A Thermodynamic Internal Variable Model for the Partition of Plastic Work into Heat and Stored Energy in Metals
The energy balance equation for elastoplastic solids includes heat source terms that govern the conversion of some of the plastic work into heat. The remainder contributes to the stored energy of cold work due to the creation of crystal defects. This paper is concerned with the fraction β of the rate of plastic work converted into heating. We examine the status of the common assumption that β is a constant with regard to the thermodynamic foundations of thermoplasticity and experiments. A general internal-variable theory is introduced and restricted to abide by the second law of thermodynamics. Experimentally motivated assumptions reduce this theory to a special model of classical thermoplasticity. The only part of the internal energy not determined from the isothermal response is the stored energy of cold work, a function only of the internal variables. We show that this function can be inferred from stress and temperature data from a single adiabatic straining experiment. Experimental data from dynamic Kolsky-bar tests at various strain rates yield a unique stored energy function. Its knowledge is crucial for the determination of the thermomechanical response in non-isothermal processes. Such a prediction agrees well with results from dynamic tests at different rates. In these experiments, β is found to depend strongly on both strain and strain rate for various engineering materials. The model is successful in predicting this dependence. Requiring β to be constant is thus an approximation of dubious validity.
© 2000 Published by Elsevier Science Ltd. Received 10 June 1998; received in revised form 16 June 1999. This work was initiated while P.R. was on leave at the California Institute of Technology; he would like to thank J. K. Knowles and the GALCIT Faculty for their hospitality, also the National Science Foundation for support through Grant MSS-9312858. G.R. and A.J.R. gratefully acknowledge support from the Office of Naval Research (Scientific Officer: Dr Y. D. S. Rajapakse) through Grant N0014-95-1-0453 and the National Science Foundation through Grant CMS-9204026.