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
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D. Columbus, M. Grujicic / Materials Science and Engineering A000 (2001) 000–000
K I/K I0=1.48, the crack extension is characterized by a
high fracture resistance (i.e. K I/K I0 increases sharply
with crack extension).
A comparison of the results shown in Fig. 3a and
Fig. 4a indicates that the density of dislocations on
both slip systems has increased while their activity
remains localized within two broad bands emanating
from the crack tip region.
By comparing the results shown in Fig. 3b and Fig.
4b the following observations can be made:
1. the three 22 stress regions observed at the onset of
crack extension are maintained at higher values of
K I/K I0;
2. due to a large density of dislocations at higher
K I/K I0 values, the dislocations’ effects on the 22
stress field become more pronounced, Fig. 4b;
3. the region of the highest tensile stress ahead of the
crack tip, responsible for crack advance (the region
denoted by the darkest shade of gray), is substantially
reduced at K I/K I0=1.48, Fig. 4b, in comparison
to that at the onset of crack extension, Fig. 3b.
This finding is fully consistent with the results
shown in Fig. 2, which indicate a sharp increase in
K I/K I0. This implies that higher loading is needed to
extend the region of maximum tensile stress ahead
of the crack tip before significant crack extension
can take place.
A comparison of the results shown in Fig. 3c and
Fig. 4c indicates that as loading proceeds the deformation
bands become more developed. As in the case of
Fig. 3c, the position of the crack tip is denoted by an
arrow.
The dislocation structure, a contour plot of the total
normal stress, 22, and the distorted finite element mesh
in the process window at the normalized stress intensity
factor K I/K I0=2.10 are shown in Fig. 5a–c, respectively.
At this level of K I/K I0, the crack extends relatively
easily (i.e. the K I/K I0 versus a curve has a small
slope, Fig. 2).
Comparison of the results shown in Fig. 5a with their
counterparts shown in Fig. 3a and Fig. 4a indicates that
dislocation density increases fairly monotonically with
UNCORRECTED PROOF
Fig. 3. (a) The dislocation structure; (b) the 22 stress contour plot and (c) the deformed finite element mesh for the discrete dislocation analysis
at the onset of crack extension (K I/K I0=1.10, arrows indicate position of crack tip).