Laser Surface Hardening Considering Coupled Thermoelasticity using an Eulerian Formulations

Authors: Me. Sistaninia, G.H.Farrahi, Ma. Sistaninia

Abstract:

Thermoelastic temperature, displacement, and stress in heat transfer during laser surface hardening are solved in Eulerian formulation. In Eulerian formulations the heat flux is fixed in space and the workpiece is moved through a control volume. In the case of uniform velocity and uniform heat flux distribution, the Eulerian formulations leads to a steady-state problem, while the Lagrangian formulations remains transient. In Eulerian formulations the reduction to a steady-state problem increases the computational efficiency. In this study also an analytical solution is developed for an uncoupled transient heat conduction equation in which a plane slab is heated by a laser beam. The thermal result of the numerical model is compared with the result of this analytical model. Comparing the results shows numerical solution for uncoupled equations are in good agreement with the analytical solution.

Keywords: Coupled thermoelasticity, Finite element, Laser surface hardening, Eulerian formulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328158

References:

[1] Peyre P, Fabbro R, Berthe L, Dubouchet C. Laser shock processing of materials. J Laser Appl 1996;8:135-41.
[2] Welsh, L.P.,Tuchmqn, J.A.,and Herman, J.P., The importance of thermal stresses and strains induced in laser processing with focused Gaussian beam ,J. Appl. Phys., Vol. 64, p.6274, 1988.
[3] K.D. Schwager, B.Scholes, E.Macheraunch,and B.L.Mordike, Proc.ECLAT 92,DGM,pp.629-634
[4] M.Bouffoussi, S.Denis, J.Ch.Chevrier, A. Simon, A. Bignonnet, and J. Merlin, Proceedings of European Conference on laser Treatment of metals, ECLAT 92 DGM, 1992,pp.635-640.
[5] Germanovich, L. N.,Kill, I. D., and Tsodokova, n.s., Thermoelasstic stresses in a half-space heated by concentrated energy flux, J. of Applied Mech., Vol. 52, P. 525, 1989.
[6] P. Hosseini-Tehrani, M.R. Eslami, BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity, Engineering Analysis with Boundary Elements 24 (2000) 249-257.
[7] S. M. Rajadhyaksha and P. Michaleris, Optimization of thermal processes using an Eulerian formulations and application in laser surface hardening, Int. J. Numer. Meth. Engng. 2000; 47:1807-1823.
[8] P. Hosseini-Tehrani, M.R. Eslami, Boundary element analysis of stress intensity factor KI in some two-dimensional dynamic thermoelastic problems, Engineering Analysis with Boundary Elements 29 (2005) 232-240.
[9] ASYS Help System, Theory Reference , Ver. 10.
[10] Bagri, M.R. Eslami, Generalized coupled thermoelasticity of functionally graded annular disk considering the Lord-Shulman theory, Composite Structures xxx (2007).
[11] Andrei D. Polyanin, Handbook of linear partial differential equations for engineers and scientists, 2002.
[12] Y. S. Yang and S. J. NA, A study on residual stresses in laser surface hardening of a medium carbon steel, surface and coatings technology, 38(1989) 311-324.
[13] Tan Zhen, Guo Guangwen, editors. Thermo-physical properties of engineering alloy. Publishedby Metallurgical industry Publisher; 1994. 9pp.
[14] X.F. Wanga,b, X.D. Lua, G.N. Chenb, Sh.G. Hua, Y.P. Sua, Research on the temperature field in laser hardening, optics & Laser Technology 38 (2006) 8-13.
[15] ASM International, ASM Handbook: properties and selection, vol. 1, ASM International, 1994
[16] S. J. Na and Y. S, Yang, Influence of heating rate on the laser surface hardening of a medium carbon steel, surf. Coat. Technol., 34 (1988) 319-330.
[17] T. Inue and K. Tanaka, An elastic-plastic stress analysis of quenching when considering a transformation, Int. J. Mech. Sci., 17 (1975) 361 - 367.