Altobelli, J. and Chandrupatla, T., "Fatigue Life Calculation with Loads Varying in Magnitude and Direction," SAE Technical Paper 2013-01-0999, 2013, doi:10.4271/2013-01-0999.
In fatigue life prediction, it is common to analyze a component subjected to a load-versus-time history that varies in magnitude over time. In established methods, it is assumed that the directions of the applied loads do not change, so stresses along the same reference plane can be compared as unidimensional quantities. Put differently, these methods require that the principal stress orientation remains the same throughout the load history.This work aims to determine the fatigue life of a component experiencing a load-versus-time history that produces stresses varying in both magnitude and principal stress orientation. To accomplish this, all six components of the stress tensor are required throughout the loading history. By choosing a cut plane defined by the normal direction n, the normal stresses can be determined. The application of the rainflow counting method can then be used to convert the normal stresses into equivalent fatigue cycles. The Goodman method can compare these cycles against an S-N or Wohler curve, while Miner's rule calculates the life Lⁿ corresponding to the plane n.It is necessary to find the cut plane that minimizes Lⁿ while ensuring that n remains a unit normal. The search for min Lⁿ is completed using the Nelder and Mead optimization. The method presented in this paper can evaluate the minimum life and the plane on which a crack will initiate.