Perspectives in the mechanics of elastoplastic crystals

The mechanics of metal crystals at finite strain is reappraised, when crystallographic slip is solely responsible for inelastic deformation. Arbitrary work-conjugate variables are used throughout, together with a slip measure that is unaffected by lattice distortion. The pioneering analysis of R. Hill and J.R. Rice (J. Mech. Phys. Solids20, 401. 1972) is amplified and in part recast. The existence of a plastic potential is proved from a new standpoint, which is believed to be more readily understandable and direct. The effect of lattice strain on slip-system geometry is expressed via an influence tensor ; this has the effect of linking apparently disparate elements of the theory. Subsequently the principal formulae are made explicit in terms of Green's measure of strain, supplemented by equations of transformation to other variables. The unique yield criterion that confers a normality structure is formulated in terms of a generalized Schmid stress, and associated rules of hardening in multislip are detailed. The available experimental data are briefly reviewed, more especially in relation to the ‘simple theory’ of hardening proposed by K.S. Havner and A.H. Shalaby (Proc. R. Soc.A358, 47. 1977).