A) Ring-Cone
3. EXPERIMENTAL PROCEDURES
3.4 Mechanical Properties Measurements
room temperature (≈22 °C). The specimens were then removed and stored in the drying oven. Table X lists the glass transition and annealing temperatures.
monitored throughout with a glass-bulb thermometer. The density was calculated using the following formula:35
(3)
Three density measurements were made per specimen, then subsequently averaged. The molar volumes (cm3/mol glass) of the glasses were also calculated by dividing the molecular masses of the glasses by the measured densities. In addition, atomic molar volumes (cm3/mol atoms) were calculated by dividing the molar volumes by the number of atoms per mole of glass. Specimens were wiped clean using the reagent alcohol and laboratory towels after testing.
3.4.2 Young’s Modulus and Poisson’s Ratio
The elastic (Young’s) modulus and Poisson’s ratio were determined using the ultrasonic pulse-echo technique.54 The specimens used for the density measurements were used for this. Transit times for shear and longitudinal sound waves to traverse the thickness of the specimens were measured using a digital oscilloscope. Shear and longitudinal transducers‡ powered by an amplifier* were used to generate the ultrasonic waves. The transducers were coupled to the specimens using maple syrup. By dividing the thickness of the
) (g/cm ρ
(g) mass wet - (g) mass dry
(g) mass ) dry
(g/cm ρ
3 kerosene
3 glass
specimens, measured with digital calipers, by one-half the round-trip transit time of the waves, the shear and longitudinal sound wave velocities were calculated. Specimens were cleaned after testing. Young’s modulus and Poisson’s ratio were then calculated using the following formulas:54
(4)
where,
= Poisson’s ratio
VT= transverse (shear) sound velocity VL= longitudinal sound velocity
(5) where,
E = Young’s modulus
= glass density
Poisson’s ratio is the ratio of transverse to longitudinal strains in the material when it is pulled (elongated) in uniaxial tension.55
ν ν ν
- 1
) 2 - )(1 + ρ(1 V
= E L2
2
L T
2
L T
V 2 V 2
V 2 V 1 ν
TDS 420 Four Channel Digital Oscilloscope, Tektronix Corporation, USA
‡Shear Transducer: Parametrics V156 5 MHz, Parametric Corporation, USA Longitudinal Transducer: Parametrics V110 5 MHz
*Model 500 PR, Parametrics Corporation, USA
Shear and bulk moduli were also calculated after Young’s modulus and Poisson’s ratio were determined, using the following formulas:35
(6) where,
G = shear modulus
(7) where,
K = bulk modulus
3.4.3 Conventional Vickers Hardness (HV)
The Vickers hardness is indicative of the mean contact pressure on a glass in an indentation experiment.21 It is calculated by dividing the indentation load by the surface area of the remaining indentation after unloading. The conventional Vickers hardness of the polished glasses was measured using a Vickers hardness testing machine†, except for the vitreous silica specimen.
This was a conventional hardness testing machine utilizing dead weight loading. The atmosphere side of the float glass specimen was tested.
Specimens were gently cleaned with reagent alcohol and a laboratory towel just before testing.
) + 2(1
= E
G ν
) 2 - 3(1
= E
K ν
†HMV-2000 Microhardness Tester, Shimadzu Corporation, Japan
An applied load of 200 g, held for 15 seconds, was used for the tests. The exact loading rate was unknown, but complied with ASTM E384-89 specifications56 and was much faster than the indentation rate of the recording microindenter. Samples rested on a three-ball ring holder to minimize tilting from any unevenness. The two indentation diagonal lengths were measured in reflected light to the nearest tenth of a micrometer for each indentation, using the attached measuring unit. Ten indentations were made per specimen. Temperature ranged from 21 to 23 °C and relative humidity from 14 to 21% during the course of testing all specimens. The Vickers hardness was calculated using the following formula from ASTM E384-89:56
(8)
where,
HV= Vickers hardness F = indentation load
d = average indentation diagonal length
The average indentation diagonal length, d, was calculated by averaging the two indentation diagonals lengths measured for each indentation. Ten Vickers hardness numbers were calculated for each glass, from which an average and standard deviation were calculated.
2 2 2
V d (µm)
1854.4F(g)
= ) (Kg/mm H
3.4.4 Fracture Toughness (KIC)
The indentation technique was used to measure the fracture toughness of the glass specimens, except the vitreous silica and Pyrex™ borosilicate glasses, since they behaved ‘anomalous.’ The same specimens used in the hardness testing were used for the fracture toughness tests. The atmosphere side of the float glass specimen was tested. Twelve Vickers indentations were made on each sample using the same hardness tester used to measure the Vickers hardness. Specimens rested on a three-ball ring holder to minimize tilting from any unevenness. Immediately after making an indentation the four major median-radial crack lengths were measured from the center of indentation to the tip of the cracks using the attached measuring unit. The two indentation diagonal lengths were measured for each indentation as well.
Loads ranging from 0.5 Kg to 2 Kg were used, with a 15 s hold time. A load of 1 Kg was used for most specimens. Different loads were needed since for some of the glasses cracking of the indentations was too severe at 1 Kg, while for another glass a higher load was needed (2 Kg) to have 100% of the indentations form cracks. The loads used for each glass will be made clear in the results section. Throughout the course of testing, temperature was 24 ± 2
°C, and relative humidity was 43 ± 7%. The equation used to calculate the fracture toughness was that derived by Anstis et al.26in which the half-penny crack geometry is assumed to be the final shape. This assumption turned out
to be valid for the glasses tested in the current work, as fractographic evidence will show. The formula used was:26
(9)
where,
KIC= Mode I (tensile opening) plane-strain fracture toughness E = Young’s modulus
H = Hardness
F = indentation load
c = crack length measured from center of indentation to crack tip
The Vickers hardness (HV) was used for the hardness (H) in Eq. 9, and was calculated from the measured indentation diagonal lengths, using Eq. 8. The average crack length of each indentation was used for ‘c’ in Eq. 9. Twelve fracture toughness values were calculated for each glass, from which an average and standard deviation were calculated.
3.4.5 Fracture Surface Energy (γf)
The plane-strain fracture surface energy, γf, was calculated using the following fracture mechanics relation:57
(10) E
2 ν) - 1 ( γ K
2 2 IC
f
3/22 / 1
IC
c
F H
016 E
.
0
K
where,
γf= plane-strain fracture surface energy
Values of KIC, E, and were obtained from the fracture toughness and Young’s modulus measurements. Twelve values of the fracture surface energy were calculated for each glass, one for each indentation, from which an average and standard deviation were calculated.
3.4.6 Brittleness Index (B)
The brittleness index (B) was calculated for each glass using the equation of Lawn and Marshall13 who proposed that brittleness in indentation testing be defined by the ratio of indentation hardness to fracture toughness:
(11)
The average Vickers hardness and fracture toughness values previously calculated were used to calculate the average brittleness index for each of the glasses.
KC
BH