마이크로 / 나노 스케일에서 다결정체의 크기 효과 연구

Abstract

Recent experiments with non-uniform plastic deformation have shown the size effects in micro/nano scale. The mechanism based strain gradient (MSG) 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 macro-scale deformation of the statistically stored dislocation (SSD) and the geometrically necessary dislocation (GND) to meso-scale deformation using the strain gradient. However, MSG plasticity can not predict the size effect for polycrystalline materials because the effect of grain boundary is not considered in the constitutive equation. Objective of this paper is to develop an analytic model of the size effect for the polycrystalline materials in experiments with the strain gradient, such as microbending test and nano-indentation, using modified MSG plasticity. The modified strain gradient plasticity theory is based on the assumption that the polycrystalline materials are nonhomogeneous. In this theory, grains of the materials are associated with the generation of the geometrically necessary dislocations (GNDs) on the boundary during deformation. These GNDs are the basis of the modified strain gradient plasticity theory, which retains the mathematical form of the mechanism-based strain gradient (MSG) plasticity using the GNDs on the grain boundaries and the free surface effect. This model predicts the flow stress in pure tension for polycrystalline materials well.The bending model is proposed using the assumption that the GNDs on the grain boundary are considered in the plastic region only. The proposed bending model can explain the size effect in bending behavior of beams of polycrystalline material by comparison with experimental results.For indentation model, the effect of grain boundary is considered by calculating the GNDs density on the grain boundaries and calculated total density of the GNDs changes with indentation depth. Then, this model can explain both the hardening and softening effects experienced in the polycrystalline materials.The effects of grain size and indenter tip angle on the indentation behavior of Al plate have been studied using the Nano-indentation XP. The hardness measured by cube-corner tip is higher than that of Berkovich tip because of the difference between the densities of GNDs caused by indenter tip angle. This difference caused that higher density of dislocation caused the larger plastic zone. These results agree with the proposed indentation model.