Effect of Grain Size Distribution on Recrystallisation Kinetics in an Fe-30Ni Model Alloy
Round 1
Reviewer 1 Report
In the manuscript, the authors have assessed the recrystallization kinetics of a model Fe-30Ni alloy, initially heat treated for mode grain sizes 100 and 160 µm, cold deformed at two different strain levels and recrystallization-annealed at two different temperatures. The experimental results are correlated with the classic ‘JMAK’ theory of recrystallization kinetics and the deviation of the Avrami exponent from theoretical values are briefly discussed.
This body of work (though short) provides a good systematic assessment of the recrystallization kinetics of the alloy under consideration. The fitting of the data with existing models is also appreciated. Hence, I recommend this manuscript for publication in the current form.
Author Response
The proposed model will be validated for more conditions, i.e. temperature, strain and alloy composition. Therefore, future work will be present to expand the results and discussion as a next step.
Reviewer 2 Report
See Attached file!
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 2 Comments
Point 1: The method to predict the Avrami-index from the initial grain size distribution is simple and intriguing. However, at the same time it based on a number of simplifying assumptions (about the material and the deformation and recrystallization behavior, incl. the small deformations involved (necessary to mainly retain the initial grain structure (although compressed) also after deformation?), which makes me skeptical about the general validity and usefulness of it to more general cases. Only one example to test the validity is also not completely convincing. These aspects should at least be given some attention in the discussion and conclusions parts.
Response 1: The revision has emphasis on the applicability and the limitations of the proposed model. It has been mentioned in the discussion and conclusion section that the model is only applicable for a low strain deformation, i.e. up to 0.3 strain, without the interference of the shear bands.
Point 2: the first part of the Abstract (l. 11-17) should not be a part of the abstract, - it is more of a general introduction and should as such also belong to the Introduction.
Response 2: Abstract (line 11-17) has been moved to introduction section.
Point 3: p. 2, l 41-43 The Avrami exponent n is only time-dependent for the nucleation and growth rate of recrystallisation (i.e. temperature independent); for example, Sellars reported that the exponent showed independence to temperature and strain rate [1].
Not well phrased. Suggested changed to: The Avrami exponent n is supposed to depend only on time for the nucleation and growth rate of recrystallisation (i.e. temperature independent); …….
Response 3: Sentence has changed to the suggested version.
Point 4: p. 2, l- 54 ..recovery would be expected to reduce the stored energy not modify the time dependence of nucleation and growth. Not strictly correct; recovery and recrystallization do take place concurrently, and since recovery reduces the stored energy, it is continuously reduced during RX, which will affect the growth rate and the thus also the Avrami-index (Cf. Furu et al 1990, Ref. 3; see also the text by Humphreys and Hatherly, Recrystallization and related annealing phenomena)
Response 4: The revision has clarified that the recovery occurring prior to recrystallisation will not affect the Avrami exponent. The paper compared the Avrami exponent variation due to grain size distribution under the same deformation and annealing condition, therefore the effect of recovery on recrystallisation was not the main focus in this case. Additionally, in Furu’s experiment, the aluminium was cold deformed to a strain of 3, which was out of the strain range discussed in this paper.
Point 5: However, there was not a fitting parameter made in the models to predict 80 the Avrami exponent based on different grain size distribution Not well phrased. Please revise!
Response 5: The phrase has changed to: No fitting parameters in these models have been developed to predict the Avrami exponent based on different grain size distribution.
Point 6: …. it has been reported that recovery does not affect the recrystallisation kinetics (Avrami exponent), which is being considered in this paper, although it will affect the recrystallisation start and finish times. Please provide relevant references!
Response 6: The section has been rephrased: …. Recovery prior to recrystallisation, to clarify the statement. Additionally, the reference, i.e. F. Humphreys and M.Hatherly, Recrystallisation and Related Annealing Phenomena, 2nd ed., Oxford: Elsevier, 2004. has been provided.
Point 7: p. 6 Fig. 5a Something missing for the legends?
Response 7: the legends have been updated.
Point 8: It can be seen that, for the 160 μm mode grain size specimens, recrystallisation starting and finishing times are one order of magnitude slower for the lower strain value, and, at all temperatures and strains. To me a factor of 5 seems more correct?
Response 8: The revised paper has changed the statement to a factor of 5.
Point 9: Additionally, it can be seen from Figure 6c that the grains over 200 μm are still shown as being predominantly unrecrystallised at 850 °C for 90 s, i.e. 50% of the area fraction is from grains > 200 μm and the sample is 50% recrystallised at this point p. 7, l. 219 … however no grains over 200 μm were detected at 90s although coarse (160–180 μm are still present). It seems that the latter statement contradicts the previous one?
Response 9: The revised paper has updated the grain size distribution, and corrected the error in the grain size distribution of 50 % recrystallised sample (850 C, 90s) in the previous version. The grains over 200 μm were still present at 50 % recrystallisation, which could be seen in Figure 6 (c).
Point 10: As a result, finer grains in the distribution recrystallise quicker, attributed to a larger number of nucleation sites per unit area, and coarser grains recrystallise more slowly. This will also imply that the spatial distribution of the nuclei are no longer randomely distributed (some degree of clustering in the fine grain regions), which also will affect the recrystallization kinetics (Avrami-index), even for site saturated nucleation kinetics where all nuclei start to grow at the same time (t = 0)! (Cf. e.g. Fridy et al, Scripta 1998). Should be commented?
Response 10: The revised paper has commented on the early impingement of the recrystallisation nuclei. The comment is shown as follow: Additionally, the early impingement of the recrystallisation nuclei could also lead to the decreasing in Avrami exponent attributed to the preferred nucleation along the grain boundary regions.
Point 11: It is strictly not correct that the Avrami exponent is given by Eq. 3. The Avrami index is given by the slope of a plot of ln(ln(1/(1-X(t))) vs ln(t)! (As in eq. 4).
Response 11: The equation has corrected to ln(ln(1/(1-X(t))) vs ln(t).
Point 12: I am a bit confused concerning Eq. 4 and 5 and the associated text. In Eq. 2 Rs is introduced as the RX starting time, while in Eq. 4 it seems to be used to give the time to a RX fraction of X = 0.85?
Response 12: The section has been rewritten to clarify the assumptions. It is assumed that each individual grain size class recrystallises separately, as a result, the recrystallisation starting time for each grain size class is assumed to be equivalent to the time to achieve the overall recrystallised fraction.
For example, grain size class 160 μm is the 50 % in the cumulative area fraction, see Figure 9. Therefore, the recrystallisation starting time for grain size class 160 μm is assumed to be the time to achieve 50% of overall recrystallisation.
Point 13: (p. 7, l. 274) The recrystallisation time for 5% and 85% are approximately equal to the recrystallisation starting time for D0.05 and D0.85. What is the meaning of 5% and 85% on this sentence; X = 0.05 and X = 0.85 respectively?
Response 13: The revised paper has clarified that the 0.05 and 0.85 represent the overall recrystallised fraction of 5% and 85% of recrystallisation respectively.
Point 14: And what about D0.05 and D0.85 ?; D0.85 and D0.05 are the grain size at the 85% and 5% cumulative area fractions.
Response 14: The revised paper has clarified that D0.85 and D0.05 are the grain size class at the 85% and 5% of the cumulative grain size distribution respectively, as shown in Figure 9.
Point 15: Due this confusion it is not obvious to me how you get from Eq. 4 to Eq. 5, e.g. where is the number 3 coming from? In Eq. 5, D0.02 also show up! Where does 0.02 come from?
Response 15: The number 3 was supposed to be 3.6, and it came from the calculation of the equation 4. That is, = 3.6
The equations 4 and 5 has been updated. D0.02 should have been D0.05.
Author Response File: Author Response.pdf
Reviewer 3 Report
Please see the attached referee report.
Comments for author File: Comments.pdf
Author Response
Response to reviewer 3
Point 1: Introduction; Page 2, line 89: Define the full names for the used techniques, SEM and EBSD, at the first place.
Response 1: The definition of SEM and ESBD have been provided in the introduction section.
Point 2: Caption for figure 1: “mm” instead for “um”.
Response 2: The revised paper has changed um to mm.
Point 3: Table 1: I could not find any explanation for the duplicated temperatures for 0.2 strain in the last four lines.
Response 3: The explanation of the last four lines of the results have been emphasised in the result chapter as follow: “That is, a higher Avrami exponent has been observed for the samples with a tighter grain size distribution (mode grain size 100 µm) compared to the samples with a wider grain size distribution (mode grain size 160 µm) under the same condition, i.e. strain 0.2, temperature range 900- 850 °C.”
Point 4: There are a few formatting errors in the references, which hopefully will be corrected during publication process.
Response 4: The references have been checked and updated.
Round 2
Reviewer 2 Report
The Authors have responded adequately to mainly all my comments and questions and done a serious job in revising the manuscript accordingly.
I have a few remaining issues:
1. Line 34: 'nucleation rate N' should be dN/dt (or N With a dot above)
2. Re Eq.3. The Avrami index is given by the slope of a plot of ln(ln(1/(1-X(t))) vs ln(t)!
As far as I can see this is not corrected in the revised manuscript!?
Author Response
Point 1: Line 34: 'nucleation rate N' should be dN/dt (or N With a dot above)
Response 1: Changed the nucleation rate N to N with a dot above.
Point 2: Eq.3. The Avrami index is given by the slope of a plot of ln(ln(1/(1-X(t))) vs ln(t)! As far as I can see this is not corrected in the revised manuscript!?
Response 2: X has been changed to X(t) to be explicitly stated as a function of time.
