# Damage Characteristics Analysis of the Truncated Cone-Shaped PELE Projectile

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structural Design of the Truncated Cone-Shaped PELE Projectile

#### 2.1. Design Idea of the Truncated Cone-Shaped PELE Projectile

#### 2.2. Determination of Structural Parameters of the Truncated Cone-Shaped PELE Projectile

_{0}corresponding to d

_{0}is:

_{1}corresponding to d

_{1}is:

## 3. Numerical Simulation

#### 3.1. Finite Element Model

#### 3.2. Material Model and Parameters

_{T}= 0.5 GPa. The plastic strain failure model is adopted for the target material, that is, when the plastic strain reaches a certain level, the material will fail. An artificial erosion algorithm (Erosion) is added to all materials to ensure normal calculations, and the failure erosion algorithm (Failure) is added to the target materials to delete the failed mesh. The geometric strain erosion algorithm (Geometric Strain) is used to the rest of the materials, it can delete the meshes whose instantaneous geometric strain are greater than the given value. In summary, all material parameters are shown in Table 3.

#### 3.3. Simulation Condition

- (1)
- Keep the initial kinetic energy of the two different types of PELE projectiles consistent.
- (2)
- The material and thickness of the target plate and the after-effect target are consistent with those of conventional PELE projectile in literature [15].

## 4. Comparative Analysis of the Numerical Simulation Results

#### 4.1. Comparison of Penetration Ability between the Truncated Cone-Shaped PELE Projectile and Conventional PELE Projectile

_{1}~c

_{4}are the resistance coefficients. In general, the second term (viscous effect term) and the fourth term (additional mass term) of the resistance expression can be neglected, and the expression of the penetration resistance of projectile can be rewritten as follows:

#### 4.2. Comparison of Fragmentation Effect between the Truncated Cone-Shaped PELE Projectile and Conventional PELE Projectile

_{0}+ l

_{0}for the truncated cone-shaped PELE projectile. Then, the expressions of the fragment conversion rate η of the two different types of PELE projectile can be obtained as follows.

## 5. Conclusions

- 1)
- In order to facilitate the comparative analysis with the conventional PELE projectile, the design principle of the truncated cone-shaped PELE projectile is to ensure that the four indexes of the impact end (projectile head), the length-diameter ratio of projectile, the thickness of outer casing and the sealing thickness of projectile rear are the same. Based on the structural parameters of the PELE projectile given in this paper, the range of angle α of the truncated cone-shaped PELE projectile was determined to be 86.2°–90°.
- 2)
- There is little difference in penetration ability between the conventional PELE projectile and the truncated cone-shaped PELE projectile. In fact, the kinetic energy loss of the truncated cone-shaped PELE projectile is slightly larger, but it can be reasonably explained. According to the penetration resistance formulas, with the increase of impact velocity, the penetration resistance will increase, the corresponding energy consumption or the kinetic energy loss of projectile will increase. The impact velocity of the truncated PELE projectile is higher under the same initial kinetic energy condition, which means that the kinetic energy loss of the truncated cone-shaped PELE projectile must be slightly larger.
- 3)
- If the initial kinetic energy of the projectile and the thickness and material of the target plate is consistent, the fragment conversion rate η and the damage area radius R of the truncated cone-shaped PELE projectile are obviously larger. In other words, the results indicate that the fragmentation effect of the truncated cone-shaped PELE projectile is better than that of the conventional PELE projectile.
- 4)
- In summary, the damage power of the truncated cone-shaped PELE projectile is better than that of the conventional PELE projectile. Therefore, the results show that the design idea of applying the truncated cone-shaped structure to the PELE projectile is feasible and reasonable. The conclusions lay a foundation for further exploring the relationship between the optimum angle α and the material and thickness of the target.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kesberg, G.; Schirm, V.; Kerk, S. PELE—The future ammunition concept. In Proceedings of the 21st International Symposium on Ballistics (ISB’21), Adelaide, Australia, 19–23 April 2004. [Google Scholar]
- Paulus, G.; Chanteret, P.Y.; Wollmann, E. PELE: A new penetrator-concept for the generation of lateral effects. In Proceedings of the 21st International Symposium on Ballistics (ISB’21), Adelaide, Australia, 19–23 April 2004. [Google Scholar]
- Rheinmetall Waffe Munition. 105/120/125 mm PELE Firing Results. Available online: https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2005/garm/wednesday/borngen.pdf (accessed on 12 July 2019).
- Gloude, D. Capabilities of Penetrator with Enhanced Lateral Efficiency. Available online: https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2007/gun_missile/GMTueAM1/GloudePresentation.pdf (accessed on 12 July 2019).
- Paulus, G.; Schirm, V. Impact behavior of PELE projectiles perforating thin target plates. Int. J. Impact Eng.
**2006**, 33, 566–579. [Google Scholar] [CrossRef] - Ding, L.; Zhou, J.; Tang, W.; Ran, X.; Hu, Y. Impact energy release characteristics of PTFE/Al/CuO reactive materials measured by a new energy release testing device. Polymers
**2019**, 11, 149. [Google Scholar] [CrossRef] [PubMed] - Du, Z.; Song, L.; Zhong, K.; Wang, F. Influence of the ratio of inner to outer diameter on penetrator with enhanced lateral efficiency. J. Comput. Theor. Nanosci.
**2011**, 4, 1525–1528. [Google Scholar] [CrossRef] - Zhu, J.; Zhao, G.; Du, Z.; Li, D. Experimental study of the influence factors on small caliber PELE impacting thin target. Chin. J. Exp. Mech.
**2007**, 22, 505–510. [Google Scholar] - Tu, S.; Wang, J.; An, Z.; Chang, Y. Influence of thickness of armor on the burst-effect of steel shell PELE. In Proceedings of the 9th International Conference on Electronic Measurement & Instruments, Beijing, China, 16–19 August 2009. [Google Scholar]
- Fan, Z.; Ran, X.; Tang, W.; Ke, Y.; Li, Z. The model to calculate the radial velocities of fragments after PELE perforating a thin plate. Int. J. Impact Eng.
**2016**, 95, 12–16. [Google Scholar] [CrossRef] - Verreault, J.; Hinsberg, N.; Abadjieva, E. PELE fragmentation dynamics. In Proceedings of the 27th International Symposium on Ballistics (ISB’27), Freiburg, Germany, 22–26 April 2013. [Google Scholar]
- Verreault, J. Modeling of the PELE fragmentation dynamics. In Proceedings of the 18th Biennial International Conference of the APS Topical Group on Shock Compression of Condensed Matter held in Conjunction with the 24th Biennial International Conference of the International Association for the Advancement of High Pressure Science and Technology, Seattle, WA, USA, 7–12 July 2013. [Google Scholar]
- Verreault, J. Analytical and numerical description of the PELE fragmentation upon impact with thin target plates. Int. J. Impact Eng.
**2015**, 76, 196–206. [Google Scholar] [CrossRef] - Century Dynamics Inc. Interactive Non-Linear Dynamic Analysis Software AUTODYN User Manual; Century Dynamics Inc.: Oakland, CA, USA, 2003. [Google Scholar]
- Ding, L.; Zhou, J.; Tang, W.; Ran, X.; Cheng, Y. Research on the crushing process of PELE casing material based on the crack-softening algorithm and stochastic failure algorithm. Materials
**2018**, 11, 1561. [Google Scholar] [CrossRef] [PubMed] - Bedon, C.; Kalamar, R.; Eliášová, M. Low velocity impact performance investigation on square hollow glass columns via full-scale experiments and Finite Element analyses. Compos. Struct.
**2017**, 182, 311–325. [Google Scholar] [CrossRef]

**Figure 1.**Simplified diagrams of the conventional PELE (penetrator with enhanced lateral efficiency) projectile structure.

**Figure 3.**Geometric structure of the truncated cone-shaped PELE projectile with different angle α. (

**a**) α = 90°; (

**b**) α = 88°; (

**c**) α = 86.2°.

**Figure 5.**Schematic diagram of penetration process of the conventional PELE projectile and the truncated cone-shaped PELE projectile corresponding to #5 working condition. (

**a1**~

**d1**): Conventional PELE projectile; (

**a2**~

**d2**): Truncated cone-shaped PELE projectile. (

**a1**) t = 0 µs; (

**a2**) t = 0 µs; (

**b1**) t = 47 µs; (

**b2**) t = 40 µs; (

**c1**) t = 126 µs; (

**c2**) t = 108 µs; (

**d1**) t = 174 µs; (

**d2**) t = 148 µs.

**Figure 6.**Local enlargement diagrams of the conventional PELE projectile and the truncated cone-shaped PELE projectile penetrating the target plate. (

**a**) Conventional PELE projectile; (

**b**) truncated cone-shaped PELE projectile.

**Figure 7.**Histogram of kinetic energy loss of the conventional PELE projectile and the truncated cone-shaped PELE projectile penetrating the target plate. (

**a**) 3 mm Al target plate; (

**b**) 8 mm Al target plate; (

**c**) 3 mm steel target plate.

**Figure 10.**The status of two different types projectile before impacting the after-effect target. (

**a1**–

**f1**): Conventional PELE projectile; (

**a2**–

**f2**): Truncated cone-shaped PELE projectile.

**Figure 11.**After-effect target damage situation corresponding to different working conditions. (

**a1**) #1-1 (3 mm Al–929 m/s); (

**a2**) #1-2 (3 mm Al–1081 m/s); (

**b1**) #2-1 (3 mm Al–1275 m/s); (

**b2**) #2-2 (3 mm Al–1483 m/s); (

**c1**) #3-1 (8 mm Al–937 m/s); (

**c2**) #3-2 (8 mm Al–1090 m/s); (

**d1**) #4-1 (8 mm Al–1254 m/s); (

**d2**) #4-2 (8 mm Al–1459 m/s); (

**e1**) #5-1 (3 mm steel–925 m/s); (

**e2**) #5-2 (3 mm steel–1076 m/s); (

**f1**) #6-1 (3 mm steel–1261 m/s); (

**f2**) #6-2 (3 mm steel–1467 m/s).

**Figure 12.**Comparison of the fragment conversion rate and damage area radius under different working conditions. (

**a**) 3 mm Al target plate; (

**b**) 8 mm Al target plate; (

**c**) 3 mm steel target plate.

D | D_{0} | d_{0} | d_{1} | L | h | δ |
---|---|---|---|---|---|---|

10 mm | 6.6 mm | 6 mm | 2.8 mm | 50 mm | 5 mm | 2 mm |

Condition Number | M (g) | v (m/s) | M′ (g) | v′ (m/s) |
---|---|---|---|---|

#1 | 51.4 | 929 | 38.0 | 1081 |

#2 | 1275 | 1483 | ||

#3 | 937 | 1090 | ||

#4 | 1254 | 1459 | ||

#5 | 925 | 1076 | ||

#6 | 1261 | 1467 |

Variable | Material | |||
---|---|---|---|---|

Tungsten | Al-6061 | Al-7075 | Steel-4340 | |

ρ_{0} (g/cm^{3}) | 18 | 2.65 | 2.8 | 7.823 |

c_{0} (km/s) | 4.03 | 5.24 | 5.2 | 4.57 |

s | 1.237 | 1.4 | 1.36 | 1.49 |

Grüneisen Coefficient | -- | 1.97 | -- | -- |

C_{p} (J/kg∙K) | -- | 885 | -- | -- |

Shear Modulus G (GPa) | 139.02 | 27.5 | 26.7 | 77 |

Yield Stress Y (GPa) | 1.5 | 0.3 | 0.4 | 0.8 |

Principle Tensile Stress σ_{T} (GPa) | 2.8 | 0.5 | -- | -- |

Principle Tensile Strain ε_{T} | 0.035 | -- | -- | -- |

Fracture Energy G_{f} (J/m^{2}) | 45 | -- | -- | -- |

Stochastic Variance γ | 36.5 | -- | -- | -- |

Inst. Geometric Strain | 0.6 | 0.8 | Failure | Failure |

Condition Number | Inner Core Material | Target Plate Material | Target Plate Thickness | After-Effect Target Material | After-Effect Target Thickness | Impact Velocity |
---|---|---|---|---|---|---|

#1 | Al | Al | 3 mm | Al | 1 mm | 1081 m/s |

#2 | Al | 3 mm | 1483 m/s | |||

#3 | Al | 8 mm | 1090 m/s | |||

#4 | Al | 8 mm | 1459 m/s | |||

#5 | Steel | 3 mm | 1076 m/s | |||

#6 | Steel | 3 mm | 1467 m/s |

Condition Number | Projectile Type | Initial Kinetic Energy of Projectile (KJ) | Residual Kinetic Energy of Projectile (KJ) | Kinetic Energy Loss of Projectile (KJ) |
---|---|---|---|---|

#1-1 | Conventional | 22.2 | 20.7 | 1.5 |

#1-2 | Truncated cone-shaped | 22.0 | 20.3 | 1.7 |

#2-1 | Conventional | 41.9 | 39.1 | 2.8 |

#2-2 | Truncated cone-shaped | 41.3 | 38.3 | 3.0 |

#3-1 | Conventional | 22.6 | 18.9 | 3.7 |

#3-2 | Truncated cone-shaped | 22.3 | 18.4 | 3.9 |

#4-1 | Conventional | 40.5 | 35.1 | 5.4 |

#4-2 | Truncated cone-shaped | 40.0 | 34.2 | 5.8 |

#5-1 | Conventional | 22.1 | 20.0 | 2.1 |

#5-2 | Truncated cone-shaped | 21.8 | 19.3 | 2.5 |

#6-1 | Conventional | 41.0 | 37.2 | 3.8 |

#6-2 | Truncated cone-shaped | 40.4 | 36.5 | 3.9 |

Condition Number | Projectile Type | Residual Length of Projectile (mm) | Mass Loss of Outering Casing (g) | Fragment Conversion Rate (%) |
---|---|---|---|---|

#1-1 | Conventional | 29.2 | 16.1 | 31.3 |

#1-2 | Truncated cone-shaped | 35.3 | 20.3 | 35.6 |

#2-1 | Conventional | 25.1 | 17.9 | 34.9 |

#2-2 | Truncated cone-shaped | 31.0 | 38.3 | 44.5 |

#3-1 | Conventional | 32.7 | 19.1 | 37.2 |

#3-2 | Truncated cone-shaped | 33.1 | 18.4 | 40.2 |

#4-1 | Conventional | 29.7 | 21.8 | 42.5 |

#4-2 | Truncated cone-shaped | 29.0 | 34.2 | 48.5 |

#5-1 | Conventional | 31.4 | 20.3 | 39.5 |

#5-2 | Truncated cone-shaped | 27.2 | 19.3 | 52.1 |

#6-1 | Conventional | 28.5 | 22.9 | 44.6 |

#6-2 | Truncated cone-shaped | 22.5 | 36.5 | 61.0 |

Condition Number | Projectile Type | Impact Velocity (m/s) | Target Plate Type | Damage Area Radius R (mm) |
---|---|---|---|---|

#1-1 | Conventional | 929 | 3 mm/Al | 23.5 |

#1-2 | Truncated cone-shaped | 1081 | 24.9 | |

#2-1 | Conventional | 1275 | 25.0 | |

#2-2 | Truncated cone-shaped | 1483 | 26.4 | |

#3-1 | Conventional | 937 | 8 mm/Al | 26.0 |

#3-2 | Truncated cone-shaped | 1090 | 28.9 | |

#4-1 | Conventional | 1254 | 28.6 | |

#4-2 | Truncated cone-shaped | 1459 | 31.4 | |

#5-1 | Conventional | 925 | 3 mm/steel | 32.9 |

#5-2 | Truncated cone-shaped | 1076 | 38.9 | |

#6-1 | Conventional | 1261 | 33.6 | |

#6-2 | Truncated cone-shaped | 1467 | 40.3 |

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**MDPI and ACS Style**

Ding, L.; Zhou, J.; Tang, W.; Ran, X.
Damage Characteristics Analysis of the Truncated Cone-Shaped PELE Projectile. *Symmetry* **2019**, *11*, 1025.
https://doi.org/10.3390/sym11081025

**AMA Style**

Ding L, Zhou J, Tang W, Ran X.
Damage Characteristics Analysis of the Truncated Cone-Shaped PELE Projectile. *Symmetry*. 2019; 11(8):1025.
https://doi.org/10.3390/sym11081025

**Chicago/Turabian Style**

Ding, Liangliang, Jingyuan Zhou, Wenhui Tang, and Xianwen Ran.
2019. "Damage Characteristics Analysis of the Truncated Cone-Shaped PELE Projectile" *Symmetry* 11, no. 8: 1025.
https://doi.org/10.3390/sym11081025