The mechanics of crystalline aggregate deformations

Abstract

The homogeneous plastic distortion of an aggregate of face-centered cubic crystalline grains is examined theoretically using a hypothetical model similar in many respects to that considered earlier by G. I. Taylor. Both continuity and equilibrium demands are, however, fully satisfied in the present model in contrast with that of Taylor's which explicitly accounts only for continuity. In particular, each grain is assumed to take up the average stress and deformation of the entire aggregate. Physical considerations, together with the neglect of elasticity, are then shown to restrict the crystallographic shearings within the individual grains to make the entire grain deformation instead of just the strain portion as assumed in the Taylor theory. Yield strengths are calculated for the case of polycrystalline tubes subjected to combined tension and torsion loadings, and these are shown to be about 10 per cent greater than actual experimental measurements. The difference is concluded to be due primarily to the additional constraints imposed by the assumed homogeneous inelastic deformation.