ENERGY INVARIANTS IN THEORY OF ELASTOPLASTIC CRACKS

Abstract

The paper considers a problem on a rectilinear crack in hardening elastoplastic material with load which is applied at infinity under plane-strain deformation conditions. While distributing J-integral in this case it is necessary to take into account specific characteristics associated with strain potential for environments with nonholonomic state equations. While considering a problem on a crack in elastoplastic material a principal term of asymptotic expansion in crack tip vicinity has an unknown singularity index in addition to an indefinite multiplier. It has been shown for steel 12X18H9T that while having invariance of energy integral it is possible to trace a singularity index for a principal term of stresses. The paper presents dependences of crack length compared to permissible Griffith’s length in accordance with the applied load which is associated with yield strength. Conceptions of J-integrals have been described for solution of a quasi-static problem. The developed approach can be used to formulate a criterion for destruction of elastoplastic material containing a rectilinear crack. The obtained theoretical dependences pertaining to determination of structure limit state characteristics have permitted to make a motivated selection of geometric parameters with due account of material strength properties. Results of the investigations can be used while preparing recommendations for development of structures with prescribed properties. The given approach makes most sense to be applied for determination of critical forces and critical value of crack length for elastoplastic material.