When testing and appraising the quality of steel structures in service, it is the basis for accurate quality evaluation to determine the grade and strength of steel.
The traditional method of steel strength detection is to take samples from members for tensile test, but this will damage the original structure, and some structures are not allowed to take samples.
Therefore, it is of great practical significance to calculate the grade and strength of steel by nondestructive testing.
Scholars at home and abroad have studied the nondestructive testing of steel strength in the engineering site, mainly from the chemical composition and hardness, and obtained some empirical formulas.
Related reading: Metal Hardness: The Definite Guide (with Hardness Chart)
These empirical formulas can be summarized into two categories: the first category is to calculate the tensile strength from the chemical composition, such as the formula mentioned in GB/T 506212010 Technical Standard for Onsite Testing of Steel Structures.
However, the chemical composition and manufacturing process (casting, forging, rolling, heat treatment) will affect the strength of steel materials, and the calculation of steel strength only based on chemical composition will have a large deviation.
The second type is to calculate the tensile strength from the hardness.
Relevant research shows that the hardness and tensile strength of steel are positively correlated.
The tensile strength of materials can be estimated from the hardness test results, which is also a method widely used in engineering practice.
The tensile strength can be calculated from the hardness.
At present, the main domestic standards that can be used are GB/T 333622016 Conversion of Hardness Values of Metallic Materials and GB/T 11721999 Conversion of Hardness and Strength of Ferrous Metals.
The translation method used in GB/T 333622016 is equivalent to ISO 18265:2013 Conversion of Hardness Values of Metallic Materials (English version).
The hardness conversion table of unalloyed steel, low alloy steel and cast steel given in Table A.1 of this standard is obtained by the German Association of Metallurgical Engineers through comparison tests with verified and calibrated hardness meters in several different laboratories.
GB/T 11721999 is obtained through a lot of tests and research by many research institutions such as the China Academy of Metrology.
Table 2 in the standard gives the conversion relationship mainly applicable to low carbon steel.
However, these two standards do not provide reliable data with statistical significance for the uncertainty of conversion values, and the deviation range of conversion results is unknown.
Researchers studied the correlation between the hardness and strength of the steel used for building steel structures through regression analysis, and compared it with national standards, which is also a verification and supplement of GB/T 333622016 and GB/T 11721999 standards;
At the same time, combined with the existing portable detection instruments, the detection method suitable for the steel structure project site is discussed.
1. Test sample
Q235 and Q345 steel plates commonly used in steel structure engineering are selected as research objects.
Related reading: Q235 vs Q345 Steel
In order to make the samples representative, 162 steel plates were collected from 86 steel structure manufacturers in Jiangsu Province, including 82 pieces of Q235 steel plates and 80 pieces of Q345 steel plates.
The thickness specification of steel plates is 6,8,10,12,14,18,20,30 mm.
The steel plate shall be processed into a 20mm×400mm strip sample, and the tensile test shall be carried out using a microcomputer controlled electrohydraulic servo tensile testing machine according to the requirements of GB/T 228.12010.
The test results of upper yield strength and tensile strength of the Q235 steel plate and Q345 steel plate are statistically analyzed, and the distribution frequency is shown in Fig. 1.
Fig. 1 Strength Distribution Frequency of Q235 Steel Plate and Q345 Steel Plate
It can be seen from Fig. 1 that the upper yield strength range of Q235 steel plate is 261~382MPa, and the tensile strength range is 404~497MPa;
The upper yield strength range of the Q345 steel plate is 345~477MPa, and the tensile strength range is 473~607MPa.
The intensity frequency distribution is basically a normal distribution, and the test results are generally consistent with the daily entrusted inspection experience data, so the sample can be considered to be very representative.
2. Test results and analysis
The test samples shall be sampled and processed according to the standard requirements, and Rockwell hardness, Vickers hardness, Brinell hardness and tensile test shall be carried out respectively.
According to the principle of the least square method, SPSS software shall be used for regression analysis of hardness and strength test results.
2.1 Correlation between Rockwell hardness and strength
2.1.1 Rockwell hardness test results and analysis
Grind the surface of the sample with a grinder to make it flat and smooth.
Select the B scale, check the instrument with a standard hardness block, and conduct the Rockwell hardness test according to the requirements of Metallic Materials Rockwell Hardness Test Part 1: Test Method (GB/T 230.12018). Measure 3 points for each sample and take the average value.
Fig. 2 Regression Analysis of Rockwell Hardness and Strength
SPSS software is used to conduct linear regression, quadratic regression, power regression and exponential regression analysis on Rockwell hardness, upper yield strength and tensile strength. The regression analysis diagram is shown in Fig. 2, and the regression results are shown in Table 1 and Table 2.
Table 1 Regression Model Data of Rockwell Hardness and Upper Yield Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 Regression Model Data of Rockwell Hardness and Tensile Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 
It can be seen from Table 1 and Table 2 that Rockwell hardness has a good correlation with strength, and the correlation with tensile strength is better than that with upper yield strength.
Among the four regression models of the relationship between Rockwell hardness and strength, the significance P is less than 0.05, and the goodness of fit R^{2} is close.
Considering that the conversion relationship between Rockwell hardness and tensile strength of low carbon steel given in the standard is close to the polynomial model, it is recommended to convert according to the quadratic model.
The formula after fitting is:
Where: R_{eH} is the upper yield strength; R_{m} is the tensile strength; H_{RB} is Rockwell hardness.
2.1.2 Relative deviation analysis of conversion results
According to the fitted quadratic regression model, the relative deviations between the converted values of upper yield strength and tensile strength and the tensile test results are calculated respectively, and the relative deviations are statistically analyzed.
The statistics are 162, and the results are shown in Table 3.
The relative deviations are basically normal distribution, and the frequency distribution is shown in Fig. 3.
Table 3 Statistical Table of Relative Deviation from Rockwell Hardness to Strength
Statistical items 
Minimum value 
Maximum 
Average deviation 
Standard reference 
Relative deviation of upper yield strength conversion value 
16.56 
+16.61 
±5.46 
6.84 
Relative deviation of converted tensile strength 
13.31 
+11.16 
±4.12 
5.03 
Fig. 3 Relative deviation from Rockwell hardness to strength
2.1.3 Comparison with national standard conversion value
Put the conversion value of tensile strength given in the standard, the conversion value of the fitted quadratic regression formula, and the scatter plot of the corresponding relationship between Rockwell hardness and tensile strength on the same chart for comparison, as shown in Fig. 4.
Fig. 4 Comparison Chart of Tensile Strength Converted by Rockwell Hardness
It can be seen from Fig. 4 that the overall trend of the three curves is consistent.
The conversion value of tensile strength given in GB/T 11721999 is close to that given by the author, with an average deviation of 2.7% and a maximum deviation of 5.7% within 370630MPa.
The conversion value of tensile strength given in GB/T 333622016 is low for Q235 steel (tensile strength 370~500MPa) and high for Q345 steel (tensile strength 470~630MPa).
2.2 Correlation between Vickers hardness and strength
2.2.1 Vickers hardness test process and result analysis
Use a grinder to polish the surface of the sample, check the instrument with a standard hardness block, and conduct Vickers hardness test according to the requirements of Metallic Materials Vickers Hardness Test Part 1: Test Method (GB/T 4340.12009). Measure 3 points for each sample and take the average value.
SPSS software is used to conduct linear regression, quadratic regression, power regression and exponential regression analysis on Vickers hardness, upper yield strength and tensile strength.
The regression analysis diagram is shown in Fig. 5, and the regression results are shown in Table 4 and Table 5.
Table 4 Regression Model Data of Vickers Hardness and Upper Yield Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 
2.020 

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 Regression Model Data of Vickers Hardness and Tensile Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 
It can be seen from Table 4 and Table 5 that Vickers hardness has a good correlation with strength, and the correlation with tensile strength is better than that with upper yield strength.
In the four regression models for the relationship between Vickers hardness and strength, the significance P is less than 0.05, and the goodness of fit R^{2} is close.
Considering that the conversion relationship between Vickers hardness and tensile strength of low carbon steel given in the standard is close to a linear relationship, it is recommended to convert according to the linear relationship.
The formula after fitting is:
Where: H_{V} is Vickers hardness.
2.2.2 Relative deviation analysis of conversion results
According to the fitted linear regression model, the relative deviations between the converted values of upper yield strength and tensile strength and the tensile test results are calculated respectively, and the relative deviations are statistically analyzed.
The statistics are 162, and the results are shown in Table 6.
The relative deviations are basically normal distribution, and the frequency distribution is shown in Fig. 6.
Table 6 Statistical Table of Relative Deviation from Vickers Hardness to Strength
Statistical items 
Minimum value 
Maximum 
Average deviation 
Standard reference 
Relative deviation of upper yield strength conversion value 
19.30 
+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 to strength
2.2.3 Comparison with national standard conversion value
Put the conversion value of tensile strength given in the standard, the conversion value of the linear regression formula fitted by the author, and the scatter plot of the corresponding relationship between Vickers hardness and tensile strength on the same chart for comparison, as shown in Fig. 7.
Fig. 7 Comparison Chart of Tensile Strength Converted by Vickers Hardness
It can be seen from Fig. 7 that the overall trend of the three curves is consistent.
The conversion value of tensile strength given in GB/T 11721999 is very close to the conversion value given by the author.
Within the range of 370~630MPa, the difference between them increases slightly with the increase of hardness value, with an average deviation of 1.2% and a maximum deviation of 3.3%.
The conversion value of tensile strength given in GB/T 333622016 is generally lower.
2.3 Correlation between Brinell hardness and strength
2.3.1 Brinell hardness test process and result analysis
Grind the surface of the sample with a grinder to make the surface roughness not greater than 1.6μm.
After checking the instrument with a standard hardness block, conduct the Brinell hardness test according to Metallic Materials Brinell Hardness Test Part 1: Test Method (GB/T 231.12018).
The cemented carbide indenter with a diameter of 10mm is used, and the test force is 29.42kN.
Measure 3 points for each sample and take the average value.
SPSS software is used to conduct linear regression, quadratic regression, power regression and exponential regression analysis on Rockwell hardness, upper yield strength and tensile strength.
The regression analysis diagram is shown in Figure 8, and the regression results are shown in Table 7 and Table 8.
Fig. 8 Regression Analysis of Brinell Hardness and Strength
Table 7 Regression Model Data of Brinell Hardness and Upper Yield Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 Regression Model Data of Brinell Hardness and Tensile Strength
Equation 
Model Summary 
Model parameter 

R^{2} 
F 
Significance P 
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 
It can be seen from Table 7 and Table 8 that Brinell hardness has a good correlation with strength, and the correlation with tensile strength is better than that with upper yield strength.
In the four regression models of the relationship between Brinell hardness and strength, the significance P is less than 0.05, and the goodness of fit R^{2} is close.
Considering that the conversion relationship between carbon steel Brinell hardness and tensile strength given in the standard is close to a linear relationship, it is recommended that the conversion should also be based on a linear relationship.
The fitted formula is:
Where: H_{BW} is Brinell hardness.
2.3.2 Relative deviation analysis of conversion results
According to the fitted linear regression model, the relative deviations between the converted values of upper yield strength and tensile strength and the tensile test results are calculated respectively, and the relative deviations are statistically analyzed.
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. 9.
Table 9 Statistical Table of Relative Deviation from Brinell Hardness to Strength
Statistical items  Minimum value  Maximum  Average deviation  Standard reference 
Relative deviation of upper yield strength 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 to strength
2.3.3 Comparison with national standard conversion value
In the standard GB/T 11721999, the ratio of test force to indenter ball diameter of Brinell hardness test is 10.
The author’s test is carried out according to GB/T 231.12018. With reference to the provisions of the standard, the ratio of test force to indenter ball diameter is 30.
Therefore, it is no longer compared with GB/T 11721999 in comparison with the national standard conversion value.
The standard conversion value of tensile strength given in GB/T 333622016, the conversion value of the linear regression formula fitted by the author, and the scatter plot of the corresponding relationship between Brinell hardness and tensile strength are compared on the same chart, as shown in Fig. 10.
Fig. 10 Comparison Chart of Tensile Strength Converted by Brinell Hardness
It can be seen from Fig. 10 that the conversion value of tensile strength given in GB/T 333622016 almost coincides with the regression curve of tensile strength fitted by the author, with an average deviation of 0.4% and a maximum deviation of 1.2% within 370630MPa.
In recent years, the rapid development of various portable hardness testers has brought great convenience to onsite testing.
At present, many types of portable Rockwell hardness tester and portable Brinell hardness tester can be purchased in the market.
The equipment is portable, simple to operate, fast to measure, and the detection accuracy also meets the requirements of national standards, which is suitable for onsite engineering detection.
There is also various portable processing equipment for sample surface treatment, which can meet the test requirements.
Therefore, it is feasible to use Rockwell hardness and Brinell hardness to calculate the steel strength in the field inspection of steel structures.
3. Conclusion
(1) Rockwell hardness, Vickers hardness and Brinell hardness show good correlation with strength. Based on material test, the conversion formula of Rockwell hardness, Vickers hardness and Brinell hardness and strength is obtained, and the relative deviation of conversion is within the allowable range of the project.
The relative deviation between Brinell hardness and tensile strength is obviously lower than that of Rockwell hardness and Vickers hardness.
(2) The converted tensile strength of Rockwell hardness given in GB/T 333622016 is low for Q235 steel and high for Q345 steel.
The converted tensile strength of Vickers hardness is slightly lower.
The converted tensile strength of Brinell hardness is consistent with the test results.
The values of tensile strength converted by Rockwell hardness and Vickers hardness given in GB/T 11721999 are close to the test results.
(3) Combined with the 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.