One of the most successful applications of the theory of fracture mechanics is in the characterization of fatigue crack propagation. An analysis of fatigue flaw growth based on fracture mechanics inevitably requires a thorough understanding of the assumptions, significance and limitations underlying the development of various crack tip parameters. An important part of such a study of fracture mechanics is the identification of the regions of dominance of the leading terms of asymptotic crack tip singular fields. The appropriate conditions for the dominance of critical fracture parameters are obtained from a knowledge of the accuracy of asymptotic continuum solutions and from the mechanistic understanding of microscopic deformation at the fatigue crack tip.

In this chapter, we present a focused discussion of the theories of linear elastic and nonlinear fracture mechanics that are relevant to applications in fatigue. Details of the mechanisms of fatigue crack propagation are examined in the following chapters.

Griffith fracture theory

Modern theories of fracture find their origin in the pioneering work of Griffith (1921) who formulated criteria for the unstable extension of a crack in a brittle solid in terms of a balance between changes in mechanical and surface energies. Consider a through-thickness crack of length 2a located at the center of a large brittle plate of uniform thickness B, which is subjected to a constant far-field tensile stress σ (Fig. 9.1).