A step towards understanding the heating phase of laser transmission welding in polymers.

In recent years, laser transmission welding has gained in significance by displaying its specific advantages among the established welding processes for thermoplastics. However, a deep understanding of the developed process variants is so far missing. Useful results for temperature development were obtained in cases of high absorption constants by setting up an analytical model by analogy to single-sided heat impulse welding. Yet there is no physico-mathematical model considering the different energy conditions for joining parts with various absorption properties. This investigation is a first step towards a deep and detailed insight into the heating phase of the laser transmission welding process. Experimental data for temperature progression was collected for polypropylene. In addition, an analysis of the heat transfer problem using the finite element method showed a good level of agreement with the experimental results.

INTRODUCTION

During the past few years, laser welding has become established as a new joining technique in plastics technology, because it selectively exploits certain advantages over conventional methods. Particular mention can be made of the contact-free energy introduction with the laser welding methods that have been developed and the high flexibility that they frequently offer. It is expected that a number of these processes will not only replace conventional plastic joining processes in future, but will also serve to open new fields of application and design that are made possible only through laser welding.

The transmission principle has emerged as the basic principle for all the process variants. This permits a molded part that is transparent to laser beams to be joined to a molded part that absorbs these beams. The laser beam is transmitted virtually unimpeded through the first part before being completely absorbed in the surface layers of the second part (high absorption constant) (see Fig. 1). The heat thus created is transported both into deeper layers of the semi-finished product that absorbs the laser beam and into the semi-finished product that is transparent to the beam. This absorption leads to a temperature increase in the joining plane.

The molten plastic that forms improves the heat contact between the parts and causes an internal joining pressure to build up through volume expansion in cases where there is pressure-free contact between the parts being joined right from the start of the welding process (1). As in film welding, the heating and joining phase take place simultaneously.

All thermoplastics in common use behave essentially transparently to radiation in the near infrared range (MR range, with a wavelength of around 1 [micro]m), despite the highly differing absorption bands at different wavelengths (2, 3). In semicrystalline materials, the laser beam is scattered by the structure, which means that transparency has to be observed as a function of the material thickness. Thermoplastics can be made into absorbing materials through "pigmentation" with appropriate pigments. The absorption will be a function of the type of pigment used and the quantity added (4).

Since the transparency and absorption behavior of pigments in the visible range (visible to the human eye) do not have to correspond to the optical behavior in the laser-beam wavelength range, the very latest developments in this field permit virtually unlimited coloring of both parts to be joined. Hence, two parts that look black to the human eye can still be joined by laser transmission welding. One part has carbon black added to it, for instance, as a classical absorbing pigment, while the part that is transparent to the laser beam includes a special pigment characterized by high transparency in the NIR range and a high absorption in the visible range. It is similarly possible to weld together two non-pigmented transparent plastics by the laser transmission method. This is done by having the beam absorbed in a thin intermediate layer that displays only a high absorption in the laser wavelength range. The heat is conducted from this layer into both parts resulting in a weld (5).

New variants on the laser transmission welding process have been developed only recently alongside the so-called contour welding process, in which the laser beam is conducted once or twice along the joining contour (6). While these variants have advantages in certain applications, they often entail a loss of flexibility. Variants include simultaneous welding, where the entire surface to be joined is heated simultaneously by a number of high-performance diode lasers (7-10), mask welding (11), where only the areas that are not covered by a mask are plasticized by the laser beam, and quasi-simultaneous welding (12), in which the laser beam is run along the weld several times at high frequency by means of a system of scanner mirrors.

A feature common to all the transmission processes is that the two parts being joined are in contact for the entire welding process.

PROBLEM

Contour welding is the first laser transmission welding process to be developed that both offers a high flexibility and can also be used to produce bead-free weld seams. A fundamental process analysis is conducted of this process principle in respect to the heating phase, employing experimental investigations and finite element calculations. The aim is to acquire a comprehensive, in-depth understanding of the process. This will then provide a systematic and simplified basis for working out process parameters, which have so far been determined in preliminary tests by the trial-and-error principle.

So far, no physico-mathematical model is available to describe the energy conditions that prevail during laser transmission welding on a comprehensive basis. Initial attempts to compile an analytical model by analogy to thermal impulse welding (13) provided serviceable results for temperature progression in cases where the absorbing part had a high absorption constant. With lower absorption constants, also, the introduction of a correction factor gave calculated melt layer thicknesses that tallied well with the measured thicknesses.

This model, however, assumes that the energy is introduced evenly into the two parts and hence that the temperature peak in the joining zone corresponds to the contact temperature between the absorbing part and the transparent part.

With low absorption constants, in particular, this precondition is no longer fulfilled. The laser beam penetrates further into the absorbing part and is thus absorbed over a broader layer of material. This is no longer surface absorption, and the energy applied is not introduced into the two parts in identical quantities. An extensive temperature gradient still prevails at the contact surface, which means that energy still penetrates the transparent part. The temperature gradient in the (broader) absorbing layer beneath the joining surface, however, is less pronounced, which means that less energy is conducted into the deeper layers of the absorbing part here. A temperature profile can thus develop in the joining zone that has the peak temperature in a layer beneath the joining surface in the absorbing part rather than directly on the contact surface.

The physico-mathematical model is unable to correctly reflect the true temperature profile in this case. In addition, the course of the temperature over time during the heating phase cannot be described with the aid of this analytic formulation.

The physico-mathematical model previously described is thus inadequate for achieving comprehensive insight into the process of laser transmission welding. Since a closed analytical solution can no longer be found to the 3D heat transfer problem by simple means, in view of the complexity of the influences involved, the finite element method is employed for purposes of analyzing the temperature progression in the heating phase.

This analysis also provides the basis for a further-reaching process analysis to cover the development of inherent stresses through cooling in laser transmission welded components.

EXPERIMENTAL INVESTIGATIONS

A fundamental difficulty encountered in process control for all laser welding methods that operate by the transmission principle derives from the fact that the parts being joined are in contact throughout the entire process. This makes it more difficult for temperatures to be recorded. Thermocouples cannot be used, since they similarly absorb laser radiation, and the signal they supply does not therefore correspond to the temperature in the plastic.

One solution would seem to be to employ contact-free temperature measurement methods with the aid of radiation pyrometers and thermography systems. Temperatures can be recorded at different points of the weld geometry, depending on the measuring wavelength. If the wavelength of the temperature radiation to be recorded is selected in the range of around 1 [mu]m. it is possible to record the temperature in the joining plane through the transparent part. Most plastics are transparent in this near infrared range, which provides the essential basis for the laser transmission welding principle. Radiation pyrometers with a measuring wavelength in the 0.5 to 10 [mu]m range can be used to record surface temperatures on transparent plastics also.

Calibrating the measuring systems poses problems for all radiation pyrometers. It is necessary to know the emission factor of the surface whose temperature is to be measured on the basis of the temperature radiation it emits. The determination of the emission factor was seen to be highly imprecise in the measurements conducted; the temperatures measured with the pyrometers are thus not considered.

The most accurate means of obtaining an indication of the temperature development that takes place in the heating phase of laser transmission welding has been found to be by determining the melt layer thicknesses on thin sections of the Joining zone under a transmitted-light microscope. With a measuring accuracy of 0.0625 mm, it is still possible to detect even small differences in the melting depth. The sole limitation on this method is that it can be used only for semicrystalline thermoplastics where the boundaries of the molten layer thickness can be detected by virtue of dissimilar structures. This investigation method is, unfortunately, unsuitable for amorphous thermoplastics because they lack a crystalline structure.

When the heating tests were conducted on polypropylene with carbon black contents of 0.1% and 0.3% by weight of gas black, the joining surface was not scanned in its entirety, as is clear from Fig. 2. This made it possible to avoid a squeeze flow in the region of the weld seam. The small welding bead, depicted in Fig. 3, is attributable to the thermal material expansion and to the prevailing joining pressure. It is possible to exclude any relative movement between the two parts. The concave molten layer profile also has to be attributed to this small welding bead, which leads to deeper melting of the edge zone. In this first approach, the effect of the thermal expansion during the heating phase and the formation of a welding bead were neglected in the finite element model. Thus, a comparison between the calculated 2-dimensional melt profile (which was found convex) with the real melt profile (concave) was considered impossible. However, the influence on the melt layer thickness in the center of the sample wa s assumed to be very small. Further investigations are planned that take these effects into account and make it reasonable to set up a 2-dimensional model.

Figures 4 and 5 show the melt layer thicknesses established as a function of the parameters of scanning speed and laser power for the transparent and the absorbing part. The pronounced reduction in the melting depth with a lower level of energy introduction. i.e., a lower laser power and an increased scanning speed, is clear to see. It can additionally be seen that a higher carbon black content in the absorbing part leads to a clear reduction in the melting depth precisely in this part, while the transparent material undergoes deeper plasticization. An increase in the absorption constant and hence the introduction of the laser radiation into the layers close to the surface of the absorbing component (surface absorption) ultimately lead to uniformly deep melting in both parts being joined by laser transmission.

IMPLEMENTATION OF THE FINITE ELEMENT METHOD

The most important boundary condition for a calculation with the finite element method is knowledge of the amount of energy introduced, i.e., the intensity of the laser radiation. This intensity is not constant over the radius of the beam or, therefore, over the beam cross section. The power behind the transparent part being joined (= in the joining plane) was thus measured experimentally with the aid of an aperture plate (diameter 1 mm), as shown in Fig. 6.

The scatter of the laser radiation is clear from Fig. 7. this being associated with the expansion of the beam. While the beam diameter was set at some 4 mm in front of the transparent part being joined, a diameter of 7 mm can be read off the intensity values established for the joining plane (behind the transparent part being joined).

The course of the experimentally established intensity values behind the transparent PP specimen corresponds to a Gaussian bell-shaped curve for the optical fiber used (graded-index fibres)--Fig. 7--and is rotationally symmetric around the beam axis. The profile can thus be approximated with the function

[I.sub.0](r) = a . [e.sup.-b.[r.sup.3]] (1)

where: [I.sub.o]: intensity

r: radius coordinate in the polar coordinate system 

a, b: approximation coefficients

If the overall power is then established, in turn, through integration of the intensity function

[P.sub.tot] = [[integral].sup.R.sub.0] [[integral].sup.2[pi].sub.0] [I.sub.0](r) . r . d[phi] . dr = 2 . [phi] . [[integral].sup.R.sub.0] r. a . [e.sup.-b.[r.sup.2]] . dr = [pi] . a/b . (1 - [e.sup.-b.[R.sup.2]]) (2)

where: [phi]: angle coordinate in the polar coordinate system

R: beam radius (behind the transparent part in the joining plane) then, for R [right arrow] [infinity], this will give:

[P.sub.tot, cal] = [pi] . a/b. (3)

Compared with the total measured power of [P.sub.tot,meas'] too small a value is obtained when the total power [P.sub.tot,cal] is calculated according to Eq 3 (from the approximation calculation). This is attributed to the imprecise power measurement through the aperture plate. The approximation calculation was thus corrected by a factor [f.sub.p] in each case (Table 1), so that the measured total power [P.sub.tot,meas] and the total power calculated from integration of the measured and approximated intensity function [P.sub.tot,cal] (Eq 3) tally with each other:

[I.sub.o] (r) = [f.sub.P] . a . [e.sup.-b.[r.sup.2]] (4)

where: [f.sub.P]: correction factor for total power.

Linear material behavior is assumed to prevail in the absorbing part to begin with, so that the intensity reduction due to absorption of the beam can be described by the Lambert-Bouguer Law:

(z) = [I.sub.0](r) . [e.sup.-K.z] (5)

where K is the absorption constant describing the absorption properties of the material. The finite element analysis makes allowance for the radiation energy introduced in the same way as for a location-dependent internal heat source (13). The intensity of the internal heat source in a material layer [DELTA]z (Fig. 8) is then

[DELTA]I(z) = [I.sub.0](r) . ([e.sup.-K.z] - [e.sup.-K.(z+[DELTA]z)]) (6)

where [DELTA]z: thickness of the material layer

The absorption constant that describes the absorption properties of the colored part being joined is the sole degree of freedom in the simulation of temperature profiles with the aid of finite element analysis. Further details will be given of the values assumed and the profiles of this parameter in the discussion of the results.

The reduced two-dimensional model as per Fig. 9 is taken for calculating the temperature progression with the aid of finite element analysis. This reduction can be assumed on symmetry grounds in order to shorten the computing time. The network division was selected as 0.1 mm in the y-direction and 0.0125 mm in the z-direction. Elements of the second order were used, as is recommended for the calculation of heat transition problems with ABAQUS (14). While these increase the computing time, they also give a more precise approximation of highly curved temperature profiles of the type that can be expected for laser transmission welding on account of the small heat-affected zone.

Heat transfer coefficients for convection and radiation as in (13) are assumed by way of external boundary conditions. These have been successfully used to achieve good results for simulation of the heating phase in the similar process of laser butt welding. The ABAQUS FEM program incorporates facilities for defining material characteristic values as a function of temperature. The density, specific heat capacity, and thermal conductivity were thus implemented in the corresponding variable manner over the expected temperature range.

RESULTS

Figure 10 shows a comparison of the calculated melting depths and the experimental values for both the absorbing and the transparent part being joined, with different laser powers and scanning speeds. An effective absorption constant that remains constant over the entire temperature range was assumed here for polypropylene with 0.1% by weight carbon black. While the low melting depths of the transparent parts can be calculated highly accurately with the assumed absorption constants, a clear difference compared with the experimental values is seen for the bigger melting depths of the absorbing part. All in all, the calculation gives rise to excessively large melt layer thicknesses. It proved possible to reduce these thicknesses somewhat by increasing the absorption constant. Despite this, it is not possible to achieve the desired level of agreement with the experimental values using an absorption constant that remains constant.

Korte assumed (13) that the absorption properties of plastics cannot be regarded as temperature-independent. In this publication, it was assumed that a clear increase results in the absorption constant in the melting range of the material, in particular. Transposing these assumptions did not, however, effect the desired improvement in the heat transfer problem being studied for laser transmission welding. The melting depths in the absorbing part were still calculated at too high a level. The authors are unfortunately unaware of any absorption measurements having been conducted at above the flow temperature for plastics. It was thus assumed that the absorption constant behaves in the same way as the temperature-dependent density profile of the material over the temperature range observed. A ramp-shaped profile was therefore taken for the absorption constant, with only the level at room temperature and in the molten range needing to be assumed. The profile between these was assumed to be similar to the density function (Fig. 11). Employing an iterative procedure, it thus proved possible to establish a ramp-shaped profile for the absorption constants, permitting the experimentally determined melt layer thicknesses to be calculated.

Viewed in physical terms, a profile of this type in the absorption properties of the plastic means that as the temperature increases in the region of the phase transition from the solid to the melt, the laser radiation penetrates ever further into the absorbing material. As the temperature rises, the molecules and the pigments distributed in them start oscillating to an increasing extent, and hence it would be conceivable for the radiation absorption of this "oscillating matrix" to be impaired in this way. The laser radiation can "penetrate" the material more easily and is only absorbed in deeper and, hence, colder material layers.

Figures 12 and 13 show that a temperature-dependent profile of this type for the absorption properties of the absorbing part gives satisfactory agreement between the calculated and the experimentally established melting depths in both the absorbing and the transparent part. For the material with the low carbon black content of 0.1% by weight, a ramp-shaped profile of between 2.4 and 1.1 [mm.sup.-1] for the effective absorption constant can be used to calculate the measured melt layer thicknesses, with just slight deviations that can be attributed to the measuring inaccuracy. A profile between 7.8 and 1.8 [mm.sup.-1] gives good results for the higher carbon black content, albeit with somewhat higher fluctuations.

CONCLUSION

Through the investigations presented here and with the aid of finite element analysis, it has proved possible to describe the heating phase in the laser transmission welding of polypropylene by the contour method in a representative manner on the basis of the melting depth. The molten layer thickness in the two parts can be calculated on a satisfactory basis for different energy conditions. For subsequent investigations it would be desirable to establish precise temperatures with the aid of contact-free measuring methods so that an analysis of the heating phase can be conducted for the laser transmission welding of amorphous plastics as well. This would make it possible to establish a basis for this group of materials also, which could then be used to analyze the inherent stresses due to cooling more closely.

ACKNOWLEDGMENT

The Institut fur Kunststofftechnik of the University of Paderborn (KTP) would like to thank the Deutsche Forschungsgemeinschaft (DFG) for its financial support of the tests presented in this report. Thanks also go to Targor GmbH (formerly Hoechst AG) and DSM Deutschland GmbH for their provision of test materials.

[Figure 4 omitted]

[Figure 5 omitted]

[Figure 7 omitted]

[Figure 8 omitted]

[Figure 10 omitted]

[Figure 11 omitted]

[Figure 12 omitted]

[Figure 13 omitted]

Table 1

Intensity Profiles and Correction of Total Power.


Total          Total Measured       Approximated
Laser           Power in the     Intensity Function
Power           Joining Zone       (Joining Zone)

[P.sub.Laser]   [P.sub.tot,       [I.sub.o](r) = a *
                   meas]         [e.sup.-b.r.sup.2]


30 W               22.0 W      1273239. 54 W/[m.sup.2] *
                                  [e.sup.-0.2701m]

40 W               28.6 W      1909859. 32 W/[m.sup.2] *
                                  [e.sup.-0.2681m]

                    Total
Total          Calculated Power
Laser           in the Joining       Correction
Power                Zone              Factor

[P.sub.Laser]  [P.sub.tot, cal]      [f.sub.P] =
                 = [phi] * a/b   [P.sub.tot, meas]/
                                  [P.sub.tot, cal]

30 W
                   14.52 W              1.5

40 W
                   22.07 W              1.3

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