Numerical Simulations of Asperity Crushing Using Boundary Conditions Encountered in Cold-Rolling
Authors: Carretta Yves , Boman Romain , Legrand Nicolas , Laugier Maxime , Ponthot J.P. 
Published: June 2013

The general framework of this paper is in the field of numerical simulation of asperity crushing. Different material forming processes, such as strip-rolling and deep drawing, imply mixed lubrication. In this lubrication regime, two types of contact are present at the same time: a direct contact between the two solids at the asperity level and also valleys filled with pressurized oil. Theses contact conditions have a large influence on friction and wear taking place during the upsetting process. As this mixed type of contact is not yet fully understood from the physics point of view, numerical models are essential to achieve a better understanding. For example, semi-analytical asperity crushing models have been developed by Wilson&Sheu [1] and Sutcliffe [2] to take into account the influence of bulk plastic deformations on asperity crushing. The finite element method has also been used to model asperity crushing. Ike&Makinouchi [3] studied the behavior of 2D triangular-shaped asperities under different boundary conditions. Krozekwa et al. [4] modeled 3D triangular asperities behavior, for various bulk strain directions. More recently, Lu et al. [5] compared experimental results of pyramid-shaped asperity and ridge-shaped asperity crushing with finite element simulation results. As in the three former references mentioned above, it has been decided, to study the interaction between a rigid plane and a simplified geometry asperity without lubricant. In this article, numerical asperity crushing results obtained with Metafor[6], a home made large strains software, will be presented. Those results will illustrate the influence of boundary conditions, contact pressure, large bulk strain and geometry of asperities on the evolution of the contact area. As the asperity crushing behaviour is known to be very sensitive to the boundary conditions, in this article, we will also present results using boundary conditions from a cold rolling model named MetaLub. MetaLub [7-8] is a software developed at the University of Liege in partnership with ArcelorMittal R&D center. It iteratively solves the equations resulting from the discretisation using the slab method of the strip coupled to a mixed lubrication model at the interface. This lubrication model takes into account the evolution of the oil film thickness as well as the asperity crushing along the roll bite. We will compare the evolution of the relative contact area obtained with MetaLub to the results obtained with finite elements simulations using the same boundary conditions. [1] Wilson, W.R.D and Sheu, S. Real area of contact and boundary friction in metal forming. Int. J. Mech. Sci. 1988, 30(7), 475-489. [2] Sutcliffe, M.P.F Surface asperity deformation in metal forming processes. Int. J. Mech. Sci., 1988, 30(11), 847-868. [3] Ike, H. and Makinouchi, A. Effect of lateral tension and compression on plane strain flattening processes of surface asperities lying over a plastically deformable bulk. Wear, 1990, 140, 17-38. [4] Korzekwa, D.A., Dawson, P.R. and Wilson W.R.D., Surface asperity deformation during sheet forming. Int. J. Mech. Sci., 1992, 34(7), 521-539. [5] Lu, C., Wei, D., Jiang, Z., and Tieu, K., Experimental and theoretical investigation of the asperity flattening process under large bulk strain, Proc. Inst. Mech. Eng. J. 222 (2008), 271–278. [6] LTAS-MN2L. ULg. http://metafor.ltas.ulg.ac.be/. [7] Stéphany, A., Contribution à l’étude numérique de la lubrification en régime mixte en laminage à froid. PhD dissertation (in French), Université de Liège (2008) [8] Carretta, Y., Stephany, A., Legrand, N., Laugier, M., and Ponthot, J.-P., MetaLub – A slab method software for the numerical simulation of mixed lubrication regime. Application to cold rolling. In Proceedings of the 4th International Conference on Tribology In Manufacturing Processes (ICTMP), 2010,799-808.