Thermomechanics and kinetics of generalized second-order phase transitions in inelastic materials. Application to ductile fracture
This paper is devoted to the study of second-order phase transformations (SOPT) in inelastic solids, named generalized SOPT, which are considered as a particular case of the first-order phase transformations (FOPT) treated earlier by the author [Int. J. Solids and Structures 35, No. 9-10, 855-887 (1998; Zbl 0931.74071)]. The main difficulty is impossibility to use for solids the classical definition of FOPT for liquids, because in the general case neither the Gibbs potential nor its arguments (stress and temperature) are fixed during FOPT. First, the problem for FOPT is formulated in an appropriate form, and the generalized SOPT is defined as a thermomechanical process of change in thermomechanical material properties from initial to final values in some regions at zero transformation strain and transformation entropy. By this, the process cannot be stopped at a material point in the intermediate state. Then an order parameter (internal dimensionless time) is introduced which is related to all variable parameters and describes the start and finish of phase transformation (PT). All variable parameters are included in its definition. The consideration of the second law of thermodynamics in the form of Clausius-Duhem inequality under some assumptions allows to determine the dissipative forces conjugated to dissipative rates, and to derive evolution equations. The kinetic equation is studied only for description of PT. Then, it is shown that in the frame of standard thermodynamical approach the transformation can be stopped at arbitrary instant value of internal dimensionless time, which contradicts the definition of SOPT. Therefore the averaging of thermodynamical parameters over the PT time is necessary. Because the PT takes place in some infinite volume, the author considers the total dissipation rate due to PT in the transforming volume, taking into account the surface energy, and derives conditions for nucleation and interface propagation. To determine all unknown parameters, the obtained kinetic equation is supplemented by the postulate of realizability proposed by the author. This allows to formulate an extremum principle for determination of unknown parameters. Next, a consideration based on the use of entropy balance equation leads to the temperature evolution equation. The author presents some specifications of this equation under concrete conditions. Finally, the theory is applied to the description of fracture, namely to the study of pore and crack nucleation and growth in elastic perfectly plastic materials. To this end, the fracture is defined in a region as a thermomechanical process of change in material properties from initial values to zero. The kinetic equation leads to threshold-type and size-dependent generalization of Arrhenius-type kinetics. The approach suggested in the paper allows to determine the dissipation rate by using the fracture only, and to express it as product of dissipative force and rate. The approach is valid for an arbitrary dissipative materials, because the constitutive equations are not used in the derivation.
generalized second-order phase transitions
scientific article; zbMATH DE number 1445954