Probabilistic formulation of the multiaxial fatigue damage of Liu

The Virtual Strain Energy (VSE) model proposed by Liu to study the multiaxial fatigue damage phenomenon is ordinarily used in its deterministic standard form. This model tries to compensate for the lack of adherence to rigorous continuum mechanics fundamentals of energy-based fatigue models like those of Garud or Ellyin, including not only an energetic approach but also a critical plane approach to the multiaxial fatigue phenomenon. In this paper, a new probabilistic formulation for the multiaxial fatigue damage model proposed by Liu [Int. J. Fatigue 23 (2001) S129] is established. With this random formulation, based on the perturbation method, the two main statistical moments (mean and variance) of the random variable fatigue lifetime (Nf) are obtained. These probabilistic results can be subsequently used to undertake reliability studies of the fatigue behavior of metal components.