Influence of Free Surface on Mutual Restriction between Grains in Elastic Deformation of Polycrystals

Abstract

Elastic deformation of polycrystalline metals under uniaxial loading is investigated by analyzing a model of polycrystals by finite element method. Influence of free surface on deformation behavior of grains and three-dimensional restriction of grains are mainly studied. It was found that the effect of free surface on distribution of stresses, strains or constraint ratios in the stress direction in surface grains is small and confined to a very thin layer near the surface. The stress normal to surface is nearly equal to zero in the surface grain, while the strain or constraint ratio normal to surface changes. There is little effect of free surface on the distribution of stresses, strains and constraint ratios in the inner grains adjacent to the surface grains. Group of grains placed near the surface of polycrystals is found to rotate during deformation. The distribution of constraint ratios in the stress direction in the surface grains is approximately represented with cosine curve as well as that in the interior grain. It is suggested, however, that the mean constraint ratio in the surface grain is about 75-89 % of that in the interior grain, because grains are cut by surface randomly and hence the depth of the surface grains is random. It is also suggested that three-dimensional restriction is nearly double the two-dimensional one.