TABLE OF CONTENTS This chapter deals with the influence of cracks on the behavior of a linearly elastic solid. We consider solutions of some idealized problems in which the crack is assumed to be straight, finite, or semi-infinite. Of particular interest is the stress distribution near the tip of the crack. Thus the concept of a stress intensity factor (SIF) is introduced. The stress intensity factor helps in predicting the possibility of fracture damage. The concept of the J integral is also introduced, and its relation to the energy release rate in the case of linearly elastic materials is determined.
All materials crack due to such conditions as material imperfections, overload, or drying out. Fracture mechanics deals with the effects of cracking on the load-bearing ability of structural elements. In this chapter we merely introduce certain fundamental concepts of fracture mechanics. We consider only two-dimensional brittle fracture (with small exceptions) and assume that the cracks are rectilinear. We also assume that the cracked solid is made of a linearly elastic material. Let us not overlook the fact that a crack can be beneficial. Take, for instance, wood chopping: we introduce a crack artificially by hitting wood with an ax. We can then enlarge the crack thus formed by inserting a wedge and hammering this wedge down. This operation will cause crack propagation and ends with splitting the piece of wood. Consider another example: tearing a perforated sheet of paper starts with a crack forming at one end, and propagating...
