Because of the complexity of several simultaneous physical processes, most heat transfer models of keyhole mode laser welding require some simplifications to make the calculations tractable. The simplifications often limit the applicability of each model to the specific materials systems for which the model is developed. In this work, a rigorous, yet computationally efficient, keyhole model is developed and tested on tantalum, Ti–6Al–4V, 304L stainless steel and vanadium. Unlike previous models, this one combines an existing model to calculate keyhole shape and size with numerical fluid flow and heat transfer calculations in the weld pool. The calculations of the keyhole profile involved a point-by-point heat balance at the keyhole walls considering multiple reflections of the laser beam in the vapour cavity. The equations of conservation of mass, momentum and energy are then solved in three dimensions assuming that the temperatures at the keyhole wall reach the boiling point of the different metals or alloys. A turbulence model based on Prandtl's mixing length hypothesis was used to estimate the effective viscosity and thermal conductivity in the liquid region. The calculated weld cross-sections agreed well with the experimental results for each metal and alloy system examined here. In each case, the weld pool geometry was affected by the thermal diffusivity, absorption coefficient, and the melting and boiling points, among the various physical properties of the alloy. The model was also used to better understand solidification phenomena and calculate the solidification parameters at the trailing edge of the weld pool. These calculations indicate that the solidification structure became less dendritic and coarser with decreasing weld velocities over the range of speeds investigated in this study. Overall, the keyhole weld model provides satisfactory simulations of the weld geometries and solidification sub-structures for diverse engineering metals and alloys.

https://iopscience.iop.org/article/10.1088/0022-3727/40/18/037/pdf

Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti–6Al–4V, 304L stainless steel and vanadium

Numerical simulation of molten pool dynamics in high power disk laser welding

Numerical modelling of welding

A three-dimensional laser-keyhole welding model is developed, featuring the self-consistent evolution of the liquid/vapor (L/V) interface together with full simulation of fluid flow and heat transfer. Important interfacial phenomena, such as free surface evolution, evaporation, kinetic Knudsen layer, homogeneous boiling, and multiple reflections, are considered and applied to the model. The level set approach is adopted to incorporate the L/V interface boundary conditions in the Navier-Stokes equation and energy equation. Both thermocapillary force and recoil pressure, which are the major driving forces for the melt flow, are incorporated in the formulation. For melting and solidification processes at the solid/liquid (S/L) interface, the mixture continuum model has been employed. The article consists of two parts. This article (Part I) presents the model formulation and discusses the effects of evaporation, free surface evolution, and multiple reflections on a steady molten pool to demonstrate the relevance of these interfacial phenomena. The results of the full keyhole simulation and the experimental verification will be provided in the companion article (Part II).

Modeling of laser keyhole welding: Part I. mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution

A three-dimensional sharp interface model is proposed to investigate the self-consistent keyhole and weld pool dynamics in deep penetration laser welding. The coupling of three-dimensional heat transfer, fluid flow and keyhole free surface evolutions in the welding process is simulated. It is theoretically confirmed that under certain low heat input welding conditions deep penetration laser welding with a collapsing free keyhole could be obtained and the flow directions near the keyhole wall are upwards and approximately parallel to the keyhole wall. However, significantly different weld pool dynamics in a welding process with an unstable keyhole are numerically found. Many flow patterns in the welding process with an unstable keyhole, verified by x-ray transmission experiments, were successfully simulated and analysed. Periodical keyhole collapsing and bubble formation processes are also successfully simulated and believed to be in good agreement with experiments. The mechanisms of keyhole instability are found to be closely associated with the behaviour of humps on the keyhole wall, and it is found that the welding speed and surface tension are closely related to the formation of humps on the keyhole wall. It is also shown that the weld pool dynamics in laser welding with an unstable keyhole are closely associated with the transient keyhole instability and therefore modelling keyhole and weld pool in a self-consistent way is significant to understand the physics of laser welding.

https://iopscience.iop.org/article/10.1088/0022-3727/44/2/025301/pdf

A three-dimensional sharp interface model for self-consistent keyhole and weld pool dynamics in deep penetration laser welding

A linear correlation between the depth and the length of the weld pool is found in laser beam welding experiments with varied laser beam power and constant welding speed. On the other hand, the weld pool length changes only slightly with increased welding speed and constant laser beam power. The existing analytical and numerical models fail to explain these dependences. The observed effects are essentially conditioned by the fluid flow in the weld pool caused by the thermocapillary effect, by the friction forces of the metal vapour passing through the capillary and by the convexity of weld pool and fusion zone caused by thermal expansion of the weld pool and the joined workpieces. In order to predict the weld pool length more accurately the model developed by Sudnik et al in 1996 is enlarged by the heat transport produced by the recirculating flow in radial sections of the weld pool. Verification of the model for 16MnCr5 steel with sheet thicknesses of 2 and 6 mm shows that it is suitable for predicting the weld pool geometry and for analysing the thermodynamics of the process. In order to gain a better understanding of the structure of heat transport in the weld pool, the different modes of transport are compared in respect of their contribution to the depth-to-length ratio of the weld pool. A calculation of the weld pool length for welding speeds of 1-8 m min-1 with a laser beam power of 2.5 kW shows that the relative contributions of the transport modes are as follows. Approximately 50-90% of the weld pool length (increasing with welding speed) results from conductive and translatory heat transport (with the fusion zone convexity contributing approximately 20-30%). The remaining 50-10% of the weld pool length (decreasing with welding speed) result from convective heat transport. The model predicts the shoulder in the weld pool trough. It also explains the change in the weld pool length by the effect of the gap width, by the transition from through welding to penetration welding and by improvements in beam quality.

http://iopscience.iop.org/article/10.1088/0022-3727/33/6/312/pdf

Numerical simulation of weld pool geometry in laser beam welding

The theoretical basis for the numerical simulation of stationary penetration welding with a laser beam is presented. The characteristics of the self-consistent model are the following. Vapour channel, weld pool and solid are considered as a nonlinear thermodynamic continuum. The laser-induced channel formation, multiple reflection of the laser beam in the channel, and plasma generation are taken into account. The absorption coefficient of the plasma is assumed as dependent on the degree of ionization. The geometry of the channel is determined on the basis of the pressure equilibrium at the channel surface taking the enthalpy of the molten mass into account. The input parameters for the simulation are the geometry of the workpiece, the material characteristic values dependent on temperature and the technological parameters such as laser beam power, beam diameter at focus, focus position, divergence angle of the beam, type of working gas and welding velocity. The results comprise the distribution of enthalpy and temperature, the shape and dimensions of the vapour channel of the weld pool and of the completed weld, and the energy losses by reflection, vaporization, thermal radiation and plasma shielding. The model was verified with welding experiments on steel and aluminium alloy. Data taken from the literature were also used for verification.

https://iopscience.iop.org/article/10.1088/0022-3727/29/11/013/pdf

Computerized simulation of laser beam welding, modelling and verification

A model of laser beam weld shape formation which comprises butt and overlap joints with a small gap between the parts to be joined is considered. It is the goal of the simulation to predict the effect of technological parameters on the reinforcement or concavity of the weld or weld root and on the area of the load-carrying cross section which controls the strength of the joint. The model is based on the equations of energy transport and of equilibrium at the free surfaces for balancing vapour pressure, capillary pressure and a correction term. The correction term allows balancing the metal volume taking into account thermal expansion and shrinkage during welding and the gap width between the parts to be joined. Verification of the simulation results for gap widths in the range 0-0.2 mm shows that the model corresponds sufficiently well to the experimental data when considering laser beam weld formation in butt and overlap joints of 1.5-6.0 mm sheet thickness. The model explains the weld concavity occurring with gaps in butt and overlap joints, the increase in penetration depth for butt welds with gaps and the widening of the molten zone near the gap in overlap joints.

https://iopscience.iop.org/article/10.1088/0022-3727/31/24/011/pdf

W Sudnik

Papers

Numerical simulation of weld pool geometry in laser beam welding

Computerized simulation of laser beam welding, modelling and verification

Computerized simulation of laser beam weld formation comprising joint gaps

Simulation des Laserstrahlschweissens auf dem Computer : Konzept und Realisierung