Normal stress differences can be determined by capillary rheometry

In polymeric flows, the material generally exerts a force in a direction II normal to the flow. For example, when a polymer is sheared between parallel plates (eg., in a parallel plate rheometer), it is found to exert a normal thrust which tends to separate the plates. This behavior is characterized in terms of the first and second normal stress differences, N1 and N2, measurable quantities which are used to describe fluids with elastic behavior. It is found that at low shear rates, the normal stress difference becomes proportional to the square of the shear rate, leading to the definition of a normal stress coefficient (yP=N/y2). The first and second normal stress coefficients, along with the viscosity, represent the viscometric functions which are used to characterize the behavior of materials subject to simple steady shear.

First normal stress difference measurements are available from Datapoint Testing Services.

The direct measurement of stress differences is traditionally performed using steady shear measurements on a cone and plate rheometer. The technique is specialized and data are highly sensitive to the test conditions, rendering good experimental data difficult to obtain. In 1980, Gleissle proposed a set of empirical ‘mirror relations” by which it would be possible to estimate the first normal stress coefficient using data gathered by a capillary rheometer. The relationships have been evaluated by several researchers and found to be a reasonable approximation for many materials. The scheme suggests itself as an attractive means to generate normal stress difference data for commercial and real-life applications. An advantage of the technique is that, unlike steady shear cone and plate measurements, the data are available over a wide range of shear rates, even covering ranges used in actual applications. Consequently, although the final result depends on the applicability of the mirror relations, the estimation of the first normal stress difference may still be comparable in accuracy to direct measurement, due to the large potential for errors involved in actual measurement.

Datapoint Testing Services grows: new capabilities, more employess

In response to clients needs for viscoelastic testing, Datapoint Testing Services has acquired a Rheometrics DMA. This instrument is extremely versatile, with capabilities to test in both solid and melt states, at sub-ambient as well as elevated temperatures. A wide range of frequencies can be covered, up to 500 rad/s.

DMA data is used for a number of applications. Extrusion analysis and blow molding simulations often require viscoelastic data. These properties are found to dramatically affect simulation results, particularly for elastomeric materials. Data are usually supplied in the form of a time- temperature superposition curve (TTS), along with WLF shift parameters.


Stress relaxation modulus vs. time. Master plot for an impact-modified PS.

Expanded Priority offerings

Datapoint Testing Services is increasing the number of tests available with PRIORITY service. Results are now available within 48 hours for pressure - volume - temperature (PVT) measurements, visco-elastic measurements, and many mechanical properties. A new price list will be released shortly, reflecting these changes. Until then, call for pricing details.

LS-DYNA3D supported

Users of LS-DYNA3D report striking success in predicting the results of impacts. Many of the measurements required for simulating impact can be performed by Datapoint Testing Services, and the results supplied ready for input into the software. Call to discuss testing appropriate for your application.

New employees welcomed

Joining the Datapoint Testing Services staff are Mike Tylenda and Gary Timpe. Mike has a degree in mechanical technologies and brings expertise in mechanical properties measurement to the company. Gary, who has a BS in chemical engineering and management experience, will be interacting with clients to develop testing schemes customized to their needs.

These new positions reflect an increasing emphasis on structural analysis industrywide. Datapoint Testing Services is responding to a need for more sophisticated mechanical properties testing, based on an understanding of the way these properties are applied by structural analysis software.

Upcoming Events

Selected meetings, conferences, and symposia: ‘Design for the 21 Si Century”, sponsored by SPE Eastern New England Section and I Product Design and Development Division,
Oct. 16-18, Andover, MA.

“Durability, Weatherability, and Aging of Plastics and Rubber”, sponsored by SPE Akron Section and Plastics Analysis Division, Oct. 28-29, Akron, OH.

ASTM Committee D-20 on Plastics meeting, Nov. 18-21, New Orleans, LA. Selected symposia: D30 on Composite Materials in Non-Aerospace Applications, E37 on Oxidative Behavior of Materials by Thermoanalytic Techniques.

Polymer Melt Rheology A Guide for Industrial Practice

F. N. Cogswell. Woodhead Publishing Ltd., Cambridge, England. First published in 1981; revised in 1994. 178 pp.

“Two approaches to polymer processing rheology are discernible; by theoreticians. who are concerned with a fundamental description of what would be happening if certain idealized criteria are met; and by practitioners, who are concerned with the results of what is actually happening.” In his newly revised book, Mr. Cogswell skillfully treads the middle ground between these camps, providing an interesting, informative guide to rheology for the design engineer.

The book, while acknowledging the strong theoretical basis that has been built to explain the complicated rheological behavior of polymers, provides a clean and pragmatic vision without resorting to complex mathematical notation.

Of particular interest are the chapters on “Physical Features and Flow” and “Adventitious Flow Phenomena”. The former provides highly readable explanations of the different phenomena that govern polymer flow, while drawing on the understanding that has been developed from the intense theoretical study that has occurred in this field. The phenomena of shear stress, temperature and pressure dependencies are covered, followed by treatments of viscoelasticity and extensional flow. In the chapter on adventitious flow, an interesting discussion on the causes of flow instability is commenced with a number of guidelines for the design engineer to control or eliminate problems associated with these phenomena.

In all this, Mr. Cogswell brings his tremendous experience at ICI to bear, providing meaningful insights into these complex phenomena and the effect they have on the processing of polymers.

—Reviewed by Hubert Lobo, president of Datapoint Testing Services. Review copy provided courtesy of Technomic Publishing, 1-800-233-9936.

Creep, stress relaxation now offered

Another application of the TTS concept is in the prediction of the long-term behavior of a material using data gathered over a very short period of time. DMA data are used to generate predictive creep curves, used as input by structural analysis programs to evaluate long term deformation of products. These techniques provide a more objective means of performing life cycle analysis, permitting designers to estimate product life and anticipate problems right at the design stage. The DMA can also be used to generate the stress relaxation master curves used in warpage predictions in high-end injection molding simulations. This information is used to predict how the molded-in stresses will be relieved as the part cools and relaxes.

Friction measurements improve screw design

One of the key questions regarding a polymer material is, “How does it feed?” This is a deceptively simple question that may take quite a while to answer. Feeding is a function of several factors: there are density issues to consider as well as the frictional properties of the material in question.

The bulk density of the raw material must be evaluated. In processing, a higher density pellet will tend to feed better than a powder or film regrind due to its density. Regrind is often put through a “densifying” system prior to being re-extruded. Powders are often pelletized in order to increase their bulk density so that they may feed better. Of course, pelletizing adds heat history to the material which may lead to material degradation or a loss in mechanical properties. In certain cases a stutter or crammer feeder is used directly in line with the extruder to force low bulk density material on to the main screw. A crammer feeder typically consists of a screw type auger installed in the hopper that will push the material on to the screw.

Another important factor in material feed is the frictional property of the material, a measurement of how the material tends to slip or stick to the screw or barrel surface. The primary concern is that the material stick to the barrel and slip on the screw in order to get maximum teeding capacity. Sometimes this factor is related to the finish on the screw or barrel: at other times it is temperature or pressure dependent. Another factor is the screw speed itself which relates to the frictional property of the material.

Plot of dynamic friction vs. temperature and velocity at 1 psi.

Scientific Process and Research has developed a method for testing the frictional properties of a polymer. The SPR Friction Tester is used to test the dynamic friction of a material against the screw or barrel surface at different temperatures, pressures, and rpm. The system consists of a rotating sample holder placed against a stationary surface representative of the screw or barrel. The surface can be heated and its temperature accurately controlled and monitored by a computerized data acquisition and control system. The rotation of the specimen can also be controlled. The operator is also able to adjust the applied pressure from 0.5 to 300 psi. The operator sets up a regime of experiments for the friction tester to perform. A range of temperatures, pressures and speeds are specified. The tester then automatically runs the sample through each experiment. Typically, over 500 individual tests are performed on each sample. The SPR regression analysis program generates a 55 term function characterizing the material response to different variables.

It is important to maintain high friction on the barrel while maintaining low friction on the screw. This may be done by cooling the barrel. Sometimes grooving the barrel improves material feeding by utilizing material to material friction which is usually much higher than material to metal friction. The material “trapped” in the grooves rubs against the material carried by the screw and improved feeding results.

When designing the feed section of your extruder screw you should take into account these differences. The channel depth and flight lead should minimize surface friction at the rpm requested. This also applies to designing take off equipment where the material may tend to stick to winders or other machinery during the process.

Ron Klein is president of Scientific Process & Research, Inc., designers and manufacturers of extrusion screws and developers of the EXTRUD -PC program.

Modeling and measuring slip

Slip is believed to play an important role in flows near the extruder die. Under some conditions of stress and strain, the melt undergoes some fracture at or near the wall. This results in uncertainty in the prediction of the flow of the melt, and can result in flow instability. In some cases, pressure drop predictions in capillary flow experiments reflect observations only when slip is incorporated in the problem formulation. Slip has also been implicated as a possible cause of melt fracture phenomena. It is widely accepted that slip along the wall plays a crucial role in melt flow instability of polyolefins. Extensive experimental results by Piau [Piau et al. (1990), Piau and El Kissi (1992)] and by Hatzikiriakos and Dealy (1992) provide convincing evidence of the importance of slip in the formation of surface defects. These observations justify the effort involved in slip modeling and measurement.

Numerical predictions of extrudate shapes for materials such as PVC or rubber should reflect experimental results when slip at the boundary is included in the mathematical model. Polyflow implements a model for slip as a relationship between the wall shear stress f_s and the fluid velocity at the wall v_s. A vanishing normal velocity component and a relationship between the shear force and the tangential relative velocity are simultaneously imposed:

 

where v₂ is the tangential velocity of the fluid, v_wall,1 is the tangential velocity of the wall, and F_slip and EX_slip are material coefficients. Note that full slip is obtained when F_slip = 0. The slip law (1) is either linear, with EX_slip = 0, or of the power law type, with EX_slip <0. We note that the case EX_slip = 0 preserves the linear character of the Newtonian flow problem. When EX_slip < 0, the problem becomes non-linear and requires an iterative solution technique, even for Newtonian flow. There seems to be experimental (not theoretical) evidence that for a power-law fluid described by the following viscosity/shear-rate relationship:

an acceptable correlation between EX_slip in (1) and n in (2) is EX_slip = n-i. This observation is based on comparisons between pressure drop measurements in capillary dies and numerical simulation results.

In order to determine parameters of law and in particular F_slip, it is necessary to perform specific experiments. Techniques are either based on global pressure drop data in capillary dies or on local measurements at the die wall. The Mooney experiment is based on global pressure drop data in capillary dies of different diameters. Another global technique is based on pressure drop/flow rate measurements in a smooth die and in a corrugated die of identical diameter. The difference in pressure drop between the two dies for the same flow rate is an indication of the amount of slip in the smooth die. Recent work has concentrated on local measurement of the velocity field very close to the wall, and on local measurements of the wall shear stress.

-Jean Marie Marchal is director, R&D. of Polyflow. References for this article are available from Datapoint Testing Services.