A Method for the Analysis of the Growth of Short Fatigue Cracks

摘要

The behavior of short fatigue cracks is a matter of importance not only because much of the fatigue lifetime is spent in propagating these cracks, but also because the boundary between propagation and non-propagation separates the safe from the potentially unsafe fatigue regimes. The method of analysis is based upon the following equation: where a is the crack length (in the case of crack starting from a hole, a is taken to be equal to the radius of the hole plus X, the actual length of the crack), N is the number of cycles, A is a material constant, triangle open K_(eff) is the effective value of the stress intensity factor (given by K_(max)-K_(op), where K_(max) is the maximum value of the stress intensity factor in a loading cycle and K_(op) is the crack opening level), and triangle open K_(eff) is the effective value of the stress intensity factor at the threshold level. In order to analyze the crack growth behavior of short fatigue cracks three modifications of Eq. 1 are needed. These are: (1) an elastic-plastic modification because the fatigue strengths are high with respect to the yield strength, (2) a modification to take into account that in the short crack range the fatigue strength rather than the threshold level becomes the dominant factor in affecting fatigue crack growth, and (3) a modification to account for the development of crack closure in the wake of a newly formed fatigue crack. With these modifications Eq. la becomes: where r_c is a material constant of the order of 1 urn in size, F, the elastic-plastic correction factor, equals Y is a geometric factor, triangle sigma is the stress range, k is a material constant which determines the rate of crack closure development, X is the length of a newly formed crack, i.e., the length measured from a free surface or from the root of a notch, and K_(opmax) is the crack opening level for a macroscopic crack. A number of examples will be provided to demonstrate the general applicability of Eq. 2a to situations involving short fatigue crack growth.