Structural changes without stable intermediate state in inelastic material. Part I. General thermomechanical and kinetic approaches

We define a structural change in inelastic material as a thermomechanical process of change in some region of material properties (elastic moduli, heat capacity, thermal expansion coefficient, entropy, yield strength), as well as a transformation strain from initial to final values. This process cannot be stopped at a material point in the intermediate state. Such a definition includes various phase transitions (martensitic, diffusional-displacive and second-order phase transitions), twinning, ductile fracture (nucleation and growth of void and cracks), solid-state chemical reactions, generation of point defects, dislocations, disclinations, deformation of amorphous materials, and so on. A theory suggested represents a generalization of the theory of martensitic phase transformations developed earlier by Levitas [Levitas, V.I., 1998a. Thermomechanical theory of martensitic phase transformations in inelastic materials. Int. J. Solids and Structures 35(9-10), 889-940] and its extension to the above phenomena. The theory includes a nonlocal thermodynamic criterion of structural changes in some finite region, a kinetic equation for the transformation rate (=inverse transformation time) and principle of minimum of transformation time derived for determination of all variable parameters (e.g. shape and volume of transforming region) and is Valid for arbitrary inelastic material. Instead of surface-independent and path-independent integrals, which are an ideal tool for the description of various phenomena in elastic media (e.g. fracture, motion and interaction of various defects and singularities), the theory suggests a region-independent integral which represents a dissipation increment due to the structural change only during the complete structural change in transforming region. In some cases the principle of the minimum of transformation time reduces to the principle of the minimum of transforming mass and the characteristic size of the transforming region (nucleus) is determined either from the thermodynamic criterion of structural changes or is equal to the interatomic distance. A new kinetic concept of a thermodynamically admissible nucleus (void, crack) follows from the theory. A number of examples. related to displacive and diffusional-displacive phase transitions, strain-induced chemical reactions and ductile fracture, are considered in Part II of the paper. (C) 2000 Elsevier Science Ltd. All rights reserved.