Application of the weakest‐link concept to the endurance limit of notched and multiaxially loaded specimens of carburized steel 16MnCrS5

Abstract

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...

Fatigue of metals under nonuniform stressed state. part 2. methods of the analysis of research results

“…The d c value obtained by criterion (39) was found to be substantially higher than that by criterion (38). In particular, with ρ = 0.127 mm and K t = 2.85 and high stress ratios R the d c was 0.06 and 0.024 mm, respectively.…”

“…Analysis of expressions (38) and (39) shows that the value of d c will be larger in the case of using criterion (39), rather than (38).…”

“…Figure 13 provides a graphical interpretation of criterion (38); b) the mean stress in a layer of depth d c is equal to stresses in a smooth specimen,…”

“…Specifically, during the investigation of a titanium alloy under various stress ratios, with K t ranging from 1.97 to 4.07 and notch radii ρ from 0.127 to 0.330 mm, Lanning et al [50] found out that the d c value computed according to formula (38) for fatigue limits on a base of 10 6 cycle varied in the range between 0.023 and 0.255 mm in the case of using maximum normal stresses and between 0.012 and 0.114 mm when employing the stresses by the Mises criterion.…”

Influence of inclusion type and size on the fatigue strength of high strength steels

“…Cracks are formed either at the surface or in the interior of the specimen which propagate and lead finally to the fracture of the specimen. In case of internal failures inclusions frequently act as crack initiating sites, where oxides, nitrides and sulphides are the most frequently mentioned inclusion types [2][3][4][5]. It is well known that with increasing inclusion size the fatigue strength of steel specimens is reduced [6].…”