US-China Winter School
New Functionalities in Glass
Why Does Glass Break?
Some considerations of the mechanical
properties of glass
Richard K. Brow
Missouri University of Science & Technology
Department of Materials Science & Engineering
2010 US-China
Winter School
Richard K. Brow
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IMI-1
If glass was 100X stronger, what
*new* applications would result?
2010 US-China
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IMI-2
New applications will benefit from stronger glass…..
2010 US-China
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IMI-3
Apple Store, 5th Ave., NYC
2010 US-China
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Glasgow, Scotland
Richard K. Brow
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IMI-4
Train Station/Strasbourg, France
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IMI-5
Emilio Spinosa, O-I, Vancouver, June 2009
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IMI-6
Strong glass comes in handy for other applications
2010 US-China
Winter School
Richard K. Brow
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IMI-7
Our Outline
1. Background Information
• Elastic modulus
• Fracture mechanics and strength
• Fatigue
• Strengthening
2. Two-point bend studies of pristine glass
2010 US-China
Winter School
Richard K. Brow
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IMI-8
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] 3019–3039 (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] 1371-1382 (2009)
• M. Ciccotti, “Stress-corrosion mechanisms in silicate glasses,” J.
Phys. D: Appl. Phys. 42, 214006 (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).
2010 US-China
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Richard K. Brow
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IMI-9
Can we connect mechanical performance to the molecular
structure of glass?
U
r0
r
U0
E
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IMI-10
Elastic Modulus
Definitions?
Why should we care about modulus?
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IMI-11
Elastic Modulus- resistance to deflection
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
x
E
Poisson‟s Ratio
y,
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z
IMI-12
Elastic Modulus Is Related To The Strength of Nearest
Neighbor Bonds
U
F
r0
r
U0
Force = F = - dU/dr
Stiffness = S0 = (dU2/dr2) r = r0
Elastic Modulus: Pascals = J/m3
a measure of the volume density
of strain energy (E≈U0/V0)
Elastic Modulus = E = S / r0
Bulk Modulus:
2
K
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r
r0
Richard K. Brow
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V0
U
V
mn
2
V0
9V 0
U
0
IMI-13
From atomistic to continuum properties:
2
K
V0
U
V
mn
2
U
9V 0
V0
0
Multi-component glasses:
U
0
fi H
V0
H
ai
x H
0
f
ai
( A)
/
fiM
y H
0
f
i
/
(B )
i
H
0
f
( AxB y )
i:
density
fi: molar fraction of ith component
Mi: molar mass of ith component
Hai: enthalpy of ith component (Born-Haber cycle)
2010 US-China
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IMI-14
E and Tg are related within a composition class
Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)
2010 US-China
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IMI-15
More cross-links:
greater E
Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)
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IMI-16
Poisson‟s ratio appears to be sensitive to structure: packing
density and „network dimensionality‟
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IMI-17
2010 US-China
Rouxel,
J. Am.
Winter School
Richard K. Brow
Ceram. Soc., 90 [10] 3019–3039
(2007)
[email protected]
IMI-18
2010
IMI
Rouxel,
Richard K. Brow
J. Am. Ceram. Soc., 90 [10] 3019–3039
(2007)
[email protected]
IMI-19
The temperature-dependence of the Poisson‟s ratio may
indicate changes in structure through the glass transition
2010
IMI
Rouxel,
Richard K. Brow
J. Am. Ceram. Soc., 90 [10] 3019–3039
(2007)
[email protected]
IMI-20
Summary: Elasticity
•There is a limited correlation between E and Tg 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
Tg may be related to “fragile” and “strong” viscosity
behavior.
2010 US-China
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IMI-21
Glass Strength
What factors determine the strength of glass?
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IMI-22
Theoretical Strength Can Be Estimated
From the Potential Energy Curve (Orowan)
m
=
2 f=
E / a0
sin( x/ ) dx
= m/( )
m
1/2
=
[
E
/
a
]
m
f
0
a0
If E = 70 GPa, f = 3.5 J/m2
and a0 = 0.2nm, then
m=
2010 US-China
Winter School
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35 GPa !
IMI-23
How does the addition of Na2O affect the
Young’s modulus and fracture surface
energy of silica glass? Consider what Prof.
Pantano discussed the other day….
2010 US-China
Winter School
Richard K. Brow
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IMI-24
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
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14-70 MPa
70-140 MPa
14-35 MPa
3-7 MPa
350-500 MPa
350-700 MPa
700-2100 MPa
140-350 MPa
IMI-25
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
1/2
(c/
)
a
Calculated strength with
critical flaw c*:
f = [2
1/2
E
/
c*]
f
If E = 70 GPa, and f = 3.5 J/m2
Then a crack of 100 microns will
result in a failure stress of ≈ 25 MPa
2010 US-China
Winter School
Richard K. Brow
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IMI-26
Fracture mechanics allow the evaluation of stresses in
the vicinity of a propagating crack
ij
= [K / (2
r)1/2] fij ( )
Fracture criterion when
stress intensity exceeds
the strain energy release
rate (depends on E, f)
KIc =
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1/2
(
c)
a
IMI-27
Cathodoluminescence measurements of stress distributions around crack tips
(Pezzotti and Leto, 2007)
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IMI-28
PF, cumulative failure prob.
2010 US-China
Winter School
1
m P
d
(
exp
m
2d
2
)
2
ln
2
ln 1
ln ln (1-PF)-1
P, probability density
An aside: Weibull Statistics
d
, applied stress
PF
m ln
ln
0
m
m
1.0
PF
1
ln
exp
0
m1
m2
Note: same „average‟
fracture strength, but
m1<m2 (broader distribution of strengths).
, applied stress
Richard K. Brow
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IMI-29
Room temperature tensile tests of pristine silica fibers
drawn and tested in vacuum- bimodal distribution
14GPa
9GPa
Smith and Michalske, 1992
2010 US-China
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IMI-30
Flame-attenuation of optical fibers
Failure strength (GPa)
The Ultimate Strength of Glass Silica Nanowires, G. Brambilla and DN Payne, Nano
Letters, 9[2] 831 (2009)
Fiber diameter (nm)
2010 US-China
Winter School
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IMI-31
E-glass fibers (tensile tests, in air)
Lower soak temperatures
lead to bimodal strength
distributions
Cameron, 1968
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Winter School
Richard K. Brow
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IMI-32
Concentric ring tests,
abraded Corning glass 1737,
two different thicknesses.
Gulati, et al., Ceramic Bulletin,
83[5] 14, 2004
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Winter School
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IMI-33
Mechanical properties depend on glass structure
K/Al-metaphosphate glasses
Baikova, et al. Glass Phys. Chem., 21[2] (1995) 115.
E
Hv
LN
RT
2010 US-China
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IMI-34
Pukh et al., 2005
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IMI-35
MD Simulations of fracture
reveal the development of
cavities that coalesce to
form the failure site
Pedone et al., 2008
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Winter School
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IMI-36
Quenched and annealed soda-lime glasses at 5GPa tension
S. Ito and T. Taniguchi, JNCS (2004)
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IMI-37
There may be experimental evidence for cavitation near
the tips of slow-moving cracks
Aluminosilicate glass, 10-11 m/s, 45% RH, AFM Images
Célarié, et al., PRL (2003)
Formation of „nano-cavities‟ interpreted as evidence for „nanoductile‟ fracture of glass!
2010 US-China
Winter School
Richard K. Brow
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IMI-38
„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)
2010 US-China
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IMI-39
Fatigue
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IMI-40
An example of fatigue in glass
http://www.youtube.com/watch?v=r8q-R9ZISac
2010 US-China
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IMI-41
F a ilu r e S t r e n g t h ( M P a )
10000
In
s ta
P r is t in e , A s - D r a w n
nt
St
1000
En
100
du
an
at
eo
us
ic
Fa
ra
nc
P r is t in e , A n n e a le d
St
t ig
e L
im
it
re
ng
F o r m e d G la s s
th
ue
U s e d G la s s
Ef
fe
ct
Dam aged
G la s s
10
In h e re n t S tru c tu ra l
F la w s
F la w s
F a b r i-
- s c o p ic
c a t io n
Dam age
V is ib le
Dam age
1
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)
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IMI-42
Stress Corrosion: source for static fatigue- the
reduction in strength with time
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IMI-43
Fatigue data on silica fibers
Liquid nitrogen
Room temperature, vacuum
Room temperature, ambient conditions
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IMI-44
Note: residual
stresses increase
susceptibility to
static fatigue
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IMI-46
Double-Cantilever Beam
(DCB) used for controlled
stress intensity and crack
velocity experiments
c
V=dc/dt
K=P2/f(geometry)
S. W. Freiman, D. R. Mulville and P. W. Mast, J. Mater. Sci., 8[11] 1573 (1973).
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IMI-47
Crack propagation kinetics
depend on the stress
intensity
Region I: stress-corrosion
Region II: diffusion-limited
Region III: rapid fracture (KIC)
Region 0: propagation threshold
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Winter School
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IMI-48
Water and stress enhance
crack growth in glass
v=AKIn, where n is the
„stress corrosion
susceptibility factor‟
30%
10%
III
Crack velocity (m/s)
Region I: stresscorrosion
100%
1.0%
0.2%
H2O(l)
0.017%
II
I
SM Wiederhorn, JACerS, 50 407 (1967)
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IMI-49
Stress Intensity Factor, KI (Nm-1/2
)
Richard K. Brow
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Compositionaldependence of vK behavior in
Region I
Borosilicate
Silica
Soda-Lime
Different glasses are
more or less
susceptible to
fatigue effects –
Aluminosilicate
We do not
understand this
compositional
dependence!
2010 US-China
Winter School
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IMI-50
Temperaturedependence of v-K
behavior in Region I
Wiederhorn and Bolz, JACerS, 53, 545 (1970)
2010 US-China
Winter School
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IMI-51
Slow crack growth is a thermally activated process
Chemical rate theory has been used to explain the exponential
form of the V –KI curves:
V
V 0 exp(
E
bK
I
/ RT )
where V0 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
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IMI-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
2010 US-China
Winter School
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IMI-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 (H2N-NH2),
formamide (CH3NO)
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IMI-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)
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IMI-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] 540-45 (1992).
W.B. Hillig, “Model of effect of environmental attack on flaw growth kinetics of glass,” Int. J.
Fract. 143 219-230 (2007)
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IMI-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+-H3O+ inter-diffusion
• Alkali depletion from crack-tip region leads to stress-relaxation
• Crack extension threshold
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IMI-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.
2010 US-China
Winter School
Richard K. Brow
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IMI-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
2010 US-China
Winter School
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IMI-59
Strengthening- What can we do to make
glass stronger (or more reliable)?
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IMI-61
• 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
2010 US-China
Winter School
Richard K. Brow
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IMI-62
Annealed vs. chemically tempered glass
From Jill Glass, Sandia National Labs
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Winter School
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IMI-63
Two-point bend studies of
the failure characteristics of silicate glasses
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Winter School
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IMI-64
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 – www.TNLTool.com
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IMI-65
We have measured failure strains using
a Two-Point Bend technique
1 . 198
TNL Tool and Technology, LLC – www.TNLTool.com
• Face plate velocities: 1 – 10,000 mm/sec
• Liquid nitrogen, room temp/variable humidity.
• Small test volume (25-100mm gauge length).
2010 US-China
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f
D
d
d
*M.J. Matthewson, C.R. Kurkjian, S.T.
E
Gulati,
f J. Am. fCer. Soc., 69, 815 (1986).
IMI-66
The inert failure strain measurements are
reproducible
C u m u la tiv e F a ilu r e P r o b a b ility ( % )
99
90
80
E - G la s s
m = 119
60
A vg
40
= 1 2 .8 1 %
Eight sets of E-glass
fibers, tested in liquid
nitrogen, collected
over two years
20
10
S ilic a
5
m = 103
3
= 1 7 .9 8 %
A vg
1
9
10
11
12
13
14
15
16
17
18
19
20
F a ilu r e S tr a in ( % )
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IMI-67
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) 2343.
Failure strain (%)
13.2
13.0
12.8
12.6
12.4
~180yE-glass
fibers/LN
2 tests
= -0.00013x
+ 12.82
12.2
70
90
110
130
150
170
190
Fiber diameter ( m)
2010 US-China
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IMI-68
Fibers fail at lower strains
in ambient conditions
2.0
ln(ln(1/1-f))
1.0
E-glass3 C1 P1 LN
E-glass3 C2 P1 LN
E-glass3 C3 P1 LN
E-glass3 C3 P1 RH
20%RH, 26ºC
0.0
-1.0
-2.0
m = 117, 12.08%
m = 113, 12.05%
m = 131, 12.09%
m = 142, 6.29%
LN2
-3.0
-4.0
-5.0
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
ln(failure strain, %)
2010 US-China
Winter School
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IMI-69
Fatigue effects can be characterized
Weibull Plot of 4A (0.0% B2O3)
Chamber purged with
controlled humidity
RH / Temp. Sensor
Cumulative Failure Probability (%)
99
4A
o
24 C, varied RH
mAvg = 181
90
80
60
40
80%
RH
20
10%
RH
Increasing RH
10
5
Tested at 24 C and
different relative
humidities.
FPV = 4000 m/s
3
1
5
5.5
6
6.5
7
Failure Strain (%)
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IMI-70
Aging effects have also been characterized
Ca-aluminoborosilicates
4A Aged at
o
80% RH, 50 C
Tested using:
LN2, 4000 m/s
90
80
60
16.0
40
Fresh
2 days
4 days
7 days
14 days
28 days
20
10
5
Aging of 4A
Aging of 4A2
Aging of 4C (set 1)
Aging of 4C (set 2)
15.0
Failure Strain (%)
Cumulative Failure Probability (%)
99
14.0
13.0
12.0
11.0
10.0
9.0
B-free composition
8.0
3
7.0
6.0
0.0
1
3
4
5
6 7 8 9 10 12 14 1618
10.0 20.0 30.0 40.0 50.0
Time (Days)
Failure Strain (%)
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IMI-71
What might inert 2pb studies tell us about
the failure characteristics of silicate glasses?
2010 US-China
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IMI-72
Compositions Studied
• xNa2O * (100-x)SiO2
• x = 0, 7, 10, 15, 20, 25, 30, 35
• xK2O * (100-x)SiO2
• x = 0, 4.5, 7, 10, 15, 20, 25
• 25Na2O * xAl2O3 * (75-x)SiO2
• x = 0, 5, 10, 15, 20, 25, 30, 32.5
• xNa2O * yCaO * (100-x-y)SiO2
– Compositions studied by Ito, et al.
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IMI-73
Na-silicate inert failure strains depend on composition
Cumulative Failure Probability (%)
99
0-100
NaSi
90
80
25-75
NaSi
60
40
20
7-93
NaSi
15-85
NaSi
10
5
3
10-90
NaSi
30-70
NaSi
20-80
NaSi
35-75
NaSi
xNa2O * (100-x)SiO2
Avg m ~ 259
1
14
15
16
17
18
19
20
21
22
23
24 25
Failure Strain (%)
2010 US-China
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IMI-74
Sodium silicate properties
UMR
Bokin
Takahashi K.
Karapetyan
Livshits
70.0
Increasing NBO‟s
65.0
25.0
LN4000
23.0
Failure Strain (%)
Elastic Modulus (GPa)
75.0
60.0
21.0
19.0
17.0
xNa2O * (1-x)SiO2
55.0
0.00
0.10
0.20
0.30
0.40
15.0
0.00
0.20
0.30
0.40
Mole Fraction Na2O
Mole Fraction Na2O
2010 US-China
Winter School
0.10
Richard K. Brow
[email protected]
IMI-75
Na-Al-silicate inert failure strains depend on
composition
Cumulative Failure Probability (%)
99
25-32.5-42.5
90
NaAlSi
80
60
25-30-45
NaAlSi
25-10-65
NaAlSi
25-25-50
NaAlSi
25-5-70
NaAlSi
40
20
10
5
3
1
12
25-75
Na-Si
25-20-55
NaAlSi
25-15-60
NaAlSi
13
25Na2O * (x)Al2O3 * (75-x) SiO2
14
15
16
17
18
19
20
21
22
Failure Strain (%)
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-76
Na-Al-silicate properties depend on structure
21.0
85.0
75.0
70.0
65.0
60.0
55.0
0.00
Greater cross-linking:
“stiffer” structure
0.10
0.20
0.30
19.0
18.0
Fully
„cross-linked‟
17.0
16.0
15.0
14.0
0.40
13.0
0.00
0.10
0.20
0.30
Mole Fraction Al2O3
Mole Fraction Al2O3
2010 US-China
Winter School
0.25Na2O * (x)Al2O3
(0.75-x) SiO2
20.0
Failure Strain (%)
Elastic Modulus (GPa)
80.0
UMR
Livshits
Yoshida
Richard K. Brow
[email protected]
IMI-77
Inert failure strain decreases for ‘crosslinked’ structures
26.0
NAS
Failure Strain, %
24.0
NS
KS
22.0
SLS
20.0
18.0
16.0
14.0
12.0
2.80
3.00
3.20
3.40
3.60
3.80
4.00
Bridging Oxygens/Former
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-78
Failure strain depends on elastic modulus
NAS
NS
KS
NB
SLS
Silica
CABS
TV Panel
E-Glass
C-0317
Failure Strain, %
25.0
20.0
15.0
10.0
5.0
25.0
35.0
45.0
55.0
65.0
75.0
85.0
Elastic Modulus (GPa)
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-79
Do these measurements provide information
about the strength of glass?
…depends on what we know about
the elastic modulus
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-80
Elastic modulus depends on strain
E-glass fibers
Na/Li-phosphate fibers
Bruckner, Strength of Inorg. Glass 1986
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-81
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( ) = Y0+Y1 +(Y2/2) 2 ;
2010 US-China
Winter School
f
= f[(2/3)Y0+(Y1/6) f]
Richard K. Brow
[email protected]
IMI-82
Failure strengths can be calculated if Y( ) is known
25.0
14.0
20.0
stress
12.0
Pukh, et al.
10.0
15.0
strain
8.0
10.0
Inert Failure Strain (%)
Mechanical Property (GPa)
16.0
6.0
4.0
5.0
0.0
10.0
20.0
30.0
40.0
mole % Na2O
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-83
• 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.
Failure Strength (GPa) .
What role is played by ‘critical flaws’?
16
14
12
10
f
2010 US-China
Winter School
c
6GPa -> 6.7 nm flaw
8
6
4
2
0
0
1
2E
13GPa -> 1.4 nm flaw
2
5
10
15
Griffith Flaw Size (nm)
Recall processing effects
Richard K. Brow
[email protected]
IMI-84
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.
99
Advantex C2P5
o
2:00 at 1180 C
m=7
Avg = 10.36%
90
80
60
Cumulative Failure Probability (%)
Cumulative Failure Probability (%)
99
Advantex C2 P4
o
2:00 at 1200 C
m=9
Avg = 10.88%
40
20
10
5
3
Advantex C2 P3
o
2:00 at 1250 C
m = 60
Avg = 12.11%
1
6
2010 US-China
Winter School
7
8
Advantex C2 P2
12:00 at 1350oC
m = 129
Avg = 12.18%
9
10
90
80
60
40
20
Advantex C2 P10
o
2:00 at 1350 C
m = 35
Avg = 11.73%
10
5
Advantex C2 P9
o
1:00 at 1350 C
m=4
Avg = 9.34%
3
1
11 12 13
Failure Strain (%)
Advantex C2 P2
o
12:00 at 1350 C
m = 129
Advantex C2 P8
o
Avg = 12.18%
0:30 at 1350 C
m=3
Avg = 8.51%
Richard K. Brow
[email protected]
4
5
6
7
Advantex C2 P11
o
3:00 at 1350 C
m = 55
Avg = 11.88%
8
9 10 11 12 13
Failure Strain (%)
IMI-85
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?
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 TL+50ºC.
1 3 .0
G la s s b e h a v e s
s t r a n g e ly a t T L - 5 0
T F ~ 1 3 5 0 ºC
1350
1 2 .0
1300
D e g r a d in g
I m p r o v in g
F a ilu r e S t r a in , %
1 0 .0
9 .0
1250
8 .0
I m p r o v in g
1200
7 .0
T L ~ 1 2 0 0 ºC
M e lt in g T e m p e r a t u r e ( C )
1 1 .0
Crystallites form
6 .0
1150
F a ilu r e S t r a in s
5 .0
M e lt in g T e m p e r a t u r e
T h e r m a l H is t o r y
4 .0
1100
0 :0 0
2010 US-China
Winter School
2 :0 0
4 :0 0
6 :0 0
8 :0 0
1 0 :0 0 1 2 :0 0 1 4 :0 0 1 6 :0 0 1 8 :0 0 2 0 :0 0 2 2 :0 0 2 4 :0 0 2 6 :0 0 2 8 :0 0
Richard
T im eK. Brow
[email protected]
IMI-87
How does glass break?
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-88
Inert ‘failure rate’ studies
99
99
90
m
1 0 -1 0 -8 0
C u m u la tiv e F a ilu r e P r o b a b ility ( % )
C u m u la tiv e F a ilu r e P r o b a b ility ( % )
S ilic a
=132
A vg
80
60
40
20
5
‘Normal’ Inert
m / s Fatigue 1 0 , 0 0 0
10
m /s
5
3
In c r e a s i n g V fp
1
1 6 .5
90
SLS
80
m A vg= 1 8 9
60
40
20
10
5
3
4 ,0 0 0
m /s
5
m /s
D e c r e a s i n g V fp
1
17
1 7 .5
18
1 8 .5
F a ilu re S tra in (% )
2010 US-China
Winter School
Inert Delayed Failure
Effect
16
1 6 .5
17
1 7 .5
18
F a ilu re S tra in (% )
Richard K. Brow
[email protected]
IMI-89
ln (failure strain, %)
Inert ‘failure rate’ studies
2.9
2.89
2.88
2.87
2.86
2.85
2.84
2.83
2.82
2.81
2.8
n = 1 / (d ln( / d ln(Vfp) )
10-10-80 SLS
Silica
0.0
2010 US-China
Winter School
n = 365
1.0
2.0
3.0
4.0
5.0 6.0
ln (Vfp)
Richard K. Brow
[email protected]
7.0
8.0
9.0 10.0
IMI-90
The inert delayed failure effect depends on structure
Inert Delayed Failure Effect
( 50- 4000)/ 50)
0.100
NAS
NS
KS
SLS
0.080
0.060
0.040
0.020
0.000
-0.020
2.80
3.00
3.20
3.40
3.60
3.80
4.00
Bridging Oxygens/Former
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-91
Failure strain measurements also correlate with
crack initiation loads
0.25Na2O * (x)Al2O3 * (0.75-x) SiO2
21
2.0
20
Failure Strain (%)
19
1.5
1.2
More Brittle
Crack initiation load (N)
1.7
1.0
0.7
17
16
15
14
0.5
Satoshi Yoshida, 2003
0.2
-0.10
0.00
0.10
0.20
0.30
0.40
Mole Fraction Al2O3
2010 US-China
Winter School
18
Richard K. Brow
[email protected]
13
-0.10
0.00
0.10
0.20
0.30
0.40
Mole Fraction Al2O3
IMI-92
Failure strain measurements may provide
information about ‘less brittle’ glasses
Setsuro Ito,
2002
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-93
“Brittleness parameter” has been determined from
indentation measurements
3/2
Brittlenes
s
B
2 . 39 P
1/ 4
C
a
P is applied load, C is crack
length, and a is Vickers
indentation diagonal length
Setsuro Ito, 2002
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-94
Soda-lime silicate glasses exhibit the ‘delayed failure’
effect
Cumulative Failure Probability (%)
99
90
80
15-5-80
SLS
mAvg = 345
60
40
20-10-70
SLS
mAvg = 326
Closed symbols
4000 mm/sec,
Open symbols
50 mm/sec
20
10
5
15-10-75
SLS
mAvg = 261
3
Each glass possesses a large IDFE.
1
17.5
18
18.5
19
19.5
20
20.5
21
Failure Strain (%)
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-95
‘Brittleness’ and ‘inert delayed failure’
may be related
IDFE (Missouri S&T)
7.0
6.0
Soda-lime &
borosilicate glasses
5.0
4.0
3.0
2.0
1.0
0.0
Silica
-1.0
-2.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Brittleness (Ito)
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-96
Is IDFE related to network relaxation?
Na diffusion
NBO motion?
Day & Rindone, 1962
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-97
Is there a universal dependence of glass failure
characteristics on network structure?
WOULD ‘INSTANTANEOUS’ FAILURE
STRAINS ALL FALL ON A STRAIGHT
LINE??
Failure strain, %
24.0
20.0
16.0
12.0
NS
NAS
KS
SLS
Silica
CABS
TV Panel
E-glass
C-0317
TiMgAlSi
8.0
35.0
45.0
LN2 tests at 4000 /sec
2010 US-China
Winter School
depends on E (IDFE≤0)
2. Silica is anomalous
LN depends on network relaxation (IDFE>0)
LN
55.0
65.0
75.0
85.0
95.0
105.0
Young's modulus (GPa)
Richard K. Brow
[email protected]
IMI-98
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
(Vfp).
 Structure with non-bridging oxygens fail at larger strains with
slower Vfp.
 ‘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?
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-99
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
2010 US-China
Winter School
Richard K. Brow
[email protected]
IMI-100