Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal

Abstract

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.