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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 fracture toughness and the critical strain energy release rate for plane stress are related by = where is the Young's modulus. If an initial crack size is known, then a critical stress can be determined using the strain energy release rate criterion.
the stored elastic strain energy which is released as a crack grows. This is the thermodynamic driving force for fracture. the dissipated energy which includes plastic dissipation and the surface energy (and any other dissipative forces that may be at work). The dissipated energy provides the thermodynamic resistance to fracture.
Using the compliance method, the critical strain energy release rate is given by G I c = 3 P C δ C 2 B a {\displaystyle G_{Ic}={\frac {3P_{C}\delta _{C}}{2Ba}}} (2) where P C {\displaystyle P_{C}} and δ C {\displaystyle \delta _{C}} are the maximum load and displacement respectively by determining when the load deflection curve has become ...
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:
This allows the strain energy release rate, , to be defined by the critical crack opening displacement, = or the critical cohesive zone size, , as follows: [6] G c = 2 ∫ 0 ν c σ y y d ν = 8 σ t h 2 r c o π E = 2 γ s {\displaystyle G_{c}=2\int _{0}^{\nu _{c}}\sigma _{yy}d\nu ={\frac {8\sigma _{th}^{2}r_{co}}{\pi E}}=2\gamma _{s}}
The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . [1] When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the ...