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In fracture mechanics, the stress intensity factor (K) is used to predict the stress state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses. [1] It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle ...
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 ...
where E is the Young's modulus, ν is Poisson's ratio, and K I is the stress intensity factor in mode I. Irwin also showed that the strain energy release rate of a planar crack in a linear elastic body can be expressed in terms of the mode I, mode II (sliding mode), and mode III (tearing mode) stress intensity factors for the most general ...
Since fatigue crack grows in a stable fashion below the critical stress-intensity factor for fracture (fracture toughness), the process is called sub-critical crack growth. The diagram on the right shows typical fatigue-crack-growth behavior. In this log-log plot, the crack-propagation velocity is plotted against the applied stress-intensity ...
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.
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 ...
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