Study on the Influence of the Gurson–Tvergaard–Needleman Damage Model on the Fatigue Crack Growth Rate
Round 1
Reviewer 1 Report
The authors in this paper have presented the influence of the GTN parameters on fatigue crack growth rate. Crack closure as a key effect being relatable to the porosity values that are reached despite the connection between the porosity and plastic strain, the effect of the initial porosity on the predicted crack growth rate is small. The sensitivity analysis identified the nucleation amplitude and Tvergaard’s loss of strength parameter as the main factors, whose variation leads to larger changes in the crack growth rate, which is interesting and helpful. I think that this paper should be accept.
Author Response
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Reviewer 2 Report
The authors offer a research, which I consider important and interesting for the readership of the “Metals”.
This well organised and well-written paper presents a well-done work, which is important for the comprehension of the fatigue cracking phenomenon. This is valuable contribution that forwards the fatigue crack growth theory implementing advanced constitutive equations to describe material behaviour with damage. The investigation is nicely designed, correctly performed and mostly adequately described.
That is why I recommend this work for publication, however, not in its present form.
For me, some points are missed, and some issues are not clear.
1. Although the introduction is nice (it is concise, but comprehensive, and free from superfluous adornments), I miss there a formulation of the work objectives. I suggest that a paragraph exposing the work aims should be put in the introduction section before explaining the organisation of the paper. BTW, it could help understanding the modelling approach regarding which I have some comprehension gaps, which I put next.
2. As regards the Sect. 2 “Numerical Model”, beyond the description of the model geometry and loading presented in the Sect. 2.2 and the part of Sect. 2.3, it is not clear for me, what relation to the undertaken study have the denominated there “Material constitutive model” (sect. 2.1) and the crack propagation criterion in terms of the attainment of the critical plastic strain (sect. 2.3). I mean, I did not find any mention about the results of crack propagation modelling implementing the model of the Sect 2.
I suspect, Sect. 2 does not present the entire model, but the skeleton within which the GTN damage model were incorporated counting on the description of the matrix material behaviour, so that all them together could form the closed model setup. But it has not been clearly said.
It does not help the matter that the meaning of the variable Y in eq. (1) has not been defined. I, again, suspect that this could be what appears later in eq. (4) as σy nominated “the isotropic hardening rule”. As a matter of fact, this σy does not represent any rule, but merely a variable, which might be defined (or not) by some relation representing the hardening rule, like, e.g., the one given by eq. (1), but with σy instead of Y. (Though, the rule (1)-(2) is not isotropic.)
BTW, in the presentations of GTN model published elsewhere (by Tvergaard, Nedleman, etc.), the variable in the place of σy of the present paper is denominated the equivalent tensile flow stress in the matrix material, which, in due course, can be established according to certain hardening rule or somehow else. Anyhow, the authors have never defined this σy, although I suspect that the unexplained variable Y could be what is commonly used in GTN model as the equivalent tensile flow stress in the matrix material.
3. Concerning the material constitutive model presented by eqs. (1)-(2), which is of the type usually implemented in monotonic-load analyses, I wonder, which equivalent plastic strain is meant there? I mean, although there is no place for misunderstanding in monotonic load case where the notion of equivalent plastic strain is unambivalent, but it is not so under cyclic (oscillating) straining where two equivalent strain notions appear: the equivalent accumulated (or cumulative) and the (nominal or measured) strain [about the difference between them, see Suresh “Fatigue of Materials” sec. 2.1, and especially, sec. 3.6.1 and Fig. 3.6].
4. Having stated that the plane stain conditions are imposed, it is needless to indicate the specimen thickness. Many readers can figure out that this is merely a computational procedure issue, but some readers may ask you for the proofs that plane strain could be achieved at 1 mm thickness.
5. Could you, please, comment your choice of the critical plastic strain value of 1.1 as the criterion of crack advance? Can you, please, substantiate this?
May be I have missed this, but which strain do you mean: the equivalent strain of the type ~(εijεij)1/2 or the “linear” one like, e.g., ε11?
6. High resolution of the strain field is crucial for the implementation of the critical strain type criteria. To this end, large-deformation elastoplastic formulations are preferable. I have not it clear which – small or large deformation – formulation was implemented in the present modelling. If you chose the small-strain option, could you, please, substantiate the choice?
7. I wonder, why do you consider two different crack lengths a0? If I understand you well, it is to generate different K levels applying the same load. Would not it be easier to adjust the applied load for obtaining definite K-s with the same model geometry (exactly the same FE mesh)?
8. Another issue that I have not clear. In CT specimen under given load, K and ΔK increase with the increasing crack size, i.e., with the crack growth. All your results about the growing crack refer to constant ΔK. Did you really adjust the load to keep ΔK fixed during the crack extension? Or, have I missed something?
9. Regarding Fig. 4, what do the dotted lines mean there?
10. What do “natural scales” mean in figure captions and the text referring to the modelling results?
11. Regarding the porosity and plastic strain evolution graphs, all them are oscillating, but the oscillations, are nearly impossible to discern (excepting Fig. 5b, amplification of ~800% is needed to see them) because they are hidden under the point symbols. I suggest presentation of these results by plain lines without symbols for visibility
12. Finally, to improve the paper, it would be nice to perform once more careful spelling, grammar and style checking to get rid of such things as “experimental… fatigue tests” (line 86) or the orphan line 210, or a formatting issue with framing eqs. (1) to (10), or ill constructed phrases like “Although the importance of this parameter, it is not capable to explain...” (lines 26-27), etc.
Author Response
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Reviewer 3 Report
I have attached my comment.
Comments for author File: Comments.pdf
Author Response
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Round 2
Reviewer 2 Report
Although the authors corrected several deficiencies that I indicated in my previous review, I’m rather disappointed by the authors’ slipshod attitude about the paper revision. It is regrettable.
In the previous review, I suggested the authors to take away in their graphs the large-size points that contribute nothing, but hide the really oscillating nature of variables presented on some graphs (e.g., Fig. 5a among others) and mask the subtle differences between result curves displayed in other figures (e.g., Fig 6 and 9a among others). The authors did nothing about the matter. (Although they claim that they improved the visibility of results upon revision, this is false.)
In the former review I pointed out the issue of ill-formatted eqs. (1) to (10). Nothing has been done to fix the matter.
To justify in my former revision the recommendation to improve English, I put there few examples of language deficiencies, but not the exhaustive list of all faults. Unfortunately, the authors did not attend even those few deficiencies that I pointed out directly in my former review.
At any rate, the authors did not do their best to improve English. Limiting to pointing out some of the deficiencies that appear only on the first two pages of the revised manuscript, they are as follows:
* line 14 (and 142) – GTN: the meaning of an abbreviature should be defined at the first use (and not repeated afterwards);
* line 36 – Crack Tip Opening Displacement is the term in common use, but not Open Displacement;
* line 58 – “materials strength”: nouns acting as adjectives always go in singular, so that instead of “materials strength” there should be “material strength”;
* line 68: “The value of these parameters defines ....”: do these parameters (in plural) have the unique value?
In the revised manuscript, there re-appears the line 231, which I pointed out in the former review as an orphan line. If I was mistaken, what is this and what does it mean now?
The authors say “In the fourth section there is the presentation and discussion of the results obtained by ...”, but I found in the revised paper the section “4. Sensitivity analysis”.
The authors denote σ (with a macron) as the equivalent stress (line 100), and denote q as the von Mises equivalent stress (line 148). Are they different things? Or this is a mere carelessness?
Here is another similar incidence. The authors denote σ‘ as the deviatoric component of the Cauchy stress tensor (line 99), and denote S as the deviatoric stress tensor (line 160). Are they different things? Or this is a mere carelessness?
I ask the authors to take more care about their manuscript and to be more respectful to the potential readership.
To terminate, I do regret, but I recommend resubmission of the paper after major careful and respectful revision.
Author Response
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Reviewer 3 Report
The manuscript has been modified adequately.
Author Response
Thank you very much for your positive comment.
Round 3
Reviewer 2 Report
Now it's OK.
Thank you.
