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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 test is performed with multiple specimen loading each of the specimen to various levels and unloading. This gives the crack mouth opening compliance which is to be used to get crack length with the help of relationships given in ASTM standard E 1820, which covers the J-integral testing. [19]
When the size of the plastic zone at the crack tip is too large, elastic-plastic fracture mechanics can be used with parameters such as the J-integral or the crack tip opening displacement. The characterising parameter describes the state of the crack tip which can then be related to experimental conditions to ensure similitude. Crack growth ...
J-integral path for the DCB specimen under tensile load. Consider the double cantilever beam specimen shown in the figure, where the crack centered in the beam of height 2 h {\displaystyle 2h} has a length of a {\displaystyle a} , and a load P {\displaystyle P} is applied to open the crack.
CTOD is a single parameter that accommodates crack tip plasticity. It is easy to measure when compared with techniques such as J integral. It is a fracture parameter that has more physical meaning than the rest. However, the equivalence of CTOD and J integral is proven only for non-linear materials, but not for plastic materials.
The above relations can also be used to connect the J-integral to the stress intensity factor because ... Compact tension specimen for fracture toughness testing.
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.
A discontinuity may exist as a single feature (e.g. fault, isolated joint or fracture) and in some circumstances, a discontinuity is treated as a single discontinuity although it belongs to a discontinuity set, in particular if the spacing is very wide compared to the size of the engineering application or to the size of the geotechnical unit.