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Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

The electrofusion welding process is widely used to join polyethylene components in gas distribution networks. This article provides experimental and 3D-finite element tools capable of reproducing the major phenomena that occur during an electrofusion process. A specific version of the 3D- finite element model simulation software Forge® has been developed to take into account the fitting parameters such as polyethylene thermal properties (i.e., melting and crystallization kinetics, phase transition, and thermal contact resistance) and the electrical and geometrical settings (i.e., welding input parameters). From a numerical point of view, a well refined highly anisotropic mesh adaptation is applied to well capture the contact condition between the heat source and the polyethylene. The computed results (temperature, melted, and cold areas) were compared with experimental data and gave very good agreement in terms of temperature and liquid phase fraction distribution. POLYM. ENG. SCI., 55:123–131, 2015. © 2014 Society of Plastics Engineers


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Polyethylene is the most commonly used thermoplastic material for the gas distribution piping systems due to its main advantages (e.g., toughness, flexibility, and chemically inert) compared with metallic materials such as steel for example. Since the 1960s, when polyethylene pipe networks were first introduced, the joints were made using heated tool fusion techniques such as butt welding or socket fusion welding [1]. Nowadays electrofusion is widely used to join polyethylene components in the gas and water distribution networks.

Classical electrofusion welding setup involves an electrofusion fitting including a metal coil integrated at the time of part injection. Two polyethylene pipes to be welded are introduced at both sides of the fitting. Once the fitting is connected to a welding machine, the metal coil generates by Joule effect the energy required for the fusion and interdiffusion of polyethylene macromolecules at the fitting/pipe interface [2, 3].

The melting zones are separated by cold areas, which provide the locking of the molten polymer inside the melting zones and ensure a sufficient pressure in the melting zone and thus strong welding. Other fitting geometries are more complex, such as the one used to connect a new pipe to an existing one, but the heat needed to melt the polymer is still brought by Joule effect in an embedded metal wire.

During an electrofusion welding process, several physical phenomena are coupled: heat flux generated by Joule effect, heat transfer, polymer deformation, fusion and crystallization, and macromolecules interdiffusion.

Information about the polyethylene material parameters (e.g., melting and crystallization enthalpy, phase transition, and thermal conductivity), electrical (voltage and intensity) and geometrical parameters (e.g., initial gap between the parts to be welded) are key features for improving the joints quality and preventing any defaults during the manufacturing and the in-service phases. The determination of such parameters and the identification of their optimal combination can be obtained either through numerical simulations [4-6] or through experimental studies [7-9].

Most numerical simulations are two-dimensional whereas the process is usually three-dimensional both in terms of heat transfer and mechanical aspects. Numerical simulations must be as close as possible to the real process and should take into account the clamping and welding conditions. A focus should be made on temperature's evolution at the fitting/pipe interface during the heating-cooling cycle, since it is one of the key parameters responsible for the molecular interdiffusion phenomenon.

A lot of parameters may have an impact on welding reliability. Among others, it has been shown that the success of the welding stage is greatly dependent on the power supplied by the heating machine and on the heating time. During a thermal welding process, the region surrounding the wire zone is subjected to thermal changes. The polyethylene physical properties also vary during the process and, in turn, affect the mechanical properties in the coupled system. We did not find in literature any 3D model that takes into account all the physical phenomena that occur during the overall welding process. That is why we decided to develop our own model.

The objective of this work is to develop a full 3D numerical thermal model of the electrofusion welding process, and to validate it by comparing to a real situation the temperature evolution and the thermally affected areas in a simple planar welding geometry chosen to make easier the instrumentation. This simple geometry has the same dimensional characteristics as a real fitting.

This article describes first the materials and experimental device allowing the measurement of the temperature evolution during welding. Then, the physical models and the numerical resolution are presented. We finally present the comparison between experiments and computation.

EXPERIMENTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Materials

The polyethylene is an ethylene-butene copolymer categorized as PE100 and widely used for injection molding of fittings. Figure 1a represents the evolution of polyethylene density with temperature, according to Hehn [10]. Figure 1b gives the evolution of the thermal conductivity that we have measured using Lees' disk apparatus [11]. Explanations of this technique can be found in various physics textbooks (e.g., [12]).

image

Figure 1. Evolution of the polyethylene thermal properties with temperature. (a) Density. (b) Heat conductivity. (c) Heat capacity. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Figure 1c shows the evolution of cp with respect to temperature during the solid and melted phase. It was measured using a DSC (PerkinElmer 8500) with cooling rate of 10°C/min. This technique does not allow one to characterize the evolution of the cp during transition phase. The value of cp in the crystallization and fusion transitions used is obtained using a linear interpolation.

We lately show how to compute its value during this phase for different cooling rates. The material properties of the copper heating wire are assumed to be constant; they do not vary significantly with temperature over the temperature range of the electrofusion process (from −40 to 380°C). The specific heat, density, and thermal conductivity are respectively 350 J kg−1 K−1, 8960 kg m−3, and 399 W m−1 K−1.

Design of a Simplified Model

Rather than dealing with complex 3D complex geometries, it was decided to validate further numerical developments on a simplified experimental setup designed to be able to control each parameter, which can have an influence on the welding results. Figure 2a shows a CAD view of the planar assembly. It is composed of two different plates. The upper one represents the fitting with an embedded copper coil. The lower one plays the role of the pipe.

image

Figure 2. (a) 3D CAD view of the simplified model. (b) 2D view with respect to Z axis. (c) Distance (in mm) between the wire and the interface. (d) Distance in mm between two adjacent wires. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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The model is totally customizable. This means that several parameters such as the wire length, spacing between adjacent wires or loops radius can be easily modified. This can be of interest to check the influence of these parameters on the temperature distribution. The plate's dimensions are 150 × 73 × 8 mm, the wire length is 1700 mm, and the wire covers a surface of 53 × 73 mm2. Those dimensions are comparable to real fittings ones. Cold areas were also respected.

Experimental Setup Making

First, a 1 mm thick polyethylene plate was injected. Then a 0.5 mm deep groove corresponding to the coil place was engraved in the plate to set up the wire (Fig. 3a and b). Finally, this plate was over molded in an 8 mm thick rectangular cavity. We obtained therefore a plaque with a wire located at a depth of 0.5 mm from the surface, comparable to what can be found generally in real fittings. This side of the plate was put in contact with another 8 mm thick plate representing the pipe. To avoid any horizontal or vertical displacement of the two plates during welding, while allowing potential thermal expansion of the polyethylene and natural convection around the device, both plates were pressed together using three polymer cable ties (Fig. 3c). Both ends of the heating wire were fixed outside of the plate to permit the connection to the welding machine.

image

Figure 3. (a) The 1 mm grooved plate. (b) Same plate with electrical wire. (c) Assembly ready for electrofusion welding. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Welding Test

Electrofusion process consists in connecting the accessory to a welding machine and imposing the voltage (between 5 and 40 V generally). Given the wire resistivity used in this study, a nominal voltage of 7 V during 90 s was applied. Since voltage and intensity evolve during the welding process, their values are recorded all along the test (Fig. 4a). The resulting power that will be used as a thermal boundary condition in the numerical model was deduced from this recording (Fig. 4b).

image

Figure 4. Heating conditions. (a) Voltage and intensity versus time. (b) Power versus time. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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For carrying out further numerical validations, the experimental evolution of the temperature at different critical points of the sample is required. Measurements were done using type K thermocouples (diameter 0.5 mm). Figure 5a shows the location of four thermocouples located at the interface between the two plates. Thermocouples 1 and 2 were placed at the center of the area covered by the coil, and thermocouples 3 and 4 at the border of this area. A fifth thermocouple was located at the external surface of the plate embedding the electrical wire, at the center of the area covered by the coil. A sixth thermocouple was put in contact with the wire before over molding of the thin plate supporting the wire (Fig. 5b).

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Figure 5. Thermocouples location. (a) At the interface between the two plates. (b) In contact with the wire. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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The position of the thermocouples is estimated at ±1 mm accuracy due to the movement of the thermocouples before and during the assembly.

MODELING

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Physical Models

Heat Transfer Equation

Two steps characterize electrofusion process: the heating stage during which a given energy is provided to the fitting by the power unit and the cooling stage during which the assembly cools down freely. The governing equation of heat transfer during an electrofusion process is given by

  • display math(1)

where ρ is the polyethylene density and k its thermal conductivity. H is the power per unit volume corresponding to crystallization or fusion. It can be expressed as a function of the crystallization enthalpy per unit mass for a pure crystal ΔHC100% (290 J/g [10]) and on the degree of crystallinity XC:

  • display math(2)

with

  • display math(3)

Equation (1) thus becomes

  • display math(4)

which is equivalent to

  • display math(5)
  • display math(6)

with

  • display math(7)

This allows us to compute the value of the modified heat capacity (cpm) with respect to temperature for a given cooling rate. Similar equations are used for the fusion step.

Crystallization Kinetics and Fusion

The determination of the crystallization kinetics is often described in literature [13-16]. The model is based on Nakamura's modification of Avrami equation [13] for nonisothermal crystallization. According to [10, 17-19], the solid phase fraction αS(t,T) can be expressed as

  • display math(8)

where nc is the Avrami exponent and Kc is the Ozawa constant.

The fusion process is not thermally activated, and no kinetics law can be applied. Nevertheless, Hehn [10] with the same polyethylene as the one used in this study observed an influence of the cooling rate on the fusion process, which has been confirmed by our measurements. Therefore, fusion kinetics has been introduced with the same form as the crystallization one. This model was used by Ageorges et al. [17] and seems to well represent the melting phenomenon. Following the same approach, the liquid phase fraction αL(t,T) is computed during the fusion as follows:

  • display math(9)

Kf is a constant similar to the Ozawa's one. The phase fractions α(t,T) are actually not directly computed using Eq. (8) or (9) but through the variation of the degree of crystallization XC which is written as follows [10, 17-19].

During Fusion
  • display math(10)

with XC∞ the maximal degree of crystallization obtained after cooling.

During Crystallization
  • display math(11)

The solid and liquid transformed volume fractions are then deduced from:

  • display math(12)
  • display math(13)

Kc, Kf, nC, and nf were identified by DSC for cooling rates ranging from 5 to 40°C/min. Having the variation of the degree of crystallization XC, the model computes at each time step the value of the modified heating capacity (cpm) to take into account the crystallization enthalpies (Eq. (7)). Figure 6 shows the evolution of the modified cpm in terms of temperature for different cooling rates.

image

Figure 6. Evolution of the heat capacity with respect to temperature for different cooling rates. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Numerical Model

Our electrofusion model is built on the basis of a 3D finite element software Forge® designed for metal forming. This model uses an Updated Lagrangian formulation. Existing heat transfer equation was modified to take into account the energy due to crystallization and melting enthalpies according to Eq. (5). As a first approximation, only the thermal calculation is considered.

Equations (10)-(13) being nonlinear, they are solved thanks to a Newton-Raphson iterative method. At each time step i, the evolution of the transformed volume fraction α(i) is computed as a function of the phase fraction at previous time step α(i − 1):

  • display math(14)

For the sake of simplification, subscripts referring to solid and liquid are not indicated here. The geometry was generated using the Gmsh® software that provides a fine and controlled mesh. Three subdomains were distinguished: the first polymer plaque, which embeds the electrical wire, the heating wire and the second polymer plaque. The wire was meshed to compute its temperature evolution. Conformal meshes allow having coincident nodes of different subdomains at each interface insuring a good thermal transition between the different domains (wire/polymer, polymer/polymer; Fig. 7a). The computational domain was discretized using tetrahedral stabilized finite elements (P1+/P1).

image

Figure 7. (a) Two cutting planes showing the adapted anisotropic mesh. (b) Conformed mesh at wire/polymer interface. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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To accurately catch the high temperature gradients due to the heating power, an anisotropic mesh adaptation procedure is used. This has the advantage of correctly reproducing interfaces between the different subdomains and ensuring accurate thermal transitions, with an acceptable number of elements [20] (Fig. 7b).

Thanks to the symmetric design of the assembly and to reduce the computing time, only half was modeled. The symmetric plane was set perpendicular to the y direction (Fig. 7). The number of nodes and elements is, respectively, about 240,000 and 1.2 million. Computation was carried out on a cluster of 16 processors. The CPU time is about 20 h.

Boundary Conditions

The measured electrical power (Fig. 4) was applied as a boundary condition inside the wire. Two different thermal contact resistances were introduced between the wire and the polymer and between the two plates. Although they depend on different parameters, such as the pressure that exists between them and the roughness of the surfaces, they were considered constant in our computation. As far as we know, no study was carried out to determine the thermal contact resistance either between a polymer and a wire or between two polymers during an electrofusion process. However, this parameter has been measured at the interface between a polymer and a mold in injection molding [21-23]. Rather than performing further studies, we decided as a first approximation, to start with the values taken from literature and then to perform a sensitivity analysis to determine the influence of this parameter on the computed results. We have set this parameter to 2 × 10−4 m2 K W−1 and 2.5 × 10−4 m2 K W−1 [23], respectively, at the wire/polymer and at the interface between the two plates to be welded. The heat transfer coefficient between the different bodies and the air was set to 15 W m−2 K−1. Room temperature was set to 23°C.

RESULTS AND DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Comparison Between Experimental and Numerical Results

Temperature Distribution

Because of the low polyethylene conductivity, high temperature gradients are expected. This is confirmed by the finite element model. Figure 8 shows a maximum difference of about 15°C between two points 1 mm away near the position of thermocouple number 4.

image

Figure 8. Evolution of the computed temperature in two neighboring points. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Except for the thermocouple located at the wire, and the thermocouple on the outer surface of the plaque, it is difficult to know accurately its exact position. To improve the comparison between experimental and numerical results, we will show the evolution of the temperature at two locations surrounding (distance <1 mm) the desired position.

Figure 9a shows the evolution of the experimental and computed temperature of the electrical wire. During the heating stage, the numerical model predicts a temperature increase slightly faster than what is measured. The maximum value is of the same order of magnitude, around 400°C. The model reproduces almost perfectly the temperature decrease during the cooling stage.

image

Figure 9. Experimental and computed temperature evolution at different locations. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Figure 9b–d shows the comparison between computed and measured temperatures at thermocouples 1, 2, 3, and 4 (Fig. 4a–c). The measured and computed temperatures for thermocouples 1 and 2 are very close. The agreement is very good, even if the same kind of differences mentioned for the wire temperature is still observed during the heating stage. Thanks to our numerical developments that take into account the crystallization enthalpy, the crystallization plateau is perfectly reproduced during the cooling stage around 120°C. The cooling rate at this time is of the order of 30°C/min, which is comparable to the cooling rates used in DSC to identify crystallization kinetics.

Temperature at the outer surface of the plate embedding the electrical wire is also well reproduced (Fig. 9e). This means that thermal properties of our materials and thermal boundary conditions are correctly identified and taken into account in the model.

Melted Area

Following Gueugnaut et al. [24], a polished cross section in the thickness was superficially heated by a hot air jet at a temperature around 80°C for around 90 min. The authors have shown that the transition visible on the micrographs corresponds to the limit between the area that has been melted during the welding operation and the area which did not reach the fusion temperature (Fig. 10 a and c).

image

Figure 10. (a,c): Observation of a cross section after thermal treatment at two magnifications. (b,d): Computed isovalues of αL when the maximum melted domain is reached. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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This area corresponds almost perfectly, qualitatively (same shape), and quantitatively (same thermally affected distance), to the maximal liquid phase fraction (αL) predicted by the numerical finite element model.

Other Results

Nonhomogeneity of the Temperature in the Wire

The finite element model shows that the wire temperature is homogenous in the section but varies along its length, as shown on Fig. 11. The temperature is lower on the border, by about 80°C, and near the curves, by about 20°C, compared with the central area. As one can see on Fig. 11, the temperature evolution is clearly inhomogeneous in the x, y, and z directions. This solely result justifies the necessity to use a three dimensional approach, even in the case of a plane geometry such as the one we studied.

image

Figure 11. Computed temperature at the end of heating: (a) along the wire, (b) in a first cut plane, and (c) in a second cut plane. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Sensitivity Analysis
Polyethylene Thermal Conductivity

Most papers dealing with polyethylene welding use a constant value for the thermal conductivity. To check whether this assumption is correct or not, we performed a sensitivity analysis of this parameter on the temperature evolution during a heating/cooling cycle. Four computations with four different conductivity values are presented: a constant value equal to 0.34 W m−1 K−1; a constant value equal to 0.4 W m−1 K−1; a variable value ranging from 0.37 W m−1 K−1 at 20°C to 0.25 W m−1 K−1 at 128°C (our measurements, see Fig. 1b); a variable value ranging from 0.45 W m−1 K−1 at 20°C to 0.25 W m−1 K−1 at 128°C.

Figure 12a–c shows that the conductivity has a direct influence on the highest temperature reached after 90 s of heating. This temperature varies from 238°C (for a constant value equal to 0.34 W m−1 K−1) to 280°C (for variable value ranging from 0.37 to 0.25 W m−1 K−1) at the end of the heating. Such a significant difference is detrimental to the precision of phase transformation or macromolecule interdiffusion computation.

image

Figure 12. Evolution of the temperature at different locations, depending on conductivity and thermal resistance contact values. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Thermal Resistance Contact

Heat exchange between the wire and the polymer is controlled by the heat flux and the thermal resistance contact between the two materials. The thermal resistance contact (R) between the wire and the material was determined so that the evolution of the computed temperature in the wire corresponds to the measured one. As mentioned before, the thermal resistance contact, found in literature, between a metal and a polymer is about 2 × 10−4 m2 K W−1. We have compared the temperature evolution in the wire for three other values (10−3 m2 K W−1, 10−4 m2 K W−1, and 10−6 m2 K W−1). Results are shown in Fig. 12d. With 10−3 m2 K W−1, the difference between the computed results and the experimental measurements is quite high, whereas it is negligible for values lower than 2 × 10−4 m2 K W−1. As a conclusion, any values lower than the one taken from literature would lead to the same result since we tend towards a perfect contact between both materials.

CONCLUSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES

The major objective of this work was to design new experimental and numerical tools, which describe the thermal and physical phenomena that occur during the electrofusion process of polyethylene pipes and fittings used in the gas distribution networks. A specific version of the 3D- finite element simulation software Forge® has been developed. It takes into account the fitting geometrical parameters, the thermal properties, the crystallization, and melting kinetics of the polyethylene. All parts of the electrofusion assembly were taken into account (heating coil, electrofusion fitting, and pipe).

In parallel to the numerical work, a new experimental setup based on the real geometrical parameters of an electrofusion fitting was developed. From a simulation point of view, the geometry was generated using the Gmsh® software that provides a fine and controlled mesh. Thus, the temperature fields can be precisely computed. The numerical dimensions corresponds exactly to the one used for the experimental device. The heating conditions needed for the simulation have been deduced from the experimental work.

The computed temperature evolution at different points and the melted area are in good agreement with the experiments. The evolution of the temperature inside the wire demonstrates the need to model the entire wire. It is the same for the evolution of the temperature and of the melted area in the plates that cannot be represented by 2D approaches and therefore it confirms the necessity to use a three-dimensional approach. Based on these promising results, this work is now ready to be applied to real 3D fittings. We have seen that for the chosen heating conditions, the temperature inside the assembly and even more specifically at the outer surface of the hotplate was quite high compared with what is requested on real fittings. Thus, further works will be focused on optimizing the heating conditions and the fitting design using the finite element model.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. EXPERIMENTS
  5. MODELING
  6. RESULTS AND DISCUSSION
  7. CONCLUSION
  8. REFERENCES