13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- boundary is released resulting in a significant increase of the crack tip slide displacement and the crack propagation rate. This mechanism yields an oscillating crack growth rate that is characteristic of microstructurally short fatigue cracks. Figure 4. Stage I-crack model with boundary element discretisation. In the plastic zone in front of the crack tip a differentiation between two cases is made, which results in different crack growth mechanisms. In the first case the crack propagates on a slip band and plastic slip occurs on this slip plane, if the resolved shear stress τ reaches the critical value for dislocation motion τ b. In the second case the crack grows on a grain boundary, which does not represent a slip system of the crystal. Therefore, the only way to reduce the stress intensity in front of the crack tip is a plastic deformation inside the neighboring grains leading to a crack tip opening displacement. As the grains at each side of the grain boundary have different orientations, in general it is likely that more than one slip system is activated in each grain in order to ensure a compatible plastic deformation (Fig. 5a). In the model this plastic deformation is projected onto the yield strip on the grain boundary where both a tangential and a normal relative displacement is possible. As the plastic deformation occurs on multiple slip systems in the neighboring grains, the von Mises stress σ m is used as the criterion for plastic deformation (Fig. 5b). Figure. 5. Crack on grain boundary: a) plastic zone around the crack tip and b) yield strip model of the plastic zone.
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