Constitutive relations of metal crystals at arbitrary strain

At any generic state, the tangent moduli and compliances of a metal crystal are derived in terms of its elastic moduli and compliances, and its physical slip system hardening moduli h_ij. The structure of h_ij is explored in conjunction with a mixed hardening law. It is found that the latent hardening moduli (h_ij, i≠j) are related to the active hardening moduli (h_ij, i+j) through the latent hardening coefficients, and that each active hardening modulus is composed of the selfhardening, single slip modulus h and the latent structural-change hardening moduli h_ij^′. The theory is supplemented with some suggested functions for h and h_ij^′, suitable for metal forming analysis. The derived constitutive relations are finally applied to calculate the tensile stress-strain relations of aluminum and zinc crystals under finite strains.