A phenomenological model of twinning based on dual reference structures
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abstract
A large class of solids, including certain metals and polymers, when subject to significant deformations undergo microstructural changes that engender a response that is distinctly different from that before which the microstructural changes occurred. Such microstructural changes usually lead to inelastic response. This paper is devoted to the study of one such microstructural change, attributed to deformation induced twinning, from a macroscopic point of view, within the framework of a general continuum theory originally developed for polymers by Rajagopal and Wineman [1] and modified appropriately to model crystalline materials 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 of twinning. The onset of twinning is determined purely by energy considerations. We show that the entire constitutive structure of the material can be reduced to the specification of three scalar functions to model "quasi equilibriated twinning": the Helmholtz free energy potential , the rate of dissipation function and the activation function g. For the dynamical case (when inertial effects cannot be ignored), an additional constitutive function for the kinetic energy associated with the process of twinning must be specified. 1998 Acta Metallurgica Inc.
