Henryk Petryk

A procedure for the modelling of microstructural changes induced by non-uniform large plastic deformation of metals is developed. For a given plastic working process, a set of deformation paths for different initial locations of a material element is generated first for a non-hardening material by using the finite element method. Next, changes of a cellular microstructure and related hardening effects along each path are calculated by using a recently proposed model. The procedure is applied to a non-conventional process of cold extrusion assisted by cyclic rotation of the die. The evolution of microstructural parameters, their effect on strain hardening and a distribution map over the specimen cross-section are calculated.

A distinctive feature of the examined class of solids is that a part of the entropy production is due to rate-independent dissipation, as in models of plasticity, damage or martensitic transformations. The standard condition for thermodynamic stability is shown to be too restrictive for such solids and, therefore, an extended condition for stability of equilibrium is developed. The classical thermodynamic theory of irreversible processes is used along with the internal variable approach, with the emphasis on the macroscopic effects of micro-scale instabilities in the presence of two different scales of time. Specific conditions for material stability against internal structural rearrangements under deformation-sensitive loading are derived within the incremental constitutive framework of multi-mode inelasticity. Application to spontaneous formation of deformation bands in a continuum is presented. Conditions for stability or instability of a quasi-static process induced by varying loading are given under additional constitutive postulates of normality and symmetry. As illustration of the theory, the stability of equilibrium or a deformation path under uniaxial tension is analysed for a class of inelastic constitutive laws for a metal crystal deformed plastically by multi-slip or undergoing stress-induced martensitic transformation.