FFAG4, Nov.5-7, 2007

Setsuro Ito

Brittleness and

Look Beyond

Asahi Glass Co., Ltd. Research Center

Nano-Structure of Glass

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Outline1. What is brittleness?

2. Cracking Behavior vs Brittleness

3. Deformation by Indentation

4. Deformation and Fracture behavior by MD Simulation

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ρσσ C

ac 2=

)(100

1)( cthaf σσσσ =≈=

Si

Si

O

ρ≒1.5nm

0.5 μm

σa

σcC

Theoretical Strength

30 nm

Griffth Theoryσf＝（2Eγ／πC）1/2

Strength and Micro-Crack

σth＝ (Si-O Bond Strength) X(No. of Bonds per Unit Area)σth ≒ 24 GPa

( by .Naray-Szabo and J. Ladric)

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Metal / Glass/Metal / Glass/Plastics Ceramics.Plastics Ceramics.

1. More 1. Less1. More 1. Less

3. Ductile 3. Brittle3. Ductile 3. Brittle

Deformation DeformationDeformation Deformation

2. Less Cracking 2. More Cracking2. Less Cracking 2. More Cracking

CrackingCrackingDeformationDeformation

B=HB=H vv/K/K CC

where, Hwhere, H is Vickers Hardness (Resistance to Deformation) is Vickers Hardness (Resistance to Deformation)

KKvv

CC is Fracture Toughness (Resistance is Fracture Toughness (Resistance to Fracture)to Fracture)

What is brittleness?

2C

2a

412

3

4.2−

⋅

⋅≈

= P

aC

KcHvB

B. R. Lawn et al., J. Am. Ceram. Soc., 62, 347-350(1979)

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Brittleness-----Alternative Idea

2C

v

KEHB =

)1(2

)1(2

20

02

2

2

νπλ

πλγ

νγ

−=∴

=

−=

aEK

aE

EK

C

C

),,( 0 νλafKHB

C

v ⋅=

J.B.Quinn & G.D.Quinn, J. Mat. Sci., 32, 4331(1997)

∝Deformation energy per unit VolumeFracture Surface energy per unit Area

3 5 7 9 11

2

4

6

8

10

12

14

16

18

H・E

/Kc2（ｘ10

8 m

-1）

H/Kc (μm-1/2)

Data Taken from “InterGlad”

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Brittleness of Glass

J. Sehgal &S. Ito, J.Non-Crystal. Solids, 253,126-132(1999)

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0

2

4

6

8

10

1.8 2.0 2.2 2.4 2.6 2.8

SiO2-based GlassB2O3-based Glass

Density (g/cm 3 )

SiO2 glass

Normal Glasses(ABDE)

Brit

tlene

ss ( μ

m)

- 1/2

A

B

C

D

E

Commercial window glass(soda-lime-silica:SL)Anomalous Glasses

(BC)

Less brittle glass : LB

Crack Initiation of Less Brittle and Soda-Lime GlassesLook Beyond

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0

1

2

3

4

5

6

7

0 0.5 1 1.5

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

S. Yoshida et al., J. Non-Cryst. Solids, 344, 37-43 (2004)

Kc

Hv

B

25Na2O-xAl2O3-(75-x)SiO2 (mol%)

Al2O3/Na2O

B=H

/Kc

(μm

-1/2

), H

v(G

Pa)

Kc

(MPa･m

1/2)

Brittleness vs Al2O3/Na2O Ratio

Increase in the content of non-bridging oxygen

(density) 2.4942.425

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S. Yoshida et al., J. Non-Cryst. Solids, 344, 37-43 (2004)

Increase in the content of non-bridging oxygen

Crack Initiation Load vs Al2O3/Na2O Ratio

25Na2O-xAl2O3-(75-x)SiO2 (mol%)

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4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

460 480 500 520 540 560 580 600

Fictive Temperature (oC)

Brittleness vs Fictive Temperature

Fictive Temperature (C)

LB-Glass (Tfis Estimated)

SL-Glass

B

ritt le

ness

( μm

-1/2

)

Brittleness = Hv/Kc

S.Ito, et al., Proc. ICG Annal. Meeting 2000, AmsterdamS1.1(2000)

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Number of Cracks vs Load as a Function of Tf

0.0

1.0

2.0

3.0

4.0

200 400 600 800 1000 3000

Indentation Load (g)

SL-Glass

Tf=500C

534C

561C

581C

Num

ber o

f Cra

cks

Crack Initiation

S.Ito, et al., Proc. ICG Annal. Meeting 2000, AmsterdamS1.1(2000)

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Why does brittleness change with

(1) glass composition, i.e., the content of network former and modifier,

(2) the content of non-bridging oxygen and(3) fictive temperature ?

To understand these phenomena, we have to clarify the behavior of

glass under an indenter.

“Less brittle glass shows less contact damage, namely more difficult crack-formation,

and hence higher mechanical reliability.”

Elastic Deformation

Plastic Flow

Densification

Indenter

During Loading

After Unloading

After Heat-Treatment Deformation Zone

Crack

Glass Surface

Tension +Compression

Effect of Deformation (flow & densification ) and stress relaxation on Cracking

Flow and Densification of Glass Look Beyond

30

35

40

45

50

55

60

65

70

75

4 5 6 7 8 9 10

dp/ d

0(%

)SL

LB

Tempax (Pyrex)

SiO2

Max. load 10N(removed 90% of max load)

Max. load 6 mN(removed 90% of max load)Max. load 10N

(removed stress)

(70 mol%)

(100mol%)

(93mol%)

(65mol%)

Indentation Depth for Various Glasses

Brittleness /μm-1/2

Lower brittleness shows larger deformation

Loading

Unloading

after Sakai et al.Toyohashi Tech. Sci. Institute

d0dp

LB

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Flow in Glass by Indentation

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-15 -10 -5 0 5 10 15 20

Cross Scan Length （μm）

SL

Tempax

LB

Sur

face

Pro

file （μ

m）

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Flow & Densification Under Indenter

At Peak LoadAfter Unloading After Heat-treatment

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-20 -15 -10 -5 0 5 10 15 20

Surface Scan ( m)µ

136oAngleDep

th P

rofil

e(μ

m)

Densification

Elastic Deformation

Flow

Side View Top View

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LB

AFM Profile of Indentation

Soda-Lime-Silica Glass

SL ν=0.23

LBν=0.21

S.Yoshida, et al., J. Mater. Res., vol.20 (12), 3404-3412(2005）

Pyrexν=0.20

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Summary of Experimental Results

Density

Brit

tlene

ss

easy

difficult

flow

difficult

easy Densifi

cation

SiO2

anomalous normal

Higher Fictive Tem.

M2O-MO-SiO2based Glass

B2O3-rich

Al/Na

Polymerized network

Modifier ions, Onb

LB

SL

Pyrex

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Less brittle glasses show greater deformation, i.e., easier densification and flow.

To understand brittle nature and create new less brittle glass , we have to know

glass structure change in nm scale during deformation under stress.

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Structure of SL and LB Glasses

0

2 0

4 0

6 0

8 0

2 3 4 5 6 7 8 9

S LL B

R in g s iz e

Rin

gs p

er 1

00 S

i & A

l ion

s

Number of Network Ring

LB

SL

(mol%)

(mol%)

Glass Composition

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Deformation is due to rearrangement of network

330

340

350

360

370

380

0 20 40 60 80 100

non-

brid

ging

oxy

gen

time /ps

Fracture

-Si-O-

Network Change of LB Glass under Tension

Tension of 6 GPa

0

10

20

30

40

0 20 40 60 80 100Time (ps)

Rin

gs p

er 1

00 S

i & A

l ion

s Fracture

6-membered ring

4-membered ring

5-membered ring

3-membered ring

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LB

SL

Structure of SL and LB glasses under Tension

Under 6GPa of tension at the same strain

Cavity formation of LB glass is more difficult due to the higher polymerized network, compared to SL

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0 ps 2.5 ps

10 ps 40 ps

LB

Change of Cavity structure under Tension of 6 GPa

r > 0.1 nm

cavity

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90.1 ps

95 ps

Change of Cavity Structure under 6 GPa

LB

95 ps

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Higher polymerized network is important for lower brittleness in normal glass region, because of more difficult cavity formation.

33.3NaO0.5-66.6SiO2 (mol%)

Structure of Glasses in the system of xNaO0.5-xAlO1.5-(1-2x)SiO2

33.3NaO0.5-33.3AlO1.5-33.3SiO2

Higher content of non-bridging oxygen

(NS) (NAS)

Glasses with the Same Content of Network Former

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0.0

0.1

0.2

0.3

0 10 20 30 40

Rel

ativ

e vo

lum

e ch

ange

, ∆V

/V

Time (ps)

NS has less polymerized network structure, but shows longer fracture time, compared to NAS.

0

20

40

60

80

2 3 4 5 6 7 8 9

NS4NAS4

Ring size

Rin

gs p

er 1

00 S

i & A

l ion

s

Network Ring and Volume Change

Fracture

Na

Na

Na

Na

NASNS

NAS

NS

NS NAS Tension of 6 GP

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Change of Number of Non-Bridging Oxygen under Tension

NAS NSFracture

Fracture

Non-bridging oxygen is useful for deformation without breaking network bond and hence leads to lower brittleness

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Na MgCa

Si-O-Si (or Al)

Annealed Quenched

Structure of Annealed and Quenched SL Glass Look Beyond

Network Ring and Strain for quenched and annealed glasses

Easier and larger deformation is due to smaller network ring in quenched glass.

SL glass under 5 GPa of Tension

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 20 40 60 80 100

quenched

Beginning of Fracture

Stra

in

Time (ps)

0

10

20

30

40

2 3 4 5 6 7 8 9

SLSL-q

Rin

gs p

er 1

00 S

i & A

l ion

s

Ring size

annealed

quenched annealed

Ring Size

Rin

gs p

er 1

00 S

i& A

l Ion

sLook Beyond

500

510

520

530

540

550

560

0 20 40 60 80 100

num

ber o

f non

-brid

ging

oxy

gen

ions

time /ps

annealed

quenched

Change of number of non-bridging oxygen during deformation

Fracture

Fracture

Annealed

Quenched

Higher amount of non-bridging oxygen ions also leads to easy deformation in quenched glass.

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Stress relaxation as a function of time

0.8

0 100 200 300

- 3

- 4

- 2

- 1

0

0.2

0.4

0.6

0.0

Time /ps

Stre

ss /

GPa

Stra

in Const. stress : – 4 GPa

Const. strain : 0.2 Quenched

Quenched

annealed

annealed

Constant strain

Under – 4 GPa

Quenched glass shows faster stress relaxation.

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150

OSiAlMgCaNa

time /ps

mea

n sq

uare

dis

tanc

e /c

m2

quenched17 ps (-4 GPa)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150

OSiAlMgCaNa

time /ps

mea

n sq

uare

dis

tanc

e /c

m2

annealed150 ps (-4 GPa)

Migration of ions in quenched and annealed glasses

Quenched Glass const. strain: 0.2 Annealed Glass

const. strain: 0.2

Quenched glass shows easier stress relaxation due to easier ion migration.

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SL-q

Cavity Formation

SL-a

Structure of quenched and annealed SL glasses

at 5 GPa of tension

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More difficult cavity formation of quenched glass is due to easy deformation and results in lower brittleness.

1 nm

Cavity formed from heterogeneity in glass structure.

S.M.Wiederhorn, et al.,J. Non-Cryst. Solids, 353, 1582-1591 (2007)

Fracture Surface and Heterogeneity in Glass

Roughness of Fracture Surface for Soda-Lime-Silicate Glass RMS: 0.5-1.0 nm (fracture velocity: 10 m/s)

Look Beyond

To design new less brittle glass, control of polymerization, ring size and ordering of network, mobility of network modifier ion, number of Onb, and homogeneity of glass is important .

Such control of glass structure probably causes more difficult cavity formation, and hence leads to lower brittleness.

Thank You