Hardness

The hardness is the opposition that materials offer to physical alterations such as penetration, abrasion and scratching.

Scales for industrial use

In metallurgy, hardness is measured using a durometer for the penetration test of an indenter. Depending on the type of point used and the range of loads applied, there are different scales, suitable for different ranges of hardness.

The interest in determining the hardness of steels lies in the existing correlation between hardness and mechanical resistance, being a cheaper and faster test method than the tensile test, which is why it is widely used.

Until the appearance of the first Brinell machine for determining hardness, it was measured qualitatively using a tempered steel file, which was the hardest material used in workshops.

The scales of current industrial use are the following:

• Brinell Hardness: Start as a tip a tempered steel ball or wolframio carbide. For hard materials, it is not accurate but easy to apply. Little precise with sheets less than 6 mm thick. It's a tough drive.
• Knoop Hardness: Measure the hardness in absolute scale values, and are valued with the depth of recorded signals on a mineral by means of a utensil with a diamond tip to which a standard force is exercised.
• Rockwell Hardness: A diamond cone (in some cases steel ball) is used as a tip. It is the most widespread, since hardness is obtained by direct measurement and is suitable for all types of materials. It is usually considered a non-destructive test due to the small size of the footprint.
• Surface Rockwell: There is a variant of the test, called superficial Rockwell, for the characterization of very thin pieces, such as shaver blades or layers of materials that have received some treatment of surface hardening.
• Rosiwal Hardness: It measures in absolute scales of hardness, it is expressed as resistance to abrasion measures in laboratory tests and based on the corindon with a value of 1000.
• Shore Hardness: Start a scleroscope. An indenter is dropped on the surface of the material and the rebound is seen. It is dimensional, but it consists of several scales. Bigger bounce, tougher. Applicable for surface quality control. It is an elastic method; not of penetration like others.
• Hardness Vickers: Start as a penetrator a diamond shaped like a quadrangular pyramid. For soft materials, Vickers values match those of the Brinell scale. Improvement of the Brinell test to perform hardness tests with sheets up to 2 mm thick.
• Webster Hardness: Start manual machines in measurement, being suitable for hard handling parts such as long extruded profiles. The value obtained is usually converted to Rockwell values.

Nanoindentation

Nanoindentation is a hardness test carried out at the nanometer length scale. A small point is used to indent the material under study. The imposed load and displacement are measured continuously with a resolution of micronewtons and subnanometers, respectively. The load and the displacement are measured simultaneously during the indentation process and for this reason it is also called “instrumented nanoindentation”. Nanoindentation techniques are important for the measurement of mechanical properties in microelectronic applications and for the deformation of micro- and nanoscale structures. The nanoindenters incorporate light microscopes to locate the area to be studied. However, unlike macro and microscale indentation methods, in the instrumented nanoindentation technique it is not possible to directly measure the area of the indentation.

Nano penetrator tips come in a variety of shapes. A common shape is known as a Berkovich indenter, which is a pyramid with 3 sides.

Oliver and Pharr invented a method to calculate the projected indentation area Ac{displaystyle A_{c}} during maximum load. The first stage of a nanoindentation test involves developing indentations on a calibration pattern. The cast silica is a common calibration pattern, because it has homogeneous and well-characterized mechanical properties. The purpose of indenting the calibration standard is to determine the projected contact area of the penetrator tip A_c as a function of the depth of indentation. For a perfect Berkovich tip,

Ac=24.5⋅ ⋅ hc2{displaystyle A_{c}=24.5cdot h_{c}^{2},}

In general, however, the tip is not perfect, it wears down and changes shape with each use. Therefore, a calibration of the tip being used must be carried out regularly. To do this, it is necessary to find the function that relates the area A_c of the cross section of the indenter at maximum load with the distance from the tip h_c that is in contact with the material being indented.

The total depth of the indentation h is the sum of the contact depth h_c and the depth h_s at the periphery of the indentation where the indenter does not make contact with the surface of the material, is say,

h=hc+hs{displaystyle h=h_{c}+h_{s}}

where,

hs={displaystyle h_{s}= ▪ PmaxS{displaystyle {frac {P_{max}}{S}}}

where P_max is the maximum load and ▪ is a geometric constant equal to 0.75 for a Berkovich penetrator. S is the rigidity when downloading, which is calculated in the nanoindentation curve: S=dP/dh{displaystyle S=dP/dh}

The hardness of a material determined by the instrumented nanoindentation is then calculated as:

HIT=PmaxAc{displaystyle H_{IT}={frac {P_{max}}{A_{c}}}}}}}{

Hardness (determined by nanoindentation) is reported in units of GPa, and results from multiple indentations are usually averaged to increase accuracy.

This analysis allows the calculation of the elastic modulus and hardness during maximum load and is known as instrumented nanoindentation; however, an experimental technique known as dynamic nanoindentation is now commonly used. During this, a small oscillating charge is superimposed on the total charge on the sample. In this way, the sample is continuously elastically discharged as the total load increases. This allows continuous measurements of elastic modulus and stiffness as a function of indentation depth.

Scale used in mineralogy

In mineralogy, the Mohs scale is used, created by the German Friedrich Mohs in 1820, which measures the scratch resistance of materials.

Hardness	Material	Chemical composition
1	Talco, (can be easily scratched with the nail)	Mg3Yeah.4O10(OH)2
2	Yeso, (can be scratched with nail with more difficulty)	CaSO4·2H2O
3	Calcita, (can be scratched with a copper coin)	CaCO3
4	Fluorite, (can be scratched with a knife)	CaF2
5	Apatite, (can be slashed hard with a knife)	Ca5(PO)4)3(OH-Cl-F-)
6	Feldespato, (can be scratched with a steel blade)	KAlSi3O8
7	Quartz.	Yes2
8	Topaz,	Al2Yes4(OH-F-)2
9	Corind, (only scratched by diamond)	Al2O3
10	Diamond, (the hardest natural mineral)	C

At a professional level, the Rosiwal and Knoop scales are used in mineralogy, since they allow the evaluation of means with an absolute quantification.

Equivalence between hardness scales

List of approximate equivalences for hardness scales of non-austenitic steels (in the range of the Rockwell C scale):

Equivalence	Factor
HBΔ Δ HV{displaystyle HBLeftrightarrow HV}	HB≈ ≈ 0,95HV{displaystyle HBapprox 0{,}95HV}
HRBΔ Δ HB{displaystyle HRBLeftrightarrow HB}	HRB≈ ≈ 176− − 1165HB{displaystyle HRBapprox 176-{frac {1165}{sqrt {HB}}}}}}
HRCΔ Δ HV{displaystyle HRCLeftrightarrow HV}	HRC≈ ≈ 116− − 1500HV{displaystyle HRCapprox 116-{frac {1500}{sqrt {HV}}}}}}
HVΔ Δ HK{displaystyle HVLeftrightarrow HK}	HV≈ ≈ HK{displaystyle HVapprox HK} (for small loads)
Rm≈ ≈ cHB{displaystyle R_{mapprox cHB}
Steel (Matriz-Fe Cúbica centred on the body)	3.5
Cu and his alloys, tempered	5.5
Cu and his alloys, deformed in cold	4.0
Al and his alloys	3.7

Dureza Rockwell C 150 kgf (HRC)	Dureza Vickers (HV)	Dureza Brinell, bola estándar de 10 mm, 3000 kgf (HBS)	Dureza Brinell, bola de carburo de 10 mm, 3000 kgf (HBW)	Dureza Knoop, 500 gf y mayor (HK)	Dureza Rockwell, escala A, 60 kgf (HRA)	Dureza Rockwell, escala D, 100 kgf (HRD)	Dureza superficial Rockwell, escala 15N, 15 kgf (HR 15-N)	Dureza superficial Rockwell, escala 30N, 30 kgf (HR 30-N)	Dureza superficial Rockwell, escala 45N, 45 kgf (HR 45-N)	Dureza escleroscopio	Dureza Rockwell C 150 kgf (HRC)
68	940	…	…	920	85,6	76,9	93,2	84,4	75,4	97,3	68
67	900	…	…	895	85,0	76,1	92,9	83,6	74,2	95,0	67
66	865	…	…	870	84,5	75,4	92,5	82,8	73,3	92,7	66
65	832	…	-739	846	83,9	74,5	92,2	81,9	72,0	90,6	65
64	800	…	-722	822	83,4	73,8	91,8	81,1	71,0	88,5	64
63	772	…	-705	799	82,8	73,0	91,4	80,1	69,9	86,5	63
62	746	…	-688	776	82,3	72,2	91,1	79,3	68,8	84,5	62
61	720	…	-670	754	81,8	71,5	90,7	78,4	67,7	82,6	61
60	697	…	-654	732	81,2	70,7	90,2	77,5	66,6	80,8	60
59	674	…	634	710	80,7	69,9	89,8	76,6	65,5	79,0	59
58	653	…	615	690	80,1	69,2	89,3	75,7	64,3	77,3	58
57	633	…	595	670	79,6	68,5	88,9	74,8	63,2	75,6	57
56	613	…	577	650	79,0	67,7	88,3	73,9	62,0	74,0	56
55	595	…	560	630	78,5	66,9	87,9	73,0	60,9	72,4	55
54	577	…	543	612	78,0	66,1	87,4	72,0	59,8	70,9	54
53	560	…	525	594	77,4	65,4	86,9	71,2	58,6	69,4	53
52	544	-500	512	576	76,8	64,6	86,4	70,2	57,4	67,9	52
51	528	-487	496	558	76,3	63,8	85,9	69,4	56,1	66,5	51
50	513	-475	481	542	75,9	63,1	85,5	68,5	55,0	65,1	50
49	498	-464	469	526	75,2	62,1	85,0	67,6	53,8	63,7	49
48	484	451	455	510	74,7	61,4	84,5	66,7	52,5	62,4	48
47	471	442	443	495	74,1	60,8	83,9	65,8	51,4	61,1	47
46	458	432	432	480	73,6	60,0	83,5	64,8	50,3	59,8	46
45	446	421	421	466	73,1	59,2	83,0	64,0	49,0	58,5	45
44	434	409	409	452	72,5	58,5	82,5	63,1	47,8	57,3	44
43	423	400	400	438	72,0	57,7	82,0	62,2	46,7	56,1	43
42	412	390	390	426	71,5	56,9	81,5	61,3	45,5	54,9	42
41	402	381	381	414	70,9	56,2	80,9	60,4	44,3	53,7	41
40	392	371	371	402	70,4	55,4	80,4	59,5	43,1	52,6	40
39	382	362	362	391	69,9	54,6	79,9	58,6	41,9	51,5	39
38	372	353	353	380	69,4	53,8	79,4	57,7	40,8	50,4	38
37	363	344	344	370	68,9	53,1	78,8	56,8	39,6	49,3	37
36	354	336	336	360	68,4	52,3	78,3	55,9	38,4	48,2	36
35	345	327	327	351	67,9	51,5	77,7	55,0	37,2	47,1	35
34	336	319	319	342	67,4	50,8	77,2	54,2	36,1	46,1	34
33	327	311	311	334	66,8	50,0	76,6	53,3	34,9	45,1	33
32	318	301	301	326	66,3	49,2	76,1	52,1	33,7	44,1	32
31	310	294	294	318	65,8	48,4	75,6	51,3	32,5	43,1	31
30	302	286	286	311	65,3	47,7	75,0	50,4	31,3	42,2	30
29	294	279	279	304	64,8	47,0	74,5	49,5	30,1	41,3	29
28	286	271	271	297	64,3	46,1	73,9	48,6	28,9	40,4	28
27	279	264	264	290	63,8	45,2	73,3	47,7	27,8	39,5	27
26	272	258	258	284	63,3	44,6	72,8	46,8	26,7	38,7	26
25	266	253	253	278	62,8	43,8	72,2	45,9	25,5	37,8	25
24	260	247	247	272	62,4	43,1	71,6	45,0	24,3	37,0	24
23	254	243	243	266	62,0	42,1	71,0	44,0	23,1	36,3	23
22	248	237	237	261	61,5	41,6	70,5	43,2	22,0	35,5	22
21	243	231	231	256	61,0	40,9	69,9	42,3	20,7	34,8	21
20	238	226	226	251	60,5	40,1	69,4	41,5	19,6	34,2	20

Equivalences of hardness and resistance

For unalloyed steels and cast irons, there is an approximate and direct relationship between the Vickers hardness and the yield strength, with the yield strength being approximately 3.3 times the Vickers hardness.

Rp0.2==3.3*HV

Table of equivalencies for elastic boundary, Brinell -, Rockwell-, Vickers hardness.

Elastic limit (approximately)	Dureza Brinell	Hardness Rockwell			Hardness Vickers
MPa	HB	HRC	HRA	HRB	HV
-	-	68	86	-	940
-	-	67	85	-	920
-	-	66	85	-	880
-	-	65	84	-	840
-	-	64	83	-	800
-	-	63	83	-	760
-	-	62	83	-	740
-	-	61	82	-	720
-	-	60	81	-	690
-	-	59	81	-	670
2180	618	58	80	-	650
2105	599	57	80	-	630
2030	580	56	79	-	610
1955	561	55	78	-	590
1880	542	54	78	-	570
1850	517	53	77	-	560
1810	523	52	77	-	550
1740	504	51	76	-	530
1665	485	50	76	-	510
1635	473	49	76	-	500
1595	466	48	75	-	490
1540	451	47	75	-	485
1485	437	46	74	-	460
1420	418	45	73	-	440
1350	399	43	72	-	420
1290	380	41	71	-	400
1250	370	40	71	-	390
1220	376	39	70	-	380
1155	342	37	69	-	360
1095	323	34	68	-	340
1030	304	32	66	-	320
965	276	30	65	-	300
930	276	29	65	105	290
900	266	27	64	104	280
865	257	26	63	102.	270
835	247	24	62	101	260
800	238	22	62	100	250
770	228	20	61	98	240
740	219	-	-	97	230
705	209	-	-	95	220
675	199	-	-	94	210
640	190	-	-	92	200
610	181	-	-	90	190
575	171	-	-	87	180
545	162	-	-	85	170
510	152	-	-	82	160
480	143	-	-	79	150
450	133	-	-	75	140
415	124	-	-	71	130
385	114	-	-	67	120
350	105	-	-	62	110
320	95	-	-	56	100
285	86	-	-	48	90
255	76	-	-	-	80