ABSTRACT
This paper describes the development of a finite element model for the 7.62×39 mm mild steel core (MSC) bullet. The derivation of the numerical model is based on results of compression testing performed on bullet components and bullets. The material constants needed are obtained using an iterative approach, where numerical models of the compression tests are carried out to match the force displacement response of the tested structures. Later, these set of constants are refined by comparing predicted deformed shapes against those observed during ballistic impact experiments. Numerical simulations of the 7.62×39 mm MSC bullet impacting a semi-infinite rigid plate are carried out over a range of impact velocities, and the predicted deformed shapes compared to experimental shapes obtained with the help of high speed photography. Soft recovery of cores and jackets are also used to perform comparisons with predicted results. It was found that our constitutive and damage models, implemented in ABAQUS Explicit, were able to accurately predict deformed shapes and failure modes without any predefined defects in the element mesh.
KEYWORDS
ABAQUS Explicit, AK-47 Kalashnikov bullet, Assault rifle bullets, Ballistics, Explicit Finite Elements Models, Johnson-Cook plasticity model, Johnson-Cook strength model, Johnson-Cook constants for steel, Johnson-Cook constants for lead, Material properties for lead, Material properties for steel, Nonlinear Finite Elements Models, Taylor impact test, 7.62×39 mm Mild Steel Core bullet, 7.62×39 mm MSC bullet.
INTRODUCTION AND OBJECTIVES
This paper covers the work done to obtain a physical – mathematical representation of small arms ammunition identified as critical for the successful design of helmet, based on results of mechanical experiments, and validated by ballistic testing. The projectile selected is the one fired from the AK-47 Kalashnikov assault rifle. The reason for selecting this bullet is the immense popularity of the AK-47 Kalashnikov assault rifle around the world [1, 2].
Among the factors affecting the penetration resistance of an armor system are the characteristics of the projectile, mass, geometry (length, shape and caliber), materials (stiffness, strength, and density), and initial impact conditions, striking velocity, and impact angle. The goal of this study is to characterize the response of one type of bullets fired by the AK-47 assault rifle. Objectives included obtaining the geometrical shapes of each bullet components, hardness, and material constants at low (1s-1) medium (100 s-1) and ballistic strain rates.
Fig. 1 AK-47 Kalashnikov assault rifle bullet components
To obtain geometrical shapes, bullets were cut in half, using water jets and wire EDM techniques (Figure 1). For each bullet component, geometric profiles were recorded 5 times using a profilometer (Figure 3), and then an average profile was obtained for each of them. Figure 4 shows the averages profile for the core, the filler and the jacket. As it can be shown in Figure 4, the steel core is flat at the top, instead of being machined to a point as it is the case with Armor Piercing rounds (AP-Armor Piercing, a bullet intended to penetrate without deformation).
Hardness measurements were conducted at several locations for each bullet component (Figure 2), and the average results are summarized in Table 1 [3].
Table 1 Rockwell Hardness for 7.62x39mm MSC components
|
Component |
Hardness |
|
Copper plated Steel |
92 HRB |
|
Jacket |
|
|
Steel Core |
23HRC |
Fig. 2 AK-47 Hardness measurements of bullet components
The average mass of whole bullet is determined to be 7.93 g, steel core has a mass of 3.58 g, while copper plated steel jacket’s mass is 2.15 g. The lead filler has a mass of 2.2 g.
Fig. 3 Bullet jacket on profilometer
Fig. 4 Projectile composition
EXPERIMENTAL
Compression Test
In order to obtain material properties of both copper plated steel jacket and steel core, bullets were cut, with high precision, by water jet (Figure 5) into cylindrical test samples, as shown on Figure 5.
Fig. 5 The way bullets are cut
Fig. 6 Core and jacket compression test samples
The average mass of the cylindrical core test samples is 2.08 g, while cylindrical jacket samples have a mass of 1.01 g.
Quasi-static Compression test results
First set of compression tests are performed under very low strain rate of 1s-1 on samples freely positioned between flat platens (Figure 7).
Fig. 7 Quasi-static compression test setup
Figure 8 shows the average, base on five repetitions, load-displacement and approximate stress-strain responses for the bullet steel core cylinders under compression.
Fig. 8 Steel Core Compression Test Result
From the graph, three different regimes of material’s response to compression can be distinguished. After first, elastic response, with the modulus of elasticity of E1=31.72 GPa, and yield point of ay=362 MPa, there are two strain hardening zones with stiffness of E2=1.24 GPa and E3=3.45 GPa, respectively, ending by load increase due to platen to platen compression.
Figure 9 represents copper plated steel jacket compression test results. Jacket showed to be stiffer, having Young’s modulus of E=42.5 GPa as well as higher yield strength of ay=603.3 MPa, then steel core. During compression, cylindrical test sample, after reaching the Yield point, gets crushed including two buckling modes, indicated by two peaks on the graph.
Fig. 9 Steel Jacket Compression Test Result
Moderate strain rate compression test
The moderate strain rate compression test is performed on MTS machine with the load limit of 30 kN, and speed range up to 17 m/s (Figure 10).
Fig. 10 High strain rate test setup
Note that because the MTS machine was not been able to maintain the loading rate, high strength steel core was able to compress only to a certain point, when the test would stop. Therefore the results on Figure 11 are valid only up to 0.5 mm displacement (shown with the arrow). After that point, the strain rate would change due to the deceleration of the test. On the other hand, the test of steel jacket results in full compression of the sample, with two buckling modes, as shown on a Figure 12.
Fig. 11 Moderate strain rate compression test results of a steel core
Fig. 12 Moderate strain rate compression test results of a steel jacket
Compared, quasi-static and moderate strain rate compression results, for both bullet core and jacket (Figure 13), show initially stiffer response (marked on graphs) of both core and jacket at higher strain rate. However, it has to be noted that even moderate strain rate of 100 s-1 (that was set by machine limitation) is still much lower than strain rates that projectile materials experience during ballistic event, which are in order of 10,000 s-1.
Fig. 13 Test strain rate comparison: (a) Core, (b) jacket
