Effect of elastic grading on fretting wear

We consider fretting wear in elastic frictional contact under influence of oscillations of small amplitude and investigate the question, how wear damage can be influenced by the introduction of material gradients. To achieve a general understanding we restrict our consideration to media with a power-law dependency of the elastic modulus on depth. In this case, a complete analytical solution can be found for the final worn shape. In the limiting case of small fretting oscillations we obtain a simple, closed-form asymptotic solution of the problem. We find that the optimum grading depends on the oscillation amplitude: for large amplitudes, the use of materials with a positive exponent decreases the wear volume whilst for very small amplitudes the use of graded materials with slightly negative exponent is beneficial. Especially interesting is the case of the Gibson-medium which may help avoiding both fretting wear and fretting fatigue.