Numerical measures of non-proportionality degree in incomplete contact subjected to fretting fatigue loading

Fretting fatigue failure is a fatigue fracture that initiates at a surface area where fretting has occurred. Fretting fatigue life assessment under multiaxial loading is a rather complex task, as the stresses at contact interface are multiaxial. A phase-shift between stress components leads to lower equivalent stress values calculated by most of available multiaxial fatigue criteria and therefore to an increased estimated fretting fatigue life. In this study a correlation based non-proportionality factor is introduced to predict the fretting fatigue lifetime under non-proportional stressing. The proposed factor is based on a statistical correlation of normal and shear stress components and does not depend on the choice of the coordinate system. A two dimensional finite element model is used to extract the stress components at crack initiation site. Moreover, to enhance the fretting fatigue lifetime assessment, stress-based Findley multiaxial fatigue criterion is modified by introducing the non-proportionality factor. A series of experimental data of high strength CrNi steel, taken from literature, are used to investigate the effect of non-proportional stressing on fretting fatigue life prediction.