Multiphysics S-N-P Fatigue Curves by Mechanistic Method Integration: Stochastic Tanaka-Mura, Klesnil-Priddle, El Haddad and Coffin-Manson, calibrated and validated against 44 published points of seven structural materials

<title>Abstract</title> <p>This work presents a stochastic numerical model for generating S-N-P fatigue curves (stress amplitude vs. number of cycles vs. probability of failure) from a single set of static mechanical properties (elastic modulus, ultimate strength, Vickers hardness, critical defect size), integrating four mechanistic methods: (i) crack initiation by Tanaka-Mura in stochastic mode; (ii) propagation with the Klesnil-Priddle threshold and El Haddad correction; (iii) the plastic branch of Coffin-Manson with exponential blending (q-blend) at the elastic-plastic transition; and (iv) spectral-load damage by Rainflow counting on Gaussian PSD synthesis. Six physical factors per material are calibrated by log-10 loss minimization with leave-one-out cross-validation. The model is validated against 44 published experimental points of seven structural materials (AISI 4340 Q&amp;T, Al 2024-T3, Al 7075-T6, annealed Ti-6Al-4V, Inconel 718, AISI 316L and Al 6061-T6): 44/44 points inside the published scatter band (mean error from 12.5% to 58.3% depending on material). In aggregate metrics over 35 finite-life points, the calibrated model achieves a mean absolute log-ratio error of 0.125 with 89% of points within a factor of 2, versus 1.12 and 16% for the classical Basquin line and 0.77 and 16% for total Coffin-Manson. The model extends the S-N curve to the environment (humidity, chloride, temperature, magnetic/electric fields, hydrostatic pressure), to mean stress (Walker equivalent), to size effect (weakest-link) and to spectral vibration (PSD), enabling engineering scenario studies without additional testing.</p>