Micro-Hardness & Toughness of Brittle Materials

* To measure the hardness of microscope glass slide by using Micro Hardness Tester. * To measure the hardness of Sintered Alumina Disk by using Vickers Hardness Tester. * To determinate the facture toughness by using the crack lengths that obtains from both of the hardness tests. * To understand the different and relationship of glass and other ceramic materials.

Theory
The cost involved in measuring ceramic-based materials is quite high. Hence, indentation techniques have been widely used to evaluating the fracture toughness of brittle materials. In order to calculate the fracture toughness, hardness should be known by using Micro Hardness Tester or Vickers hardness tester.

Hardness measurement

The term Micro Hardness Test means the load is not exceeding 1 kgf when indentation is made. Commonly, the indenter that be used is Vickers diamond pyramid and a flat and polished sample surface is needed for this testing.

While the Vickers hardness test method is apply a load of 1 to 100 kgf to the polished surface of the test material. As the diagram shows below, since the force applied in the normal direction, an included angle of 136 degrees created between two faces that made during testing. The load usually removed after force applying for 10 to 15 seconds, and then a square shape is formed on the flat surface of ceramics. The length of two diagonals of this square can be measured by using the tester, which will be used in hardness calculation.

The Vickers hardness can be calculated by using load divide area of the square that obtained during the hardness testing.

Fracture toughness measurement

Fracture toughness is an inherent property of the materials. It describes crack resistance of a material.

During the fracture toughness measurement of ceramics, A Vickers indentation is pressed on a polished ceramic surface and cracks appeared around the indentation. The cracks are considered as the artificial defects and the length of it can be used to calculate the fracture toughness. The lengths of the cracks are in inverse proportion to the toughness and in direct proportion to load applied.

The formula for calculating the fracture toughness can be written as:

Procedure

Microscope glass slide experiment
1. Take a fresh microscope glass slide, and avoid the fingerprint. 2. Place the glass slide simple in right position of the Micro Hardness Tester by using a pair tweezers. 3. Apply a 1000g load on the sample for 10 seconds to press an indentation and crack on the surface of sample. 4. Measure the two diagonal lengths and two pairs of crack lengths. 5. Repeat the steps 3 and 4 for one more time, and calculate the average of diagonal length and crack length. 6. Repeat step3 to step5 to obtain diagonal length and crack length at load 500g, 300g, 200g, 100g.

Sintered alumina disks experiment
1. Take a sintered alumina sample, and avoid the fingerprint. 2. Place the sintered alumina simple in right position of the Vickers Hardness Tester by using a pair tweezers. 3. Apply a 10kg load on the sample for 10 seconds to press an indentation and crack on the surface of sample. 4. Measure the two diagonal lengths and two pairs of crack lengths. 5. Repeat the steps 3 and 4 for one more time, and calculate the average of diagonal length and crack length. 6. Repeat step3 to step5 to obtain diagonal length and crack length at load 5kg, 3kg, 2kg, 1kg.

Observation & Result

EXPERIMENT A

Equipment: Micro hardness TesterTest Sample: Microscope Glass Slide

EXPERIMENT B

Equipment: Vickers Hardness TesterTest Sample: Sintered Alumina Disk

Analysis &discussion

1. For both glass and alumina specimens, plot the indentation load (P) versus the square of the average diagonal length (d2) and take the slope of the straight line to determinate Hv in GPa (Hint: the slope = Hv / 1.8544). For Microscope Glass Slide:

According to the formula,

For Sintered Alumina Disk:

Same with the process of calculating the Microscope Glass Slide

2. For both glass and alumina specimens, plot the indentation load (P) versus the crack length raised to the power of 3/2 (i.e. c3/2) and take the slope of the straight line to determinate the KIc in MPam1/2 (Hint: the slope = (KIC / 0.016)(H/E)1/2, where H is the hardness Hv in GPa and E is the Young’s modulus in GPa, assuming E = 70 GPa for glass and E = 400 GPa for alumina).

3. Discussion
a. Comment on the indentation method for evaluating the fracture toughness of brittle materials by considering its usefulness and limitations. The first limitation of the indentation method is that this method is not an adequate tool to determine cracks accurately. Cracks are hard to be observed by conventional optical microscopes if the indenter load is small and the material sample is thin. It’s because the width of the cracks is very narrow when the load is too small to within the resolution of the conventional optical microscope, especially near the tip of the cracks. During the glass slide experiment, the crack length cannot appear when load is 100g. We did five or six time, only one crack length appeared. In addition, the surface of ceramic substrates need to be flat and polished before it uses to do the Vickers hardness testing. Since the fracture toughness is depend on the surface, if the surface did not polished well, it will affect the actual fracture toughness. However, it’s much cheaper and simple than other methods.

b. Compare the hardness and toughness values of glass with those of alumina. Explain the different mechanical properties in terms of atomic (or ionic) bonding and microstructure. Alumina as a non-silicate oxide ceramics, it forms an ionic compound since aluminum is a metal and oxygen is non-metal, hence the bonding between them is ionic. Since alumina is form by ionic bonding, it has electrostatic attraction between atoms, and the ions pack into a regular arrangement. Hence, it gives them a relatively high hardness but a low toughness.

While for glass, it is a unique ceramic, it depends on their atomic structure. Different with most other ceramics that have ordered crystalline structure, glass is highly disordered amorphous structure. In addition, the most of glasses are formed from silica (SiO2), which have tetrahedral unit that incorporate into chains. Hence the hardness and toughness is lower than alumina.

c. The Young’s modulus should be given for a brittle material in order to determine the toughness using the indentation method. Describe three possible ways to measure the Young’s modulus. 1. According to the definition of young’s modulus, there is:

Take one set of F and delta l data in the linear potion of the stress-strain curve and submit in the above formula to obtain the young’s modulus. But sometimes, delta l is too small to measure. A system which used the reflection principle of mirror is installed, according to ratio of the position of mirror, the distance between the mirror and admeasuring apparatus, as well as the delta l, it can convent the immeasurable delta l to measurable delta y which is the direct reading from wall or admeasuring apparatus.

2. Consider the force is spring force instead of the force that applies, there is: , which can compare with Hooke’s law:
Hence
3. There is ,
Where Vs is the speed of sound,
Y is young’s modulus,
f is density of the material.
Which means the stiffer the material is, the faster the sound can travel to the other end, and the larger young’s modulus is. Inversely, if the material is more elastic, it will take a longer time for the sound reach the other end of the material and young’s modulus is lower.

Conclusion

For this experiment, it is very clear that chemical bonding and microstructure play an important role in mechanical properties of ceramics. However, generally, ceramics have high hardness and low toughness.

The normal glass is a very unique ceramic which is highly amorphous structure. The properties of it may change by adding other materials or do some other treatments.

The toughness may be not accurate due to the limitation of indentation method. In the real situation, although the indentation method is cheap and sample, other methods may be needed to obtain hardness and toughness.

References

http://www.gordonengland.co.uk/hardness/vickers.htm#hvcalc
http://www.google.com.hk/url?sa=t&rct=j&q=fracture+toughness+measurement+Kic%3D0.016&source=web&cd=4&ved=0CEcQFjAD&url=http%3A%2F%2Fbib.irb.hr%2Fdatoteka%2F300813.curkovic2.pdf&ei=-NOHUOPnEcrMrQe53oHoAw&usg=AFQjCNHBbwCiPON7GLyPLI0_M2Qry2zoMg http://www.hsctut.materials.unsw.edu.au/Ceramics/ceramics5a.htm http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-19