Effect of a graded layer on the plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

Prior work by the authors has proposed a dissipated energy theory of fatigue crack growth in ductile solids under mode I loading based on the total plastic dissipation per cycle ahead of the crack. The approach has since been extended to a general bimaterial interface geometry under mixed-mode I/II loading, with application to fatigue debonding of layered materials. An inherent assumption of this prior work is that a perfect crack exists along the interface between the two materials. The current work extends the approach to incorporate a grading of material properties between the two layers, as may occur in a variety of welding, soldering or layered manufacturing applications. Attention is restricted to elastic perfectly-plastic layers with identical elastic properties and a mismatch in yield strength across a linearly graded interface, with the crack on the boundary of the weaker material. A dimensionless plastic dissipation is extracted from 2-D plane strain finite element models over the full range of yield strength mismatches, graded layer thicknesses and mixed-mode loading conditions. Results reveal that for all modes of loading, the effect of a graded layer is to increase the total plastic dissipation per cycle, which is bounded by the extremes in plastic mismatch for a perfect crack interface. While the graded layer has a measurable effect, the plastic dissipation for all strength mismatches is dominated by the mode of loading.