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1- PURPOSE OF EXPERIMENT The object is to determine the hardness of a material (steel, aluminum etc.) for different scales.

2. THEORY
The hardness of a material can be defined as “The resistance to permanent plastic deformation”. There are three general types of hardness measurements depending on the manner in which the test is conducted. These are (1) scratch hardness, (2) indentation hardness and (3) rebound or dynamic hardness. Only indentation hardness is of major engineering interest for metals. Scratch hardness is measured according to Mohs’ scale. This consists of ten standard minerals arranged in the order of their ability to be scratched. The softest mineral in this scale is talc (Scratch hardness 1), while diamond has a hardness of 10. A fingernail has a value about 2, annealed copper has a value of 3 and martensite a hardness 7. The hardest metals fall in the Mohs’ hardness range of 4 to 8. In dynamic hardness measurements, the indenter is usually dropped on to the metal surface, and the hardness is expressed as the energy of impact.
In the indentation hardness measurements, the hardness of a metal is measured by forcing an indenter into its surface. The indenter material, which is usually a ball, pyramid or cone, is made of a material much harder than the material being tested. For example hardened steel, tungsten carbide, or diamond is commonly used. In this test, the indenter is forced into the surface of the material under a standard load at right angle (90°). After the indentation has been made, the indenter is withdrawn from the surface. An empirical hardness number is then calculated or read off a dial, which is based on the cross- sectional area or depth of the impression. * Brinell Hardness Testing:

What is “Brinell Hardness Test” ?
Dr. J. A. Brinell invented the Brinell test in Sweden in 1900. The oldest of the hardness test methods in common use today, the Brinell test is frequently used to determine the hardness of forgings and castings that have a grain structure too course for Rockwell or Vickers testing. Therefore, Brinell tests are frequently done on large parts. By varying the test force and ball size, nearly all metals can be tested using a Brinell test. Brinell values are considered test force independent as long as the ball size/test force relationship is the same.
Procedure:
In this test, a hardened steel ball is forced into the surface of material under a standard load at right angle. After the indentation has been made, the indenter is withdrawn from the surface and the diameter of spherical indentation is measured. The numerical Brinell Hardness (HB) number is equal to the applied load P, divided by the spherical surface area of the indentation A, expressed in kg/mm².

Rockwell Hardness Test:
What is “Rockwell Hardness Test”?
As The Brinell hardness test cannot be conducted on hard materials such as hardened steels, another hardness test was developed by Hugh M. Rockwell (1890-1957) and Stanley P. Rockwell (1886-1940) on July 15, 1914 . The Rockwell tests constitute the most common method used to measure hardness because they are so simple to perform and require no special skills. Several different scales may be utilized from possible combinations of various indenters and different loads, which permit the testing of virtually all metal alloys (as well as some polymers). Indenters include spherical and hardened steel balls having diameters of 1.588, 3.175, 6.350, and 12.70 mm and a conical diamond (Brale) indenter, which is used for the hardest materials.
Calculations:
* Brinell: HBn=2PπD(D-D2-d2) Where: P: applied force in Kilograms-force D: diameter of hardened ball in millimeters d: mean diameter mean diameter of indentation in millimeters
For all three materials (e.g. steel, bronze and titanium) the load was set as 187.5 Kgf
The ball diameter D is 2.5mm
For Titanium:
The mean diameter, d was measured as:
{d1=0.813, d2= 0.813} so, dTitanium=0.813+0.8132=0.813 HBTitanium=2×187.5π×2.5(2.5-2.52-0.8132)=351

For steel:
The mean diameter, d was measured as:
{d1=0.889, d2=0.868} so, dSteel=0.889+0.8682=0.8785 HBSteel=2×187.5π×2.5(2.5-2.52-0.87852)=299

For bronze:
The mean diameter, d was measured as:
{d1=1.301, d2=1.374} so, dBronze=1.301+1.3742=1.3375 HBBronze=2×187.5π×2.5(2.5-2.52-1.33752)=123

* Rockwell: The hardness Rockwell number can be obtained from Brinell hardness number including 10 % error:
For HRc between 20 and 40:
HB=25000(100-HRc)

For HRc over 40:
HB=1420000(100-HRc)2

For Steel:
299=1420000(100-HRc)2 →HRc= 32
For Titanium:

351=1420000(100-HRc)2→HRC=36

For Bronze, the above formula is not applicable as it gives a negative value.

Discussion:
For Rockwell test first we used 187.5 Kgf but when we wanted to read d1 and d2 for Bronze it was beyond the limitations of apparatus so we reduced it to 60 Kgf in order to impression be smaller so that we could read it. This event gives us the idea that the force which is applied to specimen must be set according to hardness of material. That is to say we cannot apply large forces for soft materials and vice versa.

Conclusion: When the diameter of indentation reduces, the hardness increases. We calculate d because the indentation isn't spherical, but it has oval section.

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