two civil and industrial applications of2ddic tf 2d dic ... · pdf filetwo civil and...
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Workshop 4 , June 9Workshop 4 , June 9
Two civil and industrial applications Two civil and industrial applications f 2D DIC tf 2D DIC tof 2D DIC measurements of 2D DIC measurements
combined with numerical simulationscombined with numerical simulations
Roberto FedeleRoberto Fedele and and coworkerscoworkers: : M. M. ScaioniScaioni, G. Rosati. M. , G. Rosati. M. FerrarisFerraris, V. Casalegno, V. Casalegno
D f Ci il d E i l E i i (DICA)Department of Civil and Environmental Engineering (DICA) Politecnico di Milano, Milan, Italy
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Items to be discussed
Delamination tests on FRP-reinforced masonry pillar, optical monitoring by 2D DIC and FE predictionsoptical monitoring by 2D DIC and FE predictions
coworkerscoworkers: M. : M. ScaioniScaioni, G. Rosati , G. Rosati
Sh t t t l i bli
,,
Shear tests on metal-ceramic assemblies, identification of cohesive parameters for innovative joints
coworkerscoworkers: M. : M. FerrarisFerraris, V. Casalegno, V. Casalegno
Closing remarks and future prospectsClosing remarks and future prospects
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D l i iD l i i i d FEi d FE d llid lliDelaminationDelamination experiments and FE experiments and FE modellingmodellingof FRPof FRP--reinforced masonry reinforced masonry
Roberto FedeleRoberto Fedele, M. , M. ScaioniScaioni, G. Rosati, G. Rosati
Ref: Fedele et alii, Cement & Concrete Composites, 45 (2014)
D t t f Ci il d E i t l E i i (DICA)
, p , ( )243–254.
Department of Civil and Environmental Engineering (DICA) Politecnico di Milano, Milan, Italy
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CFRP-reinforced pillar: Historical bricks (XVII century) and high strength mortar( y) g g
single-lap shear test
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Optical monitoring by 2D DIC
1 pixel footprint on the object 84 m metric object space
dcodco
1 pixel pitch on the sensor
image space
1 pixel pitch on the sensor = 6.1 m
Benchmarking
RMSE=15.9 m (0.19 Pz)
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3D heterogeneous finite element modellingCFRP
masonry
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Elastic-damageable model (Comi-Perego 2001)
“bi di i ti ” d l two isotropic damage variables:“bi-dissipative” model two isotropic damage variables:
in tension in compressiontD cDVumat (Abaqus explicit)
23(1 ) (1 ) 2ij t c v ij ijD D K G G
state equations
3( ) ( )ij t c v ij ij
l di l di diti(1 )- D
( , ) 0jt i tD f
loading-unloading conditions
0 0
j
t
t i t
ttD D
f
f
( , ) 0
0 0
jc i cD
D D
f
fdamage activation functions
0 0c tcD D f
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3D FE modelling with perfect adhesionEffective elastic modulus of the CFRP reinforcement estimated by DICEffective elastic modulus of the CFRP reinforcement estimated by DIC
h dspoon shaped mechanisms
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FOverall delamination response
sF
FE model with “ideal”constraints
“actual”
DIC corrected boundary conditions
“actual”
DIC-corrected boundary conditions
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Local slip between FRP and masonry support
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Characterization of innovative CFC/Cu joints b f ll fi ld t d fi it l tby full-field measurements and finite elements
Roberto Fedele*, Valentina Casalegno#, Monica Ferraris#
Ref: Fedele et alii, Materials Science & Engineering A, 595 (2014) 306–317.
*Dept. of Civil and Environmental # Dept of Applied Science d T h l (DISAT)Engineering (DICA)
Politecnico di Milano, Milan, Italyand Technology (DISAT)
Politecnico di Torino, Turin, Italy
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Composites for aggressive environments
2760
oC
1371
540
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ITER(International(International Thermonuclear Experimental pReactor)
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brake discs
turbine engine blades
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Single-lap shear tests on flat-tile joined samples
CFC / Cu
glue (Araldites AV 119, Ciba-Geigy)
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Macroscopic responsei t i i CFC h t th 15 20 MP !
P
intrinsic CFC shear strength 15-20 MPa !
maxmax 23.6
joint
PA
[MPa]
uncertain boundary conditions due to the glue layersto the glue layers and compliant grips!
max 34 4 [MPa]comparative assessment by different tests
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4-dofs motion for zoomed camera for optical monitoring
Z
X
X
Y
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Finite element discretization of ROI1 pixel 1 pixel 3.0 m
pixe
lp
pixel
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Joint collapse
pixe
lp
pixel
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L l hLocal approach: FE simulations driven by boundary displacements
Cuboundary displacements
plane stress schematization
CFC
plane stress schematization
(anisotropic) elastic-plastic behavior
finite thickness joint
behavior
j
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Displacement fields measured by DIC and computed
tangential component
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Displacement fields measured by DIC and computed
tangential component
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Displacement fields measured by DIC and computed
tangential component
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Joint governing parameters to be identifiedVan der Bosch Schreursinterface “di l t j ”
2
exp expn n n tp
Van der Bosch, Schreurs and Geers, EFM, 2006
interface tractions
“displacement jumps”
2
2
exp exp
2 1 exp exp
n n n tn
n n n t
t t n n t
p
p
tr
21 exp expt t n n t
tt t n n t
p
TX t t id tif
nassumed a priori
, ,n n tX
tn
parameters to identifyminimization by Trust Region, reflective, i i i h d
u1
1/2
ˆ arg min ( )t
Tk k
k
k k k
XX X R R interior point Method
in a Matlab environment
1/2 exp comp exp( )k k kk k
R W U U X U , 1,..., tk k n
boundary conditions provided by DIC were deterministically prescribed without any regularization provision
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Tangential stress evolution
maxMPa43tp traction predicted under pure mode II
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Normal stress evolution
maxMPa58np traction predicted under pure mode I
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Closing remarks and future prospects
DIC measurements especially suitable forcalibration/validation of FE modelswith special reference to :(i) accuracy of 2D/3D geometry assumptions ;(ii) boundary data estimation ;(iii) response of joint/interfaces ; (i ) i i l i hi(iv) constitutive relationships .
Information fusionfrom several sensorsand diverse testing configurations
Extension to High and Ultra High Temperature (UHT) testing (?)testing (?)
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322 ij jiJ S S [MPa2]
1 tr ij jiI σ [MPa] )( ii Dh cti ,
2 2b h k hfmeridian plane
first invariant stress tensor second invariant stress deviator hardening/softening functions
2 22 1 1, 0c c c c c c cD J a I b h I k h σf
hardening/softeninghardening/softening
2 22 1 1, 0t t t t t tt D J a I b h I k h σf
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IHaigh-Westergaad space
, 0t tD σf
II
III
= , ,i i I II IIIprincipal stresses
, 0c cD σf
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ifi f
Fracture energy regularization
(m ) iGg
specific fracture energy
(e)ch
(m )i igl
“element” characteristic length
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Local predictions of FE model
2 LVDT [ ] 0 1
2 mm
1.6
2 clip [mm]LVDT [mm]
0.08
0.1
1.2 0.06
0.8 0.04
0.4 0.02
0 1 2 3 40
di ti ti0 1 2 3 4
0
ordinative timeordinative time
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Closing remarksClosing remarks
•• SingleSingle--lap shear tests were performed under cliplap shear tests were performed under clip--controlcontrol
•• DelaminationDelamination of CFRP strips from a small masonry pillar was of CFRP strips from a small masonry pillar was simulated under the hypothesis of a perfect adhesion.simulated under the hypothesis of a perfect adhesion.
•• 3D heterogeneous FE model with elastic3D heterogeneous FE model with elastic--damageable phases damageable phases was developedwas developedpp
•• Optical monitoring was validated with correction Optical monitoring was validated with correction f ti lf ti l di t idi t iof optical of optical distorsiondistorsion
•• Information fusionInformation fusionInformation fusionInformation fusion
•• Future prospects: combining interface and bulk damageFuture prospects: combining interface and bulk damage
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Local traction predicted by FEMy1 2
3
y
3
x
1 7 MPamaxF .A
41
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FEM
12 delamination front
A
B
42
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12C
delamination frontfront
D
43
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A priori assumed parameters (“diffuse load cell”)
Ceramic phase CFC SEP NB31: Mechanical parameters at room temperature
Hill parameters Ramberg-Osgood Elastic properties
pfor plastic anisotropy
g gparameters for the
incompressible strains
107 [GPa]xE ; 15[GPa]yE ; 12 [GPa]zE ; 0 8F ; 0 5G ; 100 [MP ][ ]x [ ]y [ ]z
0.10xy ; 0.20xz ; 0.20yz ; 10 [GPa]xyG
0.8F ; 0.5G ;
0.5H ; 10N ; 0 100 [MPa] ;
/ 2083 [GPa]RE ; 7n ;
Cu phase: Mechanical parameters at room temperature
Elastic properties Ramberg-Osgood parameters
125[GP ]E ; 300 [MPa] ;125[GPa]E ;0.34 ;
0 300 [MPa] ;0.06 ; 7n ;
Ref: ITER Final Report, Material Assessment Report, 2001
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Post-mortem analyses of fracture surface by SEMFailure of CFC by interlaminar shear, carbon fibre pull-out and cracking of CCr
resolutionSEM resolutionSEM pictures
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ITER Final Design Report (July 2001): Materials
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Flat-tile mock-ups manufacturing
armour / plasma facing component
li h lcooling channel of heat sink
1) High heat flux applied on CFC surface
CFC NB31/Cu/CuCrZr
1) High heat flux applied on CFC surface up to 10 MW/m2 (3000 cycles)up to 20 MW/m2 during transient events (20 cycles)2) Neutron irradiation and radiation damage
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Problems when joining metals and CFC
Large thermal expansion mismatchbetween Cu and CFC
20Thermal expansion at 300 °C
CFC=1,7-3,3 x 10-6 K-1, Cu=16,6 x 10-6 K-1
Cu
10
15
20
16 K10 Cu 6,6 0 high residual stresses CFC
0
5
10K10
Low wettability of molten copper on CFC (contact angle= 140°)
θ=139-145°Cu
sessile drop test θ 139-145
CFC
pat 1100 oC for 30 min under Argon CFCunder Argon
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Joint manufacturing by one-step brazingF i t lii J N l M t1. Composite surface is modified by direct
reaction with chromium a carbide layer is formed: large reduction of
Ferraris et alii, J. Nucl Mat. 2008
a carbide layer is formed: large reduction of the C/C-Cu contact angle.
2 C i l b i ll (G ® ) i i ht2. Commercial brazing alloy (Gemco® ) is used to braze C/C to pure copper and pure copper to CuCrZr by the same heat
weight
pp ytreatment. Alloy does not contain any activating element ( h Ti d Si)
CFCC/C
(such as Ti and Si)
brazing alloy
pure Cu
C Cbrazing alloy CuCrZrbrazing alloy
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2D- Digital Image Correlation“ i ” d ti f th l l t t“passive” advection of the local texture (optical flow conservation)
displacement vector
( ) ( [ ])gf x x xulocal form
displacement vector
reference imagedeformed image
weak form
deformed image
2arg min ( ) ( ) ( ) df g x uxu x
weak formsimilarity measure
g ( ) ( ) ( )f gu
variational problem
1 1i i i u = u u incremental form
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Truncated expansion and stationarityEuler Lagrane d 0 LEuler-Lagrane stationarity condition
2 2 1 2grad , 0i i v v L
T 1 12 i
Ti
Tg g d v u x1 1( , )i ia u v
bilinear form
Tg g K
1( )iF v 12 ( ) ( )iT
ig g f d
xuxv xlinear form ( ) L L LL
2 2find : ( , ) ( )i i i i ia F u L u v v v L
linear form2 2 2 2( ) L L L L
semi-coercive variational problemmultiplicity of solution 0 Keru K
Galerkin finite-element discretization
u=NU(e)
1i K U Bpseudo-stiffness pseudo-load
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Tangential traction and 95% confidence strip
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Normal traction and 95% confidence strip
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Parameter sensitivity of displacement field
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Estimate dependence on a priori informationvariance assessment by -point strategy
3 99% confidence intervals
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Confidence ellipsoids and Bonferroni’s domains0 106 [GP ] 1 2T0.106 [GPa m]n
0.665 [ m]n 10.7 [ m]t X
1 2X 1( ) ( )T
,n- - X X C X X
C X CX z X z X X1C X C
ii iii i iX z X z
1 2 3i , , X(2 )/ n equivalent parallelipedic domains
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Engineering motivations
The behavior of masonry structures, strengthened with fiber-i f d l (FRP) hi h i f d i d breinforced polymer (FRP) thin sheets, is often dominated by
delamination of the FRP reinforcement from the support.
A further complication is the presence of mortar joints, where cracks may propagate preferentially.
This fundamental issue is relatively under-investigated for masonry especially from a numerical point of viewfor masonry, especially from a numerical point of view.
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Items to be discussed
engineering motivations
shear tests on joined CFC/Cu assemblies
“optical” inverse problem: from pictures to displacementsfrom pictures to displacements through 2D Digital Image Correlation
“mechanical” inverse problem: from full field data to joint properties through Finite Element Model Updating
closing remarks and future prospects
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Ceramic Matrix Composite SEP NB31NOVOLTEX
PAN=Poly-Acrylo-Nitrilex
NOVOLTEX
preform
yy
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SEM (Philips 525 M)
Energy Dispersive X-ray spectroscopy
Cromium carbide (about 20 m thick) Cr7C3 and Cr23C6
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Adherent nonlinear behavior under plane stressanisotropic extension of multiaxial Ramberg-Osgood relationship
anisotropic extension of multiaxial Ramberg-Osgood relationship
deviatoris stress tensor3 parameters
Műcke & Bernhardi CMAME (2003)
1
1
eqel pl
0R
n
nE
ε ε ε σ sC M 1/2
eqσ T s sM
(tr 3) σs σ 1
equivalent stress0R
([1 : 3],[1 : 3]) 0 M
1/ / / 0x yx y zx zE E E
M
G+H -H -G 0-H H +F -F 0
/ 1/ / 0/ / 1/ 0
0 0 0 1/
xy x y zy z
xz x yz y z
E E EE E E
G
C
M-G -F F+G 00 0 0 2N0 0 0 1/ xyG
/ /ij i ji jE E , , ,i j x y z incompressible strain pltr ( ) 0ε3 parameters
7 parameters 312 2; F = G = H Nfor isotropic Cu
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First-order sensitivity analysis by Direct Differentiation Method
i ( ; ( ); )nn X X UF U 0
FE equilibrium eqs at the free dofs
unknown parameters
Here dependence only upon U!nUint ( ; ( ); ) X X UF U 0
at step nprescribed displacements along the boundary
only upon U!U
along the boundary
int intint T
n
T n T
X U
FFX X
F U 0int TT n T X U X Xpseudo-load vector
intn
FK Up
tan T T XK
Xbl d iff iassembled tangent stiffness matrix,
already available in a Newton scheme