university of the basque country

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UNIVERSITY OF THE BASQUE COUNTRY

DETERMINATION OF TRANSVERSE COMPRESSIVE STRENGTH OF LONG FIBER COMPOSITES BY THREE-POINT

BENDING OF [90m/0n] LAMINATED STRIPS

N.Carbajal, A. Arrese, G. Vargas, F. Mujika

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

2

OUTLINE

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

1. INTRODUCTION2. ANALYTICAL APPROACH3. OPTIMAL CONFIGURATION4. EXPERIMENTAL5. RESULTS AND DISCUSSION6. CONCLUSSIONS

3Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

1. INTRODUCTION

• Three-point bending tests of cross-ply laminate strips are proposed for determining transverse compressive strength.

• Stress state has been obtained based on the hypothesis of the Classical Beam Theory (CBT)

• An adequate configuration has been obtained by imposing the condition of maximum ratio between compressive stresses at 90º layer and tensile stresses at 0º layers.

• Three-point bending tests with different thicknesses and spans have been carried out.

4Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

MAIN HIPOTHESES

• Longitudinal strain on x axis ex is a linear function of z, where the reference of z coordinate is at the midplane.• The only non vanishing stress components in each ply are sx and ts.• Each ply is linearly elastic.

2. ANALYTICAL APPROACH

5Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

STRESS-STRAIN RELATIONS AT A LAYER

000

0

0 Tz

qq k

x

s

x

s

x

kss

xx

ks

x

e

ts

LTxykss

kss

xkxx

kxx

GGS

q

ES

q

1

1

zdzm

zdzm

dzn

dznh

h ss

h

h xxh

h ss

h

h xx

2/

2/

2/

2/2/

2/

2/

2/

t

s

t

s

FORCES AND MOMENTS PER UNIT LENGTH

6Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

STRAINS AND CURVATURES OF MIDPLANE

s

x

s

x

ss

xxxx

ss

xxxx

Txx

Tx

ddb

aba

mm

n

e

0

0

0000000000

0

0

n

kkk

kijij

n

kkk

kijij

n

kkk

kijij

zzqd

zzqb

zzqa

1

31

3

1

21

2

11

3121

Tzzqm

Tzzqn

n

kkk

kx

kxx

Tx

n

kkk

kx

kxx

Tx

1

21

2

11

21

000 ss

xxxxxx

Txxx

TxxxT

x

xxxxxx

xxxMx

dabndmb

dabmb

20

20

e

e

xxxxxx

Txxx

TxxxT

x

xxxxxx

xxxMx

dabnbma

dabma

2

2

7Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

STRESS RATIO

1211)1( 2

0

90

TT

TM

x

Mx

rrr

ss

1

1Tr

L

T

EE

hhr T

T

OPTIMAL THICKNESS RATIO

MAXIMUM STRESS RATIO

ss

2

0

90

Mx

Mx

8Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

STRESS RATIO, THICKNESS RATIO AND MODULUS RATIO

=0.03

=0.07=0.11

=0.23

=0.41

=0.58

=0.92

=1

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

rT

9Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

CONDITIONS IMPOSED FOR OPTIMAL CONFIGURATION

• Neutral axis has to be located as close as possible to the bottom part of 90º layer in order to avoid tensile stresses at 90º layer. • Maximum thermal stresses must be lower than transverse strength in

order to avoid premature failures in 90º layer. • Maximum tensile stresses at 0º layer must be lower than tensile strength.

3. OPTIMAL CONFIGURATION

10Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

OPTIMAL CONFIGURATION FOR T6T-F593 -> [904n/0n]

90º

0º

hT

hL

h = 5·hL

b

z

y

z0=-h/2

z2= h/2

z1=3h/10

11Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

MAXIMUM TRANSVERSE COMPRESSIVE STRESS

2

2

3

90

2563681400225

ss

p

Mx

236hmx

p s

TRANSVERSE COMPRESSIVE STRENGTH FOR T6T-F593

pM

x 390 64.0 ss

12Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

T6T-F593 CARBON/EPOXY

Sample h (mm) hT (mm) hL (mm)[909/03]-30[9016/04]-30[9020/05]-40

2.072.973.90

1.552.383.12

0.520.590.78

SAMPLES

THREE-POINT BENDING

%10L 1min01.0

dtd xeMTS electromechanical machine

Roller radius = 2.5 mm

4. EXPERIMENTAL

ET (GPa) EL (GPa) Yt (MPa) Xt (MPa) GLT (GPa) LT L (ºC-1) T (ºC-1) (ºC) 8 108 134 1564 4 0.3 -2.81·10-7 3.61·10-5 -155

13Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

-400

-16

-208

1456

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

sxM (MPa)

-418

25-371

1552

-2.00

-1.00

0.00

1.00

2.00

sx (MPa)-56542

-3381

14339

zNA= 0.62

ex·106

-19

41

-162

96

sxT (MPa)

5. RESULTS AND DISCUSSION

STRESS PROFILES [909/03]- 30

14Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

-421

9 123

1524

-2.00

-1.00

0.00

1.00

2.00

sxM (MPa)

-443

52

-22

1587

-2.00

-1.00

0.00

1.00

2.00

sx (MPa)-59473

-164

14663

zNA= 0.92

ex·106

-22

42

-14563

sxT (MPa)

STRESS PROFILES [9016/04]- 30

15Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

-404

9 118

1463

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

sxM (MPa)

-426

51

-271526

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

sx (MPa)-57449

-209

14100

zNA= 1.18

ex·106

-22

42

-14563

sxT (MPa)

STRESS PROFILES [9020/05]- 40

16Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

PHOTOS OF FAILURE

17Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

0

500

1000

1500

2000

0 0,5 1 1,5 2 2,5

P (N)

d (mm)

[9020/05]-40

"P4"

"P3"

"P2"

"P1"

LOAD UNLOAD CYCLES PRIOR TO FAILURE

18Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

• Optimal cross-ply configuration for determining transverse compressive strength by three-point bending only depends on the relation between transverse and longitudinal modulus.• For optimal configuration of a given material the ratio between maximum stresses at 90º and 0º layers are maximum and only depends on the relation between transverse and longitudinal modulus.• Transverse compressive strength values are very similar between them.• The appearance of damage agrees well with the transverse compressive failure related to end-loaded compression tests. • No tensile failure has been found prior to final failure.

6. CONCLUSIONS

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THANK YOU FOR YOUR ATTENTION

5th International Conference on Composites Testing and Model SimulationEPFL, Lausanne, 2011

Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips