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# Finite Element Analysis of Plugging Failure in Steel Plates Struck by Blunt Projectiles

[+] Author and Article Information
A. Kane, O. S. Hopperstad, M. Langseth

Department of Structural Engineering, Structural Impact Laboratory (SIMLab), Centre of Research-Based Innovation, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

T. Børvik1

Department of Structural Engineering, Structural Impact Laboratory (SIMLab), Centre of Research-Based Innovation, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; Department of Research and Development, Norwegian Defence Estates Agency, NO-0015 Oslo, Norwaytore.borvik@ntnu.no

1

Corresponding author.

J. Appl. Mech 76(5), 051302 (Jun 12, 2009) (11 pages) doi:10.1115/1.3129722 History: Received February 01, 2008; Revised October 02, 2008; Published June 12, 2009

## Abstract

In this paper, the influence of mesh sensitivity on the fracture predictions during penetration and perforation of hardened blunt-nose cylindrical steel projectiles in plates of Weldox 460E, Weldox 700E, and Weldox 900E steel has been studied. The main objective is to try to describe the experimentally obtained trend of a decrease in ballistic limit velocity with increased target strength when the plates are impacted by blunt projectiles. This behavior is due to the occurrence of highly localized shear bands as the target strength increases. The impact tests are analyzed using the explicit solver of a nonlinear finite element code. A thermoelastic-thermoviscoplastic constitutive model with coupled or uncoupled ductile damage was used in the simulations. It was found that the residual velocity continuously increases when the element size is decreased from $125 μm$ to $15 μm$ in the shear zone, and that this increase is significantly stronger for impact velocities close to the ballistic limit. The ballistic limit decreases by up to 25% when the size of the element is decreased from $125 μm$ to $30 μm$; the decrease being somewhat greater for the two steels with the highest strength. Even with the finest mesh, the experimental trend of a decreasing ballistic limit with increasing target strength was not predicted in the simulations, neither with coupled nor uncoupled damage. Nonlocal simulations based on smoothing of the damage and temperature fields, which are the two variables causing the softening, were carried out for the Weldox steels and a mesh size of $30 μm$. These simulations indicate a reduction in the mesh sensitivity for both the coupled and uncoupled damage approaches when nonlocal averaging is employed.

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## Figures

Figure 14

Perforation of Weldox 700E (coupled simulations with initial velocity vi=265 m/s and initial element size of 15 μm in the impact region): (a) damage field and (b) temperature field

Figure 15

Influence of the value of the critical element aspect ratio (from 0.001 to 0.075) on the residual velocity versus time curve in penetration for Weldox 700E (coupled simulations with element size 30 μm)

Figure 5

Axisymmetric finite element model used in the penetration analysis for a 12 mm thick plate with a diameter of 500 mm and initial element size of 30 μm in the impact region

Figure 6

Effective plastic strain field development during perforation of a Weldox 700E plate, obtained with the coupled ductile damage model for an initial projectiles velocity vi=265 m/s

Figure 7

Effective plastic strain field during penetration at t=21 μs (initial velocity vi=300 m/s, initial element size of 15 μm in the impact region): (a) Weldox 460E and (b) Weldox 700E

Figure 2

Experimentally obtained ballistic limit velocities for the three steels for blunt-, conical-, and ogival-nose steel projectiles (17)

Figure 3

Pictures of shear bands in the various steels after penetration by a blunt projectile (18)

Figure 4

Stress-strain curves obtained with the uncoupled and coupled model at quasistatic strain-rate and room temperature

Figure 1

Comparison between experimental data and model results for Weldox 460E, Weldox 700E, and Weldox 900E (17)

Figure 8

Effect of mesh-size on the velocity-time curve from simulations using an uncoupled approach during perforation of a Weldox 700E plate at an initial velocity of 300 m/s

Figure 9

Mesh-size sensitivity on the residual velocity of Weldox 460E for different initial impact velocities using an uncoupled model and a local approach

Figure 10

Mesh-size sensitivity on the ballistic limit velocity for the three steels using a local approach in the simulations

Figure 11

Ballistic limit velocities for the three steels with an initial element size of 30 μm in the impact region: comparison between uncoupled and coupled models

Figure 12

Ballistic limit velocity for the three steels showing the influence of mesh size and nonlocal averaging: uncoupled simulations to the left and coupled simulations to the right

Figure 13

Perforation of Weldox 460E (coupled simulations with initial velocity vi=265 m/s and initial element size of 15 μm in the impact region): (a) damage field and (b) temperature field

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