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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.
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 ...
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]
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.
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.
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 ...
For example, according to ASTM E399, the maximum stress intensity K max should be no larger than 0.6 during the initial stage and less than 0.8 when crack approaches its final size. [ 14 ] In certain cases grooves are machined into the sides of a fracture toughness specimen so that the thickness of the specimen is reduced to a minimum of 80% of ...
In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.