A Tribological Model for Continuous Casting Equipment of the Steel

Abstract

This paper presents a coupled thermo-elastic contact problem with tribological processes on the contact interface (friction, wear or damage). The unilateral contact between the cilindrical roll system and a deformable foundation (slab, bloom, etc) is modeled by the Kuhn-Tucker (normal compliance) conditions, involving damage and/or wear effect of contact surfaces. The continuum tribological model is based on gradient theory of the damage variable for studying crack initiation in fretting fatigue [11], [14], [15] , and the wear is described by Archard’s law. The friction law that we consider is a regularization of the Coulomb law.
The weak formulation of the quasistatic boundary value problem is described by using the variational principle of virtual power, the principles of thermodynamics and variational inequalities theory. Thus, the main results of existence for weak solution are established using a discretization method (FEM) and a fixed-point strategy [5].