Predicting high cycle fatigue life with unified mechanics theory

Fatigue life prediction of metals has been widely studied. However, most of the research is based on empirical models under the framework of Newtonian mechanics, that relies on experimental fatigue data for curve fitting a degradation evolution function. Unified mechanics theory (UMT), on the other hand, unifies the universal laws of motion of Newton by incorporating the second law of thermodynamics directly into the Newton's laws at the ab-initio level. UMT introduces an additional linearly independent axis called Thermodynamic State Index (TSI), which can have values between zero and one. Evolution along the TSI axis follows the Boltzmann's entropy formulation and the thermodynamic fundamental equation of the material. As a result, governing differential equations of any system automatically include energy dissipation, and degradation evolution. The fatigue model presented here is pure physics based and does not require an empirical evolution function obtained by curve fitting to fatigue test data. However, it does require deriving analytical thermodynamic fundamental equations of the material based on the principals of physics. Thermodynamic fundamental equation for high cycle metal fatigue is derived in this study.