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Stress concentration, explained

In Hebrew: ריכוז מאמצים

A hole, notch or sharp step raises the local stress above the nominal value by the factor K_t. A small hole in a wide plate under tension triples it.

Where it comes from

Picture the load flowing through the part like water. A hole or a step forces the flow lines to crowd around it, and where they crowd the stress peaks. The sharper the change in geometry, the higher the peak: an elliptical hole gives K_t = 1 + 2a/b, so a long thin crack across the load gives an enormous one.

K_t depends only on geometry and load type, not on the material. Values come from Peterson’s charts, plotted against ratios like fillet radius over diameter, or from a finite element model with a fine mesh at the feature.

When it matters

Under static load, a ductile metal yields locally at the peak and redistributes the stress, so designers often check the net section without K_t. Brittle materials cannot do that, and every part under fatigue loading cannot either: the crack starts at the peak. There, K_t is not optional.

In fatigue, real parts are slightly less sensitive than K_t predicts. The notch sensitivity q, between 0 and 1, scales it down to the fatigue factor K_f. High-strength steels sit near 1.

How to design it down

Use the largest fillet radius the design allows. Add relief grooves next to a necessary notch so the flow lines turn gradually. Move holes out of the high-stress region. A shoulder fillet that goes from 0.5 to 2 mm can halve the peak stress for the cost of a different cutter.

A worked number

A plate 100 mm wide and 10 mm thick has a 20 mm hole and carries 50 kN in tension. The nominal stress on the net section is 50,000/(80 × 10) = 62.5 MPa. Peterson’s chart gives K_t ≈ 2.5 for that hole-to-width ratio, so the peak at the edge of the hole is about 156 MPa.

For fatigue in a steel with q ≈ 0.8, K_f = 1 + 0.8 × 1.5 = 2.2.

Common mistakes

  • Pairing a chart’s K_t with the wrong nominal stress. Some charts use the gross section, others the net.
  • Leaving K_t out of a fatigue calculation because the static check passed.
  • Reading an FEA peak at a perfectly sharp corner. With zero radius the stress is a singularity; model the real fillet.

Mechanical engineering, explained