Strain-Life Calculator
This interactive calculator estimates the local stress-strain response at a notch using Neuber's rule combined with the cyclic Ramberg-Osgood equation, draws the resulting hysteresis loop, and predicts fatigue life with the strain-life (Coffin-Manson) equation including SWT and Morrow mean stress corrections.
Change any input and the results update instantly.
How the calculation works
The nominal stress amplitude is raised by the stress concentration factor $K_t$. Because the notch root yields locally while the surrounding material stays elastic, the elastic estimate $K_t S$ is converted to the real local stress-strain pair $(\sigma, \varepsilon)$ with Neuber's rule:
$$\sigma\,\varepsilon = \frac{(K_t\,S)^2}{E}$$
solved together with the cyclic Ramberg-Osgood material curve ($K'$, $n'$), since the material is assumed to be cyclically stabilised. The hysteresis branches follow Masing's hypothesis (the cyclic curve doubled):
$$\Delta\varepsilon = \frac{\Delta\sigma}{E} + 2\left(\frac{\Delta\sigma}{2K'}\right)^{1/n'}$$
Neuber's rule in this elastic form is only valid while the nominal (net-section) stress remains elastic. The calculator therefore checks the nominal stress against the yield stress and warns when this assumption is violated; for net-section yielding, extended methods such as Seeger's generalisation of Neuber or an elastic-plastic FEA are required.
The fatigue life $N$ then follows from the strain-life (Coffin-Manson) equation:
$$\frac{\Delta\varepsilon}{2} = \frac{\sigma'_f}{E}\,(2N)^b + \varepsilon'_f\,(2N)^c$$
Mean stress at the notch is accounted for either with Morrow (replace $\sigma'_f$ by $\sigma'_f - \sigma_m$) or with Smith-Watson-Topper:
$$\sigma_{max}\,\frac{\Delta\varepsilon}{2} = \frac{(\sigma'_f)^2}{E}\,(2N)^{2b} + \sigma'_f\,\varepsilon'_f\,(2N)^{b+c}$$
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.