Entropy and temperature of microstructure in crystal plasticity

It has been argued for quite a while that thermodynamics of solids must include two additional thermodynamic parameters, entropy of microstructure and temperature of microstructure. Entropy of microstructure was associated with the phase volume in microstructure phase space. However, the details of this picture for particular microstructures remained vague. This paper suggests an interpretation of microstructure entropy in crystal plasticity when deformation is due to motion of dislocations. In phase space the special states, p−states, are introduced which are local minima of energy for fixed values of dislocation polarization tensor p. Microstructure entropy is logarithm of the number of p−states. It is argued that negative derivative of microstructure entropy describes the rate of slip avalanches. A proposition is made on what should be an ergodic hypothesis for dislocation dynamics. This proposition yields an interpretation of microstructure temperature as an average energy dissipation in slip avalanches. The constitutive equations for internal resistance stresses are given in terms of microstructure entropy.