Role of water in fracture of glass

$: Role of water in fracture of glass$
Rensselaer Polytechnic InstituteFFAG4Shiga, Nov. 2007

RolRolee of water in fracture of glassof water in fracture of glass(Why oxide glasses become weaker in the presence (Why oxide glasses become weaker in the presence

of water?)of water?)

M. TomozawaM. TomozawaMaterials Science and Engineering Department Materials Science and Engineering Department

Rensselaer Polytechnic InstituteRensselaer Polytechnic InstituteTroy, NY 12180Troy, NY 12180--3590 USA3590 USA

2Rensselaer Polytechnic Institute

FFAG Shiga, Nov. 2007

Mechanical fatigue of silica glassMechanical fatigue of silica glass

B.A. Proctor et al., Proc. Roy. Soc. Ser. A297 (1967) 534. Bottom data: air; middle: dry air; top: liquid nitrogen.

Hirao and TomozawaJ. Am. Ceram. Soc., 70 (1987) 377.



Crack growth of sodaCrack growth of soda--lime glass and phosphate lime glass and phosphate glassglass

Wiederhorn, J. Am. Ceram. 50 (1967) 407. Soda-lime.

T. Suratwala et al. J. Non-Cryst. Solids, 316 (2003) 174.



Crack growth and mechanical fatigue of Crack growth and mechanical fatigue of glassesglasses

Crack growth rate increases exponentially with stress (or power law).

v = v0 σ n at a constant temperature. or ln v = lnv0 + n ln σ

Static fatigue ln σf = A – (1/n) ln tf

Dynamic fatigue ln σf = B + [1/(n+1)] ln (stress rate)

Same n is observed for crack growth, static fatigue and dynamic fatigue when the same glass with freshly made cracks is used.



Various possible mechanisms of strength Various possible mechanisms of strength reduction of glass by waterreduction of glass by water

•Stress-corrosion reaction. (Hillig and Charles, p.682 in High Strength Solids, Ed. by V.F. Zackay, Wiley (1965) )• Tensile stress-promoted dissolution of the crack tip.•Surface energy reduction (Orowan, Nature, 154(1944) 341.)•Adsorption-induced reduction in bond strength (Michalsekeand Freiman, Nature, 295 (1982) 511.)•Generation of tensile stress at the crack tip by ion-exchange.

Strength of pristine glass fibers (Kurkjian and Paek, Appl. Phys. Letters, 42 (1983) 251) and glasses with blunt crack tips (Hiraoand Tomozawa, J. Am. Ceram. Soc., 70 (1987) 377) also decrease in the presence of water.Both crack initiation and crack growth are promoted by water.

Many of these mechanisms involve≡Si-O-Si≡ +H2O 2≡SiOH



MichalskeMichalske and and FreimanFreiman model of strength model of strength reduction of glass by waterreduction of glass by water

Michalske and Freiman, Nature 295 (1982) 511.1. Adsorption of water 2. Reaction and 3. Cleavage.



Dissolution rate of silica glass in water under Dissolution rate of silica glass in water under different pressuredifferent pressure

S. Ito and M. Tomozawa, J. Am. Ceram. 64 (1981) C-160.

SiO2 + nH2O SiO2.nH2Oreaction product, Si(OH)4Reaction rate constantk = k0 exp (-∆V*P/RT)∆V*:Activation volume <0

= Vac – VSiO2 – nVH2O

If H2O is not under pressure, VH2O would be larger and ∆V* would be more negative.Dissolution does not seem to be accelerated by tensile stress.



Stress effect on silica glass structureStress effect on silica glass structuredetermined with IR spectroscopydetermined with IR spectroscopy

Tomozawa, Glass Sci. Technol. 75 C1 (2002) 262.Tomozawa, J. Non-Cryst. Solids

351 (2005) 1054.



Stress effect on silica glass structure Stress effect on silica glass structure examined using IR or Ramanexamined using IR or Raman

From Michalske et al.Phys. Chem. Glasses,29 (1988) 150. From Raman.

Tomozawa et al. Glass Sci. Technol.75 C1(2002) 262. From IR.

Lehman et al. Phys. Stat. Sol. B117 (1983) 698.



Fictive temperature (Fictive temperature (TTff) and glass volume) and glass volume

R. Bruckner, J. Non-Cryst. Solids, 5 (1970) 123.

Normal glass such as soda-lime glass: specific volume is higher for glass with higher Tf.

Anomalous glass such as silica glass: specific volume is lower for glass with higher Tf.



Structural change of silica glass with Structural change of silica glass with fictive temperaturefictive temperature

Tomozawa et al. J. Non-Cryst. Solids, 351 (2005) 1054.

Lehman et al. Phys. Stat. Sol. B117 (1983) 698.



Structural change of silica glass with Structural change of silica glass with fictive temperature examined with IRfictive temperature examined with IR

Tomozawa et al. J. Non-Cryst. Solids, 351 (2005) 1054.

Lehman et al. Phys. Stat. Sol. B117(1983) 698.



OH depth profile in silica glass: effects of OH depth profile in silica glass: effects of fictive temperature and applied stress.fictive temperature and applied stress.

Nogami and Tomozawa, J. Am. Ceram. Soc., 67 (1984) 151.(1) Tens i le s t ress (2) No stress (3) Compress ive s tress. 240ºC.Glass with smaller Si-O-Si angle is more reactive.

Roberts and Roberts, Phys. Chem. Glasses, 5 (1964) 26.750ºC. Glass with smaller Si-O-Siangle is more reactive.

Water diffuses as H2O and reacts with SiO2 to form SiOH



SiSi--OO--Si bond angle of silica compounds Si bond angle of silica compounds and reactivity with waterand reactivity with water

Silicates with smaller Si-O-Si bond angle has higher reactivity with water. This is consistent with stress effect and with Tf effect.Data collected by Michalske and Bunker, J. Am. Ceram. Soc. 76 (1993) 2613.

≡Si-O-Si≡ + H2O reaction is unlikely to be the stress corrosion reaction.



High diffusion coefficient in silica glass High diffusion coefficient in silica glass under tensile stressunder tensile stress

Diffusion coefficient increases under tensile stress. High water diffusion coefficient is expected near a crack tip of glasses at room temperature.

McAfee, J. Chem. Phys. 28 (1958) 218.He diffusion in silica glass under tensile stress.Max. stress 0.65 MPa.∆V ~ 38 cm3/mol

Tomozawa, Phys. Chem.Glasses, 39 (1998) 68. ~14 GPastress is expected at crack tip.




Zouine et al. Phys. Chem. Glasses, 48 (2007) 85. Diffusion coefficient of water into SiO2 glass at room temperature is ~ 10-16 cm2/s.




Nogami and Tomozawa, J. Am. Ceram. Soc., 67 (1984) 151.192ºC, uniaxial stress, ∆V=170 cm3/mol; 350ºC, hydrostatic pressure, ∆V=72 cm3/mol



Activation volume of diffusion coefficient Activation volume of diffusion coefficient for network modifiers in glassesfor network modifiers in glasses

D = D0 exp [ - ∆ED/RT] exp [ - P∆V/RT]where ∆ED: activation energy; ∆V: activation volume.P>0 for hydrostatic pressure; ∆V> 0 for network modifier.High water diffusion coefficient is expected near a crack tip of glasses at room temperature.

H2O (diffusion)∆V = 9 cm3/mol in haplogranitic melt, e.g., 4.5wt% Na2O-7.2K2O-11.9Al2O3-77.9SiO2, 800~1200ºC, 0.5~5 kbar [1]Na+ (diffusion)∆V = 14.9 cm3/mol in 0.3Na2O-0.7B2O3, 350ºC, 4.6 kbar [2]∆V =2~5 cm3/mol in Na2O-Al2O3-SiO2, 4500K <15GPa, MD [3]Na+ (conductivity)∆V = 4.7 cm3/mol in 0.2Na2O-0.8B2O3, 57ºC. 2kbar [4].



Activation volume of diffusion coefficient Activation volume of diffusion coefficient for network modifiers in glassesfor network modifiers in glasses

References[1]M. Nowak and H. Behrens, Contrib. Mineral Petrol, 126, 365 (1997) [2] U. Schoo and H. Mehrer, Solids State Ionics, 130 243 (2000).[3] J.G. Bryce, et al., Am. Mineral, 84, 345 (1999).[4] K. Arai et al., J. Non-Cryst. Solids, 13, 131 (1973).

D = D0 exp [ - ∆ED/RT] exp [ σ∆V/3RT]Water diffusion at room temperature, D = 10-16 cm2/s.Using ∆V = 10cm3/mol, under uni-axial stress of 10 GPa, D = D (RT, 1atom) exp (σ∆V/RT) = 6.3x10-11 cm2/s

In 100 s, √Dt = 800 nm.Using ∆V=20 cm3/mol, under uni-axial stress 10 GPa, D = D (RT, 1atom) exp (σ∆V/RT) = 3.98 x 10-5 cm2/s

In 100 s, √Dt = 600 µm



water solubility increases at low water solubility increases at low temperature and with modifier.temperature and with modifier.

Zouine et al. Phys. Chem. Glasses, 48 (2007) 85. 23C, 22 torr .047%Extrapolation from high T ~x500.Most of water at low T is H2O.

H. Scholze, Glass Ind. 546 (1966)



water entry into silica glass during slow water entry into silica glass during slow crack growth in watercrack growth in water

Han et al, J. Am. Ceram. Soc. 74 (1991) 2573. DCDC crack growth in water and in paraffin oil.



Water entry into silica glass during Water entry into silica glass during fracturefracture

Han et al, J. Am. Ceram. Soc. 74 (1991) 2573. Nuclear reaction method.Water: slow crack in water. Oil: rapid crack in oil. Etch: etched with HF.



Effect of water content on mechanical Effect of water content on mechanical strength and fatigue of silica glassstrength and fatigue of silica glass

Han and Tomozawa, J. Non-Cryst. Solids, 127 (1991) 97. Static fatigue of SiO2 (T08) glass in formamide. Abraded samples were soaked in hot water and then dehydrated at various temperatures.1050ºC in vacuum; 800ºC in dry N2 and 400ºC in air. Glasses with higher water contents are weaker and exhibit greater fatigue tendency.



Swelling of SiOSwelling of SiO22 glass and sodium silicate glass glass and sodium silicate glass by water: similarity to polymeric glassesby water: similarity to polymeric glasses

J.E. Shelby, J. Non-Cryst. Solids, 349 (2004) 331.

J. Acocella et al, J. Non-Cryst. Solids, 65 (1984) 355.



ModuliModuli of SiOof SiO22 glasses with different water glasses with different water contentscontents

LeParc et al, J. Phys. Cond. Matters, 18 (2006) 7507.



Effect of water on elastic constant of Effect of water on elastic constant of glassglass

Mechanical loss increases and modulus decreases with increasing water content in glass. Day and Stevels, J. Non-Cryst. Solids, 14 (1974) 165.




Mechanical loss increases and modulus decreases with increasing water content in glass. Day and Stevels, J. Non-Cryst. Solids, 14 (1974) 165.

G'

G"f

f

A small quantity of water in glass greatly reduces elastic modulus of glass and increases its time (or frequency) dependence.



A possible mechanism of stressA possible mechanism of stress--corrosion:corrosion:Swelling of glass by water and modulus reductionSwelling of glass by water and modulus reduction

• Water enters into glasses, accelerated by tensile stress. (H2O diffusion and proton (or hydronium) ion-exchange with alkali ion).

• Glass swells by water absorption.

•Modulus decreases by swelling.

•Strength decreases by swelling.

This mechanism is similar to what is happening in polymers.



Swelling and modulus of rubbersSwelling and modulus of rubbers

Treloar, The physics of rubber elasticity, Clarendon, Oxford (1975). v2 is volume fraction of solute. l1 is the specimen length.Modulus decreases with increasing swelling. Swelling can increase with tensile stress.

Modulus vs. eq. Swelling



Swelling of polymer and solubility parameterSwelling of polymer and solubility parameter

Treloar, The physics of rubber elasticity, Clarendon (1975).Swelling vs. solubility parameter.

Greater amount of swelling can take place when the solubility parameters (cohesive energy density) of solvent and solute are closer.



Swelling of porous silica glass in various solventsSwelling of porous silica glass in various solvents

Oka et al., J. Am. Ceram. Soc., 64 (1981) 456. Diffusion distance of water ~ 20 nm in 100 h.



Swelling of porous silica glass and solubility Swelling of porous silica glass and solubility parameter and polarity parameter and polarity

0.0 0.2 0.4 0.6 0.8 1.015

20

25

30

35

40

45

50

δ

(MP

a)1/

2

p

water

formamide

methanol

nitrobenzene

Oka et al. J. Non-Cryst. Solids,38/39 (1980). 397. Oka et al., J. Am.Ceram. Soc., 64 (1981) 456. Polarity p includes the molecular interaction of various polarization effect. (Gardon, J. Paint Technol. 38 (1966) 43.)



YoungYoung’’s modulus of Nas modulus of Na22OO--SiOSiO22 glasses with high water glasses with high water contents, tested in paraffin oil.contents, tested in paraffin oil.

S. Ito and M. Tomozawa, J. de Phys. C9 (1982) 611.



Fracture strength of NaFracture strength of Na22OO--SiOSiO22 glasses with high water, glasses with high water, tested in paraffin oil, as a function of stressing ratetested in paraffin oil, as a function of stressing rate..

S. Ito and M. Tomozawa, J. de Phys. C9 (1982) 611.n value is lower for samples with higher water content.



YoungYoung’’s modulus of Nas modulus of Na22OO--SiOSiO22 glass with high glass with high water contentswater contents

S. Ito and M. Tomozawa, J. de Phys. C9 (1982) 611. Q = v/vdry: degree of swelling.

0 5 10 15 20 2510

20

30

40

50

60

You

ng's

Mod

ulus

E (G

Pa)

H2O (wt%)0.00 0.05 0.10 0.15 0.20 0.25

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

log Q

log

E (G

Pa)



Fracture strength vs. YoungFracture strength vs. Young’’s modulus of Nas modulus of Na22OO--SiOSiO22 glass with high water contentsglass with high water contents

From S. Ito and M. Tomozawa, J. de Phys. C9 (1982) 611.

0.6 0.8 1.0 1.2 1.4 1.6 1.81.0

1.2

1.4

1.6

1.8

2.0

2.2 H2O 15.9wt% H2O 23.1wt% H2O 25.3wt%

log

σ f (MP

a)

log E (GPa)

Strength appears to be proportional to Young’s modulus.



Theory of brittle factureTheory of brittle facture

σ = K sin (π/a)(x-a0); From initial slope E, K = (E/π)(a/a0)The integral of curve = 2γγ = (E/a0)(a/π)2 ≈ Ea0/10

(a0 ≈ a)Theoretical strength = √Eγ/a0=E/π

Griffith Equationσf = √2Eγ/πCσf is proportional to E if C is

constant.A. Kelly, Strong Solids



Fracture toughness is proportional to EFracture toughness is proportional to E

Shinkai, Bradt and Rindone, J. Am. Ceram. Soc., 65 (1982) 123.

KIC = √2Eγ

Kelly Strong Solids

γ = Ea0/10 and

KIC = E√5a0



Crack velocity of silica glass in various Crack velocity of silica glass in various environmentsenvironments

Michalske and Freiman, J. Am. Ceram. Soc., 66 (1983) 284.

Slow crack growthwas also observedin ammonia, hydrazineand formamide in addition to water.



Solubility parameterSolubility parameter

Solubility parameter = Cohesive energy density. Correlates with solubility of solute and solvent.•Hildebrand δ is good for non-polar solvents.e.g. = (∆H – RT)0.5/V0.5 ∆H heat of evaporation; V mol vol.•Hansen δ includes polar term and hydrogen bonding term. •Hildebrand δ (Hansen δ) (MPa)0.5

water* 47.9 (47.9) ethanol 26.0 (26.6)formamide* 39.3 methanol 29.6 (29.7)hydrazine* 37.0 toluene 18.2 (18.2) ammonia* 33.3 acetonitrile 24.3 (24.6)

•Slow crack growth of SiO2 glass was observed in * marked.Solubility parameter of SiO2 glass is not known but solids have much larger values. Si 194; C 366; Al 180; Ti4O7 746 (MPa)1/2.



Fatigue parameterFatigue parameter

Slow crack growth followsv = v0 σn, . n is also a measure of fatigue.

Crack growth ln v = ln v0 + n ln σStatic fatigue ln σf = A – (1/n) ln tfDynamic fatigue ln σf = B + [1/(1+n)] ln (σ rate)

In the present model, the value of n is determined by water content in glass; higher water content leads to smaller n value.



Fatigue parameterFatigue parameter

Slow crack growth follows; v = v0 σn.

Al2O3 n=46 [1]SiO2 n=42(l) [3]Alumino-silicate glass

[57wt%SiO2; 4B2O3; 20Al2O3; 1Na2O; 12MgO; 6CaO] n =26(l) [3]

Borosilicate glass [80wt%SiO2; 14B2O3; 2Al2O3; 4Na2O] n =23 (l) [3]

Soda-lime silicate glass [72wt%SiO2; 2Al2O3; 14Na2O; 1K2O; 4MgO; 7CaO] n =13(l) [2]

[1]S.M. Wiederhorn, Int. J. Fract. Mech. 4, 171 (1968).[2] S.M. Wiederhorn, J. Am. Ceram. Soc., 50, 407 (1967).[3] S.M.Wiederhorn and L.H. Bolz, J. Am. Ceram. Soc., 53, 543 (1970).



Water solubility in glassesWater solubility in glasses

Water solubility increases with alkali content.

Higher water solubility appears to decrease n value.

Scholze, Glass Ind (1966).



ConclusionsConclusions

Mechanisms of mechanical strength reduction ofglasses by water were considered. In particular, the stress corrosion reaction was considered.

•Si-O-Si + H2O 2 SiOH is unlikely to be the stresscorrosion reaction.

•Swelling of glass by water entry and the consequent reduction of Young’s modulus is likely to be the stress-corrosion reaction.

•n value appears to scale with the amount of water entering into the glass. (more water gives smaller n).



AcknowledgementsAcknowledgements

Financial support of NSF under contract, DMR-0352773.

I appreciate discussion with Drs. S. Ito and A. Koike of Asahi Glass Co. and with Professors Doremus and Hillig of Rensselaer.



Water speciation: HWater speciation: H22O dominates at higher O dominates at higher water concentration.water concentration.




Water can be OH or HWater can be OH or H22O in glass. Higher HO in glass. Higher H22O O over over SiOHSiOH content at low temperaturecontent at low temperature

Davis and Tomozawa, J. Non-Crsyt. Solids, 185 (1995) 203.

Nowak and Behrens, Geochimca. Cosmochimica Acta, 59 (1995) 3445.K = [-OH]2/[H2O]. At low temperature, equilibrium is not maintained.



Speciation of water in sodaSpeciation of water in soda--lime glasslime glass

Stuke et al Chem. Geology, 229 (2006) 64.H2O dominates at high water concentration.





Isotope effect, H2O vs. D2O

No isotope effect on network solubility (H2O + Si-O-Si 2 SiOH)

Isotope effect on ion-exchange

Na+ (in glass) + H+ (in water) H+ (in glass) + Na+ (in water)

McGrail, J. Non-Cryst. Solids, 296 (2001) 10.



Partial molar volume of water and glassPartial molar volume of water and glass




Crack growth of sodaCrack growth of soda--lime glass silica lime glass silica glass as a function of temperatureglass as a function of temperature

Wiederhorn and Bolz, J. Am. Ceram. 53 (1970) 543.

Suratwala and Steele, J. Non-Crystalline Solids 316 (2003) 174.



Crack growth and dynamic fatigue of silica Crack growth and dynamic fatigue of silica glassesglasses

S. Crichton et al. J. Am. Ceram. Soc. 82 (1999) 3097. Phosphate glass.



g g yg g yrelated to higher water solubility in oxide related to higher water solubility in oxide

glass than in crystalline oxideglass than in crystalline oxide

Kim and Tomozawa, J. Am. Ceram. Soc. 74 (1991) 2573. Fujita et al. J. Non-Cryst. Solids,

320 (20003) 56.



Water entry can accelerate surface Water entry can accelerate surface structural relaxation kineticsstructural relaxation kinetics

Varughese et al. J. Non-Crsyt. Solids, 242 (1998) 104. Soda-lime glass with higher Tf is stronger.

Tomozawa and Hepburn, J. Non-Cryst. Solids, 345/346 (2004) 449.

Surface structural relaxation faster than bulk and accelerated by tensile stress.Physical aging of polymer—slow reduction of Tf.



Fictive temperature effect on crack growth: Fictive temperature effect on crack growth: sodasoda--lime and silica glasseslime and silica glasses

0.4 0.5 0.6 0.7 0.810-8

10-7

10-6

10-5

10-4

Tf = 450oC, RH:50%

Tf = 550oC, RH:50%

Tf = 450oC, Dry

Tf = 550oC, Dry

Cra

ck v

elos

ity, V

(m/s

ec)

Stress intensity factor, KI (MPahm1/2)

error

A. Koike and M. Tomozawa, J. Non-Cryst. Solids, 353 (2006) 5522. Surface structural relaxation cannot be the stress-corrosion reaction.

0.5 0.6 0.7 0.810-8

10-7

10-6

10-5

10-4

Stress intensity factor, KI (MPahm1/2)

Cra

ck v

elos

ity, V

(m/s

ec)

Tf = 1100oC, RH:50%

Tf = 1300oC, RH:50%

Tf = 1100oC, Dry

Tf = 1300oC, Dry

error

Role of water in fracture of glass

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