A ciência por trás do aço: dureza versus resistência

The Science Behind Steel: Hardness Versus Strength

Accurately assessing the quality of steel structures in service requires determining the grade and strength of the steel. This is the basis for reliable testing and evaluation.

The conventional method for determining the strength of steel is to extract samples from the structure for tensile testing, but this approach can cause damage to the original structure and may not be viable for certain structures.

Therefore, it is crucial to use non-destructive testing methods to calculate the grade and strength of steel.

National and international researchers have investigated non-destructive testing methods to determine the strength of steel on engineering sites. They mainly focused on chemical composition and hardness and developed some empirical formulas.

Related reading: Metal Hardness: The Ultimate Guide (with Hardness Chart)

These empirical formulas can be categorized into two types:

The first type involves calculating tensile strength based on chemical composition, as specified in the formula of Technical Standard GB/T 50621-2010 for In-Site Testing of Steel Structures. However, the strength of steel materials is affected by chemical composition and manufacturing process (such as casting, forging, rolling, and heat treatment), so relying solely on chemical composition to calculate steel strength may result in significant deviation.

The second type involves calculating tensile strength based on hardness. Research has shown that there is a positive correlation between the hardness and tensile strength of steel. The tensile strength of materials can be estimated from the results of hardness tests, which is a widely used method in engineering practice.

Currently, the main national standards that can be used for this purpose are GB/T 33362-2016 Conversion of Hardness Values ​​of Metallic Materials and GB/T 1172-1999 Conversion of Hardness and Strength of Ferrous Metals. GB/T 33362-2016 is equivalent to the ISO 18265:2013 conversion of hardness values ​​of metallic materials. The hardness conversion table for non-alloy steel, low-alloy steel and cast steel in Table A.1 of this standard was obtained through comparison tests with hardness meters verified and calibrated in different laboratories by the German Association of Metallurgical Engineers. GB/T 1172-1999 was obtained through extensive testing and research by institutions such as the Chinese Academy of Metrology. Table 2 of the standard mainly provides the conversion ratio applicable to low-carbon steel.

However, none of these standards provide reliable data with statistical significance for the uncertainty of conversion values, and the range of deviation of conversion results is unknown. The researchers studied the correlation between hardness and strength of steel used in the construction of steel structures using regression analysis and compared it with national standards, which serve as a verification and complement to standards GB/T 33362-2016 and GB/ T 1172-1999. They also discussed the detection method suitable for steel structure project sites by incorporating existing portable detection instruments.

1. Test sample

The research objects of this study are Q235 and Q345 steel plates commonly used in metal structure engineering.

Related Reading : Q235 vs Q345 Steel

In order to ensure representative samples, 162 steel plates were collected from 86 steel structure manufacturers in Jiangsu Province, comprising 82 pieces of Q235 steel plates and 80 pieces of Q345 steel plates. The thickness specifications of the steel plates were 6, 8, 10, 12, 14, 18, 20 and 30 mm.

The steel plates were processed into 20mm x 400mm strip samples and tensile tests were carried out using a microcomputer-controlled servo electro-hydraulic tensile testing machine in accordance with the requirements of GB/T 228.1-2010 .

The test results of superior yield strength and tensile strength of Q235 and Q345 steel plates were statistically analyzed, and the distribution frequency is shown in Figure 1.

Fig. 1 Resistance distribution frequency of Q235 steel plate and Q345 steel plate

As shown in Figure 1, the upper yield strength range of Q235 steel plate is 261 to 382 MPa, and the tensile strength range is 404 to 497 MPa. The upper yield strength range of Q345 steel plate is 345 to 477 MPa, and the tensile strength range is 473 to 607 MPa.

The intensity frequency distribution is approximately normal and the test results are in line with the daily inspection data, indicating that the samples are highly representative.

2. Test results and analysis

Test samples were collected and processed in accordance with standard requirements and subjected to Rockwell hardness, Vickers hardness, Brinell hardness and tensile testing.

To carry out the regression analysis of the results of the hardness and resistance tests, the least squares method was used and the SPSS software was used.

2.1 Correlation between Rockwell hardness and strength

2.1.1 Rockwell hardness test results and analysis

The sample surface was sanded with a grinder to ensure it was flat and smooth. Scale B was selected and the instrument was calibrated using a standard hardness block. The Rockwell hardness test was carried out in accordance with the requirements of the Rockwell hardness test of metallic materials GB/T 230.1-2018, part 1: test method. Three points were measured for each sample and the average value was obtained.

Fig. 2 Regression analysis of Rockwell hardness and strength

SPSS software was used to perform linear regression, quadratic regression, power regression and exponential regression analysis on Rockwell hardness, upper yield point and tensile strength. The regression analysis diagram is represented in Figure 2, and the regression analysis results are presented in Table 1 and Table 2.

Table 1 Data from the Rockwell hardness regression model and upper yield point

Equation Model summary Model Parameter
R 2 F P Significance constant b1 b2
Linear quadratic exponent 0.736 446,897 0.000 -143,077 6,426 0.081
0.741 227,290 0.000 341,852 -6,141
0.740 456,461 0.000 0.828 1,392
0.744 464,965 0.000 86,806 0.018

Table 2 Rockwell hardness and tensile strength regression model data

Equation Model summary Model Parameter
R 2 F P Significance constant b1 b2
Linear quadratic exponent 0.780 565,900 0.000 -71,394 7,241 0.074
0.783 286,412 0.000 372,980 -4.274
0.778 560,887 0.000 3,477 1,137
0.782 574,207 0.000 155,315 0.015

As indicated by Table 1 and Table 2, Rockwell hardness has a strong correlation with strength, and the correlation with tensile strength is stronger compared to top yield strength.

Of the four regression models between Rockwell hardness and strength, all have a significance P less than 0.05 and a goodness of fit close to R 2 .

Since the conversion relationship between Rockwell hardness and the tensile strength of low carbon steel specified in the standard is similar to the polynomial model, it is recommended to use the quadratic model for conversion.

The formula after adjustment is:

Where: R Eh is the upper yield limit; R i is the tensile strength; H RB is Rockwell hardness.

2.1.2 Relative deviation analysis of conversion results

Based on the fitted quadratic regression model, the relative deviations between the converted values ​​of the upper yield point and tensile strength and the tensile test results were calculated and statistically analyzed. The sample size was 162 and the results are presented in Table 3.

The relative deviations follow a normal distribution, and the frequency distribution is shown in Figure 3.

Table 3 Statistical Table of Relative Deviation of Rockwell Hardness to Strength

Statistical Items Minimum value Maximum Average deviation Standard reference
Relative deviation of the upper yield point conversion value -16.56 +16.61 ±5.46 6.84
Relative deviation of converted tensile strength -1:31 p.m. +11.16 ±4.12 5.03

Fig. 3 Relative deviation of Rockwell hardness in relation to strength

2.1.3 Comparison with national standard conversion value

Figure 4 shows a comparison of the tensile strength conversion value specified in the standard, the fitted quadratic regression formula conversion value, and the scatterplot of the corresponding relationship between Rockwell hardness and tensile strength, all on the same graph .

Fig. 4 Comparison chart of tensile strength converted by Rockwell hardness

As seen in Figure 4, the general trend of the three curves is consistent. The tensile strength conversion value given in GB/T 1172-1999 is similar to that of the author, with an average deviation of 2.7% and a maximum deviation of 5.7% in the range of 370 to 630 MPa.

However, the tensile strength conversion value given in GB/T 33362-2016 is lower for Q235 steel (with tensile strength in the range of 370 to 500 MPa) and higher for Q345 steel (with tensile strength in the range of range from 470 to 630 MPa).

2.2 Correlation between hardness and Vickers resistance

2.2.1 Vickers hardness testing process and results analysis

The surface of the sample was polished with a grinder and the instrument was calibrated with a standard hardness block. The Vickers hardness test was carried out in accordance with the requirements of the Vickers hardness test of metallic materials GB/T 4340.1-2009, part 1: test method. Three points were measured for each sample and the average value was obtained.

SPSS software was used to perform linear regression, quadratic regression, power regression and exponential regression analysis on Vickers hardness, upper yield point and tensile strength. The regression analysis diagram is represented in Figure 5, and the regression analysis results are presented in Table 4 and Table 5.

Table 4 Vickers hardness regression model data and upper yield point

Equation Model summary Model Parameter
R 2 F P Significance constant b1 b2
Linear quadratic exponent 0.727 426,980 0.000 -9,332 2,530 0.002
0.728 212,272 0.000 27,358 2020
0.731 433,768 0.000 2,215 1,021
0.731 435,083 0.000 126,740 0.007

Fig. 5 Regression analysis of Vickers hardness and strength

Table 5 Vickers Hardness and Tensile Strength Regression Model Data

Equation Model summary Model Parameter
R 2 F P Significance Constant b1 b2
Linear quadratic exponent 0.753 486,507 0.000 84,099 2,818 0.002
0.753 241,944 0.000 133,182 2,136
0.748 475,262 0.000 8,189 0.823
0.751 483,330 0.000 213,597 0.006

As indicated by Table 4 and Table 5, Vickers hardness has a strong correlation with strength, and the correlation with tensile strength is stronger compared to top yield strength.

Of the four regression models between Vickers hardness and strength, all have a significance P less than 0.05 and a goodness of fit close to R 2 .

Since the conversion relationship between Vickers hardness and the tensile strength of low carbon steel specified in the standard is close to a linear relationship, it is recommended to use the linear relationship for conversion.

The formula after adjustment is:

Where: H V is the Vickers hardness.

2.2.2 Relative deviation analysis of conversion results

Based on the fitted linear regression model, the relative deviations between the converted values ​​of the upper yield limit and tensile strength and the tensile test results were calculated and statistically analyzed. The sample size was 162 and the results are presented in Table 6.

The relative deviations follow a normal distribution, and the frequency distribution is shown in Figure 6.

Table 6 Statistical Table of Relative Deviation of Vickers Hardness for Strength

Statistical Items Minimum value Maximum Average deviation Standard reference
Relative deviation of the upper yield point conversion value -7:30 p.m. +17.55 ±5.75 7.09
Relative deviation of converted tensile strength -12:32 +15.83 ±4.88 5.44

Fig. 6 Relative deviation of Vickers hardness converted into strength

2.2.3 Comparison with national standard conversion value

Figure 7 shows a comparison of the tensile strength conversion value specified in the standard, the conversion value of the linear regression formula obtained by the author and the scatterplot of the corresponding relationship between Vickers hardness and tensile strength, all on the same graph .

Fig. 7 Comparison chart of tensile strength converted by Vickers hardness

As seen in Figure 7, the general trend of the three curves is consistent. The tensile strength conversion value specified in GB/T 1172-1999 is very close to the conversion value obtained by the author. In the range of 370 to 630 MPa, the difference between them increases slightly with increasing hardness value, with an average deviation of 1.2% and a maximum deviation of 3.3%. However, the tensile strength conversion value given in GB/T 33362-2016 is generally lower.

2.3 Correlation between hardness and Brinell resistance

2.3.1 Brinell hardness testing process and results analysis

The surface of the sample was polished with a grinder to ensure a surface roughness of no more than 1.6 μm. The instrument was calibrated with a standard hardness block and the Brinell hardness test was performed in accordance with the requirements of GB/T 231.1-2018 Brinell hardness test of metallic materials Part 1: Test method. A carbide indenter with a diameter of 10 mm was used and the test force was 29.42 kN. Three points were measured for each sample and the average value was obtained.

SPSS software was used to perform linear regression, quadratic regression, power regression and exponential regression analysis on Brinell hardness, upper yield strength and tensile strength. The regression analysis diagram is represented in Figure 8, and the regression analysis results are presented in Table 7 and Table 8.

Fig. 8 Regression analysis of Brinell hardness and strength

Table 7 Data from the Brinell hardness and upper yield point regression model

Equation Model summary Model Parameter
R 2 F P Significance constant b1 b2
Linear quadratic exponent 0.756 495,403 0.000 -59,965 2,846 -0.001
0.758 246,186 0.000 -86,188 3,205
0.757 497,365 0.000 1,048 1,168
0.756 494,881 0.000 110,318 0.008

Table 8 Brinell hardness and tensile strength regression model data

Equation Model summary Model Parameter
R 2 F P Significance constant b1 b2
Linear quadratic exponent 0.887 1253.313 0.000 -2.613 3,377 -0.001
0.888 631,852 0.000 -225,666 6,424
0.889 1286.205 0.000 3,204 1,009
0.886 1238,834 0.000 179,073 0.007

As indicated by Table 7 and Table 8, Brinell hardness has a strong correlation with strength, and the correlation with tensile strength is stronger compared to top yield strength.

Of the four regression models between hardness and Brinell strength, all have a significance P less than 0.05 and a goodness of fit close to R 2 .

Since the conversion relationship between the Brinell hardness of carbon steel and the tensile strength specified in the standard is close to a linear relationship, it is recommended to use a linear relationship for conversion.

The adjusted formula is:

Where: H PN is Brinell hardness.

2.3.2 Relative deviation analysis of conversion results

According to the adjusted linear regression model, the relative deviations between the converted values ​​of the upper yield strength and tensile strength and the tensile test results are calculated respectively, and the relative deviations are analyzed statistically.

The statistics are 162 and the results are shown in Table 9.

The relative deviations are basically normal distribution, and the frequency distribution is shown in Fig.

Table 9 Statistical Table of Relative Deviation of Brinell Hardness to Strength

Statistical Items Minimum value Maximum Average deviation Standard reference
Relative deviation of the upper yield point conversion value -16.78 +18.67 ±5.38 6.75
Relative deviation of converted tensile strength -9.25 +8.55 ±2.89 3.59

Fig. 9 Relative deviation of Brinell hardness converted into strength

2.3.3 Comparison with national standard conversion value

In GB/T 1172-1999, the relationship between the test force and the indenter ball diameter of the Brinell hardness test is 10.

Author testing is carried out in accordance with GB/T 231.1-2018. With reference to the provisions of the standard, the relationship between the test force and the diameter of the indenter ball is 30.

Therefore, it is no longer compared with GB/T 1172-1999 compared to the national standard conversion value.

The standard conversion value of tensile strength given in GB/T 33362-2016, the conversion value of the linear regression formula adjusted by the author and the scatterplot of the corresponding relationship between Brinell hardness and tensile strength are compared in same graph, as shown in Figure 10.

Fig. 10 Comparison chart of tensile strength converted by Brinell hardness

It can be seen from Figure 10 that the tensile strength conversion value given in GB/T 33362-2016 almost coincides with the tensile strength regression curve adjusted by the author, with an average deviation of 0.4% and a maximum deviation of 1.2% within 370-630MPa.

In recent years, the rapid development of various portable hardness testers has brought great convenience to on-site testing.

At present, many types of portable Rockwell hardness tester and portable Brinell hardness tester can be purchased on the market.

The equipment is portable, simple to operate, quick to measure, and the detection accuracy also meets the requirements of national standards, which is suitable for on-site engineering detection.

There are also various portable processing equipment for sample surface treatment, which can meet testing requirements.

Therefore, it is feasible to use Rockwell hardness and Brinell hardness to calculate the strength of steel in field inspection of steel structures.

3. Conversion of hardness to strength for ferrous metals (GB/T 1172-1999)

Toughness Tensile strength
σb /MPa
Rockwell Rockwell Surface Vickers Brinell Carbon steel Chrome steel Barium chrome steel Nickel chrome steel Chrome molybdenum steel Chrome Nickel Molybdenum Steel Chrome-manganese-silicon steel Ultra-high strength steel Stainless steel No specific type of steel specified
CDH HR HR15N HR30N HR45N High voltage HB30D 2 d 10. 2 d 5. 4 d 2.5
/mm
17 67.3 37.9 15.6 211 211 4.15 73.6 706 705 772 726 757 703 724
18 67.8 38.9 16.8 216 216 4.11 753 723 719 779 737 769 719 737
19 68.3 39.8 18 221 220 4.07 771 739 735 788 749 782 737 752
20 68.8 40.7 19.2 226 225 4.03 790 757 751 797 761 796 754 767
21 69.3 41.7 20.4 231 227 4 809 775 767 807 775 810 773 782
22 69.8 42.6 21.5 237 234 3.95 829 794 785 819 789 825 792 799
23 70.3 43.6 22.7 243 240 3.91 849 814 803 831 805 840 812 816
24 70.8 44.5 23.9 249 245 3.87 870 834 823 845 821 856 832 835
25 71.4 45.5 25.1 255 251 3.83 892 855 843 860 838 874 853 854
26 71.9 46.4 26.3 261 257 3.78 914 876 864 876 857 876 892 875 874
27 72.4 47.3 27.5 268 263 3.74 937 898 886 893 877 897 910 897 895
28 73 48.3 28.7 274 269 3.7 961 920 909 912 897 918 930 919 917
29 73.5 49.2 29.9 281 276 3.65 984 943 933 932 919 941 951 942 940
30 74.1 50.2 31.1 289 283 3.61 1009 967 959 953 943 966 973 966 904
31 74.7 51.1 32.3 296 291 3.56 1034 991 985 976 967 991 996 990 989
32 75.2 52 33.5 304 298 3.52 1060 1016 1013 1001 993 1018 1020 1015 1015
33 75.8 53 34.7 312 306 3.48 1086 1042 1042 1027 1020 1047 1046 1041 1042
34 76.4 53.9 25.9 320 314 3.43 1113 1068 1072 1054 1049 1077 1073 1067 1070
35 77 54.8 37 329 323 3.39 1141 1095 1104 1084 1079 1108 1101 1095 1100
36 77.5 55.8 38.2 338 332 3.34 1170 1124 1136 1115 1111 1141 1130 1126 1131
37 78.1 56.7 39.4 347 341 3.3 1200 1153 1171 1148 1144 1176 1161 1153 1163
38 78.7 57.6 40.6 357 350 3.26 1231 1184 1206 1132 1179 1212 1194 1184 1197
39 70 79.3 58.6 41.8 367 360 3.21 1263 1216 1243 1219 1216 1250 1228 1218 1216 1232
40 70.5 79.9 59.5 43 377 370 3.17 1296 1249 1282 1257 1254 1290 1264 1267 1250 1268
41 71.1 80.5 60.4 44.2 388 380 3.13 1331 1284 1322 1298 1294 1331 1302 1315 1286 1307
42 71.6 81.1 61.3 45.4 399 391 3.09 1367 1322 1364 1340 1336 1375 1342 1362 1325 1347
43 72.1 81.7 62.3 46.5 411 401 3.05 1405 1361 1407 1385 1379 1420 1384 1409 1366 1389
44 72.6 82.3 63.2 47.7 423 413 3.01 1445 1403 1452 1431 1425 1467 1427 1455 1410 1434
45 73.2 82.9 64.1 48.9 436 424 2.97 1488 1448 1498 1480 1472 1516 1474 1502 1457 1480
46 73.7 83.5 65 50.1 449 436 2.93 1533 1497 1547 1531 1522 1567 1522 1550 1508 1529
47 74.2 84 65.9 51.2 462 449 2.89 1581 1549 1597 1584 1573 1620 1573 1600 1563 1581
48 74.7 84.6 66.8 52.4 478 401 2.85 1631 1605 1649 1640 1626 1676 1627 1652 1623 1635
49 75.3 85.2 67.7 53.6 493 474 2.81 1686 1666 1702 1698 1682 1733 1683 1707 1688 1692
50 75.8 85.7 68.6 54.7 509 488 2.77 1744 1731 1758 1758 1739 1793 1742 1765 1759 1753
51 76.3 86.3 69.5 55.9 525 501 2.73 1803 1816 1821 1799 1854 1804 1827 1817
52 76.9 86.8 70.4 57.1 543 1881 1875 1887 1861 1918 1870 1894 1885
53 77.4 87.4 71.3 58.2 561 1937 1955 1925 1985 1938 1967 1957
54 77.9 87.9 72.2 59.4 579 2000 2025 2010 2045 2034
55 78.5 88.4 73.1 60.5 599 2066 2098 2086 2131 2115
56 79 88.9 73.9 61.7 620 2224 2201
57 79.5 89.4 74.8 62.8 642 2324 2293
58 80.1 89.8 75.6 63.9 664 2437 2391
59 80.6 90.2 76.5 65.1 688 2558 2496
60 81.2 90.6 77.3 66.2 713 2691 2607
61 81.7 91 78.1 67.3 739
62 82.2 91.4 79 68.4 766
63 82.8 91.7 79.8 69.5 795
64 83.3 91.9 80.6 70.6 825
65 83.9 92.2 81.3 71.7 856
66 84.4 889
67 85 923
68 85.5 959
69 86.1 997
70 86.6 1037

3. Conclusion

(1) Rockwell hardness, Vickers hardness and Brinell hardness have good correlation with strength. Based on the material test, the conversion formula of Rockwell hardness, Vickers hardness and Brinell hardness and strength is obtained, and the relative conversion deviation is within the design allowable range.

The relative deviation between Brinell hardness and tensile strength is obviously smaller than that of Rockwell hardness and Vickers hardness.

(2) The tensile strength converted from Rockwell hardness given in GB/T 33362-2016 is low for Q235 steel and high for Q345 steel.

The tensile strength converted from Vickers hardness is slightly lower.

The tensile strength converted from Brinell hardness is consistent with the test results.

The tensile strength values ​​converted by Rockwell hardness and Vickers hardness given in GB/T 1172-1999 are close to the test results.

(3) Combined with existing portable hardness testing instruments and sample processing equipment, the use of Rockwell hardness and Brinell hardness to calculate the strength of steel is operable in practical projects and can be applied to engineering practice.

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