Shot Impact on a Steel Target Plate Experimental and Theoretical Analysis Review Paper

Introduction

In modern warfare, the fragment anti-missile warhead is widely applied to intercept and destroy the incoming missile. The warhead is a key component of the missile to destroy the targets. Its capability confronting fragments penetration is an important prerequisite to ensure the completion of the given mission. Due to its low cost and high strength, G50 (28CrMnSiNi4MoNb) ultra-loftier strength steel, a kind of low alloy steel without cobalt, has been widely used as material for penetrating warhead shell (Zhang et al., 2019). Tungsten alloy has become the main choice for the design of anti-missile warhead fragments with its skillful concrete and mechanical capabilities of high density, small attenuation coefficient and strong ability of piercing armor. Therefore, it is of swell significance to study the damage characteristics of G50 ultra-high strength steel nether the touch on of tungsten alloy fragments for designing the penetrating warhead beat.

The failure characteristics of tungsten alloy projectiles penetrating into steel targets have been studied over decades due to the continually armed forces interest. Martineau et al. (2004) studied the penetration characteristics of the high-strength depression-blend (HSLA-100) steel impacted past 6.4 mm diameter tungsten carbide spheres at velocities ranging from 0.eight to 2.v km/due south experimentally. The results demonstrate that the diameter of the resulting crater increases linearly as a function of impact velocities. But the relationship between the depth of penetration and the bear upon velocity is non-linear. Schaer and Herrwerth (2001) proposed a theoretical model to predict the depth of penetration of tungsten projectiles with rotationally symmetric ellipsoid shape into semi-space targets at hypervelocity. The shape influences of projectiles on the depth of penetration were further discussed by boosted numerical simulations. Hohler and Stilp (1977) conducted a series of tests to obtain the penetration characteristics of tungsten alloy rods into semi-infinite armored steel targets. The corresponding test information take become the standard reference data for theoretical analysis and numerical simulations. Anderson et al. (1995) and Anderson and Walker (1995) proposed an technology model in accord of the penetration mechanism and failure features of hypervelocity penetration of metal targets impacted by cylindrical tungsten projectiles. Wu (1999) conducted an series of experiments to study the failure mechanism of 93 W alloy fragments of 2–4 m penetrating into armored steel targets at velocities ranging from 500 to 1,300 thou/south. The fracture properties of 93 W alloy fragments were discussed intensively. Duan et al. (2003) conducted the experiments of two kinds of steel target plates (45# steel and 30CrMnMo) penetrated past sintered tungsten alloy projectiles. The microstructures of the targets showed that no adiabatic shear ring was observed in the low strength 45# steel. While there were several kinds of adiabatic shear bands in the high strength 30CrMnMo steel under similar impact conditions which is also observed in perforation experiments of several kinds of steel targets (Atapek and Karagoz, 2010; Atapek, 2013). Rama Subba Reddy et al. (2019) conducted the ballistic tests of an amour steel against a scaled-down tungsten alloy projectile at velocities ranging from 900 to one,400 m/s. Microstructural observations performed by SEM showed that the mushroom head of projectile is formed and cracks occurs originally at the both sides of the remnant and propagates to the head and the tungsten blend projectile fails due to the adiabatic shear localization afterward deforming severely.

However as our knowledge G50 (28CrMnSiNi4MoNb) ultra-high forcefulness steel penetrated by tungsten blend fragments take non been investigated before. In this paper, an experimental investigation is reported into the failure characteristics of ultra-loftier strength steel targets subjected to impact past tungsten alloy fragments at velocity ranging from 923 to 1870 m/s which are all the same defective. The expected results may provide a significantly experimental and theoretical footing for the blueprint of the penetrating warhead beat.

Experiments

The plate material used in the experiments is a kind of low alloy steel without cobalt, ultra-high strength G50 steel which is supplied by ChangChen Special Steel Co. and the tungsten blend is supplied by Xi'an Huashan Tungsten Products Co., Ltd. The chemical composition of G50 steel is given in Tabular array 1. The experiment organization for the nowadays tests is shown in Figure 1. The G50 ultra-high strength steel targets with the thickness of 100 mm was struck commonly past the 15 mm diameter tungsten alloy spherical fragments with velocities ranging from 923 to 1870 m/south. The fragments were fired from a Φthirty mm ballistic gun afterward placed in a specifically designed sabot which is shown in Effigy ii. The velocity measurement placed betwixt the gun and target was used to measure the velocity of fragments. High-speed photographic camera was further used to calibrate the impact velocity.

Tabular array ane. Chemical composition of G50 steel in wt%.

FIGURE i. Sketch of the experiment setup.

Effigy 2. Tungsten blend fragment and specifically designed sabot.

The 15 mm diameter spherical fragments used in the experiment are made from W93 tungsten alloy, with density of 17.half-dozen m/cm³ and total mass of 31 thousand. Assembled fragments with the sabot are shown in Figure 2. By adjusting the mass of the propellant, the velocity of fragments can be controlled in the range from 900 to 1,800 m/due south. The G50 target was placed on a steel base equally shown in Effigy 3.

Effigy 3. G50 steel target and velocity measurement.

The velocities of tungsten alloy fragments were measured past a pair of sensor aluminum foils which formed a part of electrical circuits and were connected to a multi-channel velocity measurement system. So the time it takes the fragment to fly between two aluminum foils was recorded by the sensor. The velocity of fragments could be calculated from dividing the distance between ii aluminum foils by the time interval. The high-speed camera system was used to record the flight attitude and penetration process of fragments as shown in Figure iv.

Effigy 4. The layout of high-speed photographic camera system.

Results and Discussions

Figure five shows the cut airplane view of G50 steel targets. The experimental observations prove that there are no obvious balance tungsten alloy fragments at the bottom of the crater, which suggests that the fragments are broken into pieces and ejected out of the crater during the penetration. It can be plant from the G50 steel target subsequently impact that a raised lip on the front surface combined with spall is produced by the tungsten alloy fragment and layered cracks occurs at the rough crater surface. The crater formed in the G50 steel target afterward impact by a tungsten blend spherical fragment is conic-similar, which is different from that in the low forcefulness steel target tests.

Figure 5. Photographs of cross sections of G50 steel target after bear upon by a tungsten alloy spherical fragment. (A) v = 923 g/south (B) v = ane,158 m/s (C) five = 1,426 m/southward (D) 5 = one,600 grand/s (E) v = 1,800 k/s, and (F) v = 1,870 m/s.

The depth of penetration and the crater book of six shots are summarized in Table 2. Figure six shows the experimental data of the depth of penetration and the crater book at unlike touch velocities, respectively. It is shown that both the depth of penetration and the crater volume increase nearly linearly with the increase of impact velocities.

TABLE 2. Depth of penetration and crater volume of the G50 steel targets at unlike impact velocities.

Figure half-dozen. (A) Depth of penetration, and (B) crater volumes.

Much effort Zhao et al. (2015) and Wang et al. (2013) has been defended toward the cratering features of tungsten alloy projectiles penetrating into ductile metal targets with low yield forcefulness (such as low carbon steel). The schematic diagrams of the penetration procedure are shown in Figure 7. When the projectile penetrates into the ductile metal targets at high velocities, the stress at the projectile-target interface is much higher than the dynamic yield strength of projectile material. The projectile materials deformed and eroded at the projectile-target interface. The target material flows in a hydrodynamic fashion in the depth and radial directions when intruded by a projectile. A raised lip on the front surface produced by the tungsten alloy fragment appears due to the effect of the rarefaction wave which is a typical miracle of the loftier velocity penetration when the touch on pressure exceeds the strength of the target material. After the transient entrance phase, the projectile is continuously eroded, and intrudes the targets with the crater expanding and deepening to form a uniform cylindrical target crater under the effect of force per unit area and inertia.

FIGURE vii. Schematical diagrams of penetration process of low carbon steel target impacted by a tungsten ball (Zhao et al., 2015). (A) Transient archway phase, (B) intruding phase, (C) expanding phase, and (D) penetration finished.

However as to our knowledge, much fewer researches were institute to investigate the failure features and penetration machinery of G50 ultra-high forcefulness steel targets impacted by tungsten blend fragments. Co-ordinate to the failure features and penetration mechanism of the G50 steel target impacted by the tungsten blend fragment, the pressure at the projectile-target interface is extremely loftier, and due to the potent rarefaction wave produced past boundary effect stretches target surface, a raise lip with spall are produced past rarefaction wave. With the increase of the impact velocity, the impact pressure and forcefulness of the rarefaction wave increases, which makes the tensile spall area on the front surface of the target larger. It is also demonstrated that the failure mode of G50 steel develops from ductile fracture to semi-brittle fracture under high tensile strain charge per unit. Obvious macro-cracks tin be observed on the crater surface, which is slightly undulating in a wavy manner. At the surface of the crater, grain distortion flow is considered to be acquired due to the adiabatic shear, and a severely deformed strip parallel distribution appears. At the same time, at that place are macro tensile cracks deepening into the targets, which suggests that local tensile failure occurs in the G50 target under the outcome of the tungsten alloy fragment penetration.

During the penetration process, under the conditions of high temperature, high pressure and high strain rate, inhomogeneous stress distribution in the tungsten fragment occurs, and the fragment continuously erodes to "mushroom-similar" caput and the products of erosion are ejected out of the target. Local sudden unloading of craters, and the tensile stress are produced by the unloading wave interaction. Meanwhile, the adiabatic shear bands effectually the target crater greatly reduces the material strength in this surface area. Under the influence of shear stress, micro-cracks are nucleating, propagating and penetrating in the shear bands, and and then macro-cracks are generated in the local unloading surface area.

With the penetration process going on, the random macro-cracks in the thickness direction occurs and the textile departs from the target locally, which make the stress distribution concentrate, macro-cracks propagate and material locally fails in the tungsten alloy fragment. The front section of the fragment sharpens, which reduces the contact expanse between the fragment and the target, and thus the penetration resistance decreases. Figure 8 shows the schematic diagrams of failure features of tungsten alloy fragments penetrating into G50 steel target at high speed. It tin can be inferred that the failure style of the target and the fragment is closely related.

Effigy eight. Schematical diagram of penetration process G50 steel target impacted by a tungsten ball (Zhao et al., 2015). (A) Transient entrance stage, (B) intruding stage, (C) expanding phase, and (D) penetration finished.

According to the dynamic cavity expansion theory, the radial stress on the crenel surface of the ideal elasto-plastic material is (Forrestal and Luk, 1988):

${\sigma }_r=\frac{2Y}{\mathrm{iii}}\left[\ln \left(\frac{2E}{3Y}\right)+1\right]+\frac{3}{\mathrm{ii}}\rho u^2(\mathrm{one})$

where Y is the yield strength, E is the elastic modulus, $\rho$ is the cloth density, and u is the cavity surface expansion velocity. According to Eq. (1), the radial stress on the cavity surface is closely correlated to the yield strength of the target plate. G50 steel has a ultra-loftier yield strength of one,590 MPa (Wang et al., 2009), which makes a loftier radial stress. The college radial stress acted on tungsten blend fragments will cause greater stress concentration and inhomogeneous distribution of stress in the fragments. Greater concentration and inhomogeneous distribution of stress in the fragments will consequently lead the inhomogeneity and concentration of deformation, which finally atomic number 82 the fragment pause and fall into pieces.

In order to farther investigate and verify the reason of conic-like crater forming, numerical simulations on the penetration of the tungsten alloy spherical fragment into the G50 steel target at velocities ranging from 923 to one,870 thou/s were carried out. Among them, Johnson-Cook constitutive relations and Gruneisen EOS are adopted for both the G50 steel target. The flow stress of Johnson-Cook model tin can exist expressed in the following form:

$\sigma =\left(A+B{\overline{\epsilon }}^{\mathrm{northward}}\right)\left(\mathrm{ane}+C\ln {\dot{\epsilon }}^{\ast }\right)\left(\mathrm{ane}-T^{\ast m}\right)(2)$

where $\sigma$ is the flow stress, A, B, C, n, thou are abiding parameters, ${\dot{\epsilon }}^{\ast }=\dot{\epsilon }/{\dot{\epsilon }}_0$ , ${\dot{\epsilon }}_0$ is the reference strain rate which is taken to be 10^−v/due south $T^{\ast }=\left(T-T_r\right)/\left(T_g-T_r\right)$ , $T_r$ is the reference temperature, $T_m$ is the cook temperature, $\overline{\epsilon }$ is the equivalent plastic stain. The parameters of constitutive relation are shown in Tabular array three (Wang et al., 2009). The equation of Gruneisen EOS can be expressed in the post-obit class:

$P=\{\begin{array}{cc}\frac{{\rho }_0{C}^{\mathrm{two}}\mu \left[\mathrm{one}+\left(1-\frac{\gamma }{2}\right)\mu -\frac{a^2}{2}\mu \right]}{1-\left(S_{\mathrm{one}}-1\right)\mu -S_2\frac{{\mu }^2}{\mu +1}-S_3\frac{{\mu }^{\mathrm{iii}}}{{\left(\mu +1\right)}^2}}& \mu \ge 0\\ {\rho }_0{C}^2\mu +\left(\gamma +a\mu \right)E& \mu <0\end{array}(3)$

where P is the pressure, East is the relative internal energy, ${\rho }_0$ is the initial density, C ₀ is the intercept of the curve of 5 _s to v _p, Southward ₁, Southward ₂, South ₃ are parameter of the curve of five _s to v _p, v _southward and v _p are the velocities of shock wave and particles respectively. $\mu$ is the book strain, $\gamma$ is the Gruneisen constant, a is the correction gene which is taken to be nothing in this study. The parameters of EOS are listed in Table 4 (Li and Chen, 2001). Plastic kinematic model is used for tungsten blend fragments and the parameters are listed in Tabular array 5.

Tabular array 3. Constitutive properties for the G50 steel target and tungsten alloy spherical fragment.

Table iv. Parameters of EOS for G50 steel target.

TABLE five. Material parameter for the tungsten alloy fragments.

The finite element model is shown in Effigy 9A. Co-ordinate to the symmetry of the model, 1/2 3-D solid model was established. The mesh for the fragment consisted of 78,609 elements with an elements size of 0.25 mm. The diameter and thickness of G50 target plate are 80 and 40 mm. The mesh for the targets consisted of 1,389,216 hexahedral elements. The unit of measurement sized of 0.5 mm were used to mesh the model and the grids in the circular area with a radius of 40 mm nigh the impact point is locally encrypted with the unit sized of 0.25 mm. Symmetric constraints are practical on the aeroplane of symmetry, and the boundary conditions are reinforced around the target plate.

Figure 9. Schematic diagrams of penetration of tungsten sphere into G50 steel at the impact velocity of 1,800 m/s at unlike times. (A) T = 0 µs, (B) T = 5 µs, (C) T = 10 µs, (D) T = twenty µs, (East) T = 30 µs, (F) T = 40 µs, (G) T = 50 µs, and (H) T = 60 µs.

The depth of penetration predicted by present model is 27 mm which is in good understanding with experimental data. The crater volume predicted by numerical simulation is xiv.5 cm³ approximately while the crater volume obtained by experiment is xix cm³. It should be mentioned here that the crate volume obtained past experiments includes the volume in tensile spall area which is not included in numerical results. This may be the reason why the crater book obtained by experiments is higher than that predicted by numerical simulations.

A sequence of vi images at different time, illustrating the section view of the fragment penetrating into the G50 steel target at impact velocity of 1,800 thousand/s are shown in Figure 9. At the transient entrance phase, the fragment deforms and forms a conic-like caput with hemi-spherical part backside. With the fragment beingness continuously eroded, the textile of the hemi-spherical function of the fragment flows into the conic-like head and the erosion products of the fragment grade debris which is ejected out of the crater until the hemi-spherical part is completed eroded. The conic-similar craters formed due to the shape of the fragment' head. Information technology is noteworthy that the configuration of crater obtained by the numerical simulation is similar with the experimental observation, which verifies that the tungsten fragment falls into pieces during the penetration procedure.

Decision

G50 ultra-high strength steel, which has been widely used as warhead trounce, is a depression blend steel without cobalt. The ballistic gun experiments of the G50 steel target struck normally by the tungsten alloy fragment at impact velocities ranging from 923 to i,807 1000/s has been conducted past using the commercially available software, LS-DYNA. The depth of penetration, crater volume and failure behaviors of G50 steel targets were obtained. The ballistic experimental results show that the crater is conic-like in the G50 steel target later struck by a tungsten alloy spherical fragment, which is dissimilar from that in the depression strength steel target tests. It tin can be observed in the G50 steel target after touch that obvious layer cracks in the crimps of the crater surface and a raised lip on the front end surface combined with spall produced by the tungsten blend fragment. These phenomena mentioned above provide show that the tungsten fragment is eroded, sharpened and intermission into pieces during the penetration procedure. In add-on, several tensile cracks are found in G50 steel targets, which are considered to exist acquired by tensile stress induced by the superposition of rarefaction at some local areas of the impacted interface.

Numerical simulations of the penetration of a tungsten alloy fragment into the G50 steel target were carried out to predict failure characteristics of the G50 target. It is noteworthy that the configuration of crater obtained by numerical simulations is similar with the experimental observations, which provide evidence that the tungsten fragment falls into pieces during the penetration process.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author Contributions

HP and WS annotate and maintain inquiry data for initial use. LuZ and LJ bear investigation procedure and perform the experiments and data collection. FX is responsible for the research activity planning and execution. ZX performs the numerical simulations. LiZ and LuZ write the initial draft.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Classification

Y yield forcefulness
E elastic modulus
$\rho$ material density
u cavity surface expansion velocity
A, B, Northward parameters related to strain hardening relations in Johnson-Cook constitutive model
C parameter related to strain rate outcome in Johnson-Cook constitutive model
M parameter related to temperature softening upshot in Johnson-Cook constitutive model
T _melt melting temperature
P pressure
v _s velocities of shock wave
v _p velocities of particles
Due south ₁, South _two, Due south _iii parameter of the curve of v _s to 5 _p
$\gamma$ Gruneisen abiding
$\mu$ book strain
${\sigma }_{\text{y}}$ _{yield stress}
Due east_t plastic modulus

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Source: https://www.frontiersin.org/articles/10.3389/fmats.2020.618771/full

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