Thermomechanics and kinetics of generalized second-order phase transitions in inelastic materials. Application to ductile fracture
type: Item
instance of: scholarly article
title: Thermomechanics and kinetics of generalized second-order phase transitions in inelastic materials. Application to ductile fracture
zbMATH Open document ID: 0964.74042
DOI: 10.1016/S0093-6413(98)00056-1
published in: Mechanics Research Communications
publication date: 2000-09-25T00:00:00Z
review text: 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 …
Mathematics Subject Classification ID: 74N20
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74R20
zbMATH DE Number: 1445954
zbMATH Keywords: generalized second-order phase transitions
zbMATH Keywords: ductile fracture
zbMATH Keywords: first-order phase transformations
zbMATH Keywords: order parameter
zbMATH Keywords: internal dimensionless time
zbMATH Keywords: second law of thermodynamics
zbMATH Keywords: Clausius-Duhem inequality
zbMATH Keywords: dissipative forces
zbMATH Keywords: dissipative rates
zbMATH Keywords: kinetic equation
zbMATH Keywords: averaging of thermodynamical parameters
zbMATH Keywords: entropy balance equation
zbMATH Keywords: temperature evolution equation
zbMATH Keywords: crack nucleation
zbMATH Keywords: elasto-perfectly plastic materials
author: Valery I. Levitas
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
Wikidata QID: Q126989513
description: scientific article; zbMATH DE number 1445954