Manfred Achenbach
Head of Engineering and
Analytical Services
Pradifa Packing Div.
Parker Hannifin GmbH
Bietigheim, Germany

Edited by Kenneth Korane

Finite-element modeling is an attractive alternative to physical testing for predicting seal life, particularly when aging poses major concerns and seal replacement is expensive.

Finite-element modeling is an attractive alternative to physical testing for predicting seal life, particularly when aging poses major concerns and seal replacement is expensive.


For years, seal manufacturers and users alike have been searching for their industrial Holy Grail — a method for predicting how long seals will last in service.

Traditional methods for evaluating an elastomer's potential as a static or dynamic seal use ASTM or other standard immersion tests. These tests involve immersing the material in a test fluid for a specific time. Technicians then compare physical properties such as hardness and ultimate tensile strength, before and after immersion, and make a judgement as to the material's suitability as a seal.

Immersion testing certainly plays a role in screening potential materials. A good engineer, obviously, would not choose a material that severely deteriorated in the immersion test. However, some physical degradation and volume swell can generally be tolerated, so results are often ambiguous.

The problem is, elastomers are not tested in their final form — compressed and with little surface exposed to the fluid or environment. Thus, immersion tests do not predict how long elastomers will seal in specific environments. Yet many industrial seals must remain serviceable for 20 years or more in severe environments. That makes physical tests impractical.

Fortunately, another method is emerging for evaluating the long-term performance of elastomeric seals — numerical simulation using appropriate aging models.

FINITE-ELEMENT METHODS
Elastomers rely on pressure exerted against a housing for their sealing properties. But this stress decays over time, a well-known phenomenon accelerated by high temperatures and aggressive fluids. As sealing force decreases, at some point the seal leaks and fails. The process is commonly known as aging.

Elastomers age through two mechanisms: diffusion of fluid molecules and chemical reactions involving the molecular chain network. The finite-element method can model both behaviors and works with widely available commercial codes.

Applying finite-element methods to molecular diffusion and chemical reactions is relatively straightforward, as the equations that describe aging in elastomers are analogous to those describing heat conduction in solids.

AGING BEHAVIOR
General equations for nonlinear elasticity in elastomeric sealing materials are expressed in terms of strain-energy density. However, high temperatures change the molecular networks and, in turn, the strain energy. This is due to scission, or breaking, of primary cross links formed during curing and the creation of a secondary crosslinking molecular network. This can substantially change mechanical response and lead to compression set — the permanent deformation of the seal.

There are two rather different approaches to modeling rubber elasticity. On one hand, statistical (or kinetic) theory derives elastic properties from idealized models of the rubber structure. The other, phenomenological theory, takes a continuum-mechanics viewpoint. It constructs a mathematical framework to characterize rubbery behavior and solve stress and strainanalysis problems without reference to microscopic structure or molecular concepts.

Our approach takes into account both models. Phenomenological theory provides the needed continuum-mechanics framework, while certain aspects of kinetic theory help describe changes in the network of chain molecules. It lets us use FEA to design rubber seals and account for long-term behavior and irreversible effects.

We developed a rather simple strain-energy function for describing elastic properties of rubbers (the so-called neo-Hookean law) that also considers longterm effects and temperature dependency. While a simple procedure does sacrifice some precision and accuracy, results remain within customary rubberengineering design tolerances.

Next, we conducted experiments to measure long-term relaxation behavior of sealing materials. (Several tests are suitable for determining aging parameters, such as ISO Standard 11346.) Rubber strips at room temperature were subjected to fixed uniaxial stretch and then held at high, constant temperatures for a specified time. At high temperatures, stress decreases with time. And the higher the temperature the more stress decreases. Tests were carried out for different temperatures and time intervals, and technicians measured tensile-stress losses and permanent stretch. With this data, researchers established a relation between tensile stress and uniaxial stretch ratio.

We then developed a 3D framework using uniaxial relations as a guide. It models an infinitesimal volume element of rubbery material in a stress-free reference configuration at ambient temperature, as well as how it behaves at higher pressures and temperatures over time, where network junctions can undergo time dependent scission and a secondary network of links between chain molecules is developing in the squeezed state. The material then consists of molecular networks with different reference states. These may create anisotropy and lead to permanent set as well as to irreversible stress relaxation. We also present a constitutive equation based on the experimental findings. For additional information on the mathematical models and simulation techniques, see "A Deeper Look."

CHEMICAL REACTIONS
Chemical reactions present another challenge in FE analysis. The rate of change of an elastomer's tensile stress in a stressrelaxation experiment primarily depends on the rate at which polymer chains, and molecules linking adjacent chains, rupture.

For instance, in the case of steady-state diffusion of a fluid into a seal that causes irreversible chemical reactions and proceeds at a known rate, FEA can correlate chemical changes and mechanical response — and, thus, sealing ability.

Many chemicals and reactions can be handled by letting multiple scalar fields replace the single scalar field (temperature) in heat-conduction problems. Experience in applying this method to practical problems shows that it requires mass transport and chemical-reaction parameters for all relevant chemicals. Additionally, it requires data on relationships between relevant chemical concentrations and mechanical properties to assess structural and performance changes due to aging.

However, experimentally determining all the coefficients and how they depend on concentration and temperature is labor intensive and expensive, requiring elaborate experiments and equipment. Thus, even for this numerical procedure, it takes a number of basic tests results to qualify the material and establish parameters for the governing equations.

The FEA method applies not only to static seals, but also to dynamic ones like pneumatic piston seals. Sealing components inexpensive enough to periodically replace are not normally analyzed for long-term performance. But when seal replacement is prohibitively expensive, aging behavior and its impact on performance become major concerns. As elastomers become increasingly important in high-performance sealing applications, FEA can predict changes as seals age and suggest corrective actions.

Please or Register to post comments.

Search Parts

 

powered by:

 

 

Sponsored Introduction Continue on to (or wait seconds) ×