The influence of applied stress, crack length, and stress intensity factor on crack closure
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I.
INTRODUCTION
C R A C K closure is now widely accepted as a fundamental phenomenon in fatigue crack growth. Changes in crack opening levels have been associated with many significant effects on crack growth rates. There remains widespread disagreement, however, on the functional relationship of crack opening levels to the most basic parameters of the fatigue problem. In view of the significance of the stress intensity factor, K, to the behavior of the fatigue crack, many researchers have attempted to develop a relationship between K and U, the fraction of the applied stress intensity range during which the crack is effectively open. Other workers have suggested that U is dependent on the remote applied stress, o,, but not on the crack length, a, so that properly speaking, no K dependence exists. Confusion can arise because K is a function of both a and tr. Literally dozens of research programs have attempted to address this basic issue. Most have been experimental in nature. Investigators have selected a specific materialgeometry system and then attempted to measure directly the crack opening levels under different loading conditions. Other researchers have developed analytical or numerical schemes to simulate the growth of a fatigue crack in some idealized fashion and, hence, to calculate the crack opening level. Unfortunately, there have been few attempts to synthesize the large and growing body of information about U and its relationship to such basic parameters as K, a, and or. As a result, the literature can now be divided into collections of articles which argue either for or against various types of U dependencies. In particular, there is an unfortunate shortage of dialogue between the experimental closure community, which tends to be dominated by materials scientists, and the
R.C. M c C L U N G , Senior Research Engineer, is with the Materials and Mechanics Department, Southwest Research Institute, San Antonio, TX 78228-0510. Manuscript submitted June 15, 1990. METALLURGICAL TRANSACTIONS A
analytical community, which is populated more frequently by specialists in mechanics. Few research efforts in crack closure have been based on a truly joint experimental-numerical investigation. Comparisons are generally brief. Should there be disagreement, as has frequently been the case when comparing experiments with analysis, it is relatively easy to question the validity or usefulness of the simple mathematical model. And many analysts and experimentalists are simply unfamiliar with previous research conducted and reported in the other community. The purpose of this article is to critically compare and evaluate the experimental and analytical evidence for the relationship between U and the basic fatigue crack growth parameters K, tr, and a. It will be shown that the large majority of this evidence appears to be completely consistent. Several individual results which seem to be contradictory at first glance will be shown to represent different pieces of the total picture. A master framework will be presented to
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