A comparative discrete-dislocation/nonlocal crystal-plasticity

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typeset2:/sco3/jobs1/ELSEVIER/msa/week.17/Pmsa15088y.001 Wed May 16 07:53:37 2001 Page Wed 12 D. Columbus, M. Grujicic / Materials Science and Engineering A000 (2001) 000–000 The results shown in Fig. 6a indicate that plastic deformation is localized into two deformation bands, emanating from the region surrounding the crack tip. The deformation band associated with the =60° slip system is more developed and contains the region of highest equivalent plastic strain. This finding is consistent with the dislocation structure at a comparable K I/K I0 level, Fig. 3a. The contour plot of the 22 stress shown in Fig. 6b indicates that the stress field around the crack tip is partitioned into three regions, each characterized by a different level of average stress. The region ahead of the Fig. 5. (a) The dislocation structure; (b) the 22 stress contour plot and (c) the deformed finite element mesh for the discrete dislocation analysis at the normalized stress intensity factor K I/K I0=2.10 (arrows indicate position of crack tip). Table 2 Material parameters used in the nonlocal crystal-plasticity analyses (Model-I and Model-II) Parameter Symbol Units Magnitude (Model-I) Magnitude (Model-II) Equation where used s 0.001 0.010 −1 Reference plastic shearing rate 0 Eq. (20) Material rate sensitivity parameter m N/A 0.01 0.01 Eq. (20) Initial local slip resistance sS,0 MPa 11.0 11.0 Eq. (23) Latent hardening parameter ql N/A 1.4 1.4 Eq. (25) Initial local hardening rate h MPa 380 100 0 Eq. (26) Local saturation slip resistance s MPa 1 160 160 Eq. (26) Local hardening exponent r N/A 1.2 1.2 Eq. (27) Ashby’s constant c N/A 0.3 0.3 Eq. (28) Interaction coefficient a11=a 22 N/A 0.45 0.20 Eq. (29) Interaction coefficient a12=a 21 N/A 0.45 0.20 Eq. (29) UNCORRECTED PROOF
typeset2:/sco3/jobs1/ELSEVIER/msa/week.17/Pmsa15088y.001 Wed May 16 07:53:37 2001 Page Wed D. Columbus, M. Grujicic / Materials Science and Engineering A000 (2001) 000–000 13 Fig. 6. (a) The equivalent plastic strain contour plot; (b) the 22 stress contour plot and (c) the deformed finite element mesh for the nonlocal crystal plasticity (Model-I) analysis at the onset of crack extension (K I/K I0=1.18, arrows indicate position of crack tip). addition, the stress levels in the corresponding three regions are comparable for the two types of analyses. A comparison of the distorted finite element mesh resulting from the crystal-plasticity analysis, Fig. 6c, with the corresponding mesh resulting from the discrete-dislocation analysis, Fig. 3c, indicates very similar crack profiles in the two cases. However, the deformation bands observed in Fig. 3c, can not be readily identified in Fig. 6c. To show the role of the nonlocal crystal-plasticity phenomenon on mode I crack growth behavior, the equivalent plastic strain, the normal, 22, stress contour plot, and the distorted mesh obtained from a crystal-plasticity analysis based on Model-I parameters, but with the nonlocal parameters (c, a0 and a1) turned off, at the same level of stress intensity factor as in Fig. 6a–c (KI/KI0= 1.18), are shown in Fig. 7a–c. This analysis is referred to as a local crystal-plasticity analysis. The main differences in the distribution of equivalent plastic strain in local (Fig. 7a) and nonlocal (Fig. 6a) crystal-plasticity analyses can be summarized as follows: 1. higher values of equivalent plastic strain are observed in the local-plasticity case and the highest plastic-strain region is located at the crack tip. In the nonlocal crystal-plasticity case, the highest plastic-strain region is slightly removed from the crack tip; 2. the plastic strain bands, while well formed in both cases, appear to be narrower in the local-plasticity case. A comparison of the local, Fig. 7b, and nonlocal, Fig. 6b, 22 stress distributions indicates that while the distributions are quite similar, ca. 8% higher tensile stress levels are attained in the nonlocal crystal-plasticity case. A comparison of the local, Fig. 7c, and nonlocal, Fig. 6c, deformed finite element meshes indicates significant differences in the crack profile especially near the crack tip. In the local crystal-plasticity case, the crack tip is quite blunted and no crack advance is observed. In sharp contrast, the crack tip is considerably sharp and crack extension is observed in the case of nonlocal crystal plasticity. The equivalent plastic strain, the normalized 22 stress contour plot, and the deformed finite element mesh at the onset of crack extension (KI/KI0=1.53) for the Model-II nonlocal crystal-plasticity analysis are shown in Fig. 8a–c, respectively. A comparison of the equivalent plastic strain distributions obtained using Model-II (Fig. 8a) and Model-I (Fig. 6a) nonlocal crystal-plasticity analyses indicates that higher plastic strain levels are attained in the former case. In addition, the highest plastic strain region in the case of Model-II is located at the crack tip. These findings are consistent with the fact that in order to delay the onset of crack extension in the Model-II UNCORRECTED PROOF crack tip is associated with the highest tensile stress values while the region behind the crack tip contains low-magnitude primarily negative 22 stress values. These observations are fully consistent with the ones made during the discrete-dislocation analysis, Fig. 3b. In
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A comparative discrete-dislocation/nonlocal crystal-plasticity

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