Chapter 2 - Stress Concentration

Abstract

This chapter provides an introduction to stress concentration. The stress at the edge of a hole, or at a notch root, has a higher value than the remote stress. This phenomenon is called “stress concentration.” Fatigue cracks mostly initiate at the sites of stress concentrations. Once a crack initiates, one has to consider the stress concentration of the crack. Unlike holes and notches, a crack has a sharp tip whose root radius ρ is zero. The definition of a crack, in elastic analysis, is the limiting shape of an extremely slender ellipse. As an extremely slender elliptical hole is reduced toward the limiting shape, the stress concentration ahead of the elliptical hole that is at the tip of the crack becomes unbounded regardless of the length of the crack. If a crack is close to another crack or near a cavity, or an internal crack is close to a free surface, the interaction between the crack and another crack, a cavity, or a free surface causes an increase in the value of the stress intensity factor compared with that for the isolated crack case. Although this interaction effect cannot be expressed by a simple equation, it is considered that the interaction effect for three-dimensional cracks is always smaller than for two-dimensional cracks.