The first finite element model for fretting wear was created by I.R. McColl, J. Ding, and S.B. Leen at the University of Nottingham in the early to mid 00′s.  Previously fretting models had relied on analytical solutions to solve the contact problem, but the Nottingham research group was the first to use the finite element method.

This model uses Abaqus to solve the contact and elasticity problem for a cylinder and a flat (a classical Hertzian contact) during a single fretting cycle.  The normal pressure and slip at the contact were then used to calculate the change in surface height using Archard’s equation.  The modified surface profile is then used to update the old finite element mesh to match the worn surface.  The stress during the next cycle was then calculated using Abaqus and the process is repeated.

To save computational time, the wear rate was assumed to be constant over the span of a number of cycles.  This allows a the simulation to be completed in a reasonable amount of time and does not significantly change the results.  It also avoids problems with significant figures when trying to update the location of nodes by very small amounts.  There is, however, a critical cycle increment above which the model becomes unstable.

Switching from theoretical contact mechanics to finite element modeling makes a wide variety of options available.  The finite element model can be used to study the effect of coatings, the variation of material properties within a body, heterogeneity, and nonstandard contact geometries to name a few options.  Furthermore, these changes can be implemented in a matter of minutes without the need to solve extremely difficult math problems.

Researchers in the same lab have used this model for studying fretting fatigue and fretting wear as well as phenomena including the third body effect.

• McColl, I.R., Ding, J., Leen, S.B., 2004, "Finite element simulation and experimental validation of freting wear," Wear, Vol. 256, pp. 1114-1127.