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STANDARD HARDNESS METHOD FOR KNOOP INDENTATION HARDNESS OF GLASS

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Abstract

The experiment was performed to study knoop indentation hardness of glass by the use of

an accessory which is available to existing microscopes. The glass is usually fitted on an

inverted-stage microscope. The range of the test ranges from 100-1000 when it is specified in the

conventional units of g

-2

. Results were favorable with the theoretical aspects of the

experiment.

Table of Contents

1. Introduction ........................................................................................................................................... 4

2. Theoretical principle ............................................................................................................................. 4

3. Experimental Method ............................................................................................................................ 5

4. Results ................................................................................................................................................... 6

5. Discussion of the Results ...................................................................................................................... 7

6. Conclusions and Recommendations ..................................................................................................... 7

7. References ............................................................................................................................................. 8

8. Nomenclature ....................................................................................................................................... 9

9. Appendices .......................................................................................................................................... 10

1. Introduction

A Knoop hardness test is a test for mechanical hardness which is usually used especially

for thin sheets or very brittle material where only a small indentation may be made for testing

purposes (Rouxel, 2015). The purpose of the experiment was to measure the Knoop indentation

hardness of a glass by the use of knop indenter and a microscope. The idea was to see the

permanent change of the glass surface after indentation with a solid material to determine its

hardness with the use of the Knoop hardness formula. The approach taken for the experiment

was using an indenter and a microscope with the help of HK formula to determine the hardness

of the glass. The machines and measurements used had a generally precision of +_2% coefficient

variation. However, lower load statistics could also increase the coefficient variation to +_6%.

2. Theoretical principle

The knop hardness KHN or HK is given by the formula:

KHN = (P/A)

=P/d

Where:

L = Length of indentation along its axis

= projected area of the indentation, mm

= Length of the diagonal of the indentation, mm.

Cp = ½ (cot A/2 * tan B/2),

A = Included longitudinal edge angle,

B = included transverse edge angle

For the Knoop indentation hardness test for a glass, the test load is made at 100 gf

(Rouxel, 2015). The rate of the indenter motion prior to contact with the specimen was

020+_0.05. The reason for such a low rate of load was to alleviate the effects of the magnitude of

the load on Knoop hardness number.

The standard deviation for the test is

S=√∑(KHN-KHN

)

(n-1)

Where:

S = Standard deviation of a single observation,

KHN = Mean KHN

KHN

= KHN obtained from nth indentation,

n = number indentations.

3. Experimental Method

The specimen was placed on the stage machine in such a way that the specimen could not

shift or rock when carrying out the experiment. The specimen’s surface lied at a normal plane to

the axis of the indenter. A leveling device was used to ensure that the plane was normal. The

machine was then started smoothly. The machine was loaded by a dash-pot lever system. It was

then mounted on shock absorbers which its function was to dampen out vibrations. To produce

indentation, the test force was applied for 20s (Zhang & Bradt, 2014).

The diagonal dimensions are used to calculate the Knoop hardness number (Zhang &

Bradt, 2014). The specimen was then carefully raised off the sample after some time to avoid

vibration impact. The specimen was then taken for testing where the measuring system was

carefully calibrated with a grating. The measurement reading was checked twice. All these were

done within 6 minutes period after removing the specimen from the test force. A green filter was

used all the time during the experiment.

4. Results

The Knoop hardness number KHN 0.1/20 was calculated from the numerical value in the

equation below.

HK0.1/20-1.423/d

The length (d) from the experiment was in millimeters. This was the distance of the long

indentation diagonal. It was obtained by determination from a straight line.

The initial equation was given by KHN = p/d

Where d is the length of the long diagonal indentation in mm.

Due to the finite resolving power of the light microscope, the formula becomes;

D=d

+7 ƛ /2NA

Where:

= apparent length of the diagonal measured with light microscope mm, mm,

ƛ = wavelength of light, mm

NA = numerical aperture of objective used in microscope.

Combining both equations and including the conversion from filar units to millimeters in the

table, the equation becomes:

KHN = P/ (LK=7 ƛ /2NA)

Where:

L = the length of the long diagonal in filar units as measured with the light microscope

K = the fraction of millimeter (calibration constant) represented by a filar unit.

5. Discussion of the Results

The results are consistent. There was a variation of +_0.0002 when the specimen was

measured more than twice. These variations were not excessive in that it could affect the

experiment. When the results vs. theory are compared, it corresponds to each other, in that the

experiment reflects the theory. Although there were differences between the two, the differences

were not enough to discredit either. One of the sources of error in the experiment was placement

of the specimen. Additionally, the inclination of the microscope was a source of error. Both

sources of errors were corrected during the experiment.

6. Conclusions and Recommendations

In conclusion, the experiment was successful and the Knoop hardness of glass was

identified. The experiment had a few errors but all were corrected before arriving at the final

value. It is recommended that a person taking the experiment should be very vigilant to avoid

unnecessary errors which might lead to a wrong final value.

7. References

Rouxel, T. (2015). Driving force for indentation cracking in glass: composition, pressure and

temperature dependence. Phil. Trans. R. Soc. A, 373(2038), 20140140.

Zhang, L., & Bradt, R. C. (2014). A Comparison of the Indentation Size Effect in Fused Silica

and Crystalline Quartz. Journal of North Carolina Academy of Science, 129(4), 180-183.

8. Nomenclature

ƛ – This is the wavelength of light. Light is the electromagnetic radiation within a certain portion

of the electromagnetic spectrum. The visible light usually has wavelength in the range of

400-700 nm. This translates to 4.00 * 10

-7

to 7.00 * 10

-7

9. Appendices

Equation for estimating Knoop hardness indentation of glass

Equation 1

KHN =P/d

Equation 2

D=d

+7 ƛ /2NA

Equation 3 Combine 1 and 2

KHM + P/ (d

-7 ƛ/2NA)

Equation 4

KHN = P/ (LK=7 ƛ /2NA)

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