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Capturing polycrystal plasticity and intergranular cracks with a novel DIC method
Li Li, Félix Latourte, Jean Michel Muracciole, Laurent Waltz, Laurent Sabatier, Bertrand Wattrisse
To cite this version:
Li Li, Félix Latourte, Jean Michel Muracciole, Laurent Waltz, Laurent Sabatier, et al.. Capturing polycrystal plasticity and intergranular cracks with a novel DIC method. 11th World Congress on Computational Mechanics (WCCM XI), Jul 2014, Barcelone, Spain. �hal-01175898�
E.Oñate,J.OliverandA.Huerta(Eds)
CAPTURING POLYCRYSTAL PLASTICITY AND
INTERGRANULAR CRACKS WITH A NOVEL DIC
METHOD
L. LI
1
, F. LATOURTE
2
, J.-M. MURACCIOLE
1,3
, L. WALTZ
1,3
,
L. SABATIER
1,3
AND B. WATTRISSE
1,3
1
Laboratoire de MéaniqueetGénieCivil(LMGC), Montpellier 2University, CNRS,Frane,
[li.li,jean-mihel.muraiole,laurent .waltz,la urent.sabat ier,bertr and.watt risse℄univ-montp2.fr
2
EDF R&D,MMCDept.,les Renardières,Frane, felix.latourteedf.fr
3
Laboratoire de Miroméanique etdIntégrité desStrutures(MIST),
IRSN-CNRS-Montpellier 2University,Frane.
Key words: Digital Image Correlation (DIC), Polyrystalline materials, Intergranular
raking,Numerialvalidating.
Abstrat. The aim of this paper is to validate a novel DIC method whih allows to
apture kinemati elds of potentially raked polyrystalline aggregates. A key feature
ofthemethodintroduedisthatintergranularandintragranulareetsanbeonsidered
expliitlyinthe data proessing. In this paper, we mainlyfous onthe validationproe-
dure, whih was performed on numerial examples assoiated to raked polyrystalline
aggregates.
1 Introdution
Surfae displaement eld measurements of materials subjeted to various loadings
(e.g. mehanial loading or thermal loading) are an important task for experimentalists
onduting researh in the eld of solid mehanis. Aside from the widely used strain
gauge tehnique, various full-eld non-ontat optial monitoring methods [1℄, inluding
both interferometri tehniques and non-interferometri tehniques, havebeen developed
and applied forthis purpose.
In reent years, we have witnessed an inreasing numberof spetaular developments
in optial full-eld measurement tehniques [2℄. The interferometri tehniques involve
deliate proedures whih are not always suited for experiments in onventional testing
laboratories. Conversely, the DigitalImage Correlation (DIC) methodwidely onsidered
as a representative non-interferometri optial tehnique, has been widely aepted and
ommonlyused asapowerfuland exible toolfor the surfai strainmeasurement inthe
eld of experimental solid mehanis[3, 4,5℄.
Crystal plastiity is usually used as the onstitutive model to desribe the response
of rystal grains. The objetive of single rystal plastiity is to introdue knowledge
of disloation theory into plastiity of a ontinuum of solids [6℄. In material siene,
rystalplastiityisnowlassiallyusedtodesribethe singlerystalmehanialresponse
involvingitsslipsystemativity. Onemajorinterest ofmiromehanisof heterogeneous
polyrystalline materials is to aess loal mehanial elds in a given mirostruture
assoiated to surfai strain elds that an be measured [7, 8, 9℄, in order to ontribute
toabetterunderstandingof themirostruturedependene ofyieldbehaviourduringthe
mehanialloadingatgranularsales,andtoassessloalstresseldsinviewofdeveloping
physially baseddamage models.
Inthispaper, anewmethodisproposedtoperformtheloalstraineldmeasurements
relying on DIC algorithms, with a spei treatment of intergranular and intragranular
disontinuities. The objetive of this paper is to present and to validate this novel pro-
essing method,whihallowsus heneforth to evaluatethe material behaviouratboth a
miro and maro sales.
2 Numerial Validation
2.1 Numerial example generation
In order to validate the proposed methodology on heterogeneous strain elds, it was
hosen to use omputer-generated spekle raked images assoiated to a ompletely
known straineld.
The strain eld wasobtained by diretrystal plastiityFiniteElement(FE) analysis
foragivenrystal plastiitylaw[10℄and foragiven set ofboundary onditionsandgrain
orientations. For this numerial study, a realisti aggregates of 50 grains was generated
by using a lassial Voronoï tessellation, the hosen material behaviour obeys to the
Méri-Cailletaud model, desribed in [10℄. The simulation of experimental tensile test
was performed using the nite element pakage Aster with a mesh of 11300 quadrati
triangularelements ina bi-dimensionalframeworkunder a planestrain assumption [11℄.
The aim of this FE omputation is to provide realisti kinemati elds assoiated
to equilibrated stress elds. Afterwords, the simulated displaement eld was then in-
trodued in the virtual image generation proedure, as desribed in [4℄, to mimi the
aquisition of the series of spekle images by a digital visible amera. It was hosen not
tointrodue any imagedistortionin the syntheti images.
2.2 Spatial disretizationof the syntheti image
In order to determine preisely the loal strain eld, partiular are should be given
on the meshing. With a known mirostruture (Figure 1a), where the rak is indiated
usingayanolorline, thespatialdisretizationisperformedusinganunstruturedmesh
in orderto represent the grainboundaries of the material(Figure 1b).
In this unstrutured mesh (Figure 1b), the smallest mesh unit is alled "element",
200 400 600 800 1000 1200 100
200 300 400 500 600 700 800 900 1000 1100
(a)Mirostrutureforsynthetiimage
200 400 600 800 1000 1200
100 200 300 400 500 600 700 800 900 1000 1100
(b)Unstruturedmesh
Figure1: Mirostruturewith unstrutured mesh. Initialrak is indiated using ayan
line.
whih is the equivalent of the Correlation Zone (CZ) for lassial DIC tehnique. Eah
element is onstituted by a set of pixelswithin a polygon. The elements'boundaries are
determined aurately and retained in order to apply spei adjaeny ondition with
otherelements. Knowing thegrain boundariesfor thematerial,withthis mirostrutural
disretization method, no element belongs to more than one grain. Therefore, this is a
suitable omputationalmesh for dealing with disretestruture problem (polyrystalline
metallimaterials,et.).
3 Numerial Results
One the omputational mesh isobtained, we introdue the dierentkinemati onti-
nuity onstraints inorder todesribe the mehanialfeatures of materialat the dierent
physialsale.
The rst solution is to impose no ontinuity onstraints at all between elements (see
Figure 2b, where the displaement eld is ontinuous only inside element). The seond
possibilityistoimposenormalandtangentialontinuityontheboundariesofallelements
belongingtoagivengrain. Thedisplaementeldisthusontinuouswithineahgrainbut
possibly disontinuousbetween twoadjaentgrains (seeFigure2). The third possibility
proposedhereis toenfore thenormaland tangentialontinuity ofthe displaementeld
atthe boundaries of allelements, exept the ones orrespondingto the rak (see Figure
2d).
Figure2 shows the equivalentstrain eld mapsin the Von Mises sense forthe raked
polyrystalline aggregates.
The Finite-Element referene omputations whih are performed with the raked ag-
gregateup to2% marosopi strainis represented in Figure2a. AndFigure 2b, 2, and
0 200 400 600 800 1000 1200 0
200
400
600
800
1000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
(a)SimulationAster
0 200 400 600 800 1000 1200
0
200
400
600
800
1000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
(b)Intra-elementontinuity
0 200 400 600 800 1000 1200
0
200
400
600
800
1000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
()Intra-granularontinuity
0 200 400 600 800 1000 1200
0
200
400
600
800
1000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
(d)Inter-granularontinuity
Figure2: Equivalent Von Mises strain elds for the raked polyrystal aggregates
2dshowequivalentVonMisesstrain eldsobtainedwith themethodintroduedwiththe
three dierent ontinuity levels. In the DIC omputation, the kinemati shape funtion
is bi-linear. The mesh ismade of 1513 elements distributed inthe 50 grains.
Thelessonstrainedsituationorrespondstonoontinuityonditionexeptinsideeah
element(Figure2b), whihorresponds tolassialloalDIC approahes [4,12℄,and the
displaementeldsaredesribed by1513×4×2 = 12104DegreesOfFreedom(DOFs). In this irumstane, the omputationis suitablefor desribing the intragranular behaviour
of the polyrystallineaggregates, but itisvery sensibletothe noise (the noise sensitivity
is not disussed in the present paper).
Themostonstrainedsituationisassoiatedwiththeintergranularontinuity,whihis
very similartothe globalDIC approahes proposed in [5,13℄, exept that the ontinuity
of the displaement eld isenfored in the real spae and not in the isoparametrispae
ofthe referene element. Thisleadstomuhonstrained displaementeldsompared to
the abovementionedglobalapproahes. Forour study,the kinematields are desribed
using only 170 DOFs. Figure 2d shows that this set is too small to represent aurately the displaement elds. In this ase, the ontinuity onditions should be restrained in
order toimprovethe auray of the measurements.
Theintermediatesituationonsistsofintragranularontinuity(Figure2)whihorre-
sponds to 1372DOFs. It isthusmore robustwith respet to imagenoise. This situation is partiularly suited to desribe intragranular strain heterogeneities and intergranular
disontinuities (suh asgrain boundary slip).
4 Conluding Comments
The omparison of strain elds alulated by DIC and obtained by FE simulation
is onlusive to validate our methodology. Furthermore, this method will be validated
numerially onthe noisyimages before applyingtoexperimentalvisibleimages olleted
during atensile test ona polyrystalline aluminum sample,whih ouldproess the full-
eld kinemati data grain per grain in order to establish the relationship between loal
strain elds and mirostruture at grainsale.
REFERENCES
[1℄ PramodK. Rastogi. Priniples of holographi interferometry and spekle metrol-
ogy. In PramodK. Rastogi,editor, Photomehanis,volume 77of Topis in Applied
Physis, pages 103151.Springer Berlin Heidelberg, 2000.
[2℄ MihaelA. Sutton, StephenR. MNeill, JereyD. Helm, and YuhJ. Chao. Advanes
in two-dimensional and three-dimensional omputer vision. In PramodK. Rastogi,
editor, Photomehanis, volume 77 of Topis in Applied Physis, pages 323372.
Springer Berlin Heidelberg, 2000.
[3℄ M.A. Sutton, W.J. Wolters, W.H. Peters, W.F. Ranson, and S.R. MNeill. Deter-
minationof displaements usinganimproved digitalorrelation method. Image and
Vision Computing, 1(3):133 139, 1983.
[4℄ B. Wattrisse, A. Chrysohoos, J.-M. Muraiole, and M. Nemoz-Gaillard. Analysis
of strain loalizationduring tensile tests by digital image orrelation. Experimental
Mehanis,41:2939, 2001.
[5℄ F. Hild and S.Roux. Digital image orrelation: from displaement measurement to
identiationof elasti properties areview. Strain, 42(2):6980, 2006.
[6℄ A M Cuitino and M Ortiz. Computational modelling of single rystals. Modelling
and Simulation in Materials Siene and Engineering,1(3):225,1993.
[7℄ D. Raabe,M. Sahtleber, Z.Zhao, F.Roters, andS.Zaeerer. Miromehanialand
maromehanial eets in grain sale polyrystal plastiity experimentation and
simulation. Ata Materialia,49(17):3433 3441, 2001.
[8℄ M. Sahtleber, Z. Zhao, and D. Raabe. Experimental investigation of plasti grain
interation. Materials Siene and Engineering: A,336(12):81 87,2002.
[9℄ E. Héripré, M. Dexet, J. Crépin, L. Gélébart, A. Roos, M. Bornert, and D. Calde-
maison.Couplingbetweenexperimentalmeasurementsandpolyrystalniteelement
alulations for miromehanial study of metalli materials. International Journal
of Plastiity, 23(9):1512 1539, 2007.
[10℄ L. Meri, P. Poubanne, and G. Cailletaud. Single rystal modeling for strutural
alulations.i,modelpresentation. Journalof mehanialdesign(1990),113(1):162
170, 1991. eng.
[11℄ F.Latourte,N.Rupin,andJ.-M.Proix. Plastiitéristallinedansunaierbainitique
revenu : simulations pour la validation de modèles à partir de mesures de hamps.
In 11e Colloque Nationalen Calul des Strutures, Frane,May 2013.
[12℄ B.Wattrisse,A.Chrysohoos,J.-M.Muraiole,andM.Nemoz-Gaillard. Kinemati
manifestations of loalisationphenomena in steels by digital image orrelation. Eu-
ropean Journal of Mehanis - A/Solids, 20(2):189 211, 2001.
[13℄ Stéphane Rouxand FrançoisHild. Stress intensityfator measurements fromdigital
imageorrelation: post-proessingand integrated approahes. International Journal
of Frature, 140(1-4):141157,2006.
