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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. Polishing cannot detect a crack.
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 ...
Today, it is the critical stress intensity factor K Ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics. Crack tip plastic zone [ edit ]
The energy release rate is directly related to the stress intensity factor associated with a given two-dimensional loading mode (Mode-I, Mode-II, or Mode-III) when the crack grows straight ahead. [3] This is applicable to cracks under plane stress, plane strain, and antiplane shear.
In this case, the material's fracture toughness is given by the critical stress intensity factor K Ic. [2] Approach
The stress intensity range can be calculated from the maximum and minimum stress intensity for a cycle Δ K = K max − K min {\displaystyle \Delta K=K_{\text{max}}-K_{\text{min}}} A geometry factor β {\displaystyle \beta } is used to relate the far field stress σ {\displaystyle \sigma } to the crack tip stress intensity using
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.
Linear elastic fracture mechanics predicts that a crack will extend when the stress intensity factor at the crack tip is greater than the fracture toughness of the material. Therefore, the critical applied stress can also be determined once the stress intensity factor at a crack tip is known.