A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of fatigue cracks can result in catastrophic failure, particularly in the case of aircraft. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing.
Fatigue life can be divided into an initiation period and a crack growth period.[1] Crack growth equations are used to predict the crack size starting from a given initial flaw and are typically based on experimental data obtained from constant amplitude fatigue tests.
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Many crack propagation equations have been proposed over the years to improve prediction accuracy and incorporate a variety of effects. The works of Head,[6] Frost and Dugdale,[7] McEvily and Illg,[8] and Liu[9] on fatigue crack-growth behaviour laid the foundation in this topic. The general form of these crack propagation equations may be expressed as
Crack growth equations of the form d a / d N \displaystyle da/dN are not a true differential equation as they do not model the process of crack growth in a continuous manner throughout the loading cycle. As such, separate cycle counting or identification algorithms such as the commonly used rainflow-counting algorithm, are required to identify the maximum and minimum values in a cycle. Although developed for the stress/strain-life methods rainflow counting has also been shown to work for crack growth.[10] There have been a small number of true derivative fatigue crack growth equations that have also been developed.[11][12]
A d a / d N \displaystyle da/dN equation gives the rate of growth for a single cycle, but when the loading is not constant amplitude, changes in the loading can lead to temporary increases or decreases in the rate of growth. Additional equations have been developed to deal with some of these cases. The rate of growth is retarded when an overload occurs in a loading sequence. These loads generate are plastic zone that may delay the rate of growth. Two notable equations for modelling the delays occurring while the crack grows through the overload region are:[16]
The NASGRO equation is used in the crack growth programs AFGROW, FASTRAN and NASGRO software.[20] It is a general equation that covers the lower growth rate near the threshold Δ K th \displaystyle \Delta K_\textth and the increased growth rate approaching the fracture toughness K crit \displaystyle K_\textcrit , as well as allowing for the mean stress effect by including the stress ratio R \displaystyle R . The NASGRO equation is
There are many computer programs that implement crack growth equations such as Nasgro,[24] AFGROW and Fastran. In addition, there are also programs that implement a probabilistic approach to crack growth that calculate the probability of failure throughout the life of a component.[25][26]
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