and vitrified wasteforms Russell J Hand ISL Department of - - PowerPoint PPT Presentation

Mechanical properties of glasses and vitrified wasteforms

Russell J Hand ISL Department of Materials Science and Engineering University of Sheffield

Acknowledgements

• Colleagues in the ISL, University of Sheffield
• Yordanos Bisrat, Andy Connolly, Norfadhilah

Ibrahim, Erhan Kilinç, Owen McGann, Jesús González Rodríguez, Damir Tadjiev, Ben Whittle, Peng Zeng

• IAEA-ICTP

Background

• Glasses are brittle (at RT)

– Low toughness – Flaw sensitive – Low strains to failure – Usually low strength – Hard

• Waste glasses are not usually annealed

– Residual stresses – Cracking is expected in the canister

• Handling strength supplied by the

canister

– Cracking increases the surface area available for attack by water once the canister is breached

What can we measure?

• Material properties

– Modulus

• Stiffness

– Hardness

• Resistance to deformation

– Fracture toughness

• Resistance to crack growth

– Brittleness

• Hardness / fracture toughness
• Sample property

– Fracture strength

• Depends on the defects present

Useful

Moduli

Normal stress Young's modulus, Normal strain E 

• Glasses are isotropic materials

– Hence only 2 independent moduli

Fractional lateral contraction Poisson's ratio, Fractional longitudinal extension   Shear stress Shear modulus, Shear strain G  Pressure Bulk modulus, Volumetric strain K 

 

2 1 E G   

 

3 1 2 E K   

Modulus testing

• Acoustic methods

– Measure longitudinal, Vl, and transverse (shear) velocities, Vt – Can also define a longitudinal modulus

2 t

G V  

2 2 2 2 2

3 4

l t t l t

V V E V V V    

2 l

M V  

Indentation depth Load

Modulus testing

• Instrumented (nano-)indentation

– Analysis of the unload curve gives reduced modulus – where

• i indicates properties of the indenter
• g indicates properties of the glass

– From this we can obtain the plane strain modulus

• For a diamond indenter and where E’ and Er are in GPa

     

2 2

1 1 1

g i r i g

E E E

2 4 2

1 1 1 1 1 8.721 10 1

g i r i r g

E E E E E  



                    

Tg/T 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Shear modulus /GPa

20 40 60 80

Young’s modulus

• Generally increases with Tg

BUT atomic packing density also important

• For a glass

i i x y i

A B



 

B

3 3 A

4 3

i

i i i i g i i i

f xr yr C N fM   

 

Data from SciGlass database

Packing density

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Poisson's ratio

0.05 0.15 0.25 0.35 0.45

Rouxel Makashima & Mackenzie Data used by Rouxel

Data from SciGlass database

RTg/Mv

0.10 0.15 0.20 0.25 0.30 0.35 0.40

G /GPa

5 10 15 20 25 30 35 40

Li borates (Kodama) Na borates (Kodama) K borates (Kodama) Cs borates (Kodama) Rb borates (Kodama) Sodium borosilicates SLS (Tille) SLS (Kilinc & Hand) Ba titanosilicates

Isomechanical groups

• Originally used in analysis of crystalline

materials

– Different structures give different values of b

• For glasses

B m

bk T G  

m V

bRT G M 

Moduli

• Data of Zheng et al. (2012)

– Nominal composition 15Na2OxAl2O35B2O3(80 – x)SiO2 – x = 0, 1, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20 – Minimum in moduli when no NBOs

[Na2O] [Al2O3] N4x[B2O3]

• 6
• 4
• 2

2 4 6 8 10 12

Young's modulus /GPa

60 65 70 75 80

Increasing NBOs due to Na2O Increasing NBOs due to Al2O3

[Na2O] [Al2O3] N4x[B2O3]

• 6
• 4
• 2

2 4 6 8 10 12

Shear modulus /GPa

26 28 30 32 34

Increasing NBOs due to Na2O Increasing NBOs due to Al2O3

[Na2O] [Al2O3] N4x[B2O3]

• 6
• 4
• 2

2 4 6 8 10 12

Bulk modulus /GPa

36 38 40 42 44

Increasing NBOs due to Na2O Increasing NBOs due to Al2O3

[Na2O]+[MO] [Al2O3] [B2O3]

• 15
• 10
• 5

5 10 15

Bulk modulus /GPa

36 38 40 42 44 46 48 50

MgO CaO SrO BaO Increasing NBOs due to Na2O + RO Increasing NBOs due to Al2O3

Moduli

• Data of Potuzak et al (2014)

– Nominal composition 12Na2O6MOxAl2O36B2O3 (76 – x)SiO2 – M = Mg, Ca, Sr and Ba – x = 0, 3, 6, 9, 12, 15, 18, 21, and 24 – Position of minima in E and G depends on alkaline earth

• Larger alkaline earths are less

capable of creating B4 units

– But no clear minima for bulk moduli or Poisson’s ratio

[Na2O]+[MO] [Al2O3] [B2O3]

• 15
• 10
• 5

5 10 15

Young's modulus /GPa

60 65 70 75 80

MgO CaO SrO BaO Increasing NBOs due to Na2O + RO Increasing NBOs due to Al2O3

[M2O+M'O] [Al2O3] [B2O3]

• 20
• 15
• 10
• 5

5 10 15 20

Shear modulus /GPa

20 25 30 35

N7.6M1.1C3B7.6AxS79 x N15C5AxB10 xS70 N15C5AxB20 xS60 N15CxA15 xB10S60 N15BaxA15 xB10S60 N10CxA20 xB10S60 N10BaxA20 xB10S60 N10CxA2B10S78 x N15CxA2B10S73 x N10CxBa2AyB10S78 x y

Moduli

• However this sort
• f relationship is

not always seen

– Ibrahim & Hand (unpublished data)

[M2O+M'O] [Al2O3] [B2O3]

• 20
• 15
• 10
• 5

5 10 15 20

Young's modulus /GPa

60 65 70 75 80

N7.6M1.1C3B7.6AxS79 x N15C5AxB10 xS70 N15C5AxB20 xS60 N15CxA15 xB10S60 N15BaxA15 xB10S60 N10CxA20 xB10S60 N10BaxA20 xB10S60 N10CxA2B10S78 x N15CxA2B10S73 x N10CxBa2AyB10S78 x y

Hardness

• Resistance of a material to

permanent penetration by another harder material

• Usually measured via

indentation

• Exact form depends on

indenter geometry

• May be expressed as a

hardness number or in GPa

– The latter is more common when dealing with glass

indentation load indentation area H 

Projected area

• r actual surface area

Tg/T 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Hardness /GPa

3 6 9 12

Data from SciGlass database

Hardness

• Vicker’s indentation

– Pyramid shaped indenter – Surface area of indentation

• Knoop indentation

– Elongated pyramid indenter – Projected area – Some authors claim

• n unloading b  b’

(a is little changed)

• Berkovich

indentation

– Used in nanoindentation

• Instrumented tests
• Measure H and E

– Surface area of indentation – Has the same area/depth dependence as Vickers indentation

• Standard

Berkovich – same actual area

• Modified

Berkovich – same projected area 2a 68ᵒ 65.3

2

0.4635

V

P H a 

2

14.2

K

P H a 

max

P H A 

a b

0.45Ha E b b   

Hardness

• Nuclear borosilicates relatively high

hardnesses and Young’s moduli

E /GPa

78 80 82 84 86 88 90

Hardness /GPa

5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5

UK HLW glass Novel ILW glasses Other nuclear glasses

Plane strain modulus /GPa

20 40 60 80 100 120 140 160

Indentation hardness /GPa

2 4 6 8 10 12 14

Nuclear borosils SciGlass E Other silicates

Fracture toughness

• Intrinsic resistance of a

material to crack growth

– σ is strength – a is crack depth – C is a “geometric” constant

• Material property

– Residual stresses will affect results

Ic

K T C a    

Mode 1 Mode 2 Mode 3

x x x y y y z z z

Diagram taken from J Lemaitre & J-L Chaboche Mechanics of Solid Materials

Normally report mode I –

• pening mode

Ic r r

K C a C a T C a            

T = Fracture toughness KIc = Critical stress intensity factor for failure

Fracture toughness testing

• General procedure is to introduce a controlled

defect and measure stress at which failure

• ccurs

– Plane strain fracture toughness – Related to initiation of crack growth

• Controlled defect

– Metals

• Notch and then fatigue pre-crack.

– Brittle materials

• Notch and then?

Single edge notched bend (SENB) test

max 2

3 2 FL bW  

• ASTM C1421-10
• Crack “popped-in” from pre-sawn notch or line of

indents

1/2 I max

a K f a W        

2 3/2

1.99 1 2.15 3.93 2.7 1 2 1 a a a a W W W W a f W a a W W                                                         W a F b L 0.35 0.6 a W  

• Can use indents as the strength controlling

defect

– Vicker’s indent – Knoop indent

• Newman and Raju solution for SIF
• In this case ASTM standard specifies grinding back

much of the indent to leave sub-surface crack

• Also recommends no annealing
• But residual stresses arises from

– Indentation of glass – Grinding and polishing of glass

• These will affect crack initiation

Single edge notched bend (SENB) test

 

1/8 3/4 1/3 f

E T F H         

Indentation toughness testing

• Use cracks generated by a

Vickers hardness indentation

– Arrest toughness

• Not a true fracture toughness

measure

• Might be OK for comparative

purposes

– Cracks (may) continue growing slowly due to stress corrosion

       

I I I

, 1 / 1 /

R d

K a a k a K a a C K a a C    

• 2 types of cracking possible

– Median / radial – Palmqvist

• Former usually assumed but you should

always check which is happening

Median cracks c a Palmquist cracks l a c

Indentation toughness testing

• Assuming median-radial

cracking the simplest relationship is based on semi-circular flaws where

– F is the indentation load – χ is a constant – c is half the surface crack length (or the crack depth)

Ic 3/2

F K c  

Simple relationship seems to work even with approximately semi-elliptical cracks (data shown for soda-lime-silica glass)

Indentation toughness testing

• But a variety of different equations have been

proposed e.g.

• Evans & Charles
• Blendell
• Matzke et al. used

Ic 3/2

0.0824 F K c 

 

 

2/5 1/2 Ic

0.0303 log 8.4 /

V V

E K H a a c H       

Indentation toughness testing

 

2/5 2/5 3/2 1/2 Ic 3/2

0.0264 0.057

V v v

E c F E K H a H a c H



                   

Indentation toughness testing

• Imperfect correlation between indentation

and conventional fracture toughness

• Data shown for SLS glasses

Indentation fracture toughness/ MN m 3/2

0.52 0.56 0.60 0.64 0.68 0.72 0.76

Bend test fracture toughness /MN m 3/2

0.70 0.75 0.80 0.85 0.90 0.95 1.00

MgO CaO MgO (High silica) CaO (High silica) One to one line

Poisson's ratio

0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26

Fracture toughness /MN m-3/2

0.6 0.7 0.8 0.9 1.0 1.1 1.2

MgO-SiO2 series CaO-SiO2 series MgO-CaO series Data from Rouxel & co-workers Resilient Semi-resilient Easily damaged

• However different

trend with conventional fracture toughness measurements

Kilinc & Hand J. Non-Cryst. Solids 429 (2015) 190-197

[MgO]/[MgO+CaO]

0.0 0.2 0.4 0.6 0.8 1.0

Fracture toughness /MN m 3/2

0.70 0.75 0.80 0.85 0.90 0.95 1.00

MgO-SiO2 series CaO-SiO2 series MgO-CaO series

[MgO]/[MgO+CaO+BaO]

0.0 0.2 0.4 0.6 0.8 1.0

Indentation fracture toughness /MN m 3/2

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Nuclear waste glasses

• Other nuclear glasses

– Data from Matzke and co-workers

• Waste glasses tend to have higher indentation

toughnesses than “simple” silicates

H /GPa

5 6 7 8 9 10

Indentation fracture toughness /MN m 3/2

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

MW-HLW glass ILW glasses Other nuclear glasses Modified MW

E /GPa

78 80 82 84 86 88 90

Indentation fracture toughness /MN m 3/2

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

MW-HLW glass Novel ILW glasses Other nuclear glasses

Brittleness index

• Defined as B = H/KIc
• For Evans & Charles analysis of indentation this gives
• Sehgal et al give
• High B – more brittle
• Usually measured at a fixed indentation load

– e.g. 5 kg

 

3/2 1/2

5.6262 / B a c a 

 

3/2 1/4

/ B dP c a





Essentially equivalent definitions

General trends – brittleness

• Sehgal & Ito

suggest lower density = more brittle

• Reality is

more complex Density /Mg m-3

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

Brittleness / m 1/2

2 4 6 8 10

MA/MAE glasses Nuclear glasses S&I silicates S&I borosilicates Homeny oxycarbides Homeny oxynitrides MW & modified MW

• For plane strain
• But γp ~ 0 for

glasses

• γe does not vary

greatly with composition

 

 

      

2 2 Ic Ic

2 1

e p

K G E

“Surface” energy

Fracture "surface" energy /J m 2

5 10 15 20 25 30 35

Brittleness / m 1/2

4 8 12 16

Hand & Tadjiev silicates Nuclear glasses SciGlass E = 40 GPa E = 80 GPa E = 120 GPa

Oxynitrides Oxycarbides

 

2 2 Ic 1

2

e

K E    

Irradiation

• Borosilicates containing

iron show little change in mechanical properties on γ- irradiation

β-irradiation

• Iwata et al. (2005)

– 4.5Na2O 1.9Al2O3 10.7B2O3 84.8SiO2 (mol%)

• Mir et al. (2016)

irradiation dose /MGy

0.0 0.1 0.2 0.3 0.4 0.5

Hardness /GPa

5.0 5.5 6.0 6.5 7.0 7.5

irradiation dose /GGy

1 2 3 4 5

Percentage change in hardness

• 25
• 20
• 15
• 10
• 5

5

BS3 SON68

Hardness variation with α and heavy ion irradiation

• More significant effects for α and heavy ion-

irradiation

• Data from Weber & Matzke (1987), Peuget et
• al. (2006), Karakurt et al. (2016)

Reduced modulus /GPa

79 80 81 82 83 84 85 86 87

Hardness /GPa

3.5 4.0 4.5 5.0 5.5 6.0 6.5

Irradiated - 5 mN Irradiated - 10 mN Unirradiated

High temperature behaviour

• Centreline temperature of HLW glass can be

close to Tg

• In this region glass will behave viscoelastically

– Creep

• High temperature contact also occurs during

commercial glass manufacture

Experimental Apparatus

• Mounted on a Hounsfield universal

testing machine –Loads from 10 to 1000 N –Speeds from 0.001 to 5 mm/min

• Split tube furnace

–Temperature control ±1°C –Maximum furnace temperature 1050°C –Testing maximum temperature 650°C

• Indenters

–Vickers (diamond) –Carbide Rockwell ball 6mm diameter

• Controlled loading/ unloading rates
• Controlled hold at maximum load

Analysis

• Creep / viscoelastic behaviour at high

temperatures has to be accounted for

• Modified Oliver and Pharr analysis (Lu et al,
• Exp. Mech. 50 (2010) 491–499

 

max max creep

0.75

c e

P h h h S      1 1

v e

h S S P

Creep rate at end of dwell time Unloading rate

• Longer dwells are required to avoid “nose”

feature

• Example data

– 520ᵒC, 30 s hold

High temperature indentation

Air side hardness

Temperature /oC

100 200 300 400 500 600 700

Vickers hardness /GPa

1 2 3 4 5 6 7

Le Bourhis & Metayer 2000 Watanabe et al. 2001 Le Bourhis & Rouxel 2003 Michel 2004 Shang et al. 2006 Kese et al. 2008 Wilantewicz & Varner 2008 Sheffield data Tg

Tg

High temperature properties

• Soda lime silica (float

glass)

– Air side hardness – Fracture toughness ↑ (as assessed by crack numbers) as T ↑

Dwell time /s

20 40 60 80 100 120 140 160

Vickers hardness /GPa

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

520oC air side 540oC air side 560oC air side 560oC tin side

Dwell time /s

20 40 60 80 100 120 140

Apparent plane strain modulus /GPa

30 40 50 60 70 80

520oC 540oC

50 100 150 200

Displacement / m

5 10 15 20 25 30

180 s dwell 2 a+bt^(1/3)+ct

Time /s

50 100 150 200

Displacement / m

5 10 15 20 25 30

180 s dwell 2 a(1-exp(-bt))

Time /s

Creep

Kelvin model Andrade + linear Kelvin + Maxwell model

50 100 150 200

Displacement / m

5 10 15 20 25 30

520oC 120 s 540oC 120 s 560oC 120 s

Time /s

Temperature a b c r2 520ᵒC 4.09 ± 0.15 0.087 ± 0.006 0.016 ± 0.002 0.995 540ᵒC 6.07 ± 0.08 0.042 ± 0.001 0.016 ± 0.001 0.989 560ᵒC 10.25 ± 0.15 0.036 ± 0.001 0.090 ± 0.001 0.998

 

 

    1 exp h a bt ct

Fitted with Maxwell + Kelvin element

50 100 150 200

Displacement / m

5 10 15 20 25 30

520oC 120 s 1 520oC 120 s 2 540oC 120 s 1 540oC 120 s 2 560oC 180 s 1 560oC 180 s 2

Time /s

Creep

KI /MPa m1/2

2 3 4 5 6 7

Crack velocity /m s 1

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4

SLS Borosilicate Aluminosilicate Silica

Stress corrosion • Strained Si-O bonds are

susceptible to attack by water

• At a crack tip this can

give

– Crack growth – Crack blunting

Weiderhorn & Bolz (1967)

d ln d a t      

I II III KI = T KI

KI /MN m 3/2

0.5 0.6 0.7 0.8

Crack velocity /m s 1

• 2x10-12

2x10-12 4x10-12 6x10-12 8x10-12 10x10-12 12x10-12

Aged in solution at 90oC Aged in air at 22oC Aged in air at 90oC

Stress corrosion

• Ji et al. (2005)

– SON68 – Solution = water enriched in Si, B and Na – Stress corrosion assessed by the growth of indentation cracks

Time /d

10 20 30 40 50 60

Fracture toughness /MN m 3/2

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

30 3.1 I

d 9.75 10 d a v K t



  

Nanoindentation calibration

• Need to know how the

tip shape varies with depth

– Calibrate using pure silica – Concentrate on low indentation depths – Equivalent radius preferable to area

Equivalent radius

• The use of area in calibration

gives more weight to larger depth data

• For an equivalent

axisymmetric body note that

• i.e. rc should be linearly

proportional to hc

• Hence more equal weighting
• f data
• Also

/

c

r A   2

c r

S r E  

1/2

2.0115 12.1929 19.7669 48 nm 2.897 61.67 48 nm

c c c c c c c

r h h r r h r       

2

2.899 23.5 0.990

c c

r h r   

hc /nm

20 40 60 80 100

Er /GPa

20 40 60 80 100 120

Calibration 1 Calibration 2 Correct value

• If TAF calibration is

self-consistent then re-analysis of the calibration data should give a horizontal straight line

– In this case equivalent radius approach better for initial fit – Note this does not prove that the TAF is correct

hc /nm

20 40 60 80 100

Er /GPa

20 40 60 80 100 120

Calibration 1 O&P 9 term fit Calibration 2 O&P 9 term fit Correct value

20K2O 15CaO 65SiO2 15Na2O 10CaO 75SiO2

Alkali lime silicate glasses

Nanoindentation of hydrated layers

• Compared durable and non-durable “simple”

glasses

• Also assessed layer depths using TEM

– Samples prepared by FIB lift-out technique

• Quanta 200 3D FIB (FEI)
• Gold coated prior to FIB

– TEM Philips EM 430

• 300 kV

5 um

• 20K2O 15CaO 65SiO2

– Layer thickness 47 ± 5 nm

Au Ion damage

Comparison with TEM

20K2O 3.75BaO 6.25MgO 70SiO2 20K2O 10BaO 70SiO2

Alkali barium silicate glasses

• 20K2O 3.75BaO

6.25MgO 70SiO2

– 165 ± 5 nm

Au

Comparison with TEM

Weathered float glass 40⁰C, 95%RH

Air side Tin side

Weathered layer on float glass

• Near surface modulus constrained by

unaltered glass

Summary

• Moduli
• Hardness
• Fracture toughness

– Use bend tests if possible

• Brittleness
• Irradiation

– Significant changes in E and H observed with alpha/ heavy ion irradiation – Reduction of Cg

• Hydration reduces near surface modulus and hardness

– Also fracture toughness – Small compositional changes can lead to significant differences in hydration resistance