A non-linear damage accumulation fatigue model for predicting strain   life at variable amplitude loadings based on constant amplitude fatigue data
  A new phenomenological technique for using constant amplitude loading data to predict fatigue life from a variable amplitude strain history is presented. A critical feature of this reversal-by-reversal model is that the damage accumulation is inherently non-linear. The damage for a reversal in the variable amplitude loading history is predicted by approximating that the accumulated damage comes from a constant amplitude loading that has the strain range of the particular variable amplitude reversal. A key feature of this approach is that overloads at the beginning of the strain history have a more substantial impact on the total lifetime than overloads applied toward the end of the cycle life. This technique effectively incorporates the strain history in the damage prediction and has the advantage over other methods in that there are no fitting parameters that require substantial experimental data. The model presented here is validated using experimental variable amplitude fatigue data for three different metals. 
S. P. Beckman and P. J. Huffman
cond-mat.mtrl-sci