Failure Strain Studies ofFailure Strain Studies ofSilicate Glass FibersSilicate Glass Fibers
Nathan P. Lower and Richard K. BrowUniversity of Missouri-Rolla
Ceramic Engineering DepartmentRolla, MO 65409
American Ceramic Society MeetingApril 20, 2004
Mechanical Properties Depend on Glass Structure
Baikova, et al. Glass Phys. Chem., 21[2] (1995) 115.
E
Hv
σLN
σRT
K/Al-metaphosphate glasses
Bulk properties are often studied.
Flaw Size (m)1e-9 1e-8 1e-7 1e-6 1e-5 1e-4
Failu
re S
treng
th (M
Pa)
1
10
100
1000
10000
InherentFlaws
StructuralFlaws
Fabri-cation
µ-scopicDamage
VisibleDamage
Pristine, As-Drawn
Pristine, Annealed
Formed Glass
Used Glass
DamagedGlass
StaticFatigue
Effect
Instantaneous StrengthEndurance Limit
Intrinsic Strength is Difficult to Measure
Mould, R.E. (1967)
Theoretical Strength
Fiber Puller Used to Produce Pristine Fibers
Box FurnaceBox Furnace
Drawing CageDrawing Cage
• Glass is thermally conditioned then transferred to a box furnace.
• Cooling coil controls surface viscosity.• Pulling speed controls fiber diameter.• “Pristine” 10 cm length fibers produced.• Fiber diameters ~125 µm.• Fibers can be tested immediately.TNL Tool and Technology, LLC – www.TNLTool.com
Failure Strains are Measured Using a Two-Point Bender
• Face plate velocities: 1 – 10,000 µm/sec• Liquid nitrogen, room temp/variable humidity.• Small test volume (25-100µm gauge length).• E~Young’s modulus; acoustic pulse.
EdD
d
ff
f
×=
⎟⎠⎞
⎜⎝⎛
−⋅
=
εσ
ε 198.1
*M.J. Matthewson, C.R. Kurkjian, S.T. Gulati, J. Am. Cer. Soc., 69, 815 (1986).
TNL Tool and Technology, LLC – www.TNLTool.com
Elastic Modulus Changes with Applied Strain
Bruckner, Strength of Inorg. Glass 1986
Glasses Studied
E-Glass.Commercial TV Panel Glass.XNa2O * (100-X)SiO2
X = 0, 7, 10, 15, 20, 25, 30, 35
25Na2O * XAl2O3 * (75-X)SiO2X = 0, 5, 10, 15, 20, 25, 30, 32.5
XK2O * (100-X)SiO2X = 0, 4.5, 7, 10, 15, 20, 25
Failure Distributions Depend on Processing History
Failure Strain (%)5 6 7 8 9 10 11 12 13 15 17 19 21 23 25
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
80
90
99
Optimized Processingm = 237, εAvg = 20.85%
LN2 Strains25Na2O * 75SiO2
Increasing Melt Time
Each set representsa new batch ~35g
Failure Strain (%)5 6 7 8 9 10 11 12 13 14 15 16
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
1550oC (short melt time)m = 5, εAvg = 10.63%
1550oC for 0:45m = 8, εAvg = 11.93%
LN2 Strains20Ca-17.5Al2O3-2.5B2O3-60SiO2
1550oC (short melt time)m = 36, εAvg = 10.36%
1550oC for 8:35m = 192, εAvg = 13.9%
Commercial Glasses
Failure Strain (%)5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
1400oC 6 hrs (crushed)m = 218, εAvg = 17.34%
1350oC for 0:30m = 8, εAvg = 11.93%
LN2 Strains
1350oC (30 min)m = 6.5, εAvg = 13.89%
1550oC for 4:00m = 141, εAvg = 12.99%
E-Glass TV Glass
Longer melting times and better mixing significantly improves the failure distributions.
What Causes These Thermal History Effects?
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.
Does melt / glass homogeneityplay a role?
02468
10121416
0 5 10 15
Griffith Flaw Size (nm)
Failu
re S
treng
th (G
Pa)
13GPa -> 1.4 nm flaw
6GPa -> 6.7 nm flaw
Two Na-borosilicate melts withdifferent colorants. One melt was quenchedthen added to the second. Combined glasswas melted for 2 hrs at 1100oC and poured.
21
2⎟⎠⎞
⎜⎝⎛=
cE
f πγσ
How Can We Characterize Homogeniety?
Light Scattering?
1.435
1.44
1.445
1.45
1.455
1.46
1.465
1.47
1.475
0 25 50 75 100Temperature (C)
Ref
ract
ive
Inde
x (n
)
RI Oil (Cargille)Silica
V. I. Shelyubskii, 1987
Differentproductionrates
How Can We Characterize Homogeniety?
V. I. Shelyubskii, 1987Failure Strain (%)
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
1400oC 6 hrs (crushed)m = 218, εAvg = 17.34%
1350oC for 0:30m = 8, εAvg = 11.93%
LN2 Strains
1350oC (30 min)m = 6.5, εAvg = 13.89%
1550oC for 4:00m = 141, εAvg = 12.99%
E-Glass TV Glass
TV Panel Glass
0.00
0.20
0.40
0.60
0.80
1.00
1.20
10.0 30.0 50.0 70.0 90.0Temperature (C)
% M
ax T
rans
mis
sion
Narrow Failure StrainsBroad Failure Strains
nG <> nO
nG = nO
Failure Strain (%)14 15 16 17 18 19 20 21 22 23 24 25
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
35
10
20
40608090
99
15-85NaSi
0-100NaSi
20-80NaSi
25-75NaSi
30-70NaSi
35-75NaSi10-90
NaSi
7-93NaSi
Na-Silicate Inert Failure Strains
Avg m ~ 259 XNa2O * (100-X)SiO2
55.0
60.0
65.0
70.0
75.0
0.00 0.10 0.20 0.30 0.40Mole Fraction Na2O
Ela
stic
Mod
ulus
(GP
a)
UMRBokinTakahashi K.KarapetyanLivshits
Sodium Silicate Properties
15.0
17.0
19.0
21.0
23.0
25.0
0.00 0.10 0.20 0.30 0.40
Mole Fraction Na2O
Failu
re S
train
(%)
LN4000
Increasing NBO’s
XNa2O * (1-X)SiO2
Failure Strain (%)15 16 17 18 19 20
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
35
10
20
4060809099
15-85KSi
7-93KSi 10-90
KSi
4-96KSi
20-80KSi
25-75KSi
0-100KSi
K-Silicate Inert Failure Strains
Avg m ~ 267 XK2O * (100-X)SiO2
15.0
16.0
17.0
18.0
19.0
20.0
21.0
0.00 0.10 0.20 0.30
Mole Fraction K2O
Failu
re S
train
(%)
Potassium Silicate PropertiesLN4000
35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0
0.00 0.10 0.20 0.30 0.40
Mole Fraction K2O
Ela
stic
Mod
ulus
(GP
a)
UMRFuxiGamberg
XK2O * (1-X)SiO2
Failure Strain (%)12 13 14 15 16 17 18 19 20 21 22
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
25-5-70NaAlSi
25-10-65NaAlSi
25-75Na-Si
25-25-50NaAlSi
25-15-60NaAlSi
25-20-55NaAlSi
25-30-45NaAlSi
25-32.5-42.5NaAlSi
Na-Al-Silicate Inert Failure Strains
25Na2O * (X)Al2O3 * (75-X) SiO2
55.0
60.0
65.0
70.0
75.0
80.0
85.0
0.00 0.10 0.20 0.30 0.40Mole Fraction Al2O3
Ela
stic
Mod
ulus
(GP
a)
UMRLivshitsYoshida
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
0.00 0.10 0.20 0.30Mole Fraction Al2O3
Failu
re S
train
(%)
Na-Al-Silicate Properties
Greater cross-linking:“stiffer” structure
Fullycross-linked
0.25Na2O * (X)Al2O3 * (0.75-X) SiO2
What is Responsible for the Change in the Inert Failure Strains?
13.0
15.0
17.0
19.0
21.0
23.0
-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20Non-bridging oxygens/network former
LN2 F
ailu
re S
train
, %
Na-silicatesNa-aluminosilicatesK-SilicatesSilica
Fully cross-linked:25-30-45 NaAlSi25-32.5-42.5 NaAlSi
0.0
5.0
10.0
15.0
20.0
25.0
30.0
20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0Elastic Modulus (Gpa)
Iner
t Fai
lure
Stra
in (%
)
Sodium SilicatesSodium AluminosilicatesSodium BoratesSilicaE-Type GlassesPotassium SilicatesTV Panel Glass20-10-70 SLS
What is the Dependence of Elastic Modulus on Failure Strain?
Increase Eo → Decrease εf
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
-5.0 5.0 15.0 25.0 35.0Mole Fraction Na2O
100∗((ε f
(50 µm
/s) -ε f
(400
0 µm
/s)/ ε
f(50µm
/s))
IDFE - Inert Delayed Failure Effect
Failure Strain (%)13 14 15 16 17 18 19 20 21 22 23 24 25 26
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
25-75NaSi
15-85NaSi
30-70Na-Si
7-93NaSi
XNa2O * (100-X)SiO2
Testing at different speeds produces different failure strains.
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
4.5
5.5
-0.05 0.05 0.15 0.25 0.35
Mole Fraction Al2O3
100∗((ε f
(50 µm
/s) -ε f
(400
0 µm
/s)/ ε
f(50µm
/s))
IDFE - Inert Delayed Failure Effect
Failure Strain (%)13 14 15 16 17 18 19 20 21 22 23
Cum
ulat
ive
Failu
re P
roba
bilit
y (%
)
1
3
5
10
20
40
60
8090
99
25-5-70NaAlSi
25-10-65NaAlSi
25-75Na-Si
25-25-50NaAlSi
25-32.5-42.5NaAlSi
0.25Na2O * XAl2O3 * (0.75-X)SiO2
Fully cross-linked
What is Responsible for the Inert Delayed Failure Effect?
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20Non-bridging oxygens/network former
Iner
t Del
ayed
Fai
lure
Eff
ect,
( ε50
- ε40
00)/ ε
50
Na-silicatesNa-aluminosilicatesK-SilicatesSilica
Unanswered Questions
What do the failure properties tell us about glass structure?
Why do NaSi failure strains increase when the glass network should be “weakening”?
Internal friction studies – structural relaxation?
Are the decreases in NaAlSi failure strains with the addition of Al2O3 related to nano-indentation studies?
Is the IDFE Effect Related to Internal Friction?
Day & Rindone, 1962
NBO relaxation?
Na hopping
Unanswered Questions
What do the failure properties tell us about glass structure?
Why do NaSi failure strains increase when the glass network should be “weakening”?
Internal friction studies – structural relaxation?
Are the decreases in NaAlSi failure strains with the addition of Al2O3 related to nano-indentation studies?
Are the Failure Strains Related to Crack Initiation?
13
14
15
16
17
18
19
20
21
-0.10 0.00 0.10 0.20 0.30 0.40Mole Fraction Al2O3
Failu
re S
train
(%)
0.2
0.5
0.7
1.0
1.2
1.5
1.7
2.0
-0.10 0.00 0.10 0.20 0.30 0.40Mole Fraction Al2O3
Cra
ck in
itiat
ion
load
(N)
Satoshi Yoshida, 2003
0.25Na2O * (X)Al2O3 * (0.75-X) SiO2
How are High εf and IDFE Related to “Less Brittle” Glasses?
Setsuro Ito, 2002
Do large failure strains, or a large IDFE suggest a more responsive,“less brittle” structure?
ConclusionsInert failure strains are sensitive to the composition/structureof glass fibers.
εf increases when NBO’s replace BO’sAlkali silicate and sodium aluminosilicate series.
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 ‘anomalous inert delayed failure effect’.Is the IDFE effect due to relaxation of NBO’s?
Thermal history effects appear to be related to melt homogeneity.
The length scale has yet to be determined.
Acknowledgements
We would like to thank the NSF/Industry/University Center for Glass Research for support in the development of the fiber preparation and testing equipment at UMR.
Lucas and Trent Lower (Tool & Die specialists –TNL Tool and Technology, LLC) for their assistance in producing the fiber drawing and testing equipment.
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