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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.
If a very sharp crack, or a V-notch can be made in a material, the minimum value of can be empirically determined, which is the critical value of stress intensity required to propagate the crack. This critical value determined for mode I loading in plane strain is referred to as the critical fracture toughness ( K I c {\displaystyle K_{\mathrm ...
The crack is expected to propagate when the strain energy release rate exceeds a critical value - called the critical strain energy release rate. The fracture toughness and the critical strain energy release rate for plane stress are related by
Compute the change in the free energy (surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a critical crack length, beyond which the free energy decreases as the crack length increases, i.e. by causing fracture. Using this procedure, Griffith found that
The critical load and strain gauge measurements at the load are noted and a graph is plotted. The crack tip opening can be calculated from the length of the crack and opening at the mouth of the notch. According to the material used, the fracture can be brittle or ductile which can be concluded from the graph.
A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing.
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Critical value or threshold value can refer to: A quantitative threshold in medicine, chemistry and physics; Critical value (statistics), boundary of the acceptance region while testing a statistical hypothesis; Value of a function at a critical point (mathematics) Critical point (thermodynamics) of a statistical system.