The maximum stress that appears near the tip of a crack appears in the region of smallest radius of curvature. For an elliptical crack of length and width , under an average applied stress , it reaches two maxima about the two ends of the semimajor axis given by:.

where ρ is the radius of curvature of the crack tip. A stress concentration factor is the ratio between the maximum stress compared to the average stress or reference stress for the section (assuming that there was no stress concentration). The elastic analysis implies that the radius of curvature approaches zero, the maximum stress grows without limit (in reality, when the stress grows sufficiently, local yielding is reached). Note that the stress concentration factor is a function of the geometry of the crack or defect causing the stress concentration, and not its size. The most common factors can be found in engineering reference manuals and are used to estimate the value of the actual stresses that could appear. In this procedure, the reference or average stresses are calculated using materials resistance methods, and these values ​​are corrected using stress concentration factors.

There are experimental methods to estimate concentration factors, including photoelasticity, brittle coatings or strain gauges. Although all of these procedures are suitable, they all have experimental, environmental, or precision disadvantages.

During the design phase, there are various approaches to estimating stress concentration factors and, in fact, numerous compendia have been published collecting concentration factors. Perhaps the most famous of these is Peterson's, Stress Concentration Design Factors, first published in 1953. Estimates based on the finite element method (FEM) are now frequently used. Other theoretical approaches that use considerations about the elasticity or resistance of materials allow us to arrive at equations similar to those obtained previously.

There are small differences between the factors published in compendiums, those calculated by the MEF and the theoretical values. Each method has advantages and disadvantages. Many published data were obtained from experimental setups, while the FEM calculates the peak stress directly and nominal stresses can be obtained by averaging over the material around the peak.

The maximum stress that appears near the tip of a crack appears in the region of smallest radius of curvature. For an elliptical crack of length and width , under an average applied stress , it reaches two maxima about the two ends of the semimajor axis given by:.

where ρ is the radius of curvature of the crack tip. A stress concentration factor is the ratio between the maximum stress compared to the average stress or reference stress for the section (assuming that there was no stress concentration). The elastic analysis implies that the radius of curvature approaches zero, the maximum stress grows without limit (in reality, when the stress grows sufficiently, local yielding is reached). Note that the stress concentration factor is a function of the geometry of the crack or defect causing the stress concentration, and not its size. The most common factors can be found in engineering reference manuals and are used to estimate the value of the actual stresses that could appear. In this procedure, the reference or average stresses are calculated using materials resistance methods, and these values ​​are corrected using stress concentration factors.

There are experimental methods to estimate concentration factors, including photoelasticity, brittle coatings or strain gauges. Although all of these procedures are suitable, they all have experimental, environmental, or precision disadvantages.

During the design phase, there are various approaches to estimating stress concentration factors and, in fact, numerous compendia have been published collecting concentration factors. Perhaps the most famous of these is Peterson's, Stress Concentration Design Factors, first published in 1953. Estimates based on the finite element method (FEM) are now frequently used. Other theoretical approaches that use considerations about the elasticity or resistance of materials allow us to arrive at equations similar to those obtained previously.

There are small differences between the factors published in compendiums, those calculated by the MEF and the theoretical values. Each method has advantages and disadvantages. Many published data were obtained from experimental setups, while the FEM calculates the peak stress directly and nominal stresses can be obtained by averaging over the material around the peak.