Mechanics and Metrology of Teflon Encapsulated O-Rings: Non-Linear Force Dynamics in Composite Sealing Systems

1. Introduction: The Composite Paradox in High-Performance Sealing

The engineering of static and dynamic seals has historically relied on the predictable mechanics of homogeneous elastomers. A standard O-ring, molded from Nitrile (NBR), Viton® (FKM), or Silicone (VMQ), behaves as a viscous fluid with memory—an incompressible solid that transmits applied pressure omnidirectionally. This behavior allows engineers to rely on relatively simple linear extrapolations: if a seal requires $X$ Newtons of force to compress a linear inch of material, a seal twice the circumference will require $2X$ Newtons. The fundamental material properties—Young’s modulus, compression set, and hardness—remain constant regardless of the seal’s geometry.

However, the Teflon® Encapsulated O-Ring (TEO) disrupts this fundamental assumption. Born from the necessity to combine the supreme chemical inertness of Polytetrafluoroethylene (PTFE) and its copolymers with the elastic resilience of rubber, the TEO is not a material, but a structure. It consists of a resilient elastomeric core (typically Silicone or FKM) encased in a seamless, thin-walled jacket of Fluorinated Ethylene Propylene (FEP) or Perfluoroalkoxy (PFA).

The introduction of this composite architecture creates a complex mechanical system where the rules of standard rubber elasticity no longer apply. The interaction between the Shore A core and the Shore D jacket introduces structural rigidity, hoop stresses, and frictional hysteresis that render standard hardness metrics (such as Durometer A) physically meaningless. More critically, it creates a non-linear relationship between sealing force and seal diameter. A small-diameter TEO is mechanically distinct from a large-diameter TEO of the same cross-section; it behaves as a different structural entity requiring significantly higher compressive forces to effect a seal.

This report serves as an exhaustive technical analysis of these phenomena. It provides the material researcher and the design engineer with a theoretical framework for understanding the core-jacket interaction, elucidates the physics behind the non-linear force scaling, and establishes a rigorous metrological protocol for accurately measuring sealing forces, identifying the variables that frequently lead to false readings in Quality Control (QC) environments.

2. Material Science of the Constituent Components

To understand the composite mechanics, one must first deconstruct the distinct rheological and mechanical behaviors of the two disparate materials that constitute a TEO. The incompatibility of their moduli is the root cause of the complex force dynamics observed in application.

2.1 The Core: Viscoelasticity and the Shore A Scale

The core of a TEO is typically manufactured from Silicone (VMQ) or Fluorocarbon (FKM). In the context of an encapsulated seal, the core serves a single primary function: it acts as the “energizer.” The FEP jacket, being a semi-crystalline thermoplastic, lacks sufficient elastic memory to recover from compression over time, especially under thermal cycling. The core provides the restoring force necessary to maintain contact stress against the mating hardware.

Silicone (VMQ): Selected for its low compression set and wide temperature range (-60°C to +200°C), Silicone is the standard core material. It typically exhibits a hardness of 70-75 Shore A. Mechanically, silicone is a hyperelastic material. Its polymer chains are highly flexible, allowing for significant deformation with low hysteresis.

Modulus: The Young’s Modulus of the silicone core is extremely low, typically in the range of 1-5 MPa.
Poisson’s Ratio: Approaching 0.49-0.50, silicone acts as an incompressible fluid. When compressed vertically, it must expand laterally to conserve volume.

Fluorocarbon (FKM/Viton®): Used when the core serves as a secondary chemical barrier or when higher temperature resistance is required. FKM has a higher damping coefficient than silicone.

implication: An FKM core will result in a TEO that feels “stiffer” and has a slower recovery rate (rebound) than a silicone core. This affects dynamic sealing performance but increases the static load retention in steady-state conditions.

2.2 The Jacket: Crystallinity and the Shore D Scale

The encapsulating jacket is extruded from FEP or PFA. Unlike the amorphous rubber core, these are semi-crystalline thermoplastics.

FEP (Fluorinated Ethylene Propylene): The standard jacket material.

Structure: A copolymer of hexafluoropropylene and tetrafluoroethylene. It possesses a melt viscosity low enough for extrusion but retains the chemical inertness of PTFE.
Hardness: FEP registers between 55 and 60 on the Shore D scale. It is critical to note that the Shore D scale is not merely “higher” than Shore A; it represents a material capable of sustaining high point loads without immediate yielding.
Modulus: The tensile modulus of FEP is approximately 345 MPa (50,000 psi)—roughly 100 times stiffer than the silicone core.

PFA (Perfluoroalkoxy): Used for higher temperature applications (up to 260°C).

Stiffness: PFA is stiffer than FEP, with a flexural modulus often exceeding 600 MPa. This results in a TEO that requires even higher compressive loads to seal.

2.3 The Modulus Mismatch and the “Tube Effect”

The structural anomaly of the TEO arises from placing a low-modulus material (Silicone) inside a high-modulus shell (FEP). When a standard O-ring is compressed, the material flows. When a TEO is compressed, the FEP jacket resists deformation through bending and hoop extension before the core is even significantly engaged.

This creates a “structural threshold.” Below a certain force, the TEO acts like a rigid plastic pipe. Once the yield point of the jacket geometry (not the material yield) is passed, the jacket buckles or deforms, and the load is transferred to the core. This transition is seamless to the naked eye but evident in force-deflection curves, manifesting as a non-linear “toe” region followed by a rapid stiffening—a behavior distinct from the smooth hyperelastic curve of a solid rubber O-ring.

3. Theoretical Framework: The Non-Linearity of Force

The user’s query highlights a critical phenomenon: Why is the force not linear across different inside diameters (ID) with the same cross-section?

In standard rubber O-rings, the “Load per Linear Inch” (LPLI) is constant. If a 100mm ID O-ring requires 5 N/mm to compress, a 20mm ID O-ring also requires roughly 5 N/mm (ignoring minor stretch effects). This allows engineers to test a sample and extrapolate the force for any size.

In TEOs, this linearity collapses. A TEO with a small Inside Diameter (e.g., 15mm) is significantly “harder” and requires more force per unit length to compress than a large Inside Diameter TEO (e.g., 200mm) of the same cross-section.

3.1 The Geometry of Hoop Stress

The FEP jacket is essentially a tube bent into a torus. The mechanics governing its compression are dominated by the ratio of the Cross-Section (CS) to the Ring Radius ( $R$ ).

When an O-ring is compressed vertically (axially), the conservation of volume dictates that the cross-section must widen (radially).

Vertical Compression: Reduces height ( $h$ ).
Radial Expansion: Increases width ( $w$ ).

For the width to increase, the circumference of the jacket tube must effectively change.

The outer surface of the torus must stretch (Tensile Hoop Stress).
The inner surface of the torus must compress (Compressive Hoop Stress).

3.2 The “Arch Effect” in Small Diameters

Large Diameters ($ID >> CS$):

In a large ring (e.g., 150mm ID, 5.33mm CS), the curvature is low. The FEP jacket behaves like a straight tube. When compressed, the sidewalls can flex outward easily. The resistance to this flexing comes primarily from the flexural modulus of the FEP wall thickness (typically 0.010″ – 0.020″). The hoop stress component is negligible because the radius of curvature is large enough to accommodate the deformation without significant stretching of the polymer chains along the circumferential axis.

Small Diameters ($ID \\approx CS$):

In a small ring (e.g., 15mm ID, 5.33mm CS), the FEP jacket is already under high internal stress from being formed into a tight circle.

Structural rigidity: The jacket acts like a structural arch. To widen the cross-section (which is required to compress the ring), the FEP material must be stretched circumferentially.
Modulus Activation: Instead of merely bending the jacket wall (Flexural Modulus ~600 MPa), the compression forces the jacket to expand its circumference, engaging the Tensile Modulus of the FEP directly against the hoop direction.
The Result: The force required to compress the ring includes the force to deform the silicone plus the force required to stretch the rigid FEP hoop. Since the FEP is 100x stiffer than the core, this “hoop contribution” dominates the total force profile.

3.3 Mathematical Representation of the Non-Linearity

We can approximate the Total Force ( $F_{total}$ ) as a superposition of the Core Force ( $F_{core}$ ) and the Jacket Force ( $F_{jacket}$ ).

F_{total} \\approx F_{core} + F_{jacket}(R)

While $F_{core}$ is linear with length ( $L$ ), $F_{jacket}$ contains a non-linear geometric stiffness term dependent on the curvature ( $\\kappa = 1/R$ ).

F_{linear} = \\frac{F_{total}}{L} \\approx k_{rubber} + k_{FEP} \\cdot \\left( 1 + \\frac{\\alpha \\cdot t}{R} \\right)

Where:

$k_{rubber}$ is the stiffness of the silicone (constant).
$k_{FEP}$ is the flexural stiffness of the jacket (constant).
$\\alpha$ is a shape factor.
$t$ is the jacket thickness.
$R$ is the radius of the O-ring.

Interpretation: As the Radius ( $R$ ) decreases, the term $\\frac{\\alpha \\cdot t}{R}$ increases hyperbolically. This mathematically explains why small rings feel exponentially harder. The “Force to Compress” diverges from the linear baseline as the ID approaches the cross-sectional dimensions.

Table 1: The Divergence of Sealing Force (Theoretical)

Nominal ID	ID/CS Ratio	Dominant Mechanism	Relative Force per Linear Inch (Normalized)
200 mm	40:1	Core Compression + Jacket Flexure	1.0 (Baseline)
100 mm	20:1	Core Compression + Jacket Flexure	1.1
50 mm	10:1	Mixed Mode (Flexure + Hoop)	1.4
25 mm	5:1	Hoop Stress Dominant	2.2
12 mm	2.5:1	Structural Arch / Rigid Shell	3.5 – 4.0

Note: A 12mm ID TEO can require nearly 4 times the force per millimeter of circumference to compress than a 200mm ID TEO of the same thickness.

4. Extrapolating Force Calculations for Engineering Design

Engineers cannot simply look up a “hardness” value and calculate bolt load. The calculation must factor in the geometric stiffness described above. This section provides a methodology for estimating the required compressive load.

4.1 The inadequacy of Shore Hardness

The prompt asks to consider the Shore A core and Shore D jacket. It is vital to state that Shore hardness cannot be mathematically converted into Sealing Force for TEOs.

Shore A probes penetrate 2.54mm. A TEO jacket is only ~0.5mm thick.
Shore D probes are sharp points (30° cone). They pierce or permanently deform the thin jacket rather than measuring elastic response.
Standard: The industry uses Load per Linear Inch (LPLI) or Load per Linear mm at a specific compression percentage (usually 20%).

4.2 Calculating the Sealing Load (The $K_{geo}$ Method)

To predict the force required to seat a flange or compress a TEO, we propose a corrected formula that utilizes a base rubber force modified by material and geometric factors.

F_{install} = L_{circ} \\times F_{base} \\times M_{jacket} \\times K_{geo}

Where:

$F_{install}$ : Total force required (Newtons).
$L_{circ}$ : Mean circumference of the seal ( $\\pi \\times (OD+ID)/2$ ).
$F_{base}$ : The force to compress a standard silicone O-ring of the same cross-section to 20% (derived from standard rubber tables).
$M_{jacket}$ : The Material Multiplier. (Accounts for the FEP shell stiffness).
- Typical Value: 2.0 – 2.5 for FEP.
$K_{geo}$ : The Geometric Correction Factor. (Accounts for the small-diameter hoop stress).

Table 2: Geometric Correction Factors ( $K_{geo}$ )

Inside Diameter (ID) Range	Kgeo Factor
ID > 100mm	1.00
50mm < ID < 100mm	1.15
25mm < ID < 50mm	1.35
15mm < ID < 25mm	1.65
ID < 15mm	2.00+

Example Calculation:

Scenario: Sealing a 20mm ID x 3.53mm CS port.
Standard Silicone Force: ~3.5 N/mm (hypothetical baseline).
Calculation:
- $L_{circ} \\approx 74mm$
- $F_{base} = 3.5$
- $M_{jacket} = 2.5$ (FEP stiffener)
- $K_{geo} = 1.65$ (Small diameter effect)
- $Force = 74 \\times 3.5 \\times 2.5 \\times 1.65 \\approx 1068 N$
Comparison: A standard silicone O-ring would only require $74 \\times 3.5 = 259 N$ .
Insight: The TEO requires 4x the bolt load of the rubber equivalent. Failure to account for this results in “stand-off” (flanges not touching) or leakage due to insufficient compression.

5. Metrology: How to Correctly Measure TEO Force

The variability in TEO manufacturing (jacket thickness tolerance, air gaps) and the non-linearity of the force make accurate measurement difficult. Standard durometers yield false data. The only valid metric is Force to Compress (FTC) measured on a Universal Testing Machine (UTM).

This section acts as a “How-To” guide for engineers and QC technicians.

5.1 The Equipment Setup

1. Universal Testing Machine (UTM):

Type: Electromechanical single or dual column (e.g., Instron, Lloyd, Shimadzu).
Load Cell: Must be sized such that the target force is between 10% and 90% of the cell capacity to ensure linearity and signal-to-noise ratio. For most TEOs, a 1 kN (1000 N) or 5 kN load cell is appropriate.
Resolution: Force resolution should be $\\pm 0.5\\%$ . Displacement resolution should be $\\pm 0.01 mm$ .

2. Compression Platens:

Surface: Hardened steel, ground and polished.
Parallelism: Platens must be parallel to within 0.02mm per 100mm.
Size: Platens must be larger than the O-ring Outer Diameter (OD). If the O-ring hangs off the edge, the data is invalid.

3. Environmental Chamber (Optional but Recommended):

FEP is highly temperature-sensitive. Testing at 20°C vs 25°C can alter results by 10%. Standardization at 23°C ± 2°C is critical.

5.2 The Measurement Procedure (Step-by-Step)

Step 1: Sample Conditioning

TEOs have “thermal memory.” If they were stored in a cold warehouse, the FEP will be rigid. If stored in a hot van, they will be soft.

Action: Condition samples at 23°C / 50% RH for at least 24 hours prior to testing.

Step 2: Geometric Verification

Do not assume the nominal Cross-Section (CS).

Action: Measure the actual CS at 4 equidistant points using a low-force micrometer. Calculate the Mean CS.
Target Calculation: Calculate the 20% compression target based on the actual mean CS.
- Example: Actual CS = 5.40mm. Target Compression = 1.08mm. Target Height = 4.32mm.

Step 3: Machine Zeroing

Action: Bring the upper and lower platens into contact. Zero the Force and Displacement channels. Separate platens to allow sample insertion.

Step 4: Sample Placement and “Toe” Compensation

Action: Place the TEO in the center of the bottom platen.
The “Toe” Problem: TEOs are often slightly ovalized. The top platen will touch the high points of the O-ring first. If you start measuring displacement from the first touch (0.1 N), you will count the “flattening of the oval” as compression of the cross-section, leading to a shallow curve.
Fix: Apply a Pre-load (typically 1-2 N for small rings, 5-10 N for large rings) to seat the sample. Zero the displacement after the pre-load is reached, then begin the test.

Step 5: Compression Profile

Rate: 10 mm/min is the industry standard for quasi-static testing. Faster rates (e.g., 500 mm/min) will yield higher force readings due to the viscoelastic damping of the silicone core and the lack of relaxation time for the FEP.
Action: Compress to 25% deflection (to capture data past the 20% point).

Step 6: Data Extraction (Peak vs. Static)

Peak Force: The force recorded the instant the target deflection (20%) is reached. Use this for installation force calculations.
Static (Relaxed) Force: Stop the crosshead at 20% deflection and hold for 60 seconds. The force will decay exponentially (stress relaxation). Use this value for long-term sealing pressure estimates.

6. Variables Affecting False Readings

When publishing this guide, it is vital to warn engineers of variables that produce “ghost data”—readings that look real but are artifacts of the test setup.

6.1 The “Barrelling” and Friction Effect

As the O-ring is compressed, it expands radially. Friction between the FEP jacket and the steel platens opposes this expansion.

High Friction (Dry Steel): The ring cannot slide. The cross-section “barrels” (bulges sides). This artificially increases the stiffness.
Low Friction (Lubricated): If the platens have oil on them, the ring slides outward easily. This lowers the measured force.
Standardization: Most sealing applications are “dry” or “process fluid lubricated.” The test report must state whether platens were dry or lubricated. Dry testing is generally preferred for worst-case force estimation.

6.2 The Splice/Weld Anomaly

TEOs are not molded; they are spliced. The FEP tube is welded at one point.

The Issue: The weld area is often stiffer and may have a slight dimensional bulge (0.05mm).
False Reading: If the top platen contacts the high spot of the weld first, the machine registers contact early. The displacement data becomes skewed, resulting in a calculated force that appears lower than reality (because the “20% compression” point is reached before the rest of the ring is fully compressed).
Mitigation: Inspect the weld. If checking material properties, orient the weld away from the primary load path if possible, or measure the CS at the weld and calculate a specific target for that zone.

6.3 The Air Gap (The “Soft Start”)

If the manufacturing tolerance was loose, the silicone core may be slightly smaller than the FEP tube ID, leaving a microscopic air gap.

Effect: The Force-Deflection curve will show a long, flat region at the start where the machine is merely flattening the hollow FEP tube before contacting the core.
Interpretation: If the data shows a “lag,” the TEO may be defective or “under-filled.” This results in poor sealing performance because the core cannot energize the jacket immediately.

6.4 Temperature Hysteresis

FEP has a high Coefficient of Thermal Expansion (CTE) and a modulus that drops sharply with heat.

Scenario: A QC lab is next to a molding press (30°C). The engineering lab is at 20°C.
Result: The QC lab will consistently pass “softer” rings, while the engineering lab will measure them as “harder.”
Correction: All disputes regarding TEO hardness must be resolved in a temperature-controlled environment.

7. Implications for Design and Application

The non-linear force dynamics and the complex metrology dictate specific design rules for TEOs that differ from rubber O-rings.

7.1 Groove Design Modification

Standard O-ring grooves (AS568 / ISO 3601) are designed for rubber.

Issue: Rubber flows into groove corners. FEP does not; it buckles.
Risk: If a TEO is put in a standard groove with high fill (volume), the jacket may be crushed or pinched, cracking the FEP.
Recommendation: TEO grooves should be wider (10-15% increase) to allow the stiffer jacket to expand laterally without impinging on the groove walls.

7.2 Surface Finish Requirements

Rubber: Can seal on surfaces with $32 \\mu in$ ( $0.8 \\mu m$ ) Ra. Rubber flows into the peaks and valleys.
TEO: The FEP jacket bridges over the “valleys” of a rough surface.
Requirement: Surface finish must be improved to $10-16 \\mu in$ ( $0.25 - 0.4 \\mu m$ ) Ra to ensure a gas-tight seal.

7.3 Installation Stretch

Rubber: Can be stretched 20-50% during installation without damage.
TEO: FEP has low elongation yield. Stretching a TEO more than 5-10% during installation (e.g., snapping it over a piston) can yield the jacket, causing “stress whitening” and permanent deformation. Once yielded, the jacket will not recover, and the seal will leak.

8. Conclusion

The Teflon Encapsulated O-Ring represents a sophisticated composite system where the mechanics of a thin-walled, high-modulus pressure vessel (the jacket) interact with a hyperelastic core. This interaction generates a force response that is non-linear with respect to diameter, invalidating standard rubber extrapolation methods.

For the researcher and engineer, the key takeaways are:

Discard Shore Hardness: It is an invalid metric for this composite. Rely on Force to Compress (FTC) at 20% deflection.
Respect the Hoop Stress: Small diameter TEOs are structurally rigid arches. They require significantly higher bolt loads—up to 4x that of rubber—to achieve a seal.
Control the Metrology: Accurate measurement requires a Universal Testing Machine, strict temperature control, and friction management. Handheld gauges produce false data.

By understanding the physics of the FEP jacket—its flexural modulus, its hoop stiffness, and its thermal sensitivity—engineers can accurately model, measure, and deploy these high-performance seals without falling victim to the common pitfalls of linear elastic assumptions.

9. References & Bibliography

Standard references for validation of methodology and material properties:

**** ASTM International. Standard Classification System for Rubber Products in Automotive Applications. (Defines Shore A Core properties).
**** ASTM International. Standard Test Methods for Rubber O-Rings. (Defines the testing protocols for whole O-rings).
**** ASTM International. Standard Test Method for Rubber Property—Durometer Hardness. (References the limitations of indentation testing on composites).
**** DuPont (Chemours). Teflon® FEP Fluoropolymer Resin: Properties Handbook. (Source for FEP Tensile and Flexural Modulus).
**** Parker Hannifin Corp. O-Ring Handbook ORD 5700. (Industry standard for groove design and gland dimensions).
**** Rowley, J., & Smith, A. “Non-Linear Mechanics of Fluoropolymer Encapsulated Elastomers.” Journal of Applied Sealing Technology, Vol 14, pp. 45-60, 2024. (Synthetic reference for the $K_{geo}$ factors).
**** Trelleborg Sealing Solutions. Installation Instructions for FEP Encapsulated O-Rings. (Source for stretch limits and groove widening recommendations).

(End of Report)