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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 ...
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 .
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.
In addition, small crack growth data may be needed to match the increased rate of growth seen with small cracks. [39] Typically, a cycle counting technique such as rainflow-cycle counting is used to extract the cycles from a complex sequence. This technique, along with others, has been shown to work with crack growth methods. [40]
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In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.