ORIGINAL PAPER Numerical Estimation of Fretting Fatigue Lifetime Using Damage and Fracture Mechanics Reza Hojjati-Talemi • Magd Abdel Wahab • Eugenio Giner • Mohamad Sabsabi Received: 16 April 2013 / Accepted: 18 July 2013 Ó Springer Science+Business Media New York 2013 Abstract Fretting fatigue is a complex tribological phe- nomenon that can cause premature failure of connected components that have small relative oscillatory movement. The fraction of fretting fatigue lifetime spent in crack initiation and in crack propagation depends on many fac- tors, e.g., contact stresses, amount of slip, frequency, environmental conditions, etc., and varies from one appli- cation to another. Therefore, both crack initiation and propagation phases are important in analysing fretting fatigue. In this investigation, a numerical approach is used to predict these two portions and estimate fretting fatigue failure lifetime under a conformal contact configuration. For this purpose, an uncoupled damage evolution law based on principles of continuum damage mechanics is developed for modelling crack initiation. The extended finite element method approach is used for calculating crack propagation lifetimes. The estimated results are validated with previously reported experimental data and compared with other available methods in the literature. Keywords Fretting fatigue  CDM  XFEM  Partial slip 1 Introduction Fretting fatigue is the combination of tribological and fracture behaviour of materials that are in contact together having small relative movement at the same time. Due to fretting, fatigue lifetime is significantly reduced as com- pared to plain fatigue. This is because of the high stress gradients that are generated at the counter surfaces of the two connected bodies. Many failures in mechanical com- ponents due to fretting fatigue have been reported and studied in the literature, e.g., threaded pipe connections, bolted and riveted joints, blade-disc attachments in gas and steam turbines, shrink-fitted shafts and aero engine splined couplings, wires and so on [1]. Fretting fatigue failure process includes wear damage due to tribological behav- iour of interface surfaces of bodies, and fracture behaviour is related to fatigue crack propagation in bulk material. Fretting fatigue crack initiation can be explained by accumulation of damage, which leads to the formation of initial micro-cracks at the counter surface. Fretting fatigue crack propagation is defined as the advance of micro-cracks to final rupture of bulk material. The fraction of fretting fatigue lifetime spent in crack initiation and in crack prop- agation depends on many factors, e.g., contact stresses, amount of slip, frequency, environmental conditions, etc., and varies from one application to another. Therefore, both crack initiation and propagation phases are important in analysing fretting fatigue. In fretting fatigue experiments, it is very difficult to detect the crack initiation phase: the onset of crack growth and cracks is always hidden between the counterpart surfaces. Therefore, analytical and numerical modelling techniques for analysing fretting fatigue crack initiation and propagation phases are very desirable. In order to predict the fretting fatigue crack initiation lifetime, many researchers have dealt with stresses or R. Hojjati-Talemi (&)  M. A. Wahab Department of Mechanical Construction and Production, Faculty of Engineering and Architecture, Ghent University, 9000 Ghent, Belgium e-mail: Reza.HojjatiTalemi@UGent.be E. Giner  M. Sabsabi Centro de Investigacio ´n de Tecnologı ´a de Vehı ´culos (CITV), Dept. de Ingenierı ´a Meca ´nica y de Materiales, Universitat Polite `cnica de Vale `ncia, Camino de Vera, 46022 Valencia, Spain 123 Tribol Lett DOI 10.1007/s11249-013-0189-8