A Maximum Likelihood Method for Estimating Probabilistic Strain Amplitude–Fatigue Life Curves

The fatigue lives of materials and structures at different strain levels show heteroscedasticity. In addition, when the number of test specimens is insufficient, the fatigue strength coefficient and fatigue ductility coefficient of the fitting parameters in the total strain life equation may not have definite physical significance. In this work, a maximum likelihood method for estimating probabilistic strain amplitude–fatigue life curves is presented based on the fatigue lives at different strain levels. The proposed method is based on the general basic assumption that the logarithm of fatigue life at an arbitrary strain level is normally distributed. The relationship among the parameters of total strain life equation, monotonic ultimate tensile stress and percentage reduction of area is adopted. The presented approach is finally illustrated by two applications. It is shown that probabilistic strain amplitude–fatigue life curves can be easily estimated based on the maximum likelihood method. The results show that fatigue lives at different strain levels have heteroscedasticity and the values of fatigue strength coefficient and fatigue ductility coefficient obtained by the proposed method are close to those of the true tensile fracture stress and true tensile fracture strain.

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