peel nonlinear fab results(1)
TRANSCRIPT
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.