Crack Propagation Analysis by Finite Differences

A finite-difference scheme for treating the dynamic stress field around a crack tip under plane-strain conditions, is proposed. The scheme is initially applied to the case of a crack of constant length which is suddenly opened in an infinite elastic medium loaded by a remotely uniform stress. By this, a numerical solution corresponding to the static state of stress is obtained which is compared with analytic solutions. It is shown that the numerically evaluated strain-energy-release rates are close to values calculated analytically. A modified scheme which presupposes a cuspated crack tip results in nearly the same strain-energy-release rates. Hence the validity of both numerical schemes is confirmed. For the numerical schemes adjusted to handle the propagating crack problem, the results represent a situation which is very close to reality; namely, the crack velocity accelerates up to a stage where propagation continues with a practically constant velocity. This terminal velocity moves from about 0.77 C₂ to about 0.57C₂ (C₂ being the shear wave velocity). The last-mentioned velocity value corresponds to the cuspated crack model.