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 15
crystal-plasticity analysis. This finding can be attributed
to the aforementioned less pronounced role of the
nonlocal effects in the Model-II analysis.
The crack profile, in Fig. 8c, is more blunted in
comparison to that for Model-I, Fig. 6c. This is another
indication of the less pronounced role of nonlocal
crystal-plasticity effects in the former case.
Above, results shown in Fig. 6 and Fig. 8 were used
to compare the corresponding fields and deformed finite
element meshes from Model-I and Model-II crystalplasticity
analyses at the respective onsets of crack
extension. Therefore, the K I/K I0 values where different
in the two cases. The results shown in Fig. 9a–c are
used to show the effect of nonlocal crystal-plasticity
parameters at the same level of K I/K I0. That is, the
results shown in Fig. 9a–c are obtained using the
Model-I crystal-plasticity analysis at a level of the stress
intensity factor of 1.53 (level of K I/K I0 at which crack
advance begins for the Model-II analysis).
The equivalent plastic strain distribution results
shown in Fig. 9a can be summarized as follows:
1. The deformation band associated with the =60°
slip system broadens as the crack extends. Band
broadening takes place mainly in the direction of
crack extension.
2. The highest plastic strain region remains removed
from the crack tip, while the plastic deformation
band as a whole, expands and increases in
magnitude.
3. The region just ahead of the crack tip is characterized
by low plastic strain values. It appears that the
crack tip is advancing into an elastic region.
The normal, 22, stress contour plot shown in Fig. 9b
indicates that the stress field possesses the same basic
features previously identified in Fig. 6b, Fig. 7b, and
Fig. 8b. The new feature of the stress field shown in
Fig. 9b is the lateral movement of the region of maximum
tensile stress with the crack tip.
The deformed mesh shown in Fig. 9c, as well as the
one shown in Fig. 7c indicate that the crack profile
remains sharp as it advances. Again, no well-defined
deformation bands can be observed.
3.3. Comparison of discrete-dislocation and
crystal-plasticity analyses
A comparison of the corresponding results shown in
Figs. 3–9 suggests that the dislocation/plastic strain
and 22 stress fields as well as distorted finite element
meshes and crack profiles obtained using the discretedislocation
and crystal-plasticity analyses are quite
comparable. Nevertheless, some significant differences
can be identified:
1. the 22 stress fields, which in both analyses consists
of three well defined regions, can be locally very
different due to the ˜ 22 stress contribution in the
discrete-dislocation analysis. This is particularly
pronounced within the two deformation bands emanating
from the crack tip region which contain high
densities of dislocations;
UNCORRECTED PROOF
Fig. 9. (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 normalized stress
intensity factor KI/KI0=1.53 (arrows indicate position of crack tip).