James L. Throne
Sherwood Technologies, Inc.
Dunedin FL 34698-3347


This work focuses on the interface between a semi-solid polymer and a non-polymeric surface. More to the point, it focuses on the interface between polymer and non-polymer when one or both are in motion. And to a further point, it focuses on the interfacial resistance between the two – in short, sliding friction. Like Gaul, the work is divided into three parts. The first part discusses sliding friction experiments. The second part is concerned with the question: What is sliding on what? And the third part focuses on the various types of interfacial interaction that might be found when plugs contact hot plastic sheet.


Why is sliding friction important? Ready for some ancient 1900-1903 history?

There is no other element in connection with lubrication that has received so much consideration as that of the coefficient of friction, and yet there is no other that is in so indeterminable a state. (1)

Consider this more modern quotation from Rauwendaal (2), discussing the feed section dynamics in extrusion:

Because of the inherent non-isothermal nature of the solids conveying process (in extrusion), accurate prediction of the actual solids conveying process becomes quite difficult. Not because the mathematics are so complicated – they are relatively straightforward – but because the coefficient of friction should be known as a function of temperature and pressure. This information is generally not available.

In thermoforming, there are two areas where polymer-non-polymer sliding friction is important. The first is between the plastic sheet and the plug assist. Consider this from a CMT Materials 2001 publication:

In an effort to better predict polymer response in the thermoforming plug assist process, CMT Materials has initiated an investigation into plug assist and polymer interactions. Initially a detailed scope of work for the coefficient of friction between polymer and plug assist has been generated and work has progressed.

We’ll revisit this later. A second area is the frictional characteristics between the polymer sheet and the mold wall. Consider this from Throne (3):

In certain mold designs, the sheet must not stick against the (mold) surface. Olefins tend to alternately slip and stick when vacuum formed. This causes visible ridges on the part surface. Roughening the mold surface does little to prevent sliding and may aggravate the problem. A better alternative is to treat the surface with a high frictional coefficient substance.

Thus, there is ample justification for examining polymer-non-polymer sliding friction. In this part of the treatise, we focus on the interaction between a solid plug or pusher and the hot plastic sheet.

The Problem

So why don’t we just go out and measure the coefficient of friction? I mean, after all, we learned in high school physics that the sliding force, F, is directly proportional to the normal applied load, N: F = μN, where μ is the sliding coefficient of friction, right? And recall the very simple experiment of placing a weight on a flat surface and tilting the surface until the block began to slide [Figure 1].

Sliding Block Experiment

Figure 1. The Classical Sliding Block Exeriment

The problem is that, for even well defined material interfaces, frictional coefficients are very difficult to accurately measure. Consider this 1903 viewpoint:

While the coefficient of friction must always be taken into consideration when designing and constructing machinery, it is not always practicable to calculate it with any degree of accuracy, [and] in fact it can only be determined absolutely by experiment. (4)

The study of friction is encompassed in tribology, a study of friction, lubrication, and wear. According to Persson (5), the subject is approached through both the nanoscale response – what is going on on a molecular or macromolecular level at the tips of the asperities of the interacting solids [Figure 2] – and the macroscale response – what is sliding resistance as a function of applied load and temperatures of the interacting solids. Coulomb, one of the giants of frictional technology, identified the following factors that affect frictional resistance:

  • The extent of the surface area (not the visual area, but the contact area)
  • The nature of the materials in contact
  • The surface coating on either or both of these surfaces
  • The force applied normal to the surface
  • The time the two surfaces have been in contact with each other
  • Environmental factors such as temperature, air pressure between the surfaces, and for some materials, humidity

Concept of Asperities

Figure 2. The Concept of Asperities

For many solid materials, the general effect is one of mechanical abrasion or wearing away of the asperities over moderate to extended periods of time [Figure 3]. This wearing away is of course counteracted by introducing a lubricant (thus the tribological triumvirate). According to Persson, this subject has been of major interest for centuries and it appears that both engineers and physicists are nearing the time when they can “get their arms around” the subject, as it were.

Not so with polymers. Although Persson discusses polymers at some length, it appears that the problem offers a greater challenge than the ones he outlines. And so to the discussion in this treatise.

Erosion of Asperities

Figure 3. The Erosion of Asperities

What’s So Difficult Here?

Consider pristine polymer and metal interfaces. For the moment, consider the metal surface to have no surface oxidation or lubrication, either intentional or deliberate. Consider the polymer to have no surface coating, such as blooming agent, external lubricant or antiblocking agent. Again, pristine surfaces. If the two surfaces are microscopically planar and the two surfaces are mated in such a fashion to eliminate all air pockets, it would be impossible to slide one surface against the other. So the frictional coefficient would be unity (on a scale from zero to one).

But, the latter condition is not real world. As Persson points out, asperities exist even on a nanoscale (and usually on a much greater scale). Coulomb envisioned rough surfaces as having regular, interlocking asperities, much like two pieces of peeled-back cardboard. When the two surfaces are slid, the asperities must ride up and over one another. The upward motion offers resistance in addition to the applied normal force. So his model assumes a slip-stick or jog-stop motion. However, you can show that the jog-stop action would yield a sliding force (in the surface direction) that would increase with increasing sliding velocity. But, wait! It appears that frictional coefficients are in fact independent of the sliding velocity. So, this model doesn’t work, at least not for polymerics.

So, What Is Happening?

Consider first polymers that do not yield. At any temperature. Instead, they simply elongate to break. Brittle polymers, if you wish. We can all agree that the moduli of polymers – all polymers – are substantially below the moduli of metals such as aluminum or steel. Now consider our two pristine but not molecularly smooth surfaces. Surfaces with asperities. The asperities either touch – asperity tip to asperity tip – or nest – asperity tip between asperity tips. (As we’ll see in a moment, it really doesn’t make a difference which case we consider.) Now we apply a suitable normal force, and then apply sliding force. Immediately, instantaneously some of the polymer asperities are going to be broken off by the higher modulus metal ones. Detritus! If we continue to apply sliding force, more and more polymer asperities are broken. We are in effect smoothing the plastic surface by drawing it against a metal “micro-rasp”! Depending on the roughness of the metal surface, we would anticipate needing to move the plastic only a few microinches before the resistance to sliding decreases.

Aha, you say! The only thing you’ve done is overcome static friction! Okay, we can test that theory. We know for example that static frictional coefficients are always greater than sliding frictional coefficients. If we slide metal-to-metal (say P13 steel to P13 steel), we observe this. But we also observe that the static frictional coefficient is essentially the same, regardless of how many times we stop and start the sliding test! Not so with plastics! The first resistance of the pristine surface is always greater than the second, or third, or for that matter, the nth. Why? Because we’ve deliberately smoothed the plastic surface. Fewer asperities, shorter asperities, lower resistance to initial force, lower resistance to sliding force.

Now remember, we’re assuming that the plastic is brittle. In other words, the little plastic bumps are sheared off by the metal bumps. How can we verify this hypothesis? Well, we take two pristine but matte surfaces and carefully SEM (scanning electron microphotograph) the surfaces. Then we mate them, apply normal force, and slide one against the other for a short distance. We carefully separate the two surfaces and SEM them once again. We should see less plastic asperities and we may see “plow” lines in the plastic from the metal surface. If we’re really careful, we should see “polymer dust” on the metal surface.

Is That Really Important?

That, in and of itself, is really not very exciting. What it does indicate, however, is that the polymer surface is very quickly abraded by the metal surface. The next portion of the exercise is important, however. Recall that we assumed that the polymer failed brittlely. What would happen if the polymer yielded instead? Suppose the polymer was a polyolefin? Or an elastomer? Or even a brittle polymer above its glass transition temperature, where it is rubbery? Note in Figure 4 that friction is maximum and wear is minimum at the polymer glass transition temperature.

Temperature-Dependent Friction and Wear

Figure 4. Temperature-Dependent Friction and Wear

Consider one scenario. Suppose we had the same conditions as in the brittle example, but instead of fracturing, the polymer simply yielded. So instead of seeing detritus “dust”, we should expect to see the polymer surface with microfibrils, the manifestation of localized drawing. Do we see them? Dunno. Haven’t done the test. We’re just hypothesizing right now.

Remember that we’re still thinking “semi-solidly” here. If we were to tear asperities from the sheet, we should see these not as chips but as microballs. Why? Because the polymer asperity should attempt to recover to a sphere as soon as the shearing force is released.

Now let’s bump up the temperature or increase the applied force. The first thing we notice is that the amount of force needed to begin the slide is much greater. Why? Because the softer plastic has been pressed or deformed into and around the metal surface irregularities, thereby yielding greater surface area contact. (Think adhesive!) Does this mean the frictional mechanism has changed? If this were the only thing that happened, probably not. But something else may happen and probably does happen. As the asperities distort, they may melt locally (or at least become very soft). And instead of forming microballs or microfibrils, the plastic may simply adhere to the metal surface. (Think adhesive again!)

Is this bad? Yes! Decidedly so. Because now not only has the plastic surface morphology been changed but so has the nonplastic surface. And now instead of polymer interfacing with non-polymer, we have a polymer-mostly polymer interface. Of course, the rougher the non-polymer surface is, the less general effect polymer separation and adhesion will have. At least in the beginning of the slide.

What About Long-term Effects?

Consider now a long-term slide. Picture two disks, one of plastic and one of nonplastic, brought together under fixed normal stress and rotated for a substantial length of time. The only appropriate measure of the sliding frictional resistance would be torque. (If there’s a concern that the outer portion of the disks see greater velocity and longer contact time than the inner portion, replace the disks with rings and redo the tests.) After the initial overcoming of the static friction, we should see the resistance to applied load decrease, perhaps quite rapidly, to a constant value (assuming of course that the sliding friction is not converted to heat, which would further soften the plastic). So, now we have the true coefficient of sliding friction, right? No, we have a frictional coefficient that relates the now-smoother polymer to the perhaps polymer-coated non-polymer surface.

But isn’t that what we want? I mean, after all, a plug on a thermoformer is in contact with the plastic sheet many, many times over a relatively short time. And certainly if there is a transfer of polymer to the non-polymer surface, the long-term frictional coefficient is really more representative of reality than the first values obtained from pristine surfaces, right?

This is right to a point, of course. But as I pointed out earlier, we need to establish first principles. What is the value under pristine conditions? Then we can experiment with all the vagaries of the process ? mechanical vagaries such as variation in temperature, variation in applied load, sliding speed, and polymer variations such as initial sheet smoothness, morphological characteristics of the first few microns of the sheet surface, and any non-polymer stuff that might be exuded or diffused from the polymer to the interface. More important than just establishing first principles is the development of a device that will yield reproducible results, not just on the same polymer-non-polymer combination in our lab, but in other labs across the country.

So What Kind of Device Do We Need?

Now consider most friction coefficient measuring systems. Very early on, Tabor invented an “abrasor” [ASTM D1044], which slides a weighted rotating abrasive wheel against a stationary plastic surface. After a fixed number of revolutions, the plastic is weighed to determine the weight loss due to abrasion. Other frictional devices are found in Progelhof and Throne (6). Insofar as I can tell, the Tabor Abraser and other sliding or rolling friction tests are not sensitive enough or versatile enough to accurately determine sliding frictional coefficients.

It is certain that any device needs a method of applying a normal stress to the two surfaces. And the device needs a very accurate way of measuring the sliding force. And of course, temperature (and perhaps pressure) must be controlled very carefully. But we need more than the mechanical device. We need to carefully examine both the polymer and non-polymer surfaces, using ESCA and SEM and maybe FTIR (scrapings or dissolutions from the non-polymer surface, perhaps). Most of the friction coefficient measuring systems use gross rotating or sliding devices. However, since the effect we are seeking should manifest itself at very small sliding distances, a device having one oscillating plate and one stationary plate, where the extent of oscillations is in milliinches, is more appropriate. The device, therefore, is quite small, allowing the entire assembly to be mounted on a hot plate or in a temperature-controlled environment. Bartenev and Lavrentev (7) demonstrate a strong correlation between sliding velocity-dependent frictional force and frequency-dependent loss tangent. This supports the theory that an oscillatory device should serve the need here.

What Does the Device Look Like?

Sliding Device Concept

Figure 5. A Sliding Device Concept

Figure 5 is a schematic of one type of sliding device. A is the plug material. B is the sheet supported on a hot plate. P is the applied load. Two experiments were done:

Experiment 1

  • E&C Syntactic Foam, sanded w/180 grit, blown with oil-free air
  • Normal stress= 3 lb/in2
  • Hot plate temp setting = 162+/-2oF
  • 0.120 inch black GP-PS sheet
  • Block held on sheet 10 s, moved 10 cm in 10 sec, then removed and cooled 15 s
  • Force measured once block moved
  • Concluded after 10 contacts

Experiment #2

  • E&C Syntactic Foam, sanded w/180 grit, blown with oil-free air
  • Normal stress= 3 lb/in2
  • Hot plate temp setting = 162+/-2oF
  • 0.120 inch black GP-PS sheet
  • Block immediately moved 10 cm in 10 s, then removed and cooled 15 s
  • Force measured once block moved
  • Concluded after 40 contacts

The sheet and heater temperatures were fixed, as was the sliding and contact time protocols. Measurements were made of the sliding force, being the force measured once the block began to slide, and the block temperature after sliding was complete. After each contact was completed, the block was moved to a new position on the sheet. The measured sliding forces for these two experiments are shown below in Figure 6.

Sliding Force Experiment

Figure 6. Sliding Force Experiment

The measured syntactic foam temperatures are shown below in Figure 7.

Measured Syntactic Foam Block Temperatures

Figure 7. Measured Syntactic Foam Block Temperatures

A scatter diagram of the sliding force dependency on block temperature is shown below in Figure 8.

Relationship Between Sliding Force and Syntactic Block Temperature

Figure 8. Relationship Between Sliding Force and Syntactic Block Temperature

Other research efforts indicate that the coefficient of friction increases with increasing sheet temperature (8,9). In our experiments, the sliding force decreases with increasing block temperature at constant sheet temperature.

So, why should our results differ? They may not differ but there are experimental differences. First, we kept the sheet temperature constant. Second, we moved the foam block to a new position on the sheet after each sliding contact. Third, we are comparing the sliding force against block temperature, not sheet temperature.

Having said that, Figure 5 in Ref. 9 shows a decrease in frictional coefficient with increasing sheet temperature. According to the authors of that paper:

[m]easuring at higher temperatures (above 130oC or 266oF) yields just the dynamic coefficient. Here most probably a pure shear of the polymer (HIPS) and a total stick between the polymer and the plug (HYTAC B1X from CMT) occurs. Indication for pure shear is also indicated by the decreasing value for the coefficient with further increase in temperature. This may be linked to the lower viscosity of polystyrene at higher temperatures.

And in Ref. 8, the researchers found that “as the temperatures of the plug and sheet increase, the peak force decreases.” So, while we’re measuring different things, there does seem to be a sense of agreement that at forming temperatures, there may be increased lubrication occurring at the interface between the plug and the sheet. The nature of the lubrication will be discussed in Part 3 of this report.


  1. Mr. Hall, Car Lubrication, ca. 1900 – cited in W.M. Davis, Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903. [The “car” referred to here is a rail car!]
  2. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich, 1986, p. 246.
  3. J.L. Throne, Technology of Thermoforming, Hanser/Gardner Publishers, Cincinnati, 1996, p. 434
  4. 4.W.M. Davis, Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.
  5. Bo N.J. Persson, Sliding Friction: Physical Principles and Applications, 2nd Ed., Springer-Verlag, Berlin, 2000.
  6. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser/Gardner Publications, Inc., Cincinnati, 1993, pp. 666-679.
  7. G.M. Bartenev and V.V. Lavrentev, Friction and Wear of Polymers, Elsevier, New York, 1981.
  8. B. Hegemann, P. Eyerer, N. Tessier, and T. Bush, “Various Plug Assist Materials and Their Effect on the Thermoforming Characteristics of Polymer Sheet,” Thermoforming Quarterly, 21:4, 2002, pp. 12-16.
  9. B. Hegemann, P. Eyerer, N. Tessier, K. Kouba, and T. Bush, “Polymer-Polymeric Friction at Temperatures and Rates Simulating the Thermoforming Process,” Thermoforming Quarterly, 22:1, 2003, pp. 10-13.

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