3 - Further results for a stationary crack

Summary

Introduction

In the preceding chapter, the transient stress intensity factor history resulting from the application of a spatially uniform crack face traction was examined. The particular situations analyzed represent the simplest cases of transient loading of a stationary crack for each mode of crack opening. There are many similar situations that can be analyzed by the methods outlined in Chapter 2. For example, consider the plane strain situation of a plane tensile stress pulse propagating through the material toward the edge of the crack, which lies in the half plane −∞ < x < 0, y = 0. Suppose that the x and y components of the unit vector normal to the wavefront are − cos θ and − sin θ, respectively, and that the pulse front reaches the crack edge at time t = 0. Suppose further that the incident pulse carries a jump in the normal stress component from the initial value of zero to σ_inc. If the solid is uncracked, then the incident pulse will induce a tensile traction of magnitude σ* = σ_inc{1 − (1 − 2v) cos² θ/(1 − v)} and a shear traction of magnitude τ* = σ_inc[1 − 2v) sin θ cos θ/(1 − v) on the plane y = 0 over the interval −C_dt/ cos θ < x 0. This particular stress wave diffraction problem was studied by de Hoop (1958) in his pioneering work on the subject.