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