Bullet Frangibility Factor Quantification by Using Explicit Dynamic Simulation Method

Round 1

Reviewer 1 Report

This paper investigates the bullet frangibility factor with a focus on the material properties and projectile design of the bullets. The paper is useful for readers who are interested in using computation to investigate protective structures. However, there are some concerns that should be addressed before accepting.

1. Many paragraphs are duplicated. Please carefully check it.
2. What kind of material model did the author use for the bullet model?
3.  What kind of interaction did the author use for the bullet and plate
4. In Fig 11. please compare with the numerical results
5. The protective structures for the ballistic impact can be found in review paper
   
6. The reviewer can not find the reference Firmansyah et al. (line 282)
     

Author Response

1. I have made a mistake about the paragraph and there are some pictures that were missing, and I have revised in the following document.
2. The materials properties are stated in the table 1 and 2, which use Cu-Sn metal matrix composite. The material model used is explicit dynamic which applying lagrangian frameworks
3. The plate become the fixed support and the bullet is free moving body
4. I have already attached the comparison between the simulation and the actual result
5. Sorry I am not quite understand about this point
6. I have inserted the missing reference

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is devoted to the calculation of the Frangibility Factor parameter for a bullet by using numerical simulation, which is an interesting problem in itself. However, in my opinion, the the article does not solve the stated problem.

There are a number of significant remarks to the article:

1. The information is presented very inaccurately: the text is often repeated several times: (lines 23-39 are a complete copy of lines 40-56, lines 73-79 repeat the text of lines 84-90, etc.) There is no reference and commentary on Figure 1 in the text.The numbering of figure 10 is repeated 2 times. Judging by the text, the number of the second figure should be 11. There is no figure 12, which the authors refer to in the text of the article. etc.
2. The description of an explicit scheme for solving a dynamic problem (implemented apparently in Ansys Autodyn) in the introduction (lines 122-140) is, in my opinion, inappropriate and unnecessary.
3. On the left side of equation (4) «twovklim» is a typo?
4. Models and parameters for the deformation and fracture of the bullet are not given, although these data are critical for the problem being solved and completely determine the result.
5. What is a and S in equation (8)?
6. The procedure for calculating the acceleration line 193 is not clear. What two speeds are used for this?
7. The procedure for estimating the desired characteristic is not clear.If there is an experiment, then it is clear from what considerations the initial velocity of the bullet is chosen. In the absence of an experiment, what velocity to take and how to build an estimation algorithm? The algorithm must be clearly described.
8. It is known that the simulation result strongly depends on the finite element mesh discretization. For fragmentation simulation, the mesh size is a critical parameter. Has the influence of the mesh on the result obtained been analyzed? Summing from Figure 4, for one version of the bullet, partitioning by tetrahedra was used, for the second, by hexahedra. Is it reasonable to compare such calculations without analyzing grid convergence?
9. What is the reason for the increase in bullet speed before a sharp drop in graphs 6 and 8?
10. It is stated that in Fig.10 the scattering pattern for the bullet after impact is shown. What is the meaning of this diagram? I believe that at the time of rendering, the nodes in the cloud have non-zero velocities and the scattering pattern will depend on time.
11. The reasoning in the last paragraph on page 11 (lines 265-274) is moot. The compaction process of molding a bullet can most likely be considered quasi-static due to the small size of the bullet. Therefore, the force acting on the bottom approximately corresponds to the force acting on the head part by virtue of Newton's 2nd law. Moreover, during molding, the head part undergoes more intensive shaping, i.e. in the head part, on the contrary, the material should be strengthened more strongly due to plastic deformation. The tail part of the bullet does not fracture upon impact, not because it is more durable, but because the interaction with the target is localized in the head part and a significant part of the energy is absorbed during the fracture and plastic deformation of the material.

In general, I think that the research topic is relevant, but the material is very raw and requires significant revision before publication in the journal.

Author Response

1. I have made a mistake about the paragraph and there are some pictures that were missing, and I have revised in the following document.
2. After few considerations, we agreed to delete the scheme picture of the autodyne
3. Yes, it is a typo and I have revised it
4. I have added the Poisson’s ratio, bulk and shear modulus for the fracture deformation
5. I have added the information bellow the equation.
6. The speed used is the initial velocity acquired from real shooing experiment
7. These velocities are acquired from actual experiment. Every ammunition caliber has its own velocity standard that can be obtained from the bullet data sheets
8. The simulation used the automatic method so the shape of the elements and nodes can be varied depend on the complexity of the geometry. For the AMMO 1, due to its sharp bullet head the most suitable is triangular element mesh. On the other hand, AMMO 2 has tertrahedral shape that generated by the automatic meshing. However, the element size used during the simulation have the same size (0.5 mm) which created a nearly same element quantity at 59577 elements for AMMO 1 and 59458 elements for AMMO 2.
9. Both graphs show small velocity increase before sharp drop because this simulation considers the total velocity from all axis which the resultant can cause a small velocity increase and considered as error.
10. The diagram just compare the maximum scattering diameter at a certain time step which indicate and compare how far do the fragmentation take place.
11. I agreed that the tails were not deformed because the interaction with the target is localized in the head part and a significant part of the energy is absorbed during the fracture and plastic deformation of the material. But the single acting compaction process also affect he density of the solid body which can be illustrated in the following figure which has denser particle where the force is applied.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

It can be accepted.

Reviewer 2 Report

I thank the authors for the clarifications. I think that in its current form the article can be published.