The effects of heterogeneous mechanical properties on the response of a ductile material

We investigate numerically the small-strain, elastic-plastic response of statistically isotropic materials with non-uniform spatial distributions of mechanical properties. The numerical predictions are compared to simple bounds derived analytically. We explore systematically the effects of heterogeneity on the macroscopic stiffness, strength, asymmetry, stability and size dependence. Monte Carlo analyses of the response of statistical volume elements are conducted at different strain triaxiality using computational homogenisation, and allow exploring the macroscopic yield behaviour of the heterogeneous material. We illustrate quantitatively how the pressure-sensitivity of the yield surface of the solid increases with heterogeneity in the elastic response. We use the simple analytical models developed here to derive an approximate scaling law linking the fatigue endurance threshold of metallic alloys to their stiffness, yield strength and tensile strength.