A unified expression for low cycle fatigue and extremely low cycle fatigue and its implication for monotonic loading

It is well-known that the empirical Manson–Coffin law tends to over-predict the cyclic life under extremely low cycle fatigue condition. In the present paper, a new unified expression is proposed to overcome this shortcoming. By introducing an exponential function, this new expression is capable of capturing the cyclic life over the entire span of extremely low cycle fatigue to low cycle fatigue with an additional material parameter to calibrate. Experimental data from existing literature are used to demonstrate the applicability of the proposed expression for several polycrystalline metals. The implication of the new expression to monotonic plastic fracture is discussed. It is also identified that the exponent in the unified expression is sensitive to temperature. Examples are given for the thermal influence on the material constants.