Research Proposal for Properties

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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
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
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
 Introduction to Research - Cont’d
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.
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.

 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%.
Previous Work - Japan
   Flexible micro-actuators, rubber fingers, ‘snakes’ were
    found at Toshiba, Okayama Univ., and Okayama Science
Objectives of Research
 Develop low-cost (non-calendering) fabrication technique,
  with high fiber volume fractions, high quality specimens.
 Fabricate simple application.
 Characterize elastomer, fiber and FRE properties.
 Obtain high quality test results from FRE angle-ply specimens.
 Modify laminated plate model to include material and
  geometric nonlinearity.
 Predict response of FRE “rubber muscle” application.
Materials Used
   Fiberglass         PP&G 1062
    High strength, high stiffness, common aerospace fiber.
   Cotton             Wellington twine
    Used in Japan, fibrils promote adhesion, inexpensive.
 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.
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
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.
Fabrication Methods - Lamination
   Prepreg is laminated
    using silicone or
    urethane rubber.

   Vacuum-bagged

   Cured in autoclave again.

   Specimens are ‘dog-boned’ using a water-jet cutter.
   Fiber volume fractions 12% to 62%.
  Experimental -Tension Test Articles
   Elastomers       Fibers
   5 silicone      Dry cotton
   5 urethane      Rubber-
                   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.
 Experimental - Cotton Behavior
Dry   cotton
Silicone   - impregnated
Urethane    - impregnated
Surprising Results
  Ec = 47 ksi
  Es/c = 82 ksi
  Eu/c = 107 ksi
  Experimental - FRE Behavior

        Vf = 17.9%                   Vf = 59.4%
Urethane - linear and softening   Silicone - stiffening
  Experimental - FRE Behavior

           Vf = 62.4%                 Vf = 12.1%
Urethane - linear and softening   Silicone - stiffening,
Experimental - Material Properties

          G12 vs ex                         E2 vs ex
   Nonlinearity a function of elastomer matrix.
   Magnitude a function of Vf and fiber type.
Classical Laminated Plate Theory
   Assumes small strains and
    material properties are constant.
   E1 E2, G12, n12  stiffnesses Qij.                            x
   Qij rotated  Qij.
   Rotated stiffnesses assembled for each layer,
    become laminate stiffnesses Aij, Bij, and Dij.
   Laminate forces Ni, and moments Mi; Ni=[Aij]{ej}+[Bij]{kj},
    Mi =[Aij]{ej}+[Bij]{kj}, ej - midplane strains, kj - curvatures.
   The modified theory considers nonlinear material
    properties and nonlinear strain-displacement theory.
Nonlinear Model - Material
   Ogden model

    s =S cj(abj-1-a-(1+0.5bj))   a (extension ratio) = e +1
   Polynomial Model
    s = a1 + a2e + a3e2 + a4e3   e = strain
   Mooney-Rivlin Model (2-coefficient)
    s = 2(a-a-2)(c1+c2a-1)       a (extension ratio) = e +1
   Mooney-Rivlin Model (3-coefficient)
    s =2(c1a-c2/a3+c3(1/a3-a))   a (extension ratio) = e +1
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-(2+0.5bj))

6 constants: c1, c2 , c3, b1,b2, b3.
Nonlinear Model - Geometric
   Geometrically nonlinear
    Includes high elongation
   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.
Nonlinear Model - Predictions

        Vf=12.1%                          Vf=62.4%

   Predictions compare very well for most data points
Nonlinear Model - Predictions

        Vf = 17.9%                      Vf = 59.4%
   Trends and magnitudes predicted well (except u/g 37,
Nonlinear Model - Poisson’s Ratios

   Nonlinear model will predict Poisson’s ratios at each angle, and
    as a function of strain. Poisson’s ratios may be nonlinear.
Rubber Muscle - Predictions

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

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