Antiplane Elastodynamic Analysis of a Half-Plane Weakened by Multiple Cracks

Abstract

The distributed dislocation technique is used to analyze the defects in the forms of cracks in a half-plane under timeharmonic anti-plane excitation. The stress fields are obtained for a half- plane containing a Volterra screw dislocation. The method of images is utilized to derive the solution of a screw dislocation under time-harmonic conditions for an elastic half-plane from the solution of infinite planes. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The displacement and stress components are obtained for a half-plane under concentrated anti-plane, time-harmonic traction. The dislocation solution is employed to analyze a half-plane weakened by cracks under anti-plane point load. The solution may be viewed as the Green's function for a half-plane under arbitrary self-equilibrating traction. The effects of load frequency and crack orientation on the stress intensity factors are studied.