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

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

Bond Breaking Leads to Characteristic Features Log U v   K c r Log K = Log (Y  c ½ ) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 2

Elastic Modulus Is Related To The Strength of Nearest Neighbor Bonds F U r 0 r r 0 r Force = F = - dU/dr Stiffness = S 0 = (dU 2 /dr 2 ) r = r0 Elastic Modulus = E = S / r 0 jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 3

There Are Several Important Properties in Mechanical Behavior: Elastic Modulus – Governs Deflection S e Hardness Measures Surface Properties Strength – Governs Load Bearing Capacity Toughness – Governs Crack Propagation jmech@mse.ufl.edu 4 Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11

P Stress = P / A A = Cross-sectional Area =  r 2 P = Load On Sample r P jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 5

Strain =  L / L P A = Cross-sectional Area =  r 2 L L = Length  L = Change In Length  L r P jmech@mse.ufl.edu 6 Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11

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 ) jmech@mse.ufl.edu 7 Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11

Special Cases of Loading Often Occur (a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure. jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 8

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

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

(a) Tensile stress. (b) Shear stress. (c) Hydrostatic pressure. jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 11

In the case of hydrostatic pressure, the bulk modulus is appropriate.   V/ V 0 jmech@mse.ufl.edu 12 Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11

There is a relationship between E, G and K (and of course Poisson’s ratio,  ) 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.). jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 13

There is a relationship between E, G and K (and of course Poisson’s ratio,  ) G = E / [2 (1+  )] K = E / [3(1-2  )] So, when we determine any two parameters, (for isotropic materials) we can calculate the others. jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 14

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

Elastic Modulus = Stress / Strain P A = Area =  r 2 A = Brittle B = Ductile S or  Strain = e or  S =Stress = P / A r Strain =  L / L P jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 16

To measure E from flexure, need to calculate the stress and strain. P  b h A A  = 3PL / (2 b h 2 )  / L jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 17

Pulse echo technique is often used to measure modulus C. Kittel, Intro. To Solid State Physics, J. Wiley & Sons jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 18

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

In the simplest case for isotropic materials there are direct relationships. v L = [ E /  ] 1/2 (Longitudinal waves) v S = [ G /  ] 1/2 (Shear waves) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 20

For the beam vibration technique, we stimulate the flexural modes. For beam bending: E = (0.946 L 4 f 2  S) / h 2 f = frequency S = shape factor H = width and height L = length  = density Fig 8-5 jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 21

In general, E decreases as the size and concentration of the alkali cations increases Fig 8-6a jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 22

E decreases as the size and concentration of the alkali cations increase E K  x  G Fig 8-6b jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 23

E decreases as the size and concentration of the alkali cations increases Fig 8-6c jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 24

E increases with addition of metal oxide (MO) [except PbO] Na 2 O  x MO  5SiO 2 Fig.8-7 (Varshneya) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 25

Lithia-aluminosilicates have greater E values than SiO 2 Fig.8-8 jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 26

In general, bulk moduli of silicate glasses increase with temperature (except at low temperatures [0 - 60K]) N.B. - the compressibility,  is being graphed in the figure (Fig. 8-9). (The compressibility is the reciprocal of the bulk modulus.) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Charge Conduction in Glass - Lecture 1 27

Composition and structure affect the values of elastic moduli. N.B.: at low (< 10mol%) alkali content, E with B 2 O 3 addition. However, with greater alkali content glasses addition of B 2 O 3 leads to a maximum in E. jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 28

Complications of silicate glasses makes predictions difficult F = [-a / r n ]+ b / r m (Condon-Morse) Force = F = - dU/dr Stiffness = S 0 = (dU 2 /dr 2 ) r = r0 Elastic Modulus = E = S / r 0 jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 29

Complications of silicate glasses makes predictions difficult F = [-a / r n ]+ b / r m (Condon-Morse) Force = F = - dU/dr Stiffness = S 0 = (dU 2 /dr 2 ) r = r0 Elastic Modulus = E = S / r 0 General rules: x decreases 1. E increases as r 0 2. E increases as valence, i.e., q a x q c 3. E affected by bond type (covalent, ionic, metallic). 4. E affected by structure (density, electron configuration, etc.) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 30

Microhardness is a measure of surface properties and can be related to elastic modulus, toughness and surface tension. Hardness = Force / Area jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 31

Many hardness tests are available jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 32

The most common microhardness diamond tips for glasses are Vickers and Knoop Fig. 8-12 Hardness = Force / Area Hv = 1.854 F / D 2 (Actual area) KHN = 14.23 F / L 2 (Projected area) jmech@mse.ufl.edu Virtual Course on Glass - The Properties of Glass: Mechanical Properties of Glass - Lecture 11 33