1. Overview
Hardness: the ability to resist local indentation deformation or scratch fracture.

Two kinds of Mohs hardness sequence tables
Order |
Material |
Order |
Material |
1 |
talc |
1 |
talc |
2 |
gupse |
2 |
gupse |
3 |
calcite |
3 |
calcite |
4 |
fluorite |
4 |
fluorite |
5 |
apatite |
5 |
apatite |
6 |
orthoclase |
6 |
orthoclase |
7 |
quartz |
7 |
SiO2 glass |
8 |
topaz |
8 |
quartz |
9 |
corindon |
9 |
topaz |
10 |
adamas |
10 |
garnet |
– |
11 |
Fused zirconia |
|
– |
12 |
corindon |
|
– |
13 |
silicon carbide |
|
– |
14 |
Carbonization shed |
|
– |
15 |
diamond |
2. Brinell hardness
(1) Principle
Press the spherical indenter with diameter D into the metal surface with a load F of a certain size, and keep it for a period of time to form a spherical indentation.
The load value that can be borne on the unit indentation area is the Brinell hardness of the metal material.

Measuring indentation diameter

Indenter material:
- Hard alloy ball (HBW) HB=450~650
- Hardened steel ball (HBS) HB<450
(2) Representation method
For example: 280HBS10/3000/30
1kgf=9.81N
- 280 – Hardness value
- HBS – Hardness symbol
- 10 – Diameter of steel ball mm
- 3000 – Load size kgf
- 30 – Load holding time s
General conditions: 10mm steel ball diameter; 3000kg load; 10s pressure holding time, namely HB280
(3) Test steps

(4) Selection of F and D (principle of geometric similarity of indentation)
When measuring Brinell hardness with indenters of different diameters and loads of different sizes, the principle of geometric similarity must be met to obtain the same HB value, that is, the opening angleφ of the indentation is equal.
Method: The same HB shall be measured for samples with the same material but different thickness, or materials with different hardness and softness.
When selecting D and F, F/D2 shall be the same.
Principle of geometrical similarity of indentation:

It can be seen that as long as F/D remains constant, HB only depends on the pressing angle φ.
F/D2 ratio: 30,15,10,5,2.5,1.25,1
According to the engineering regulations, the ratio of F/D2 is 30, 10 and 2.5, which are selected according to the material hardness and sample thickness.
See various standards and test specifications for details.

Fig. 1-21 Application of similarity principle
Selection Table of Brinell Hardness Test P/D2
Material type |
Brinell hardness number/HB |
Sample thickness/mm |
Relationship between load P and indenter diameter D |
Diameter of indenter D/nm |
Load P/kgf |
Load holding time/s |
Ferrous metal |
140~450 |
6~3 4-2 <2 |
P=30D2 |
10 5 2.5 |
3000 750 187.5 |
10 |
<140 |
>6 6~3 <3 |
P=10D2 |
10 5 2.5 |
1000 250 62.5 |
10 |
|
Nonferrous metals |
>130 |
6~3 4-2 <2 |
P=30D2 |
10 5 2.5 |
3000 750 187.5 |
30 |
36~130 |
9~3 6~2 <3 |
P=10D2 |
10 5 2.5 |
1000 250 62.5 |
30 |
|
8-35 |
>6 6~3 <3 |
P=2.5D2 |
10 5 2.5 |
250 62.5 15.6 |
60 |
The experiment shows that HB is stable and comparable when 0.25D<d<0.5D.
(5) Load holding time:
If it has influence on the test, it shall be carried out in strict accordance with the regulations, generally 10s and 30s.
(6) Characteristics and Application of Brinell Hardness
With large indentation area and high measurement accuracy, it is suitable for coarse or heterogeneous materials;
The indentation is large, and the finished product inspection is difficult.
It is mainly used for raw material inspection:
The indenter material is limited to the softer material (HB450~650);
The efficiency of indentation measurement is low.
3. Rockwell hardness
Test principle: Use indentation depth to reflect material hardness.
In order to use the same hardness tester to adapt to different soft and hard materials, different indenters and loads are used in many grades.
Common Grade C, HRC: the total load is 150kgf, and the 120 ° diamond cone indenter is loaded twice.
First, the initial load P1=10kgf is added to make the indenter contact the material surface well, and then the main load P2=140kgf is added.
After removing P2, the indentation depth is h.

Fig. 3-17 Schematic Diagram of the Principle and Test Process of Rockwell Hardness Test
(a) Add preload (b) Add main load (c) Unload main load
Hardness symbol | Head used | Total test force N | Scope of application | Applied range |
HRA | Diamond cone | 588.4 | 20-88 | Carbide, hard alloy, quenched tool steel, shallow case hardening steel |
HRB | φ 1.588mm steel ball | 980.7 | 20-100 | Mild steel, copper alloy, aluminum alloy, malleable cast iron |
HRC | Diamond cone | 1471 | 20-70 | Quenched steel, quenched and tempered steel, deep case hardened steel |
Indenter: 120 diamond cone or hardened steel ball
Rockwell hardness definition:
0.002mm residual indentation depth is a Rockwell hardness unit.

K – constant, 130 for steel ball indenter and 100 for diamond indenter
Table 3-6 Test Specification and Application of Rockwell Hardness
Ruler |
Type of indenter |
Initial test force/N |
Main test force/N |
Total test force/N |
Constant K |
Hardness range |
application examples |
A |
Diamond circular dimension |
100 |
500 |
600 |
100 |
60~85 |
High hardness thin parts and cemented carbides |
B |
φ1.588mm steel ball |
900 |
1000 |
130 |
25~100 |
Non ferrous metals, malleable cast iron and other materials |
|
C |
Diamond circular dimension |
1400 |
1500 |
100 |
20~67 |
Heat treated structural steel and tool steel |
|
D |
Diamond cone |
900 |
1000 |
100 |
40-77 |
Surface hardened steel |
|
E |
φ3.175mm steel ball |
900 |
1000 |
130 |
70~100 |
Plastic |
|
F |
φ1.588mmm steel ball |
500 |
600 |
130 |
40~100 |
Non ferrous metals |
|
G |
φ1.588mm steel ball |
1400 |
1500 |
130 |
31~94 |
Pearlitic steel, copper, nickel, zinc alloy |
|
H |
φ3.175mm steel ball |
500 |
600 |
130 |
– |
Annealed copper alloy |
|
K |
φ3.175mm steel ball |
1400 |
1500 |
130 |
40~100 |
Non ferrous metals and plastics Soft metal and non-metallic soft materials High hardness thin parts and cemented carbides Non ferrous metals, malleable cast iron and other materials |
|
L |
φ6.350mm steel ball |
500 |
600 |
130 |
– |
||
M |
φ6.350mm steel ball |
900 |
1000 |
130 |
– |
||
P |
φ6.350mm steel ball |
1400 |
1500 |
130 |
– |
||
R |
φ12.70mm steel ball |
500 |
600 |
130 |
– |
Heat treated structural steel and tool steel |
|
S |
φ12.70mm steel ball |
900 |
1000 |
130 |
– |
||
V |
φ12.70mm steel ball |
1400 |
1500 |
130 |
– |
Characteristics and Application of Rockwell Hardness
() Direct reading of hardness value, high efficiency, suitable for batch inspection;
(2) The indentation is small and basically “nondestructive”, which is suitable for finished product inspection;
(3) The indentation is small, and the representativeness is poor, which is not suitable for coarse or non-uniform materials;
(4) It is divided into various scales and has a wide range of applications;
(5) The Rockwell hardness values of various scales are not comparable.
4. Vickers hardness
1. Principle
Press a diamond pyramid into the metal surface with a certain load F to form a pyramid indentation.
The load value on the unit indentation area is the Vickers hardness of the metal material.
When the unit of test force F is kgf:

When the unit of test force F is N:

Indenter material: diamond pyramid with an included angle of 136 °
2. Representation method
For example: 270HV30/20, if the holding time is 10-15s, it can be recorded as 270HV
- 270 – Hardness value
- 30 – Load size kgf
- 20 – Load holding time s

3. Microhardness
Vickers hardness with very small load, the load is 5-200gf.
Indicated by Hm, it can be used to test the hardness of single grain or phase.

Vickers hardness test |
Low load Vickers test |
Micro Vickers hardness test |
|||
Hardness symbol |
Test force/N |
Hardness symbol |
Test force/N |
Hardness symbol |
Test force/N |
HV5 |
49.03 |
HVO.2 |
1.961 |
HVO.01 |
0.09807 |
HV10 |
98.07 |
HVO.3 |
2.942 |
HVO.015 |
0.1471 |
HV20 |
196.1 |
HVO.5 |
4.903 |
HVO.02 |
0.1961 |
HV30 |
294.2 |
HV1 |
9.807 |
HVO.025 |
0.2452 |
HV50 |
490.3 |
HV2 |
19.61 |
HVO.05 |
0.4903 |
HV100 |
980.7 |
HV3 |
29.42 |
HVO.1 |
0.9807 |
Note: 1. The Vickers hardness test can use a test force greater than 980.7N; 2. The micro Vickers test force is recommended. |
Characteristics and Application of Vickers Hardness
(1) The geometrical shape of the indentation is always similar, and the load is optional;
(2) The corner cone indentation contour is clear and the measurement accuracy is high;
(3) The diamond indenter has a wide range of applications and can provide continuous and consistent hardness scales for various materials:
(4) The indentation measurement efficiency is low, and it is not suitable for on-site batch inspection;
(5) The indentation is small and not suitable for coarse or heterogeneous materials;
However, if the metallographic specimen is made, the hardness or hardness distribution of various phases can be measured.
5. Improvement of hardness strength relationship and test method
(1) Hardness test characteristics
① The stress state is very soft (α>2), which is widely applicable;

Hardness of some materials
Material |
Condition |
Hardness/(kgf/mm ²) |
|
Metallic Materials |
99.5% aluminum |
annealing |
20 |
|
|
cold rolling |
40 |
|
Aluminum alloy (A-Zn Mg Cu) Mild steel (tc=0.2%) |
annealing |
60 |
|
|
Precipitation hardening |
170 |
|
Bearing steel Aluminum alloy (A-Zn Mg Cu) |
normalizing |
120 |
|
|
cold rolling |
200 |
|
Mild steel (tc=0.2%) |
normalizing |
200 |
|
|
Quenching (830 ℃) |
900 |
|
|
Tempering (150 ℃) |
750 |
ceramic materials |
WC |
agglutination |
1500~2400 |
|
Cermet (Co=6%, allowance WC) |
20℃ |
1500 |
|
|
750℃ |
1000 |
|
Al2O3 |
|
~1500 |
|
B4C |
|
2500~3700 |
Material |
Condition |
Hardness/(kgf/mm ²) |
BN (cubic meter) |
|
7500 |
diamond |
|
6000-10000 |
Glass |
|
|
Silica |
|
700-750 |
Soda lime glass |
|
540~580 |
optical glass |
|
550-600 |
Polymer |
|
|
High pressure polyethylene |
|
40-70 |
Phenolic plastic (filler) |
|
30 |
polystyrene |
|
17 |
organic glass |
|
16 |
polyvinyl chloride |
|
14~17 |
ABS |
|
8-10 |
polycarbonate |
|
9-10 |
Polyoxymethylene |
|
10~11 |
Polytetraethylene oxide |
|
10~13 |
polysulfone |
|
10~13 |
Covalent bond ≥ ionic bond>metal bond>hydrogen bond>Van’s bond
② The method is simple, nondestructive and suitable for field inspection;
③ The physical meaning is not clear, and it is difficult to design quantitatively.
(2) Relationship between hardness and strength

σb≈KH
Steel: K=0.33~0.36
Copper alloy, stainless steel, etc.: K=0.4~0.55
Relationship between hardness and strength of annealed metals
Name of metal and alloy |
HB |
σb/MPa |
k(σb/HB) |
σ-1/MPa |
σ(σ-1/HB) |
|
Non ferrous metals Ferrous metal Non ferrous metals |
copper |
47 |
220.30 |
4.68 |
68.40 |
1.45 |
aluminium alloy |
138 |
455.70 |
3.30 |
162.68 |
1.18 |
|
Duralumin |
116 |
454.23 |
3.91 |
144.45 |
1.24 |
|
Ferrous metal |
Industrial pure iron |
87 |
300.76 |
3.45 |
159.54 |
1.83 |
20 steel |
141 |
478.53 |
3.39 |
212.66 |
1.50 |
|
45 steel |
182 |
637.98 |
3.50 |
278.02 |
1.52 |
|
18 Steel |
211 |
753.42 |
3.57 |
264.30 |
1.25 |
|
T12 steel |
224 |
792.91 |
3.53 |
338.78 |
1.51 |
|
1Cr18Ni9 |
175 |
902.28 |
5.15 |
364.56 |
2.08 |
|
2Cr13 |
194 |
660.81 |
3.40 |
318.99 |
1.64 |
Note: Unit of hardness!
(3) Nano indentation test
During the loading process, the elastic deformation first occurs on the surface of the specimen, and with the further increase of the load, the plastic deformation starts to appear and gradually increases;
The unloading process is mainly the process of elastic deformation recovery, and the plastic deformation finally makes the sample surface form an indentation.

Load displacement curve of nano indentation
Principle of nano indentation test


- H – Nano hardness;
- S – Contact stiffness;
- A – Contact area;
- β – Constants related to the geometry of the indenter;
- Er – equivalent modulus
There are important differences between nano hardness and traditional hardness:
First of all, the two definitions are different.
Nanohardness: the instantaneous force borne by a unit area on the projection of the surface area of the base indentation during the indentation process of the sample, which is a measure of the sample’s ability to withstand the contact load;
Vickers hardness is defined as the average force per unit area on the surface area of the indentation retained after the unloading of the indenter, which reflects the ability of the specimen to resist linear residual deformation.
In the process of hardness measurement, for the process dominated by plastic deformation, the results of the two definitions are similar: for the contact process dominated by elastic deformation, the results will be different.
In the process of pure elastic contact, the residual contact area is very small, so the traditional hardness definition will lead to infinite hardness, and the true hardness value of the sample cannot be obtained.
Secondly, the measurement ranges of the two are different.
Traditional hardness measurement is only applicable to large size samples: not only because of the limitations of the measuring instrument itself, but more importantly, when the indentation is small to the micro nano scale, the residual indentation can no longer correctly reflect the true hardness of the sample.
New measurement techniques and calculation methods are used for nano hardness measurement, which can more accurately reflect the hardness characteristics of the sample at the micro nano scale.
The important difference between the two is the calculation of indentation area.
The nano hardness is to measure the indentation depth and then calculate the contact area according to the empirical formula;
The traditional hardness measurement method is to obtain the surface area of the indentation according to the photos of the indentation after unloading.
(4) Nanoindentation test method
The basic components of nano hardness tester can be divided into several parts, such as control system, moving coil system, loading system and indenter.
The indenters are generally all diamond indenters, which are divided into triangular cones or four-edge dimensions.
During the test, the initial parameters are input first, and the subsequent detection process is completely controlled by the microcomputer automatically.
By changing the current in the moving coil system, the loading system and the action of the indenter can be manipulated.
The measurement and control of the indenter pressing load are completed by the strain gauge.
At the same time, the strain gauge also feeds back the signal to the moving coil system to achieve closed-loop control, so that the test can be completed according to the input parameter settings.