Evaluation of the elastic-plastic mixity barameters on the base of different crack propagation criteria. Part 2. Solution and results - Shlyannikov, V.N.; Sakhabutdinov, Zh.M. (Проблемы прочности, 2005)
We propose a new scheme of mixed-mode problem solution based on the deformation theory o f plasticity with a power-law hardening stressstrain 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.