A PHENOMENOLOGICAL MODEL OF TWINNING BASED ON DUAL REFERENCE STRUCTURES

A large class of solids, including certain metals and polymers, when s ubject to significant deformations undergo microstructural changes tha t engender a response that is distinctly different from that before wh ich the microstructural changes occurred. Such microstructural changes usually lead to inelastic response. This paper is devoted to the stud y of one such microstructural change, attributed to deformation induce d twinning. From a macroscopic point of view, within the framework of a general continuum theory originally developed for polymers by Rajago pal and Wineman [1] and modified appropriately to model crystalline ma terials by Rajagopal and Srinivasa [2,3]. In this paper, we elucidate the intricate interplay between the storage and dissipation of energy due to deformation and their influence on the propagation and arrest o f twinning. The onset of twinning is determined purely by energy consi derations. We show that the entire constitutive structure of the mater ial can be reduced to the specification of three scalar functions to m odel ''quasi equilibriated twinning'': the Helmholtz free energy poten tial psi, the rate of dissipation Function xi and the activation funct ion g. For the dynamical case (when inertial effects cannot be ignored ), an additional constitutive function for the kinetic energy associat ed with the process of twinning must be specified. (C) 1998 Acta Metal lurgica Inc.