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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.
It is denoted by critical stress intensity factor or critical strain energy release rate. [15] For unidirectional fiber reinforced polymer laminate composites , ASTM provides standards for determining mode I fracture toughness G I C {\displaystyle G_{IC}} and mode II fracture toughness G I I C {\displaystyle G_{IIC}} of the interlaminar matrix.
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 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 ...
The strain energy density is defined as the energy invested into the volume unit of polymeric material for deformation, also known as the elastic energy per unit volume in the solid. In crack nucleation approach, no crack is introduced into the sample initially, and crack initiation is observed under loadings. Crack Growth Approach
Resistance curve of crack extension force versus crack extension for a brittle and ductile material, showing , the critical strain energy release rate. The resistance curve (R-curve) is utilized to study crack propagation and toughness development of a material by plotting the crack extension force versus crack extension. In bone literature ...