No abstract

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.

We propose and assess a procedure to measure the damage evolution in solids as a function of the applied strain, by conducting stiffness-sensing mechanical tests. These tests consist in superimposing to a monotonically increasing applied strain numerous, low-amplitude unloading/reloading cycles, and extracting the current stiffness of the specimens from the slope of the stress–strain curve in each of the unloading/reloading cycles. The technique is applied to a set of polymeric and metallic solids with a wide range of stiffness, including CFRP laminates loaded through the thickness, epoxy resins, injection-moulded and 3D printed PLA and sintered Ti powders. The tests reveal that, for all the materials tested, damage starts developing at the very early stages of deformation, during what is commonly considered an elastic response. We show that the test method is effective and allows enriching the data extracted from conventional mechanical tests, for potential use in data-driven constitutive models. We also show that the measurements are consistent with the results of acoustic and resistive measurements, and that the method can be used to quantify the viscous response of the materials tested.