Abstract
The strain rate in an inclusion embedded in a matrix undergoing large strains is investigated theoretically. The inclusion is either a spheroid (axisymmetric loading), or an elliptical cylinder (plane strain loading), and both are assumed to be made of incompressible power law viscous materials, including the limit case of perfect plasticity. Localization factors (i.e., normalized strain rates) derived from various approaches (viz, linearization models, variational principle, finite element method) are first compared for a sphere and a circular cylinder. The influence of the inclusion aspect ratio is then investigated by means of the variational approach. Finally, an original and practical purpose of the paper is to propose approximate analytical equations to fit the dependence of the localization factor on the strain rate sensitivity parameter, as well as on the inclusion hardness and aspect ratios.
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