N Postacioglu

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.

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.

Upwelling in the liquid region surrounding the keyhole in penetration welding with a laser

In penetration welding with a laser, the pressure in the keyhole is in excess at atmospheric pressure. A pressure gradient related to this is produced in the liquid region surrounding it, with the result that there is a flow parallel to the axis of the laser. The velocity of this flow is found as a function of the material constants, and the volume flow rate calculated. From this it is possible to construct an estimate of the elevation or depression of the surface of the weld. the shape of the surface cross section is discussed, and some deductions made about the pressure distribution in the liquid metal.

Capillary waves on the weld pool in penetration welding with a laser

In penetration welding with a laser, a ripple pattern is frozen into the weld bead. The causes of this are not clear but the frequencies most readily observed are likely to be related to the natural frequencies of oscillation of the weld pool when in its molten state. These frequencies are investigated by a combination of analytical and numerical methods which allow for the presence of inner and outer boundaries to the weld pool, the finite depth of the pool and the dependence of the surface tension on temperature. The effect of oscillations on the weld pool forced by pulsations in the keyhole is also studied.

Theory of the oscillations of an ellipsoidal weld pool in laser welding

The weld bead formed when a laser is used for penetration welding usually exhibits a ripple pattern superimposed on the surface. The reasons for this are not clear but the frequencies most likely to be observed will be related to the natural frequencies of oscillation of the weld pool when it is molten. Postacioglu et al. (see ibid., vol.22, p.1050, 1989) have already studied these frequencies in the case when the weld pool is almost circular and deep. When the welding speed is higher however, the weld pool is nearer to being ellipsoidal in shape. The frequency of the first asymmetric mode of oscillation is calculated, and is found to depend on the shape of the weld pool.

A theoretical model of thermocapillary flows in laser welding

Surface tension variations on the surface of the weld pool produced by a laser during the process of welding, can produce very strong currents. A linearized description of the process is constructed, as well as a non-linear boundary layer model that takes account of thermal conduction and fluid convection. It is found that there is a considerable difference between the predictions of the two approaches. The non-linear model produces results that are compatible with what is believed to occur in practice.

The thermal stress generated by a moving elliptical weldpool in the welding of thin metal sheets

In the welding of metal sheets by lasers or electric arcs, a problem of considerable interest and importance is the formation of stresses and strains in the material undergoing the welding process. This paper investigates the process making use of the linear theory of elasticity. The non-uniform heating of the metal is allowed for by the presence of an appropriate term in the stress tensor representing the temperature field. The weld pool is approximated by an elliptic region which is constant in cross sectional shape with depth. This paper calculates the stresses in metal outside the molten region in the frame of the laser using mainly analytical techniques and in its final stages evaluates these numerically for the cases of an unclamped as well as a clamped metal sheet. The results are found to be largely independent of the particular metal when the stresses are expressed in dimensionless form. The effects of welding the metal with a laser are essentially reversible in character when the analysis is restricted to linear elastic theory without phase changes.

A mathematical model of heat conduction in a prolate spheroidal coordinate system with applications to the theory of welding

The steady-state heat conduction equation is solved in a prolate spheroidal coordinate system. Some simple solutions are derived in the limiting cases of both low and high Peclet numbers. The analysis was carried out in such a way as to avoid the physical details of conditions inside the weld pool, so that the solutions are restricted to the solid region outside the weld pool. This procedure was specifically adopted because these conditions are difficult to gain access to experimentally, as is the precise detailed shape of the pool; the solutions obtained can be verified experimentally. The high-Peclet-number approximation is likely to be particularly useful in the case of laser welding where large translation speeds of the weld piece are of interest. The solution of the problem is given in the form of a series as well as in an asymptotic form. The asymptotic method of solution presented can be adapted to any smooth shape of weld pool with only minor alterations, since the method involves integration in the tangent plane to the weld pool and the results of such an integration are independent of the global form of the weld pool. The asymptotic result is compared with the exact solution in a number of special geometric configurations. These are prolate spheroidal weld pool geometries with various aspect ratios and cylindrical weld pool geometries with elliptical or circular cross sections. The results of these comparisons were found to be satisfactory.

Distortion generated by a moving weld pool of elliptical cross section in the welding of thin metal sheets

Much analytical work exists dealing with distortion in thin metallic sheets produced by moving heat sources. We consider here the case of the distortion generated in a weld pool whose cross section is in the form of an ellipse in a thin sheet of metal, but with some allowance for variations through the thickness of the material. An essential feature is the presence of this molten pool. The presence of the molten region ensures that stresses arising from viscous flow and pressure are many orders of magnitude smaller then those present in the solid region and can therefore be neglected. In the present analysis all deformations that arise are associated with the equations of linear thermoelastic theory. The problem is tackled analytically and expressions obtained for the stresses in the work piece.

WAVE PATTERN PRODUCED BY A HEAT SOURCE MOVING WITH CONSTANT VELOCITY ON THE TOP OF AN INFINITE PLATE

Within the framework of linear, isotropic elasticity theory the wave pattern produced by a heat source moving with constant velocity on the top of an infinite plate is computed. Both the transient effects associated with the initial conditions and the damping of the waves are neglected. If the travel speed of the heat source is smaller than the velocity of the surface waves, dispersive flexural waves will be excited. The frequency of these waves is proportional to the square of the wave number if the wavelength is much larger than the thickness of the sheet. In this limiting case it is found that the crest of the waves makes an angle of 90 degrees with the travel direction, and this result is independent of the travel speed as long as the parabolic approximation remains valid for the dispersion relation of flexural waves.