Interface crack loaded by a time-harmonic plane wave
The two-dimensional problem of a finite crack along the interface of two dissimilar solids loaded by a plane wave has been studied. Fourier transform has been used for reducing the problem to that of solving a vectorial Cauchy singular integral equation for dislocation density on the crack face. This singular integral equation is solved numerically by the well-known Jacobi polynomial technique. Physical quantities such as crack shape and stress intensity factors have been obtained for various values of incident frequencies and incident angles. The crack faces are found to interpenetrate at the crack tip, and the stress field at the crack tip is found to be oscillatory. For practical purposes, an engineering approximation is suggested to overcome these situations at the crack tip.
vectorial Cauchy singular integral equation
scientific article; zbMATH DE number 527582