A new model of fatigue life dispersion in rolling contact

The dispersion of rolling contact fatigue life is modelled assuming defects of uniform severity randomly distributed in the stressed volume. The probability of a defect occurring in a material volume is assumed to follow a Poisson distribution. The life N to failure at any defect is obtained as a deterministic function of a stress related hazard parameter t_R at the defect location. Defining equi-hazard contours as loci of constant hazard parameter, the area S_A enclosed by any equi-hazard contour is related to the hazard factor t_R at the contour through Hertzian analysis. A toroidal material volume bounded in each cross section by an equi-hazard contour with an identical hazard parameter value t_R contains all points at which a defect fails after a life not exceeding N. The probability S(N) of survival beyond N is equal to the Poisson probability P(0) that there is no defect within this volume and is obtained by transformation of P(0). It yields a three parameter Weibull distribution with a dispersion exponent β depending solely on the Hertzian stress distribution and presupposing no defect severity dispersion. It is estimated to be of the order β = 0.4-1.3, which reasonably coincides with the life dispersions obtained experimentally. The minimum life N₀ can be set equal to the experimental value N = 0.05 N₁₀, where N₁₀ is the 10% failure life quantile.