John Dowden

A keyhole model in penetration welding with a laser

Discusses the interaction of conditions in the liquid metal surrounding the keyhole which is formed when a laser is used as the source of power for welding, with conditions in the vapor itself. The transfer of power and matter across the interface is considered, and a simple model set up for the energy interchange and vapor flow in the keyhole itself. The principal processes are identified. The model is then used to calculate keyhole shapes, and the variation with depth of the related quantities is found.

A point and line source model of laser keyhole welding

The keyhole formed during penetration welding with a laser is modelled so far as its thermal absorption characteristics are concerned by the combination of a point and a line source. In this way a representation of the broader surface section of the weld is obtained in addition to the lower section. A simple analytical form for the temperature distribution is obtained and possible weld profiles are found numerically from this. These are compared with examples of actual welds; it is possible in this way to estimate the proportion of the laser power absorbed in each section of the weld. Graphs and some simple approximations are given which allow it to be done easily for a given weld.

Theoretical approach to the humping phenomenon in welding processes

The conjecture which explains the humping phenomenon in terms of Marangoni convection is discussed and rejected. Instead, Rayleighs theory of the instability of a free liquid cylinder due to surface tension is applied. The width-to-length ratio of the weld pool has to exceed 1/2 pi to avoid humping. The growth time of a disturbance is found to be approximately the same as the growth time of a hump. The analysis of a bounded cylinder provides a new stability criterion which allows the introduction of a bounding function to distinguish between arc and laser welding. The weld pool dimensions are estimated in terms of a simple heat conduction model. The threshold value predicted theoretically for the travel speed above which humping commences agrees well with the experimental value. It decreases with increasing power, which is in qualitative agreement with experimental results.

The laser welding of thin metal sheets: an integrated keyhole and weld pool model with supporting experiments

An integrated mathematical model for laser welding of thin metal sheets under a variety of laser material processing conditions has been developed and tested against the results of experiments. Full account is taken in the model of the interaction of the laser-generated keyhole with the weld pool. Results calculated from the model are found to agree well with experiment for appropriate values of the keyhole radius. The analysis yields values for power absorption in the metal. In a complementary calculation the total absorption of the laser energy is determined from detailed consideration of the inverse Bremsstrahlung absorption in the plasma and Fresnel absorption at the keyhole walls. To test these results, experiments were performed on 1 mm mild steel using a high-speed video camera, which measured the surface dimensions of the melt pool. Processing parameters were varied to study the effect on the melt pool; parameters considered included traverse speed, laser power and shroud gas species. The general shape of the weld pool was found to depend on whether penetration was full, partial or blind; only the results for full penetration were compared with the theory, which is for complete penetration only.

An analytical model for the laser drilling of metals with absorption within the vapour

A mathematical model for the laser drilling of metals is given for the cases of constant and pulsed laser sources. Attenuation of the laser beam within the vapour is considered through an averaged absorption coefficient . The experimentally observed logarithmic dependence of the hole depth on the laser energy is predicted theoretically. A singular perturbation technique is used in order to find solutions valid for different regimes of time, namely pre-vaporization and post-vaporization times. Uniformly valid solutions are found for the one-dimensional analysis of the drilling-front position and speed by matching the inner and outer solutions. First-order approximations for the time-dependent hole profile for the various laser source profiles considered are also found. The model is compared with experimental data in the literature for the drilling speed of copper. An additional set of experiments is specifically carried out to allow comparison with the theoretical hole profiles for titanium. The predictions of the model are found to agree well with the experiments.

An analysis of the laser-plasma interaction in laser keyhole welding

In penetration welding with a laser, a plasma is formed in the keyhole. In the energy exchange process it is to be expected that a substantial part of the power is absorbed directly at the walls of the keyhole, but another exchange mechanism is the interaction of the laser beam with the plasma. A simple model of this part of the process is described and its properties are investigated. It is found to be consistent, and estimates are obtained for the parameters. The existence of a linking intensity is deduced. This relates the power absorbed by the workpiece per unit thickness of the workpiece to the laser power available at each cross section of the keyhole.

Some aspects of the fluid dynamics of laser welding

When a laser beam is used as the energy source for welding two pieces of metal together, a hole is formed perpendicular to the plane of the workpiece. The latter is moved relative to the laser and metal is transferred from the front to the rear by fluid flow round the hole. The equations governing the process are set out and the conditions at the two boundaries in the problem (one between the hole and the molten metal, and the other between the liquid and the solid states of the metal) are considered. Approximate solutions of the problem for low welding speeds are obtained for four different models. The first is one in which the viscosity is taken to be constant. In the second, the viscosity is allowed to depend linearly on temperature. The third model divides the liquid into a region in which the cooler part is taken to be viscous and the hotter part inviscid; the fourth model is then constructed as a limit, with the liquid motion considered as wholly inviscid. It is found that the motion is not irrotational in this last model. The models all display a downstream displacement of the boundary between the solid and liquid states, in agreement with observations. An expression for the minimum power of the laser is calculated.

Heat hardening of metal surfaces with a scanning laser beam

The hardening of steel by means of a rapidly scanning laser is investigated from a theoretical viewpoint based on the equation of heat conduction. The criteria for hardening are considered and related to parameters of the steel and the laser. With the aid of approximations a simple formula is obtained for the depth of hardening in terms of these parameters. The predictions of this model were compared with the results of a set of experiments on En8 steel, and were found to be in good agreement.

Heat conduction in high-speed laser welding

The three-dimensional, time-dependent temperature distribution in a moving solid of finite thickness due to a laser beam with a Gaussian power distribution on its surface is investigated. The effects due to latent heat and the keyhole are neglected. The model is determined by Peclet number Pe=r0U/2 kappa , a non-dimensional melting temperature Theta m= lambda r0 pi 32/(Tm-T0)/P and a non-dimensional thickness xi 0=h/r0. An upper limit for the time needed to establish the steady state is 0.1 s in the case of iron for all travel speeds. Accounting for the effects due to the finite thickness of the specimen is essential for the thin metal sheets used in high-speed laser welding. Asymptotic solutions for high Pe are provided. The resulting weld pool for high Pe are long, narrow and shallow; the weld pool may be approximated by a cylinder. For a given value of the power, the weld pool length depends only slightly on Pe, and consequently a simple approximate formula for the dependence on laser power P is possible and is presented.

A mathematical investigation of the penetration depth in keyhole welding with continuous CO2 lasers

Continuous CO2 lasers have been used for many years to weld a variety of materials. A problem of importance is the question of what is the thickest work piece that can be reliably welded with complete penetration occurring at all times. Empirical results indicate that the size of the keyhole radius at the top of the work piece is almost exactly three times the radius at the bottom in the case of maximum penetration. A mechanism based on the instability inherent in the variable absorption capabilities of the work piece when absorbing energy from a laser beam with an interference pattern which is itself the result of reflection at the wall of the keyhole has been suggested and the implications investigated. A simple model has been studied in which the beam has a uniform intensity at any given cross section; an analysis in terms of geometrical optics and a parallel beam supports the empirical observation. The effect of the curvature of the keyhole wall was studied and found not to make a great difference to the results of the theory. The same techniques were used to investigate the effect of the convergence and subsequent divergence of the laser beam as it passes through the focal plane. The estimates provided by the theory have been compared with experimental results and shown to agree very well with them.