Neutron and X-ray Microbeam Diffraction Studies around a 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 distributions and plastic deformation around a crack tip after overload. The lattice-strain profiles around a crack tip were measured as a function of the applied load during the tensile loading cycles after overload. Dislocation densities calculated from the diffraction peak broadening were presented as a function of the distance from the crack tip. Furthermore, the crystallographic orientation variations were examined near a crack tip using polychromatic X-ray microdiffraction combined with differential aperture microscopy. Crystallographic tilts are considerably observed beneath the surface around a crack tip, and these are consistent with the high dislocation densities near the crack tip measured by neutron peak broadening. DOI: 10.1007/s11661-008-9606-2 Ó The Minerals, Metals & Materials Society and ASM International 2008
I.
INTRODUCTION
THE accurate understanding of the micromechanism for the load-interaction effects during fatigue crack growth is essential for the damage tolerance design and the development of the lifetime prediction model. One aspect that is still not fully understood is the overload effect and crack closure behavior in the structural materials subjected to cyclic loading. A variety of crack closure measurements have been used to investigate the crack growth retardation mechanisms for structural materials.[1–9] However, the various closure measurements between the surface and bulk resulted in different closure levels.[10] In addition, due to a lack of experimental capabilities to measure strain/stress fields within the bulk under the applied load, the relationship 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 and Engineering, The University of Tennessee, TN 37996. Contact e-mail:
[email protected] R.I. BARABASH, Research Professor, is with the Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, and the Center for Materials Processing, The University of Tennessee, Knoxville. J.-S. CHUNG, Associate Professor and Department Head, is with the Department of Physics, Soongsil University, Seoul 156-743, Republic of Korea and the Materials Science and Technology Division, Oak Ridge National Laboratory. H. CHOO, Associate Professor, is with the Department of Materials Science and Engineering, The University of Tennessee, and the Materials Science and Technology Division, Oak Ridge National Laboratory. D.W. BROWN, Instrument Scientist, is with the Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, NM 87545. G.E. ICE, Group Leader and Corporate Fellow, is with the Materials Science and Technology Division, Oak Ridge National Laboratory. This article is based on a presentation given in the symposium entitled ‘‘Neutron and X-Ray Studies for Probing Materials Behavior,’’ which occurred during the TMS Spring Meeting in New Orleans, LA, March 9–13, 2008, under the auspices of the National Science Foundation, TMS, the TMS Structural Materials Division, and the TMS Advanced Characterization, Testing, and Simulation Committee. Article published online August 5, 2008 3164—VOLUME 39A, DECEMBER 2008
between overload and retardation has not been quantitatively established. Recently, a neutron-diffraction measurement was performed to probe the crack closure phenomena after an overload during fatigue crack growth.[11,12] The deep penetration capability of neutrons enables the nondestructive studies of the bulk crack closure behavior as compared to the surface crack closure phenomena observed using strain gauge.[4] Furthermore, the changes in internal strains can be measured in situ under the applied load using the load frame as a function of the distance from the crack tip. At the same time, the dislocation density can be carried out from the diffraction peak profile analyses.[13–15] On the other hand, polychromatic X-ray microdiffraction is an emerging tool for studying mesoscale structure and dynamics in materials. From the polychromatic methods combined with differential aperture X-ray microscopy,[16] the local crystal phase, orientation (texture), and local defect distribution including elastic and plastic strain can be determined.[17,18] In this study, the evolutions of elastic-lattice strains around a crack tip were investigated as a function of the applied load during tensile loading cycles immediately after overload using in-situ neutron diffraction. The crack opening load was determined by neutron diffraction. The dislocation density distributions around a crack tip were estimated from the diffraction peak broadening. Moreover, the local lattice orientation variations near a crack tip were examined using polychromatic X-ray microdiffraction.
II.
EXPERIMENTAL PROCEDURES
A compact-tension (CT) specimen of a type 316 nitrogen-added stainless steel was used for the fatigue crack propagation experiment, as shown in Figure 1. METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 1—Geometry of a CT specimen. Diffraction patterns were measured along the cracking path with a scattering volume of 4 mm3.
Fig. 2—Fatigue-crack-growth rate as a function of the stress-intensity-factor range.
The specimens were prepared according to the American Society for Testing and Materials (ASTM) standard E647-99.[19] The crack growth experiments were performed under a constant-load-range-control mode with a frequency of 10 Hz and a load ratio, R, of 0.1 (R = Pmin/Pmax, Pmin and Pmax are the applied minimum (988 N) and maximum (9880 N) loads, respectively). The crack length was measured by the compliance method using the crack-opening-displacement gauge. The stress-intensity factor, K, was obtained:[20] Pð2 þ aÞ K ¼ pffiffiffiffiffi B Wð1 aÞ3=2 ð0:886 þ 4:64a 13:32a2 þ 14:72a3 5:6a4 Þ ½1 where P = applied load, B = thickness, W = width, a = a/W, a = crack length for a CT specimen, and DK = Kmax – Kmin (Kmax and Kmin are the maximum and minimum stress-intensity factors, respectively). When the crack length reaches 15.3 mm, a single tensile overload, 13,189 N, which is 133 pct of Pmax, is applied. After the overload was imposed, the fatigue crack retardation period was observed, as presented in Figure 2. In-situ neutron diffraction measurements were conducted on the Spectrometer for Materials Research at Temperature and Stress (SMARTS)[21] at the Los Alamos Neutron Science Center (LANSCE). The specimens were aligned 45 deg from the incident neutron beam, which is the continuous energy spectrum. The entire diffraction pattern was recorded in two stationary detector banks with diffraction angle 2h = ±90 deg. Thus, the diffraction vectors were parallel to the in-plane (IP) and through-thickness (TT) directions of the specimen. The incident beam was defined by 2-mm horizontal and 1-mm vertical slits, and the diffracted beams were collimated by 2-mm radial collimators, resulting in a 4-mm3 scattering volume. The lattice METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 3—Tensile loading and unloading sequence applied immediately after an overload. At each load point, neutron strain mapping was performed as a function of the distance from the crack tip. Note that the number in the lower graph is a load ratio (e.g., 0.6 means that 60 pct of Pmax is applied).
parameters were obtained using the Rietveld refinement[22] in the General Structure Analysis System (GSAS),[23] and the lattice strains were calculated by the changes in the lattice parameter, a, at different applied loads during tensile loading and unloading cycles with respect to the stress-free reference lattice parameter, a0, measured away from the crack tip, as shown in the following equation: a a0 e¼ ½2 a0 Spatially-resolved strain mapping was performed during the tensile loading cycle immediately after overload, as shown in Figure 3. At each load, the 20 diffraction VOLUME 39A, DECEMBER 2008—3165
FWHMG dhkl 2 n C j bj
Fig. 4—Locations from the crack tip measured by polychromatic X-ray microdiffraction combined with differential aperture microscopy.
patterns in both IP and TT directions were measured as a function of the distance from the crack tip. The pseudo-Voigt function is employed to decompose the Gaussian and Lorentzian peak broadening component from the single peak fitting in GSAS. The full-width at half-maximum of Gaussian (FWHMG) and Lorentzian (FWHML) can be used as an input to calculate the randomly distributed dislocation density and the distance between dislocation walls, respectively.[24] As a first approximation, the dislocation density is calculated, assuming that dislocation activities for all primary slip systems are equal. The randomly distributed dislocation density (n) is calculated as follows:[15,24]
½3
where FWHMG is the full-width at half-maximum of Gaussian, dhkl is the d-spacing for each hkl plane, C is the contrast factor, and b is the Burgers vector. Polychromatic X-ray microdiffraction combined with differential aperture microscopy was used to study the local plastic deformation around a crack tip on the beamline ID-34-E at the Advanced Photon Source. A focused 0.5-lm-diameter polychromatic synchrotron beam penetrates a specimen, and the beam produces a Laue pattern from each subgrain that it intercepts. With a differential aperture microscopy technique, the depthresolved three-dimensional crystal orientation distributions were investigated. The surface of the specimen is inclined at 45 deg from the incident beam, and a charge coupled device area detector is placed at 90 deg relative to the incident beam.[25] The crystallographic orientation distributions are examined as a function of depth at two locations near a crack tip after overload, as indicated in Figure 4. Note that z is the TT direction of the specimen.
III.
RESULTS AND DISCUSSION
A. Lattice Strain Evolution The internal strain evolution was investigated with increasing the applied load near a crack tip after an overload. The IP lattice strain profiles were measured as a function of the applied load, as shown in Figure 5. After a single tensile overload was imposed, the large compressive strains were observed within ±3 mm near a crack tip. At 1 mm in front of the crack tip, the largest compressive strain of -410 le (microstrain) was examined.
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, strain changes from compressive to tensile. The maximum tensile strain was observed at about 8 mm ahead of the crack tip. As the applied load increases, it can be noted that strains behind the crack tip do not change much, while strains in front of the crack tip evolve with increasing the applied load. When about 0.3 Pmax (30 pct of maximum load) was applied, all compressive strains 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, strain gradually increases, especially at the region in front of the crack tip. At Pmax, the maximum tensile strain of 1100 le was observed at 1.5 mm ahead of the crack tip. Figure 6 presents the lattice strain variations as a function of the applied load at the specific locations from the crack tip. It should be noted that the load response of lattice strain was dependent on the location from the crack tip. Strains do not change much with increasing the applied load at the region behind the crack tip, while strains increase linearly with increasing the applied load at locations in front of the crack tip. Especially, at 1 mm ahead of the crack tip, the latticestrain change is the largest and strain changes are diminished, as the distance from the crack tip increases. Note that the lattice-strain change corresponds to the slope of the load ratio vs lattice strain. A slope is steep at the region behind the crack tip, and it is the lowest at 1 mm in front of the crack tip; then it becomes higher, as the distance from the crack tip increases. A high slope indicates that the lattice strains do not change much with increasing the applied load. In other words, as the applied load increases, stress is not effectively applied at the region behind the crack tip and far away from the crack tip. On the other hand, a low slope means that the lattice strain changes greatly, as the applied load increases. Thus, it could be thought that stress is systematically imposed with increasing the applied load
near the location in front of the crack tip, resulting in larger lattice-strain change and lower slope. As a result, it should be emphasized that the changes of slope at specific locations from the crack tip correspond exactly to the stress distributions in front of the crack tip. Various crack closure measurements have been empolyed to precisely investigate the crack opening load.[1–10] Neutron diffraction can be used as a unique tool for the bulk crack closure measurement, which facilitates the measurements of bulk strain/stress fields around a crack tip under the applied loads. There are several approaches to determine the crack opening load. The common method is to measure the deviation point from the linearity in the plot of load (or stress) vs strain. The other method we proposed is to examine the load value to remove the compressive lattice strain presented in Figure 6. The fatigue crack should overcome the compressive residual strain/stress near a crack tip for the crack propagation. The load ratio values to remove the compressive residual strains at various locations from the crack tip are indicated in Figure 7. It was found that the compressive residual strains were removed with load values of 0.36 Pmax at the crack tip and 0.15 Pmax at 3 mm ahead of the crack tip. As a result, 0.36 Pmax is determined as the crack opening load right after overload, which enables all compressive residual strains at regions in front of the crack tip as well as the cracktip position to disappear and become zero. B. Dislocation Density and Crystallographic Tilt The dislocation density was measured from Gaussian peak broadening deconvoluted by a pseudo-Voigt function in GSAS. Figure 8 shows the dislocation density distributions along the IP direction as a function of the distance from the crack tip right after an overload. For the grains of (111) orientation, high dislocation densities of 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
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Fig. 7—Crack-opening load at specific locations from the crack tip.
Fig. 9—Change of misorientation at location ‘‘a’’ shown in Fig. 4.
beneath the surface. Figure 10(a) shows that the rotation angle changes with increasing the depth at the close location from the crack tip (location ‘‘b’’ in Figure 4). As the depth increases, two distinct groups of rotation angles are examined, revealing that another grain appears at 11 lm below the surface. The rotation angle between two grains was 32 deg. The rotation angles of grains 1 and 2 are shown in Figures 10(b) and (c), respectively. The maximum tilt angles of 0.58 and 0.57 deg were observed in grains 1 and 2, respectively. As a result, the crystallographic tilts were significantly observed around a crack tip immediately after overload using a differential aperture X-ray microscopy technique. It should be noted that severe lattice distortions measured from X-ray microdiffraction are consistent with the high dislocation densities near the crack tip calculated from neutron peak broadening. Fig. 8—Dislocation density distributions around a crack tip in the IP direction.
crack tip. As the distance from the crack tip increases, the dislocation density decreases tremendously. Note that the average dislocation density obtained from the broadening of several hkl diffractions means the randomly distributed dislocation density in the gauge volume investigated. The high dislocation densities of approximately 8.5 9 1010 cm-2 are examined near a crack tip, supporting that the overload induced the severely large plastic deformation at the crack tip. From the dislocation density distribution, the plastic zone size occurring by an overload seems to be approximately 5 mm in front of the crack tip. In order to study the localized plastic deformation on the submicron scale, polychromatic X-ray microdiffraction was applied to investigate the lattice distortions beneath the specimen surface around a crack tip. Figure 9 presents the relative orientation change of C-axes as compared to the starting point, which is the specimen surface. The location examined is 200 lm far away from the crack tip along the y direction (location ‘‘a’’ in Figure 4). As the depth increases, the lattice distortions are obviously measured. The crystallographic tilt angle of 0.67 deg was observed at 25 lm 3168—VOLUME 39A, DECEMBER 2008
IV.
CONCLUSIONS
A retardation period in the fatigue-crack-growth rate was observed after overload. From an in-situ neutron diffraction measurement, the bulk elastic-lattice strains near a crack tip were measured as a function of the applied load. The large compressive residual strains were observed within ±3 mm near a crack tip right after overload. As the applied load increases, strains gradually increase at the region in front of the crack tip. However, strains behind the crack tip do not change much with increasing the applied load. From neutron peak profile analyses, high dislocation densities were measured near a crack tip and sharply decreased with increasing the distance from the crack tip. Moreover, the local orientation variations were examined near a crack tip using polychromatic X-ray microdiffraction combined with differential aperture microscopy. This reveals that crystallographic tilts are considerably observed beneath the surface around a crack tip, which is in good agreement with high dislocation densities near a crack tip measured by peak profile analyses using neutron diffraction. METALLURGICAL AND MATERIALS TRANSACTIONS A
Institutes (IMI) Program under Contract No. DMR0231320, with Dr. C. Huber as the program director. This work has benefited from the use of the Los Alamos Neutron Science Center at the Los Alamos National Laboratory. This facility is funded by the United States Department of Energy under Contract No. W-7405ENG-36. This research is also sponsored, in part, by the Division of Materials Sciences and Technology, Office of Basic Energy Sciences, United States Department of Energy, under Contract No. DE-AC05-00OR22725 with UT–Battelle, LLC. One of the authors (J.-S. Chung) is supported by the Korea Research Foundation (Grant No. KRF-2005-005-J01103). Data collection with polychromatic X-ray microdiffraction has been carried out on beamline ID-34-E at the Advanced Photon Source (Argonne, IL).
REFERENCES
Fig. 10—(a) Change of misorientation at location ‘‘b’’ shown in Fig. 4; (b) change of misorientation in grain 1; and (c) change of misorientation in grain 2.
ACKNOWLEDGMENTS This work is supported by the United States National Science Foundation (NSF) International Materials
METALLURGICAL AND MATERIALS TRANSACTIONS A
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