13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- introducing a dependence of plastic deformation (or the FIP) on the grain size. Such a definition can be ambiguous since the ―cross sectional area of the grain‖ differs for each slip plane that cuts through it. For example, the grain size can be computed for each band as the square root of the cross sectional area or as the diameter of a spherical grain with equivalent volume. Figure 6 presents the distributions of the size of the bands (scales as the square root of the number of elements within) and grains (scales as the cubic root of the number of elements within) normalized by the reference grain size ( ref gr d =18µm.); the distributions are clearly different, with the same extreme values but a lower mean value for the band size distribution. In previous work [3][8] we have estimated the fatigue life to nucleate a crack by assuming a proportional dependence of the FIP on the normalized grain size, gr d , (either the size of the band or the diameter of the grains) described by = gr ref gr d A d (5) By multiplying A by the FIP we obtain the normalized driving force = gr ref gr d A FIP FIP d (6) Distributions in Figure 7 present normalized values of A FIP . It is noted that, because the extreme values associated with FIPband do not tend to be associated with the center of grains, the cross sectional dimension of their associated planes is usually smaller than the grain diameter based the cube root of the grain volume. Accordingly, the distributions of band A FIP and grain A FIP are very similar. However, the maximum extreme values of the grain-averaged FIPs are somewhat higher. Figure 6. Distributions of the normalized size of bands (left) and grains (right).
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