Probabilistic high cycle fatigue models - volumetric approaches

Abstract: Fatigue is the most frequent failure mode and must be considered in a mechanical designof actual operating components. The fact that mechanical design is most often linkedwith existence of stress raisers and multiaxial time-varying stresses has in the last decadesincreased the research effort worldwide. The goal is to put forward methods and ideasto explain the fatigue phenomenon so that costs can be decreased and reliability can beincreased. The ultimate goal is reliable performance of mechanical components.Most of the available models for High Cycle Fatigue (HCF) assessment are deterministicand are applied to experimental fatigue limits for a failure probability of 50%.These models are not intended to describe the statistical nature of HCF even with theknowledge that HCF has a degree of randomness (stochastic), often showing considerablescatter even in well controlled environments. In traditional product design, safetyfactors, or design factors, are usually assigned in order to assure reliability since thefatigue process is influenced by many different factors, i.e. size effect, gradient effect andload effect, which inherently exhibit scatter.Probabilistic approaches in fatigue design are practical due to the uncertainties associatedwith service loads, material properties, geometrical attributes, and mathematicaldesign models. This approach allows a quantification of risk that is not possible withdeterministic design approaches.In HCF assessment, both the deterministic and probabilistic models share a commoncritical point. The critical point is the transferability of the models, i.e. transferringfatigue data in between different geometries. In order to address the problem of transferability,and hence the prediction capability of the fatigue models in new situations,many engineers and researchers have contributed.The stress gradient and the structural size are known to be important factors affectingthe fatigue life of components. The volumetric approaches based on threshold stresslevels have indicated on good predictive capabilities. In these approaches, it is assumedthat only in some highly stressed material volume, fatigue processes take place.For describing the scatter around the fatigue limit, the weakest link (WL) model iswidely used. In theWL-model, the spatial stress field acting in a component is integratedover either the component material volume or surface and thus the failure probability isobtained. The model is considered to be the state of the art approach in HCF field.In this work, new probabilistic HCF models based on ideas originating from thehighly loaded region concept and the Theory of Critical Distances (TCD) are presented.The new HCF models stem from the hypothesis that fatigue damage can initiate at anyspatial point that is stressed higher than a material specific threshold stress value. Allpoints that fulfill this condition form the highly loaded regions. The new models arefound to have good transferability and improved predictive capability compared to theWL-model when validated with fatigue test data obtained from conducted experimentsusing cylindrical specimens loaded by uniaxial and rotating bending loading modes.