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where K is the stress intensity factor (with units of stress × length 1/2) and is a dimensionless quantity that varies with the load and geometry. Theoretically, as r goes to 0, the stress σ i j {\displaystyle \sigma _{ij}} goes to ∞ {\displaystyle \infty } resulting in a stress singularity. [ 5 ]
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 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.
Since the quantity is dimensionless, the stress intensity factor can be expressed in units of . Stress intensity replaced strain energy release rate and a term called fracture toughness replaced surface weakness energy. Both of these terms are simply related to the energy terms that Griffith used:
In a 1961 paper, P. C. Paris introduced the idea that the rate of crack growth may depend on the stress intensity factor. [4] Then in their 1963 paper, Paris and Erdogan indirectly suggested the equation with the aside remark "The authors are hesitant but cannot resist the temptation to draw the straight line slope 1/4 through the data" after reviewing data on a log-log plot of crack growth ...
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.
= in units of MPa, where HV is the Vickers hardness in N/mm 2 (or MPa) (i.e., 9.81 x numerical HV), P is the indentation load in N (typically 30 kgf is used) and T is the total crack length (mm) after application of the indenter.
The stress intensity factor is given by K = β σ π a , {\displaystyle K=\beta \sigma {\sqrt {\pi a}},} where σ {\displaystyle \sigma } is the applied uniform tensile stress acting on the specimen in the direction perpendicular to the crack plane, a {\displaystyle a} is the crack length and β {\displaystyle \beta } is a dimensionless ...