Issues for the life prediction of Ceramic Matrix … · Hi-Nicalon tows at 500°C and 800°C Lamon, J. Am. Ceram. Soc. 2009) t sn = A t sn = A 0 exp (Ea/RT) 1 10 100 1000 10000 100000

Issues for the life prediction of

Ceramic Matrix Composite

components

Jacques Lamon

LMT, CNRS/ENS/Paris-Saclay University, France

[email protected]

C a c h a n

Summary

• CMCs are of interest to thermostructural applications.

• They were developed initially for military and aerospace applications.

• Effort on CMCs in France started in the seventies

• They have now a high level of technological development.

• The issues have moved from processing methods and basic characteristics to issues relative to resistance to high temperatures and aggressive environments, life of material and components, predictive models and simulation.

• Predictions and control of life are fundamental issues for safe introduction and reliable use of Ceramic Matrix Composites (CMCs) in industrial systems running at high temperature or in aggressive environments.

- Applications

- Some exceptional properties of CMCs: Features of fast fracture Features of delayed fracture at high temperature

- Significance of microstructure/properties relationships

- Multiscale Modeling for lifetime prediction and composite design by tailoring properties to service conditions

Summary

4

Issue : lifetime control and prediction

for long term applications

APPLICATIONS

Ceramic Matrix Composites (CMC) : FIBRES + Interphase + MATRIX

(SiC, C) (SiC, C) (PyC, BN)

High temperature structural applications • Space and Defence • Aeronautical applications • Nuclear reactors

Gas Fast Reactor

Composite Ceramics

Fuel Element Core Lay-out

Core VesselGFR Core Vessel

NUCLEAR POWER PLANTS

Fuel cladding Control rods (SiC/SiC)

ARIANE LAUNCHER

PROPULSION

SPACE CRAFT THERMAL PROTECTION

HERMES EUROPEAN SPACE SHUTTLE PROJECT

Thermal protection components

AERONAUTICAL APPLICATIONS

C/C FORMULA 1 BREAKS

CERAMIC MATRIX COMPOSITES

CMC continuous fiber reinforced ceramics display remarkable properties

- resistance to high temperature

- resistance to high temperature fatigue

- versatile stiffness

- damage tolerance

- crack arrest capability

- decreased flaw sensitivity

- quite infinite toughness/notch insensitivity

- reliability

- versatility

400

300

200

100

00.2 0.4 0.6 0.8 1.0

2D-C/C

2D-SiC/SiCcvi

2D-SiC/CAS

2D-SiC/C

STRAIN (%)

STRE

SS (

MPa

)

(after A. G. Evans)

Tensile behavior: influence of Young’s modulus contrast

VERSATILITY of CMCs

macropore

longitudinal tow

transverse tow

layer

0.5mm

2D woven SiC/SiC microstructure

Matrix damage and tensile behavior

Microstructure – damage – behavior relationship

(Guillaumat, Lamon, 1993)

E f .V f

2.E 0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

E

/ E

0

Strain (%)

G D

A

F

DAMAGE: Load transfer from matrix to fibers during

matrix damage in 2D woven SiC/SiC

A: Ni/(PyC20/SiC50)10/SiC

D: Ni/PyC100/SiC

F: Hi-Ni/(PyC20/SiC50)10/SiC

G: Hi-Ni/(PyC100/SiC

RELATIVE YOUNG’S MODULUS

TOP DOWN PROCESS

load

fibre

matrix

matrix crack

load

debonded

zone

fibre/matrix

interfacial shear

bonded

zone

bonded

zone

load

fibre

matrix

matrix crack

load

debonded

zone

fibre/matrix

interfacial shear

bonded

zone

bonded

zone

(Bertrand, Pailler, Lamon, 2001)

Tensile strength of composite

sTS = VL stow

Tensile strength of tow

Predictions for 2D Nicalon / SiC composites

Nt = 500 aC = 0.17 VL 0.2 Rf = 7.5 mm

tow 2

t C f

F=

N 1 Rs

a

Minimum Tow strength

F(N)

Composite strength

sTS (MPa)

ELS 90 245

LLS 70 190

RLLS (br = 0.35) 40 109

RLLS (br = 1) 25 68

Tensile strength: tow – controlled fracture of 2D composite

Strength density functions for SiC fibers (NLM 202), SiC fiber tows,

SiC/SiC (1D) minicomposites and 2D SiC/SiC composites

0

0.002

0.004

0.006

0.008

0.01

0.012

0 500 1000 1500 2000 2500 Stress (MPa)

Density (

1/M

Pa)

Fibers

Tows

Composites (1D)

Composites (2D)

Reliability: Ultimate failure of CMCs:

from single filaments to woven composites

(Calard, Lamon, 2002)

Reliability: Ultimate failure of CMCs:

statistical distributions of failure strengths

limited effects of stress-state s3p / sR 1.15

(Calard, Lamon, 2002)

Multiscale modeling of tensile

behavior

Ultimate failure of filaments and multifilament tows

Tensile behavior Damage mode Statistical distribution

[Calard, Lamon, 1996]

Flaw-induced stochastic process

Matrix fragmentation in CMCs

[Calard, Lamon, 1998] [Lebrun, Lamon, 1996]

Matrix damage: Fragment dichotomy based model

Strength data have Weibulll distribution

i

i

V

m

Vrup dV

VP

00

1exp1

s

s

Fragment volume (equivalent to length li ) is a statistical variable such as

ii lSV

di

dx

ll

lxP

2)(

ldi ldi ldi ldi

ldi 2li-ldi 2li x

sm

fragment i

0

2li

Stress-state in fragment i

Fibre

(Lissart, Lamon, 1997, 2009, 2010)

Prediction of composite tensile behavior

0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Déformation(%)

Fo

rce

(N)

expérience

simulation

Longueur du minicomposite : 25.04

tau = 84 MPa

Vf = 0.4

Em = 400 GPa

Ef = 300 GPa

mm=5.03

mf=4.2

S0m=5.7 MPa

S0f=6 MPa

Srf=0 MPa

nombre de fibres : 500

rayon des fibres : 7 microns

Tow damage mode

[Pailler, Lamon, 2004]

Matrix damage mode

Damage tolerance and notch sensitivity

Resistance to crack propagation

C/C and C/SiC are notch insensitive

SiC/SiC may be notch insensitive

2D woven SiC/SiC fabricated

By polymer conversion process

(Kagawa, Goto (1997))

Notch sensitivity

A. G. Evans (1997)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

sR/sR(a=0)

a/w

without Fatigue

after Fatigue at450°C

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

sR/sR(a=0)

a/w

this study

Damage sensitivity

Notch insensitivity: sR = sR (a=0).(1-a/w)

a= diameter of equivalent hole

Residual strength after static fatigue

Post impact tensile strength

w

a s = F/(w-a)b

Resistance to crack propagation

Fracture toughness:

Material property which characterizes

the initiation of fracture from a sharp crack

(obtained by fatigue cracking under plane

Strain conditions)

2D SiC/SiC composites

(Droillard, Lamon, 1996)

High Temperature behavior:

- monotonous loading rate

- static fatigue

Tensile behavior at high temperature

(Forio, Lamon, 2001)

Mechanical loads

Matrix cracking

Degradation of interphases High temperature

oxidation

Fiber overloading

Fiber weakening

Temperature

Environment

Delayed failure of fibers

Ultimate failure

degradation

oxidation

Creep T>1200°C

slow crack growth

T<1000°C

Durability

creep of the matrix

T>1200°C

Delayed failure and lifetime at high temperature

Crack healing in 2D woven SiC/SiBC composite

Cyclic fatigue (20 Hz) at 1200°C

Static fatigue at 1200°C (load150 MPa) (Carrere, Lamon, 1999)

Lifetimes in fatigue at high temperature

700°C Minicomposite BN interphase [Morscher 1998] 600°C NLM 207 treated 700°C NLM 202 as-received [Lavaire 1999] 600°C 1D SiC/Si-B-C

100

1000

10 4

10 5

10 6

10 7

100 1000

Life

tim

e

(s)

Stress on fiber (MPa)

600°C NLM 207 treated 600°C 1D SiC/Si-B-C 600°C 2D SiC/Si-B-C

100

1000

10 4

10 5

10 6

100 1000

Life

tim

e (s

)

Stress on fiber (MPa)

Composite 2D 120 MPa

Composite 2D 220 MPa

Static fatigue: slow crack growth in SiC fibers

500°C 900°C 1000°C 1200°C

SiC tows

SiC/SiC composite

Slow crack growth

Growth of oxide layer at fiber surface Protection of fiber by oxide layer and SiC

matrix: slowing down SCG phenomenon

Slow crack growth

Surface oxidation

Creep

Fracture surface of a fiber after static

fatigue on Nicalon tows at 700°C

Fiber

Silica thin layer

flaw

Stress intensity factors estimated from

crack sizes

crack length KI KI/KIC

0.62 0.47 0.23

1.23 0.66 0.33

1.85 0.81 0.40

3.08 1.04 0.52

Penny shaped cracks :

I

aK 2 s

ICK 2MPa m

Static fatigue: slow crack growth in SiC Nicalon tows

(Forio, Lamon. JACS, 2004)

34

Static fatigue of SiC filaments and tows

n ≈ 8.4

A0 = 5,62.1017 Ea = 182 kJ.mol-1

y = 3,15.10 26 x

-7,25

y = 3,29.10 24 x

-7,24

1

10

100

1000

10000

100000

1000000

10000000

100 300 500 700 900 1100 1300 1500 1700 1900

stress ( MPa )

lifet

ime

( s

)

Fils Hi - Nicalon S 600 °C

Fils Hi - Nicalon S 800 °C

Fils Hi - Nicalon S 800 °C

1 mois

1 sem

1 j

1 h

1 min

1000

100

10

1

0,1

0,01

0,001

dd

v (h

) Hi-Nicalon S tows at 600°C and 800°C

n ≈ 7,2 A0 = 7,38.1015 Ea = 178 kJ.mol-1

Hi-Nicalon tows at 500°C and 800°C

(Gauthier, Lamon, J. Am. Ceram. Soc. 2009)

t sn = A0 exp (Ea/RT) t sn = A

1

10

100

1000

10000

100000

1000000

10000000

100 300 500 700 900 1100 1300 1500 1700 1900

applied stress (MPa)

life

tim

e (

s)

tows 500°C

tows 800°C

single fibres 800°C

1000

100

10

1

0,1

0,01

0,001

life

tim

e (

h)

Theory: fiber lifetime distribution

V =da

dt= V *

K I

K IC

æ

è ç

ö

ø ÷

n

t =2K IC

2

V *Y 2s2(n - 2)

sf

s

æ

è ç

ö

ø ÷

n-2

-1é

ë ê ê

ù

û ú ú

P(t,s,v) =1 - exp -v

vo

æ

è ç

ö

ø ÷

s

s0

æ

è ç

ö

ø ÷

m

1 +t

t*

n - 2

2

æ

è ç

ö

ø ÷

m

n-2é

ë

ê ê

ù

û

ú ú

- Subcritical crack growth

- Stress-strength-rupture time relation

- Lifetime distribution

t* =K IC

2

V *s2Y 2

sfj

= s0(-v

0

vLn(1 - P

j))

1

m

(R’Mili, Lamon, 2011, 2012)

Distribution of lifetimes under constant stresses

Hi Nicalon S filaments @800°C in air

(R’Mili, Lamon, 2015)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.E-04 1.E-01 1.E+02 1.E+05 1.E+08

Pro

ba

bil

ity

Rupture time (hours)

1100 MPa 700 MPa

400 MPa

Critical fiber

Fibre Fibre

L1 L2

PyC coating t1 t2

Influence of oxidation of PyC interphase in SiC/SiC: size effects

On lifetime of SiC filament (P=0.1) at 500°C under 700MPa

Size dependence of rupture time

P(t,s,v) =1 - exp -v

vo

æ

è ç

ö

ø ÷

s

s0

æ

è ç

ö

ø ÷

m

1 +t

t*

n - 2

2

æ

è ç

ö

ø ÷

m

n-2é

ë

ê ê

ù

û

ú ú

(R’Mili, Lamon, 2011, 2012)

t2

t1

=L

1

L2

æ

èçç

ö

ø÷÷

n-2

m

0,1

1

10

100

1000

10000

100000

1000000

10000000

100000000

0 50 100 150 200 250 300 350 400

Stress on composite (MPa)

Experimental data

Predicted data

t s 2= cste

75%

0%

25%

50%

p 90%

Ru

ptu

re t

ime

(h)

Stress-Probability-Time diagrams for 2D SiC/SiC

(Loseille, Lamon, 2010)

Static fatigue at 500°C

• CMCs are versatile and smart materials

• Significance of microstructure/properties relationships

• Theoretically, composites can be designed with respect to end use applications

• Empirism still prevails

• But, composite design can be based on models

• Multiscale bottom up models are required: damage processes, failure mechanisms at pertinent scales, constituents properties, interface mechanics, and scale to scale changes

• Interface engineering, processing, treatment and new fibres and matrices (?)

ACKNOWLEDGMENTS

• Financial support: CNRS, Snecma, CEA, Conseil Régional d’Aquitaine, European Commission.

• Ph. D. students: S. Bertrand, K. Rugg, L. Guillaumat, N . Godin, P. Forio, S. Pasquier, S. Pompidou, F. Pailler, P. Carrère, C. Droillard, F. Rebillat, V. Calard, C. Sauder, O. Loseille, V. Calard, J. El Yagoubi, M. R’Mili, A. Laforêt