### Ball indentation hardness test

Hardness refers to the body's ability to withstand the introduction of foreign bodies into the surface layers.
This ability depends on the properties of the material and on the shape and properties of the counterbody.

In most European countries, the definition of Brinell hardness is accepted, and in England and the USA, according to Rockwell.

But in both methods, a ball indenter is introduced into the surface of the material under study .

The pressure p along the plane of contact during the introduction of the sphere into an elastic flat surface is distributed according to the Hertz law:

$p=\frac{3}{2}\frac{P}{a^{3}\pi}\sqrt{a^2-x^2}$

where P is the total load on the sphere; a is the radius of the pressure circle (or crushing area); x is the distance of this point from the center of the pressure circle.

Maximum pressure equal to $\frac{3P}{2a^{2}\pi}$ , is observed in the center of the circle, and the minimum pressure is on the edge. The pressure distribution over the contact surface has the shape of a semicircle.

The elastic displacement h at an arbitrary point of the collapse site is determined by the formula

$h=\frac{3}{2}\frac{P}{a}(1-\frac{x^2}{2a^2})\frac{m^2-1}{m^2E}$

where m is the reciprocal of the Poisson's ratio; E — elastic modulus of the material.

It follows that the displacement in the center of the site (at x = 0) is two times greater than at the edge of the site (at x = a).

The radius of the crushing area a is determined by the formula

$a=\frac{1}{\pi}\sqrt[3]{\frac{3(1-\frac{1}{m^2})RP}{2E}}$

where R is the radius of curvature of the indenter

The pressure in the center of the circle p0 is determined by the formula

$p_0=\frac{1}{\pi}\sqrt[3]{\frac{3PE^2}{2R(1-\frac{1}{m^2})}}$

The radius of the pressure circle is determined empirically. With an increase in P , the pressure p increases until a circular crack is formed, which is characteristic of brittle bodies.

According to Hertz, "absolute" hardness $p^H_0$ equal to po at the time of crack formation is calculated by the formula

$p^H_0=\frac{3P^*}{2a^2\pi}$

where P * is the total indentation force at the moment of crack formation; a is the radius of the pressure circle.

The “absolute” Hertz hardness index can only be determined for brittle bodies, for which, when the nndenter is introduced, a brittle crack is formed.

The Brinell hardness Nk when indenting the ball is determined by the formula

$H_k=\frac{P}{{\pi}Dh}$

where P is the maximum load; D is the diameter of the ball; h — depth of implementation.

### Rockwell Hardness

The Rockwell hardness test method also includes a method for measuring the imprint depth under load. For this, it is supplemented by method B, in which the so-called Rockwell a-hardness is determined, which is directly related to the imprint depth under load.

Name of hardness scale Preload, N The main load, N Ball diameter, mm
R 98.1 589 12.7 ± 0.0025
L 98.1 589 6.35 ± 0.0025
M 98.1 981 6.35 ± 0.0025
F 98.1 981 3.175 ± 0.0025
TO 98.1 1472 3.175 ± 0.0025
IN 98.1 981 1,588 ± 0,0025

Rockwell hardness (method A) is determined by changing the penetration depth per cycle application of preload - application of the main load - removal of the main load - exposure under preload - measurement of the imprint depth.

Scale E is used only to calibrate the instrument in accordance with the requirements of the standard. Typically, the E scale is used to determine the hardness of cast iron, steel, aluminum, and magnesium.

Scale K is used to determine the hardness of steels and other soft and thin metallic materials. In this case, the smallest ball and the largest load are used, which allow avoiding the influence of the support table when determining the hardness of thin sheets.

Scale B is used to determine the hardness of alloys of copper, aluminum, mild steel, ductile iron and other metallic materials.

The symbol of the scales, which is recorded together with the hardness indicator, allows you to identify the size of the ball and the magnitude of the main load at which the determination was made.

The Rockwell hardness tester differs little from the Brinell hardness tester

If the device is not graduated in Rockwell units, then Rockwell hardness n r can be found by the formula
$H_R=130-\frac{h}{0.002}$

where h is the depth of the print after removal of the main load, mm

If the material has a lower hardness than the Rockwell R scale requires, then the hardness is determined on a Shore instrument.

In front of the numerical value of Rockwell hardness, the letter designation of the scale on which it is determined is indicated. For example, hardness R 90

Rockwell scales are somewhat overlapping, and therefore for the same material hardness can be obtained on two scales.

The hardness of some metals can be seen in the table. Mechanical properties of pure metals at room temperature

### MOOS SCALE

It is mainly used to determine the comparative hardness of minerals.

The German mineralogist Friedrich Mohs (1773–1839) proposed a scale according to which minerals are grouped according to their relative hardness on a ten-point scale called the mineralogical hardness scale, or Mohs scale. Each mineral that occupies a specific place on this scale scratches all minerals with a lower hardness value, but at the same time, it is scratched by harder minerals standing above it. Minerals with equal hardness values ​​do not scratch each other.

By comparing with this scale, the hardness of any mineral can be established - Mohs hardness. Minerals with hardness 1 and 2 are considered soft, from 3 to 6 - medium hardness, and above 6 - hard. Minerals with a hardness of 8-10 are said to have the hardness of precious stones.

Mohs scale is a relative scale. With its help, it can only be established which mineral is harder. It is impossible to say how hardness increases in quantitative terms from step to step on the Mohs scale.
In the table below, this scale is compared with the absolute values ​​of hardness - this is the hardness of grinding in water according to Rosival. Comparison shows how abruptly increases absolute hardness. For a layman, the determination of absolute hardness, requiring complex equipment, is almost impossible.

Hardness scale Mineral Mohs hardness Grinding hardness
one Talc Toenail 0,03
2 Gypsum Scratched with a fingernail 1.25
3 Calcite Scratched by a copper coin 4,5
4 Fluorite Easily scratched with a penknife 5
5 Apatite Hardly scratched with a penknife 6.5
6 Orthoclase Scratched by a file 37
7 Quartz Window glass scratches 120
8 Topaz Easily scratches quartz 175
nine Corundum Scratches topaz easily 1,000
10 Diamond Not scratched by anything 140,000

When determining Mohs hardness, use sharp-edged specimens and scratch them on even, fresh (not affected by weathering) surfaces. In ribbed formations, leafy crystals, weathered from the surface of minerals, the values ​​of scratching hardness are underestimated. The application of the Mohs scale to rocks is generally impossible due to their heterogeneity - the presence of heterogeneous components.

The main advantage of the Mohs scale is its ease of use. Using reference samples and scratch sets, the hardness of minerals can be easily determined in the field, during walks and excursions. Even if you don’t have control samples at hand, you can use other simple aids. So, our nail scratches minerals with a hardness of up to 2, a penknife - with a hardness of up to 5-6, the glass is easily scratched by quartz (its Mohs hardness is 7). Of course, for a professional diagnosis of a mineral or gemstone, the Mohs hardness test is too inaccurate. In addition, precious stones can be damaged when scratched. Therefore, in such cases, resort to the determination of the so-called grinding hardness, which is measured by the amount of mineral polished from the surface of the sample under certain conditions.

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