A Statistical Methodology of Cyclic Plasticity Inhomogeneity at Grain Scale

The inhomogeneous plastic deformation has important effects on the manufacturing process and the fatigue property of mechanical products. To directly and correctly evaluate the deformation inhomogeneity of grain scale under cyclic loading, a statistical method is proposed and named as the normalized standard deviation. The method is comprised of the following steps: (1) Construct a representative volume element (RVE) of polycrystalline by Voronoi tessellation and electron backscatter diffraction, and calculate the grain strain by a constitutive model of crystal cyclical plasticity. (2) Deal with grain strain data of RVE by Min-max normalization method. (3) Compute the standard deviation of the normalized data as the identification of mesoscopic inhomogeneity. In order to validate the proposed normalized standard deviation, the contrastive analyses with the strain contours, the weighted standard deviation and the coefficient of variation are conducted at the same conditions of cyclic loading. The results demonstrated that the normalized standard deviation was the best as the indication of cyclic plasticity inhomogeneity among the above methods.