Evaluation of the Elastic-Plastic Mixity Parameters on the Base of Different Crack Propagation Criteria. Part 2. Solution and Results

Abstract

We propose a new scheme of mixed-mode problem solution based on the deformation theory of plasticity with a power-law hardening stress-strain response and on application of elastic and plastic mixity parameters. Depending on the mixed-mode loading conditions and the initial crack line direction, this approach allows one to analyze a wide range of possible crack propagation paths controlled by shear and tensile mechanisms. The equilibrium equation with Airy function is used for a two-dimensional problem in the polar coordinate system. The Ramberg-Osgood model is applied to a material with power-law hardening behavior. Using the finite difference method we obtained a numerical solution of the mixed-mode loading problem with boundary conditions corresponding to two cases of crack propagation. Within the framework of the proposed approach we estimated the dependencies between mixity parameters and various loading parameters and crack inclination angle for a range of strain hardening exponent values, which dependencies closely fit the experimental data.

Mode Mixity Parameters for Mathematical Crack Type

“…Как правило, для решения подобных задач применяют метод пристрелки и разностный метод. В настоящей работе использован разностный метод, подробные детали реализации которого в приложении к задаче смешанных форм деформирования изложены в работе [4].…”