Non‐local stress approach for fatigue assessment based on weakest‐link theory and statistics of extremes

Abstract

A B S T R A C T In the present paper a non-local stress approach for fatigue assessment based on weakestlink theory and statistics of extremes is presented. It is a non-local stress approach in the sense that it takes the complete stress field into account rather than just the highest local stress. The statistical distribution of fatigue strength data from smooth standard specimens serves as a starting point for the computation of the probability of fatigue failure of a mechanical component under cyclic loading. The probability of fatigue failure can be obtained by post-processing results from a standard finite element stress analysis. It is shown that the non-local stress approach can be linked to the probability of finding the fatigue critical defect in the most highly stressed volume of the component. A numerical procedure is presented that is fully compatible with the results from a standard finite element stress analysis. It is further shown how the fatigue strength distribution can be transformed into a fatigue life distribution by using Basquin's equation. Finally, the nonlocal stress approach is used for predicting the fatigue limit of several specimens and predictions are compared with test results.Keywords block maximum method; effective stress amplitude; defects; finite element analysis; finite-element post-processor; statistics of extremes; surface effect; stress field; volume effect; weakest-link model. N O M E N C L A T U R E A = surface areaA 0 = reference surface area a = 'intrinsic' crack length a 0 = scale parameter in the generalized extreme value distribution a * 0 = characteristic largest defect size a crit = critical defect size B = Basquin coefficient b σ , b n = Weibull exponent G(a) = generalised extreme value distribution FEA = finite element analysis |J| = Jacobian determinant l = gauge length m = Basquin exponent n = number of cycles n = element face normal N = fatigue life (random variable) N * 0 = characteristic fatigue life N = element shape functions Correspondence: A. Wormsen.

Base material fatigue data for low alloy forged steels used in the subsea industry. Part 1: In air S–N data

“…5. The weakest-link method may be used for taking into account the influence of the size of the highly stressed volume of the component in a rational manner [56,57]. It is also worth noting that for notched components, especially with high stress concentration factors, the resulting fatigue strength is less dependent on the tensile strength than a smooth specimen [52].…”

Fatigue testing and analysis of notched specimens with typical subsea design features

“…• Exploring the capability of non-local stress methods (notch support factor method [10] and the weakest-link method [6,29,30]) in estimating the fatigue life of the tested notched specimens compared to using the local stress approach.…”

“…While the local stress approach is an excellent tool for performing design screening and design optimization of fatigue exposed equipment, it is well recognised [6,7] that this method will yield a conservative fatigue life estimate especially for equipment having design features with high stress concentration factors. In order to reduce the conservatism of the local stress approach, several non-local stress approaches for fatigue assessment have been developed .…”

“…In the notch support factor method, the peak stress in the component is adjusted with respect to the stress gradient in front of the notch. The stressed volume sensitivity on the fatigue strength is taken into account in the weakest-link method [6].…”

Fatigue damage criteria classification, modelling developments and trends for welded joints in marine structures

“…largest, critical) one defines the fatigue resistance and the probability of fatigue induced failure can conceptually be estimated using a series system description: a geometry (i.e. structural member assembly) is as weak as its weakest (material) link, introducing the statistics of extremes to the adopted process zone along the weld seam (Danzer et al 2007;Wormsen et al 2007;Todinov 2009). …”