Why Does Glass Break?

Transcription

1 US-China New Functionalities in Glass Why Does Glass Break? Some considerations of the mechanical properties of glass Missouri University of Science & Technology Department of Materials Science & Engineering IMI-1

2 If glass was 100X stronger, what *new* applications would result? IMI-2

3 New applications will benefit from stronger glass.. IMI-3

4 Apple Store, 5 th Ave., NYC Glasgow, Scotland IMI-4

5 Train Station/Strasbourg, France IMI-5

6 Emilio Spinosa, O-I, Vancouver, June 2009 IMI-6

7 Strong glass comes in handy for other applications IMI-7

8 Our Outline 1. Background Information Elastic modulus Fracture mechanics and strength Fatigue Strengthening 2. Two-point bend studies of pristine glass IMI-8

9 Some useful references: A. Varshneya, Fundamentals of Inorganic Glasses, Society of Glass Technology (2006)- chap. 18 Elastic Properties and Short-to Medium-Range Order in Glasses, Tanguy Rouxel, J. Am. Ceram. Soc., 90 [10] (2007) Environmentally Enhanced Fracture of Glass: A Historical Perspective, S. W. Frieman, S.M. Weiderhorn, and J.J. Mecholsky, J. Am. Ceram. Soc. 92[7] (2009) M. Ciccotti, Stress-corrosion mechanisms in silicate glasses, J. Phys. D: Appl. Phys. 42, (2009). C. R. Kurkjian, P. K. Gupta, R. K. Brow, and N. Lower, The intrinsic strength and fatigue of oxide glasses, J. Noncryst. Solids, 316, 114 (2003). IMI-9

10 Can we connect mechanical performance to the molecular structure of glass? U U 0 r 0 r E IMI-10

11 Elastic Modulus Definitions? Why should we care about modulus? IMI-11

12 Elastic Modulus- resistance to deflection x x Why is the elastic modulus of a glass important? Stiffer hard-drive disks (minimize deflection at high rpm s) Stiffer glass-fiber reinforces composites (larger windturbine blades) Reduce the thickness (and weight) of architectural glass) Increase the stiffness of glass-bearing structures (buildings, bio-glass scaffolds, etc.) Design glass or glass-ceramic matrices for aerospace applications x E Poisson s Ratio y, z IMI-12

13 Elastic Modulus Is Related To The Strength of Nearest Neighbor Bonds U r 0 F U 0 r r 0 r Force = F = - du/dr Stiffness = S 0 = (du 2 /dr 2 ) r = r0 Elastic Modulus: Pascals = J/m 3 a measure of the volume density of strain energy (E U 0 /V 0 ) Elastic Modulus = E = S / r 0 Bulk Modulus: K V 0 2 V U 2 V 0 mn 9V 0 U 0 IMI-13

14 From atomistic to continuum properties: K V 0 2 V U 2 V 0 mn 9V 0 U 0 Multi-component glasses: U V 0 0 f i H ai / f i M i / i H ai x H 0 f ( A ) y H 0 f ( B ) H 0 f ( A x B y ) i: density f i : molar fraction of i th component M i : molar mass of i th component H ai : enthalpy of i th component (Born-Haber cycle) IMI-14

15 E and T g are related within a composition class Rouxel, J. Am. Ceram. Soc., 90 [10] (2007) IMI-15

16 More cross-links: greater E Rouxel, J. Am. Ceram. Soc., 90 [10] (2007) IMI-16

17 Poisson s ratio appears to be sensitive to structure: packing density and network dimensionality IMI-17

18 Rouxel, J. Am. Ceram. Soc., 90 [10] (2007) IMI-18

19 2010 Rouxel, IMI J. Am. Ceram. Soc., 90 [10] (2007) IMI-19

20 The temperature-dependence of the Poisson s ratio may indicate changes in structure through the glass transition 2010 Rouxel, IMI J. Am. Ceram. Soc., 90 [10] (2007) IMI-20

21 Summary: Elasticity There is a limited correlation between E and T g within compositional series, but not necessarily between compositional types High elastic moduli are favored by structural disorder and atomic packing seems to be more important than bond strength Poisson s ratio ( ) correlates with atomic packing density and with network dimensionality (polymerization) The temperature dependence of elastic properties above T g may be related to fragile and strong viscosity behavior. IMI-21

22 Glass Strength What factors determine the strength of glass? IMI-22

23 Theoretical Strength Can Be Estimated From the Potential Energy Curve (Orowan) m = E / a 0 2 f = m sin( x/ ) dx = m / ( ) a 0 m = [ f E / a 0 ] 1/2 If E = 70 GPa, f = 3.5 J/m 2 and a 0 = 0.2nm, then m = 35 GPa! IMI-23

24 How does the addition of Na 2 O affect the Young s modulus and fracture surface energy of silica glass? Consider what Prof. Pantano discussed the other day. IMI-24

25 Practical strengths are significantly less than the theoretical strengths: Common glass products Freshly drawn glass rods Abraded glass rods Wet, scored glass rods Armored glass Handled glass fibers Freshly drawn glass fibers Most metals, including steels MPa MPa MPa 3-7 MPa MPa MPa MPa MPa IMI-25

26 C. E. Inglis (1913): flaws acted as stress concentrators A.A Griffith (1921): critical flaws determine strength Stress enhancement by flaws with length 2c and radius : yy 2 a (c/ ) 1/2 Calculated strength with critical flaw c*: f = [2 f E / c*] 1/2 If E = 70 GPa, and f = 3.5 J/m 2 Then a crack of 100 microns will result in a failure stress of 25 MPa IMI-26

27 Fracture mechanics allow the evaluation of stresses in the vicinity of a propagating crack ij = [K / (2 r) 1/2 ] f ij ( ) Fracture criterion when stress intensity exceeds the strain energy release rate (depends on E, f) K Ic = a ( c) 1/2 IMI-27

28 Cathodoluminescence measurements of stress distributions around crack tips (Pezzotti and Leto, 2007) IMI-28

29 P, probability density P F, cumulative failure prob. An aside: Weibull Statistics m P d 1 2 exp ( 2 d 2 m ) 2 ln ln 1 P F m ln ln 0 d, applied stress ln ln (1-P F ) -1 m 1.0 P F 1 exp m ln 0 m 1 m 2 Note: same average fracture strength, but m 1 <m 2 (broader distribution of strengths)., applied stress IMI-29

30 Room temperature tensile tests of pristine silica fibers drawn and tested in vacuum- bimodal distribution 14GPa 9GPa Smith and Michalske, 1992 IMI-30

31 Failure strength (GPa) The Ultimate Strength of Glass Silica Nanowires, G. Brambilla and DN Payne, Nano Letters, 9[2] 831 (2009) Flame-attenuation of optical fibers Fiber diameter (nm) IMI-31

32 E-glass fibers (tensile tests, in air) Lower soak temperatures lead to bimodal strength distributions Cameron, 1968 IMI-32

33 Concentric ring tests, abraded Corning glass 1737, two different thicknesses. Gulati, et al., Ceramic Bulletin, 83[5] 14, 2004 IMI-33

34 Mechanical properties depend on glass structure K/Al-metaphosphate glasses Baikova, et al. Glass Phys. Chem., 21[2] (1995) 115. E Hv LN RT IMI-34

35 Pukh et al., 2005 IMI-35

36 MD Simulations of fracture reveal the development of cavities that coalesce to form the failure site Pedone et al., 2008 IMI-36

37 Quenched and annealed soda-lime glasses at 5GPa tension S. Ito and T. Taniguchi, JNCS (2004) IMI-37

38 There may be experimental evidence for cavitation near the tips of slow-moving cracks Aluminosilicate glass, m/s, 45% RH, AFM Images Célarié, et al., PRL (2003) Formation of nano-cavities interpreted as evidence for nanoductile fracture of glass! IMI-38

39 Nano-ductility interpretation is not universal Post-mortem AFM analyses of the opposing fracture surfaces show no evidence for the formation of nano-cavities Note the relatively rough surface Guin and Wiederhorn, PRL (2004) IMI-39

40 Fatigue IMI-40

41 An example of fatigue in glass IMI-41

42 F a ilu re S tre n g th (M P a ) In s ta n ta n e o u s S tre n g th S ta tic F a tig u e E ffe c t E n d u ra n c e L im it P ris tin e, A s -D ra w n P ris tin e, A n n e a le d F o rm e d G la s s U s e d G la s s D a m a g e d G la s s In h e re n t S tru c tu ra l F a b ric -s c o p ic V is ib le F la w s F la w s a tio n D a m a g e D a m a g e 1 e -9 1 e -8 1 e -7 1 e -6 1 e -5 1 e -4 F la w S iz e (m ) After Mould (1967) IMI-42

43 Stress Corrosion: source for static fatigue- the reduction in strength with time IMI-43

44 Fatigue data on silica fibers Liquid nitrogen Room temperature, vacuum Room temperature, ambient conditions IMI-44

45 Note: residual stresses increase susceptibility to static fatigue IMI-46

46 Double-Cantilever Beam (DCB) used for controlled stress intensity and crack velocity experiments c V=dc/dt K=P 2 /f(geometry) S. W. Freiman, D. R. Mulville and P. W. Mast, J. Mater. Sci., 8[11] 1573 (1973). IMI-47

47 Crack propagation kinetics depend on the stress intensity Region I: stress-corrosion Region II: diffusion-limited Region III: rapid fracture (K IC ) Region 0: propagation threshold IMI-48

48 Crack velocity (m/s) Water and stress enhance crack growth in glass Region I: stresscorrosion v=ak I n, where n is the stress corrosion susceptibility factor H 2 O(l) 100% 30% 10% III 1.0% 0.2% 0.017% SM Wiederhorn, JACerS, (1967) I II Stress Intensity Factor, K I (Nm -1/2 ) IMI-49

49 Compositionaldependence of v- K behavior in Region I Soda-Lime Borosilicate Silica Different glasses are more or less susceptible to fatigue effects Aluminosilicate We do not understand this compositional dependence! IMI-50

50 Temperaturedependence of v-k behavior in Region I Wiederhorn and Bolz, JACerS, 53, 545 (1970) IMI-51

51 Slow crack growth is a thermally activated process Chemical rate theory has been used to explain the exponential form of the V K I curves: V V exp( E bk / RT 0 I ) where V 0 is a constant, E is the activation energy for the reaction, R is the gas constant, T is the temperature, and b is proportional to the activation volume for the crack growth process, ΔV*. Wiederhorn, et al., JACerS, 1974 IMI-52

52 Stress-corrosion in silicate glass: a. Adsorption of a water molecule on a strained siloxane bond at a crack tip; b. Reaction based on proton and electron transfer; c. Separation of silanol groups after rupture of the hydrogen bond. Net result: extension of the crack length by one tetrahedral unit IMI-53

53 Stress-corrosion in silicate glass: a. Reactive molecules can donate both protons and electrons to the ruptured siloxane bond; b. Reactive molecules are small enough to reach the crack tip (<0.5 nm). Water, ammonia, hydrazine (H 2 N-NH 2 ), formamide (CH 3 NO) IMI-54

54 Other crack-tip chemistries lead to strength increasing with time Controlled flaws (Vicker s indents) in S-L-S Aging in different environments Tensile tests in inert conditions (silicone oil) May be due to stress release- not crack geometry? Lawn et al., JACerS, 68[1] 25 (1985) IMI-55

55 Crack-tip sharpness depends on glass structure and corrosion conditions Change in crack tip geometry due to corrosion: (a) Flaw sharpening for stresses greater than the fatigue limit; (b) Constant flaw sharpness for stresses equal to the fatigue stress; (c) Flaw blunting for stresses below the fatigue limit..t.-j. Chuang and E.R. Fuller, Jr. Extended Charles-Hillig Theory for Stress Corrosion Cracking of Glass, J. Am. Ceram. Soc. 75[3] (1992). W.B. Hillig, Model of effect of environmental attack on flaw growth kinetics of glass, Int. J. Fract (2007) IMI-56

56 AFM detects significant morphological changes around the crack-tip in aged samples SLS glass, 45% RH Célarié, et al., JNCS (2007) Formation of alkali-rich regions modeled by Na + -H 3 O + inter-diffusion Alkali depletion from crack-tip region leads to stress-relaxation Crack extension threshold IMI-57

57 The corrosion reactions at a crack tip are similar to those that occur at glass surfaces From Prof. Jain: A clear glass plate is made of soda lime silicate glass by pressing molten gob. It shows the following undesirable pattern upon washing in a dishwasher. Discuss this problem with your roommate. Then develop a collaborative research program to characterize and solve the problem. The proposal should be about 1500 words long. IMI-58

58 Water plays many roles at a crack-tip 1. Chemical attack on strained bonds to extend flaws 2. Water films adsorbed on crack surfaces 3. Capillary condensation at the crack tip 4. Water diffusion into the glass network, changing elastic properties 5. Inter-diffusion with alkali ions, changing ph and attacking glass IMI-59

59 Strengthening- What can we do to make glass stronger (or more reliable)? IMI-61

60 Polished surfaces Surface dealkalization Protective coatings Relaxation of residual stresses (annealing) Reduction of expansion coefficients (thermal shock) Thermal tempering Chemical tempering Modified compositions: Increasing elastic modulus and/or surface energy Reducing stress-corrosion Propagation threshold Crack healing IMI-62

61 Annealed vs. chemically tempered glass From Jill Glass, Sandia National Labs IMI-63

62 Two-point bend studies of the failure characteristics of silicate glasses IMI-64

63 We have produced and tested pristine fibers Drawing Cage Box Furnace Pristine 10 cm length fibers Fiber diameters ~125 mm. Fibers can be tested immediately. TNL Tool and Technology, LLC IMI-65

64 We have measured failure strains using a Two-Point Bend technique Face plate velocities: 1 10,000 mm/sec Liquid nitrogen, room temp/variable humidity. Small test volume (25-100mm gauge length). TNL Tool and Technology, LLC f f f D *M.J. Matthewson, C.R. Kurkjian, S.T. Gulati, J. Am. Cer. Soc., E 69, 815 (1986). d d IMI-66

65 The inert failure strain measurements are reproducible 99 C u m u la tiv e F a ilu re P ro b a b ility (% ) E -G la s s m = A v g = % Eight sets of E-glass fibers, tested in liquid nitrogen, collected over two years S ilic a m = A v g = % F a ilu re S tra in (% ) IMI-67

66 Failure strain (%) The inert failure strain measurements are intrinsic Criteria for intrinsic failure properties* Narrow failure distributions: s(failure) < s(fiber diameter) Failure property (strength, strain) independent of diameter *Gupta and Kurkjian, JNCS 351 (2005) ~180 E-glass fibers/ln 2 tests y = x Fiber diameter ( m) IMI-68

67 ln(ln(1/1-f)) Fibers fail at lower strains in ambient conditions E-glass3 C1 P1 LN E-glass3 C2 P1 LN E-glass3 C3 P1 LN E-glass3 C3 P1 RH 20%RH, 26ºC m = 117, 12.08% m = 113, 12.05% m = 131, 12.09% m = 142, 6.29% -3.0 LN ln(failure strain, %) IMI-69

68 Fatigue effects can be characterized Chamber purged with controlled humidity RH / Temp. Sensor Cumulative Failure Probability (%) % RH Weibull Plot of 4A (0.0% B 2 O 3 ) 10% RH 5 Tested at 24 C and 3 different relative humidities. FPV = 4000 m/s Failure Strain (%) 4A 24 o C, varied RH m Avg = 181 Increasing RH IMI-70

69 Cumulative Failure Probability (%) Failure Strain (%) Aging effects have also been characterized A Aged at 80% RH, 50 o C Tested using: LN 2, 4000 m/s Fresh 2 days 4 days 7 days 14 days 28 days Failure Strain (%) Ca-aluminoborosilicates Aging of 4A Aging of 4A2 Aging of 4C (set 1) Aging of 4C (set 2) B-free composition Time (Days) IMI-71

70 What might inert 2pb studies tell us about the failure characteristics of silicate glasses? IMI-72

71 Compositions Studied xna 2 O * (100-x)SiO 2 x = 0, 7, 10, 15, 20, 25, 30, 35 xk 2 O * (100-x)SiO 2 x = 0, 4.5, 7, 10, 15, 20, 25 25Na 2 O * xal 2 O 3 * (75-x)SiO 2 x = 0, 5, 10, 15, 20, 25, 30, 32.5 xna 2 O * ycao * (100-x-y)SiO 2 Compositions studied by Ito, et al. IMI-73

72 Na-silicate inert failure strains depend on composition Cumulative Failure Probability (%) NaSi NaSi NaSi NaSi NaSi NaSi Failure Strain (%) NaSi Avg m ~ 259 xna 2 O * (100-x)SiO NaSi IMI-74

73 Elastic Modulus (GPa) Failure Strain (%) Sodium silicate properties UMR Bokin Takahashi K. Karapetyan Livshits LN Increasing NBO s xna 2 O * (1-x)SiO Mole Fraction Na 2 O Mole Fraction Na 2 O IMI-75

74 Na-Al-silicate inert failure strains depend on composition Cumulative Failure Probability (%) NaAlSi NaAlSi NaAlSi NaAlSi NaAlSi NaAlSi NaAlSi Na-Si 25Na 2 O * (x)al 2 O 3 * (75-x) SiO Failure Strain (%) IMI-76

75 Elastic Modulus (GPa) Na-Al-silicate properties depend on structure Failure Strain (%) UMR Livshits Yoshida Na 2 O * (x)al 2 O 3 (0.75-x) SiO Fully cross-linked Greater cross-linking: stiffer structure Mole Fraction Al 2 O Mole Fraction Al 2 O 3 IMI-77

76 Failure Strain, % Inert failure strain decreases for crosslinked structures NAS NS KS SLS Bridging Oxygens/Former IMI-78

77 Failure Strain, % Failure strain depends on elastic modulus NAS NS KS NB SLS Silica CABS TV Panel E-Glass C Elastic Modulus (GPa) IMI-79

78 Do these measurements provide information about the strength of glass? depends on what we know about the elastic modulus IMI-80

79 Elastic modulus depends on strain E-glass fibers Na/Li-phosphate fibers Bruckner, Strength of Inorg. Glass 1986 IMI-81

80 Strain dependence of modulus has been modeled Converting failure strain to failure stress requires knowledge of Y( ): Gupta and Kurkjian, JNCS 351 (2005) 2343 Y( ) = Y 0 +Y 1 +(Y 2 /2) 2 ; f = f [(2/3)Y 0 +(Y 1 /6) f ] IMI-82

81 Failure strengths can be calculated if Y( ) is known Mechanical Property (GPa) Inert Failure Strain (%) stress Pukh, et al. strain mole % Na 2 O 5.0 IMI-83

82 Failure Strength (GPa). What role is played by critical flaws? There are no apparent surface heterogeneities. If Griffith flaws are responsible for low strengths, they will be in the range of 2-7 nm, depending on the flaw (stress concentrator) geometry. f 2 E c GPa -> 1.4 nm flaw GPa -> 6.7 nm flaw Griffith Flaw Size (nm) Recall processing effects IMI-84

83 Cumulative Failure Probability (%) Advantex C2 P4 2:00 at 1200 o C m = 9 Avg = 10.88% Advantex Failure Strains Weibull distributions of fibers drawn after different melt histories. Weibull modulus (m), average failure strain ( Avg ), and melt history are reported for each data set Advantex C2 P2 Advantex C2P5 90 2:00 at 1180 o C 90 12:00 at 1350 o C m = m = 7 80 = 10.36% = 12.18% Avg Avg 3 Advantex C2 P3 Advantex C2 P2 2:00 at 1250 o C 12:00 at 1350 o C m = 60 m = 129 Avg 1 = 12.11% = 12.18% Avg Failure Strain (%) Cumulative Failure Probability (%) Advantex C2 P8 0:30 at 1350 o C m = 3 Avg = 8.51% Advantex C2 P10 2:00 at 1350 o C m = 35 Avg = 11.73% 3 Advantex C2 P9 Advantex C2 P11 1:00 at 1350 o C 3:00 at 1350 o C m = 4 m = 55 1 = 9.34% Avg = 11.88% Avg Failure Strain (%) IMI-85

84 Some questions related to Prof. Sen s lecture: What type of heterogeneities might account for these distributions in failure strains? What techniques could you use to characterize these heterogeneities?

85 F a ilu re S tra in, % M e ltin g T e m p e ra tu re (C ) Advantex Thermal History Summary When the glass was melted at 1350ºC, the failure strain distributions narrow with time. Failure strain distributions begin to broaden when melts are cooled to T L +50ºC. G la s s b e h a v e s s tr a n g e ly a t T L T F ~ º C Im p ro v in g D e g ra d in g Im p ro v in g 7.0 T L ~ º C Crystallites form F a ilu re S tra in s M e ltin g T e m p e ra tu re T h e rm a l H is to ry :0 0 2 :0 0 4 :0 0 6 :0 0 8 : : : : : : : : : : :0 0 Richard T im ek. Brow 1100 IMI-87

86 How does glass break? IMI-88

87 Inert failure rate studies C u m u la tiv e F a ilu re P ro b a b ility (% ) S ilic a m A v g = Normal Inert Fatigue 5 m /s 1 0,0 0 0 In c re a s in g V fp m /s C u m u la tiv e F a ilu re P ro b a b ility (% ) S L S m A v g = Inert Delayed Failure Effect 4,0 0 0 m /s F a ilu re S tra in (% ) D e c r e a s in g V fp 5 m /s F a ilu re S tra in (% ) IMI-89

88 ln (failure strain, %) Inert failure rate studies n = 1 / (d ln( / d ln(vfp) ) n = SLS Silica ln (V fp ) IMI-90

89 Inert Delayed Failure Effect ( )/ 50) The inert delayed failure effect depends on structure NAS NS KS SLS Bridging Oxygens/Former IMI-91

90 Crack initiation load (N) More Brittle Failure Strain (%) Failure strain measurements also correlate with crack initiation loads 0.25Na 2 O * (x)al 2 O 3 * (0.75-x) SiO Satoshi Yoshida, Mole Fraction Al 2 O Mole Fraction Al 2 O 3 IMI-92

91 Failure strain measurements may provide information about less brittle glasses Setsuro Ito, 2002 IMI-93

92 Brittleness parameter has been determined from indentation measurements Brittlenes B 2.39 P is applied load, C is crack length, and a is Vickers indentation diagonal length s P 1 / 4 C a 3 / 2 Setsuro Ito, 2002 IMI-94

93 Soda-lime silicate glasses exhibit the delayed failure effect 99 Cumulative Failure Probability (%) SLS m Avg = 345 Closed symbols 4000 mm/sec, Open symbols 50 mm/sec Each glass possesses a large IDFE. SLS m Avg = Failure Strain (%) SLS m Avg = 326 IMI-95

94 IDFE (Missouri S&T) 7.0 Brittleness and inert delayed failure may be related Soda-lime & borosilicate glasses Silica Brittleness (Ito) IMI-96

95 Is IDFE related to network relaxation? Na diffusion NBO motion? Day & Rindone, 1962 IMI-97

96 Failure strain, % Is there a universal dependence of glass failure characteristics on network structure? WOULD INSTANTANEOUS FAILURE STRAINS ALL FALL ON A STRAIGHT LINE?? NS NAS KS SLS Silica CABS TV Panel E-glass C-0317 TiMgAlSi LN depends on E (IDFE 0) 2. Silica is anomalous LN depends on network relaxation (IDFE>0) LN 2 tests at 4000 /sec Young's modulus (GPa) IMI-98

97 Summary Inert failure strains are sensitive to the composition/structure of glass fibers. f increases when NBO s replace BO s f increases when Young s modulus decreases Inert failure strains are dependent on the applied stressing rates (V fp ). Structure with non-bridging oxygens fail at larger strains with slower V fp. Framework structures do not exhibit this inert delayed failure effect. Is IDFE due to relaxation of the network? What role is played by the NBO s? IMI-99

98 The NSF/Industry/University Center for Glass Research sponsored the two-point bend studies at Missouri S&T Nate Lower and Zhongzhi Tang collected the data Chuck Kurkjian (retired, AT&T) inspired the work IMI-100