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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.
The crack relaxes the stress and hence reduces the elastic energy near the crack faces. On the other hand, the crack increases the total surface energy of the specimen. Compute the change in the free energy (surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a ...
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 .
The crack is expected to propagate when the strain energy release rate exceeds a critical value - called the critical strain energy release rate. The fracture toughness and the critical strain energy release rate for plane stress are related by
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
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 ...
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Relationship to energy release rate and J-integral [ edit ] In plane stress conditions, the strain energy release rate ( G {\displaystyle G} ) for a crack under pure mode I, or pure mode II loading is related to the stress intensity factor by: