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 t erms 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 beta of the rate of plastic work converted into heating. We examine the status of the c ommon assumption that beta is a constant with regard to the thermodynamic f oundations of thermoplasticity and experiments. A general internal-variable theory is introduced and restricted to abide by the second law of thermody namics. Experimentally motivated assumptions reduce this theory to a specia l model of classical thermoplasticity, The only part of the internal energy not determined from the isothermal response is the stored energy of cold w ork, a function only of the internal variables. We show that this function can be inferred from stress and temperature data from a single adiabatic st raining experiment. Experimental data from dynamic Kolsky-bar tests at vari ous strain rates yield a unique stored energy function. Its knowledge is cr ucial for the determination of the thermomechanical response in non-isother mal processes. Such a prediction agrees well with results from dynamic test s at different rates. In these experiments, beta is found to depend strongl y on both strain and strain rate for various engineering materials. The mod el is successful in predicting this dependence. Requiring beta to be consta nt is thus an approximation of dubious validity. (C) 2000 Published by Else vier Science Ltd. All rights reserved.