The Butt-fusion welding of polymers

Cheanical Enpineehg Science, Vol. 48. No. 17. pp. 3071-3082. ,959 Printed in Great Britain.

THE BUTT-FUSION WELDING

ooo9-2509/93 $6.00 + 0.00 0 1993 Pcrgamon Press Ltd

OF POLYMERS

A. S. WOOD University of Bradford, Department of Mathematics, Bradford, West Yorkshire BD7 IDP, U.K.

(First received 27 May 1992; accepted in revised form 8 January 1993)

Abstract-A predictive model, based on the definition of an enthalpy function, is constructed for the evolutionary heat transfer behaviour of the butt-fusion welding process for polymer pipes. The model is implemented using standard finite difference techniques and is shown to be robust for a wide range of operating conditions. Its usefulness to relevant industrial and commercial areas is demonstrated.

INTRODUCTION

Polyethylene pipes are now used extensively for the local and national transmission of our gas and water supplies. They are recognisable as the piles of yellow or blue thermo-plastic pipes frequently seen by road- side trenching, generally in the vicinity of gas and/or water company vehicles. The adavantages of their use include resistance to corrosion and, with regard to installation costs, the relatively simple process used to join two pipe lengths together. This process, known as butt-fusion welding (BFW), is carried out in situ by operators using portable equipment and consists of five main stages (schematically represented in Fig. 1): (a) bead-up involves two pipe lengths being brought

Load + H Hot Plate

(a) t

Load

/ \

J---r Cd)

Load

(e)

Fig. 1. Five stages of butt-fusion welding: (a) bead-up, (b) heat soak, (c) dwell, (d) jointing and (e) cooling.

to bear, under pressure, against a hot plate. The pipe ends melt and a layer, or bead, of liquid plastic is squeezed out along the face of the plate. (b) During heat soak the pressure is relaxed so that the pipes just touch the plate, and continue to melt. (c) At the dwell stage, the pipes are moved back from the hot plate, which is then removed. During this stage the pipe ends start to cool. (d) At the jointing stage the pipes are butted together to form a fusion weld which, de) during the cooling stage, solidifies. This process has been used to successfully joint many thousands of kilometres of polyethylene pipe (see Fig. 2).

Crucial to facilitating conditions which may opti- mise the integrity of the joint (such as strength, leak- age, etc.) is a need to understand and control the heat transfer processes involved during the five stages. For this we can model the physical situation as a system of partial differential equations, which is then solved using numerical techniques. The full model (including pipe movement and deformation) is useful to both material and pipe manufacturers and to pipe in- stallers, allowing practitioners of BFW to determine a priori the best conditions for welding, for example, hot plate temperature. bead-up time, etc.

Several models for the BFW process are described in the literature, much of it concerned with the mech- anisms active during the bead-up stage [Lyashenko and Zaitsev (1968), Budak (1970), Lyashenko and Istratov (1973, who ignored melt flow, Potente (1977, 1982), Potente et al. (1986)]. Shillitoe (1988) described a series of experiments concerned with the determina- tion of material properties. Subsequently, Shillitoe et al. (1990) presented a finite element simulation of the bead-up stage for BP Rigidex, making use of the commercially available general-purpose modelling package ABAQUS which requires considerable “user experience” and setting up for separate simulations. Its use has been in identifying the characteristic behaviour of the welding process. To be of practical use to the welding industry a model needs to be dedicated to the fusion welding process allowing multiple simulations via portable compact code and straightforward user-supplied data, such as hot plate temperature, bead-up time, etc. These are typically the parameters that an on-site practitioner can set. To this end Benkreira et al. (1991a) described a lubrication model

3071

3072 A. S. WOOD

Fig. 2. Microtome section of the weld region.

for the steady-state behaviour of the melt flow during bead-up. The work was extended to a full model of the butt-fusion welding process by Benkreira et al. (1991 b). However, the resulting procedure was rather cumbersome and required several concatenated process steps (including use of ABAQUS) to generate, albeit useful, results. Subsequently, the present work illustrates a methodology for describing and simula- ting the evolutionary heat transfer behaviour within the thermoplastic pipes during all stages of the BFW process. The approach may be coupled with the squeeze flow description of pipe movement and bead formation (Shillitoe et al., 1990; Benkreira et al., 199la) to provide a simplified but “user-friendly” BFW simulator.

A HEAT TRANSFER MODEL

With symmetry about the hot plate we need consider only a single circular pipe made of material with a unique melting temperature, U,, and initially solid at a temperature Ue < U,. At time t* = 0 the pipe end is brought to bear (under pressure) against a hot plate maintained at a temperature U,, > U, The pipe subsequently melts (bead-up), with the process being characterised by a small motion of the pipe and by a moving melt front f(t*, z*, t*) = 0 separating the liquid and solid regions. During heat soak the pressure

on the pipe is removed but the thermal boundary conditions remain the same. If pipe movement is ignored during bead-up (discussed later in this section) then, from a heat transfer analysis point of view, bead-up and heat soak may be treated as a single stage. Axial symmetry reduces this consideration to the semi-infinite region r: < r* < r:, z* 2 0 (see Fig. 3).

In each of the liquid and solid regions the temperature U(r*, z*, t*) is governed by the equation

pCg=K [

I au a2u a2u FF+-+- ar*2 az*2 1

+(~)[(~>‘+(~>‘] r-t < r* -z r:, Z* > 0, t* > 0. (1)

Thermal conductivity, K, density, p, and specific heat capacity, c, are all (possibly) functions of temperature which gives rise to the non-linear form of eq. (1). Axially, eq. (1) is subject to the isothermal Dirichlet conditions

U(r*, 0, t*) = U,, r:=Sr*Gr.*,OGt*Gt.+

(2)

lim U(r*,.z*, t*) = Uo, 2, - m

ri* G r* sG r:, t* 2 0. (3)

The butt-fusion welding of polymers 3073

Adjacent i Pipe -i I

I ;

Z'

I: 0 Melt Front

Fig. 3. Typical pipe cross-section and physical solution region for the present analysis.

Condition (2) implies perfect contact between the pipe and the hot plate. rb and t: are the times at the end of bead-up and heat soak, respectively. At the internal and external pipe surfaces, heat loss by convection to the surrounding medium (air) is governed by

Kg= h(U - u.), r*=rt,z*z=O,t*&O (4)

+ = h(U, - U), r*=r:,z*>o,t*>o. (5)

Strictly speaking, we might expect h to be different on the inner and outer pipe surfaces, although in practice the variability of ambient and process conditions renders unnecessary all but a reasonable estimate of h. There will also be some variation of air temperature inside the Ripe as it is welded. This change is likely to be exaggerated for small-bore pipes although, con- versely, for such pipes the process heating times will be smaller and hence reduce heat flow into the surrounding air. Certainly, if critical process parameters (such as melt depth) were acutely sensitive to these factors then some account for variations in h and U, would need to be made. However, this does not ap- pear to be the case (see Table 2, for example).

During the dwell stage the hot plate is removed and at the pipe end there is con,vective heat loss:

Kg = h(U - U,,), rr<r*<r:,

z* = 0, t: < t’ d td* (6)

in which tz is the time at the end of this stage. Finally, during jointing and cooling (treated as a single stage), symmetry across the jointing interface implies

There is no analytical solution for the problem de- fined by eqs (l)-(7) and a numerical solution is im- peded by several factors:

(ii)

(iii)

There is a non-linear (Stefan) condition at the liquid/solid boundary governing the motion of the melt front, namely

Lpv, = [KlVV[];, f(r*, z*, t*) = 0 (8)

in which v, is the normal velocity of the melt front. The pipe is essentially semi-infinite in the axial direction and so, for practical and numerical reasons, we need an idea of the size of the heat-aficted zone (HAZ). During bead-up and jointing there is a small movement of the pipe and melt flow in the liquid phase.

The first of these difficulties can be overcome by using what is commonly known as the enthalpy method (Rose, 1960, Atthey, 1974). For this we define an enthalpy function Q(U) to he the sum of the volumetric sensible (pcU) and latent (pL) heats. At a point in the solid region,

” Q(U) =

i PC du, u < u, (9)

u.

in which UR is a reference temperature. Specifically,

s “’ Q,, = pcdu and Qm = 0. s

urn pc du.

rJI

At the melting temperature U,, the enthalpy ranges over an interval of size pmL,

Q,~QVJ,)CQ,+P,~ U=U, (10) in which pm = p (U,). We assume that there is no change in density at melting or solidification, that is, the density is continuous across the melt front. Finally, at points in the liquid region,

” QW) = Qm +

s pcdu + pL

U”

-Qm+ ” s

pcdu + p,,,L, V > U,. (11) u”.

In particular,

Q,=Q,+ UPpcdu+pmL. I u,

Figure 4 illustrates typical behaviour of Q(U). Since aQ/at* = pcXJ/at* eq. (1) can be written as

which is valid over the entire liquid/solid region. The temperature on the right-hand side of eq. (1) is not

A. S. WOOD

tion (14) is replaced by

3074

Q(U)

QP.

Qti

QO

PmL I I I t I

I I

I I I

"0 Urn “P U

Fig. 4. Typical enthalpy behaviour as a function of temperature.

replaced since Q and its spatial derivatives are discon- tinuous at the melt front. Having determined Q(U), the temperature can be obtained from relations (9)-(11). This approach has been successfully em- ployed by various authors to generate numerical solutions to a variety of Stefan problems, from the simple one-dimensional case (Wood et al., 1981), including the so-called mushy region (Voller and Cross, 1981), to multidimensional problems (Meyer, 1973; Crowley, 1978; Bell and Wood, 1983; Wood, 1986).

To overcome the necessity of determining a HAZ, and to simplify the solution region (which becomes a square), we adopt the change of variables

r* - r: I=- z=l-exp(-s) andt=t*

r: - r:’

in which a is a scaling parameter (quantified in the following section). Defining E = rf/(rr - rp), the heat transfer model (12) and conditions (2H7) become

ae K

[

1 dcr azu -= -- at (ro* - ri*)2 E + r dr + p - “(l - ‘1X

+ a’(1 - z)‘$ + 1 (r* 2 rtJ2 [$J[cij c au 2 + a2(1 - z)~ aZ

C >I O<rc 1,

Otzt 1,t>o (13)

subject to (during bead-up and heat soak)

U(r, 0, t) = UP, O<r< 1,Og t<t,. (14)

U(r, 1, t) = UIJ. OGrGl,t20 (1%

au h - = &rt - rf)(U - U.), ar r = 0, z 3 0, t 2 0

(161 au h - = ,(rZ - rt)(U, - U), dr

r = 1, z 2 0,1> 0.

(17) During the dwell and jointing/cooling stages, condi-

au h -_= i?Z j&r: - rf)(U - U,)

0 < r < 1, z = 0, t. e t Q Cd (18) and

au -=0, O<r< l,z=O, t>td dz (19)

respectively. Finally, we consider the pipe movement. During

bead-up a steady state is reached when the applied force and hydrodynamic pressure are in equilibrium, that is, when the rate of pipe movement equals the rate of melt flow into the bead. Typical measured values of the steady-state melting rate of solid cylin- ders of polymer lie in the range 0.35-3.83 x 10e5 m/s for values of (applied force, temperature) ranging from (9.81 N, 183’C) to (78.5 N, 236°C) (Table 4, Benkreira et al., 1991a) and so, in general, the pipe movement during bead-up is small [ - 0.12 mm, for example, in Shillitoe (1988)]. The flow of melt along the hot plate also operates under a long time scale and, coupled with the relatively large thermal conductivity (u 0.3 W/m K), in practice the temperature profile can “catch up” with the Aow field and melt layer growth can be considered in the absence of movement. The primary use of the squeeze film model of Benkreira et al. (1991a) was to determine the final steady-stat? melt depth at the end of bead-up. This was achieved by solving the steady-state continuity, momentum and energy equations for the velocity and temperature profiles. The approach does not yield the amount of melt flow into the bead. An estimate of this critical quantity may be obtained by subtracting the steady-state squeeze film prediction from the present (no load, no flow) heat transfer prediction.

A NUMERICAL SOLUTION

The region 0 < r G 1,O c z d 1 is subdivided into n, radial elements of size Ar and n, axial elements of size AZ and nodes (rir zj). Typically, n, will be greater than n, since the bulk of the heat flow takes place in the axial direction, particularly at nodes close to the pipe end. For this reason, a finer z-mesh is appropriate and for the numerical results presented in this paper n, = 4n,. Further, due to the exponential relation between I* and z, a uniform mesh in z corresponds to a graduated mesh in the physical coordinate z*, with a finer mesh size closer to the pipe end. This mimics the expectation that most of the heat flow takes place in this region, due to both the poor trans- port properties of plastic pipe materials and the sud- den thermal loading by the hot plate. Finally, to facilitate a reasonably accurate description of the melt front motion in the early stages, the scaling parameter a is chosen so that a value of z = 0.1 corresponds to a value z* = 0.001 m, namely

a= _(r$--rri*)ln0.9 0.001 .

Hence,

z+= _(r.*-~:)ln(l--z)=OOOlln(l--z) a In 0.9

and with, for example, n, = 10 radial elements the penultimate axial node, n. - 1, corresponds to a physical distance of about 35 mm. This value should, under typical working conditions, provide a strict upper limit for the maximum melt depth in any simulation. If this were not the case, difficulties would arise with interpolation routines used to determine the melt depth at the end of certain stages of the BFW process. This occurs since the last axial node (in physical space) is located at infinity and so the melt front will never reach this point, precluding interpolation.

Defining r,=iAr, z,=jAz, t,=mAt, UT’- V(ri, z,, t,,,) and Q~j _ Q( Vkj), an explicit difference replacement for eq. (13) is

(20) in which KT, 5 K(VT,), @, m dK/dV (at V = VT,)*


and

uE+l.j= VE-l,j + +(Lz, - vZ.j) ar.j

l<j<n,- 1,maO (23)

in which y, = 2 Ar(r$ - r:)h. During the dwell and jointing/cooling stages, conditions (18) and (19) can be replaced by

VT_, = VT, - $--$(V% -V,), OGi<n,

(24) and

UC-1 = UT,, OdiGn,

respectively, in which y. = 2 Az(r$ - r,+)h.

(25)

It is well known that explicit difference methods operate in restricted domains due to stability problems (Smith, 1978). Since the updating formula (20) is non-linear, the usual matrix or Van Neumann ap proaches to stability analysis ar qpractical. Instead, we employ a heuristic argum erfe t, namely that a virtual increase in the value of VT, should produce a virtual increase in the value of QTf ’ and hence in Vzi+ I. To ensure this physically appropriate behaviour, the CO- efficient of VTj in eq. (20) must be positive. On incor- porating the convective boundary conditions (22)-(24) this approach leads to the time step bound

At < &?(r: - r,)): (A#

2R(1 + 16a2) + (r.l - r?)h Ar [2 + Ar/(z + 1) + cc(Ar + 8)] (26)

1 Vl:l,j- uE1.j AT,=-

8 + ri 2Ar

+ Vl;l,i- 2uy, + VT- 1.j (Ar)2

- a2(1 - zi) VTJ+l- VTj-1

2Az

+ a2(1 - Zj)’ u;lj+i - 2Vllj + V&l

(AZ)*

W.j = lVT+l,j - vF-‘-l,j)2

4(Ar)l

+ aZ(l _ zj)2(UG+;(;zYPl)2.

During bead-up and heat soak eq. (20) is applied at thespatialnodes(ri,zj),O<i<h,l<j<n,-l.At the pipe ends we have

Vr, = VP and UT,,. = V,,, 0 G i C b. (21)

Assuming that eq. (13) is satisfied at all internal nodes, as well as nodes lying along the internal and external surfaces of the pipe, the fictitious values U?‘,,i and UrP+ i, i appearing in eq. (20) can be obtained by using appropriate central difference replacements for the boundary conditions (16) and (17). We obtain

u’ll.j= UT.j-&(W.j- vn)

ICiGn.-- 1, .mbO (22)

in which the minimum values of density (D) and specific heat (E),_and the maximum value of thermal conductivity (K), are taken.

By the nature of the relation (10) between V and Q, a naive interpretation of the results from the difference method will lead to erroneous conclusions regarding the evolutionary behaviour of the melt depth and the temperature history at any point in the solution region, as noted and remedied by Voller and Cross (1981) and analysed by Bell (1982). While the moving boundary is in the vicinity of a node, the temperature at that node is held at the melting temperature for a finite number of time steps and tracking the temperature and/or melt front at every time step produces a step-like profile. This behaviour is entirely a result of using a difference replacement of the enthalpy model and may be overcome if we can predict the times at which the melt front actually passes through a node. To proceed, we define a critical enthalpy equal to Qm plus one-half of the phase-change energy, namely

If, during one time step, the enthalpy at zj passes through the critical value then we may assume that the melt front has moved through the node in that time step. Simple interpolation gives us an estimate of that time (see Fig. 5),

tori, = t, + At Q wit - QTj ?#I+1 Qi.i - Q? >

3076 A. S. WDOD

m+l

)

I I I I

tm hit tm+l

At

Fig. 5. Calculation of nodal interface times.

with corresponding melt front location z,. If these times and locations are plotted then a smooth profile results which is demonstrably accurate (Voller and Cross, 1981). More recently, Date (1992) has proposed an efficient implicit remedy to the “waviness’ problem.

NUMERICAL EXPERIMENTS AND DISCUSSION

We concentrate on simulations involving pipes made from a typical medium-density polyethylene (BP Rigidex) and use two readily available material data sets. Table 1 shows the constant thermal properties used by Benkreira et nl. (1991a) (the liquid value c = 3 160 J/kg K appeared incorrectly as 2160) and the temperature-dependent properties used by Shillitoe et al. (1990). Finally, we make use of the values U, = 135°C and L = 390,600 J/kg (Benkreira et al., 199la). To conform with the convention adopted by pipe manufacturers and users, sizes are presented in terms of the pair (rz, SDR), in which SDR is the standard diameter ratio.

3.5 i

Table 1. Constant and variable thermal properties of BP Rigidex

u (“Cl

20 40 42 60 80

100 120 126 140 150 160 179 180 200 201 220

Solid Liquid

K W/m K)

- 0.328

- 0.318

-

- 0.273

-

- -

0.273 -

0.3099 0.2643

P (kg/m3 ) c (J/kg K)

940.0 1750 930.9 2200

922.0 2500 910.3 2750 898.8 3500 880.8 6Wo

11,200 749.0 2600

737.4 - 2700

725.8 - 714.2 2725

- 2750 940.0 2680 785.0 3160

Figure 6 shows the predicted development of the melt depth and pipe interface temperature, along an axial line that lies midway through the pipe wall for a simulation using n, = 10 radial elements. The fol- iowing process and environment parameters were used: bead-up 25 s, heat soak 180 s, dwell 10 s, cooling 50 s, U,, = U,-, = lO”C, UP = 23O”C, h = 15 W/mZK (still air), I-: = 0.125 m and SDR = 17. There are several relevant observations:

(i) Contrary to frequently stated simplifications, it is clearly not valid to assume constant thermal properties. The results based on temperature- dependent properties (dashed line) show a de- parture from those based on constant properties (solid line) and we might reasonably expect that conclusions based on the use of this model will be sensitive to the material data provided.

-180 8

E

‘-._ --___ - ‘t-

0.0 , ‘. I I I I I I

0 100 200 300 400 500 800 700 Tirrm (0)

Fi8. 6. Mid-wall melt depth and interface temperature as functions of time.


(ii)

(iii)

Primarily, the difference is due to using a temperature-dependent specific heat capacity c(U). In the vicinity of the melting temperature, c behaves like log1 U - U,1-the so- called R-transition (Hsieh, 1975). A fixed value of c in each phase gives completely the wrong behaviour-a first- or second-order phase transition. In both curves the melt front traces a smooth profile, validating the nodal interpolation procedure described previously. Further, during bead-up and heat soak, the behaviour re- sembles a ti relation, typical of the classical one-dimensional Stefan problem. This is to be expected since along the mid-wall axial line there is little radial heat flow. For constant properties, the melt depths at the end of bead-up and heat soak are, respectively, s$ = 1.044 mm and s.* = 3.014 mm. These values agree quite well with Shillitoe’s (1988) ABAQUS simulations of 1.07 and 3.15 mm (which also included a pipe movement of 0.12 mm). Further, the predicted mid-wall interface temperature at the end of the dwell stage is 182.2”C, which agrees well with the value of 183°C predicted by ABAQUS simulation. This indicates that, perhaps, when look- ing at the thermal behaviour of the fusion process, pipe movement for “typical” problems can be ignored, substantially simplifying the analysis.

Figure 7 shows the mid-wall motion of the melt front, during bead-up, as predicted by the present zero-load analysis. The variable data set was used with U, = 200°C r: = 0.0625 m and SDR = 11.36. For comparison, experimental values for three different load forces are also shown (Benkreira et al., 199la, Fig. 5). For smaller bead-up times there is some correlation between predicted and experimental data.

The dotted line shows the predicted effect of using Potente’s experimentally measured value h = 43 W/m’ K (still air).

Figure 8 shows predicted and measured (British Gas, 1991) mid-wall pipe interface temperatures during the dwell stage. In this case the conditions V. = V, = 20°C applied. A smooth profile is predicted and the value of l75.7”C at the end of the dwell stage (variable properties) agrees well with the measured value of 174.7”C. The improvement when using the variable thermal properties (dashed line) in place of the constant properties (solid line) is evident.

Figure 9 shows zero-load bead-up (that is, heat soak) and dwell stage temperature profiles along the mid-wall axis using variable data and the value h = 43 W/m2 IL There is excellent correlation between the non-linear ABAQUS simulation of Shillitoe (1988, Figs 5.14 and 5.15) and the present analysis. Both predictive models indicate the correct trend for the temperature behaviour. It seems fairly clear that the present model can provide an adequate picture of the evolving thermal behaviour in the BFW process.

Tables 24 simply serve to illustrate the use of the model as a look-and-see tool, showing the predicted dependence of several critical mid-wall BFW process parameters on selected applied conditions. In all three tables the data for Fig. 6 were used with oariable thermal properties.

Table 2 suggests that the surface heat transfer has least effect on the heat soak melt depth, the value of s$ decreasing by approximately 3.5% over the range shown. The bead-up melt depth remained essentially unaffected at 1.010 mm. More significant is the dependence of dwell stage interface temperature and the time to attain total solidification. U, is reduced by about 28% and, for values of h in excess of about 80 W/m2 K, the interface temperature (for this simulation) reaches the fusion temperature before the dwell stage is complete. This situation is undesirable for the BFW process since jointing would be prevented.

I I I I

0 50 100 150 200 Tim (s)

Fig. 7. Predicted and experimental melt depths during bead-up.

3078 A. S. WOOD

180-

170 ' I I I f I 206 208 210 212 214

Time (s)

Fig. 8. Predicted and experimental evolution of dwell stage mid-wall interface temperature.

t = 20s Soak

oil d5 1:o 1; io io &l is io 4; ;o Distance (mm)

t = 60s Soak

0, , , ‘ ) , , , I , , 0.0 0.5 l.0 ld 2.4 2.5 x0 3.3 +,a 4,s a.0

Distance (mm)

t = 40s Soak

t = 60s Soak + 10s Dwell

Fig. 9. Predicted and experimental zero-load axial temperature profiles.

Typically, temperatures should be maintained at least 10°C above the melting temperature up to the jointing stage. The values of Ud on the pipe surface show that solidification will start in the dwell stage for values of h as low as 40 W/m2 K. On the contrary, the negat- ive-slope behaviour is desirable (although perhaps less crucial) regarding total solidification, the value of tzO, decreasing by some 41% as h is increased.

The hot plate temperature clearly has a great effect on the melt depth, with sb and s: both increasing by about 40% over the typical range of U,, values. U1 and t& behave much as in Table 2, except that now there is a positive slope.

With the exception of t.*,,, there is little effect in changing the pipe size. The increase in t$,, is predict- able since larger pipes will have a larger total heat


Table 2. Effect of surface heat transfer h on selected process parameters, for BP Rigidex

Melt depth (mm)

(V&K) s: r :

Interface temperatures (“C) Solid at

Mid-wall Surface G,(s)

0

:8 30 40 50 60 70 80 90

100

2.944 2.918 188 188 2.929 2.896 179 167 2.914 2.878 170 151 2.902 2.862 I62 136 2.890 2.849 155 I35 2.880 2.838 148 134 2.870 2:828 142 131 2.860 2.819 136 128 2.852 2.811 135 127 2.844 2.805 I35 126 2.837 2.798 135 125

835 736 670 624

:z

z; 515 504 494

Table 3. Effect of hot plate temperature U, on sekcted process parameters, for BP Rigidex

Melt depth (mm) Interface temperatures (“C) Solid at

s+ . Mid-wall Surface 12, (s)

0.697 2.056 I45 I35 512 0.859 2.520 I59 I46 611

230 1.010 2.922 174 I58 699 250 I.129 3.278 189 172 782

Table 4. Effect of pipe size on selected process parameters

r: (mm)

I25 250 500

SDR

17 II IO

Interface temperatures (“C) Solid at

s: (mm) Mid-wall Surface t4 (s)

2.922 174 I58 699 2.944 I75 I65 820 2.944 I75 168 822

content to disperse. Further, as the pipe wall size is varied, the temperature profile across the wall is modified, “flattening” as the wall thickness increases (see Fig. 10). Again, this is to be expected since more of the pipe wall lies far enough from the surfaces to be (effectively) unaffected by the wall conditions.

As an aside it should be noted that the curvature of the temperature surfaces, at least during bead-up, would typically be away from the pipe end (due to the squeeze film deformation of the pipe end). However, once the loading has been removed, the profile will move to the usual inward curving profiles, seen in Fig. 10, due to surface convection. Consequently, it is clear that the dwell stage temperature should prefer- ably be monitored at the external surface of the pipe since the temperature cools more rapidly here. Clarifi- cation of this presented in Fig. 11.

As explained, total solidification has been measured at a point midway through the pipe wall. Figure 10 indicates why. It is clear from the temperature surfaces that the pipe solidifies inwards from the internal and external surfaces. Whilst a BFW practitioner is

likely to be aware of this, his only evidence of solidification will be a view of the state of the pipe surface. Moving the jointed pipes too soon could impair the joint (out of sight). Further, even if temperatures at internal points of the joint could readily be monitored on site, misleading conclusions might still easily be reached. Referring back to Fig 6, it is quite clear that the temperature has effectively reached the value U, while there is still some 2 mm of melt remaining. This phenomenon occurs because heat is lost more rapidly at the pipe interface than it can be replaced by con- duction. This gives rise to an internal “hot spot” of molten polymer (see Fig. 12) and would be extremely difficult to determine from measured observations. Again, the model provides essential information for improving the probability of making “good” joints.

CONCLUSIONS

An easily programmable numerical scheme has been developed, based on a flexible enthalpy model,

3080 A. S. WOOD

0.0 0.0 0.5 1.0

Heat Soak

1.0

20.0

0.5------- - 100.0 -i

o..

0.0 0.5 1.0 Heat Soak

L

0.5--- 90.0

- 150.0 - _pp--q--

0.0-j

Dwell Stage

0.5-- 90.0 -_ / -_

Cc

130.0 . /- N.

0.0 , ( , , , , , , ,

0.0 0.5 1.0 Dwell Stage

0.0 0.0 0.5 1.0

Solidification

*_, _” .,-, 1 r ,.,.,.. “.,. , , , I _ ,

0.0 0.5 Solidification

Fig. 10. Temperature surfaces, on the normal&d solution region, at the end of soak, dwell and total’ solidification (a) for a pipe of size T, * = 125 mm (SDR = 17) and (b) for a pipe of size r: = 500 mm

(SDR = 10).

2j10 242 I

214 Time (s)

Fig. 1 I. Predicted interface temperature at the mid-wall point and pipe surfaces during the dwell stage.

for describing the transient heatjfow in the butt-fusion welding process and it has been shown to yield sensible results for the evolving temperature surface in the pipes, validated against experimental data and ABAQUS simulations. Further, its use as a predictive tool (for determining both optimum and undesirable process conditions) has been indicated. It is particularly useful in detecting situations in which action

might be taken by practitioners which may damage the joint (such as moving the fused pipes before total solidification). The ideas presented in this paper have been combined with a squeeze film lubrication model (Benkreira et al., 1991a) of the bead-up pipe deformation for estimating the bead size and pipe movement. The resulting software package based on these works runs on a PC.


Dwell Stage

901 , , , , , , , , , , 0.0 0.5 1.0 l.S 2.0 25 3.0 35 4.0 45 *

Distance (mm)

Fig. 12. Internal “hot spot” of molten polymer.

Acknowledgemenrs-Financial support and in-kind contri- butions from the following companies are gratefully acknow- ledged: British Gas, Glynwed Plastics, Wavin, Stewarts & Lloyds, BP, Welding Institute. Water Research Council, Fusion Plastics, Uponor Aldyl, FINA. The author would also like to thank Andrew Day, Haj Benkreira and Nouri Dib for useful discussions about this work.

; h K L

n, n, Q r r* t*, t V z z*

NOTATION

specific heat capacity, JjkgK liquid+olid interface (melt front) surface heat transfer coefficient, W/m2 K thermal conductivity, W/m K latent heat of fusion, J/kg number of radial elements number of axial elements enthalpy, J/m3 dimensionless radial coordinate radial coordinate, m time, s temperature, “C dimensionless axial coordinate axial coordinate, m

Greek letters a scaling factor (see text) Yr parameter [ = 2 Ar(r: - rr)h] Yz parameter [ = 2 Az(r$ - r(*)h] Ar dimensionless radial mesh size At time Step AZ dimensionless axial mesh size

8 V” P

parameter [ = r:/(r: - rr )] normal melt front speed, m/s density, kg/m3

Superscript m time step index

Subscripts 0 initial pipe value a ambient (air) b bead-up stage d dwell stage e external pipe surface i internal pipe surface i, j finite difference nodal indices m melting (or fusion) P hot plate R reference value s heat soak stage

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The Butt-fusion welding of polymers