Formación de la población

Flyer-plate tests were developed to examine shock wave propagation in materi- als, and these experiments take the material to extremely high strain rates.

(a)

(b)

(c) 10 mm(d)

FIGURE 2.15

High-speed photography showing how zirconium samples exited a die after extrusion (a and b). Stereographic images of reassembled Zr specimens (c and d). (Reprinted from Escobedo, J. P. et al., Acta Materialia, 60 (11), 4379–4392, Copyright 2012, with permission from Elsevier.)

A typical experimental set-up is shown in Figure 2.16. Here, a flyer plate is accelerated towards the target and arrives so that all points on the projectile’s surface make contact with the target simultaneously. Consequently, both the flyer plate (projectile) and the target need to be lapped to very high toler- ances (typically <±5 μm). Projectile alignment before impact is also impor- tant. The impact of a flyer plate generates a planar shock wave in the target. In this situation, all strain is accommodated along the impact axis, whilst the orthogonal components of strain are zero due to inertial confinement. Consequently, the orthogonal components of stress are non-zero. Therefore, in summary, the conditions of stress and strain are written in the target as

εx≠ εy = εz = 0 and σx≠ σy = σz≠ 0, (2.60)

where the subscript x denotes the condition along the impact axis, and the subscripts y and z denote the conditions orthogonal to the impact axis.

The set-up shown in Figure 2.16 denotes a gun-launched flyer plate mounted on a sabot, although it is also possible to explosively accelerate a flyer plate. In this experimental set-up, two spatially separated gauges are shown to measure the shock wave velocity in the material (attached to a suit- able digital storage oscilloscope) and stress within the sample. A cover plate is necessary to protect the first gauge and would be made from the same material as the flyer plate. The first gauge records a rapid rise in stress due to the arrival of the shock wave followed by a plateau stress (referred to as the Hugoniot stress) and an elastic–plastic release. The second gauge records a precursor wave that has separated out from the main shock front, and this is apparent when the shock wave velocity is slower than the elastic wave speed in the material. The magnitude of the precursor is known as the Hugoniot elastic limit (HEL) and is analogous to the yield strength of the material. The HEL has been linked to the ballistic performance of certain materials such

Flyer-plate Gauge assemblies Target specimen Backing ma te rial (a) Sabot Stress (GP a) Time (µs) Δt (b) HEL Cover-plate _{1 2} 1 2 FIGURE 2.16

(a) A schematic of the flyer-plate technique where gauges are employed and (b) the expected gauge response when the backing material has the same shock impedance as the target material.

as ceramics. This is followed by post-yield flow and the ‘plastic’ shock front. The shock velocity is then established by measuring Δt, and with knowledge of the sample thickness, it is possible to calculate the shock wave velocity.

These types of experiments are fundamental to the establishment of an equation of state for the material by providing a reference curve called a Hugoniot. Once a Hugoniot is established, the parameters for the equation of state can be calculated that can be input into hydrocodes (such as ANSYS AUTODYN™ or LS-DYNA), which are commonly used to simulate the bal- listic response of materials. It is important to realise that the Hugoniot is not a plot of the history of pressure increase as a shock is formed but rather that it is a locus of all the possible shock states achievable. This will be discussed in more detail in Chapter 5 where stress waves and shock are examined.

2.8 Summary

Material science plays a large role in armour designs, and having a good understanding of how materials behave under load is crucial for good designs. In particular, bullets, bombs and blast push materials to their extreme limits of strength, and therefore, it is good to know how materials fail. Materials have a theoretical strength – that is, the maximum strength that can be achieved for a perfectly uniform structure that is defect-free. However, all materials possess defects that compromise their ability to with- stand load. We have seen in this chapter that crystals have natural defects called dislocations, and these play a role in how a material will deform plastically.

We have seen that the behaviour of materials at elevated deformation rates is generally different than at lower deformation rates. Therefore, the behav- iour of a bullet striking a target cannot be predicted just from knowing the quasi-static values of strength and ductility (although they do serve as a good approximation in the first instance). A complete picture of the work hardening, strain-rate sensitivity and thermal-softening characteristics of the jacket, core and target will help us understand how the bullet penetrates.

There are a number of techniques that can be employed to investigate the high strain-rate response of a material, and these have been quickly reviewed here. These techniques subject the material to different loading rates and subject the sample to different stress states. The results from these tests can then be used to input into computer codes to simulate complex loading problems.

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3

Bullets, Blast, Jets and Fragments

3.1 Introduction

Before we look at the technologies that help in saving lives, we need to assess what has historically been designed to take life away. It is only with a full understanding of these technologies that we can begin to assess how to pro- tect. The mechanisms of damage can be quite varied, and therefore, an intro- duction to bullets, blast, jets and fragments is given here.