The Rapid Tearing of a Half Plane

The surface of an elastic half space is subjected to sudden antiplane mechanical disturbances. Crack initiation and subsequent crack instability are examined via two idealized problems; the first is concerned with instantaneous crack bifurcation and the second with instantaneous skew crack propagation. In either problem, crack propagation occurs at a constant subsonic velocity under an angle κπ with the normal to the surface. For the externally applied disturbances that are considered here, and for contstant crack-tip velocities, the particle velocity and τ_θz are functions of r/t and θ only, which allows Chaplygin’s transformation and conformal mapping to be used. The problems can then be solved using analytic function theory. For various values of the angle of crack propagation, the dependence of the elastodynamic stress intensity factors on the crack propagation velocity is investigated. For certain specific geometries, fully analytical solutions are derived to provide check cases.