Hardness is a measure of the surface resistance of a metal to permanent plastic deformations. The metal specimen hardness is measured through a penetrator, usually with spherical, pyramidal or conical shape, which is pressed against its surface. The penetrator bit is made of tempered or tungsten carbide steel, so that it is tougher than the tested specimen material. Standard hardness tests are based on the slow application of a known force that compresses the penetrator in a perpendicular direction to the metal surface to be tested. After the impression is made, the penetrator is removed from the surface and then an empirical hardness value, based on either the impression area or the imprint depth, is calculated or read directly on the test machine. The hardness value derived from Brinell, Vickers or Rockwell tests depends on both the impression shape and the applied force.

Being achieved essentially in a conventional way, the hardness values ​obtained by different methods or with different scales can be compared to each other only by means of purely experimental conversion tables, which are valid for individual classes of materials.

Normally hardness tests use dedicated machines called durometers (Fig. 1), so that each test is calibrated on the force value related to the used penetrator bit type.

Fig. (1). Instrumentations used for Rockwell (a), Brinell (b) and Vickers (c) hardness tests.

Fig. (2). Samples from plates and sheets with different thickness.

The aim of this research work is to verify the reliability of results from non-destructive tests with the Leeb method using portable micro-durometers on steel samples with different shape, nature and origin. This allows to:

• − Verify the test reliability with respect to the hardness values ​provided by ASTM A956 [7] and UNI EN ISO 18265 [8] standards;
• − Define, whenever possible, the corrective coefficients to be applied to the Leeb tests for the indirect determination of the carpentry steel classes using the tabular expressions defined in ASTM A956 and UNI EN ISO 18265 standards.

The used steel samples, provided by the Tecnolab srl company, an authorised laboratory for investigation tests on construction materials, are represented by specimens having different shape, origin and material type. In particular, the available samples are:

• Plates and sheeting of different thickness (Fig. 2);
• HE and IPE profiles (Fig. 3);
• Smooth bars with different diameters (Fig. 4).

The above samples have been tested and the achieved test values have been ordered on the basis of the average values of the achieved Brinell hardness. After these non-destructive tests, in the cases where certificates on the steel properties were not available, the various samples have been subjected to destructive mechanical tensile tests in the laboratory, to classify the steel type (S235, S275 or S355) depending on the yielding stress achieved.

For the purpose of the tests, a durometer type MH100 Leeb Hardness Tester, manufactured by the Mitech CO. Ltd company, is used (Fig. 5).

Fig. (3). Samples from HE and IPE profiles.

Fig. (4). Samples from smooth round bars having different diameters.

Fig. (5). MH100 Leeb Hardness Tester manufacturer by the Mitech CO. Ltd company.

Fig. (6). Technical specifications of the MH100 Leeb Hardness Tester.

Such an instrument has a lot of useful advantages, such as:

• Easiness of measurement, since the tester is portable and compact, with the impacting tip integrated into the instrument main body;
• Large measuring range, based on the principle of steel Leeb hardness;
• Large LCD display for viewing parameters and functions, with direct reading of test values ​in HB, HS, HV, HRB, HRC and HRA scales;
• Possibility to vary both the angle of inclination of the impact surface and the type of test to be carried out;
• Large memory, that can hold up to 100 measurement, impact, angle information and impact time values;
• Software for transferring data directly to a PC;
• Simplicity of use, due to the limited geometrical dimensions (148mm x 33mm x 28mm).

From the technical specifications (Fig. 6), the working conditions are described, allowing for very wide use of the device, which is extremely easy to be used even by not highly specialized workers.

The instrument use conditions are:

• Working temperature: -10°C ÷ 50°C;
• Storage temperature: -30°C ÷ 60°C;
• Relative humidity: <90%;
• Preparation of the contact surfaces.

With reference to the last issue, the manufacturer requires the preliminary preparation of the test surfaces for the elimination of residues of oil or fat, traces of rust and/or varnishes. Therefore, the specimens are preliminarily cleaned using a counter-top grinder (Fig. 7), so to make the surface perfectly flat and free from oxidation spots.

This operation is particularly important and delicate, since the durometer support ring must adhere orthogonal to the surface to properly perform the measurement. Otherwise, the device returns default values only, which require to repeat the test. The test consists of three measurement gauges, carried out at different points of the sample, spaced according to the manufacturer's specifications (Table 1).

Initially, the loading test is carried out by pushing the loading column in contact with the surface and slowly releasing it to the rest position, so as to control the efficiency of the column stroke, paying close attention to check that the test surface adheres to the micro-durometer head ring. After positioned the tool, the release button is pressed, marking the load direction coincident with the device axis.

For each sample five tests are carried out, checking that the result data do not have values ​that deviate from ± 1.5HL. Excluding the largest and smallest test values, the arithmetic mean of the remaining three test values is performed.

Generally, the device has memorized a number of materials, which there are already conversion ratios in terms of hardness (Table 2) or resistance (Table 3) for, to be selected before testing. Contrary, if it is required to correlate Leeb hardness values to another hardness values for special materials (aluminium alloys, steels with different carbon content or special steels), it is necessary to execute a new static hardness test campaign to get the conversion ratios.

Fig. (7). Bench grinder for preparation of samples (https://cdn0.grizzly.com/manuals/g0596_m.pdf).

The specimens have been prepared for the execution of the test, assigning an acronym to each of them. In particular, the used abbreviation is ST-X-N, where ST means mild steel, X indicates the specimen type (P = plate; S = sheet; R = round) and N is the progressive number of samples of the same typology.

The samples have been cleaned by solvents from oils and fats detected on the surface. Each sample has been weighed and the related thickness (Tables 4 and 5 for plates and sheets, respectively) or diameter (Table 6), the latter in the case of round specimens, have been measured. Moreover, the steel class has been determined by destructive tensile tests. On each specimen, the area to be used for test has been delimitated by chalk lines. In addition, each sample has been cleaned by means of a bench grinder, bringing the test surface to “white iron”.

Subsequently, the specimens have been left to rest for at least 6 hours in a room at standard temperature and humidity, so to allow both any remaining residual stresses and the abrasion heat to be discharged. The preparation lasted about 12 hours. The day after the preparation of specimens, Leeb micro-hardness tests have been performed. The equipment has been calibrated on mild and cast steels (with index 0 in Tables 2 and 3), taking care to carry out the test by keeping the device as firm as possible and perpendicular to the impact surface of the sample.

The tests have been conducted in three points of the test area, with a distance among them and from the sample edges not less than 5 mm (Table 1). For each specimen, the test values ​have been annotated separately on a laboratory register. Subsequently, the steel class (S235, S275 or S355) has been assigned to each sample according to either the material origin certificate or the result of destructive tensile tests (Tables 4, 6).

The hardness measurements recorded for the different specimens have been renumbered in ascending order based on the average value derived from the three tests, taking care to discard the minimum and maximum values from the performed five test readings (Table 7). Subsequently, the strengths of tested specimens have been derived from conversion tables provided by ASTM and ISO standards, interpolating between two values when test results have not been found in the resistances of reference tables (Table 8).

Later on, the envelope curves of the obtained data (Table 9) have been determined, as shown in Fig. (8), on the basis of the following (Eq. 1-3) :

(1)

(2)

(3)

where:

R_m^ASTM is the tensile strength according to the ASTM standard, expressed in MPa;

R_m^UNI is the tensile strength according to the UNI standard, expressed in MPa;

R_{m_avg} is the average tensile resistance, expressed in MPa;

HB is the Brinell scale static hardness.

Considering the conversion tables shown in the UNI EN ISO 18256 (Table 10) and ASTM A370-03a (Table 9) standards, the formulations encompassing the values of these tables (Fig. 8) have been deduced for S235, S275 and S355 metal carpentry steels with nominal ultimate tensile strengths f_uk,max in the range from 510 to 530 MPa.

Fig. (8). Hardness-strength curves (Brinell method) achieved from conversion tables.

Fig. (9). Hardness-strength curves (Brinell method) achieved from conversion tables for structural steels.

For simplicity, the envelope curves of these strength values for structural carpentry steels have been obtained from the tables as a function of the hardness value HB on the basis of the following expressions (Eq. 4 and 5) (Fig. 9):

(4)

(5)

where:

R_m^ASTM is the tensile strength according to the ASTM standard, expressed in MPa;

R_m^UNI is the tensile strength according to the UNI standard, expressed in MPa.

Thus, from the surface hardness measurements, it is possible to achieve the tensile strengths of tested steels.

By implementing all the values contained in the conversion tables given from both the UNI EN ISO 18256 standard (Table 10) and the ASTM A370-03a one (Table 9), the envelope formulations (Fig. 10), depending on the measurement of hardness HB, are obtained as: Eq. (6 and 7).

(6)

(7)

where:

R_m^ASTM is the tensile strength according to the ASTM standard, expressed in MPa;

R_m^UNI is the tensile strength according to the UNI standard, expressed in MPa.

Comparing the values ​deriving from the ASTM A370-03a standard conversion tables (Table 9) with those achieved from relationships (1), (4) and (6), very similar trends of related curves have been observed (Fig. 11).

The errors committed by using the envelope curve from the whole ASTM table have been evaluated for all the steel classes (Table 11).

From this comparison it has been observed a maximum negative error =-4.37%, a maximum positive error =2.35% and a maximum percentage scatter =6.72% (Fig. 12 and Table 12). Contrary, using the partial tables for structural steels only, a maximum negative error =-2.30%, a maximum positive error =1.83%, and a maximum percentage scatter =4.13%, have been detected. Analysing separately the errors committed for the different steel classes (Table 12), it has been observed that errors found for S235 steels (Fig. 13) are lower than those obtained with S275 steels (Fig. 14).

Fig. (10). Hardness-strength curves (Brinell method) achieved from the complete conversion tables.

Fig. (11). Comparison among hardness-strength curves (Brinell method – ASTM A370-03a standard; tensile tests curve from conversion tables).

Table 11. Comparison among mechanical strengths obtained by hand conversions and data envelopes and relative percentage errors with respect to the ASTM whole table values.

Code	Sample n°	HBavg					e(eq.1-test) (%)	e(eq.4-test) (%)	e(eq.6-test) (%)
							(1)	(2)	(3)
ST-P-01	1	88,7	308,5	311,8	311,7	313,7	1,06	1,03	1,69
ST-P-02	2	89,3	310,6	313,5	313,4	315,6	0,93	0,91	1,63
ST-P-25	3	89,7	312	314,4	314,3	316,6	0,76	0,74	1,48
ST-P-09	4	90,3	314,0	316,1	316,1	318,5	0,67	0,67	1,45
ST-P-15	5	90,7	315,7	317,0	317,0	319,5	0,40	0,41	1,20
ST-P-23	6	90,7	315,7	317,0	317,0	319,5	0,40	0,41	1,20
ST-P-24	7	93,0	323,5	323,1	323,2	326,3	-0,13	-0,08	0,86
ST-S-01	8	94,0	330,0	325,7	326,0	329,2	-1,29	-1,23	-0,25
ST-P-13	9	96,0	337,0	331,1	331,4	335,0	-1,75	-1,66	-0,60
ST-P-03	10	96,7	339,5	332,9	333,2	336,9	-1,94	-1,84	-0,76
ST-S-04	11	100,3	341,0	343,0	343,4	347,7	0,58	0,70	1,95
ST-R-01	12	100,7	342,4	343,9	344,3	348,6	0,44	0,56	1,82
ST-P-08	13	103,7	352,4	352,3	352,8	357,4	-0,02	0,11	1,43
ST-P-05	14	104,0	353,4	353,3	353,7	358,4	-0,04	0,10	1,42
ST-P-07	15	105,0	360	356,1	356,6	361,4	-1,08	-0,95	0,38
ST-P-26	16	106,7	364	360,9	361,4	366,3	-0,86	-0,72	0,63
ST-P-10	17	107,3	366,6	362,8	363,3	368,3	-1,03	-0,90	0,45
ST-R-02	18	109,0	366,6	367,7	368,1	373,2	0,29	0,41	1,80
ST-R-03	19	109,0	366,6	367,7	368,1	373,2	0,29	0,41	1,80
ST-P-16	20	109,0	369	367,7	368,1	373,2	-0,36	-0,24	1,14
ST-R-04	21	109,7	369	369,6	370,1	375,2	0,17	0,29	1,67
ST-S-02	22	109,7	370	369,6	370,1	375,2	-0,10	0,01	1,40
ST-S-06	23	110,7	370	372,6	373,0	378,1	0,69	0,80	2,20
ST-R-05	24	110,7	370	372,6	373,0	378,1	0,69	0,80	2,20
ST-P-12	25	111,0	373,4	373,6	374,0	379,1	0,04	0,15	1,54
ST-P-04	26	111,3	374,4	374,5	374,9	380,1	0,04	0,14	1,53
ST-R-06	27	111,7	375,7	375,5	375,9	381,1	-0,05	0,06	1,44
ST-P-22	28	112,0	376,7	376,5	376,9	382,1	-0,05	0,05	1,44
ST-S-03	29	113,0	380,1	379,5	379,8	385,1	-0,16	-0,07	1,31
ST-P-21	30	113,7	382,4	381,5	381,8	387,1	-0,23	-0,15	1,22
ST-R-07	31	114,3	384,5	383,5	383,8	389,1	-0,26	-0,18	1,19
ST-R-08	32	114,7	385,8	384,5	384,8	390,1	-0,33	-0,26	1,10
ST-P-06	33	116,0	385	388,6	388,8	394,0	0,93	0,98	2,35
ST-R-09	34	117,0	395	391,6	391,8	397,0	-0,85	-0,81	0,51
ST-R-10	35	117,7	397,3	393,7	393,8	399,0	-0,91	-0,88	0,43
ST-R-11	36	118,0	398,4	394,7	394,8	400,0	-0,93	-0,90	0,41
ST-P-27	37	122,7	410,7	409,3	409,1	414,1	-0,35	-0,40	0,82
ST-P-18	38	122,7	410,7	409,3	409,1	414,1	-0,35	-0,40	0,82
ST-P-31	39	125,7	422,4	418,8	418,4	423,1	-0,84	-0,95	0,17
ST-P-32	40	133,0	443,3	442,9	441,6	445,4	-0,09	-0,37	0,48
ST-P-19	41	130,3	435	434,0	433,1	437,3	-0,22	-0,43	0,53
ST-P-17	42	131,7	440,7	438,4	437,4	441,4	-0,51	-0,76	0,15
ST-P-11	43	135,3	451,7	450,7	449,2	452,6	-0,21	-0,55	0,19
ST-S-06	44	136,3	454,3	454,1	452,5	455,6	-0,04	-0,41	0,29
ST-P-29	45	139,7	462,3	465,6	463,4	465,9	0,70	0,24	0,77
ST-P-28	46	149,3	490,8	499,8	496,0	495,8	1,83	1,05	1,02
ST-S-08	47	153,0	505	513,2	508,6	507,3	1,63	0,72	0,45
ST-P-14	48	154,7	510,6	519,4	514,5	512,5	1,72	0,76	0,37
ST-P-20	49	155,7	513,9	523,1	518,0	515,6	1,79	0,79	0,34
ST-P-34	50	156,7	532,4	526,9	521,5	518,8	-1,04	-2,05	-2,56
ST-R-12	51	158,0	536,8	531,9	526,2	523,0	-0,91	-1,97	-2,57
ST-S-07	52	162,0	560	547,1	540,5	535,6	-2,30	-3,48	-4,35
ST-P-33	53	163,3	564,5	552,3	545,3	539,8	-2,16	-3,40	-4,37
ST-R-13	54	166,3	569,5	564,0	556,2	549,4	-0,97	-2,33	-3,54
ST-R-14	55	167,7	574,2	569,2	561,1	553,6	-0,87	-2,28	-3,59
ST-P-30	56	169,0	570	574,5	566,0	557,9	0,79	-0,70	-2,13
ST-S-05	57	169,7	572,3	577,1	568,5	560,0	0,85	-0,67	-2,15
(*) Tensile strength from conversion tables (1) Percentage error from the comparison between the curves deriving from the ASTM A370-03a data envelope (eq. 1) and the hardness data resulting from manual conversion with ASTM A370-03a tables (test values) (2) Percentage error from the comparison between the ASTM A370-03a partial conversion curves for carpentry steels (eq. 4) and the hardness data resulting from manual conversion with ASTM A370-03a tables (test values) (3) Percentage error from the comparison between the ASTM A370-03a full table curve (eq. 6) and the hardness data resulting from manual conversion with ASTM A370-03a tables (test values)

Table 12. Minimum, maximum and average errors and deviation values among achieved strengths determined according to ASTM methods.

Comparison Case
(1)	-2,30	1,83	-0,10	4,13
(2)	-3,48	1,05	-0,33	4,54
(3)	-4,37	2,35	0,42	6,72
S235 - (1)	-1,94	1,06	/	3,01
S235 - (2)	-1,84	1,03	0,06	2,87
S235 - (3)	-0,76	1,95	1,04	2,71
S275 - (1)	-1,08	0,93	-0,22	2,01
S275 - (2)	-0,95	0,98	-0,16	1,93
S275 - (3)	0,17	2,35	1,17	2,18
S355 - (1)	-2,30	1,83	/	4,13
S355 - (2)	-3,48	1,05	-0,91	4,54
S355 - (3)	-4,37	1,02	-1,24	5,39
(1) Percentage error between the ASTM A370-03a data envelope curves and the hardness data resulting from manual conversion with ASTM A370-03a tables (2) Percentage error between the ASTM A370-03a partial conversion curves for carpentry steels and the hardness data resulting from manual conversion with ASTM A370-03a tables (3) Percentage error between the ASTM A370-03a full table curve and the hardness data resulting from manual conversion with ASTM A370-03a tables

Fig. (12). Percentage errors with respect to the envelope curve of the ASTM whole table.

Fig. (13). Percentage errors in predicting the Brinell Hardness for S235 steels (ASTM standard).

The increase of the resistance class from S275 to S355 (Fig. 15) results in errors higher than the ones obtained with lower resistance classes. Comparing the data from non-destructive Leeb tests (Table 11) with the results of tensile tests, it has been observed that for samples ST-P-05 (n.14) and ST-P-07 (n. 15) the passage of class from S235 to the S275 takes place.

The maximum scatter between the resistances of the two samples is equal to 6.60 MPa. In general, for 1 out of 15 samples of S235 steel class, there is an error in the identification of a higher resistance class, with a percentage error referred to the number of specimens investigated. Regarding the classification between S275 steels and S355 ones, from the data (Table 11) the passage is observed for the samples ST-P-32 (n.40) and ST-P-19 (n.41). The maximum scatter among resistances is equal to 20.9 MPa. In the transition between S275 class and the S355 one, for 1 out of 26 samples made of S275 steel an error is committed in the assignment of the class with respect to the higher one.

Fig. (14). Percentage errors in predicting the Brinell Hardness for S275 steels (ASTM standard).

Fig. (15). Percentage errors in predicting the Brinell Hardness for S355 steels (ASTM standard).

With regard to the samples ST-P-26, ST-P-11 and ST-S-06, the detected hardness values ​have been noticed in disagreement with the actual steel class deriving from either tensile test results or origin certificates. Moreover, comparing the resistance values ​for the different steel classes gotten from the different conversions from Leeb tests, it has been observed for S235 steels a maximum positive error and a maximum negative error (Table 13). Therefore, the tests tend to underestimate the resistance values, going on the safe side in terms of classification. For S275 steel (Table 14), the conversion gives rise to a maximum positive error and a maximum negative error .

Table 13. Comparison among strength values obtained from ASTM tables and envelopes and mechanical resistances for S235 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-01	1	-14,31	-13,39	-13,42	-12,85
ST-P-02	2	-13,72	-12,92	-12,93	-12,32
ST-P-25	3	-13,33	-12,68	-12,69	-12,05
ST-P-09	4	-12,78	-12,20	-12,20	-11,52
ST-P-15	5	-12,31	-11,96	-11,95	-11,25
ST-P-23	6	-12,31	-11,96	-11,95	-11,25
ST-P-24	7	-10,14	-10,25	-10,21	-9,37
ST-S-01	8	-8,33	-9,52	-9,46	-8,56
ST-P-13	9	-6,39	-8,03	-7,94	-6,95
ST-P-03	10	-5,69	-7,52	-7,43	-6,41
ST-S-04	11	-5,28	-4,73	-4,61	-3,43
ST-R-01	12	-4,89	-4,47	-4,35	-3,16
ST-P-08	13	-2,11	-2,14	-2,00	-0,71
ST-P-05	14	-1,83	-1,87	-1,74	-0,44
ST-P-07	15	/	-1,08	-0,95	0,38
ST-P-26	16	1,11	0,25	0,38	1,75
–		1,11	0,25	0,38	1,75
–		-14,31	-13,39	-13,42	-12,85
–		-7,64	-7,78	-7,72	-6,76
–		15,42	13,64	13,80	14,60
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Table 14. Comparison among strength values obtained from ASTM tables and envelopes and mechanical resistances for S275 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-07	15	-16,28	-17,19	-17,07	-15,96
ST-P-26	16	-15,35	-16,07	-15,96	-14,82
ST-P-10	17	-14,74	-15,62	-15,52	-14,36
ST-R-02	18	-14,74	-14,50	-14,39	-13,21
ST-R-03	19	-14,74	-14,50	-14,39	-13,21
ST-P-16	20	-14,19	-14,50	-14,39	-13,21
ST-R-04	21	-14,19	-14,04	-13,94	-12,75
ST-S-02	22	-13,95	-14,04	-13,94	-12,75
ST-S-06	23	-13,95	-13,36	-13,26	-12,06
ST-R-05	24	-13,95	-13,36	-13,26	-12,06
ST-P-12	25	-13,16	-13,13	-13,03	-11,83
ST-P-04	26	-12,93	-12,90	-12,81	-11,60
ST-R-06	27	-12,63	-12,67	-12,58	-11,37
ST-P-22	28	-12,40	-12,44	-12,35	-11,14
ST-S-03	29	-11,60	-11,74	-11,66	-10,45
ST-P-21	30	-11,07	-11,28	-11,20	-9,98
ST-R-07	31	-10,58	-10,81	-10,74	-9,52
ST-R-08	32	-10,28	-10,58	-10,51	-9,29
ST-P-06	33	-10,47	-9,64	-9,58	-8,36
ST-R-09	34	-8,14	-8,92	-8,89	-7,67
ST-R-10	35	-7,60	-8,45	-8,42	-7,20
ST-R-11	36	-7,35	-8,21	-8,18	-6,97
ST-P-27	37	-4,49	-4,82	-4,87	-3,71
ST-P-18	38	-4,49	-4,82	-4,87	-3,71
ST-P-31	39	-1,77	-2,60	-2,70	-1,60
–		5,65	5,61	5,22	5,96
–		-16,28	-17,19	-17,07	-15,96
–		-8,92	-9,13	-9,12	-7,99
–		21,93	22,79	22,30	21,92
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Table 15. Comparison among strength values obtained from ASTM tables and envelopes and mechanical resistances for S355 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-19	41	-14,71	-14,90	-15,08	-14,26
ST-P-17	42	-13,59	-14,03	-14,24	-13,46
ST-P-11	43	-11,43	-11,62	-11,92	-11,26
ST-S-06	44	-10,92	-10,96	-11,28	-10,66
ST-P-29	45	-9,35	-8,71	-9,14	-8,65
ST-P-28	46	-3,76	-2,00	-2,75	-2,78
ST-S-08	47	-0,98	0,63	-0,26	-0,53
ST-P-14	48	0,12	1,84	0,88	0,49
ST-P-20	49	0,76	2,57	1,56	1,11
ST-P-34	50	4,39	3,31	2,25	1,72
ST-R-12	51	5,25	4,29	3,18	2,55
ST-S-07	52	9,80	7,28	5,98	5,02
ST-P-33	53	10,69	8,29	6,92	5,85
ST-R-13	54	11,67	10,58	9,06	7,72
ST-R-14	55	12,59	11,61	10,02	8,55
–		12,59	13,17	11,46	9,80
–		-14,71	-14,90	-15,08	-14,26
–		0,85	0,82	-0,14	-0,55
–		27,29	28,06	26,54	24,06
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Fig. (16). Comparison among hardness-strength curves (Brinell method – UNI ISO 18265 standard; tensile tests curve from conversion tables).

Table 16. Comparison among mechanical strengths obtained by hand conversions and data envelopes and relative percentage errors with respect to the UNI ISO whole table values.

Code	Sample n°	HBavg					e(eq.2-test) (%)	e(eq.5-test) (%)	e(eq.7-test) (%)
							(1)	(2)	(3)
ST-P-01	1	88,7	295,6	329,9	334,7	304,8	11,61	13,22	3,12
ST-P-02	2	89,3	297,7	332,4	337,1	307,0	11,65	13,25	3,12
ST-P-25	3	89,7	299	333,6	338,4	308,1	11,57	13,17	3,03
ST-P-09	4	90,3	305,3	336,0	340,9	310,2	10,07	11,65	1,61
ST-P-15	5	90,7	306,7	337,3	342,1	311,3	9,97	11,54	1,49
ST-P-23	6	90,7	306,7	337,3	342,1	311,3	9,97	11,54	1,49
ST-P-24	7	93,0	314,5	345,8	350,8	318,8	9,97	11,53	1,37
ST-S-01	8	94,0	317,8	349,5	354,5	322,0	9,98	11,54	1,33
ST-P-13	9	96,0	323,4	356,9	361,9	328,5	10,35	11,91	1,58
ST-P-03	10	96,7	325,7	359,3	364,4	330,6	10,32	11,88	1,52
ST-S-04	11	100,3	336,7	372,8	378,1	342,5	10,73	12,29	1,72
ST-R-01	12	100,7	338,0	374,1	379,3	343,6	10,67	12,22	1,65
ST-P-08	13	103,7	348,1	385,1	390,5	353,3	10,64	12,18	1,49
ST-P-05	14	104,0	349,1	386,4	391,8	354,4	10,67	12,22	1,51
ST-P-07	15	105,0	355,7	390,0	395,5	357,6	9,66	11,19	0,54
ST-P-26	16	106,7	357,6	396,2	401,7	363,0	10,79	12,34	1,52
ST-P-10	17	107,3	370	398,7	404,2	365,2	7,75	9,25	-1,30
ST-R-02	18	109,0	370	404,8	410,4	370,6	9,41	10,93	0,16
ST-R-03	19	109,0	370	404,8	410,4	370,6	9,41	10,93	0,16
ST-P-16	20	109,0	372,4	404,8	410,4	370,6	8,71	10,22	-0,48
ST-R-04	21	109,7	372,4	407,3	412,9	372,8	9,37	10,89	0,10
ST-S-02	22	109,7	375,4	407,3	412,9	372,8	8,50	10,00	-0,70
ST-S-06	23	110,7	375,8	411,0	416,7	376,0	9,36	10,88	0,06
ST-R-05	24	110,7	375,8	411,0	416,7	376,0	9,36	10,88	0,06
ST-P-12	25	111,0	376,8	412,2	417,9	377,1	9,40	10,92	0,08
ST-P-04	26	111,3	377,8	413,5	419,2	378,2	9,44	10,95	0,10
ST-R-06	27	111,7	379,1	414,7	420,4	379,3	9,39	10,90	0,04
ST-P-22	28	112,0	380,2	415,9	421,7	380,3	9,40	10,91	0,04
ST-S-03	29	113,0	381,6	419,6	425,4	383,6	9,97	11,49	0,52
ST-P-21	30	113,7	384	422,1	427,9	385,8	9,92	11,44	0,46
ST-R-07	31	114,3	386	424,6	430,4	387,9	9,99	11,51	0,50
ST-R-08	32	114,7	387,4	425,8	431,7	389,0	9,91	11,43	0,42
ST-P-06	33	116,0	391,8	430,7	436,7	393,4	9,94	11,46	0,40
ST-R-09	34	117,0	393,3	434,5	440,4	396,6	10,46	11,99	0,84
ST-R-10	35	117,7	395,6	436,9	442,9	398,8	10,45	11,97	0,80
ST-R-11	36	118,0	396,6	438,2	444,2	399,9	10,48	12,00	0,82
ST-P-27	37	122,7	410,6	455,5	461,7	415,1	10,93	12,46	1,09
ST-P-18	38	122,7	410,6	455,5	461,7	415,1	10,93	12,46	1,09
ST-P-31	39	125,7	420,7	466,6	473,0	424,9	10,92	12,44	0,99
ST-P-32	40	133,0	450	494,0	500,7	448,9	9,77	11,27	-0,25
ST-P-19	41	130,3	437,7	484,0	490,7	440,1	10,58	12,10	0,55
ST-P-17	42	131,7	442,4	489,0	495,7	444,5	10,53	12,05	0,47
ST-P-11	43	135,3	457,8	502,7	509,6	456,5	9,80	11,31	-0,28
ST-S-06	44	136,3	461,2	506,4	513,3	459,8	9,80	11,31	-0,31
ST-P-29	45	139,7	470,7	518,9	526,0	470,7	10,24	11,74	/
ST-P-28	46	149,3	502,7	555,1	562,7	502,5	10,42	11,94	-0,04
ST-S-08	47	153,0	513,4	568,9	576,7	514,6	10,81	12,32	0,23
ST-P-14	48	154,7	519,1	575,1	583,0	520,1	10,80	12,32	0,19
ST-P-20	49	155,7	522,4	578,9	586,8	523,4	10,82	12,34	0,19
ST-P-34	50	156,7	532,4	582,7	590,7	526,7	9,44	10,94	-1,07
ST-R-12	51	158,0	536,8	587,7	595,8	531,1	9,48	10,98	-1,06
ST-S-07	52	162,0	545	602,8	611,1	544,3	10,60	12,12	-0,12
ST-P-33	53	163,3	549,4	607,8	616,2	548,8	10,63	12,15	-0,12
ST-R-13	54	166,3	561,0	619,1	627,7	558,7	10,36	11,88	-0,41
ST-R-14	55	167,7	565,7	624,2	632,8	563,1	10,34	11,86	-0,46
ST-P-30	56	169,0	570,1	629,2	637,9	567,5	10,37	11,89	-0,45
ST-S-05	57	169,7	572,5	631,7	640,4	569,8	10,35	11,87	-0,48
(*) Tensile strength from conversion tables (1) Percentage error from the comparison between the curves deriving from the UNI ISO 18265 data envelope (eq. 2) and the hardness data resulting from manual conversion with UNI ISO 18265 tables (test values) (2) Percentage error from the comparison between the UNI ISO 18265 partial conversion curves for carpentry steels (eq. 5) and the hardness data resulting from manual conversion with UNI ISO 18265 tables (test values) (3) Percentage error from the comparison between the UNI ISO 18265 full table curve (eq. 7) and the hardness data resulting from manual conversion with UNI ISO 18265 tables (test values)

The percentage scatter in terms of stress between the S275 class and the S235 one is defined as Eq. (8):

(8)

and herein assumes the value of 16.28%, which is greater than the maximum negative error recorded. However, the test does not imply problems in the class assignment.

For S355 steel class (Table 15), the conversion provides a maximum positive error and a maximum negative error .

The percentage scatter between these two steel classes is 15.69%, a value greater than the maximum negative error recorded.

The tests conducted on 2 out of the total 19 specimens have provided values with an error in the class assignment, while for higher values this problem is not felt.

Comparing the results deriving from relationships (2), (5) and (7), the achieved curves have trends very similar to each other (Fig. 16).

Nevertheless, these values are very far from those gotten from the UNI ISO 18265 standard conversion tables (Table 16). In particular, when values deriving from the previously mentioned relationships are compared with the UNI complete table ones, it has been recorded a maximum error , a minimum error and a maximum percentage scatter (Fig. 17 and Table 17).

Fig. (17). Percentage errors with respect to the envelope curve of the UNI ISO whole table.

Fig. (18). Percentage errors in predicting the Brinell Hardness for S235 steels (UNI ISO standard).

Contrary, in the case of conversion using either only partial tables for carpentry steels or envelope formulas from manual conversion data, it has been noticed that the committed errors are higher than the previous case (Table 17). In fact, the maximum error is , the minimum error is and the maximum scatter is . Analysing the error detected for the different steel classes (Table 17), it has been observed that for S235 (Fig. 18), S275 (Fig. 19) and S355 (Fig. 20) steels, the errors tends to reduce only in the case of relationship (7).

Analyzing the data from non-destructive Leeb tests (Table 18), the transition from S235 class to S275 class does not take place in a univocal manner, depending on the different assessments made. The error committed is much wider and implies that, according to the criterion used for 9 out of 17 samples of class S235 (samples n.9-17), an error in the identification of a higher resistance class can be made (Table 18), with a percentage error . Similarly, in the transition from S275 steel to S355 one, it is observed that for 10 out of 26 samples a percentage error is committed in the assignment to a higher class (Table 19).

Fig. (19). Percentage errors in predicting the Brinell Hardness for S275 steels (UNI ISO standard).

Fig. (20). Percentage errors in predicting the Brinell Hardness for S355 steels (UNI ISO standard).

Table 17. Minimum, maximum and average errors and deviation values among achieved strengths determined according to UNI ISO methods.

Comparison Case
(1)	9,79	12,41	11,06	2,62
(2)	8,23	10,88	9,54	2,65
(3)	-3,03	1,32	-0,53	4,35
S235 - (1)	9,79	10,55	10,11	0,76
S235 - (2)	8,23	9,02	8,56	0,79
S235 - (3)	-3,03	-1,32	-1,82	1,71
S275 - (1)	10,59	11,56	10,93	0,97
S275 - (2)	9,07	10,05	9,42	0,98
S275 - (3)	-1,49	1,32	-0,30	2,81
S355 - (1)	11,48	12,41	12,04	0,93
S355 - (2)	9,98	10,88	10,52	0,90
S355 - (3)	-0,55	1,08	0,19	1,63
(1) Percentage error between the UNI ISO 18265 data envelope curves and the hardness data resulting from manual conversion with UNI ISO 18265 tables (2) Percentage error between the UNI ISO 18265 partial conversion curves for carpentry steels and the hardness data resulting from manual conversion with UNI ISO 18265 tables (3) Percentage error between the UNI ISO 18265 full table curve and the hardness data resulting from manual conversion with UNI ISO 18265 tables

Table 18. Comparison among strength values obtained from UNI ISO tables and envelopes and mechanical resistances for S235 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-01	1	-17,89	-8,35	-7,04	-15,32
ST-P-02	2	-17,31	-7,67	-6,35	-14,73
ST-P-25	3	-16,94	-7,33	-6,00	-14,43
ST-P-09	4	-15,19	-6,65	-5,32	-13,83
ST-P-15	5	-14,81	-6,31	-4,97	-13,53
ST-P-23	6	-14,81	-6,31	-4,97	-13,53
ST-P-24	7	-12,64	-3,93	-2,56	-11,44
ST-S-01	8	-11,72	-2,91	-1,53	-10,55
ST-P-13	9	-10,17	-0,87	0,53	-8,75
ST-P-03	10	-9,53	-0,19	1,22	-8,15
ST-S-04	11	-6,47	3,56	5,02	-4,86
ST-R-01	12	-6,11	3,91	5,36	-4,56
ST-P-08	13	-3,31	6,98	8,47	-1,86
ST-P-05	14	-3,03	7,32	8,82	-1,56
ST-P-07	15	-1,19	8,35	9,86	-0,66
ST-P-26	16	-0,67	10,06	11,59	0,84
ST-P-10	17	2,78	10,74	12,28	1,44
–		2,78	10,74	12,28	1,44
–		-17,89	-8,35	-7,04	-15,32
–		-9,35	0,02	1,44	-7,97
–		20,67	19,09	19,32	16,76
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Table 19. Comparison among strength values obtained from UNI ISO tables and envelopes and mechanical resistances for S275 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-26	16	-16,84	-7,86	-6,58	-15,58
ST-P-10	17	-13,95	-7,29	-6,00	-15,07
ST-R-02	18	-13,95	-5,85	-4,55	-13,81
ST-R-03	19	-13,95	-5,85	-4,55	-13,81
ST-P-16	20	-13,40	-5,85	-4,55	-13,81
ST-R-04	21	-13,40	-5,28	-3,97	-13,31
ST-S-02	22	-12,70	-5,28	-3,97	-13,31
ST-S-06	23	-12,60	-4,42	-3,10	-12,56
ST-R-05	24	-12,60	-4,42	-3,10	-12,56
ST-P-12	25	-12,37	-4,13	-2,81	-12,30
ST-P-04	26	-12,14	-3,85	-2,52	-12,05
ST-R-06	27	-11,84	-3,56	-2,23	-11,80
ST-P-22	28	-11,58	-3,27	-1,93	-11,55
ST-S-03	29	-11,26	-2,41	-1,06	-10,79
ST-P-21	30	-10,70	-1,84	-0,48	-10,29
ST-R-07	31	-10,23	-1,26	0,10	-9,78
ST-R-08	32	-9,91	-0,98	0,39	-9,53
ST-P-06	33	-8,88	0,17	1,55	-8,52
ST-R-09	34	-8,53	1,04	2,43	-7,77
ST-R-10	35	-8,00	1,61	3,01	-7,26
ST-R-11	36	-7,77	1,90	3,30	-7,01
ST-P-27	37	-4,51	5,93	7,38	-3,47
ST-P-18	38	-4,51	5,93	7,38	-3,47
ST-P-31	39	-2,16	8,52	10,01	-1,19
ST-P-32	40	4,65	14,88	16,45	4,38
–		4,65	14,88	16,45	4,38
–		-16,84	-7,86	-6,58	-15,58
–		-10,13	-1,34	0,03	-9,85
–		21,49	22,74	23,03	19,96
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Analyzing the resistance values deriving from the different conversions from Leeb tests to the reference values of classes, for S235steels a maximum error and a minimum error is observed (Table 18).

The test, therefore, tends to overestimate the resistance values, classifying S235 steel samples as S275 steel ones, and, thus, operating not on the safe side in terms of classification. For S275 class steel (Table 19) the conversion involves a maximum error and a minimum error . Given a percentage difference between S235 class and S275 one, defined by h) is equal to , it is not possible to assign the class in an unambiguous way.

For S355 steel class (Table 20) the conversion involves a maximum error and a minimum error . The percentage difference between S275 class and S355 one is , higher than the minimum error committed. The tests conducted for 2 out of 19 samples provide limited values, which could lead to an error in the assignment to the samples of a steel lower class.

Using the average values deriving from formulations provided by ASTM A370-03a and UNI ISO 18265 methods (Table 21), an intermediate trend between the two curves ones is achieved (Fig. 21).

Table 20. Comparison among strength values obtained from UNI ISO tables and envelopes and mechanical resistances for S355 grade steels.

Code	Sample n°	e1 (%)	e2 (%)	e3 (%)	e4 (%)
		(1)	(2)	(3)	(4)
ST-P-31	39	-17,51	-8,50	-7,25	-16,69
ST-P-32	40	-11,76	-3,14	-1,82	-11,99
ST-P-19	41	-14,18	-5,09	-3,79	-13,70
ST-P-17	42	-13,25	-4,12	-2,81	-12,85
ST-P-11	43	-10,24	-1,43	-0,09	-10,49
ST-S-06	44	-9,57	-0,70	0,66	-9,85
ST-P-29	45	-7,71	1,74	3,13	-7,70
ST-P-28	46	-1,43	8,84	10,33	-1,47
ST-S-08	47	0,67	11,55	13,07	0,90
ST-P-14	48	1,78	12,77	14,32	1,98
ST-P-20	49	2,43	13,51	15,07	2,63
ST-P-34	50	4,39	14,25	15,82	3,28
ST-R-12	51	5,25	15,23	16,82	4,14
ST-S-07	52	6,86	18,19	19,81	6,73
ST-P-33	53	7,73	19,18	20,82	7,60
ST-R-13	54	10,00	21,40	23,07	9,55
ST-R-14	55	10,92	22,39	24,07	10,41
ST-P-30	56	11,78	23,37	25,08	11,28
ST-S-05	57	12,25	23,87	25,58	11,72
–		12,25	23,87	25,58	11,72
–		-17,51	-8,50	-7,25	-16,69
–		-0,61	9,65	11,15	-0,76
–		29,76	32,37	32,82	28,41
Conversion with:  (1) Manual use of the table  (2) Envelope from manual conversion values  (3) Envelope from partial tables for carpentry steels  (4) Envelope from the complete table

Table 21. Comparison among mechanical strengths obtained by hand conversions and data envelopes and relative percentage errors with respect to the average values between the UNI ISO whole table values and the ASTM whole table ones.

Code	Sample n°	HBavg					e(b-a)%	e(c-a)%	e(d-a)%
			[MPa]	[MPa]	[MPa]	[MPa]	(1)	(2)	(3)
ST-P-01	1	88,7	302,1	305,3	323,2	309,3	1,06%	6,99%	2,39%
ST-P-02	2	89,3	304,2	307,3	325,3	311,3	1,02%	6,95%	2,36%
ST-P-25	3	89,7	305,5	308,3	326,4	312,3	0,90%	6,83%	2,24%
ST-P-09	4	90,3	309,7	310,3	328,5	314,4	0,20%	6,08%	1,53%
ST-P-15	5	90,7	311,2	311,3	329,5	315,4	0,02%	5,89%	1,35%
ST-P-23	6	90,7	311,2	311,3	329,5	315,4	0,02%	5,89%	1,35%
ST-P-24	7	93,0	319,0	318,3	337,0	322,5	-0,21%	5,65%	1,11%
ST-S-01	8	94,0	323,9	321,4	340,2	325,6	-0,78%	5,04%	0,53%
ST-P-13	9	96,0	330,2	327,5	346,7	331,7	-0,83%	4,99%	0,47%
ST-P-03	10	96,7	332,6	329,5	348,8	333,8	-0,94%	4,88%	0,36%
ST-S-04	11	100,3	338,9	340,8	360,7	345,1	0,57%	6,46%	1,84%
ST-R-01	12	100,7	340,2	341,8	361,8	346,1	0,47%	6,36%	1,74%
ST-P-08	13	103,7	350,3	351,1	371,6	355,4	0,24%	6,11%	1,46%
ST-P-05	14	104,0	351,3	352,1	372,7	356,4	0,26%	6,12%	1,47%
ST-P-07	15	105,0	357,9	355,3	376,0	359,5	-0,72%	5,08%	0,46%
ST-P-26	16	106,7	360,8	360,5	381,5	364,7	-0,09%	5,75%	1,07%
ST-P-10	17	107,3	368,3	362,6	383,7	366,7	-1,55%	4,19%	-0,43%
ST-R-02	18	109,0	368,3	367,8	389,3	371,9	-0,12%	5,70%	0,98%
ST-R-03	19	109,0	368,3	367,8	389,3	371,9	-0,12%	5,70%	0,98%
ST-P-16	20	109,0	370,7	367,8	389,3	371,9	-0,77%	5,01%	0,32%
ST-R-04	21	109,7	370,7	369,9	391,5	374,0	-0,20%	5,61%	0,88%
ST-S-02	22	109,7	372,7	369,9	391,5	374,0	-0,74%	5,04%	0,34%
ST-S-06	23	110,7	372,9	373,1	394,8	377,1	0,06%	5,88%	1,12%
ST-R-05	24	110,7	372,9	373,1	394,8	377,1	0,06%	5,88%	1,12%
ST-P-12	25	111,0	375,1	374,2	395,9	378,1	-0,25%	5,56%	0,80%
ST-P-04	26	111,3	376,1	375,2	397,1	379,1	-0,23%	5,57%	0,81%
ST-R-06	27	111,7	377,4	376,3	398,2	380,2	-0,29%	5,50%	0,74%
ST-P-22	28	112,0	378,5	377,4	399,3	381,2	-0,29%	5,51%	0,73%
ST-S-03	29	113,0	380,9	380,5	402,6	384,3	-0,08%	5,72%	0,92%
ST-P-21	30	113,7	383,2	382,7	404,9	386,4	-0,14%	5,66%	0,84%
ST-R-07	31	114,3	385,3	384,8	407,1	388,5	-0,12%	5,68%	0,84%
ST-R-08	32	114,7	386,6	385,9	408,2	389,5	-0,19%	5,60%	0,76%
ST-P-06	33	116,0	388,4	390,1	412,7	393,7	0,45%	6,27%	1,36%
ST-R-09	34	117,0	394,2	393,4	416,1	396,8	-0,20%	5,57%	0,68%
ST-R-10	35	117,7	396,5	395,5	418,4	398,9	-0,23%	5,53%	0,62%
ST-R-11	36	118,0	397,5	396,6	419,5	399,9	-0,23%	5,54%	0,61%
ST-P-27	37	122,7	410,7	411,8	435,4	414,6	0,27%	6,03%	0,95%
ST-P-18	38	122,7	410,7	411,8	435,4	414,6	0,27%	6,03%	0,95%
ST-P-31	39	125,7	421,6	421,6	445,7	424,0	0,01%	5,73%	0,58%
ST-P-32	40	133,0	446,7	446,0	471,2	447,1	-0,15%	5,49%	0,11%
ST-P-19	41	130,3	436,4	437,1	461,9	438,7	0,16%	5,85%	0,54%
ST-P-17	42	131,7	441,6	441,5	466,5	442,9	-0,01%	5,66%	0,31%
ST-P-11	43	135,3	454,8	453,8	479,4	454,5	-0,21%	5,42%	-0,05%
ST-S-06	44	136,3	457,8	457,2	482,9	457,7	-0,13%	5,49%	-0,01%
ST-P-29	45	139,7	466,5	468,5	494,7	468,3	0,42%	6,04%	0,38%
ST-P-28	46	149,3	496,8	501,8	529,3	499,2	1,01%	6,56%	0,49%
ST-S-08	47	153,0	509,2	514,6	542,7	510,9	1,06%	6,57%	0,34%
ST-P-14	48	154,7	514,9	520,4	548,7	516,3	1,09%	6,58%	0,28%
ST-P-20	49	155,7	518,2	524,0	552,4	519,5	1,12%	6,61%	0,26%
ST-P-34	50	156,7	532,4	527,5	556,1	522,7	-0,92%	4,45%	-1,81%
ST-R-12	51	158,0	536,8	532,2	561,0	527,0	-0,85%	4,51%	-1,82%
ST-S-07	52	162,0	552,5	546,5	575,8	540,0	-1,09%	4,21%	-2,27%
ST-P-33	53	163,3	557,0	551,3	580,7	544,3	-1,02%	4,27%	-2,27%
ST-R-13	54	166,3	565,3	562,1	591,9	554,0	-0,56%	4,72%	-1,99%
ST-R-14	55	167,7	570,0	566,9	596,9	558,4	-0,53%	4,73%	-2,03%
ST-P-30	56	169,0	570,1	571,8	601,9	562,7	0,30%	5,59%	-1,29%
ST-S-05	57	169,7	572,4	574,2	604,5	564,9	0,31%	5,60%	-1,32%
(*) Average tensile strength between ASTM 370-03a standard resistance and UNI ISO 18265 standard one (1) Percentage error between the curves deriving from the average data envelope of ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables (2) Percentage error between the average values from the partial conversion curves for carpentry steels deriving from ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables (3) Percentage error between the average values from the full table curve of ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables

Fig. (21). Comparison among hardness-strength curves deriving from average values between ASTM standard and UNI ISO one (Brinell method).

Table 22. Minimum, maximum and average errors and deviation values with respect to average strengths between the ASTM method and the UNI ISO one.

Comparison case
(1)	-1,55	1,12	-0,06	2,67
(2)	4,19	6,99	5,65	2,80
(3)	-2,27	2,39	0,48	4,67
S235 - (1)	-0,94	1,06	0,14	2,00
S235 - (2)	4,88	6,99	6,02	2,12
S235 - (3)	0,36	2,39	1,44	2,03
S275 - (1)	-1,55	0,45	-0,22	2,00
S275 - (2)	4,19	6,27	5,57	2,07
S275 - (3)	-0,43	1,36	0,74	1,79
S355 - (1)	-1,09	1,12	0,01	2,21
S355 - (2)	4,21	6,61	5,46	2,40
S355 - (3)	-2,27	0,54	-0,72	2,81
(1) Percentage error between the curves deriving from the average data envelope of ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables (2) Percentage error between the average values from the partial conversion curves for carpentry steels deriving from ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables (3) Percentage error between the average values from the full table curve of ASTM 370-03a and UNI ISO 18265 standards and the average hardness data resulting from the manual conversion from ASTM 370-03a and UNI ISO 18265 tables