Geometry and Material Property Uncertainty Model for Fatigue Life Predictions

ABSTRACT The objective of the present work is the development and demonstration of a statistical model for the prediction of fatigue life of metal and alloys under different probability and confidence levels. This model is based on the assumption that fatigue life of a component follows log normal distribution. It describes an analytical model which is derived from energy theorem and coupled with the uncertainty associated with material properties and geometrical parameters to estimate fatigue life and crack growth at different level of probability and confidence level. A substantial amount of published data has been used to validate the proposed model for predicting S-N curve as well as fatigue crack growth of steel, aluminum alloys, copper alloys and titanium alloys. INTRODUCTION The analysis of cracks in a structure is an important aspect if the damage tolerance and durability of structures and components are to be predicted. As part of the engineering design process, engineers have to assess not only how well the design satisfies the performance requirements but also how durable the product will be over its life cycle. Often cracks cannot be avoided in structures; however the fatigue life of the structure depends on the location and size of these cracks. In order to predict the fatigue life for any component, crack growth study needs to be performed. Fatigue life is related to and is affected to a great extent with the uncertainties in both the material properties and the specimen or component geometrical parameters. The present work contributes to the fundamental understanding of fatigue life and its relation with these uncertainties. Several methods [1-27] have been discussed in the literature to predict the fatigue life but the problem of uncertainty associated with material and specimen geometry has not been addressed so far. In the present work an approximate analytical model derived from the energy theorem and probabilistic nature of material properties and specimen geometry parameters are combined and correlated to determine the associated error in the predicted fatigue life. The Error in estimating the fatigue life is derived from the expected values of fatigue life. The prediction is based on minimization of the error.