Silvestre T Pinho [email protected]
Damage in composites:
experiments and simulation
LCC Symposium, 12 September 2014
World-Wide Failure Exercise - II
0%
20%
40%
60%
80%
100%
Pin
ho
Ca
rrere
Wolf
Puck
Ha
nse
n
Tsai-H
a
Hu
an
g
Cuntz
e
Ha
shin
Rote
m
Bog
etti
Ch
riste
nsen
Perc
enta
ge s
co
re
Combined quantitative and qualitative assessment
based on blind predictions from Kaddour & Hinton, J. Composite Materials 2013 47: 925
Score C
Score A and B
Matrix cracking in LaRC
• Mohr-Coulomb
approach
• Follows work from
Puck et al (1998)
Pinho, Camanho, Davila, Robinson, Iannucci. NASATM 213530 (2005)
0
50
100
150
200
250
-800 -700 -600 -500 -400 -300 -200 -100 0 100
s1 = s2 = s3 (MPa)
t 12 (
MP
a)
Predictions, matrix cracking
Experimental
Experimental
Input data
Matrix cracking: validation
Pinho, Darvizeh, Robinson, Schuecker, Camanho. WWFE-II (2013)
h La02h La0202a
02a La02hLa02
Matrix cracking: size effects
Camanho, Davila, Pinho, Robinson, Iannucci. Composites Part A, 2006
1
23
2
m1
m2
3
Kink plane
3
Matrix fracture plane
m2
3
LaRC failure criteria
Pinho, Camanho, Davila, Robinson, Iannucci. NASATM 213530 (2005)
Kink bands: sequence of events
Pimenta, Gutkin, Pinho, Robinson. Comp Sci Tech 69(7-8) 948-955 (2009)
Gutkin, Pinho, Robinson, Curtis. Mechanics of Materials 43(11) 730-739 (2011)
Kink bands: fibre failure
Pimenta, Gutkin, Pinho, Robinson. Comp Sci Tech 69(7-8) 948-955 (2009)
Gutkin, Pinho, Robinson, Curtis. Mechanics of Materials 43(11) 730-739 (2011)
sinusoid
al fibres
150
straight
fibres
Kink bands: simulation @
microscale
Pimenta, Gutkin, Pinho, Robinson. Comp Sci Tech 69 (7-8) 956-964 (2009)
0
1
2
3
4
5
6
7
0 25 50 75 100 125 150 175 200
v(L) [mm]
P [N/mm]
analytical numerical
numerical
(no stab)
Kink bands: analytical vs. FE
• Good agreement
P
P
M
M
t
t
x, u
y, v
Pimenta, Gutkin, Pinho, Robinson. Comp Sci Tech 69 (7-8) 956-964 (2009)
Longitudinal compression and
shear
0
20
40
60
80
100
120
-1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0
t12 (MPa)
s1 (MPa)
Soden et al (1994)
Transition compressive shear failure to kinking
Inputs model
Gutkin, Pinho, Robinson, Curtis. Comp Sci Tech 70(8) 1223-1231 (2010)
Deterministic predictions
fft : Fibre Tensile Failure
fmat : Matrix Failure
fsplit : Fibre Splitting Failure
fkink : Fibre Kinking Failure
fft : Fibre Tensile Failure
fmat : Matrix Failure
fsplit : Fibre Splitting Failure
fkink : Fibre Kinking Failure
Stochastic analyses
Whiteside, Pinho. Reliability Engineering & System Safety 108 1-9 (2012)
Translaminar toughness
0
20
40
60
80
100
120
140
Baselin
e
Half
in-p
lane
Tw
ice
in-p
lane
More
90°
plie
s
Tw
ice
th
ick
Fracture toughness of 0° plies
Translaminar toughness
0
20
40
60
80
100
120
140
Baselin
e
Half
in-p
lane
Tw
ice
in-p
lane
More
90°
plie
s
Tw
ice
th
ick
Blo
cked
0°
plie
s
Fracture toughness of 0° plies
Open Hole Compression
Delamination Splitting Matrix damage
Experiment: 424 MPa ± 45 MPa
Predicted : 451 MPa
Lee and Soutis (2008) 1
2
Gutkin, Pinho, ICCM-18, Jeju, Korea (2011)
Unit Cell Periodic BC Homogenised
Response
A knot and a Mobius strip
a) b) c)
Potter, Pinho, Robinson, et al Comput Mater Sci 51(1) 103-1011 (2012)
Unit Cell Periodic BC Homogenised
Response
3D woven composites
Potter, Pinho, Robinson, et al Comput Mater Sci 51(1) 103-1011 (2012)
Unit Cell Periodic BC Homogenised
Response
Reduced Unit Cells
Carvalho, Pinho, Robinson. Comp Sci Tech 71(7) 969-979 (2011)
Unit Cell Periodic BC Homogenised
Response
Reduced Unit Cells
dx
uxuxu
= )()( BA
Carvalho, Pinho, Robinson. Comp Sci Tech 71(7) 969-979 (2011)
Unit Cell Periodic BC Homogenised
Response
Exploiting symmetry
EoAA ˆ)()(
ˆ
Txx
uxTuxu
=
1 0 0
1 1 0
0 0 1 1 0 0
0 1 1
0 0 1 E
Ê
EO ˆx
Â
A
EOx
Carvalho, Pinho, Robinson. Comp Sci Tech 71(7) 969-979 (2011)
Unit Cell Periodic BC Homogenised
Response
Accurate stress fields
Tows Matrix
Tows
Carvalho, Pinho, Robinson. Composites Part A, 43 (8), 1326-1337 (2012)
Failure envelope generation
Biaxial Loading
-800
-600
-400
-200
0
200
400
600
800
-800 -400 0 400 800
Average
Experiments
IP
OP
Tensile
Failure
Compressive
Failure
σ1
[MPa]
σ2
[MPa]
Carvalho, Pinho, Robinson. Composites Part A, 43 (8), 1326-1337 (2012)
Analytical model for woven
Model Details
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
P
V
dxdx
dVV
Pdx
dx
dMM
M
p
t
t
xwT
dx
towt
Model Details
Equilibrium of a beam
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
LA
x
w0
y
LB
y×y Twill
LA
Model Details
Equilibrium of a beam
Which represents a
reduced Unit Cell
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
LA
x
w0
y
LB
y×y Twill
LA
Model Details
Equilibrium of a beam
Which represents a reduced
Unit Cell
Loaded Axially
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
Model Details
Equilibrium of a beam
Which represents a reduced
Unit Cell
Loaded Axially
With an elastic foundation
due to:
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
Model Details
Equilibrium of a beam
Which represents a reduced
Unit Cell
Loaded Axially
With an elastic foundation
due to:
Adjacent Tows
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
DeformedUndeformed
θ
h
dx
dw
dw
dw
du
towt
DeformedUndeformed
dw
w
Both dwhBot 2
dx
w
towt
dwhTop 2Toph
Model Details
Equilibrium of a beam
Which represents a reduced
Unit Cell
Loaded Axially
With an elastic foundation
due to:
Adjacent Tows
Adjacent plies
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
Model Details
Equilibrium of a beam
Which represents a reduced
Unit Cell
Loaded Axially
With an elastic foundation
due to:
Adjacent Tows
Adjacent plies
Failure Criteria
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
y
x
-50
0
50
100
0 0.2 0.4 0.6 0.8 1
σ12
[MPa]
x/L
Analytical
Numerical
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
Analytical model for woven
570 562 544
0
100
200
300
400
500
600
700
Analytical Numerical Experimental
Tension
-529 -550 -564
-700
-600
-500
-400
-300
-200
-100
0
Analytical Numerical Experimental
Compression
σ1
[MPa]
σ1
[MPa]
Carvalho, Pinho, Robinson. Composite Structures 94 (9), 2724-2735 (2012)
rCFRP and Discontinuous Carbon
Systems
0
25
50
75
100
2009 2012 2015 2018
CF use (1000 ton/year)
Acmite Market Intelligence
0.5 mm 0.5 mm 0.5 mm
A B C
Architecture
• Different degrees of bundling
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
Toughening mechanisms
• Compact tension
testing
• Fractography
Optical microscopy
SEM analysis
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
0
2
4
6
0 5 10 15 20
CT tests
• Fracture toughness vs. fracture surface
A
Crack extension (mm)
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
Failure of bundles
• Bundle pull-out • Single-fibre pull-out
Self similar
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
500 μm
Failure of bundles
• Defibrillation
Hierarchic
al
failure
100 μm 50 μm
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
0
2
4
6
8
0 5 10 15 20 25 30 35
CT tests
• Fracture toughness vs. fracture surface
B
Crack extension (mm)
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
0
10
20
30
0 5 10 15 20 25 30 35
CT tests
• Fracture toughness vs. fracture surface
C
Crack extension (mm)
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
0
10
20
30
0 10 20 30 40 50 60 70
Fracture toughness
• Comparison
Crack extension (mm)
A
B
C Bundles
Toughness
Pimenta, Pinho, Robinson, Wong, Pickering. Comp Sci Tech 70(2) 1713-25 (2011)
0
10
20
30
0 10 20 30 40 50 60 70
Modelling
• Experimental vs. Analytical
Crack extension (mm)
A
B
C
Pimenta, Pinho, Robinson. ICCM-18, Jeju, Korea (2011)
Conclusions
• Mechanical response of composites:
– There is a lot we still don’t know,
– but there is a lot we have learnt
• Modelling of mechanical response:
– Increasing use for design
– Potential for integration with manufacturing
– Potential for innovative microstructure design
Silvestre T Pinho [email protected]
Damage in composites:
experiments and simulation
LCC Symposium, 12 September 2014