Numerical and analytical methods for simulation of growth and interaction of cracks

The problem of predicting the trajectories of cracks or a system of interacting cracks in elastic bodies is of theoretical and practical interest in multiply fields, as the presence of such structures affects not only the strength characteristics, but also many other properties of the material under consideration. However, the calculating of the growth paths of cracks is a complex challenge analytically because every increment of crack growth modifies the stress field globally and changes the stress intensity factors at all other cracks. A numerical iterative method is presented and used for the simulation of quasi-static crack growth in linear elastic plane bodies. The modeling of crack growth is performed using a finite element method in conjunction with a remeshing algorithm carried out on each iteration. To describe properly the stress-strain state in the vicinity of the crack tip, the singular elements are used. The crack growth and its direction are determined by the maximum hoop stress criterion. Using the developed numerical method, some basic problems are considered, namely, the problem on growth of a crack in the vicinity of two closely spaced pores, and also a detailed research of the trajectories of two interacting collinear cracks of equal length in a plate subjected to tension load. An analytical solution of the latter problem is also considered. Using the Kolosov-Muskhelishvili potentials approach, the coefficients of the Williams expansion are obtained which are necessary for cracks trajectories calculation. Within the region of the analytical model applicability, the numerical and analytical results are in good agreement.