sloan andrew
DESCRIPTION
Failureof Dual-Phase Steels; Micro-Void Damage Accumulation; ferriteTRANSCRIPT
The Role of Non-Ferritic Phase in the
Micro-Void Damage Accumulation and Failure
of Dual-Phase Steels
by
Andrew D.C. Sloan
A thesis submitted to the
Department of Mechanical and Materials Engineering
in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
September 2011
Copyright c© Andrew D.C. Sloan, 2011
For Sarah
There’s no question, you’re the answer.
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Abstract
Dual-phase (DP) sheet steels are a class of advanced high strength steels which boast a
desirable combination of properties for the forming of automotive components, includ-
ing: high strength, continuous yielding behaviour, and a high initial work hardening
rate. The higher strength of DP steels relative to predecessors used to form automo-
tive components allows for a reduction in part gauge, translating to the potential for
reduced automobile weight, emissions, and fuel consumption.
However, a form of premature failure during component forming known as ‘shear
fracture’ has become a prominent challenge to manufacturers’ adoption of DP steels.
Martensite particles in DP steel microstructures act as nucleation sites for the de-
velopment of void damage during deformation, resulting in a deleterious effect upon
formability and thought to contribute to the observed shear fractures.
This dissertation contributes to the overall goal of offering guidance for the im-
provement of DP steel microstructures for more desirable fracture behaviour. Specif-
ically, the role of non-ferritic phase/constituent (NFP) volume percent and spatial
distribution in the accumulation of void damage in DP steels was investigated. Void
damage accumulation in ten DP steel microstructural variants tested to failure under
near plane-strain deformation was qualified and quantified in three dimensions using
an X-ray micro-computed tomography technique. These results were correlated to the
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microstructural parameters of the variants, which clearly indicated the detrimental
effects of NFP banding in DP steels.
It was observed that DP microstructures with increased severity of NFP banding
(generally aligned in the sheet rolling direction) incurred a reduced strain to failure.
Often, microstructural variants with NFP bands aligned transverse to the major
loading direction incurred a reduced strain to failure, accumulated a greater number
of voids, and exhibited a larger void volume percent than a specimen with oppositely
oriented NFP bands. Void damage spatial distribution was generally reflective of
the spatial distribution of the most coarse NFP bands through the sheet thickness.
In microstructural variants with NFP bands aligned transverse to the major loading
direction, accumulated void damage was often observed to be highly elongated in the
direction of NFP banding.
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Acknowledgments
I would like to extend my sincerest thanks to my supervisors Dr. Keith Pilkey and
Dr. Doug Boyd. Your genorosity, candor, and genuine interest in the success of my
graduate studies at Queen’s University have made this journey a most enjoyable one.
Thank you for all of your guidance, the independence you have granted me, and the
Tuesday afternoon shinny.
I am grateful for all of the assistance of Charlie Cooney; he is a true MacGyver
of materials science problems. His resourcefulness and extensive practical knowledge
prevented many hours of fruitless experimentation. The McLaughlin Hall machine
laboratory technicians, particularly Andy Bryson, deserve my thanks for all of their
assistance in mechanical testing specimen preparation.
Many thanks are extended to Dr. Brent Lievers for his expertise in the use of
Linux and Tesselation3DSuite. Hossein Seyedrezai has been an excellent colleague
for discussing the minutiae of dual-phase steels with. Of course, thanks go to Eric
Tulk too for his friendship and comic relief; especially the SSMB and the materials
engineering puns.
Luke Hunter and Tiffany Fong of Xradia Inc. were most helpful in tackling tomo-
graphic issues. The work of Drew Marshall, Sean Cunningham, and Brandon Haw,
NSERC Undergraduate Summer Research Award (USRA) students, was invaluable
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to the completion of this thesis.
I acknowledge the financial support of Queen’s University, the AUTO21 Network
of Centres of Excellence, and the U.S. Steel Canada graduate fellowship. Thank you
to U.S. Steel and Jian Wang for supplying the sheet steel used in this study.
Sarah, this thesis is dedicated to you for enduring the endless hours of materials
banter between Eric and I, the nights and weekends at the lab, and for your unwaver-
ing encouragement. Most of all, thank you to my family. Without your love, support,
and teachings, I would not be half the man I am today.
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List of Abbreviations
AHSS Advanced high-strength steelAT Austempering/AustemperedBCC Body-centered cubicBCT Body-centered tetragonalCCD Charge-coupled deviceCCT Continuous cooling transformationCR Cold-rolledDP Dual-phaseFCC Face-centered cubicFEM Finite element methodFLC Forming limit curveFLD Forming limit diagramFOV Field of viewfps Frames per secondGA GalvannealedHSLA High-strength low-alloyHSS High-strength steelIC IntercriticalIPPS In-plane plane-strainIR InfraredLAC Linear absorption coefficientMSE Mean squared errorND Through-thickness direction of sheetNDT Non-destructive testingNFP Non-ferritic phase(s) and/or constituent(s)NL-means Non-local meansRD Rolling direction of sheetROI Region of interestSEM Scanning electron microscopeSMB Sodium MetabisulfiteSNR Signal-to-noise ratioTD Transverse direction of sheetUTS Ultimate tensile strengthXµCT X-ray micro-computed tomography
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Nomenclature
Ac1 Eutectoid temperature
Ac3 Minimum austenitizing temperature
Ar3 Austenite to ferrite start temperature
Ms Martensite start temperature
Mf Martensite finish temperature
φ Spherical coordinate azimuth orientation of a void.
θ Quasi-spherical coordinate inclination orientation. See Table 4.8
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Contents
Abstract ii
Acknowledgments iv
List of Abbreviations vi
Nomenclature vii
List of Tables xvi
List of Figures xviii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2: Literature Review . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 DP Steel Microstructures . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2.1 Commercial DP Steel Processing . . . . . . . . . . . 12
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2.1.2.2 Austenite Formation during IC Annealing . . . . . . 14
2.1.2.3 Transformation of Austenite to Martensite . . . . . . 15
2.1.2.4 Evolution of Microstructural Banding . . . . . . . . 16
2.2 DP Steel Mechanical Properties . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Constituent Strain Incompatibility . . . . . . . . . . . . . . . 22
2.2.3 Work Hardening . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Ductility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.5 Sheet Metal Formability . . . . . . . . . . . . . . . . . . . . . 24
2.2.6 In-Plane Plane-Strain Tensile Testing . . . . . . . . . . . . . . 24
2.3 Ductile Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Void Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1.1 Void Nucleation Mechanisms . . . . . . . . . . . . . 27
Effect of Martensite Particle Size . . . . . . . . . . . . 29
Effect of Martensite Particle Shape . . . . . . . . . . . 31
Effect of Martensite Spatial Distribution . . . . . . . . 32
Effect of Martensite Carbon Content . . . . . . . . . . 34
2.3.1.2 Critical Nucleation Strain . . . . . . . . . . . . . . . 35
2.3.2 Void Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.3 Void Coalescence . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.4 Fracture Surface Orientation . . . . . . . . . . . . . . . . . . . 37
2.4 Damage Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.1 X-ray Micro-computed Tomography . . . . . . . . . . . . . . . 39
2.4.1.1 Micro-focus X-ray Sources . . . . . . . . . . . . . . . 39
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2.4.1.2 X-ray attenuation . . . . . . . . . . . . . . . . . . . 40
2.4.1.3 Tomography Fundamentals . . . . . . . . . . . . . . 42
2.4.1.4 Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . 44
Beam Hardening . . . . . . . . . . . . . . . . . . . . . 44
Ring Artifacts . . . . . . . . . . . . . . . . . . . . . . . 45
Streak Artifacts . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Previous XµCT Experimentation . . . . . . . . . . . . . . . . 48
2.5 Digital Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5.1 Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5.2 Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . 56
Chapter 3: Experimental Methods and Materials . . . . . . . . . . . 58
3.1 Received Material Characteristics . . . . . . . . . . . . . . . . . . . . 58
3.2 DP Steel Microstructural Variant Design . . . . . . . . . . . . . . . . 59
3.2.1 Thermal Path One . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.2 Thermal Path Two . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2.3 Heat Treatment Procedures and Apparatus . . . . . . . . . . . 61
3.2.4 IPPS Specimen Heat Treatment Schedule . . . . . . . . . . . . 65
3.2.4.1 Austempering Apparatus . . . . . . . . . . . . . . . 69
Tube Furnace Preparation . . . . . . . . . . . . . . . . 69
Custom Salt Bath Preparation . . . . . . . . . . . . . . 70
3.2.4.2 Austempering Procedure . . . . . . . . . . . . . . . . 70
3.2.4.3 IC Annealing Apparatus . . . . . . . . . . . . . . . . 71
Salt Bath Preparation . . . . . . . . . . . . . . . . . . 72
3.2.4.4 IC Annealing Procedure . . . . . . . . . . . . . . . . 72
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3.3 Metallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.1 Specimen Preparation . . . . . . . . . . . . . . . . . . . . . . 75
3.3.1.1 Grinding and Polishing . . . . . . . . . . . . . . . . . 75
Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Polishing . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1.2 Etching . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.2 Microstructure Characterization Methods . . . . . . . . . . . . 79
3.3.2.1 Volume Percent Measurement . . . . . . . . . . . . . 79
3.3.2.2 Particle Size Measurement . . . . . . . . . . . . . . . 81
3.4 In-Plane Plane-Strain Mechanical Testing . . . . . . . . . . . . . . . . 81
3.4.1 Sample Geometry and Preparation . . . . . . . . . . . . . . . 82
3.4.1.1 Specimen Cleaning . . . . . . . . . . . . . . . . . . . 83
3.4.2 IPPS Testing Methodology . . . . . . . . . . . . . . . . . . . . 85
3.4.2.1 IPPS Testing Procedure . . . . . . . . . . . . . . . . 86
3.4.3 Image Processing and Strain Analysis . . . . . . . . . . . . . . 90
3.4.4 Experimental Error Analysis . . . . . . . . . . . . . . . . . . . 93
3.5 X-ray Micro-computed Tomography Damage Analysis . . . . . . . . . 95
3.5.1 Sample Preparation and Geometry . . . . . . . . . . . . . . . 97
3.5.2 Tomography Acquisition . . . . . . . . . . . . . . . . . . . . . 101
3.5.2.1 Tomography Acquisition Procedure . . . . . . . . . . 101
3.5.2.2 Projections . . . . . . . . . . . . . . . . . . . . . . . 103
3.5.2.3 Exposure Time . . . . . . . . . . . . . . . . . . . . . 104
3.5.2.4 Source Power . . . . . . . . . . . . . . . . . . . . . . 104
3.5.2.5 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . 104
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3.5.2.6 Binning . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.5.2.7 Dynamic Ring Removal . . . . . . . . . . . . . . . . 105
3.5.2.8 Multiple Reference Imaging . . . . . . . . . . . . . . 106
3.5.3 3-D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.3.1 Projection Post-processing . . . . . . . . . . . . . . . 106
3.5.3.2 Reconstruction Procedure . . . . . . . . . . . . . . . 108
Center Shift Correction . . . . . . . . . . . . . . . . . . 108
Beam Hardening Correction . . . . . . . . . . . . . . . 109
Other Reconstruction Parameters . . . . . . . . . . . . 110
3.5.4 Slice Post-processing . . . . . . . . . . . . . . . . . . . . . . . 110
3.5.4.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . 112
3.5.4.2 Quantitative and Qualitative Volume Analysis . . . . 118
3.6 Fractography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.7 Metallographic Damage Analysis . . . . . . . . . . . . . . . . . . . . 122
Chapter 4: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.1 Microstructure Characterization . . . . . . . . . . . . . . . . . . . . . 123
4.1.1 Cold-rolled DP Steels . . . . . . . . . . . . . . . . . . . . . . . 124
4.1.2 Galvannealed DP Steels . . . . . . . . . . . . . . . . . . . . . 124
4.1.3 TP1-treated DP Steels . . . . . . . . . . . . . . . . . . . . . . 126
4.1.4 TP2-treated DP Steels . . . . . . . . . . . . . . . . . . . . . . 128
4.1.5 Summary of Microstructures . . . . . . . . . . . . . . . . . . . 131
4.2 IPPS Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.3 Void Damage Accumulation and Failure . . . . . . . . . . . . . . . . 139
4.3.1 Galvannealed DP Steels . . . . . . . . . . . . . . . . . . . . . 142
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4.3.1.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 142
4.3.1.2 Damage Distribution . . . . . . . . . . . . . . . . . . 143
4.3.1.3 Void Orientations . . . . . . . . . . . . . . . . . . . . 143
4.3.1.4 Failure Mechanism . . . . . . . . . . . . . . . . . . . 143
4.3.2 TP1-treated DP Steels . . . . . . . . . . . . . . . . . . . . . . 164
4.3.2.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 164
4.3.2.2 Damage Distribution . . . . . . . . . . . . . . . . . . 164
4.3.2.3 Void Orientations . . . . . . . . . . . . . . . . . . . . 165
4.3.2.4 Failure Mechanism . . . . . . . . . . . . . . . . . . . 165
4.3.3 TP2-treated DP Steels . . . . . . . . . . . . . . . . . . . . . . 226
4.3.3.1 Degree of Damage . . . . . . . . . . . . . . . . . . . 226
4.3.3.2 Damage Distribution . . . . . . . . . . . . . . . . . . 226
4.3.3.3 Void Orientations . . . . . . . . . . . . . . . . . . . . 226
4.3.3.4 Failure Mechanism . . . . . . . . . . . . . . . . . . . 226
Chapter 5: Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.1 Microstructural Variants . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.1.1 TP1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.1.2 TP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
5.1.2.1 Explanation of Residual Banding for TP2 . . . . . . 248
5.2 IPPS Variant Ductility and Failure . . . . . . . . . . . . . . . . . . . 248
5.2.1 Effect of NFP Content on Ductility . . . . . . . . . . . . . . . 248
5.2.2 DP Steel Variant Failure Behaviour . . . . . . . . . . . . . . . 249
5.3 XµCT for Characterization of Damage . . . . . . . . . . . . . . . . . 250
5.4 DP Steel Damage Accumulation in Plane-Strain Fracture . . . . . . . 251
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5.4.1 Void Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . 251
5.4.2 Failure Behaviour Variation with Degree of NFP Banding . . . 252
5.4.3 Explanation for Reduced Ductility with Increased NFP Banding 253
5.5 Effects of Microstructure on Damage Accumulation . . . . . . . . . . 259
5.5.1 Effect of NFP Volume Percent . . . . . . . . . . . . . . . . . . 259
5.5.2 Effect of NFP Morphology . . . . . . . . . . . . . . . . . . . . 260
5.5.3 Effect of NFP Spatial Distribution . . . . . . . . . . . . . . . 261
5.5.4 Importance of NFP Banding to Damage . . . . . . . . . . . . 263
Chapter 6: Conclusions and Recommendations . . . . . . . . . . . . . 264
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Appendix A: Preliminary IC Annealing Experiments . . . . . . . . . 281
A.1 Preliminary Heat Treatment Experiment . . . . . . . . . . . . . . . . 281
A.1.1 Alloy Intercritical Temperature Ranges . . . . . . . . . . . . . 282
A.1.2 IC-Annealing Calibration Curves for NFP Content . . . . . . 283
A.1.2.1 Optical Microscopy Procedure . . . . . . . . . . . . . 284
A.2 Optical vs. SE Quantitative Metallography . . . . . . . . . . . . . . . 285
Appendix B: IPPS Blanks - Time to Heat to IC Temperature . . . . 291
Appendix C: IPPS Specimen Cleaning Procedure . . . . . . . . . . . 295
Appendix D: NL-Means Denoising Parametric Study . . . . . . . . . 298
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Appendix E: Complete IPPS Testing Results . . . . . . . . . . . . . . 304
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List of Tables
2.1 DP steel typical alloying elements . . . . . . . . . . . . . . . . . . . . 10
3.1 Experimental sheet steel elemental compositions . . . . . . . . . . . . 59
3.2 Experimental sheet steel thicknesses . . . . . . . . . . . . . . . . . . . 59
3.3 IPPS specimen production schedule . . . . . . . . . . . . . . . . . . . 68
3.4 Metallographic specimen preparation grinding stages . . . . . . . . . 76
3.5 Metallographic specimen preparation polishing stages . . . . . . . . . 78
3.6 Metallographic specimen etchants . . . . . . . . . . . . . . . . . . . . 79
3.7 Micro-XCT 400 Specifications . . . . . . . . . . . . . . . . . . . . . . 95
3.8 X-ray micro-computed tomography acquisition parameters . . . . . . 101
4.1 Cold-rolled sheet steel constituent volume percents . . . . . . . . . . 124
4.2 NFP particle characteristics of the galvannealed DP steels . . . . . . 126
4.3 NFP particle characteristics of the TP1-treated DP steels . . . . . . . 128
4.4 NFP particle characteristics of the TP2-treated DP steels . . . . . . . 131
4.5 NFP microstructural characteristics summary for all DP steel variants 134
4.6 IPPS specimen failure strains . . . . . . . . . . . . . . . . . . . . . . 136
4.7 IPPS match-head specimen void accumulation quantitative measures 140
4.8 IPPS match-head specimen void accumulation quantitative measures(2)141
4.9 Galvannealed specimen damage observations . . . . . . . . . . . . . . 144
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4.10 7TP1-treated specimen damage observations . . . . . . . . . . . . . . 166
4.11 9TP1-treated specimen damage observations . . . . . . . . . . . . . . 167
4.12 TP2-treated specimen damage observations . . . . . . . . . . . . . . . 227
A.1 Approximated alloy solid state transformation temperatures . . . . . 283
A.2 NFP content - galvannealed and preliminary heat-treatment specimens 285
E.1 Complete IPPS failure strain results. . . . . . . . . . . . . . . . . . . 305
E.1 Complete IPPS failure strain results. . . . . . . . . . . . . . . . . . . 306
E.1 Complete IPPS failure strain results. . . . . . . . . . . . . . . . . . . 307
E.1 Complete IPPS failure strain results. . . . . . . . . . . . . . . . . . . 308
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List of Figures
1.1 Historical view of DP steel use in automobiles . . . . . . . . . . . . . 4
1.2 Elongation vs. strength ranges for several classes of steel . . . . . . . 5
1.3 Example automotive component forming shear fracture . . . . . . . . 5
2.1 Effect of manganese alloying on austenite hardenability . . . . . . . . 11
2.2 Typical industrial continuous annealing schedule . . . . . . . . . . . . 13
2.3 Microstructural banding in 1020 steel hot-rolled plate . . . . . . . . . 17
2.4 As-solidified crystal morphologies of a section of steel . . . . . . . . . 18
2.5 Schematic of dendritic solidification . . . . . . . . . . . . . . . . . . . 19
2.6 Manganese segregation in 4140 steel . . . . . . . . . . . . . . . . . . . 20
2.7 DP steel tensile stress-strain behaviour . . . . . . . . . . . . . . . . . 22
2.8 General categories of fracture processes in metals . . . . . . . . . . . 27
2.9 Void nucleation with respect to local strain . . . . . . . . . . . . . . . 28
2.10 Void damage in DP steels of differing banded microstructures . . . . 34
2.11 XµCT beam and detector geometries . . . . . . . . . . . . . . . . . . 40
2.12 Bremsstrahlung and characteristic radiation . . . . . . . . . . . . . . 41
2.13 Lab-scale XµCT schematic . . . . . . . . . . . . . . . . . . . . . . . . 43
2.14 Beam hardening artifact . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.15 Ring artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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2.16 Streak artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.17 Damage anisotropy in steel due to inclusion orientation . . . . . . . . 49
2.18 Damage distribution evolution in DP600 steel tension specimen . . . 51
2.19 NL-means denoising scheme . . . . . . . . . . . . . . . . . . . . . . . 53
2.20 Effectiveness of various denoising methods on a natural image . . . . 54
2.21 Method noise produced by various denoising methods . . . . . . . . . 55
2.22 Effectiveness of various denoising methods on a periodic image . . . . 56
3.1 Heat treatment path representations . . . . . . . . . . . . . . . . . . 62
3.2 Tube furnace used for austenitization . . . . . . . . . . . . . . . . . . 63
3.3 Salt bath used for bainite hold portion of austempering . . . . . . . . 63
3.4 Salt bath used for IC annealing . . . . . . . . . . . . . . . . . . . . . 64
3.5 IC annealing IPPS rectangular blank holder . . . . . . . . . . . . . . 74
3.6 IPPS metallographic specimen extraction location . . . . . . . . . . . 75
3.7 IPPS tension test specimen geometry . . . . . . . . . . . . . . . . . . 82
3.8 Custom paint plotting press for IPPS grid application . . . . . . . . . 84
3.9 Inter-dot spacing for the grid applied to IPPS specimens. . . . . . . . 84
3.10 Alignment of IPPS specimens in bottom grip . . . . . . . . . . . . . . 87
3.11 Alignment of IPPS specimens in top grip . . . . . . . . . . . . . . . . 88
3.12 IPPS testing experimental setup . . . . . . . . . . . . . . . . . . . . . 89
3.13 IPPS grid image segmentation process Fig. 1/2 . . . . . . . . . . . . 91
3.14 IPPS grid image segmentation process Fig. 2/2 . . . . . . . . . . . . 92
3.15 Example IPPS specimen strain path . . . . . . . . . . . . . . . . . . 94
3.16 Micro-XCT 400 instrument . . . . . . . . . . . . . . . . . . . . . . . . 96
3.17 Schematic of match-head extraction location . . . . . . . . . . . . . . 98
xix
3.18 Micro-XCT 400 interior components . . . . . . . . . . . . . . . . . . . 99
3.19 X-ray source to specimen and detector distances . . . . . . . . . . . . 100
3.20 Reconstructed XµCT slice greyscale intensity mapping variation . . . 113
3.21 Poor preliminary reconstructed slice thresholding results . . . . . . . 114
3.22 Poor reconstructed slice thresholding results due to noise . . . . . . . 115
3.23 Poor thresholding results for uncropped reconstructed slices . . . . . 116
3.24 Locally adaptive thresholding of uncropped reconstructed slice . . . . 119
3.25 Custom threshold mask overlay software . . . . . . . . . . . . . . . . 120
4.1 Cold-rolled DP steel microstructures . . . . . . . . . . . . . . . . . . 125
4.2 Galvannealed DP steel microstructures . . . . . . . . . . . . . . . . . 127
4.3 DP780CR-TP1-treated DP steel microstructures . . . . . . . . . . . . 129
4.4 DP980CR-TP1-treated DP steel microstructures . . . . . . . . . . . . 130
4.5 TP2-treated DP steel microstructures . . . . . . . . . . . . . . . . . . 132
4.6 7-series IPPS specimen failure strain vs. NFP volume percent . . . . 137
4.7 9-series IPPS specimen failure strain vs. NFP volume percent . . . . 138
4.8 7GA-R4 void accumulation 3-D rendering . . . . . . . . . . . . . . . 145
4.9 7GA-R4 through-thickness void accumulation 3-D rendering . . . . . 146
4.10 Optical micrographs of 7GA-R4 match-head specimen . . . . . . . . . 147
4.11 SEM fractographs of 7GA-R4 match-head specimen . . . . . . . . . . 148
4.12 7GA-T2 void accumulation 3-D rendering . . . . . . . . . . . . . . . . 149
4.13 7GA-T2 through-thickness void accumulation 3-D rendering . . . . . 150
4.14 Optical micrographs of 7GA-T2 match-head specimen . . . . . . . . . 151
4.15 SEM fractographs of 7GA-T2 match-head specimen . . . . . . . . . . 152
4.16 9GA-R3 void accumulation 3-D rendering . . . . . . . . . . . . . . . 153
xx
4.17 9GA-R3 through-thickness void accumulation 3-D rendering . . . . . 154
4.18 Optical micrographs of 9GA-R3 match-head specimen . . . . . . . . . 155
4.19 SEM fractographs of 9GA-R3 match-head specimen . . . . . . . . . . 156
4.20 9GA-T4 void accumulation 3-D rendering . . . . . . . . . . . . . . . . 157
4.21 9GA-T4 through-thickness void accumulation 3-D rendering . . . . . 158
4.22 Optical micrographs of 9GA-T4 match-head specimen . . . . . . . . . 159
4.23 SEM fractographs of 9GA-T4 match-head specimen . . . . . . . . . . 160
4.24 Galvannealed DP steel variant void size histograms . . . . . . . . . . 161
4.25 Galvannealed DP steel variant void spatial distribution histograms . . 162
4.26 Galvannealed DP steel variant void volume profiles in ND . . . . . . 163
4.27 Effect of NFP volume percent on void volume % in 7TP1 variants . . 168
4.28 Effect of NFP volume percent on void volume % in 9TP1 variants . . 169
4.29 Effect of NFP volume percent on # of voids in 7TP1 variants . . . . 170
4.30 Effect of NFP volume percent on # of voids in 9TP1 variants . . . . 171
4.31 7TP1-15-R4 void accumulation 3-D rendering . . . . . . . . . . . . . 172
4.32 7TP1-15-R4 through-thickness void accumulation 3-D rendering . . . 173
4.33 Optical micrographs of 7TP1-15-R4 match-head specimen . . . . . . 174
4.34 SEM fractographs of 7TP1-15-R4 match-head specimen . . . . . . . . 175
4.35 7TP1-15-T11 void accumulation 3-D rendering . . . . . . . . . . . . . 176
4.36 7TP1-15-T11 through-thickness void accumulation 3-D rendering . . 177
4.37 Optical micrographs of 7TP1-15-T11 match-head specimen . . . . . . 178
4.38 SEM fractographs of 7TP1-15-T11 match-head specimen . . . . . . . 179
4.39 7TP1-33-R11 void accumulation 3-D rendering . . . . . . . . . . . . . 180
4.40 7TP1-33-R11 through-thickness void accumulation 3-D rendering . . 181
xxi
4.41 Optical micrographs of 7TP1-33-R11 match-head specimen . . . . . . 182
4.42 SEM fractographs of 7TP1-33-R11 match-head specimen . . . . . . . 183
4.43 7TP1-33-T10 void accumulation 3-D rendering . . . . . . . . . . . . . 184
4.44 7TP1-33-T10 through-thickness void accumulation 3-D rendering . . 185
4.45 Optical micrographs of 7TP1-33-T10 match-head specimen . . . . . . 186
4.46 SEM fractographs of 7TP1-33-T10 match-head specimen . . . . . . . 187
4.47 7TP1-43-R3 void accumulation 3-D rendering . . . . . . . . . . . . . 188
4.48 7TP1-43-R3 through-thickness void accumulation 3-D rendering . . . 189
4.49 Optical micrographs of 7TP1-43-R3 match-head specimen . . . . . . 190
4.50 SEM fractographs of 7TP1-43-R3 match-head specimen . . . . . . . . 191
4.51 7TP1-43-T5 void accumulation 3-D rendering . . . . . . . . . . . . . 192
4.52 7TP1-43-T5 through-thickness void accumulation 3-D rendering . . . 193
4.53 Optical micrographs of 7TP1-43-T5 match-head specimen . . . . . . 194
4.54 SEM fractographs of 7TP1-43-T5 match-head specimen . . . . . . . . 195
4.55 9TP1-15-R7 void accumulation 3-D rendering . . . . . . . . . . . . . 196
4.56 9TP1-15-R7 through-thickness void accumulation 3-D rendering . . . 197
4.57 Optical micrographs of 9TP1-15-R7 match-head specimen . . . . . . 198
4.58 SEM fractographs of 9TP1-15-R7 match-head specimen . . . . . . . . 199
4.59 9TP1-15-T1 void accumulation 3-D rendering . . . . . . . . . . . . . 200
4.60 9TP1-15-T1 through-thickness void accumulation 3-D rendering . . . 201
4.61 Optical micrographs of 9TP1-15-T1 match-head specimen . . . . . . 202
4.62 SEM fractographs of 9TP1-15-T1 match-head specimen . . . . . . . . 203
4.63 9TP1-33-R10 void accumulation 3-D rendering . . . . . . . . . . . . . 204
4.64 9TP1-33-R10 through-thickness void accumulation 3-D rendering . . 205
xxii
4.65 Optical micrographs of 9TP1-33-R10 match-head specimen . . . . . . 206
4.66 SEM fractographs of 9TP1-33-R10 match-head specimen . . . . . . . 207
4.67 9TP1-33-T10 void accumulation 3-D rendering . . . . . . . . . . . . . 208
4.68 9TP1-33-T10 through-thickness void accumulation 3-D rendering . . 209
4.69 Optical micrographs of 9TP1-33-T10 match-head specimen . . . . . . 210
4.70 SEM fractographs of 9TP1-33-T10 match-head specimen . . . . . . . 211
4.71 9TP1-43-R11 void accumulation 3-D rendering . . . . . . . . . . . . . 212
4.72 9TP1-43-R11 through-thickness void accumulation 3-D rendering . . 213
4.73 Optical micrographs of 9TP1-43-R11 match-head specimen . . . . . . 214
4.74 SEM fractographs of 9TP1-43-R11 match-head specimen . . . . . . . 215
4.75 9TP1-43-T7 void accumulation 3-D rendering . . . . . . . . . . . . . 216
4.76 9TP1-43-T7 through-thickness void accumulation 3-D rendering . . . 217
4.77 Optical micrographs of 9TP1-43-T7 match-head specimen . . . . . . 218
4.78 SEM fractographs of 9TP1-43-T7 match-head specimen . . . . . . . . 219
4.79 TP1-treated DP steel variant void size histograms . . . . . . . . . . . 220
4.80 TP1-treated DP steel variant void size histograms . . . . . . . . . . . 221
4.81 TP1-treated DP steel variant void spatial distribution histograms . . 222
4.82 TP1-treated DP steel variant void spatial distribution histograms . . 223
4.83 TP1-treated DP steel variant void volume profiles in ND . . . . . . . 224
4.84 TP1-treated DP steel variant void volume profiles in ND . . . . . . . 225
4.85 7TP2-25-R4 void accumulation 3-D rendering . . . . . . . . . . . . . 228
4.86 7TP2-25-R4 through-thickness void accumulation 3-D rendering . . . 229
4.87 Optical micrographs of 7TP2-25-R4 match-head specimen . . . . . . 230
4.88 7TP2-25-T2 void accumulation 3-D rendering . . . . . . . . . . . . . 231
xxiii
4.89 7TP2-25-T2 through-thickness void accumulation 3-D rendering . . . 232
4.90 Optical micrographs of 7TP2-25-T2 match-head specimen . . . . . . 233
4.91 SEM fractographs of 7TP2-25-T2 match-head specimen . . . . . . . . 234
4.92 9TP2-37-R4 void accumulation 3-D rendering . . . . . . . . . . . . . 235
4.93 9TP2-37-R4 through-thickness void accumulation 3-D rendering . . . 236
4.94 Optical micrographs of 9TP2-37-R4 match-head specimen . . . . . . 237
4.95 SEM fractographs of 9TP2-37-R4 match-head specimen . . . . . . . . 238
4.96 9TP2-37-T1 void accumulation 3-D rendering . . . . . . . . . . . . . 239
4.97 9TP2-37-T1 through-thickness void accumulation 3-D rendering . . . 240
4.98 Optical micrographs of 9TP2-37-T1 match-head specimen . . . . . . 241
4.99 SEM fractographs of 9TP2-37-T1 match-head specimen . . . . . . . . 242
4.100TP2-treated DP steel variant void size histograms . . . . . . . . . . . 243
4.101TP2-treated DP steel variant void spatial distribution histograms . . 244
4.102TP2-treated DP steel variant void volume profiles in ND . . . . . . . 245
5.1 Schematic proposing failure sequences dependent upon NFP banding 255
5.2 Galvannealed DP steel failure schematic . . . . . . . . . . . . . . . . 256
5.3 TP1- and TP2-treated DP steel failure schematic . . . . . . . . . . . 257
A.1 DP780 preliminary heat treatment microstructures . . . . . . . . . . 286
A.2 DP980 preliminary heat treatment microstructures . . . . . . . . . . 287
A.3 IPPS rectangular blank metallographic specimen extraction . . . . . . 288
A.4 IC annealing NFP content calibration curve for CR alloys . . . . . . . 289
A.5 Example optical micrograph and grid for volume percent counting . . 290
B.1 IPPS rectangular blank heating rates . . . . . . . . . . . . . . . . . . 293
xxiv
B.2 Salt bath transient temperature response to IC annealing . . . . . . . 294
C.1 Acid cleaning of IPPS specimens; “before” and “after” photographs . 297
D.1 Test images for NL-means denoising parametric study . . . . . . . . . 300
D.2 NL-means denoising parametric study results . . . . . . . . . . . . . . 301
D.3 NL-means denoising algorithm filtering parameter testing . . . . . . . 303
xxv
Chapter 1
Introduction
This thesis focuses on the detection and quantification of void damage accumulated in
dual-phase steels under near plane-strain loading using X-ray micro-computed tomog-
raphy, working towards developing an increased understanding of the microstructural
features and mechanisms which contribute to the failure of this family of steels.
1.1 Motivation
At the forefront of current trends influencing automobile design worldwide are ris-
ing oil prices, increasingly stringent emissions regulations, stronger safety legislation,
and the heightened environmental consciousness of consumers. This new industry
trajectory has necessitated rapid innovation and product mix turnover on the part of
steel producers and auto parts manufacturers to maintain market share in response to
consumer desires for lightweight, fuel-efficient vehicles with reduced greenhouse gas
emissions. A cost-effective and straightforward means to producing automobiles that
meet these desires is a reduction in vehicle weight via the implementation of thinner
1
CHAPTER 1. INTRODUCTION 2
gauge, higher strength sheet steels for the manufacture of structural components.
Steel remains the material of choice for structural component weight reduction
despite the availability of many other lower density material choices such as aluminum
and magnesium. Some keys to this distinction are the relatively low cost and volatility
in the price of steels, their high level of recyclability, and the weldability and re-
workability of steels necessary to repair defects and in-service damage [1]. Dual-
phase (DP) steels, a grade of advanced high-strength steels (AHSS), have emerged as
a frontrunner for vehicle light-weighting, with many steel producers having invested
in continuous annealing facilities and further development of these sheet steels.
DP sheet steels boast a desirable combination of properties for the forming of auto-
motive components: high strengths, continuous yielding behaviour, and a high initial
work hardening rate. The higher strengths of DP steels relative to high-strength steel
(HSS) predecessors allow for a reduction in sheet thickness necessary for component
weight reduction. It follows that reduced automobile structural weight leads to re-
duced emissions and fuel consumption. Also, the reduction in structural weight allows
for power-train downsizing to further improve fuel efficiency. It has been estimated
that an overall vehicle weight reduction of 9% can be made in a typical five-passenger
automobile by replacing the main frame structure with an optimized blend of AHSS
products [2]. This weight savings translates into a decrease in fuel consumption of ap-
proximately 0.4 L per 100 km and an elimination of approximately 1800 kg of carbon
dioxide emissions over a 200 000 km vehicle lifetime [3]. One other important benefit
of DP steels for structural automotive components is their positive strain rate sensi-
tivity, which elicits a high level of energy absorption during crash scenarios, thereby
enhancing vehicle crashworthiness.
CHAPTER 1. INTRODUCTION 3
Research of DP steels began as early as the 1960s [4], but intensified research
interest in DP steels first began in 1975-76 after the 1973 world oil crisis produced
a strong demand for lightweight, fuel-efficient transport [5, 6]. It is only recently,
however, that widespread adoption of DP steels has occurred amongst automotive
parts manufacturers, as shown in Fig. 1.1. This rapid introduction of DP steels to
parts manufacturing regimes has not been without challenges. While a reduction in
ductility with increased steel strength is generally to be expected (as illustrated in
Fig. 1.2), many premature component forming failures have been reported within the
predicted formability limits of DP steels by automotive manufacturers.
Until about two decades ago, stamping of newly designed steel components from
sheet required months to years of experimental die tryout and modifications [11].
With the emergence of improved processing power for computers and non-linear finite
element software, these arduous trial periods have been all but eliminated [11]. Today,
dies for a part forming operation are designed and tested in a virtual environment
using finite element models tied to experimentally determined forming limit diagrams,
which delineate in principal strain space the limit strains within which a material can
be deformed without the occurrence of local necking. Such a method has been highly
successful for the relatively ductile alloys for which dies have been designed in the
past. However, the method has failed to predict so-called ‘shear fractures’ of DP steels
in high-curvature regions of dies (Fig. 1.3) when used with DP steels. Shear fracture
is typically associated with a lack of significant sheet thinning near the failure region
and occurs most frequently in die regions of low bending ratio, i.e. the ratio of the
bend radius to the sheet thickness [11].
The constant applied strain path inherent to the creation of experimental forming
CHAPTER 1. INTRODUCTION 4
(a)
(b)
(c)
Figure 1.1: Demonstration of the rapid implementation of DPsteels in automobile structures in the early 21st century: a)Typical steel mix for automobile bodies in 1980 and 2000 [1]; b)Steel grades used in the body of a small-size vehicle introducedin Japan in 2002, adapted from [7]; c) Steel grades used in astate of the art automobile body as of 2004 [8].
CHAPTER 1. INTRODUCTION 5
Figure 1.2: Typical ultimate tensile strength and total elon-gation ranges for several classes of steel, demonstrating thegeneral decline in ductility with increasing strength [9].
Figure 1.3: Shear fracture of a stamped DP600 automotive railpart in a region of near plane-strain bending [10].
CHAPTER 1. INTRODUCTION 6
limit curve (FLC) locii can result in situations where the formability for a more
complex strain path is over-predicted. However, the far more likely contributors
to the unpredicted shear fractures are the nucleation and growth of void damage
at martensite particles in DP steel microstructures [10, 12, 13] and the deleterious
softening effect of deformation induced heating [11]. The latter concern is typically
unaccounted for in an FEM + FLC approach, where FLCs that are experimentally-
determined under low-rate, near-isothermal conditions are used to predict failure
during quasi-adiabatic, high-rate commercial forming operations [11]. Developing an
improved understanding of how the two aforementioned mechanisms contribute to the
premature failure of DP steels is imperative to the realization of their full potential
for automobile light-weighting through both improved prediction of low and high-rate
failures (forming and in-service) and new DP microstructures that are less prone to
damage.
1.2 Research Objectives
In this thesis, focus is placed upon studying the role of void damage in the fail-
ure of DP steels subject to a near plane-strain path. Particularly, developing an
improved understanding of the interaction between martensite particles, voids, and
shear bands in the failure of DP steels is a milestone target of this research, looking
towards the greater goal of modeling these interactions. In the past, investigations
into these relationships have been undertaken using two-dimensional metallographic
methods [14–19]. However, the data collected using such techniques tend to lack
a robustness due to the sampling of 2-D planes at large finite spacings relative to
void size. Recently, it has been shown that the most reliable method for obtaining
CHAPTER 1. INTRODUCTION 7
quantitative 3-D information concerning damage in materials is through X-ray ab-
sorption microtomography [20, 21]. Three known studies to date have made use of
the technique to examine damage in DP steels, including its evolution in the case of
Maire et al. [22], but none have provided insight into the role of the microstructural
parameters of the martensitic phase in the accumulation of void damage [22–24].
The unique contribution of this thesis is the quantitative and qualitative study
of void damage in ten DP steel microstructural variants using lab-scale X-ray micro-
computed tomography (XµCT) to acquire reliable 3-D measurements. To date, such
use of a lab-scale X-ray source to image damage in steel has only been reported once
by Gupta et al. [23]. The primary goal of the present study is to employ mechanical
testing of the DP steel variants to failure under a critical strain path representative of
typical automotive forming failures and observe the damage accumulation produced
using XµCT. DP steel microstructural variants were selected and designed to: a)
be representative of current microstructures used commercially to form automotive
components (i.e. commercially available sheet); b) be of varied martensite volume
percent while maintaining morphology; and c) be of varied martensite morphology
and distribution while maintaining volume percent. These variants were selected to
provide useful insight into how non-martensitic second phases in commercial DP steels
affect damage accumulation and the significance of variation in the volume percent
and morphology of martensite in a DP steel microstructure to damage and failure.
CHAPTER 1. INTRODUCTION 8
1.3 Organization
The remainder of this thesis is divided into five chapters as outlined below:
Chapter 2 provides a pertinent review of the literature and explains the
principles underlying X-ray absorption micro-computed tomography.
Chapter 3 details the DP steel alloys used in this study, outlines the heat
treatment methods used to produce DP steel microstructural variants,
chronicles the microstructural characterization methods employed, doc-
uments the procedures of the mechanical testing protocol, and describes
the experimental and analytical procedures of the XµCT examination
of failed mechanical testing specimens.
Chapter 4 presents the results of the experiments outlined in Chapter
3.
Chapter 5 provides a discussion of the results and methodologies and
their significance with respect to the existing literature.
Chapter 6 draws the primary conclusions of this study and offers guid-
ance for future work in this particular field.
Chapter 2
Literature Review
2.1 DP Steel Microstructures
The microstructure of dual-phase steels consists mainly of ferrite and martensite.
Small amounts of bainite, pearlite, and retained austenite may also be present. A typi-
cal microstructure consists of a matrix of 70-95% ferrite with 5-30% dispersed marten-
site islands [8]. The unique tensile behaviour of DP steels, examined in Sec. 2.2, is a
direct result of the use of a hard second phase dispersed in a soft matrix.
2.1.1 Chemistry
Many alloying elements are used in DP steels to assist in their production and final
properties. These elements and their functions are summarized in Table 2.1. Carbon
content of DP steels is generally kept low to improve weldability. By weight percent,
the largest elemental alloying additions in many DP steels for strengthening purposes
are manganese, silicon, and molybdenum. The remainder of the alloying content of
9
CHAPTER 2. LITERATURE REVIEW 10
the steel is carefully tweaked to provide a hardenability which allows for a martensitic
transformation to occur through carefully controlled cooling. Manganese content is
a particular point of interest as it has been demonstrated in many studies to be the
alloying element most responsible for the development of microstructural banding
during the production of low alloy steels [25–27]. A poignant example of the effect
of manganese content on hardenability is provided in the continuous cooling trans-
formation (CCT) diagrams of Fig. 2.1, displaying transformation differences between
low- and high-Mn 5140 steels. The addition of manganese is shown to push austen-
ite decomposition to bainite, pearlite, and ferrite to longer times under continuous
cooling.
Table 2.1: Typical alloying elements in DP steels and theirfunction. Adapted from [28].
Element Function
C, Mn, Si, Ni, Cr, MoIncreases solid-solution strength and hardnessIncreases hardenability
V, Cb, NbIncreases strength and hardness through grain refinementIncreases hardenability
Al, Ti Increases strength and hardness through grain refinement
B Increases hardenability
N Increases amount of nitrides, required for strengthening or grain refinement
2.1.2 Processing
At its most basic, the process for producing a DP steel microstructure is as follows. A
steel of appropriately low carbon content is intercritically heat treated (heating to the
ferrite + austenite region of the iron-carbon phase diagram). Following a short hold in
the intercritical region to produce a ferrite-austenite mixture, the steel is put through
accelerated cooling to cause a diffusionless transformation of the FCC austenite to
BCT martensite, resulting in a dual phase microstructure completely composed of
CHAPTER 2. LITERATURE REVIEW 11
(a)
(b)
Figure 2.1: CCT diagrams for 5140 steel containing: a) 1.83pct Mn and b) 0.82 pct Mn [29].
CHAPTER 2. LITERATURE REVIEW 12
ferrite and martensite. Carbon atoms in the austenite remain as interstitial alloying
elements in the martensite, resulting in a metastable supersaturated solid solution.
2.1.2.1 Commercial DP Steel Processing
To produce DP steel sheet in an economical manner at high volumes, a complex
thermomechanical procedure is necessary. Cast steel slab is taken through a hot
rolling process involving several roughing and finishing stages to produce sheet of
uniform thickness (typically 2-3 mm) and properties. Cold rolling is applied to the
sheet to further reduce its thickness to a gauge which is appropriate for the forming
of automotive components (∼1 mm). At this stage, the steel typically consists of
ferrite and pearlite elongated in the rolling direction, but may also contain bainite
and martensite. Commercial DP steel sheets are typically produced on a continuous
annealing line + hot dip galvanizing/galvannealing line, which provides a protective
surface layer to the sheet to guard against corrosion. A typical industrial continuous
annealing schedule for DP steel sheet which includes constituent evolution is provided
in Fig. 2.2.
The design of an economical physical facility line for implementing a galvanneal-
ing schedule limits cooling rates to levels that are often too low to produce a purely
dual-phase microstructure, such that epitaxial ferrite, bainite, or pearlite may form
in some small portion from intercritical austenite. These transformations are not as
desirable because these constituents do not provide the high strength of martensite
and do not result in the production of a highly mobile dislocation network in sur-
rounding ferrite grains (as is the case for the martensitic transformation). As such,
CHAPTER 2. LITERATURE REVIEW 13
Figure 2.2: Schematic of a typical industrial continuous anneal-ing schedule for the production of dual-phase steel. Neitherthe time nor the temperature axis is scaled due to the minorvariations in scheduling from producer to producer. ‘F’ repre-sents ferrite, ‘B’ represents bainite, ‘P’ represents pearlite, ‘A’represents austenite, and ‘M’ represents martensite. Adaptedfrom the work of [30].
CHAPTER 2. LITERATURE REVIEW 14
partitioning a greater amount of carbon into austenite during intercritical (IC) an-
nealing is advantageous to increase the hardenability of the austenite and thus shift
pearlite and bainite transformation to lower temperatures and slower cooling rates.
Utilizing lower IC annealing temperatures produces a greater concentration of carbon
in austenite for a given IC annealing hold time. As well, further carbon enrichment
of the austenite phase occurs during slow cooling from IC temperature as carbon
is redistributed from “new ferrite” to austenite grains [30]. As shown in Table 2.1,
manganese, silicon, nickel, chromium, and molybdenum also serve the purposes of
increasing austenite hardenability.
2.1.2.2 Austenite Formation during IC Annealing
It is well known that austenite forms by a nucleation and growth mechanism upon
heating. Speich et al. [6] have shown that the formation of austenite in low-carbon
1.5 weight percent Mn steels during IC annealing can be broken into three steps:
(1) nearly instantaneous nucleation of austenite in pearlite, followed by rapid growth
until complete pearlite dissolution, (2) slow growth of austenite into ferrite primarily
controlled by carbon diffusion in austenite, and (3) very slow equilibration of ferrite
and austenite controlled by manganese diffusion in austenite. Step (1) is completed on
the order of seconds due to the short range diffusion of carbon atoms, step (2) requires
hours to fully complete, and step (3) is never completed under normal annealing times
[6]. It should be noted that other microstructural regions of high carbon concentration
may also act as austenite nucleation sites, such as martensite particles and ferrite grain
boundaries [31, 32].
The preceding generally accepted mechanisms of austenite formation are largely
CHAPTER 2. LITERATURE REVIEW 15
drawn from isothermal studies using hot-rolled or fully annealed steels [31]. As such,
they pay no heed to the effects of the cold rolling which is performed prior to IC
annealing during DP steel production, or to the effect of heating rate to IC annealing
temperature. Huang et al. [31] demonstrated that heating rate is a very important
variable affecting the nucleation and growth of austenite, especially in cold-rolled DP
steel. For a high heating rate (∼100◦C/s), it is purported that concurrent ferrite
recrystallization and austenite nucleation during IC annealing of cold-rolled ferrite-
pearlite steel allows for unabated growth of pearlite-nucleated austenite due to a lack
of any ferrite-nucleated austenite presenting any competition [31]. For high heating
rates to IC temperature, this results in a higher austenite transformation rate and
coarser austenite grains elongated in a continuous fashion in the rolling direction [31].
2.1.2.3 Transformation of Austenite to Martensite
Rapid cooling below the martensite start temperature from the IC temperature range
causes a diffusionless transformation of FCC austenite to BCT martensite. All carbon
atoms in the austenite remain as interstitial impurities in the martensite, resulting in
a metastable supersaturated solid solution. Depending upon the carbon content of the
parent austenite, martensite morphology can vary from lath substructure, typical of
low-carbon martensite, to internally twinned substructure plate martensite, typical of
high-carbon martensite. The former is associated with high toughness and ductility,
but low strength; the latter with high strength, but low ductility and toughness. It
should be mentioned that the low- and high-carbon terms used in this section refer
to the relative changes that may be made to the carbon content of parent austenite
by varying IC annealing temperature, i.e. on the order of 0.5%.
CHAPTER 2. LITERATURE REVIEW 16
A small fraction of austenite that has been sufficiently stabilized with carbon
and other solid-solution alloying elements may remain after cooling in the form of
retained austenite in DP steels due to a resultant shift of the martensite start and
finish temperatures to lower levels. For steels with low- or medium-carbon martensite,
austenite is believed to be retained as interlath films within martensite [33]. For
steels with high-carbon martensite, austenite is believed to be retained as isolated
particles [34, 35].
The final microstructure of a DP steel post-IC annealing is heavily dependent
upon the microstructure of the input steel prior to the annealing treatment. It has
been demonstrated that the resultant size, morphology, and distribution of marten-
site in DP steels is dependent upon the IC annealing heating rate, temperature, hold
time, cooling rate, and the distribution of carbon and manganese prior to IC an-
nealing [6, 31, 36–38]. Thermomechanical processing may be used to influence the
latter via alteration of the size, spatial distribution, morphology, and composition of
microstructural constituents.
2.1.2.4 Evolution of Microstructural Banding
In hot rolled low alloy steels, it is well known that ferrite and pearlite are normally
arranged in layers [39]. In an etched metallographic section showing a plane defined
by the sheet rolling direction and through-thickness direction (RD-ND), this arrange-
ment is visually apparent as a banded microstructure [25, 29] such as in Fig. 2.3.
Some degree of banding is present in all types of steel [29]. The root cause of this
banding is known to be the segregation of alloying elements, both macroscopically
and microscopically, in cast steel products.
CHAPTER 2. LITERATURE REVIEW 17
Figure 2.3: Ferrite (light) and pearlite (dark) bands in 1020steel hot-rolled plate. Nital etch, light micrograph. [29].
The typical crystal morphologies of a transverse section in an as-cast steel shape
are shown in Fig. 2.4. The columnar and interior equiaxed grains form by a dendritic
solidification mechanism due to constitutional supercooling and preferred crystallo-
graphic growth [29]. Partitioning of alloying elements between parent liquid and the
solidifying secondary dendritic arms produces a non-uniform distribution of these
elements through the thickness of sheet steel [29], exemplified in Fig. 2.5. As so-
lidification proceeds, the concentration of solutes in the remaining liquid increases,
translating into the highest solute content of the steel being partitioned into the last
liquid to freeze [29], i.e. at the sheet centerline. Secondary dendrite arm spacing
grows with increasing section size, increasing distance from the slab surface, and with
decreasing cooling rate [29]. Therefore, segregation in sheet steel may be minimized
CHAPTER 2. LITERATURE REVIEW 18
through the casting of thinner gauges [29]. Hot rolling aligns the inter-dendritic seg-
regation of alloying elements into bands along the rolling direction [29]. Due to the
low diffusion coefficients of substitutional alloying elements, the homogenizing effects
of hot-rolling are minimal [29].
Figure 2.4: Schematic diagram of zones of crystal morphologiesin an as-solidified section of steel [40]. Shown are the outerchill zone, the columnar zone, and the interior equiaxed zone.
Solute elements with a lower equilibrium partition ratio have the greatest tendency
to segregate, but the amount of element present in the steel is another important
factor [29]. Manganese, generally present in very high concentrations relative to other
alloying additions in DP steels, is generally accepted to play a more important role in
segregation and banding [29,39]. An example of this concentration of manganese into
CHAPTER 2. LITERATURE REVIEW 19
Figure 2.5: Schematic of dendritic solidification [41]. The darkshading in liquid adjacent to dendrites represents concentra-tions of solute atoms rejected from solid. Due to the thin gaugeof sheet product, primary dendritic arms would predominantlybe aligned along the through-thickness direction.
CHAPTER 2. LITERATURE REVIEW 20
bands is provided in Fig. 2.6 for a quench and tempered 4140 steel bar, containing
by heat analysis 1.00 pct. Mn. The longitudinal banding of ferrite and pearlite in
hypoeutectoid steels, such as in Fig. 2.3, is explained by the banded distribution of
manganese. Manganese acts to stabilize austenite and thus reduces Ar3 temperature.
Upon cooling, ferrite forms first in austenite with a low concentration of manganese,
i.e. along low-Mn bands, and rejects carbon into high-Mn bands as it grows [29]. Thus,
the austenite in these high-Mn, high-C bands eventually transforms into pearlite [29].
It is worth noting that with austenite grain sizes greater than the wavelength of
chemical segregation, microstructural constituent banding upon cooling is eliminated
[29].
Figure 2.6: Variations in Mn and C concentrations across aquench and tempered 4140 steel bar, 95.25 mm in diameterand containing by heat analysis 1.00 pct. Mn [42]. Electronmicroprobe analysis.
CHAPTER 2. LITERATURE REVIEW 21
2.2 DP Steel Mechanical Properties
The mechanical properties of a DP steel are highly dependent upon the volume
fraction, carbon concentration, and spatial distribution of non-ferritic phases and
constituents (NFP) in the microstructure [31]. The transformation of austenite to
martensite requires a volume expansion of approximately 2 to 4 percent [43,44]. Sur-
rounding ferrite grains must plastically accommodate this volume expansion, which
produces a high dislocation density in the ferrite near the ferrite-martensite interface
and produces residual stresses. The highly mobile dislocations and residual stresses
result in a low yield stress for DP steels [34, 44, 45]. Plastic flow generally begins
simultaneously at many sites throughout a DP steel tensile specimen, suppressing
discontinuous yielding [46]. These characteristics are clearly evident when compared
to the higher yield stress and yield point phenomena of a microalloyed steel shown
in Fig. 2.7. The naming of DP steels follows the convention of DP-UTS, where UTS
is the ultimate tensile strength of the steel quoted in MPa. For instance, a steel
classified as DP780 is expected to have a UTS of 780 MPa.
2.2.1 Strength
The relatively high strength of DP steels is a result of a composite strengthening
effect contributed by hard martensite in a ductile ferrite matrix. The yield and
tensile strengths of DP steels have been reported to increase in a linear [45, 47, 48]
and a non-linear [49–52] manner with increasing martensite volume fraction by many
researchers. It has been proposed that the non-linear relationship, deviating from the
rule of mixtures, is a result of changing martensite strengths due to differing carbon
content in the martensite; a result of the range of IC annealing temperatures used
CHAPTER 2. LITERATURE REVIEW 22
Figure 2.7: Tensile stress-strain behaviour of a DP steel and amicroalloyed steel [8].
to vary martensite volume fraction. The cause of the differences in these findings is
unclear, but may be related to scatter in experimental data and testing of DP steels
with a limited range of martensite volume fractions [6]. Changes in the strength of
the ferrite phase, resultant from grain size, solid solution hardening, and precipitation
hardening can also affect the strength of the mixture.
2.2.2 Constituent Strain Incompatibility
Despite DP steels exhibiting macroscopically homogeneous and uniform deformation,
the microscopic plastic deformation is inherently heterogeneous due to the differing
strength levels of martensite and ferrite [53]. Shen et al. [54] used a scanning electron
microscope (SEM) equipped with an in-situ tensile straining stage to demonstrate the
inhomogeneous strain distributions between ferrite grains and martensite particles in
CHAPTER 2. LITERATURE REVIEW 23
DP steels. The group observed that, in general, ferrite grains deformed immediately
and at a much higher rate than martensite particles, whose deformation was delayed.
These results have been confirmed via in-situ SEM testing by Ghadbeigi et al. and
Tasan et al. [55, 56].
2.2.3 Work Hardening
During deformation of a DP steel, strain is not distributed evenly between ferrite
and martensite; a plastic incompatibility exists between the two. This leads to a
rapid buildup of back stresses in ferrite and coincident with this is the elimination of
residual stresses caused by the martensitic transformation, contributing to the very
high initial work hardening rate of DP steels [6]. Work hardening of DP steels can
be simplified to three stages [34,57,58], with the aforementioned classified as stage 1
between 0.1-0.5% strain. Stage 2, from approximately 0.5-4.0% strain, consists of a
reduced work hardening rate of ferrite due to strain incompatibility constraining the
plastic flow of ferrite. Stage 3 involves the formation of dislocation cell structures,
cross slip and dynamic recovery of ferrite, and eventual yielding of martensite.
2.2.4 Ductility
Many factors are known to influence the ductility of DP steels [6]: volume fraction of
martensite, carbon content of martensite, plasticity of martensite, spatial distribution
of martensite, alloy content of ferrite, amount of epitaxial ferrite, and the amount
of retained austenite. Uniform elongation is known to decrease non-linearly with
increasing martensite volume fraction [47,49] and to increase slightly with decreasing
martensite carbon content [49]. The former effect is presumably produced by an
CHAPTER 2. LITERATURE REVIEW 24
increase in the number of voids nucleated with increasing martensite volume fraction.
The latter effect may be due to reduced strain incompatibility between martensite
and ferrite, leading to a reduction in the ease with which void damage may form [49].
A uniform spatial distribution of widely-spaced small martensite particles is desirable
for increased ductility [6]. A banded martensite distribution offers an easy crack
propagation path (stress-state dependent), thus adversely affecting ductility [6, 27].
2.2.5 Sheet Metal Formability
The history, construction, and use of forming limit diagrams (FLDs), created to
delimit the maximal safe deformation in strain space for sheet product, is clearly
described in the works of Pilkey, Valletta, Kilfoil, and Lawrence [59–62]. For the sake
of brevity, the reader is referred to these resources for detailed information on the
subject matter.
2.2.6 In-Plane Plane-Strain Tensile Testing
The formability limits, i.e. the occurrence of local necking, of sheet material are
typically lower in plane-strain than any other proportional forming path. As men-
tioned previously, DP steel components have been known to fail prematurely via
shear fracture during forming in plane-strain bending areas. In-plane plane-strain
(IPPS) tensile testing is advantageous in that it may be performed on sheet material
to produce an approximate plane-strain forming path using typical tensile testing
equipment. The wide geometry of the tensile IPPS specimens used and their notch
geometry produce a condition of near full constraint of strain in the minor direc-
tion at the center of specimens, with deformation occurring mainly in the major and
CHAPTER 2. LITERATURE REVIEW 25
through-thickness directions. Again, for the sake of brevity, the reader is referred to
the works of Valletta, Kilfoil, and Lawrence [60–62] for detailed information concern-
ing the history and development of IPPS tensile testing. The methods corresponding
to this mechanical testing protocol are clearly outlined in Sec. 3.4.
2.3 Ductile Failure
The failure of DP steels has been reported by many researchers to take place through
ductile failure [49, 53, 58, 63–78], i.e. microscopic deformation behaviour leading to
plastic strain localization. Critically, plastic strain localization is preceded by diffuse
necking. Deformation of a metal prior to the occurrence of diffuse necking is re-
soundingly believed to be controlled by elemental plastic properties; crystallographic
texture being the most dominant of these [79]. The development of plastic strain
localization, also referred to as local necking, is believed to be controlled by mi-
crostructural inhomogeneities [79]. For DP steels, hard NFP particles plus inclusions
and the voids formed in association with each represent the inhomogeneities critical
to plastic localization.
For a high purity BCC or FCC polycrystalline metal with negligible second phase
or impurity content, final failure under tensile load occurs through nearly 100% area
reduction of the external neck [80, 81]. This form of ductile failure is termed plastic
failure [82]. However, practical engineering alloys, such as DP steels, contain large
numbers of microstructural inhomogeneities in the form of second phase particles
and inclusions among others. As such, DP steels fail in a ductile manner not through
plastic failure, but via two other mechanisms described according to Ashby et al. [82]
as ductile fracture and shear fracture; both of which are the focus of this study. These
CHAPTER 2. LITERATURE REVIEW 26
mechanisms, along with plastic failure, are illustrated in Fig. 2.8.
Ductile fracture takes place by three non-mutually exclusive [59] component mech-
anisms; namely void nucleation, void growth, and void coalescence [83]. During plastic
flow, voids nucleate at microstructural inhomogeneities and continuously grow due to
the externally applied stress and strain-rate field [83]. Eventually, these voids become
numerous and large enough to cause localization of strain and increased void-void in-
teractions; resulting in the breaking or necking-down of inter-void ligaments. This
interplay of void nucleation, growth, and coalescence continues until a critically-sized
flaw activates final fracture [59].
Shear fracture, in the sense of a ductile failure, is produced by the formation of a
macroscopic shear band across a developing neck [59]. Often this process is facilitated
in part by the production of planar sheets of microvoids in regions of intense plastic
flow [59]. This form of failure typically exhibits reduced degrees of through-thickness
thinning compared to ductile fracture.
2.3.1 Void Nucleation
It has generally been assumed throughout a great portion of literature that all damage
nucleates solely at the onset of plastic deformation, followed purely by growth and
no further nucleation [85–89]. It has been verified through experimentation that this
assumption is invalid; damage nucleation in ductile materials is progressive [20,90,91].
Maire et al. [22] found two distinct regimes of void nucleation with respect to local
strain during XµCT in-situ tensile testing of a DP600 steel: a linear void nucleation
rate with local strain up until the point of necking, at which time voids began to
nucleate at an exponential rate due to increased stress triaxiality (Fig. 2.9). Poruks
CHAPTER 2. LITERATURE REVIEW 27
(a) Plastic failure (b) Ductile fracture (c) Shear fracture
Figure 2.8: General categories of fracture processes in metals[84]. Note that final failure in ductile and shear fracture maybe transgranular as shown or intergranular.
et al. [92] and Avramovic-Cingara et al. [14] have confirmed this void nucleation trend
for a bainitic and DP600 steel respectively. Void density has been shown throughout
the literature to increase towards the fracture surface and to be greater in samples
which exhibit localized necking [14,22,72]. This is of course explained by an increasing
strain gradient with increasing proximity to the fracture surface.
2.3.1.1 Void Nucleation Mechanisms
Void nucleation occurs at material discontinuities such as second phase particles,
inclusions, and grain boundary triple points [59, 83]. In the case of DP steels, void
nucleation has been reported by many investigators to occur as a result of both
martensite particle fracture and ferrite-martensite interfacial decohesion [22, 66, 68–
72,93,94]. It has been pointed out by Balliger [70], Gladman [69], and Koo [71] that
CHAPTER 2. LITERATURE REVIEW 28
Figure 2.9: The evolution of void nucleation in a DP600 tensilespecimen with a clear linear regime prior to necking and anexponential regime post-necking [22]. Data captured in 3-Dusing synchrotron XµCT.
the largest voids are nucleated via martensite particle fracture. Speich and Miller [49]
observed void nucleation to occur only via ferrite-martensite interfacial decohesion for
low martensite volume fractions, while martensite cracking also operated for higher
martensite volume fractions. Szewczyk and Gurland [75] echoed these results by
failing to observe any martensite particle cracking for martensite volume fractions in
the range of 15-20%. Avramovic-Cingara et al. and Poruks et al. [15, 92] reported
that void nucleation via ferrite-martensite interfacial decohesion occurs generally on
the interface perpendicular to the tensile axis.
Many other researchers have reported that void nucleation occurs primarily due
to ferrite-martensite interfacial decohesion [49,58,67,75,76]. Nam and Bae [76] stated
that overwhelming reports find the majority of voids which lead to fracture are nucle-
ated via ferrite-martensite interfacial decohesion, rather than via martensite particle
CHAPTER 2. LITERATURE REVIEW 29
cracking.
Steinbrunner and Krauss [72] observed void nucleation to occur via the aforemen-
tioned mechanisms plus the separation of deformed martensite particles. Ahmed et
al. [77] reported a unique mechanism of void nucleation via decohesion at ferrite-ferrite
interfaces with minimum plastic deformation. They reported that for low to interme-
diate martensite volume fraction, void formation was due to ferrite-martensite inter-
facial decohesion. Otherwise for martensite volume fractions above 32%, martensite
particle cracking and ferrite-ferrite decohesion mechanisms also operated. Avramovic-
Cingara et al. observed a small number of voids to have nucleated at inclusions [15].
These voids were relatively large and non-negligible in terms of their contribution to
void volume fraction [15].
The variation reported for the aforementioned void nucleation mechanisms ap-
pears to be a function of DP steel chemical compositions, heat treatment histories,
and microstructural differences [15]. Some of these characteristics and their potential
effects on void damage nucleation in DP steels under uniaxial tension are outlined in
the following subsections.
Effect of Martensite Particle Size
Martensite particle size has been shown in the literature to have a significant effect on
the strength and damage behaviour of DP steels [14,15,19]. It has been emphasized by
many research workers that the probability of fracture of martensite increases with
increasing martensite grain size [95–97]. For a Fe-2Si-0.1C DP steel with a coarse
martensite structure, Kim and Thomas [74] have reported uniaxial tensile failure
via ferrite cleavage due to maximum localized stress concentrations in these grains.
CHAPTER 2. LITERATURE REVIEW 30
For both fine fibrous and fine globular martensite microstructures of the DP steel
chemistry used, it was reported that failure occurred via void nucleation, growth,
and coalescence after large degrees of straining. These voids formed at the ferrite-
martensite interfaces.
He et al. [19] studied the evolution of damage in Fe-Mn-C DP600 steels with 17%
volume fraction of martensite; one with coarse martensite particles and the other
with fine martensite. Under uniaxial tension it was reported that coarse structures
of martensite tend to initiate voids due to cracking of the martensite at very low
strain levels, i.e. in the uniformly elongated region [19]. This was followed by interfa-
cial decohesion at ferrite-martensite interfaces for higher strain levels; the dominant
mechanism in the necked region. Cracks that initiated within martensite particles
always traversed the entire particle and were always arrested by ferrite grains [19].
For the material with finer martensite grains, the majority of voids were observed
to form via decohesion of the ferrite-martensite interfaces, attributed to the strain
incompatibility between the two phases [19]. Most of this decohesion was observed
in the non-uniformly elongated region. The size of voids in the strained material was
reported to be directly related to the size of martensite islands, for both modes of void
nucleation. It should be mentioned that the coarse martensite material failed via void
nucleation and coalescence at the center of the sample (via both martensite cracking
and ferrite-martensite decohesion), with ferrite cleavage at the sample edges due to
sharp rises in the stress level as damage accumulated in the center of the sample. The
fine-grained martensite material failed purely in a ductile manner.
The work of Erdogan [98] agreed with the aforementioned void nucleation mecha-
nism observations. Coarse martensite that was interconnected and distributed along
CHAPTER 2. LITERATURE REVIEW 31
ferrite grain boundaries cracked easily. Finer martensite that was not as intercon-
nected, but still distributed along ferrite grain boundaries, cracked less easily. Kad-
khodapour et al. [53] also observed that the interfacial decohesion of ferrite grains
mainly occurs in regions where two ferrite grains have a long contact surface with
the martensite. This was explained by the strain incompatibility between ferrite and
martensite.
Effect of Martensite Particle Shape
The shape of martensite particles is an important factor to consider. Elongated
particles experience a stress similar to that of fibers in a composite material [19].
That is, the stress in elongated second phase particles is thought to be proportional
to the ratio of the length to the width of the particle [19]. As well, martensite particles
elongated in the tensile direction are thought by Han et al. [99] to produce multiple,
sequential nucleation of voids which join by coalescence. This sentiment is echoed by
Avramovic et al. [14], reporting that elongated martensite particles with the major
axis aligned with the tensile axis of the sample will fracture preferentially. This is
in contrast to the work of Nam and Bae [76] who reported that unlike martensite
particles aligned nearly parallel with the drawing axis, which are thinned to fibrous
shape, those particles aligned transverse to the drawing axis are severely bent and
even fractured with increasing drawing strain.
Sun and Pugh [66] reported that void nucleation occurs by both ferrite-martensite
decohesion and martensite cracking, depending upon the martensite morphology.
Elongated martensite ribbons were observed to be most prone to martensite cracking.
CHAPTER 2. LITERATURE REVIEW 32
Effect of Martensite Spatial Distribution
Distribution of martensite particles carries strong implications for the strength and
damage behaviour of dual phase steels. In terms of the spatial distribution of marten-
site with respect to ferrite grains, martensite grains located close together produce rel-
atively undesirable damage properties. The strain incompatibility between the closely
situated martensite particles and ferrite grains results in a condition that prevents
deformation of ferrite due to a need to maintain grain boundary coherence between
the two phases [19]. Being that martensite is very brittle, cracking typically occurs
for these clustered particles, firstly those with quenching flaws, with the subsequent
nucleation and growth of a void to geometrically allow for ferrite deformation [19].
Such a process quickly leads to an increase in the volume fraction of voids present,
resulting in the rapid formation of a neck. Decohesion of ferrite-martensite interfaces
within the necked region nucleates further voids which grow and coalesce to produce
a central cavity in the sample. This results in a high stress level in the tensile sample
that the microstructure is incapable of supporting, resulting in rapid cleavage failure.
A microstructure that contains well dispersed martensite islands provides much
more desirable mechanical properties and delayed nucleation of void damage. This
is because plastic flow of ferrite grains is not as restricted due to reduced interfacial
constraints at the ferrite grain boundaries [19]. Plastic deformation of ferrite grains
reduces stress concentrations in the microstructure and prevents cracking of marten-
site particles [19]. As plastic deformation of the ferrite grains increases, voids form
via ferrite-martensite decohesion as a result of the strain incompatibility between the
two phases [19]. However, these voids form progressively with strain and result in a
ductile fracture that occurs after a large elongation [19].
CHAPTER 2. LITERATURE REVIEW 33
Avramovic et al. [14] performed a uniaxial tension study on two galvannealed
DP600 steels with differing chemistry, both with roughly 20% martensite volume
fraction, and both with differing banded microstructures. DP600A exhibited strong
banding of martensite along the sheet centerline in the rolling direction, whereas
DP600B exhibited martensite bands aligned in the rolling direction dispersed rela-
tively uniformly throughout the sheet thickness. Void damage in the DP600A steel
was highly concentrated at the sheet centerline where a coarse martensite band was
located, as seen in Fig. 2.10(a). The largest voids were also located at the sheet
centerline, nucleated by martensite cracking. Away from this band, voids nucleated
typically by ferrite-martensite decohesion. In the DP600B steel, void damage was
distributed relatively uniformly throughout the thickness as in Fig. 2.10(b), reflect-
ing the distribution of martensite bands throughout the thickness. The steel with a
more uniform distribution of martensite, DP600B, showed a slower rate of damage
growth and a continuous void nucleation during the deformation process, which re-
sulted in a higher void density before fracture. The steel with coarse sheet centerline
banding of martensite through the thickness exhibited accelerated void growth and
catastrophic coalescence in the transverse orientation to the applied load. Interest-
ingly, void growth and coalescence was observed preferentially along the plane normal
to applied load in DP600A, the opposite of DP600B for which void growth occurred
preferentially along ferrite grain boundaries parallel to applied load. As well, the
ductile dimples of the fracture surfaces of both steels closely reflected the distribution
of martensite in the microstructures.
CHAPTER 2. LITERATURE REVIEW 34
(a) (b)
Figure 2.10: Voids revealed by light microscopy in a polishedthrough-thickness longitudinal cross-section of (a) DP600A and(b) DP600B steels. Strong concentration of voids at the sheetcenterline is visible in DP600A. [14]
Effect of Martensite Carbon Content
Mazinani and Poole [100] have reported that martensite plasticity is capable of re-
ducing strain incompatibility between ferrite and martensite particles and thus makes
decohesion of these interfaces and subsequent void nucleation more difficult, resulting
in both higher fracture stresses and strains. For martensite particles to be capable of
significant plastic deformation, their strength must be reduced via decreased carbon
content [100]. This can be achieved through tempering or through an increase of the
martensite volume fraction due to a mass balance [100]. Szewczyk and Gurland [75]
have also reported this martensite plasticity effect for DP steels, particularly in the
neck of tensile specimens. Speich and Miller [49] observed that low volume fractions
and high carbon contents of martensite resulted in easier ferrite-martensite decohesion
than in microstructures of high volume fractions and low carbon contents of marten-
site. Avramovic-Cingara et al. [14] observed in two DP600 steels of similar martensite
CHAPTER 2. LITERATURE REVIEW 35
volume fraction but differing carbon content that the higher carbon martensite pro-
duced a higher tendency for void nucleation via ferrite-martensite decohesion.
In contrast, Kang and Kwon [73] identified void nucleation to occur predominantly
by ferrite-martensite interfacial decohesion for lath-type martensite, i.e. low-carbon
martensite. Plate martensite, typically of higher carbon content, was observed to
nucleate voids predominantly via cleavage cracking.
2.3.1.2 Critical Nucleation Strain
A critical stress/strain must be achieved prior to nucleation of a microvoid by in-
terfacial decohesion or particle cracking. Avramovic-Cingara et al. [15] calculated a
critical nucleation thickness strain for a banded DP600 steel of 0.15. Steinbrunner et
al. [72] observed void nucleation via fractured martensite particles at global strains
as low as 0.05 for DP steel of a similar chemical composition. For another banded
DP600 steel of the same NFP volume fraction, but different chemical composition and
significantly coarser banding at the sheet centerline, Avramovic-Cingara et al. [14] re-
ported a critical local true void nucleation strain of 0.029 for martensite cracking and
0.09 for ferrite-martensite decohesion.
2.3.2 Void Growth
Subsequent to the nucleation of microvoids, an externally applied stress and plastic
strain-rate field results in the continuous plastic growth of microvoids [83]. Experi-
mental studies have shown that void growth is primarily extensional in nature along
the tensile axis in the central regions of necked tension specimens where the maxi-
mum mean normal stress was approximately 0.7 times that of the yield strength [83].
CHAPTER 2. LITERATURE REVIEW 36
Work with DP steels under uniaxial tension has confirmed this observation, with
Avramovic-Cingara et al. [15] reporting that nucleated microvoids grew longitudi-
nally along ferrite grain boundaries parallel to the tensile loading direction.
Factors experimentally determined to influence void growth behaviour include
stress state and strain hardening rate [59]. It has been demonstrated that a state of
increased stress triaxiality increases both dilational void growth [101] and void growth
rates [85,101]. This dependance of void growth rate upon tensile stress triaxiality has
been shown to be exponential in nature [102–107]. Rationally, the application of a
hydrostatic pressure upon deforming tensile specimens reduces tensile stress triaxiality
and thus dilational void growth [108]. The rate of void growth has been demonstrated
in maraging steels to depend upon yield strength, with increasing yield strength
resulting in increased growth rates [109,110]. This effect has been explained by a lower
strain-hardening rate and higher applied stresses in steels of greater strength [59].
2.3.3 Void Coalescence
Void coalescence is the least understood portion of ductile failure due to the ra-
pidity with which it typically precipitates final failure [59]. Two prevailing forms
of coalescence behaviour have been experimentally observed [59]. The first is the
formation of a shear band between closely-spaced voids which ultimately severs the
inter-void ligament [111,112]. As well, this intense plastic shear can nucleate a plane
of voids, known as void sheeting, which assist in the severing of the inter-void liga-
ment. The other form of void coalescence simply involves stable void growth until
the inter-void ligament has necked down entirely, impinging the two voids upon one
another [112–114].
CHAPTER 2. LITERATURE REVIEW 37
2.3.4 Fracture Surface Orientation
The orientation(s) of a ductile fracture surface for a mechanical testing specimen is
heavily dependent upon the volume fraction of second phase present, the specimen
geometry, and the loading of the specimen. For instance, to elicit the typical cup-
cone ductile fracture surface of uniaxial tensile testing of round bar, clearly a critical
condition must precipitate intervention from void coalescence across the plane normal
to the tensile direction in a macroscopically homogeneous state of plastic flow to
a localized mode of internal microscopic necking across a sheet of microvoids [83].
This intervention is mathematically equivalent to the development of a stationary
velocity-discontinuity in the plastic velocity-field [83]. The work of Hill [115] provides
an invariant formulation of the conditions necessary for determining the location of
characteristic surfaces on which fracture surfaces can develop in a plastic velocity
field. Applying Hill’s formulated condition to a state of plane-strain plastic velocity-
fields, it has been shown that the characteristic surfaces upon which fractures tend to
form along are oriented 45◦ with respect to the major strain direction [83]. However,
despite this tendency for final ductile fracture under plane-strain to occur on a plane
45◦ with respect to the major strain direction, this is not always the case. Final
ductile fracture surfaces are not confined to their respective characteristic surfaces of
a particular plastic field and can develop on other surfaces under certain circumstances
[83]. As pointed out by Thomason [116], this is because the internal necking form of
microvoid coalescence differs to first order from the previous stable, macroscopically
homogeneous state of plastic flow.
CHAPTER 2. LITERATURE REVIEW 38
2.4 Damage Characterization
Typically, investigation into the process of ductile failure of steels via void nucle-
ation, growth, and coalescence has been undertaken with scanning electron or light
microscopy of strained and failed mechanical testing samples [14–19]. This technique
is beset with many drawbacks, including the need to use a sectioning technique that
accurately preserves the integrity of the void structure developed during deformation,
such as electric discharge machining or the use of a focused ion beam. This act of
sectioning irreversibly destroys the integrity of the original failed specimen. As well,
SEM analysis provides only two-dimensional data at the discrete planes of sectioning
concerning the morphology of voids. As such, extracting robust 3-D data concerning
void morphology and spatial distribution requires a time-intensive serial-sectioning
technique whereby a small layer of material is removed between subsequent 2-D im-
age captures, which can later be stacked to form a 3-D reconstruction of the volume
sampled.
These limitations, and recent advancements in the resolution of synchrotron beam-
lines have led to the use of synchrotron X-ray micro-computed tomography (XµCT)
to characterize damage evolution in materials as dense as automotive structural steels.
The advantages of such a technique include that it is non-destructive, relatively fast,
and provides 3-D information on the morphology of voids. However, unlike SEM
study, phases of similar density cannot be differentiated by greyscale contrast using
XµCT. This limitation prevents simultaneous analysis of the microscopic features
and mechanisms that can lead to premature failures during typical forming opera-
tions for DP steels due to the very similar densities of ferrite and martensite phases.
Thus, it is necessary to couple light or scanning electron microscopy analysis of failed
CHAPTER 2. LITERATURE REVIEW 39
or interrupted mechanical samples with XµCT results. It has been demonstrated
that X-ray absorption micro-computed tomography is the most reliable method for
obtaining three-dimensional quantitative information about void damage in mate-
rials [20, 21]. The following subsection presents the basic theory encompassing the
XµCT technique.
2.4.1 X-ray Micro-computed Tomography
XµCT makes use of an X-ray source to image materials in three dimensions at high
spatial (below 1 µm) resolutions [117]. The technique is based upon X-ray radiogra-
phy: X-ray photons are directed at a sample for a defined period of time and those
photons that are transmitted through or around the sample are counted/recorded by a
detector. For X-ray tomography, charge-coupled device (CCD) detectors are typically
used. Detectors may be 1-D (linear) or 2-D as shown in Fig. 2.11, the latter providing
faster acquisition times by eliminating the need for sample vertical translation.
2.4.1.1 Micro-focus X-ray Sources
Lab X-ray sources, also known as micro-focus sources, produce polychromatic, conical
X-ray beams. High potential differences on the order of tens of kV are produced be-
tween the cathode and anode (target) of an X-ray tube. This large potential difference
causes electrons to travel from the cathode to the anode, impacting the atoms of the
target. When these incident electrons interact with shell electrons of the target atoms,
it is possible that a shell electron may be ejected and the incident electron scattered.
This results in an electron vacancy in said shell that will be filled by an electron
dropping from a higher-energy shell, producing an x-ray photon (of discrete energy
CHAPTER 2. LITERATURE REVIEW 40
Figure 2.11: XµCT beam and detector geometries. (a) Fanbeam geometry: micro-focus X-ray source with 1D detector.The sample requires vertical translation to be scanned. (b)Cone-beam geometry: micro-focus source with 2D detector.The sample is magnified on the detector. (c) Parallel beamgeometry: synchrotron source ensures nearly parallel X-raybeams. The sample is negligibly magnified on the detector.Not shown are a scintillating material that is used to convertthe wavelength of the radiation from X-ray to visible light andan optical objective for image magnification [118].
level) with the latent energy; i.e. characteristic X-ray generation. Bremsstrahlung
radiation, carrying a continuum of photon energy levels, is also produced in lab X-ray
sources due to incident electron path changes resulting from interactions with tar-
get atom electrons. Both characteristic and Bremsstrahlung radiation are shown in
Fig. 2.12.
2.4.1.2 X-ray attenuation
X-ray beams produced from a synchrotron source are typically monochromated. This
is useful in X-ray tomography as it eliminates artifacts due to beam hardening and
can allow for quantitative phase analysis due to a direct relationship between the grey
level of projections and the absorption coefficient of phases [118]. This absorption
coefficient is linked to the density and the atomic number of materials, plus the energy
CHAPTER 2. LITERATURE REVIEW 41
Figure 2.12: X-ray spectrum of a molybdenum target asa function of applied voltage. Shown are the continuousBremsstrahlung radiation and the discretely peaked character-istic radiation produced. [119]
of impinging X-rays. Thus, when a beam is monochromated to a single energy, E,
grey levels in projections become purely a function of the material density, ρ, and
atomic number, Z, plus a constant K as in Eq. 2.1 [117]. Monochromators for lab-
scale tomography, i.e. micro-focus X-ray sources, are currently prohibitively costly for
many research groups. In the case of a polychromatic beam, grey levels in projections
are not purely a function of material density and thus reconstructions from these
projections are inherently subject to slightly increased noise.
µ(x, y, z) = KρZ4
E3(2.1)
The probability of X-ray attenuation in a material is a function of the probability
of photoelectric absorption and the probability of Compton scattering, both of which
CHAPTER 2. LITERATURE REVIEW 42
are related to the density and atomic number of the material. As mentioned previ-
ously, the basis of X-ray tomography is X-ray radiography. X-rays pass through a
material sample according to the Beer-Lambert law [118]. The ratio of the number
of transmitted to incident photons is related to the integral of the absorption coef-
ficient, µ, along the path that the photons follow through the sample [118] and is
also dependent upon the energy of the incident photons. This can be represented in
Eq. 2.2 [117] with the number of incident photons, N0, of energy E, the number of
transmitted photons, N1, of energy E, and the corresponding attenuation coefficient,
µ, of the sample along the X-ray path, s :
N1
N0= e[−
∫sεray
µ(s)δs] (2.2)
2.4.1.3 Tomography Fundamentals
Transmitted photons are recorded by a detector, typically a CCD, with counts recorded
at each pixel. It is necessary to use a scintillating material between the sample and
detector to change the wavelength of the transmitted photons from the X-ray spec-
trum to the visible light spectrum. Optical objectives are often placed between the
scintillator and the detector as well for magnification purposes. The counts collected
by the CCD are transposed into grey level intensities of an image of the sample. This
image represents a two-dimensional projection of the three-dimensional object. In
order to obtain 3D information about the sample, a large number of 2D projections
of the sample are radiographically recorded between periodic rotations of the sample
between 0◦ and 180◦ about a single axis. With enough projections of high signal to
noise ratio throughout the 180◦ scan, a 3-D reconstruction of the sample comprised
CHAPTER 2. LITERATURE REVIEW 43
of stacked 2D slices can be produced using a filtered back-projection algorithm. An
explanation of the calculations made during filtered back-projection are beyond the
scope of this dissertation. A simplified representation of a tomographic setup is pro-
vided in Fig. 2.13.
Figure 2.13: Simplified schematic of an X-ray tomographicsetup [120]. The source shown is that of a lab-scale X-ray tubeproducing a conical beam. The sample is typically mountedon a stage capable of rotation and Cartesian translation. Itshould be noted that unlike what is depicted in the schematic,specimens are typically of lesser width than field of view madeavailable at the CCD by the optics of the system.
There are three typical modes in which to perform tomography: absorption mode,
phase contrast mode, and holotomography mode. Absorption mode is the most typ-
ical and develops contrast between constituents in a material based upon their re-
spective absorption coefficients. The greater the difference in the density and the
atomic number of constituents, the greater the contrast that is developed between
them. The detector needs to be placed close to the sample to avoid phase effects [118].
The degree of transmission through the sample is also of importance; too great, and
CHAPTER 2. LITERATURE REVIEW 44
sufficient contrast is not developed between constituents; too low, and the signal to
noise ratio of projections is inadequate [118]. For synchrotron XµCT, a reasonable
compromise between both effects is a transmission of around 10% [118].
2.4.1.4 Artifacts
In the context of XµCT, an artifact refers to any systematic discrepancy between
greyscale values in a reconstructed volume and the true attenuation coefficients of
the material within that volume [121]. These artifacts may hinder qualitative and
quantitative interpretation of reconstructions. The most common artifacts to affect
reconstructions of tomographic datasets captured using lab-scale XµCT are outlined
below.
Beam Hardening
Beam hardening is a phenomenon that affects tomographic reconstructions produced
using a polychromatic X-ray beam. The spectra of energy levels which the photons of
the beam possess is the root cause of this type of artifact. As the polychromatic X-ray
beam passes through an object, its mean energy level increases as lower-energy pho-
tons are attenuated more easily than higher-energy photons; hence the term “harden-
ing”. Obviously, attenuation of lower-energy photons occurs to a greater degree with
increasing path length through an attenuating material. Thus, X-ray projections
of an object of uniform attenuation coefficient, but variable thickness, i.e. variable
photon path length, will exhibit a characteristically darker intensity in the regions
of greater thickness where the beam has been hardened. In reconstructions, beam
hardening artifacts are exhibited as a distinct cupping effect in greyscale intensity
CHAPTER 2. LITERATURE REVIEW 45
through specimen thickness, such as in Fig. 2.14.
Beam hardening can be minimized by using physical filters to attenuate some of
the lower-energy photons from the X-ray beam prior to interaction with the specimen
being imaged. As well, post-processing may be applied to provide a correction to
reconstructions suffering from beam hardening artifacts.
Figure 2.14: Intensity profiles plotted across a reconstructedslice of a uniform water phantom: a) suffering from a beamhardening artifact; and b) corrected for beam hardening viapost-processing [121].
Ring Artifacts
Inhomogeneities, i.e. defects, in the scintillators used to convert radiation from the X-
ray spectrum to the visible light spectrum produce repeatable artifacts in tomographic
projections. These artifacts occur at the same locations relative to the field of view
(FOV) and result in ring artifacts in reconstructed slices, such as in Fig. 2.15.
CHAPTER 2. LITERATURE REVIEW 46
Figure 2.15: Severe ring artifacts in a reconstructed slice of afailed DP steel uniaxial tension specimen. It should be notedthat the signal to noise ratio in this reconstruction is very pooras well.
CHAPTER 2. LITERATURE REVIEW 47
Streak Artifacts
Higher energy X-rays, i.e. 100 to 150 kV, are likely to sometimes pass right through the
thinner scintillating screens on the 10x and 20x objectives of Xradia’s Micro-XCT 400.
When this occurs, the X-ray photons may carry on and impact the CCD, resulting
in a saturated pixel which will appear as a bright “speckle” in single projections and
line or streak artifacts in reconstructed slices as shown in Fig. 2.16.
Figure 2.16: A streak artifact (line) in a reconstructed sliceof a failed DP steel IPPS tension specimen, resultant from aspeckle in projection data.
CHAPTER 2. LITERATURE REVIEW 48
2.4.2 Previous XµCT Experimentation
Previous studies have taken advantage of XµCT’s capability to provide a wealth of
information regarding void damage morphology in steels for uniaxial tensile loading
[22,24,122], but these have been performed on a synchrotron beamline where current
generation synchrotron X-ray sources can deliver fluxes greater than 1000 times those
generated by X-ray tubes [118]. This high flux allows for better quality images in
terms of signal-to-noise ratio. The highly collimated nature of synchrotron X-ray
photons also allows for submicron resolutions in some setups [123].
Due to the high linear absorption coefficient (LAC) of steel, the only study in the
literature to date that is known to have used a lab-scale X-ray tube source to perform
micro-computed tomography of a steel specimen is that of Gupta et al. [23]. Such
a high LAC leads to reduced contrast development between voids and surrounding
material. For a CrMoV steel uniaxial tensile specimen loaded to a nominal strain of
17%, Gupta et al. reported 11261 voids within the reconstructed region of the neck
(1.4 mm3), with the largest voids generally elongated in the tensile direction. This
represented a void volume fraction of 0.03%. Voids were predominantly in the range
of 5-19 µm in size.
An important conclusion drawn from the synchrotron XµCT in-situ tensile testing
of cold forging steel by Bouchard et al. [122] was the influence of inclusion orienta-
tion on damage anisotropy. Voids were observed to nucleate and grow at inclusions
primarily in the direction of inclusion orientation. Thus, tensile specimens in which
inclusions were oriented perpendicular to the principal loading direction were observed
to nucleate and grow voids primarily through the thickness of the tensile specimen, as
evident in the radial ‘R’ specimens of Fig. 2.17. This led to void coalescence, strain
CHAPTER 2. LITERATURE REVIEW 49
localization, and final fracture occurring more rapidly in specimens with transversely
oriented inclusions compared to specimens with longitudinally oriented inclusions.
(a)
(b)
Figure 2.17: Void evolution observed by XµCT for a longitudi-nal and radial cold forging steel tensile specimen on: a) a radialcutting plane; and b) a longitudinal cutting plane. [122]
CHAPTER 2. LITERATURE REVIEW 50
For synchrotron XµCT in-situ uniaxial tensile testing of dual-phase steel, Maire
et al. [22] have quantitatively computed void fraction to increase with increasing
proximity to the center of a neck. This trend becomes stronger with increasing strain,
especially after diffuse necking begins (Fig. 2.18(a)). As well, void fraction has been
shown to decrease with increasing proximity to the specimen surface (Fig. 2.18(b)).
This is explained by increased stress triaxiality at the center of a tension specimen.
A novel finding was a quasi-stagnation of the average equivalent diameter of voids
during tension testing of the DP steel studied due to nucleation of new small voids
balancing the growth of larger voids.
2.5 Digital Image Processing
2.5.1 Image Denoising
It is imperative that a filtering operation used on reconstructed tomography slices for
the purposes of denoising not cause any significant loss of fidelity of void morphology.
A typically used Gaussian filter essentially produces a convolution of an image by a
linear symmetric kernel [124]. This form of filtering is optimal for harmonic functions
but does not perform as well in image regions with texture or edges [124]. In these
regions, a blurring effect is produced by a Gaussian filter and results in a loss of fine
detail. A loss of fine detail in the slices produced by tomographic study of deformed
steel specimens would result in a removal of distinctly contrasted edges between voids
and surrounding steel, translating to a degradation in the accuracy of subsequent
thresholding operations’ capture of true void morphology.
A review of image denoising methods performed by Buades et al. [124] revealed a
CHAPTER 2. LITERATURE REVIEW 51
(a)
(b)
Figure 2.18: Profiles of the fraction of voids produced fromin-situ XµCT data for a DP600 steel tension specimen in slicesperpendicular to: a) the tensile axis for various deformationsteps prior to failure; and b) the tensile axis and the two or-thogonal directions in the last deformation stage recorded priorto fracture. [22]
CHAPTER 2. LITERATURE REVIEW 52
Non Local Means (NL-Means) algorithm to be optimal in removing noise from natu-
ral images while preserving fine structures. The method takes advantage of the high
degree of redundancy present in natural images by comparing small windows within
an image for similarity. The estimated true greyscale intensity value for every pixel in
an image is computed as a weighted average of all the pixels in the image, with similar
pixel neighbourhoods given a larger weighting than dissimilar neighbourhoods [125].
This concept is given visual context in Fig. 2.19. An example of the superior perfor-
mance of the NL-means algorithm in preserving fine detail while smoothing greyscale
gradients relative to conventional filtering techniques is demonstrated in Fig. 2.20 and
Fig. 2.21 for a natural image and in Fig. 2.22 for a periodic image. Fig. 2.21 provides
the method noise produced by various algorithms, which is equivalent to the point
operation of subtracting the denoised image from the original image. Ideally, the
method noise resembles white noise as much as possible, is as small as possible, and
does not show any detail from the original image.
CHAPTER 2. LITERATURE REVIEW 53
Figure 2.19: Scheme of NL-means strategy. Similar pixel neigh-borhoods give a large weight, w(p,q1) and w(p,q2), while muchdifferent neighborhoods give a small weight w(p,q3). [125]
CHAPTER 2. LITERATURE REVIEW 54
(a) Original image.
(b) From left to right and from top to bottom: noisy image (standard deviation 20), Gaussian
filtering, anisotropic filtering, Total variation, Neighborhood filtering and NLmeans algorithm. The
removed details must be compared with the method noise (see Fig. 2.21).
Figure 2.20: Denoising of a typical natural image, “Lena”, usingvarious algorithms [125].
CHAPTER 2. LITERATURE REVIEW 55
(a) Original image.
(b) Image method noise. From left to right and from top to bottom: Gaussian
convolution, Mean curvature motion, Total Variation, Iterated Total Varia-
tion, Neighborhood filter, Hard TIWT, Soft TIWT, DCT empirical Wiener
filter and NL-means.
Figure 2.21: Denoising of a typical natural image, “Lena”, usingvarious algorithms. [124]
CHAPTER 2. LITERATURE REVIEW 56
Figure 2.22: Denoising experience on a periodic image. Fromleft to right and from top to bottom: noisy image (standard de-viation 35), Gaussian filtering, Total variation, Neighborhoodfilter, Wiener filter (ideal filter), Hard TIWT, DCT empiricalWiener filtering, NL-means algorithm. [124]
2.5.2 Image Segmentation
An exhaustive review performed by Sezgin et al. [126] of image thresholding tech-
niques and their performance distinguished six general categories of thresholding tech-
niques: histogram shape-based methods, clustering-based methods, entropy-based
methods, object attribute-based methods, spatial methods, and local methods.
Forty algorithms encompassing the six thresholding technique categories were used
to threshold each of forty different non-destructive testing (NDT) images. Perfor-
mance of the algorithms was based upon five criteria: misclassification error, edge
mismatch, relative foreground area error, modified Hausdorff distance, and region
nonuniformity. The clustering-based method of Kittler and Illingworth [127] and the
CHAPTER 2. LITERATURE REVIEW 57
entropy-based methods of Kapur, Sahoo, and Wong [128], and Sahoo, Wilkins, and
Yeager [129], were determined, in that order, to be the best performing thresholding
algorithms in the case of NDT images.
Chapter 3
Experimental Methods and
Materials
This chapter contains a description of the sheet steels provided by U.S. Steel Corpora-
tion for this study. The metallographic techniques employed to characterize the steel
microstructures are described. The heat treatment paths and methodologies used to
produce variants of ferrite-martensite microstructures are documented. Mechanical
testing methods are outlined along with XµCT techniques for subsequent analysis of
void damage within failed specimens.
3.1 Received Material Characteristics
Four steels were used for this study: two classified as DP780 and two as DP980. The
DP780 and DP980 sheets were received in both a cold-rolled (CR) and a galvannealed
(GA) condition. This material was provided by U.S. Steel Corporation. The chem-
ical compositions for these four sheets are given in Table 3.1. It is clear that the
58
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 59
compositions of the two DP780 and DP980 sheets respectively are comparable and
that the carbon content of each alloy is relatively low. The thickness of each sheet is
listed in Table 3.2. It is evident that the gauges of the two DP780 and DP980 sheets,
respectively, are comparable as well.
Table 3.1: Elemental compositions of the sheet steels providedby U.S. Steel Corporation (wt.%); balance is iron. ‘GA’ signi-fies commercial galvannealed sheet and ‘CR’ signifies sheet inthe cold-rolled condition.
DP780 DP780 DP980 DP980GA CR GA CR
C 0.09 0.09 0.1 0.11Mn 2.05 2.1 2.34 2.42P 0.007 0.012 0.01 0.014S 0.006 0.006 0.004 0.006Si 0.016 0.02 0.02 0.02Cu 0.01 0.03 0.02 0.02Ni 0.01 0.01 0.01 0.01Cr 0.25 0.26 0.24 0.25Mo 0.285 0.29 0.33 0.362Sn 0.001 0.003 0.011 0.002Al 0.044 0.039 0.036 0.046N 0.006 0.004 0.004 0.004V 0.001 0.001 0.001 0.001B 0.0001 0 0.0001 0.0001Ti 0.001 0.001 0.001 0.001Cb 0.001 0.002 0.001 0.002
Table 3.2: Thicknesses of the sheet steels provided by U.S. SteelCorporation. ‘GA’ signifies commercial galvannealed sheet and‘CR’ signifies sheet in the cold-rolled condition.
DP780 DP780 DP980 DP980GA CR GA CR
Thickness (mm) 1.02 0.98 1.18 1.19
3.2 DP Steel Microstructural Variant Design
The primary goal of this study was to examine the effects of NFP (particularly marten-
site) volume percent, spatial distribution, and morphology on the failure behaviour
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 60
and accumulation of damage for strained DP steels. As such, microstructural variants
of DP steels with differing martensite particle populations had to be produced. To
accomplish this task, heat treatment procedures were tailored to make use of the cold-
rolled sheet available. A particular goal was to develop two microstructural variants
per cold-rolled alloy with similar NFP volume percent to that of the galvannealed DP
steel alloy of corresponding chemical composition; both variants were to be comprised
entirely of ferrite and martensite, but with differing martensite populations.
To produce these variants, two forms of thermal treatment path were applied
to cold-rolled specimens and various IC annealing temperatures were employed to
control the NFP volume percent.
3.2.1 Thermal Path One
Thermal Path One (TP1) consisted of a simple IC annealing of the cold-rolled steels.
TP1 is represented graphically in Fig. 3.1(a) and described in detail in Sec. 3.2.4.4.
Cold-rolled steel blanks were rapidly heated to a temperature within the alloy’s IC
range (715◦C or 733◦C or 743◦C) and held for 2 minutes before rapidly quenching in
an ice-water bath. This treatment produced a microstructure of banded NFP in a
ferrite matrix due to the highly deformed microstructure of the cold-rolled steel which
also contained banded NFP.
A short IC hold time of 2 minutes was selected to mimic industrial annealing times
and reduced experimental heat treatment time. As well, the short IC hold minimized
the slow growth of austenite into ferrite grains during annealing, leading to desirable
finer-scaled NFP after quenching, while still likely providing sufficient time for full
carbide dissolution.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 61
3.2.2 Thermal Path Two
Thermal Path Two (TP2) consisted of an austempering pretreatment of the cold-
rolled steels prior to IC annealing. TP2 is represented graphically in Fig. 3.1(b) and
described in detail in Sec. 3.2.4.2. Austempering produces a bainitic microstructure,
causing a redistribution of carbon relative to the microstructures of the cold-rolled
steels. The bainite laths spatially segregate carbides in a relatively uniform fashion.
Upon subsequent IC annealing, this results in a uniform spatial distribution of NFP
with a bi-modal distribution of particle sizes: coarse grains with a high aspect ratio
and fine grains with a low aspect ratio.
Cold-rolled steel blanks were heated to 917◦C for 30 minutes to transform the
microstructure to 100% austenite. The blanks were then rapidly transferred to a
custom salt bath, quickly cooling to the bath temperature of 500◦C, and then held
in the bath for 20 minutes before being quenched in water. At this point, the blanks
were IC annealed as per TP1 at a temperature of 725◦C or 737◦C. The same IC
annealing time of 2 minutes was used for reasons explained in Sec. 3.2.1.
3.2.3 Heat Treatment Procedures and Apparatus
Three apparatus were used for the heat treatments employed in this study. Austem-
pering was performed using a Lindberg type 54232 tube furnace coupled to a Lindberg
type 59344 temperature controller for austenitizing (Fig. 3.2) and using a custom-built
salt bath furnace for the bainite hold (Fig. 3.3). IC annealing was performed in a salt
pot fit within a Lindberg type 56622 vertical crucible furnace coupled to a Lindberg
type 59344 temperature controller (Fig. 3.4).
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 62
(a)
(b)
Figure 3.1: Representative heat treatment paths for a) ThermalPath One (TP1); and b) Thermal Path Two (TP2). Not toscale.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 63
Figure 3.2: Lindberg type 54232 tube furnace coupled to aLindberg type 59344 temperature controller. Used for austen-itization during austempering heat treatments.
Figure 3.3: Custom-built salt bath used for the bainite holdportion of austempering heat treatments.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 64
Figure 3.4: Lindberg type 56622 vertical crucible furnace andsalt pot coupled to a Lindberg type 59344 temperature con-troller. Used for IC annealing heat treatments.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 65
3.2.4 IPPS Specimen Heat Treatment Schedule
IC annealing heat treatment temperatures for IPPS specimens were selected based on
the NFP content calibration curves presented in Appendix A. First, an IC annealing
temperature for each cold-rolled alloy was selected which would produce a microstruc-
ture with comparable NFP content to its corresponding galvannealed alloy: 733◦C
for cold-rolled DP780 and 743◦C for cold-rolled DP980. These IC annealing temper-
atures were used to generate DP variants for both alloys in an effort to minimize
necessary salt bath temperature changes. To produce a clearer trend between NFP
volume percent and void damage accumulation, a third IC annealing temperature
(715◦C) was selected to produce a DP steel variant with lower NFP volume percent.
This approach was expected to produce three DP steel microstructural variants with
similar NFP morphology, but varying NFP content.
To determine the effect of a differing population of NFP on damage accumulation,
an IC annealing temperature for TP2 was selected for each cold-rolled DP steel alloy
with the intent of producing the same volume percent of NFP as in the corresponding
galvannealed alloys. Due to the bainitic microstructure produced during austemper-
ing, a larger proportion of carbides existed in TP2 specimens prior to IC annealing
than in the TP1 specimens. It was expected that this increased carbide content would
result in a higher volume percent of NFP for any given IC-annealing temperature on
the calibration curve of Fig. A.4. This is because the first step in the formation of
austenite during IC annealing is almost instantaneous nucleation at cementite parti-
cles, followed by rapid growth until the carbide phase is fully dissolved [6]. Speich
show that this takes less than 1 minute to complete for low-carbon 1.5-Mn steels [6].
With the second step of austenite formation being slow growth into ferrite grains,
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 66
which takes hours to fully complete [6], it was assumed that the higher bainite content
of the austempered blanks relative to the cold-rolled blanks would result in a higher
NFP content for equivalent IC annealing treatments of the two input microstructures.
Based on the experience of Seyedrezai [130] with austempering and IC annealing of
the DP780 cold-rolled alloy, it was predicted that shifting the IC annealing calibra-
tion curve of Fig. A.4 by approximately 7◦C to the left would result in a reasonable
prediction of NFP content. As such, IC annealing temperatures of 725◦C and 737◦C
were selected for TP2 for the DP780 and DP980 cold-rolled alloys, respectively.
Given the highly banded nature of NFP along the rolling direction in the mi-
crostructure of TP1-treated blanks, it was postulated that both mechanical proper-
ties and void damage accumulation would vary between IPPS specimens in which the
tensile direction was aligned with either the sheet rolling direction or the transverse
direction. To determine if this was the case, IPPS specimens for all heat treatments
were produced with both sheet orientations.
The location at which failure occurs within the gauge region of IPPS mechani-
cal testing specimens was known to be highly unpredictable for the inhomogeneous
microstructures of the DP steel variants used in this study. As such, production of
a large number of IPPS specimens per variant batch was necessary to result in a
sufficient number of failed specimens suitable for accurate analysis of strain at failure
(via tracking of the deformation pattern of a grid of dots painted onto the specimen
surface). Seven specimens per heat-treated variant batch were produced. The full
schedule for the IPPS specimens is presented in Table 3.3.
A naming convention was applied to specimens as follows, where # represents a
numerical digit and n represents an alphabetic character: #(TP#)-(##)-n#. The
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 67
first digit, #, is either a 7 or 9, identifying respectively whether the specimen was pro-
duced from DP780 or DP980 sheet. The next three alphanumeric characters, (TP#),
represent the thermal path undertaken by the specimen; TP1 or TP2. The brackets
signify that these characters will not appear for galvannealed material; rather, a ‘GA’
will take their place. The next two numerical digits, (##) are representative of the
IC annealing temperature used during heat treatment. All IC annealing temperatures
were within the range of 715◦C to 743◦C, thus the 7 is dropped and only the remain-
ing 2 digits are used in the naming convention. Again, these two numerical digits will
not appear for galvannealed material. The alphabetic character, n, represents the
principal sheet direction of the specimen aligned with the tensile axis: ‘R’ indicates
the rolling direction is aligned with the tensile axis and ‘T’ indicates the transverse
direction is aligned with the tensile axis. The final numerical digit, #, indicates the
specimen number within the given condition/treatment batch.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 68
Table 3.3: Full schedule for the production of IPPS rectangularblank specimens, detailing their condition/treatment prior tomechanical testing.
(a) DP780 blanks.
Condition / TreatmentIC Annealing
Temperature (◦C)
Alignment of
Tensile
Direction
Number of
Specimens
Galvannealed N/A RD 7
Galvannealed N/A TD 7
TP1 715 RD 7
TP1 715 TD 7
TP1 733 RD 7
TP1 733 TD 7
TP1 743 RD 7
TP1 743 TD 7
TP2 725 RD 7
TP2 725 TD 7
(b) DP980 blanks.
Condition / TreatmentIC Annealing
Temperature (◦C)
Alignment of
Tensile
Direction
Number of
Specimens
Galvannealed N/A RD 7
Galvannealed N/A TD 7
TP1 715 RD 7
TP1 715 TD 7
TP1 733 RD 7
TP1 733 TD 7
TP1 743 RD 7
TP1 743 TD 7
TP2 737 RD 7
TP2 737 TD 7
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 69
3.2.4.1 Austempering Apparatus
Austempering was performed in a tube furnace with a custom-made glass tube, shown
in Fig. 3.2, and with the custom-built salt bath shown in Fig. 3.3. The tube furnace
was used for austenitizing, while the salt bath was used for a bainite hold at 500◦C.
Treatment of steel at high temperature results in accelerated oxidation. The tube
furnace allowed for the treatment of steel blanks at high temperature without oxida-
tion by using a steady flow of argon to provide an inert atmosphere. The salt used
for the bainite hold was draw salt #275.
Tube Furnace Preparation
With an exit nozzle clamped to the glass tube, the temperature controller for the
tube furnace was set to a target temperature of 900◦C and the system was allowed
to heat up. Upon temperature stabilization, the volume of air within the glass tube
was purged with argon gas at a flow rate of 2000 cc/minute. The argon was al-
lowed to continue to flow at this rate for the duration of heat treatments. A 915 mm,
Chromega R©-Alomega R© Omega R© brand K-type thermocouple with Inconel sheath was
inserted into the glass tube through its exit nozzle such that the tip of the thermocou-
ple was located at the center of the tube furnace and suspended at the center of the
circular tube cross-section. The target temperature on the controller was adjusted
until the thermocouple reading stabilized at 917◦C.
For a stabilized hold temperature while argon was flowing, a temperature gradient
existed within the glass tube. For a temperature of 917◦C at the center of the tube
furnace within the glass tube, the temperature 43 mm away from this location along
the length of the tube was 7◦C lower, which means the temperature at the edge of an
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 70
IPPS steel blank may have been nominally lower than the center of the blank during
austenitization for TP2.
Custom Salt Bath Preparation
The temperature controller for the salt bath was set to a target temperature of 500◦C.
Upon reaching the target, a 610 mm long Chromega R©-Alomega R© Omega R© brand K-
type thermocouple with 304 stainless steel sheath was suspended in the molten salt
with its tip at a depth of 135 mm. This depth is where the center of the sample
gauge region would be located during heat treatment. The target temperature of
the salt bath temperature controller was adjusted until the temperature of the salt
measured using the suspended thermocouple reached 500◦C. A piece of steel rebar
was laid across the top of the salt bath to hang blanks from during heat treatments.
Due to the very large volume of salt within the custom-designed bath, no vertical
temperature gradient was detected within the molten salt after stabilization to target
temperature.
3.2.4.2 Austempering Procedure
A steel blank was wrapped in thermocouple wire around its 50 mm side length. A
small loop was made in the free end of the thermocouple wire 245 mm away from the
top of the blank. This loop would facilitate the hanging of the blank from the rebar
positioned above the salt bath such that the center of the blank gauge region was at
the same depth as the tip of the suspended thermocouple. After confirming the tube
furnace and custom salt bath had stabilized at the desired temperature, the blank
and thermocouple wire were pushed into the tube furnace and located such that the
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 71
center of the blank was at the center of the furnace.
The blank remained within the tube furnace for 30 minutes before being quickly
extracted and dipped into the custom salt bath. The transfer from the tube furnace
to the salt bath was made rapidly to ensure the cooling rate between austenitization
temperature and bainite hold temperature was high enough to prevent any austenite
within the blank from transforming to pearlite. After being held in the salt bath
for 20 minutes, producing a bainitic microstructure, the blank was extracted and
quenched in water.
At this time, the blank was taken through the procedure for TP1, producing
a ferrite-martensite microstructure. The IC annealing temperatures used for the
AT blanks are provided in Sec. 3.2.4, as well as the reasons underlying the selected
temperatures.
3.2.4.3 IC Annealing Apparatus
IC annealing was performed in a bath of molten salt to provide a nearly uniform tem-
perature environment around specimens during treatment; the temperature gradient
in the salt from the top to the bottom of specimens was approximately 3◦C. The salt
selected for IC annealing was NuSal based on its recommended operating tempera-
ture range, low reactivity with the surface of steel, and its melting temperature [131].
NuSal is produced by APCO Industries Co. Ltd. and is a mixture of potassium and
sodium chlorides.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 72
Salt Bath Preparation
Prior to IC annealing of specimens, the temperature controller for the salt bath
furnace was set to 840◦C which allowed the solid salt within the pot to melt after a
period of time. After the salt was completely molten, more salt was gradually added
to the pot until the top surface of the molten salt was 25 mm from the top of the
pot. This allowed for complete immersion of specimens in the molten salt, well away
from the surface where a significant temperature gradient existed.
At this time, a 610 mm, Chromega R©-Alomega R© Omega R© brand K-type thermo-
couple with 304 stainless steel sheath was suspended into the salt bath and clamped
into position 10 mm from the edge of the salt pot. The tip of the thermocouple was
located at the same depth as the center of the gauge region of IPPS specimen blanks
being IC annealed, 82 mm below the surface of the salt. Bricks were located on either
side of the thermocouple on top of the salt pot to minimize convection between the
salt and the atmosphere. A gap of approximately 40 mm was maintained between
the bricks.
For simplicity and time-saving reasons, the thermocouple was not welded or
peened onto the sample. It is shown in Appendix B that the heating response of
the rectangular steel blanks being treated is quite predictable for a specified target
temperature.
3.2.4.4 IC Annealing Procedure
The set-point of the furnace controller was adjusted until the temperature reported
using the submerged thermocouple stabilized to the desired value within ±1◦C for 10
minutes. A rectangular blank sheet specimen, 85 mm x 50 mm, was then secured to a
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 73
custom specimen holder, detailed in Fig. 3.5, by wrapping thermocouple wire around
the specimen and forks. The blank was oriented with its 85 mm edges horizontal to
prevent any variation in microstructure along the width of the gauge region of the
blank due to the small vertical temperature gradient within the salt bath. Due to
the lack of an intimate interface between the specimen holder and steel blanks, and
the short annealing times (<3 minutes), diffusion of elements between the specimen
holder and blanks was highly improbable and therefore considered negligible.
The blank was submerged quickly in the center of the salt pot and the three legs
of the specimen holder rested on the bricks located on top of the salt pot. The blank
remained in the salt pot for as long as was required to heat up to the target temper-
ature, calculated in Appendix B, plus 2 minutes. At this time, the specimen holder
and attached blank were rapidly withdrawn from the molten salt and submerged in
an ice-water bath for quenching. The rapid nature of this sample extraction was
employed to minimize the production of any non-martensitic NFP.
The blank and specimen holder were blown dry shortly thereafter to prevent cor-
rosion of the blank and to prevent any water from entering the salt pot and causing
potentially harmful bubbling during a subsequent treatment. Before another blank
was IC annealed in the salt pot, the salt pot temperature was allowed to stabilize
within its target range again. This required time is calculated in Appendix B. To con-
firm that the target temperature was reached after this time period, the temperature
reported by the suspended thermocouple in the salt bath was also examined. After
every 7 blanks were IC annealed, the depth of the molten salt surface below the top of
the pot was measured and more salt added accordingly. If salt was added, no further
treatments were performed until the salt had stabilized at the target temperature,
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 74
±1◦C, for 15 minutes.
Figure 3.5: Custom-built IC annealing IPPS rectangular blankspecimen holder. Center rod collinear with axis of dipping intosalt pot.
3.3 Metallography
This section describes in detail the metallographic procedures applied to character-
ize the microstructures of the steels used in this study. Metallographic specimen
extraction is described, followed by preparatory procedures for microscopy, includ-
ing etchant descriptions, and techniques for quantitative analysis of microstructural
constituents. Procedures described within this section were developed as per the
recommendations of ASM Handbook Volume 9 [132], and ASTM Standards E3 and
E407 [133, 134].
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 75
3.3.1 Specimen Preparation
Sectioning of metallographic specimens from ‘D’-shaped cutouts at the location of
the IPPS specimen gauge region (Fig. 3.6) was performed using a Struers Accutom
precision cut-off machine equipped with an aluminum oxide cut-off wheel and contin-
uously flowing coolant. The scrap ‘D’-shaped cutouts were considered representative
of undeformed gauge regions for IPPS specimens. Referring to the IPPS specimen
heat treatment schedule (Table 3.3), one ND-RD and one ND-TD metallographic
section were extracted per IPPS specimen condition.
Figure 3.6: IPPS specimen with waterjet-cut ‘D’-shaped scrapsused for the production of ND-RD and ND-TD metallographicspecimens at the center of the gauge region.
3.3.1.1 Grinding and Polishing
Prior to grinding and polishing, metallographic sections were mounted in short-glass
reinforced diallyl phthalate using a Simplimet 1000 automatic mounting press. The
heat developed in the mounting process was not expected to affect the microstructures
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 76
of the steels examined.
Grinding
Rough grinding using 80 grit silicon carbide rotary discs was performed initially for
one minute to remove any heat affected zone that may have resulted from the unlikely
possibility of insufficient cooling during sectioning with the cut-off saw. Grinding and
polishing media with progressively finer particle sizes were used in sequence to remove
all artifacts and deformation produced by the previous step of grinding/polishing until
the specimen surface became free of any artifacts. The full sequence of grinding media
used is presented in Table 3.4. Grinding papers were continuously flushed with water
to keep specimens cool and to remove debris.
Table 3.4: Stages of grinding employed for metallographic spec-imen preparation.
Grinding Stage Details
Rough
• 80 grit silicon carbide• rotary wheel manual grind• moderate-heavy pressure• one minute• water flush
1
• 220 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• water flush
2
• 320 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• water flush
3
• 400 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• water flush
4
• 600 grit silicon carbide• stationary paper manual grind• moderate-heavy pressure• cotton and water clean, ethanol flush, compressed air jet dry
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 77
Polishing
The polishing stages employed for all specimens are outlined in Table 3.5. Etching
was performed immediately after the final polishing stage to prevent passivation of
the specimen surface.
3.3.1.2 Etching
Several attack etchants and tint etchants were used in this study to develop contrast
between microstructural constituents for the purposes of optical and scanning electron
microscopy. Most of these etchants were mixed and applied following the procedures
outlined in ASTM Standard E407-07 [134]. A summary of the etchants used, their
purpose in microstructural characterization, and associated procedures is provided in
Table 3.6.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 78
Table 3.5: Stages of polishing employed for metallographic spec-imen preparation.
Polishing Stage Details
1
• 6 µm diamond solution with 50% glycerin lube
• rotary wheel manual polish
• cotton cloth
• heavy pressure
• 2 minutes
• cotton and water clean, ethanol flush, compressed air jet dry
2
• 1 µm diamond solution with 50% glycerin lube
• rotary wheel manual polish
• cotton cloth
• heavy pressure
• 1 minute
• cotton and water clean, ethanol flush, compressed air jet dry
3
• 0.05 µm colloidal suspension of silicon dioxide
• rotary wheel manual polish
• Alphalap synthetic cloth (Micro Metallurgical Ltd.)
• light pressure
• 1 minute
• ethanol flush, compressed air jet dry
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 79
Table 3.6: Etchants used for microstructural characterizationand their associated procedures. The ‘Stage’ column denotesthe step number in a multi-stage etching procedure.
Microstructural CharacterizationMicroscopy
MethodDetails
• 10% Sodium metabisulfite (SMB)
NFP Volume Percent in Specimens of
Preliminary Heat TreatmentsOptical • 20 s immersion with light agitation
• ethanol flush, warm air dry
NFP Volume Percent in Cold-rolled Steels • 2% Nital
NFP Volume Percent in IPPS SpecimensScanning
Electron• 13 s immersion
NFP Particle Size in IPPS Specimens • ethanol flush, compressed air jet dry
• 2% Nital
Void Nucleation Sites in XµCT Match-head
Specimens
Scanning
Electron• 40 s immersion
• ethanol flush, compressed air jet dry
3.3.2 Microstructure Characterization Methods
This section outlines the procedures undertaken for quantitative analysis of the mi-
crostructural characteristics of metallographic specimens prepared from the DP steel
variants of this study.
3.3.2.1 Volume Percent Measurement
The volume percentages of microstructural constituents within metallographic spec-
imens were statistically estimated according to the guidelines for systematic point
counting of ASTM standard E562-08 [135]. This technique actually measures area
fraction; however, it has been shown that stereological area fraction measurements
are directly related to volume percent [136]. A JEOL JSM-840 SEM instrument was
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 80
used in secondary electron mode to capture greyscale micrographs measuring 1024
x 768 pixels. Mounted, nital-etched specimens were gold-coated and grounded with
copper tape attached to the specimen holder prior to being placed in the SEM cham-
ber. A working distance of 15 mm and an accelerating voltage of 20 kV were used.
For each DP steel microstructural variant examined from Table 3.3, 15 micrographs
were captured from each of the ND-RD and ND-TD sections at a magnification of
5000x. These micrographs were captured along the through-thickness centerline of
the steel sheet where NFP banding was most prevalent. A manual stage control knob
was rotated a random magnitude while looking away from the SEM display to move
the specimen along the sheet centerline to the location of the next field to avoid any
operator field selection bias.
A regular grid of test points was overlayed onto these micrographs using ImageJ
software and the number of test points falling within the constituent of interest were
counted, using manual tally software, and then divided by the total number of test
points. The average of the mean point fraction for ten ND-RD fields and the mean
point fraction for ten ND-TD fields provided an estimate of the volume percent of said
constituent within the DP steel variants. The 95% confidence interval and percent
relative accuracy were calculated for each volume percent estimate.
Due to the periodicity of the distribution of NFP in many of the microstructures
examined, a custom grid of 131 test points in the shape of five equidistant circles was
developed and used as a Java plug-in within ImageJ for point-counting, as opposed to
a typical rectangular array of grid-points. The use of circles eliminated any bias that
would be associated with NFP regularly falling on the horizontal grid-lines of a rect-
angular array. The test points of the grid were made to be as small as possible while
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 81
remaining visually detectable, thereby reducing bias caused by operator perception
when points appear to fall upon multiple constituents.
3.3.2.2 Particle Size Measurement
The sizes of NFP particles within metallographic specimens were measured according
to the guidelines for determining average grain size in ASTM standard E112-96 [137].
A modified Abrams Three-Circle Intercept Procedure was used to produce an unbi-
ased particle size measurement because of the non-equiaxed NFP particles within
many of the DP steel microstructures examined. Circular test arrays automatically
compensate for non-equiaxed grain shapes, without overweighting any local region of
the field [137].
Secondary electron micrographs captured for NFP volume percent measurements
as in Sec. 3.3.2.1 were used for the NFP particle size measurement procedure. Three
concentric, equidistant circles with a total circumference of 121.1 µm were overlaid
onto the micrographs using ImageJ freeware. Intercept counting was performed with
manual tally software for 10 micrographs in each of the ND-RD and ND-TD sections.
A minimum of 500 total counts were recorded, a number found to produce acceptable
precision [137]. The mean lineal intercept length, 95% confidence interval, and percent
relative accuracy were calculated for each DP steel variant.
3.4 In-Plane Plane-Strain Mechanical Testing
It was expected that mechanically testing the DP steels along a near plane-strain
forming path and performing XµCT examinations of failed specimens would shed
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 82
insight into the significance of void damage accumulation in the failure of these ma-
terials.
3.4.1 Sample Geometry and Preparation
The IPPS specimens used in this study were prepared from 85 x 50 mm rectangular
blanks of the DP steel sheets received from U.S. Steel. The blanks were first rough
cut with a hydraulic shear press. After heat treating the cold-rolled blanks, according
to the schedule of Table 3.3, the blanks were waterjet cut into the IPPS geometry
detailed in Fig. 3.7. This geometry allowed for testing to failure for all of the DP
steel microstructural variants using an 8521 Instron tensile testing machine equipped
with custom wide grips and a 100 kN load cell.
Figure 3.7: IPPS tension test specimen dimensions, adaptedfrom the work of Kilfoil [61].
The IPPS testing required the application of a grid of dots to each specimen
surface to facilitate measurement of the strains developed during testing based upon
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 83
tracking the deformation produced between dot centroids using a digital camera and
intervalometer. These dots were applied in an 8 x 8 array with the center of the array
located at the center of the gauge region of the IPPS specimen, where deformation
conditions are nearest to plane-strain. The dots were applied using a custom marker-
press attached to a micro-controlled microscope stage (Fig. 3.8). A script written
in Image-Pro PlusR© was used to move the stage in 3.175 mm intervals, producing
a uniform, square array of dots using a SharpieR© Paint marker. As mentioned by
Kilfoil [61], this grid application method was found to be superior to silk-screening
prior to machining as it helped prevent rubbing off or smudging of the dots. As
well, the custom tray used to hold IPPS specimens during the dot application process
allowed for consistent location of the array at the center of the gauge region [61].
The dots applied were approximately 1 mm in diameter. The small diameter dots
assisted in producing failure surfaces between rows of dots rather than through the
dots themselves [61]. The spacing of the dot array is detailed in Fig. 3.9.
3.4.1.1 Specimen Cleaning
Preliminary testing was performed to determine if cleaning of the IPPS specimens
to remove any oxide developed during heat treatments was necessary to produce
sufficient contrast between the dots and background steel for accurate image analysis.
Both a red and a green paint were applied to oxide-covered IPPS specimens which
were taken through the full testing procedure described in Sec. 3.4.2 and Sec. 3.4.3.
Subsequent thresholding of captured digital photographs of the dot arrays during
testing proved difficult to threshold with accurate representation of dot geometry due
to the dark oxide. The cleaning procedures of Kitney [131], detailed in Appendix C,
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 84
Figure 3.8: Custom paint plotting press used for application ofa grid of dots to IPPS specimens.
Figure 3.9: Inter-dot spacing for the grid applied to IPPS spec-imens.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 85
were thus applied to IPPS specimens prior to subsequent application of a grid of
dots. Only IPPS specimens which had been heat treated were given an inhibited acid
cleaning; the galvannealed sheets had a matte finish which provided sufficient contrast
between dots and the steel in digital images. It was determined from preliminary
testing that red paint provided for more accurate segmentation than green paint
using the thresholding methods outlined in Sec. 3.4.3.
3.4.2 IPPS Testing Methodology
Custom 101.6 mm wide grips with a load rating of 133 kN [61] were attached to the
8521 Instron machine to apply the tensile force to IPPS specimens. Grip modifications
were previously made by Kilfoil [61] and Kitney [131] to the wedge-style grips to
facilitate more consistent alignment of specimens and reduce setup time. A constant
actuator speed of 2.5 mm/min was employed for all tests until specimens failed,
providing a nominal initial strain rate of approximately 0.01 s-1 averaged over the
entire gauge region. Clearly the local strain rate in the central region of specimens
differed from that near sample edges due to the differing strain states caused by
varying degrees of physical constraint in the minor direction.
Throughout the IPPS testing, an intervalometer equipped with an infrared (IR)
emitter was used to trigger digital camera exposures of the grid of dots. A Nikon D70
6.0 MP DSLR camera with CCD dimensions of 3008 x 2000 pixels was used. The
camera was mounted on a tripod and equipped with a 2x teleconverter lens followed
by 105 mm macro lens. The teleconverter acts to increase the camera’s focal length,
which was helpful considering the macro lens is suited to close-range applications.
The macro lens alone would not allow for fitting of a grid of dots in the field of view
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 86
(FOV). However, the teleconverter lens reduced light intake [61]; thus, additional
lighting was necessary to maintain contrast between the dots and the surrounding
steel. A distance of 890 mm between the IPPS specimen surface and the front face of
the macro lens was used to maintain both the grid of dots and a digital timer within
the FOV during testing. A single undeformed grid, i.e. four nearest-neighbour dots
forming a square, had dimensions of 93 x 93 pixels measured centroid to centroid in
captured images.
3.4.2.1 IPPS Testing Procedure
IPPS specimens were vertically aligned in the bottom grip using a squared block of
steel seated on the grip housing as a visual reference, as shown in Fig. 3.10. The
IPPS specimen was re-aligned within the grips until the top edge of the steel block
was parallel with top edge of the IPPS specimen before tightening the bottom grip.
The top grip’s center of mass was not coincident with the central axis of the shaft
used for attachment to the tensile testing machine. Since the top grip attached to a
universal joint to maintain uniaxial loading during testing, it did not hang plumb. To
ensure proper initial alignment of the top grip with respect to the IPPS specimen, a
level was placed on the upper housing surface of the top grip. The wedges of the top
grip were allowed to tighten on the IPPS specimen once it had been rotated about
the universal joint to be plumb, as depicted in Fig. 3.11. The experimental apparatus
setup for IPPS testing is displayed in Fig. 3.12.
At the beginning of each test, an image of the grid of dots in the un-deformed
condition was captured as a reference for subsequent calculation of strains developed
throughout the test. An intervalometer, The Time MachineTM, manufactured by
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 87
Mumford Micro Systems, was used to remotely trigger exposures of the deforming
grid every 30 seconds during each test. Shortly before failure of a specimen, the
IR trigger rate was increased to 20 Hz, activating the maximal exposure rate of the
camera (approximately 1.5 fps). Only specimens which failed between rows of dots
were used for strain analysis and tomographic analysis of damage accumulation.
Figure 3.10: Squared steel block used to visually align IPPSspecimens in bottom grip. The block was seated on the griphousing and the top edge of the IPPS specimen was alignedwith the top edge of the block.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 88
Figure 3.11: Alignment of top grip using a level to ensureuniaxial loading of IPPS specimens.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 89
Figure 3.12: Experimental setup of the apparatus for IPPStesting.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 90
3.4.3 Image Processing and Strain Analysis
The segmentation technique used to binarize the digital images of dot grids captured
during IPPS testing was based upon the methods of Kitney [131]. This technique
allowed for semi-automation of the segmentation procedure and a more accurate
capture of dot geometry than a simple greyscale histogram shape-based thresholding
method. This procedure led to more accurate calculation of strains.
Images of IPPS specimens in the undeformed condition and throughout testing
were first cropped to contain only the grid of dots on the specimen (see Fig. 3.13(a)).
The RGB colour model used to record .jpeg images of grids was converted to a Lu-
minance, In-Phase, and Quadrature (YIQ) model using Image-Pro PlusR© software
(see Fig. 3.13(b) and Fig. 3.13(c)). The In-phase and Quadrature channels were then
automatically thresholded using a simple automatic convex hull thresholding. The
resulting black masks on white backgrounds were then combined using an OR logic
operation as shown in Fig. 3.14. The OR operation produced a new image where bits
are turned on (white) if the corresponding bit is on in either one of the input images.
Using Image-Pro PlusR©, the centroids of each dot were calculated and written to a
.txt file. These .txt files were imported into MicrosoftR© Excel and used with a macro
to calculate major and minor engineering strains for each group of four dots within
the gridded region of IPPS specimens. The strain calculation for each grid is one
used for 4-noded quadrilateral elements in FEM software, based upon the changing
distance between dot (node) centroids. Major and minor engineering strains were
calculated within the entire gridded region of the specimens for the last 5 images
captured prior to specimen failure. A check was made to ensure that strain within
the specimen was increasing reasonably with respect to time for these five exposures.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 91
(a)
(b) (c)
Figure 3.13: IPPS grid image segmentation process (part 1 of2) showing: a) cropped RGB colour image of dots on an IPPSspecimen; b) In-Phase channel of a YIQ colour model for theimage of dots; c) Quadrature channel of a YIQ colour modelfor the image of dots.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 92
(a) (b)
(c)
Figure 3.14: IPPS grid image segmentation process (part 2 of 2)showing: a) automatic convex hull thresholding of Fig. 3.13(b);b) automatic convex hull thresholding of Fig. 3.13(c); c) finalthresholded image used for strain calculations, created from anOR logic operation of the masks in a) and b).
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 93
It was assumed that the principal engineering strains were aligned with the principal
sheet directions (rolling and transverse).
The major and minor engineering strains just prior to failure within the grid row
where final specimen failure occurred were averaged for comparative purposes with
respect to specimens of other microstructural variants. As well, the major and minor
engineering strains were calculated at the position of the coupons removed for XµCT
analysis.
An example strain path for the central region of a TP2-treated DP780 IPPS
specimen is provided in Fig. 3.15, illustrating that the applied strain path is very
close to plane-strain.
3.4.4 Experimental Error Analysis
An error analysis was performed to determine the systematic error and variance in-
herent in the procedures previously outlined for image capture, post-processing, and
strain analysis. Using a typical IPPS test setup (including camera placement), an
undeformed, dotted specimen placed within the grips was imaged 40 times in succes-
sion at approximately 1.5 fps using the intervalometer and DSLR camera. The strain
analysis techniques outlined in Sec. 3.4.3 were applied to these 40 images with the
expectation that the strains calculated with respect to image capture time would be
normally distributed around a mean of zero. A 95% confidence interval for engineering
strain measurements was calculated to be ± 0.00003.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 94
-0.08 -0.04 0.00 0.04 0.08
0.05
0.10
0.15
Minor Engineering Strain
Maj
or E
ngin
eeri
ng S
trai
n
Figure 3.15: An example strain path for a TP2-treated DP780IPPS specimen (7AU25-R4). Strain data points shown are theaverage of the strains calculated for the 7 grid points withinthe failure row.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 95
3.5 X-ray Micro-computed Tomography Damage
Analysis
X-ray micro-computed tomography was the technique of choice for probing the in-
ternal structure of failed IPPS specimens in order to determine the degree of void
damage present. It allowed for the extraction of quantitative data concerning void
morphology in 3-D, using a non-destructive approach. Time and complexity for spec-
imen preparation and testing were greatly reduced by using XµCT compared to serial
2-D metallography methods.
The instrument used to perform XµCT projection capture was a Micro-XCT 400
produced by Xradia Inc. (Fig. 3.16). The approximately 5 µm spot size of the X-ray
source for this system allows for high resolution tomographic imaging. Specifications
of the instrument pertinent to this study are presented in Table 3.7.
Table 3.7: Micro-XCT 400 Specifications. 1Modulation transferfunction (MTF) measured using Xradia’s standard 2-D resolu-tion target.
Source
Max Voltage (kV) 150Min Voltage (kV) 40Max Power (W) 10
Objective Best Resolution at 10% MTF1 (µm)
Macro-70 204x 510x 2.520x 1.5
CCD
Pixel Array 2048 x 2048
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 96
Figure 3.16: Micro-XCT 400 instrument produced by XradiaInc.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 97
3.5.1 Sample Preparation and Geometry
To achieve the best resolution possible with the Micro-XCT 400 system and thus
garner the most accurate information regarding void morphology in the failed IPPS
specimens, the 20x objective was used for this study. So-called “match-head” speci-
mens were produced from the failed IPPS specimens for tomographic analysis because
specimens that fit completely within the field of view (FOV) of an X-ray tomogra-
phy imaging system avoid truncated projection artifacts during image reconstruc-
tion [138]. The most common artifact produced is bright shading near the edge of
truncation [138, 139].
The “match-head” specimens for tomographic analysis were extracted from se-
lected IPPS specimens using a wafering saw so as to minimize artifacts near the plane
of sectioning, while minimizing the cost of the process. Twenty “match-head” speci-
mens were produced in total: one per IPPS specimen condition outlined in Table 3.3.
The selection criteria applied to determine which satisfactorily failed IPPS specimen
per condition would be sectioned to produce a tomography sample were: failure oc-
curred between two rows of dots, failure initiated from the center of the specimen (if
this was visually perceptible during mechanical testing), and, if possible, the major
engineering failure strain was representative of all satisfactorily failed specimens of
that particular DP steel microstructure.
The size of the match-head specimens was determined by the size of the FOV
available using the 20x lens of the Micro-XCT 400. For the conditions of placing
the X-ray source and 20x lens as close as physically possible (which is optimal for
producing a high flux of X-ray photons) the FOV was approximately 1.3 mm x 1.3 mm.
Match-head specimens were thus sectioned with a geometry of 1 mm x sheet thickness
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 98
x arbitrary height from the center of the width of IPPS specimens, where height
refers to the direction of tensile loading during mechanical testing. This location fell
directly between the 4th and 5th columns of dots on IPPS specimens, as detailed in
the schematic of Fig. 3.17.
In order to bring the X-ray source and detector as close to the match-head speci-
mens as possible during tomographic scanning (Fig. 3.18 and Fig. 3.19), an extension
mount was required to provide vertical clearance of the sample mount from the X-ray
source and detector. Match-head specimens were mounted to 60 mm long sections of
steel welding rod using LePageR© Epoxy SteelR©, as depicted in Fig. 3.19.
Figure 3.17: Schematic detailing the location within IPPSspecimens from which match-head specimens (green) were ex-tracted. Not to scale.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 99
Figure 3.18: Micro-XCT 400 interior components set up intypical positions for a tomography capture of this study.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 100
Figure 3.19: Close-up photograph detailing the small sourceto specimen and specimen to detector distances. These weremade possible by use of an extension rod mount for match-headspecimens.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 101
3.5.2 Tomography Acquisition
The acquisition parameters for tomographic captures in this study are summarized
in Table 3.8. The acquisition procedure is outlined in the following sections.
Table 3.8: XµCT acquisition parameters used for IPPS match-head specimens.
Projections 3400
Exposure Time (s) 45
Source Voltage (kV) 100
Source Power (W) 10
Objective 20x
Source to Sample Distance (mm) 27.5
Sample to Detector Distance (mm) 4.0
Sample Rotation (◦) 184
Filter Xradia’s LE#5
Binning 2
Multiple Reference Imaging Average of 5 exposures every 850 projections
Dithering (Dynamic Ring Removal) On
Camera Readout Time Fast
3.5.2.1 Tomography Acquisition Procedure
A pin-vice sample holder equipped with kinematic stops was used to hold and kine-
matically locate a match-head specimen for tomographic capture. The source and
detector were carefully moved towards the specimen with incremental movements,
being sure to avoid any collisions. These were not brought as close as possible to the
specimen at this time, due to the specimen not yet being aligned with the stage axis of
rotation. Thus, stage rotation would result in a circular path of the sample, possibly
colliding with the stage or detector. The stage and sample holder were then taken
through a procedure of iterative rotation and translation in the X and Z axes to align
the central longitudinal axis of the match-head specimen with the rotational axis of
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 102
the stage. This alignment procedure is important for keeping the specimen within the
FOV throughout tomography capture while the stage rotates through 184◦. At this
time, the source and detector were then moved to the positions specified in Table 3.8.
The match-head specimen was then translated vertically along the Y axis to place
the top of its fracture surface just inside the top of the FOV. At this time, a physical
filter was selected to minimize global beam hardening using Xradia’s application notes
for filter selection. The filter attenuates X-ray photons from the lower end of the radi-
ation spectrum produced by the X-ray source, which are more likely to be attenuated
by following a path through thick specimen regions, but are likely to pass through
the specimen and reach the detector along shorter paths such as specimen corners.
Filtering these low energy photons helps minimize a “cupping effect” in greyscale in-
tensity variation traversing the cross-section of reconstructed specimen slices. Using
a source power of 10 W, the source voltage necessary to produce a transmission ratio
of 0.25-0.35 in the region of interest (ROI) below the fracture surface was experi-
mentally determined. This transmission ratio is recommended as optimal by Xradia
applications engineers. Finally, the exposure time necessary to produce a minimum of
2000 counts within the ROI at the specimen orientation which produced the longest
photon paths through the specimen was determined experimentally. It was observed
that photon counts received by the CCD generally have a linear relationship with
exposure time. The minimum value of 2000 counts was recommended by Xradia Inc.
to produce an adequate signal-to-noise ratio (SNR) for quality reconstructions.
After completing the above steps, the determined parameters were entered into a
recipe interface of Xradia’s XM Controller software and the tomography acquisition
was started. Projections were saved in a proprietary .xrm file.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 103
3.5.2.2 Projections
The number of projections selected for each tomographic scan in this study was
determined based upon capturing a minimum number of views, Nmin, to satisfy the
Nyquist criterion for angular sampling: theoretically, the length of a 180◦ arc divided
by the linear sampling distance, defined by:
Nmin ≥ πd
2∆r(3.1)
where Nmin represents the minimum number of projections required to satisfy the
Nyquist criterion, D represents the diameter of the FOV, and ∆r represents the
linear sampling distance.
Equation 3.1 is valid for a parallel beam geometry and acts only as an approxima-
tion of the Nyquist criterion for the cone beam geometry produced in the Micro-XCT
400. As well, other factors beyond satisfying the Nyquist criterion must be considered
when determining the minimum number of projections that produce the best image
quality using tomography: the noise floor of data acquisition electronics, availabil-
ity of X-ray photon flux, etc [140]. As such, “oversampling” beyond the criterion of
Eq. 3.1 was performed in this study.
For the 2048 x 2048 CCD used in this study, the resulting minimum number
of projections dictated by Eq. 3.1 is 3217. However, a binning of 2 was used during
projection capture to increase SNR. Thus, 1609 projections are the minimum required
to approximately satisfy the Nyquist criterion for a parallel beam geometry. This
value was significantly “oversampled”, as 3400 projections were captured for each
tomography scan. This “oversampling” should not be viewed as detrimental due to
the extra projection capture time involved; rather, the “oversampling” increases the
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 104
SNR of the final reconstruction due to the additional data it provides for filtered back
projection reconstruction.
3.5.2.3 Exposure Time
A tradeoff exists between achieving higher resolution reconstructions and the photon
fluxes possible with higher magnification objectives during projection capture. Due
to the scale of microvoid damage within the IPPS specimens, a high resolution was
necessary. This was the reasoning underlying the selection of the 20x objective for all
tomographic captures performed in this study. However, the photon flux through the
20x objective is significantly lower than that possible for any of the lower magnifica-
tion objectives. To maintain a satisfactory SNR at this relatively lower flux, longer
projection exposures were necessary to produce a minimum of 2000 counts in the
ROI. At the same time, it was necessary to avoid saturation of projections in regions
of specimens which were very thin, i.e. at the top of fracture surfaces. A balance was
struck with a 45 second exposure time for the tomographic setup previously outlined
for the match-head specimens.
3.5.2.4 Source Power
The maximum power of the X-ray source, 10 W, was used to generate as great a
photon flux as possible, thereby decreasing tomography acquisition time.
3.5.2.5 Rotation
Using 180◦ of rotation for XµCT capture with a cone-beam source may produce cone
angle defects in reconstructions due to insufficient sampling. Extending this range of
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 105
rotation to 184◦ assisted in avoiding these defects.
3.5.2.6 Binning
Binning is the process of combining charges from adjacent pixels in a CCD during
readout. The parameter quoted for binning represents the side length of the square
matrix of pixels that have their charges averaged into one new superpixel after CCD
readout. It was determined from preliminary experiments that the SNR produced
using the 20x lens in conjunction with a binning of 1 was far too low to justify the
increased resolution offered with this setup. Exposures on the order of 7 minutes were
required to produce a minimum of 2000 counts in the ROI of projections; translating
to tomographic captures that would have required 18 days to complete per specimen.
Thus, a binning of 2 was used which required only 45 second exposures to produce
adequate counts.
3.5.2.7 Dynamic Ring Removal
Dithering, also known as dynamic ring removal, was used for all tomographic captures
to minimize ring artifacts caused by the defects in the scintillating material located
on the objective lens. Between projections, the stage is randomly translated a few
micrometers in the three principal axes. These stage movements are recorded by the
software and accounted for during reconstruction, with the end result being a “smear-
ing” of the ring artifacts produced by scintillator defects across several reconstructed
slices rather than resulting in a distinct, high contrast ring artifact.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 106
3.5.2.8 Multiple Reference Imaging
Also known as flat-fielding, reference imaging divides projections by an image with
the sample out of the FOV (at the same magnification and with the same source
settings) to remove background noise. This includes dust particles in the imaging
apparatus and the “fish bowl” effect of most photons from the conical beam being
centralized in the FOV of the CCD, leaving the fringes of projections darker. The
intensity across projections is thus “flattened” after application of a reference image.
In general, it is best to have multiple referencing enabled, which acquires several
reference images throughout the course of the tomography and averages these into
one reference image which is applied to all of the projections captured throughout
the tomography scan. In this manner, variations in the environment within the
instrument over the duration of the tomography scan are better accounted for than
if a single reference image is used. A good rule of thumb according to Xradia Inc. is
to set the number of frames between references to one quarter of the total number
of projections to be taken in the tomography scan and to use an average of 5 images
at each interval. This translated to a reference image being captured after every 850
projections in the current study.
3.5.3 3-D Reconstruction
3.5.3.1 Projection Post-processing
Prior to reconstruction of the 2-D data captured in the form of X-ray projections of
match-head specimens, two forms of post-processing were applied to the projections.
The first was a plug-in included in Xradia’s software package which “de-speckled”
projections. The de-speckling filter was applied only to those projection sets which
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 107
suffered from speckling. It should be mentioned that when using the term ‘slice’,
reference is being made to reconstruction of the internal structure at a 1 voxel thick
plane through the cross-section of match-head specimens; i.e. this plane has a normal
vector parallel to the longitudinal axis of the match-head.
The other post-processing applied to projection sets was a correction to account for
any source/specimen drift during the course of tomographic acquisition. The plasma,
or spot, of the X-ray source has a tendency to drift location slightly, especially shortly
after the source has been aged. This drift would slightly change the typical path
followed by X-ray photons compared to paths taken during earlier projections, thereby
causing a shift of the specimen within the FOV that would not be accounted for during
filtered backprojection reconstruction. As well, any motion of the specimen itself
during the course of tomographic capture would produce the same effect; however,
for the non-biological specimens examined in this study, the likelihood of specimen
motion was very low. To account for both of these possible motions, a drift file is
automatically acquired during tomography acquisition to correct for both specimen
and source drift. A projection of the specimen at 0◦ of stage rotation is automatically
captured after every 60 non-reference image exposures and these drift projections are
automatically correlated to determine how much drift occurred. A plug-in was used
for each projection in this study to apply the source/specimen drift file recorded for
each specimen and make corrections to projections by corresponding translations.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 108
3.5.3.2 Reconstruction Procedure
Center Shift Correction
After importing projections into Xradia’s proprietary reconstruction software, the first
step to producing a 3-D stack of 2-D reconstructed slices representing the match-head
volume being examined was to determine a center shift correction factor to prevent a
center shift artifact. This type of artifact arises from the vertical axis of the specimen
not being perfectly centered upon the CCD, even if it is centered upon the stage
rotation axis. Symptoms of this type of artifact are reconstructed slices which appear
blurry and out of focus. A center shift correction factor equal to the distance in
pixels that the rotation axis is offset from the center of the CCD must be determined
experimentally. This correction is accomplished via reconstruction of a single slice
using a range of center shift values and manually selecting the value which appears
to render an artifact free slice reconstruction.
The correct center shift value was relatively easy to determine by reconstructing,
with a range of center shift correction values, a slice in a region of a match-head
specimen that contained voids. For center shift values progressively further from the
true value, voids became progressively more ‘C’-shaped in the corresponding slices.
As such, the correct center shift correction factor effectively eliminated the ‘C’-shaped
void artifact. To be certain the correct value was selected for final reconstruction of
the entire stack of slices, several other specimen slice reconstruction locations were
tested with this procedure.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 109
Beam Hardening Correction
A correction factor was also determined to minimize beam hardening in reconstructed
slices. Due to the non-uniform shape of the failed match-head IPPS specimens, a sin-
gle correction factor (which is all that is available using Xradia’s proprietary XM
Reconstructor software) does not perfectly minimize beam hardening for all slices
within the reconstructed stack. In fact, selecting a correction factor which adequately
minimized beam hardening for reconstructed slices in the thickest region of the spec-
imen would cause a very slight over-correction in reconstructed slices in thin regions
of the specimen, i.e. near the fracture surface. As the population of voids tended
to be concentrated near the fracture surface in many specimens, this over-correction
effect could possibly be detrimental to later thresholding of slices due to the resulting
reduction in greyscale contrast between voids near the specimen surface and sur-
rounding steel. As such, the “test” slice selected for determination of the optimal
beam hardening correction constant was chosen from a moderately thin region of the
specimen; a region which would yield a correction factor that would adequately min-
imize beam hardening in upper slices of the reconstructed stack without producing a
reverse-cupping radial greyscale intensity distribution artifact (over-correction).
After selecting this “test” slice location, the slice was reconstructed with a range
of beam hardening correction factors. A lineal greyscale intensity plot was produced
for each reconstructed slice; beam hardening was evident as a “cupping” artifact
in the intensity distribution through the thickness of the specimen. The correction
factor which eliminated this cupping effect and produced a flat greyscale intensity
distribution through the thickness of the specimen was selected. This factor was 0.25
for all match-head specimens.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 110
Other Reconstruction Parameters
To produce the best contrast possible within reconstructed slices via better use of the
effective intensity range, manual byte scaling was used during reconstruction. A mini-
mum and maximum greyscale intensity value for slices within the reconstructed stack
were selected which would map the greyscale intensity histogram of reconstructed
slices as broadly across available bins as possible without saturation. If manual byte
scaling had not been employed, the proprietary reconstruction software would have
automatically set the min and max greyscale intensity histogram bins by first recon-
structing and sampling 6 slices from unknown specimen regions. Thus, clipping and
saturation could occur for some of the slices in the fully reconstructed stack.
Reconstructions were performed using 16-bits in order to have a large number
of greyscale bins and thus increase dynamic range. Final reconstruction of the full
stack of slices for each projection set was performed using the filtered backprojection
algorithms of Xradia’s XM Reconstructor software, producing a .txm file.
3.5.4 Slice Post-processing
Once a stack of slices had been fully reconstructed as a .txm file, they were converted
to a stack of uncompressed .tiff images to avoid data loss. These images were then
cropped about the largest match-head specimen cross-section, removing background
corresponding to the air surrounding the specimen, which would only lengthen post-
processing calculations. The goal with these slices was to perform segmentation of
voids from within slices to allow for automated quantitative analysis of void mor-
phology, size, and spatial distribution. However, unlike a synchrotron X-ray source
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 111
equipped with a monochromator, the beam produced in the Micro-XCT 400 is poly-
chromatic. Thus, greyscale intensity in reconstructed slices is not directly linked to
absorption coefficient. This translates to greyscale intensity mapping variation for a
material with an essentially homogeneous absorption coefficient throughout its vol-
ume. Noise inherent to reconstruction from projections of finite exposure time also
contributes to this greyscale intensity mapping variation (shown in Fig. 3.20 for a
cropped 16-bit slice of IPPS match-head specimen 9TP1-33-R10).
This greyscale intensity mapping variation led to poor results for preliminary
testing of thresholding methods, where pixels with low-level greyscale intensities that
were incorrectly captured as voids. Examples of these poor thresholding results are
provided in Fig. 3.21. As such, it was determined that a filtering operation prior to
thresholding was required to smooth out the noise. As described in Chap. 2, the filter
of choice for preserving void morphology in slices is the NL-means algorithm. The
algorithm was expected to perform well in preserving fine void detail while flattening
noise, given the high degree of redundancy produced by the pixels corresponding to
steel in the slices.
In order to make effective use of the NL-Means Denoising algorithm, a parametric
study was required to determine the optimal values for the window and patch size
used by this algorithm, detailed in Appendix D. These optimal parameters were used
for the NL-means denoising of all of the match-head specimen .tiff slice stacks. This
denoising step was performed using a scripted MATLAB implementation of the NL-
means algorithm written by Jose Vicente Manjon-Herrera, available on the MATLAB
Central File Exchange. The script was modified to process a folder containing a stack
of reconstructed slices using parallel computing; one image was denoised per CPU
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 112
core at a time, which vastly improved processing times.
3.5.4.1 Segmentation
NL-means denoising vastly improved thresholding results for cropped slices by accu-
rately capturing voids in the resulting masks without capturing low-intensity pixels
related to noise. This improvement is evident in Fig. 3.22. However, the thresholding
algorithms used up to this point performed very poorly with uncropped slices. As
shown in Fig. 3.23, even after NL-means denoising, the following algorithms from
five of the six categories outlined in Chap. 2 failed to elicit proper thresholding
masks of uncropped slices: histogram shape-based methods, clustering-based meth-
ods, entropy-based methods, object attribute-based methods, and spatial methods.
The clustering-based method of Kittler and Illingworth [127] and the entropy-based
methods of Kapur, Sahoo, and Wong [128], and Sahoo, Wilkins, and Yeager [129],
determined by Sezgin et al. [126] to be optimal for the thresholding of NDT images,
were included in this set. It appears that the relatively dark background surround-
ing the specimen in uncropped slices, which had lower greyscale intensity than void
pixels, was the most detrimental factor contributing to the poor thresholding results.
It was necessary to use uncropped slices because one single crop size for an entire
stack of slices would either leave background in upper slices near the specimen frac-
ture surface for a large crop window, or would eliminate some portion of the specimen
volume from analysis for a smaller crop window. It was desirable to extract as much
void damage data as possible in IPPS specimens. Therefore, the idea of cropping slice
stacks was discarded. It should be noted that each slice could have been individually
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 113
(a)
(b) (c)
Figure 3.20: a) A cropped 16-bit slice reconstructed from spec-imen 9TP1-33-R10 showing a large variation in greyscale in-tensity throughout. The yellow line represents the location ofsampling for the line intensity plot shown in b). The greyscaleintensity histogram for the cropped image is provided in c).
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 114
(a)
(b) (c)
Figure 3.21: a) A raw, cropped slice containing dark voids froma DP steel failed mechanical testing specimen of preliminarytesting. Poor thresholding results due to noise with: b) algo-rithm 2 of Pal and Pal [141]. c) algorithm of Sahoo, Wilkins,and Yeager [129].
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 115
(a) (b) (c)
(d) (e) (f)
Figure 3.22: a) A raw, cropped slice from a DP steel failed me-chanical testing specimen of preliminary testing. Poor thresh-olding results of a) due to noise using: b) algorithm 2 of Paland Pal [141]; c) algorithm of Sahoo, Wilkins, and Yeager [129].d) The slice of a) after being denoised with the NL-means algo-rithm. Accurate thresholding of voids from d) without captureof noise pixels using: e) algorithm 2 of Pal and Pal [141]; f)algorithm of Sahoo, Wilkins, and Yeager [129].
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 116
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m) (n)
Figure 3.23: a) A denoised, uncropped slice reconstructed froman XµCT scan of a match-head IPPS specimen. Poor thresh-olding results for this slice are displayed for the algorithms of:b) Abutaleb [142]; c)3-class fuzzy c-means clustering; d) Ka-pur, Sahoo, and Wong [128]; e) Kittler and Illingworth [127];f) Li and Lee [143]; g) Otsu [144]; h) Pal and Pal (algorithm1) [141]; i) Pal and Pal (algorithm 2) [141]; j) Ridler and Cal-vard [145]; k) Sahoo, Wilkins, and Yeager [129]; l) Tsai [146];m) Wong and Sahoo [147]; n) Yen, Chang, and Chang [148].
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 117
cropped to eliminate most background from the slice, but alignment of these vari-
ously sized slices into a 3D stack for void accumulation analysis would have proved
challenging.
A locally adaptive thresholding method was found to be the most viable option
for accurately segmenting voids in uncropped slices. The algorithm of choice, con-
tributed to the MATLAB Central File Exchange by Guanglei Xiong, makes use of
local contrast data to threshold an image. Pixels within a specified neighbourhood
window size in an image have their intensity compared to the average intensity of
the entire neighbourhood. If the intensity of any given pixel is significantly darker
than the average (beyond a set threshold controlled by a filtering parameter within
the algorithm), it is classified as foreground; otherwise it is classified as background.
The algorithm was used within MATLAB to threshold all of the NL-means denoised
slices from the match-head specimen tomography stacks.
The local contrast thresholding method performed very well in accurately cap-
turing void morphology in masks of uncropped slices for the IPPS match-heads, as
shown in Fig. 3.24. However, due to the high contrast with background at specimen
surfaces, these regions were captured as “voids” in masks. Typically, due to the con-
tinuous nature of these specimen edge artifacts in thresholded slices when stacked in
3-D, it was possible to eliminate them by applying a maximum volume criterion in
later void image analysis. However, some isolated pixels were produced in masks at
the specimen edge regions of slices which needed to be manually removed. Streak
artifacts were also often captured in masks.
All thresholded slices from each match-head specimen stack were visually cor-
related to their corresponding raw slices to ensure accurate thresholding had taken
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 118
place and to manually remove any artifacts present. If an accurate thresholding had
not taken place, i.e. some voids had not been captured in the resulting masks or were
of improper shape, then the local thresholding algorithm parameters (window size
and filtering degree) were modified and thresholding was re-performed until all slices
had accurately produced masks. To improve the ease with which manual correlation
could be made between masks and their corresponding raw slices, custom software
(Fig. 3.25) was developed which overlaid a red mask in a semi-transparent fashion
onto its corresponding raw slice.
3.5.4.2 Quantitative and Qualitative Volume Analysis
The thresholded stacks corresponding to each IPPS match-head specimen reconstruc-
tion were imported into Avizo R© Fire software for quantitative analysis of void dam-
age present. The pixel sizes calculated by Xradia’s proprietary software for the slices
within these stacks were used as calibrations for the voxel size of reconstructed vol-
umes. The accuracies of these calibrations were confirmed to within ±1% by com-
paring match-head specimen widths measured with the calibrated software with mea-
surements using Vernier calipers. Voids were identified within the segmented volume
by the software and their geometric parameters automatically calculated.
A size criterion was used to remove voids that approached the resolving power of
the Micro-XCT 400 instrument. To be confident that foreground pixels captured in
binary masks truly represented voids within specimens and not just noise, a minimum
volume criterion was applied to the 3D threshold image. Voids were required to be
a minimum size of 27 voxels, i.e. (3 x pixel size)3 in volume, in order to be included
in the analysis. Data that was calculated for each void identified included: volume,
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 119
(a)
(b)
Figure 3.24: a) The denoised slice from Fig. 3.23(a). b) Athreshold mask accurately capturing the morphology of thevoids from a); produced using a locally adaptive thresholdingalgorithm.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 120
Figure 3.25: Custom software capable of overlaying a red maskproduced from thresholding in a semi-transparent fashion ontoits corresponding raw slice.
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 121
surface area, centroid location within the 3D volume bounding box, maximal length,
and spherical coordinates of the orientation of the maximal length vector.
The denoised match-head slices were also thresholded using an automated greyscale
histogram shape-based method to produce a mask of the steel volume. These stacks
of slices were analyzed in Avizo R© Fire in the same manner outlined above for the
void mask slice stacks to determine the total volume of each match-head specimen
that was reconstructed. Using these calculated match-head specimen volumes, the
volume percent of void damage within each specimen was computed.
Finally, 3-D renderings of the voids were produced using the Avizo R© Fire soft-
ware. A closed 3-D surface was generated for the binarized voids. A semi-transparent
rendering of the IPPS match-head specimen volume was produced using raw recon-
structed slices around this void surface rendering to lend context to the locations of
voids within the specimen.
3.6 Fractography
The match-head specimen fracture surfaces were examined using a JEOL JSM-840
SEM instrument in secondary electron mode to capture greyscale micrographs mea-
suring 1024 x 768 pixels. Fractographs were captured at 85x magnification to image
the entire fracture surface. Fractographs were also captured at 500x magnification
at locations that were one-quarter and one-half through the sheet thickness at the
location of failure. These locations detailed any transition in fracture mode from
ductile to shear.
Despite being stored in a dessicator, the match-head specimens oxidized to a minor
degree. Hence, prior to fractographic examination a cleaning procedure was applied
CHAPTER 3. EXPERIMENTAL METHODS AND MATERIALS 122
to remove the oxidation while introducing minimal artifacts to the fracture surface. A
15 second dip in the inhibited sulphuric acid described in Appendix C was employed
based upon the recommendations of Tartaglia [149]. This was followed immediately
by an ultrasonic cleaning in ethanol to remove any dust and debris which may have
collected in the fracture surface.
3.7 Metallographic Damage Analysis
Post SEM-examination, the match-head specimens were mounted in epoxy for metal-
lographic examination of through-thickness tensile axis plane. These mounted spec-
imens were ground and polished as per the procedures outlined in Table 3.4 and
Table 3.5, but with a significantly longer rough grind to be certain artifacts were not
introduced into the polished surface from the wafer-saw sectioning. A 10% Sodium
metabisulfite etchant was used to stain and provide colour contrast between ferrite
grains and NFP particles. A Zeiss Axioskop 2 MAT light microscope equipped with
an Olympus EvolutionTMMP Colour CCD camera was used to capture colour micro-
graphs measuring 2560 x 1920 pixels for each match-head specimen. A 100x Zeiss
Epiplan-NEOFLUAR oil immersion lens was used during micrograph acquisition.
Micrographs were captured in regions where void damage was evident to allow for
interpretation of void nucleation mechanisms active in each specimen.
Chapter 4
Results
This chapter presents the results of the experiments outlined in Chap. 3. The mi-
crostructures of the ten DP steel variants used for the IPPS mechanical testing pro-
tocol are quantitatively and qualitatively characterized. The failure strains of valid
IPPS specimens are reported. Void damage accumulation within “match-head” spec-
imens, extracted from the failure surface of IPPS specimens, as determined by XµCT
is quantified and qualified.
4.1 Microstructure Characterization
The quantitative measures of microstructural parameters which are presented in the
succeeding sub-sections were calculated in the manner dictated in Sec. 3.3. The mi-
crostructures of the cold-rolled DP steels are presented. Microstructures of DP steel
variants used for the IPPS mechanical testing protocol are presented and described
in the following order: commercial galvannealed DP steels, TP1-treated DP steels,
and TP2-treated DP steels. The fine-grained nature of the steels necessitated high
123
CHAPTER 4. RESULTS 124
magnifications not achievable via light microscopy for accurate microstructural char-
acterization. Thus, colour contrast was not available for the differentiation of phases
and constituents. This led to a simplified characterization of NFP as a whole in
the microstructures, due to a lack of readily physically-distinguishable features be-
tween martensite, pearlite, bainite, and austenite at 5000x magnification in scanning
electron micrographs.
4.1.1 Cold-rolled DP Steels
The sheets received in the cold-rolled condition contained ferrite and NFP in a heavily
deformed microstructure, as shown in Fig. 4.1. Both ferrite grains and NFP particles
were elongated in the rolling direction. The volume percents of constituents for both
cold-rolled steels are provided in Table 4.1.
Table 4.1: As-received cold-rolled sheet steel constituent volumepercents with 95% confidence interval.
NFP Ferritevolume % volume %
DP780 CR 9.8 ± 1.1% balanceDP980 CR 11.8 ± 1.0% balance
4.1.2 Galvannealed DP Steels
The microstructures of the multiphase galvannealed DP780 and DP980 steels received
from U.S. Steel are presented in the representative optical micrographs of Fig. 4.2.
Both the DP780GA and DP980GA steels were observed to consist of a matrix of
ferrite grains which were elongated in the rolling direction. The NFP particles in
these microstructures were observed to be located at ferrite grain boundaries.
CHAPTER 4. RESULTS 125
(a) DP780CR (b) DP780CR
(c) DP980CR (d) DP980CR
Figure 4.1: Representative optical micrographs of a) and b)cold-rolled DP780 steel at the sheet centerline; c) and d)cold-rolled DP980 steel at the sheet centerline. 10% Sodiummetabisulfite etch. Martensite and bainite/pearlite tinted dark,ferrite tinted light.
CHAPTER 4. RESULTS 126
Both the volume percent and size of NFP particles are clearly larger in the
DP980GA steel than in the DP780GA steel. The results of quantitative measure-
ments are summarized in Table 4.2. For both steels, NFP was observed to be dis-
tributed heterogeneously. Heavy and continuous banding of NFP was present along
the rolling direction and to a lesser extent along the transverse direction for both
steels. This banding was most prevalent at the sheet centerline, with NFP bands
becoming slightly more discontinuous and finer in scale with increasing proximity to
the sheet surface.
Table 4.2: Volume percent and mean lineal intercept of NFPparticles in the galvannealed DP steel sheets provided by U.S.Steel. A 95% confidence interval and percent relative accuracy(R.A.) are provided for both measures.
DP Steel Variant NFP Vol. % % R.A. NFP mean lineal intercept (µm) % R.A.
DP780GA 22.5 ± 2.9 12.9 1.07 ± 0.07 6.5
DP980GA 36.3 ± 3.5 9.6 1.43 ± 0.10 7.0
4.1.3 TP1-treated DP Steels
The microstructures of the DP steel variants produced via TP1-treatment of the
DP780 and DP980 cold-rolled steel received from U.S. Steel are presented respectively
in the representative micrographs of Fig. 4.3 and Fig. 4.4. TP1-treated microstruc-
tures were somewhat similar to those of the commercial galvannealed sheets; both
consisted of a matrix of ferrite grains which were elongated in the rolling direction
and NFP particles in both microstructures were located at ferrite grain boundaries.
For TP1-treated DP780CR steels, NFP bands were present along both the RD and
TD. The bands aligned along the RD were thicker and more continuous. Banding of
NFP along the RD and TD near the sheet centerline was observed to be more severe
CHAPTER 4. RESULTS 127
(a) DP780GA (b) DP780GA
(c) DP980GA (d) DP980GA
Figure 4.2: Representative optical micrographs of a) and b)galvannealed DP780 steel at the sheet centerline; c) and d)galvannealed DP980 steel at the sheet centerline. 10% Sodiummetabisulfite etch. Martensite and bainite/pearlite tinted dark,ferrite tinted light.
CHAPTER 4. RESULTS 128
and continuous in TP1-treated DP780CR steels than in the galvannealed DP780 steel.
As well, this banding was heavily concentrated and most continuous at the sheet
centerline with little banding observed elsewhere through the sheet thickness. The
7TP1-33-T10 IPPS specimen in particular was noted to contain a singular continuous
NFP band at the sheet centerline in the RD.
For TP1-treated DP980CR steels, NFP was observed to be dispersed in clusters
and slightly more discontinuous bands due to irregularly shaped ferrite grains. The
volume percent and mean lineal intercept of NFP particles in TP1-treated IPPS spec-
imens are provided in Table 4.3. It is clear that increasing IC annealing temperature
resulted in increased NFP content.
Table 4.3: Volume percent and mean lineal intercept of NFPparticles in TP1-treated DP steel variants. A 95% confidenceinterval and percent relative accuracy (R.A.) are provided forboth measures.
DP Steel VariantIC AnnealingTemperature
(◦C)NFP Vol. % % R.A.
NFP meanlineal intercept
(µm)% R.A.
7TP1-15 715 11.7 ± 0.8 6.8 0.59 ± 0.04 6.8
7TP1-33 733 29.4 ± 3.3 11.2 1.22 ± 0.09 7.4
7TP1-43 743 37.8 ± 2.4 6.3 1.2 ± 0.07 5.8
9TP1-15 715 17.3 ± 1.6 9.2 0.79 ± 0.09 11.4
9TP1-33 733 38.3 ± 2.3 6.0 1.29 ± 0.07 5.4
9TP1-43 743 40.4 ± 2.1 5.2 1.39 ± 0.08 5.8
4.1.4 TP2-treated DP Steels
The microstructures produced by TP2-treatment of the cold-rolled steels of this study
are presented in the representative micrographs of Fig. 4.5. The relatively discontinu-
ous, uniform distribution of NFP is evident, but so is some residual banding of NFP at
the sheet centerline. This banding was more continuous for the TP2-treated variants
CHAPTER 4. RESULTS 129
(a) 7TP1-15 (IC annealed @ 715◦C) (b) 7TP1-15 (IC annealed @ 715◦C)
(c) 7TP1-33 (IC annealed @ 733◦C) (d) 7TP1-33 (IC annealed @ 733◦C)
(e) 7TP1-43 (IC annealed @ 743◦C) (f) 7TP1-43 (IC annealed @ 743◦C)
Figure 4.3: Representative optical micrographs captured at thesheet centerline for DP780CR steel after TP1-treatment. Con-tinuous banding of NFP is present in both ND-RD and ND-TDsections. 10% Sodium metabisulfite etch. Martensite tinteddark, ferrite tinted light.
CHAPTER 4. RESULTS 130
(a) 9TP1-15 (IC annealed @ 715◦C) (b) 9TP1-15 (IC annealed @ 715◦C)
(c) 9TP1-33 (IC annealed @ 733◦C) (d) 9TP1-33 (IC annealed @ 733◦C)
(e) 9TP1-43 (IC annealed @ 743◦C) (f) 9TP1-43 (IC annealed @ 743◦C)
Figure 4.4: Representative optical micrographs captured at thesheet centerline for DP980CR steel after TP1-treatment. Con-tinuous banding of NFP is present in both ND-RD and ND-TDsections. 10% Sodium metabisulfite etch. Martensite tinteddark, ferrite tinted light.
CHAPTER 4. RESULTS 131
produced from DP980CR than from DP780CR. For TP2-treated variants produced
from DP980CR, the banding in the longitudinal direction was also not confined solely
to the sheet centerline. Like DP980GA, banding was most prevalent at the material
centerline, with NFP bands becoming slightly more discontinuous and finer in scale
with increasing proximity to the sheet surface.
The NFP particles in TP2-treated microstructures had a bimodal size distribution,
with many thin, elongated particles, but this was not taken into account during
measurement of NFP particle size. The mean sizes of NFP particles in the TP2-
treated specimens were relatively similar to those of the galvannealed steels. The
volume percent and mean lineal intercept of NFP particles in TP2-treated IPPS
specimens are provided in Table 4.4.
Table 4.4: Volume percent and mean lineal intercept of NFPparticles in TP2-treated DP steel variants. A 95% confidenceinterval and percent relative accuracy (R.A.) are provided forboth measures.
DP Steel Variant NFP Vol. % % R.A. NFP mean lineal intercept (µm) % R.A.
7TP2-25 30.5 ± 1.8 5.9 0.84 ± 0.03 3.6
9TP2-37 34.2 ± 2.2 6.4 1.23 ± 0.09 7.3
4.1.5 Summary of Microstructures
The volume percent and mean lineal intercept of NFP particles in all of the DP steel
variants used for IPPS testing are summarized in Table 4.5. The goal of performing
heat treatments on cold-rolled sheet to produce two DP steel variants with similar
NFP volume percent to the galvannealed DP steels was accomplished for the DP980
series of steels with 9TP1-33 and 9TP2-37. However, for the DP780 series of steels,
two variants were produced with similar NFP volume percent through 7TP1-33 and
CHAPTER 4. RESULTS 132
(a) 7TP2-25 (b) 7TP2-25
(c) 9TP2-37 (d) 9TP2-37
Figure 4.5: Representative optical micrographs captured at thesheet centerline for DP780CR and DP980CR steel after TP2-treatment. Residual banding of NFP is present in both ND-RDand ND-TD sections. 10% Sodium metabisulfite etch. Marten-site tinted dark, ferrite tinted light.
CHAPTER 4. RESULTS 133
7TP2-25 treatments, but this volume percent was not similar to that of the corre-
sponding DP780GA steel.
The galvannealed DP steel microstructures consisted of NFP, heavily and contin-
uously banded at the sheet centerline in the rolling direction, embedded in a ferrite
matrix. The NFP banding was finer and more discontinuous with increasing prox-
imity to the sheet surface. The TP1-treated DP780 steel microstructures consisted
of NFP, heavily and continuously banded at the sheet centerline in the rolling direc-
tion, embedded in a ferrite matrix. The NFP banding was heavily concentrated at
the sheet centerline with little banding observed away from this region. In the TP1-
treated DP980CR steels, NFP was observed to be dispersed in clusters and slightly
more discontinuous bands. The TP2-treated DP steel microstructures consisted of
relatively uniformly spatially distributed NFP, with light banding at the sheet cen-
terline in the rolling direction, embedded in a ferrite matrix. The NFP particles
in TP2-treated microstructures were bimodal in size with many elongated particles
present. Mean NFP particle size varied throughout the microstructures, essentially
increasing in a relatively linear fashion with NFP volume percent.
4.2 IPPS Mechanical Testing
The results of the IPPS tensile testing are provided in this section. For all specimens
which failed in a satisfactory manner according to the criteria outlined in Sec. 3.5.1,
strains in the grid row where final failure occurred were calculated just prior to frac-
ture. The strains calculated for the 7 grid-points in this failure row were averaged
to a single value. The failure strains for the entire population of valid specimens are
presented in Appendix E.
CHAPTER 4. RESULTS 134
Table 4.5: Volume percent and mean lineal intercept of the NFPparticles in all of the DP steel variants used for IPPS testing.A 95% confidence interval and percent relative accuracy (R.A.)are provided for both measures.
DP Steel Variant NFP Vol. % % R.A. NFP mean lineal intercept (µm) % R.A.
DP780GA 22.5 ± 2.9 12.9 1.07 ± 0.07 6.5
DP980GA 36.3 ± 3.5 9.6 1.43 ± 0.10 7.0
7TP1-15 11.7 ± 0.8 6.8 0.59 ± 0.04 6.8
7TP1-33 29.4 ± 3.3 11.2 1.22 ± 0.09 7.4
7TP1-43 37.8 ± 2.4 6.3 1.2 ± 0.07 5.8
9TP1-15 17.3 ± 1.6 9.2 0.79 ± 0.09 11.4
9TP1-33 38.3 ± 2.3 6.0 1.29 ± 0.07 5.4
9TP1-43 40.4 ± 2.1 5.2 1.39 ± 0.08 5.8
7TP2-25 30.5 ± 1.8 5.9 0.84 ± 0.03 3.6
9TP2-37 34.2 ± 2.2 6.4 1.23 ± 0.09 7.3
To elucidate the general behaviour of each of the DP steel variants tested, the
mean failure row strains for specimens of a given condition/treatment were averaged
and are provided in Table 4.6(a). As only one or two specimens failed satisfactorily for
many of the DP steel variants tested, a measure of standard deviation is not provided
for the failure strain results. For the IPPS specimens selected for XµCT analysis, the
strain measured at the gridpoint which was in the middle column of the failure row
where the match-head specimens were extracted is reported in Table 4.6(b). For both
of the aforementioned tables, results are not ordered numerically by failure strain,
but rather by the heat treatment/condition and orientation of DP steel variants.
Due to problems with surface pitting caused by improper acid cleaning procedures,
some IPPS specimen batches required reproduction; hence the identification numbers
greater than 7 for some of the XµCT specimens.
In many cases, IPPS specimens oriented with the rolling direction along the tensile
axis (RD specimens) had a higher major failure strain than those with the transverse
CHAPTER 4. RESULTS 135
sheet direction aligned with the tensile axis. The DP steel variants which were the ex-
ception to this observation were the 7TP1-15 and the 7TP2-25 variants. The variant
with the highest major failure strains was 7TP1-15 and the lowest 9TP2-43. These
variants respectively had the lowest and highest volume percents of NFP in their
microstructures. Major engineering failure strain and NFP volume percent are corre-
lated in Fig. 4.6 and Fig. 4.7 for all valid IPPS specimens produced from DP780 and
DP980, respectively. A general trend of major engineering strain at failure decreasing
with increasing NFP content was clearly evident.
CHAPTER 4. RESULTS 136
Table 4.6: Strain just prior to failure in IPPS DP steel variantspecimens.
(a) Mean major and minor engineer-
ing strains computed in the failure
row, just prior to failure, averaged
for the IPPS specimens of a given
condition/treatment. The numerals
in brackets appended to the variant
name indicate the number of valid
tests used to compute the mean strain
values.
VariantEngineering Strain
Major Minor
7GA-R(2) 0.106 -0.005
7GA-T(2) 0.093 -0.005
9GA-R(3) 0.070 0.000
9GA-T(2) 0.049 -0.001
7TP1-15-R(1) 0.202 -0.015
7TP1-15-T(1) 0.242 -0.016
7TP1-33-R(1) 0.131 -0.008
7TP1-33-T(3) 0.125 -0.007
7TP1-43-R(5) 0.063 -0.003
7TP1-43-T(3) 0.053 -0.003
9TP1-15-R(2) 0.157 -0.010
9TP1-15-T(5) 0.138 -0.010
9TP1-33-R(3) 0.087 -0.005
9TP1-33-T(2) 0.076 -0.006
9TP1-43-R(2) 0.051 -0.003
9TP1-43-T(4) 0.020 -0.001
7TP2-25-R(1) 0.129 -0.006
7TP2-25-T(2) 0.135 -0.007
9TP2-37-R(2) 0.093 -0.004
9TP2-37-T(3) 0.064 -0.003
(b) Major and minor engineering
strain computed in the central grid-
point of the failure row, just prior to
failure, for IPPS specimens subjected
to XµCT analysis.
SpecimenEngineering Strain
Major Minor
7GA-R4 0.109 -0.004
7GA-T2 0.079 -0.004
9GA-R3 0.059 0.002
9GA-T4 0.040 0.001
7TP1-15-R4 0.197 -0.010
7TP1-15-T11 0.229 -0.014
7TP1-33-R11 0.130 -0.003
7TP1-33-T10 0.136 -0.006
7TP1-43-R3 0.065 -0.002
7TP1-43-T5 0.051 -0.002
9TP1-15-R7 0.179 -0.012
9TP1-15-T1 0.125 -0.009
9TP1-33-R10 0.094 -0.005
9TP1-33-T10 0.072 -0.008
9TP1-43-R11 0.052 0.000
9TP1-43-T7 0.020 -0.001
7TP2-25-R4 0.118 -0.006
7TP2-25-T2 0.092 -0.005
9TP2-37-R4 0.090 -0.003
9TP2-37-T1 0.071 -0.002
CHAPTER 4. RESULTS 137
Figure 4.6: Relationship between NFP volume percent in IPPSspecimens produced from DP780 and mean major engineeringstrain in the failure row just prior to specimen failure. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars,derived from the systematic error associated with IPPS gridstrain measurements, are too small to be visible.
CHAPTER 4. RESULTS 138
Figure 4.7: Relationship between NFP volume percent in IPPSspecimens produced from DP980 and mean major engineeringstrain in the failure row just prior to specimen failure. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars,derived from the systematic error associated with IPPS gridstrain measurements, are too small to be visible.
CHAPTER 4. RESULTS 139
4.3 Void Damage Accumulation and Failure
The results of the XµCT scans of the 20 match-head IPPS specimens are presented in
this section. For each of the reconstructions produced, voxel size was 1.1815 x 1.1815
x 1.1815 µm. The size distribution, spatial distribution, and number of microvoids
varied throughout the reconstructed specimens. Microvoid damage was generally
concentrated most densely near the fracture surface, but significant damage was ob-
served hundreds of microns away from the fracture surface for many specimens. As
well, there was a significant localization of void populations to a region near the sheet
centerline for many specimens.
Fracture surfaces and micrographs of polished through-thickness tensile axis planes
for the match-head specimens are also presented in this section. It was clear from the
metallographic micrographs that the smallest voids in match-head specimens were
not captured using XµCT and the minimum void volume criterion of Sec. 3.5.4.2.
However, the distribution of larger voids observed in metallographic micrographs
and XµCT reconstructions had a high degree of correlation. A general trend of
reduced through-thickness specimen thinning with decreasing nominal failure strain
was observed.
The data computed for the reconstructed voids of each specimen is summarized
in Table 4.7 and Table 4.8. For all specimens examined, void volume percent within
the reconstructed volumes totalled less than 0.3%. To more clearly illustrate the re-
lationships between microstructure, void damage accumulation, and strain at failure
each specimen will be discussed in a subsection devoted to DP steel variants of its
particular treatment/condition. The order of presentation begins with the commer-
cial galvannealed DP steel, followed by TP1-treated DP variants, and TP2-treated
CHAPTER 4. RESULTS 140
DP variants. A summarial examination of the role played by NFP volume percent,
morphology, and spatial distribution in damage accumulation for the IPPS DP steel
variants follows in Chap. 5.
Table 4.7: Number of voids, void volume percent, and total voidvolume in the XµCT reconstructed portions of IPPS match-head specimens. Standard deviation is represented by σ.
Specimen # of Voids Volume Percent (%)Volume (µm3)
Mean (x 103) σ (x 103) Max (x 103)
7GA-R4 116 0.006 0.361 0.42 2.1
7GA-T2 318 0.024 0.448 1.07 12.6
9GA-R3 51 0.005 0.559 1.15 7.5
9GA-T4 84 0.014 0.977 2.02 12.5
7TP1-15-R4 65 0.020 1.956 7.31 57.6
7TP1-15-T11 158 0.032 1.129 2.88 26.5
7TP1-33-R11 167 0.025 0.855 2.47 21.2
7TP1-33-T10 260 0.273 5.719 32.12 453.9
7TP1-43-R3 165 0.071 2.561 15.07 189.8
7TP1-43-T5 83 0.011 0.736 3.16 28.2
9TP1-15-R7 304 0.031 0.692 1.57 13.9
9TP1-15-T1 551 0.037 0.446 0.95 12.9
9TP1-33-R10 60 0.006 0.527 1.16 7.7
9TP1-33-T10 593 0.044 0.521 1.32 13.0
9TP1-43-R11 42 0.001 0.181 0.18 0.7
9TP1-43-T7 123 0.009 0.392 0.49 3.9
7TP2-25-R4 63 0.008 0.705 1.95 14.9
7TP2-25-T2 282 0.036 0.722 1.67 19.6
9TP2-37-R4 155 0.036 1.216 2.93 20.4
9TP2-37-T1 282 0.016 0.324 0.46 3.2
CHAPTER 4. RESULTS 141
Table 4.8: Equivalent spherical diameter, maximum length ofFeret distribution (Length3D), and modified spherical coordi-nate orientations of voids in the XµCT reconstructed portionsof IPPS match-head specimens. Phi, φ, was defined as the an-gle between the principal inertia axis of a void and the globalZ-axis in degrees between [0,+90]. The major strain axis ofIPPS specimens was assumed to be aligned with global Z-axisof XµCT reconstructions. Theta, θ, was defined as the an-gle between the principal inertia axis projection of a void inthe global XY-plane and the global X-axis in degrees between[0,+90]. The minor strain axis of IPPS specimens was assumedto be aligned with the global X-axis of XµCT reconstructions.Standard deviation is represented by σ.
SpecimenEq. Diameter (µm) Length3D (µm) φ (◦) θ (◦)
Mean σ Mean σ Mean σ Mean σ
7GA-R4 6.47 8.8 11.8 15.5 85 25 32 24
7GA-T2 5.67 5.3 13.0 8.7 78 74 12 15
9GA-R3 12.85 17.6 24.8 24.5 3 37 35 27
9GA-T4 5.21 6.5 9.2 11.6 66 86 18 23
7TP1-15-R4 5.01 9.7 13.8 18.9 59 89 27 27
7TP1-15-T11 7.97 10.5 12.1 20.2 71 84 11 15
7TP1-33-R11 5.21 6.7 7.1 9.8 16 28 21 24
7TP1-33-T10 8.90 5.2 34.3 10.6 90 83 5 9
7TP1-43-R3 5.86 4.7 14.2 7.5 83 64 17 22
7TP1-43-T5 5.64 4.6 10.6 7.5 80 7 7 8
9TP1-15-R7 9.74 4.4 18.2 7.9 23 10 33 29
9TP1-15-T1 4.60 6.2 10.9 9.8 72 57 8 11
9TP1-33-R10 5.83 8.4 8.5 13.0 77 11 33 26
9TP1-33-T10 4.93 4.5 8.7 7.9 65 16 9 13
9TP1-43-R11 4.70 8.4 7.8 13.0 78 86 30 24
9TP1-43-T7 4.55 4.9 8.7 8.5 43 75 11 15
7TP2-25-R4 6.52 6.0 10.6 10.5 17 27 33 26
7TP2-25-T2 12.80 4.7 27.2 6.8 78 45 14 17
9TP2-37-R4 5.83 5.8 10.6 11.8 30 87 22 26
9TP2-37-T1 8.43 6.4 13.2 9.2 13 11 10 14
CHAPTER 4. RESULTS 142
4.3.1 Galvannealed DP Steels
4.3.1.1 Degree of Damage
The degree of damage in each of the galvannealed XµCT specimens is qualitatively
provided in 3-D renderings of the outer surfaces of voids within a semi-transparent
rendering of the match-head specimen volumes in Fig. 4.8 through Fig. 4.21. These
images highlight in 3-D the size of voids (shown in red), their shape, and their spatial
arrangement within the reconstructed match-head volumes. For instance, Fig. 4.8 and
Fig. 4.9 illustrate a general concentration of sphere-shaped voids accumulated near the
fracture surface of the 7GA-R4, that the voids were generally distributed throughout
the sheet thickness, but with some concentration towards the sheet centerline, and
that many small voids are visible hundreds of microns away from the fracture surface.
Fig. 4.10(a) displays a polished RD-ND plane of the 7GA-R4 specimen, providing
evidence to back-up the void damage accumulation observed via XµCT. Fig. 4.10(b)
exhibits detail of void nucleation sites in the 7GA-R4 specimen using a 2% nital
etch to colour NFP a tan/blue hue, leaving ferrite light and voids black. Fig. 4.11
provides fractographs of the 7GA-R4 specimen fracture surface at two magnifications
to provide insight to the failure mechanisms which were at work.
The size distribution of accumulated void damage for each specimen is provided
in Fig. 4.24. The frequency distribution of void damage through the thickness is
presented in Fig. 4.25 and the distribution of void volumes through the thickness by
geometric centroid is presented in Fig. 4.26. All of the aforementioned figures have
been prepared for each of the specimens of galvannealed, and TP1- and TP2-treated
condition in the following subsections; for the sake of brevity, these figures will not be
introduced in the text. Summarial tables are provided for each of the the three types
CHAPTER 4. RESULTS 143
of DP steel variants highlighting the important damage accumulation observations
for each specimen. Table 4.9 provides this summary for the galvannealed specimens.
4.3.1.2 Damage Distribution
Void damage was generally more concentrated within the region just below the frac-
ture surface of the galvannealed match-head specimens, where strains were larger. No
significant trends were elicited in the spatial distribution of void damage through the
thickness of specimens in terms of the number of voids present (Fig. 4.25) or their vol-
umes (Fig. 4.26). At the most, it can be stated that the distribution of voids through
the sheet thickness resembles a normal distribution and that voids were somewhat
clustered towards the mid-thickness of the sheet. This spatial distribution of void
damage through the thickness of the sheet closely mimics the spatial distribution of
NFP bands through the thickness of the galvannealed sheets.
4.3.1.3 Void Orientations
For the most part, void orientation in the galvannealed match-head specimens was
relatively random (see Table 4.8). However, the 7GA-T2 specimen had a large pro-
portion of voids which were very much aligned with its minor strain axis as evidenced
qualitatively in Fig. 4.12 and quantitatively by its low mean θ value in Table 4.8 with
relatively low standard deviation.
4.3.1.4 Failure Mechanism
The galvannealed specimens tended to fail via a shear-dominated mechanism. Signif-
icant surface roughening is evident for 7GA-R4 and 7GA-T2 respectively in Fig. 4.9
CHAPTER 4. RESULTS 144
and Fig. 4.13.
Table 4.9: Damage accumulation observations, inferences, andcomputations for galvannealed DP steel specimens.
Specimen # of Voids
Void Volume (µm3)
ObservationsMean σ Max(x 103) (x 103) (x 103)
7GA-R4 116 0.361 0.42 2.1
• Moderately ductile cup-cone type failure• NFP particle cracking dominated voidnucleation• Uniform size distribution of fracture sur-face dimples (2-4 µm)• Mild clustering of void damage to sheetcenterline
7GA-T2 318 0.448 1.07 12.6
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples elongatedin RD, surrounded by uniform size dimples(2-5 µm)• Random spatial distribution of voiddamage through sheet thickness
9GA-R3 51 0.559 1.15 7.5
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Uniform size distribution of fracture sur-face dimples (1-3 µm)• Mild clustering of void damage to sheetcenterline
9GA-T4 84 0.977 2.02 12.5
• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples very elon-gated in RD• Mild clustering of void damage to sheetcenterline region
CHAPTER 4. RESULTS 145
Figure 4.8: 3-D semi-transparent volume rendering of the 7GA-R4 IPPS match-head specimen displaying an isosurface render-ing of the void damage within (three-point perspective). Theperspective view makes the insertion of a scale bar inappropri-ate. The dimensions of the bounding box of the reconstructionare 1066 x 963 x 1152 µm.
CHAPTER 4. RESULTS 146
Figure 4.9: 3-D semi-transparent volume rendering of the 7GA-R4 IPPS match-head specimen displaying an isosurface render-ing of the spatial distribution of void damage in the ND-RDplane (one-point perspective). The perspective view makes theinsertion of a scale bar inappropriate. The dimensions of thefrontal plane of the bounding box of the reconstruction are 963x 1152 µm.
CHAPTER 4. RESULTS 147
(a) Polished
(b) 2% Nital etch
Figure 4.10: Typical optical micrographs of the failed 7GA-R4match-head specimen showing void damage.
CHAPTER 4. RESULTS 148
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.11: SEM fractographs of the failed 7GA-R4 match-head specimen.
CHAPTER 4. RESULTS 149
Figure 4.12: 3-D semi-transparent volume rendering of the7GA-T2 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 987 x 932 x 1150 µm.
CHAPTER 4. RESULTS 150
Figure 4.13: 3-D semi-transparent volume rendering of the7GA-T2 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are932 x 1150 µm.
CHAPTER 4. RESULTS 151
(a) Polished
(b) 2% Nital etch
Figure 4.14: Typical optical micrographs of the failed 7GA-T2match-head specimen showing void damage.
CHAPTER 4. RESULTS 152
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.15: SEM fractographs of the failed 7GA-T2 match-head specimen.
CHAPTER 4. RESULTS 153
Figure 4.16: 3-D semi-transparent volume rendering of the9GA-R3 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 1081 x 1087 x 1148 µm.
CHAPTER 4. RESULTS 154
Figure 4.17: 3-D semi-transparent volume rendering of the9GA-R3 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are1087 x 1148 µm.
CHAPTER 4. RESULTS 155
(a) Polished
(b) 2% Nital etch
Figure 4.18: Typical optical micrographs of the failed 9GA-R3match-head specimen showing void damage.
CHAPTER 4. RESULTS 156
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.19: SEM fractographs of the failed 9GA-R3 match-head specimen.
CHAPTER 4. RESULTS 157
Figure 4.20: 3-D semi-transparent volume rendering of the9GA-T4 IPPS match-head specimen displaying an isosurfacerendering of the void damage within (three-point perspective).The perspective view makes the insertion of a scale bar inap-propriate. The dimensions of the bounding box of the recon-struction are 958 x 1081 x 1147 µm.
CHAPTER 4. RESULTS 158
Figure 4.21: 3-D semi-transparent volume rendering of the9GA-T4 IPPS match-head specimen displaying an isosurfacerendering of the spatial distribution of void damage in the ND-RD plane (one-point perspective). The perspective view makesthe insertion of a scale bar inappropriate. The dimensions ofthe frontal plane of the bounding box of the reconstruction are1081 x 1147 µm.
CHAPTER 4. RESULTS 159
(a) Polished
(b) 2% Nital etch
Figure 4.22: Typical optical micrographs of the failed 9GA-T4match-head specimen showing void damage.
CHAPTER 4. RESULTS 160
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.23: SEM fractographs of the failed 9GA-T4 match-head specimen.
CHAPTER 4. RESULTS 161
0 10 20 300
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(a) 7GA-R4
0 10 20 300
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(b) 7GA-T2
0 10 20 300
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(c) 9GA-R3
0 10 20 300
10
20
30
40
50
60Freq
uenc
y
Equivalent Diameter (µm)
(d) 9GA-T4
Figure 4.24: Histograms of equivalent spherical void diame-ter in reconstructed galvannealed DP steel variant match-headspecimens.
CHAPTER 4. RESULTS 162
-400 -300 -200 -100 0 100 200 300 4000
5
10
15
20
25
30
35
40
Freq
uenc
y
Distance to Center (µm)
(a) 7GA-R4
-400 -200 0 200 4000
5
10
15
20
25
30
35
40
Freq
uenc
y
Distance to center (µm)
(b) 7GA-T2
-400 -200 0 200 4000
5
10
15
20
25
30
35
40
Freq
uenc
y
Distance to center (µm)
(c) 9GA-R3
-400 -200 0 200 4000
5
10
15
20
25
30
35
40Freq
uenc
y
Distance to center (µm)
(d) 9GA-T4
Figure 4.25: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed galvannealed DPsteel variant match-head specimens.
CHAPTER 4. RESULTS 163
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(a) 7GA-R4
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(b) 7GA-T2
-500 -400 -300 -200 -100 0 100 200 300 400 500
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(c) 9GA-R3
-400 -200 0 200 400
100
1000
10000V
olum
e (µ
m3 )
Distance to center (µm)
(d) 9GA-T4
Figure 4.26: Profiles of the volumes of voids through thesheet thickness in reconstructed galvannealed DP steel variantmatch-head specimens.
CHAPTER 4. RESULTS 164
4.3.2 TP1-treated DP Steels
Table 4.10 and Table 4.11 highlight the important damage accumulation observations
for each of the 7TP1-treated and 9TP1-treated specimens, respectively. The effect of
NFP content on damage accumulation is examined in terms of void volume percent
in Fig. 4.27 and Fig. 4.28 for 7TP1 and 9TP1 variants, respectively; and in terms of
number of voids in Fig. 4.29 and Fig. 4.30 for 7TP1 and 9TP1 variants, respectively.
No clear trends are evident.
4.3.2.1 Degree of Damage
The degree of damage in each of the TP1-treated XµCT specimens is qualitatively
provided in 3-D renderings of the outer surfaces of voids within a semi-transparent
rendering of the match-head specimen volumes in Fig. 4.31 through Fig. 4.76. Several
of the TP1-treated specimens contained the largest void volume percent of all the
variants.
4.3.2.2 Damage Distribution
For all TP1-treated specimens, damage was concentrated most populously just below
the fracture surface. As well, voids were often concentrated heavily in the sheet center-
line plane, especially those of the largest volume, reflective of the spatial distribution
of microstructural NFP banding in these variants. A spatial and volumetric distri-
bution of void damage which was heavily centerline clustered in many of the more
ductile microstructures (i.e. lower NFP volume percent) can be seen in Fig. 4.81,
Fig. 4.82, Fig. 4.83, and Fig. 4.84.
CHAPTER 4. RESULTS 165
4.3.2.3 Void Orientations
Significant alignment of voids in directions within the plane produced by the major
and minor strain axes was present for the TP1-treated specimens in which the sheet
rolling direction aligned with the minor strain axis. This is evident in Table 4.8 for
7TP1-15-T11, 7TP1-33-T10, 7TP1-43-T5, 9TP1-15-T1, 9TP1-33-T10, and 9TP1-43-
T7, and is qualitatively observed in Fig. 4.35, Fig. 4.43, Fig. 4.51, Fig. 4.59, Fig. 4.67,
and Fig. 4.75 respectively.
4.3.2.4 Failure Mechanism
The failure mechanism of TP1-treated specimens progressed from a mixed ductile-
shear mechanism to a progressively more shear-dominated mechanism with increasing
NFP content.
CHAPTER 4. RESULTS 166
Table 4.10: Damage accumulation observations, inferences, andcomputations for 7TP1-treated DP steel specimens.
Specimen # of Voids
Void Volume (µm3)
ObservationsMean σ Max(x 103) (x 103) (x 103)
7TP1-15-R4 65 1.956 7.31 57.6
• Mixed ductile-shear type fracture• NFP particle cracking dominated voidnucleation• Large size distribution of deep fracturesurface dimples (1-11 µm), largest dimpleslocated near sheet centerline• Mild clustering of void damage to sheetcenterline
7TP1-15-T11 158 1.129 2.88 26.5
• Mixed ductile-shear type fracture• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples very elon-gated in RD• Mild clustering of void damage to sheetcenter region
7TP1-33-R11 167 0.855 2.47 21.2
• Mixed ductile-shear type fracture• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Large size distribution of fracture surfacedimples (1-9 µm)• Major clustering of void damage to sheetcenter region
7TP1-33-T10 260 5.719 32.12 453.9
• Shear mechanism dominated failure• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Many fracture surface dimples very elon-gated in RD at sheet centerline, moreequiaxed elsewhere• Major clustering of void damage to sheetcenter region
7TP1-43-R3 165 2.561 15.07 189.8
• Shear mechanism dominated failure• NFP particle cracking at sheet centerline• Relatively uniform size distribution offracture surface dimples (1-5 µm)• Major clustering of void damage to sheetcenter region
7TP1-43-T5 83 0.736 3.16 28.2
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples very elon-gated in RD• Uniform spatial distribution of voiddamage through sheet thickness
CHAPTER 4. RESULTS 167
Table 4.11: Damage accumulation observations, inferences, andcomputations for 9TP1-treated DP steel specimens.
Specimen # of Voids
Void Volume (µm3)
ObservationsMean σ Max(x 103) (x 103) (x 103)
9TP1-15-R7 304 0.692 1.57 13.9
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Large size distribution of deep fracturesurface dimples (1-13 µm), largest dimplesgenerally located near sheet centerline• Major clustering of void damage to sheetcenter region
9TP1-15-T1 551 0.446 0.95 12.9
• Shear mechanism dominated failure• Particle cracking dominated void nucle-ation at NFP bands• Many fracture surface dimples very elon-gated in RD• Relatively uniform spatial distribution ofvoid damage through sheet thickness
9TP1-33-R10 60 0.527 1.16 7.7
• Shear mechanism dominated failure• Particle cracking dominated void nucle-ation at NFP bands• Large size distribution of fracture surfacedimples (2-9 µm)• Uniform spatial distribution of voiddamage through sheet thickness
9TP1-33-T10 593 0.521 1.32 13.0
• Shear mechanism dominated failure• NFP particle cracking at sheet center-line and some ferrite-NFP decohesion voidnucleation elsewhere• Many fracture surface dimples increas-ingly elongated in RD with increasingproximity to sheet centerline• Relatively uniform spatial distribution ofvoid damage through sheet thickness
9TP1-43-R11 42 0.181 0.18 0.7
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Relatively uniform size distribution offracture surface dimples (1-3 µm)• Uniform spatial distribution of voiddamage through sheet thickness
9TP1-43-T7 123 0.392 0.49 3.9
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Many fracture surface dimples increas-ingly elongated in RD with increasingproximity to sheet centerline• Relatively uniform spatial distribution ofvoid damage through sheet thickness
CHAPTER 4. RESULTS 168
Figure 4.27: Relationship between NFP volume percent in IPPSspecimens and the volume percent of void damage accumulatedin the 7TP1 match-head region examined using XµCT. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars arenot provided as systematic error in computing the number ofvoids present in match-head specimens was not performed inthis study.
CHAPTER 4. RESULTS 169
Figure 4.28: Relationship between NFP volume percent in IPPSspecimens and the volume percent of void damage accumulatedin the 9TP1 match-head region examined using XµCT. Hori-zontal error bars are derived from the 95% confidence intervalof NFP volume percent measurements. Vertical error bars arenot provided as systematic error in computing the number ofvoids present in match-head specimens was not performed inthis study.
CHAPTER 4. RESULTS 170
Figure 4.29: Relationship between NFP volume percent inIPPS specimens and the number of voids accumulated in the7TP1 match-head region examined using XµCT. Horizontal er-ror bars are derived from the 95% confidence interval of NFPvolume percent measurements. Vertical error bars are not pro-vided as systematic error in computing the number of voidspresent in match-head specimens was not performed in thisstudy.
CHAPTER 4. RESULTS 171
Figure 4.30: Relationship between NFP volume percent inIPPS specimens and the number of voids accumulated in the9TP1 match-head region examined using XµCT. Horizontal er-ror bars are derived from the 95% confidence interval of NFPvolume percent measurements. Vertical error bars are not pro-vided as systematic error in computing the number of voidspresent in match-head specimens was not performed in thisstudy.
CHAPTER 4. RESULTS 172
Figure 4.31: 3-D semi-transparent volume rendering of the7TP1-15-R4 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 1063 x 838 x 1145 µm.
CHAPTER 4. RESULTS 173
Figure 4.32: 3-D semi-transparent volume rendering of the7TP1-15-R4 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 838 x 1145 µm.
CHAPTER 4. RESULTS 174
(a) Polished
(b) 2% Nital etch
Figure 4.33: Typical optical micrographs of the failed 7TP1-15-R4 match-head specimen showing void damage.
CHAPTER 4. RESULTS 175
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.34: SEM fractographs of the failed 7TP1-15-R4 match-head specimen.
CHAPTER 4. RESULTS 176
Figure 4.35: 3-D semi-transparent volume rendering of the7TP1-15-T11 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 938 x 793 x 1145 µm.
CHAPTER 4. RESULTS 177
Figure 4.36: 3-D semi-transparent volume rendering of the7TP1-15-T11 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 793 x 1145 µm.
CHAPTER 4. RESULTS 178
(a) Polished
(b) 2% Nital etch
Figure 4.37: Typical optical micrographs of the failed 7TP1-15-T11 match-head specimen showing void damage.
CHAPTER 4. RESULTS 179
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.38: SEM fractographs of the failed 7TP1-15-T11match-head specimen.
CHAPTER 4. RESULTS 180
Figure 4.39: 3-D semi-transparent volume rendering of the7TP1-33-R11 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 945 x 828 x 1151 µm.
CHAPTER 4. RESULTS 181
Figure 4.40: 3-D semi-transparent volume rendering of the7TP1-33-R11 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 828 x 1151 µm.
CHAPTER 4. RESULTS 182
(a) Polished
(b) 2% Nital etch
Figure 4.41: Typical optical micrographs of the failed 7TP1-33-R11 match-head specimen showing void damage.
CHAPTER 4. RESULTS 183
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.42: SEM fractographs of the failed 7TP1-33-R11match-head specimen.
CHAPTER 4. RESULTS 184
Figure 4.43: 3-D semi-transparent volume rendering of the7TP1-33-T10 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 925 x 837 x 1148 µm.
CHAPTER 4. RESULTS 185
Figure 4.44: 3-D semi-transparent volume rendering of the7TP1-33-T10 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 837 x 1148 µm.
CHAPTER 4. RESULTS 186
(a) Polished
(b) 2% Nital etch
Figure 4.45: Typical optical micrographs of the failed 7TP1-33-T10 match-head specimen showing void damage.
CHAPTER 4. RESULTS 187
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.46: SEM fractographs of the failed 7TP1-33-T10match-head specimen.
CHAPTER 4. RESULTS 188
Figure 4.47: 3-D semi-transparent volume rendering of the7TP1-43-R3 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 1043 x 917 x 1145 µm.
CHAPTER 4. RESULTS 189
Figure 4.48: 3-D semi-transparent volume rendering of the7TP1-43-R3 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 917 x 1145 µm.
CHAPTER 4. RESULTS 190
(a) Polished
(b) 2% Nital etch
Figure 4.49: Typical optical micrographs of the failed 7TP1-43-R3 match-head specimen showing void damage.
CHAPTER 4. RESULTS 191
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.50: SEM fractographs of the failed 7TP1-43-R3 match-head specimen.
CHAPTER 4. RESULTS 192
Figure 4.51: 3-D semi-transparent volume rendering of the7TP1-43-T5 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 968 x 913 x 1151 µm.
CHAPTER 4. RESULTS 193
Figure 4.52: 3-D semi-transparent volume rendering of the7TP1-43-T5 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 913 x 1151 µm.
CHAPTER 4. RESULTS 194
(a) Polished
(b) 2% Nital etch
Figure 4.53: Typical optical micrographs of the failed 7TP1-43-T5 match-head specimen showing void damage.
CHAPTER 4. RESULTS 195
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.54: SEM fractographs of the failed 7TP1-43-T5 match-head specimen.
CHAPTER 4. RESULTS 196
Figure 4.55: 3-D semi-transparent volume rendering of the9TP1-15-R7 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 923 x 926 x 1148 µm.
CHAPTER 4. RESULTS 197
Figure 4.56: 3-D semi-transparent volume rendering of the9TP1-15-R7 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 926 x 1148 µm.
CHAPTER 4. RESULTS 198
(a) Polished
(b) 2% Nital etch
Figure 4.57: Typical optical micrographs of the failed 9TP1-15-R7 match-head specimen showing void damage.
CHAPTER 4. RESULTS 199
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.58: SEM fractographs of the failed 9TP1-15-R7 match-head specimen.
CHAPTER 4. RESULTS 200
Figure 4.59: 3-D semi-transparent volume rendering of the9TP1-15-T1 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 984 x 1033 x 1150 µm.
CHAPTER 4. RESULTS 201
Figure 4.60: 3-D semi-transparent volume rendering of the9TP1-15-T1 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 1033 x 1150 µm.
CHAPTER 4. RESULTS 202
(a) Polished
(b) 2% Nital etch
Figure 4.61: Typical optical micrographs of the failed 9TP1-15-T1 match-head specimen showing void damage.
CHAPTER 4. RESULTS 203
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.62: SEM fractographs of the failed 9TP1-15-T1 match-head specimen.
CHAPTER 4. RESULTS 204
Figure 4.63: 3-D semi-transparent volume rendering of the9TP1-33-R10 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 871 x 970 x 1146 µm.
CHAPTER 4. RESULTS 205
Figure 4.64: 3-D semi-transparent volume rendering of the9TP1-33-R10 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 970 x 1146 µm.
CHAPTER 4. RESULTS 206
(a) Polished
(b) 2% Nital etch
Figure 4.65: Typical optical micrographs of the failed 9TP1-33-R10 match-head specimen showing void damage.
CHAPTER 4. RESULTS 207
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.66: SEM fractographs of the failed 9TP1-33-R10match-head specimen.
CHAPTER 4. RESULTS 208
Figure 4.67: 3-D semi-transparent volume rendering of the9TP1-33-T10 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 949 x 1043 x 1150 µm.
CHAPTER 4. RESULTS 209
Figure 4.68: 3-D semi-transparent volume rendering of the9TP1-33-T10 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 1043 x 1150 µm.
CHAPTER 4. RESULTS 210
(a) Polished
(b) 2% Nital etch
Figure 4.69: Typical optical micrographs of the failed 9TP1-33-T10 match-head specimen showing void damage.
CHAPTER 4. RESULTS 211
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.70: SEM fractographs of the failed 9TP1-33-T10match-head specimen.
CHAPTER 4. RESULTS 212
Figure 4.71: 3-D semi-transparent volume rendering of the9TP1-43-R11 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 868 x 1046 x 1151 µm.
CHAPTER 4. RESULTS 213
Figure 4.72: 3-D semi-transparent volume rendering of the9TP1-43-R11 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 1046 x 1151 µm.
CHAPTER 4. RESULTS 214
(a) Polished
(b) 2% Nital etch
Figure 4.73: Typical optical micrographs of the failed 9TP1-43-R11 match-head specimen showing void damage.
CHAPTER 4. RESULTS 215
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.74: SEM fractographs of the failed 9TP1-43-R11match-head specimen.
CHAPTER 4. RESULTS 216
Figure 4.75: 3-D semi-transparent volume rendering of the9TP1-43-T7 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 975 x 1138 x 1150 µm.
CHAPTER 4. RESULTS 217
Figure 4.76: 3-D semi-transparent volume rendering of the9TP1-43-T7 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 1138 x 1150 µm.
CHAPTER 4. RESULTS 218
(a) Polished
(b) 2% Nital etch
Figure 4.77: Typical optical micrographs of the failed 9TP1-43-T7 match-head specimen showing void damage.
CHAPTER 4. RESULTS 219
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.78: SEM fractographs of the failed 9TP1-43-T7 match-head specimen.
CHAPTER 4. RESULTS 220
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(a) 7TP1-15-R4
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(b) 7TP1-15-T11
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(c) 7TP1-33-R11
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(d) 7TP1-33-T10
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(e) 7TP1-43-R3
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Equivalent Diameter (µm)
(f) 7TP1-43-T5
Figure 4.79: Histograms of equivalent spherical void diame-ter in reconstructed TP1-treated DP steel variant match-headspecimens.
CHAPTER 4. RESULTS 221
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(a) 9TP1-15-R7
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(b) 9TP1-15-T1
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(c) 9TP1-33-R10
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(d) 9TP1-33-T10
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(e) 9TP1-43-R11
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
100
110
120
Freq
uenc
y
Equivalent Diameter (µm)
(f) 9TP1-43-T7
Figure 4.80: Histograms of equivalent spherical void diame-ter in reconstructed TP1-treated DP steel variant match-headspecimens.
CHAPTER 4. RESULTS 222
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(a) 7TP1-15-R4
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(b) 7TP1-15-T11
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(c) 7TP1-33-R11
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(d) 7TP1-33-T10
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(e) 7TP1-43-R3
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Freq
uenc
y
Distance to center (µm)
(f) 7TP1-43-T5
Figure 4.81: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed TP1-treated DPsteel variant match-head specimens.
CHAPTER 4. RESULTS 223
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(a) 9TP1-15-R7
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(b) 9TP1-15-T1
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(c) 9TP1-33-R10
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(d) 9TP1-33-T10
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(e) 9TP1-43-R11
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90
100
110
Freq
uenc
y
Distance to center (µm)
(f) 9TP1-43-T7
Figure 4.82: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed TP1-treated DPsteel variant match-head specimens.
CHAPTER 4. RESULTS 224
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(a) 7TP1-15-R4
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(b) 7TP1-15-T11
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(c) 7TP1-33-R11
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(d) 7TP1-33-T10
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(e) 7TP1-43-R3
-400 -200 0 200 400
100
1000
10000
100000
1000000
Vol
ume
(µm
3 )
Distance to center (µm)
(f) 7TP1-43-T5
Figure 4.83: Profiles of the volumes of voids through the sheetthickness in reconstructed TP1-treated DP steel variant match-head specimens.
CHAPTER 4. RESULTS 225
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(a) 9TP1-15-R7
-400 -200 0 200 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(b) 9TP1-15-T1
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(c) 9TP1-33-R10
-400 -200 0 200 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(d) 9TP1-33-T10
-400 -200 0 200 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(e) 9TP1-43-R11
-400 -200 0 200 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(f) 9TP1-43-T7
Figure 4.84: Profiles of the volumes of voids through the sheetthickness in reconstructed TP1-treated DP steel variant match-head specimens.
CHAPTER 4. RESULTS 226
4.3.3 TP2-treated DP Steels
4.3.3.1 Degree of Damage
The degree of damage for each of the TP2-treated XµCT specimens is qualitatively
provided in 3-D renderings of the outer surfaces of voids within a semi-transparent
rendering of the match-head specimen volumes in Fig. 4.85 through Fig. 4.97.
4.3.3.2 Damage Distribution
For the most part, damage was concentrated near the fracture surface where strains
were larger. Again the void damage spatial distribution closely mimicked the distri-
bution of NFP in the TP2-treated microstructures.
4.3.3.3 Void Orientations
Void orientation in the TP2-treated variants was fairly randomized. As observed for
the previously discussed variants subject to NFP banding along the RD, alignment
of voids in the plane produced by the major and minor strain axes was present for
the TP2-treated specimens in which the sheet rolling direction was aligned with the
minor strain axis. Evidence of this observation is provided by the low θ values in
Table 4.8 for specimens 7TP2-25-T2 and 9TP2-37-T1 and the corresponding rela-
tively low standard deviations.
4.3.3.4 Failure Mechanism
A shear dominated failure mechanism was apparent for all TP2-treated specimens.
CHAPTER 4. RESULTS 227
Table 4.12: Damage accumulation observations, inferences, andcomputations for TP2-treated DP steel specimens.
Specimen # of Voids
Void Volume (µm3)
ObservationsMean σ Max(x 103) (x 103) (x 103)
7TP2-25-R4 63 0.705 1.95 14.9
• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• No fractographs due to severe corrosionartifacts• Moderate clustering of void damage tosheet center region
7TP2-25-T2 282 0.722 1.67 19.6
• Shear mechanism dominated failure• Mix of NFP particle cracking and ferrite-NFP decohesion void nucleation• Some fracture surface dimples elongatedin RD, sparse population of small dimples(1-4 µm), evidence of cleavage• Moderate clustering of void damage tosheet centerline
9TP2-37-R4 155 1.216 2.93 20.4
• Shear mechanism dominated failure• NFP particle cracking dominated voidnucleation• Large size distribution of shallow frac-ture surface dimples (1-9 µm)• Severe clustering of void damage to sheetcenterline
9TP2-37-T1 282 0.324 0.46 3.2
• Shear mechanism dominated failure• NFP particle cracking and some ferrite-NFP decohesion void nucleation• Many fracture surface dimples elongatedin RD, large size distribution (1-8 µm)• Very mild clustering of void damage tosheet centerline region
CHAPTER 4. RESULTS 228
Figure 4.85: 3-D semi-transparent volume rendering of the7TP2-25-R4 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 1076 x 893 x 1150 µm.
CHAPTER 4. RESULTS 229
Figure 4.86: 3-D semi-transparent volume rendering of the7TP2-25-R4 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 893 x 1150 µm.
CHAPTER 4. RESULTS 230
(a) Polished
(b) 2% Nital etch
Figure 4.87: Typical optical micrographs of the failed 7TP2-25-R4 match-head specimen showing void damage.
CHAPTER 4. RESULTS 231
Figure 4.88: 3-D semi-transparent volume rendering of the7TP2-25-T2 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 983 x 860 x 1150 µm.
CHAPTER 4. RESULTS 232
Figure 4.89: 3-D semi-transparent volume rendering of the7TP2-25-T2 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 860 x 1150 µm.
CHAPTER 4. RESULTS 233
(a) Polished
(b) 2% Nital etch
Figure 4.90: Typical optical micrographs of the failed 7TP2-25-T2 match-head specimen showing void damage.
CHAPTER 4. RESULTS 234
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.91: SEM fractographs of the failed 7TP2-25-T2 match-head specimen.
CHAPTER 4. RESULTS 235
Figure 4.92: 3-D semi-transparent volume rendering of the9TP2-37-R4 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 927 x 976 x 1145 µm.
CHAPTER 4. RESULTS 236
Figure 4.93: 3-D semi-transparent volume rendering of the9TP2-37-R4 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 976 x 1145 µm.
CHAPTER 4. RESULTS 237
(a) Polished
(b) 2% Nital etch
Figure 4.94: Typical optical micrographs of the failed 9TP2-37-R4 match-head specimen showing void damage.
CHAPTER 4. RESULTS 238
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.95: SEM fractographs of the failed 9TP2-37-R4 match-head specimen.
CHAPTER 4. RESULTS 239
Figure 4.96: 3-D semi-transparent volume rendering of the9TP2-37-T1 IPPS match-head specimen displaying an isosur-face rendering of the void damage within (three-point perspec-tive). The perspective view makes the insertion of a scale barinappropriate. The dimensions of the bounding box of the re-construction are 962 x 1037 x 1148 µm.
CHAPTER 4. RESULTS 240
Figure 4.97: 3-D semi-transparent volume rendering of the9TP2-37-T1 IPPS match-head specimen displaying an isosur-face rendering of the spatial distribution of void damage in theND-RD plane (one-point perspective). The perspective viewmakes the insertion of a scale bar inappropriate. The dimen-sions of the frontal plane of the bounding box of the recon-struction are 1037 x 1148 µm.
CHAPTER 4. RESULTS 241
(a) Polished
(b) 2% Nital etch
Figure 4.98: Typical optical micrographs of the failed 9TP2-37-T1 match-head specimen showing void damage.
CHAPTER 4. RESULTS 242
(a) Entire fracture surface detailing locations of
higher magnification fractographs.
(b)
(c) Center of sheet thickness.
Figure 4.99: SEM fractographs of the failed 9TP2-37-T1 match-head specimen.
CHAPTER 4. RESULTS 243
0 5 10 15 20 25 30 350
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(a) 7TP2-25-R4
0 5 10 15 20 25 30 350
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(b) 7TP2-25-T2
0 5 10 15 20 25 30 350
10
20
30
40
50
60
Freq
uenc
y
Equivalent Diameter (µm)
(c) 9TP2-37-R4
0 5 10 15 20 25 30 350
10
20
30
40
50
60Freq
uenc
y
Equivalent Diameter (µm)
(d) 9TP2-37-T1
Figure 4.100: Histograms of equivalent spherical void diame-ter in reconstructed TP2-treated DP steel variant match-headspecimens.
CHAPTER 4. RESULTS 244
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90Freq
uenc
y
Distance to center (µm)
(a) 7TP2-25-R4
-400 -300 -200 -100 0 100 200 300 4000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Distance to center (µm)
(b) 7TP2-25-T2
-600 -400 -200 0 200 400 6000
10
20
30
40
50
60
70
80
90
Freq
uenc
y
Distance to center (µm)
(c) 9TP2-37-R4
-400 -200 0 200 4000
10
20
30
40
50
60
70
80
90Freq
uenc
y
Distance to center (µm)
(d) 9TP2-37-T1
Figure 4.101: Histograms of the spatial distribution of voidsthrough the sheet thickness in reconstructed TP2-treated DPsteel variant match-head specimens.
CHAPTER 4. RESULTS 245
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(a) 7TP2-25-R4
-400 -300 -200 -100 0 100 200 300 400
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(b) 7TP2-25-T2
-600 -400 -200 0 200 400 600
100
1000
10000
Vol
ume
(µm
3 )
Distance to center (µm)
(c) 9TP2-37-R4
-400 -200 0 200 400
100
1000
10000V
olum
e (µ
m3 )
Distance to center (µm)
(d) 9TP2-37-T1
Figure 4.102: Profiles of the volumes of voids through the sheetthickness in reconstructed TP2-treated DP steel variant match-head specimens.
Chapter 5
Discussion
5.1 Microstructural Variants
The production of microstructural variants of DP steels in this study was accom-
plished though intercritical heat treatment; that is, intercritical temperature and
input microstructure were varied to produce DP microstructures of different NFP
volume percentages and different NFP particle morphology. Explanation is provided
within this section for the microstructural variation observed between TP1- and TP2-
treated DP steel variants.
5.1.1 TP1
Thermal Path One (TP1) consisted of a rapid IC annealing of cold-rolled steel spec-
imens. During the two minute hold within the IC temperature range, austenite was
expected to have nucleated at cementite grains within pearlite colonies, consumed the
pearlite colonies entirely, and then continued to slowly grow into ferrite grains. It is
246
CHAPTER 5. DISCUSSION 247
believed that due to the highly banded nature of the distribution of pearlite colonies
within the cold-rolled DP microstructure, the austenite phase formed in grains that
were highly banded as well. Upon rapid quenching from the IC annealing temperature
to 5◦C, the FCC austenite within the now ferrite-austenite microstructure underwent
a diffusionless transformation to BCT martensite. Martensite grains were observed at
ferrite grain boundaries and triple points due to parent austenite having nucleated in
pearlite colonies at these locations. There is a possibility that some very small frac-
tion of stabilized austenite was retained within the microstructure after quenching.
The effects of any metastable austenite content within TP1-treated mechanical test
specimens were considered to be negligible. Due to the high rate of cooling produced
by ice-water quenching, it is expected that no austenite transformed to pearlite or
bainite.
5.1.2 TP2
Thermal Path Two (TP2) consisted of an austempering pre-treatment of cold-rolled
DP steel specimens followed by rapid IC annealing. The austempering pre-treatment
was employed to produce a more uniform spatial distribution of carbon relative to the
cold-rolled material via the production of a bainitic microstructure. A microstructure
composed mostly of bainite resulted in the segregation of carbon into the partitioned
cementite laths of bainite, spread uniformly throughout the microstructure. This
more uniform spatial distribution of cementite relative to the cold-rolled sheet resulted
in a more uniform spatial distribution of nucleation sites for austenite grains during
IC annealing, which subsequently resulted in a more uniform spatial distribution of
NFP upon quenching. Microstructures after austempering were not directly observed
CHAPTER 5. DISCUSSION 248
metallographically, thus the actual bainite volume percent at this stage of treatment
is unknown.
5.1.2.1 Explanation of Residual Banding for TP2
Residual banding of NFP in the TP2 microstructure likely persists due to presumed
manganese segregation to the sheet centerline region. Manganese is an austenite sta-
bilizer, so it is quite plausible that a higher concentration of manganese present within
the sheet centerline region (for reasons explained in Sec. 2.1.2.4) lead to an increased
hardenability of the austenite formed within this region. Thus, during the bainite hold
portion of the austempering treatment, it is believed that austenite which had been
sufficiently stabilized by an increased manganese content, remained stable at 500◦C
and did not transform to bainite prior to quenching to room temperature. Therefore,
the austenite would have presumably transformed to martensite upon quenching, pro-
viding a preferable nucleation site for austenite under subsequent IC annealing and
thus resulting in a banded final microstructure.
5.2 IPPS Variant Ductility and Failure
5.2.1 Effect of NFP Content on Ductility
The macroscopic major engineering failure strain, computed as the average of the
seven grid measurements within the failure row, serves as a first approximation of the
ductility of each IPPS specimen. As observed in Fig. 4.6 and Fig. 4.7, the general
trend quoted within the literature of ductility decreasing with increasing martensite
content [47,49] has been confirmed. Whether or not this trend is linear or non-linear
CHAPTER 5. DISCUSSION 249
for the IPPS specimens of this study cannot be ascertained from the limited data-set.
5.2.2 DP Steel Variant Failure Behaviour
Failure of all DP steel IPPS variant specimens appears to have been ductile in nature
from the dimples evident in captured fractographs, an observation in agreement with
the literature [49,53,58,63–78]. Mean dimple size generally increased with increasing
fracture strain of specimens. Logically, this makes sense as increasing strain to failure
would allow for increased void growth and coalescence prior to fracture. Transition
from a more ductile, cup-cone type fracture to a shear fracture generally occurred with
increasing NFP content. This is interpreted to be a result of increased NFP content
providing a greater number of microstructural inhomogeneities, leading to earlier
onset of strain localization and increased ease of shear band formation, explained
further in Sec. 5.4.3. Most DP variant IPPS specimens failed via shear fracture.
Given the near plane-strain nature of the deformation, this behaviour was expected
as shear fracture of DP steels has been reported in regions of plane-strain bending
during premature forming failure [10].
Nearly all of the shear-mechanism dominated fracture surfaces were oriented ap-
proximately 45◦ with respect to the tensile axis. This agrees with the characteristic
surfaces upon which failure was predicted to occur under plane-strain conditions in
Sec. 2.3.4. Fracture surfaces were reflective of the spatial distribution of NFP in
the plane formed by the through-thickness and minor strain directions. Long, deep
cracks/dimples were observed for specimens with the sheet RD aligned along the mi-
nor strain direction. This was interpreted to be reflective of the NFP bands aligned
in the rolling direction causing void nucleation via particle cracking, subsequent void
CHAPTER 5. DISCUSSION 250
growth, and possibly coalescence.
It should be noted that significant surface roughening is evident for 7GA-R4 and
7GA-T2, respectively, in Fig. 4.9 and Fig. 4.13. Surface roughening may be partially a
result of the galvannealed sheet surface containing zinc. This surface roughening could
have resulted in a field of reduced thickness inhomogeneities [59] which contributed
to the initiation of a final shear mechanism of failure. The DP980GA material did
not exhibit notable surface roughening, but also incurred reduced strain to failure.
5.3 XµCT for Characterization of Damage
XµCT proved to be a very valuable tool for assessing void size, morphology, and dis-
tribution in 3-D. Tomographic reconstructions of the internal structure of the failed
IPPS DP steel variant specimens of this study confirmed three-dimensionally the
general trend within the literature of void damage density increasing towards the
fracture surface of DP steel tension specimens [14, 22, 72]. As well, a trend of signif-
icantly sized void damage generally being concentrated at the sheet centerline was
observed for many of the DP steel variants. The smallest voids were not detected
using the XµCT protocol of this study as any void computed to be less than 44.53
µm3 in volume was removed from the analysis, but it is the larger voids which are
more likely to have an important effect on the failure process [22]. Systematic er-
ror in computing the quantitative characteristics of voids via the XµCT protocol of
this study was not examined. Hence, no confidence interval is provided for void size
measurements.
CHAPTER 5. DISCUSSION 251
5.4 DP Steel Damage Accumulation in Plane-
Strain Fracture
5.4.1 Void Nucleation
Voids were generally inferred via post-failure metallography to have nucleated via
NFP particle cracking for the galvannealed and TP1-treated DP steel variants, espe-
cially at NFP bands and large particles. Coarse NFP bands were inferred to produce
the most number and the largest voids. This agrees with the results of Winkler et
al. [18] who observed void nucleation to occur preferentially at the thicker or denser
martensitic bands for both DP steels of their study. Some void nucleation via ferrite-
NFP decohesion was inferred in this study to have occurred away from NFP bands
for the galvannealed and TP1-treated DP steel variants. In general, the amount of
damage nucleated via ferrite-NFP decohesion decreased with increasing NFP content
for these variants. According to a mass balance, carbon content of the martensite
would have decreased with increasing NFP content. As such, these results agree with
the bulk of the literature with lower-carbon martensite producing a tendency for void
nucleation via martensite particle cracking and higher-carbon martensite producing a
tendency for void nucleation via ferrite-martensite decohesion [14,49,75,100]. A mix
of ferrite-NFP decohesion and NFP particle cracking was inferred to have produced
the void damage in TP2-treated DP steel variants.
CHAPTER 5. DISCUSSION 252
5.4.2 Failure Behaviour Variation with Degree of NFP Band-
ing
The two DP780-series variants with similar NFP volume percent (within uncertainty),
but differing particle populations, were 7TP1-33 and 7TP2-25. Both variants had
quite similar mean major engineering strains at failure for RD and TD specimens,
respectively (see Table 4.6(a)). However, it is evident from Fig. 4.6 that the 7TP2-
25 series had a much larger variance in failure strains for TD specimens than did
the 7TP1-33 series. The lack of an increased ductility for the 7TP2-25 specimens
composed of more uniformly spatially distributed NFP particles relative to the 7TP1-
33 series may be in part caused by the residual NFP banding present in the 7TP2-25
specimens. Increased nucleation and growth of void damage at these residual bands
may have led to an earlier onset of localization and formation of a critical flaw leading
to failure.
Interestingly, both of the aforementioned variants had mean failure strains for RD
and TD oriented specimens more than 22% higher than those of the DP780 galvan-
nealed steel, despite both having a larger volume percent of NFP by approximately
7%. Although, these results are subject to a small sample size and an associated
high uncertainty, the disparity cannot be explained simply by the DP780GA steel
containing a small portion of bainite comprising its NFP content. It seems likely that
the larger prevalence of NFP banding throughout the thickness of the DP780GA ma-
terial led to earlier strain localization within the gauge region of the DP780GA IPPS
specimens. This explanation is plausible when considering the cooperative interaction
between voids and shear bands in precipitating strain localization [150].
For the DP980-series of variants, the 9TP1-33 and 9TP2-37 variants both had
CHAPTER 5. DISCUSSION 253
similar NFP volume percent (within uncertainty) to the DP980 galvannealed steel.
The RD-oriented and TD-oriented specimens of the TP1- and TP2-treated variants
had higher mean major engineering strains at failure than the correspondingly ori-
ented DP980GA specimens. While the small number of samples casts some doubt
upon this observation, the greater frequency of NFP banding across the thickness
of the galvannealed steel leading to earlier strain localization represents a plausible
explanation for these results.
5.4.3 Explanation for Reduced Ductility with Increased NFP
Banding
A schematic depicting how increased void nucleation in a microstructure with in-
creased NFP banding frequency through the sheet thickness is thought to lead to
earlier strain localization and failure is shown in Fig. 5.1. The steps leading to failure
shown in Fig. 5.1 are outlined more clearly for the two degrees of banding in the
cropped schematics of Fig. 5.2 and Fig. 5.3. The term NFP banding describes a mi-
crostructural state of highly aligned, highly proximal NFP particles, so proximal in
fact that under a light microscope at 1000x magnification, these bands often appear
to be a continuous particle.
The reasoning for a greater strain to failure in a less banded microstructure is
thought to be its effect of delaying strain localization and the formation of shear
bands. Voids were observed to have formed preferentially at NFP bands throughout
the microstructural variants of this study. The low critical local void nucleation strain
of 0.029 for martensite cracking and 0.09 for ferrite-martensite decohesion reported
by Avramovic-Cingara et al. [14] for a DP steel assists in explaining this behaviour.
CHAPTER 5. DISCUSSION 254
As discussed in Sec. 2.3.1.1, coarser NFP particles are predicted to crack first and
the coarsest NFP particles were generally located within bands. This leads to the
idea that the first voids to nucleate during deformation of the IPPS specimens do so
primarily at NFP bands, as shown in Fig. 5.1. It is predicted that these voids grow
by continued cracking while further voids are nucleated at the bands and eventually
away from the bands via ferrite-NFP decohesion, as reported by Avramovic-Cingara
et al. [14]. This behaviour continues until the void inhomogeneities result in a loss of
load carrying capacity and strain localization [14].
It follows that, an increasing number of NFP bands through the thickness of a
sheet represents a greater number of void nucleation sites for producing a critical
string of void inhomogeneities, leading to strain localization at a lower level of global
strain. Thus, as shown in Fig. 5.1, the formation of a shear band across the neck
of a specimen due to the presence of a critical population of microstructural inho-
mogeneities (voids, NFP particles, inclusions) occurs at a lower global strain for a
DP steel microstructure with increased NFP banding. It is worth noting that the
intense strain within the shear band likely causes a rapid nucleation of secondary
voids, called void sheeting, assisting in the final failure process of inter-void ligament
shearing. Void sheeting during shear fracture of DP steel has also been considered by
Avramovic-Cingara et al. [14].
Despite specimen 7TP1-33-T10 accumulating the largest total volume of void dam-
age of all specimens, it still maintained a higher failure strain than that of 7GA-T2,
which had significantly lower damage accumulation and NFP content. To demon-
strate that this is not just a singular event, consider the 7TP1-33 and 7TP2-25 series
of variants in comparison to the 7GA specimens; the lab-treated variants had mean
CHAPTER 5. DISCUSSION 255
Figure 5.1: Schematic depicting how the proposed increasedvoid nucleation in a microstructure with increased NFP band-ing frequency through the sheet thickness is thought to leadto earlier strain localization in IPPS specimens. The uppersequence roughly depicts typical galvannealed DP steel mi-crostructural NFP banding; bands are situated throughout thesheet thickness. The lower sequence depicts typical TP1- andTP2- treated DP steel variant microstructural NFP banding;the bands are concentrated at the sheet centerline. Step 1: voidnucleation via particle cracking at NFP bands and growth; step2a: void nucleation via ferrite-martensite decohesion through-out the sheet thickness; step 2b: formation of a shear bandalong a plane weakened by inhomogeneities; step 3: void sheet-ing and coalescence across shear band; step 4: fracture.
CHAPTER 5. DISCUSSION 256
(a) Step 1 - void nucleation via particlecracking at NFP bands and growth
(b) Step 2b - formation of a shear bandalong a plane weakened by inhomogeneities
(c) Step 3 - void sheeting and coalescenceacross the shear band
Figure 5.2: Detailed schematic depicting what is thought tobe the simplified typical stages leading to failure of the gal-vannealed DP steels of this study exhibiting a large number ofNFP bands throughout the sheet thickness.
CHAPTER 5. DISCUSSION 257
(a) Step 1 - void nucleation via particlecracking at NFP bands and growth
(b) Step 2a - void nucleation via ferrite-martensite decohesion throughout thesheet thickness
(c) Step 2b - formation of a shear bandalong a plane weakened by inhomogeneities
(d) Step 3 - void sheeting and coalescenceacross the shear band
Figure 5.3: Detailed schematic depicting what is thought to bethe simplified typical stages leading to failure of the TP1- andTP2-treated DP steels of this study exhibiting a small numberof NFP bands concentrated at the sheet centerline.
CHAPTER 5. DISCUSSION 258
failure strains more than 22% higher than those of the DP780 galvannealed steel,
despite both having a 7% higher volume percent of NFP. The major microstructural
difference between the lab-treated variants and the galvannealed sheet is the greater
number and more continuous nature of NFP bands throughout the thickness of the
galvannealed sheet. This provides further evidence that, from the perspective of de-
signing DP steels which have improved formability under plane-strain conditions, it
is desirable to design microstructures where strain localization is not induced at early
global strains due to void damage developing rapidly at many “easy” nucleation sites
throughout the sheet thickness. It seems that a reduction of NFP banding through
the thickness of DP sheet would assist in delaying the onset of strain localization by
providing fewer sites for void nucleation.
To elaborate using one final example, the one coarse NFP band and finer surround-
ing NFP bands were localized distinctly to the sheet centerline within the 7TP1-33-
T10 microstructure. While these bands caused a very high volume of void damage to
be produced at the sheet centerline, they did not result in a critical flaw leading to
failure until a much higher strain than for 7GA-T2. This difference was due to the
increased prevalence of banding in multiple RD-TD planes throughout the thickness
of the 7GA-T2 sheet. In turn, voids readily nucleated at many points through the
thickness of the sheet, leading to an inhomogeneity sufficient for strain localization
and the formation of a shear band along a characteristic surface (45◦ with respect to
the tensile axis), and rapid failure assisted by void sheeting.
CHAPTER 5. DISCUSSION 259
5.5 Effects of Microstructure on Damage Accumu-
lation
5.5.1 Effect of NFP Volume Percent
For a higher NFP volume percent, it is expected that the resulting increase in the
number of void nucleation sites would result in an increased amount of void damage
measured using XµCT. However, the confounding factors of strain to failure, and the
rapidity of onset of strain localization must also be considered when analyzing the
void damage data of the TP1-treated specimens. A reduced strain to failure and
earlier strain localization would afford reduced opportunity for void nucleation and
growth to occur globally, thereby concentrating void damage to the specimen region
which would in turn become the fracture surface, reducing void damage accumulation
in a failed specimen.
The TP1-treated IPPS specimens may be compared in terms of void damage ac-
cumulation due to their similar NFP morphology. Fig. 4.27 and Fig. 4.28 provide
such a comparison in terms of void volume percent measured within the portion of
match-head specimens reconstructed using XµCT. A bias is introduced into the re-
sults because of the variance in the distance of specimens below the fracture surface
that was fit into the FOV during XµCT capture. It should be mentioned that the data
point for the 7TP1-33-T10 specimen is interpreted as an outlier due to the uncharac-
teristically coarse NFP band contained at its sheet centerline shown in Fig. 4.45(b).
Fig. 4.27 and Fig. 4.28 provide no evidence of a strong relationship between NFP con-
tent and void damage accumulation. As well, no clear trend is evident in Fig. 4.29 or
Fig. 4.30 for the number of voids present in the reconstructions of TP1-treated IPPS
CHAPTER 5. DISCUSSION 260
match-head specimens with respect to NFP volume percent. No consideration was
given to the effect of NFP particle size as this was moderately similar throughout the
TP1-treated DP steel variants. IPPS testing of additional TP1-treated DP variants
with a further variety of NFP volume percents, plus performing XµCT analysis of
multiple match-head specimens per DP steel variant may have elicited a more clear
trend.
It is postulated that there exists an NFP volume percent for a singular DP steel
microstructural morphology which would produce a peak level of void damage accu-
mulation away from the failure surface. This NFP volume percent would provide the
optimal damage accumulation blend of having a large number of void nucleation sites
at NFP particles, but not so large as to cause rapid onset of strain localization, thus
allowing void growth and further void nucleation to occur for a longer period prior
to failure. The relationship between DP steel NFP content and void damage accu-
mulation for a singular NFP morphology is expected to hold a Chi-Square-type fit.
Such a trend may be very weakly fit to the data of this study in Fig. 4.27, Fig. 4.28,
Fig. 4.29, and Fig. 4.30.
5.5.2 Effect of NFP Morphology
No evidence of a strong correlation between NFP morphology and void damage accu-
mulation was observed when comparing TP1-treated, TP2-treated, and galvannealed
DP steel variants. However, it is thought that the more uniformly spatially distributed
NFP of TP2-treated DP steel variants relative to the TP1-treated and galvannealed
DP steels caused the greater occurrence of ferrite-NFP decohesion; a notion that
agrees with the work of He et al. [19]. In order to better determine morphological
CHAPTER 5. DISCUSSION 261
effects, if any exist, residual banding in the TP2-treated DP steel variants must be
eliminated.
5.5.3 Effect of NFP Spatial Distribution
Many major trends were observable in void damage spatial distribution with respect
to NFP morphology. The first is that the largest volume of void damage was generally
observed to be concentrated at the sheet centerline in both TP1- and TP2-treated
DP steel variants. This observation is presumably due to NFP banding being concen-
trated to this region for the aforementioned variants. Polished and etched match-head
specimens revealed that void nucleation was most prevalent at NFP bands and that
the bands were the most coarse and continuous near the sheet centerline. The lack
of a concentration of void damage at the sheet centerline for the galvannealed DP
sheets is reflective of the greater frequency of NFP banding throughout the thickness
of these steels.
Generally, more voids and a greater void volume percent were computed in match-
head variants with the sheet RD aligned with the minor strain direction of IPPS spec-
imens. As well, these ‘TD’ specimens exhibited slightly lower failure strains in general
than their ‘RD’ counterparts. These trends are attributed to the increased prevalence
of NFP banding aligned in the sheet rolling direction relative to the transverse di-
rection. It has been shown by Thomson et al. [151] through finite element modeling
that the orientation of particle clusters/stringers with respect to major loading di-
rection in a ductile material plays an important role in the evolution of damage. In
agreement with the present work, transverse particle clusters/stringers were shown
to produce higher damage rates and lower failure strains than those aligned with the
CHAPTER 5. DISCUSSION 262
major loading direction. This behaviour also agrees with the work of Bouchard et
al. [122] described in Sec. 2.4.2. Further evidence supporting the idea that transverse
orientation of the NFP banding relative to the major loading direction is respon-
sible for higher damage rates is observed in the 3-D reconstruction images of such
‘TD’ specimens, the histograms of the spatial distribution of voids through the sheet
thickness, the profiles of the volumes of voids through the sheet thickness, and in the
fractographs of Chap. 4.
The 7TP1-33-T10 specimen stands out as a prime example due to the relatively
large volume of sheet centerline damage evident in Fig. 4.43 and Fig. 4.44. This
damage was due to the presence of an exceptionally coarse and exceptionally con-
tinuous NFP band aligned in the rolling direction at the sheet centerline of this
variant, shown in Fig. 4.45(b). High levels of void damage nucleated and coalesced
at this band, resulting in the sheet centerline concentrated distribution of damage
highlighted in Fig. 4.81(d) and Fig. 4.83(d). Fractographs reveal long, deep dimples
at the sheet centerline (Fig. 4.46(c)) where NFP banding was most prevalent and gen-
erally smaller, less elongated dimples approaching the sheet surfaces (Fig. 4.46(b));
reflective of the microstructure described in Sec. 4.1.3. The corresponding 7TP1-33-
R11 specimen also exhibited void concentration at the sheet centerline where NFP
banding was most prevalent (Fig. 4.40), but its fracture surface lacks any elongated
dimples, providing further evidence that NFP bands aligned transverse to the major
loading direction are responsible for increased damage rates.
Localization of voids at the sheet centerline was generally greater for ‘RD’ speci-
mens than ‘TD’ specimens. This trend is to be expected as once localization begins
to occur void formation would be confined to a smaller region of the specimen where
CHAPTER 5. DISCUSSION 263
strains are large enough for nucleation. It is readily recognizable that more NFP
bands aligned in the major strain direction would fall into this neck region than those
aligned in the minor strain direction. Thus, as void nucleation has been shown to
occur preferentially at NFP bands, it would occur in greater frequency at the sheet
centerline for ‘RD’ specimens than ‘TD’ specimens.
5.5.4 Importance of NFP Banding to Damage
Understanding the anisotropy of damage behaviour in DP steels due to NFP banding
in the rolling direction, as presented in this study, is important to both steel producers
and auto parts manufacturers. For parts manufacturers, this knowledge could possibly
lead to simple solutions for avoiding premature part-forming failures. An act as
straightforward as being sure DP steel sheet used in a part forming operation is always
oriented such that the rolling direction is aligned parallel to the largest imposed strains
could potentially prevent many premature failures, if this practice is not already in
place. The same idea applies to orienting sheet during a part forming operation
in order to minimize damage and thus maximize ductility and energy absorption
during a crash-scenario. For steel producers, the present study highlights the need
for developing a cost-effective method to reduce or eliminate NFP banding in DP
steels in order to obtain improved levels of formability.
Chapter 6
Conclusions and Recommendations
6.1 Conclusions
An in-plane plane-strain (IPPS) tensile testing methodology, originally devel-
oped by Valletta [60] and modified by Kilfoil and Kitney [61,131], was used to
deform DP steel microstructural variants in a near plane-strain forming path
under constant crosshead displacement at a nominal initial strain rate of ap-
proximately 0.01 s-1 averaged over the entire specimen gauge region. Testing
was performed to the point of fracture while tracking major and minor strain
developed. Failure strains, a first approximation of ductility, were observed
to decrease with increasing non-ferritic phase/constituent (NFP) content.
264
CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 265
Fractured specimens were examined for damage accumulation in the bulk us-
ing 3-D X-ray micro-computed tomography (XµCT) with a spatial resolution
of approximately 2 µm and 2-D metallographic procedures, and at the sur-
face via scanning electron fractography. The DP steel microstructural variants
failed in a ductile manner with a shear mechanism becoming more dominant
with increasing NFP content.
It was observed that DP microstructures with an increased severity of NFP
banding (generally aligned in the sheet rolling direction) incurred reduced
strain to failure. In many cases, particularly for the DP980 microstructural
variants, IPPS specimens with the sheet rolling direction transverse to the ma-
jor loading direction incurred a reduce strain to failure than the same variants
with the sheet rolling direction aligned with the major loading direction.
This study has clearly demonstrated the capability of extracting quantitative
and qualitative measures of void damage in 3-D for deformed DP steel sheet
using lab-scale XµCT.
Void damage in all DP steel microstructural variants was observed to be
concentrated most populously near the fracture surface.
No quantitative relationship could be established between NFP content and
void damage accumulation.
Void damage was inferred metallographically to nucleate preferentially at mi-
crostructural bands of NFP via particle cracking, especially at the coarsest of
bands.
CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 266
Void damage spatial distribution was generally reflective of the spatial distri-
bution of the most coarse NFP bands through the sheet thickness, i.e. voids
were concentrated to regions in which NFP banding was observed to be most
severe.
In general, microstructural variants with the sheet rolling direction transverse
to the major loading direction were observed to accumulate a greater number
of voids and a larger void volume percent than the same variants with the
sheet rolling direction aligned with the major loading direction. This damage
anisotropy reflected the general alignment of NFP bands in the sheet rolling
direction.
In microstructural variants with NFP bands aligned transverse to the major
loading direction, accumulated void damage was often observed to be highly
elongated in the direction of NFP banding.
6.2 Recommendations
Future studies elaborating upon the work of this dissertation may consider the fol-
lowing:
An increased number of valid IPPS specimens per microstructural variant
may afford a more robust analysis of the effect of NFP content and spatial
distribution on ductility and damage accumulation under plane-strain defor-
mation.
CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 267
Further TP1-treated specimens could be produced using additional IC an-
nealing temperatures and tested to better elucidate the relationship between
NFP content and damage accumulation.
Producing multiple match-head specimens per microstructural variant, ex-
tracted from different valid IPPS specimens, for XµCT scanning would have
provided insight into how representative the damage accumulation behaviour
observed for each variant was.
Eliminating residual NFP banding in a DP steel microstructural variant would
provide an opportunity to better determine the importance of NFP spatial
distribution to damage accumulation.
Examination of the void populations in microstructural variants prior to test-
ing may reveal pre-existing voids.
Performing plane-strain testing at a rate closer to that of typical automotive
forming operations and observing the accumulated damage would be useful
in eliciting strain rate effects for this deformation path.
Ideally, interrupted IPPS tests could be performed to garner some data con-
cerning the development of void damage within the DP steel variants for this
deformation path.
In-situ sub-size tensile testing of DP steel variants within the Micro-XCT 400
may be performed to determine the differences in void evolution behaviour
during straining in relation to known NFP content and spatial distribution.
CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 268
Digital image correlation (DIC) software (freeware available for MATLAB
made by Christoph Eberl) may be paired with smaller media applied to the
IPPS specimen surface to possibly track strains in IPPS specimens with an in-
creased spatial resolution and thus better capture the strain gradient existing
within regions of intense localization.
The effect of ferrite grain size should be investigated. The rate of surface
roughening increases with grain size, which may result in a field of reduced
thickness inhomogeneities and through-thickness shearing under severe con-
ditions [59]
The effects of what were thought to be manganese sulfide stringers present in
the microstructures of the DP steel variants of this study on void nucleation
could be assessed.
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Appendix A
Preliminary IC Annealing
Experiments
This appendix details the experiment conducted to produce a calibration curve for
NFP content in the cold-rolled steels of this study after IC annealing treatments at
various temperatures. This curve was used to select three IC annealing temperatures
used for the production of DP microstructural variants for IPPS tensile testing.
A.1 Preliminary Heat Treatment Experiment
Lacking software, such as Thermo-CalcR©, to calculate the phase diagram for the cold-
rolled dual-phase steel alloys used in this study for heat treatments, an experiment
was designed to create a calibration curve correlating the volume percent of NFP in
TP1-treated microstructures to IC annealing temperature.
281
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 282
A.1.1 Alloy Intercritical Temperature Ranges
Firstly, the eutectoid (Ac1) and minimum austenitizing (Ac3) temperatures needed to
be determined to distinguish the intercritical treatment temperature range for each
of the cold-rolled DP steel alloys. Andrews’ formulae [152], provided in Eq. A.1 and
Eq. A.2, were used to provide an estimate of these temperatures where elemental
composition is input in weight percent. These equations are valid for low alloy steels
with less than 0.6%C. The martensite start (Ms) and finish (Mf) temperatures of
these alloys were also calculated using Andrews’ formulae [152], provided in Eq. A.3
and Eq. A.4 respectively. These equations are valid for low alloy steels with less than
0.6%C, 4.9%Mn, 5.0%Cr, 5.0%Ni, and 5.4%Mo. The results of the calculations of
the aforementioned temperatures are provided for both cold-rolled DP steel alloys in
Table A.1.
Ac1 (◦C) = 723− 10.7Mn− 16.9Ni+ 29.1Si+ 16.9Cr + 290As+ 6.38W (A.1)
Ac3 (◦C) = 910− 203
√C − 15.2Ni+ 44.7Si+ 104V + 31.5Mo+ 13.1W (A.2)
Ms (◦C) = 512− 453C − 16.9Ni+ 15Cr − 9.5Mo
+ 217(C)2 − 71.5(C)(Mn)− 67.6(C)(Cr)
(A.3)
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 283
Mf (◦C) = Ms − 215 (A.4)
Table A.1: Approximated solid state transformation tempera-tures for the cold-rolled DP steel alloys.
Ac1 Ac3 Ms Mf
(◦C) (◦C) (◦C) (◦C)
DP780 CR 705 859 459 244DP980 CR 702 855 444 239
A.1.2 IC-Annealing Calibration Curves for NFP Content
With knowledge of the approximate range of temperatures falling within the inter-
critical region for each alloy, five IC annealing temperatures were selected from within
this range to produce microstructural variants of DP steel with varying NFP volume
percent. The five semi-arbitrarily selected temperatures were: 707◦C, 716◦C, 729◦C,
739◦C, and 751◦C. These temperatures were selected from the lower portions of the
approximated cold-rolled alloy IC annealing ranges in an attempt to produce typi-
cal dual-phase steel microstructures in which the ferrite content is greater than NFP
content. IC annealing treatments of IPPS blanks at these temperatures for both of
the cold-rolled DP steel alloys were undertaken following the procedures for TP1 in
Sec. 3.2.4.4.
After treatment, a microstructural characterization of NFP volume percent was
performed for each specimen. Metallographic through-thickness (ND) sections were
extracted from the blanks along the rolling direction (RD) and transverse direction
(TD) from the locations detailed in Fig. A.3 using a Struers Accutom precision cut-
off machine equipped with an aluminum oxide cut-off wheel and continuously flowing
coolant. Samples were also sectioned from the DP780 and DP980 galvannealed steel
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 284
and subjected to the same microstructural characterization to determine the volume
percent of NFP present. The etchant used was 10% sodium metabisulfite (SMB)
which left ferrite untinted and tinted both martensite and bainite dark.
A.1.2.1 Optical Microscopy Procedure
This section describes point counting procedures specific to NFP volume percent es-
timates for preliminary heat treatment DP steel specimens. A Zeiss Axioskop 2 MAT
light microscope equipped with an Olympus EvolutionTMMP Colour CCD camera
was used to capture colour micrographs measuring 2560 x 1920 pixels. A 100x Zeiss
Epiplan-NEOFLUAR oil immersion lens was used during micrograph acquisition.
Each captured micrograph was the average of 10 accumulated exposures to account
for any vibrations of the system during acquisition.
For each DP steel microstructural variant, 10 micrographs were captured each from
ND-RD and ND-TD sections. These micrographs were captured along the through-
thickness centerline of the steel sheet where banding of NFP was most prevalent. A
software-driven microcontroller was used to automatically shift the microscope stage
0.5 mm along the through-thickness sheet centerline between micrograph captures,
thereby eliminating operator bias in field selection. The capture of fields along sheet
centerlines introduces a bias into the constituent volume percent estimates; however
this region is thought to control plane strain formability for the IPPS testing method
[131].
ImageJ, image analysis freeware written in Java, was used to overlay a grid of
test points over acquired micrographs. A custom grid consisting of 110 test points
distributed about five equidistant circles was developed as a Java plug-in within
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 285
ImageJ for the optical micrographs and used for point-counting.
Representative micrographs of the resulting microstructures for each IC annealed
variant and of the galvannealed steel are provided in Fig. A.1 for DP780 and in
Fig. A.2 for DP980. The NFP contents measured for the galvannealed and heat-
treated blanks are summarized in Table A.2 and presented graphically in Fig. A.4.
Table A.2: Volume percent of NFP measured in the as-receivedgalvannealed DP steels and in the gauge region of the TP1-treated IPPS blanks of preliminary heat treatments.
ConditionNFP
ConditionNFP
Volume % Volume %
DP780 Galvannealed 34.9 ± 1.2 % DP980 Galvannealed 47.2 ± 1.3DP780CR + TP1 @ 707◦C 20.6 ± 1.2 % DP980CR + TP1 @ 707◦C 23.0 ± 1.1 %DP780CR + TP1 @ 716◦C 27.5 ± 1.4 % DP980CR + TP1 @ 716◦C 27.3 ± 1.4 %DP780CR + TP1 @ 729◦C 31.2 ± 1.4 % DP980CR + TP1 @ 729◦C 35.7 ± 1.7 %DP780CR + TP1 @ 739◦C 40.0 ± 1.3 % DP980CR + TP1 @ 739◦C 41.5 ± 1.9 %DP780CR + TP1 @ 751◦C 50.5 ± 1.5 % DP980CR + TP1 @ 751◦C 60.2 ± 1.8 %
A.2 Optical vs. SE Quantitative Metallography
The attentive reader will note that the NFP contents predicted in Fig. A.4 for the
TP1 IC annealing temperatures used do not correlate within uncertainty with the
NFP contents measured for the TP1-treated DP steel variants in Chap. 4. The ex-
planation for this non-correlation hinges primarily on the ineffectiveness of 1000x
optical micrographs in magnifying the fine-grained microstructures of the sheet steels
used in this research to a size which allowed for accurate delineation of whether or
not grid-points fell upon a constituent. A micrograph demonstrating the difficulty in
performing manual volume percent counting using 1000x optical micrographs due to
the low ratio of grid-point size to NFP particle size is provided in Fig. A.5. Despite
having provided a high degree of precision in measuring NFP volume percent, the
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 286
(a) (b)
(c) (d)
(e) (f)
Figure A.1: Representative microstructures at the sheet centre-line of: a) as-received DP780 galvannealed steel; b) DP780CRTP1 @ 707◦C; c) DP780CR TP1 @ 716◦C; d) DP780CR TP1@ 729◦C; e) DP780CR TP1 @ 739◦C; and f) DP780CR TP1@ 751◦C. (10% SMB etch)
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 287
(a) (b)
(c) (d)
(e) (f)
Figure A.2: Representative microstructures at the sheet centre-line of: a) as-received DP980 galvannealed steel; b) DP980CRTP1 @ 707◦C; c) DP980CR TP1 @ 716◦C; d) DP980CR TP1@ 729◦C; e) DP980CR TP1 @ 739◦C; and f) DP980CR TP1@ 751◦C. (10% SMB etch)
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 288
Figure A.3: IPPS blank detailing the locations of ND-RD (red)and ND-TD (green) metallographic specimen extraction at thecenter of the gauge region for preliminary heat treatments.
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 289
700 710 720 730 740 750
20
30
40
50
60
70
DP780 DP980
NFP
Vol
ume
Per
cent
IC Annealing Temperature (°C)
Figure A.4: NFP content calibration curve constructed for TP1heat treatment of the DP780 and DP980 cold-rolled alloys.Lines of best fit are polynomial functions.
APPENDIX A. PRELIMINARY IC ANNEALING EXPERIMENTS 290
accuracy of point counting using optical micrographs was clearly questionable. As
such, all point counting of NFP for non-preliminary experiments was performed using
5000x SE micrographs. The superior resolving power of the SEM and the increased
magnification allowed for what was expected to be quantitative metallographic mea-
surements of greater accuracy. A convergence study was not performed to assess
the accuracy of 5000x SE micrographs in mean lineal intercept and volume percent
measurements.
Figure A.5: Optical micrograph taken at 1000x of TP1-treatedDP780 (729◦C IC annealing temperature) demonstrating thedifficulty inherent in classifying whether grid points (small reddots) fall on a NFP particle. The etchant used was 10% SMB.
Appendix B
IPPS Blanks - Time to Heat to IC
Temperature
The heating times required within the vertical crucible furnace salt bath to reach
desired IC temperature for 85 mm x 50 mm x sheet thickness rectangular blanks of
cold-rolled DP780 and DP980 were measured using a thermocouple and data acqui-
sition software. Small slots were cut into the 50 mm side at the center of the gauge
region of a blank from each steel grade. A K-type thermocouple’s two wires were
peened tightly into place using a hammer and punch to plastically deform the mouth
of each slot. Prior to IC annealing heat treatment, the other end of the thermocouple
was connected to a data acquisition (DAQ) card on a PC with Instrunet data acqui-
sition software. The blank was then dipped in the salt bath following the procedures
outlined in Sec. 3.2.1, being sure to prevent the bare thermocouple wires from touch-
ing conductive objects. The temperature of the salt bath in the location of the gauge
region of the submerged blanks as recorded by the shielded thermocouple submerged
in the salt bath was approximately 700◦C. This is shown in Appendix A to be above
291
APPENDIX B. IPPS BLANKS - TIME TO HEAT TO IC TEMPERATURE 292
the Ac1 temperature for both steels. The transient temperature responses of the cold-
rolled DP780 and DP980 blanks for repeated TP1 trials are provided in Fig. B.1(a)
and Fig. B.1(b) respectively. It was determined that the time for the IPPS blanks
to heat to target IC annealing temperature was approximately 37 seconds and 50
seconds for the DP780 and DP980 cold-rolled alloys respectively. The longer time for
the DP980 material is due to its increased thickness.
The response of the salt bath to the addition of the steel blanks was also recorded
using the data acquisition software. The shielded K-type thermocouple suspended
in the salt bath 10 mm away from the pot edge was connected to the DAQ card.
The transient response of the bath was recorded to determine what length of time
was necessary between IC annealing treatments for the salt bath to re-stabilize at
the target temperature. The transient temperature responses of the salt bath for
repeated trials with the DP780CR and DP980CR blanks are provided in Fig. B.2(a)
and Fig. B.2(b) respectively. It was determined that the time for the salt bath to re-
stabilize to target IC annealing temperature was approximately 18 minutes between
TP1 treatments of both the DP780 and DP980 cold-rolled alloys.
APPENDIX B. IPPS BLANKS - TIME TO HEAT TO IC TEMPERATURE 293
(a)
(b)
Figure B.1: Heating curves for the TP1 heat treatment of: a)cold-rolled DP780 IPPS rectangular blanks; and b) cold-rolledDP980 IPPS rectangular blanks. Also shown are ±1% K-typethermocouple accuracy bounds on the target temperature of700◦C. The short plateau prior to reaching the target temper-ature of 700◦C is explained by energy rapidly being consumedin the transformation of carbides to austenite.
APPENDIX B. IPPS BLANKS - TIME TO HEAT TO IC TEMPERATURE 294
(a)
(b)
Figure B.2: Salt bath transient temperature response for theTP1 heat treatment of: a) cold-rolled DP780 IPPS rectangu-lar blanks; and b) cold-rolled DP980 IPPS rectangular blanks.Also shown are ±1% K-type thermocouple accuracy bounds onthe target temperature of 700◦C.
Appendix C
IPPS Specimen Cleaning
Procedure
The inhibited acid cleaning solution was prepared in a fume hood. Seven-hundred
milliliters of water was added into a 1000 milliliter volumetric flask. One-hundred
milliliters of concentrated (98%) sulphuric acid was added to the flask. Seventeen
drops of Activol inhibitor, produced by Harry Miller Corporation, were added to the
solution. This inhibitor assists in facilitating attack of the oxide layer only and not
the base steel [131]. Finally, the solution was diluted to one liter with water, mixed
well, and allowed to cool to room temperature.
Prior to inhibited acid treatment, all heat-treated IPPS specimens were wiped
with acetone to remove any grease. Two-hundred milliliters of inhibited acid solution
were poured into a glass dish of 100 mm inner diameter. This 200 mL of solution was
used to treat seven IPPS specimens in succession before being disposed of following
standard waste acid disposal procedures. A treatment consisted of immersing an IPPS
specimen in the inhibited solution for 2 minutes with the sheet surface flat on the
295
APPENDIX C. IPPS SPECIMEN CLEANING PROCEDURE 296
bottom of the glass dish. During this time, the specimen was given a light scrub with
a soft-bristled toothbrush, scrubbing in the direction of the major strain axis only to
prevent development of any small surface striations perpendicular to the applied load
direction of mechanical testing. The specimen was then flipped and re-immersed in
solution for 2 minutes with light-scrubbing taking place throughout. After this, the
specimen was dunked in a flask filled with water, flushed under running water, rinsed
with ethanol, and dried using compressed air. Example photographs of the condition
of a heat-treated IPPS specimen prior to and after an inhibited acid cleaning are
provided in Fig. C.1.
APPENDIX C. IPPS SPECIMEN CLEANING PROCEDURE 297
(a) Heavy oxidation of an IPPS specimen resulting from both theIC annealing process and water remaining on the surface of thespecimen after waterjet-cutting.
(b) IPPS specimen after inhibited acid bath treatment and dot plot-ting.
Figure C.1: a) ‘Before’ and b) ‘after’ photographs of a heat-treated IPPS specimen subjected to inhibited sulfuric acidcleaning.
Appendix D
NL-Means Denoising Parametric
Study
In order to make effective use of the NL-Means Denoising algorithm, a parametric
study was required to determine the optimal values for a window and patch size used
by the algorithm. The window size, t, determines the side length of a square region
(window) of pixels within an image that will be compared with other windows within
the image. A patch size parameter, f, determines the square pixel array sample size
within these windows that will be sampled and compared to the same patch locations
within other windows for contribution to the weighted average computation resulting
in image denoising.
For experimental purposes, it was ideal to use a test image with the parametric
study for which the method noise was known, i.e. the true pixel intensities that should
result from denoising were known. To accomplish this, a manually produced image
simulating a reconstructed slice of a failed DP steel mechanical testing specimen
was produced. This image, shown in Fig. D.1(a), would act as the standard for
298
APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 299
a noise free reconstruction. Thresholding of the slice was performed manually to
produce a standard for what a 100% accurate thresholding operation would result
in (Fig. D.1(b)). Gaussian noise of a standard deviation equivalent to that seen in
reconstructions of the match-head specimens was added to Fig. D.1(a) to simulate
true noisy reconstruction conditions (Fig. D.1(c)).
NL-means denoising was performed on the test image with added Gaussian noise
using 100 combinations of window and patch parameters, varying both with integers
from one to ten. Subsequently, these denoised images were thresholded using the
algorithm of Sahoo, Wilkins, and Yeager [129]. The mean squared error (MSE)
between the thresholds of the denoised image and the standard for 100% accurate
thresholding were compared. The results are presented graphically in Fig. D.2. Just
as Buades stated, the results indicate that a 7 x 7 similarity window is large enough
to be robust to noise, but small enough to preserve fine structure and detail [125].
Combined with a patch size of 1 x 1, the most optimal thresholding results in terms
of MSE were obtained. Visual comparison of the threshold masks of the denoised
images and the standard for 100% accurate thresholding confirmed that a window
size of 7 combined with a patch size of 1 produced the most accurate correlation and
retention of fine detail.
The last parameter that needed to be determined to use the NL-means algorithm
optimally was a filtering factor, h. A reconstructed and cropped slice of a failed DP
steel specimen was tested with the NL-means denoising algorithm with the newly
selected window size of 7 and patch size of 1. The filtering factor was varied through
a range of values to determine the optimal degree of filtering. It was determined, that
the standard deviation of the pixel greyscale intensities in regions correlating to steel
APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 300
(a)
(b) (c)
Figure D.1: a) Standard NL-means denoising parametric studytest image for a noise free reconstruction. b) Standard for a100% accurate thresholding of the “voids” in a). c) Gaussiannoise added to a) to simulate noisy reconstructions producedby X-ray tomography of match-head specimens.
APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 301
Figure D.2: Mean square error between the threshold masks(produced using the algorithm of Sahoo, Wilkins, and Yea-ger [129]) of images resulting from NL-means denoising ofFig. D.1(c) and the standard for 100% accurate thresholdingfrom Fig. D.1(b).
APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 302
in reconstructed slices provided the best value for h in terms of flattening intensity
distribution while preserving detail (Fig. D.3). Based upon the recommendations of
Buades, this made sense; the optimal filtering parameter is dependent mainly upon
the standard deviation of noise in the image [124].
APPENDIX D. NL-MEANS DENOISING PARAMETRIC STUDY 303
(a)
(b) (c) (d)
(e) (f) (g)
Figure D.3: a) Reconstructed and cropped slice of a failed DPsteel mechanical testing specimen. This image was denoisedwith the NL-means algorithm with a window size of 7, patchsize of 1, and filtering parameter, h, of the following factorsof the standard deviation, σ, of the greyscale intensities of theoriginal cropped slice: b) 0.42σ; c) 0.83σ; d) 1.0σ; e) 1.25σ; f)1.67σ; g) 2.08σ.
Appendix E
Complete IPPS Testing Results
Table E.1 below provides a complete list of the mean strains just prior to fracture in
the failure row for all the IPPS specimens which failed satisfactorily according to the
criteria outlined in Sec. 3.5.1.
304
APPENDIX E. COMPLETE IPPS TESTING RESULTS 305
Table E.1: Mean major and minor engineering strain just prior tofailure within the row of the grid of IPPS dots in which fractureoccurred. All IPPS specimens which failed satisfactorily areprovided, ordered according to treatment/condition.
SpecimenEngineering Strain
Major Minor
7GA-R4 0.1141 -0.0051
7GA-R1 0.0974 -0.0047
7GA-T2 0.0843 -0.0051
7GA-T1 0.1022 -0.0041
9GA-R3 0.0658 -0.0002
9GA-R4 0.0795 -0.0012
9GA-R5 0.0641 -0.0007
9GA-T4 0.0451 -0.0005
9GA-T1 0.0524 -0.0007
APPENDIX E. COMPLETE IPPS TESTING RESULTS 306
Table E.1: Mean major and minor engineering strain just prior tofailure within the row of the grid of IPPS dots in which fractureoccurred. All IPPS specimens which failed satisfactorily areprovided, ordered according to treatment/condition.
SpecimenEngineering Strain
Major Minor
7TP1-15-R4 0.2019 -0.0149
7TP1-15-T11 0.2423 -0.0162
7TP1-33-R11 0.1308 -0.0083
7TP1-33-T10 0.1369 -0.0067
7TP1-33-T9 0.1138 -0.0069
7TP1-33-T12 0.1244 -0.0076
7TP1-43-R3 0.0699 -0.0034
7TP1-43-R2 0.0577 -0.0039
7TP1-43-R5 0.0488 -0.0020
7TP1-43-R7 0.0685 -0.0028
7TP1-43-R1 0.0679 -0.0033
7TP1-43-T1 0.0609 -0.0029
7TP1-43-T5 0.0507 -0.0032
7TP1-43-T4 0.0467 -0.0032
APPENDIX E. COMPLETE IPPS TESTING RESULTS 307
Table E.1: Mean major and minor engineering strain just prior tofailure within the row of the grid of IPPS dots in which fractureoccurred. All IPPS specimens which failed satisfactorily areprovided, ordered according to treatment/condition.
SpecimenEngineering Strain
Major Minor
9TP1-15-R7 0.1816 -0.0122
9TP1-15-R6 0.1323 -0.0078
9TP1-15-T1 0.1301 -0.0089
9TP1-15-T3 0.1423 -0.0094
9TP1-15-T2 0.1286 -0.0109
9TP1-15-T4 0.1671 -0.0134
9TP1-15-T5 0.1235 -0.0088
9TP1-33-R10 0.0965 -0.0046
9TP1-33-R12 0.0929 -0.0052
9TP1-33-R13 0.0723 -0.0042
9TP1-33-T10 0.0714 -0.0069
9TP1-33-T8 0.0814 -0.0044
9TP1-43-R11 0.0563 -0.0016
9TP1-43-R12 0.0452 -0.0035
9TP1-43-T7 0.0206 -0.0008
9TP1-43-T1 0.0179 -0.0007
9TP1-43-T4 0.0211 -0.0005
9TP1-43-T5 0.0207 -0.0007
APPENDIX E. COMPLETE IPPS TESTING RESULTS 308
Table E.1: Mean major and minor engineering strain just prior tofailure within the row of the grid of IPPS dots in which fractureoccurred. All IPPS specimens which failed satisfactorily areprovided, ordered according to treatment/condition.
SpecimenEngineering Strain
Major Minor
7TP2-25-R4 0.1290 -0.0061
7TP2-25-T2 0.0963 -0.0066
7TP2-25-T4 0.1730 -0.0076
9TP2-37-R4 0.0962 -0.0030
9TP2-37-R3 0.0898 -0.0044
9TP2-37-T1 0.0783 -0.0028
9TP2-37-T5 0.0645 -0.0033
9TP2-37-T4 0.0481 -0.0017