Magnetic Signal Characteristics in Critical Yield State of Steel Box Girder Based on Metal Magnetic Memory Inspection

Round 1

Reviewer 1 Report

 

In this paper, the author presented a four-point bending static loading test on the steel box girder. The author analyzed the magnetic signal characteristics of different parts of the specimen and proposed two magnetic characteristic parameters that could be used as early warning signs before the deformation or failure of the specimen or quantitatively characterize the shear capacity. My detailed comments are as follows:

1)      The pictures and captions should be aligned and they need to be revised, such as Figure 1, Figure 8 and Figure 10-12.

2)      The title of the third part and the body should be together, please modify it.

3)      In Figure 12(a), The lines are too thick, resulting in more difficult observation. Please vary the thickness of the lines.

4)      In Figure 15 and Figure 16, the diagrams and captions should be on one page.

5)      The format of the units should be consistent. For example, the units of kN on page 10.

6)      The formulas should be aligned in 3.3.1.

7)      On page 15 and 16, there has too much space between the words. It may be a formatting problem. Please correct it.

Therefore, I recommend a few revision.

Author Response

1): The pictures and captions should be aligned and they need to be revised, such as Figure 1, Figure 8 and Figure 10-12.

Response: Thank you very much for reviewing this article scrupulously. We apologize for
oversights in our work. We have aligned pictures and captions of all in this paper, including Figure1, Figure 8, and Figure 10-12.

2): The title of the third part and the body should be together, please modify it.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have modified the position of the title of the third part and body to them together.

3): In Figure 12(a), The lines are too thick, resulting in more difficult observation. Please vary the thickness of the lines.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We reduced the size of the lines in Figure 12(a) to make the observation clearer.

4): In Figure 15 and Figure 16, the diagrams and captions should be on one page.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have modified the position of diagrams and captions in Figure 15 and Figure 16 to make them on one page.

5): The format of the units should be consistent. For example, the units of kN on page 10.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have checked and modified all the formats of the units in the paper, including the unit kN on page 10.

6): The formulas should be aligned in 3.3.1.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have modified the positions of all formulas in the paper, including subsection 3.3.1, to align them.

7): On page 15 and 16, there has too much space between the words. It may be a formatting problem. Please correct it.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have modified the formatting of pages 15 and 16 to make the proper spacing between the words. In addition, we have checked and modified the incorrect format in the paper, such as the wrong font in the formula, redundant spaces, the omission of punctuation marks and spaces, etc. All the modifications are marked in red font in the revised version.

Reviewer 2 Report

1. What was the effect of butt welds on the failure process and the load-bearing capacity of the specimen tested?

2. Subsection “4.1. Damage warning analysis based on magnetic characteristic parameter” –location of the analysed different force parts of the specimen (Fig. 16) should be presented.

3. Subsection “4.2. Quantitative evaluation based on magnetic characteristic parameters” – Authors discuss the relationship between the average value of the absolute value of the magnetic signals of the six inspection lines on the same section and the load F. The scheme of tested area (lines 250 mm up to 750 mm) should be included to make the analysis clearer.

4. Authors presented an example relation between the magnetic signal and the shear bearing capacity of the web. Is it possible to define a critical and universal value for the H_SF parameter that signals the possibility of damage?

5. Conclusion No 2. – Authors wrote: The safety margin for warning damage using this magnetic feature was the web >bottom flange > top flange. This should be clearly proven.

Author Response

1: What was the effect of butt welds on the failure process and the load-bearing capacity of the specimen tested?

Response: Thank you very much for your question. We have added the relevant contents about the effect of butt welds on the failure process and the load-bearing capacity of the specimen tested.

The modification is as follows:

    The V-groove butt weld in the middle span of the specimen was welded using E50 welding electrodes and the strength and stiffness of the weld were slightly higher than that of the steel. Due to the impact of the butt weld, the buckling deformation that should have occurred in the mid-span location of the top flange was shifted, and the final buckling area occurred between 1550 mm and 1650 mm. Among them, the number represents the distance from the left support to a certain inspection point, and the buckling deformation photo is shown in Figure 9. The buckling area occurred on the steel, and the welded joint was not in a weak position, so the weld did not weaken the load-bearing capacity of the specimen. Relevant studies showed that high-quality welds had some influence on the location of buckling deformation, and generally had little impact on improving load-bearing capacity [25,26].

[25]Qiao, G.Y.; Liu, Y.M.; Han, X.L.; Wang, X.; Xiao, F.R. Simulation study on effects of geometry size of weld joint on bearing capacity of steel pipe. Transactions of the China Welding Institution. 2017, 38, 33–36, 130.

[26]Broniewicz, M.; Broniewicz, F. Welds assessment in k-type joints of hollow section trusses with I or H section chords. Buildings, 2020,10, 43.

2: Subsection “4.1. Damage warning analysis based on magnetic characteristic parameter” –location of the analysed different force parts of the specimen (Fig. 16) should be presented.

Response: Please accept our sincere thanks for reviewing this manuscript. We apologize for oversights in our work. In subsection 4.1, we have described the locations of different force parts, inspection lines, and strain gauges of the specimen to make this part of the content more complete and clear.

The modification is as follows:

Figure 16 shows thecurves at the top flange, bottom flange, and web of the specimen, where T and TS were the numbers of the inspection line and strain gauge on the top flange, respectively. Similarly, B and BS, W and WS were on the bottom flange and web, respectively. The specific locations of inspection lines and strain gauges at different force parts correspond to Figure 4 (a), (b), and (c) (d), respectively.

3: Subsection “4.2. Quantitative evaluation based on magnetic characteristic parameters” – Authors discuss the relationship between the average value of the absolute value of the magnetic signals of the six inspection lines on the same section and the load F. The scheme of tested area (lines 250 mm up to 750 mm) should be included to make the analysis clearer.

Response: Thank you very much for reviewing this article scrupulously. We apologize for failing to clearly describe this part of the content. In subsection 4.2, we have added the scheme of the tested area (lines 250 mm up to 750 mm) on the web. In addition, to express the meaning ofmore clearly, we listed the expression of.  

The modification is as follows:

 In the web, the average value of the absolute value of the magnetic signals of the six inspection lines on the same section, |H_SF(y)|_ave was defined to characterize the force-magnetic relationship, and the expression is as follows

|H_SF(y)|_ave=[∑|H_SF(y)_i|] / N        (11)

Where H_SF(y)_i is the magnetic signal value of different inspection lines on a cross-section, N is the number of inspection lines on the same cross-section, that is, N=6.

When loaded to the preset load, stop loading and collected magnetic signals. The probe was placed vertically on the web surface to collect magnetic signal data from left to right. Three magnetic signals were collected at each measuring point and the average value was calculated to reduce the effect of random errors. The specific locations of inspection lines, points, and strain gauges on the web are shown in Figure 4(c)(d). Because the loading end and support had a great impact on the magnetic signal value of the inspection points beside them, this paper did not analyze these inspection points that were greatly affected, only the inspection points between 250mm-750mm were analyzed.

4: Authors presented an example relation between the magnetic signal and the shear bearing capacity of the web. Is it possible to define a critical and universal value for the HSF parameter that signals the possibility of damage?

Response: Thank you very much for the hard work of the reviewer. It is of great significance to the engineering application of MMMT for defining a critical and universal value for the magnetic parameter that signals the possibility of damage. We are sorry cannot define explicit critical and universal value for a magnetic parameter that signals the possibility of damage, and the reasons are as follows.

MMMT is a kind of weak magnetic detection technology. The structure form, loading mode and loading position, steel type, and steel thickness may have an impact on the magnetic signal amplitude, which may lead to differences in the magnetic signal amplitude on different specimens. Therefore, it is difficult to give a critical value of damage only depending on the experimental data in this paper. More tests are needed to verify the fitting relation in this paper, so as to achieve the purpose of inversion force state of the web by magnetic signal value.

In addition, in subsection “4.2. Quantitative evaluation based on magnetic characteristic parameters”, we discussed the problem that MMMT was difficult to implement accurate quantitative evaluation from two aspects of controllable and uncontrollable factors. “Significantly, there were two reasons for the dispersion of magnetic signals at different inspection points under the same load. One was the human factor, the lift-off value and angle of the probe were inevitably slightly different during the inspection process. Second, steel is an uneven material, the stress and the surface self-leakage magnetic field on it were not uniform. In addition, the loading speed, temperature, chemical composition of the material, and size of the SCZ also affect the strength of the magnetic signal. These factors make MMMT difficult to achieve accurate quantitative evaluation, and more methods to reduce quantitative errors are needed to verify. ”

It is noteworthy that the magnetic signal is particularly sensitive to the yield behavior of the steel box girder in this paper, and similar phenomena have been found in plate tests with different load forms and material thicknesses. Therefore, combined with Figure 17, the phenomenon of rapid decrease ofvalue can be used as an early warning sign that the web reaches the critical yield state.

In this paper, we have added a conclusion and the reasons that cannot define explicit critical and universal value for the HSF parameter that signals the possibility of damage.

The modification is as follows:

Supplemented and perfected the factors affecting the amplitude of magnetic memory signal, as shown below

In addition, the structure form, loading form and loading position, steel type, steel thickness, loading speed, chemical composition of the material, and size of the SCZ also affect the strength of the magnetic signal[40-42].

[40]Bao, S,; Yang, J.; Gu, Y.B. Effect of strain rate history on the piezomagnetic field of ferromagnetic steels. J. Magn. Magn. Mater. 2021, 526, 167760.

[41]Huang, H.H.; Qian, Z.C. Effect of Temperature and Stress on Residual Magnetic Signals in Ferromagnetic Structural Steel. IEEE. Trans. Magn. 2017,53, 6200108.

[42]Zhao, X.R.; Su, S.Q.; Wang.W.; Zhang, X.H. Metal magnetic memory inspection of Q345B steel beam in four point bending fatigue test. J. Magn. Magn. Mater. 2020,514, 167155. 

A sentence has been added in the conclusion (3), as shown below

Through the reversal of the-F curve could accurately judge the critical yield state of the web.

5: Conclusion No 2. – Authors wrote: The safety margin for warning damage using this magnetic feature was the web >bottom flange > top flange. This should be clearly proven.

Response: Please accept our sincere thanks for reviewing this manuscript. We apologize for hastily conclusions that have not been clearly proven. We have deleted this part of the conclusion that “the safety margin for warning damage using this magnetic feature was the web >bottom flange > top flange ”and the specific reasons are as follows.

The analysis in subsection “3.2. Force magnetic relationship” could clearly present this conclusion, but it cannot be clearly presented in subsection “4.1 Damage warning analysis based on magnetic characteristic parameter’’. At present, the conclusion is hastily and needs further verification, so this part of the content is deleted.

The contents deleted are as follows:

Subsection 3.2. Force magnetic relationship – “According to the-F curves of different parts of the steel box girder, it can be obtained that the safety reserve of warning damage was the web >bottom flange > top flange by the sudden and rapid reversal of the trend of the curves.”

Conclusion 2. – “The safety margin for warning damage using this magnetic feature was the web >bottom flange > top flange.”

Attached please find the response letter contains revised version.

Author Response File: Author Response.docx

Reviewer 3 Report

In the Reviewer opinion the research paper entitled “Magnetic Signal Characteristics of Steel Box Girder Based on Metal Magnetic Memory Inspection” is good.

The present paper propose the law of distribution of the magnetic signal,△HSF(y), at different stress parts of a steel box girder and the quantitative relationship between the magnetic characteristic parameters and the external load. The results showed that the MMMT could accurately detect the early stress concentration zone (SCZ) and predict final buckling zone of steel box girders. All the evaluation methods are expected to provide a basis for effectively evaluating the stress state of steel box girders with the MMMT method.

Some comments which greatly enhance the understanding of the paper and its value are presented below. Specific issues that require further consideration are:

1. The title of the manuscript is matched to its content.
2. The Introduction generally covers the cases.
3. The methodology was clearly presented.
4. In the Reviewer’s opinion, the current state of knowledge relating to the manuscript topic has been presented, but the author's contribution and novelty are not enough emphasized.
5. Experimental program and results looks interesting and was clearly presented.
6. In the Reviewer’s opinion, the bibliography, comprising 31 references, is more less representative.
7. An analysis of the manuscript content and the References shows that the manuscript under review constitutes a summary of the Author(s) achievements in the field.
8. In the Reviewer’s opinion the manuscript is well written, and it should be published in the journal after minor revision.

Author Response

1: The title of the manuscript is matched to its content.

Response: Thank you very much for reviewing this article scrupulously. We apologize for oversights in our work. We have revised the title of the manuscript to match the content of this paper.

The modification is as follows:

Magnetic Signal Characteristics in Critical yield State of Steel Box Girder Based on Metal Magnetic Memory Inspection

2: The Introduction generally covers the cases.

Response: Many thanks to the reviewers for their suggestions. We apologize for oversights in our work. In the introduction, we have added cases related to the necessity of nondestructive testing (NDT), especially metal magnetic memory testing (MMMT).

The modification is as follows:

When the SCZ reaches the yield load, the components will appear local buckling phenomenon, and the structural damage caused by the buckling instability of components will have a serious impact on the safety of human life and property. There have been many accidents caused by buckling instability in history. Li [3] reported that during the construction of the Westgate bridge near Melbourne, the top flange plate at the midspan lost stability after buckling, leading to the collapse of the entire span of 112 m. The former Soviet Union counted 59 major steel structure accidents during the 27 years, of which 29% were the overall lost stability or local lost stability of the structure. In the 1970s, in less than two years, four orthotropic deck slab bridges under construction in Europe suffered from collapse after local buckling. In recent years, there had been many accidents caused by the bridge's local buckling. Because the steel box girder is prone to local buckling, Many scholars [4-7] have studied how to improve the local stiffness and strength and how to enhance the local stability of the steel box girder.

Aiming at the instability phenomenon of bridge steel structure after local buckling, if the location of local stress concentration and critical yield state of steel structure can be identified and early warned through the results of non-destructive testing (NDT), the potential safety risks can be found in time and disasters can be avoided. Therefore, early identification of stress concentration location and critical yield state of steel structures in service by NDT method is an important basis for evaluating structure reliability [8]. However, it is difficult for traditional NDT to effectively evaluate such invisible hidden damage [9,10].

3: The methodology was clearly presented.

Response: Thank you very much for reviewing this article scrupulously. As the reviewer commented, we detailed presented the inspection line, inspection point, inspection equipment, inspection method, and inspection measures to reduce measurement error in subsection "2. Experiences".

4: In the Reviewer’s opinion, the current state of knowledge relating to the manuscript topic has been presented, but the author's contribution and novelty are not enough emphasized.

Response: Thank you very much for the hard work of the reviewer. We modified part of the introduction in this paper to better emphasize the novelty and the author's contribution.

The modification is as follows (the first and second paragraphs have appeared in the response to comment 2) :

When the SCZ reaches the yield load, the components will appear local buckling phenomenon, and the structural damage caused by the buckling instability of components will have a serious impact on the safety of human life and property. There have been many accidents caused by buckling instability in history. Li [3] reported that during the construction of the Westgate bridge near Melbourne, the top flange plate at the midspan lost stability after buckling, leading to the collapse of the entire span of 112 m. The former Soviet Union counted 59 major steel structure accidents during the 27 years, of which 29% were the overall lost stability or local lost stability of the structure. In the 1970s, in less than two years, four orthotropic deck slab bridges under construction in Europe suffered from collapse after local buckling. In recent years, there had been many accidents caused by the bridge's local buckling. Because the steel box girder is prone to local buckling, Many scholars [4-7] have studied how to improve the local stiffness and strength and how to enhance the local stability of the steel box girder.

Aiming at the instability phenomenon of bridge steel structure after local buckling, if the location of local stress concentration and critical yield state of steel structure can be identified and early warned through the results of non-destructive testing (NDT), the potential safety risks can be found in time and disasters can be avoided. Therefore, early identification of stress concentration location and critical yield state of steel structures in service by NDT is an important basis for evaluating structure reliability [8]. However, it is difficult for traditional NDT to effectively evaluate such invisible hidden damage [9,10].

Currently, MMMT is still an emerging NDT method. Previous experimental studies mainly focused on the uniaxial tension or compression of steel plates, and the conclusions were only applicable to the case of macroscopic defects in specimens. However, the problems related to invisible hidden damage in steel components, such as inspection·of local buckling location, identification and warning of critical yield state had not been considered. To further study the feasibility of MMMT for invisible hidden damage monitoring of complex steel structures, and also to extend the application of MMMT to bridge steel structures, a four-point bending static loading test was carried out on the steel box girder in this paper. We analyzed the feasibility of identifying the location of invisible hidden damage on different parts of the steel box girder through magnetic signal characteristics. Then, two magnetic parameters were proposed to be used as warning signs of critical yield state on different parts of the steel box girder. Finally, the relationship between the magnetic signal value and the magnetic parameters was obtained to inverse the force state of the web.

5: Experimental program and results looks interesting and was clearly presented.

Response: Please accept our sincere thanks for reviewing this manuscript.

6: In the Reviewer’s opinion, the bibliography, comprising 31 references, is more less representative.

Response: Thank you very much for your question. We apologize for oversights in our work. This paper includes two aspects: steel box girder and metal magnetic memory technology (MMMT). Several representative literatures on the aspect of steel box girders have been added to make this paper's literature more comprehensive. In the literature on MMMT, we have used the representative literature of recent years to replace the literature of long ago. In addition, we have modified the wrong format of references in this paper.

The modification is as follows:

1. Li, X.Y.; Zhang, G.; Kodur, V.; He,S.H.; Huang, Q. Designing method for fire safety of steel box bridge girders. Steel. Compos. Struct. 2021, 38, 657–670.
2. Gao, C.; Zhu, L.; Han, B.; Tang, Q.C.; Su, R. Dynamic Analysis of a Steel–Concrete Composite Box–Girder Bridge–Train Coupling System Considering Slip, Shear–Lag and Time–Dependent Effects. Buildings. 2022, 12, 1389.
3. Li, L.F. The analytieal theory and model test research on local stability of orthotropie steel box girder[D]. Changsha, Hunan University, 2005.(in Chinese)
4. Stamatelos, D.G.; Labeas, G.N.; Tserpes, K.I. Analytical calculation of local buckling and post–buckling behavior of isotropic and orthotropic stiffened panels. Thin–Walled. Struct, 2011, 49 422–430.
5. Wang, F.; Lv, Z.D.; Zhao, Q.K.; Chen, H.L.; Mei, H.L. Experimental and numerical study on welding residual stress of U–rib stiffened plates. J. Construct. Steel. Res. 2020, 175, 106362.
6. Wang, F.; Tian, L.J.; Lv, Z.D.; Zhao, Z.; Chen, Q.K.; Mei, H.L. Stability of full-scale orthotropic steel plates under axial and biased loading: Experimental and numerical studies. J. Construct. Steel. Res. 2021, 181, 106613.
7. Wang, F.; Lv, Z.D.; Gu, M.J.; Chen, Q.K.; Zhao, Z.; Luo, J. Experimental study on stability of orthotropic steel box girder of self–anchored suspension cable–stayed bridge. Thin–Walled. Struct, 2021, 163, 107727.
8. Shi, P.P.; Su, S.Q.; Chen, Z.M. Overview of researches on the nondestructive testing method of metal magnetic memory, status and challenges. J. Nondestruct. Evl. 2020, 39, 1–37.
9. Shi, P.P.; Jin, K.; Zheng, X.J. A magnetomechanical model for the magnetic memory method. Int. J. Mech. Sci. 2017, 124, 229–241.
10. Shi, P.P.; Bai, P.G.; Chen, H.E.; Su S.Q.; Chen Z.M. The magneto-elastoplastic coupling effect on the magnetic flux leakage signal. J. Magn. Magn. Mater. 2020, 504, 166669.
11. Bao, S.; Jin, P.; Zhao, Z.; Fu, M. A Review of the Metal Magnetic Memory Method. J. Nondestruct. Eval. 2020, 39, 1–14.
12. Kashefi, M.; Clapham, L.; Krause, T.W.; Krause, P.; Ross, U.; Anthony, K.K. Stress–Induced Self–Magnetic Flux Leakage at Stress Concentration Zone. IEEE. Trans. Magn. 2021, 57, 6200808.
13. Zhang, H.; Leng, L.; Zhao, R.Q.; Zhou, J.T.; Yang, M.; Xia, R.C. The non–destructive test of steel corrosion in reinforced concrete bridges using a micro–magnetic sensor. Sensors 2016, 16, 1439.
14. Roskosz, M.; Bieniek, M. Evaluation of residual stress in ferromagnetic steel based on residual magnetic feld measurements. NDT&E. Int. 2012, 45, 55–62.
15. Roskosz, M.; Bieniek, M. Analysis of the universality of the residual stress evaluation method based on residual magnetic feld measurements. NDT&E. Int. 2013, 54, 63–68.
16. Dong, L.H.; Xu, B.S.; Dong, S.Y.; Chen, Q.Z. Characterisation of stress concentration of ferromagnetic materials by metal magnetic memory testing. Nondestruct. Test. Eva. 2010, 25, 145–151.
17. Huang, H.H.; Jiang. S.L.; Yang, C.; Liu, Z,F. Stress concentration impact on the magnetic memory signal of ferromagnetic structural steel. Nondestruct. Test. Eva. 2014, 29, 377–390.
18. Bao, S.; Fu, M.L.; Lou, H.J.; Bai, S.Z.; Hu, S. Evaluation of stress concentration of a low-carbon steel based on residual magnetic field measurements. Insight. 2016, 58, 678–682.
19. Dubov, A. Diagnostics of austenitic steel tubes in the superheaters of steam boilers using scattered magnetic fields. Therm. Eng. 1999, 46, 369–372.
20. Liu, L.L.; Yang, L.J.; Gao, S.W. Propagation Characteristics of Magnetic Tomography Method Detection Signals of Oil and Gas Pipelines Based on Boundary Conditions. Sensors. 2022, 22, 6055.
21. Shi, M.J.; Liang, Y.B.; Zhang, M.F.; Huang, Z.Q.; Feng, L.; Zhou, Z.Q. Pipeline Damage Detection Based on Metal Magnetic Memory. Trans. Magn. 2021, 57, 1–15.
22. Roskosz, M.; Rusin, A.; Kotowicz, J. The metal magnetic memory method in the diagnostics of power machinery component. J. Achiev. Mater. Manuf. Eng. 2010, 1, 362–370.
23. Su,Q.; Zhao, X.R.; Wang, W.; Zhang, X.H. Metal Magnetic Memory Inspection of Q345 Steel Specimens with Butt Weld in Tensile and Bending Test. J. Nondestruct. Eval. 2019, 38, 64.
24. Su,Q.; Ma, X.P.; Wang, W.; Yang, Y.Y. Stress-dependent magnetic charge model for micro-defects of steel wire based on the magnetic memory method. Res. Nondest. Eval. 2020, 31, 24–47.
25. Li, M.L.; Yao, H.; Feng, J.R.; Yao, E.T.; Wang, P.; Shi, Y. Calculation and experimental verification of force-magnetic coupling model of magnetised rail based on density functional theory. Insight. 2021. 63, 597–603.
26. Broniewicz, M.; Broniewicz, F. Welds assessment in k–type joints of hollow section trusses with I or H section chords. Buildings, 2020,10, 43.
27. Qiao, G.Y.; Liu, Y.M.; Han, X.L.; Wang, X.; Xiao, F.R. Simulation study on effects of geometry size of weld joint on bearing capacity of steel pipe. Transactions of the China Welding Institution. 2017, 38, 33–36, 130.
28. Gorkunov, E. Different remanence states and their resistance to external effects. Discussing the "method of magnetic memory". Russ. J. Nondestruct. 2014, 50, 617–633.
29. Gatelier–Rothea, C.; Chicois, J.; Fougeres, R.; Fleischmann,P. Characterization of pure iron and (130 P.P.M.) carbon–iron binary alloy by Barkhausen noise measurements, study of the influence of stress and microstructure. Acta. Materialia. 1998, 46, 4873–
30. Chen, X.; Liu, C.K.; Tao, C.H.; Dong, S.Y.; Wang, D.; Shi, C.L. Research on metal magnetic memory signal change of a ferromagnetic material under static tension. Nondestruct. Test. 2009, 31, 345–348.(In Chinese)
31. Su, S.Q.; Yi, S.C.; Wang, W.; Sun, H.J.; Ren, G.C. Bending experimental study of structural steel beam on magnetic field gradient based on modified Jiles-Atherton model. Int. J. App Electrom. 2017, 55, 409–421.
32. Guo ; Su S.Q.; Wang W.; Ma X.P.; Yi S.C.; Zhao X.R. Relationship between applied force and magnetic field in a pseudo-static test of a portal frame. Int. J. Appl. Electrom. 2021, 66, 1–19.
33. Su, S.Q.; Qin, Y.L.; Wang, W.; Zuo, F.F.; Deng, R.Z.; Liu, X.W. Stress–magnetization of the state of flange damage to a bridge steel box beam based on magnetic memory inspection. Chinese Journal of Engineering. 2022, 44, 900–910.(In Chinese)
34. Yi, S.C.; Wang, W.; Su, S. Bending experimental study on metal magnetic memory signal based on von Mises yield criterion. Int. J. Appl. Electrom. 2015, 49, 547–556.
35. Sablik, M.J.; Jiles, D. Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis. IEEE. Trans. Magn. 1993, 29, 2113.
36. Jiles, D.C.; Devine, M. Recent developments in modeling of the stress derivative of magnetization in ferromagnetic materials. J. Appl. Phys. 1994, 76, 7015.
37. Jiles, D. Theory of the magnetomechanical effect. J. Phys. D. Appl. Phys. 1995, 28, 1537.
38. Yang, E.; Li, L.M.; Chen, Magnetic field aberration induced by cycle stress. J. Magn. Magn. Mater. 2007, 312, 72–77.
39. Cullity, B.D.; Graham, C. Introduction to Magnetic Materials. John. Wiley. Press. 2008.
40. Pitman, K. The influence of stress on ferromagnetic hysteresis. IEEE. T. Magn. 1990, 26, 1978–1980.
41. Bao, S,; Yang, J.; Gu, Y.B. Effect of strain rate history on the piezomagnetic field of ferromagnetic steels. J. Magn. Magn. Mater. 2021, 526, 167760.
42. Huang, H.H.; Qian, Z.C. Effect of Temperature and Stress on Residual Magnetic Signals in Ferromagnetic Structural Steel. IEEE. Trans. Magn. 2017,53, 6200108.
43. Zhao, X.R.; Su, S.Q.; Wang.W.; Zhang, X.H. Metal magnetic memory inspection of Q345B steel beam in four point bending fatigue test. Magn. Magn. Mater. 2020, 514, 167155.

7: An analysis of the manuscript content and the References shows that the manuscript under review constitutes a summary of the Author(s) achievements in the field.

Response: Thank you very much for reviewing this article scrupulously.

8: In the Reviewer’s opinion the manuscript is well written, and it should be published in the journal after minor revision.

Response: Please accept our sincere thanks for reviewing this manuscript.

Attached please find the response letter containing revised version.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Authors response: In subsection 4.2, we have added the scheme of the tested area (lines 250 mm up to 750 mm) on the web.

I can't find this in the revised paper.