Modified crack-analogy methodology: the equivalent theory

The crack initiation process of fretting fatigue is a complex phenomenon, and various approaches have been instigated to investigate fretting fatigue damage tolerance and crack initiation. The Crack-Analogy Methodology (CAM) is one approach, which is introduced by Giannakopoulos et al. It utilizes the similarity between contact mechanics and fracture mechanics to investigate fretting fatigue life. The present study is motivated by the crack-analogy methodology where a Modified Crack-Analogy Methodology (MCAM) is developed to extend CAM capabilities and to improve its prediction of crack initiation. The modified form extends CAM to include various indenter–substrate geometries as well as modifying its crack initiation parameter to include the effect of the bulk stress in the substrate. MCAM uses the change of the stress intensity factor (ΔK-parameter) as a fretting fatigue crack initiation parameter, since the change is consistent with the cyclic mechanism of fretting fatigue. It uses experimental data to establish ΔK-parameter–life curves similar to the stress–life S–N curve prototype in fatigue and to validate crack initiation for various geometric configurations under various load conditions. The results show similar trends to plain fatigue with lower damage tolerance as expected. By including the bulk stress, the crack initiation predictions of fretting fatigue show better consistency with the experimental data than without it where it exhibits fatigue characteristics consistent with S–N curves. In general, the ΔK-parameter–life trends show dependency on applied load and pad geometry. Reduced scatter is observed when bulk stress is included in the analyses as compared to that without it. It further demonstrates that the presence of bulk stress in general shifts fretting fatigue characteristics toward low cycle fatigue. The MCAM also predicts the limit of high cycle fatigue. The MCAM formulation shows potentials in life prediction such that it can be used as a tool in the design of components under fretting fatigue.