Abstract
It is shown that dimensionless equations for the force and contact area in finite element models of flattening the sphere were obtained for a very narrow range of relative displacements, which is ten times smaller than for the indentation models. The analysis of the Drozd-Matlin analytical model, which is based on the concept of «plastic hardness» and the linear dependence of the residual deformation on the applied load. It is indicated that this approach does not take into account the strain hardening of the material, and its use for calculating the flattening of the sphere leads to incorrect results. To account for strain hardening, plastic hardness is represented through the characteristics of the power law of hardening. The model under consideration was modernized and dimensionless equations for the relative deformation were obtained depending on the degree of loading and the characteristics of the power law of hardening. To simulate the flattening of the sphere, we used the results of finite element modeling to determine the residual deformation in view of their identical values for different flattening models that take into account strain hardening. A comparison of the developed model with the known finite-element flattening models for large relative displacements for different values of the characteristics of the power law of hardening is shown.
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