measuring overload effects during fatigue crack growth in bainitic steel

7/24/2019 Measuring Overload Effects During Fatigue Crack Growth in Bainitic Steel

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Measuring overload effects during fatigue crack growth in bainitic steel

by synchrotron X-ray diffraction

P. Lopez-Crespo a,, A. Steuwer b,c, T. Buslaps d, Y.H. Tai e, A. Lopez-Moreno f, J.R. Yates g, P.J. Withers h

a Department of Civil and Materials Engineering, University of Malaga, C/Dr Ortiz Ramos, s/n, 29071 Malaga, Spainb MAX IV Laboratory, Lund University, Box 118, SE-221 00 Lund, Swedenc NMMU, Gardham Avenue, 6031 Port Elizabeth, South Africad ESRF, 6 rue J Horowitz, 38000 Grenoble, Francee Rolls-Royce plc, PO Box 31, Derby DE24 8BJ, UKfDepartment of Materials Science and Metallurgy Engineering, University of Jaen, Campus Las Lagunillas, 23071 Jaen, Spaing Simuline Ltd., Derbyshire S18 1QD, UKh School of Materials, University of Manchester, Grosvenor St., Manchester M13 PL, UK

a r t i c l e i n f o

Article history:

Received 28 October 2013

Received in revised form 9 March 2014

Accepted 17 March 2014

Available online 26 March 2014

Keywords:

Overload effect

Fatigue crack closure

Residual stress

X-Ray diffraction

a b s t r a c t

In this work we present the results of in situ synchrotron X-ray diffraction measurements of fatigue

crack-tip strain fields following a 100% overload (OL) under plane strain conditions. The study is made

on a bainitic steel with a high toughness and fine microstructure. This allowed a very high (60lm) spatial

resolution to be achieved so that fine-scale changes occurring around the crack-tip were captured along

the crack plane at the mid-thickness of the specimen. We have followed the crack as it grew through the

plastic/residually stressed zone associated withthe OL crack location. We observed two effects; one when

the enhanced plastic zone is ahead of the crack and one after it has been passed. Regarding the former it

was found that the compressive stress at the crack-tip initially falls sharply, presumably due to the

increased plastic stretch caused by the OL. This is associated with a concomitant fall in peak tensile stress

atKmax, the elastic excursion between KminandKmaxremaining essentially unchanged from before OL.

Subsequently discontinuous closure as seen previously for plane stress caused by crack face contact at

the OL location limits the elastic strain range experienced by the crack tip and thereby retards crack

growth.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

The concept of crack closure has been used to explain many

crack retardation effects in the fatigue of materials. Closure encom-

passes effects that cause the crack faces to close early during

unloading so that the crack-tip does not experience the full

crack-opening fatigue cycle. Plasticity induced crack closure isone of the most important mechanisms of crack closure, but is still

a hotly debated subject with some researchers suggesting it does

not occur at all[1],while others believe that it can only occur un-

der plane stress[2]. To date, experimental measurements of crack

closure for plane strain samples have been inconclusive relying on

either (i) measuring some secondary property of the cracked body

such as compliance or electrical resistance or (ii) measurement of

crack-opening displacements on the surface of the cracked body.

Third generation synchrotron X-ray facilities allow experimental

measurement of the strain field within the interior of the speci-

men. Recently it has been shown that it is possible to map in 2D

the strain fields around the crack-tip, both with neutron diffraction

[3]and synchrotron X-ray diffraction[46].

Croft et al.[6,7]have studied the crack-tip stress fields during

and after an overload event in 4 mm thick (approximately planestress) steel samples. In some well-designed experiments they

found evidence of discontinuous crack closure in the locality of

the overload event at distances as large as 1.5 mmbehind the crack

tip. This work has also been corroborated by synchrotron strain

mapping in 5 mm Ti6Al4V samples[8].

Under plane strain conditions the evidence obtained to date for

crack closure is not so clear. The highest spatial resolution crack-

tip strain measurements (25 lm) have been made on a very fine

grained AlLi alloy, but the low fracture toughness meant that un-

der plane strain conditions the plastic zone was very small [9].

Nevertheless it was possible to extract accurate measures of the

http://dx.doi.org/10.1016/j.ijfatigue.2014.03.015

0142-1123/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author.

E-mail address: [email protected](P. Lopez-Crespo).

International Journal of Fatigue 71 (2015) 1116

Contents lists available at ScienceDirect

International Journal of Fatigue

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j f a t i g u e
http://dx.doi.org/10.1016/j.ijfatigue.2014.03.015mailto:[email protected]://dx.doi.org/10.1016/j.ijfatigue.2014.03.015http://www.sciencedirect.com/science/journal/01421123http://www.elsevier.com/locate/ijfatiguehttp://www.elsevier.com/locate/ijfatiguehttp://www.sciencedirect.com/science/journal/01421123http://dx.doi.org/10.1016/j.ijfatigue.2014.03.015mailto:[email protected]://dx.doi.org/10.1016/j.ijfatigue.2014.03.015http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://crossmark.crossref.org/dialog/?doi=10.1016/j.ijfatigue.2014.03.015&domain=pdfhttp://-/?-


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crack-tip stress intensity factor at minimum, maximum and over-

load stresses,Kmin,KmaxandKOL. More recent experiments have al-

lowed the measurement of crack-tip strains under plane stress

conditions with characteristically larger plastic zones [10,11].

Overload events have been studied at the surface via digital image

correlation[11]and microscopy[7,12]and in the interior, via syn-

chrotron X-ray diffraction[13]. However, the large grain sizes in-

volved in previous studies (50lm) did not allow sufficiently

high resolution strain mapping to resolve the changes occurring

immediately local to the crack-tip. The current work aims to exam-

ine the effect of overload during fatigue crack growth in a bainitic

steel. The attractions of using such a steel are firstly the high frac-

ture toughness which allows high levels of applied DKduring fati-

gue and hence a large plastic-zone, and secondly the very fine grain

size, which allows excellent resolution when mapping the strain

fields around the crack-tip. In the work that we report here, it

has been possible to track the crack-tip strain field in a single sam-

ple at various stages of crack growth past the overload event.

2. Experimental procedure

2.1. Material and specimen

A compact tension (CT) fatigue specimen was machined from

quenched and tempered steel similar to Q1N (HY80) [14]. Its

chemical composition is summarised inTable 1. The tensile prop-

erties are as follows: Yield Stress = 570 MPa and Ultimate Tensile

Stress = 663 MPa. The CT specimen had a width of 62.5 mm and

thickness (B) of 12 mm.

The steel has a typical bainitic microstructure, shown inFig. 1,

with an approximate grain size of 5 lm.

2.2. X-ray diffraction experimental setup

The crack-tip elastic strain fields were measured on beam line

ID15A at the European Synchrotron Radiation Facility (ESRF) inGrenoble, using the same arrangement as that described in [5]as

shown schematically in Fig. 2. The scattering angle was 2h= 5.

The strains were derived by analysing the shifts in the (211) dif-

fraction peak. The incident beam slits were opened to

60 60lm giving a lateral resolution (x,y) of 60 lm and a nominalgauge length through-thickness (z) of around 1.4 mm. This allowed

a 10 times greater resolution than in previous plastic zone map-

ping experiments under plane strain conditions[11]. Such a good

resolution was possible because of the very fine microstructure

of the bainitic steel used here (see Fig. 1), meaning that even at

such small gauge volumes, sufficient number of grains in the gauge

volume contribute to the diffracted signals to allow powder analy-

sis of the diffraction patterns[16].

There are a number of methods for identifying the stress free

lattice parameter, as discussed by Withers et al. [17]. The initial

selection of a stress free lattice parameter far from the crack tip

gave a residual strain of400 106 across the crack faces at Kmax.This may be the result of Poissons ratio effects or plastic anisot-

ropy [18]. Instead a stress-free lattice parameter was chosen so

as to give zero strain across the (open) crack faces at Kmaxfor the

baseline fatigue case (OL 1). It is noteworthy that previous stud-ies have seen similar slightly negative (compressive) strains in the

crack wake[5,6].

Great care was taken throughout the experiment to ensure that

any sample movement during loading toKmaxor unloading toKminwas taken account of. Since the crack-tip lies deep within the bulk

it is not possible to unambiguously determine the crack-tip loca-

tion. For an ideal crack tip stress field it would be a simple matter

to determine the crack position simply from the locationof the sin-gularity. However in reality the crack-tip is not so sharp, in part be-

cause of plasticity, in part because the gauge volume is 60lm wide

and in part because the crack will not be perfectly straight or par-

allel to the z direction noting that the gauge is 1.4 mm long

through thickness. This was studied by cooling the sample to liquid

nitrogen temperature and cracking it open once the XRD experi-

ment was finished. Beach markings indicated that at least for the

OL condition the crack front was essentially straight with around

1 mm difference in length from side to side.

For plane stress the plastic zone, rp, would be expected to be

approximately (DKI/rYS)2/2p= 380 lm or around approximately

(DKI/rYS)2/6p= 120 lm for plane strain (although considerably

smaller along the line of the crack) which is close to the gauge

dimension. From a gauge volume smoothing view point one couldtake the crack-tip to be located at the mid-height of the rising

Table 1

Chemical composition in weight % of Q1N steel. The balance is Fe.

Alloy C Si Mn P S Cr Ni Mo Cu

Q1N 0.16 0.25 0.31 0.010 0.008 1.42 2.71 0.41 0.10

Fig. 1. Optical micrograph of the bainitic steel used in the current work. The

micrograph was obtained at 1000X magnification.

Fig. 2. Schematic of the diffraction geometryshowinga CT specimen with the crack

plane horizontal, andthe two detectors measuring two directions of strain; note the

coordinate system forexx andeyyadopted after[5]. Given that h = 2.5, these strains

can be taken as representative of those in the loading (y) and crack growth (x)

directions.

12 P. Lopez-Crespo et al. / International Journal of Fatigue 71 (2015) 1116


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elastic strain curve. Here we have takenthe crack-tip to lie near the

top of the elastic strain response which is possibly around rp in

advance of the actual crack-tip position.

2.3. Fatigue experiment

The specimen was fatigue pre-cracked for 43,000 cycles at a fre-

quency of 10 Hz and stress intensity range DK= 28 MPapm andload ratio Kmin/Kmax= 0.05. Plane strain conditions were met at

the mid-plane through the thickness for all loads applied during

the experiment[19]. The crack length was measured perpendicu-

larly to the loading direction from the centre of the loading holes

[15]. Once the fatigue crack had grown to a length of 12.75 mm,

a 100% overload (OL) was applied. Strain measurements were

made on a number of occasions, namely, during the cycle immedi-

ately before the overload (OL 1); during the overload (OL); 20 cy-cles after the overload (OL + 20); 1000 cycles after the overload

(OL + 1000); 11,000 cycles after the overload (OL + 11,000); and

21,000 cycles after the overload (OL + 21,000). By measuring

around 50 strain points along the crack plane (y= 0), a profile of

the strain evolution behind and ahead of the crack-tip was pro-

duced for each of the stages of fatigue crack growth.

3. Results and discussion

Historically, it has been the practice to correlate long fatigue

crack propagation with a single fracture mechanics parameter

based on the applied range of stress intensity factor. As an engi-

neering approximation for constant amplitude loading this has

served engineers well for more than half a century. In the presence

of overloads, and cycles of varying amplitude, the correlations

breakdown as process of crack growth is more complex than sim-

ply described by the range of the elastic crack tip displacements.

The elegant work by Liu and others [20,21] clearly show the

non-linear relationship between external load and crack tip

displacements.The traditional approach to modifying the stress intensity factor

crack in the presence of closure is to define the level at which the

crack faces touch, represented by Kcl, and contrive an effective

range ofDK. This is often identified by a knee in the crack compli-

ance during unloading from Kmax, as recorded by a back-face strain

gauge[22]or by DIC[23]. A recent, and more promising, approach

has been proposed by James and co-workers [24] in which they use

four parameters to capture the different influences on the crack tip

stress field. The important feature of this work is the separation of

a retardation parameter, governed by the plastic enclave, from the

conventional elastic opening terms of the field.

To investigate the manner in which the crack-tip strain field

varies with unloading a series of measurements were made during

an unloading cycle (Kmax, 0.7Kmax, 0.2Kmax, Kmin) and the results areshown in Fig. 3a. Furthermore the changes in elastic strain through

the loading cycle are shown inFig. 3b with reference to the strains

at Kmin and compared directly with those expected for linear elastic

fracture mechanics:

eyyx KIffiffiffiffiffiffiffiffiffi2px

p 1 2t1 tE

where t is Poissons ratio, Eis Youngs modulus andxis the distance

along the crack line as shown in Fig. 2.FromFig. 3b it is clear that

the strains increase in accordance with linear elastic fracture

mechanics fromKminexcept in the immediate vicinity of the crack

tip where the linear elastic curve becomes singular while yielding

limits the elastic strains achieved in practice. The maximum elastic

strain is consistent with a multi-axial stress around (1650 MPa,1650 MPa, 990 MPa) suggesting multiaxial yielding at around

660 MPa (under the Tresca yield criterion) which is close to the

UTS for uniaxial loading. The plastic zone radius appears to bearound 100 lm along the x direction, in accordance with

predictions.

From these measurements it is clear that compressive stresses

have started to develop by the time the load has fallen to 0.2Kmax.

Although this compressive trough is normally depicted in terms of

stresses [25,26], it is common to represent it in terms of strain

when experiments are performed with XRD[11,27]. Indeed the

compressive zone appears to increase only marginally both in

terms of depth and extent with further unloading to Kminalthough

the peak tensile strain ahead of the crack at the edge of the plastic

zone continues to fall to a value of around 400 106 atKminlo-cated approximately 250 lm ahead of the crack tip. Very similar

behaviour has been observed in the region of the crack tip by Croft

et al.[7]. While it is difficult to ensure completely faithful registrybetween scans atKmaxandKmin, in both their work and our work

the compressive zone appears to span the crack-tip in our case

spanning a distance of around -360 lm. Of course stress equilib-

rium requires stress balance across thexz plane at zero load. At

Kmin the essentially residual stresses along the centreline (z= 0,

y= 0) do not appear to balance; the tensile residual stresses ahead

of the crack being larger than the compressive stresses in the vicin-

ity of the crack. That might suggest that crack is being held open

somewhat at the mid-plane (z= 0) by the material towards the sur-

faces of the CT specimen.

Fig. 4shows the evolution in the strain field in the crack open-

ing direction along the crack plane (y= 0) at mid-thickness (z= 0)

both at maximum and minimum loading as the sample undergoes

the overload event (at x = 0) and then as the crack grows past it.The peak tensile strain at overload is around 4750 106 which

-2 0 2 4 6

Distance from Crack-tip (mm)

-1000

0

1000

2000

3000

4000

Elasticstrain(10-

6) Kmax

0.7Kmax

0.2Kmax

Kmin

5000

8

-2 0 2 4 6

Distance from Crack-tip (mm)

8

-1000

0

1000

2000

3000

4000

Realativeelasticstrain(10-6)

5000

Kmax

0.7Kmax

0.2Kmax

Fig. 3. (a) The variation in the crack opening elastic strain measured mid-thickness

(z= 0)along the crack plane (y = 0) as the sample was unloaded from Kmaxto Kminat

OL 1 (1 cycle prior to overload), and (b)the change in elastic strainrelative to Kmincompared to the ideal elastic crack-tip response (dashed lines). Note that the crack-

tiplocation (x= 0) wastakento be the pointof maximumtensile strainand so could

berp (60120 lm) ahead of the actual crack tip position.

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represents a triaxial stress of around (1780 MPa, 1780 MPa,

1070 MPa) which is equivalent to mutli-axial yield at a level

around 710 MPa. It is clear that very little crack growth has takenplace after 20 and 1000 cycles, since in each case the tensile crack-

tip stress field is located at approximately the same location as for

the OL curve. After 10,000 additional cycles the crack has pro-

gressed around 300 lm while after an additional 20,000 cycles

the crack has progressed 1070 lm beyond the overload event. It

should be noted that during the loading cycles the CT sample

moves slightly in response to the applied load, however we have

tried to correct for movement in both the crack growth direction

(x) and perpendicular to it (y). Given the overload the broad and

shallow residual compressive residual stress at the crack at Kminat OL is surprising and may be because the scan line just misses

the actual crack tip location. For cycles (OL + 20 and OL + 1000) it

is clear that at Kmin there is an extensive compressive trough at

the crack location arising from the OL. This has the effect ofdepressing the tensile peak at Kmax compared to that just before

the overload (OL 1). With the crack having moved away fromthe OL location there is clear evidence of a compressive stress

(compression across the crack faces) at the OL location (x= 0) for

OL + 11,000 atKminand limited evidence of crack face compression

at OL + 21,000 as observed by Croft et al. for plane stress[7]. The

low level tensile strains (


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the synchrotron beam both vertically (y) and horizontally (x).

While great care was taken to ensure that the linescans were accu-

rately aligned with the crack tip, it is possible these differences in

the location and extent of the compressive zone are due to slight

differences in the locations of the linescans and 2D strain maps

are currently being acquired [11] to check this. Besides the changes

in the immediate vicinity of the crack tip, the compressive contact

stresses in the region of the crack tip at overload atKminare clearly

evident in Fig. 6 as positive peaks in the KmaxKmin curves for

OL + 11,000 and OL + 21,000. These compressive stresses appearto hold open the crack reducing the extent of the excursion in

elastic strain at the crack tip by 30% for OL + 11,000 and to a lesser

extent (25%) for OL + 21,000. Of course it is possible that compres-

sive stresses also arise behind the crack after 20 and 1000 cycles

but as is clear fromFig. 5b they are much less extensive.

The effect of the overload is studied in Fig. 7 in terms of the var-

iation in the maximum strain excursion (i.e. the maximum strain

difference betweenKmaxand Kmincurves inFig. 4), the maximum

tensile strain and the maximum compressive strain as a function

of crack growth past the OL crack tip location. It is clear that the

OL modifies the strain curve for each fatigue stage. Both maximum

compression and maximum tensile strain show a similar trend.

Similar trends were found in 4140 steel specimens also subjected

to 100% OL[12]. However further experiments are required to cor-

relate them with crack growth rates. Before the OL the compressive

zone peaks at 300 106 and deepens to1500 106 twentycycles after overload. It then falls back to the baseline fatigue value

(

300

106) by the time the crack has grown

1 mm beyond

the overload event (OL + 21,000). One of the most accepted theo-ries is that the effect of the OL extends for a length equal to the size

of the plastic zone [11,28,29], however the compressive zone here

(closure plus plastic zone) is considerably smaller along x, being

around 600lm.It is also worth noticing the striking resemblance between Fig. 7

and crack growth curves (see for exampleFig. 1in[7]), suggestive

of a relation between maximum compressive strain at Kmin or max-

imum tensile strain atKmaxand crack growth data while the crack

grows through the OL plastically affected zone. The increase in the

compressive strain at Kmin after OL is probably because of the in-

crease in plastic (stretch) deformation in the increased plastic zone

ahead of the crack rather than crack closure. The OL also increases

the crack opening thus promoting a decrease in crack face closure

behind the crack-tip as the faces come together on unloading.Whilst the four parameter stress field model of James et al.[24]

has yet to be applied to synchrotron data, it is clear from our work

that there would be value in doing so. The dramatic changes ob-

served in the strain field data after the OL event will provide valu-

able insight into the role of the changing retardation and shear

stress parameters on fatigue crack propagation.

4. Conclusions

Using very high spatial resolutions (60 lm inx,y) we have been

able to explore the elastic strains in the crack opening direction e

(x,y= 0), in the vicinity of a fatigue crack before and after an over-

load event. We have followed the crack until it is 1 mm beyond theoverload location. Unlike most of the work to date, the crack-tip

Fig. 5. Strain evolution mid-thickness along the crack plane at (a)Kmaxand (b)Kminfor all the stages of fatigue crack growth analysed. The coordinate along the crack

plane (horizontal axis) has been shifted so that the crack-tip positions coincide for

all cases.

Fig. 6. Plots showing the change in elastic strain between Kmax and Kmin as afunction of number of cycles, i.e.KmaxKmincurve.The dashed lines show the ideally

elastic curves.

-2000

-1000

0

1000

2000

3000

4000

5000

6000

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Distance from the OL (mm)

Relative

elasticstrain(10-6)

Max excursion

Max tensile

Max compression

Fig. 7. Maximum strain excursion (i.e. maximum strain difference betweenKmaxand Kmin curves in Fig. 4), maximum tensile strain and maximum compressive

strain as a function of crack growth from the OL location. The second data point for

each curve represents the OL.

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measuring overload effects during fatigue crack growth in bainitic steel

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