RESEARCH ARTICLE


Non-Destructive Tests on Carpentry Steels



Antonio Formisano1, *, Enzo Jr. Dessì1, Giovanni Chiumiento1
1 Department of Structures for Engineering and Architecture, University of Naples "Federico II" Piazzale Tecchio n. 80, Naples, Italy


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Creative Commons License
© 2019 Formisano et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Structures for Engineering and Architecture, University of Naples "Federico II" Piazzale Tecchio n. 80, Naples, Italy; Fax: +390815934792; Tel: +390817682438;
E-mail: antoform@unina.it


Abstract

Background:

Industrial archaeology represents a modern branch of urbanism and architecture that studies, applying an interdisciplinary method, all the evidence inherent the process of industrialization from its origins to the actuality.

Aim:

Looking at the cities of our epoch, more and more are the testimonies of these historical artefacts, which in fact represent our cultural identity and are often intended to be recovered and converted into modern destinations of use.

Methods:

If the identification of constructive schemes is based on direct essays and surveys, the definition of material properties requires material testing and investigation. For metal structures, the standards involve destructive investigations only, with a sampling of specimens, which often conflict with the protection requirements of the artefact. This leads to the need to refine and make reliable non-destructive investigations using the Leeb method, by means of portable micro-durometers, for in-situ characterization of carpentry steels, so to suggest new regulatory guidelines for existing structures surveys.

Results:

In the paper, the classification of carpentry steels based on non-destructive hardness test was illustrated and discussed. Firstly, for the evaluation of the resistance class of a structural steel, it was recorded that the execution of tests required a careful cleaning of the surface of samples.

Subsequently, analyzing the data obtained from the experimentation, it was clear that the best methodology of data conversion from micro-hardness (Leeb method) tests for the determination of the steel class was given by tables and formulations of the ASTM standard. In the case of a few values to be converted, the most effective method was the manual use of the tables, with an average error of 0.10%.

Conclusion:

In conclusion, it should be remarked that differently from the reinforced concrete structures, where the non-destructive tests are allowed by the current Italian technical code on, for metallic structures only, destructive tests are permitted, so that the use of non-destructive ones should be encouraged, especially when interventions on cultural heritage constructions are of concern.

Keywords: Steel structures, Mechanical tests, Hardness, Brinell tests, Leeb tests, Micro-durometers.



1. INTRODUCTION

Industrial archaeology represents a modern branch which studies, through an interdisciplinary method, all the experiences (material and immaterial, direct and indirect) of the industrialization process in order to deepen the knowledge from the past history to the current techniques. In this architectural and urbanism framework, there are numerous testimonies of historical artefacts, which represent an important social trace of the collective and urban development, becoming witnesses of an epoch. Nowadays, the renewed technical sensitivity is aimed at rediscovering and recovering such evidence with intervention methods having the prerequisites to be eco-sustainable, according to the dictates of bio-architecture, and innovative, according to home automation and intelligent architecture fundamentals [1, 2]. In this context, if the architectural challenge is to adapt volumes to new spaces and activities, the true competition starts at the engineering level in terms of both plants, being the modern functional needs always more specialized, and structures, having to operate on a historic built conceived and erected according to project and executive methodologies often disused or totally in conflict with current design philosophies and relevant regulatory frameworks. Through a project of cognitive investigations, it is possible to find adequate knowledge levels of the structure [3, 4], which allow to identify the used materials, so to carefully simulate the behaviour of structural systems.

On one hand, if it is possible to attain the whole knowledge of these systems by means of surveys and in-situ tests, in order to identify mechanical characteristics and physical properties of materials and their degradation state, it is necessary to perform an adequate campaign of tests. About metal structures, the current regulations allow to use an appropriate number of sampled specimens only [5], achieved from structural zones not too much stressed, to be subjected to destructive laboratory tests able to provide under semi-probabilistic way their mechanical and physical features. Such types of investigative campaigns, however, are often in conflict with the architectural protection constraints of artefacts under consideration, which do not allow to operate the normal sampling of specimens. On the other hand, given the need to pursue minimum levels of knowledge, the use of non-destructive testing methods, instead of destructive investigations, would allow to protect the artefact, without limiting the cognitive framework useful to carry out a proper design intervention. Among non-destructive investigations, the surface hardness measurements of steel specimens performed with portable equipment allow, within certain limits of use, for a supplementary investigation campaign partly substitutive of destructive tests.

Hardness assessment methods are multiple, they being referred to the different reading methods (Brinell - HB, Rockwell - HR, Vickers - HV), related to the type of penetrator adopted, to the value of the applied static force and to the test response value, expressed as the incision energy on the surface of the metal sample. This energy is a function of the shape and size of the impression on the basis of the predetermined load adopted for the test. Micro-hardness or “Leeb” tests are carried out with portable devices equipped with different bits which, providing rebound energy based on their impression on the metal surface, allow to see on the tool display the hardness value to be converted from the Leeb scale (HL) to a predefined more common scale (HB, HR or HV) [6]. Compared to the static tests, such investigations are much more affected by a number of factors, such as the sample thickness, the surface cleaning and imperfections, and thus have a reliability degree lower than the traditional hardness tests one.

The objective of the current experimentation is to test the reliability of the Leeb procedure, carried out with a piece of portable equipment, on different types of samples. The inspected procedure results are compared to the nominal hardness values determined by static tests, according to ASTM A956 [7] and UNI EN ISO 18265 [8] standards, which define in tabular way, the transformation and conversion parameters regulating the use of static durometers. The test is carried out in longitudinal direction according to the methodology defined in the ASTM A30-03a code [9], subsequently evaluating the type of steels according to the UNI EN 10002-1 standard [10], or using the material accompanying certificates, obtained from acceptance tests [3-5]. Currently, in the market, there are various types of equipment for Leeb hardness tests, although reliability and compliance with international standards are still being tested [11].

It should also be noted that for reinforced concrete structures, the existing Italian regulations [3-5] allow for the use of non-destructive tests, replacing 50% of destructive tests with at least a double number of non-destructive tests, such as the SONREB (SONic REBound) ones [12, 13], which are correlated to the compression resistances of cylindrical samples extracted from structural members. Contrary, for metallic structures, current standards do not envisage non-destructive tests. It seems, therefore, indispensable to prove the reliability of the Leeb tests in order to integrate and modify the regulatory contents with the purpose to both optimize and improve the goodness of experimental campaigns, working properly on existing artefacts protected by Superintendence rules, and to limit the damage to structures, where latent hazards situations can be hypothesized. So, the innovation of the present work is to set up appropriate theoretical relationships for carpentry steels able to put in relationship Leeb hardness test values with experimental tensile strengths. In this way, it will be possible to indirectly evaluate, starting from Leeb hardness values measured in-situ on carpentry steels, the strengths of those materials to be used for their mechanical characterization in the field of seismic assessment of steel artefacts.

2. TESTING METHODOLOGY

2.1. The Hardness Test

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.

2.2. Specimens

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.

2.3. Test Equipment

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).

Table 1. Specifications of the manufacturer for Leeb tests.
Type of Impact Device Distance Between Centres
of Two Indentations
Distance from the Centre of the Indentation to the Sample Edge
Not Less Than (mm) Not Less Than (mm)
D 3
1.5
5
6,2-20
DL 3
0,6-1,1
5
11-32
C 2
1.35
4
12

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).

Table 2. Different material types for conversion in terms of hardness.
Index Material
0 Steel and cast steel
1 Cold work tool steel
2 Stainless steel
3 Gray cast iron
4 Nodular cast iron
5 Cast aluminum alloys
6 Copper-Zinc alloys
7 Copper –Aluminum alloys
8 Wrought copper
9 Wrought steel

3. THE EXPERIMENTAL ACTIVITY

3.1. Preparation of Samples for Leeb Test

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”.

Table 3. Different material types for conversion in terms of strength.
Index Material
0 Mild steel
1 High carbon steel
2 Cr steel
3 Cr-V steel
4 Cr-Ni steel
5 Cr-Mo steel
6 Cr-Ni-Mo steel
7 Cr-Mn-Si steel
8 Super strenght steel
9 Stainless steel
Table 4. Numbering, steel type and thickness of plate samples.
Code Sample Number Thickness
[mm]
Steel Class
[MPa]
ST-P-01 1 4,7 S235
ST-P-02 2 5,3 S235
ST-P-25 3 10,2 S235
ST-P-09 4 8,0 S235
ST-P-15 5 8,9 S235
ST-P-23 6 10,2 S235
ST-P-24 7 10,2 S235
ST-P-13 9 8,5 S235
ST-P-03 10 5,3 S235
ST-P-08 13 7,9 S235
ST-P-05 14 6,1 S235
ST-P-07 15 7,3 S275
ST-P-26 16 10,2 S235(*)
ST-P-10 17 8,2 S275
ST-P-16 20 8,9 S275
ST-P-12 25 8,4 S275
ST-P-04 26 5,3 S275
ST-P-22 28 10,1 S275
ST-P-06 33 6,5 S275
ST-P-27 37 10,2 S275
ST-P-18 38 9,9 S275
ST-P-31 39 13,0 S275
ST-P-32 40 13,7 S275
ST-P-19 41 9,9 S355
ST-P-17 42 9,3 S355
ST-P-11 43 8,2 S275
ST-P-29 45 11,8 S355
ST-P-28 46 10,2 S355
ST-P-14 48 8,8 S355
ST-P-20 49 9,9 S355
ST-P-34 50 20,4 S355
ST-P-33 53 20,4 S355
ST-P-30 56 12,3 S355
(*) Test not performed, class assigned from the material certification
Table 5. Numbering, steel type and thickness of sheet samples.
Code Sample Number Thickness
[mm]
Steel Class
[MPa]
ST-S-01 8 5,0 S235
ST-S-04 11 9,0 S235
ST-S-02 22 7,5 S275
ST-S-06 23 10,0 S275
ST-S-03 29 8,0 S275
ST-S-06 44 15,0 S275
ST-S-08 47 20,0 S355
ST-S-07 52 20,0 S355
ST-S-05 57 9,0 S355
Table 6. Numbering and steel type of round samples.
Code Sample Number Steel Class
[MPa]
ST-R-02 18 S275
ST-R-03 19 S275
ST-R-04 21 S275
ST-R-05 24 S275
ST-R-06 27 S275
ST-R-07 31 S275
ST-R-08 32 S275
ST-R-09 34 S275
ST-R-10 35 S275
ST-R-11 36 S275
ST-R-12 51 S355
ST-R-13 54 S355
ST-R-14 55 S355

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).

3.2. Classification of Samples According to the Leeb-HB Tests

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).

Table 7. Leeb hardness values resulting from tests.
Code Sample Number Leeb - HB Hardness Conversion Average HB Hardness
HBmin HB_1 HB_2 HB_3 HBmax HBavg
ST-P-01 1 78,0 81,0 87,0 98,0 99,0 88,7
ST-P-02 2 80,0 82,0 94,0 92,0 95,0 89,3
ST-P-25 3 91,0 93,0 86,0 90,0 93,0 89,7
ST-P-09 4 91,0 91,0 98,0 82,0 85,0 90,3
ST-P-15 5 87,0 92,0 82,0 98,0 101,0 90,7
ST-P-23 6 80,0 82,0 96,0 94,0 97,0 90,7
ST-P-24 7 94,0 97,0 89,0 93,0 96,0 93,0
ST-S-01 8 94,0 95,0 91,0 96,0 99,0 94,0
ST-P-13 9 91,0 92,0 95,0 101,0 104,0 96,0
ST-P-03 10 85,0 86,0 107,0 97,0 100,0 96,7
ST-S-04 11 97,0 99,0 102,0 100,0 102,0 100,3
ST-R-01 12 90,0 92,0 107,0 103,0 105,0 100,7
ST-P-08 13 105,0 108,0 98,0 105,0 107,0 103,7
ST-P-05 14 97,0 98,0 112,0 102,0 104,0 104,0
ST-S-06 15 105,0 107,0 105,0 120,0 122,0 110,7
ST-P-07 16 121,0 123,0 95,0 97,0 99,0 105,0
ST-P-26 17 106,0 108,0 105,0 107,0 109,0 106,7
ST-P-10 18 101,0 103,0 120,0 99,0 101,0 107,3
ST-R-02 19 99,0 100,0 112,0 115,0 117,0 109,0
ST-R-03 20 115,0 117,0 101,0 109,0 111,0 109,0
ST-P-16 21 101,0 104,0 108,0 115,0 117,0 109,0
ST-R-04 22 115,0 120,0 106,0 103,0 105,0 109,7
ST-S-02 23 113,0 117,0 116,0 96,0 98,0 109,7
ST-R-05 24 115,0 117,0 97,0 118,0 120,0 110,7
ST-P-12 25 112,0 113,0 117,0 103,0 105,0 111,0
ST-P-04 26 102,0 106,0 110,0 118,0 120,0 111,3
ST-R-06 27 115,0 119,0 110,0 106,0 108,0 111,7
ST-P-22 28 107,0 110,0 114,0 112,0 114,0 112,0
ST-S-03 29 121,0 124,0 106,0 109,0 111,0 113,0
ST-P-21 30 107,0 111,0 116,0 114,0 116,0 113,7
ST-R-07 31 130,0 132,0 100,0 111,0 113,0 114,3
ST-R-08 32 97,0 100,0 124,0 120,0 122,0 114,7
ST-P-06 33 114,0 117,0 124,0 107,0 109,0 116,0
ST-R-09 34 112,0 115,0 114,0 122,0 124,0 117,0
ST-R-10 35 122,0 125,0 127,0 101,0 103,0 117,7
ST-R-11 36 115,0 118,0 123,0 113,0 115,0 118,0
ST-P-27 37 115,0 116,0 123,0 129,0 131,0 122,7
ST-P-18 38 119,0 124,0 119,0 125,0 127,0 122,7
ST-P-31 39 116,0 117,0 124,0 136,0 137,0 125,7
ST-P-32 40 126,0 127,0 133,0 139,0 140,0 133,0
ST-P-19 41 125,0 128,0 124,0 139,0 140,0 130,3
ST-P-17 42 137,0 140,0 125,0 130,0 131,0 131,7
ST-P-11 43 128,0 129,0 130,0 147,0 148,0 135,3
ST-S-06 44 135,0 136,0 129,0 144,0 145,0 136,3
ST-P-29 45 142,0 143,0 147,0 129,0 130,0 139,7
ST-P-28 46 142,0 144,0 157,0 147,0 148,0 149,3
ST-S-08 47 145,0 147,0 160,0 152,0 153,0 153,0
ST-P-14 48 151,0 153,0 146,0 165,0 166,0 154,7
ST-P-20 49 147,0 148,0 164,0 155,0 156,0 155,7
ST-P-34 50 162,0 162,0 168,0 140,0 141,0 156,7
ST-R-12 51 159,0 160,0 152,0 162,0 163,0 158,0
ST-S-07 52 160,0 162,0 160,0 164,0 165,0 162,0
ST-P-33 53 174,0 175,0 153,0 162,0 163,0 163,3
ST-R-13 54 164,0 166,0 159,0 174,0 175,0 166,3
ST-R-14 55 159,0 159,0 175,0 169,0 170,0 167,7
ST-P-30 56 170,0 171,0 167,0 169,0 170,0 169,0
ST-S-05 57 172,0 173,0 186,0 150,0 152,0 169,7

Table 8. Conversion from tensile test values to Leeb hardness ones.
Tensile Strength Rm
Code Sample Number Steel Class [MPa] (*) Average HB Hardness HBmed ASTM A370-03a [MPa] UNI ISO 18265 [MPa] Rm,avg [MPa] Average Deviation [%]
ST-P-01 1 S235 88,7 308,5 295,6 302,1 -4,27
ST-P-02 2 S235 89,3 310,6 297,7 304,2 -4,24
ST-P-25 3 S235 89,7 312 299 305,5 -4,26
ST-P-09 4 S235 90,3 314,0 305,3 309,7 -2,81
ST-P-15 5 S235 90,7 315,7 306,7 311,2 -2,89
ST-P-23 6 S235 90,7 315,7 306,7 311,2 -2,89
ST-P-24 7 S235 93,0 323,5 314,5 319,0 -2,82
ST-S-01 8 S235 94,0 330,0 317,8 323,9 -3,77
ST-P-13 9 S235 96,0 337,0 323,4 330,2 -4,12
ST-P-03 10 S235 96,7 339,5 325,7 332,6 -4,15
ST-S-04 11 S235 100,3 341,0 336,7 338,9 -1,27
ST-R-01 12 S235 100,7 342,4 338,0 340,2 -1,29
ST-P-08 13 S235 103,7 352,4 348,1 350,3 -1,23
ST-P-05 14 S235 104,0 353,4 349,1 351,3 -1,22
ST-P-07 15 S275 105,0 360 355,7 357,9 -1,20
ST-P-26 16 S235 106,7 364 357,6 360,8 -1,77
ST-P-10 17 S275 107,3 366,6 370 368,3 0,92
ST-R-02 18 S275 109,0 366,6 370 368,3 0,92
ST-R-03 19 S275 109,0 366,6 370 368,3 0,92
ST-P-16 20 S275 109,0 369 372,4 370,7 0,92
ST-R-04 21 S275 109,7 369 372,4 370,7 0,92
ST-S-02 22 S275 109,7 370 375,4 372,7 1,45
ST-S-06 23 S275 110,7 370 375,8 372,9 1,56
ST-R-05 24 S275 110,7 370 375,8 372,9 1,56
ST-P-12 25 S275 111,0 373,4 376,8 375,1 0,91
ST-P-04 26 S275 111,3 374,4 377,8 376,1 0,90
ST-R-06 27 S275 111,7 375,7 379,1 377,4 0,90
ST-P-22 28 S275 112,0 376,7 380,2 378,5 0,92
ST-S-03 29 S275 113,0 380,1 381,6 380,9 0,39
ST-P-21 30 S275 113,7 382,4 384 383,2 0,42
ST-R-07 31 S275 114,3 384,5 386 385,3 0,39
ST-R-08 32 S275 114,7 385,8 387,4 386,6 0,41
ST-P-06 33 S275 116,0 385 391,8 388,4 1,75
ST-R-09 34 S275 117,0 395 393,3 394,2 -0,43
ST-R-10 35 S275 117,7 397,3 395,6 396,5 -0,43
ST-R-11 36 S275 118,0 398,4 396,6 397,5 -0,45
ST-P-27 37 S275 122,7 410,7 410,6 410,7 -0,02
ST-P-18 38 S275 122,7 410,7 410,6 410,7 -0,02
ST-P-31 39 S275 125,7 422,4 420,7 421,6 -0,40
ST-P-32 40 S275 133,0 443,3 450 446,7 1,50
ST-P-19 41 S355 130,3 435 437,7 436,4 0,62
ST-P-17 42 S355 131,7 440,7 442,4 441,6 0,39
ST-P-11 43 S275 135,3 451,7 457,8 454,8 1,34
ST-S-06 44 S275 136,3 454,3 461,2 457,8 1,51
ST-P-29 45 S355 139,7 462,3 470,7 466,5 1,80
ST-P-28 46 S355 149,3 490,8 502,7 496,8 2,40
ST-S-08 47 S355 153,0 505 513,4 509,2 1,65
ST-P-14 48 S355 154,7 510,6 519,1 514,9 1,65
ST-P-20 49 S355 155,7 513,9 522,4 518,2 1,64
ST-P-34 50 S355 156,7 532,4 532,4 532,4 0,00
ST-R-12 51 S355 158,0 536,8 536,8 536,8 0,00
ST-S-07 52 S355 162,0 560 545 552,5 -2,71
ST-P-33 53 S355 163,3 564,5 549,4 557,0 -2,71
ST-R-13 54 S355 166,3 569,5 561,0 565,3 -1,50
ST-R-14 55 S355 167,7 574,2 565,7 570,0 -1,49
ST-P-30 56 S355 169,0 570 570,1 570,1 0,02
ST-S-05 57 S355 169,7 572,3 572,5 572,4 0,03
(*) Classification by destructive tensile tests

Table 9. Conversion among hardness values for mild and alloy steels according to the ASTM A370-03a code.
HV HRC HV HRC HV HRC HV HRC HV HRC
2270 85 1950 81 1633 77 1323 73 1004 69
2190 84 1865 80 1556 76 1245 72 940 68
2110 83 1787 79 1478 75 1160 71 920 67,5
2030 82 1710 78 1400 74 1076 70 900 67
HRC Diamond cone HV Vickers 30 HBBrinell 29400 N HRA Diamond cone Rm (MPa) HRB Sphere 1/16” HV Vickers 30 HB Brinell 29400 N HRA Diamond cone Rm (MPa)
68 940 / 85,6 / 100 240 240 61,5 800
67 900 / 85,0 / 99 234 234 60,9 785
66 865 / 84,5 / 98 228 228 60,2 750
65 832 739 83,9 / 97 222 222 59,5 715
64 800 722 83,4 / 96 216 216 58,9 705
63 772 706 82,8 / 95 210 210 58,3 690
62 746 688 82,3 / 94 205 205 57,6 675
61 720 670 81,8 / 93 200 200 57,0 650
60 697 654 81,2 / 92 195 195 56,4 635
59 664 634 80,7 2420 91 190 190 55,8 620
58 653 615 80,1 2330 90 185 185 55,2 615
57 633 595 79,6 2240 89 180 180 54,6 605
56 613 577 79,0 2160 88 176 176 54,0 590
55 595 560 78,5 2070 87 172 172 53,4 580
54 577 543 78,0 2010 86 169 169 52,8 570
53 560 525 77,4 1950 85 165 165 52,3 565
52 544 512 76,8 1880 84 162 162 51,7 560
51 528 496 76,3 1820 83 159 159 51,1 550
50 513 482 75,9 1760 82 156 156 50,6 530
49 498 468 75,2 1700 81 153 153 50,0 505
48 484 455 74,7 1640 80 150 150 49,5 495
47 471 442 74,1 1580 79 147 147 48,9 485
46 458 432 73,6 1520 78 144 144 48,4 475
45 446 421 73,1 1480 77 141 141 47,9 470
44 434 409 72,5 1430 76 139 139 47,3 460
43 423 400 72,0 1390 75 137 137 46,8 455
42 412 390 71,5 1340 74 135 135 46,3 450
41 402 381 70,9 1300 73 132 132 45,8 440
40 392 371 70,4 1250 72 130 130 45,3 435
39 382 362 69,9 1220 71 127 127 44,8 425
38 372 353 69,4 1180 70 125 125 44,3 420
37 363 344 68,9 1140 69 123 123 43,8 415
36 354 336 68,4 1110 68 121 121 43,3 405
35 345 327 67,9 1080 67 119 119 42,8 400
34 336 319 67,4 1050 66 117 117 42,3 395
33 327 311 66,8 1030 65 116 116 41,8 385
32 318 301 66,3 1010 64 114 114 41,4 /
31 310 294 65,8 970 63 112 112 40,9 /
30 302 286 65,3 950 62 110 110 40,4 370
29 294 279 64,6 630 61 108 108 40,0 /
28 286 271 64,3 900 60 107 107 39,5 /
27 279 264 63,8 880 59 106 106 39,0 360
26 272 258 63,3 860 58 104 104 38,6 /
25 266 253 62,8 850 57 103 103 38,1 350
24 260 247 62,4 820 56 101 101 37,7 /
23 254 243 62,0 810 55 100 100 37,2 340
22 248 237 61.5 790 54 / / 36,8 /
21 243 231 61.0 770 51 / 94 35,5 330
20 238 226 60.5 760 49 / 92 34,6 320
Legend:
Bold values are reliable, but out of the ASTM table. Italic values are due to the passage from Table 2 to Table 3 of the ASTM A 370 standard.
HRA: Rockwell hardness with diamond cone - load: 588 N - duration: 30”
HRB: Rockwell hardness with 1/16” sphere - load: 980 N - duration: 30”
HRC: Rockwell hardness with 120° diamond cone - load: 1470 N-duration: 30”
HB: Brinell hardness with 10 mm diameter sphere - load: 29400 N-duration: 15”
HV: Vickers hardness with 136° diamond pyramid - load: 294 N-duration: 15”
Rm: Tensile strength (MPa)

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:

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

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

Rm_avg is the average tensile resistance, expressed in MPa;

HB is the Brinell scale static hardness.

3.3. Determination of Hardness Conversion Curves (Brinell Method)

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 fuk,max in the range from 510 to 530 MPa.

Table 10. Conversion of hardness-to-hardness or hardness-to-tensile-strength values for unalloyed and low alloy steels and cast steels according to the UNI EN ISO 18265 standard.
* Brinell hardness values up to 450 HB were determined using a steel ball indenter, those above this value were determined with a hard metal ball.
NOTE 1 Values in parentheses are those lying outside the defined range of the standard test method but which may used as estimates.
Tensile Strength MPa Vickers Hardness HV10 Brinell Hardness HB* Rockwell Hardness
HRB HRF HRC HRA HRD HR15N HR30N HR45N
255 80 76
270 85 80,7 41
285 90 58,5 48 82,6
305 95 90,2 52
320 100 95 56,2 57
335 105 99,8
350 110 105 62,3 90,5
370 115 109
385 120 114 66,7 93,6
400 125 119
415 130 124 71,2 96,4
430 135 128
450 140 133 75 99
465 145 138
480 150 143 78,7 (101,4)
495 155 147
510 160 152 81,7 (103,6)
530 165 156
545 170 162 85 (105,5)
560 175 166
575 180 171 87,1 (107,2)
595 185 176
610 190 181 89,5 (108,7)
625 195 185
640 200 190 91,5 (110,1)
660 205 195 92,5
675 210 199 93,5 (111,3)
690 215 204 94
705 220 209 95 (112,4)
720 225 214 96
740 230 219 69,7 (113,4)
755 235 223
770 240 228 98,1 (114,3) 20,3 60,7 40,3 69,6 41,7 19,9
785 245 233 21,3 61,2 41,1 70,1 42,5 21,1
800 250 238 99,5 115,1) 22,2 61,6 41,7 70,6 43,4 22,2
820 255 242 23,1 62 42,2 71,1 44,2 23,2
835 260 247 (101) 24 62,4 43,1 71,6 45 24,3
850 265 252 24,8 62,7 43,7 72,1 45,7 25,2
865 270 257 (102) 25,6 63,1 44,3 72,6 46,4 26,2
880 275 261 26,4 63,5 44,9 73 47,2 27,1
900 280 266 (104) 27,1 63,8 45,3 73,4 47,8 27,9
915 285 271 27,8 64,2 46 73,8 48,4 28,7
930 290 276 (105) 28,5 64,5 46,5 74,2 49 29,5
950 295 280 29,2 64,8 47,1 74,6 49,7 30,4
965 300 285 29,8 65,2 47,5 74,9 50,2 31,1
995 310 295 31 65,8 48,4 75,6 51,3 32,5
1030 320 304 32,2 66,4 49,4 76,2 52,3 33,9
1060 330 314 33,3 67 50,2 76,2 52,3 33,9
1095 340 323 34,4 67,6 51,1 77,4 54,4 36,5
1125 350 333 35,5 68,1 51,9 78 55,4 37,8
1155 360 342 36,6 68,7 52,8 78,6 56,4 39,1
1190 370 352 37,7 69,2 53,6 79,2 57,4 40,4
1220 380 361 38,8 69,8 54,4 79,8 58,4 41,7
1255 390 371 39,8 70,3 55,3 80,3 59,3 42,9
1290 400 380 40,8 70,8 56 80,8 60,2 44,1
1320 410 390 41,8 71,4 56,8 81,4 61,1 45,3
1350 420 399 42,7 71,8 57,5 81,8 61,9 46,4
1385 430 409 43,6 72,3 58,2 82,3 62,7 47,4
1420 440 418 44,5 72,8 58,8 82,8 63,5 48,4
1455 450 428 45,3 73,3 59,4 83,2 64,3 49,4
1465 460 437 46,1 73,6 60,1 83,6 64,9 50,4
1520 470 447 46,9 74,1 60,7 83,9 65,7 51,3
1555 480 456 47,7 74,5 61,3 84,3 66,4 52,2
1595 490 466 48,4 74,9 61,6 84,7 67,1 53,1
1630 500 475 49,1 75,3 62,2 85 67,7 53,9
1665 510 485 49,8 75,7 62,9 85,4 68,3 54,7
1700 520 494 50,5 76,1 63,5 85,7 69 55,6
1740 530 504 51,1 76,4 63,9 86 69,5 56,2
1775 540 513 51,7 76,7 64,4 86,3 70 57
1810 550 523 52,3 77 64,8 86,6 70,5 57,8
1845 560 532 53 77,4 65,4 86,9 71,2 58,6
1880 570 542 53,6 77,8 65,8 87,2 71,7 59,3
1920 580 551 54,1 78 66,2 87,5 72,1 59,9
1955 590 561 54,7 78,4 66,7 87,8 72,7 60,5
1995 600 570 55,2 78,6 67 88 73,2 61,2
2030 610 580 55,7 78,9 67,5 88,2 73,7 61,7
2070 620 589 56,3 79,2 67,9 88,5 74,2 62,4
2105 630 599 56,8 79,5 68,3 88,8 74,6 63
2145 640 608 57,3 79,8 68,7 89 75,1 63,5
2180 650 618 57,8 80 69 89,2 75,5 64,1
660 58,3 80,3 69,4 89,5 75,9 64,7
670 58,8 80,6 69,8 89,7 76,4 65,3
680 59,2 80,8 70,1 89,8 76,8 65,7
690 59,7 81,1 70,5 90,1 77,2 66,2
700 60,1 81,3 70,8 90,3 77,6 66,7
720 61 81,8 71,5 90,7 78,4 67,7
740 61,8 82,2 72,1 91 79,1 68,6
760 62,5 82,6 72,6 91,2 79,7 69,4
780 63,3 83 73,3 91,5 80,4 70,2
800 64 83,4 73,8 91,8 81,1 71
820 64,7 83,8 74,3 92,1 81,7 71,8
840 65,3 84,1 74,8 92,3 82,2 72,2
860 65,9 84,4 75,3 92,5 92,7 73,1
880 66,4 84,7 75,7 92,7 83,1 73,6
900 67 85 76,1 92,9 83,6 74,2
920 67,5 85,3 76,5 93 84 74,8
40 68 85,6 76,9 93,2 84,4
75,4
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:

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

RmUNI 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.

3.4. Hardness Estimation by the Complete Conversion Curves (Brinell Method)

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:

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

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

4. DISCUSSION

4.1. Determination of Steel Class Using ASTM Methods

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
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
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
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
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
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.

4.2. Determination of Steel Class Using UNI ISO Methods

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
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
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.

4.3. Relationship Between the Two Conversion Methods

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
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
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
Table 23. Comparison among strength values obtained from ASTM and UNI ISO tables and envelopes and mechanical resistances for S235 grade steels.
Code Sample
e1
(%)
e2
(%)
e3
(%)
e4
(%)
(1) (2) (3) (4)
ST-P-01 1 -16,10 -15,20 -10,23 -14,09
ST-P-02 2 -15,51 -14,65 -9,64 -13,52
ST-P-25 3 -15,14 -14,37 -9,35 -13,24
ST-P-09 4 -13,99 -13,81 -8,76 -12,67
ST-P-15 5 -13,56 -13,54 -8,46 -12,39
ST-P-23 6 -13,56 -13,54 -8,46 -12,39
ST-P-24 7 -11,39 -11,58 -6,39 -10,41
ST-S-01 8 -10,03 -10,73 -5,49 -9,55
ST-P-13 9 -8,28 -9,04 -3,70 -7,85
ST-P-03 10 -7,61 -8,48 -3,11 -7,28
ST-S-04 11 -5,87 -5,34 0,20 -4,14
ST-R-01 12 -5,50 -5,06 0,51 -3,86
ST-P-08 13 -2,71 -2,47 3,24 -1,29
ST-P-05 14 -2,43 -2,18 3,54 -1,00
ST-P-07 15 -0,60 -1,31 4,45 -0,14
ST-P-26 16 0,22 0,14 5,98 1,29
0,22 0,14 5,98 1,29
-16,10 -15,20 -10,23 -14,09
-8,88 -8,82 -3,48 -7,66
16,32 15,34 16,21 15,38
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. (22). Percentage errors with respect to the envelope curves of the complete tables from ASTM and UNI ISO standards.

Comparing the values deriving from the different formulas with the average values ​from the table and evaluating the error committed (Table 22), it is observed (Fig. 22) a maximum error and a minimum error , with a maximum percentage scatter .

Analyzing the errors committed for the different steel classes (Table 22), it is observed that the use of average values tends to reduce the errors detected using the UNI ISO tables. As seen before, the use of the envelope curve, obtained from the partial use of the tables for carpentry steels only, entails the greatest errors for all the steel classes.

Analyzing data from non-destructive Leeb tests due to the use of partial envelope curves (Table 16), for some samples the passage from S235 class to S275 one takes place from sample ST-S-04 (sample n.11). For 6 out of 16 samples of S235 class a percentage error occurs in the detection of a higher resistance class.

With reference to the transition from S275 steel to S355 one, the change of class is observed for the sample ST-P-27 (sample n.37) adopting all the evaluation methods. Compared to the total number of S275 class steel samples, for 4 out of 26 samples, the assignment to a higher class is committed, with a percentage error .

Analyzing the resistance values deriving from the different conversions from Leeb tests to the classes reference values, for S235 steels a maximum error and a minimum error is gotten (Table 23). Therefore, the tests do not tend to overestimate the resistance values, but they appropriately classify the samples.

For S275 class steels the conversion involves a maximum error and a minimum error (Table 24).

Given the percentage scatter between S235 class and S275 one, for n.1 sample the assignment to a lower class occurs. For S355 class steels the conversion involves a maximum error and a minimum error (Table 25).

Table 24. Comparison among strength values obtained from ASTM and UNI ISO tables and envelopes and mechanical resistances for S275 grade steels.
Code Sample
e1
(%)
e2
(%)
e3
(%)
e4
(%)
(1) (2) (3) (4)
ST-P-07 15 -16,78 -17,38 -12,55 -16,40
ST-P-26 16 -16,09 -16,16 -11,27 -15,20
ST-P-10 17 -14,35 -15,68 -10,76 -14,71
ST-R-02 18 -14,35 -14,46 -9,47 -13,51
ST-R-03 19 -14,35 -14,46 -9,47 -13,51
ST-P-16 20 -13,79 -14,46 -9,47 -13,51
ST-R-04 21 -13,79 -13,97 -8,95 -13,03
ST-S-02 22 -13,33 -13,97 -8,95 -13,03
ST-S-06 23 -13,28 -13,23 -8,18 -12,31
ST-R-05 24 -13,28 -13,23 -8,18 -12,31
ST-P-12 25 -12,77 -12,98 -7,92 -12,07
ST-P-04 26 -12,53 -12,74 -7,66 -11,83
ST-R-06 27 -12,23 -12,49 -7,40 -11,58
ST-P-22 28 -11,99 -12,24 -7,14 -11,34
ST-S-03 29 -11,43 -11,50 -6,36 -10,62
ST-P-21 30 -10,88 -11,01 -5,84 -10,14
ST-R-07 31 -10,41 -10,51 -5,32 -9,65
ST-R-08 32 -10,09 -10,26 -5,06 -9,41
ST-P-06 33 -9,67 -9,27 -4,02 -8,44
ST-R-09 34 -8,34 -8,52 -3,23 -7,72
ST-R-10 35 -7,80 -8,02 -2,70 -7,23
ST-R-11 36 -7,56 -7,77 -2,44 -6,99
ST-P-27 37 -4,50 -4,24 1,26 -3,59
ST-P-18 38 -4,50 -4,24 1,26 -3,59
ST-P-31 39 -1,97 -1,95 3,65 -1,40
ST-P-32 40 3,87 3,71 9,58 3,99
3,87 3,71 9,58 3,99
-16,78 -17,38 -12,55 -16,40
-10,62 -10,81 -5,64 -9,97
20,65 21,09 22,13 20,38
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 25. Comparison among strength values obtained from ASTM and UNI ISO tables and envelopes and mechanical resistances for S355 grade steels.
Code Sample
e1
(%)
e2
(%)
e3
(%)
e4
(%)
(1) (2) (3) (4)
ST-P-31 39 -17,34 -17,33 -12,60 -16,86
ST-P-32 40 -12,42 -12,56 -7,61 -12,33
ST-P-19 41 -14,44 -14,30 -9,44 -13,98
ST-P-17 42 -13,42 -13,43 -8,52 -13,15
ST-P-11 43 -10,83 -11,02 -6,00 -10,88
ST-S-06 44 -10,25 -10,36 -5,31 -10,25
ST-P-29 45 -8,53 -8,14 -3,00 -8,18
ST-P-28 46 -2,60 -1,62 3,79 -2,12
ST-S-08 47 -0,16 0,90 6,40 0,18
ST-P-14 48 0,95 2,05 7,60 1,24
ST-P-20 49 1,60 2,74 8,32 1,87
ST-P-34 50 4,39 3,43 9,04 2,50
ST-R-12 51 5,25 4,36 10,00 3,34
ST-S-07 52 8,33 7,16 12,90 5,88
ST-P-33 53 9,21 8,09 13,87 6,72
ST-R-13 54 10,83 10,22 16,06 8,63
ST-R-14 55 11,75 11,16 17,04 9,48
ST-R-30 56 11,77 12,11 18,03 10,33
ST-S-05 57 12,24 12,59 18,52 10,76
12,24 12,59 18,52 10,76
-17,34 -17,33 -12,60 -16,86
-0,72 -0,73 4,69 -1,41
29,58 29,92 31,12 27,62
Conversion with:
Manual use of the table
Envelope from manual conversion values
Envelope from partial tables for carpentry steels
Envelope from the complete table

Since the percentage scatter between the 275 class and the S355 one equal to 15.69%, for n.1 out of 19 samples the assignment on the safe side to a lower steel class occurs with an error .

CONCLUSION

In the paper, the classification of carpentry steels based on non-destructive hardness test was illustrated and discussed.

Firstly, for the evaluation of the resistance class of structural steel, it was recorded that the execution of tests required a careful cleaning of the surface of samples.

Subsequently, analyzing the data obtained from the experimentation, it was clear that the best methodology of data conversion from micro-hardness (Leeb method) tests for the determination of the steel class was given by tables and formulations of the ASTM standard. In the case of a few values to be converted, the most effective method was the manual use of the tables, with an average error of 0.10%. However, with the increase in the number of samples, the manual use involved a significant increase in the working time. In this case, the most reliable method for conversion was given by the formula deriving from the envelope of the entire ASTM table, which provides an average error of 0.42%. Even in the case of combined use of the ASTM and UNI standards values, the presence of the greatest errors deriving from the UNI standards led to the increase of the average error committed in the conversion.

By dividing the different samples according to the steel classes deriving from either tensile tests or origin certificates, it was noted that for all types of steel, the use of ASTM standard tables (or of the envelope formulas derived from them) allows to reduce errors obtained from using the UNI standard. In fact, the errors committed with ASTM tables were contained in a limited range, with a maximum value of 6.67%. Contrary, the maximum error detected when using the UNI tables for carpentry steels was equal to 52.94%. More in detail, with regard to the S235 class, the most reliable method was that given by the formulas deriving from the envelope of the ASTM partial tables for carpentry steels, which provided error and scatter , respectively, against the corresponding values and when the complete envelope of tables was used.

Passing to the S275 and S335 classes, the most reliable method derived from the envelope of partial tables, where only the data of carpentry steels were present. The detected errors were 0.16% and 0.91% for S275 steel and S355 one, respectively. Moreover, percentage scatters of 1.93% and 4.54% were achieved when S275 steels and S355 ones, respectively, are of concern. However, it is important to remember that tables of both ASTM and UNI standards do not cover a large range of low hardness values and, therefore, in these cases a linear interpolation process to find intermediate values is often required. For this reason, further experimental destructive and non-destructive tests on carpentry steels should be performed in order to complete the tables of the used reference standards for obtaining reliable conversion formulas from hardness values to tensile strengths.

In conclusion, it should be remarked that, differently from reinforced concrete structures, where non-destructive tests are allowed by the current Italian technical code, for metallic structures, only destructive tests are permitted. Therefore, in this framework, to know the reliability of Leeb tests appears to be indispensable in order to both integrate and modify the regulatory contents with the purpose of completing the experimental campaign so to work properly also on existing artefacts protected by Superintendence rules, where the damage to structures must be either avoided or limited as much as possible.

Definitely, in the present work, the introduction of theoretical relationships for carpentry steels able to put in relationship Leeb hardness test values with experimental tensile strengths represents a very novel application in the field of seismic assessment of historical metal structures. In this way, it will be possible to indirectly evaluate, starting from Leeb hardness values measured in-situ on carpentry steels, the strengths of those materials to be used for their mechanical characterization when seismic analysis and improvement/ retrofitting of steel artefacts are of concern.

LIST OF ABBREVIATIONS

e = Percentage error;
e355-275 = Percentage error in the assignment of the S355 class instead of the S275 one;
emax = Maximum positive error;
emin = Maximum negative error;
fuk,max = Nominal ultimate tensile strength;
HB = Brinell Hardness;
HB = Brinell Hardness with 10 mm diameter sphere – load: 29400 N – duration: 15”;
HBavg = Brinell Hardness average value;
HL = Leeb Hardness;
HR = Rockwell Hardness;
HRA = Rockwell Hardness with diamond cone – load: 588 N – duration: 30”;
HRB = Rockwell Hardness with 1/16” sphere – load: 980 N – duration: 30”;
HRC = Rockwell Hardness with 120° diamond cone – load: 1470 N – duration: 30”;
HV = Vickers Hardness;
HV = Vickers Hardness with 136° diamond pyramid – load: 294 N – duration: 15”;
RASTM-UNI = Average tensile strength between ASTM 370-03a standard resistance and UNI ISO 18265 standard one;
Rm,avg = Medium value between ASTM A370-03a strength value and UNI EN ISO 18256 one;
Rm = Tensile strength (MPa);
RmASTM = Steel average strength according to the ASTM A370-03a standard;
RmUNI = Steel average strength according to the UNI EN ISO 18256 standard;
SONREB = SONic REBound test;
Δ275-235 = Percentage scatter in terms of stress between the S275 class and the S235 one;
δmax = Maximum positive scatter;
δmin = Maximum negative scatter.

CONSENT FOR PUBLICATION

Not applicable.

AVAILABILITY OF DATA AND MATERIALS

The data that support the findings of this study are available from the corresponding author upon request.

FUNDING

None.

CONFLICT OF INTEREST

The authors declare no conflict of interest, financial or otherwise.

ACKNOWLEDGEMENTS

The Authors would like to acknowledge the Tecnolab s.r.l. company and his Technical Director Eng. Andrea Basile for the invaluable help in performing the non-destructive tests object of the current research activity.

REFERENCES

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