What really happens - current theories for welding plastics

TWI Bulletin, May - June 1997

Roger Wise joined TWI in 1986, and spent four years in the Electron Beam group before starting work on polymer welding. He is currently a member of TWI's New Technology Unit, working on novel materials joining solutions.

Thermoplastics are used today more than ever before in a wide range of applications from packaging to gas pipes and medical products. The technology of welding thermoplastics has been known for at least fifty years but the science underlying this technology is much less well known.

Roger Wise describes how a TWI collaboration with Cambridge University is producing some interesting insights into welding plastics.

How welds form - early theory

Have you ever wondered how two pieces of plastic can be made to weld together? This was the question puzzling researchers in the 1950s who realised that the answer would provide the key to many industrial processes. They decided to study welding rubber in some detail to see if this could shed light on the more general case of welding any polymer. The advantage to studying rubber was that no additional heat is required to cause a weld to form. In fact, gentle pressure between two pieces of uncrosslinked rubber is enough to cause them to stick together (this is called 'tack').

Fig. 1: Contact temperature against autohesion, Au, for polyisobutylene. ^[2]

There were two research groups looking at welds in rubber, one in Europe ^[1] and the other in Russia ^[2] . They soon showed that the strength of the joint is related to joining temperature (Fig. 1), welding time and welding pressure. The interpretation of these results by the Russian researcher Voyutskii was that weld strength was due to the diffusion of polymer chains across the interface. This was an intuitive interpretation, but Voyutskii developed a pictorial view of the process (Fig. 2) and with the help of colleagues, some mathematics to predict weld strength: ^[3]

Fig. 2: Scheme of coalescence of high polymers. ^[2]

where

t = time of contact before testing.

This rather complicated expression agreed well with experimental results although only for certain polymer types (eg. uncrosslinked rubbers). Voyutskii's theory did not please everyone and there was another school of thought, led by Anand ^[4] , which believed that significant weld strength could be developed by chemical bonds. Anand picked up on the fact that, according to the Russian theory, there should be no weld strength at the instant of contact, whereas experiments showed that this was not true. As is usual in these cases, it is now believed that both sides were right, Anand for his explanation of initial strength and Voyutskii for the concept of weld strength development by interdiffusion.

Recent Theory

The technology of polymer welding was successfully harnessed in the 1950s and 60s for such applications as manufacture of inflatable lifejackets and plastic pipelines without any significant addition to the understanding of the science.

Fig. 3: The chain P is free to move between the fixed obstacles O, but cannot cross any of them

However, in the 1970s a theory describing the way that polymer chains move was developed by de Gennes and others ^[5] . This theory was called reptation (after the Latin reptare - to creep) and was based on the idea of the oscillatory motion of a single polymer chain in a crosslinked polymer gel (Fig. 3). The gel provided a regular pattern of obstacles for the chain which had to wriggle between them.

De Gennes worked out mathematics for how the chain should move including an expression for the diffusion coefficient D for the chains:

where
M = molecular weight of the polymer (a measure of how long the chain is).

When he went on to try to apply this idea to polymer chains in the molten state, de Gennes found that it worked well with a few modifications. He had to use the idea that each chain was imprisoned in a cage whose bars were defined by the positions of other surrounding chains ^[6] .

Fig. 4: Chain segment AB in a polymer. The dots represent other chains which in this drawing are assumed to be perpendicular to the paper. As a result of entanglements the chain is confined to the tube-like region shown by the broken line

This cage defined a tube around the chain as shown in (Fig. 4). De Gennes again calculated that for the chain in the tubular cage, D∞1/M² . This was actually confirmed by measurement by various people using techniques such as nuclear magnetic resonance (NMR) ^[7] . 

This confirmed de Gennes' reptation model as currently the best model for how polymer chains move in the molten state ^[8] .

Reptation theory was then used by Wool in the 1980s to explain how weld strength develops in amorphous thermoplastics, such as polystyrene ^[9] . Wool mainly studied simple welding processes such as heated tool welding or compression moulding, to eliminate complicating factors such as variations in weld temperature and melt flow. Nevertheless, Wool developed a detailed theory for how welds form and checked this against numerous careful experiments. Wool's theory makes the following assumptions:

1. The two polymers being welded are nominally the same material.
2. The two polymers being welded comprise chains having the same length.
3. The polymers are amorphous and weld at one fixed temperature which is above the glass transition temperature.
4. Surface effects are not considered.
5. The surfaces come into intimate contact (called 'wetting') everywhere at the instant they touch.

These conditions are, of course, never encountered in 'real' welding situations such as hot plate welding polethylene pipes for example. In this case, the pure theory cannot be applied because maybe the polymers are polydisperse(chains can have many different lengths), semicrystalline, have complicated surface characteristics, surfaces may not wet instantly, the weld is not isothermal etc.

The Wool theory is, however, very valuable in predicting the main mechanism for weld strength development and chain interdiffusion.

The key step in Wool's model for welding was in trying to imagine how a single chain at the weldline would behave according to reptation theory (Fig. 5). Wool and his student Kim ^[10] developed the concept of the mechanism for the end of a polymer chain at the weldline leaving its tubular cage and diffusing across the weldline (Fig. 6). Wool called these chain ends 'minor chains' and worked out how far they should move into the material on the other side of the weld X as a function of time t.

Fig. 5: Disengagement of a chain from its initial tube near the interface. Only portions of the tube that confine the initial chain are shown

Fig. 5: Disengagement of a chain from its initial tube near the interface. Only portions of the tube that confine the initial chain are shown Fig. 6: The interdiffusion process at a polymer-polymer interface:

a) minor chains

b) minor chains spherical envelopes. Only one side of the interface is shown for convenience and instantaneous wetting at t = 0 is assumed

Wool calculated X∞t^1/4 until the chains left their tubular cage. After this Wool calculated that X∞t^1/2 . Having predicted these relationships, Wool then set about trying to prove them experimentally. He eventually succeeded using secondary ion mass spectrometry ^[11] .

Mechanical Strength

Wool had managed to show how simple welds form using modern theories of how polymer chains move but, unfortunately, this is only half of the full story. Of greatest importance to engineers using polymer welding is an understanding ofhow welds fail. Wool approached this by working on materials which obey the principles of linear elastic fracture mechanics such as polystyrene and polymethylmethacrylate (eg. Perspex). In these cases, Wool realised that when a crackruns through a weld, polymer chains are either pulled out (chain disentanglement) or break (chain scission). The proportion of these failure mechanisms depends on a number of factors including chain length (molecular weight), how farthe chains have interpenetrated and the conditions of the mechanical test (Fig. 7).

Fig. 7: A simplified representation of micromechanisms of failure in a weld in a polydisperse glassy amorphous thermoplastic (failures involving crazing are not represented). All welds made at the same temperature at different weld times t ₁<t ₂<t ₃<t ₄. Weld model verification is simplest at time t ₁ and t ₂.

In simple terms, for short welding times, the minor chains will have penetrated relatively short distances into the entangled chains on the other side of the weld. In this situation the most likely result of a mechanical test is chain disentanglement. Using this idea Wool derived an expression for how the critical stress intensity should vary with weld time and molecular weight .

where t is weld time and M is molecular weight. This expression was obeyed in several tests on real specimens ^{[9] [12]} .

It is interesting to compare Wool's expression (ii) with Voyutskii's (i), where it can be seen that only the time dependency is the same. However, it is important to remember that Wool worked on glassy, amorphous thermoplastics such as polystyrene while Voyutskii worked on semicrystalline rubbers such as polyisoprene.

Wool's ideas on the formation of weld strength in glassy amorphous polymers are now fairly well established. They can be applied to several commercial employed welding techniques as well as compression moulding and the formation of weldlines in injection moulding.

Unfortunately, semicrystalline thermoplastics are most often used in engineering applications and here simple chain scission and disentanglement theories for fracture are not sufficient. The locus of failure or crack may pass through amorphous areas, through crystalline areas and at the boundary between the two. The failure type may also change with factors such as test rate, molecular orientation in the amorphous regions and as a function of ambient temperature for the test. For these reasons it is often very difficult to predict the welding parameters or morphological features which play the dominant role in controlling mechanical properties of welds in semicrystalline thermoplastics.

Future Challenges

What is now required is an extension to Wool's ideas to allow modelling of weld strength development in all 18 commercially available welding techniques. For convenience these techniques have been classified into three groups by heating method:

Friction Heating Techniques

• vibration welding
• spin welding
• ultrasonic welding
• orbital welding

• hot plate welding
• hot bar welding
• impulse welding
• hot gas welding
• extrusion welding
• bead and crevice free (BCF) welding
• solvent welding

• resistive implant welding
• induction welding
• electromagnetic (EMA) welding
• dielectric welding
• microwave welding
• infra red welding
• laser welding

A description of these techniques is given in the literature ^[13] .

Several factors must be incorporated into current theory before a predictive model for welding thermoplastics can be produced.

A simplified representation of how the necessary conceptual bridges could be built is shown in Fig. 8. These factors include polydispersity, crystallinity, additives and fillers, surface effects, non isothermal welds and melt shear.

TWI is approaching this task via a collaboration with Cambridge University which will develop a computer based simulation using the Monte Carlo technique. The aim is to be able to include the following factors in the simulation : polydispersity, additives and fillers, surface effects, non isothermal welds and melt orientation. This model should be able to simulate many of the 18 welding processes as well as the development of strength at weldlines in injection mouldings.

Fig. 9: Monte Carlo simulation of molten polymer chains at the 'meso' scale at:

a) initial contact and

b) some time later when chains at the interface have begun to interdiffuse

An example of the model is shown in Fig. 9, where two pieces of molten polymer are represented, corresponding to initial contact and later when chains at the interface have begun to interdiffuse.

It is envisaged that the computer simulation will enable welding engineers to predict the optimum welding conditions for any polymer system (polymer and fillers or additives) without having to carry out time consuming laboratory trials. With sufficient information concerning the polymer system and the physics of the welding process, the software will simulate the chain diffusion process and deliver the chain interpenetration distance as a function of welding parameters. It will however be necessary to carry out a small number of laboratory trials to confirm the solution but the majority of work will be conducted using a computer.

For companies supplying polymers, polymer systems or welding equipment, this should offer a real advantage in many ways. For polymer suppliers, there is the prospect of a greatly enhanced customer support service for applications where mechanical properties of welds or weldlines are important. Similarly for manufacturers of welding equipment, new applications can be simulated using the model. This would eliminate the many lengthy experimental trials required to assess the suitability of a certain technique or welding condition for a particular application.

Of perhaps more strategic importance, the computer model offers the prospect of designing polymers or polymer systems with enhanced weldability. In the field of metallurgy, this is a well known concept involving modification of, for example, a grade of steel by the addition of certain elements to bring about better weldability by microstructural modification.

For polymers this concept is only just being addressed and it is not yet clear which parameters govern weldability. However possibilities include molecular weight distribution, macro molecular architecture (degree of branching etc.) and additives such as plasticisers or fillers. In each case, a polymer system with enhanced weldability will have to be designed such that other marketable qualities, such as mechanical properties, are not compromised. This will form one of the central challenges for this approach.

References