Thermomechanics and kinetics of generalized second-order phase transitions in inelastic materials. Application to ductile fracture

Abstract

A number of simple examples demonstrate the applicability of the general theory developed in Part I of this paper to various structural changes in solids, namely to displacive and generalized second-order phase transformations, twinning and reorientation of crystal lattice, ductile fracture, and strain-induced chemical reactions. The theory is extended to diffusional-displacive phase transitions. The following problems for elastic and elastoplastic materials are solved analytically: displacive and diffusional–displacive phase transitions in a spherical particle inside the space under external pressure, martensitic phase transition and twinning in ellipsoidal inclusion under applied shear stress, spherical void nucleation, crack propagation in a similar framework to the Dugdale model for a plane stress state. In most cases explicit expressions for the thermodynamic and kinetic conditions for structural changes and the geometric parameters of the nucleus are obtained and analyzed. The following typical cases in the determination of the geometric parameters of nucleus are found: solely from the principle of the minimum of transformation time and the kinetic equation without any constraints or with thermodynamic constraint; from the principle of the minimum of transformation mass and the thermodynamic criterion of structural changes (thermodynamically admissible nucleus); as an interatomic distance. For diffusional–displacive phase transformations, additional variants are related to the necessity to consider the diffusion equation (for the diffusion-controlled transformation) and constraints related to the maximum and minimum possible volume fraction of solute atoms. The nucleation kinetics for various nucleus geometries is compared.