Theoretical Model of Structural Phase Transitions in Al-Cu Solid Solutions under Dynamic Loading Using Machine Learning

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article is interesting, well-written and at a good scientific level. I think some additional information could be added:

1. For dipper analyze of FCC-BCC phase transformations in Cu-Al alloys,  a Cu–Al diagram should be added.

I determined that Cu in Al. it is very slightly soluble, while in Cu a maximum of approx. 18% Al can be dissolved. With higher amount of AL in Cu alloy, some intermetallic phases were formed, mainly as a result of peritectoid transformations. In the article might be write about these phases, their crystal lattices and their properties.

2. The obligation to store that FCC lattice is only up to approx. 18% Al.

3. No information on the presence of other alloying elements in the tested material.

Author Response

Reviewer 1

R1.G. The article is interesting, well-written and at a good scientific level. I think some additional information could be added:

A1.G. Thank you for your kind feedback and for suggestions!

 

R1.1. For dipper analyze of FCC-BCC phase transformations in Cu-Al alloys,  a Cu–Al diagram should be added. I determined that Cu in Al. it is very slightly soluble, while in Cu a maximum of approx. 18% Al can be dissolved. With higher amount of AL in Cu alloy, some intermetallic phases were formed, mainly as a result of peritectoid transformations. In the article might be write about these phases, their crystal lattices and their properties. The obligation to store that FCC lattice is only up to approx. 18% Al.

A1.1. The following explanation is added to Section 2.1:

“Usually, the proportion of the additive element in alloys is small–less than 5% of Cu in Al matrix and up to 18% of Al in Cu matrix, but the alloying element can locally reach high concentrations during plastic deformation.”

 

R1.2. No information on the presence of other alloying elements in the tested material.

A1.2. There are no other alloying elements; therefore, there is no this information.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This is  a very nice study and well written paper. Based on the large volume of computed data, the authors come up with the model of structural transitions in shock compressed Al-Cu alloy. I believe the paper can be published as is.

Comments on the Quality of English Language

I am not a native speaker, so my opinion is partial yet at times I felt that phrases could be written better.

Author Response

Reviewer 2

R2.G. This is a very nice study and well written paper. Based on the large volume of computed data, the authors come up with the model of structural transitions in shock compressed Al-Cu alloy. I believe the paper can be published as is.

A2.G. Thank you for this kind evaluation of our research!

 

R2.1. I am not a native speaker, so my opinion is partial yet at times I felt that phrases could be written better.

A2.1. We have checked English one more time.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a numerical study on the determination of mechanical properties of Al-Cu systems by means of MD and ANN models. Although this work is comprehensive, the authors should carry out various modifications to their manuscript before it can be considered for publication.

Some more specific quantitative data should be added in the Abstract section. 

Moreover, at the beginning of the Abstract section the authors should clarify the purpose of this research and its significance.

The Introduction section is very brief and insufficient to clear present the studied topic. The authors should radically expand the Introduction section by discussing the works which they mention instead of only referring them. References to many works at once are not recommended, as the authors used more than 40 references for only a single paragraph.

More works on machine learning modeling of material properties should be discussed.

The novelty of this work should be appropriately justified in comparison with existing works.

Why did the authors choose to study the mechanical behaviour of materials in conditions similar to those achieved under picosecond laser irradiation?

How many atoms are used in the simulations? Which are the boundary conditions? The authors should provide a relevant schematic.

Apart from phase fractions and shear stresses, the authors should present results regarding dislocation density evolution in each case.

The authors should discuss the validity of their results in subsection 2.2 in comparison to available experimental data, even qualitatively.

How many simulations were carried out for the development of the data for ANN? What is the range of the input variables for ANN models?

Why did the authors compare their results with experimental ones with only up to 6% Cu? The authors should compare their data with additional experimental data under different conditions, covering most of their range of conditions.

Author Response

Reviewer 3

R3.G. This manuscript presents a numerical study on the determination of mechanical properties of Al-Cu systems by means of MD and ANN models. Although this work is comprehensive, the authors should carry out various modifications to their manuscript before it can be considered for publication.

A3.G. Thank you very much for careful reading and useful comments!

 

R3.1. Some more specific quantitative data should be added in the Abstract section.

A3.1. Done:

“In particular, pure Al reveals an almost complete phase transition from FCC to BCC structure at pressure of about 36 GPa, while pure copper does not reveal it at least till 110 GPa.”

 

R3.2. Moreover, at the beginning of the Abstract section the authors should clarify the purpose of this research and its significance.

A3.2. Done:

“Development of dynamic plasticity models with accounting of interplay between several plasticity mechanisms is an urgent problem for the theoretical description of complex dynamic loading of materials. Here we consider dynamic plastic relaxation by means of the combined action of dislocations and phase transitions using Al-Cu solid solutions as model materials and uniaxial compression as a model loading. We propose a simple and robust theoretical model combining molecular dynamics (MD) data, theoretical framework and machine learning (ML) methods.”

 

R3.3. The Introduction section is very brief and insufficient to clear present the studied topic. The authors should radically expand the Introduction section by discussing the works which they mention instead of only referring them. References too many works at once are not recommended, as the authors used more than 40 references for only a single paragraph.

A3.3. Done. The following additional text discusses the cited papers:

“Under dynamic loading, the equivalent shear stress exceeds the quasi-static yield stress due to a finite rate of defect microstructure evolution, and the purpose of a dynamic plasticity model is to take this finite rate of relaxation into account. The simplest way to describe the dynamic plasticity is to introduce a dynamic yield stress as a material parameter [1–2], which is, unfortunately, valid only for specific test conditions. Semi-empirical constitutive models [3–5] were created to determine the strain rate and temperature dependence of material yield behavior from the consideration of defect microstructure evolution, typically the thermally activated dislocation motion with parameter fitting to experiments [6]. In general, the dislocation-mediated plasticity is the main mechanism for most crystalline metals, which is supported by both molecular dynamics (MD) simulations [7] and experimental studies [8]. Incorporation of a crystal plasticity approach with explicit description of the dislocation activity in different slip planes is a fruitful approach for quasi-static [9] and dynamic [10–12] applications. This approach is successfully used to describe the shock wave processes in solid metals [13–15].”

“Levitas and Javanbakht [39,40] proposed a phase field model with in-deep thermodynamics consideration for description of martensitic transformations. Yeddu and Lookman [41] developed a variant of the phase field model based on the time-dependent Ginzburg–Landau kinetics equation for assessment of the β(BCC)-to-ω(hexagonal) phase transformation in Zr–Nb alloys. Consideration of multiple possible variants of austenite-to-martensite transformation in a quenching and partitioning steel QP1180 allowed Yang et al. [42] to describe correctly the strain path and orientation dependencies of the transformation process.”

 

R3.4. More works on machine learning modeling of material properties should be discussed.

A3.4. Done:

“The ML is increasingly being used in material science and mechanics of materials [47,48]. ML methods are efficient than accounting for changes in mechanical properties of materials is quite difficult to implement by classical methods and requires analysis of a large amount of experimental data and simulation results. The problem statement such as prediction, recognition and classification determines the choice of the most effective ML algorithm such as linear and logical regression, decision trees, clustering, etc. [49–51]. Among various ML methods, ANNs and Bayesian global optimization of model parameters are of particular interest for the present study. An ANNs can be used to approximate the strain, strain rate and temperature effect on the yield surface more precisely in comparison with the known analytical dependencies [52,53], to establish the structure-property relationships [54–56] and to construct a surrogate model of material [57,58]. Bayesian calibration of model parameters was fruitfully used to calibrate empirical Johnson-Cook model using the data on plate impact [59] and Taylor tests [60], as well as to fit a dislocation plasticity model to the Taylor test data [61–63].”

 

R3.5. The novelty of this work should be appropriately justified in comparison with existing works.

A3.5. The following statement is included in Introduction:

“In spite of these efforts, there is still lacking of a simple and robust model of plastic relaxation with the interplay of dislocation activity and phase transitions. Combining MD data, theoretical framework and machine learning (ML) methods for optimization of model parameter is a prospective approach in the field.”

 

R3.6. Why did the authors choose to study the mechanical behaviour of materials in conditions similar to those achieved under picosecond laser irradiation?

A3.6. We formulated our theoretical model to predict material properties under impact loading conditions. Sub-picosecond laser irradiation is one example of an experiment, where high strain rates are achieved comparable with the MD. It is computational resources-consuming to reach much lower strain rates in the MD. The following explanation is provided in the text:

“… which is close to that is achieved in the state-of-art experiments on irradiation of thin metal foils with powerful sub-picosecond laser pulses [48–51]; thus, this strain rate is experimentally attainable.”

 

R3.7. How many atoms are used in the simulations? Which are the boundary conditions? The authors should provide a relevant schematic.

A3.7. The system size and the boundary conditions were previously specified in Section 2.1. We have added the schematic representation of crystal loading in MD modeling as new Figure 1 in the revised text.

 

R3.8. Apart from phase fractions and shear stresses, the authors should present results regarding dislocation density evolution in each case.

A3.8. Done, see Figure 6b.

 

R3.9. The authors should discuss the validity of their results in subsection 2.2 in comparison to available experimental data, even qualitatively.

A3.9. Section 3 compares the artificial neural network data with experimental data for aluminum, copper, and solid solution. The ANN was trained on the molecular dynamics data described in Section 2. In addition, a comparison of pressures with experimental data from Dewaele et al. (2004)(quasi-static measurements with a diamond anvil cell) and DFT calculations by Panchenko (2022) is given in Section 2.

 

R3.10. How many simulations were carried out for the development of the data for ANN? What is the range of the input variables for ANN models?

A3.10. Subsection 2.1 explained that MD simulations were performed for copper concentrations of 0, 10, 20, 30, 50, 70, 80 and 100 % and the temperatures of 100 to 900 K in steps of 100 K. “Thus, 72 MD simulations were performed in total.” Each MD simulation introduces multiple data points for ANN training. The number of data points for ANN training now indicated in Section 3:

“The datasets contain a total of 285 715 data vectors (…) for the first ANN and 133 763 data vectors (…) for the second ANN.”

Table 1 was also supplemented with the data ranges.

 

R3.11. Why did the authors compare their results with experimental ones with only up to 6% Cu? The authors should compare their data with additional experimental data under different conditions, covering most of their range of conditions.

A3.11. The following explanation is added to Conclusions:

“Most of the considered solid solutions are thermodynamically unstable in traditional metallurgical casting and the experimental data are still lacking, but in the case they reveal unique dynamic-protecting properties, novel production techniques, such as additive manufacturing can be applied to produce such metastable alloys. Therefore theoretical analysis of their properties is relevant”

and in Section 2.1:

“although a part of the considered solid solutions can be thermodynamically unstable in traditional metallurgical casting. On the other hand, in the case they reveal unique dynamic-protecting properties, novel production techniques, such as additive manufacturing can be applied to produce such metastable alloys; therefore theoretical analysis of their properties is relevant.”

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors performed the necessary modifications to their manuscript. Thus, it can be accepted for publication.