# Disputation - Salar Sadek

Probabilistic high cycle fatigue models - volumetric approaches

Salar Sadek defended his PhD thesis on December 18th 2015. The thesis was titled “Probabilistic high cycle fatigue models - volumetric approaches”. The supervisor was Mårten Olsson and the faculty opponent was Prof. Anders Ekberg, Applied Mechanics, Chalmers.

Fatigue is the most frequent failure mode and must be considered in a mechanical design of actual operating components. The fact that mechanical design is most often linked with existence of stress raisers and multiaxial time-varying stresses has in the last decades increased the research effort worldwide. The goal is to put forward methods and ideas to explain the fatigue phenomenon so that costs can be decreased and reliability can be increased. The ultimate goal is reliable performance of mechanical components. Most of the available models for High Cycle Fatigue (HCF) assessment are deterministic and 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 the knowledge that HCF has a degree of randomness (stochastic), often showing considerable scatter even in well controlled environments. In traditional product design, safety factors, or design factors, are usually assigned in order to assure reliability since the fatigue process is influenced by many different factors, i.e. size effect, gradient effect and load effect, which inherently exhibit scatter. Probabilistic approaches in fatigue design are practical due to the uncertainties associated with service loads, material properties, geometrical attributes, and mathematical design models. This approach allows a quantification of risk that is not possible with deterministic design approaches. In HCF assessment, both the deterministic and probabilistic models share a common critical point. The critical point is the transferability of the models, i.e. transferring fatigue 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 affecting the fatigue life of components. The volumetric approaches based on threshold stress levels have indicated on good predictive capabilities. In these approaches, it is assumed that only in some highly stressed material volume, fatigue processes take place. For describing the scatter around the fatigue limit, the weakest link (WL) model is widely used. In the WL-model, the spatial stress field acting in a component is integrated over either the component material volume or surface and thus the failure probability is obtained. 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 the highly 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 any spatial point that is stressed higher than a material specific threshold stress value. All points that fulfill this condition form the highly loaded regions. The new models are found to have good transferability and improved predictive capability compared to the WL-model when validated with fatigue test data obtained from conducted experiments using cylindrical specimens loaded by uniaxial and rotating bending loading modes.