A compatible regression Weibull model for the description of the three-dimensional fatigue σM–N–R field as a basis for cumulative damage approach. (February 2022) - Castillo, Enrique; Fernández-Canteli, Alfonso
Abstract: Different considerations suggest that the fatigue crack growth mechanism, in particular, the threshold between propagating and non-propagating conditions is factually governed by maximum stress rather than stress range values. This propitiates the consideration of σ M, as the primary variable to which the S–N field should be referred to whereas R = σ m / σ M would act as a secondary variable. Based on physical and statistical principles, notably the compatibility condition between both distributions F ( N ; σ M, R ) and F ( σ M ; N, R ), a functional equation is established whose solution provided the analytical expression of the σ M – N – R field representing the more general solution of the S–N field characterized by the common fatigue endurance limit. Higher reliability in the model S–N assessment is achieved because of the pooling of all results irrespective of the R -value. The essential point is that the normalizing variable V derived from the σ M – N – R field for certain load history can be identified as a state of cumulative damage and as such related to the probability of failure. The validity of the new model is confirmed by its application to data from experimental campaigns performed on AlMgSi 1 and Inconel 718 alloys. Highlights: A three-dimensional S–N model, including σ M as driving force, is proposed and the R-ratio effect. The model allows different pairs of σ M -R results to be jointly assessed as a unique sample. Damage life prediction for any load is predicted from the univariate single normalized variable V. Application to different metallic materials provides satisfactory definition of the 3D S–N field.