Probabilistic stress and strain-life fatigue crack initiation models with mean stress effects and life-dependent scatter considering runouts

A powerful probabilistic framework is proposed to account for life-dependent data scatter in fatigue crack initiation (FCI) predictions considering mean stress effects. It is applicable to any stress, strain, or energy-based fatigue damage parameter (DP), as long as the logarithm of DP for a given FCI life Nf can be assumed to follow a three-parameter Weibull (W3P) distribution. The proposed approach, named P-DP-N, does not require the assumption of any particular statistical distribution for Nf, thus it can fit the shape of virtually any equation correlating DP and Nf. Hence, it can deal simultaneously with LCF, HCF and VHCF FCI data, considering mean stress effects and runout statistics. The approach deals with heteroscedasticity through a user-defined lifedependent scedastic function of Nf, allowing the consideration of variable data scatter in log-log scales. The PDP-N performance is evaluated using the Walker Equivalent Strain (WES) equation proposed by the authors, which is generalized to explicitly consider fatigue limits. Procedures are proposed to calibrate both stress and strain-based versions of the deterministic WES-life FCI model, as well as to optimize the W3P parameters from the resulting P-WES-N probabilistic model, considering runout data when available. A compact computational implementation of the calibration routines is presented as well. The W3P-based P-WES-N probabilistic model is evaluated for 31 metallic alloy data sets from the literature that include non-zero mean stresses and at least twenty specimens each, totaling 1,498 uniaxial fatigue specimens, including 141 runouts. This comprehensive evaluation shows that the proposed probabilistic model is able to account for tensile and compressive mean stress effects, as well as to calibrate the usually observed increase in experimental scatter for longer FCI lives.