Crack Growth in Rolling Bodies under the Conditions of Dry Friction and Wetting

Abstract

Within the framework of a two-dimensional mathematical model, we study the development of a surface macrocrack in the course of unidirectional rolling under the conditions of dry friction and wetting. The damaged body in a rolling couple is modeled by an elastic half plane with an edge cut (crack) and the action of the counterbody is simulated by the translational motion of Hertzian contact forces along the boundary of the half plane with taking into account the friction forces. We compute the crack-growth paths depending on the coefficient of contact friction between the bodies and the orientation and length of the crack. The numerical calculations are performed by the step-by-step method based on the use of the singular integral equations of the theory of elasticity for bodies with curvilinear cracks and the criterion of generalized opening. It is shown that, for high coefficients of friction between the bodies of the rolling couple (f = 0.20–40; dry friction), a branch propagates from the original fatigue shear macrocrack into the bulk of the material of the driven body. In the case of low friction coefficients (f < 0.20; wetting), a branch mainly propagates along the boundary of the body in the direction of motion of the counterbody. We propose an explanation of the mechanism of development of burrow-type defects often encountered in railroad rails.