Parameter identification of superplastic constitutive model based on heteroscedastic maximum likelihood estimator

摘要

In this paper, the material parameters of a macro–micro coupled superplastic constitutive model,nwhich considers grain growth and metal flow behaviour, are identified by inverse analysis. Basednon the heteroscedastic maximum likelihood estimator, the objective function is provided. Thenobjective function couples the information of stress–strain data, grain size–time data, strain ratensensitivity and a priori knowledge. And then, a hybrid optimisation method is developed and usednto identify the parameters. An optimisation method, which incorporates the strengths of geneticnalgorithm and the variable error polyhedron algorithm is developed. The difficulty of choosingnappropriate initial values for the parameters in the traditional optimisation technique is overcomenby applying the genetic algorithm and the shortcoming of the slow convergent speed of thengenetic algorithm is surmounted by applying the variable error polyhedron algorithm. The nichingnmethod is used to maintain the population diversity and to choose the initial value for the variablenerror polyhedron algorithm. A transition criterion between the genetic algorithm and the variablenerror polyhedron algorithm is proposed, through the improvement on the average objectivenfunction value of the chromosomes and the objective function value of the best chromosome innthe population. At last, taking Ti–6Al–4V as an example, a set of satisfactory material parametersnis obtained. The calculated results agree well with the experimental results.