INELASTIC BEHAVIOR OF MATERIALS .2. ENERGETICS ASSOCIATED WITH DISCONTINUOUS DEFORMATION TWINNING

Following the recent work of Rajagopal and Srinivasa (''On the inelast ic behavior of solids-part I. Twinning,'' Int. J. Plasticity, 11, 653) on the development of a macroscopic theory to model the inelastic def ormation twinning of polycrystals, we provide in this paper a thermome chanical framework for the study, albeit under the assumption that the process is isothermal. A criterion based on energetics is proposed fo r the initiation and propagation of twinning. The theory is based on t he notion of multiple natural configurations which was introduced earl ier by Wineman and Rajagopal (''On a constitutive theory for materials undergoing microstructural changes'', Arch. Mech., 42, 53) and Rajago pal and Wineman (''A constitutive equation for non-linear solids which undergo deformation induced microstructural changes'', Int. J. Plasti city, 8, 385) for the study of the inelastic behavior of polymer netwo rks. In this paper, we bring out the important role played by the diss ipative processes on the onset and arrest of twinning. We show that th e 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 psi, the rate of diss ipation function xi and the activation function g. For the dynamical c ase (when inertial effects are not negligible), an additional constitu tive function for the kinetic energy due to the growth of the twinned regions must be specified. We demonstrate the versatility and the effi cacy of the theory by choosing special forms for these functions and a pplying them to the slow compression of steel at 4.2K. The results agr ee very well with the experiments of Madhava et al. (''Discontinuous T winning during essentially elastic compression of steel at 4.2 K'', Ph il. Mag., 25, 519) We also include a generalization of the theory to a ccount for multiple twin orientations. (C) 1997 Elsevier Science Ltd.