Elastic Deformation of Polycrystalline Metal : 2nd Report, Effect of Slenderness of Grains on Deformation Mode

Abstract

Elastic deformation of polycrystalline metal was studied analytically with simplified models of polycrystals. The stress and the strain distributions in a plate having discontinuity of elastic constant were calculated adoping continuum elasticity theory. Both successive approximation method with Fourier series and finite element method were used. The deformation mode of a grain is represented with constraint ratio defined previously. It was found that the deformation mode of polycrystalline metal is affected markedly with the ratio of the width to the length along the stress axis of each grain. When the grain is long enough in the direction of stress axis, the strain becomes nearly constant across the grain. On the other hand, when the grain is flat in shape, the stress is nearly constant. The distribution of constraint ratio or strain across the grain boundary parallel to the stress axis is represented approximately with a sine curve.