draw-bend fracture prediction with dual-phase steels r. h. wagoner september 25, 2012 ampt...
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R. H. Wagoner 3 1.Background – Shear Fracture, 2006TRANSCRIPT
Draw-Bend Fracture Prediction with Dual-Phase Steels
R. H. Wagoner
September 25, 2012
AMPTWollongong, Australia
R. H. Wagoner
Outline
1. Background – Shear Fracture, 2006
2. DBF Results & Simulations, 2011Intermediate Conclusions
3. Practical Application, 2012Ideal DBF TestRecommended Procedure
4. No Ideal Test?Results,Recommended Procedure
2
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1. Background – Shear Fracture, 2006
R. H. Wagoner 4
Shear Fracture of AHSS – 2005 Case
Jim Fekete et al, AHSS Workshop, 2006
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Shear Fracture of AHSS - 2011
Forming Technology Forum 2012 Web site: http://www.ivp.ethz.ch/ftf12
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Unpredicted by FEA / FLD
Stoughton, AHSS Workshop, 2006
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Shear Fracture: Related to Microstructure?
Ref: AISI AHSS Guidelines
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Conventional Wisdom, 2006
Shear fracture…•is unique to AHSS (maybe only DP steels)•occurs without necking (brittle)•is related to coarse, brittle microstructure•is time/rate independent
Notes:•All of these based on the A/SP stamping trials, 2005.•All of these are wrong.•Most talks assume that these are true, even today.
R. H. Wagoner 999
NSF Workshop on AHSS (October 2006)E
long
atio
n (%
)
Tensile Strength (MPa)
0
10
20
30
40
50
60
70
0 600 1200300 900 1600
DP, CP
TRIP
MART
HSLA
IF
MildIF- HS
BHCMn
ISO
Elo
ngat
ion
(%)
600
TWIPAUST. SS
L-IP
ISO
R. W. Heimbuch: An Overview of the Auto/Steel Partnership and Research Needs [1]
R. H. Wagoner 10
2. DBF Results & Simulations, 2011
R. H. Wagoner
References: DBF Results & Simulations
J. H. Kim, J. H. Sung, K. Piao, R. H. Wagoner: The Shear Fracture of Dual-Phase Steel, Int. J. Plasticity, 2011, vol. 27, pp. 1658-1676.
J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation Incorporating Strain, Strain-Rate, and Temperature, Int. J. Plasticity, 2010, vol. 26, pp. 1746-1771.
J. H. Sung, J. H. Kim, R. H. Wagoner: The Draw-Bend Fracture Test (DBF) and Its Application to DP and TRIP Steels, Trans. ASME: J. Eng. Mater. Technol., (in press)
11
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DBF Failure Types
Type I
Type IIType III
65o
65o
V2
V1
Type I: Tensile failure (unbent region) Type II: Shear failure (not Type I or III)Type III: Shear failure (fracture at the roller)
12
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DBF Test: Effect of R/t
13
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“H/V” Constitutive Eq.: Large-Strain Verification
600
700
800
900
1000
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Effe
ctiv
e St
ress
(MPa
)
Effective Strain
H/V <>=1MPa
DP590(B), RDStrain Rate=10-3/sec25oC
Tensile TestVoce <>=1MPa
Hollomon <>=4MPa
Bulge Test (r=0.84, m=1.83)
FitRange Extrapolated, Bulge Test Range
R. H. Wagoner 15
0 0.05 0.1 0.15 0.2 0.25 0.3300
400
500
600
700
Engi
neer
ing
Stre
ss (M
Pa)
Engineering Strain
Experiment(D-B)
Voce HollomonH/V model
DP590(B), RDStrain Rate=10-3/s100oC, Isothermal
FE Simulated Tensile Test: H/V vs. H, V
R. H. Wagoner
Predicted ef, H/V vs. H, V: 3 alloys, 3 temperatures
16
Hollomon Voce H/V
DP590 0.05 (23%) 0.05 (20%) 0.02 (7%)
DP780 0.03 (18%) 0.04 (22%) 0.01 (6%)
DP980 0.04 (30%) 0.03 (21%) 0.01 (5%)
Standard deviation of ef: simulation vs. experiment
R. H. Wagoner 17
FE Draw-Bend Model: Thermo-Mechanical (T-M)
hmetal,air = 20W/m2K
hmetal,metal = 5kW/m2K
= 0.04
U1, V1
U2, V2
• Abaqus Standard (V6.7)• 3D solid elements (C3D8RT), 5 layers• Von Mises, isotropic hardening• Symmetric model
Kim et al., IDDRG, 2009
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Front Stress vs. Front Displacement
18
0
200
400
600
800
1000
0 20 40 60 80
Fron
t Str
ess,
1
Front Displacement, U1 (mm)
Measured
DP780-1.4mm, RDV
1=51mm/s, V
2/V
1=0
R/t=4.5
IsothermalSolid, Shell
T-M
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Displacement to Maximum Front Load vs. R / t
19
0
20
40
60
80
0 2 4 6 8 10 12 14
UM
ax. L
oad (m
m)
R / t
Type I
Type III
DP780-1.4mm, RDV
1=51mm/s, V
2/V
1=0
T-M, Solid
Measured
Isothermal, SolidIsothermal, Shell
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Is shear fracture of AHSS brittle or ductile?
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Fracture Strains: DP 780 (Typical)
21
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Fracture Strains: TWIP 980 (Exceptional)
22
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Directional DBF : DP 780 (Typical)
23
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Directional DBF Formability: DP980 (Exceptional)
24
0
5
10
15
20
25
30
0 30 60 90
Elon
gatio
n to
Fra
ctur
e (m
m)
Angle to RD (degree)RD TD
DP980R/t = 3.3
R. H. Wagoner 25
Interim Conclusions
• “Shear fracture” occurs by plastic localization.
• Deformation-induced heating dominates the error in predicting shear failures.
• Brittle cracking can occur. (Poor microstructure or exceptional tensile ductility, e.g. TWIP).
• T-dependent constitutive equation is essential.
• Shear fracture is predictable plastically. (Challenges: solid elements, T-M model.)
R. H. Wagoner 26
3. Practical Application - 2012
R. H. Wagoner
DBF/FE vs. Industrial Practice/FE
Ind.: Plane strainHigh rate ~Adiabatic
FE: ShellIsothermalStatic
DBF: General strain Moderate rates
Thermo-mech.FE: Solid element
Thermo-mech.27
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Ideal DBF Test: Plane Strain, High Rate
28
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Ideal Test Results - Stress
29
400
600
800
1000
1200
0 2 4 6 8 10 12 14
Peak
Eng
inee
ring
Stre
ss (M
Pa)
Bending Ratio, R / t
DP780-1.4mm
Analytical PS Result
(UTS)
(R/t)*
R. H. Wagoner
Ideal Test Results - Strain
30
0
0.1
0.2
0.3
0.4
0 2 4 6 8 10 12 14 16
True
Str
ain
Bending Ratio, R / t
Analytical PS ResultsDP 780 - 1.4mm
Outer Strains
Inner Strains
Center Strains(Membrane) FLD
o
(R/t)*
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How to Use Practically: Bend, Unbend Regions
31
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Practical Application of SF FLD – (1) Direct
32
For each element in contact
Known: R, t *membrane
Predicted Fracture: FEA > *membrane
R. H. Wagoner
Practical Application of SF FLD – (2) Indirect
33
For each element drawn over contact
Known: (R, t)contact Pmax *PS tension *PS tension
Predicted Fracture: FEA > *PS tension
Wu, Zhou, Zhang, Zhou, Du, Shi: SAE 2006-01-0349.
R. H. Wagoner
Calculation: Indirect Method
34
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Recommended Procedure with Industrial FEA
35
1. Use adiabatic law in FEA, use rate sensitivity
2. Classify each element based on X-Y position (tooling)a) Bend (plane-strain)b) After bend (plane-strain)c) General (not Bend, not After)
3. Apply 4 criteria:a) FLD (Bend, After)b) Direct SF (Bend)c) Indirect SF (After)d) Brittle Fracture* (All?)
R. H. Wagoner 36
4. No Ideal Test?(What to do?)
R. H. Wagoner
What is Needed?
37
Pmax = f(R/t)(PS, high-speed DBF)
400
600
800
1000
1200
0 2 4 6 8 10 12 14
Peak
Loa
d (M
Pa)
Bending Ratio, R / t
0
0.1
0.2
0.3
0.4
0 2 4 6 8 10 12 14 16
Mem
bran
e St
rain
Bending Ratio, R / t
membrane = f(R/t)(PS, high-speed DBF)
R. H. Wagoner 38
FE Plane Strain DBF Model
= 0.06
U1, V1
U2, V2 = 0
• Abaqus Standard (V6.7)• Plane strain solid elements (CPE4R), 5 layers• Von Mises, isotropic hardening• Isothermal, Adiabatic, Thermo-Mechanical
R. H. Wagoner
0
400
800
1200
1600
0 0.2 0.4 0.6 0.8 1
True
Str
ess
(MPa
)
True Plastic Strain
DP980(D)-GA-1.45mmd/dt=10-3/s
Adiabatic
25oC75oC
125oC
-5% -12%
Adiabatic Constitutive Equation
0p
T dC
( , ) ( , , )adiabatic T
39
R. H. Wagoner
Peak Stress, Plane-Strain: DP980
40
600
800
1000
1200
1400
0 2 4 6 8 10 12 14
Peak
Eng
inee
ring
Stre
ss (M
Pa)
R / t
DP980-1.43mm
Analytical Model,Plane StrainPS FE Model,
m=0, =0
UTS
DBF measured(RD, TD)
R. H. Wagoner
Membrane Strains at Maximum Load
41
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8 10 12 14 16
s, T
rue
Mem
bran
e St
rain
Bending Ratio, R / t
Analytical Adiabatic ModelStopped at Maximum LoadDP590
DP780
DP980
R. H. Wagoner
Analytical Model: Model vs. Fit
42
0
0.02
0.04
0.06
0.08
0.1
0 0.1 0.2 0.3 0.4 0.5 0.6
s,
Tru
e M
embr
ane
Stra
in
1 / Bending Ratio, t / R
Analytical Adiabatic ModelStopped at Maximum Load
DP590S = 0.167,
so = 0.138
DP780S = 0.198,
so = 0.101
DP980S = 0.221, s
o = 0.088
maxmax
oss R
tRtS
Rt
Rt
R. H. Wagoner
Analytical Model: Model vs. Fit
43
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8 10 12 14 16
s, Tru
e M
embr
ane
Stra
in
Bending Ratio, R / t
Analytical Adiabatic ModelStopped at Maximum Load
DP590: S = 0.168,
so = 0.138
DP780: S = 0.198, s
o = 0.101
DP980: S = 0.221,
so = 0.088
maxmax
oss R
tRtS
Rt
Rt
R. H. Wagoner 44
Conclusions
• Shear fracture is predictable with careful testing or careful constitutive modeling and FEA.
• “Shear fracture” occurs by plastic localization.
• “Shear fracture” is an inevitable consequence of draw-bending mechanics. All materials.
• Brittle fracture can occur, but is unusual. (Poor microstructure or v. high tensile tensile limit, e.g. TWIP).
• T-dependent constitutive equation is essential for AHSS because of high plastic work. (But probably not Al or many other alloys.)
R. H. Wagoner 45
Thank you.
R. H. Wagoner 46
References
• R. H. Wagoner, J. H. Kim, J. H. Sung: Formability of Advanced High Strength Steels, Proc. Esaform 2009, U. Twente, Netherlands, 2009 (CD)
• J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation Incorporating Strain, Strain-Rate, and Temperature, Int. J. Plasticity, (accepted).
• A.W. Hudgins, D.K. Matlock, J.G. Speer, and C.J. Van Tyne, "Predicting Instability at Die Radii in Advanced High Strength Steels," Journal of Materials Processing Technology, vol. 210, 2010, pp. 741-750.
• J. H. Kim, J. Sung, R. H. Wagoner: Thermo-Mechanical Modeling of Draw-Bend Formability Tests, Proc. IDDRG: Mat. Prop. Data for More Effective Num. Anal., eds. B. S. Levy, D. K. Matlock, C. J. Van Tyne, Colo. School Mines, 2009, pp. 503-512. (ISDN 978-0-615-29641-8)
• R. H. Wagoner and M. Li: Simulation of Springback: Through-Thickness Integration, Int. J. Plasticity, 2007, Vol. 23, Issue 3, pp. 345-360.
• M. R. Tharrett, T. B. Stoughton: Stretch-bend forming limits of 1008 AK steel, SAE technical paper No.2003-01-1157, 2003.
• M. Yoshida, F. Yoshida, H. Konishi, K. Fukumoto: Fracture Limits of Sheet Metals Under Stretch Bending, Int. J. Mech. Sci., 2005, 47, pp. 1885-1896.
R. H. Wagoner 47
Extra Slides
R. H. Wagoner
DP Steels
48
0
200
400
600
800
1000
1200
0 5 10 15 20 25
Engi
neer
ing
Stre
ss(M
Pa)
Engineering Strain (%)
DP590(B)-1.4mm
DP780(D)-1.4mm
DP980(D)-1.45mm
Strain Rate: 10-3/secRoom Temp.Rolling Direction
R. H. Wagoner 49
“H/V” Constitutive Framework
Special:
Standard:
( , , ) ( , ) ( ) ( )T f T g h T
( , ) ( ) (1 ( ))Hollo Vocef T T f T f
1 2( ) ( )RTT T T nHollof K [1 exp( )]Vocef A B C
[log ]
0
( )a b
g
( ) (1 ( ))RTh T D T T Sung et al., Int. J. Plast. 2010
R. H. Wagoner
Simulated D-B Test: Effect of Draw Speed
50
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25 30 35
F/F U
TS
Front Displacement (mm)
DP980(D)R/t=4.4, V
2/V
1=0
51mm/s(d/dt=2.5/s)
Adiabatic
Isothermal
2.5mm/s(0.13/s)
0.001mm/s(5x10-3/s)
13mm/s(0.6/s)
R. H. Wagoner
DBF Formability: DP980(A), RD vs. TD (Typical)
51
* Directional Formability: TD=RD
0
10
20
30
40
50
2.2 3.4 4.5 5.5 6.6 7.8 10 13.3
Fron
t Dis
p. to
Fai
lure
(Uf, m
m)
R/t
RDTD
DP980(A)V
1=51mm/sec
V2/V
1=0
R. H. Wagoner
DBF Formability: DP980(D), RD vs. TD (Exceptional)
52
* Directional Formability: RD>TD
0
10
20
30
40
50
60
2.2 3.3 4.4 5.4 6.6 7.7 9.9 13.1
Fron
t Dis
p. to
Fai
lure
(Uf, m
m)
R/t
DP980(D)V
1=51mm/sec
V2/V
1=0
RD
TD
R. H. Wagoner
Analytical Model – Curvilinear Derivation
Rrn
Neutral liner
t
T T
lnn
r
r
2 2ln
3 3ij ij
n
r
r
53
Fracture Criterion: Fracture occurs at Tmax for given R, to
2 2 2( ) ( )3 3 3
n
n
rR t
r r
r dr dr r
0R tR t
R R
Trdr d
2 2( ) ( )3 3
R t
r
r dr r
Materially embedded coordinate :
nr
rdr d dr
0 2 2( ) ( )3 3
R t r d
0 2 2 2( ) ( )3 3 3
n
n
R t r rd d
nr r
nr r
n
n
R. H. Wagoner
DBF Interpretation: Plane-strain vs. Tension
400
600
800
1000
1200
0 2 4 6 8 10 12 14
Peak
Eng
inee
ring
Stre
ss (M
Pa)
R / t
DP780-1.4mm
Analytical Model,Plane Strain
Simplified FE Model,m=0, =0
UTS
54
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Inner and Outer Strains at Maximum Load
55
0
0.1
0.2
0.3
0.4
0 2 4 6 8 10 12 14 16
True
Str
ain
Bending Ratio, R / t
Analytical Adiabatic ModelStopped at Maximum Load
DP590
DP780
Inner Strains
DP980
Outer Strains
R. H. Wagoner
Membrane Strains (R/t Affected Only)
56
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8 10 12 14 16
s,
Tru
e M
embr
ane
Stra
in
Bending Ratio, R / t
Analytical Adiabatic ModelStopped at Maximum Load
DP590
DP780DP980
R. H. Wagoner
R/t-Affected Membrane Strains vs. t/R
57
0
0.05
0.1
0.15
0.2
0.25
0 0.1 0.2 0.3 0.4 0.5 0.6
s,
Tru
e M
embr
ane
Stra
in
1 / Bending Ratio, t / R
Analytical Adiabatic ModelStopped at Maximum Load
DP590
DP780
DP980
R. H. Wagoner
Forming Limit Diagram
58
Ref: Hosford & Duncan
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PS T-M Model: Model vs. Fit
59
-0.05
0
0.05
0.1
0.15
0.2
0.25
0 0.1 0.2 0.3 0.4
s, T
rue
Mem
bran
e St
rain
1 / Bending Ratio, t / R
Plane Strain Thermo-Mechanical ModelStopped at Maximum Load DP590
S = 0.753, s
o = 0.149
DP780S = 0.330,
so = 0.123
DP980S = 0.051,
so = 0.133
maxmax
oss R
tRtS
Rt
Rt
R. H. Wagoner
PS T-M Model: Model vs. Fit
60
0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12 14 16
s, Tru
e M
embr
ane
Stra
in
Bending Ratio, R / t
Plane Strain Thermo-Mechanical ModelStopped at Maximum Load
DP590S = 0.753,
so = 0.149
DP780: S = 0.330, so = 0.123
DP980: S = 0.051, s
o = 0.133
maxmax
oss R
tRtS
Rt
Rt
R. H. Wagoner 61
Draw-Bend Fracture Test (DBF): V1, V2 Constant
Star
t
Max. Finish
Max
. Fin
ish
V1
Start
R
444.5 mm (10”)190.5 mm
190.
5 m
m
444.
5 m
m(1
0”)
V2 = V1
uf
Specimen width: 25mm
Tool radius choices: 2/16, 3/16, 4/16, 5/16, 6/16, 7/16, 9/16, 12/16 inch 3.2, 4.8, 6.4, 7.9, 9.5, 11.1, 14.3, 19 mm
= V2/V1: 0 and 0.3
Wagoner et al., Esaform, 2009
R. H. Wagoner
AHSS vs. HSLA
62
Ref: AISI AHSS Guidelines