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Simulation of vapour keyhole and weld pool dynamics during laser beam welding

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Abstract

To help get a deeper insight into highly-complex characteristics of laser beam welding, a mathematical model, closely mapping all prominent phenomena, is useful. Some phenomena such as surface tension induced forces, recoil back pressure, multiple reflections of laser rays and angle dependent energy absorption of hot surfaces are all crucial. Encompassing all those presences, a simulation model has thereby been developed. A laser power transmission model built in conformity with the ray tracing scheme is proposed along with a consistently-adaptive system of time stepping and meshing. The simulation results demonstrate a tailing, deepening weld pool wrapping around an unsettled vapour keyhole forming and collapsing in a fickle manner. Besides, the development pattern of the total laser power literally conveyed to the workpiece seems well matching with the prevalent understanding on broad deep-penetration welding processes. Experimental verification comes in the end. The simulated weld pool shape at its presumably-mature state is compared with that from the laboratory. A continuous-wave multimode Ytterbium-doped fibre laser was employed in the experiment to weld a plain 6-mm-thick stainless steel plate. Apart from the computed weld pool depth appearing somewhat deeper than it is supposed to be, the calculated weld pool width and length are in good agreement with the measured ones.

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Abbreviations

\(A\) :

Area

\(Ab_0\) :

Absorption coefficient for circularly-polarised laser

\(Ab_{\parallel }\) :

Absorption coefficient for P-polarised laser

\(Ab_{\perp }\) :

Absorption coefficient for S-polarised laser

\(C\) :

Factor

\(C_i\) :

Laser beam focal point coordinates

\(CFL\) :

Courant–Friedrichs–Lewy number

\(c\) :

Mean curvature

\(c_p\) :

Mixture-phase specific heat

\(c_{pl}\) :

Liquid-phase specific heat

\(c_{ps}\) :

Solid-phase specific heat

\(f_l\) :

Liquid mass fraction

\(f_s\) :

Solid mass fraction

\(g_i\) :

Gravitational acceleration vector

\(g_l\) :

Liquid volume fraction

\(g_s\) :

Solid volume fraction

\(h\) :

Mixture-phase enthalpy or axial distance with respect to the laser beam focal point

\(h_{conv}\) :

Convective thermal transfer coefficient

\(h_l\) :

Liquid-phase enthalpy

\(h_p\) :

Axial distance from a reflection point to the laser beam focal point

\(h_s\) :

Solid-phase enthalpy

\(I_i\) :

Striking-ray direction vector

\(I_{LB}\) :

Laser beam power intensity

\(K\) :

Permeability

\(K_0\) :

Permeability coefficient

\(k\) :

Mixture-phase thermal conductivity

\(k_l\) :

Liquid-phase thermal conductivity

\(k_s\) :

Solid-phase thermal conductivity

\(L_m\) :

Latent heat of fusion

\(L_v\) :

Latent heat of evaporation

\(\dot{m}_{evap}\) :

Rate of evaporative mass loss

\(n\) :

Refractive index

\(n_i\) :

Unit normal vector

\(P\) :

Pressure or power

\(P_i\) :

Reflection point coordinates

\(P_{Laser}\) :

Laser beam nominal power

\(P_r\) :

Evaporative recoil back pressure

\(R_i\) :

Reflected-ray direction vector

\(r\) :

Radial distance from a reflection point to the laser beam axis

\(r_0\) :

Laser beam radius

\(S_c\) :

Sulphur concentration

\(T\) :

Temperature

\(T_a\) :

Ambient temperature

\(T_b\) :

Boiling temperature

\(T^0_i,\, T^1_i,\, T^2_i\) :

Triangle vertex coordinates

\(T_l\) :

Liquidus temperature

\(T_s\) :

Solidus temperature

\(t\) :

Time

\(u_i\) :

Laser beam axial unit vector

\(V\) :

Volume

\(v_f\) :

Laser feed rate

\(v_i\) :

Mixture-phase velocity vector or laser beam radial unit vector

\(v^l_i\) :

Liquid-phase velocity vector

\(v^s_i\) :

Solid-phase velocity vector

\(v_{\perp }\) :

Normal component of velocity vector

\(w_0\) :

Laser beam waist radius

\(\beta\) :

Reflection angle

\(\beta _T\) :

Thermal expansion coefficient

\(\gamma\) :

Surface tension coefficient

\(\varDelta t\) :

Timestep size

\(\varDelta x\) :

Element size

\(\varepsilon\) :

Radiative emissivity

\(\theta\) :

Laser beam divergence angle

\(\theta _p\) :

Laser ray divergence angle

\(\kappa\) :

Extinction coefficient

\(\mu _l\) :

Liquid-phase dynamic viscosity

\(\rho\) :

Mixture-phase density

\(\rho _l\) :

Liquid-phase density

\(\rho _s\) :

Solid-phase density

\(\sigma\) :

Stefan–Boltzmann constant

\(\phi\) :

Signed distance (level set) function

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Acknowledgments

The author expresses his cordial gratitude for the financial support of the project “Melt Geometry Dependent Distortion” by the Scientific Computing in Engineering (SCiE) programme from the University of Bremen.

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  1. Bremer Institut für angewandte Strahltechnik GmbH (BIAS), Klagenfurter Str. 2, 28359, Bremen, Germany

    Komkamol Chongbunwatana

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Correspondence to Komkamol Chongbunwatana.

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Chongbunwatana, K. Simulation of vapour keyhole and weld pool dynamics during laser beam welding. Prod. Eng. Res. Devel. 8, 499–511 (2014). https://doi.org/10.1007/s11740-014-0555-x

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