Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion

Journal of Thermal Analysis and Calorimetry

Volumn 97, Issue 3, 2009, Pages 911-915

  Belhadj, Asma ^a   Bessrour, Jamel ^b   Bouhafs, Mahmoud ^b   Barrallier, Laurent ^a  

^a ARTS ET MÉTIERS PARISTECH   (France)

^b UNIVERSITY OF TUNIS EL MANAR   (Tunisia)

Author keywords

Boubaker polynomials; Cooling velocity; Keyhole model; Laser welding; Temperature profiling

Indexed keywords

BOUBAKER POLYNOMIALS; COOLING VELOCITY; KEYHOLE MODEL; LASER WELDING; TEMPERATURE PROFILING;

COOLING; LASER WELDING MACHINES; LASERS; POLYNOMIALS; QUENCHING; SMELTING; VELOCITY;

LASER BEAM WELDING;

EID: 70350423094     PISSN: 13886150     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10973-009-0094-4     Document Type: Conference Paper

References (32)

1. RK Singh J Narayan 1990 Pulsed-laser evaporation technique for deposition of thin films: physics and theoretical model Phys Rev B 41 8843 59 10.1103/PhysRevB.41.8843
2. SI Anisimov BS Luk'yanchuk A Luches 1996 An analytical model for three-dimensional laser plume expansion into vacuum in hydrodynamic regime Appl Surf Sci 96-98 24 32 10.1016/0169-4332(95)00373-8 (Pubitemid 126373502)
3. DW Koopman 1971 Langmuir probe and microwave measurements of streaming plasmas generated by focused laser pulses Phys Fluids 14 1707 16 10.1063/1.1693667
4. B Toftmann J Schou TN Hansen JG Lunney 2000 Evolution of the plasma parameters in the expanding laser ablation plume of silver Phys Rev Lett 84 3998 4001 10.1103/PhysRevLett.84.3998 1:CAS:528:DC%2BD3cXis1alsLs%3D
5. I Weaver GW Martin WG Graham T Morrow CLS Lewis 1999 The Langmuir probe as a diagnostic of the electron component within low temperature laser ablated plasma plumes Rev Sci Instrum 70 1801 5 10.1063/1.1149672 1:CAS:528: DyaK1MXhsFGls74%3D
6. B Doggett C Budtz-Joergensen JG Lunney P Sheerin MM Turner 2005 Behaviour of a planar Langmuir probe in a laser ablation plasma Appl Surf Sci 247 134 8 10.1016/j.apsusc.2005.01.035 1:CAS:528:DC%2BD2MXltVOgs7w%3D
7. A Chaouachi K Boubaker M Amlouk H Bouzouita 2007 Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition Eur Phys J Appl Phys 37 105 9 10.1051/epjap:2007005 (Pubitemid 46308171)
8. J Ghanouchi H Labiadh K Boubaker 2008 An attempt to solve the heat transfer equation in a model of pyrolysis spray using 4q-order Boubaker polynomials Int J Heat Technol 26 49 53 1:CAS:528:DC%2BD1cXnsFWhtLw%3D
9. OB Awojoyogbe K Boubaker 2009 A solution to Bloch NMR flow equations for the analysis of homodynamic functions of blood flow system using m-Boubaker polynomials Curr Appl Phys 9 278 83 10.1016/j.cap.2008.01.019
10. K Boubaker 2007 On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving bi-varied heat equation Trends Appl Sci Res 2 540 4 10.3923/tasr.2007.540.544
11. H Labiadh 2007 A Sturm-Liouville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials J Differ Equ Control Process 2 117 33
12. R Gallusser K Dressler 1971 Application of the coulomb approximation to the Rydberg transitions of the NO molecule Z Angew Math Phys 22 792 4 10.1007/BF01587809 1:CAS:528:DyaE3MXltlGhurY%3D
13. BH Armstrong KL Purdum 1966 Extended use of the Coulomb approximation: mean powers of r, a sum rule, and improved transition integrals Phys Rev 150 51 8 10.1103/PhysRev.150.51 1:CAS:528:DyaF28XkvFGmuro%3D
14. A Paul T Debroy 1988 Free surface flow and heat transfer in conduction mode laser welding Metall Mater Trans B 19 851 8
15. E Andreassen OJ Myhre F Oldervoll EL Hinrichsen K Grøstad MD Braathen 1995 Nonuniform cooling in multifilament melt spinning of polypropylene fibers: cooling air speed limits and fiber-to-fiber variations J Appl Polym Sci 58 1619 32 10.1002/app.1995.070580925 1:CAS:528:DyaK2MXptVahtbY%3D
16. Belcher SL. Practical guide to injection blow molding. Boca Raton, FL: CRC Press; 2007. ISBN 0824757912, 9780824757915.
17. Santos CAC, Quaresma JNN, Lima JA. Convective heat transfer in ducts: the integral transform approach. Brazil: E-papers Servicos Editoriais Ltd; 2001. ISBN 8587922238, 9788587922236.
18. MP Mughal H Fawad R Mufti 2006 Finite element prediction of thermal stresses and deformations in layered manufacturing of metallic parts Acta Mech 183 61 79 10.1007/s00707-006-0329-4 (Pubitemid 43814296)
19. J Dowden N Postacioglu M Davis P Kapadia 1987 A keyhole model in penetration welding with a laser J Phys D Appl Phys 20 36 44 10.1088/0022-3727/20/1/006 1:CAS:528:DyaL2sXovVOmtA%3D%3D
20. VV Semak WD Bragg B Damkroger S Kempka 1999 Transient model for the keyhole during laser welding J Phys D Appl Phys 32 61 4 10.1088/0022-3727/32/15/ 103
21. H Ki J Mazumder PS Mohanty 2002 Modeling of laser keyhole welding: Part II: simulation of keyhole evolution, velocity, temperature profile, and experimental verification Metall Mater Trans A 33 1831 42 10.1007/s11661-002- 0191-5
22. R Rai SM Kelly RP Martukanitz T DebRoy 2008 A convective heat-transfer model for partial and full penetration keyhole mode laser welding of a structural steel Metall Mater Trans A 39 98 112 10.1007/s11661-007-9400-6
23. H Al-Kazzaz M Medraj X Caoand M Jahazi 2008 Nd:YAG laser welding of aerospace grade ZE41A magnesium alloy: modeling and experimental investigations Mater Chem Phys 109 61 76 1:CAS:528:DC%2BD1cXjtVWht7k%3D
24. A Kaplan 1994 A model of deep penetration laser welding based on calculation of the keyhole profile J Phys D Appl Phys 27 1805 14 10.1088/0022-3727/27/9/002 1:CAS:528:DyaK2MXovFWnsQ%3D%3D
25. C Lampa AFH Kaplan J Powell C Magnusson 1997 An analytical thermodynamic model of laser welding J Phys D Appl Phys 30 1293 9 10.1088/0022-3727/30/9/004 1:CAS:528:DyaK2sXjtFKlsr0%3D
26. X Jin L Li Y Zhang 2002 A study on fresnel absorption and reflections in the keyhole in deep penetration laser welding J Phys D Appl Phys 35 2304 10 10.1088/0022-3727/35/18/312 1:CAS:528:DC%2BD38XnsFKisbc%3D (Pubitemid 35167244)
27. P Solana G Negro 1997 A study of the effect of multiple reflections on the shape of the keyhole of the keyhole in the laser processing of materials J Phys D Appl Phys 30 3216 22 10.1088/0022-3727/30/23/006 1:CAS:528:DyaK1cXlslGl
28. CS Wu HG Wang YM Zhang 2006 A new heat source model for keyhole plasma arc welding in FEM analysis of the temperature profile Weld J 85 284 9
29. R Puchert U Menzel A Bärwolff M Vo Ch Lier 1997 Influence of heat source distributions in GaAs/GaAlAs quantum-well high-power laser arrays on temperature profile and thermal resistance J Therm Anal Calorim 48 1273 82 10.1007/BF01983437 1:CAS:528:DyaK2sXltVyjtLc%3D
30. G Hakvoort CM Hol 1999 DSC calibration during cooling J Therm Anal Calorim 56 717 22 10.1023/A:1010193803783 1:CAS:528:DyaK1MXnt1Ghur4%3D
31. J Holender J Solstroktys R Kozubski 1988 Numerical method of non-isothermal curve analysis by means of electrical resistance measurement during cooling J Therm Anal Calorim 33 223 8 10.1007/BF01914604
32. É Hidvégi EK Csetényi Gy Keébe 1977 The effects of concentration and heating or cooling rate on the DTA curves of Al-Ce alloys J Therm Anal Calorim 11 221 9 10.1007/BF01909959