About estimation of sensitivity of statistical multilevel polycrystalline metal models to parameter variations

Analysis of the influence of variations of the parameters characterizing the properties of a modeled object on response change (sensitivity analysis for model parameter perturbations) is an important stage in studying the features of nonlinear mathematical models. The relevance of this research for material models is based on stochasticity of most material characteristics, and therefore constitutive mathematical models used in technological processes calculations must be stable with regard to variation of material parameters, which allows one to avoid precise experimental identification of product material properties in each particular case. It is reasonable to use multilevel constitutive models of materials, which makes it possible to describe explicitly the mechanisms of inelastic deformation, as well as the material structure evolution and the corresponding changes in physical and mechanical properties. This article provides the method of sensitivity estimation to parameter perturbations for models of this type, which is based on an integral comparison of response histories for perturbed and unperturbed sets of parameters for several types of loading. The results of application of the proposed technique to the two-level statistical model of polycrystalline metals, which includes the description of intragranular dislocation sliding and crystallite lattice rotations, and to the modified three-level model, which additionally contains the description of grain-boundary sliding mechanism, are presented. The obtained results demonstrate the stability of the considered mathematical models with respect to parameter changes. The ordering of model parameters by their sensitivity to perturbations is performed on the basis of the analysis carried out in this study.