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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.

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The proposed equation for estimating J makes use of the linear elastic and the fully plastic solution to interpolate over the entire range from small-to large-scale yielding. The elastic geometry factor is obtained by means of the stress intensity factor. In the fully plastic formulation, the plastic geometry factors are obtained by considering a pure power-hardening solid, which reduces at one limit to an incompressible linear elastic solid, and at the other to a perfectly plastic solid. The solutions are given for three basic configurations: a double-edgecracked plate under tension and bending; a notched plate under tension with a crack at the root of the notch; a single-edge-cracked plate under bending. Both force control and displacement control are considered. The accuracy of the formulae is assessed using the finite element calculations in Part 2.

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