It is shown that simple shear can be considered a “near ideal” deformation method for structure and texture formation in metal-working. Equal channel angular extrusion (ECAE) is a special industrial process employed to realize this method. In comparison with traditional metal-working operations, this process has a number of advantages; the most important is that extra-large, strictly uniform and unidirectional deformations can be produced under relatively low pressure and load for massive products. The unusual effects that are observed in both the structure and physical-mechanical properties of various metals and alloys suggest many new applications of the simple shear method in materials synthesis and processing.

Materials processing by simple shear

Overview no. 42 Texture development and strain hardening in rate dependent polycrystals

An analysis of nonuniform and localized deformation in ductile single crystals

Publisher Summary This chapter focuses on micromechanics of crystals and polycrystals. In Section II of the chapter, a brief outline of only some of the important features of the micromechanics of crystalline plasticity is given. The discussion is confined to plastic flow caused by dislocation slip, and face-centered-cubic crystals are used in the examples of dislocation mechanisms. Particular attention is paid to kinematics and to the phenomenology of strain hardening, because these are shown to play dominant roles in macroscopic response. In Section III, constitutive laws for elastic-plastic crystals are developed. The framework draws heavily on Hill's analysis of the mechanics of elasticplastic crystals, but the theory is extended by incorporating the possibility of deviations from the Schmid rule of a critical resolved shear stress for slip. Deviations from the Schmid rule are motivated by micromechanical models for dislocation motion and are shown to lead to deviations from the “normality flow rule” of continuum plasticity. The implications of these “non-Schmid effects” regarding the stability of plastic flow are brought out via some examples of models for kinks bands and shear bands in Section IV. In Section IV some examples of analyses of elastic-plastic deformation in crystals are discussed. The chapter concludes with some suggestions for fruitful research. These involve extensions of the theory to finite-strain rate-dependent polycrystalline models.

Micromechanics of Crystals and Polycrystals

Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials

Preface 1. A historical introduction 2. The kinematics of double slip 3. A general theory of elastoplastic crystals 4. Axial-load experiments and latent hardening in single crystals 5. Analysis of crystals in channel die compression 6. Theoretical connections between crystal and aggregate behaviour 7. Approximate polycrystal models Appendix: the general theory of work-conjugate stress and strain References Index.

Finite Plastic Deformation of Crystalline Solids

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).

Perspectives in the mechanics of elastoplastic crystals

A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f.c.c. crystals and reduces to Taylor's rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.

A Simple Mathematical Theory of Finite Distortional Latent Hardening in Single Crystals

E lastic-plastic constitutive behavior of cubic crystals (and aggregates) at large pressure is investigated taking account of a thermodynamic basis for lattice straining. Particular attention is directed to quasi-static processes in which an explicit Schmid law governing active slip systems is adopted. Connections between a precise normality rule and the pressure-dependence of moduli and critical shear strengths are analyzed and their implications assessed.

Kerry S. Havner

Papers

Finite Plastic Deformation of Crystalline Solids

Perspectives in the mechanics of elastoplastic crystals

A Simple Mathematical Theory of Finite Distortional Latent Hardening in Single Crystals

On the mechanics of crystalline solids

A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity