# Hardness (material)

With the difference of the minerals whose hardness is historically characterized by scratching (cf Scale of hardness Mohs), one generally uses tests of bounce or penetration to characterize the hardness of the metals.

These tests have the advantage of being simpler to realize and of giving reproducible results.

## Measure hardness by bounce: Shore test

This test is mainly used to test the hardness of rubbers and elastomers. For that one lets fall well vertically and a height a small steel mass fixes finished by a round diamond. The mass is guided in its fall by a smooth tube. Hardness is evaluated then according to the height of the rebound.

This test measures the elastic deformation energy absorptive by material. For including/understanding that well it is necessary to observe the traction diagrams of an elastomer with cycle of load and discharge in the elastic range. (missing illustration). It is thus noticed that in the case of the elastomers, the load and the elastic discharge do not take the same way as that can be the case with a crystalline material.

In a " plan; constraint-déformation" surface under the curve with the dimension of an energy. The surface under the elastic traction diagram thus corresponds to the elastic energy absorptive by materials. The surface under the curve of discharge corresponds to energy restored by materials. The difference of two surfaces corresponds to the elastic energy degraded by material. A material " caoutchouteux" thus all energy does not return absorptive, it is besides for that which they are so often used to deaden the vibrations. The harder the elastomer will be, the more it will behave like an ordinary material of crystalline type. The softer the elastomer will be, the more it will absorb elastic energy. One thus notices here the difference in significance of the words " dur" and " mou" between polymers and crystalline lenses.

There exists also an alternative of this test for metal alloys. The procedure remains identical but interpretation is different. It is a question in this case of measuring the plastic deformation energy absorptive by material. If the shock is perfectly elastic (not plastic deformation, part to be tested very hard), the point theoretically rebounds until its height to release (by neglecting frictions); one can connect the difference in height H to the kinetic energy Δ Ec absorptive at the time of the shock:

$\ Delta E_c=m \ cdot G \ cdot h$

where m is the released mass and G is the acceleration of the revolved. In the case of an extremely soft object, the point is inserted and does not rebound. The apparatuses are calibrated in theory to obtain a hardness of 100 for a tempered steel with carbon 0,9% and approximately 35 for the mild steels.

Let us note however that the test results Shore depend much on the surface quality of the part tested. The apparatus must be obliged to quite vertical manner to avoid having frictions which would distort measurement. The mass of the part to be measured must be much more important than the mass of the mass used in the measuring device.

(information to be checked and supplement, the other sites does not have at all the same definition for Shore hardness;)

## Measurements of hardness per penetration

They are the tests most usually practiced. The principle is always identical: an indeformable penetrant leaves a print in material be tested. One measures dimensions of the print and one from of deduced hardness.

In a first approach, one can connect in a rather simple way the elastic limit Re with surface of the print: the more the penetrating object is inserted, the more surface S of pressure increases, therefore the force F being constant, the more the Contrainte decreases. When the constraint is not sufficient any more to deform the solid plastically to be tested, the penetrating object stops, and one thus has:

$R_e= \ frac \left\{F\right\} \left\{S\right\} \, \!$

The values of hardness obtained thanks to the various protocols and testing apparatuses indicated below are this elastic limit Re but the results are not identical because these simplified calculations take into account the surface of the projection of the print (like a disc or a square) instead of taking into account the true surface of the print (as the surface of the segment of a sphere or the facets of the pyramidal print). A brinell test and a Vickers test on the same test-tube do not give the same value in result, but while bringing back by calculation the value of the force to the true surface of the print (respectively a segment of a sphere or a pyramid), one falls into both cases on the same value which is the value “of pressure” of solid material.

They do not take into account the work hardening which is different for each type of test.

### Test Brinell hardness

#### Principle

The test consists in making penetrate by applying a force F a penetrant having the shape of ball in a metal in order to deduce hardness from it from this material.

HB : Brinell hardness
D : diameter of the penetrant (mm)
d1 and d2: measure print carried out with 90° (mm)
H : depth (mm)
F : charge with test (NR)
G : acceleration of gravity

$\begin\left\{matrix\right\}$

& H_B & = & {\ rm Constante} \ cdot \ frac {\ rm (Load \ of \ the test)} {\ rm (Surface \ of \ the print)} \ \ \ \ & & = & 0,102 \ cdot \ frac {2F} {\ pi \ cdot D (D \ sqrt {D^2-d^2})} \end{matrix} with
$\left\{\ rm Constante\right\} = \ frac \left\{1\right\} \left\{G\right\} = \ frac \left\{1\right\} \left\{9,8066\right\} =0,102$
$d= \ frac \left\{d_2+d_1\right\} \left\{2\right\}$

#### The penetrant

Matter: generally polished carbide

Dimension: diameter D

#### The material to be tested

Surface must be plane and cleaned (without lubricant, oxide or calamine). It is necessary to have a sufficient thickness so that the penetration of the ball does not deform material. In the contrary case, measurement would not be reliable. One needs a thickness of at least eight times the depth H of the print.

#### Procedure

To place the penetrant in contact with the surface of material. To apply the force. To maintain this load during 10 to 15 seconds.

To measure on the print two diameters with 90° one of the other. Measurement is taken using a device growing bigger and of a scale taking account of the factor of enlargement.

#### Standard

• European standards (CEN) and international (ISO):

*EN ISO 6506-1: Metallic materials - Test Brinell hardness - Part 1: Testing method.

*EN ISO 6506-2: Metallic materials - Test Brinell hardness - Part 2: Checking and calibration of the testing machines.
*EN ISO 6506-3: Metallic materials - Test Brinell hardness - Part 3: Calibration of the blocks of reference.
• American (ASTM)
* ASTM E10: Standard method for Brinell hardness off metallic materials.

### Hardness test Meyer

The penetrant is identical to the penetrant of Brinell hardness. In a more general way, one uses the same durometer as that used for Brinell hardness.

Measurement is taken with same the principles as Brinell hardness. The values of Meyer hardness are calculated with the following formula:

$\begin\left\{matrix\right\}$

H_M & = & 0,102 \ cdot \ frac {4F} {\ pi \ cdot d^2} \end{matrix} with
$\left\{\ rm Constante\right\} = \ frac \left\{1\right\} \left\{G\right\} = \ frac \left\{1\right\} \left\{9,8066\right\} =0,102$
$d= \ frac \left\{d_2+d_1\right\} \left\{2\right\}$

### Test Vickers hardness

#### Principle

The measurement of Vickers pyramid hardness is made with a pyramidal point standardized out of basic diamond square and of point angle between face equal to 136°. The print thus has the form of a square ; one measures the two diagonals d1 and d2 of this square using an optical apparatus. One obtains the value D by carrying out the average of d1 and d2. It is D which will be used for the calculation of hardness. The force and the duration of the support are also standardized.

* HV : Vickers pyramid hardness

*d1 and d2: measure print carried out with 90° (2 diagonals of square of the print) (mm)
* F : charge with test (NR)
* G : acceleration of gravity

$\begin\left\{matrix\right\}$

& H_V & = & {\ rm Constante} \ cdot \ frac {\ rm (Load \ of \ the test)} {\ rm (Surface \ of \ the print)} \ \ \ \ & & = & 0,102 \ cdot \ frac {2F \ cdot \ sin (\ frac {136^ \ circ} {2})}{d^2} \ \ \ \ & & = & 0,189 \ cdot \ frac {F} {d^2} \end{matrix}

with

$\left\{\ rm Constante\right\} = \ frac \left\{1\right\} \left\{G\right\} = \ frac \left\{1\right\} \left\{9,8066\right\} =0,102$
$d= \ frac \left\{d_2+d_1\right\} \left\{2\right\}$

The degree of hardness, noted Hv, is then read on an abacus (a table); there is an abacus by force of support.

#### Standards

• International (ISO) and European (CEN)

* IN ISO 6507-1: Metallic materials - Test Vickers hardness - Part 1: testing method
• American (ASTM)

* Metals
* E92: Standard Test Method for Vickers Hardness off Metallic Materials
*Ceramic
*C1327: Standard Test Method for VICKERS Indentation Hardness off Advanced Ceramics

### Test Rockwell hardness

#### Principle

Tests the Rockwell hardness are tests of penetration. There exists in fact several types of penetrants which consist of a diamond cone or a polished ball in soaked Acier. To obtain a value of Rockwell hardness, one measures a remanent penetration of the penetrant to which one applies a weak load.

The test proceeds in three phases:

• Application on the penetrant of an initial load F0= 98 NR (either 10 kgf). The penetrant is inserted an initial depth I. This depth being the origin which will be used for measurement Rockwell hardness.
• Application of an additional force F1. The penetrant is inserted a depth of P.
• Relâchement of the F1 force and reading of the indicator of depression.

The value of R being the remanent depression obtained while applying then by slackening the F1 force.

The value of hardness is then given by the following formula:

* Scale B, E and F

$HRB = 130 - R \,$

* Scale C

$HRC = 100 - R \,$

A unit of Rockwell hardness corresponding to a penetration of 0,002 Misters.

#### Various scales

The two most used scales are the scale B and C.

#### Surface Rockwell hardness

These scales are used for very thin products and the measurement of hardness of coatings.

The two scales used are the scale NR (Cone of diamond) and T (steel ball). In both cases, the initial load (F0) is of 29,4 NR. Each one among it can be used by using a load total of 147 NR, 294 NR or 441 NR. One will note that there exist also scales W (ball with a diameter 3,175 mm), X (ball of diameter 6,350) and Y (ball with a diameter 12,70 mm).

In this case a unit of Rockwell hardness corresponds to a depression of 0,001 Misters.

For the scales NR and T hardness is given by the formula:

#### Standards

• International (ISO) and European (CEN)

* IN ISO 2039-2: Plastics - Determination of hardness - Part 2: Rockwell hardness.
* IN ISO 6508-1: Metallic materials: test Rockwell hardness Left 1: testing method (scales has, B, C, D, E, F, G, H, K, NR, T) .
• American

* ASTM E18: Standard methods for Rockwell hardness and Rockwell superficial hardness off metallic materials.

## Measurements of microhardness

Made under very weak load, the tests of microhardness allow very localized measurements (on approximately 100 µm2). Using a microdurometer, one can for example determine the hardness of a phase given in a polyphase sample or that of a very fragile and thin sample.