A comparative discrete-dislocation/nonlocal crystal-plasticity

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