Keywords: contact problems, sliding wear, heat generation, steady-state, periodic sliding, optimal contact surface, p-version of finite elements.

The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process tends to a steady state occuring at fixed contact stress and strain distribution. This state corresponds to the minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. This paper extends the previous analyses [1,2,3,4,5] of the steady state conditions to cases of periodic sliding of contacting bodies, assuming cyclic steady state conditions for both mechanical and thermal fields.

This technique for solution of the coupled thermo-elastic-wear problem provides reasonable results for engineering applications The coupled thermo-mechanical problem is solved by an operator split technique. The mechanical and thermal fields discretized by the finite element approximation are specified separately in consecutive time steps.

The wear effect is calculated incrementally by applying the Archard type wear rule. The wear is accumulated at the end of half period of motion, so the contact pressure is fixed (at the iteration level), and the transient heat conduction problem is next solved for the given temperature field at the beginning of half period. The iterative process for one half period is terminated when the convergence criterion satisfies the error constraint for gap modification.

Numerical examples for different geometrical support conditions confirm the validity of prediction of the maximum value of temperature in the contact zone for the periodical motion of the strip. The results for the monotonic punch motion in the steady state wear state can be used to generate periodic solution.

1

I. Páczelt, Z. Mróz, "On optimal contact shapes generated by wear", Int. J. Num. Meth. Eng., 63, 1310-1347, 2005. doi:10.1002/nme.1321

2

I. Páczelt, Z. Mróz, "On the analysis of steady sliding wear process", Trib. Int., 42, 275-283, 2009. doi:10.1016/j.triboint.2008.06.007

3

I. Páczelt, Z. Mróz, "Variational approach to the analysis of steady state thermo-elastic wear regimes", Int. J. Num. Meth. Eng., 81, 728-760, 2010.

4

Z. Mróz, I. Páczelt, "Analysis of thermo-elastic wear problems", J. Thermal Stresses, 34-35, 569-606, 2011. doi:10.1080/01495739.2011.564026

5

I. Páczelt, Z. Mróz, "Numerical analysis of steady thermo-elastic wear regimes induced by translating and rotating punches", Computers and Structures, 89, 2495-2521, 2011. doi:10.1016/j.compstruc.2011.06.001

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