# Little more than a cure curve.

Little more than a cure curve

Normally, when we talk about rheology on rubber products, most of us think of cure curves, two point rises and [T.sub.c]90s. Rheology, however, is much more than that. Both much more powerful and useful.

Rheology is actually defined as the science that studies the deformation and flow of materials. Solids, liquids or melts can be studied in terms of the material's viscosity and elasticity. From this study, performance properties of the material can be determined and predicted

Before we can talk about some of the things that can be done with rheology, we will review some basics

First, definitions. Rubber, both normal thermoset materials and the newer TPEs, is a viscoelastic material. It combines both elastic and viscous behavior. Elasticity is defined as the ability of a material to store energy applied during deformation and return to its original shape. Viscous behavior, viscosity, is the resistance of the material to flow and the rate at which deformational energy can be relieved through flow

Next, stress and strain. Stress is the force applied to an object. Strain is the amount of movement that the object undergoes. Shear rate is the amount of change in strain with time.

The relationship between stress and strain is related in one of the following ways. For an ideal solid,

stress = modulus x deformation. This is related in Hooke's Law.

Newton's Law for a viscous fluid is similar. The only real difference is that a coefficient of viscosity is substituted for modulus. A fluid is said to be Newtonian if the viscosity does not change with shear rate. Likewise a solid is said to be Hookean in the region where its modulus is linear.

Polymers are also very sensitive to temperature. Physical properties change as the temperature changes. These changes are dependent on other properties of the polymer such as crystallinity, molecular weight, molecular weight distribution, etc.

Okay, now what?

Viscoelastic materials combine the behavior of Newtonian fluids and Hookean solids. Water is an example of a Newtonian fluid. It will deform continuously as stress is applied. As soon as the stress is removed, it stops and stays where it is.

A steel spring is an example of a Hookean solid. When stress is applied, it deforms to a given strain. As soon as the stress is removed, it snaps back to its original position.

When these properties are combined in a viscoelastic material we can begin to understand "creep." Under a constant load, these materials will change shape over time. This property is quantified in a term known as "creep compliance." This property becomes very important in determining load bearing capabilities, long term dimensional stability, etc.

If a material deforms in such a way that the ratio between stress and strain is constant at a given frequency and temperature, it is considered to be "linearly viscoelastic." Without going into the detailed mathematics used to derive it, this can be simplified into the following equation:

G(t) = s(t)/d where

* G(t) is the stress relaxation modulus as a function of time.

* s(t) is the stress applied as a function of time.

* d is the deformation.

Two models have been constructed to describe the behavior of a polymer. Both involve a spring and a dashpot operating simultaneously (see figure 1). In the Maxwell model, the spring and the dashpot operate in series. In the Voigt model, the elements act in parallel.

Using the Maxwell element, the relaxation modulus can be defined by

G(t) = [Ge.sup.-t/[Lambda]] where

* G = the shear rigidity of the spring

* [Lambda] = the relaxation time of a dashpot with a viscosity of [Eta] and

* [Lambda] = [Eta]G

Using the Voigt model, the creep compliance J(t) can be defined by:

J(t) = [1/G][1-e.sup.-t/[Lambda]]

In this formula, [Lambda] is the retardation time required for a spring to extend to its equilibrium length while being retarded by a dashpot.

In both cases, a group of elements will have a spectrum of discrete relaxation and retardation times. Each time will be associated with a relaxation modulus G or compliance J.

When a number of Maxwell type elements is connected in parallel, a spectrum of relaxation times will result. Each of these relaxation times will be associated with a relaxation modulus G of an individual element. These stresses are additive in the parallel array so that the viscoelastic functions can be determined by adding them all up. This will result in a continuous relaxation spectrum, H.H is defined as: [Mathematical Expression Omitted] where [G.sub.e] is the equilibrium shear modulus.

In a similar fashion, if a number of Voigt elements are connected in series, there will be a spectrum of retardation times. Each of these compliance times will be associated with a compliance J. Again, these compliances in series are additive, and will produce a continuous compliance spectrum L. L is defined by: [Mathematical Expression Omitted] where:

* [J.sub.e] = the instantaneous glass-like compliance and

* [Eta.sub.e] = the zero shear viscosity

These relaxation spectra define the response of a given material to any strain history. With this information, a material's response to any arbitrary strain history can be determined.

The rheological tests can be performed in three different test modes: steady shear, dynamic mechanical and transient. The steady shear applies a constant shear rate and measures the shear stress as a function of shear rate. The ratio of the two yields the steady state shear viscosity.

In the dynamic mechanical mode, an oscillating strain is applied to the sample and the resulting stress is measured. This stress is separated into two components: elastic stress (in phase with the strain) and viscous stress (90 [degrees] behind the strain). The ratio of elastic stress to strain is the storage modulus, G', while the ratio of viscous stress to strain is the loss modulus, G". The ratio of G"/G' is tan delta which measures the damping quality and heat build-up in the material.

Transient testing measures the stress relaxation characteristics of the material. These tests involve deforming the sample to a predetermined strain, then measuring the stress required to maintain that strain over time. These numbers can be related to molecular weight and molecular weight distribution.

Now that I've got it, what do I do with it?

One non-Newtonian property of polymers, particularly thermoplastic polymers, is shear thinning. In this phenomenon, the melt viscosity drops at higher shear rates. By using this property, material flow can be speeded up and heat generation can be reduced. It is also known that materials with a broad molecular weight distribution exhibit shear thinning at lower shear rates than those with narrow molecular weight distributions.

Using information noted previously, the molecular weight distribution is mirrored by the slope of the modulus vs. frequency curve. From these parameters, problems such as sag and surface smoothness on thermoplastic materials can be varied. Also, once the proper control numbers are established, they can be used for screening of material to ensure that no unusable products are manufactured.

Likewise, chain branching can affect the final performance as well as the processibility of a material. Since more highly branched polymers exhibit a greater degree of shear thinning than non-branched polymers at the same molecular weight, control of these parameters can improve process uniformity and final product performance.

With regard to rubber products, there has been a significant amount of work done in the last few years with respect to explosive decompression in products used in the oil field and with improving the life of tank treads. A great deal of the work done in this area has related performance of the products to modulus and loss tangent of the materials. In the case of tank treads, work is under way to provide for testing of the final product non-destructively so that testing can be used for screening of the product to ensure performance in the field. Using these types of rheological measurements, performance of many dynamic rubber, TPE and plastic parts can be understood and improved.

Figure 2 shows the interrelationship of these properties and how they can by used to improve products.

Summary

To summarize, I would like to quote from a recent publication by Rheometrics on rheological testing: "Rheology provides a window into a polymer, allowing the molecular innerworkings to reveal themselves by their measurable reactions to external stresses and strains. And modern rheometry provides the necessary tools. When a stress is applied, the polymer deforms. But the stress is unwelcome, and the structure attempts to relieve itself of it. In this stress relaxation process, the chains shift to less stressed positions each chain taking a time interval to relax which is, characteristic of its size, shape and spatial arrangement.

"Because a polymer's molecular weight is a matter of chain length and degree of branching, and we have a distribution of molecular weights, we also have a distribution of relaxation times, represented by the relaxation spectrum.

"This spectrum can be calculated from rheological data. In turn, other viscoelastic parameters can be calculated from it, along with the response expected from other types of deformation. The spectrum can also be used to calculate polymer molecular weight distribution.

"And because rheological testing provides a direct link between a polymer's response to a stress or strain and its molecular architecture, a link is forged between molecular weight, molecular weight distribution, chain branching and the polymer's behavior in processing.

"Thus, rheology provides an accurate means for relating molecular structure to process behavior, establishing design criteria and predicting product performance."

Rheology and understanding how our polymers and compounds function and can be better tuned goes hand in hand with statistical process control, total quality management and other techniques to better control what we are making. Like these other disciplines, knowledge of rheology will help prepare us and propel us into the 21st century. [Figures 1 and 2 Omitted]
COPYRIGHT 1991 Lippincott & Peto, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.