Multi-axial response of idealized cermets

Abstract

The yield response of two idealized cermets comprising mono and bi-disperse steel spheres in a Sn/Pb solder matrix has been investigated for a range of axisymmetric stress states. Proportional stress path experiments are reported, from which are extracted the initial yield surfaces and their evolution with increasing plastic strain. The initial yield strength is nearly independent of the hydrostatic pressure but the strain hardening rate increases with stress triaxiality up to a critical value. For higher triaxialities, the responses are independent of hydrostatic pressure. Multi-axial measurements along with X-ray tomography were used to demonstrate that the deformation of these idealized cermets occurs by two competing mechanisms: (i) a granular flow mechanism that operates at low levels of triaxiality, where volumetric dilation occurs under compressive stress states, and (ii) a plastically incompressible mechanism that operates at high stress triaxialities. A phenomenological viscoplastic constitutive model that incorporates both deformation mechanisms is presented. While such multi-axial measurements are difficult for commercial cermets with yield strengths on the order of a few GPa, the form of their constitutive relation is expected to be similar to that of the idealized cermets presented here.