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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 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.
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 ...
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 ...
The J-integral represents the energy that flows to the crack, hence, it is used to calculate the energy release rate, G. Additionally, it can be used as a fracture criterion. This integral is found to be path independent as long as the material is elastic and damages to the microstructure are not occurring.
Strain energy release rate per unit fracture surface area is calculated by J-integral method which is a contour path integral around the crack tip where the path begins and ends on either crack surfaces. J-toughness value signifies the resistance of the material in terms of amount of stress energy required for a crack to grow.
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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 .