Mechanical Properties of Glass Elastic Modulus and Microhardness - - PowerPoint PPT Presentation

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Mechanical Properties of Glass Elastic Modulus and Microhardness - - PowerPoint PPT Presentation

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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.

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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)

jmech@mse.ufl.edu 1 Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11

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SLIDE 2

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 2

  Log v Log K = Log (Yc ½) U r

Kc

Bond Breaking Leads to Characteristic Features

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SLIDE 3

Elastic Modulus Is Related To The Strength of Nearest Neighbor Bonds

jmech@mse.ufl.edu 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 r0 F r

r0

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SLIDE 4

jmech@mse.ufl.edu Virtual 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 Capacity Toughness – Governs Crack Propagation

S e

Hardness Measures Surface Properties

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SLIDE 5

jmech@mse.ufl.edu 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

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SLIDE 6

jmech@mse.ufl.edu Virtual 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

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SLIDE 7

jmech@mse.ufl.edu Virtual 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)

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SLIDE 8

Special Cases of Loading Often Occur

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 8

(a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure.

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SLIDE 9

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

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Charge Conduction in Glass - Lecture 1 9

 

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SLIDE 10

In the case of shear loading, the shear modulus is appropriate

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 10

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SLIDE 11

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 11

(a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure.

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SLIDE 12

jmech@mse.ufl.edu 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.

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SLIDE 13

There is a relationship between E, G and K (and of course Poisson’s ratio, )

jmech@mse.ufl.edu 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.).

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SLIDE 14

There is a relationship between E, G and K (and of course Poisson’s ratio, )

jmech@mse.ufl.edu 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

  • thers.
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SLIDE 15

There are several techniques used to measure the elastic modulus:

  • A. Stress-strain directly (load-displcament)
  • 1. tension
  • 2. 3-pt flexure
  • 3. 4-pt flexure
  • 4. Hydrostatic pressure
  • 5. Torque on rod
  • B. Ultrasonic wave velocity
  • 1. Pulse echo
  • 2. Direct wave
  • C. Beam Vibration

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 15

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SLIDE 16

jmech@mse.ufl.edu 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

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SLIDE 17

To measure E from flexure, need to calculate the stress and strain.

jmech@mse.ufl.edu 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

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SLIDE 18

Pulse echo technique is often used to measure modulus

jmech@mse.ufl.edu 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
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Pulse Echo technique is one of the most reliable.

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 19

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In the simplest case for isotropic materials there are direct relationships.

jmech@mse.ufl.edu 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)

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SLIDE 21

For the beam vibration technique, we stimulate the flexural modes.

jmech@mse.ufl.edu 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 = frequency S = shape factor H = width and height L = length  = density

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SLIDE 22

In general, E decreases as the size and concentration of the alkali cations increases

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 22

Fig 8-6a

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SLIDE 23

E decreases as the size and concentration of the alkali cations increase

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 23

E K G

x 

Fig 8-6b

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SLIDE 24

E decreases as the size and concentration of the alkali cations increases

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 24

Fig 8-6c

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E increases with addition of metal oxide (MO) [except PbO]

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 25

Na2O x MO  5SiO2

Fig.8-7 (Varshneya)

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SLIDE 26

Lithia-aluminosilicates have greater E values than SiO2

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 26

Fig.8-8

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SLIDE 27

In general, bulk moduli of silicate glasses increase with temperature (except at low temperatures [0 - 60K])

jmech@mse.ufl.edu 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.)

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SLIDE 28

Composition and structure affect the values of elastic moduli.

jmech@mse.ufl.edu 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.

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SLIDE 29

Complications of silicate glasses makes predictions difficult

jmech@mse.ufl.edu 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/dr Stiffness = S0 = (dU2/dr2) r = r0 Elastic Modulus = E = S / r0

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SLIDE 30

Complications of silicate glasses makes predictions difficult

jmech@mse.ufl.edu 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/dr Stiffness = S0 = (dU2/dr2) r = r0 Elastic Modulus = E = S / r0

General rules:

  • 1. E increases as r0

x decreases

  • 2. E increases as valence, i.e., qa x qc
  • 3. E affected by bond type (covalent, ionic,

metallic).

  • 4. E affected by structure (density, electron

configuration, etc.)

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SLIDE 31

Microhardness is a measure of surface properties and can be related to elastic modulus, toughness and surface tension.

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 31

Hardness = Force / Area

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SLIDE 32

Many hardness tests are available

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 32

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The most common microhardness diamond tips for glasses are Vickers and Knoop

jmech@mse.ufl.edu 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
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SLIDE 34

jmech@mse.ufl.edu Virtual 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
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SLIDE 35

Diamond hardness indentations can result in elastic and plastic deformation.

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 35

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SLIDE 36

Microhardness can be measured dynamically

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 36

HvL = 37.84 F / h2

max

(from loaded depth, hmax) Hvf = 37.84 F / h2

f

(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.
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Microhardness can be measured dynamically

jmech@mse.ufl.edu 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-i

2)/ Ei

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SLIDE 38

jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 38

Materials & Methods

  • 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.

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SLIDE 39

Elastic Moduli and microhardness are two important mechanical properties.

jmech@mse.ufl.edu 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