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.