Glossary: What is a stress concentration factor in CAE? Examples included

Stress Concentration Factor (Kt) is a coefficient that represents the degree to which stress becomes locally concentrated at points of geometric discontinuity (such as holes, notches, steps, or sharp bends) in materials or structures when external forces are applied.

Definition

Stress Concentration Factor Kt

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For example, consider a flat plate with a small circular hole at its centre. Stress concentrates at the hole's edge, where maximum stress occurs. This maximum stress is greater than the average stress when no hole is present. The ratio of these values is the “stress concentration factor”.

Characteristics

Shape-dependent: Kt tends to increase as the hole diameter or notch curvature radius decreases.

Load mode-dependent: The value also varies depending on the type of loading, such as tension, bending, or torsion.

Material-independent: Theoretical Kt is determined solely by geometric factors and does not directly depend on material strength or elastic modulus.

Engineering Significance

Stress concentration zones are prone to becoming initiation points for fracture or fatigue cracks. Therefore, designs should avoid such concentrations by employing shapes that mitigate them (e.g., adding fillets, enlarging holes, smoothing abrupt steps).

The actual impact on fracture strength relates to the material's plastic deformation capacity and fatigue strength. Hence, the concept of the ‘effective stress concentration factor (fatigue stress concentration factor Kf)’ is also employed.

We shall now present several concrete examples of the representative stress concentration factor Kt.

1. Tension in a flat plate with a circular hole

When a flat plate of width W has a hole of diameter d at its centre, tension loading causes stress concentration around the hole.

In other words, the greater the ratio of the hole, the stronger the stress concentration becomes.

2. Notches with sharp corners on flat plates

When a ‘rectangular notch’ is present on a flat plate, stress concentrates more intensely the sharper the corners are.

Large curvature radius ρ at the notch base → Stress concentration is small

Very small ρ (sharp angle) → Kt increases sharply

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3. Stepped Round Bars (Where Shaft Diameter Changes Abruptly)

In the common mechanical element known as a ‘stepped shaft’, stress concentration occurs at the step transition.

A smaller fillet radius r at the step results in a larger Kt value.

This relationship is proportional: the greater the D/d ratio, the greater the stress concentration.

Example (for tension and bending):

4. Transverse holes in shafts (such as pin holes)

When applying tensile load by drilling a transverse hole through the centre of a round bar:

Key Points Summary

Holes, notches, steps, sharp corners → Cause stress concentration

Increase the radius of curvature, smooth out steps, reinforce holes → Can mitigate stress concentration

As a guideline, Kt values commonly encountered in design practice are typically around 2 to 3.