Modeling of the Complexity Propagation of Crack in a Ductile Material Under Complex Solicitation in Crack Tip: Introduction of a Matrix of Stress Intensity Factors of Bifurcation

Abstract

In fracture and damage mechanics, modeling of crack propagation has always been a source of difficulties. Numerous works have been carried out on this case at the crack tip, introducing new parameters: the Stress Intensity Factor (K); which is the local Irwin parameter, and also the Rice integral (J), the Griffith's energizing method, in which J and G are the global parameters around the crack tip. The problem of the crack remains very complex and difficult problem to be solved. Several methods are used to investigate the crack problem, namely the method of gradient, the numerical methods by finite elements, as well as the thermodynamic approach and the classical methods of Irwin, Griffith or Rice, according to the Intensity Stress Factor. This study adds to the work already carried out. Using the analytical analysis method of equations, we manage to show that the Stress Intensity Factor has a matrix of rank 3 at the crack tip, which is a better form since it includes complex combination cases of crack mode and bifurcation. Furthermore, when the material is subjected to complex stress, after analysis we emerge from a new singularity in (r) which is different from the classical mode. Finally, we are shown the new form of singularity, which is frequency dependent. This work can explain many situations, for example, the case of certain structural disasters showing the presence of cracks for complex or uncontrollable stress.