Elastodynamic Near-Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials

Abstract

The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The two-dimensional near-tip displacement fields are assumed in the general form rp T(t, c) K(θ, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(θ, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(θ, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.