Limiting shape due to fretting wear in an adhesive contact in Dugdale approximation

We consider fretting wear in an adhesive contact due to tangential oscillations of small amplitude. While both wear in non-adhesive contacts and adhesive contacts without wear have been studied in detail, there still have been no attempts to combine both approaches. In the present paper, we study the problem of wear in adhesive contacts under the simplified assumption, that the adhesive (attractive) stress is constant up to some critical distance h and vanishes beyond this range (Dugdale approximation). In this approximation, the normal adhesive contact problem can be solved to a great extent analytically. In a series of previous works, it was shown that the worn shape due to fretting wear tends to some limiting shape which is determined solely by the solution of the normal contact problem. In the present paper, we exploit these ideas to derive the limiting shape of the worn body in an adhesive contact.