## Stress concentration

• A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated. An object is stronger when force is evenly distributed over its area, so a reduction in area, e.g., caused by a crack, results in a localized increase in stress. A material can fail, via a propagating crack, when a concentrated stress exceeds the material's theoretical cohesive strength. The real fracture strength of a material is always lower than the theoretical value because most materials contain small cracks or contaminants (especially foreign particles) that concentrate stress. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue strength.

Geometric discontinuities cause an object to experience a local increase in the intensity of a stress field. Examples of shapes that cause these concentrations are cracks, sharp corners, holes, and changes in the cross-sectional area of the object. High local stresses can cause objects to fail more quickly, so engineers must design the geometry to minimize stress concentrations.

A counter-intuitive method of reducing one of the worst types of stress concentrations, a crack, is to drill a large hole at the end of the crack. The drilled hole, with its relatively large diameter, causes a smaller stress concentration than the sharp end of a crack. This is however, a temporary solution that must be corrected at the first opportune time.

It is important to systematically check for possible stress concentrations caused by cracks—there is a critical crack length of 2a for which, when this value is exceeded, the crack proceeds to definite catastrophic failure. This ultimate failure is definite since the crack will propagate on its own once the length is greater than 2a. (There is no additional energy required to increase the crack length so the crack will continue to enlarge until the material fails.) The origins of the value 2a can be understood through Griffith's theory of brittle fracture.

Another method used to decrease the stress concentration is by creating the fillet at the sharp edges. It gives smooth flow of stress streamlines. In a threaded component force flow line is bent as it passes from shank portion to threaded portion as a result stress concentration takes place. To reduce this a small undercut is taken between shank and threaded portion.

${\displaystyle \sigma _{max}=\sigma \left(1+2{\cfrac {a}{b}}\right)=\sigma \left(1+2{\sqrt {\cfrac {a}{\rho }}}\right)}$
• ESDU64001: Guide to stress concentration data ()
• Pilkey, Walter D, Peterson's Stress Concentration Factors, Wiley, 2nd Ed (1999).
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