A study of microindentation hardness tests by mechanism-based strain gradient plasticity

We recently proposed a theory of mechanism-based strain gradient (MSG) plas ticity to account for the size dependence of plastic deformation at micron- and submicron-length scales. The MSG plasticity theory connects micron-sca le plasticity to dislocation theories via a multiscale, hierarchical framew ork linking Taylor's dislocation hardening model to strain gradient plastic ity. Here we show that the theory of MSG plasticity, when used to study mic ro-indentation, indeed reproduces the Linear dependence observed in experim ents, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model. In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformati on in the hierarchical framework.