S-N & Haigh Diagram Calculator

How the calculation works

The endurance limit of the part is built from the rotating-beam value with the Marin modification factors (Shigley):

$$S_e = k_a\,k_b\,k_c\,k_e\,k_{misc}\,S'_e, \qquad S'_e = 0.5\,S_{ut} \;\; (\text{steel, capped at } 700\,\text{MPa})$$

The finite-life S-N curve between $10^3$ and $10^6$ cycles follows the Basquin form $S = a\,N^b$ with

$$a = \frac{(f\,S_{ut})^2}{S_e}, \qquad b = -\tfrac{1}{3}\,\log_{10}\!\frac{f\,S_{ut}}{S_e}$$

Mean stress is handled on the Haigh diagram. With a load line through the origin (proportional loading), the safety factors are:

$$\text{Goodman: } \frac{1}{n} = \frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_{ut}} \qquad \text{Soderberg: } \frac{1}{n} = \frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_y}$$

$$\text{Gerber: } \frac{n\,\sigma_a}{S_e} + \left(\frac{n\,\sigma_m}{S_{ut}}\right)^{\!2} = 1 \qquad \text{ASME-elliptic: } \left(\frac{n\,\sigma_a}{S_e}\right)^{\!2} + \left(\frac{n\,\sigma_m}{S_y}\right)^{\!2} = 1$$

together with the Langer line for first-cycle yielding, $n_y = S_y/(\sigma_a + |\sigma_m|)$. For life prediction, the operating point is converted to an equivalent fully reversed stress, e.g. for Goodman $S_{ar} = \sigma_a/(1 - \sigma_m/S_{ut})$, which is then entered into the Basquin equation.

Conventions and assumptions: for compressive mean stress the beneficial effect is conservatively ignored ($\sigma_a$ is simply checked against $S_e$). The $S'_e = 0.5\,S_{ut}$ rule and the endurance-limit plateau apply to steels; aluminium and other alloys without a fatigue limit need a different treatment. In torsion ($k_c = 0.59$, shear-based $S_e$) the inputs are shear stresses and the criteria are anchored to the shear static strengths $S_{su} \approx 0.67\,S_{ut}$ and $S_{sy} = S_y/\sqrt{3}$. Room temperature is assumed ($k_d = 1$); the optional factor $k_{misc}$ can carry $k_d$, $1/K_f$, or any other modification. Below 7.62 mm the size factor is conservatively clamped at $k_b = 1$. The $S'_e$ cap is fixed at 700 MPa ($\approx 101.5$ ksi) in both unit systems, so the computed $S_e$ never depends on the unit selection (Shigley's US-customary convention rounds this to 100 ksi). A notch is accounted for by dividing $S_e$ by the fatigue notch factor $K_f$ from the stress concentration calculator. Below about $10^3$ cycles the stress-life method loses validity and the strain-life method should be used.

This calculator is provided for educational purposes and accompanies our course Introduction to Fatigue Calculations with FEA. Verify results against applicable standards before using them in design.