On temperature in thermoelastoplasticity

Abstract

Nowadays, the determination of temperature needs often to be treated in the framework of thermoplasticity or thermoviscoplasticity, for example, during metal forming, crashes, … There are still many great difficulties. Some concern the numerical integration of the equations involved; we can say that they are solved reasonably well. Others are more fundamental, and concern the basic constitutive equations and the writing of the thermodynamical equations; they still belong to unsolved problems. Recently, many papers have been published in this area (for ex. [P. Germain, E.H. Lee, in: A. Sawczuk (Ed.), Problems of Plasticity, Noorthoff Int. Publ., 1974. [14]] and [D. Rittel, Z.G. Wang, M. Merzer, Adiabatic shear failure and dynamic stored energy of cold work, Phys. Rev. Lett. 96 (7) (2006) 075502. [18]]); we have thought that it would be useful to discuss our old paper that appeared, in French, in the Journal Archives of Mechanics 26 (4) (1974) 701–715, and to underline what our contributions were at that time: (i) on a possible definition of the homogenized temperature of an aggregate (polycrystals or composites); (ii) on a possible interpretation of the occurrence of ‘adiabatic bands’ by considering only the influence of temperature, for ex. [A. Baltov, T. Vinh, C. R. Acad. Sci. Paris Sér. A 291 (1972) 275. [13]] and [D. Rittel, Z.G. Wang, M. Merzer, Adiabatic shear failure and dynamic stored energy of cold work, Phys. Rev. Lett. 96 (7) (2006) 075502. [18]]. For this, with the help of a physical microscopical model, we have explained where some energy could be stored in the aggregate, and we have shown that only in the case of elastic and thermal isotropy, were we able to defined its temperature T, as the mean of the local temperature θ, of its constituents. Then we wrote the thermodynamical equations (assuming small perturbations) for various hypotheses: isothermic, adiabatic or general heat condition. Finally, we analyzed a simple rod that is subjected to a quasi-static loading at a constant strain rate and then, when the rod is dynamically loaded as during the Taylor test i.e. during the impact of the rod on a rigid wall. We have shown that there is a non-constant ratio between the plastic power and the stored power and that there was no concentration (adiabatic band), while taking into account the influence of the temperature in the equations. To cite this article: W.K. Nowacki, J. Zarka, C. R. Mecanique 336 (2008).