Molecular Dynamics Study on Crack Angle Effect on Amorphous Silica Fracture Performance
Round 1
Reviewer 1 Report
General Comment:
The paper investigated the effect of crack angle on mechanical properties and energy evolution in amorphous silica utilizing reactive molecular dynamics method. The main research contents include the influence of crack angle on stress-strain curve, complete fracture surface form, bond length analysis and input energy, elastic energy, new surface energy and energy efficiency.
Detailed Comments:
1. The ReaxFF document is not mentioned in the paper. Is there any literature about parameter fitting of ReaxFF in amorphous silica or a resemble system? Please attach the relative research paper.
2. Chemical reactions are generally engaged in the reactive molecular dynamics process, and the choice of time step will be hence subjected to the reaction rate. The timestep is generally set as 0.1fs or 0.25fs. Is it too large to set the step size of reaction force field to 0.5fs?
3. In lines 110-112, the author argues “the mechanical properties of the model will be relatively stable, when the atomic scale is large than 5×104 in PBC conditions.” What is the scale here? Volume scale or atomic number scale?
4. In table 1, Model II is obtained by high-temperature polymerization, annealing and relaxation of Model 1 under NPT ensemble, why do the densities of the two models distinguish much? Are there any references to indicate what the appropriate system density of amorphous silica should be?
5. The specific surface energy of the model is much smaller than other simulation results and experimental results. If is it correlated to the density or some other causes?
6. Is there any research paper to demonstrate that the models with cracks established in this paper are stable? That is, whether the size (5nm×0.5nm) and angles of cracks compared to the unit cell size are reasonable.
7. Can you give several stress-strain stages according to the stress-strain curve, such as elastic stage? Why does the calculation of elastic modulus get a strain of 0.05?
8. How is F in equation (2) obtained? What is the difference between stress here and that output by LAMMPS?
9. Can the author explain the distinction between stress-strain curves with various crack angles at the atomic level, such as the breakage of Si-O? Will the amorphous silica show the phenomenon of silicon chain rearrangement during the stress process, thus producing certain toughness?
10. Are the cloud diagrams obtained in Figure 7 by taking a slice parallel to the tensile direction?
11. It is mentioned in this paper that the crack development direction presents a “Z” shape because of the influence of shear stress. Did the author calculate or output the shear stress change in the crack area? If so, it is suggested to supplement it in the text.
12. The formation and fracture of bonds in the ReaxFF are determined by the distance, and the fracture of bonds is thus caused by the long distance between atoms. In Table 5 and Figure 9, why does the average bond length become shorter during stretching?
13. In line 240, “the input energy is mainly stored in the model in the form of elastic energy”, so what is the difference between input energy and elastic energy? How can elastic energy be calculated?
14. The new surface energy, as well as the fracture surface area of the model peak when the crack angle is 45°. Is it because the fracture area affects the new surface energy?
15. A kind of dissipative energy is mentioned in this paper. How to understand this energy from the atomic point of view?
16. Reaxff is originally an abbreviation for the reaction force field, so there is a duplication in the way of the description of “the Reaxff force field”.
17. What is the reason why the specific surface energy calculated in this paper is lower than other literature?
18. It is better to add the data of this study in Table 3 to facilitate comparison and viewing.
19. As far as this reviewer knows, the value obtained from the authors' simulation (of the first peak of RDF of Si-O bond) is small, so is the choice of force field parameters reasonable?
20. What is the basis for the selection of the crack size?
See the previous table.
Author Response
Dear Editor and Reviewer,
We would like to thank the reviewers for carefully reading our manuscript (minerals-2499694). We appreciate the comments and suggestions. In the following, we include a point-by-point response to the comments from each reviewer. In the revised manuscript, all the changes have been highlighted in red.
Response 1: Thank you for your suggestion. We have added a relevant reference regarding the ReaxFF version in line 87.
Response 2: Because the fracture process takes longer time than the chemical reaction with the chemical bond breaking, a step size of 0.5 fs is sufficient. Similar time steps were also used in previous relevant studies ( Fang [1], Chowdhury [2], Vo [3] and et al. ).
[1] Fang, T.H.; Shen, C.Y.; Fan, Y.C.; Chang, W.J. Fracture characteristics of silicene nanosheet with a crack under tension estimated using molecular dynamics simulation. Superlattices Microstruct. 2019, 129, 124-129, doi:10.1016/j.spmi.2019.03.021.
[2] Chowdhury, S.C.; Wise, E.A.; Ganesh, R.; Gillespie, J.W. Effects of surface crack on the mechanical properties of Silica: A molecular dynamics simulation study. Engineering Fracture Mechanics 2019, 207, 99-108, doi:10.1016/j.engfracmech.2018.12.025.
[3] Vo, T.; He, B.; Blum, M.; Damone, A.; Newell, P. Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF. Computational Materials Science 2020, 183, 10, doi:10.1016/j.commatsci.2020.109881.
Response 3: Thank you for your reminder. It is atomic number scale and has been corrected in line 110.
Response 4: In this paper, Model I is the original SiO2 crystal, Model II is amorphous SiO2 (i.e. quartz glass), and the two models are SiO2 homogeneous multiphase with different structures (i.e. Model II has more and larger pores). The density of amorphous SiO2 (Model II) is greatly affected by the simulated environmental pressure, and its density has been compared with existing simulation and related experimental results in Table 3, which is in good agreement.
Response 5: The specific surface energy is closely related to the number of chemical bond per unit area. So as the porosity of Model II increases slightly, the density will decrease and affect the specific surface energy of the model. The reason for this difference is that the simulation conditions are not completely consistent with those of others’. We have added Rimsza‘s [1] reference and the results are close to ours. Overall, our simulation results are within the range of existing research results.
[1] Rimsza, J.M.; Jones, R.E.; Criscenti, L.J. Surface Structure and Stability of Partially Hydroxylated Silica Surfaces. Langmuir 2017, 33, 3882-3891, doi:10.1021/acs.langmuir.7b00041.
Response 6: The ratio of the model’s long edge to crack length in this article is 5.4. In previous studies about pre-cracks, the ratio of the model's long edge to crack length or region in Vo’s [1], Fang’s [2] and Chowdhury’s [3] models are 5.9, 6.67 and 12 respectively. In the simulation, we have tried to reduce the ratio, and found that under the periodic boundary conditions, the larger the ratio is, the smaller the impact of the crack size effect on the model will be. Based on the previous simulation, we chose a ratio that is relatively small but sufficient to reflect the differences in simulation results.
For the crack width, the research object of this paper is a long and narrow crack, so a large aspect ratio of the crack is required. However, during the relaxation after pre cracking, it is found that if the crack width is too small, the entire crack will heal. Considering the above situations, a crack size of 5nm × 0.5nm was ultimately selected.
After determining the crack size, atoms in the selected area are rotated and removed to obtain pre-cracks at different angles.
[1] Vo, T.; He, B.; Blum, M.; Damone, A.; Newell, P. Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF. Computational Materials Science 2020, 183, 10, doi:10.1016/j.commatsci.2020.109881.
[2] Fang, T.H.; Shen, C.Y.; Fan, Y.C.; Chang, W.J. Fracture characteristics of silicene nanosheet with a crack under tension estimated using molecular dynamics simulation. Superlattices Microstruct. 2019, 129, 124-129, doi:10.1016/j.spmi.2019.03.021.
[3] Chowdhury, S.C.; Wise, E.A.; Ganesh, R.; Gillespie, J.W. Effects of surface crack on the mechanical properties of Silica: A molecular dynamics simulation study. Engineering Fracture Mechanics 2019, 207, 99-108, doi:10.1016/j.engfracmech.2018.12.025.
Response 7: Due to the fact that amorphous SiO2 belongs to brittle materials, the entire process is divided into two stages: elastic deformation of the model and crack instability propagation. Before the curve reaches its peak, it is in the elastic deformation stage, during which stress and strain show a linear growth trend. After reaching the peak (threshold), the crack in the model begins to be unstable and propagate, causing the stress-strain curve to rapidly decline.
In the process of calculating Young's modulus E, due to the need for unified calculation standards and the strong linear trend of the stress-strain curve in the elastic stage, we ultimately referred to the calculation method of Vo [1], which uses the curve at 0~0.05 strain to calculate Young's modulus E.
[1] Vo, T.; He, B.; Blum, M.; Damone, A.; Newell, P. Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF. Computational Materials Science 2020, 183, 10, doi:10.1016/j.commatsci.2020.109881.
Response 8: Equation (2) is only a simple schematic for calculating stress during the simulation, and the stress is output through LAMMPS after programming.
Response 9: Thank you for your valuable questions and analytical methods. We will use these analytical perspectives you mentioned in our future researches.
Response 10: Due to the model been already thin enough and the periodic boundary in the z-direction, no slicing is done when drawing the cloud diagrams.
Response 11: Thank you for your valuable suggestion. In the simulation, we only considered the stress in the load direction (y-direction) and did not calculate and analyze the shear stress. Based on your suggestion, we will take this into account in future researches.
Response 12: Thank you for your reminder. Table 5 and Figure 9 show the bond length distribution of the model after the ultimate stress ( i.e. crack instability propagation stage), rather than that of elastic deformation stage. So during this period, the bond length has reached its maximum value and decreases with crack propagating. It has been supplemented in line 220 and 301.
Response 13: In rock mechanics, the input energy comes from the load on the material, which is converted into the elastic energy of the material and the dissipated energy emitted to the outside. In the laboratory, the elastic energy and dissipated energy of a specific material are usually determined through cyclic loading and unloading tests.
In the simulation, because the environment under the NPT ensemble is open, the system energy mainly represents the elastic energy (internal energy) of the model, and does not include dissipative energy. So we calculate the input energy through the stress-strain curve and represent the elastic energy of the model using the difference in system energy before and after loading.
Response 14: For a model with a crack angle of 45°, the fracture area is more easy for crack to branch under the coupling effect of tensile and shear loads. When the miner crack heals, it will have an impact on the surface of the main crack, thereby affecting the new surface energy, which as shown in the following figure.
Response 15: During the stretching deformation stage, the model absorbs energy and the bond length between atoms increases. When unloading, the model cannot restore its original length, that is, the chemical bond appears permanent plastic deformation, and the energy used to make the chemical bond produce plastic deformation is dissipated energy.
Response 16: Thank you for your reminder, It has been corrected in the manuscript.
Response 17: This question has been answered in Point 5.
Response 18: Thank you for your suggestion. It has been revised in the manuscript.
Response 19: The position of the first peak of RDF of Si-O bond in this model is closer to the experimente’s [3] than previous simulations’ [1, 2], which as shown in the table below.
[1] Fogarty, J.C.; Aktulga, H.M.; Grama, A.Y.; van Duin, A.C.T.; Pandit, S.A. A reactive molecular dynamics simulation of the silica-water interface. J. Chem. Phys. 2010, 132, 10, doi:10.1063/1.3407433.
[2] Vo, T.; Reeder, B.; Damone, A.; Newell, P. Effect of Domain Size, Boundary, and Loading Conditions on Mechanical Properties of Amorphous Silica: A Reactive Molecular Dynamics Study. Nanomaterials 2020, 10, 16, doi:10.3390/nano10010054.
[3] Rouxel, T. Fracture surface energy and toughness of inorganic glasses. Scripta Materialia 2017, 137, 109-113, doi:10.1016/j.scriptamat.2017.05.005.
Response 20: This question has been answered in Point 6.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This manuscript using molecular dynamics simulation to evaluate the evolution of stress and strain within silica, with a pre-existing pre-crack at varying angles to the direction of the applied load. The results are interesting and would be of broad interest to several different technical communities. Ther are some concerns with the methods and reporting
1. Analysis of the surface energy is not general consistent with best practices. It is unclear how removing the atoms at both ends of the structure would be necessary prior to slicing. Typically, a vacuum gap is introduced which generated two surfaces. Additionally, from Figure 3 it looks like there are four surfaces introduced into the bulk system. This would change the denominator in Equation 1 to 4 (from 2). This would drop the value to ~1.1-1.2 J/m2 which is consistent with previous values reported for unhydroxylated surfaces simulated with ReaxFF (https://pubs.acs.org/doi/full/10.1021/acs.langmuir.7b00041). Comparison to surface energies from silica simulations using other forcefields are likely to be different and should be noted when they occur in the text.
2. The location of the cut-through in the systems for calculation the surface energy should be irrelevant since the structure is disordered. It would be better to collapse Table 1 into a single value with error bars. Also, the referenced value of 2.75 J/m2 from Sanjib et al is actually from Ref. 16 within that paper. References should be to the original manuscript, and not reference manuscripts that contain those references.
3. The authors have referenced Sanjib’s manuscript twice for the use of the method. Typically, references are identified by the last name of the first author, not the first name.
4. If Chowdhury et al. recommends a strain-rate of 2.5x1011 1/s, why was 5/x109 1/s used? Was any strain rate testing performed here? It would be expected that this would have a significant effect on the results.
5. For Figure 7 is this the total stress per-atom? Or just the per-atom stress in the YY direction? Also 405 GPa*A^3 is an unusual unit. It is possible to estimate a per-atom volume in lammps which could be used to get the values in GPa. How is the surface defined as “completely stable”? There appear to be free atoms in the crack volume in all the snapshots in Figure 7 (right hand column).
6. It is very unusual that the average Si-O bond length decreases with increasing tensile loading. Is this analysis over the entire system? Or are the bonds closer to the pre-crack smaller than those farther away? Relaxation of the surface might account for some of this effect, but the very definition of elasticity suggests that there should be elongation of the interatomic bonds. Are the O…O and Si…Si distances also decreasing? Decreasing Si-O bond length with increasing Si…Si distances might suggest that its extension of the Si-O-Si bond angle that is accommodating the applied load. But without additional analysis the origin of the phenomena is unclear.
7. Data in Figure 11 and Figure 12 is intriguing, but without errors bars it is difficult to believe such tight correlations (R2 = 0.994). Due to intrinsic disorder is its common to perform a minimum of 3 and as many as 12 replicates to confirm trends.
8. Energy values in J are very odd to use here and make it very difficult to connect with published data from other sources. Could energy dissipation, fracture toughness, or other types of values be reported? Example: https://www.sciencedirect.com/science/article/pii/S1359645416306838
9. The exact parametrization of ReaxFF used here needs to be reported. There are at least four different Si/O ReaxFF versions that could be used here with different parameters (Pitman et al. 2012, Hahn et al. 2018, Fogarty et al. 2010, Van Duin et al. 2003). Additionally, the parameters themselves should be included in the SI. The simulation time step also needs to be included.
Author Response
Dear Editor and Reviewer,
We would like to thank the reviewers for carefully reading our manuscript (minerals-2499694). We appreciate the comments and suggestions. In the following, we include a point-by-point response to the comments from each reviewer. In the revised manuscript, all the changes have been highlighted in red.
Response 1: Thank you for your suggestion, Rimsza's reference has been inserted in line 132. The energy of the original complete model was not calculated when calculating the specific surface energy in our simulation. The first energy calculation in our simulation is performed after removing the atoms at both ends and the second after slicing, so only two surfaces were generated between the two calculations. In addition, hydroxylation is not used in this model.
Response 2: Thank you for your suggestion, but the table here better reflects the details and workload of the simulation than picture. The value of 2.75 J/m2 is obtained by Sanjib according to the method in the reference, rather than the original data in the reference.
Response 3: Thank you for your reminder. We have corrected the relevant positions in the manuscript.
Response 4: In Chowdhury's simulation, if the strain rate is higher than 2.5×1011 1/s, the mechanical properties of the model will significantly change. We have tried to different strain rates including 2.5×1011, it was found that if the strain rate is too high, more small fragments (i.e. atoms that do not have time to react) will appear during the model fracture process, and properties such as stress-strain curves will become more unstable. Based on this and Chowdhury's research [15], we chose the strain rate of 5×109 1/s.
Response 5: The stress is in the YY direction and it has been supplemented in line 182. We normalized the stress cloud map to better display the stress state of each atom, so the unit of the stress cloud map here is GPa·A3. The same representation was also used in Vo's research [1].
In our simulation, we define that the fracture surface has reached stability when the model is completely fractured, the crack in the model is completely healed, and there is no significant fluctuation on the fracture surface. The free atoms are mostly oxygen generated after model fracture and no longer react with the surface. A similar phenomenon also occurred in Chowdhury's research [2], which as shown in the following figure.
[1] Vo, T.; He, B.; Blum, M.; Damone, A.; Newell, P. Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF. Computational Materials Science 2020, 183, 10, doi:10.1016/j.commatsci.2020.109881.
[2] Chowdhury, S.C.; Wise, E.A.; Ganesh, R.; Gillespie, J.W. Effects of surface crack on the mechanical properties of Silica: A molecular dynamics simulation study. Engineering Fracture Mechanics 2019, 207, 99-108, doi:10.1016/j.engfracmech.2018.12.025.
Response 6: Thank you for your question. Table 5 and Figure 9 show the bond length distribution of the model after the ultimate stress ( i.e. crack instability propagation stage), rather than that of elastic deformation stage. So during this period, the bond length has reached its maximum value and decreases with crack propagating. It has been supplemented in line 220 and 301.
Response 7: Thank you for your reminder. However, the consistency of the simulation results under the same conditions is good. Referring to previous researches (reference [1], [2], [3] and et al.), scholars only conducted once simulation under the same conditions. We also have simulated many times under a certain condition and found that it is indeed the case. Therefore, in order to improve computational efficiency, we only conducted once simulation under the same conditions.
In the future, we will also continue to explore the coupling effects of crack length, width, and angle on model fracture.
[1] Xie, Y.F.; Feng, F.; Li, Y.J.; Hu, Z.Q.; Shao, J.L.; Mei, Y. Mechanical and microstructural response of densified silica glass under uniaxial compression: Atomistic simulations*. Chin. Phys. B 2020, 29, 8, doi:10.1088/1674-1056/aba5fe.
[2] Chowdhury, S.C.; Haque, B.Z.; Gillespie, J.W. Molecular dynamics simulations of the structure and mechanical properties of silica glass using ReaxFF. J. Mater. Sci. 2016, 51, 10139-10159, doi:10.1007/s10853-016-0242-8.
[3] Vo, T.; Reeder, B.; Damone, A.; Newell, P. Effect of Domain Size, Boundary, and Loading Conditions on Mechanical Properties of Amorphous Silica: A Reactive Molecular Dynamics Study. Nanomaterials 2020, 10, 16, doi:10.3390/nano10010054.
Response 8: Thank you for your suggestion. However, in the crushing of mineral processing engineering, the energy unit is J. We also have considered unit normalization, so all energy units in the paper are represented by J. We will adopt your suggestion and apply different representation and analysis methods in later researches.
Response 9: Thank you for your suggestion. We have added a relevant reference regarding the ReaxFF version in line 87. The time step is mentioned in line 109.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors should look into several papers on brittle fracture studies using ReaxFF by the author Markus Buehler. Their methods are similar to his, and at the very least his analysis might help them improve their own.
I also think the paper would benefit from more atomistic analysis. After all, there are many faster, easier methods for modeling fracture than ReaxFF. If you are going to use an atomistic method, you should provide more atomistic scale analysis. Buehler's papers do a good job of this.
The quality of the English is quite good. I didn't find any serious problems, or even minor mistakes.
Author Response
Dear Editor and Reviewer,
We would like to thank the reviewers for carefully reading our manuscript (minerals-2499694). We appreciate the comments and suggestions. In the following, we include a point-by-point response to the comments from each reviewer. In the revised manuscript, all the changes have been highlighted in red.
Response 1: Thank you for your valuable suggestions on this article. We previously attempted to use Tersoff to simulate the fracture process, but its accuracy and simulation phenomenon were not ideal. Then according to reference [1-4], the ReaxFF was selected. Although ReaxFF has a relatively slow speed, it is in good agreement with the experimental results, so it was chosen. We will also study Buehler's papers carefully and try different force fields for relevant simulations in the later. If conditions permit in the future, we will also expand the atomic number scale and use more analytical methods at the molecular level.
[1] Vo, T.; Reeder, B.; Damone, A.; Newell, P. Effect of Domain Size, Boundary, and Loading Conditions on Mechanical Properties of Amorphous Silica: A Reactive Molecular Dynamics Study. Nanomaterials 2020, 10, 16, doi:10.3390/nano10010054.
[2] Vo, T.; He, B.; Blum, M.; Damone, A.; Newell, P. Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF. Computational Materials Science 2020, 183, 10, doi:10.1016/j.commatsci.2020.109881.
[3] Chowdhury, S.C.; Haque, B.Z.; Gillespie, J.W. Molecular dynamics simulations of the structure and mechanical properties of silica glass using ReaxFF. J. Mater. Sci. 2016, 51, 10139-10159, doi:10.1007/s10853-016-0242-8.
[4] Chowdhury, S.C.; Wise, E.A.; Ganesh, R.; Gillespie, J.W. Effects of surface crack on the mechanical properties of Silica: A molecular dynamics simulation study. Engineering Fracture Mechanics 2019, 207, 99-108, doi:10.1016/j.engfracmech.2018.12.025.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
No additional comments.
