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A B S T R A C T Based on the weakest-link concept a method is developed, from which the endurance probability of every surface and volume element of a case-hardened part, which is loaded near the endurance limit, can be calculated. A prerequisite for the calculation is knowledge of the hardness and residual stress distribution, the surface roughness and the surface oxidation depth. By multiplication of the endurance probabilities of neighboured elements the endurance probability of a limited region or of the whole part can be calculated, which includes an endurance limit determination. It is shown, that this model can be applied successfully to specimens of a carburized steel. The necessary model parameters can be gained from a set of reference specimens. Because of the possibility to formulate an endurance probability for every volume and surface element, there are no geometrical restrictions on the parts to be assessed. N O M E N C L A T U R EA 0 = reference area AT = alternating torsion F = distribution function m = exponent of the two-parametric Weibull distribution M = mean stress sensitivity N F = number of cycles to failure p = hydrostatic stress P E = endurance probability P F = failure probability R = load ratio RB = rotary bending RT = repeated tension S a = nominal stress amplitude S D = median of the endurance limit described as nominal stress S m = nominal mean stress SO = surface oxidation TC = tension compression V 0 = reference volume x SO = depth of surface oxidation λ = X-ray wave length c 2005 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 28, 983-995 983 984 H. BOMAS and M. SCHLEICHERσ a = local stress amplitude σ aeq = equivalent stress amplitude σ m = local mean stress σ W = local endurance limit for symmetric tension-compression τ W = local endurance limit for symmetric shear I N T R O D U C T I O NFor a long time, the calculation of the endurance limit of case-hardened parts has been a subject of scientific and practical interest. Starting from the early work of Woodvines, 1 in the last years especially the results of carburizing, 2,3 nitriding, 2,4-7 induction hardening 8,9 and laser hardening 10,11 have been investigated with respect to the endurance limit. The following contribution describes a calculation method for carburized steels, which allows the prediction of the endurance limit of parts of arbitrary geometry based on data that have been gained from tests on a set of reference specimens under certain load conditions. The endurance limit refers to a number of cycles equal to 10 7 . It is known that fatigue failure of high-carbon steel may also occur after passing this number of cycles, 12 this is a feature that could not be examined in this work.For the development of this calculation method, the endurance limits of smooth and notched specimens under tension-compression, repeated tension, rotary bending and alternating torsion have been determined experimentally. Hereby, the influence of mean stresses, multiaxial stress conditions, stress gradients and gradients of the...

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A B S T R A C T The endurance limit and the mechanisms of fatigue crack initiation in the high-cycle regime were investigated using round specimens of the bearing steel SAE 52100 in a bainitic condition under longitudinal forces, torsional moments and combinations of these loads. Three specimen types were examined: smooth specimens and specimens with circumferential notches with radii of 1.0 and 0.2 mm. The surfaces of the specimens including the notches were ground resulting in compressive residual stresses in the nearsurface region. The influence of mean and multiaxial stresses on the endurance limit can be understood by consideration of crack initiation mechanisms and micromechanics. Crack initiation occurred at oxides, carbonitrides and at the surface. The oxides had little adhesion to the bainitic matrix and acted like pores. The carbonitrides were well bonded to the matrix and caused stress concentrations due to their higher elastic modulus when compared to that of the matrix. The mechanisms of crack initiation could be related to the load type: loads with rotating principal stresses cause more damage for nitrides than for oxides. Increasing maximum stresses are more dangerous for nitrides than for oxides, and damage the surface more than the nitrides. Normal stresses produce more damage for oxides than shear stresses. The endurance limits were calculated by means of an extended weakest-link model which combines volume and surface crack initiation with individual fatigue criteria. For volume crack initiation, the criterion of Dang Van was used. For the correct description of the surface crack initiation, a criterion proposed by Bomas, Mayr and Linkewitz was applied. With this concept, a prediction of the endurance limit is possible. The influence of the notch geometry on the endurance limit is well characterized. A 0 = reference surface d = net diameter of the specimens E = elastic modulus f = load frequency F = longitudinal load, distribution function K t,σ = concentration factor for normal stress K t,τ = concentration factor for shear stress m = exponent of the Weibull distributionCorrespondence: H. Bomas.