Crack modelling: A novel technique for the prediction of fatigue failure in the presence of stress concentrations

Abstract

Finite element (FE) analysis and other computational methods have developed rapidly in recent years, allowing accurate predictions of elastic stresses in components of complex geometry. However, the prediction of fatigue failure in these components is still a non-trivial problem; one reason for this is the difficulty of assessing stress concentrations and regions of high stress-gradient.

This paper describes a new technique, called “crack modelling”, which addresses the problem through a modification of linear-elastic fracture mechanics (LEFM). LEFM is designed to deal with cracks in nominally elastic stress fields, using elastic analysis to derive a characteristic stress intensity, K or, for cyclic loading, a range ΔK. This methodology is modified in two ways. Firstly it is shown that LEFM can be extended to predict the fatigue behaviour of bodies containing notches of standard geometry, instead of cracks. Secondly, FE analysis is used in conjunction with a modelling exercise in order to extend the method to include bodies of arbitrary shape subjected to any set of loads.

The method was first tested using standard notch geometries (blunt and sharp notches in beams), where accurate predictions of fatigue limit could be achieved. It was then applied to an industrial problem, giving a prediction of high-cycle fatigue behaviour for an automotive crankshaft. The method requires only simple mechanical-property data (the material fatigue limit and stress-intensity threshold) and uses only linear-elastic FE modelling. It allows fracture mechanics theory to be used without the need to specifically model the presence of a crack and uses far-field elastic stresses to infer behaviour in the region of a stress concentration.