This paper investigates the accuracy of the linear‐elastic Theory of Critical Distances (TCD) in estimating high‐cycle fatigue strength of notched metallic materials experiencing elevated temperatures during in‐service operations. The TCD postulates that the fatigue damage extent can be estimated by directly post‐processing the entire linear‐elastic stress field acting on the material in the vicinity of the crack initiation locations. The key feature of this theory is that the high‐cycle fatigue assessment is based on a scale length parameter that is assumed to be a material property. The accuracy of this design method was checked against a number of experimental results generated, under axial loading, by testing, at 250 °C, notched specimens of carbon steel C45. To further investigate the reliability of the TCD, its accuracy was also checked via several data taken from the literature, these experimental results being generated by testing notched samples of Inconel 718 at 500 °C as well as notched specimens of directionally solidified superalloy DZ125 at 850 °C. This validation exercise allowed us to prove that the linear‐elastic TCD is successful in estimating high‐cycle fatigue strength of notched metallic materials exposed to elevated temperature, resulting in estimates falling within an error interval of ±20%. Such a high level of accuracy suggests that, in situations of practical interest, reliable high‐cycle fatigue assessment can be performed without the need for taking into account those non‐linearities characterising the mechanical behaviour of metallic materials at high temperature, the used critical distance being still a material property whose value does not depend on the sharpness of the notch being designed.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. b s t r a c tThis paper assesses and quantifies the detrimental effects of complex tri-dimensional notches subjected to uniaxial and multiaxial fatigue loading. A number of experimental results taken from the technical literature and generated by testing specimens containing complex geometrical features were reanalysed using a critical distance/plane method. The investigated notched samples were tested under uniaxial and multiaxial constant amplitude load histories, considering also the effects of non-zero mean stresses as well as non-proportional loading. The common feature of the considered notched geometries was that the position of the critical location changed as the degree of multiaxiality of the applied loading varied. The relevant linear-elastic stress fields in the vicinity of the crack initiation points were calculated by the Finite Element method and subsequently post-processed using the Modified Wöhler Curve Method in conjunction with the Theory of Critical Distances (the latter theory being applied in the form of the Point Method). This validation exercise confirms the accuracy and reliability of our multiaxial fatigue life assessment technique, which can be efficiently used in situations of practical interest by directly postprocessing the relevant linear-elastic stress fields calculated with commercial Finite Element software packages.

Engineering components often contain notches, keyways or other stress concentration features. These features raise the stress state in the vicinity of their apex which can lead to unexpected failure of the component. The Theory of Critical Distances has been proven to predict accurate results, but, conventionally, requires two key ingredients to be implemented: the first is a stress-distance curve which can be obtained relatively easily by means of any finite element software, the second is two additional material parameters which are determined by running appropriate experiments. In this novel reformulation, one of these additional parameters, namely the critical distance, can be determined a priori, allowing design engineers to assess components whilst reducing the time and cost of the design process. This paper investigates reformulating the Theory of Critical Distances to be based on two readily available material parameters, i.e., the Ultimate Tensile Strength and the Fracture Toughness. An experimental data base was compiled from the technical literature. The investigated samples had a range of stress concentration features including sharp V-notches to blunt U-notches, and a range of materials that exhibit brittle, quasi-brittle and ductile mechanical behaviour. Each data set was assessed and the prediction error was calculated. The failure predictions were on average 30% conservative, whilst the non-conservative predictions account for less than 10% of the tested data and less than 2% of the non-conservative error results exceed -20%. It is therefore recommended that a safety factor of at least 1.2 is used in the implementation of this version of the Theory of Critical Distances.

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