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Modelling of the butt fusion welding process
Chemical En@zeering Printed in Great
Schce,
Vol. 46, No.
Brimin.
1. pp. 133-142,
imo9-2509p1$3.00
1991.
0
MODELLING
OF THE BUTT PROCESS
H. BENKREIRA, Polymer
Research
Unit,
University
FUSION
1990 Pergamon
+ 0.00 Press plc
WELDING
S. SHILLITOE and A. J. DAY of Bradford, Bradford, West Yorkshire
BD7
IDP,
U.K.
(First received 31 August 1989; accepted in revised form 22 January 1990) Abstract-The bead up stage of the butt fusion welding of plastic pipes is modellad by treating the melt layer as a squeeze film contained between two parallel annular rings to which fluid is supplied by the melting of the pipe ends. The lubrication approximation is used to simplify the solution of the governing equations with the melt treated as a non-isothermal power law fluid. Predicted melt layer thicknesses agree well with experimental data over a wide range of operating conditions. Also, this model is used to determine flow characteristics such as the radius of flow separation and the plane of zero shear stress in the melt layer, both of which influence the microstructure of the joint.
analysis. He first prescribed a nominal, arbitrary shear rate, effectively carrying out a Newtonian analysis. He then improved on this by using a power law model (r = Ky”) with the coefficient K averaged over the temperature distribution. In the present paper, the treatment is more comprehensive: flow is assumed at the onset and a general power law is taken with both the variation in temperature and shear rate accounted for using the prevailing boundary conditions. Also, an annular (rather than rectangular) section is studied, which is more appropriate when dealing with the welding of pipes.
INTRODUCTION
The use of thermoplastic pipes, particularly for the distribution of water and gas, has increased rapidly over the last 30 years and now some 5000 km of polyethylene gas pipes ranging in diameter from 16 to 800 mm are installed annually in the U.K. One attractive feature of thermoplastic pipe materials is the ease with which they can be joined using the butt fusion welding technique, which involves several stages. The first is the bead up stage, where the pipe ends are pressed against a hot plate and a melt layer with inner and outer beads is formed (Fig. 1). Reduction of the load on the pipe ends until it is just sufficient to keep them in contact with the hot plate then follows and the heat soak stage commences, in the course of which the melt layer thickness increases. At the end of the heating stage, the pipes are retracted from the hot plate and pressed together to form the joint, which is allowed to cool sufficiently before handling. From a consideration of the process it is possible to identify several important welding parameters, e.g. hot plate temperature, heating time, joint cooling time and joining pressure, which when optimised allow a joint with almost lOO%parent material strength to be made. Despite the wide use of this process, optimum welding parameters have been arrived at empirically; such parameters for polyethylene pipes are shown in Table 1. This ad hoc approach (Barber and Atkinson, 1972, 1974; decourcy and Atkinson, 1977, 1981; Colaluca et al., 1983) is very reliable but it would benefit from a fundamental understanding of the roles played by heat transfer and melt flow in the formation of a-butt fusion joint. This is clearly a complex problem to model and many investigators (Lyashenko and Zaitsev, 1968; Budak, 1970; Lyashenko and Istratov, 1975) simply ignored melt flow during bead up and calculated the rate of melt layer growth throughout the heating stage using ID heat conduction. Potente (1977, 1986) extended this approach by coupling the temperature distribution (linear) so obtained with a squeeze film
THEORETICAL
ANALYSIS
During the bead up stage, melting is initially transient but a steady state is reached when an equilibrium exists between the applied load and the hydrodynamic pressure generated in the melt layer separating the hot plate and the pipe end. This situation arises when the rate at which the melt flows into the beads, II,,,,equals the rate at which the pipe advances towards the hot plate and this is accompanied by the attainment of a constant melt layer thickness, h,. The objective of this analysis is to formulate a model capable of predicting v, and h, as a function of the process parameters; namely applied load and hot plate temperature, material properties and pipe geometry. The prediction of h, is particularly attractive because several investigators (Neubert and Wolfgang, 1973) have shown it has a decisive effect on joint quality. For the small dimensions of the melt layer in comparison with the pipe wall thickness (see Fig. 2), the lubrication approximation may be used and the governing equations in a cylindrical coordinates system (see Fig. 3) at steady state become in a dimensionless form (see Notation): Continuity
135
136
H. BENKREIRA pipe
wall -I
Fig. 1. Schematic representation of the bead up stage.
Momentum i?P _=aR
al-
(2)
az
Energy (3) where Pe is the Peclet number, a measure of the relative importance of convection to conduction in the melt layer. A constitutive equation which relates shear stress to shear rate and temperature must also be introduced. For polymeric melts the power law model expressed in dimensionless form is applicable:
la--l
I I
r=e-TE$
av
-&_
Butt fusion is clearly a low shear rate deformation where melt thickness and melting rate are typically 1 mm and 1 mm/s, respectively, i.e. shear rate z 1 s-r. Viscosity data for three pipe material melts are shown in Fig. 4, where in the low shear rate range, a power law model may be used to describe approximately the behaviour of these materials. Now the following dimensionless velocity, pressure and temperature boundary conditions may be identified: At the hot plate surface (Z = 0):
V,(R, 0) = V,(R, 0) = 0 T(R, 0) = N,, At the melt-solid
(5) (6)
interface (Z = 1): v&z,
1) = 0
(7)
Vz(R, 1) = 1
(8)
T(R, 1) = 0
(9)
At the outer (R = 1) and inner pipe (R = R,) walls: P(1, Z) = P(R,, Z) = 0
(10)
where N,, is a dimensionless temperature difference across the melt layer, and R, the radius ratio. Two further constraints on the temperature arise from a consideration of the heat conduction at the hot
et al.
Modelling of the butt fusion welding process
137
Fig. 2. Microtome section of the weld region showing the size of the melt layer to be much smaller than the pipe wall thickness.
plate and at the melt-solid
interface: (11)
E(R,1) =
Fig. 3. Simplified flow field and co-ordinate system.
10-Z
10-l 100 shear rate
10’ j’ d’
102
lo=
Fig. 4. Rheological data of the polymer material used.
Peiv,
(12)
where IV, is a modified Stefan number representing the ratio of the heat necessary to raise the temperature of the solid polymer from-the ambient to the melting temperature to the heat used in raising the temperature of the melt. Equation (12) is a crude approximation for semi-crystalline polymers because it assumes the latent heat change occurs at a single sharply defined temperature when in reality it occurs over a temperature range. In a squeeze film the flow is characterised by two parameters: the plane of zero shear stress, Z,, which is the plane along which the fluid velocity reaches a maximum, and the radius of flow separation, R,, at which the flow divides into two regions, whose velocity components are of opposite sign (Fig. 3). In isothermal, planar systems the position of each flow characteristic coincides with the axes of symmetry to which it is parallel, but, in the case of a pipe geometry, R, is displaced towards the outer pipe wall because it is also the point at which the maximum of the pressure distribution lies. When there is a temperature profile across the fluid layer, 2, is displaced towards the warmer fluid layers because the fluid in this region is less viscous and flows faster. The determination of these parameters must therefore be an integral part of
H.
138
BENKREIRA
this model because they are used as limits of integration in the solution of the governing equations. This information also gives a useful insight into the distribution of the melt flow during butt fusion welding. By integrating eq. (2) twice with respect to Z, together with the velocity boundary conditions and the power law equation req. (4)], two equations for the radial velocity distribution in the melt layer are obtained: dP
Z>Z,,VR=sgn-
et al.
Tho displaccmcnt of Z, towards the hot plate will have the effect of narrowing the velocity profile and causing a “fountain flow”, where the melt will be squirted out of the melt layer into the beads in 8, narrow jet. The position of the radius of flow separation, R,, can be found by integrating the dimensionless continuity eq. (1) with respect to R and Z, and substituting into it eqs (13), i.e. dP dR=sgn(R
dP Ifn
-
dR I dR I
s sgnglgy s z
1
z < z,, v, = -
([Z
- Z,]eT)““dZ
(13a)
I =
2. ss0 +
- Z]er)l’“dZ
(13b)
0
where “sgn” means sign of. The position of the plane of zero shear stress, Z,, can be found from the condition that, at Z,, the velocity V, must be continuous, i.e.
(16)
where
2
([Z,
-R.)(IR’_&R+y
z 0 1
ss2.
eT/“(Z 0 - Z)‘@dZ
dZ
1 2
er’“(Z
- Z,)““dZdZ.
Integrating eq. (16) and applying the pressure boundary condition [eq. (S)] yields an expression for the radial pressure distribution: R,>
-(‘i>“~z~(R’~R2~dR
R,P,=
(17a)
2. 5I
([Z
- Z,ler)l“‘dZ =-
R, < R,P, z0 ([Z, s0
- Z-Je’)““dZ.
(14)
Equation (14) is solved numerically by substituting the temperature, T, which is expressed by a polynomial in Z compatible with the four available temperature boundary conditions, i.e. T=
O.S[PeN,
+ N,,]Z3
+ 3N,,]Z
- O.S[PeN,
+ N,,.
(15)
Table 2 lists dimensionless values of Z, as a function of the power law index, n, and the dimensionless temperature difference, N,,, across the melt layer for Pe IV, = 0 to assess the simple case of a nonNewtonian fluid being squeezed between two plates held at different temperatures. These results show that, as the temperature difference across the melt layer increases, then Z, is displaced towards the hot plate and, for a given tempcrature difference across the melt layer, Z, is further displaced towards the hot plate as the degree of shear thinning behaviour exhibited by the melt increases.
=
+ (;>”
JI”(R2$‘J
Since the pressure is continuous
dR.
(17b)
at R = R,:
Computed values of R, as a function of the power law index n and the radius ratio R, are presented in Table 3. Identical results were obtained by Elkouh er al. (1982), who modelled the isothermal squeeze flow of a power law fluid between parallel annular rings. These results show that an increase in radius ratio or shear thinning behaviour displaces R, towards the outer wall of the pipe. This causes more melt to flow towards the inner pipe wall, hence producing a larger inner weld bead as commonly observed in practice (see Fig. 2). Such beads form a significant obstruction to flow in the pipe and are usually removed. Two equations are now required to determine V, and h,. The first may be obtained by integrating the pressure distribution over the area of the pipe end to obtain an expression for the dimensionless load required to cause squeeze flow:
Table 2. Predicted zero shear plane, Z,, for annular pure squeeze flow (no melting) of a power law fluid between two hot plates held at different temperatures N AT n
0.2
0.4
0.6
0.8
1.0
1.0 0.8 0.6 0.4 0.2
0.4833 0.4807 0.4772 0.4722 0.4643
0.4665 0.4614 0.4544
0.4497 0.4420 0.4317 0.4169 0.3942
0.4329 0.4228 0.4092 0.3900 0.3907
0.4162 0.4037 0.3871 0.3637 0.3288
Medelling of the butt fusion welding process
w=
P,RdR
+
P,RdR
=
139
I
Table 3. Predicted radius of flow separation, K,, for annular squeeze flow (with or without melting) of a power law fluid
R, 0.01
?I
1.0
0.3295
0.8 0.6 0.4 0.2
The integrals with solved analytically give the following numerically for the
w = - (0.5)”
(1 -
0.3593 0.3925 0.4284 0.4662
0.1
0.2
0.6
0.4637 0.4765 0.4913 0.5083 0.5277
0.5461 0.5540 0.5630 0.5735 0.5857
0.7915 0.7927 0.7941 0.7957 0.7977
respect to R in eq. (19) can be by multiple parts integration to equation which may be solved dimensionless load, W: R:)“+’
an
R:-“(R:
-
R:)“”
+ 3)U r
1 S[o
Id --(RFRT)
+ $(V,T)
RdR
1 1 s dZ =
d2T dZ.
o dZ2
1
s0
V, TdZ
= ;(Pe
N,
+ N,,).
(22)
It must be noted here that the cubic profile suggested in eq. (15) does not necessarily satisfy the energy conservation eq. (3) merely its boundary conditions (9)-(12). These are, however, the essential energy features of the process and justify such an approach. Substituting eqs (13) for V, into the above equation gives the following equation which can be solved numerically for Pe: TeT’“(jZo -
2)“”
Beelc (1969) list melting rate data for cylindrical bars of Alkathene and Hostaform C (polyoxymethylene) together with their relevant thermal and rheological property data, and before applying the model to butt fusion welding it was decided to validate it by comparison with this data. Therefore the model was modified to treat melt flow between parallel circular (not annular) plates and a power law model was fitted to the given rheological data. Table 4 compares the measured melting rate data of Hostaform C with that predicted by the model developed by Stammers and Beek (1969) and that developed as part of this study. It can be seen that the more comprehensive treatment of the polymer melt rheology results in better agreement with experimental data.
(21)
Integrating eq. (21) over the melt layer together with the velocity boundary conditions [eqs (5)--(7)-J and the temperature profile equation introducing [eq. (19)] yields Pegp
0.9496 0.9496 0.9497 0.9498 0.9499
I.(20)
A second equation which allows the determination of the Peclet number can be found by combining the dimensionless energy equation [es_ (3) 3 with the continuity equation [eq. (l)] to yield Pe
0.9
dZ dZ + I
Knowing the values of Wand Pe then v, and h, may be calculated. The theoretical approach used here is similar to, but more comprehensive than, that used by Stammers and Beek (l969), who modelled the contact melting process using a Newtonian analysis. Stammers and
EXPERIMENTAL
STUDIES
A detailed description of the experimental studies can be found in Shillitoe (1988). Three pipe materials, which represent the wide range of materials used in pipe applications were used in this study: two medium-density polyethylenes, BP rigidex (PEX) and Du Pont Aldyl (PEA), and one high molecular weight, high-density polyethylene, Philip’s Drisco (PED). The viscosity of these pipe material melts was measured at various temperatures (16%24O”C) and over a wide range of shear rates (0.01400 s - ’), using a combination of two techniques: the Instron capillary and Weissenberg cone and plate rheometers. At low shear rates (up to 10 s- ‘), PEA, PEX and PED have widely
Te=‘“(Z - Z,)““dZdZ = i(PeiV,
+ N,,).
(23)
different melt viscosities, with PED being the most viscous and PEA the least. At high shear rates ( > 100 s- ’), PEA and PED exhibit similar viscosities lower than those of PEX (Fig. 4). A power law model was fitted to this data over a low shear rate range
H. BENKREIRAet al.
140
Table 4. Apphcation of this model to squeeze melting polymer
of a cylindrical
bar of
Melting rate (m/s x 10e5) Force F (NJ
Temperature T c-7
78.5 49.1 9.81 78.5 29.4 78.5 49.1 78.5 78.5 9.81 49.1 ‘Calculated (1969).
Measured
This study
t
0.73 0.58 0.35 1.50 1.38 1.78 2.50 2.87 3.83 2.20 3.40
0.97 0.80 0.40 1.69 1.10 1.94 2.30 3.09 4.42 1.45 3.52
1.49 1.41 1.10 2.43 2.27 2.74 3.51 4.09 5.54 3.33 5.04
by Stammers
and Beek
179 180 183 190 193 194 211 213 236 237 238
using the expression developed
Table 5. Properties of polymer materials used in this study Mean thermal conductivity W/m K)
Mean specific heat capacity
Mean density
&J/kg K)
Material
Solid phase
Melt phase
Solid phase
Melt phase
PEA PEX PED
0.2606 0.3099 0.2795
0.2812 0.2643 0.2438
2.1 2.68 2.18
2.63 2.16 2.63
Latent heat of fusion
b/m3)
Melting temperature
O
(“Cl
Solid phase
Melt phase
135 135 142
940 940 960
785 785 819
Table 6. List of operating conditions
Material PEA/PEX PED
because of the dynamics pipe advances
towards
Outer pipe radius (mm)
Pipe wall thickness (mm)
Bead up time (s)
Hot plate temperature (“C)
62.5 50.0
11.0 9.0
7.5-240 7.5-240
167-240 167-240
of the system. Typically, the the hot plate at a rate of less
than 1 mm/s and the melt flow is confined within a layer of approximately 1 mm in thickness. The thermal conductivity of the pipe materials in the solid and melt phases was measured using the apparatus developed by Hands and Horsfall(1975), in which a steady-state temperature difference is generated across a disc-shaped specimen. The specific and latent heats were measured using differential scanning calorimetry and the melting temperature using the Kofler method. These data, together with density, which was determined from specific volume data in Matsuoka (1962), are listed in Table 5. The melt layer thickness generated over a wide range of conditions (see Table 6) was measured using transmitted polarised light microscopy of thin sections. The thin sections were microtomed from across the end of the pipe that had been headed up using an
automatic butt fusion welding lowed to COOL
Bead up force
(N) 482-1642 482-1642
machine and then al-
RESULTS AND DISCUSSION
Figure 5(a) shows the measured variation of melt layer thickness with time during the bead up stage of PEX. The melt layer thickness increases to a constant value which decreases with bead up force. Similar results were obtained with PEA but not with PED, whose higher viscosity prevented the attainment of a constant thickness as illustrated in Fig. 5(b). Therefore, the lubrication model developed above cannot be applied to this material. Instead, the model was used to predict the variation of the constant melt layer thickness of PEX and PEA with hot plate temperature. Clearly, the predictions are in good agreement with experimental data (see Fig. 6). Und5r identical conditions the melt layer thickness at steady state of PEX is greater than that of PEA on
Modelling of the butt fusion welding process
141
4.0 ,
I
* z E I f +I! E 8 p
l
3.0
I .
2.0
I . .
.
1.0
*
1.0
5
0.8
=
0.6
I
I
I
I
._
0.4
0.2
MATERIAL : PED HOT PLATE TEMP
:
ma
0
:
1
MATERIAL HOT
PLATE
1
: 200% I
: PEX TEMP
: 200%
.
I
30
0
I
60
SO Bead
120 up time
150
160
210
240
Is)
Fig. 5. Measured variationof melt thicknesswith timeduringthe bead up stage of PEX and PEA [bead up
force:(o)482N,(A)1112N,(m)lf542N].
150
170
180
to0
Hot plate Fig. 6. Comparison of predicted (-)
IMPLICATIONS
210
220
230
240
(‘C)
and measured (0) melt thicknessat steady state for PEX and PEA.
account of its higher melt viscosity at low shear rates. Additionally it is apparent that the melt layer thickness of both materials increases very little with hot plate temperature. This is because the increased rate of heat penetration into the pipe as a result of the higher hot plate temperature is offset by the reduction in the ability of the melt to support a load caused by the decrease in melt viscosity resulting from its temperature dependence. PRACTICAL
200
temperature
OF THIS WORK
The results of this investigation are now discussed in relation to the actual practice of plastic pipe welding. The attainment of a large melt film thickness is essential for the formation of a good joint. With a large film thickness, adequate melt flow ensures the removal of contamination from the melt surface caused by cooling and oxidation, while retaining sufficient hot melt at the pipe ends to promote transcrystallinity across the joint interface (Neubert and
Wolfgang, 1973). The work here has demonstrated that steady-state conditions are reached quickly with PEX and PEA (of order 60 s) but not with PED (see Fig. 5). An immediate conclusion is to favour PEX and PEA where the limiting growth of the melt film thickness can be predicted. Also, it was shown that increasing hot plate temperature during bead up altered little the film thickness for both PEX and PEA, hence the practice of a heat soak stage where the pressure is removed and melt layer growth via conduction prevails. A favoured method thus would be to use a large hot plate temperature rather than a longer heat soak time. Again this is used in practice. Also, the examination of both theoretical and experimental data suggests that, under identical conditons, larger film thicknesses are produced with PEX than with PEA due to the lower viscosity of the former. Again in practice, PEX is favoured and conforms with this observation. Finally, the model shows a significant increase in melt layer with decreasing pressure, corres-
H. BENKREIRA
142
ponding with the use of small loads in actual practise. However, it must be recognised that other factors pertinent to the production of a good weld (e.g. cooling/crystallisation) are not considered here and are now being addressed in our laboratory. CONCLUSIONS
The bead up stage of the butt fusion welding operation was modelled using lubrication approximation coupled takes
with into
viscosity
the general
power
account
both
the
of the melt
with
shear
ature. This approach and melt layer
yields
thickness
law
equation
variation
which
of melting
are in good
rate
agreement
experimental data. Furthermore, the model enables calculations of flow characteristics (R,, 2,) to be made. It can also be extended to calculate the melt layer thickness after the heat soak and joining stages, and the joining displacement, all factors which influence joint quality. Acknowledgements-We would like to express our appreciation to the SERC and the Engineering Research Station of British Gas for supporting this work. NOTATION
hm I K k n NIlI N AT P P Pe R
heat capacity, kJ/kg K steady-state melt layer thickness after the bead up stage, m doube integrals in eq. (16) consistency index in the power law equation, N C/m2 thermal conductivity, W/m K power law index (aA*/cp,) (modified Stefan’s number) ~$0, - 0,) (dimensionless temperature difference across the melt layer) pressure, N/m2 (ph,/rjv,)(h,/r,)2 (dimensionless pressure) specific
(Peclet
(cp,v,h,p,)/k, r/r2 [radius radius
R, r
t-r/r2 (radius ratio) radial coordinate
r1
inner outer
r2 T
a(0
v,
pipe
of flow
separation
0,)
(dimensionless)
m
pipe radius, pipe radius, -
number)
(dimensionless)]
RO
m
[temperature
(dimensionless)]
W
rate, m/s (Q/U,) (hm/r2) (dimensionless radial melt velocity) v,/v, (dimensionless axial melt velocity) load, N
W
(wh~)/(ifu,27rr’:)
Z z
axial coordinate, m z/h,,, (dimensionless axial
Z*
plane
VIl Vz
melting
of zero
[load
shear
(dimensionless shear stress) ’ (dimensionless viscosity)
temperature, K hot plate temperature, K initial temperature, K melting temperature, K latent heat, kJ/kg 1 + cp,(O, - Oi) (reduced density, kg/m3 shear stress, N/m2
latent heat), kJ/kg
apparent
with
CP
(th,/tjv,)(h,/r,) K [(v,/h,)(r,/h,)~“-
rate and the temper-
predictions
which
in
et al.
(dimensionless)] distance)
stress (dimensionless)
Greek
letters
cc
viscosity temperature dependence power law equation, K- ’
term
in the
REFERENCES
Barber, P. and Atkinson, J. R., 1972, Some microstructural features of the- welds in butt-welded polyethylene and polybutene-1 pipes. J. Mater. Sci. 7, 1131-1136. Barber, P. and Atkinson, J. R., 1974, The use of tensile tests to determine the optimum conditions for butt fusion welding certain grades of polyethylene, polybutene-1 and polypropylene pipes. J. Mater. Sci. 9, 1456-1466. Boenig, H. V., 1966, Polyolejins,Structure and Properties, p. 49. Elsevier, Amsterdam. Budak, V. M., 1970. Investigation of the thermal aspects of contact butt welding in polyethylene tubes. Weld. Prod. 1, 5-7. Colaluca, M., Earles, L. and Malguarnera, S., 1983, Fractional factorial testing to determine processing parameters producing acceptable heat fused joints in polyethylene nipe. Polym. Plast. Technol. 20, 180-195. deCourcy, D. R. and Atkinson, J. R., 1977, The use of tensile tests to determine the optimum conditions for butt fusion welding polyethylene pipes of different melt flow index. J. Mater. Sci. 12, 15351551. decourcy, D. R. and Atkinson, J. R., 1981, The assessment of fusion joint quality and some evidence for the presence of molecular orientation in butt fusion welds in polyethylene pipes. Plast. Rubb. Process. Applic. 1, 289-292. Elkouh, A. F., Nigro, N. J. and Liou, Y. S., 1982, NonNewtonian soueeze film between two plane annuli. J. Lubrication 7’echnol. 104, 275-278. Hands. D. and Horsfall. F., 1975, A thermal conductivity apparatus for solid and molten polymers. J. Phys. E scien;. Znstrum. 8, 687-690. Lyashenko, V. F. and Zaitsev, K. I., 1968, Research into the thermal processes taking place during the butt welding of tubes made of thermoplastic substances. Aut. Suarka 1, 37-39. Lyashenko, V. F. and Istratov, I. F., 1975, The butt fusion welding of thermoplastic tubes in winter conditions. Weld. Prod. 22, 58-60. Matsuoka, S.. 1962, The effect of pressure and temperature on the specific volume of polyethylene. J. Polym. Sci. 57, 569-587. Nuebert, W. and Wolfgang, M. A., 1973, Getting a bead on welding of plastic pipe and fittings. Plast. Engng August, 4043. des HeizelementstumPotente, H., 1977, Die theorie pfschweissens. Kunststof67, 98-102. Potente, H., 1982, An analysis of the heated tool butt welding of pipes made of semi-crystalline thermopIastics. Department of Polymer Technology, internal report, University of Paderborn. Potente, H., Michel, P. and Tappe, P., 1986, Heated tool butt welding of semi-crystalline thermoplastics. Department of Polymer Technology, internal report, University of Paderborn. Shillitoe, S., 1988, A study of the butt fusion welding of thermoplastic pipes. Ph.D. thesis, University of Bradford. Stammers, E. and Beek, W. J., 1969, The melting of a polymer on a hot surface. Polym. Engng Sci. 9, 49-55.
Schce,
Vol. 46, No.
Brimin.
1. pp. 133-142,
imo9-2509p1$3.00
1991.
0
MODELLING
OF THE BUTT PROCESS
H. BENKREIRA, Polymer
Research
Unit,
University
FUSION
1990 Pergamon
+ 0.00 Press plc
WELDING
S. SHILLITOE and A. J. DAY of Bradford, Bradford, West Yorkshire
BD7
IDP,
U.K.
(First received 31 August 1989; accepted in revised form 22 January 1990) Abstract-The bead up stage of the butt fusion welding of plastic pipes is modellad by treating the melt layer as a squeeze film contained between two parallel annular rings to which fluid is supplied by the melting of the pipe ends. The lubrication approximation is used to simplify the solution of the governing equations with the melt treated as a non-isothermal power law fluid. Predicted melt layer thicknesses agree well with experimental data over a wide range of operating conditions. Also, this model is used to determine flow characteristics such as the radius of flow separation and the plane of zero shear stress in the melt layer, both of which influence the microstructure of the joint.
analysis. He first prescribed a nominal, arbitrary shear rate, effectively carrying out a Newtonian analysis. He then improved on this by using a power law model (r = Ky”) with the coefficient K averaged over the temperature distribution. In the present paper, the treatment is more comprehensive: flow is assumed at the onset and a general power law is taken with both the variation in temperature and shear rate accounted for using the prevailing boundary conditions. Also, an annular (rather than rectangular) section is studied, which is more appropriate when dealing with the welding of pipes.
INTRODUCTION
The use of thermoplastic pipes, particularly for the distribution of water and gas, has increased rapidly over the last 30 years and now some 5000 km of polyethylene gas pipes ranging in diameter from 16 to 800 mm are installed annually in the U.K. One attractive feature of thermoplastic pipe materials is the ease with which they can be joined using the butt fusion welding technique, which involves several stages. The first is the bead up stage, where the pipe ends are pressed against a hot plate and a melt layer with inner and outer beads is formed (Fig. 1). Reduction of the load on the pipe ends until it is just sufficient to keep them in contact with the hot plate then follows and the heat soak stage commences, in the course of which the melt layer thickness increases. At the end of the heating stage, the pipes are retracted from the hot plate and pressed together to form the joint, which is allowed to cool sufficiently before handling. From a consideration of the process it is possible to identify several important welding parameters, e.g. hot plate temperature, heating time, joint cooling time and joining pressure, which when optimised allow a joint with almost lOO%parent material strength to be made. Despite the wide use of this process, optimum welding parameters have been arrived at empirically; such parameters for polyethylene pipes are shown in Table 1. This ad hoc approach (Barber and Atkinson, 1972, 1974; decourcy and Atkinson, 1977, 1981; Colaluca et al., 1983) is very reliable but it would benefit from a fundamental understanding of the roles played by heat transfer and melt flow in the formation of a-butt fusion joint. This is clearly a complex problem to model and many investigators (Lyashenko and Zaitsev, 1968; Budak, 1970; Lyashenko and Istratov, 1975) simply ignored melt flow during bead up and calculated the rate of melt layer growth throughout the heating stage using ID heat conduction. Potente (1977, 1986) extended this approach by coupling the temperature distribution (linear) so obtained with a squeeze film
THEORETICAL
ANALYSIS
During the bead up stage, melting is initially transient but a steady state is reached when an equilibrium exists between the applied load and the hydrodynamic pressure generated in the melt layer separating the hot plate and the pipe end. This situation arises when the rate at which the melt flows into the beads, II,,,,equals the rate at which the pipe advances towards the hot plate and this is accompanied by the attainment of a constant melt layer thickness, h,. The objective of this analysis is to formulate a model capable of predicting v, and h, as a function of the process parameters; namely applied load and hot plate temperature, material properties and pipe geometry. The prediction of h, is particularly attractive because several investigators (Neubert and Wolfgang, 1973) have shown it has a decisive effect on joint quality. For the small dimensions of the melt layer in comparison with the pipe wall thickness (see Fig. 2), the lubrication approximation may be used and the governing equations in a cylindrical coordinates system (see Fig. 3) at steady state become in a dimensionless form (see Notation): Continuity
135
136
H. BENKREIRA pipe
wall -I
Fig. 1. Schematic representation of the bead up stage.
Momentum i?P _=aR
al-
(2)
az
Energy (3) where Pe is the Peclet number, a measure of the relative importance of convection to conduction in the melt layer. A constitutive equation which relates shear stress to shear rate and temperature must also be introduced. For polymeric melts the power law model expressed in dimensionless form is applicable:
la--l
I I
r=e-TE$
av
-&_
Butt fusion is clearly a low shear rate deformation where melt thickness and melting rate are typically 1 mm and 1 mm/s, respectively, i.e. shear rate z 1 s-r. Viscosity data for three pipe material melts are shown in Fig. 4, where in the low shear rate range, a power law model may be used to describe approximately the behaviour of these materials. Now the following dimensionless velocity, pressure and temperature boundary conditions may be identified: At the hot plate surface (Z = 0):
V,(R, 0) = V,(R, 0) = 0 T(R, 0) = N,, At the melt-solid
(5) (6)
interface (Z = 1): v&z,
1) = 0
(7)
Vz(R, 1) = 1
(8)
T(R, 1) = 0
(9)
At the outer (R = 1) and inner pipe (R = R,) walls: P(1, Z) = P(R,, Z) = 0
(10)
where N,, is a dimensionless temperature difference across the melt layer, and R, the radius ratio. Two further constraints on the temperature arise from a consideration of the heat conduction at the hot
et al.
Modelling of the butt fusion welding process
137
Fig. 2. Microtome section of the weld region showing the size of the melt layer to be much smaller than the pipe wall thickness.
plate and at the melt-solid
interface: (11)
E(R,1) =
Fig. 3. Simplified flow field and co-ordinate system.
10-Z
10-l 100 shear rate
10’ j’ d’
102
lo=
Fig. 4. Rheological data of the polymer material used.
Peiv,
(12)
where IV, is a modified Stefan number representing the ratio of the heat necessary to raise the temperature of the solid polymer from-the ambient to the melting temperature to the heat used in raising the temperature of the melt. Equation (12) is a crude approximation for semi-crystalline polymers because it assumes the latent heat change occurs at a single sharply defined temperature when in reality it occurs over a temperature range. In a squeeze film the flow is characterised by two parameters: the plane of zero shear stress, Z,, which is the plane along which the fluid velocity reaches a maximum, and the radius of flow separation, R,, at which the flow divides into two regions, whose velocity components are of opposite sign (Fig. 3). In isothermal, planar systems the position of each flow characteristic coincides with the axes of symmetry to which it is parallel, but, in the case of a pipe geometry, R, is displaced towards the outer pipe wall because it is also the point at which the maximum of the pressure distribution lies. When there is a temperature profile across the fluid layer, 2, is displaced towards the warmer fluid layers because the fluid in this region is less viscous and flows faster. The determination of these parameters must therefore be an integral part of
H.
138
BENKREIRA
this model because they are used as limits of integration in the solution of the governing equations. This information also gives a useful insight into the distribution of the melt flow during butt fusion welding. By integrating eq. (2) twice with respect to Z, together with the velocity boundary conditions and the power law equation req. (4)], two equations for the radial velocity distribution in the melt layer are obtained: dP
Z>Z,,VR=sgn-
et al.
Tho displaccmcnt of Z, towards the hot plate will have the effect of narrowing the velocity profile and causing a “fountain flow”, where the melt will be squirted out of the melt layer into the beads in 8, narrow jet. The position of the radius of flow separation, R,, can be found by integrating the dimensionless continuity eq. (1) with respect to R and Z, and substituting into it eqs (13), i.e. dP dR=sgn(R
dP Ifn
-
dR I dR I
s sgnglgy s z
1
z < z,, v, = -
([Z
- Z,]eT)““dZ
(13a)
I =
2. ss0 +
- Z]er)l’“dZ
(13b)
0
where “sgn” means sign of. The position of the plane of zero shear stress, Z,, can be found from the condition that, at Z,, the velocity V, must be continuous, i.e.
(16)
where
2
([Z,
-R.)(IR’_&R+y
z 0 1
ss2.
eT/“(Z 0 - Z)‘@dZ
dZ
1 2
er’“(Z
- Z,)““dZdZ.
Integrating eq. (16) and applying the pressure boundary condition [eq. (S)] yields an expression for the radial pressure distribution: R,>
-(‘i>“~z~(R’~R2~dR
R,P,=
(17a)
2. 5I
([Z
- Z,ler)l“‘dZ =-
R, < R,P, z0 ([Z, s0
- Z-Je’)““dZ.
(14)
Equation (14) is solved numerically by substituting the temperature, T, which is expressed by a polynomial in Z compatible with the four available temperature boundary conditions, i.e. T=
O.S[PeN,
+ N,,]Z3
+ 3N,,]Z
- O.S[PeN,
+ N,,.
(15)
Table 2 lists dimensionless values of Z, as a function of the power law index, n, and the dimensionless temperature difference, N,,, across the melt layer for Pe IV, = 0 to assess the simple case of a nonNewtonian fluid being squeezed between two plates held at different temperatures. These results show that, as the temperature difference across the melt layer increases, then Z, is displaced towards the hot plate and, for a given tempcrature difference across the melt layer, Z, is further displaced towards the hot plate as the degree of shear thinning behaviour exhibited by the melt increases.
=
+ (;>”
JI”(R2$‘J
Since the pressure is continuous
dR.
(17b)
at R = R,:
Computed values of R, as a function of the power law index n and the radius ratio R, are presented in Table 3. Identical results were obtained by Elkouh er al. (1982), who modelled the isothermal squeeze flow of a power law fluid between parallel annular rings. These results show that an increase in radius ratio or shear thinning behaviour displaces R, towards the outer wall of the pipe. This causes more melt to flow towards the inner pipe wall, hence producing a larger inner weld bead as commonly observed in practice (see Fig. 2). Such beads form a significant obstruction to flow in the pipe and are usually removed. Two equations are now required to determine V, and h,. The first may be obtained by integrating the pressure distribution over the area of the pipe end to obtain an expression for the dimensionless load required to cause squeeze flow:
Table 2. Predicted zero shear plane, Z,, for annular pure squeeze flow (no melting) of a power law fluid between two hot plates held at different temperatures N AT n
0.2
0.4
0.6
0.8
1.0
1.0 0.8 0.6 0.4 0.2
0.4833 0.4807 0.4772 0.4722 0.4643
0.4665 0.4614 0.4544
0.4497 0.4420 0.4317 0.4169 0.3942
0.4329 0.4228 0.4092 0.3900 0.3907
0.4162 0.4037 0.3871 0.3637 0.3288
Medelling of the butt fusion welding process
w=
P,RdR
+
P,RdR
=
139
I
Table 3. Predicted radius of flow separation, K,, for annular squeeze flow (with or without melting) of a power law fluid
R, 0.01
?I
1.0
0.3295
0.8 0.6 0.4 0.2
The integrals with solved analytically give the following numerically for the
w = - (0.5)”
(1 -
0.3593 0.3925 0.4284 0.4662
0.1
0.2
0.6
0.4637 0.4765 0.4913 0.5083 0.5277
0.5461 0.5540 0.5630 0.5735 0.5857
0.7915 0.7927 0.7941 0.7957 0.7977
respect to R in eq. (19) can be by multiple parts integration to equation which may be solved dimensionless load, W: R:)“+’
an
R:-“(R:
-
R:)“”
+ 3)U r
1 S[o
Id --(RFRT)
+ $(V,T)
RdR
1 1 s dZ =
d2T dZ.
o dZ2
1
s0
V, TdZ
= ;(Pe
N,
+ N,,).
(22)
It must be noted here that the cubic profile suggested in eq. (15) does not necessarily satisfy the energy conservation eq. (3) merely its boundary conditions (9)-(12). These are, however, the essential energy features of the process and justify such an approach. Substituting eqs (13) for V, into the above equation gives the following equation which can be solved numerically for Pe: TeT’“(jZo -
2)“”
Beelc (1969) list melting rate data for cylindrical bars of Alkathene and Hostaform C (polyoxymethylene) together with their relevant thermal and rheological property data, and before applying the model to butt fusion welding it was decided to validate it by comparison with this data. Therefore the model was modified to treat melt flow between parallel circular (not annular) plates and a power law model was fitted to the given rheological data. Table 4 compares the measured melting rate data of Hostaform C with that predicted by the model developed by Stammers and Beek (1969) and that developed as part of this study. It can be seen that the more comprehensive treatment of the polymer melt rheology results in better agreement with experimental data.
(21)
Integrating eq. (21) over the melt layer together with the velocity boundary conditions [eqs (5)--(7)-J and the temperature profile equation introducing [eq. (19)] yields Pegp
0.9496 0.9496 0.9497 0.9498 0.9499
I.(20)
A second equation which allows the determination of the Peclet number can be found by combining the dimensionless energy equation [es_ (3) 3 with the continuity equation [eq. (l)] to yield Pe
0.9
dZ dZ + I
Knowing the values of Wand Pe then v, and h, may be calculated. The theoretical approach used here is similar to, but more comprehensive than, that used by Stammers and Beek (l969), who modelled the contact melting process using a Newtonian analysis. Stammers and
EXPERIMENTAL
STUDIES
A detailed description of the experimental studies can be found in Shillitoe (1988). Three pipe materials, which represent the wide range of materials used in pipe applications were used in this study: two medium-density polyethylenes, BP rigidex (PEX) and Du Pont Aldyl (PEA), and one high molecular weight, high-density polyethylene, Philip’s Drisco (PED). The viscosity of these pipe material melts was measured at various temperatures (16%24O”C) and over a wide range of shear rates (0.01400 s - ’), using a combination of two techniques: the Instron capillary and Weissenberg cone and plate rheometers. At low shear rates (up to 10 s- ‘), PEA, PEX and PED have widely
Te=‘“(Z - Z,)““dZdZ = i(PeiV,
+ N,,).
(23)
different melt viscosities, with PED being the most viscous and PEA the least. At high shear rates ( > 100 s- ’), PEA and PED exhibit similar viscosities lower than those of PEX (Fig. 4). A power law model was fitted to this data over a low shear rate range
H. BENKREIRAet al.
140
Table 4. Apphcation of this model to squeeze melting polymer
of a cylindrical
bar of
Melting rate (m/s x 10e5) Force F (NJ
Temperature T c-7
78.5 49.1 9.81 78.5 29.4 78.5 49.1 78.5 78.5 9.81 49.1 ‘Calculated (1969).
Measured
This study
t
0.73 0.58 0.35 1.50 1.38 1.78 2.50 2.87 3.83 2.20 3.40
0.97 0.80 0.40 1.69 1.10 1.94 2.30 3.09 4.42 1.45 3.52
1.49 1.41 1.10 2.43 2.27 2.74 3.51 4.09 5.54 3.33 5.04
by Stammers
and Beek
179 180 183 190 193 194 211 213 236 237 238
using the expression developed
Table 5. Properties of polymer materials used in this study Mean thermal conductivity W/m K)
Mean specific heat capacity
Mean density
&J/kg K)
Material
Solid phase
Melt phase
Solid phase
Melt phase
PEA PEX PED
0.2606 0.3099 0.2795
0.2812 0.2643 0.2438
2.1 2.68 2.18
2.63 2.16 2.63
Latent heat of fusion
b/m3)
Melting temperature
O
(“Cl
Solid phase
Melt phase
135 135 142
940 940 960
785 785 819
Table 6. List of operating conditions
Material PEA/PEX PED
because of the dynamics pipe advances
towards
Outer pipe radius (mm)
Pipe wall thickness (mm)
Bead up time (s)
Hot plate temperature (“C)
62.5 50.0
11.0 9.0
7.5-240 7.5-240
167-240 167-240
of the system. Typically, the the hot plate at a rate of less
than 1 mm/s and the melt flow is confined within a layer of approximately 1 mm in thickness. The thermal conductivity of the pipe materials in the solid and melt phases was measured using the apparatus developed by Hands and Horsfall(1975), in which a steady-state temperature difference is generated across a disc-shaped specimen. The specific and latent heats were measured using differential scanning calorimetry and the melting temperature using the Kofler method. These data, together with density, which was determined from specific volume data in Matsuoka (1962), are listed in Table 5. The melt layer thickness generated over a wide range of conditions (see Table 6) was measured using transmitted polarised light microscopy of thin sections. The thin sections were microtomed from across the end of the pipe that had been headed up using an
automatic butt fusion welding lowed to COOL
Bead up force
(N) 482-1642 482-1642
machine and then al-
RESULTS AND DISCUSSION
Figure 5(a) shows the measured variation of melt layer thickness with time during the bead up stage of PEX. The melt layer thickness increases to a constant value which decreases with bead up force. Similar results were obtained with PEA but not with PED, whose higher viscosity prevented the attainment of a constant thickness as illustrated in Fig. 5(b). Therefore, the lubrication model developed above cannot be applied to this material. Instead, the model was used to predict the variation of the constant melt layer thickness of PEX and PEA with hot plate temperature. Clearly, the predictions are in good agreement with experimental data (see Fig. 6). Und5r identical conditions the melt layer thickness at steady state of PEX is greater than that of PEA on
Modelling of the butt fusion welding process
141
4.0 ,
I
* z E I f +I! E 8 p
l
3.0
I .
2.0
I . .
.
1.0
*
1.0
5
0.8
=
0.6
I
I
I
I
._
0.4
0.2
MATERIAL : PED HOT PLATE TEMP
:
ma
0
:
1
MATERIAL HOT
PLATE
1
: 200% I
: PEX TEMP
: 200%
.
I
30
0
I
60
SO Bead
120 up time
150
160
210
240
Is)
Fig. 5. Measured variationof melt thicknesswith timeduringthe bead up stage of PEX and PEA [bead up
force:(o)482N,(A)1112N,(m)lf542N].
150
170
180
to0
Hot plate Fig. 6. Comparison of predicted (-)
IMPLICATIONS
210
220
230
240
(‘C)
and measured (0) melt thicknessat steady state for PEX and PEA.
account of its higher melt viscosity at low shear rates. Additionally it is apparent that the melt layer thickness of both materials increases very little with hot plate temperature. This is because the increased rate of heat penetration into the pipe as a result of the higher hot plate temperature is offset by the reduction in the ability of the melt to support a load caused by the decrease in melt viscosity resulting from its temperature dependence. PRACTICAL
200
temperature
OF THIS WORK
The results of this investigation are now discussed in relation to the actual practice of plastic pipe welding. The attainment of a large melt film thickness is essential for the formation of a good joint. With a large film thickness, adequate melt flow ensures the removal of contamination from the melt surface caused by cooling and oxidation, while retaining sufficient hot melt at the pipe ends to promote transcrystallinity across the joint interface (Neubert and
Wolfgang, 1973). The work here has demonstrated that steady-state conditions are reached quickly with PEX and PEA (of order 60 s) but not with PED (see Fig. 5). An immediate conclusion is to favour PEX and PEA where the limiting growth of the melt film thickness can be predicted. Also, it was shown that increasing hot plate temperature during bead up altered little the film thickness for both PEX and PEA, hence the practice of a heat soak stage where the pressure is removed and melt layer growth via conduction prevails. A favoured method thus would be to use a large hot plate temperature rather than a longer heat soak time. Again this is used in practice. Also, the examination of both theoretical and experimental data suggests that, under identical conditons, larger film thicknesses are produced with PEX than with PEA due to the lower viscosity of the former. Again in practice, PEX is favoured and conforms with this observation. Finally, the model shows a significant increase in melt layer with decreasing pressure, corres-
H. BENKREIRA
142
ponding with the use of small loads in actual practise. However, it must be recognised that other factors pertinent to the production of a good weld (e.g. cooling/crystallisation) are not considered here and are now being addressed in our laboratory. CONCLUSIONS
The bead up stage of the butt fusion welding operation was modelled using lubrication approximation coupled takes
with into
viscosity
the general
power
account
both
the
of the melt
with
shear
ature. This approach and melt layer
yields
thickness
law
equation
variation
which
of melting
are in good
rate
agreement
experimental data. Furthermore, the model enables calculations of flow characteristics (R,, 2,) to be made. It can also be extended to calculate the melt layer thickness after the heat soak and joining stages, and the joining displacement, all factors which influence joint quality. Acknowledgements-We would like to express our appreciation to the SERC and the Engineering Research Station of British Gas for supporting this work. NOTATION
hm I K k n NIlI N AT P P Pe R
heat capacity, kJ/kg K steady-state melt layer thickness after the bead up stage, m doube integrals in eq. (16) consistency index in the power law equation, N C/m2 thermal conductivity, W/m K power law index (aA*/cp,) (modified Stefan’s number) ~$0, - 0,) (dimensionless temperature difference across the melt layer) pressure, N/m2 (ph,/rjv,)(h,/r,)2 (dimensionless pressure) specific
(Peclet
(cp,v,h,p,)/k, r/r2 [radius radius
R, r
t-r/r2 (radius ratio) radial coordinate
r1
inner outer
r2 T
a(0
v,
pipe
of flow
separation
0,)
(dimensionless)
m
pipe radius, pipe radius, -
number)
(dimensionless)]
RO
m
[temperature
(dimensionless)]
W
rate, m/s (Q/U,) (hm/r2) (dimensionless radial melt velocity) v,/v, (dimensionless axial melt velocity) load, N
W
(wh~)/(ifu,27rr’:)
Z z
axial coordinate, m z/h,,, (dimensionless axial
Z*
plane
VIl Vz
melting
of zero
[load
shear
(dimensionless shear stress) ’ (dimensionless viscosity)
temperature, K hot plate temperature, K initial temperature, K melting temperature, K latent heat, kJ/kg 1 + cp,(O, - Oi) (reduced density, kg/m3 shear stress, N/m2
latent heat), kJ/kg
apparent
with
CP
(th,/tjv,)(h,/r,) K [(v,/h,)(r,/h,)~“-
rate and the temper-
predictions
which
in
et al.
(dimensionless)] distance)
stress (dimensionless)
Greek
letters
cc
viscosity temperature dependence power law equation, K- ’
term
in the
REFERENCES
Barber, P. and Atkinson, J. R., 1972, Some microstructural features of the- welds in butt-welded polyethylene and polybutene-1 pipes. J. Mater. Sci. 7, 1131-1136. Barber, P. and Atkinson, J. R., 1974, The use of tensile tests to determine the optimum conditions for butt fusion welding certain grades of polyethylene, polybutene-1 and polypropylene pipes. J. Mater. Sci. 9, 1456-1466. Boenig, H. V., 1966, Polyolejins,Structure and Properties, p. 49. Elsevier, Amsterdam. Budak, V. M., 1970. Investigation of the thermal aspects of contact butt welding in polyethylene tubes. Weld. Prod. 1, 5-7. Colaluca, M., Earles, L. and Malguarnera, S., 1983, Fractional factorial testing to determine processing parameters producing acceptable heat fused joints in polyethylene nipe. Polym. Plast. Technol. 20, 180-195. deCourcy, D. R. and Atkinson, J. R., 1977, The use of tensile tests to determine the optimum conditions for butt fusion welding polyethylene pipes of different melt flow index. J. Mater. Sci. 12, 15351551. decourcy, D. R. and Atkinson, J. R., 1981, The assessment of fusion joint quality and some evidence for the presence of molecular orientation in butt fusion welds in polyethylene pipes. Plast. Rubb. Process. Applic. 1, 289-292. Elkouh, A. F., Nigro, N. J. and Liou, Y. S., 1982, NonNewtonian soueeze film between two plane annuli. J. Lubrication 7’echnol. 104, 275-278. Hands. D. and Horsfall. F., 1975, A thermal conductivity apparatus for solid and molten polymers. J. Phys. E scien;. Znstrum. 8, 687-690. Lyashenko, V. F. and Zaitsev, K. I., 1968, Research into the thermal processes taking place during the butt welding of tubes made of thermoplastic substances. Aut. Suarka 1, 37-39. Lyashenko, V. F. and Istratov, I. F., 1975, The butt fusion welding of thermoplastic tubes in winter conditions. Weld. Prod. 22, 58-60. Matsuoka, S.. 1962, The effect of pressure and temperature on the specific volume of polyethylene. J. Polym. Sci. 57, 569-587. Nuebert, W. and Wolfgang, M. A., 1973, Getting a bead on welding of plastic pipe and fittings. Plast. Engng August, 4043. des HeizelementstumPotente, H., 1977, Die theorie pfschweissens. Kunststof67, 98-102. Potente, H., 1982, An analysis of the heated tool butt welding of pipes made of semi-crystalline thermopIastics. Department of Polymer Technology, internal report, University of Paderborn. Potente, H., Michel, P. and Tappe, P., 1986, Heated tool butt welding of semi-crystalline thermoplastics. Department of Polymer Technology, internal report, University of Paderborn. Shillitoe, S., 1988, A study of the butt fusion welding of thermoplastic pipes. Ph.D. thesis, University of Bradford. Stammers, E. and Beek, W. J., 1969, The melting of a polymer on a hot surface. Polym. Engng Sci. 9, 49-55.