Development And Applications Of Mechanism Based Strain Gradient Plasticity

Recent experiments at the micron scale have repeatedly shown that metallic materials display significant size effect. Classical plasticity theories do not possess internal material lengths and therefore cannot explain the observed size dependence of material behavior. However, there is an impending need to deal with design and manufacturing issues at the level of microns and submicrons. Moreover, to explain the cleavage fracture in ductile materials also needs the development of strain gradient theory. In this paper, some problems of the mechanism-based strain gradient plasticity are researched. The following objectives have been achieved:1. The constitutive relations of MSG flow theory are given, with consideration of the effect of friction stress.2. For the flow theory of MSG plasticity, we developed a finite element formulation which is then used to study the problems of micro-indentation and fracture of static crack. It is established that the flow theory of MSG plasticity as well as deformation theory, agrees very well with the micro-indentation experiments. There is an approximate linear relation between the square of indentation hardness and the inverse of indent depth. The stress level in vicinity of crack tip in MSG plasticity is significantly higher than that in classical plasticity (HRR field). The stress singularity of MSG plasticity is not only larger than HRR field, but also equals to or exceeds the square-root singularity of elastic field. And that singularity is independent of the plastic hardening exponent. The dominance zone size of near-tip field in MSG plasticity is very small and insensitive to the level of the remote applied stress intensity.3. Mode I crack under steady-state growth and plane strain is analyzed employing MSG flow theory. The results show that during crack growth, the normal separation stress will achieve considerably high value within a sensitive zone of strain gradient near the crack tip. The crack tip stress singularity within the dominance zone of MSG plasticity is much stronger, even than elasticity singularity.