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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 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.
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.
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 ...
In a molecule, strain energy is released when the constituent atoms are allowed to rearrange themselves in a chemical reaction. [1] The external work done on an elastic member in causing it to distort from its unstressed state is transformed into strain energy which is a form of potential energy.
The chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes. This means that cases involving multiple out-of-phase load inputs, or crack closure can be treated with high ...
The usage of R-curves in fracture analysis is a more complex, but more comprehensive failure criteria compared to the common failure criteria that fracture occurs when where is simply a constant value called the critical energy release rate. An R-curve based failure analysis takes into account the notion that a material's resistance to fracture ...