Novel Methods for Testing and Modelling Composite ... Douglas Composite Materials Laboratory School of Aeronautics and Astronautics, Purdue University Novel Methods for Testing and

McDonnell Douglas Composite Materials LaboratorySchool of Aeronautics and Astronautics, Purdue University

Novel Methods for Testing and Modelling Composite Materials and Laminates

C. T. SunSchool of Aeronautics and Astronautics

Purdue UniversityWest Lafayette, Indiana

September 23, 20042nd International Conference on

Composites Testing and Model Identification


Outline

•Testing Notch Strength in Laminates

•Oblique End Tab for Off Axis Testing

•Testing and Modeling Nonlinear Behavior of Composites

•Testing and Modeling Compressive Strength of Composite

• Dynamic Interlaminar Fracture Toughness


Free Edge Stresses

R.B Pipes , " Interlaminar Stresses in Composite Laminates ,"

Air Force Materials Laboratory , Technical Report AFML -TR-72-18 , 1972

θ

z

yxb

b 3h0

0.0 0.25 0.50 0.75 1.00- 0.10

- 0.05

0.00

0.05

0.10

0.15

0.20

0.25

Graphite - Epoxy

Glass - Epoxy

y / b

[ 45 / -45 / 0 / 0 / -45 / 45 ]

z / h= 1.0

Interlaminar Normal Stress


Strength without Edge Effect

2000

3000

4000

5000

6000

0.00 7.50 15.00 22.50 30.00 37.50 45.00

Loading Angle

AS4/3501-6[0/90/45/-45]Swith adhesive

Well polished free edge


Strength in Off-Axis Directions

2000

3000

4000

5000

6000

0.00 7.50 15.00 22.50 30.00 37.50 45.00

Loading Angle

AS4/3501-6[0/90/45/-45]S

Well polished free edge


[ ]S45/90/0 ±Failure Loads of Laminate

Notch TypeUnnotched1 2 3 4 5

0o 4700 (lb/in) 3710 3730 3730 3705 38107.5o 2730 (lb/in) 3350 3400 3220 3385 354015o 2510 (lb/in) 3150 3200 3100 3300 3300


Notch Strength of Composite Laminates

Two Failure Mechanisms

•Stress Concentration

•Free Edge Stress


Net-section Strength

0

100

200

300

400

500

0 7.5 15Loading Angle

Edge unnotchedEdge notched

AS4/3501-6[0/90/45/-45]S


Off-Axis Tension

Simple Tension

0,0 =σ=σσ=σ xyyyxx

Clamped End

0,0 ≠σ≠σ xyxx


Displacements in Off-Axis Tension

ySxSU xx16xx11x σ+σ=

11

16

SScot

dydx

−=φ=


Oblique Tab Angley

x

end tab

AS4/3501-6


Undeformed (a) and (c) and deformed shapes (b) and (d)of 20o off-axis carbon/ epoxy specimens


Axial strains in 20 deg off-axis specimen with rectangular end tabs


Strain Distribution in 20 deg Specimen with Oblique Tabs


Nonlinear Behavior in Fiber Composites

• Off-Axis Stress-Strain Curves

0 0.004 0.008 0.012 0.016Strain (mm/mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

01530456090

Unidirectional S2Glass/8553

AnisotropicNonlinear


Plastic Potential and Flow Rule

•Flow Rule •One-Parameter Plastic Potential

( ) ( ) ( )[ ]212

21366

223

23322 24

21 σσσσσσ +++−= af ij

Transversely isotropicpij

eijij ddd εεε +=

λσ

ε dfdij

pij ∂

∂=

•No plastic strain in the fiber directionf3=σ

ppijij

p dddW εσεσ == •Satisfies transverse isotropy

=

σσ

σελ dddd

p

23


Off-Axis Test-Plane Stress

x12

x2

22

x2

11

cossin sin

cos

σθθσσθσ

σθσ

−==

=

xh σθσ )(=

ppppx dddd 1222

211

2 cossin sin cos γθθεθεθε −+=

)(/ θεε hdd px

p =)(/ θεε hp

xp =

2/122

664 cossin2(sin

23)(

+= θθθθ ah

( )npA σε =Power Law


Master Curve in Effective Stress and Effective Plastic Strain

0 0.002 0.004 0.006 0.008 0.01Effective Plastic Strain (mm/mm)

0

20

40

60

80

100

120

Eff

ectiv

e St

ress

(MPa

)

1530456090Master Curve

( )npAσε =

0 0.004 0.008 0.012 0.016Strain (mm/mm)

0

50

100

150

200

250

300

Stre

ss (M

Pa)

01530456090

a66 = 6

λσ

ε dfdij

pij ∂

∂=


Compression Test of Off-Axis CompositesCompression tests were performed on off-axis S2/8552

glass/epoxy composites at strain rates from 10-4/s to 1000/s.

SpecimenHard steel

θ

x

Y10 mm

6 mm6 mm

Applied displacement Strain gageGage A Gage B

Incident Bar Transmission BarSpecimen

Striker Bar Throw-off Bar

Gage A Gage B

Incident Bar Transmission BarSpecimen

Striker Bar Throw-off Bar

Dynamic(Hopkinson bar)

Quasi-Static(MTS machine)

Lapped and Lubricated


A Model for Rate –Dependent Nonlinear BehaviorOf Fiber Composites

np A )(σε =&

f3=σ

)](a24)[(21f 2

1321266

223

23322 σσσσσ −++−=

mp )(A εχ &=

Master Curves

Off-Axis Curves

10-3/s

AS4/3501-6

a 66 7.0 χ 1.1E-17(MPa)-n m -0.1425 n 5.26

λσ

ε &&ij

pij

f∂∂

=


Failure Modes Produced in Off-Axis Test

• Fiber Microbuckling Failure - fiber orientation equal or less than 15o.

ep12

f

epm

cr GV1

G=

−=σ (Microbuckling model)

• In-plane Shear Failure –between 15o and 45o.

• Out-of-plane Shear Failure – greater than 45o .


Strain Rate Effect on Failure Mode

Uncoated Coated withTi15 degree AS4/3501-6

Microbucklingat 10-5/s strain rate

Shear failure at1/s strain rate


Microbuckling Model

Rosen (1965):

•Idealize the composite as a series of perfectly aligned beam

embedded in elastic matrix.

•Two modes of failure: extension and shear.

Shear mode

GV1

G

f

mc ≈

−=σ 12


Microbuckling Model with Nolinear Matrix Behavior an Misalignments

Sun and Jun (1994)

• Fiber microbuckling in nonlinear matrix including fiber misalignment effect

),(G

V1G

crep

f

epm

cr

φσ≈

−=σ

σσf

σm

τm


EFFECT OF SHEAR STRESSCompression-Torsion Test

EXAS HIS/DX6002 Carbon/epoxy composites, Vf =65%

0

400

800

1200

1600

2000

-100 -50 0 50 100

Applied shear stress τ (Mpa)

Com

pres

sive

str

engt

h σ c (M

pa)

Test (Jelf and Fleck)

Model prediction Fiber misalignment = 2 o


Model Predictions and Test DataAS4/3501-6 (misalignment angle = 2.5 deg)

1

122

66122

p

1222

66e12

122

cx ))(cosa2)((sinH)(cosa6

G1)(cos

−

++++

+=+γθγθ

γθγθσep

12cr G=σ

626597.211940934.95

~150/s

530487.011801837.75

10-1/s

401366.415472460.911706729.45

10-3/s

355331.715419420.911627649.75

10-5/s

Model Prediction (MPa)

Test Result(MPa)

Off-axis Angle (o)

Strain Rate


Longitudinal Compressive StrengthLongitudinal Compressive Strength

10-5/s 10-3/s

15471392Model prediction (MPa)

15571324Strength projection from test data (MPa)

10-3/s10-5/sStrain rate


y = 0.0832x + 113.96

y = 0.0325x + 133.22

y = 0.0455x + 99.147

y = 0.1001x + 157.85

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200 250σ22 (MPa)

σ 12

(MPa

)

500/s

1/s

0.01/s

0.0001/s

15 deg

Shear Failure Mode


In-Plane Shear Strength

Transverse normal stress = 0σ22

1300600158

1.731133

0.020.01114

0.000230.000199

Shear strain rate(1/s)

Nominal axial strain rate (1/s)

Pure shear strength (MPa)


Shear Strength vs Shear Strain Rate

0

40

80

120

160

200

1.0E-4 1.0E-2 1.0E+0 1.0E+2 1.0E+4

Shear strain rate (1/s)

In-p

lane

she

ar s

tren

gth

(MPa

)

Exp

Curve-fit

γγ

+= s12

12log73.84.98S&

&


Montmorillonite Clay Structure

Layer dimension length (width)= 0.5 ~ 1 micron, thickness =1nm

= Sodium ions

ExfoliatedIntercalated Unseparated (Tactoids)


Comparison of Stress-Strain Behavior of Resin with Different Clay Loadings


Compressive Strength of 0 Degree Composites


Longitudinal (0 deg) Compressive Strength

Fiber volume 35%

0

100

200

300

400

500

600

700

Com

pres

sive

Str

engt

h (M

Pa)

No Clay (0%) 5% Clay

TestPrediction

33.9 % 34.2 %


Interlaminar fracture Test

DCB

ENF


Delayed Crack Initiation

(FM73)


Crack Extension History

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

-1E-4 0E+0 1E-4 2E-4 3E-4 4E-4 5E-4 6E-4

Time (s)

Vol

tage

(v)


Typical Crack Speed HistoryMode I

0

50

100

150

200

250

300

350

400

0 0.01 0.02 0.03 0.04 0.05

Crack Extension (m)

Cra

ck S

peed

(m/s

)


Mode I Fracture Toughness for AS4/3501-4

0

50

100

150

200

250

300

350

400

450

50 100 150 200 250 300 350Crack Speed (m/s)

Dyn

amic

Ene

rgy

Rel

ease

Rat

e (N

/m

GIC

500


ENF Test for Mode II Fracture

Aluminum line

Copper fingers


Mode II Dynamic Fracture Toughness for S2/8553

0

500

1000

1500

2000

2500

3000

3500

4000

300 400 500 600 700Crack speed (m/s)

Crit

ical

Ene

rgy

Rel

ease

Rat

e (J

/m2 )

GIIC


Copper fingers

Aluminum line

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200Crack Speed (m/s)

Stra

in E

nerg

y R

elea

se R

ate

(J/m

2 ) Static GcZT13ZT1ZT17ZT16

Mixed Mode Dynamic Fracture Toughness

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Novel Methods for Testing and Modelling Composite ... Douglas Composite Materials Laboratory School of Aeronautics and Astronautics, Purdue University Novel Methods for Testing and