Accounting for elastic anisotropy in crystal plasticity within the context of olivine dynamic recrystallization using a level-set framework

(1)

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Accounting for elastic anisotropy in crystal plasticity within the context of olivine dynamic recrystallization

using a level-set framework

Jean Furstoss, David Ruiz Sarrazola, Marc Bernacki, Carole Petit, Clément Ganino, Daniel Pino Muñoz

To cite this version:

Jean Furstoss, David Ruiz Sarrazola, Marc Bernacki, Carole Petit, Clément Ganino, et al.. Accounting for elastic anisotropy in crystal plasticity within the context of olivine dynamic recrystallization using a level-set framework. AGU Fall Meeting 2019, Dec 2019, San Francisco, United States. �hal-02440169�

(2)

Accou

ntin

g for

elasti

c ani

sotr

opy in

a

ﬁ

ni

te element ap

proa

ch of

olivi

ne cry

stal

deforma

tion

J. F

urs

toss

a, b

, D. R

uiz Sar

razola

b

, M. Ber

nac

ki

b

, C.

Petit

a

, C.

Ganino

a

, D. P

ino Muñ

oz

b a Geoazur , 250 rue Albert Eins tein, 06 560 V albonne, F ran ce b Mines P arisT ech-C EME F, r ue Clau de Daun esse, 06 904 Sophia-Antipolis cede x, F ran ce

Does the elast

ic anisotr

opy have an

in

ﬂ

u

ence

on the

mecha

nical beha

viour an

d LPO development

during

plastic defor

mation,

in the

case of olivine ?

Context :

Cryst

al plasticity for

mulation

(Marin 2006)

furstoss

@geoazur

.unic

e.fr

Abstra

ct :

Because

olivine

is

the

major

constitu

ent

of

upper

mant

le

rocks,

its

mech

anical

pr

operties

and

micr

ostruc

tura

l

evolutions

play

an

importan

t

role

in

the

lithospher

e

rheology

.

In

this

study,

we

investigate

the

defor

mation

of

olivine

polycrystals

thr

ough

a

numer

ical

framewor

k

coupling

the

crys

tal

plasticity

and

the

ﬁ

nite

element

method

(CPFE

M).

The

rheology

of

the

olivine

aggr

egate

is

described

thr

ough

a

crys

tal

plasticity

model

that

we

have

developed

and

that

tak

es

into

accou

nt

the

elastic

anisotr

opy

of

the

olivine

cryst

al,

based

on

published

e

xperiment

al

data.

The

mix

ed

velocity/pr

essur

e

ﬁ

nite

element

for

mulation

has

also

been

modi

ﬁ

ed

in

or

der

to

tak

e

into

accou

nt

the

infor

mations

coming

fr

om

crys

tal

plasticity

comput

ation.

In

addition

to

pr

edicting

polycrystal

mecha

nical

behaviour,

this

methodology

also

per

mits

to

trac

k

the

development

of

lattice

pr

efer

red

orientat

ion

(LPO)

during

defor

mation.

These

important

featur

es

ar

e

pr

edicted

using

the

pr

oposed

appr

oach

during

the

defor

mation

of

olivine

aggr

egate

with an

d withou

t acc

ountin

g for elastic

anisotr

opy

.

Our

results

suggest

that

the

elastic

anisotr

opy

e

xerts

a

weak

in

ﬂ

uen

ce

on

the

subsequ

ent

plastic

defor

mation

and

thus

on polycrys

tal mech

anica

l behaviour,

LPO development a

nd local pr

essur

e and

str

ess.

Finite element

framework

Results fo

r ini

tia

lly textu

red an

d non

textured po

lycr

ystal

Discu

ssio

n/Con

clu

sion

:

No

stro

ng

in

ﬂ

uenc

e

is

obser

ved

between

mod

els

acc

ount

ing

or

not

for an

isot

ropi

c elas

tici

ty :

• neither on

macr

osco

pic

mecha

nic

al beh

aviou

r,

• nor on textur

e developm

ent,

• nor on lo

cal

total

disl

ocat

ion d

ensity

,

and

this fo

r ini

tia

lly textu

red or n

ot mat

erial

Same tr

ends wit

h loc

al di

ﬀ

erenc

es abou

t few tens of perc

ent on :

• local

pressu

re

• local

stresses

At

this

poin

t,

there

is

no

clear

eviden

ce

for

the

in

ﬂ

uence

of

ani

sotro

pic

elasti

city

on pla

stic

deform

atio

n

Perspecti

ves :

The

in

ﬂ

uence

of

elasti

c

ani

sotro

py

has

to

be

tested

withi

n

dyna

mic

recry

stal

liza

tion

simu

lati

ons

Nuc

leati

on

cri

teriu

m

based

on

loca

l

diso

rient

atio

n

or

loca

l

stress

ma

y

imp

ly som

e chan

ges

References :

A

.

Tommasi,

M. Knoll,

A

.

V

auc

hez,

J. W

.

Signor

elli,

C. Thora

val,

R

.

Logé.

Struc

tur

al

reactivat

ion

in

plate

tectonic

s

contr

olled

by

olivine

cryst

al

anisotr

opy

. Natu

re Geoscien

ce, 2,

423-4

27, 20

09.

D.

G. Isaak

,

O

.

L. Anderson

,

T. Goto,

I. Suzuk

i.

Elasticity

of

single

‐cr

ystal

forsterite m

easur

ed to 170

0 K. JG

R : Solid Ea

rth,

94, 5

895-590

6, 198

9

E.

B. Marin

.

On

the

for

mulation

of

a

crys

tal

plasticity

model.

Mecha

nics

of Materials,

Sandia Nat

ional Laboratories,

2006.

J. Durinc

k,

P. Car

rez,

P. Cor

dier

.

Application

of

the

Peierls-Nabar

ro

model

to dislocations in

forsterite.

Eur

. J. M

ineral, 1

9, 631

-639,

2007.

P. Phack

ey,

G. Dollinger,

J. Christ

ie.

Trans

mission

Electr

on

Micr

oscopy

of

Experimen

tally

Defor

med

Olivine

Crys

tal.

Flow

and

fractu

re

of

rocks,

16,

117-13

8, 197

2.

M.

M. Mehra

badi

and

S.

C. Cowin.

Eigenten

sors

of

linear

anisotr

opic

elastic

materials.

The

Quart

erly

Jour

nal

of

Mecha

nics

and

Applied

Mathem

atics,

43, 15

-41, 1

990.

J. Gasc

,

S. Demouchy,

F. Bar

ou,

S. K

oizumi,

P. Cor

dier

.

Cr

eep

mecha

nisms

in

the

lithospheric

mant

le

infer

red

fr

om

defor

mation

of

ir

on-fr

ee

forsterite

aggr

egates

at

900–12

00 °C.

Tectonoph

ysics,

761,

16–

30, 20

19. Ackno

wledgm

ents :

This wor

k was

support

ed by CNRS

INSU 2018

-pr

ogramme T

elluS-SYSTER

.

The

supports

of

the

Fr

ench

Agence

Nationale

de

la

R

echer

che

(ANR),

Ar

celorMittal,

Ar

eva,

ASCOMET

AL,

AUBER

T&DUV

AL,

CEA,

S

AFR

AN

thr

ough

the DIGIMU

Indus

trial Ch

air an

d cons

ortium a

re grat

efully ackn

owledged.

Most r ocks e xhibit a mec han ical behaviour str ongly anisotr opic This is m ainly due t o lack of indepen dent s lip systems a ccommodat ing str ain dur ing plastic defor mation Consequ ently, plast ic defor mation of r ocks of ten leads to the developmen t of mark ed lattice pr efer red orientation (LPO) Orthor hombic cryst allographic s truc tur e of forsterite (M g rich end

member of olivine) _Forsterite

elastic c onstan ts fr om Isaak et al. 1 989 Numeric al simulation of a shear zone cr eation an d act ivation with the cor responding LPO development fr om T ommasi et a l. 2009

Num

erica

l im

plemen

tati

on :

A list of sl

ip sy

stem :

The elasti

c beha

viou

r :

The

ﬂ

ow rul

e :

The hard

enin

g beha

viou

r :

The for mulation is based on a set of 3 equations describing the equilibrium of strain , the rotation of the lattic e and t he evolution of th e str ength .

A set of cons

titutive laws

has

to de

ﬁ

ne

:

P1+/P1 mix ed velocity pr essur e for mulation The fi rst r esidual is bas ed on : with The sec ond r esidual is bas ed on : Cr oss cu t onto t he su rface fl ow for th e di ff er ent list of slip systems W ith initial C RSS ( ) disc riminatin g slip systems with [ 100] a nd [001 ] Bur gers vec tor fr om dislocation dyn amics simulation ( Durinc k et al. 2007) Dislocation density evolution : wher e K1 an d K2 ar e tak en to bes t fi t m onocryst al defor mation e xperiment s (Ph ack ey 1989 )

CP calc

ula

tion

prov

ides : - d

eviato

ric

stress

- tangent

matr

ix

A

ccoun

ting for elas

tic an

isotr

opy

All tensors a re e xpr essed with in the appr opriate K elvin base which acc ounts for crys tal type (M ehraba di et al. 19 90) : the 6 tensors of the bas e ar e the eigentensor s of the elas tic con stant matr ix Str ess an d stra in become : and th e Hook e's law is reduced to : Ini tial pole ﬁ g ures Cube ( 2mm as ide) compr ession Isotr opic mesh (1 million element) r emeshed ever y 1% of macr oscopic str ain 300 gr ains of 0.1 8mm mea n gra in size

Initial total dislocat

ion density 1 0 5 mm − 2 Macr oscopic st rain r ate 10 − 3 s − 1 and in cr ement of 0.1% a t every s tep Mac rosc opic mecha nic al b ehavi our

(full line with

anisotr opy, dashed line without anisotr opy) With elasti c ani sotr opy With out ela stic anis otrop y

Results a

t loca

l sca

le

Deviato ric stress co mpon ents al ong a lin e passin g thr oug h a gr ain boun dar y Pressur e evoluti on between two op posi te edges Ini tial ly no n textured Ini tial ly textur ed