Page 343 - Biaxial Multiaxial Fatigue and Fracture

Variability in Fatigue Lives: An Effect of the Elastic Anisotropy of Grains? 327

anisotropy of the copper crystal (Table 1). The most interesting result is that regular patterns
are found in the calculations. Though the distribution of the local orientations was defined to be
random, the local stress distribution is definitely not random. In uniaxial extension, it was
checked that the direction of the maximum principal stress is close to the vertical axis
everywhere in the sample. However, vertical links appear in the model that sustain higher
stresses. With the same model, if the mean principal stress directions are rotated, the directions
of the links follow the principal stress directions (e.g. see Fig. 5 (b)). This observation is very
similar to previous results obtained with granular media [ 101.

t

V
-.-
Fig. 5. Intensity maps (MPa) of the maximum principal stress component in the case of copper.
(a) uniaxial extension E~ = 0.1 %, (b) shear strain yxy = 0.1 %, (c) biaxial extension E,, = E~ =
0.1 %. The displacements are magnified by a factor 100.

h

Fig. 6. Intensity maps of the maximum principal strain component (in %) in the case of copper.
(a) uniaxial extension E~ = 0.1 %, (b) shear strain yxy = 0.1 %, (c) biaxial extension E,, = E~ =
0.1 %. The displacements are magnified by a factor 100.