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© 2012 Spinu and Amarandei, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Numerical Simulation of Slip-Stick Elastic Contact** 

Fretting defines a condition in which mechanical contacts are subjected to alternating tangential displacements, small compared to dimensions of contact area, due to oscillating loading conditions. Fretting wear and fretting fatigue are between the most important factors responsible for contact failure, especially when high loads are transmitted through non-conforming contacts, leading to highly localized stress concentrators in the vicinity of the contact region. Prediction of life span of machine elements working in such conditions requires assessment of stress and strain in the contacting bodies, which is the main subject of Contact Mechanics. Although fretting is intrinsically a multidisciplinary process, involving adhesion, oxidation, abrasion and pitting, modern approach suggests that contact stresses

While analytic solutions in this research field lead to complex mathematical models, many without closed-form solution, numerical approach reveals itself as a useful engineering tool, capable of extending the few existing analytical results to technologically important contact scenarios. A numerical study may advance the understanding of fretting contact and

Elastic contact analysis considering interfacial friction and slip-stick behaviour originated in the works of Cattaneo (Cattaneo, 1938) and Mindlin (Mindlin, 1949). They proved independently that, even when the contacting bodies are globally sticking, a peripheral region of slip is to be assumed in order to remain in the frame of Linear Theory of Elasticity and to obey the Coulomb's law of friction. Based on these results, Johnson (Johnson, 1985) advanced the closed-form solution for the contact between similarly elastic materials

In case of dissimilarly elastic materials, when the effects of normal and tangential tractions are coupled, an iterative solution has been achieved (Hills et al., 1993) only for the plane (i.e. cylindrical) contact. Many authors employ the so-called Goodman approximation

and reproduction in any medium, provided the original work is properly cited.

provide assistance to the design of contacts with improved load-carrying capacity.

Sergiu Spinu and Dumitru Amarandei

http://dx.doi.org/10.5772/48451

**1. Introduction** 

play a chief role.

undergoing a fretting loop.

Additional information is available at the end of the chapter
