Stress Concentration Factor Calculator

Use this stress concentration factor calculator to estimate the localized high stresses in the regions of geometric discontinuities.

Stress concentration factor2.50646Howland's fit at d/W = 0.2. In an INFINITELY wide plate it is exactly 3, independent of hole size — a small hole concentrates stress just as much as a large one

Peak local stress250.6464 MPaK_t times the nominal 100 MPa, right at the feature. It falls back to the nominal value within roughly one feature diameter

Nominal stress100 MPa

Extra stress from the feature150.6464 MPa150.646% above nominal

K_t is a STATIC elastic factornot the fatigue factorin fatigue the effective factor K_f is usually LOWER than K_t, because materials are notch-sensitive to differing degrees. Using K_t for fatigue is conservative rather than correct

Ductile materials tolerate itlocal yielding redistributesa ductile material yields at the notch and sheds the peak into its surroundings, so K_t matters far less under static load than under fatigue. A brittle material has no such relief, which is why glass and cast iron are so notch-sensitive

In an infinitely wide plate3.0000the classic Kirsch result, and it does not depend on the hole size at all

Net section stress125 MPathe hole also removes material, raising the average stress on what remains — a separate effect from the concentration

The formula

K_t = 1 + 2√(a/ρ); circular hole K_t = 3

A small hole is as bad as a large one

In a wide plate the stress concentration factor for a circular hole is exactly 3, whatever the hole's diameter. Halving the hole does not halve the peak stress — it just shrinks the region over which the peak acts. What matters is the SHAPE of the feature, not its size, and that is the single most counter-intuitive result in the subject.

Sharpness is what really hurts. An elliptical hole gives 1 + 2√(a/ρ), so as the tip radius goes to zero the concentration goes to infinity. A perfectly sharp crack has no finite K_t at all, which is precisely why fracture mechanics abandons stress concentration and works with stress intensity instead.

Ductility forgives, fatigue does not

Under static load a ductile material yields locally at the notch and redistributes the peak into its surroundings, so a high K_t often does little harm. A brittle material has no such relief, which is why glass and cast iron are so notch-sensitive and why scoring glass makes it break where you want.

Under fatigue there is no forgiveness at all: cracks start at stress concentrations, and most fatigue failures begin at a hole, a sharp corner or a tool mark. The fatigue factor K_f is usually somewhat below K_t because materials vary in notch sensitivity, so using K_t for fatigue is conservative rather than exact.