Development and determination of unified viscoplastic constitutive equations for predicting microstructure evolution in hot forming processes

This paper reports the development of advanced unified viscoplastic constitutive equations for the modelling of microstructure evolution and their effects on viscoplastic flow of materials. The material parameters within constitutive equations are determined by minimising the difference between predicted results and the corresponding experimental data. To achieve this, firstly, new methods have been developed to overcome different scale problems in a set of constitutive equations. This enables that all the equations can be integrated accurately with a specified single tolerance. Secondly, objective functions have been formulated to enable all the data to be optimised with equal opportunity. Thus, the selection of weighting factors is eliminated. Thirdly, based on the analysis of the failure of gradient-based, genetic algorithm (GA)-based and evolutionary programming (EA)-based optimisation techniques in determining the constants within constitutive equations, a new combined method has been proposed to increase the chance to get the global minimum.