Ballistic limit predictions for perforation of multi-layered aluminium armour targets by rigid, nose-pointed projectiles

https://doi.org/10.1016/j.ijimpeng.2021.103900Get rights and content

Highlights

  • A model for estimating ballistic performance of multi-layered targets is developed.

  • The resistance of each layer is influenced by its relative position in the stack.

  • Ballistic experiments and numerical simulations are used to validate the model.

  • Nearly constant deceleration phase is identified as part of the perforation process.

  • New and unexpected prediction of the model is verified by numerical simulations.

Abstract

We have developed a heuristic, closed-form model for estimating the ballistic performance of layered, in-contact aluminium targets that are penetrated by a rigid projectile through ductile hole growth. The model uses an estimated material resistance for each layer, based on the specific cavitation energy concept. Weighting of the material resistance by the corresponding layer thickness leads to the effective (or average) target resistance of the in-contact layers, which we termed as the target stack resistance. For in-contact layers, we propose that the resistance of each layer is influenced by its relative position in the stack. The in-contact plates that are subsequent to the layer that is being penetrated (the backing layers), provide additional support (a reinforcement effect) and by that increase the resistance to ductile hole growth in the penetrated layer. A campaign of ballistic experiments and numerical simulations is performed to compare the performance of monolithic and in-contact layered 6061-T651 aluminium targets against 7.62 mm APM2 projectiles. The developed model is compared with the experimental and numerical results and is found to provide good agreement. An unexpected prediction of the model is verified by numerical simulations.

Introduction

Penetration and perforation processes are regarded amongst the most challenging fields in impact engineering, and have been under extensive continuous research since World War II due to their military applications. Analytical methods for penetration and perforation mechanics date back to the pioneering studies [1], [2], where quasi-static and dynamic cavitation pressures were used to estimate target material resistance. Plane-strain, cylindrical cavitation models [3], [4], [5], [6] have been shown to provide accurate predictions for ballistic perforation by ductile hole growth under plane-strain conditions. However, such models are not accurate enough for prediction of ballistic limit velocity in other conditions, such as plane-stress target response. The plane-stress analysis in [7] for ductile perforation under plane-stress conditions has led to the specific cavitation energy concept. Further, the heuristic approach in [8] has inspired a logarithmic expression for the specific cavitation energy of monolithic ductile targets. Comprehensive comparisons to experimental data [8], [9], [10], [11] have shown that specific cavitation energy is essential in calculating the ballistic limit velocity of monolithic aluminium alloy plates perforated by rigid projectiles in ductile hole formation.

Besides perforation of monolithic ductile targets, extensive experimental, numerical and analytical research has been done on ballistic perforation of multi-layered protective shields. The studies [12], [13], [14], [15], [16], [17] compared ballistic performance of monolithic targets and multi-layered shields manufactured from the same material and having the same total thickness, while other studies [12,[18], [19], [20], [21] analyse the effect of non-identical layers on shield performance. Comprehensive reviews can be found in [22], [23], [24], [25], which together provide a complete overview of the state-of-the-art in the field of multi-layered targets.

The dominant failure mode of a protective shield depends on target and projectile characteristics, and the present study focuses on target perforation by ductile hole formation. For perforation under ductile hole growth conditions, several experimental studies [26], [27], [28], [29], [30] have shown that monolithic targets are more effective shields than multi-layered targets which, in turn, are more effective than air-gapped targets. The reduction in ballistic limit velocity due to splitting of monolithic target into separate, thinner plates with air gaps, was explained in [7] by the specific cavitation energy concept. Later, this reduction was quantified in [8] and it was observed that the worst splitting of a monolithic shield, in terms of its effect on ballistic performance, is to identical thickness plates separated by air-gaps.

With regard to ductile hole growth perforation of multi-layered targets, the authors of [31,32] consider perforation of a rigid sharp-nosed striker into a shield consisting of several metal plates in-contact, but they used the assumption that the layers do not interact and are perforated independently. Hence, the same researchers have mentioned in review [22] that ”The problem of determining a more-or-less general law, which will enable predicting the change of the ballistic limit velocity by varying the shield structure, has not been solved as yet”, and in the more recent review [23] they emphasized that ”At present is not feasible to predict effect of shield layering and spacing for a particular case of high velocity penetration, and one can only consider general dominant patterns.”.

In the absence of a generalised analytical law, numerical simulations, such as [19,28,33,34], have been utilized to provide further insight into the comparative performance of monolithic and multi-layered metallic plates subject to ballistic impact. These numerical simulations, typically performed using explicit finite element solvers, have been shown to replicate the experimental findings for metallic targets perforated in ductile hole formation, namely that the protective performance of monolithic plates is superior to that of layered, in-contact and layered, air-gapped targets. Furthermore, simulations can provide additional insight into the penetration event, the initiation and development of target failure modes, as well as the evaluation of additional impact conditions.

The present research goal is to suggest a new heuristic, closed-form method for predicting the ballistic limit velocity of a multi-layer metallic target consisting of identical layers (material and thickness) and perforated in ductile hole formation. We propose that the resistance of each layer is influenced by its relative position in the stack, so that the in-contact plates that are subsequent to the penetrated layer provide additional support. In Section 2 we derive the new heuristic resistance model for multi-layered targets consisting of identical in-contact layers. To demonstrate the validity of the proposed model, we present in Section 3 the results of ballistic experiments against monolithic and equivalent-thickness, in-contact layered aluminium 6061-T651 targets impacted by 7.62 mm APM2 armour piercing projectiles. Section 4 presents numerical simulations for monolithic and multi-layered aluminium targets, initially for validation against the ballistic experiments and then for evaluation of the heuristic model against additional configurations. The suggested closed-form model is compared with the experimental and numerical results and is found to provide good agreement, and a new and unexpected prediction of the model is verified by numerical simulations. While the present research is focused on identical in-contact layers, its extension to non-identical layers will be given in a follow-on paper.

Section snippets

Background

Ballistic performance of a ductile plate of thickness h perforated at normal incidence by a rigid, nose-pointed projectile of mass M and diameter D can be estimated by an energy-balance, in which the elastoplastic work done in expanding the perforation cavity can be approximated byW=πD24hsc.Here sc refers to the specific cavitation energy of the target material [7]. The heuristic approach in [8] has inspired a logarithmic expression for the specific cavitation energy during perforation of

Ballistic impact experiments

To check the validity of the proposed model for multi-layered targets, a series of ballistic experiments have been conducted on monolithic and multi-layer stacks of 6061-T651 aluminium alloy with 7.62 mm x 63 APM2 projectiles at normal incidence. This projectile consists of an armour piercing, hardened tool steel core with lead nose filler, lead base filler, and copper jacket. The target plates used during the experiments measured 300 mm x 300 mm laterally and were fixed in place using a rigid

Numerical simulations

An in-depth numerical study was performed to provide further insight into the perforation process and explore additional target configurations for further validation of the heuristic model. All simulations were performed using the explicit structural mechanics solver in LS-DYNA from LSTC. Simulations were performed in 3D using quarter symmetry. The target plates and projectiles were modelled using 8-node, reduced integration (constant stress) hexahedral solid elements. The in-plane length of

Concluding remarks

We have suggested a heuristic approach for estimating the ballistic performance of targets constructed of multiple, identical in-contact layers perforated in ductile hole growth. The proposed model defines a material resistance sci for each layer, which depends on the position of the layer in a multi-layered target stack. This layer material resistance is affected by the target layers not yet perforated by the projectile, suggesting a reinforcement effect which provides greater resistance than

CRediT authorship contribution statement

Rami Masri: Conceptualization, Methodology, Formal analysis, Writing - original draft, Writing - review & editing. Shannon Ryan: Validation, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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      Citation Excerpt :

      However, for multi-layered, in-contact targets, the material resistance that the projectile feels during penetration of each layer is influenced by the layers ahead of it [17]. From Ref. [17] we recall that, for a target composed of two identical, in-contact layers, the material resistance to penetration of the first layer is dependent on the total thickness of material ahead of the projectile, while material resistance to penetration of the second layer is not affected by the first layer, and the second layer acts as an independent monolithic target. Hence, to model the material resistance of a target consisting of two non-identical in-contact layers, we will propose in Section 4 to replace the second layer by a ballistically-equivalent layer of the same material as the first layer.

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    Current affiliation: Applied Artificial Intelligence Institute (A2I2), Deakin University, Waurn Ponds, Australia

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