rate in ductile and brittle materials is given by where, and are material parameters. Based on different crack-advance and crack-tip shielding mechanisms in metals, ceramics, and intermetallics, it is observed that the fatigue crack growth rate in metals is significantly dependent on term, in ceramics on , and intermetallics have almost similar dependence on and terms. Prediction of fatigue life Computer programs There are many computer programs that implement crack growth equations such as Nasgro, 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. Crack growth programs grow a crack from an initial flaw size until it exceeds the fracture toughness of a material and fails. Because the fracture toughness depends on the boundary conditions, the fracture toughness may change from plane strain conditions for a semi-circular surface crack to plane stress conditions for a through crack. The fracture toughness for plane stress conditions is typically twice as large as that for plane strain. However, because of the rapid rate of growth of a crack near the end of its life, variations in fracture toughness do not significantly alter the life of a component. Crack growth programs typically provide a choice of: cycle counting methods to extract cycle extremes geometry factors that select for the shape of the crack and the applied loading crack growth equation acceleration/retardation models material properties such as yield strength and fracture toughness Analytical solution The stress intensity factor is given by where is the applied uniform tensile stress acting on the specimen in the direction perpendicular to the crack plane, is the crack length and is a dimensionless parameter that depends on the geometry of the specimen. The alternating stress intensity becomes where is the range of the cyclic stress amplitude. By assuming the initial crack size to be , the critical crack size before the specimen fails can be computed using as The above equation in is implicit in nature and can be solved numerically if necessary. Case I For crack closure has negligible effect on the crack growth rate and the Paris–Erdogan equation can be used to compute the fatigue life of a specimen before it reaches the critical crack size as Crack growth model with constant value of 𝛽 and R = 0 For the Griffith-Irwin crack growth model or center crack