A study of micro bending test for polycrystalline by modified strain gradient theory

Abstract

Recent experiments with non-uniform plastic deformation have shown the size effects in micro/nano scale. But the classical continuum plasticity can't predict these size effects in micro/nano scale, since the constitutive equation of the classical mechanics doesn't include the internal length as a parameter for the deformation. The mechanism based strain gradient plasticity is one of the methods to analyze non-uniform deformation behavior in micro/nano scale. The MSG plasticity is the multi-scale analysis connecting the micro-scale notion of the statistically stored dislocations and the geometrically necessary dislocation to meso-scale deformation using the strain gradient. In this paper, modified strain gradient theory is proposed based on the nonhomogeneity of polycrystalline metallic materials and free surface effect. Consideration of the geometrically necessary dislocations on the grain boundary and the free surface effect suggests a relationship between the characteristic length, specimen size and grain size. This relationship can explain the size effects and flow stress in micro/nanoscale structures. We will propose a new model for bending tests using the modified strain gradient plasticity theory. Using the proposed model, bending behavior of polycrystalline materials in micron-scale structures is investigated, and compared with experimental results from other researchers.