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. 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. One of the earliest crack growth equations based on the stress intensity factor range of a load cycle () is the Paris–Erdogan equation where is the crack length and is the fatigue crack growth for a single load cycle . A variety of crack growth equations similar to the Paris–Erdogan equation have been developed to include factors that affect the crack growth rate such as stress ratio, overloads and load history effects. The stress intensity range can be calculated from the maximum and minimum stress intensity for a cycle A geometry factor is used to relate the far field stress to the crack tip stress intensity using . There are standard references containing the geometry factors for many different configurations. History of crack propagation equations Many crack propagation equations have been proposed over the years to improve prediction accuracy and incorporate a variety of effects. The works of Head, Frost and Dugdale, McEvily and Illg, and Liu on fatigue crack-growth behaviour laid the foundation in this topic. The general form of these crack propagation equations may be expressed as where, the crack length is denoted by , the number of cycles of load applied is given by , the stress range by , and the material parameters by . For symmetrical configurations, the length of the crack from the line of symmetry is defined as and is half of the total crack length . Crack growth equations of the form 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