Abstract
The previous chapter concluded the physical discussion of laser materials processing (LMP). In this chapter no new physical concepts or theory of physical phenomena will be introduced. The objective of this chapter is rather to give an overview of how to analyse the complex system that is LaserMaterials Processing. As has been shown in great detail, the physical level of complexity is deep and analysis becomes extremely cumbersome if it is pursued on an analytical level. Albeit giving great insight into the detailed phenomena, whole processes and their sensitivity to ambient conditions and changes in process parameters or physical setup cannot be investigated using these methods alone. Here numerical simulation comes into play for the scientist investigating processes from an engineering point of view. Numerical simulation has an almost endless scope for system complexity and is only limited by the resources available and the time the investigator is prepared to wait for results. This final chapter should be read as a guide to how to get started.Some fundamental principles of discrete numerical modelling will be introduced and reference made to work by other authors. This, in the space available, can by no means be a comprehensive review, or a textbook of all the methods available and required. Nevertheless it should be seen as a starting point for investigators, at the doctoral student level, trying to get to terms with the task ahead, or for the researcher trying to move from practice to theory, from experiment to simulation, looking for a guide on what to look out for, where to go and which pitfalls to avoid.
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References
Kaplan A (1964) Conduct of Inquiry: Methodology for Behavioral Science. Chandler Publishing Company, p 288 para 32. Reprinted (1998) Transaction Publishers, p 288.
Dowden JM (200) The Mathematics of Thermal Modeling. Chapman & Hall/CRC
Dowden J, Davis M, Kapadia P (1985) The flow of heat and the motion of the weld pool in penetration welding with a laser. J Appl Phys, 57(9): 4474–4479
Dowden J, Postacioglu N, Davis M, Kapadia P (1987) A keyhole model in penetration welding with a laser. J Physics D: Appl Phys, 20(1): 36–44
Dowden J, Kapadia P, Postacioglu N (1989) An analysis of the laser-plasma interaction in laser keyhole welding. J Physics D: Appl Phys, 22(6): 741–749
Postacioglu N, Kapadia P, Dowden JM (2000) Distortion generated by a moving weld pool of elliptical cross section in the welding of thin metal sheets. J Physics D: Appl Phys, 33(14): 1739–1746
Postacioglu N, Kapadia P, Dowden J (1989) Capillary waves on the weld pool in penetration welding with a laser. J Physics D: Appl Phys, 22(8): 1050–1061
Postacioglu N, Kapadia P, Dowden J (1991) Theory of the oscillations of an ellipsoidal weld pool in laser welding. J Physics D: Appl Phys, 24(8): 1288–1292
Postacioglu N, Kapadia P, Davis M, Dowden J (1987) Upwelling in the liquid region surrounding the keyhole in penetration welding with a laser. J Physics D: Appl Phys, 20(3): 340–345
Wei PS, Chang CY (1996) Surface ripple in electron-beam welding solidification. J Heat Transfer – Trans ASME, 118(4): 960–969
Wei PS, Shian MD (1993) 3-dimensional analytical temperature-field around the welding cavity produced by a moving distributed high-intensity beam. Journal Heat Transfer – Trans ASME, 115(4): 848–856
Colla TJ, Vicanek M, Simon G (1994) Heat transport in melt flowing past the keyhole in deep penetration welding. J Physics D: Appl Phys, 27(10): 2035–2040
Matsunawa A, Semak V (1997) The simulation of front keyhole wall dynamics during laser welding. J Physics D: Appl Phys, 30(5): 798–809
Kroos J, Gratzke U, Vicanek M, Simon G (1993) Dynamic behaviour of the keyhole in laser welding. J Physics D: Appl Phys, 26(3): 481–486
Kroos J, Gratzke U, Simon G (1993) Towards a self-consistent model of the keyhole in penetration laser beam welding. J Physics D: Appl Phys, 26(3): 474–480
Fabbro R, Chouf K (2000) Keyhole modeling during laser welding. J Appl Phys, 87(9): 4075–4083
Ducharme R, Williams K, Kapadia P, Dowden J, Steen W, Glowacki M (1994) The laser welding of thin metal sheets: an integrated keyhole and weld pool model with supporting experiments. J Physics D: Appl Phys, 27(8): 1619–1627
Steen WM, Dowden JM, Davis M, Kapadia PD (1988) A point and line source model of laser keyhole welding. J Physics D: Appl Phys, 21(8): 1255–1260
Davies M, Kapadia P, Dowden J (1986) Modeling the fluid-flow in laser-beam welding. Welding J, 65(7): S167–S174
Akhter R, Davis M, Dowden J, Kapadia P, Ley M, Steen WM (1989) A method for calculating the fused zone profile of laser keyhole welds. J Physics D: Appl Phys, 21: 23–28
Gratzke U, Kapadia PD, Dowden JM, Kroos J, Simon G (1992) Theoretical approach to the humping phenomenon in welding processes. J Physics D: Appl Phys, 25(11): 1640–1647
Ki H, Mohanty P, Mazumder J (2002) Multiple reflection and its influence on keyhole evolution. J Laser Appl, 14: 39–45
Kar A, Mazumder J (1995) Mathematical modeling of key-hole laser welding. J Appl Phys, 78(11): 6352–6360
Farooq K, Kar A (1999) Effects of laser mode and scanning direction on melt pool shape. J Appl Phys, 85(9): 6415–6420
Choi JH, Lee J, Yoo CD (2001) Dynamic force balance model for metal transfer analysis in arc welding. J Physics D: Appl Phys, 34(17): 2685–2664
Tsai FR, Kannatey-Asibu E (2000) Modeling of conduction mode laser welding process for feedback control. Trans ASME, 122: 420–428
Kaplan A (1994) A model of deep penetration laser welding based on calculation of the keyhole profile. J Physics D: Appl Phys 27(9): 1805–1814
Schubart D, Otto A (1997) Process development of laser melt ablation. In: Laser Assisted Net shape Engineering 2 (LANE 97), 865–876
Chung JD, Lee JS, Whang KH, Kim TH (1996) Analysis of striation formation in laser material cutting process. J Mater Process Manuf Sci 5: 3–15
DiPietro P, Yao YL (1995) A numerical investigation into cutting front mobility in co-2 laser cutting. International Journal of Machine Tools & Manufacture 35(5): 673–688
O'Neill W, Steen WM (1995) A three-dimensional analysis of gas entrainment operating during the laser-cutting process. J Physics D: Appl Phys 28(1): 12–18
Kim MJ, Majumdar P (1995) Computational model for high-energy laser-cutting process. Numerical Heat Transfer, Part A 27: 717–733
Prusa JM, Venkitachalam G, Molian PA (1999) Estimation of heat conduction losses in laser cutting. International Journal of Machine Tools & Manufacture 39(3): 431–458
Kim MJ, Zhang J (2001) Finite element analysis of evaporative cutting with a moving high energy pulsed laser. Appl Math Modelling 25(3): 203–220
Kim MJ, Chen ZH, Majumdar P (1993) Finite element modelling of the laser cutting process. Computers & Structures 49(2): 231–241
Chryssolouris G, Choi WY (1989) Gas jet effects on laser cutting. In: Proc. SPIE, vol 1042 of Proc. SPIE, pages 86–96
Chen K (2000) Gas jet-workpiece interactions in laser machining. J Manuf Sci and Engineering-Trans ASME 122(3): 429–438
Mazumder J, Steen WM (1980) Heat transfer model for cw laser materials processing. J Appl Phys 51(2): 941–947
Vicanek M, Simon G, Urbassek HM, Decker I (1987) Hydrodynamical instability of melt flow in laser cutting. J Physics D: Appl Phys 20(1): 140–145
Chen K, Yao YL (2000) Interactive effects of reactivity and melt flow in laser machining. High Temp Mater Process 4: 227–252
Yilbas BS, Davies R, Gorur A, Yilbas Z, Begh F, Akcakoyun N, Kalkat M (1992) Investigation into the development of liquid layer and formation of surface plasma during co2 laser cutting process. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 206(B4): 287–298
Kim BC, Kim TH, Jang YS, Chung KH (2001) Investigation of striation formation in thin stainless steel tube during pulsed nd : Yag laser cutting process by numerical simulation. Metall Mater Trans A-Phys Metall Mater Sci 32: 2623–2632
Xie J, Kar A (1997) Mathematical modeling of melting during laser materials processing. J Appl Phys 81(7): 3015–3022
Rao BT, Nath AK (2002) Melt flow characteristics in gas-assisted laser cutting. Sadhana 27(5): 569–575
Vicanek M, Simon G (1987) Momentum and heat transfer of an inert gas jet to the melt in laser cutting. J Physics D: Appl Phys 20(9): 1191–1196
Leidinger D, Schuoecker D, Deinzer G, Geiger M, Haensel A, Herbig N (1994) Nozzle design and simulation of gas flow for the laser cutting process. In: Proc. SPIE vol 2207 of Proc. SPIE, pages 469–479
Bukharov NN, Barinov VV, Mishina MV, Prokoshev VG, Arakelian SM (1997) Numerical modeling laser thermochemical processes on metals surface. In: Laser Assisted Net shape Engineering 2 (LANE 97), 683–686
Chen K, Yao YL, Modi V (1999) Numerical simulation of oxidation effects in the laser cutting process. Int J Advanced Manufacturing Technology 15(11): 835–842
Lim CK, Molian PA, Brown RC, Prusa JM (1998) Numerical studies of gas jet/molten layer interaction during laser cutting. J Manuf Sci and Engineering, Trans ASME 120(3): 496–503
Finke BR, Simon G (1990) On the gas kinetics of laser-induced evaporation of metals. J Physics D: Appl Phys 23(1): 67–74
Rand C, Sparkes M, O'Neill W, Sutcliffe C, Brookfield D (2003) Optimisation of melt removal in laser cutting. In: ICALEO 2003 Congress Proceedings. LIA, Orlando
Mas C, Fabbro R, Gouédard Y (2003) Steady-state laser cutting modeling. J Laser Applics 15(3): 145–152
Semak VV, Damkroger B, Kempka S (1999) Temporal evolution of the temperature field in the beam interaction zone during laser material processing. J Physics D: Appl Phys 32: 1819–1825
Yilbas BS, Kar A (1998) Thermal and efficiency analysis of co2 laser cutting process. Optics and Lasers in Engineering 29(1): 17–32
Semak V, Matsunawa A (1997) The role of recoil pressure in energy balance during laser materials processing. J Physics D: Appl Phys 30(18): 2541–2552
Modest M (1996) Three-dimensional, transient model for laser machining of ablating/decomposing materials. Int J Heat Mass Transfer 39(2): 221–234
Modest MF, Mallison TM (2001) Transient elastic thermal stress development during laser scribing of ceramics. J Heat Transfer 123(1): 171–177
Kim MJ (2000) Transient evaporative laser-cutting with boundary element method. Appl Math Modelling 25(1): 25–39
Ganesh RK, Faghri A (1997) A generalized thermal modeling for laser drilling process – ii. numerical simulation and results. Int J Heat Mass Transfer 40(14): 3361–3373
Ganesh RK, Faghri A, Hahn Y (1997) A generalized thermal modeling for laser drilling process – i. mathematical modeling and numerical methodology. Int J Heat Mass Transfer 40(14): 3351–3360
Solana P, Kapadia P, Dowden JM, Marsden PJ (1999) An analytical model for the laser drilling of metals with absorption within the vapour. J Physics D: Appl Phys 32(8): 942–952
Chan CL, Mazumder J, Chen MM (1988) Effect of surface tension gradient driven convection in a laser melt pool: Three-dimensional perturbation model. J Appl Phys 64(11): 6166–6174
Ko SH, Choi SK, Yoo CD (2001) Effects of surface depression on pool convection and geometry in stationary gtaw. Welding research supplement pp 39s–45s
Westerberg K, McClelland M, Finlayson B (1998) Finite element analysis of flow, heat transfer, and free interfaces in an electron-beam vaporization system for metals. Int J Numer Methods Fluids 26: 637–655
Preston RV, Shercliff HR, Withers PJ, Smith SD (2003) Finite element modelling of tungsten inert gas welding of aluminum alloy 2024. Science and Technology of Welding and Joining 8(1): 10–18
Koo SH, Farson DF, Choi SK, Yoo CD (2000) Mathematical modeling of the dynamic behavior of gas tungsten arc weld pools. Metallurgical and Materials Transactions B-Process Metallurgical and Materials Processing Science 31(6): 1465–1473
Callies G, Schittenhelm H, Berger P, Hügel H (1997) Modeling and simulation of short pulse laser ablation with feeding speed. In: Laser Assisted Net shape Engineering 2 (LANE 97) 825–834
Zhou J, Wang PC (2003) Modeling of hybrid laser-mig keyhole welding process. In: ICALEO 2003 Congress Proceedings
Ki H, Mohanty PS, Mazumder J (2002) Modeling of laser keyhole welding: Part ii. simulation of keyhole evolution, velocity, temperature profile, and experimental verification. Metallurgical and Materials Transactions A-Physical Metallurgical and Materials Science 33(6): 1831–1842
Ki H, Mohanty PS, Mazumder J (2002) Modeling of laser keyhole welding: Part i. mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution. Metallurgical and Materials Transactions A-Physical Metallurgical and Materials Science 33(6): 1817–1830
Amara EH, Fabbro R, Bendib A (2003) Modeling of the compressible vapor flow induced in a keyhole during laser welding. J Appl Phys 93(7): 4289–4296
Hu J, Tsai HL, Lee YK (2003) Modeling of weld pool dynamics during dual-beam laser welding process. In: ICALEO 2003 Congress Proceedings
Thompson ME, Szekely J (1989) The transient behavior of weldpools with a deformed free surface. Int J Heat Mass Transfer 32(6): 1007–1019
Chan CL, Mazumder J, Chen MM (1987) Three-dimensional axisymmetric model for convection in laser-melted pools. Materials Science and Technology 3(4): 306–311
Chan CL, Zehr R, Mazumder J, Chen MM (1986) Three-dimensional model for convection in laser weld pool. In: Proc. 3rd conf modeling & control of casting & welding processes pp 229–246
Tufte ER (2006) The Cognitive Style of PowerPoint: Pitching Out Corrupts Within. Graphics Press
Patankar SV (1997) Numerical Heat Transfer and Fluid Flow. Series in computational methods in mechanics and thermal sciences. Hemisphere Publishing Corporation
Courant R, Friedrichs K, Lewy H (1928) über die partiellen differenzengleichun-gen der mathematischen physik. Mathematische Annalen 100(1): 32–74
Courant R, Friedrichs K, Lewy H (1967) On the partial difference equations of mathematical physics. IBM Journal 215–234
Saad Y, Schultz MH (1986) Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3): 856–869
Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics The finite volume method. Prentice Hall
Leonard BP (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Eng 19: 59–98
Leonard BP (1991) The ultimate conservative difference scheme applied to unsteady one-dimensional advection. Comput Meth Appl Mech Eng 88: 17–74
Leonard BP (1988) Simple high-accuracy resolution program for convective modelling of discontinuities. Int J Numerical Methods in Fluids 8: 1291–1318
Thuburn J (1996) Multidimensional flux-limited advection schemes. J Comput Phys 123: 74–83
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations. J Comp Phys 79: 12–49
Shyy W, Udaykumar HS, Rao MM, Smith RW (1996) Computational fluid dynamics with moving boundaries. Taylor & Francis
Iida T, Guthrie RI (1988) The Physical Properties of Liquid Metals. Oxford Science Publications
Colella P, Woodward PR (1984) The piecewise parabolic method (ppm) for gas-dynamical simulations. J Comput Phys 54: 174–201
Ducharme R, Kapadia PD, Dowden JM (1993) A mathematical model of the defocusing of laser light above a workpiece in laser material processing. In: Proc ICALEO, vol 75 of Proc ICALEO, pp 187–197. Laser Institute of America
Gladstone JH, Dale TP (1863) Researches on the refraction, dispersion and sensitiveness of liquids. Phil Trans Roy Soc 153: 317–343
Lee WHK, Stewart SW (1981) Principles and applications of microearthquake networks. Adv Geophys Supplement No. 2 p 293
Brankin RW, Gladwell I (1994) A fortran 90 version of rksuite: an ode initial value solver. Ann Numer Math 1: 363–375
Dagum L, Menon R (1998) Openmp: An industry-standard api for shared-memory programming. IEEE Computational Science & Engineering pages 46–55
Rapaport DC (2004) The Art of Molecular Dynamics Simulation. Cambridge University Press
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Gross, M. (2009). Comprehensive Numerical Simulation of Laser Materials Processing. In: Dowden, J. (eds) The Theory of Laser Materials Processing. Springer Series in Materials Science, vol 119. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9340-1_11
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