Perforation of 5083-H116 Aluminum Armor Plates with Ogive-Nose Rods and 7.62 mm APM2 Bullets

Abstract

We conducted an experimental and analytical study to understand the mechanisms and dominant parameters for ogive-nose rods and 7.62 mm APM2 bullets that perforate 5083-H116 aluminum armor plates. The 20-mm-diameter, 95-mm-long, ogive-nose, 197 g, hard steel rods were launched with a gas gun to striking velocities between 230–370 m/s. The 7.62-mm-diameter, 10.7 g, APM2 bullet consists of a brass jacket, lead filler, and a 5.25 g, ogive-nose, hard steel core. The brass and lead were stripped from the APM2 bullets by the targets, so we conducted ballistic experiments with both the APM2 bullets and only the hard steel cores. These projectiles were fired from a rifle to striking velocities between 480–950 m/s. Targets were 20, 40, and 60-mm-thick, where the 40 and 60-mm-thick targets were made up of layered 20-mm-thick plates in contact with each other. The measured ballistic-limit velocities for the APM2 bullets were 4, 6, and 12% smaller than that for the hard steel cores for the 20, 40, and 60-mm-thick targets, respectively. Thus, the brass jacket and lead filler had a relatively small effect on the perforation process. In addition, we conducted large strain, compression tests on the 5083-H116 aluminum plate material for input to perforation equations derived from a cavity-expansion model for the ogive-nose rods and steel core projectiles. Predictions for the rod and hard steel core projectiles are shown to be in good agreement with measured ballistic-limit and residual velocity data. These experimental results and perforation equations display the dominant problem parameters.

Appendix: Perforation Models

We give a full discussion of the cylindrical, cavity-expansion, perforation models in [1]. Briefly, the aluminum plate deformations are dominated by ductile hole-growth and the holes had nearly the diameter of the projectile shanks. To approximate ductile hole growth, the cylindrical, cavity-expansion method idealizes the target as thin independent layers that are compressed normal to the perforation direction. Thus, the analysis is simplified to one-dimensional motion in the radial plate dimension for an elastic-plastic material. We perform a cylindrically symmetric, cavity-expansion analysis, use these results to develop the perforation equations, and obtain closed-form perforation equations that predict the ballistic-limit and residual velocities.

A cylindrically symmetric cavity is expanded from zero initial radius at constant expansion velocity V. This expansion produces an elastic-plastic response. The elastic region has Young’s modulus E and Poisson’s ratio ν, and the plastic response region is taken as an incompressible, power-law hardening material. Data from uniaxial compression tests were curve fit with equations (2a,b) and results are shown in Fig. 2.

Our perforation models require the radial stress σ _r at the cavity surface versus cavity-expansion velocity V. From [1]

$$ {\sigma_r} = {\sigma_s} + {\rho_t}B{V^2} $$

(3a)

$$ {\sigma_s} = \frac{Y}{{\sqrt 3 }}\left\{ {1 + {{\left[ {\frac{E}{{\sqrt 3 Y}}} \right]}^{^n}}\int\limits_0^b {\frac{{{{\left( { - \ln x} \right)}^n}}}{1 - x}dx} } \right\}\,\,\,\,,\,\,b = 1 - {\gamma^2} $$

(3b)

$$ B = \frac{1}{2}\left\{ {\frac{1}{{\left( {1 - \nu } \right)\sqrt {1 - {\alpha^2}} }}\ln \left[ {\frac{{1 + \sqrt {1 - {\alpha^2}} }}{\alpha }} \right] + {\gamma^2} - 2\ln \left[ \gamma \right] - 1} \right\} $$

(3c)

$$ {\alpha^2} = \frac{{\sqrt 3 \left( {1 - 2\nu } \right)}}{{2\left( {1 - \nu } \right)}}\left( {\frac{{{\rho_t}{V^2}}}{Y}} \right) $$

(3d)

$$ {\gamma^2} = \frac{{2\left( {1 + \nu } \right)Y}}{{\sqrt 3 E}} $$

(3e)

where σ _s is the quasi-static radial stress required to open the cylindrical cavity and ρ _t is the target density. As discussed in [16], the integral in equation (3b) is improper because of the integrand behavior near x = 0. However, this singularity is integrable and the integral can be evaluated with an open formula such as the extended midpoint rule [17].

As discussed in [1], we accurately approximate equations (3c–e) with

$$ {\sigma_r} = {\sigma_s} + {\rho_t}{B_0}{V^2} $$

(4)

where B ₀ is a dimensionless constant obtained from curve-fitting equations (3c–e). The approximation given by equation (4) is required to obtain closed-form perforation equations because α and B ₀ depend on V. Figure 6 shows the dimensionless radial stress at the cavity surface versus dimensionless cavity-expansion velocity from equations (3c–e) and equation (4) with B ₀ = 3.105.

We now present closed-form perforation equations for rigid, ogive-nose projectiles that perforate aluminum target plates. For an ogive-nose projectile with striking velocity V _s , the ballistic-limit V _bl and residual velocity V _r are given by

$$ {V_{bl}} = {\left( {\frac{{2{\sigma_s}}}{{{\rho_p}}}\frac{h}{{\left( {L + {k_1}l} \right)}}} \right)^{1/2}}{\left[ {1 + C + \frac{2}{3}{C^2}} \right]^{1/2}} $$

(5)

$$ {V_r} = {V_{bl}}{\left[ {{{\left( {\frac{V_s}{{{V_{bl}}}}} \right)}^2} - 1} \right]^{1/2}}{\left[ {1 - C + \frac{1}{2}{C^2}} \right]^{1/2}} $$

(6)

$$ C = \frac{h}{{\left( {L + {k_1}l} \right)}}\frac{{{\rho_t}}}{{{\rho_p}}}{B_0}N\left( \psi \right) $$

(7)

$$ N\left( \psi \right) = 8{\psi^2}\ln \left( {\frac{{2\psi }}{{2\psi - 1}}} \right) - \left( {1 + 4\psi } \right) $$

(8)

In equations (5–8), the ogive-nose rod projectile has density ρ _p, shank length L, nose length l, diameter 2a, caliber-radius-head ψ, and k ₁ is given by equation (1b). The target plate has density ρ _t , thickness h, σ _s is given by equation (3b), and B ₀ is given by equation (4).

As explained in [1], the terms in C in equations (5) and (6) come from a power-series expansion that is truncated after three terms. For the applications in [1] and this study, C is small enough that the next terms are negligible. For some applications [1], the value of C is very small compared to unity and equation (6) for residual reduces to

$$ {V_r} = {V_{bl}}{\left[ {{{\left( {\frac{V_s}{{{V_{bl}}}}} \right)}^2} - 1} \right]^{1/2}} $$

(9)

Based on the conservation laws and some assumptions, Recht and Ipsen [18] published equation (9) as an analytical model. They then determined V _bl experimentally and found that equation (9) could accurately predict V _r for many data sets. Later, Lambert and Jonas [19, 20] observed that a modification of equation (9) provided a better fit to some experimental data. The Lambert-Jonas empirical equation is given by

$$ {V_r} = {\left( {V_s^p - V_{bl}^p} \right)^{1/p}} $$

(10)

where p is the empirical constant used to best fit the data with the least squares method. Equation (10) reduces to equation (9) for p = 2. In this study and a previous study [6], we use equation (10) to curve-fit the residual velocity versus striking velocity data.