Spherical Cavity Expansion Approach for the Study of Rigid-Penetrator’s Impact Problems
Abstract
:1. Introduction
2. Literature Review
- Spherical Cavity Expansion (SCE): Starting with a small hollow sphere in the body of an infinite block of ductile material to determine the pressure that will enlarge the spherical hole indefinitely.
- Cylindrical Cavity Expansion (CCE): Starting with a cylindrical hole of infinite length to find the pressure that will enlarge the hole indefinitely.
Summary of the Literature Review
- Penetration of undeformed projectiles into soft targets is valid at low and medium penetration velocities.
- Cavity pressure on the target can be calculated using the spherical cavity expansion theory.
3. Spherical Cavity Expansion Formulation
3.1. Conservation Laws in Spherical Coordinates
3.2. Material Response
3.3. Different Cases of the SCE Theory
3.3.1. Compressible-Dynamical Solution
3.3.2. Incompressible-Dynamical Solution
4. Formulation of the Engineering Model of Penetration
4.1. Projectile Deceleration
4.2. SCE Theory in Penetration Problems
4.3. Model Solution
5. Results and Discussion
5.1. Comparison to the Forrestal et al. SCE Solution
5.2. Comparison to the Masri and Durban SCE Solution
5.3. Results of SCE Model for 7075-T6 Aluminum Alloys and Comparison to FE Models
6. Conclusions
- Verified using elastic, perfectly plastic, 6061-T6 aluminum.
- Verified using four elastic, strain-dependent materials: titanium B120VCA, stainless steel, D6AC steel, and 7076-T6 aluminum.
- Verified and validated by FE numerical simulations and experimental data using semi-infinite, strain-dependent, 7075-T6 aluminum targets in the range of 250 m/s to 500 m/s.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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(kg/m) | E (GPa) | (-) | (MPa) | |
---|---|---|---|---|
6061-T6 Al | 2700 | 68.9 | 0.33 | 300 |
Material | (kg/m) | E (GPa) | (-) | k (-) | n (-) |
---|---|---|---|---|---|
Titanium B120VCA | 4400 | 106 | 0.333 | 2.4 × | 16.5 |
Stainless steel | 7800 | 206 | 0.3 | 5.78 × | 3 |
Steel D6AC | 7800 | 213 | 0.27 | 2.52 × | 28 |
Aluminum7075-T6 | 2700 | 72.4 | 0.32 | 3.94 × | 10.9 |
(kg/m) | E (GPa) | (-) | Y (MPa) | B (MPa) | n (−) |
---|---|---|---|---|---|
2700 | 72.4 | 0.32 | 601 | 765 | 0.09174 |
(kg/m) | E (GPa) | (-) |
---|---|---|
2700 | 189 | 0.3 |
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Buchely, M.; Marañon, A. Spherical Cavity Expansion Approach for the Study of Rigid-Penetrator’s Impact Problems. Appl. Mech. 2020, 1, 20-46. https://doi.org/10.3390/applmech1010003
Buchely M, Marañon A. Spherical Cavity Expansion Approach for the Study of Rigid-Penetrator’s Impact Problems. Applied Mechanics. 2020; 1(1):20-46. https://doi.org/10.3390/applmech1010003
Chicago/Turabian StyleBuchely, Mario, and Alejandro Marañon. 2020. "Spherical Cavity Expansion Approach for the Study of Rigid-Penetrator’s Impact Problems" Applied Mechanics 1, no. 1: 20-46. https://doi.org/10.3390/applmech1010003