Transient Analysis of Stress Waves around Cracks under Antiplane Strain

Abstract

This paper carries out a mathematical formulation of the antiplane strain problem of a crack with finite width subjected to any time‐dependent loadings. It is based on integral tranforms and a technique employed originally by Cagniard and simplified subsequently by De Hoop in geophysical‐layer problems. The procedure obviates the contour‐integration difficulties and permits the explicit recovery of the transient result by insepction. An illustrative example is given for the case in which a finite crack suddenly appears in an elastic solid under anitplane shear. A Fredholm integral equation of the second kind is obtained in the Laplace transform domain and solved numerically on the computer. Asymptotic forms for the transient stresses near the crack tip are found and a dynamic stress‐intensity factor, which is held important in the current theory of crack propagation, is defined. Numerical results showing that the transient stress reaches a peak very rapidly and then oscillates about the static value are displayed graphically.