Quasi-static crack growth in three-layer media: a numerical experiment

Quasi-static growth of planar three-dimensional cracks in homogeneous and three-layer media is studied numerically using the particle dynamics method. It is shown that in the homogeneous medium cracks with different convex and nonconvex initial shapes tend to become circular (penny-shaped). The crack "forgets" its initial chape approximately when its front reaches the corresponding circumscribed circle and further propagates in the penny-shaped mode. In the three-layer medium, a crack grows in the plane orthogonal to the layers, having either different Young's moduli or different strength. In simulations, the ratio of crack's length (size along the layers) to its height (size across the layers) is calculated. It is shown that with increasing crack volume the ratio tends to some limiting value, dete272rmined by contrast in properties of the layers. Empirical dependencies of the limiting length/height ratio on parameters of the layers are derived. The conditions, corresponding to arresting of the crack in the central layer, are estimated.