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A B S T R A C T A sickle-shaped surface crack in a round bar under complex Mode I loading is considered.First, the stress-intensity factor (SIF) along the front of the flaw is numerically determined for five elementary Mode I stress distributions (constant, linear, quadratic, cubic and quartic) directly applied on the crack faces. The finite element method and linear elastic fracture mechanics concepts are employed. Then, a numerical procedure to calculate approximate values of SIF for a complex Mode I stress distribution on the crack faces is proposed based on both the power series expansion of the function describing such a stress distribution and the superposition principle. In order to validate the results obtained through the above procedure, a comparison with numerical data available in the literature is made. a = crack depth at the most internal point A on the crack front (Fig. 1) a el = ellipse semi-axis (along the Y -axis) b el = ellipse semi-axis (along the X -axis) B i(L) = ith polynomial coefficient describing the generic complex Mode I stress distribution σ I(L) B i(L lin) = ith polynomial coefficient describing the linear complex Mode I stress distribution σ I(L lin) B i(L quad) = ith polynomial coefficient describing the quadratic complex Mode I stress distribution σ I(L quad) D = diameter of the round bar E = Young's modulus h = distance of point B (intersection between the crack front and the external boundary of the bar cross-section) from the Y -axis (Fig. 1) K I(i) , K * I(i) = stress-intensity factor (SIF) and dimensionless SIF, respectively, for the ith elementary Mode I stress distribution σ I(i) K I(L) , K * I(L)= stress-intensity factor (SIF) and dimensionless SIF, respectively, for the generic complex Mode I stress distribution σ I(L) K I(L lin) , K * I(L lin) = stress-intensity factor (SIF) and dimensionless SIF, respectively, for the linear complex Mode I stress distribution σ I(L lin) K I(L quad) , K * I(L quad) = stress-intensity factor (SIF) and dimensionless SIF, respectively, for the quadratic complex Mode I stress distribution σ I(L quad) u = coordinate related to the U-axis, with origin at point O ( Fig. 1) X , Y , Z = cartesian coordinate axes (Fig. 1) w x , w y , w z = displacements along the X -, Y -, Z-axis, respectively α = a el /b el = aspect ratio of the elliptical-arc crack front Correspondence: A. Carpinteri.

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In the present paper, a high-cycle critical plane-based multaxial fatigue criterion, recently proposed by the authors to determine the fatigue strength of smooth components, is extended to notched components by using the so-called point method. Accordingly, once the location of the 'hot spot' on the notch surface is determined, the orientation of the critical plane (material plane where fatigue strength assessment has to be performed) is assumed to be correlated with the principal stress directions in the hot spot itself. Some experimental results related to round bars with a surface circular notch (an artificially drilled surface hole) submitted to cyclic loading are compared with the theoretical predictions of the proposed extension. The comparison, which is instrumental in highlighting the notch size-effect (as the hole diameter varies) under uniaxial and biaxial far-field stress conditions, appears to be quite satisfactory.