Fabrication and Mechanics of FiberReinforced Elastomers

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Fabrication and Mechanics of Fiber-Reinforced
Elastomers

• Final Defense
• Larry Peel
• Department of Mechanical Engineering
• Advisor - Dr. David Jensen
• Center for Advanced Structural Composites
• Brigham Young University
• Nov. 5, 1998

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Presentation Outline

• Introduction
• Review Previous Work
• Objectives of Current Work
• Fabrication and Processing
• Experimental Data
• Nonlinear Model and Predictions
• Demonstrate Simple Application (Rubber Muscle)
• Conclusions
• Questions

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Introduction to Research

• What are Fiber-Reinforced Elastomers (FRE)?
• Flexible rubber structures with embedded fibers
• Tires - rigid, linear properties, low elongation
• Why conduct research?
• Increase awareness
• Resolve processing and experimental issues
• Improve predictive capability
• Create new applications
• Flexible underwater vehicles
• Aircraft surfaces
• Bio-mechanical devices
• Inflatable space structures

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Introduction to Research - Contd

• Special Considerations
• Material and Geometric nonlinearity of FRE
  composites,
• Processing concerns,
• Testing (gripping) difficulties,
• Little published processing information,
• Few published experimental results,
• Calendering process (tires, belting) not suitable.

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Previous Work

• Processing and Experimental
• Philpot et al. -- Conducted filament winding with
  elastomers, concerned with elastomer curing.
• Krey, Chou, and Luo -- Arranged fibers by hand,
  1-2 fiber-volume processes, have potential for
  fiber mis-alignment.
• Bakis Gabrys -- Elastomer as matrix for
  composite flywheels.
• Theoretical
• Lee et al. -- Conducted tire research (linear
  material models),
• Clark -- Used a bi-linear stress-strain model on
  tire-composites.
• Chou, Luo -- Specimens had wavy fibers, model
  used quadratic material nonlinearity, considered
  strains up to 20.

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Previous Work - Japan

• Flexible micro-actuators, rubber fingers,
  snakes were found at Toshiba, Okayama Univ.,
  and Okayama Science Univ.

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Objectives of Research

• Fabrication
• Develop low-cost (non-calendering) fabrication
  technique, with high fiber volume fractions, high
  quality specimens.
• Fabricate simple application.
• Experiment
• Characterize elastomer, fiber and FRE properties.
• Obtain high quality test results from FRE
  angle-ply specimens.
• Theory
• Modify laminated plate model to include material
  and geometric nonlinearity.
• Predict response of FRE rubber muscle
  application.

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Materials Used

• Fibers
• Fiberglass PPG 1062
• High strength, high stiffness, common aerospace
  fiber.
• Cotton Wellington twine
• Used in Japan, fibrils promote adhesion,
  inexpensive.
• Matrix
• Silicone Rubber Dow-Corning Silastic
• Green, 2-part, low viscosity, 700 elongation,
  stiffens as stretched, needs primer for good
  adhesion with fiberglass.
• Urethane Rubber Ciba RP 6410-1
• Yellow, 2-part, low viscosity, 330 elongation
  softens as stretched, exhibits good adhesion with
  fiberglass and cotton.

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Fabrication Methods - Winding

• Fibers wound,
• Elastomer applied
• to dry fibers,
• Teflon-coated
• peel-ply wrapped
• over elastomer and fiber layer,
• Process is repeated for 4 or 5 layers.

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Fabrication Methods - Curing

• Bleeder cloth,
• Flat caul plates,
• Vacuum bagged,

• Autoclave Cure Parameters 40 psi , 160 F, 45
  minutes.
• High quality fiber-reinforced elastomer prepreg.

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Fabrication Methods - Lamination

• Prepreg is laminated using silicone or urethane
  rubber.
• Vacuum-bagged again.

• Cured in autoclave again.
• Specimens are dog-boned using a water-jet
  cutter.
• Fiber volume fractions 12 to 62.

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Experimental -Tension Test Articles

• Elastomers
• 5 silicone
• 5 urethane

• Fibers
• Dry cotton
• Rubber-impregnated
• cotton
• Fiberglass not tested

• Fiber-Reinforced Elastomer Coupons
• 4 specimens each at 0, 15, 30, 45, 60, 75, 90
• Silicone/cotton, Silicone/fiberglass,
• Urethane/cotton, Urethane/fiberglass.

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Experimental - Cotton Behavior

• Dry cotton
• Silicone - impregnated cotton
• Urethane - impregnated cotton

Surprising Results Ec 47 ksi Es/c 82
ksi Eu/c 107 ksi
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Experimental - FRE Behavior
Vf 17.9 Vf 59.4
Urethane - linear and softening
Silicone - stiffening
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Experimental - FRE Behavior
Vf 62.4 Vf 12.1
Urethane - linear and softening Silicone -
stiffening, elongation
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Experimental - Material Properties
G12 vs ex E2 vs ex

• Nonlinearity a function of elastomer matrix.
• Magnitude a function of Vf and fiber type.

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Classical Laminated Plate Theory

• Assumes small strains and material properties are
  constant.
• E1 E2, G12, n12 ? stiffnesses Qij.
• Qij rotated ? Qij.

• Rotated stiffnesses assembled for each layer,
• become laminate stiffnesses Aij, Bij, and Dij.
• Laminate forces Ni, and moments Mi
  NiAijejBijkj,
• Mi AijejBijkj, ej - midplane strains,
  kj - curvatures.
• The modified theory considers nonlinear material
  properties and nonlinear strain-displacement
  theory.

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Nonlinear Model - Material

• Ogden model
• s S cj(abj-1-a-(10.5bj)) a
  (extension ratio) e 1
• Polynomial Model
• s a1 a2e a3e2 a4e3 e strain
• Mooney-Rivlin Model (2-coefficient)
• s 2(a-a-2)(c1c2a-1) a (extension
  ratio) e 1
• Mooney-Rivlin Model (3-coefficient)
• s 2(c1a-c2/a3c3(1/a3-a)) a (extension
  ratio) e 1

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Nonlinear Model - Material

• Linear E1 assumed,
• Nonlinear Ogden model
• chosen for E2, G12.
• Form E2, G12 ds / da
• S cj((bj-1)abj-2(1.5bj)a-(20.5bj))
• 6 constants c1, c2 , c3, b1,b2, b3.

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Nonlinear Model - Geometric

• Geometrically nonlinear
• strain-displacement relations.
• Includes high elongation terms.
• Addition of nonlinear components changes method
  of solution to iterative or incremental.

• Load is incrementally applied in form of strain.
• Fiber re-orientation is function of geometry.

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Nonlinear Model - Predictions
Vf12.1 Vf62.4

• Predictions compare very well for most data points

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Nonlinear Model - Predictions
Vf 17.9 Vf 59.4

• Trends and magnitudes predicted well (except u/g
  37, 53).

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Nonlinear Model - Poissons Ratios

• Nonlinear model will predict Poissons ratios at
  each angle, and as a function of strain.
  Poissons ratios may be nonlinear.

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Rubber Muscle - Predictions

• Can be an actuator, integral part of flexible
  structure, high force.

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Conclusions - Fabrication

• Modified standard composites processes to
  fabricate high quality fiber-reinforced elastomer
  prepreg
• Fiber-rubber adhesion -- Autoclave pressure,
  primer, careful choice of fiber/elastomer
  combinations.
• High fiber volume fraction -- Filament winder
  allows user to adjust fraction (12 - 62).
• Parallel, straight fibers -- Caul plate,
  filament winder, and rectangular mandrel.
• Improved process facilitates fabrication of more
  complex FRE applications.

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Conclusions - Experimental

• Acquired high quality elastomer, fiber, and FRE
  stress-strain results and nonlinear properties.
• Elastomer stress-strain results show nonlinear
  trends.
• Extensional stiffnesses for rubber-impregnated
  cotton are 74 to 128 higher than for dry
  cotton.
• New test fixture works well (except with 0
  fiberglass-reinforced rubber).
• Nonlinearity is a function of elastomer and fiber
  angle.
• Shear and transverse properties functions of Vf ,
  fiber type, and elastomer type.
• Nonlinear material properties used in nonlinear
  CLT model.

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Conclusions - Nonlinear Model

• Incorporated material and geometric nonlinearity
  into a modified classical laminated plate model.
  Fiber re-orientation is incorporated into a
  rubber muscle model.
• A six-coefficient Ogden rubber model used for
  nonlinear material properties.
• Extensional terms of Lagrangian
  strain-displacement tensor included.
• Nonlinear model provides good to excellent
  correlation with tensile stress-strain data.
• Rubber muscle model predicts force, fiber angle
  change, displacement, provides valuable insights
  into muscle behavior.
• Research provides new and valuable tools for FRE
  research.

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Many Thanks to

• Wife - Makayla,
• Advisor - Dr. David Jensen,
• Committee - Pitt, Eastman, Cox, Howell
• Family, office-mates, and Brigham Young
  University.
• This effort was sponsored in part by the Air
  Force Office of Scientific Research, Air Force
  Material Command, USAF, under grant number
  F49620-95-1-0052, US-Japan Center of Utah.