Consistency for two multi-mechanism models in isothermal plasticity

Abstract

A new class of constitutive equations (the multi-mechanism models) devoted to the prediction of ratcheting and of complex material behavior, for instance of steel, has developed during the last years. The main difference between these models and the “Chaboche” type models is the representation of different mechanisms of plastic strain with a possible interaction between them. This sophistication has a cost related to the complexity to understand well how the various parameters act. The identification process thus becomes more difficult as it will be difficult to give reasonable bounds. Two multi-mechanism models have been proposed during the last decade, see Cailletaud and Sai [Cailletaud, G., Sai, K., 1995. Study of plastic/viscoplastic models with various inelastic mechanisms. International Journal of Plasticity 11, 991], Taleb et al. [Taleb, L., Cailletaud, G., Blaj, L., 2006. Numerical simulation of complex ratcheting tests with a multi-mechanism model type. International Journal of Plasticity, 22, 724], and Sai and Cailletaud [Sai, K., Cailletaud, G., 2007. Multi-mechanism models for the description of ratcheting: effect of the scale transition rule and of the coupling between hardening variables. International Journal of Plasticity 23, 1589]. In this paper, we would like to ensure a kind of “after-sales service” by exploring the thermodynamic way in order to see if there exist any restrictions on the parameter values. We prove thermodynamic consistency of some two-mechanism models under suitable conditions. As a result, we obtain conditions for the parameters which ensure the non negativity of the free energy and the fulfilling of the Clausis–Duhem inequality. Besides this, we perform numerical simulations, considering classical histories (monotonic tension, cyclic strain controlled, uniaxial ratcheting, biaxial ratcheting). These simulations show that the violation of the established restrictions may lead to anomalous predictions.