![Page 1: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/1.jpg)
Mechanical Properties of Glass
Elastic Modulus and Microhardness[Chapter 8 – The “Good Book”*]
Strength and Toughness [Chapter 18] Fracture mechanics tests Fractography Stress Corrosion Fracture Statistics
*A. Varshneya, “Fundamentals of Inorganic Glasses”,Society of Glass Technology (2006)
[email protected] 1Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11
![Page 2: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/2.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 2
Log v
Log K = Log (Yc ½)
U
rKc
Bond Breaking Leads to Characteristic Features
![Page 3: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/3.jpg)
Elastic Modulus Is Related To The Strength of Nearest Neighbor Bonds
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 3
U
r
Force = F = - dU/dr
Stiffness = S0 = (dU2/dr2) r = r0
Elastic Modulus = E = S / r0
r0F
rr0
![Page 4: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/4.jpg)
[email protected] Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11
4
There Are Several Important Properties in Mechanical Behavior:
Elastic Modulus – Governs Deflection
Strength – Governs Load Bearing CapacityToughness – Governs Crack Propagation
S
e
Hardness Measures Surface Properties
![Page 5: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/5.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 5
P
P
A = Cross-sectional Area = r 2
Stress = P / A
r
P = Load On Sample
![Page 6: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/6.jpg)
[email protected] Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11
6
P
P
A = Cross-sectional Area = r 2
Strain = L / L
r
L
L
L = Length
L = Change In Length
![Page 7: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/7.jpg)
[email protected] Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11
7
Infinitesimal cube represents triaxial state of stress.
y = (1 /E)[y - ( x + z)] xy = [2(1+) / E] (xy)x = (1 /E)[x - ( y + z)] yz = [2(1+) / E] (yz)z = (1 /E)[z - ( y + x)] zx = [2(1+) / E] (zx)
![Page 8: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/8.jpg)
Special Cases of Loading Often Occur
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 8
(a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure.
![Page 9: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/9.jpg)
In uniaxial loading in the x direction, E (or Y) relates the stress, x, to the strain, x.
x = E x
y = z= - x
xy = G p = K V
[email protected] Virtual Course on Glass - The Properties of Glass: Charge Conduction in Glass - Lecture 1 9
![Page 10: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/10.jpg)
In the case of shear loading, the shear modulus is appropriate
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 10
![Page 11: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/11.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 11
(a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure.
![Page 12: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/12.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 12
V/ V0
In the case of hydrostatic pressure, the bulk modulus is appropriate.
![Page 13: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/13.jpg)
There is a relationship between E, G and K (and of course Poisson’s ratio, )
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 13
G = E / [2 (1+)]
K = E / [3(1-2)]
Note: -1 ≤ ≤ 0.5.
(When = 0.5, K ∞ and E 3G. Such a material is called incompressible.).
![Page 14: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/14.jpg)
There is a relationship between E, G and K (and of course Poisson’s ratio, )
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 14
G = E / [2 (1+)]
K = E / [3(1-2)]
So, when we determine any two parameters, (for isotropic materials) we can calculate the others.
![Page 15: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/15.jpg)
There are several techniques used to measure the elastic modulus:
A. Stress-strain directly (load-displcament)1. tension2. 3-pt flexure3. 4-pt flexure4. Hydrostatic pressure5. Torque on rod
B. Ultrasonic wave velocity1. Pulse echo2. Direct wave
C. Beam [email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 15
![Page 16: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/16.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 16
P
P
A = Area = r 2
r
Elastic Modulus = Stress / Strain
S or
Strain = e or
A = Brittle
B = Ductile
S =Stress = P / A
Strain = L / L
![Page 17: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/17.jpg)
To measure E from flexure, need to calculate the stress and strain.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 17
A A
= 3PL / (2 b h2) / L
b
h
P
![Page 18: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/18.jpg)
Pulse echo technique is often used to measure modulus
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 18
C. Kittel, Intro. To Solid State Physics, J. Wiley & Sons
![Page 19: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/19.jpg)
Pulse Echo technique is one of the most reliable.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 19
![Page 20: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/20.jpg)
In the simplest case for isotropic materials there are direct relationships.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 20
vL = [ E / ]1/2
(Longitudinal waves)
vS = [ G / ]1/2
(Shear waves)
![Page 21: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/21.jpg)
For the beam vibration technique, we stimulate the flexural modes.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 21
Fig 8-5
For beam bending:E = (0.946 L4 f2 S) / h2
f = frequencyS = shape factorH = width and heightL = length = density
![Page 22: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/22.jpg)
In general, E decreases as the size and concentration of the alkali cations increases
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 22
Fig 8-6a
![Page 23: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/23.jpg)
E decreases as the size and concentration of the alkali cations increase
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 23
E
K
Gx
Fig 8-6b
![Page 24: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/24.jpg)
E decreases as the size and concentration of the alkali cations increases
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 24
Fig 8-6c
![Page 25: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/25.jpg)
E increases with addition of metal oxide (MO) [except PbO]
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 25
Na2O x MO 5SiO2
Fig.8-7 (Varshneya)
![Page 26: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/26.jpg)
Lithia-aluminosilicates have greater E values than SiO2
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 26
Fig.8-8
![Page 27: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/27.jpg)
In general, bulk moduli of silicate glasses increase with temperature (except at low temperatures [0 - 60K])
[email protected] Virtual Course on Glass - The Properties of Glass: Charge Conduction in Glass - Lecture 1 27
N.B. - the compressibility, is being graphed in the figure (Fig. 8-9).
(The compressibility is the reciprocal of the bulk modulus.)
![Page 28: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/28.jpg)
Composition and structure affect the values of elastic moduli.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 28
N.B.: at low (< 10mol%) alkali content, E with B2O3 addition.
However, with greater alkali content glasses addition of B2O3 leads to a maximum in E.
![Page 29: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/29.jpg)
Complications of silicate glasses makes predictions difficult
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 29
F = [-a / rn ]+ b / rm
(Condon-Morse)Force = F = - dU/drStiffness = S0 = (dU2/dr2) r = r0Elastic Modulus = E = S / r0
![Page 30: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/30.jpg)
Complications of silicate glasses makes predictions difficult
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 30
F = [-a / rn ]+ b / rm
(Condon-Morse)Force = F = - dU/drStiffness = S0 = (dU2/dr2) r = r0Elastic Modulus = E = S / r0
General rules:1. E increases as r0
x decreases2. E increases as valence, i.e., qa x qc3. E affected by bond type (covalent, ionic,
metallic).4. E affected by structure (density, electron
configuration, etc.)
![Page 31: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/31.jpg)
Microhardness is a measure of surface properties and can be related to elastic modulus, toughness and surface tension.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 31
Hardness = Force / Area
![Page 32: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/32.jpg)
Many hardness tests are available
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 32
![Page 33: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/33.jpg)
The most common microhardness diamond tips for glasses are Vickers and Knoop
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 33
Hv = 1.854 F / D2 (Actual area) KHN = 14.23 F / L2 (Projected area)
Hardness = Force / Area Fig. 8-12
![Page 34: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/34.jpg)
[email protected] Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11
34
Note plastic flow in silicate glass using a Vickers microhardness indenter.
Plastic flow in Se glass using a Brinell microhardness indentation.
Fig. 8-13 a & b
![Page 35: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/35.jpg)
Diamond hardness indentations can result in elastic and plastic deformation.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 35
![Page 36: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/36.jpg)
Microhardness can be measured dynamically
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 36
HvL = 37.84 F / h2max
(from loaded depth, hmax)
Hvf = 37.84 F / h2f
(from unloaded depth, hf)
F = a1h + a2 h2 (equation fit to curve)
HvL2 (GPa)= 37.84 a2 { load independent hardness; a2 = N/m2}
Refs. 34 and 35 in Chapter 8.
![Page 37: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/37.jpg)
Microhardness can be measured dynamically
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 37
Measure dF/dh on initial unloading
Er = ( / 2 A) [dF/dh]
Er =[(1-2)/E] + [(1-i2)/ Ei
![Page 38: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/38.jpg)
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 38
Materials & Methods o The energy spent during the nanoindentation process can be categorized as plastic energy (Wpl) and elastic energy (Wel). The indenter penetrates the sample and reaches the maximum penetration (hmax) at Pmax. During the unloading process, the compressed zone recovers and the final depth of the indent (hf)is often much less than hmax.
![Page 39: [Chapter 8 – The “Good Book”*] - · PDF fileMechanical Properties of Glass Elastic Modulus and Microhardness [Chapter 8 – The “Good Book”*] Strength and Toughness [Chapter](https://reader033.vdocuments.net/reader033/viewer/2022051507/5a7778267f8b9aa3618df933/html5/thumbnails/39.jpg)
Elastic Moduli and microhardness are two important mechanical properties.
[email protected] Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 39
Elastic modulus is a macroscopic measure of the strength of bonds at the atomic scale.
Hooke’s law (stress proportional to strain) defines the moduli of linear elastic solids.
For isotropic glasses only two constants are required – others can be calculated. Note: -1 ≤ ≤ 0.5. (When = 0.5, K ∞ and E 3G).
Elastic modulus is best measured using the “pulse echo” or similar technique. For silicate glasses, E 70≈ GPa and ≈ 0.22.
Hardness is a measure of the resistance to penetration. Both densification and material pile-up are observed in glasses.
Vickers indentation is the most common diamond indenter for glasses.For a silicate glass, H v ≈ 5.5 GPa