Cylindrical cavity expansion in compressible Mises and Tresca solids

摘要

The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.