Inelastic behavior of materials .2. Energetics associated with discontinuous deformation twinning
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Following the recent work of Rajagopal and Srinivasa ("On the inelastic behavior of solids - part I. Twinning," Int. J. Plasticity, 11, 653) on the development of a macroscopic theory to model the inelastic deformation twinning of polycrystals, we provide in this paper a thermomechanical framework for the study, albeit under the assumption that the process is isothermal. A criterion based on energetics is proposed for the initiation and propagation of twinning. The theory is based on the notion of multiple natural configurations which was introduced earlier by Wineman and Rajagopal ("On a constitutive theory for materials undergoing microstructural changes", Arch. Mech., 42, 53) and Rajagopal and Wineman ("A constitutive equation for non-linear solids which undergo deformation induced microstructural changes", Int. J. Plasticity, 8, 385) for the study of the inelastic behavior of polymer networks. In this paper, we bring out the important role played by the dissipative processes on the onset and arrest of twinning. We show that the entire constitutive structure of the material can be reduced to the specification of three scalar functions to model "quasi-equilibriated deformation twinning": the Helmholtz potential , the rate of dissipation function and the activation function g. For the dynamical case (when inertial effects are not negligible), an additional constitutive function for the kinetic energy due to the growth of the twinned regions must be specified. We demonstrate the versatility and the efficacy of the theory by choosing special forms for these functions and applying them to the slow compression of steel at 4.2K. The results agree very well with the experiments of Madhava et al. ("Discontinuous Twinning during essentially elastic compression of steel at 4.2 K", Phil. Mag., 25, 519) We also include a generalization of the theory to account for multiple twin orientations. 1997 Elsevier Science Ltd.
