Multi-Fiber, MT Ferrule Endface Fiber Tip Displacement
`Model for Physical Contact Interconnects
`Michael Gurreri, James Kevern, Michael Kadar-Kallen, Lou Castagna
`Tyco Electronics
`PO Box 3608, Harrisburg, PA 17105
`email: mgurreri@tycoelectronics.com
`
`Darrell Childers, Mike Hughes
`US Conec, Ltd.
`1555 4th Avenue SE, Hickory, NC 28602
`email: mikehughes@USConec.com
`
`1.
`
`Abstract: This paper describes a simplified model linking MT ferrule and connector attributes to positive
`contact performance. Validation with FEA, experimental apparatus and empirical results are described, along
`with topics for future study.
`©2006 Optical Society of America
`OCIS codes: (060.2340) Fiber Optics Components; (120.3180) Interferometry
`Introduction
`Multi-fiber, monolithic MT ferrules are used in a wide variety of optical interconnect applications including
`bulkhead feed-through connectivity, optical backplanes and outside plant passive optical networks. The typical MT
`ferrule is comprised of at least one fiber array with up to twelve 125μm diameter fibers on 250μm centerline spacing.
`The MT ferrule has a rectangular cross-section of 2.4mm X 6.4mm and a depth of 8mm. The ferrules are generally
`molded from a highly glass-filled, thermoplastic or thermoset resin, which combines the durability and stability
`required of a connector with the precision necessary to maintain low-loss singlemode core-to-core alignment across
`multiple fibers. Although single row ferrules with four, eight or twelve fibers are the most common, multi-row MT
`ferrules with up to 72 fibers are now readily available. This high density interconnect package offers a compact,
`convenient means for quickly and effectively distributing large numbers of fibers.
`To assure precision alignment between two mating MT ferrule based connectors, a non-interference, dual guide
`pin and hole system is used. One connector in the pair typically houses both guide pins while the mating, unpinned
`connector ferrule receives the guide pins when mated. The pinned and unpinned ferrules have identical geometry.
`In order to establish a reliable, dry, low insertion loss and low reflectance junction, physical contact between
`each fiber tip is imperative. Even with very accurate core-to-core alignment, power loss from Fresnel effects, which
`are associated with gaps between fiber tips, will not meet the requirements of today’s WDM and Passive Optical
`Network applications. To achieve physical contact, the ferrule endface is prepared such that the fiber tips are
`protruding from the ferrule surface.
`Optical transmission systems have historically employed physical contact connectors that are based on single-
`fiber cylindrical ferrules. To establish dimensional limits on the end face geometry, such that physical contact is
`maintained, the mechanics of single-fiber connectors have been studied extensively [1,2]. These studies employed
`finite element analysis (FEA), boundary element methods, Hertzian analysis, and experimentation to develop a
`comprehensive understanding of the interface under various environmental and mechanical conditions [3-7]. Given
`that MT connectors have emerged as a de facto standard for high density applications, similar evaluations will allow
`for meaningful specification of the governing end face variables.
`The two primary parameters, which impact the ability to obtain physical contact in an MT connector system are
`(1) the coplanarity of the protruded fiber tip and (2) the angular accuracy in both axes of the ferrule endface relative
`to the guide pin bores. Even the most advanced and well-controlled mass production processes today produce fiber
`arrays with some variation in fiber tip protrusion and angular endface accuracy. Any imprecision of this nature must
`be overcome by deformation due to the connector spring mechanism to obtain physical contact of mating fiber tips.
`Gaps between the fiber tips resulting from these manufacturing inaccuracies are illustrated in Figure 1.
`
`US Conec EX1008
`IPR2024-00115
`U.S. Patent No. 11,307,369
`
`

`

`Connector
`Spring Force
`
`F
`
`Connector
`Spring Force
`
`F
`
`Figure 1: Schematic of MT ferrule pair with exaggerated manufacturing inaccuracies to be
`overcome by the connector spring mechanism
`Two primary ferrule attributes that determine the connector endface geometry requirements for physical contact
`are the fiber tip stiffness and rotational stiffness. The focus of this research is on the fiber tip stiffness. The fiber tip
`stiffness will dictate the industry specification for fiber tip coplanarity [8] across an array of fibers. Coplanarity is
`the difference between the maximum and minimum fiber tip protrusions relative to a best-fit line through the fiber
`tip array distribution.
`2.
`Theory
`A three-stage analytical approach was taken to examine the force required to displace the tip of a single fiber in
`an MT ferrule when an axial load is applied to the fiber. First, a full three-dimensional finite element model was
`created as a baseline. Then, for computational efficiency, a two-dimensional axisymmetric finite element model
`was created to explore a variety of fiber tip radii to determine a composite “fiber stiffness” that includes the
`elasticity of the ferrule, fiber and epoxy regions. This stiffness became the basis of an even more simplified model
`wherein each fiber is represented by a spring. The behavior was verified experimentally by mating specially
`prepared samples against a transparent rigid plate and using interferometry to observe fiber contact.
`2.1. Three dimensional FEA
`The three-dimensional FEA was performed on a single row, 12-fiber MT ferrule to observe the deflection with a
`single load applied to the fiber under study. The model, which included material properties for the ferrule, fibers,
`and bonding epoxy, was constrained at the base of the ferrule and subjected to a 1N distributed load on one of the
`central fibers. The compressive deflection results of the model are illustrated in Figure 2. It was observed that the
`displacement field is radially symmetric in the region of interest. This finding indicates that a two-dimensional,
`axis-symmetric model can be used to simplify the analysis. There are also larger, asymmetric displacement contours,
`due to the presence of an epoxy window on one side of the ferrule. However, this deflection, which is relatively low
`in magnitude, had an inconsequential effect on the overall system stiffness.
`
`Figure 2: 3D FEA model with load applied to one center fiber. The color gradient represents the Z-
`axis deflection field.
`
`

`

`In addition, it was determined that a foundation effect is present such that, when displacing a single fiber, the
`stress zone within the ferrule body is large enough to influence the fiber tip location of adjacent fibers. Notable
`adjacent fiber displacement was detected at fiber locations 250μm, 500μm, and 750μm away from the fiber under
`load. This discovery suggests that the displacement of each fiber tip is related not only to the reaction force of that
`particular fiber, but also to the applied forces on neighboring fibers. These discoveries led to a conceptual model
`that includes an elastic base as shown in Figure 3.
`
`RIGID PLATE
`
`2
`
`3
`
`Fiber Tip 1
`
`4
`
`1
`
`2
`
`3
`
`4
`
`INITIAL
`
`DEFORMED
`
`Figure 3: Simplified conceptual model of four fiber MT ferrule fiber tips compressed by a rigid
`plate showing the foundation effect.
`
`2.2. Two dimensional axisymmetric FEA
`Based on evaluation of the complete, three-dimensional model results, an axisymmetric FEA was generated.
`This yielded a streamlined approach that allowed parametric adjustment of the dominant variables, including the
`geometry, material properties, and load conditions. As shown in Figure 4, a cross-sectional slice was taken through
`one of the individual fiber centers. This cross-section included regions for the optical fiber, epoxy layer, and ferrule,
`and the material properties were based on published literature values. The boundary conditions included a fixed
`displacement to a rigid plate, which contacts a spherically shaped fiber tip, and fixed constraints on the ferrule
`exterior. Other pertinent details of the model are defined in Appendix A.
`
`
`CONTACT CONTACT
`ELEMENTS
`
`
`RIGID RIGID
`
`PLATEPLATE
`
`DISPLACEMENT
`DISPLACEMENT
`
`
`
`FERRULEFERRULE
`
`EPOXY
`EPOXY
`
`
`
`FIBERFIBER
`
`SYMMETRY
`
`SYMMETRY
`
`W
`
`p
`
`FERRULE
`
`EPOXY
`
`FIBER
`
`FIBER
`
`L
`
`A
`
`FERRULE
`
`LCLC
`SECTION A-A
`
`
`CC
`
`LL
`Figure 4: 2D Axisymmetric Model Concept with load applied to one fiber.
`To validate this two-dimensional model, the fiber reaction force and displacements were compared to the more
`computationally intense, three-dimensional analysis. It was found that the two models produced nearly identical
`results for the fiber under load, as well as the neighboring unloaded fibers at 250μm, 500μm and 750μm. The
`
`

`

`contour plot shown in Figure 5 illustrates the axial deflection of the system given a 2μm displacement of the rigid
`plate. This demonstrates that a significant portion of the system elasticity is attributable to compression of the
`ferrule region due to the relatively large displacement zone.
`
`FERRULE
`
`EPOXY
`
`FIBER
`
`SYMMETRY AXIS
`
`Axial Displacement (μm)
`Figure 5: Axial deflection results for a 2μm displacement of the fiber tip
`Several iterations of the model were run with various fiber tip profiles and loads to understand how these
`parameters influence the overall system stiffness. To summarize the results, Figure 6 shows a graph of the fiber
`reaction forces, which are plotted as a function of tip displacement, for a family of different radius cases. This data
`reveals several critical traits of the overall system behavior. As the fiber tip radius decreases, the equivalent spring
`constant, as illustrated by the slope of the curves, is significantly reduced. The case with the highest stiffness, which
`is associated with a flat fiber tip (infinite radius), has a spring rate of about 4.2 N/μm while the 1mm case has a rate
`of about 2.1 N/μm. Furthermore, as the fiber tip radius decreases, the linearity of the spring constant diminishes.
`This suggests that there are two components to the fiber tip displacement: (1) The composite stiffness of the ferrule,
`fiber, and epoxy, and (2) the classical Hertzian contact deformation of the glass fiber tip. For large fiber tip radii,
`the composite stiffness is largely responsible for tip displacement, while the Hertzian effect plays a minor role;
`whereas, for small radii, the impact of the Hertzian component becomes noticeable.
`
`

`

`Fiber Tip Radius
`R = 1 mm
`R = 2 mm
`R = 3 mm
`R = 10 mm
`R = Infinity
`
`0.2
`
`0.4
`0.6
`Fiber Compression (microns)
`
`0.8
`
`1.0
`
`5
`
`4
`
`3
`
`2
`
`1
`
`Fiber Tip Reaction Force (N)
`
`0
`0.0
`
`Figure 6: Fiber tip reaction force as a function of compression and fiber tip radius. Note the
`nonlinear behavior increases as the tip radius decreases.
`Figure 7 demonstrates the foundational effect: the displacement of fibers other than the fiber to which the force
`is applied, caused by the deformation of the MT ferrule "foundation". The displacements of the other fibers are
`linear functions of the applied force, independent of the radius of the tip of the fiber to which the force is applied.
`
`Fiber Location
`250 um
`500 um
`750 um
`
`0.05
`
`0.10
`0.15
`0.20
`Adjacent Fiber Displacement (microns)
`
`0.25
`
`0.30
`
`Figure 7: Fiber tip reaction force as a function of adjacent fiber displacement.
`
`6
`
`5
`
`4
`
`3
`
`2
`
`1
`
`Fiber Tip Reaction Force (N)
`
`0
`0.00
`
`

`

`3.
`
`Simplified Mathematical Model
`A simplified mathematical model based on the fiber tip displacement vs. force FEA analysis was developed to
`quickly and accurately predict the forces required for physical contact for actual ferrule geometries. Figure 8
`defines the parameters that were used to generate this model.
`
`RIGID PLATE
`
`F1
`
`F2
`
`F3
`
`F4
`
`p1
`
`d1
`
`z2
`
`u2=d2
`
`z
`
`1
`
`2
`
`3
`
`4
`
`1
`
`2
`
`3
`
`4
`
`FERRULE
`
`(b)
`(a)
`Figure 8: Model Parameters: (a) Fiber protrusion in the absence of an applied force; (b) A rigid
`plate is at a distance z such that some fibers are in contact with the plate.
`The displacement of an individual fiber tip di is the difference between the initial protrusion pi and the protrusion
`zi under an applied load:
`
`d
`p
`z
`i
`i
`i
`Note that zi is measured with respect to the initial, undeformed ferrule surface. This displacement consists of
`two components:
`
`−
`
`.
`
`=
`
`d
`
`u
`
`,
`
`+Δ=
`i
`i
`i
`where Δi is the compression of the fiber i due to the force Fi applied to fiber i and ui is the displacement of the
`foundation of fiber i due to the forces applied to the other fibers.
`From Figure 7 it can be seen that the displacement of the foundation of fiber i due to the forces applied to the
`other fibers is a linear function. The displacement of the foundation of fiber i can therefore be modeled as a series of
`springs such that:
`
`(1)
`
`(2)
`
`j
`
` ,
`
`(3)
`
`kF
`∑<
`
`>
`
`i
`
`j
`
`u
`
`i
`
`=
`
`ij
`where kij is the spring constant which couples fiber i and fiber j.
`By combining Equations 1, 2, and 3, the following equation for the fiber tip protrusion under load is derived:
`
`j
`
`.
`
`(4)
`
`kF
`∑<
`
`>
`
`i
`
`j
`
`z
`
`i
`
`=
`
`p
`
`i
`
`−Δ−
`i
`
`ij
`The force Fi applied to a fiber tip is related to the compression Δi caused by this force and to the radius of
`curvature ri of the fiber, as shown in Figure 6. Note that Δi = 0 if and only if Fi = 0.
`
`

`

`i
`
`≥
`
` if
`
`i
`
`−
`
`.
`
`(5)
`
`(6)
`
`Applying the following boundary conditions for a given rigid plane at a distance z from the ferrule defines a set
`of N simultaneous equations with N unknowns: the forces Fi, or the corresponding compressions Δi
`
`z
`p
`u
`zzi = if
`<
`−
`z
`p
`u
`z
`p
`u
`=
`−
`i
`i
`i
`i
`i
`By varying the value of z and solving the set of equations for each value of Fi , the minimum force required to
`achieve contact with the rigid plate can be determined. The total force applied to the rigid plate is simply
`∑=
`F
`iF
`
`.
`
`4.
`
`Experimental Methodology
`To assess the validity of the theoretical models, MT ferrule assemblies were created with end face geometries
`designed specifically to facilitate the experiment. This was accomplished by polishing such that the fiber tip
`elevations lay along a curved profile with varying deviation (coplanarity). These parts were characterized
`interferometrically for coplanarity of the fiber tips as well as for shape of the individual fibers. A sample fiber tip
`radius is shown in Figure 9.
`
`Contour
`
`X-Profile
`
`Y-Profile
`
` 0.8
`
` 0.4
`
` 0.0
`
`-0.4
`
`-0.8
`
`Figure 9: Typical interferometric endface analysis of fiber tip
`An experiment was then set up to evaluate the forces required to bring the various protruded fiber tip heights into
`contact with a transparent rigid body. By shining white light through the transparent body onto the ferrule endface,
`fiber tip contact with the body can be observed through a microscope when the reflection of light traveling through
`the body onto the polished fiber tips is eliminated by physical contact. At the point of fiber contact with the
`transparent rigid body, light is no longer reflected from the fiber tips, but rather transmitted into the fiber resulting in
`a dark contact region on the fiber tip.
`The transparent rigid body is mounted onto a stage with precision angular alignment control in both primary axes.
`The angular alignment control of the rigid body provides a means to ensure physical contact with only the protruded
`fiber tips. The MT ferrule is mounted to a load cell for capturing the forces transmitted by the rigid body for various
`stages of fiber tip physical contact. By documenting the amount of force required to bring known fiber tip heights
`into contact with the optical flat, the theoretical deflection vs. reaction force model can be compared with actual
`empirical data. A schematic of the experimental apparatus is illustrated in Figure 10.
`
`

`

`
`Load Cell Load Cell
`
`MonitorMonitor
`
`
`
`Light SourceLight Source
`
`
`Transparent Transparent
`
`Rigid Plate Rigid Plate
`
`(Sapphire Flat)(Sapphire Flat)
`
`
`
`MonitorMonitor
`
`
`Transparent Transparent
`
`Glass Slide for Glass Slide for
`
`IlluminationIllumination
`
`MicroscopeMicroscope
`
`
`
`CameraCamera
`
`
`X, Y, Z X, Y, Z
`
`StageStage
`
`
`
`MT FerruleMT Ferrule
`
`
`
`Optical BenchOptical Bench
`
`
`X-Y TiltingX-Y Tilting
`
`Optical Flat MountOptical Flat Mount
`
`Figure 10: Apparatus for measuring fiber tip deflection vs. reaction force
`The polishing process used for the experimental MT ferrules yielded a fiber tip distribution such that the fiber
`tips in the center of the array protruded the most, while the fiber tips on the ends of the protruded the least. As a
`result, the outermost fiber tips are the last to come into contact when force is applied with a flat, rigid body. An
`example of the Tip Deflection vs. Reaction Force data collected for a typical MT endface is shown in Figure 11.
`
`
`
`Rigid PlateRigid Plate
`
`
`
`FF
`
`
`
`11
`
`
`
`22
`
`
`
`33
`
`
`
`44
`
`
`
`55
`
`
`66
`
`77
`
`Fiber NumberFiber Number
`
`
`
`88
`
`
`
`99
`
`
`
`1010
`
`
`
`1111
`
`
`
`1212
`
`
`
`8F Contact: 2.05 N8F Contact: 2.05 N
`
`
`
`10F Contact: 6.36 N10F Contact: 6.36 N
`
`
`
`12F Contact: 10.01 N12F Contact: 10.01 N
`
`Figure 11: Sample tip deflection vs. reaction force data
`
`6 5 4 3 2 1 0
`6 5 4 3 2 1 0
`
`Protrusion (microns)
`Protrusion (microns)
`
`

`

`5.
`
`Empirical and Theoretical Results
`The force required to bring fiber tips into contact with the rigid plate was compared to the theoretical force as
`calculated by the simplified mathematical model. Ferrules characterized with sharp fiber tip radii (1-2mm) and flat
`fiber tips (>10mm) were analyzed. Figure 12 illustrates a comparison of theoretical and empirical results for
`ferrules that had polished fiber tip radii ranging between 1mm and 2mm.
`
`Assumed
`Fiber Radius
`1 mm
`2 mm
`
`5
`
`10
`
`15
`20
`Experimental Force (N)
`
`25
`
`30
`
`35
`
`35
`
`30
`
`25
`
`20
`
`15
`
`10
`
`0
`
`5 0
`
`Theoretical Force (N)
`
`Figure 12: A comparison of the experimental and theoretical results. For each experimental data
`force value, two theoretical points are plotted, corresponding to 1 mm and 2 mm fiber radii of
`curvature.
`To investigate system repeatability in addition to presence of any inelastic behavior, a set of previously unmated
`ferrules was measured for physical contact force over repeated compression cycles. Ten repeated iterations of
`compressing the fiber tips onto the rigid plate for various fiber tip coplanarities were followed by 50 MPO mating
`cycles. A final fiber tip compression experiment was performed. The forces required to bring all fibers into contact
`are shown in Figure 13 and suggest no hysteresis effect from repeated MT connector mating cycles.
`
`

`

`Note: Trial 11 was completed after 50 MPO
`mating cycles.
`
`Coplanarity
`0.406 um
`0.593 um
`0.665 um
`0.697 um
`0.724 um
`0.886 um
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`Trial
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`10
`
`8
`
`6
`
`4
`
`2
`
`0
`
`Measured Force (N)
`
`Figure 13: Compression force required for physical contact over repeated cycles. 50 MPO cycles
`were performed on the samples between trials 10 and 11.
`The amount of force required to bring fiber tips into contact with a rigid plate is directly related to the
`degree to which the fiber tip elevations deviate from a single plane. Typical polishing processes will yield a
`distribution of fiber tip elevations that closely follows the ferrule surface profile. Figure 14 shows the circular shape
`of MT ferrule fiber tip distributions created for this experiment.
`
`1
`
`2
`
`3
`
`4
`
`5
`6
`7
`Fiber Position
`
`8
`
`9
`
`10
`
`11
`
`12
`
`Figure 14: Exaggerated curved shape for MT fiber tip height distribution. Each curve is in fact a
`circular arc.
`
`3.0
`
`2.5
`
`2.0
`
`1.5
`
`1.0
`
`Fiber Protrusion (microns)
`
`

`

`By assuming fiber tip elevations are distributed in a circular shape, the theoretical force required for
`physical contact can be approximated as a function of fiber tip coplanarity. A Force Vs. Coplanarity curve is
`illustrated in Figure 15 for flat (10mm – Infinite) and radiused (1mm-2mm) fiber tips. Experimental results for both
`flat and radiused fiber tips are plotted along the theoretical curves. Given the degree of experimental uncertainty
`and sample variability, the correlation between the theory and experiment shows excellent agreement.
`
`A ctual Data: 1 - 2 mm Radius
`A ctual Data: >10 mm Radius
`1mm Radius - Theoretical
`2mm Radius - Theoretical
`10mm Radius - Theoretical
`Infinite Radius (F lat) - Theoretical
`
`40
`
`30
`
`20
`
`10
`
`Force (N)
`
`0
`0.00
`
`0.25
`
`0.50
`
`0.75
`1.00
`1.25
`Coplanarity (microns)
`
`1.50
`
`1.75
`
`2.00
`
`Figure 15: Force required for physical contact as a function of coplanarity for 1-2mm radius and
`>10mm fiber tips. Theoretical fiber tip distributions are radiused in shape as illustrated in Figure 14
`
`6. Conclusions
`A theoretical model to simulate MT fiber tip compression has been generated and verified empirically. This
`model will be used as a foundation to further develop MT endface geometry requirements.
`The amount of compression force required to bring differing MT fiber tip heights into contact is highly
`dependent on ferrule material modulus. The ferrule material foundation deflection due to loads applied to a single
`fiber will also result in relative deflection of adjacent fiber tips. This foundation effect requires a complex analysis
`of the interaction between all fiber tip reaction forces within a single ferrule to predict forces required for physical
`contact.
`Due to a classical Hertzian deformation component of the fiber tip deflection, the fiber tip shape is a key MT
`endface geometry parameter to be considered when formulating intermateability standards. Depending on the
`coplanarity, ferrules polished with perfectly flat shaped fiber tips can require as much as 80% more force for
`physical contact as ferrules polished with 2mm radius fiber tips.
`Future Work
`7.
`Fiber tip stiffness is but one attribute which impacts the geometric optical interface specifications required to
`establish key MT ferrule connector physical contact. Angular mismatch and rotation stiffness in both X and Y axes
`must also be thoroughly characterized to complete a room temperature physical contact model for MT ferrules. The
`impact of operating environment on these parameters must also be studied to determine endface geometry
`specifications for specific applications.
`
`

`

`8. Acknowledgements
`Eric Childers and Dr. Toshiaki Satake: Empirical experiment development
`Ton Bolhaar and Robert Peters: Fiber tip radius measurement.
`Mark Thompson: Endface geometry interferometer measurements.
`9. References
`[1] Nagase, R., Shintaku, T., Sugita, E., “Effect of Axial Compressive Force for Connection Stability in PC Optical Fibre Connectors”, IEEE
`Electronics Letters, Trans. Photonic Tech. Lett., Vol. 23, No. 3, pp. 103 – 105, (1987).
`[2] Shintaku, T., Nagase, R., Sugita, E., “Connection Mechanism of Physical-Contact Optical Fiber Connectors with Spherical Convex Polished
`Ends", Applied Optics, Vol. 30, No. 36, pp. 5260 – 5265, (Optical Society of America 1991).
`[3] Deeg, E. W., “Effect of Elastic Properties of Ferrule Materials on Fiber-Optic Physical Contact (PC) Connection”, AMP Journal of
`Technology, Vol. 1: 25-31, (1991).
`[4] Deeg, E. W., “New Algorithms for Calculating Hertizian Stresses, Deformations, and Contact Zone Parameters”, AMP Journal of
`Technology, Vol. 2, pp. 14-24, (1992).
`[5] Reith, L. A., Grimado, P. B., and Brickel, “Effect of Ferrule-Endface Geometry on Connector Intermateability”, in Technical Proceedings,
`NFOEC 1995, Vol. 4, (1995).
`[6] Breedis, J. B., and Manning, R. M., “Simulating the End-Face Deformation of Physical Contact (PC) Optical Connectors”, AMP Research
`Report, (1997).
`[7] Bolhaar, T., “PC Connector Interface Parameters for Datacom Detail Specifications”, IEC 86B (Ottawa 1996).
`[8] Knecht, D., Luther, J., Pyatt, J., and Ugolini, A., “Recent Advances in MT Ferrule Processing and MTP Hardware Design”, in Technical
`Proceedings, OFC, (Optical Society of America, 2005)
`
`Appendix A – FEA Model Material and Geometric Properties
`The finite element models were generated using properties for a glass-filled polyphenylene sulphide (PPS)
`ferrule material. Specific values of the elastic modulus, E, and Poisson’s ratio, ν, are defined in Table A.1 for the
`ferrule, fiber, and epoxy regions. The materials were assumed to behave in a linear elastic manner.
`Table A.1: Material properties used in finite element analysis
`Material
`E (MPa)
`Fiber
`73000
`Ferrule
`18000
`Epoxy
`5000
`
`ν
`0.17
`0.35
`0.40
`
`The model was constructed with a nominal fiber diameter of 125μm and an annular epoxy layer thickness of
`0.5μm. The fiber, epoxy, and ferrule regions were bonded such that no shear slippage could occur at the boundaries.
`In addition, to validate the experimental setup, there was a previous analysis that included material properties for a
`sapphire optical flat. However, it was found that this flat could be treated as infinitely rigid since the modulus,
`which is approximately 345 GPa, was several times larger than the other component moduli.
`
`