Laser Surface Hardening Considering Coupled Thermoelasticity using an Eulerian Formulations

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.

Authors:

• Me. Sistaninia
• G.H.Farrahi
• Ma. Sistaninia

Keywords:

• Coupled thermoelasticity
• Finite element
• Laser surface hardening
• Eulerian formulation.

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.