Constitutive modeling of ratcheting of metal particulate-reinforced ceramic matrix composites

Abstract

Brittle solids fail in compression by a process of progressive microfracture. If subjected to cyclic loading beyond the elastic range with non-zero mean stress, usually there is a cycle by cycle accumulation of inelastic strain related to microfracturing in the direction of mean stress similarly like an accumulation of plastic strain in steels or other metals. This phenomenon is called cyclic creep or ratcheting. In cyclic plasticity there are several models capable to describe ratcheting, among others Armstrong–Frederick model (AF), Chaboche, Ohno/Wang and/or Jiang model. AF model, however, in most situations, overpredicts ratcheting. Within the context of brittle composites reinforced by ductile inclusions one can apply these models for describing the cyclic plasticity of inclusions while matrix remains macroscopically elastic. Using a suitable composite approach a response of representative volume element of composite may be modeled. But even with the AF model we do not get any ratcheting which contradicts to experimental observations. This is due to a strong constraint exerted by matrix on inclusions. It is proposed that the weakening constraint power of the matrix caused by microfracture damage around inclusions can reconcile the model predictions with experiment. It can be easily shown that even under compression loading a local tensile stress field develops around a softer inclusion. The treatment of local stresses makes possible to introduce a microfracture damage by an approximative, self-consistent method. The microfracture damage is closely coupled with the plasticity of inclusions and provides additional inelastic strains. The effect of lateral pressures under multiaxial loading can be straightforwardly included. Numerical results are presented and compared with experimental data.