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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. The growth of a fatigue crack can result in catastrophic failure, particularly in the case ...
In a 1961 paper, P. C. Paris introduced the idea that the rate of crack growth may depend on the stress intensity factor. [4] Then in their 1963 paper, Paris and Erdogan indirectly suggested the equation with the aside remark "The authors are hesitant but cannot resist the temptation to draw the straight line slope 1/4 through the data" after reviewing data on a log-log plot of crack growth ...
where is the Young's modulus of the material, is the surface energy per unit area of the crack, and is the crack length for edge cracks or is the crack length for plane cracks. The quantity σ π a {\displaystyle \sigma {\sqrt {\pi a}}} is postulated as a material parameter called the fracture toughness .
Crack growth calculations, periodic inspections and component repair or replacement can be used to ensure critical components that may contain cracks, remain safe. Inspections usually use nondestructive testing to limit or monitor the size of possible cracks and require an accurate prediction
This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increments. [2] Both methods give an estimate of the fatigue life of a component.
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Therefore, a more general theory of crack growth is needed for elastic-plastic materials that can account for: the local conditions for initial crack growth which include the nucleation, growth, and coalescence of voids (decohesion) at a crack tip. a global energy balance criterion for further crack growth and unstable fracture.
In fracture mechanics, a crack growth resistance curve shows the energy required for crack extension as a function of crack length in a given material.For materials that can be modeled with linear elastic fracture mechanics (LEFM), crack extension occurs when the applied energy release rate exceeds the material's resistance to crack extension .