Texas A\&M University
College Station, Texas, U. S. A.
The problems of interest in this talk concern the unsteady, dynamic growth of planar cracks in elastic material. Most existing closed form solutions to such problems have been for a single semi-infinite crack propagating in an infinite isotropic, homogeneous linear elastic or viscoelastic material.
The authors report here on a method by which closed form solutions can be constructed for multiple, finite length, dynamically accelerating, co-planar cracks. In particular, expressions are constructed for crack opening displacements as well as stress intensity factors for such problems. The solution method utilizes an analog of the Dirichlet to Neumann map on the crack plane to derive an integro-differential equation for the crack opening displacement on the crack faces. This equation is then solved analytically for a single growing semi-infinite crack, a single growing finite length crack, and ultimately for multiple, growing, coplanar cracks. Simulations are shown based upon a stress intensity factor fracture criterion. The specific results presented here are in the context of anti-plane shear deformations in linear elastic material, but in principle the method can be applied to plane strain deformations and to viscoelastic as well as elastic material. One of the applications of these solutions is to the study of the process by which multiple, co-planar micro-cracks grow and coalesce into a macro-crack which is an important mechanism for damage development in many brittle materials.