fracture of materials: from physical mechanisms to

Chaire Francqui 2016, ULg

Fracture of materials : from physical mechanismsto engineering applications

Thomas Pardoen

In February and March 2016

Institute of Mechanics, Materials and Civil Engineeri ng

Chaire Francqui 2016, ULg

Opening lectureFracture , a fatality for materials, structures and life?

Thomas Pardoen

Leçon inauguraleLe mercredi 3 février 2016Salle académique de ULg, Place du 20 août 7 à 4000 Liège

Fracture is

everywhere

in the earth

Keywords : cracks, faults, fragmentation

Introduction

In plants

Keywords : cracks, delamination, fibrillation

Introduction

in the sky

Keywords : cracks, fragmentation

Introduction

In producing objects

Keywords : cutting, machining, carving

Introduction

In transportation

Keywords : fatigue, crack propagation, tearing, crash, fatigue

Introduction

DOEL3 Safety Case 2015, Electrabel, 2015Keywords : cracks, microcracks, transition temperat ure

Introduction

in buildings and structures

Le tunnel Stéphanie restera fermé jusqu'au week-end prochain (21-01-2016)

l’année prochaine

Weapons and protection systems

Keywords : cracks, tearing, penetration

Introduction

Garage Carat Duchatelet

in pipes and cables

Keywords : cracks, tearing

Introduction

Accident de Ghislenghien

In coatings

Introduction

Keywords : cracks, delamination,spalling, chipping

Faou et al. JMPS 2015

Favache et al. Wear 2015, TSF 2014

in our body

Keywords : cracks, chipping, fatigue

Introduction

in sport

Keywords : cracking, crushing, fragmentation, fatig ue

Introduction

in foods

Quality of the taste depends on crispiness, crunchiness, easiness of cutting, etc !Keywords : cracking, cutting, delamination

ciboulette57.canalblog.com

Introduction

In everyday life

Keywords : cracks, shear cracks, fragmentation, stick ing, debonding

Introduction

T. Atkins

Outline

1. First approach : fracture mechanics

2. Second approach : damage mechanics

3. Towards super tough materials

Assume a theoretically perfectlysharp crack of length a

F (N)u (mm)

1. Fracture mechanics

See lecture 1 A.A. Griffith, Phil Trans R Soc London 1921

If the load such that no cracking

external work entirely converted intodeformation energy

Energy balance

F,∆u

F,∆u

eWuF ∆=∆

If cracking

part of the energy of the system used for cracking

aBGWuF ce ∆=∆−∆

B : thickness


Define the driving and resistive force for crack propagation G and G c

{ { { { {advancecrack thicknessenergy def of change workexternal

aGBWuF ce ∆=∆−∆

Gc : critical energy release rate (J/m 2)Energy par unit area required for cracking

= fracture toughness

Define G as

∆∆−

∆∆=

aW

aFu

BG e1

As long as G<Gc, no cracking


How to estimate G ?


Sometimes analytical solutions can be worked out

Example : Double Cantilever Beam (DCB)

analytical (approximate) solution - OK for sufficiently long beams

F

F

hB

a

h

32

22

34

22 1212

hEB

aF

hEB

AFG ==

∆∆−

∆∆=

aW

aFu

BG e1

See lecture 4


Wyart et al. EFM 2009

Duflot et al.

Sometimes estimatingG is very complex

New methods like X-FEM allow calculating G (and K) in very complex 3D configurations at reasonable prize

Lani 2015 with Morfeo

Meaning of Gc

See lecture 1 to 6


F

F

hB

a

hNew surface 2 withsurface energy γγγγs

New surface 1 withsurface energy γγγγs

If perfectly brittle Gc = 2γγγγsaround 1 J/m 2 …

If perfectly brittle Gc = 2γs ~ 1 J/m2 …fortunately almost never that small

Meaning of Gc

See lecture 1 to 6

Ashby map Gc

Gc & Kc depend alsoon T°, irradiation, microstructure,

humidity, etc


Map from Edupack

Gc = 1 J/m2

Gc = 100000 J/m2

See lecture 1

Measurement of Gc

F

F

hB

a

h32

22

34

22 1212

hEB

aF

hEB

AFG ==


Example based on DCB geometry

u

acrack length

CCD camera

constant rate

PCIR source

Wedge configuration

1. Measure G c (at right T°, etc)

2. Determine G based on crack length a, load F and geometry

Fracture if G > Gc

Summary


2. Constraint effects

Unfortunately, fracture mechanicshas two major limitations

3. No link with the physics and material structure

See lectures 1, 4

See lectures 3 to 6

1. How to deal with un-cracked materials or components ?

See lecture 3, 5, 6


Outline




σσc

0r

λ/2

u = r - r0

r

0r

10

Etheorc ≈σ

The theoretical fracture stress

EF=σA

u

r0

2γs

Examples

Si E = 180GPa σσσσc = 25 GPaFe E = 260GPa σσσσc = 32 GPaNaCl E = 44GPa σσσσc = 6.3 GPaIce E = 8.5GPa σσσσc = 3.4 GPa

2. Damage mechanics

The theoretical fracture stress of Si

2. Damage mechanics

Dubois, Rignanese, Pardoen, Charlier, PRB 2006

Simulation withcode ABINIT

(UCL)

based on density-

functionaltheory

1. « Brittle » materials

Is it valid for brittle materials ?

10

Etheorc ≈σ

2. Damage mechanics

ε = ∆L/L

σ = F/A5 GPa

50 GPa

Theoreticalvalues

0.1 GPa

1 GPa

Realvalues

The real fracture stressof « brittle » materials

2. Damage mechanics

1%

Why brittle materials are brittle ?

σσσσmacro

σσσσlocal >> >> >> >> σσσσmacro

10

Etheorc

local ≈=σσFracture when theorc

macroc σσ <<

< 1 µm

2. Damage mechanics

What if smaller and smaller

Specimens are tested ?

σσσσmacro

< 1 µm

2. Damage mechanics

Nano« brittle » materials : back to theoretical fracture stress

Volume of Si cantilever beam [µm3]

Fra

ctur

e st

reng

th [G

Pa]

σσσσfracture for Si bulk

See lecture 6

~40% of

theoretical σσσσfracture

New concept of nanomechanical on-chip test

laboratory developed and patented at UCL

2. Damage mechanics

Passi et al ., Rev Sci Inst 2011, JMEMS 2012

1 wafer

2 weeks of processing

~ 10.000 test structures

UCL Nanomechanical lab on chip

2. « Ductile » materials

Is it valid for ductile materials ?

10

Etheorc ≈σ

2. Damage mechanics

ε = ∆L/L

σ = F/A

The real fracture stressof « ductile » materials

5 GPa

50 GPa

Theoreticalvalues

0.1 GPa

1 GPa

Realvalues

Meaningful parameterfracture strain5% 500%

2. Damage mechanics

What happens inside a « ductile » material when highly deformed ?

See lecture 3Tests performed at the ESRF synchrotron in Grenoble by F. Hannard (Ph. D. UCL) collaboration with Dr. E. maire INSA Lyon Hannard et al. Acta Mater 2016

2. Damage mechanics

X-ray tomography of in-situ tensile tests= scanner for materials

Al 6056

X-ray tomography of in-situ tensile tests on an aluminium alloy

εεεε = 23%

2. Damage mechanics

Al 6056


εεεε = 30%

2. Damage mechanics

Al 6056


εεεε = 38%

2. Damage mechanics

Al 6056


εεεε =50%

2. Damage mechanics

Al 6056


εεεε =60%

2. Damage mechanics

« Ductile » materials fail by a mechanism of nucleation, growth and

coalescence of damage

See lecture 3

Pardoen and Pineau, CSI 2003Benzerga et al. Acta Mater 2016

σzmean

εzmean

or

Void nucleation

Void growth

Void coalescence

2. Damage mechanics

Advanced models

Prediction of ductile failureSee lecture 3

Pardoen et al. , Comptes R Phys 2010Scheyvaerts et al. , J Mech Phys Solids 2011Tekoglu, Hutchinson, Pardoen, Phil Trans R Soc 2015

for elementary

damage mechanisms

for collective damage effects

2. Damage mechanics

The « in between » materials

See lecture 5 M.F. Ashby, 2013

Composites and other hybrids structures involvea combination of complex failure modes

2. Damage mechanics

Disdvantages of damage based approaches

• Complex models (one per phenomena)• Sophisticated experimental instruments

Advantages of damage based approaches

• Link with the physics• No constraint effects• Can guide materials development

At the interface between solids mechanics and materials sciences

Summary

2. Damage mechanics




Outline

ΓΓΓΓcinit =ΓΓΓΓ0

ΓΓΓΓcprop =ΓΓΓΓ0+ΓΓΓΓb+ΓΓΓΓp

Toughening strategies

Γb

Γp σc

δcΓ0

00

0

Xcc

cc

εσδσ

≈Γ≈Γ

0X

0X

cσIncrease

cε

3. High toughness materials

Failure mechanisms

Failure mechanisms at crack tip

i.

ii.

iii.

iv.

v.

vi. H2S

vii.

viii.

ix.

x.

xi.

xii.

bridging mechanisms


Gaps in material property space

From N.A. Fleck, Cambridge


From N.A. Fleck, Cambridge

Tough & light latticematerials


Some glues have a toughnessas high as some metals !

Tough epoxies- gluesSee lecture 1

0

1000

2000

3000

4000

5000

6000

7000

0 0,5 1 1,5 2 2,5 3

Kinloch and Shaw 1981

Adh

esiv

e jo

int t

ough

ness

(J/

m2 )

Bond line thickness (mm)

XD1493

XD4600

Betamate 73455

ESP110

Γcpropincreases by

high Γp& high Γ0

Pardoen et al , JMPS 2005Martiny et al , EFM 2013


Thickness effect on fracture toughness in thin sheetsnot yet well exploited (nor understood)

Tough thin metallic sheets

G or J (kJ/m )

c c2

Specimen thickness (mm)

20

200

100

2 10

Gc

thickness

?

0

5 104

1 105

1.5 10 5

2 105

2.5 10 5

0 1 2 3 4 5 6 7

Jc (J/m2)

we (J/m2)

t0 (mm)

24300 J/m2

28800 J/m2

33MJ/m3

29MJ/m3

Mixed mode I-III cracking

Mode I cracking or

See lecture 4

Pardoen et al , JMPS 2004


Super tough hydrogels

Sun et al Nature 489 (2012) 133


Play with roughness of substrateto control non percolating

cracking pattern

Super flexible electronicdevices

Reference lecture xxx

Lambricht, Pardoen, Yunus, Acta Mater 2013

See lecture 2

500 nm thick


Cu, 200nm thick

Super ductile thin films

Can we learn from these examples to produce extremely ductile systems ?

e.g. Coulombier et al ., Scripta Mater 2010Colla et al ., Nature Comm 2015Mompiou et al. , Acta Mater 2013

Al, 200nm thick

See lecture 6


Ultra-tough metallic glasses

Ph. D. thesis M. Ghidelli, 2015 INPG + UCLe.g. Ghidelli et al., Acta Mater 2015

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.160

500

1000

1500

2000

2500

3000

3500

4000

4500

110 nm 200 nm 360 nm Elastic Behaviour

Tru

e S

tres

s (M

Pa)

True Strain (-)

Metallic glasses are wonderful materials except for their brittleness

Can we learn from this discovery to

make ductile-tough metallic glasses ?

Zr65Ni35

15 % fracture strain !


Example of bone

Super tough materialsin nature

Ritchie, Nature Mater 2011


Nacre

Super tough materialsin nature

Ritchie, Nature Mater 2011


From Dierk Raabe, Aachen

Lobster shell

Towardssmart

evolvingmaterials

Crack healing concepts

White et al ., Nature 2001


polymer

CNT

1mm

foaming agent

Composite compound processing

Grinding and feeding compound

in honeycombFoaming Bonding of face

sheets - sandwich

1cmChemical foaming

pellets of compound

Al honeycomb

1cm500mm

50mm

CO2 supercritical foaming

Composite face sheet

T° - pressure

Tough electromagneticabsorbing materials

Long term collaboration UCL – ULG patented

e.g. Huynen et al., Acta Mater 2011


Notre multimateriauix EM absorption

6 7 8 9 10 11

x 109

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

HC+Foam 121Foam 121: PU+2%wt NTCHC+Foam 120: PU+2%wt NTCFoam 120: PU+2%wt NTCFoam 122: PU+2%wtNTCHC+Foam 122: PU+2%wtNTCHC+Foam 112: PU+2%wtNTCFoam 112: PU+2%wtNTC

Improved with honeycomb10

20

30

40

50

60

70

80

Pabso

rbed %

100

90

Example : EM absorbingmaterials

e.g. Huynen et al., Acta Mater 2011


Frequency (Hz)

Hybrid architectures to produce synergy

effects on dissipation

Tough hybrids

Bollen et al. Scripta Mater 2013Tomo at KULeuven


Why is it so important to develop tough materials ?

• Safety of installations and devices

• Lighter, hence more esthetic structures

• hence, less energy consumption (transport and producti on)

• More durable ! against planned obsolescence

Summary


Lectures (2016)

04/02 Fracture of interfaces, adhesive joints and we lds

18/02 Fracture of coatings and electronic devices

03/03 Fracture of metals and polymers - I. Damage

10/03 Fracture of metals and polymers - II. Crack p ropagation

17/03 Fracture of composites

24/03 Fracture of nanomaterials

Adresse des lectures

Institut de Mathématiques, Quartier Polytech 1, Allée de la Découverte 12, Bâtiment B37, 4000 Liège - Auditoire 02

Inscription via le site web: http://www.facsa.ulg.ac.be/chairefrancqui/2016

Program of the Chair

25 nm diameter Si nanowires

1 2 3

σ σc

12

3δ

Γ0

Γp1

Γp2

Gc = Γ0+Γp1+Γp2+Γel_stored

Acknowledgements to my colleagues(and friends) at ULg

Fe and Ti alloys, wear, etc Ti fracture, abradables, etc Mechanical metallurgy, thin films

MeMS and composites EM absorption, hybrid materials Ab initio, L’ducasse d’Ath

Acknowledgements to collaboratorsand to funding agencies

PhD (Accomplished) T. Ferracin F. Lani, D. Lassance, A. Simar, Y. Bertholet, E. Wyart, G. Lacroix, A. Lenain, M.Delincé, F. Hachez, F. Scheyvaerts, S. Kumar Yerra, F. Strepenne, M. Coulombier, P. Martiny, L. Lecarme, U. Bhaskar,A.P. Pierman, M.-S. Colla, E. Navarro, P. Bollen X. Morelle, M. Ghidelli, G. Martin, Q. Lai, B. Chehab

PhD (Running) B. Wucher, A. Van Der Rest, Q. Voleppe, C.-H. Sacré, G. Lemoine, F. Hannard, T. Djikanovic, M.Hammad, A. Ribesse, J. Chevalier, V. Rousseaux, K. Ismail, P. Lapouge

Post docs/senior researchers S. Ryelandt, A. Favache, C. Doneux, L. Brassart, L. Cousin, F. Lani, V. Destoop, Y.A.Janssens, H. Idrissi, D. Fabrègue, C. Tekoglu, S. Gravier, C. Brugger, R. Vayrette, A. Boé, M. Melchior, P.Carbonnelle, N. André, G. Guisbiers

Tech staff M. Sinnaeve and all the LACAMI team, the LEMSC team, the WINFAB team

Admin staff C. Bauwens, V. Abeels, R. Sakkal, A. Hellebrandt, I. Hennau

Colleagues and collaborators P. Jacques, A. Simar, J.P. Raskin, L. Delannay, C. Bailly, F. Delannay, J. Proost, B.Nysten, J.C. Charlier, G.M. Rignanese, B. Hackens, D. Flandre, I. Huynen, J.F. Remacle, L. Francis, S. Yunus, I.Doghri, P. Bertrand, Q. van Overmeere B. de Meester, P. Van Velthem, J. Devaux, W. Ballout, Q. Furnémont, A.Bahrami, V. Passi, S. Befahy, S. Houri, R. Delmelle, A. Vlad at UCL, T. Massart, S. Godet at ULB, colleagues at ULg,D. Schryvers, B. Amin-Ahmadi at UAntwerpen, L. Rabet at RMA, B. Verlinden, P. Van Houtte, M. Wevers, M. Seefeldt,B. Van Bael at KULeuven, L. Kestens, P. Verleysen, J. Degrieck at UG, R. Chaouadi, D. Terentyev at SCK•CEN, J.W.Hutchinson at Harvard, P. Onck at Groningen, Y. Bréchet, M. Verdier, S. Gravier, M. Braccini, M. Fivel, A. Deschamps,M. Véron, J.J. Blandin, G. Parry at INPG, A. Pineau at ENSMP, A. Benzerga, C. Landis at U. Texas, A.G. Atkins atReading, A.G. Kinloch at Imp College, R.H. Dodds at U. Illinois, O. Bouaziz U Nancy, K. Nielsen, V. Tvergaard atDTU, J Gil Sevillano CEIT, M. Geers at TUEindhoven, B. Cotterell at U. Sydney, H. Van Swygenhoven PSI, J.D.Embury at U. McMaster, F. Mompiou, M. Legros at CEMES Toulouse, J.D. Mithieux at APERAM, A. Perlade, T. Iung atArcelorMittal, L. Libralesso, Y. Marchal at SONACA, P. Guaino at CRM, I. Radu at Soitec, E. Maire INSA Lyon

Loving team Cath, Tang, Ju, Marg

Funding UCL (ARC, FSR), Belspo (PAI), FNRS, Région Wallonne, EU, ArcelorMittal, Soitec, Aperam

Lectures (2016)

04/02 Fracture of interfaces, adhesive joints and we lds

18/02 Fracture of coatings and electronic devices

03/03 Fracture of metals and polymers - I. Damage

10/03 Fracture of metals and polymers - II. Crack pr opagation

17/03 Fracture of composites

24/03 Fracture of nanomaterials

Adresse des lectures

Institut de Mathématiques, Quartier Polytech 1, Allée de la Découverte 12, Bâtiment B37, 4000 Liège - Auditoire 02

Inscription via le site web: http://www.facsa.ulg.ac.be/chairefrancqui/2016

Program of the Chair

25 nm diameter Si nanowires

1 2 3

σ σc

12

3δ

Γ0

Γp1

Γp2

Gc = Γ0+Γp1+Γp2+Γel_stored

fracture of materials: from physical mechanisms to

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