A Unified Approach to Contact and Structural Fatigue

Abstract

A unified model of fatigue that is applicable to a variety of mechanical in nature fatigue phenomena including contact and structural fatigue is introduced. The model considers two-and three-dimensional stress states. The model is based on crack mechanics, kinetics of crack propagation, and statistical treatment of material defects. The foundation of the model follows from the analysis [1,2], a model of contact fatigue [3], and the asymptotic formulas for the stress intensity coefficients (see [4]) developed earlier. The model takes into account the local stress distribution, initial statistical distribution of defects versus their size, defect location and crack propagation directions related to the specific stress state of the material, material fatigue resistance parameters, etc. The main assumptions used for the model derivation and their validity are discussed.The crack distribution versus their size satisfies a kinetic equation. Together with a crack propagation equation (for example, Paris equation) the above kinetic equation allows to determine the distribution of cracks versus their size after any number of loading cycles. The fatigue phenomenon is considered to be of a discrete nature. The expressions for the local survival probability and the probability of the solid as a whole as well as for fatigue life are proposed.A parametric qualitative and quantitative analysis of the model properties is performed. It is found that for materials like steel fatigue life is practically independent from the material fracture toughness. The fatigue life increases as the normal and frictional stresses decrease and compressive residual stress increases.