A modified conventional theory of mechanism-based strain gradient plasticity considering both size and damage effects

The in-service deformation damage cannot be avoided, even for micro-scale metallic materials. To characterize the coupling effect of size and damage in micro-metallic materials, a modified incremental constitutive model is proposed on the basis of the conventional theory of mechanism-based strain gradient plasticity (CMSG), in which the assumptions of both small strain and isotropic damage are adopted. Other than retaining the essential features of the CMSG theory, the in-service deformation damage effects on the elastic moduli, plastic yielding criterion and intrinsic length scale, are well included. Typical micro-scale experimental results, including those from the torsion of thin wires, bending of ultra-thin beams, and tension and compression of micro-particle-reinforced metal matrix composites (MPMMCs), are theoretically analyzed using the new modified theory. Good agreements between the theoretical predictions and the experimental measurements are achieved, especially for the mechanical behaviors of MPMMCs subjected to relatively large deformation. Furthermore, it is interesting to find, upon increasing the uniaxial tension, the dominant damage mode in MPMMCs will transit from interface debonding to matrix damage, while matrix damage is always dominated in MPMMCs under uniaxial compression. In this study, we provide a convenient and precise way to characterize the in-service mechanical behaviors of micro-scale material systems, especially the commonly used composites with a characteristic length scale of micrometers.