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Abstract
In this paper, the material parameters of a macro–micro coupled superplastic constitutive model, which considers grain growth and metal flow behaviour, are identified by inverse analysis. Based on the heteroscedastic maximum likelihood estimator, the objective function is provided. The objective function couples the information of stress–strain data, grain size–time data, strain rate sensitivity and a priori knowledge. And then, a hybrid optimisation method is developed and used to identify the parameters. An optimisation method, which incorporates the strengths of genetic algorithm and the variable error polyhedron algorithm is developed. The difficulty of choosing appropriate initial values for the parameters in the traditional optimisation technique is overcome by applying the genetic algorithm and the shortcoming of the slow convergent speed of the genetic algorithm is surmounted by applying the variable error polyhedron algorithm. The niching method is used to maintain the population diversity and to choose the initial value for the variable error polyhedron algorithm. A transition criterion between the genetic algorithm and the variable error polyhedron algorithm is proposed, through the improvement on the average objective function value of the chromosomes and the objective function value of the best chromosome in the population. At last, taking Ti–6Al–4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree well with the experimental results.
Finical support for this research is provided by Major National Science and Technology Program of Ministry of Industry and Information Technology of the People’s Republic of China (grant no. 2009ZX04014‐082) and the Fundamental Research Funds for the Central Universities (grant no. 20092m0150).