Notch effect factor from stress concentration and support factor

What does this quantity describe?

The stress concentration factor αk describes the purely geometric, material-independent stress magnification at a notch (e.g. a hole, shoulder or groove). The support factor n accounts for the fact that ductile materials can yield locally at the notch root, relieving part of the theoretical stress peak (a support effect). The notch effect factor βk = αk/n is the actually effective reduction factor governing fatigue strength.

Think of αk as the theoretical backup height at a bottleneck in a rigid pipe. If the pipe material is instead compliant (like a ductile material), it locally relieves part of that backup — the support factor n describes exactly this relief effect.

Formula and variables

βk = αk / n

• βk = αk / n
• αk = βk · n
• n = αk / βk

Choose the inputs correctly

αk is the theoretical stress concentration factor, taken from notch charts, tables (e.g. TB 3-6) or an FEA for the given notch geometry and load type. n is the support factor, which depends on material, relative stress gradient and part size (e.g. from TB 3-7).

How to use the calculator

First determine αk for the notch geometry at hand and n for the material and part size, then enter both here to get βk.

Worked example

αk = 2.1 and n = 1.4 give βk = 2.1/1.4 = 1.5.

Understand the result and units

βk = 1.5 means the notched part's fatigue strength must be reduced by a factor of 1.5 relative to the unnotched fatigue strength. A value near 1 would indicate near-insensitivity to the notch.

αk, n and βk are all dimensionless.

Why βk is always smaller than αk

For ductile materials, the support factor n is always greater than 1, because local yielding at the notch root relieves the stress peak relative to the purely elastic calculation described by αk. For ideally brittle materials, n approaches 1, and βk approaches αk because no yielding is available to provide support. The gap between αk and βk is thus a direct measure of the material's ductility at the notch root.

Typical applications

The notch effect factor is used in fatigue and endurance strength verification for notched parts such as shaft shoulders, holes, grooves and thread run-outs, e.g. as an input to DIN 743.

Assumptions, limits and common mistakes

βk applies to fatigue strength (cyclic loading); for static strength, the notch effect is instead accounted for separately via the plastic support factor npl. The support factor n must be correctly taken from tables for the specific material and part size and is not universal.

Common mistake: A common mistake is equating βk with αk and neglecting the support effect of ductile materials entirely — this leads to an unnecessarily conservative (too low) fatigue strength estimate. n is also sometimes set to 1 across the board, which is only correct for very brittle materials.