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Influence of Mass Ratio on Forward and Reverse Ballistic Impact Equivalence: Experiments, Simulations, and Mechanism Analysis

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Abstract

Reverse ballistic impact tests are widely used for studying dynamic responses because they provide more comprehensive and quantitative projectile/rod response results than forward impact tests. To examine equivalent forward and reverse conditions, a series of 8-cm length oxygen-free copper rods with varying length–diameter ratios was used in forward and reverse ballistic Taylor impact experiments with velocities and strain ratios of 104–215 m/s and 1.25 × 103–2.5 × 103 s-1, respectively. Digital image correlation (DIC) and traditional optical measurements were used to determine instantaneous responses at the μs level. Based on DIC, transient structural deformation, and plastic wave propagation, the forward and reverse length difference at similar velocities ranges from 2 to 6.95 %. Rules governing deformation from the perspective of energy, along with rules for changes in energy and plastic wave propagation were determined. The relative deformation energy error was below 5 % for target projectile mass ratios above 20.

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Abbreviations

A 0 :

Initial sectional area

C :

Correlation coefficient in equation (14)

Cf :

Elastic velocity in forward impact at t 1

C r :

Elastic wave velocity in reverse impact at t 1

D :

Diameter of specimen

E :

Young’s modulus of the material

E fin :

Total input energy of forward impact

E fp :

Deformation energy of forward impact

E rin :

Total input energy of reverse impact

E rk :

Kinetic energy of reverse ballistic test after impact

E rkr :

Kinetic energy of the specimen

E rkp :

Kinetic energy of the plate

E rp :

Deformation energy of reverse impact

F cr :

Yield force of the cross section

f (x y):

Pixel matrix of M in equation (14)

g (x * y *):

Pixel matrix of M 1 in equation (14)

L 0 :

Initial length of the specimen

L 1 :

Total length at t 1

L 2 :

Total length at t 2

m :

Number of pixels

m r :

Mass ratio of the rigid plate to the specimen

M :

Center point of sub-region S in Fig. 22

M 1 :

Point after M moves in Fig. 22

n j :

Vector shown in Fig. 15

n i :

Normal to the cross section in Fig. 15

N :

Axial force

R 0 :

Initial radius of the specimen

R 2 :

Radius of the specimen after impact

S :

Sub-region in Fig. 22

S 1 :

Sub-region after S moves in Fig. 22

t 0 :

Initial time of impact

t 1 :

Time during the impact process

t 2 :

Final time of the impact process

u 1f :

Particle velocity of elastic region in forward impact at t 1

u 1r :

Particle velocity of elastic region in reverse impact at t 1

u 2r :

Particle velocity of plastic region in reverse impact at t 1

u f :

Initial velocity of forward impact

u r :

Initial velocity in reverse impact

u rr :

Velocity after reverse impact

v 0 :

Initial impact velocity

v f :

Plastic velocity in reverse impact at t 1

v r :

Plastic wave velocity in reverse impact at t 1

x 1 :

Undeformed length at t 1

x 2 :

Undeformed length at t 2

Y :

Dynamic strength of material

ρ :

Specimen density

σ ij :

Stress tensor

σ s :

Tensile strength

\( \overset{\cdot }{\varepsilon } \) :

Strain ratio of material

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (No.11202029, No.11390362, No.11221202).

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Authors and Affiliations

  1. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, People’s Republic of China, 100081

    J. Liu, F. Huang, K. Xu, L. Liu, T. Zuo & A. Pi

  2. Chuannan Machinery Factory, Luzhou, Sichuan, People’s Republic of China, 646000

    L. Liu

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  1. J. Liu
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Correspondence to A. Pi.

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Liu, J., Huang, F., Xu, K. et al. Influence of Mass Ratio on Forward and Reverse Ballistic Impact Equivalence: Experiments, Simulations, and Mechanism Analysis. Exp Mech 57, 387–404 (2017). https://doi.org/10.1007/s11340-016-0225-3

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  • DOI: https://doi.org/10.1007/s11340-016-0225-3

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