Theoretical Model of Self-Magnetic Flux Leakage and Its Application in Estimating the Depth Direction of a Fatigue Crack
Round 1
Reviewer 1 Report
The manuscript submitted by Jinyi Lee, Dabin Wang, and I Dewa Made Oka Dharmawan deals with a study of the influence of the fatigue crack and stresses near it on a magnetic flux density (induction) in a ferromagnetic metal. The authors present analyzed and measured the magnetic induction induced by three type of the domain structures in presence of the cracks with different orientations.
The article consists of two main parts: the first one presents the three theoretical models of domain structure, in which the induction distribution is analyzed depending on the cracks orientation, and the second one presents the experimental measurement of the stray fields from carbon steel specimens, which were cut at an angle of 30°, 60°, and 90° to cracks. The latter part presents a distribution of the magnetic flux density on the surface of the specimen using a 3-axis TMR sensor.
First of all it is necessary to note that the title of the manuscript is not concordant with the results of the manuscript. There are static cracks, which were inset in context “by hands”. Neither initiation nor propagation of a fatigue crack are in the manuscript.
As for the theoretical part of the article, where the authors have presented the magnetic domain structures with a different magnetization orientation in domains, the many definitions and statements are clearly wrong. In order to calculate the magnetic flux density (factually stray fields) outside of the sample induced by “spontaneous magnetic flux density” near crack, it is necessary to take into account such magnetic parameters as magnetocrystalline anisotropy, exchange stiffness, magnetoelastic strain tensor, magnetostriction, demagnetizing fields, and real domain structure. See, for example, J.M.D. Coey, “Magnetism and Magnetic Materials”, Cambridge University Press, New York, 2009. Therefore, these presented “Magnetic Domain Models” are not correct and cannot be use to estimate the stray fields While I find the measurement using a 3-axis TMR sensor and analysis of the stray fields induced by a magnetization localized in vicinity of the sample cracks are interesting I have to conclude that the paper is not suitable for the journal "Applied Sciences".
Moreover, the English in this manuscript is not too good. The authors could ask somebody with native language in order to edit the manuscript if they will change and resubmit this article.
Author Response
Dear Reviewer,
Thank you for your valuable time and expertise, and for your very detailed comments on our manuscript. Your comments were very helpful to us in clarifying the content of our article. All your suggestions and advice have been carefully considered in revising the manuscript point by point. The changes in revised manuscript are highlighted in red-colored text. We attach the point-by-point response down below.
We hope that the revision of this current manuscript according to your comments will meet with your approval. We again sincerely thank you for the time and effort you put into reviewing our manuscript.
Best Regards,
Authors.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. In Equation 1, the upper limit of the summation should be only n.
2. In some places it looks like the units of some quantities are wrong, for example S’ in Eq. 7, the surface current density in Eqs. 13 to 15.
3. The dimension values 15.36 and 30.72 in Figure 11a are not consistent with the size given in the text (32 × 30 × 12.8 mm). Are the values needed to be rounded? Or just because of the machining error? The authors should clarify it.
4. Pay attention to some expressions. For example, in lines 371-372, the distance between the surface of the specimen and the sensor surface is exactly the liftoff. The first two paragraphs in Section 4 are expected to be improved. The terminology SMFL in the conclusion is not consistent with the front abbreviation SMFD.
5. The results presented in Figures 15 and 16 are difficult to understand. It is incredible that the magnetic field distributions are the same when the carbon steel specimen is present and absent, respectively. The magnetic field produced by the specimen is not the background field. Isn’t it the target field carrying information of the fatigue stress?
Author Response
Dear Reviewer,
Thank you for your valuable time and expertise, and for your very detailed comments on our manuscript. Your comments were very helpful to us in clarifying the content of our article. All your suggestions and advice have been carefully considered in revising the manuscript point by point. The changes in revised manuscript are highlighted in red-colored text. We attach the point-by-point response down below.
We hope that the revision of this current manuscript according to your comments will meet with your approval. We again sincerely thank you for the time and effort you put into reviewing our manuscript.
Best Regards,
Authors.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The revised version of the manuscript submitted by Jinyi Lee and coauthors contains the correct title, the more informative introduction, and it is written in improved English. However, the theoretical model of domain structures was remained the same, i.e. it is wrong as in the old version.
I have recommended to the authors in my previous report to check the magnetic definitions and statements according with that in the special literature, for example, in the Coey’s book [1] “Magnetism and Magnetic Materials”, Cambridge University Press, New York, 2009 or in any another book of magnetism and magnetic materials. The presented “Magnetic Domain Models” are simplified and too far from realistic. It is necessary to take into account that domain structure of ferromagnets is a result of minimizing the free energy. Thus, the domains tend to form in the lowest-energy state (See chapter 7 “Micromagnetism, domains and hysteresis” in [1]). For this reason the model CDM must be transform to the model RDM, because magnetostatic energy, localized on the domain walls in the former state is higher than in the later one.
The mistakes and remarks presented below is only part of it in the manuscript. This presented “Magnetic Domain Models” are not correct and cannot be use to estimate the stray fields, induced by spontaneous magnetic flux density localized near cracks in ferromagnetic metal. Because, the authors do not present any substantially correct results in their study, I have to conclude that the paper is not suitable for publication in the “Applied Sciences”.
In the following I will list a few issues which I would like to ask the authors to consider before resubmitting the paper to this or another journal.
- the authors indicate external magnetic field H at the Fig.1, however, later in the text it don’t use. The equations (4) and (5) are standard definitions.
- the authors write at the132 and133 lines “A magnetic dipole moment m, is assumed to be generated by electrons rotating and orbiting around the nucleus of a ferromagnetic metal”. However, the magnetic moment m in a ferromagnetic is determined, generally, by both the spin and the orbital magnetic moments of an atomic electron, which are quantum values (See chapter 3 “Magnetism of electrons” in [1]);
- it is not clear the definition of the magnetization M by equation (1), where the value of mk summarizes from k=1 (dimensionless value) to Δv (volume dimension), which is nonsense;
- it is not clear what means mk;
- line 148, the authors write, “In Equation (1), n is the number of magnetic domains”, however the index “n” in this equation absentees;
- the equation (1) doesn’t have any sense, because mk is summarizing but Δv is no;
- the authors write, that “3-dimensional model…can be replaced in…the 2-dimensional model”, however this is possible if they use a thin film, the thickness of which is smaller than the domain wall thickness in the ferromagnetic, in another case it will be bulk material, i.e. it is necessary use 3-dimensional model;
- it is not clear the definition of the magnetization Meqv by equation (2). The authors write that it “can be expressed as the average obtained by multiplying the magnetization by the area of the magnetic domain”. It is not correct, i.e. according to (2) Meqv is not multiplying by the area;
- as for the “domain models”, they don’t take into account the magnetic crystalline anisotropy and coercivity of the ferromagnetic, i.e. there is a magnetic hysteresis, it means that statement ‘When H =0, M???=0” is true in the case of a demagnetized state only;
- at lines 177-178 the statement “The MFD B outside the ferromagnetic metal can be expressed as the superposition of the external magnetic field H and the equivalent magnetization” is amiss, because M outside is equal zero, so B=?0H;
- the equation (5) is correct inside the ferromagnetic metal, so the statement H=0, M???=0 is correct only if coercive field equal zero;
- the equations (7) and (8) are not clear, because ??? and ??? are tensors;
- the equations (10) - (12) have to multiply by a permeability ? of the ferromagnetic material.
- the authors display many of the characters (for example, J?,????, M?,????, M???,14, M???,58, a?,?, a???,??, and so one), which are not explained.
Author Response
Dear Reviewer,
Thank you for your valuable time and expertise, and for your very detailed comments on our manuscript. Your comments were very helpful to us in clarifying the content of our article. All your suggestions and advice have been carefully considered in revising the manuscript point by point. The changes in revised manuscript are highlighted in red-colored text. We attach the point-by-point response down below.
We hope that the revision of this current manuscript according to your comments will meet with your approval. We again sincerely thank you for the time and effort you put into reviewing our manuscript.
Best Regards,
Authors.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Dear Authors,
Your responses to my comments are unconvincing. I would not like to open the discussion with you. I think the theoretical model of domain structures in the revised version of the manuscript was remained the same, i.e. it is wrong as in the previous versions.
