peel nonlinear fab results(1)

Fabrication and Mechanics of Fiber-Reinforced Elastomers

Final Defense

Larry Peel Department of Mechanical Engineering

Advisor - Dr. David JensenCenter for Advanced Structural Composites

Brigham Young UniversityNov. 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 ResearchWhat are Fiber-Reinforced Elastomers (FRE)? Flexible rubber structures with embedded fibers Tires - rigid, linear properties, low elongationWhy 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 WorkProcessing 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%.

Previous Work - Japan Flexible micro-actuators, rubber fingers, ‘snakes’ were found

at Toshiba, Okayama Univ., and Okayama Science Univ.

Objectives of ResearchFabrication 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.

Materials UsedFibers: Fiberglass PP&G 1062

High strength, high stiffness, common aerospace fiber.

Cotton Wellington twineUsed 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 6410-1Yellow, 2-part, low viscosity, 330% elongation softens as stretched, exhibits good adhesion with fiberglass and cotton.

Fabrication Methods - Winding

Fibers wound,

Elastomer appliedto dry fibers,

Teflon-coated peel-ply wrapped over elastomer and fiber layer,

Process is repeated for 4 or 5 layers.

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 again.

Cured in autoclave again.

Specimens are ‘dog-boned’ using a water-jet cutter. Fiber volume fractions 12% to 62%.

Experimental -Tension Test Articles Elastomers 5 silicone 5 urethane

Fibers Dry cotton Rubber-impregnated cotton Fiberglass not testedFiber-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

Surprising ResultsEc = 47 ksiEs/c = 82 ksiEu/c = 107 ksi

Dry cotton Silicone - impregnated cotton Urethane - impregnated cotton

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15

Strain (m/m)

Stre

ss (M

Pa)

0

1000

2000

3000

4000

5000

6000

7000

Stre

ss (p

si)

u/c (Average)s/c (Average)Dry CottonLinear Fit

Experimental - FRE Behavior

Urethane - linear and softening Silicone - stiffeningVf = 17.9% Vf = 59.4%

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5 1.75

Strain (m/m)St

ress

(MPa

)

0

200

400

600

800

1000

1200

1400

1600

Stre

ss (p

si)

Silicone/Cottons/c 0 avgs/c 15 avgs/c 30 avgs/c 45 avgs/c 60 avgs/c 75 avgs/c 90 avgsilicone rubber

0

2

4

6

8

10

12

14

16

18

20

0 0.25 0.5 0.75 1 1.25 1.5 1.75Strain (m/m)

Stre

ss (M

Pa)

0

500

1000

1500

2000

2500

Stre

ss (p

si)

Urethane/Fiberglassu/g 0 avgu/g 15 avgu/g 37 avgu/g 45 avgu/g 53 avgu/g 75 avgu/g 90 avgurethane rubber

Experimental - FRE Behavior

Urethane - linear and softening Silicone - stiffening, elongation Vf = 62.4% Vf = 12.1%

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5 2.0 2.5

Strain (m/m)St

ress

(MPa

)

0

200

400

600

800

1000

1200

1400

1600

Stre

ss (p

si)

Silicone/Glasss/g 0 avgs/g 15 avgs/g 30 avgs/g 60 avgs/g 75 avgs/g 90 avgsilicone rubber

0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1Strain (m/m)

Stre

ss (M

Pa)

0

500

1000

1500

2000

Stre

ss (p

si)

Urethane/Cottonu/c 0 avgu/c 15 avgu/c 30 avgu/c 60 avgu/c 75 avgu/c 90 avgurethane rubber

Experimental - Material Properties

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

G12 vs x E2 vs x

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8Strain (m/m)

Shea

r Mod

ulus

(MPa

)

0

200

400

600

800

1000

Shea

r Mod

ulus

(psi

)

Urethane/FiberglassUrethane/CottonSilicone/FiberglassSilicone/Cotton

0

1000

2000

3000

4000

5000

6000

7000

0.0 0.5 1.0 1.5 2.0Strain (m/m)

Tra

nsve

rse

Stiff

ness

(kPa

)

0

200

400

600

800

1000

Tra

nsve

rse

Stiff

ness

(psi

)Urethane/fiberglassUrethane/cottonSilicone/fiberglassSilicone/cotton

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; 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.

Classical Laminated Plate Theory

x

y

12

Nonlinear Model - Material Ogden model

= cj(abj-1-a-(1+0.5bj)) a (extension ratio) = +1 Polynomial Model

= a1 + a2 + a32 + a43 strain

Mooney-Rivlin Model (2-coefficient) = 2(a-a-2)(c1+c2a-1) a (extension ratio) = +1

Mooney-Rivlin Model (3-coefficient) =2(c1a-c2/a3+c3(1/a3-a)) a (extension ratio) = +1

Nonlinear Model - Material Linear E1 assumed, Nonlinear Ogden model

chosen for E2, G12.

Form: E2, G12 = d / da

= cj((bj-1)abj-2+(1+.5bj)a-(2+0.5bj))

6 constants: c1, c2 , c3, b1,b2, b3. 0

250

500

750

1000

1250

1500

0.1 0.3 0.5 0.7Strain (m/m)

Shea

r M

odul

us (k

Pa)

0

50

100

150

200

Shea

r M

odul

us (p

si)

s/c 45 G12Ogden 63rd order polynomialMooney-Rivlin 2Mooney-Rivlin 3

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.

Nonlinear Model - Predictions

Predictions compare very well for most data points

Vf=12.1% Vf=62.4%

0

200

400

600

800

1000

1200

1400

1600

0 0.5 1 1.5 2 2.5Strain (in/in)

Stre

ss (p

si)

s/g avg

s/g predicted

0

500

1000

1500

2000

2500

0 0.25 0.5 0.75 1Strain (in/in)

Stre

ss (p

si) u/c avg

u/c predicted

Nonlinear Model - Predictions

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

Vf = 17.9% Vf = 59.4%

0

4

8

12

16

20

24

0 0.5 1 1.5 2Strain (m/m)

Stre

ss (M

Pa)

0

500

1000

1500

2000

2500

3000

Stre

ss (p

si)

u/g Predictedu/g 0 avgu/g 15 avgu/g 37 avgu/g 45 avgu/g 53 avgu/g 75 avgu/g 90 avg

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2Strain (m/m)

Stre

ss (M

Pa)

0

500

1000

1500

2000

2500

Stre

ss (p

si)

s/c Predicteds/c 0 avgs/c 15 avgs/c 30 avgs/c 45 avgs/c 60 avgs/c 90 avg

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.

0

5

10

15

20

25

30

35

0 15 30 45 60 75 90Off-axis angle,

Pois

son'

s ra

tio, v

xy

silicone/cottonsilicone/glassurethane/cottonurethane/glass

Rubber Muscle - Predictions

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

0

500

1000

1500

2000

2500

3000

0 100 200 300 400Pressure (kPa)

Forc

e (N

)

0

100

200

300

400

500

600

0 20 40 60Pressure (psi)

Forc

e (lb

s.)

Silicone/CottonSilicone/Fiberglass

Urethane/CottonUrethane/Fiberglass

0

5

10

15

20

25

30

0 100 200 300 400Pressure (kPa)

Fibe

r Ang

le (d

egre

es)

0

5

10

15

20

25

30

0 20 40 60

Pressure (psi)

Fibe

r Ang

le (d

egre

es)

Silicone/Cotton

Silicone/Fiberglass

Urethane/Cotton

Urethane/Fiberglass

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.

Conclusions - ExperimentalAcquired 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 ModelIncorporated 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.

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.