martensitic phase transformations weak vs...
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MARTENSITIC PHASE TRANSFORMATIONS WEAK vs RECONSTRUCTIVE
Oguz Umut Salman
LSPMLaboratoiredesSciencesdesProcédésetdesMatériaux–UPR3407-ParisXIII
2
Formalisation Energétique
• Mul%-physique(techniqueflexible)• Paramètragepardessimula%onsatomis%quespossible• Méthodesspectrales(FFT),élémentsfinis,différencesfinies• Codesdehauteperformancemaison:techniquesdeparallélisa%on
Champscon%nus(plusieursparamètresd’ordre)
nm μm mm mAtomis,que Mésoscopique
(Microstructures)Macroscopique
Echelles d’intérêt
Avantages
ETotal
= EChimique
+ EInterface
+ EElastique
+ EDefaut
- “Special” Microstructure in Martensite : martensite/austenite compatibility
Cu-Zn-Al, M. Morin, INSA de Lyon Ni-Al, R.Delville, AnversTi-Ni-Pd, R.Delville, Anvers
- Dynamics of Martensitic Phase Transitions
Cu-Zn-Al,M.Morin,INSAdeLyon
To understand the macroscopique behaviour of SMA
Formalisation Energétique en fonction de paramètres d’ordre
4
Austénite
Variantsmartensi%ques
PHASE FIELD - MARTENSITIC TRANSFORMATION SMA
ETotal
= EChimique
(�) + EInterface
(r�) + EElastique
(✏ij
�)
Dynamiquepurementdissipa%ve(sansl’énergieciné%que)
austenite
martensite
Ti-Ni-Pd, R. Delville, Antwerpen University (2008)
Ti-Ni, Otsuka, Skuba University
Phase Field Simulations
Phase Field Simulations
ChampsdePhaseélas%citélinéaire,Salmanetal.JournalofAppliedPhysics,(2012)
→ Approche traditionnelle ne reproduit pas ces microstructures
Ni-Al, N. Schryvers, Université d’Anvers
→ On a développé une approche Ginzburg-Landau pour les grandes déformations, c.à.d. élasticité géométriquement non-linéaire.
Finel et al. (2010)
Transmission electron microscopy (TEM) observation NiAl :
Dynamics of Martensite
u+ u = ��ETotal
�uDynamiqued’iner%e(avecl’énergieciné%que)
Iner%aanddissipa%on onlyiner%a onlydissipa%on
LATTICE INVARIANT SHEAR
e1
e2
set of vectors generating same lattice :
C1ij = ei.ej
3
2
1
metric (non-linear strain) associated with each set of vector :
strain energy density : �(C1) = �(C2) = �(C3)
�
- we need to write an energy with infinite number of minimum in the strain space - strain space in three dimensional in 2D, six dimensional in 3D
ej = mijei m = (mij) 2 GL(2,Z)
e0
2
e0
1
e00
1
e00
2
C3ij = e
00
i .e00
j
C2ij = e
0
i.e0
j
- The problem is now to find the matrix m; - Lagrange Reduction gives the equivalent shortest and the most acute set of
vectors
FUNDAMENTAL DOMAIN by Lagrange Reduction:
�(C) = �0(C) = �0(mtCm)
C
�0(C)
the reduced metricenergy is defined only in the reduced strain domain
md�0(C)
dCmt =
d�(C)
dC
for numerical minimisation we also need the stress with respect to the reference state:
we triangulate the lattice using finite atomistic finite elements : vertices are atomistic coordinates
Reduced Domain
RECONSTRUCTIVE MARTENSITE:
fcc to bcc
� =p2 full bcc symmetry
�0(C, T ) = T (C
det1/2C) + (detC � 1)2
Reduced Domain
Dislocation Structure Formation due to thermal cycling
OUTLOOK:
•LagrangeReduc%onin3Dsymmetrygroup•FCC-BCCtransforma%onin3D,cyclicloadingintemperature•Studyofplas%cityonlyandcouplingwithaDDmodelforshortrangereac%ons
•Temperatureeffectswithastochas%cterm(diffusion?)
GL(3,Z)
Merci de votre attention