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

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

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

CFRP-reinforced pillar: Historical bricks (XVII century) and high strength mortar( y) g g

single-lap shear test

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)

3D heterogeneous finite element modellingCFRP

masonry

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

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

FOverall delamination response

sF

FE model with “ideal”constraints

“actual”

DIC corrected boundary conditions

“actual”

DIC-corrected boundary conditions

Local slip between FRP and masonry support

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

Composites for aggressive environments

2760

oC

1371

540

ITER(International(International Thermonuclear Experimental pReactor)

brake discs

turbine engine blades

Single-lap shear tests on flat-tile joined samples

CFC / Cu

glue (Araldites AV 119, Ciba-Geigy)

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

4-dofs motion for zoomed camera for optical monitoring

Z

X

X

Y

Finite element discretization of ROI1 pixel 1 pixel 3.0 m

pixe

lp

pixel

Joint collapse

pixe

lp

pixel

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

Displacement fields measured by DIC and computed

tangential component

Displacement fields measured by DIC and computed

tangential component

Displacement fields measured by DIC and computed

tangential component

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

Tangential stress evolution

maxMPa43tp traction predicted under pure mode II

Normal stress evolution

maxMPa58np traction predicted under pure mode I

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 (?)

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

IHaigh-Westergaad space

, 0t tD σf

II

III

= , ,i i I II IIIprincipal stresses

, 0c cD σf

ifi f

Fracture energy regularization

(m ) iGg

specific fracture energy

(e)ch

(m )i igl

“element” characteristic length

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

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

Local traction predicted by FEMy1 2

3

y

3

x

1 7 MPamaxF .A

41

FEM

12 delamination front

A

B

42

12C

delamination frontfront

D

43

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

Post-mortem analyses of fracture surface by SEMFailure of CFC by interlaminar shear, carbon fibre pull-out and cracking of CCr

resolutionSEM resolutionSEM pictures

ITER Final Design Report (July 2001): Materials

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

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

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

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

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

Tangential traction and 95% confidence strip

Normal traction and 95% confidence strip

Parameter sensitivity of displacement field

Estimate dependence on a priori informationvariance assessment by -point strategy

3 99% confidence intervals

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

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.

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

Ceramic Matrix Composite SEP NB31NOVOLTEX

PAN=Poly-Acrylo-Nitrilex

NOVOLTEX

preform

yy

SEM (Philips 525 M)

Energy Dispersive X-ray spectroscopy

Cromium carbide (about 20 m thick) Cr7C3 and Cr23C6

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

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