An approach to model the melt displacement and temperature profiles during the laser through-transmission welding of thermoplastics.
Over the past few years, laser through-transmission welding of thermoplastics has become established as a new joining technique in plastics technology which selectively exploits the advantages selectively over conventional methods . Particularly, by using laser radiation, non-contact energy deposition, particulate-free welding, and high process flexibility are possible. Laser welding is not expected to simply replace conventional plastic joining processes in the future, but it will serve to open up new fields of application and design possibilities for plastics that can only be processed using laser welding.
The laser through-transmission principle permits a molded part, which is transparent to the wavelength of the laser beam, to be joined to a molded part that absorbs the laser radiation. With this material combination, the laser beam is transmitted through the first part before it is completely absorbed in the surface layers of the second part (high constant of absorption, see Fig. 1). Heat is transported into deeper layers of the semi-finished product, which absorb the laser radiation. This absorption leads to a temperature increase in the joining plane. By applying a predefined joining pressure a weld can be created.
Thermoplastics commonly used today have different optical properties for laser radiation in the near infrared (NIR) range, with a wavelength of around 1 [micro]m, because of highly varying absorption bands at different wavelengths. With semi-crystalline 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 turned into laser absorbing materials by using appropriate NIR pigmentation (e.g. carbon black). Absorption is a function of the type and the concentration of the pigment used.
Since the transparency and the absorption behavior of pigments in the visible range (i.e., visible to the human eye) do not have to correspond to the optical behavior of the laser beam wavelength, latest developments permit unlimited coloring of both parts to be joined [2, 3]. Hence, two parts that--to the human--look black can still be joined using laser transmission welding. For instance, one of the joining parts will contain carbon black as a classic pigment. The transparent joining partner includes a special pigment which is characterized by high transparency in the NIR range and high absorption in the visible range. Moreover, it is state of the art to color the parts to be joined without major design limitations by using appropriate pigments. Similarly, it is possible to weld two non pigmented transparent plastics using the laser transmission welding process. To do this, a thin intermediate layer with a high absorption level for the laser beam wavelength is needed in the interface. The heat is conducted from this layer into both joining parts resulting in a weld seam [4, 5].
[FIGURE 1 OMITTED]
New modes of laser transmission welding have been recently developed apart from the so-called contour welding process. Here, the laser beam is guided once along the joining contour [6, 7]. The new modes include on one hand mask welding [8, 9], in which only the areas that are not covered by a mask are plasticized by laser radiation. On the other hand, the simultaneous and quasi-simultaneous welding modes can be differentiated. In the case of simultaneous welding, the entire surface to be joined is heated simultaneously by a number of high-performance diode lasers [10-13]. For quasi-simultaneous welding, the laser beam is guided along the weld in a predetermined repetition rate, and at high frequency using a scanner system [14, 15].
These last two modes have in common that during the welding process, the whole joining surface will be heated up and simultaneously plasticized (Fig. 2). Thus, a weld seam will be created after the melt is squeezed out by applying a predefined joining pressure.
TARGETS OF INVESTIGATIONS
Simultaneous and quasi-simultaneous welding modes are being increasingly applied besides contour welding. These modes are often used when geometrical tolerances of the joining parts have to be compensated, as well as when fixed and tight joining contours have to be established. In this study, a fundamental analysis of the heating phase and the joining phase of the quasi-simultaneous welding mode was carried out. To do so, a finite-element model (FEM) was developed to calculate temperature and melt displacement profiles. Moreover, the model was experimentally verified. The goal of this study was to gain a comprehensive and profound understanding of the underlying process, in order to be able to decrease existing process limitations. Furthermore, the temperature profiles and melt displacements were also correlated with the mechanical properties of the resulting weld seams.
[FIGURE 2 OMITTED]
This article is based on previous work in which a physico-mathematical model was introduced to characterize the heating phase during contour welding [16, 17]. This model is limited to describe the temperature development in the transparent and the absorbent joining components for a small absorption constant. According to this, more energy is transferred to the absorbent component than to the transparent one. This high temperature gradient in the contact area results in a non-uniform temperature distribution in both components. In the temperature profile developed, the maximum temperature is found in the layers below the joining surface of the absorbent partner and not directly in the joining surface.
Extending this model and transferring it to quasi-simultaneous welding will now also allow a simulation of the melt flow, apart from calculating the temperature profiles.
Heating and plasticizing the joining surface by applying pressure generates a joining displacement which must be considered in the model. After the laser energy is deposited and it has interacted with the joining pressure, an additional joining displacement is created. This is the so-called settling displacement which is to be distinguished from the joining displacement. By predefining the material data, joining geometry, and boundary conditions as well as the process parameters (energy, joining pressure and time), the temperature and melt displacement profiles can be calculated. For this purpose, the calculated data should be verified with data collected in the experiments. In this regard, the correlation of the melt flow data and the achievable weld strength is also to be demonstrated.
Because of the complexity of the three-dimensional heat transfer with simultaneous mechanical load, a complete analytical solution cannot be found. Therefore, the (FEM) is used as an approximation procedure.
MELTING DISPLACEMENT PROFILE IN LASER THROUGH-TRANSMISSION WELDING
Before starting a detailed description of the model to be developed, a few basic correlations must be discussed between simultaneous and quasi-simultaneous welding. In Fig. 3, an exemplary melting displacement diagram is represented in dependence on the welding time for the process mode of simultaneous welding. The resulting curve can be subdivided into four phases:
[FIGURE 3 OMITTED]
Phase 1: unsteady without an increasing joining displacement
Phase 2: unsteady with an increasing joining displacement
Phase 3: steady (constant melting rate and const. flow velocity)
Phase 4: cooling down.
In Phase 1, after the laser beam irradiates the joining surface, no noteworthy increase of the melting displacement can be detected. In Phase 2, the melting displacement increases continuously after a welding time of about 0.6 s. In Phase 3, the melting rate turns into a constant level after a welding time of about 1 s. This effect can be observed in the diagram with the constant slope of the displacement-time-curve. In the steady phase, the energy dissipation of the laser radiation equals the heat flow dissipated into the weld bead. After a heating time of about 2.5 s, a predefined melting path of 1.0 mm is obtained. The cooling time commences in Phase 4 and terminates the welding process.
In Fig. 4, the joining displacement and the weld strength are represented in dependence on the welding time.
The weld strength does not change considerably after reaching the steady phase, and remains constant in this example at about 39 MPa.
Similar correlations are also found for the quasi-simultaneous welding mode. In Fig. 5, the joining displacement is shown as a function of the welding time for the polymeric material polycarbonate (PC).
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
After a welding time of about 23 s, the slope of the curve reaches a constant value in which the steady phase begins.
[FIGURE 6 OMITTED]
The weld strength does not increase in the steady phase and remains invariable at a value of about 27 MPa.
Furthermore, the measured remaining melt layer thickness (using cross-sections of the weld seam) also achieves a constant value of 1.9 mm in the steady phase.
The correlations mentioned between joining displacement, weld strength, and welding time have already been observed in other joining processes, such as biaxial vibration welding .
For the investigations, the semi-crystalline polymeric material PA6 Durethan B 30 S was selected. The absorbent partner has a weight content of 0.1% carbon black. A modified AWS geometry was used as a test sample (Fig. 6).
In order to experimentally determine the melt displacement during the laser welding process, high-speed micro-focus radioscopy was used (Fig. 7).
The experimental set-up consisted of the following components: a laser beam source, a galvanoscanner, a microfocus-X-ray tube, an image converter in combination with a high-speed camera, a clamping device for the polymeric samples, and a recording system. The polymeric samples are placed between the microfocus-X-ray tube and the image converter. The X-ray tube is positioned perpendicular to the incident laser beam and irradiates the welding zone.
[FIGURE 7 OMITTED]
In order to visualize the polymeric welding zone, tracer particles are placed in the contact area of both polymeric parts. A high-speed camera operating at frequencies up to 1000 Hz registers the x-ray image sequences during the welding process. These are analyzed off-line using an image process system.
The set-up allowed the three-dimensional observation of the dynamic melting pool behavior, by recording two projections of the molten polymer pool in two predefined planes. In the range of the investigations, a diode laser was applied as a laser source, with a wavelength of 940 nm and a maximum output power of 250 W.
Prior to the laser welding process, tracer particles were embedded into the polymeric matrix (tungsten, particle diameter = 75-90 [micro]m; weight content = 0.1%). During the experiments, the chronological and spatial displacements of these particles were recorded.
In order to determine the molten area in the joining zone, the remaining melt layer thickness was measured for predetermined welding times after preparing the respective cross-sections. In addition, tensile strength tests were carried out to determine the mechanical properties of the resulting weld seams.
IMPLEMENTING OF WELDING AND BOUNDARY CONDITIONS
Precise information about the launched energy (i.e. the laser intensity) represents one of the important boundary conditions for a calculation using the FEM. Since the intensity varies with the laser beam radius, and the laser beam is scattered through the transparent partner, the laser beam profile at the joining area (i.e., behind the transparent partner) presents other characteristics. In order to characterize it, the laser output power was measured for a constant irradiated area, and the transmission value of the polymeric sample was considered for the final intensity distribution (Fig. 8).
[FIGURE 8 OMITTED]
The resulting intensity curve corresponds to a Gaussian distribution, which can be described by means of the following equation (compare also with Fig. 9):
[I.sub.0](r) = a x [e.sup.-br[.sup.2]] (1)
where [I.sub.0] is the intensity, a and b are approximation coefficients and r is the radius coordinate in the polar coordinate system.
Appropriate with the approach used in Refs. 14 and 15, the total power in the joining surface can be calculated by:
[P.sub.tot] = [R.[integral].0][2[pi].[integral].0][I.sub.0](r) x r x d[phi] x dr = 2 x [pi] x [R.[integral].0] r x a x e x [.sup.-br[.sup.2]] x dr (2)
= [pi] x [a/b] x (1 - [e.sup.-bR[.sup.2]])
where [phi] is the angle coordinate in the polar coordinate system and R is the laser radius in the joining area. This is true for R [right arrow] [infinity], following relation:
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[P.sub.tot,cal] = [pi] x [a/b]. (3)
In the total laser power [P.sub.tot,meas] measured, the resulting value is higher than the calculated one in virtue of the approximation calculation according to Eq. 3 ([P.sub.tot,cal]). Thus, for the preset laser power of 250 W, the transparency accounted is 15% (corresponds to 37.5 W). However, according to Eq. 3, the approximated laser power achieves 31 W. This discrepancy is attributed to the experimental conditions, where the laser beam irradiates the transparent partner. Therefore, a correction factor [f.sub.p] (here 1.2) is considered, so that the measured value of the total power [P.sub.tot,meas] equaled the value of the total calculated power [P.sub.tot,cal] (Eq. 3).
[I.sub.0](r) = [f.sub.p] x a x [e.sup.-br[.sup.2]] (4)
where [f.sub.P] is the correction factor for the total power. The launching of the laser radiation into the absorbent partner was assumed, in compliance with the Lambert-Bouguer law. According to this, the intensity distribution in the absorbent component is characterized as follows:
I(x) = [I.sub.0](r) x [e.sup.K[dot]x] (5)
where K is the constant of absorption, which represents the absorption properties of the FEM material, and x is the position of the propagation angle of the laser beam.
By using the FEM and the program ABAQUS 6.3, the radiation launch was specified by the spatially dependent interior heat sources [16, 17]. According to this, the intensity of the interior heat source for a material layer thickness of [DELTA]x can be delineated as follows (compare also with Fig. 10):
[DELTA]I(x) = [I.sub.0](r) x ([e.sup.-K[dot]x] [-e.sup.-K(x[dot][DELTA]x)]) (6)
[FIGURE 11 OMITTED]
where [DELTA]x is the thickness of the material layer.
The above mentioned details demonstrate that the resulting intensity curve in the joining area requires a correction factor of 1.2 if the laser beam remains in a predefined position. To transfer the actually launched intensity into the FEM, in the case of quasi-simultaneous welding, the measurements were performed at an arbitrary chosen scanning velocity of 8 m/s. In this way, the initial intensity [I.sub.0] of about 1.08 W/[mm.sup.2] was determined (Fig. 11). It is assumed that the intensity here also must be corrected, as for the fixed laser beam. On the basis of the same experimental set-up, the same correction factor of [f.sub.p] = 1.2 is used. The initial intensity [I.sub.0] is set to 1.333 W/[mm.sup.2]. For all experiments performed in this study, the scanning velocity was held constant at 8 m/s and the laser output power at 250 W.
As previously observed in Refs. 16 and 17 for the absorbent partner, a non-varying constant of absorption in compliance with the Lambert-Bouguer law in Eq. 5 cannot be assumed. According to Refs. 16 and 17, the constant of absorption decreases with an increasing temperature, just like the density of the analyzed polymer. To simplify matters, the constant of absorption K was assumed so as to adopt a value of 3 [mm.sup.-1] until the PA6 material reached the melting point of 220[degrees]C. At this point, a value of 2.6 [mm.sup.-1] was chosen. The choice of these values is adjusted to the experimentally specified melt layer thickness (pure heating without melt flow) for the FEM material. High consistency between the calculated and the measured values was attained for this constant of absorption, as demonstrated below. However, the influence of the constant of absorption in dependence on the temperature of the melt layer thickness, for the absorbent partner was not as dramatically characteristic as emphasized in Refs. 16 and 17.
[FIGURE 12 OMITTED]
The reduced two-dimensional model (Fig. 12) was chosen for symmetric reasons, to diminish the calculation period as well as the storage capacity. The intensity distribution in the spot diameter was implemented according to Fig. 11. Second-order elements were applied, which are recommended for the calculation of heat conduction systems with the program package ABAQUS.
The external boundary conditions such as the heat conduction coefficient for convection and radiation were assumed as in Ref. 17. The FEM program ABAQUS provides the opportunity to define material properties, in dependence on the temperature. Therefore, the thermodynamic state variables, such as the density, specific heat capacity, and heat conductivity were implemented in a correspondingly variable way for the expected temperature range.
Apart from setting the laser output power, the joining pressure and the welding time were also predefined in the model as a joining displacement-time curve. In Fig. 13, the profile of the measured joining displacement is represented against the welding time and the joining displacement profile implemented in the model. As mentioned above, the joining displacement curve can be divided into four phases (steps). In the first phase (Step 1), up to about 7 s, the joining displacement does not increase. In Step 2, up to about 10 s, the joining displacement increases unsteadily. In Step 3 (the steady phase), until about 13 s, the melting velocity remains constant. After 13 s, the laser beam radiation is turned off, and the cooling phase commences and lasts for about 24 s.
In addition to the measurement of the joining displacement in dependence on the welding time, the weld strength was determined (Fig. 12). It was evident that the weld strength remained almost constant in the steady phase at a value of about 33 MPa.
[FIGURE 13 OMITTED]
The mechanical and thermal loading that occurs during the welding process causes strains and tensions in the joining parts in dependence on the temperature and time (see also Fig. 13). The strains and tensions can be identified by means of the thermoelasticity and plasticity theory . This theory assumes an elastic-plastic material deformation, in which the complete strain is described by the elastic, plastic and thermal component. As soon as the loading is released, the plastic proportion remains:
[[epsilon].sub.all] = [[epsilon].sub.ij.sup.el] + [[epsilon].sub.ij.sup.th] + [[epsilon].sub.ij.sup.pl] (7)
[[epsilon].sub.ij.sup.el] = [[1 + v]/E][[sigma].sub.iJ] - [v/E][[sigma].sub.kk][[delta].sub.ij] (8)
[[epsilon].sub.ij.sup.th] = [alpha][DELTA]T[[delta].sub.ij] (9)
[[epsilon].sub.ij.sup.pl] = [3/2][alpha]([[sigma].sub.v]/[[sigma].sub.0])[.sup.n-1][[S.sub.ij]/E] (10)
[S.sub.ij] = [[sigma].sub.ij] - [1/3][[sigma].sub.kk][[delta].sub.ij] (11)
[[sigma].sub.v] = [square root of ([3/2][S.sub.ij][S.sub.ij])]. (12)
As mentioned above, ABAQUS provides the opportunity to define material properties in dependence on the temperature. Apart from the thermodynamic parameters of state, the material characteristics (i.e., the elastic modulus, Poisson number and stress--strain values) were preset in dependence on the temperature.
In Fig. 14, the calculated and the measured melt layer thicknesses without melt flow are exhibited for the transparent and absorbent partner. The entire melt layer thickness without melt flow is illustrated for both materials with their respective heating periods [t.sub.E].
The calculated melt layer thickness for the absorbent material is consistent with the associated measured values. However, the calculated melt layer thicknesses for the transparent material appear to be undersized.
[FIGURE 14 OMITTED]
[FIGURE 15 OMITTED]
Consequentially, the calculated total melt layer thicknesses are also smaller than the measured values. This can be attributed to the partial absorption of the laser beam in the transparent partner, so that its heating occurs not only as a result of a heat conduction process from the absorbent partner. In order to simplify the calculation, it was assumed for the simulation that the transparent partner is heated and plasticized solely by head conduction through the absorbent partner. To consider the absorption of the laser intensity also in the transparent partner, [I.sub.0] was preset according to Eq. 5. It was assumed here that the absorption in the transparent partner was relatively low (i.e. [K.sub.tr] [right arrow] 0). In compliance with Eq. 5, the following is described:
I(x, [K.sub.tr] [right arrow] 0) = [I.sub.0](x) x [e.sup.-Ktr[dot]x] = [I.sub.0]. (13)
As the intensity distribution decreases toward the edge of the laser beam radius, an intensity distribution (Fig. 15) was implemented in the transparent partner. The assumed rate of intensity declines toward the edge regarding the percentage of the measured intensity in the joining surface and in the absorbent partner respectively (Fig. 11).
Once the intensity distribution described was preset for the transparent partner, there was a high conformity between the calculated and measured values of melt layer thickness (Fig. 16).
In Fig. 17, the schematic model is shown in image A, and the calculated profile of the melt displacement in y-direction is represented in dependence on the welding time for the coordinates x = 0 mm and [y.sub.0] = 0.15 mm in B. These coordinates correspond to the joining plane in an offset position 0.15 mm (y axis) with regard to the center of the welding seam.
[FIGURE 16 OMITTED]
In the first instance, the calculation was performed without considering absorption of laser beam radiation in the transparent partner. The calculated values are slightly undersized, as compared to the measured ones. For example, after about 13 s, a displacement of about y = 0.33 mm is measured and a smaller displacement of 0.27 mm is calculated. The difference of 0.06 mm between the calculated and measured values corresponds to a welding time of 13 s. A higher conformity of the results can be achieved by considering the absorption of laser beam radiation in the transparent partner. As shown in Fig. 17, the calculated melt displacements with the assumption of an absorption term demonstrate better conformity with the measured values.
The profiles of the calculated melt layer and remaining layer thickness as well as the joining displacement are shown as a function of the welding time (Fig. 18).
The remaining melt layer thickness increases relatively fast after about 7 s. After a welding time of about 10 s, in the steady phase, the remaining melt layer thickness reaches a constant value of about 1.17 mm.
In Fig. 19, the temperature profile is illustrated in dependence on the x-coordinate for selected welding times. The temperature increases obviously with the welding time, and reaches the crystalline melting point of 220[degrees]C after about 7 s. For all welding times, the temperature maximum is not located in the joining area, but behind the surface of the absorbent partner. On the basis of the boundary conditions specified for the welding process, larger melt layer thicknesses in the absorbent partner are achieved in comparison to the melt layer thicknesses in the transparent partner.
[FIGURE 17 OMITTED]
In Fig. 20, the profile of the melt displacement in the xy-plane for the original coordinate [y.sub.0] = 0.15 mm in the area of -1 mm [less than or equal to] X [less than or equal to] 1 mm is illustrated in dependence on the welding time. Because of the better comparability, the melt displacement profile at t = 0 s (before the welding process starts) is represented as a function of the x-coordinate. It is remarkable, that the largest displacement in the y-direction is observed at about x = 0.23 mm in the absorbent partner for any welding time. The first detectable displacements in the absorbent partner are identified after about 8 s which can be seen in the figure. In the case of the transparent partner, first displacements can be observed after about 10 s.
In Fig. 21, the profile of the flow velocity [v.sub.y] is displayed in dependence on the x-coordinate at the point [y.sub.0] = 0.15 mm for selected welding times. As expected, the highest flow velocity was detected in the absorbent partner at about x = 0.23 mm for all measured times.
[FIGURE 18 OMITTED]
[FIGURE 19 OMITTED]
[FIGURE 20 OMITTED]
CONCLUSIONS AND OUTLOOK
In this work, a model was introduced using FEM to describe melt displacement and temperature profiles for laser through-welding, especially for the quasi-simultaneous welding mode. It was shown that a relatively high conformity could be attained between the calculated and the measured data. For the chosen boundary conditions the maximum temperature is not placed in the joining zone, but underneath the surface of the absorbent partner. Therefore, the melt layer thickness in the absorbent partner is generally greater than in the transparent one. Furthermore, the squeeze flow initially begins in the absorbent partner and then also flows to the transparent one.
In addition, temperature and melt displacement profiles could be correlated to characterize the weld seam quality. As a result, it could be shown that the weld strength and the remaining melt layer thickness remained at an almost constant level in the steady phase. Similar results are also expected during simultaneous welding regarding melt displacement and temperature profiles.
[FIGURE 21 OMITTED]
Further investigations are required to study the influences during laser through-welding by laser beam shaping and forming in order to minimize the welding time and increase the welding quality of the resulting polymeric weld seam.
Thanks to Bayer AG for the provision of test materials.
a coefficient of the Gauss function [W/[mm.sup.2]] b coefficient of the Gauss function [[mm.sup.~1]] c specific heat [J [g.sup.-1] [K.sup.-1]] [c.sub.12] radiation exchange number -- E clastic modulus [MPa] [f.sub.p] correction factor -- I intensity [W/[mm.sup.2]] [I.sub.tr] intensity in the transparent material [W/[mm.sup.2]] K constant of absorption [[mm.sup.-1]] [K.sub.tr] constant of absorption in the transparent material [[mm.sup.-1]] [P.sub.tot, cal] total calculated power [W] [P.sub.tot, meas] total measured power [W] [P.sub.r] joining pressure [MPa] r radius coordinate [mm] t welding time [s] [t.sub.E] heating time [s] [T.sub.0] ambient temperature [[degrees]C] - 20[degrees]C v, [v.sub.x], [v.sub.y] velocity [m/s] [v.sub.s] scanning velocity [m/s] x, y, z, [y.sub.0] coordinate [mm] [alpha] heat transfer coefficient [W [m.sup.-2] [K.sup.-1]] [[delta].sub.ij] Kronecker symbol [epsilon], [[epsilon].sub.ij] elongation [%] [[epsilon].sub.p], [[epsilon].sub.E] emissivity of the plastic and environment [lambda] heat conduction [W [K.sup.-1] [m.sup.-1]] [rho] density [kg/[m.sup.3]] [nu] Poisson number [sigma] Boltzmann constant [W [m.sup.-2] [K.sup.-4] [[sigma].sub.0], [[sigma].sub.v] yield stress and von Mises stress [MPa]
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H. Potente, G. Fiegler
Institut fur Kunststofftechnik KTP, Warburger Strasse 100, 33098 Paderborn, Germany
H. Haferkamp, M. Fargas, A. von Busse, J. Bunte
Laser Zentrum Hannover e.V., Hollerithallee 8, 30419 Hannover, Germany
*Presented at the 62nd ANTEC Conference, Chicago 2004 and the 57th International Institute of Welding Annual Assembly, Osaka 2004.
Correspondence to: H. Potente; e-mail: firstname.lastname@example.org, or H. Ha-ferkamp; e-mail: email@example.com
Contact grant sponsor: German Research Society (DFG).
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|Author:||Potente, H.; Fiegler, G.; Haferkamp, H.; Fargas, M.; von Busse, A.; Bunte, J.|
|Publication:||Polymer Engineering and Science|
|Date:||Nov 1, 2006|
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