Microstructure-Based Constitutive Modelling of Low-Alloy Multiphase TRIP Steels
, Linton Carvajal 3, Alfredo Artigas 3 and Alberto Monsalve 3,*Round 1
Reviewer 1 Report
The authors have made a detail extensive research. They have carried out a different heat treatments to evaluate the mechanical-microstructural relationships for three low alloy multiphase TRIP steels. I think this work is a very useful tool for the industrial applications with a precious remedy. Additionally they have used successfully a model (Becquerel’s work) for explaining stress strain flow on these materials. It merit to be published in this journal as it is.
Author Response
Referee 1 has not suggestions.
Reviewer 2 Report
The manuscript is original and interesting, is well written thus deserves to be published. Minor revisions are required to better describe the experiments.
1- Experimental details of XRD and EBSD must be carefully reported.
2- Data reported in Tables Ii, III, IV and V should be accompanied by the corresponding experimental error. The discussion must take into account the errors.
3- English should be improved.
Author Response
Referee 2
1.- Experimental details of XRD and EBSD must be carefully reported.
Answer:
X-ray measurements were carried out in a PANALYTICAL EMPYREAN diffractometer with a Co tube on samples prior and post-tensile testing. X-ray diffraction patterns were obtained in the 20º to 55º 2θ range with a step (Δθ) of 0.0065º respectively. ASTM E975 method was followed to determine the austenite volume fraction in the samples.
Electron backscattered diffraction (EBSD) analyses were carried out on a plane perpendicular to the transverse direction of samples by means of the EDAX-TSL® system (Ametek, Berwyn, PA, USA). An FEI XL30 ESEM microscope (TSS Microscopy, Boston, USA), with a LaB6 filament was used. The specimens were analyzed on a plane tilted 70° with respect to the incidence beam at 20 kV acceleration voltage. A step size of 60 nm in a hexagonal scan grid was used for for microstructure characterization. EBSD data were postprocessed with OIM (Orientation Imaging Microscopy) Analysis™ software (Ametek, Berwyn, PA, USA). The postprocessing procedure included the elimination of points with low confidence indices (lower than 0.1). Grains were considered with a minimum of six pixels, while grain boundaries were defined when a rotation between pixels was greater than 15°. Austenite identification by EBSD was done directly by indexing FCC structures. Martensite has a high density of defects; therefore, it must have a low average Image Quality (IQ) pattern. Due to it, martensite identification was done based on low IQ pattern on BCC structures.
2.- Data reported in Tables Ii, III, IV and V should be accompanied by the corresponding experimental error. The discussion must take into account the errors.
Answer:
In Table 2, the volume fraction of each phases were determined by means of X-Ray and EBSD simultaneously in only one sample, finding a good agreement between both values. So, we do not have an error to report.
In Table 3, all the standard deviations were included.
In Table 4, only the ferrite volume fraction has an error associated.
Table 5 is a consequence of the data reported in Table 2.
3.- English should be improved.
The English was reviewed by a native person.
Reviewer 3 Report
This manuscript tries to fit the stress-strain curves of TRIP-aided steels with the experimental curves. Authors should investigate the transformation behavior of retained austenite at the early stage of stress-strain curve.
Authors discussed with the true stress-true strain curves, q curves and e BM/e ferrite curves at an early stage of plastic deformation by using stability of retained austenite and multiplication of dislocation density of ferrite. In addition, authors explained that the stability of retained austenite was evaluated by the reduction of volume fraction of retained austenite after tensile tests. If TRIP-aided steels exhibit low stability of retained austenite, retained austenite transforms to martensite in an early stage of plastic deformation. Therefore, authors should consider the transformation behavior of retained austenite at the small plastic deformation region.
The other comments are as follows.
Line 34:
References ([2, 13]) did not continuously allocate.
Line 115:
Authors explained Table 4 before explaining Table 3.
Author Response
Referee 3
1.- Authors should investigate the transformation behavior of retained austenite at the early stage of stress-strain curve.
Authors discussed with the true stress-true strain curves, q curves and e BM/e ferrite curves at an early stage of plastic deformation by using stability of retained austenite and multiplication of dislocation density of ferrite. In addition, authors explained that the stability of retained austenite was evaluated by the reduction of volume fraction of retained austenite after tensile tests. If TRIP-aided steels exhibit low stability of retained austenite, retained austenite transforms to martensite in an early stage of plastic deformation. Therefore, authors should consider the transformation behavior of retained austenite at the small plastic deformation region.
Answer:
We have done an analysis of the evolution of the contribution in the deformation of the hard (Bainite plus Martensite) and soft phase (Ferrite), and therefore the hardening rates evolution based on the results obtained from the calibration. Our analysis has focused on the stability of austenite, which was measured in two ways (Table 5):
a)Transformation of austenite to martensite by deformation, measuring the initial and final quantities.
b)Transformation of austenite to martensite by cooling.
It is not the emphasis of the present work to evaluate the factors that affect the austenite stability, since these are a consequence of thermal treatments and are explained on reference 28, but we have taken into account such factors to make the calibration.
Effectively, in the initial stages of plastic deformation is where the model indicates that there is a higher hardening rate in ferrite. Therefore it would be appropriate to have transformation data from austenite to martensite in very early stages of deformation as you suggest, however we do not have such data. In the proposed model, the initial density of dislocations for the ferrite (ρ0) corresponds to that deformation-free dislocations density. Therefore, on calibration stage of the model, the parameters must be adjusted not only taking into account the dislocation increase product of transformation of austenite to martensite by strain, but also of the extra dislocations induced by the transformation from austenite to martensite by cooling. So, the treatment of both factors in isolation is complex. A proposal of interest for future research is to evaluate the austenite-martensite transformation evolution by deformation at earlier stages combined with the hardening contribution by the austenite-martensite transformation by cooling.
The following text was added to the paper, before conclusions.
“From the previous analysis, the numerical evaluation shows that an accelerated increase in the soft phase occurs in the first stages and, on this, the transformation of austenite to martensite could contribute significantly. This hardening is consistent with the different austenite stabilities of each steel, taking into account as stability the transformation of austenite to martensite by cooling and by deformation. Certainly the hardening evolution by TRIP effect is more interesting at the first stages of deformation process, but the gradual hardening on this first stages is a result of the effect of austenite transformation by two ways: cooling (heat treatment) and strain. Further study of hardening and changes in the very early stages will be addressed by the authors in a future development of the model by means of interrupted tension tests.”
The other comments are as follows.
2.- Line 34:
References ([2, 13]) did not continuously allocate.
Answer:Thank you. This was a typing error. The correct reference is [2,3]
3.- Line 115:
Authors explained Table 4 before explaining Table 3.
Answer:Thank you. Correction was made. Table 3 is now cited before Table 4.
The English was reviewed by a native person.
Reviewer 4 Report
Dear Authors,
I have read manuscript titled: “Microstructure-based constitutive modelling of low alloy multiphase TRIP steels” with great attention.The submission falls within the scope of the journal and is sufficiently original and comprehensive. The article is well organized, but I have a few remarks.
Major remarks:
1/ Introduction. You identified properly the important factors affecting the stability of retained austenite. However, you did not mention the effects of deformation temperature and strain rate. It was not the aim of your paper but you should at least mention about these important parameters. The issues are considered, for example in: Metals 10.3390/met9010002.
2/ Introduction. You noted that a grain size is very important for the stability of retained austenite. It is true. One of the ways to reduce in TRIP steels is to use microadditions (for example in TRIP steels - Materials Science and Technology 10.1179/1743284714Y.0000000742). The effects of Nb, Ti and V should be emphasized.
3/ Figure 1. Improve the figure caption
4/ Figure 2. A temperature axis is confusing. Please try to scale the temperature values better.
5/ Table 2 and 3. It is not enough clear how particular parameters (volume fraction and grain sizes) were determined ? What about errors ?
6/ Figure 3. Higher magnification images would be helpful to determine particular structural constituents.
7/ Line 143: wrong table numbering
8/ In Table 8, change commas to dots
9/ In Figure 8, please start captions with a capital letter
10/ In figures 9 and 10, please describe the Y axis
11/ Tables 6 and 7. The reference for the citied parameters should be provided.
12/ Reference [22] It should be … work hardening … Please check other typos in the whole text.
Author Response
Referee 4
1.- Introduction. You identified properly the important factors affecting the stability of retained austenite. However, you did not mention the effects of deformation temperature and strain rate. It was not the aim of your paper but you should at least mention about these important parameters. The issues are considered, for example in: Metals 10.3390/met9010002
Answer.
A major emphasis was placed on the influence of deformation temperature and strain rate on the austenite stability. Some references related to these parameters were included, such as Zhang et al. (2017), Kim et al. (2015), Grzegorcyk et al. (2019) and Hecker et al. (2018).
The following text was added to the introduction of the paper:
It is well known that the addition of elements as Al and Si inhibits the cementite formation, increasing the carbon concentration on austenite during isothermal bainitic heat treatments [5-13]. This carbon enrichment degree on austenite in linked to its stabilization at room temperature, at higher carbon concentration, higher retained austenite stability. Some studies on TRIP steels [9-12] have reported that retained austenite stability increases when its grain size decreases. Wang et al. [10] related austenite stabilization to the extra interfacial (austenite/martensite) energy required for fine austenite grains. Some authors [14-16] have shown that a temperature increment stabilizes the retained austenite. Hecker et al.[17] have found that, for a 304 stainless steel, at high strain rates, thetemperature increase resulting from adiabatic heating is sufficient to suppress the austenite transformation.
2.- Introduction. You noted that a grain size is very important for the stability of retained austenite. It is true. One of the ways to reduce in TRIP steels is to use microadditions (for example in TRIP steels - Materials Science and Technology 10.1179/1743284714Y.0000000742). The effects of Nb, Ti and V should be emphasized.
Answer.
The effect of the microaddition of elements such as Nb, Ti and V on the ferrite size, recrystallization, texture components and mechanical properties is very important especially on IF steels. The article recommended by the reviewer was included in the text of the paper. The difference of retained austenite grain size on that work seems to be linked to the difference on thermomechanical treatment. We have cited the article recommended by the reviewer as a reference of that it is not only the austenite stability that determines the mechanical properties, but also it depends of the nature of the other phases. In the cited work, different mechanical properties were obtained due to two reasons (i) differences in the matrix (ferrite-bainite and ferrite) and (ii) differences in austenite stability.
The following text was added to the introduction of the paper:
Although perhaps the main feature of multiphase TRIP steels is the austenite transformation into martensite by strain, their global response is strongly influenced by the intrinsic features of each constituent, especially ferrite and bainite, due to these phases are present in high proportion. Grajcar et al.[18], for example, obtained noticeable differences on mechanical properties for a medium carbon TRIP aided steel with Nb and Ti microaddition. These differences were mainly attributed to two factors: (i) nature of bainitic-ferritic matrix and (ii) differences onaustenite stability due to grain size and shape distribution.
In order to complement points 1 and 2, the following references were added:
14. Zhang, M.; Li, L.; Ding, J.; Wu, Q.; Wang, Y.-D.; Almer, J.; Guo, F.; Ren, Y. Temperature-dependent micromechanical behavior of medium-Mn transformation-induced-plasticity steel studied by in situ synchrotron X-ray diffraction. Acta Mater. 2017 141, 294-303. DOI: 10.1016/j.actamat.2017.09.030.
15. Kim, H.; Lee, J.; Barlat, F.; Kim, D.; Lee, M.-G. Experiment and modeling to investigate the effect of stress state, strain and temperature on martensitic phase transformation in TRIP-assisted steel. Acta Mater. 2015 97, 435-444. DOI: 10.1016/j.actamat.2015.06.023.
16. Grzegorczyk, B.; Kozlowska, A.; Morawiec, M.; Muszynski, R.; Grajcar, A. Effect of deformation temperature on the Portevin-Le Chatelier effect in medium-Mn steel. Metals, 2019 9, 2. DOI: 10.3390/met9010002.
17. Hecker, S.S.; Stout, M.G.; Staudhammer, K.P.; Smith, J.L.; Effects of strain state and strain rate on deformation- induced transformation in 304 stainless steel part I. magnetic measurements and mechanical behavior. Metall. Mater. Trans. A. 1982 13, 619-626. DOI: 10.1007/BF02644427.
18. Grajcar, A.; Kwasny, W.; Zalecki, W. Microstructure-property relationships in TRIP aided medium-C bainitic steel with lamellar retained austenite. Mater. Sci. Techno. 2015 31, 781-794, DOI: 10.1179/1743284714Y.0000000742.
3.- Figure 1. Improve the figure caption
Answer: The caption of figure 1 was modified in order to clear the description of itself.
4.- Figure 2. A temperature axis is confusing. Please try to scale the temperature values better.
Answer:The temperature values were scaled.
5.- Table 2 and 3. It is not enough clear how particular parameters (volume fraction and grain sizes) were determined ? What about errors ?
Answer:In order to better explain the method in which the parameters associated with microstructural characteristics were obtained, the following text was introduce on the document (lines 119 to 149):
A LEICA metallographic microscope (Model DM LM/P, Leica Microsystems, Wetzlar, Germany) was used to characterize the microstructures. The samples were polished and then chemically etched with a solution of 3% HNO3in ethanol (Nital, 3%) and LePera etchant (a 4% solution of picric acid in ethanol and a 1% solution of sodium metabisulfite in water, mixed in equal parts just before etching). The ferrite volume fraction was estimated from metallographic images by using the image analysis software ImageJ (version 1.5i, National Institutes of Health, Bethesda, MD, USA). The ferrite grain size was measured directly from metallographic images using the mean linear interception technique.
Fig. 4 shows SEM micrographs where the different microstructures can be observed: austenite and/or martensite (A/M), ferrite (F) and bainite (B) that appear near or inside prior austenite blocks. SEM analysis using a TESCAN Vega 3 scanning electron microscope (Tescan, Brno, Czech Republic), with tungsten filament was performed at 15 kV in the backscattered electron (BSE) mode.
Fig 5 shows IQ + phase maps for each steel obtained by the EBSD technique, where retained austenite is easily identified and martensite appears as dark zones. Electron backscattered diffraction (EBSD) analyses were carried out on a plane perpendicular to the transverse direction of samples by means of the EDAX-TSL® system (Ametek, Berwyn, PA, USA). An FEI XL30 ESEM microscope (TSS Microscopy, Boston, USA), with a LaB6 filament was used. The specimens were analyzed on a plane tilted 70° with respect to the incidence beam at 20 kV acceleration voltage. A step size of 60 nm in a hexagonal scan grid was used for for microstructure characterization. EBSD data were postprocessed with OIM (Orientation Imaging Microscopy) Analysis™ software (Ametek, Berwyn, PA, USA). The postprocessing procedure included the elimination of points with low confidence indices (lower than 0.1). Grains were considered with a minimum of six pixels, while grain boundaries were defined when a rotation between pixels was greater than 15°. Austenite identification by EBSD was done directly by indexing FCC structures. Martensite has a high density of defects; therefore, it must have a low average Image Quality (IQ) pattern. Due to it, martensite identification was done based on low IQ pattern on BCC structures.
Table 2 shows the austenite volume fraction obtained by X-Ray before and after tensile test. X-Ray measurements were carried out in a PANALYTICAL EMPYREAN diffractometer (Malvern Panalytical Ltd., Malvern, UK), with a Co tube on samples before and after tensile testing. X-Ray diffraction patterns were obtained in the 20–55° 2θ range with a step (Δθ) of 0.0065°. The ASTM E975 method was followed to determine the austenite volume fraction in the samples.
About error, it was estimated for the characteristic dimension on each constituent (Table 3). About volume fraction, only the standard deviation for ferrite was incorporated on Table 4. The following text was introduced on text in order to explain it (lines 168 to 176)Ferrite grain size was obtained by metallographic observation, bainite lath size was measured on SEM images, and austenite and martensite dimensions were directly obtained from EBSD maps analysis. Errors reported on Table 3 correspond to the standard deviation of measurements. Table 4 shows the volume fraction for each phase, where ferrite, austenite, martensite and bainite volume fractions were obtained by metallographic analysis, X-Ray diffaction, EBSD and mass balance, respectively. Only the experimental error of ferrite fraction is shown, because the other phases were determined by means of X-Ray and EBSD simultaneously in one sample, finding a good agreement between both values.
6.- Figure 3. Higher magnification images would be helpful to determine particular structural constituents.
Answer:Unfortunately, it is not possible to obtain images with high magnification. The main goal of these images is to describe the important differences between the phases in each steel. In SEM images at 6000X and EBSD IQ+phase maps it is possible to appreciate more details of each microstructure.
7.- Line 143: wrong table numbering
Answer:Table 5 was correctly cited.
8.- In Table 8, change commas to dots
Answer:Thank you, the change was done.
9.- In Figure 8, please start captions with a capital letter
Answer: Thank you. In Figures 8 and 10, the characters of each axe were changed. In Figure 8, ferrite was changed by Ferrite.
10.- In figures 9 and 10, please describe the Y axis
Answer:Thank you. In Figures 9 and 10, the captions were changed in order to increase the clarity of the information.
11.- Tables 6 and 7. The reference for the citied parameters should be provided.
Answer:Thank you. In Table 6 a reference was added (Samek) and in Table 7, a new column with references was included.
12.- Reference [22] It should be … work hardening … Please check other typos in the whole text.
Answer:Thank you. The word was corrected.
The English was reviewed by a native person.
Round 2
Reviewer 4 Report
Thank you for considering the comments
