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Note that the dimensionless stress concentration factor is a function of the geometry shape and independent of its size. [4] These factors can be found in typical engineering reference materials. Stress concentration around an elliptical hole in a plate in tension. E. Kirsch derived the equations for the elastic stress distribution around a hole.
This would be considered a stress singularity, which is not possible in real-world applications. For this reason, in numerical studies in the field of fracture mechanics, it is often appropriate to represent cracks as round tipped notches, with a geometry dependent region of stress concentration replacing the crack-tip singularity. [9]
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 ...
A geometry factor is used to relate the far field stress to the crack tip stress intensity using K = β σ π a {\displaystyle K=\beta \sigma {\sqrt {\pi a}}} . There are standard references containing the geometry factors for many different configurations.
Any pair of coordinates that differ from (,) by constant multiples of equal absolute value are also isomorphic with respect to principal stress space. As an example, pressure = / and the Von Mises stress = are not an isomorphic coordinate pair and, therefore, distort the yield surface because
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 ...
As an example, let's assume we have a state of stress with stress components ,, ,, and ,, as shown on Figure 7. First, we can draw a line from point B {\displaystyle B} parallel to the plane of action of σ x {\displaystyle \sigma _{x}} , or, if we choose otherwise, a line from point A {\displaystyle A} parallel to the plane of action of σ y ...
Stress is a measure of the average amount of force exerted per unit area. The stress distribution can be obtained from known theoretical [ 1 ] or numerical ( Finite element method ) analysis. The researcher who builds up the force lines can choose a magnitude of the internal force and the initial border where the drawing procedure starts.