Edited by Kenneth J. Korane
Finite-element analysis (FEA) has come of age for those who design and use seals. It lets engineers study the viscoelastic effects of elastomers and plastics on seal and bearing performance, and predict life and failure. It’s leading to seals that
cost less and perform better than the ones they replace. Here’s an overview of how our company developed and validated FEA methods for comparing common sealing polymers.
All plastics and elastomers inherently move and deform under load, a behavior generally called viscoelasticity. It is most commonly known as creep and stress relaxation.
Creep is the increase in deformation or strain under a constant load/stress.
Stress relaxation is the decay of stress over time while material is under a constant strain.
Stress relaxation and creep can significantly affect seal shape, deformation, and performance. Stress relaxation reduces the force or stress exerted by the seal on adjacent surfaces. And it significantly influences compressive stress relaxation (CSR) and aging, two common parameters in the sealing industry. CSR measures a material’s stress relaxation in compression at a specified temperature over a period of time. Aging is a general term describing changes in sealing stress or force, in part caused by stress relaxation.
Creep indirectly but significantly affects sealing through deformations that change the distribution of sealing stress. The terms extrusion, cold flow, set and describe shape changes, and all are related to creep. Extrusion is typically movement of seal material into the small clearances of a rod housing or piston. Cold flow, another term for creep, defines shape changes over time. And set is deformation under stress or load, partly due to creep.
To simplify FEA to study creep and stress relaxation in seals, we focused on linear viscoelasticity. It follows the principle of superposition where the relaxation (or creep) rate is proportional to the instantaneous stress (or strain).
Predicting seal performance
The seal was analyzed using an axisymmetric model, temperatures of 23 and 205°C, and Abaqus FEA software. The elastomer is a 90 durometer HBNR, and stress-strain and relaxation data were used in the modeling. After assembly, 5,000 psi was applied to the top surface of the seal.
At 23°C, sealing stress at assembly, measured at node 110 in the FE model, is 650 psi. After seal relaxation for 1,000 min, sealing stress declines to 373 psi, a decay of 43%. Applying 5,000-psi pressure to the upper surface produces sealing stress at the node of 5,935 psi. After 1,000 min of relaxation, but still under pressure, sealing stress is 5,735 psi, a decay of just 3.4%. This indicates that maximum relaxation occurs after assembly, not after pressure is applied. Data for analysis at 205°C show similar results.. Full results are summarized in the table.
This analysis provides a better understanding of how this seal performs over time and a range of temperatures. It demonstrates the value of this technique to predict long-term sealing stress distribution and ensure the product works as intended.
Elastic materials can be modeled by using hyperelastic-material models for instantaneous stress and a time-dependent function (described in the accompanying sidebar.) Modeling generally uses uniaxial stress/strain and stress (or strain)/time data. The same holds for elastic-plastic materials, except instantaneous stress is modeled using uniaxial- elastic constants and stress/strain.
With the goal of making longer-lasting seals, we tested eight of our materials. Although proprietary, they are based on common polymer formulations and results are applicable to similar materials. Materials tested under compression creep and relaxation include:
• Virgin PTFE (Turcon T01)
• PTFE mixed with bronze (Turcon T46)
• PEEK with internal lubricant (Zurcon Z43)
• Nylon (Zurcon Z60)
• Nitrile (Turel BAE)
• Fluorocarbon (Turel E)
• Polyurethane (Zurcon Z20)
• Fabric composite (Orkot TXMM)
Test samples were buttons 10 mm in diameter by 10-mm thick; O-rings (for elastomers) with a 25.64-mm diameter and 3.53-mm cross section; and rectangular rings (for plastics) measuring 25.83 mm in diameter, 3.62-mm high, and 2.97-mm wide. An Instron testing machine loaded all samples axially.
We tested samples for compression creep and relaxation. Specialists performed FE analyses of the materials using test data and Marc and Abaqus codes. Finally, we compared FEA and test results, and found good correlation, validating the FEA processes.
Material models in FEA
Elastic materials are modeled in two steps: Using hyperelastic material models for instantaneous state of stress, and using the time-dependent function:
R(t) = [1 – Σ(αi (1 – e-t/τ))].
Linear viscoelasticity can be represented by the uniaxial stress state:
σ = Eε + η(δε/δt).
The relation for stress relaxation can be written as:
σ(t) = Y(t)εo
where Y(t) is a relaxation function modeled by a Prony series:
Y(t) = Eo[1 – Σ(αi (1 – e-t/τi))],
and i = 1…n; Eo = instantaneous modulus; αi = Prony constant; and τi = Prony retardation time.
A similar equation is used for creep strain behavior,
ε(t) = J(t) σo
where J(t) = creep compliance function modeled by a Prony series:
J(t) = (1/Eo)[1 – Σ(αi (1 – e-t/τi))],
and i = 1…n; and 1/Eo = instantaneous compliance.
Here’s a closer look at test and analysis methods for one material, Turel E fluorocarbon.
Button creep test. The button was tested under compressive load of 450 N held constant for about 15 hr to determine instantaneous stress-strain data and creep-strain data.
Ring creep test. The ring was tested under compressive load of 450 N held constant for about 15 hr to generate instantaneous stress-strain and creep-strain test data.
Ring relaxation test. The ring experienced compression strain of 35%, which was held constant for about 15 hr. Instantaneous stress-strain data and shear-modulus relaxation data were converted from the button’s uniaxial stress-time test data.
We validated FEA procedures by comparing FEA results of the button sample with the button test data, as well as ring FEA and test results. Similar tests and analyses were conducted for the other materials. The accompanying tables compare test and FEA results. Changes for various plastics due to creep show that the sealing materials tested have a steep viscoelastic effect in a short time span. Zurcon Z43 had the highest strain change, compared to the other plastics, but Turcon T46 show the largest creep strain of 19%. Zurcon Z20 has the smallest strain change and creep strain.
Note that creep-strain behavior of materials does not always translate exactly to behavior of seals made of these materials. Nonetheless, results show we can model and validate the effects of creep and stress relaxation with an acceptable level of accuracy. The eight materials represent a vast range of plastics, elastomers, and composite seal materials.
FEA can help engineers understand creep and stress relaxation, and their effects. When extrusion, set, cold flow, stress relaxation, or aging are concerns, it can also predict seal behavior. This lets engineers make better materials choices, lower costs, predict seal failure more accurately, and reduce safety factors. Ultimately, the benefit is better-designed products that give outstanding field performance.