428 Fatigue Crack Growth Rates : A General Method of Analysis

Abstract

In order to deal with many aspects of fatigue crack growth such as constant amplitude fatigue crack growth, small fatigue crack growth, two-step and multiple two-step loadings, the effects of tensile overloads and compressive underloads, and the effect of mean stress on the fatigue limit, there is a need for a general approach which includes treatment of elastic-plastic behavior, the endurance limit, and the development of crack closure. For this purpose the following constitutive relation has been proposed : [numerical formula] where α is the crack length, N is the number of cycles, A is a material constant of dimensions (MPa)^<1/2>, ΔK_<eff> is the effective range of the stress intensity factor, K, ΔK_<effth> is the effective range of the stress intensity factor at the threshold level, K_c is the cyclic fracture toughness, and K_<max> is the maximum stress intensity factor in a loading cycle. An important feature of the relation is that it is dimensionally correct, a requirement long foreseen by such researchers as Frost and Liu. The expression within the second parentheses is included to deal with the contribution of so-called static modes of separation to the overall fatigue crack growth process, i.e., those modes of separation which are not cyclic in nature but are associated with tensile fracture processes such as cleavage and ductile rupture. These modes of separation become more important as K_<max> approaches K_c. Since K_<max>=ΔK/(1-R), where R is the ratio of the minimum to maximum stress in a loading cycle, the effects of R on the extent of static modes of fracture are included in Eq. 1. The expression within the first parentheses deals with purely cyclic fatigue crack growth, and as such deals with fatigue crack growth in the near-threshold range as a well as in the Paris range when the expression within the second parentheses can be neglected. In such a case Eq.1 becomes [numerical formula] Eq. 2 is deceptively simple. In order to make use of it information is needed about the crack closure level, since ΔK_<eff>=K_<max>-K_<op>, where K_<op> is the crack opening level, which under constant amplitude loading conditions is a function of the crack length and R. In order to deal with the important topic of short fatigue crack growth Eq. 2 must be modified to include consideration of (1) elastic-plastic behavior, since the maximum stress in a loading cycle may be a significant fraction of the yield stress, (2) the development of crack closure in the wake of a newly-formed crack, and (3) the role of the endurance limit (Kitagawa effect) in short fatigue crack growth. Ishihara has shown that even in the high-cycle fatigue range over 90% of the fatigue lifetime is spent in the process of growing fatigue cracks. Therefore the integration of Eq. 2 between the limits of the initial flaw size and the crack length at final fracture can lead to a reasonable estimate of the fatigue lifetime. In this presentation a review of the processes leading to the development of Eq. 1 which have taken place over the last fifty years, and illustrations of its use in dealing with fatigue crack growth, will be given.