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Figure 1: Typical plot of crack growth rate versus the stress intensity range. The Paris–Erdogan equation fits the central linear region of Regime B.. A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads.
Typical plot of crack growth rate with respect to the stress intensity range where the Paris–Erdogan equation fits the central, linear region of Regime B. Paris' law (also known as the Paris–Erdogan equation) is a crack growth equation that gives the rate of growth of a fatigue crack.
1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of plastic strain in the tip of cracks. 1961: P. C. Paris proposes methods for predicting the rate of growth of individual fatigue cracks in the face of initial scepticism and popular defence of Miner's phenomenological approach.
In true corrosion fatigue, the fatigue-crack-growth rate is enhanced by corrosion; this effect is seen in all three regions of the fatigue-crack growth-rate diagram. The diagram on the left is a schematic of crack-growth rate under true corrosion fatigue; the curve shifts to a lower stress-intensity-factor range in the corrosive environment.
Known as fatigue, it was found that for long cracks, the rate of growth is largely governed by the range of the stress intensity experienced by the crack due to the applied loading. Fast fracture will occur when the stress intensity exceeds the fracture toughness of the material.
Fastran is a computer program for calculating the rate of fatigue crack growth by combining crack growth equations and a simulation of the plasticity at the crack tip. Fastran models accelerations and retardation and other variable amplitude loading effects in crack growth using a crack closure model.
The stress intensity factor at the crack tip of a compact tension specimen is [4] = [() / / + / / + /] where is the applied load, is the thickness of the specimen, is the crack length, and is the effective width of the specimen being the distance between the centreline of the holes and the backface of the coupon.
Hence, the plasticity-induced crack closure under plane stress conditions can be expressed as a consequence of the stretched material behind the crack tip, which can be considered as a wedge that is inserted in the crack and reduces the cyclic plastic deformation at the crack tip and hence the fatigue crack growth rate. [7]