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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 Mode I critical stress intensity factor, , is the most often used engineering design parameter in fracture mechanics and hence must be understood if we are to design fracture tolerant materials used in bridges, buildings, aircraft, or even bells.
The strain energy release rate ... it is the critical stress intensity factor ... One basic assumption in Irwin's linear elastic fracture mechanics is small scale ...
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.
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 parameter in fracture mechanics is the stress intensity factor (K), which is related to the strain energy release rate (G) and the fracture toughness (G c). When the stress intensity factor reaches the material's fracture toughness, crack propagation becomes unstable, leading to failure.
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 ...