Jim Throne on January 16th, 2003
James L. Throne, Sherwood Technologies, Dunedin Florida 34698
Peter J. Mooney, Plastics Custom Research Services, Advance North Carolina 27006


Thermoforming is the process of heating and shaping plastic sheet into rigid containers, components of final assemblies, and stand-alone end-use parts. The value of all thermoformed parts produced in North America in 2003 exceeded US$10 billion. Traditionally, about ¾ of all thermoformed products are produced from sheet of 1.5 mm or less in thickness and are primarily rigid disposable packaging products. Most of the rest is produced from sheet of 3 mm or more in thickness and are primarily durable structural goods.

Thermoforming has benefited by its ability to fabricate thin-walled parts having large areas, using relatively inexpensive, single-sided aluminum tooling. Its deficiencies – variable wall thickness, the added cost of sheet and trim regrind, and extensive trimming and additional cost to reprocess the trim – are offset by the ability to economically produce low-volume, thick-walled parts or high-volume thin-walled parts.

The advances in thermoforming technology in the past decade have allowed the industry to grow at a rate that exceeded the growth rate of the plastics industry in general. However, this pattern has changed in the past few years. Newer advances in plastic materials, tooling, forming machinery, and auxiliary equipment are needed to regain earlier growth rate momentum.

This paper considers several emerging technologies such as forming composite sheet materials, surface decoration, and new material development. It also considers the effect of globalization on both thin-gauge and heavy-gauge domestic thermoformers.

“New” Technologies to Advance the Industry

As pontificated in Part I, many extant technologies have not been fully exploited. This section highlights some of those technologies that appear to provide thermoformers with future market advantage.

Forming Composite/Laminated Structures

Heavy-gauge thermoforming has very thoroughly mined the “pretty part” or “easy” applications, where the part is made of unreinforced plastic and is designed to be incorporated into or fastened onto a supporting structure. Formers now need to go beyond their current comfort zones to new materials and processing variants. There are two general types of formed structures – single-layer composite materials that are formed into non-appearance parts, and thermoformed “skins” or “shells” that are thermoformed, then backed with composite materials.

Single-Layer Composites. A military drone structure made of matched-mold glass-reinforced nylon composite was an early commercial application of a non-appearance single-layer structural product. The composite bumper structure for the recent BMW 5 vehicle is another single-layer composite application. The reinforcing medium is usually either woven or non-woven continuous glass mat. In general, matched tooling is required and the sheet must slip or slide into the mold to avoid substantial fiber breakage (1). Furthermore, the force needed to bend the composite into even gentle shapes is usually quite high. As a result, forming presses for such applications are more akin to compression molding presses than conventional thermoforming presses.

Most applications have focused on forming thick composite sheet (2). However, composite sheets having thicknesses less than 1.5 mm (0.060 inches) are now commercially available (3,4). Glass levels are typically 10% to 20% by weight, but they can be less, depending on the applications. The focus will be on structural applications where the parts have large surface areas but they must be thin-walled.

Laminated Structures. The plastics industry has had success commercializing multilayer structures where one of the layers is a high-performance composite and another layer is a cosmetic shell. The best example is found in the sanitaryware industry where spas, shower stalls, and tub surrounds are fabricated of thermoformed ABS sheet that are backed with spray-up chopped fiberglass-reinforced polyester resin (FRP). Automotive innovators such as DeLorean and Bricklin adopted similar techniques in the 1980s to produce exterior car parts. Today some models of the SMART car in Europe boast of laminated parts.

The resurgence of this technology is due in part to automated methods of handling the reinforcing layer. Robots apply the fiberglass- or filler-impregnated resin (often polyurethane) to the formed “skin” residing in the lower half of a matched mold press. Then the press is closed, expressing air and compressing, shaping, and fully reacting the reinforcing layer. Although the automotive industry was apparently the first to adopt this technology, the marine and farm equipment industries are actively pursuing it (5,6).

In-Mold Decoration

In-mold decoration is not a new concept. Paper labels with pressure-sensitive adhesive layers were developed for thin-gauge containers in the 1980s. And rotational molders have been pre-applying heat-activated decoration to mold surfaces for a decade or more. Recently the automotive industry has been considering paint film technology as a way of minimizing the economic cost and environmental hazards of conventional “wet” exterior surface painting (7).

Paint film can be either single-layered or multi-layered. Polycarbonate is the preferred single-layer paint film (8). Multi-layer films are usually structures on the order of 0.5 mm (0.020 inches) in thickness. The film consists of at least a high-gloss, weatherable and durable clear outer layer (e.g., a fluoropolymer), a pigmented color layer, and a supporting substrate (9). This film is laminated to a structural sheet. To maintain surface gloss, the laminated sheet is very carefully heated and formed, usually against a male mold. To prevent color wash, care must be taken to ensure that the film is not stretched. Although there have been a few successful applications, the high current film cost, the concern with reprocessing regrind, and the degree of difficulty forming the part are mitigating against rapid non-automotive market penetration.

Nanofillers and Nanofibers

Nanomaterials are substances having dimensions in the range of 1 to 100 nanometers (0.001 to 0.1 mm). There are at least three general categories of nanoparticles – carbon nanotubes, intercalcated platelet particles of clay, and near-spherical particles of silica. Carbon-based nanotubes and larger-diameter nanofibers are apparently destined for reinforcement of specialty plastics (10). Nanoclays, primarily intercalated montmorillonite clays, are touted for their reinforcing effects at very low weight fractions of 10% by weight or less (11). Nanosilicas are touted for their ability to increase polymer strength and stiffness without dramatically decreasing impact strength, because the particle sizes are below the Griffin crack initiation size (12). Polymer viscosities are not greatly affected even at loadings in excess of 40 wt-%.

It appears that nanoclay-filled polymers offer opportunities in thin-gauge part thermoforming where stiffness is now achieved only with increased thickness. Polyolefins have good chemical and high temperature resistance but they tend to be weak at elevated temperatures. They appear to be prime candidates for nanoclay fillers.

Nanosilicas are being considered for heavy-gauge part forming applications. To date, nanosilicas are best dispersed in prepolymers that are then polymerized. Cast PMMA is one example. Because the filler particles are so small, forming forces should be substantially more modest than those for equivalently loaded glass-fiber reinforced sheet. Improved mechanical strength can lead to substantial reduction in formed part wall thickness in many industrial parts. Moreover, down-gauging usually leads to improved cycle time and lower production cost. And because nanoparticle sizes [about 20 nm] are far below the wavelength of light [400-700 nm], highly filled cast acrylic sheet remains transparent.

Nanofillers are finding early application in low-viscosity thermosetting prepolymers. Although addition to higher-viscosity thermoplastic polymers is being intensely researched today, uniformity in particle dispersion and distribution through the polymer matrix and production cost remain major concerns. Nevertheless, the unique property improvements that might be achieved indicate that the thermoforming industry must continue to monitor this new technology.


In this section, we simply highlight some other technologies that might influence future thermoforming developments.

Porous mold materials. There are now two commercial types of porous mold materials – porous aluminum and porous ceramic. Porous aluminum is best used when vacuum or vent hole mark-offs are not acceptable on the formed parts. Open areas and pore sizes range from 8% and 5 μm (13) to 20% and 100 μm (14,15).

Porous ceramics, used for years as liquid and gas filters and high-temperature diffusion plates, can now be fabricated directly into mold structures. Open areas and pore sizes can be tailored to essentially the same characteristics as porous metal. As with porous metal, the ceramic is mixed with a volatile material such as a polymer. The slip is formed against the pattern and dried. It is then fired to vitrify the ceramic and volatilize the pore-forming material. Shrinkage is about 30% or about the same shrinkage level as porcelain. Although the porous ceramics tend to be fragile, they are usually tough enough to be used for a few hundred parts (16).

Newer Polymers. The earliest polymers – camphorated cellulose nitrate and viscose rayon – were based on biological materials. Today, oil-based polymers dominate the thermoforming material palette. However, biopolymers are finding new interest, particularly in rigid packaging applications where compostability and biodegradability are desired. Polylactic acid or PLA, invented by Wallace Carothers in 1932, patented by Dupont in 1954, and available today primarily from Cargill Dow, is the leading polymer in this area (17,18). PLA processes as a “stiff polystyrene”. Although it is currently more expensive than current packaging materials, its “earth friendliness” often outweighs the additional cost.

Biopolymers based on polyhydroxybutyrate (PHB) may also offer thermoforming opportunities. PHB is reported to be a rather brittle highly crystalline polymer with properties similar to those of polystyrene. When copolymerized with polyhydroxyvalerate (PHV), the polymer degradation rate at elevated temperature is greatly reduced (19). It is thought that these polymers are best suited for medical applications.

Polymers based on norbornene are now commercial (20). These cycloolefins are produced by reacting ethylene or propylene with cyclopentadiene. The polymers are amorphous with glass transition temperatures that can be adjusted from 30oC to 230oC by increasing the norbornene content. Commercial grades have norbornene concentrations of 40 to 60 mol-% and Tgs from 70oC to 170oC. They are FDA food contact-approved and steam-sterilizable. It is reported that cycloolefins process more like PVCs than polyolefins.

Although these materials are not yet major players in thermoforming, there appear to be many future packaging applications.

“Moldless” prototyping. Since the 1930s, heat has been used to produce generous bends in plastics (21). Strip heating was introduced during WWII and again the allowable bends were generous. Cut sheet was fabricated into sharp-edged shapes by gluing. The objective of making sharp bends without excessive gluing has always required accurate machining techniques. Computer-driven three-axis machines are now being used in conjunction with precise bending protocols and exacting gluing procedures to produce very elaborate structures directly from sheet (22). These allow designs to be very quickly reduced to prototypes or even a few functional products.


Thermoforming, being the art and engineering of fabricating functional plastic parts from sheet, is maturing into a viable, competitive technology in packaging and structural parts. The future of thermoforming depends on quickly adapting advances in composites, nanofillers, and other commercialized technologies. The global scene will undoubtedly dictate future business decisions regarding offshore production, consolidation, and diversification.


  1. Throne, J.L., Technology of Thermoforming, Hanser Verlag, Munich, 683 (1996).
  2. Azdel GMTTM, Azdel Inc., 25900 Telegraph Rd., Southfield MI 48034.
  3. PennFibre, 2434 Bristol Rd., Bensalem PA, 19020.
  4. VeriflexTM thermoset polymer, CRG Industries, 2750 Indian Ripple Rd., Dayton OH, 45440.
  5. DKI Form a.s., Rundforbivej 281, DK-2850 Naerum, Denmark.
  6. VEC LLC (formerly Virtual Engineered Composites Technology division of Genmar Holdings), 639 Keystone Rd., Greenville PA, 16125.
  7. Hilgendorf, J.S., “Automotive Exteriors – Evolving to No-Spray Paint?” Plastics Engineering, 60:9, 34, 37 (Sep 2004).
  8. LexanTM SLX polycarbonate, GE Advanced Materials, Southfield MI.
  9. Spain, P.L., et al, “Dry Paint Transfer-laminated Body Panels Having Deep-Draw High DOI Automotive Paint Coat,” U.S. Patent 5,916,643, assigned to Avery Dennison Corp., (29 Jun 1999).
  10. The NanotubeSite lists dozens of universities and research laboratories active in C60 carbon-based nanotubes (and other geometries). Insofar as can be determined, none of these sites provide applications. The NASA nanotube site index has “applications” as a topic, but the location is blank. One major university active in this area is Inorganic Chemistry Laboratory, University of Oxford, South Parks Rd., Oxford OX1 3QR, UK.
  11. Nanocor, 1500 W. Shure Dr., Arlington Hts., IL 60004.
  12. Hanse Chemie AG, Charlottenburger Str. 9, 21502 Geesthacht, Germany.
  13. MetaporTM and EsporTM, Portec, Ltd., Barbara-Reinhart-Str. 22, P.O. Box 3139, CH 8404, Winterthur, Switzerland.
  14. Pyramid Technologies, Inc., 467 Forrest Park Circle, Franklin TN 37064
  15. Porvair Technology, Inc., Clywedog Road South, Wrexham LL13 9KS, North Wales, UK.
  16. Mould D/ATLAS M 130 porous casting system, ALWA GmbH, Roentgenstrasse 1, DE 48599, Gronau, Germany. [Note: The air-permeable casting system will tolerate 90oC mold temperature. Shrinkage in the casting system is about 30%.]
  17. NatureworksTM, Cargill Dow LLC, P.O. Box 5830, MS114, Minneapolis MN 55440-5830
  18. Balkcom, M., B. Welt, and K. Berger, “Notes From the Packaging Laboratory: Polylactic Acid – An Exciting New Packaging Material,” Doc. ABE339, Agricultural and Biological Engineering Dept., Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida, Gainesville FL (Dec. 2002).
  19. PHB and PHB-PHV copolymers available from Goodfellow Corporation, 800 Lancaster Avenue, Berwyn PA 19312-1780.
  20. TopasR COC, Ticona, Div. Celanese AG, 86-90 Morris Ave., Summit, NJ, 07901.
  21. Lockrey, A.J., Plastics in the School and Home Workshop, Governor Publishing Corp., New York City, 74-75 (1937).
  22. Tool-Less Plastic Technologies, LLC, 11208 47th Ave. W., Suite B, Mukilteo WA 98275.
Jim Throne on November 21st, 2002
James L. Throne, Sherwood Technologies, Inc., Dunedin Florida 34698
Peter J. Mooney, Plastics Custom Research Services, Advance North Carolina 27006


Thermoforming is the process of heating and shaping plastic sheet into rigid containers, components of final assemblies, and stand-alone end-use parts. The value of all thermoformed parts produced in North America in 2003 exceeded US$10 billion. Traditionally, about ¾ of all thermoformed products are produced from sheet of 1.5 mm or less in thickness and are primarily rigid disposable packaging products. Most of the rest is produced from sheet of 3 mm or more in thickness and are primarily durable structural goods.

Thermoforming has benefited by its ability to fabricate thin-walled parts having large areas, using relatively inexpensive, single-sided aluminum tooling. Its deficiencies – variable wall thickness, the added cost of sheet and trim regrind, and extensive trimming and additional cost to reprocess the trim – are offset by the ability to economically produce low-volume, thick-walled parts or high-volume thin-walled parts.

The advances in thermoforming technology in the past decade have allowed the industry to grow at a rate that exceeded the growth rate of the plastics industry in general. However, this pattern has changed in the past few years. Newer advances in plastic materials, tooling, forming machinery, and auxiliary equipment are needed to regain earlier growth rate momentum.

This paper considers several emerging technologies such as forming composite sheet materials, surface decoration, and new material development. It also considers the effect of globalization on both thin-gauge and heavy-gauge domestic thermoformers.


The thermoforming process begins with an extruded sheet of plastic. It is heated between infrared heaters to its forming temperature. Then it is stretched over or into a temperature-controlled metal mold. It is held against the mold surface until it is cooled. The formed sheet is then removed from the mold and the formed part is trimmed from the sheet. The trim is then reground and returned to the extruder to be mixed with virgin plastic for extrusion into sheet.

There are two general thermoforming process categories. Sheet 1.5 mm (0.060 inches) or less in thickness is usually delivered to the thermoforming press in rolls. Thin-gauge, roll-fed thermoforming applications are dominated by rigid or semi-rigid disposable packaging products. Sheet 3 mm (0.120 inches) or more in thickness is usually delivered to the forming press cut close to final dimensions and stacked on pallets. Heavy- or thick-gauge, cut sheet thermoforming applications are primarily permanent structural components. There is a small but growing medium-gauge market that forms sheet 1.5 mm to 3 mm in thickness. Thermoformed parts are as small as thimbles with wall thicknesses less than 0.015 mm (0.0006 inches) or as large as swimming pools with wall thicknesses greater than 25 mm (1 inch).

The North American thermoforming market has traditionally been split into ¾ thin-gauge products and ¼ heavy-gauge products. There are about 150 thin-gauge thermoformers in North America. Sixty percent form proprietary products, 30% are custom formers, and 10% are OEMs with in-house forming capability. There are about a dozen thin-gauge formers having annual sales of US$100 million or more. The largest, Pactiv Corporation of Lake Forest, IL, has annual sales in excess of US$1,000 million.

There are about 250 heavy-gauge formers in North America. Nearly all are custom formers. Only a handful of heavy-gauge formers have annual sales of more than US$100 million. In 2003, the largest, Wilbert Plastic Services of St. Paul, MN, had annual sales of about US$140 million.

Historically, thermoforming is one of the oldest plastics processes (1). Baby rattles and teething rings were formed of camphorated cellulose nitrate or pyroxylinTM in the 1890s (2). The industry did not grow substantially until the 1930s when the development of cellulose acetate and acrylic provided the industry with formable sheet. The earliest roll-fed thermoforming machines were developed in the late 1930s in Europe (3). Throughout WWII, heavy-gauge forming depended on convection oven heating of the sheet and hand draping of the sheet over male or positive molds (4,5). Shuttle presses were developed in the late 1940s, and rotary machines followed in the late 1950s and early 1960s.

Growth Dynamic for the Industry

For many years, the growth rate of the industry exceeded the growth rate of the plastics industry, in general. The forming industry grew at about 8.5% to 9% annually through the 1970s. From 1984 to 2000, the heavy-gauge growth rate was in excess of 5% annually, but by the second half of the 1990s, the thin-gauge packaging business had slowed to about 3.4% annually (6). From 2000 to 2003, the overall industry growth rate dropped to zero. The forecast for the coming years for both thin-gauge and heavy-gauge forming is a growth rate below that of the plastics industry, in general (7). A maturing industry and the effects of globalization are the primary forces behind this decrease in its growth rate.

Maturation of the Industry

It is our observation that the thermoforming industry is moving into its mature stage. In the last half-century, the industry has evolved from toaster-wire heaters, using sag as a measure of formability, wooden molds, and hand trimming, to energy-efficient heaters, sheet temperature monitoring, temperature-controlled molds, and advanced trimming machines. Because of this evolution, one wag has said, “We’ve formed all the easy, pretty parts.”

Market penetration requires ratcheting up the technical level. But it also increases piece-part costs and invites competition. Injection molders, for example, for some time have been molding plastics with superior mechanical strength to compete with structural thermoformed parts, and they are now bidding for low-volume parts to just cover their variable costs. They are once again investing in large-platen, high-tonnage presses to challenge heavy-gauge formers. Rotational and blow molders are strongly resisting inroads by twin-sheet thermoformers into hollow part production (8). Yet, as we note below, new thermoforming techniques may help counter these infringements.


Over the last half-century, the three North American economies have been truly transformed by globalization. In the United States, the share of foreign trade in our gross national product has risen from roughly 5% a half-century ago to over 10% today. The opportunities for expanding production through exports have increased. At the same time, consumer choice has been enhanced through imports (9).

Although some domestic industries have benefited from globalization, the overall domestic plastics industry has suffered. Injection molders, in particular, have endured a continuing decrease in their markets as many domestic OEMs have either relocated their manufacturing operations to Asia and other regions of the world or have outsourced the production of parts – in some cases, entire assemblies – to foreign countries with comparative advantages in the form of low-cost labor. Injection molders are particularly susceptible to this trend because their mode of production has become standardized and automated, and their output is typically small in physical size and economical to transport in container ships.

Thin-gauge part formers have already been impacted by this trend to globalization as parts produced offshore are usually also packaged offshore. Heavy-gauge formers are just now beginning to feel the globalization effects. The major barrier that Asian heavy-gauge part formers faced in the past was poor quality sheet. This is now beginning to change. To meet the inevitable growing challenge of foreign competition, the domestic heavy-gauge part formers must be relentless in reviewing their entire operation to increase overall efficiency. And they need to explore export opportunities, which have traditionally been a small fraction of their customer base.

A Caveat on Newer Advances in Thermoforming

In Table 1, we list several recent advances of importance to formed sheet fabrication. However, we must keep in mind that thermoformers tend to be very pragmatic regarding new concepts. In many cases, formers are aware of these technologies, but they will only adopt them when the customer is willing to pay for the time and effort needed to learn how to use them. Technologies such as twin-sheet forming, multi-axis trimming of heavy-gauge parts, formable PP, and syntactic foam for pre-stretching thin-gauge parts were tested and available for years before thermoformers chose to employ them. Interestingly, once thermoformers learn the value of these technologies, they quickly embrace them.

Technologies Available by 1980 But Adopted Much Later by Thermoformers

Table 1

Tungsten-wire halogen heater (late 1800s)
Nichrome wire in quartz glass heater (1930s)
Low-pressure natural gas or propane heater (1800s)
Electric platen drive (1960s, injection molding)
Enclosed oven heating (1970s, Japan)
Twin-sheet forming (late 1800s)
Pressure forming (late 1800s)
Computer models for predicting heating rates (1970s)
Polypropylene for thin-gauge forming (1970s)
Oil-less bearing surfaces (1960s)
Localized matched-tool forming or “coining” (1970s, injection molding)
Syntactic foam (1970s)
In-mold labeling (1970s)
Infrared temperature measurement (1970s)
Scrapless thermoforming (Dow STP, 1970s)
Multi-axis trimming (3-axis,1930s metalworking; 5-axis,1950s woodworking)
Computer-driven machining (1960s, metalworking)
Machining and bending for assembly (1940s, hobbyists)
Computer-aided distortion printing (1970s, Hollywood morphing)
Mathematical wall thickness prediction (1970s, Fukase, blow molding)

Is Thermoforming Evolving?

Nearly a decade ago, one of us (PJM) conducted the first extended survey of North American industrial thermoforming (10). At that time, he noted that most of the companies interviewed had little or no interest in the latest thermoforming technologies. In the forward to this report, the other of us (JLT) noted that many of these same companies had recently invested heavily in pressure forming, CNC trimmers, syntactic foam plugs, epoxy foam prototype tools, extensive sheet drying equipment, ceramic, quartz, and/or natural gas heaters, and in-house vacuum and pressure systems. Many of these techniques were experimental or not fully developed only a decade earlier. So, despite thermoformers’ claims that they have no interest in the latest innovations, they do ultimately adopt them. This year he (PJM) conducted a follow-up survey of these processors (7) and once again, he concluded that this attitude toward new technological advances still prevails.

So, what new developments should formers be adopting in the days and years ahead? Table 2 lists many technologies that have been around for a while but have not yet become part of the thermoformers’ lexicon. Some of these will become economically important in the next few years.

Technologies Known Since 1980 But in Limited Use Now

Table 2

Small-particle fillers (including nanofillers)
Biodegradable and compostable polymers
In-mold decorating
Secondary reinforcement of formed part
Water jet cutting
Short, long, and continuous glass fiber-reinforced sheet
Coordinate measurement uses (other than QC)
Porous metal and porous ceramic mold materials
Formable high-performance sheet applications
Antistatic and static-dissipative sheet applications
Surface venting – poppet valve
Thin-gauge, in-mold, trim-in-place forming
High-density foam sheet
Thin-gauge wheel forming
Linear motor multi-axis trimming devices


  1. Throne, J.L., “Thermoforming: From Baby Rattles to Bed Springs and Beyond,” 60th SPE ANTEC, San Francisco, SPE Tech. Papers, 47, 4089-4095, (2002).
  2. DuBois, J.H., Plastics History U.S.A., Cahners Books, Boston, 44-45 (1972).
  3. DuBois, J.H., Plastics History U.S.A., Cahners Books, Boston, 248-249 (1972).
  4. Anon., 1941 Modern Plastics Catalog, Breskin Publishing Corp., New York, 52 and 180 (1940).
  5. Anon., 1943 Modern Plastics Catalog, Plastics Catalogue Corp., Chicago, 130, 395, 508-516, and 524-528 (1942).
  6. Mooney, P.J., “Understanding the Thermoformed Packaging Business,” Plastics Custom Research Services, Advance NC (May 2002).
  7. Mooney, P.J., “The Industrial Thermoforming Business: Review and Outlook,” Plastics Custom Research Services, Advance NC (Nov. 2004).
  8. Beall, G.L., and J.L. Throne, Hollow Plastic Parts: Design and Manufacture, Hanser Publishers, Munich (2004).
  9. Mooney, P.J., “It’s the Economy, Stupid!” Plastics News, 6, 23 (15 Nov 2004).
  10. Mooney, P.J., “An Analysis of the North American Industrial Thermoforming Business,” Plastics Custom Research Services, Advance NC (Sep. 1995).


In Part 1 of this treatise, I discussed some of the background thinking on solids sliding on polymeric surfaces. I identified friction as part of the tribological triumvirate of friction, lubrication, and wear. I reviewed the various methods for measuring frictional coefficients and concluded that for plug-polymer sheet interaction, the extent of sliding is very small. So I conducted a simple experiment using a linear motor that pulled a weighted sled very slowly across the hot PS sheet. The contact surface of the sled was syntactic foam. It showed that, at constant sheet temperature, the towing force decreased with increasing plug temperature.

In Part 2, I examined the force required to stretch a natural rubber sheet using a hemispherical plug. I changed the surface condition of the plug from very rough to very smooth and found very little difference in the force-penetration curves. I found an interesting anomaly when I deliberately coated the plug surface with a lubricant. There was little difference between the oil-coated plug force-deflection curve and the dry plug force-deflection curve. But there was measurable difference between the water-base coated plug force-deflection curve and the dry plug force-deflection curve. The possible reason for this is discussed in this part.

I still have not fully addressed the question: What is sliding on what? Or perhaps, more pertinently now: Is anything sliding on anything?

Previous Researchers’ Data

I noted in Part 2 that it appeared from my simple rubber sheet experiments, the sheet did not stretch once it contacted the plug surface. In my opinion, it appeared that the sheet simply adheres to the plug surface. In Part 1, I listed several publications of interest to this thesis. Some of the data from Ref. 8 are most interesting and are discussed here. In this work, the researchers relate the thickness of HDPE sheet at the tip of a hemispherical plug to sheet and plug temperatures and plug speed into the sheet. I have plotted their data in Fig. 19, below.

Literature Results on Sheet Thickness v. Sheet Temperature

Figure 19. Literature Results on Sheet Thickness v. Sheet Temperature

The blue line represents average sheet tip thickness at the specific sheet temperature and the red line represents the average sheet tip thickness over all sheet temperatures. In my opinion, there is no dramatic change in sheet tip thickness for the set of experiments listed on the figure legend. In essence, this seems to confirm my rubber sheet experiments. Another interesting aspect to these data is the apparent sheet tip thickness insensitivity to plug speed. I’ll discuss this very interesting aspect somewhat later.

So, can we conclude that nothing is sliding on anything? No. Not quite. Remember the water-based v. oil-based data. It is time to review the tribological thing again. We do this by reviewing the concepts of friction and frictional coefficient.

Again, Tell Me the Meaning of the Coefficient of Friction?

The best definition is that given in the 1903 Ref. 4, to wit:

The coefficient of friction is the ratio between the resistance to motion and the perpendicular pressure.

What are the various conditions that might occur between the plug and the sheet?

  • Static frictional conditions, no sliding (coefficient max)
  • Sliding frictional conditions, no static (coefficient zero)
  • Some static, some sliding
  • Slip-stick behavior

First, what are these? And then which of these – if any – are relevant when plastic stretches against plug surface?

Static frictional force is the force needed to initiate sliding. Sliding frictional force is the force needed to move one surface against another in a steady fashion. Static frictional force can often be hundreds of times greater in value than sliding frictional force. It appears from Ref. 9 experiments, that the static coefficient of friction between a syntactic foam plug material and HDPE is about two to three times greater than the sliding coefficient of friction. The ratio for syntactic foam and HIPS may be as high as five times. However, as noted in Part 1, the static frictional coefficient appears to vanish when the HIPS sheet temperature is above the polymer glass transition temperature.

As discussed in Part 1, the key to sliding focuses on the nature of the asperities at the interface between the plastic and the plug. The sliding force is proportional to the normal stress, being the load per unit contact area. The interfacial contact area may increase as the load increases. Or the sheet may creep or flow to a greater extent as the sheet temperature is increased, thus increasing the interfacial contact area. An example of this effect is seen as Figure 21. The red area represents short contact time or low temperature. The yellow is medium contact time or temperature, and the blow represents long contact time or higher temperature.

The Effect of Increased Time or Temperature on Contact Area

Figure 21. The Effect of Increased Time or Temperature on Contact Area

As a result, the sliding friction is usually independent of load.

I already discussed wear. If sliding does occur, wear probably occurs on both the plug and sheet surface. Wear would occur on the plug because it contacts sheet perhaps thousands of times. Although the plug material is brittle when compared with the sheet, after many contacts, we should expect some asperities to be worn from the plug surface. If the sheet is brittle, as it would be if it is below its melt or glass transition temperature, its asperities should also be worn away. The caveats here, however, are 1) the sheet temperature is usually substantially above its transition values when it contacts the plug, and 2) the sheet contacts the plug just one time. So wearing away is probably not a factor in polymer-to-plug siding friction.

So that leaves us with the concept of lubrication, the third of the trilogy.

Is There Lubrication Between the Sheet and the Plug?

Probably the proper question is: “Could there be lubrication?” According to Persson (5), there are two general forms of sliding friction – dry and wet. Dry sliding assumes no lubrication between the surfaces. Now we know that plastics exude small molecules, be they low molecular weight polymers, additives, processing aids, or whatever. And we would expect that these molecules would reside between the plug and the sheet. And we would suspect that these molecules could be transferred from the sheet to the plug. And if that were the case, after many contacts, the plug surface would become coated with these small molecules. If we extrapolate this thought further, we would expect that the sliding frictional coefficient of a well-used plug might be substantially lower than that of a brand-new plug or one that has just been cleaned.

Is There More Than One Type of Wet Lubrication?

Unfortunately, yes. Boundary lubrication and hydraulic or hydrodynamic lubrication. Boundary lubrication is characterized by low sliding velocity, low interfacial viscosity, and high loading levels. Hydrodynamic lubrication is characterized by high sliding velocity, high viscosity, and low loading levels. Boundary lubrication occurs when surfaces are started and stopped. Boundary lubrication sliding resistance is often much higher than hydrodynamic lubrication, as seen in Figure 22.

The Relationship Between Boundary and Hydrodynamic Lubrication

Figure 22. The Relationship Between Boundary and Hydrodynamic Lubrication

If, in fact, sliding is taking place between the plug and the sheet, we should see some effect if we add different lubricants to the interface. Lubricants such as grease and glycerin. For the results shown in Fig. 17, reproduced below, the plug speed was held constant. The force required to stretch the water-base lubed sheet was less than that for the oil-base lubed sheet. And perhaps the glycerin had a higher viscosity than the grease. If so, then the sliding resistance for the water-based lubricant may be hydrodynamic whereas that for the oil-based lubricant may be boundary.

Effect of Lubrication Between Sheet and Plug

Figure 17. Effect of Lubrication Between Sheet and Plug

So What, You Say

Well, here’s what! The dry v. wet and boundary v. hydrodynamic lubrication issues could be quite significant as a plug continues to age and as the polymer character changes. By polymer character, I mean polymer temperature and extent and nature of the additive package. As the data from References 8 and 9 demonstrate, the sliding coefficient of friction increases dramatically as the sheet heats to the forming temperature. Part of this may be due directly to improved adhesion of the sheet with the plug. But part of it may be due to increased release of small molecules that influence the interfacial conditions between the plug and the sheet.

Thickness, Revisited

In Part 2, I presented some data showing that the plane strain theory that relates the applied force directly to the sheet thickness holds for the natural rubber sheet.

But does this hold for real-world plug-assisted thermoforming? It might not. The reason for this is relatively easy to understand. Two effects might happen as the plug – or in reality, any solid object – presses into the hot, thick sheet. The first is compression, forcing the polymer away from the point of applied force and thereby thinning it locally. The second is shear. Shear is the result of differential tension on the sheet from the surface in contact with the plug to that on the free surface opposite the plug. Both effects would serve to reduce the sheet thickness at the point of contact with the plug. Certainly, with thicker sheet, the effect of shear would be more pronounced. And of course, shear implies viscoelastic deformation of the plastic.


As you probably have guessed, I have some serious reservations about the importance of the frictional coefficient in plug-assist thermoforming. Remember the original question: What is sliding on what?

I believe that for the most part, nothing is sliding on anything.

Furthermore, if something is sliding on something else, the sliding effect is limited to region where the sheet initially contacts the plug surface. Once the sheet contacts the plug, there seems to be little additional reason for it to slide. The force-penetration curves and sheet thickness on the plug show little difference between a very rough plug surface and a highly polished, waxed, and powdered surface.

If there is substantial lubrication at the initial contact area, there may be some change in the sliding characteristics. But the nature of the lubrication is apparently quite important.

Interestingly, from other research work, it appears that the speed of the plug does not dramatically alter the stretching characteristics of the sheet. If this effect can be verified with polymers other than HIPS and HDPE, it does not bode well for the hypothesis that the rate of stretching of the sheet must be included in the mathematical models currently in vogue. In simple terms, plug-assist thermoforming may be primarily an elastic process and not a viscoelastic one. At least for thin sheet.


In Part 1, I presented experimental data on sliding of E&C syntactic foam on 0.120-inch black general-purpose polystyrene sheet at a temperature substantially above its glass transition temperature. But I did not address the question: What is sliding against what? In this part, I try to identify the conditions under which the plastic sheet slides against the plug. To do this, I propose a series of experiments using a natural rubber sheet and a plug having various surface conditions.

What is Sliding on What?

Consider a hemispherical plug pushing into a plastic sheet, Figure 9:

Hemispherical Plug Entering Sheet Surface

Figure 9. Hemispherical Plug Entering Sheet Surface

It is apparent that the sheet is being stretched between the rim and the plug surface. The question is whether the sheet on the plug is being stretched to the same degree as the sheet free of the plug or whether it is being stretched at all. Consider the first scenario. If the sheet is stretching uniformly whether in contact with the plug or free of the plug, the sheet must be sliding freely on the plug. When the sheet is stretching only where it is free of the plug, it must be firmly “attached to” or “bonded with” the plug. If we relate this to frictional resistance, when the sheet is sliding, the frictional coefficient is zero. And when it is not sliding, the relative frictional coefficient is unity.

So, to test the theory I reconstructed a device I used many years ago when I was studying the theory of plane strain deformation. The device consists of a scissor jack, a kilogram scale, and a fixture that holds the sheet, Figure 10:

Experimental Setup

Figure 10. Experimental Setup

As shown on the right side of Figure 10, the plug is centered below the membrane. As the jackscrew advances, the plug pushes into the membrane. The penetration height and membrane resistance to penetration are measured. For these experiments, I used a 0.015-inch thick natural rubber membrane and wooden plugs. I used hemispherical plugs of two diameters – ¾-inch and 3-inch. The membrane was 6¾-inch in diameter.

Some Experiments on Plugs

The force-penetration curves for these two plugs are shown in Figure 11.

Force-Penetration Curves for Two Diameter Hemispheres

Figure 11. Force-Penetration Curves for Two Diameter Hemispheres

Because the ¾-inch diameter plug contact area was so small, I considered that the contact area of the sheet on the plug was very small when compared to the membrane area, as seen in Figure 12.

This allowed me to calculate the equivalent modulus, E, for the rubber from the following equation: F = 2πδET0/ln(a/b).

Where F is the force, δ is the penetration depth, t0 is initial sheet thickness, a is plug diameter, b is sheet diameter. In addition to measuring the force as a function of penetration, I also measured the contact area between the plug and the sheet.

Surface Contact for Two Diameters of Hemispheres

Figure 12. Surface Contact for Two Diameters of Hemispheres

Figure 13 compares the calculated and measured force-penetration curves for the two plugs. As expected, the experimental values for the small-diameter plug agree quite well with the calculated values. The experimental values for the large-diameter plug are quite a bit lower than the calculated values.

Calculated and Measured Force-Penetration Values

Figure 13. Calculated and Measured Force-Penetration Values

How Does the Plug Surface Affect Force-Penetration?

Dry Plug Surface

In both cases, the plugs were as-received wooden spheres. I then began to modify the surface of the large plug. In the first set of modifications, I simply smoothed the plug surface, according to the following schedule:

  • As-is (coarse, exterior PT pine)
  • Sanded w/180 grit paper, blown free
  • Sanded w/320 grit paper, blown free, waxed with furniture wax
  • Sanded, waxed, polished on rouge wheel
  • Sanded, waxed, polished, then coated with talc

The results of these experiments are shown in Figure 14.

Effect of Surface Texture on Force-Penetration

Figure 14: Effect of Surface Texture on Force-Penetration

There is relatively little difference in the force-penetration curves, as seen in the expanded scale, Figure 15.

Expanded Scale of Figure 14.

Figure 15. Expanded Scale of Figure 14.

To carry this one step further, I measured the increase in surface area of the free portion of the sheet. This was done by inscribing a 2.5 cm circle on the membrane prior to stretching. When the membrane is stretched, the circle is stretched into an ellipse. The increase in area is inversely proportional to the reduction in thickness:

Raoriginal circle = π r² , where r is the radius

Raellipse = π a b, where a is the major axis of the ellipse and b is the minor axis

The relative increase in surface area is:

Arearelative = ab/r²

Since the volume is constant, the relative decrease in thickness of the membrane that is free of the plug is:

t/t0 = 1/Arearelative = r²/ab

If the plug had zero radius, the entire sheet thickness would be reduced by this amount. As noted, the contact area of the ¾-inch diameter plug is very small, relative to that of the membrane. As a result, we would expect the free membrane thickness to be nearly identical to that of a zero radius plug. This is the case, as seen in Figure 16.

Now consider the larger ball. If the sheet easily slides on the large ball surface, the thickness of the stretched sheet should be essentially the same as that for the smaller ball. This is shown in Figure 16. If the sheet adheres in any way to the surface of the larger plug, we might expect the free membrane thickness to be reduced as the plug penetrates the membrane. Simply because a substantial portion of the sheet is in contact with the larger ball. This is also shown in Figure 16.

Calculated Reduced Thickness v. Penetration Depth

Figure 16. Calculated Reduced Thickness v. Penetration Depth

Here’s what the measurements show:

Penetration No Frict Max Frict Exptl*
2.0 in 0.832 0.813 0.805
2.4 in 0.778 0.738 0.744
* Average of 9-10 experiments

In other words, it appears that the sheet is in fact sticking to the surface of the plug.

Lubricated Plug Surface

As seen above, plug surface condition does not seem to lead to substantial alterations in the force-penetration curves. As a result, I added lubrication to the plug surface:

  • Molybdenum white grease – oil-based
  • Glycerin – water-based

It is apparent in Figure 17 that water-based lubrication leads to substantial reduction in the amount of force required to stretch the membrane. What is surprising is that the white grease did not appear to affect the stretching resistance. It could be that the rubber membrane is adhered to the grease but slides quite well on the glycerin.

Okay, What About Thickness?

Thicker rubber sheet was not available. So I chose to double and triple the 0.015-inch membrane to simulate thicker sheet. Because of the limitations of the scale, I did not increase the thickness beyond 0.045-inch. According to the plane strain force-penetration formula given earlier, the amount of force required to stretch the membrane a given amount is proportional to the initial membrane thickness. As is seen in Figure 18, the experimental values mirror the theory quite well. In other words, at least this part of the theory works.

Effect of Lubrication Between Sheet and Plug

Figure 17. Effect of Lubrication Between Sheet and Plug

Comparison of Calculated and Experimental Measurements for Thicker Sheet

Figure 18. Comparison of Calculated and Experimental Measurements for Thicker Sheet

What Can We Conclude?

We can conclude several things.

So long as the plug surface is dry-

  • The surface quality of the plug does not dramatically affect the force-penetration curves for thin membranes.
  • It appears that the sheet tends to lay on the plug surface without additional stretching, rather than sliding over the plug surface.

When the plug surface isn’t dry –

  • Plug surface lubricity affects the force-penetration curve but apparently the nature, oil v. water, of the lubricant is important.

Okay, how does this compare with the work of others? The work of References 8 and 9 represent the most comprehensive efforts to date to understand the interaction between the plug and the sheet. The focus in Ref. 8 was the measurement of the plug force-penetration of a syntactic foam plug [Formplast 2000] with either flat or hemispherical geometry. The researchers tested only dry plugs. The hemispherical plug was used either rough or polished. Their peak load data are shown in Fig 19. Their results indicate that sheet resistance is higher for smooth plugs than rough plugs, but that the differences in resistance values are not as substantial as the differences in plug and sheet temperatures. Our results with room temperature rubber sheet appear to corroborate these results.

Literature Results on Plug Force v. Sheet Temperature

Figure 19. Literature Results on Plug Force v. Sheet Temperature

So, Are We There Yet?

Not yet. Knowing what we know now, we need to reconsider the original question: What is sliding on what? This is the focus of Part 3.

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.
Jim Throne on February 16th, 2001

Recently, Profile Plastics has been winning major thermoforming awards on their thin-gauge twin-sheet thermoformed surgeon’s helmet. Although this is certainly not the first thin-gauge twin-sheet thermoformed part, it certainly has raised the bar in this area. This technical note discusses the nature of the process and some of the reasons why this technology has not blossomed in the manner of heavy-gauge twin-sheet forming. Before we get started on this discourse, let’s simplify the language. Whenever we need a shorthand phrase, let’s call thin-gauge twin-sheet forming just “thin-twin” forming.

First we need some historical information. J. Harry DuBois noted that the very first twin-sheet forming took place in the late 1800s. The products were baby rattles, teething rings, mirror cases and hairbrush backs. The company was Hyatt Brothers. And the cellulose nitrate or pyroxylin sheet was skived or sliced into very thin sheets from blocks. In other words, the very earliest twin-sheet forming was thin-twin forming. In the 1930s, table tennis (“ping pong”) balls were twin-sheet formed from Dupont Surlyn ionomer. And also in the 1930s, liquid containers were twin-sheet formed from the revolutionary new but very expensive polyethylene.

So, why did it take until the beginning of the twenty-first century to rediscover thin-twin forming? Well, it really didn’t. Let’s look at the current thermoforming market for a brief moment. First roughly three-quarters of all thermoformed products are formed from thin sheet. And nearly all of these are formed for the packaging industry. Although being disposable, a product such as the surgeon’s helmet is obviously not a package. This means that the currently developed applications for non-packaging hollow parts are apparently quite limited. This does not, however, mean that the potential markets are limited.

Does this mean that there are no markets for thin-twin packages? Consider this. In the early 1980s, Dairy Queen prototyped a twin-sheet pint PS ice cream tub for carryout. While the technical problems were mostly solved, the project was shelved in favor of expanded polystyrene foam. Ultimately, this container, too, was phased out when half-gallon containers were successfully marketed. In the early 1980s, Nestle developed a process for multi-layer forming of preforms for subsequent stretch blow molding of wide-mouth tea jars. The final product did not preserve the freshness and moisture resistance of glass. In the late 1990s, Kiefel developed a machine for thin-twin forming one-liter bottles of PP for a French dairy. The product was never marketed, the dairy preferring to continue using their flexible milk-in-a-bag container. About this same time, Kiefel developed a machine for fabricating thin-twin PS microwavable rice bowls for the Japanese market. The success of this development is unknown. I was told at the Kunststoffe 2001 show in Dusseldorf that, in the mid-1980s, OMV had developed technology to produce a twin-sheet PS “hot cup” for a Canadian company. The cup was designed to compete with expanded polystyrene foam, but the project lost out to a paper cup with a cardboard collar. Think Starbucks.

There are several ways to form a thin-twin product. If the product is needed in limited quantities, a “double-ender” shuttle press is used. In this method, a cut sheet is loaded into each of two clamp frames. The frames are then shuttled into their respective ovens at each end of the load/mold/unload station. When the sheets are at forming temperature, the frames are moved from the ovens to the molding station. The mold frame contains both mold halves, which are sequenced into the hot sheets. Typically, both mold halves are female, although this is not a requisite for the forming step. The sheets are formed independently of each other. Then the mold halves are brought together to form the seal area. Much mold design effort is devoted to achieving adequate seal, since in many cases, the seal area must be liquid-tight. Multiple-cavity molds can be used if market size warrants.

If the product quantities are large, the shuttle concept is usually not advocated. Special roll-fed machines are needed, in which the two sheets are brought into the heating ovens on separate pin-chain rails. If a nearly conventional top-and-bottom heating oven is used, the heating time must be increased by a factor of about four. Usually, however, a special oven, employing top-and-bottom heaters for the parallel sheets, is needed. These ovens are usually considerably “thicker” than conventional thin-gauge thermoforming ovens.

The sheets are conveyed between the two mold halves and simultaneously formed in the manner described above for the shuttle press. The mold halves are then brought together to form the seal. The sheets containing the formed products are then released from the top pin-chain and conveyed to the trimming press. It is believed that Kiefel used a technique similar to this to produce its PP liter bottles six-up or nine-up.

So it appears that thin-twin forming is doable and has, in fact, been developed for several applications. It is now time to discuss the reasons why it may not be the “next breakthrough” in thin-gauge thermoforming. First consider the technical limitations. First, the process is most suited to hollow products, where both mold halves are female cavities. This doesn’t mean that one half of the mold cannot be male or that the final part cannot have kiss-offs. It just means that the sheet thickness of the seal area is far better controlled with female cavities than with male molds. And since seal area integrity is of major concern, female molds are preferred.

A second technical limitation deals with sheet stretching. So far, essentially all the twin-sheet products evaluated have shallow draws. This is because that with simultaneous forming, there seems to be no practical way of plugging the sheet into the female cavities. This doesn’t mean it can’t be done. It just means that reliable technology is not in place to do it with current machine designs. Is it possible to develop a simultaneous technique that includes an active plugging step, maybe by separating the mold halves and shuttling the plug plate into the area between them? Probably, but see my comments at the end of the next paragraph.

In heavy-gauge twin-sheet forming, the plugging problem is bypassed by using sequential forming. In other words, the bottom sheet is formed first, using the top mold as a plug. Then the top sheet is formed against the top mold. Then the two sheets are mated. Is this sequential method possible with thin-twin forming? Insofar as I can tell, it hasn’t been successful to date. But keep in mind that anything is possible in thermoforming, so long as there is a suitably large money pit.

So, to this point, we’ve learned that thin-twin forming is not only possible but also that it has been technically practiced successfully in portions of three centuries. Now the question is: “Why hasn’t it been used in more applications?” After all, consider all the “hollow parts” that we see in a few minute supermarket or hardware store tour.

There are two major areas of thin-gauge rigid and semi-rigid containers that apparently compete with thin-twin products. First, consider lidded containers. There are two generic types – those with separate lids and those with integral lids. Deli containers are typical of the first type. Point-of-purchase products such as nuts and bolts are usually sold in the second type of container. Integral-lid containers are the dandies of the industry today. No lost lids. No lids that don’t fit. Containers can be easily made pilfer-proof. Containers can be closed mechanically. The forming technologies for integral-lid containers are well known. Most of the innovations focus on designing and redesigning the hinge and on methods of closure. In the latter case, the design considers whether the container must be opened more than one time by the user or whether the container is primarily a protection for the contents. The fast-food salad container is an example of the former. The point-of-purchase container protecting a portable CD player is an example of the latter. There are all manner of closures, including interference-fit buttons and bars, detents, staples and heat-sealed edges.

These containers are probably not candidates for thin-twin forming. In fact, there is strong evidence that the single-sheet forming technique used to make an integral-lid container can be used to produce a very suitable thin-twin container, by simply thermally welding the two halves together, then trimming off the integral hinge!

The second area of thin-gauge containers that compete with thin-twin containers is the so-called “nested container.” A nested container is simply two nearly identical thermoformed sheets, usually in the form of five-sided boxes. Cavities are formed in the centers of these five-sided boxes in a fashion allowing the product to nest between the two boxes. The boxes are designed so that the draft angles allow them to tightly nest around the product. The entire assembly is then either stapled or taped shut, or inserted into a cardboard sleeve. The nesting technique is used for containers that require very deep draw or must hold products are very bulky. Although this type of container is a faux thin-twin, it is doubtful that it is a strong candidate for thin-twin technology. The reason? What’s done now is cheap and easy. And it works just fine, thank you very much.

Oh, and by the way, it is not a difficult stretch to consider simply single-sheet forming the inside and outside shells of a deep-draw container in separate conventional forming machines that employ conventional plug assists, then feeding the sheets containing the formed shells into a third machine, where the shells are nested, then thermally welded and trimmed in a single step. Decoupling the two stretching processes from the welding step yields better quality control of the forming process.

So, should this prevent us from scurrying around for other thin-twin challenges? I mean, certainly if the surgeon’s helmet can engender all those awards, there certainly should be dozens of other applications just as spectacular. The importance of the surgeon’s helmet lies in the fact that it fulfills two very important aspects of innovation. First, the size of the market is relatively limited, thereby allowing adaptation of essentially existing technologies. And second, the market might be considered “mission-oriented,” in that competition was minimal and experimentation and prototyping could proceed apace to meet the unmet needs in the marketplace. Launching a thin-twin drink cup program, on the other hand, would simply not have the same advantages or luxuries, if you will. And perhaps that is why the previous thin-twin products – ice cream tub, milk bottle, “hot cup” – did not make it to the market.

Does this mean then that there will never be a thin-twin ice cream tub or milk bottle or hot cup? Of course not! It seems to me that these products represent the vanguard of high-volume thin-twin products. And that they may have been before their time from a marketing or technical viewpoint. So while it is important that we continue to scurry about seeking out the next “surgeon’s helmet,” we must also realize that major market penetration of thin-twin containers must come from high-volume products. And to penetrate these markets, efforts must be continually made to improve on or invent new methods of fabricating them.

Jim Throne on May 4th, 1999


Rotational molding focuses on the sinter-melting, densification and cooling of polymer, beginning with powder. Typically, polymer powder has a particle size range of -35 mesh to + 200 mesh. The powder is usually manually charged to the mold while the mold is in the open configuration in the servicing stage of the process cycle. This Technical Minute reviews some basic information on the way in which powder moves across the metal mold surface. Be aware that studies of polymer powder flow are just beginning.

Putting Powder Into Perspective

The typical poured but untamped powder packing fraction range is 0.35 to 0.50. The bulk density range for typical rotational molding polymers is given in Table 1.

Table 1

Powder Bulk Density

Polymer Compact Density, kg/m3 Bulk Density, kg/m3 Bulk Density, lb/ft3
LLDPE 910 345 to 390 22 to 24
HDPE 960 375 to 425 23 to 27
PS 1050 430 to 585 27 to 37
PP 910 345 to 490 22 to 31
Nylon 1100 460 to 615 29 to 38
FEP 2200 1000 to 1230 62 to 77

There are several important aspects about powder charging. First, there must be room for the powder in the mold half during charging. For asymmetric molds, the deeper portion should be that which is filled. The powder must be freely poured, and must not be tamped. Then, there needs to be free space for the tumbling powder during the early portion of the heating cycle. Nonuniform wall thickness and severe corner bridging result when the powder cannot freely flow across the mold surface. And powder must be carefully distributed when the mold has both large and small cross-sections. A classic example is a hobby horse, where the leg cross-sections are substantially less than that of the body.

Determination of the required amount of powder in a specific charge is quite straight-forward. The inner mold surface area is determined, either manually or from CAE software. Tool path software yields the most accurate surface area values. The anticipated uniform wall thickness is obtained either from prior experience or from finite element analysis. The product of the area and the wall thickness yields the volume of plastic required in the finished part. The weight of polymer is determined by multiplying the volume by the polymer density. Of course, this is the weight of the powder charge. The volume of the powder charge can be two to three times greater than the required volume of plastic.

Air-borne dust is a major problem with manual powder charging into an open mold half. Dust can be minimized by filling through an accessway in an already-closed mold, or by using a drop box mounted to the accessway. It can also be minimized by using micropellets or prilled powders.

General Process Description

Consider the following summary of the rotational molding process. The heating cycle begins with powder charging at the service station and ends when the mold assembly is removed from the oven to the cooling station. Table 2 details the various phenomenological steps. In this Technical Minute, we consider only the various ways in which powder flows in a mold, prior to tacking, coalescence and densification.

Table 2
Steps in the Heating Cycle

Step Comments/Concerns
Powder charging Bulk density of the powder, place for powder in narrow molds
Initial heating Characteristics of powder bed
Tacking condition Hot tack temperature of powder
Particle coalescence Three-dimensional structure
Densification Capillary flow, powder structure collapse, air inclusion

Powder Flow

In conventional rotational molding, rotating speeds are quite low, typically about 4 RPM or so. As a result, the powder charge remains as a powder bed near the bottom of the mold throughout the early portion of the heating cycle. Three types of bed motion have been observed, Figure 1.

Figure 1

Steady-state circulation

For steady-state circulation of the powder in the bed, the powder at the mold surface moves with the mold surface until the mass exceeds the dynamic angle of repose. For most polymer powders, this angle is between 25o and 50o from the horizontal. At that point, the mass breaks away from the mold wall, and cascades across the static surface of the bulk of the powder bed. This type of flow is continuous and the flow rate is altered only by the geometry of the mold itself. Powder having this type of flow behavior is usually characterized as spherical or squared-egg in shape and as freely flowing.

Avalanche flow

This mode of circulation is analogous to snow avalanche. Initially, the powder in the bed is static with respect to the mold surface. The mold raises the powder bed until the entire mass exceeds the dynamic angle of repose. At that point, the top portion of the mass breaks away from the mold wall, and cascades across the rest of the powder bed. The bed again becomes static and is again raised by the rotating mold. It is known that avalanche flow occurs when the powder is slightly tacky or is not free-flowing, and when the powder is acicular or two-dimensional.

Slip flow

This type of flow occurs when the mold surface is very smooth. There are two types of slip flow. The more common slip flow is really a cyclical slip-stick flow. Initially, the powder in the bed is static with respect to the mold surface, as with the avalanche flow. As the mold raises the powder bed, the entire mass reaches a point where the friction between the powder and the mold wall is no longer sufficient to prevent the mass from sliding against the mold surface. At that point, the entire static bed simply slides to the bottom of the mold, without any measurable type of powder circulation. The bed then becomes static and is again raised by the rotating mold. The less common slip flow is a steady state slip. For this type of slip, the bed essentially remains fixed relative to the horizontal axis of the mold and the mold simply slides beneath it. Powders that pack well and that have very low coefficients of friction with the mold material, such as olefins and FEP, will exhibit slip flow, particularly if the mold is also plated or highly polished. Early permanent teflon mold releases also promoted slip flow.

Table 3 summarizes these major types of powder flow.

Table 3
Types of Powder Flow – Rotational Molding

Type Comment
Steady-state circulation Ideal flow
Maximum mixing
Best heat transfer
Spherical or squared egg particle shape
Cohesive-free or freely flowing powders
Smooth powder surfaces
Relatively high friction between mold surface and powder bed
Avalanche Adequate powder flow
Relatively good powder mixing
Relatively good heat transfer
Squared egg, acicular or disk-like particles
High friction between mold surface and powder bed
Slip flow Poor powder flow
No powder mixing
Poor heat transfer
Disk-like, acicular particles
Powders with high adhesion or cohesion
Agglomerating or sticky powders
Very low friction between mold surface and powder bed

Polymer powder particles fluidize during avalanche and steady-state bed flows. From in-mold cameras and from dimunition of light through rotating beds [see comments about Exxon Canada’s experimental analyzer, below], particle size segregation and decrease in overall powder bulk density are observed, particularly in the layers farthest from the mold surface. There is substantial debate as to the best way to treat the mechanics of powder flow. In reality, flowing powders are discrete particles that are temporarily suspended in air. There have been many studies on the rheological or flow characteristics of powders. Single powder particles falling in quiescent air or another fluid are characterized by Stokes flow. That is, the drag force on the particle is directly proportional to its relative velocity, with gravity being the only body force. As the particle density increases, Stokes flow is compromised by interparticle collisions, where kinetic energy interchange occurs. Fluidization is the lifting of a stationary bed of particles by upward flow of air or another fluid.

Unfortunately, throughout most of the rotational molding process, there are so many particles interacting with one another, in swarms or as streams, that most discrete particle theories cannot be used. The possible exception is in the latter stages of powder flow, when most of the polymer is adhered to the mold surface or to other pieces of powder. The concept of viscosity of a flowing powder stream, proposed many years ago, has not received wide acceptance. This concept was based on the decrease in velocity of a falling powder layer owing to shear with a solid inclined plane. This decrease implies a shear layer or region and a resistance to flow. Additional work indicates that the velocity of a flowing powder stream is not necessarily maximum at the free surface, and that a viscosity of sorts is defined only when the shear surface is static. When the shear surface exchanges particles with the flowing surface, the flowing fluid can either increase or decrease in mass during flow across the shear surface. The change in mass is dependent on the effect of external factors such as gravity, fluid velocity, the relative size and shape of the particles, and the relative boundary conditions. 

Laboratory Studies

Since the nature of powder bed motion is so critical to the early fusion state of the powder against the mold surface, it is recommended that a simple lab-scale rotating unit be employed to evaluate the flow behavior of new polymers and new grinding techniques. The unit shown in Figure 2 yields rotation in a radial direction only, as seen in Figure 3.

Figure 2

Figure 3

Nevertheless the unit is useful for determining the effect of mold fill level on bed motion and the nature of the powder flow characteristics during dry flow and melting. In fact, at the 1997 ARM conference, Blair Graham at Exxon Canada demonstrated a correlation between measured avalanche characteristics and the processability of molding powders. The experimental device is shown in schematic in Figure 4 and the nature of the experimental data is shown in Figure 5.

Figure 4

Figure 5

It should be noted that the bed flow mechanism can change during heating. For example, as powder becomes sticky or begins to stick to the mold surface, the bed flow can change from slip flow to avalanche, or from steady-state circulation to avalanche flow. As a result, the particle-to-particle temperature uniformity can change dramatically. This aspect of rotational molding will be the subject of another Technical Minute.

Jim Throne on January 1st, 1999

It has always been my philosophy to obtain as much information as possible about the polymer with which I’m working. As techniques for predicting polymer performance during processing become more sophisticated and computer models for predicting polymer product response to applied temperature and force conditions become more exacting, our thirst for data seems to grow exponentially. There are two approaches to satisfying the demands for more information about polymer performance. Not surprisingly, the first is prediction of polymer properties from first principle. The second is experimental generation of requisite properties.

First Principle Prediction

For a century or more, physical chemists and chemical physicists have developed and fine-tuned mathematical models for small molecules. For example, in graduate school, we studied from Hirschfelder, Curtiss and Bird [J.O. Hirschfelder, C.F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, NY, 1964], where we learned that molecular properties such as PVT, surface tension and the Joule-Thompson effect, could be adequately predicted for small molecule materials in thermodynamic equilibrium. We also learned that molecular properties such as viscosity, diffusion and thermal conductivity, could be almost predicted for small molecule materials that were not in thermodynamic equilibrium. Most importantly, however, we learned that most predictive models were very shaky when they were applied to macromolecular materials, which were almost never in thermodynamic equilibrium. In the decades since, other, braver souls have accepted the challenge of first principle prediction of polymer properties. Perhaps the best summary of the state-of-art is given by Bicerano [J. Bicerano, Prediction of Polymer Properties, 2e, Marcel Dekker, Inc., NY, 1996]. It now appears that, for simple polymers at least, we can predict, within engineering accuracy, such properties as volumetric properties, glass transition and crystalline melting temperature, heat capacity, thermal conductivity, cohesive energy, solubility parameter, surface tension, optical and electrical properties, and even mechanical properties such as structure-property relationships for glassy and rubbery polymers. And there appears to be hope in predicting polymer properties for copolymers, blends and even for filled and plasticized polymers. The question remains, however, as to whether these predictive properties are sufficient for computer analyses. Insofar as I can tell, the biggest hurdle in using the predictive correlations offered today is that they are academic. By that I mean, in order to use the techniques, I need to input substantial information about the behavior of elements within the molecular structure, not at just one environmental condition, but at the wide range of environmental conditions dictated either by product use or the process used to make the product. In simple terms, then, the current technologies lack “user friendliness”, forcing the design engineer to spend his time on molecular design instead of product design.


If you can’t predict it, at least within the accuracy needed to meet QC or customer demands, then you need to measure it. In a recent conference, Dr. Shastri of Dow outlined not only the polymer performance criteria needed by computer-aided engineering [CAE] programs, but also the cost involved in obtaining the requisite data [R.K. Shastri, “The ISO Guide on Design Data for Plastics”, paper presented at SPE Plastics Product Design and Development Forum, 31 May-2 June 1998, Chicago IL]. Dr. Shastri is one of the leaders in ASTM D 20.10.24 subcommittee on Engineering Properties and Design. This ASTM subcommittee has issued D 5592-94, “Guide for Material Properties Needed in Engineering Design Using Plastics”. The following table identifies material property needs currently required for commercial CAE programs:

Table 1 – Polymer Material Property Needs

Mechanical Properties
Elastic modulus * Poisson’s ratio *
Bulk modulus Uniaxial compression
Shear modulus Creep data
Fatigue data Fracture strength
Inelastic strain rate Tension cracking stress
Tension softening modulus Crushing compression strain
Shear retention factor

* also as function of anisotropy

Thermal Properties
Thermal conductivity * Specific heat *
Melt density * PVT data **
Thermal diffusivity CLTE ***
No flow/solidification temperature Glass transition temperature
Crystallization temperature Heat of fusion
Recrystallation temperature Crystallization kinetics

* as function of temperature and pressure
** as function of cooling rate
*** coefficient of linear thermal expansion, as function of temperature and anisotropy

Rheological Properties
Viscosity as function of pressure Viscosity model coefficients
Extensional viscosity Normal stresses
Normal stress differences G’, G”
Cure kinetics for thermosets Coefficient of friction
Longitudinal shear relaxation modulus Transverse shear relaxation modulus
Relaxation time

The enormous task of collecting and disseminating physical property data is currently a joint effort between the International Technical and Standards Advisory Committee of The Society of the Plastics Industry, Inc. [ITSAC/SPI] and CAMPUS, a worldwide consortium of polymer resin suppliers. As Dr. Shastri points out, there are two huge barriers to this task. The first lies directly with the user of the information. And the second deals with the incredible cost of generating requisite data.

The Uninformed User

As Dr. Shastri points out, designers often have misconceptions about which properties are essential for the design of their products and are often confused by the lack of a standardized reporting format for the data that are available. In the first case, designers often have limited knowledge about plastics in general and the plastic they want to use, in particular. Furthermore, they frequently lack the skills to translate the “handbook” or “data sheet” values into product performance requirements, and vice versa. To complicate matters, CAE code designers frequently require physical properties that are unmeasurable, academic, or just plain irrelevant. And to compound this, CAE code designers do not provide sufficient “sensitivity analyses”, so that the product designer can determine what levels of accuracy are required for the requisite physical properties. Unfortunately, because of these barriers, the designer frequently will select polymers with properties that approximate those of traditional materials, will over-design with over-generous safety factors, or will request inordinate amounts of information from resin suppliers, with the mistaken belief that somewhere, in the mass of data, he or she will find enough information to allow the CAE program to crank away.

The Cost of Measuring

Let’s focus on the request for data from the resin supplier. Astute resin suppliers, and now CAMPUS, provide basic data on their commercial resin blends. We call that database, the “data sheet”. As we are learning, particularly in thermoforming, these data sheets have only limited use when trying to determine whether a polymer will sag in the oven. But what does it cost to generate these and other design data? According to Dr. Shastri, a consensus of seven testing facilities in the U.S., U.K, and Germany found the approximate costs given in Table 2.

Table 2 Cost of Material Data Generation

Property (Single-point data) Cost Range Per Grade Average Cost
Mechanical properties $780 – $3120 $1500
Thermal properties $1030 – $3270 $2000
Rheological properties $ 370 – $ 650 $ 500
Electrical properties $1020 – $1860 $1500
Other properties $ 170 – $ 540 $300
Property (Multi-point data)
[viz, creep, stress-strain]
Average Cost
$14,484 – $93,140

In other words, it costs nearly $6000 to achieve a relatively rudimentary database for one grade of one polymer. When you consider that there are perhaps 20,000 grades of polymers in use worldwide, you can clearly see the prohibitive cost involved. And that’s just to generate some very basic data.

So, keep in mind that when the thermoformer [or the consultant, urging on the thermoformer] decides he or she needs temperature-dependent stress-strain data for several grades of polymer, in order to determine how each of these grades performs during an FEA wall thickness calculation, he or she is asking the resin supplier to generate data that lie outside the normal measuring protocol. Of course, the resin supplier would be more than happy to do this for a customer, if there is financial incentive to do so. In other words, if you’re going to buy a few million pounds of his stuff, he’ll do it. If you’re buying a few thousand pounds, forget it!

In Short, Then

And, folks, in a nutshell, that’s why we in the thermoforming community are having a really tough time getting relevant processing data for our polymers.

Jim Throne on November 4th, 1998

Power Point: Frictional Coefficients Between Plug and Sheet

Jim Throne on September 9th, 1998

A Brief Review

Rotational molding begins with -35 mesh polymer powder tumbling in a metal mold. It ends with a monolithic layer of solid polymer against the metal mold. In between, the powder tumbles against the mold until the mold temperature reaches the tack temperature of the powder, whereupon the powder begins to stick to the mold surface. Then as the powder stuck on the mold surface heats, more powder sticks to that powder, and on and on. Sometime after the first layer of powder sticks to the mold, but before the entire mass of polymer is totally liquefied on the mold surface, the air in powder bed, for the most part, “goes away”. The question for this technical minute is “Where does all the air go?”

Some Hypotheses

First, we need to identify some possible mechanisms for air disappearance. I’ve put these in four general categories:

Bulk migration,
Bubble Disappearance by Molecular diffusion, and

Capillarity was the first mechanism proposed [M.A. Rao and J.L. Throne, “Principles of Rotational Molding”, Polym. Eng. Sci., 12 (1972), pp. 237-264]. The coalescing bed was pictured as liquidus at the mold surface but tacked granular at the free or non-mold surface. It was proposed that when the polymer powder was fused at some point but when there was still tortuous air paths, polymer would be drawn up the air channel by simple surface tension, essentially expelling the air ahead of it toward the non-mold surface. Envisage the drawing of a liquid up a soda straw. There are several problems with capillarity. First, it depends on surface tension for the driving force, but surface tension decreases with increasing temperature. Second, the drawing effect decreases in proportion to the cross-sectional area of the flow channel. In other words, the smaller the soda straw, the higher the liquid will be drawn. And then, for capillarity to be effective in a time-dependent way, the liquid viscosity must be low. And of course, the viscosities of polymers are quite high, when compared with, say, soda. So, while there may be some capillarity effect, it is probably minimal.

Bulk Migration

Sometime after the capillarity hypothesis and after substantial observances of powder being heated on a static plate, it was decided that another mechanism was in action, that of bulk migration of the air from the powder to the non-mold surface [R.C. Progelhof, G. Cellier and J.L. Throne, “New Technology in Rotational Molding: Powder Densification”, SPE ANTEC Tech. Pap., 28 (1982), pp. 627-629]. In other words, we noticed that the powder structure weakened as it heated. As a result, the ‘powder columns’ simply collapsed under their own weight. If heating was gentle, the air would be expelled toward the non-mold surface, i.e., bulk migration of air. If the heating was severe, the collapse would entrap some air, which ultimately would form into bubbles. As part of this study, it was noted that the time-dependent height of the powder bed was not altered dramatically when a substantial portion of the air was evacuated during powder bed heating. This led us to the conclusion that the underlying mechanism for air removal from the coalescing powder bed was the viscoelastic character of the polymer and not capillarity.

Bubble Disappearance via Molecular Diffusion

Recently, Dr. Roy Crawford and his team at Queen’s University at Belfast [R.J. Crawford and P.J. Nugent, “A New Process Control System for Rotational Moulding”, Plast. Rubb. Compos. Process Applic., 17 (1992), pp. 23-31] have determined that the mechanism of air migration is dramatically altered once bubbles have formed. Lord Rayleigh determined that a bubble can remain stable only if the internal gas pressure is greater than the external melt pressure:

where σ is the surface tension of the polymer and r is the bubble radius. As is apparent, small stable bubbles have higher internal gas pressure than do large stable bubbles. As an example of the differential pressure required, consider a bubble 100 microns = 0.01 cm in diameter, in a polymer with the surface tension of 30 dyne/cm. The differential pressure is:

Δ P = 30 x 2/0.005 = 12000 dyne/cm2 = 1200 Pa = 0.174 psi

If the differential pressure decreases, the bubble will grow until the equation is met. If it increases, the bubble will shrink until the equation is met. [See J.L. Throne, Thermoplastic Foams, Sherwood Publishers, 1996 for more information on bubble dynamics.] Although Lord Rayleigh was right on regarding the static condition, his equation needs tampering in order to work for time-dependent events such as bubble extinction. [See J.L. Throne, “Is Your Polymer Foamable?” Foams Conference ’96, Somerset NJ, 10-12 Dec 1997, for the “Second Rayleigh Equation”].


It has further been proposed that, owing to the differential pressure between the air in the bubble and that in the polymer, it simply disappears by dissolving in the polymer. Solubility is usually given by Henry’s law:

S = HP

where S is solubility in cm3(STP)/g plastic, P is pressure in atm and H is Henry’s constant, in cm3(STP)/g atm. Now for nitrogen in polyethylene, H has a value of 0.111. Therefore at the cell gas pressure calculated above:

S = 0.111 x 1.174/14.7 = 0.00887 cm3/g plastic

Assume for the moment that all the air brought in with the plastic powder becomes bubbles. Consider the bulk density of powder to be about 1/2 that of the monolithic polymer. If the density of the polymer is about 1 g/cm3, then the volume of air in the incoming powder is about 1 cm3/g plastic. [Because the polymer has some volume, the actual volume of air is somewhat less.]

Therefore, of the original air concentration of 1 cm3/g plastic, less than 1% will be dissolved in the polymer. But again, this is a static situation. We need to determine whether this very tiny concentration difference can cause the bubble dimension to decrease completely.

So… Where Does The Air Go?

Recent work at McMasters University [K. Kontopoulou and J. Vlachopoulos, “Bubble Dissolution in Molten Polymers and Its Role in Rotational Molding”, paper submitted to Polym. Eng. Sci., 1998] summarizes bubble disappearance in the following way:

* From a fluid mechanics viewpoint, the rate of bubble disappearance [viz, dR/dt] is given by Lord Rayleigh’s second equation, with Newtonian viscosity, h, as a measure of polymer resistance to deflation. The greater the polymer viscosity, the more rapidly the bubble disappears. This is written as:dR/dt = [R ΔP – 2σ] / η

* From a mass transfer viewpoint, the rate of bubble disappearance is a direct function of the concentration gradient. Owing to Henry’s law, the concentration of air at the bubble interface is greater than that in the bulk polymer.

Putting these ideas together, if there is a concentration gradient owing to differential solubility, regardless of how small, the result will be diffusion of air from the bubble into the bulk polymer. This causes the bubble to decrease in radius, which in turn increases the internal bubble gas pressure, according to Lord Rayleigh, which further in turn, increases the concentration of air at the bubble interface, thereby increasing the concentration gradient. In other words, in an isothermal viscous-only world [and even in a non-isothermal viscous-only world], bubble diameter decreases slowly at first, then accelerates as the bubble gets smaller and smaller, until… POOF! The bubble is gone!

It seems fair to say that, following this logic, eventually all bubbles will go poof!, regardless of their initial size. Further it seems fair to say that the rate of extinguishment of the bubble is therefore governed primarily by polymer viscosity.

What About Applied Pressure?

Accordingly, when we apply pneumatic or air pressure to the densifying bubble, the following things happen. When we increase the hydrostatic pressure on the outside of the bubble, the volume of the bubble decreases. Remember P-V-T? Of course, the internal gas pressure increases, and since the bubble radius is now smaller, the local solubility at the bubble/polymer interface increases and therefore, so does the concentration gradient. Ergo, increasing pressure causes the bubbles to go poof! more rapidly. The only remaining question is whether someone will attempt to patent this event of nature!

Short Summary

So there we have it! Capillarity is apparently out of favor. Bulk migration owing to the collapse of the friable powder columns occurs but is also probably not that significant during densification. What we really have is bubble disappearance due to the differential pressure between the air in the bubble and that in the bulk polymer which triggers a concentration gradient of air between the bubble/polymer interface and the bulk polymer. Applied pneumatic pressure hastens extinction.

What’s Wrong With This Picture?

Really not a whole lot. But…

* If I can rotationally mold PS, why can’t I rotationally mold ABS?

* And, if bubbles disappear catastrophically, why are there any bubbles, at all, in some rotomolded parts?

* And, if little bubbles disappear quicker than big bubbles, why are there so many little bubbles in some rotomolded parts? Are they just formerly big bubbles on their way to extinction?

* And finally, what happens if I apply a vacuum rather than pressure? Sure, initially, the bubbles will get bigger. But the concentration gradient gets even bigger, since there’s less air in the bulk polymer. So, shouldn’t the bubbles disappear even quicker?

Here’s a thought experiment to ponder. Suppose we try to separate diffusion from dissolution. I guess I’d use the Progelhof hot plate scheme to illustrate the effect, although I might even be able to carry it out on a microscope hot stage. I’d put polyethylene powder in a glass cylinder that sits on a hot plate. Suppose that the cylinder cavity is initially filled with a gas other than air, say, carbon dioxide. Then, at the instant of coalescence completion but before densification can begin, I swap the carbon dioxide in the mold cavity for nitrogen, say. Then the concentration of carbon dioxide in the gas bubble is unity while it is zero in the mold cavity. Obviously then carbon dioxide will diffuse from the bubbles as well as the bulk polymer. But keep in mind that nitrogen will diffuse the other way, into the polymer and the bubbles. However, for most polymers, carbon dioxide permeability is about 15 times greater than that for nitrogen. So the result should be one of diminishing of bubble radii even though the polymer and gas temperatures remain isothermal. Then I’d reverse the process, this time using a gas with a low diffusional coefficient, say, dichlorotrifluoroethane [R-123], then at the same appropriate time, swapping it in the free space with carbon dioxide. And finally, I’d repeat the original Progelhof experiment, with and without one atmosphere air in the cylinder. Will I still see the same rate of bubble disappearance?

9 June 1998