Neutron and X-ray Microbeam Diffraction Studies arounda Fatigue-Crack Tip after Overload

S.Y. LEE, R.I. BARABASH, J.-S. CHUNG, P.K. LIAW, H. CHOO, Y. SUN, C. FAN, L. LI,D.W. BROWN, and G.E. ICE

An in-situ neutron diffraction technique was used to investigate the lattice-strain distributionsand plastic deformation around a crack tip after overload. The lattice-strain profiles around acrack tip were measured as a function of the applied load during the tensile loading cycles afteroverload. Dislocation densities calculated from the diffraction peak broadening were presentedas a function of the distance from the crack tip. Furthermore, the crystallographic orientationvariations were examined near a crack tip using polychromatic X-ray microdiffraction com-bined with differential aperture microscopy. Crystallographic tilts are considerably observedbeneath the surface around a crack tip, and these are consistent with the high dislocationdensities near the crack tip measured by neutron peak broadening.

DOI: 10.1007/s11661-008-9606-2� The Minerals, Metals & Materials Society and ASM International 2008

I. INTRODUCTION

THE accurate understanding of the micromechanismfor the load-interaction effects during fatigue crackgrowth is essential for the damage tolerance design andthe development of the lifetime prediction model. Oneaspect that is still not fully understood is the overloadeffect and crack closure behavior in the structuralmaterials subjected to cyclic loading. A variety of crackclosure measurements have been used to investigate thecrack growth retardation mechanisms for structuralmaterials.[1–9] However, the various closure measure-ments between the surface and bulk resulted in differentclosure levels.[10] In addition, due to a lack of experi-mental capabilities to measure strain/stress fields withinthe bulk under the applied load, the relationship

between overload and retardation has not been quan-titatively established.Recently, a neutron-diffraction measurement was

performed to probe the crack closure phenomena afteran overload during fatigue crack growth.[11,12] The deeppenetration capability of neutrons enables the nonde-structive studies of the bulk crack closure behavior ascompared to the surface crack closure phenomenaobserved using strain gauge.[4] Furthermore, the changesin internal strains can be measured in situ under theapplied load using the load frame as a function ofthe distance from the crack tip. At the same time, thedislocation density can be carried out from the diffrac-tion peak profile analyses.[13–15] On the other hand,polychromatic X-ray microdiffraction is an emergingtool for studying mesoscale structure and dynamics inmaterials. From the polychromatic methods combinedwith differential aperture X-ray microscopy,[16] the localcrystal phase, orientation (texture), and local defectdistribution including elastic and plastic strain can bedetermined.[17,18]

In this study, the evolutions of elastic-lattice strainsaround a crack tip were investigated as a function of theapplied load during tensile loading cycles immediatelyafter overload using in-situ neutron diffraction. Thecrack opening load was determined by neutron diffrac-tion. The dislocation density distributions around acrack tip were estimated from the diffraction peakbroadening. Moreover, the local lattice orientationvariations near a crack tip were examined using poly-chromatic X-ray microdiffraction.

II. EXPERIMENTAL PROCEDURES

A compact-tension (CT) specimen of a type 316nitrogen-added stainless steel was used for the fatiguecrack propagation experiment, as shown in Figure 1.

S.Y. LEE, Y. SUN, and L. LI, Graduate Research Assistants, P.K.LIAW, Professor and Ivan Racheff Chair of Excellence, and C. FAN,Research Professor, are with the Department of Materials Science andEngineering, The University of Tennessee, TN 37996. Contact e-mail:slee40@utk.edu R.I. BARABASH, Research Professor, is with theMaterials Science and Technology Division, Oak Ridge NationalLaboratory, Oak Ridge, TN 37831, and the Center for MaterialsProcessing, The University of Tennessee, Knoxville. J.-S. CHUNG,Associate Professor and Department Head, is with the Department ofPhysics, Soongsil University, Seoul 156-743, Republic of Korea andthe Materials Science and Technology Division, Oak Ridge NationalLaboratory. H. CHOO, Associate Professor, is with the Department ofMaterials Science and Engineering, The University of Tennessee, andthe Materials Science and Technology Division, Oak Ridge NationalLaboratory. D.W. BROWN, Instrument Scientist, is with the LosAlamos Neutron Science Center, Los Alamos National Laboratory,Los Alamos, NM 87545. G.E. ICE, Group Leader and CorporateFellow, is with the Materials Science and Technology Division, OakRidge National Laboratory.

This article is based on a presentation given in the symposiumentitled ‘‘Neutron and X-Ray Studies for Probing Materials Behav-ior,’’ which occurred during the TMS Spring Meeting in New Orleans,LA, March 9–13, 2008, under the auspices of the National ScienceFoundation, TMS, the TMS Structural Materials Division, and theTMS Advanced Characterization, Testing, and Simulation Committee.

Article published online August 5, 2008

3164—VOLUME 39A, DECEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A

The specimens were prepared according to the AmericanSociety for Testing and Materials (ASTM) standardE647-99.[19] The crack growth experiments were per-formed under a constant-load-range-control mode witha frequency of 10 Hz and a load ratio, R, of 0.1(R = Pmin/Pmax, Pmin and Pmax are the applied mini-mum (988 N) and maximum (9880 N) loads, respec-tively). The crack length was measured by thecompliance method using the crack-opening-displacementgauge. The stress-intensity factor, K, was obtained:[20]

K ¼ Pð2þ aÞBffiffiffiffiffi

Wpð1� aÞ3=2

� ð0:886þ 4:64a� 13:32a2 þ 14:72a3 � 5:6a4Þ½1�

where P = applied load, B = thickness, W = width,a = a/W, a = crack length for a CT specimen, andDK = Kmax – Kmin (Kmax and Kmin are the maximumand minimum stress-intensity factors, respectively).When the crack length reaches 15.3 mm, a single tensileoverload, 13,189 N, which is 133 pct of Pmax, is applied.After the overload was imposed, the fatigue crackretardation period was observed, as presented inFigure 2.

In-situ neutron diffraction measurements were con-ducted on the Spectrometer for Materials Research atTemperature and Stress (SMARTS)[21] at the LosAlamos Neutron Science Center (LANSCE). The spec-imens were aligned 45 deg from the incident neutronbeam, which is the continuous energy spectrum. Theentire diffraction pattern was recorded in two stationarydetector banks with diffraction angle 2h = ±90 deg.Thus, the diffraction vectors were parallel to the in-plane(IP) and through-thickness (TT) directions of thespecimen. The incident beam was defined by 2-mmhorizontal and 1-mm vertical slits, and the diffractedbeams were collimated by 2-mm radial collimators,resulting in a 4-mm3 scattering volume. The lattice

parameters were obtained using the Rietveld refine-ment[22] in the General Structure Analysis System(GSAS),[23] and the lattice strains were calculated bythe changes in the lattice parameter, a, at differentapplied loads during tensile loading and unloadingcycles with respect to the stress-free reference latticeparameter, a0, measured away from the crack tip, asshown in the following equation:

e ¼ a� a0a0

½2�

Spatially-resolved strain mapping was performed duringthe tensile loading cycle immediately after overload, asshown in Figure 3. At each load, the 20 diffraction

Fig. 1—Geometry of a CT specimen. Diffraction patterns were mea-sured along the cracking path with a scattering volume of 4 mm3.

Fig. 2—Fatigue-crack-growth rate as a function of the stress-inten-sity-factor range.

Fig. 3—Tensile loading and unloading sequence applied immediatelyafter an overload. At each load point, neutron strain mapping wasperformed as a function of the distance from the crack tip. Notethat the number in the lower graph is a load ratio (e.g., 0.6 meansthat 60 pct of Pmax is applied).

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, DECEMBER 2008—3165

patterns in both IP and TT directions were measured asa function of the distance from the crack tip.

The pseudo-Voigt function is employed to decomposethe Gaussian and Lorentzian peak broadening compo-nent from the single peak fitting in GSAS. The full-widthat half-maximumofGaussian (FWHMG) andLorentzian(FWHML) can be used as an input to calculate therandomly distributed dislocation density and the distancebetween dislocation walls, respectively.[24] As a firstapproximation, the dislocation density is calculated,assuming that dislocation activities for all primary slipsystems are equal. The randomly distributed dislocationdensity (n) is calculated as follows:[15,24]

n � FWHMG � dhklC� bj j

� �2

½3�

where FWHMG is the full-width at half-maximum ofGaussian, dhkl is the d-spacing for each hkl plane, C isthe contrast factor, and b is the Burgers vector.Polychromatic X-ray microdiffraction combined with

differential aperture microscopy was used to study thelocal plastic deformation around a crack tip on thebeamline ID-34-E at the Advanced Photon Source. Afocused 0.5-lm-diameter polychromatic synchrotronbeam penetrates a specimen, and the beam produces aLaue pattern from each subgrain that it intercepts. Witha differential aperture microscopy technique, the depth-resolved three-dimensional crystal orientation distribu-tions were investigated. The surface of the specimen isinclined at 45 deg from the incident beam, and a chargecoupled device area detector is placed at 90 deg relativeto the incident beam.[25] The crystallographic orienta-tion distributions are examined as a function of depth attwo locations near a crack tip after overload, asindicated in Figure 4. Note that z is the TT directionof the specimen.

III. RESULTS AND DISCUSSION

A. Lattice Strain Evolution

The internal strain evolution was investigated withincreasing the applied load near a crack tip after anoverload. The IP lattice strain profiles were measured asa function of the applied load, as shown in Figure 5.After a single tensile overload was imposed, the largecompressive strains were observed within ±3 mm near acrack tip. At 1 mm in front of the crack tip, the largestcompressive strain of -410 le (microstrain) was examined.

Fig. 4—Locations from the crack tip measured by polychromaticX-ray microdiffraction combined with differential aperture microscopy.

Fig. 5—Lattice-strain evolution around a crack tip with an increase in the applied load.

3166—VOLUME 39A, DECEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A

As the distance from the crack tip increases, strainchanges from compressive to tensile. The maximumtensile strain was observed at about 8 mm ahead of thecrack tip. As the applied load increases, it can be notedthat strains behind the crack tip do not change much,while strains in front of the crack tip evolve withincreasing the applied load. When about 0.3 Pmax

(30 pct of maximum load) was applied, all compressivestrains around a crack tip disappeared and became zero.This load value corresponds to the crack opening load.As the load increases from 0.3 Pmax to Pmax, straingradually increases, especially at the region in front ofthe crack tip. At Pmax, the maximum tensile strain of1100 le was observed at 1.5 mm ahead of the crack tip.

Figure 6 presents the lattice strain variations as afunction of the applied load at the specific locationsfrom the crack tip. It should be noted that the loadresponse of lattice strain was dependent on the locationfrom the crack tip. Strains do not change much withincreasing the applied load at the region behind thecrack tip, while strains increase linearly with increasingthe applied load at locations in front of the crack tip.Especially, at 1 mm ahead of the crack tip, the lattice-strain change is the largest and strain changes arediminished, as the distance from the crack tip increases.Note that the lattice-strain change corresponds to theslope of the load ratio vs lattice strain. A slope is steep atthe region behind the crack tip, and it is the lowest at1 mm in front of the crack tip; then it becomes higher, asthe distance from the crack tip increases. A high slopeindicates that the lattice strains do not change muchwith increasing the applied load. In other words, as theapplied load increases, stress is not effectively applied atthe region behind the crack tip and far away from thecrack tip. On the other hand, a low slope means that thelattice strain changes greatly, as the applied loadincreases. Thus, it could be thought that stress issystematically imposed with increasing the applied load

near the location in front of the crack tip, resulting inlarger lattice-strain change and lower slope. As a result,it should be emphasized that the changes of slope atspecific locations from the crack tip correspond exactlyto the stress distributions in front of the crack tip.Various crack closure measurements have been em-

polyed to precisely investigate the crack opening load.[1–10]

Neutron diffraction can be used as a unique tool for thebulk crack closure measurement, which facilitates themeasurements of bulk strain/stress fields around a cracktip under the applied loads. There are several ap-proaches to determine the crack opening load. Thecommon method is to measure the deviation point fromthe linearity in the plot of load (or stress) vs strain. Theother method we proposed is to examine the load valueto remove the compressive lattice strain presented inFigure 6. The fatigue crack should overcome the com-pressive residual strain/stress near a crack tip for thecrack propagation. The load ratio values to remove thecompressive residual strains at various locations fromthe crack tip are indicated in Figure 7. It was found thatthe compressive residual strains were removed with loadvalues of 0.36 Pmax at the crack tip and 0.15 Pmax at3 mm ahead of the crack tip. As a result, 0.36 Pmax isdetermined as the crack opening load right afteroverload, which enables all compressive residual strainsat regions in front of the crack tip as well as the crack-tip position to disappear and become zero.

B. Dislocation Density and Crystallographic Tilt

The dislocation density was measured from Gaussianpeak broadening deconvoluted by a pseudo-Voigt func-tion in GSAS. Figure 8 shows the dislocation densitydistributions along the IP direction as a function of thedistance from the crack tip right after an overload. Forthe grains of (111) orientation, high dislocation densitiesof 10 9 1010 cm-2 are observed within ±3 mm from the

Fig. 6—Lattice-strain change as a function of the applied load at specific locations from the crack tip.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, DECEMBER 2008—3167

crack tip. As the distance from the crack tip increases,the dislocation density decreases tremendously. Notethat the average dislocation density obtained from thebroadening of several hkl diffractions means the ran-domly distributed dislocation density in the gaugevolume investigated. The high dislocation densities ofapproximately 8.5 9 1010 cm-2 are examined near acrack tip, supporting that the overload induced theseverely large plastic deformation at the crack tip. Fromthe dislocation density distribution, the plastic zone sizeoccurring by an overload seems to be approximately5 mm in front of the crack tip.

In order to study the localized plastic deformation onthe submicron scale, polychromatic X-ray microdiffrac-tion was applied to investigate the lattice distortionsbeneath the specimen surface around a crack tip.Figure 9 presents the relative orientation change ofC-axes as compared to the starting point, which is thespecimen surface. The location examined is 200 lm faraway from the crack tip along the y direction (location‘‘a’’ in Figure 4). As the depth increases, the latticedistortions are obviously measured. The crystallo-graphic tilt angle of 0.67 deg was observed at 25 lm

beneath the surface. Figure 10(a) shows that the rota-tion angle changes with increasing the depth at the closelocation from the crack tip (location ‘‘b’’ in Figure 4).As the depth increases, two distinct groups of rotationangles are examined, revealing that another grainappears at 11 lm below the surface. The rotation anglebetween two grains was 32 deg. The rotation angles ofgrains 1 and 2 are shown in Figures 10(b) and (c),respectively. The maximum tilt angles of 0.58 and0.57 deg were observed in grains 1 and 2, respectively.As a result, the crystallographic tilts were significantlyobserved around a crack tip immediately after overloadusing a differential aperture X-ray microscopy tech-nique. It should be noted that severe lattice distortionsmeasured from X-ray microdiffraction are consistentwith the high dislocation densities near the crack tipcalculated from neutron peak broadening.

IV. CONCLUSIONS

A retardation period in the fatigue-crack-growth ratewas observed after overload. From an in-situ neutrondiffraction measurement, the bulk elastic-lattice strainsnear a crack tip were measured as a function of theapplied load. The large compressive residual strainswere observed within ±3 mm near a crack tip right afteroverload. As the applied load increases, strains gradu-ally increase at the region in front of the crack tip.However, strains behind the crack tip do not changemuch with increasing the applied load. From neutronpeak profile analyses, high dislocation densities weremeasured near a crack tip and sharply decreased withincreasing the distance from the crack tip. Moreover, thelocal orientation variations were examined near a cracktip using polychromatic X-ray microdiffraction com-bined with differential aperture microscopy. This revealsthat crystallographic tilts are considerably observedbeneath the surface around a crack tip, which is in goodagreement with high dislocation densities near a cracktip measured by peak profile analyses using neutrondiffraction.

Fig. 7—Crack-opening load at specific locations from the crack tip.

Fig. 8—Dislocation density distributions around a crack tip in theIP direction.

Fig. 9—Change of misorientation at location ‘‘a’’ shown in Fig. 4.

3168—VOLUME 39A, DECEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A

ACKNOWLEDGMENTS

This work is supported by the United States NationalScience Foundation (NSF) International Materials

Institutes (IMI) Program under Contract No. DMR-0231320, with Dr. C. Huber as the program director.This work has benefited from the use of the Los AlamosNeutron Science Center at the Los Alamos NationalLaboratory. This facility is funded by the United StatesDepartment of Energy under Contract No. W-7405-ENG-36. This research is also sponsored, in part, by theDivision of Materials Sciences and Technology, Officeof Basic Energy Sciences, United States Department ofEnergy, under Contract No. DE-AC05-00OR22725with UT–Battelle, LLC. One of the authors (J.-S.Chung) is supported by the Korea Research Founda-tion (Grant No. KRF-2005-005-J01103). Data collec-tion with polychromatic X-ray microdiffraction hasbeen carried out on beamline ID-34-E at the AdvancedPhoton Source (Argonne, IL).

REFERENCES1. D.L. Davidson: Eng. Fract. Mech., 1991, vol. 38, pp. 393–402.2. M. Okayasu, D.L. Chen, and Z.R. Wang: Eng. Fract. Mech., 2006,

vol. 73, pp. 1117–32.3. S.L. Wong, P.E. Bold, M.W. Brown, and R.J. Allen: Fatigue

Fract. Eng. Mater. Struct., 2000, vol. 23, pp. 659–66.4. D.GanandJ.Weertman:Eng.Fract.Mech., 1981, vol. 15, pp. 87–106.5. A. Guvenilir, T.M. Breunig, J.H. Kinney, and S.R. Stock: Acta

Mater., 1997, vol. 45, pp. 1977–87.6. I.R. Wallhead, L. Edwards, and P. Poole: Eng. Fract. Mech., 1998,

vol. 60, pp. 291–302.7. W. Elber: ASTM STP 486, ASTM, Philadelphia, PA, pp. 230–42.8. V.S. Sarma, G. Jaeger, and A. Koethe: Int. J. Fatigue, 2001,

vol. 23, pp. 741–45.9. M. Andersson, C. Persson, and S. Melin: Int. J. Fatigue, 2006,

vol. 28, pp. 1059–68.10. C.K. Clarke and G.C. Cassatt: Eng. Fract. Mech., 1977, vol. 9,

pp. 675–88.11. Y. Sun, H. Choo, P.K. Liaw, Y. Lu, B. Yang, D.W. Brown, and

M.A.M. Bourke: Scripta Mater., 2005, vol. 53, pp. 971–75.12. Y. Sun, K. An, F. Tang, C.R. Hubbard, Y.L. Lu, H. Choo, and

P.K. Liaw: Physica B, 2006, vol. 385, pp. 633–35.13. H. Mughrabi: Acta Metall., 1983, vol. 31, pp. 1367–79.14. T. Ungar, I. Dragomir, A. Revesz, and A. Borbely: J. Appl.

Crystallogr., 1999, vol. 32, pp. 992–1002.15. R. Barabash: Mater. Sci. Eng. A, 2001, vol. 309, pp. 49–54.16. B.C. Larson, W. Yang, G.E. Ice, J.D. Budai, and J.Z. Tischler:

Nature, 2002, vol. 415, pp. 887–90.17. G.E. Ice, B.C. Larson, W. Yang, J.D. Budai, J.Z. Tischler

J.W.L. Pang, R.I. Barabash, and W. Liu: J. Synchrot. Radiat.,2005, vol. 12, pp. 155–62.

18. G.E. Ice, J.W.L. Pang, R.I. Barabash, and Y. Puzyrev: ScriptaMater., 2006, vol. 55, pp. 57–62.

19. ‘‘ASTM Standard E 647-99: Standard Test Method forMeasurement of Fatigue Crack- Growth Rates,’’ ASTM, Phila-delphia, PA, 2000, vol. 03.01, pp. 591–630.

20. S.Y. Lee, Y.L. Lu, P.K. Liaw, H. Choo, S.A. Thompson, J.W. Blust,P.F. Browning, A.K. Bhattacharya, J.M. Aurrecoechea, and D.L.Klarstrom:Mech. Time-Depend. Mater., 2008, vol. 12, pp. 31–44.

21. M.A.M. Bourke, D.C. Dunand, and E. Ustundag: Appl. Phys.Lett., 2002, vol. 74, pp. S1707–S1709.

22. H.M. Rietveld: J. Appl. Crystallogr., 1969, vol. 2, pp. 65–71.23. A.C. Larson and R.B. Von Dreele: ‘‘General Structure Analysis

System,’’ Los Alamos National Laboratory Report LAUR, LosAlamos National Laboratory, Los Alamos, NM, 2004, pp. 86–748.

24. E.-W. Huang, R.I. Barabash, Y.D. Wang, B. Clausen, L. Li, P.K.Liaw, G.E. Ice, Y. Ren, H. Choo, L.M. Pike, and D.L. Klarstrom:Int. J. Plasticity, 2008, vol. 24, pp. 1440–56.

25. G.E. Ice andR.I.Barabash: inDislocations inSolids, F.R.N.Nabarroand J.P.Hirth, eds., Elsevier, 2007, vol. 13, chap. 79, pp. 500–601.

Fig. 10—(a) Change of misorientation at location ‘‘b’’ shown inFig. 4; (b) change of misorientation in grain 1; and (c) change ofmisorientation in grain 2.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, DECEMBER 2008—3169