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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 Simulation
EPFL, 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 Simulation
EPFL, Lausanne, 2011
Determination of transverse compressive strength of long fiber composites by three-point bending of [90m/0n] laminated strips
1. INTRODUCTION2. ANALYTICAL APPROACH
3. OPTIMAL CONFIGURATION
4. EXPERIMENTAL
5. RESULTS AND DISCUSSION
6. 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 Simulation
EPFL, 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 Simulation
EPFL, 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 Simulation
EPFL, Lausanne, 2011
STRESS-STRAIN RELATIONS AT A LAYER
00
00
0 Tz
q
q kx
s
x
s
x
kss
xx
ks
x
LTxykss
kss
xkxx
kxx
GGS
q
ES
q
1
1
zdzm
zdzm
dzn
dznh
h ss
h
h xx
h
h ss
h
h xx
2/
2/
2/
2/2/
2/
2/
2/
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 Simulation
EPFL, Lausanne, 2011
STRAINS AND CURVATURES OF MIDPLANE
s
x
s
x
ss
xxxx
ss
xxxx
Txx
Tx
d
db
a
ba
mm
n
0
0
000
00
000
00
0
0
n
kkk
kijij
n
kkk
kijij
n
kkk
kijij
zzqd
zzqb
zzqa
1
31
3
1
21
2
11
31
21
Tzzqm
Tzzqn
n
kkk
kx
kxx
Tx
n
kkk
kx
kxx
Tx
1
21
2
11
2
1
000 ss
xxxxxx
Txxx
TxxxT
x
xxxxxx
xxxMx
dab
ndmb
dab
mb
20
20
xxxxxx
Txxx
TxxxT
x
xxxxxx
xxxMx
dab
nbma
dab
ma
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 Simulation
EPFL, Lausanne, 2011
STRESS RATIO
121
1)1( 2
0
90
TT
TM
x
Mx
rr
r
1
1Tr
L
T
E
E
h
hr TT
OPTIMAL THICKNESS RATIO
MAXIMUM STRESS RATIO
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 Simulation
EPFL, 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 Simulation
EPFL, 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 Simulation
EPFL, 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 Simulation
EPFL, Lausanne, 2011
MAXIMUM TRANSVERSE COMPRESSIVE STRESS
2
2
3
90
2563681
400225
p
Mx
23
6
h
mxp
TRANSVERSE COMPRESSIVE STRENGTH FOR T6T-F593
pM
x 390 64.0
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 Simulation
EPFL, 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 dt
d xMTS 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 Simulation
EPFL, Lausanne, 2011
-400
-16
-208
1456
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
xM (MPa)
-418
25
-371
1552
-2.00
-1.00
0.00
1.00
2.00
x (MPa)-56542
-3381
14339
zNA= 0.62
x·106
-19
41
-162
96
xT (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 Simulation
EPFL, Lausanne, 2011
-421
9 123
1524
-2.00
-1.00
0.00
1.00
2.00
xM (MPa)
-443
52
-22
1587
-2.00
-1.00
0.00
1.00
2.00
x (MPa)-59473
-164
14663
zNA= 0.92
x·106
-22
42
-14563
xT (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 Simulation
EPFL, Lausanne, 2011
-404
9 118
1463
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
xM (MPa)
-426
51
-27
1526
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
x (MPa)-57449
-209
14100
zNA= 1.18
x·106
-22
42
-14563
xT (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 Simulation
EPFL, 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 Simulation
EPFL, 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 Simulation
EPFL, 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