ABSTRACT

The Thermodynamics of Irreversible Processes (TPI) applied to the mechanics of materials boomed significantly in France in the 60s and 70s, under the impulse of Paul Germain. The formalization of the Generalized Standard Materials, proposed in 1975 by Bernard Halphen and Quoc-Son Nguyen, corresponds to a now “classical” framework to study thermomechanics of materials, in particular metals. This framework is most often used in an isothermal context in order to derive constitutive and evolution laws from free energy and dissipation potentials. However, the real challenge, which fully justifies TPI, is to study multiphysic couplings where temperature, the first state variable, plays a crucial role.

We will focus here on the first historically studied coupling in this context –thermoelasticity and thermoplasticity – in the case of metallic materials. We discuss the concepts of dissipation, storage and release of energy. Taylor’s pioneering work in the 1930s led to the definition of a ratio often denoted β, which corresponds to the ratio between the amount of energy stored in the material and total plastic work. We will discuss here this ratio under monotonic, cyclic, static or dynamic loadings at the macroscopic or mesoscopic scale by taking up the classical framework derived from TPI (energy balances and heat equation) and by trying to extend it to polycrystals. Some possible extensions to other couplings (chemistry, electromagnetism) will finally be discussed.

 

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