Stress Concentration

When materials are placed under stress care should be taken to ensure that all edges and surfaces are polished and smooth. Forces will concentrate around even the smallest surface imperfection causing the component to fail sooner than predicted by a theoretical calculation.

This can be catastrophic, as in the case of the Comet airliner disaster, or it can be an intended consequence, as in the case of a bar of chocolate for example.

Calculating the stress concentration, or increase in stress, (σ_max) is very complex but for a simple scratch or indentation it can be estimated as follows:

Where:

• l = length or depth of scratch
• r = the tip radius at the bottom of the scratch
• Capital I - Moment of Inertia for the material

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Note: The key point to note is that the best way to reduce the increase in stress created by a scratch or cut is to increase the radius at the tip - and that is why driling a hole at the end of a cut or tear can stop it spreading further!

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