Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

Abstract

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed. This study investigated the fragmentation performance of a new high-carbon silicon-manganese (HCSiMn) steel cylindrical shell through fragment recovery experiments. Compared with the conventional 45Cr steel shell, the number of small mass fragments produced by the HCSiMn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model. The fragmentation process of the HCSiMn shell exhibited more brittle tensile fracture characteristics, with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation. On the one hand, the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite, so that microscopic intergranular fracture reduces the characteristic mass of the fragments; on the other hand, the distribution of alloy carbides can exert a "pinning" effect on the substrate grains, causing more initial cracks to form and propagate along the brittle carbides, further improving the shell fragmentation. Although the killing power radius for light armored vehicles was slightly reduced by about 6%, the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26% based on theoretical assessment. These results provided an experimental basis for high fragmentation warhead design, and to some extent, revealed the correlation mechanism between metallographic structure and shell fragmentation.

Headnote

ABSTRACT

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed. This study investigated the fragmentation performance of a new high-carbon silicon-manganese (HCSiMn) steel cylindrical shell through fragment recovery experiments. Compared with the conventional 45Cr steel shell, the number of small mass fragments produced by the HCSiMn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model. The fragmentation process of the HCSiMn shell exhibited more brittle tensile fracture characteristics, with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation. On the one hand, the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite, so that microscopic intergranular fracture reduces the characteristic mass of the fragments; on the other hand, the distribution of alloy carbides can exert a "pinning" effect on the substrate grains, causing more initial cracks to form and propagate along the brittle carbides, further improving the shell fragmentation. Although the killing power radius for light armored vehicles was slightly reduced by about 6%, the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26% based on theoretical assessment. These results provided an experimental basis for high fragmentation warhead design, and to some extent, revealed the correlation mechanism between metallographic structure and shell fragmentation.

Keywords:

Projectile fragmentation

Fragment mass distribution

Fracture mode

Metallographic structure

Damage power

(ProQuest: ... denotes formula omitted.)

1. Introduction

The major firepower suppression weapons in modern warfare, such as grenades and bombs, have typically used metal (e.g. alloy steel) as the projectile material [1]. Driven by the high explosive, the fragmentation of the steel projectile produces natural fragments with various shapes and masses, which destroys enemy living targets and determines the effectiveness of weapons and ammunition. It is noted that the specific shape and mass of the fragments produced by natural shell fragmentation cannot be completely controlled and are random, depending on the type of explosive charge [2], the firing and detonation position [3], as well as the material and structure of the shell [4]. However, the number of fragments corresponding to different masses (quantity-mass distribution) has a certain degree of certainty according to a statistical distribution.

Early on, the size relationship of fragments during explosive loading was first studied by Mott based on the unloading wave theory, where a model was proposed to describe the quantity-mass relationship of projectile fragments [5]. Subsequently, the Mott's model was extended by Grady [6,7] when considering the energy dissipation of shell fracture, which provides an expression for the characteristic mass related to the Weibull two-parameter distribution. Taking into account different dynamic fracture characteristics, shell thickness structures, shell axial position and fragment morphology, Weimer [8], Zhang [9], Zhu [10] and Tang [11] have further elaborated and revised the Mott's theory to give a more accurate prediction of fragment mass distribution, and new statistical methods have also been applied, such as Arnold et al. [12]. who used image processing to obtain perforation information on the fragments and finally calculated the specific fragment mass distribution.

If the quantity, mass, and velocity distribution characteristics of fragments can be scientifically regulated, the warhead's damage power can be maximized and an effective attack on various targets can be achieved. On the one hand, the internal charge is the direct energy source for shell fragmentation. The higher the explosive energy, the more obvious the expansion and acceleration of the shell, and the higher the initial velocity of the fragments can be achieved [13,14], which also results in the changes in the microfracture mechanism and affects the fragments quantity-mass distribution. On the other hand, the shell material and structural design must be matched to the explosive charge to achieve better fragmentation. When using explosives with a higher detonation energy, conventional steel shells can no longer achieve the best fragmentation performance [15]. Under the same loading conditions, the material with higher ductility corresponds to a larger fracture radius [16], i.e. a higher initial fragment velocity, which is conversely reduced for hard brittle steel, while the mass distribution characteristics and ballistic performance of the fragments formed by hard brittle steel can be optimized.

To further improve the number of effective fragments after shell fragmentation, mechanical processing or surface modification methods were adopted to carve grooves on the inner/outer surface of the shell to create an ideal pre-controlled fragmentation [17-21]. However, due to the harsh environment during projectile launch, the safety of pre-grooved shells is difficult to guarantee. Changing the shell performance by designing the material composition and heat treatment process can ensure the safety of the projectile during launch and effectively regulate the fragmentation performance. For example, for 40CrMnSiB steel cylindrical shell, the number of fragments whose mass is more than 1.0 g can be increased by about 77.4% when the tempering temperature of the shell is increased from 350 to 600 °C [22]. By designing the midexplosion recovery experiment, Li et al. [23] further found that the fracture characteristic parameters of recovered 40CrMnSiB wreckage change significantly and then become essentially consistent with the increase in tempering temperature, where the alloy carbide precipitation may play a key role. In addition, there is a strong correlation between the average grain size and the characteristic fragment mass, as confirmed by the experimental research of Zhao et al. [4], i.e. the characteristic mass increased as the grain size increased. Furthermore, by investigating the fracture mode of four metallographic states for two steels (50SiMbVB and 50Si2Mn) [24], it is found that the intergranular and cleavage fracture are the main fracture modes under the impact loading, and the tempered troostite state was more likely to produce shear and tensile mixed fracture than the tempered sorbite steel.

Although many studies have investigated the influence of steel microstructure on fracture modes and failure mechanisms [24e27], it is still not clear how it controls the quantity-mass distribution of fragments and quantitatively affects the damage power of the projectile, in particular the corresponding microscopic mechanism when considering the effect of alloy element. In this paper, we compared the fragmentation performance of a new high-carbon silicon-manganese (HCSiMn) steel with normally used 45Cr steel based on fragment recovery experiments under static blast loading. We analyzed the quantity-mass distribution of the fragments formed and the influence of surface grooves. Further research focused mainly on the characteristics of fracture morphology and metallographic structure of recovered fragments by light microscopy, scanning electron microscopy (SEM) and metallographic microscopy. The picture of the microstructural effect by alloy doping on shell fragmentation was presented and the corresponding effect on the projectile killing radius was quantitatively assessed.

2. Fragmentation experiment of steel cylinder shells under explosive loading

2.1. Materials and experimental setup

The composition and heat treatment method of the steel will affect the microstructure and mechanical properties of the metal material, thereby influencing the fracture and fragmentation behavior of the cylinder shell under explosive loading [22,28]. To ensure the projectile's safe launch, a new high-carbon silicon-manganese steel material (HCSiMn) with higher strength than the usual 45Cr projectile steel was selected. The final heat treatment of both steels adopted the commonly used "quenching ＋ tempering" method, and then the mechanical properties were tested, which included yield strength (δ_s), tensile strength (δ_b), elongation (δ), shrinkage rate (ψ), and hardness (HRC), as shown in Table 1. HCSiMn was found to have lower plastic toughness. Its higher mechanical strength and hardness made it more brittle.

The cylindrical structure of the projectile was chosen to perform the fragmentation experiment according to an equivalent filling ratio design based on the typical cross-sectional structural characteristics of a natural fragmentation warhead, as shown in Fig. 1. The shell has an internal diameter of 134 mm, an external diameter of 154 mm and a height of 90 mm. The RDX-based aluminum-containing explosive was filled inside the shell, and the detonation point was then located in the center of the top of the shell cover. In addition to the natural shell's explosive fracture, V-shaped grooves with depths of 1 mm and 2 mm and lateral separation of 6 mm were pre-carved on the outer shell surface to assess the impact of groove on shell fragmentation.

2.2. Experimental procedure

To examine the fragments mass distribution produced by explosion, the fragment recovery experiments were carried out by using the "sand box" method, where over 90% of the fragments can be successfully recovered. The structural diagram of the fragment recovery chamber, consisting of an air chamber, sand box, and recovery chamber, was displayed in Fig. 2(a). The wooden sand box has dimensions of 2300 mm x 2300 mm x 1800 mm. Once the air chamber is situated inside, fill the remaining space with fine sand. The air chamber was a wooden hexagonal cuboid of 760 mm x 760 mm x 490 mm with the cylindrical projectile shell positioned vertically in its center for testing. The real photography of experiment was shown in Fig. 2(b). The experimental procedure was as follows: 1) Set up the test site as shown in Fig. 2(a), mainly including the recovery chamber and the detonation point; 2) place the projectile with detonators on the frame, fix it in the center of the air chamber, and load the air chamber into the center of the sand inside the sand box; 3) check the safety protection status of the detonator and projectile, and cover the air chamber lid with fine sand to fill the remaining space in the sand box; 4) cover the recovery chamber and connect the detonator for detonation; 5) collect the fragments, clean the sediment on the surface of the fragments and dry them in a drying oven; 6) weigh and count the mass and number of fragments, then record the experimental data.

3. Results and discussion

3.1. Mass distribution characteristics of recovered fragments

After the shell fragmentation experiments, the recovered fragments were classified and counted according to the mass range as follow: 0.5-1 g, 1-4 g, 4-8 g, 8-12 g, 12-16 g, 16-20 g, 20-30 g, 30-50 g. Fig. 3 shows the mass distribution of fragments after six independent experiments with different shell materials (45Cr and HCSiMn) and groove depths (h = 0/1/2 mm), and all recovery rates were above 90%.

It can be intuitively seen that the shell material has a significant influence on the mass distribution of fragments formed after explosive loading. The depth of the 0 mm groove corresponded to a naturally uncontrollable shell, and within the mass range of 0.5e4 g, the number of fragments formed by the 45Cr shell after blasting was 196 pieces, while the number of fragments formed by the HCSiMn shell was significantly more within this mass range, which is 497 pieces (increase by 154%). At the same time, within the mass range corresponding to larger fragments (>4 g), the number of fragments formed by 45Cr shell was 163 (increase by 14%), more than the 143 pieces formed by HCSiMn shell, suggesting that the shell material with higher strength and brittleness is more conducive to the formation of numerous small fragments under detonation.

Regarding the influence of groove depth on fragmentation, it can be found that as the groove depth increases, the number of small fragments formed by 45Cr shells significantly increases. However, for HCSiMn shell with higher strength and brittleness, grooving has less effect on fragmentation, except for the 1 mm grooved case where there is an abnormal increase in the number of fragments in the 1-4 g mass range.

To quantitatively analyze the quantity-mass distribution, the cumulative distribution function was adopted to give the statistical properties of fragments. The Mott distribution model was commonly used to describe the mass distribution of projectile fragments, which is a single parameter model and a special case of Weibull distribution [29]. The latter was a dual parameter model that not only provides fragment characteristic mass parameter, but also describes the uniformity of fragment mass distribution. Thus, Weibull distribution model was used to fit the N(>m) curves [4,9]:

... (1)

where N (>m) is the cumulative number of fragments with a mass greater than or equal to fragment mass (m), M0 is the mass of the shell, G is the gamma function, and m is the scale parameter of the Weibull distribution, denoting the characteristic mass of the fragments, which is positively correlated with the fragment average mass (m).

... (2)

In Eq. (1), Ʌ is a shape parameter that reflects the distribution uniformity of shell fragments. The closer it is to 1, the more uniform the mass distribution of fragments is. When Ʌ = 0.5, the Weibull distribution regresses to the Mott distribution as follow [30]:

... (3)

The fitting results of above six experimental results using Eq. (1) were shown in Fig. 4. It can be seen that the distribution characteristics of fragment quantity-mass distribution can be well described through Weibull distribution. After blasting, the HCSiMn shell can form more small fragments, corresponding to a larger attenuation slope of the cumulative quantity curve within the range of 1-10 g mass. More clearly, the influence of grooving on the fragmentation mass distribution of the 45Cr shell was greater than that of the HCSiMn shell, because the change in the distribution curve of the latter is relatively small.

Fig. 5 illustrated the results of fitted μ and Ʌ. It can be shown that the μ of the HCSiMn shell was lower than that of the 45Cr shell under all groove depths. For instance, the m of natural 45Cr shell (groove depth of 0 mm) was 3.14 g, which was much higher than the 0.57 g for HCSiMn natural shell. The better fragmentation of the HCSiMn shell can be qualitatively understood based on the HallPetch theory [4,31], which means that the higher yield strength of HCSiMn may benefit from smaller grain sizes and thus lead to a significant reduction in μ.

Meanwhile, as the groove depth increases from 0 to 2 mm, μ decreased from 3.14 to 1.21 g for 45Cr shell (a decrease of 61%) and from 0.57 to 0.30 g for HCSiMn shell with a decrease amplitude of 47%, indicating that grooving can further enhance the shell fragmentation, which is more significant for 45Cr steel. Due to the higher plasticity and toughness of the 45Cr steel, the degree of expansion and deformation can be effectively promoted [32], so as to support the macro shell fracture along the groove position. In addition, the material properties had a greater influence on Ʌ than the shell grooving, as it is approximately around 0.65 for the 45Cr shell and around 0.45 for the HCSiMn shell, regardless of the grooves on shell surface. The 45Cr shell demonstrated better plasticity and toughness, resulting in greater uniformity of fragment distribution. Conversely, the HCSiMn shell produced more small fragments upon explosion, leading to a reduction in large fragments and an exacerbation of non-uniform distribution.

3.2. Microscopic fracture mechanisms by analyzing the fracture morphology and metallographic structure

To study the fracture mechanism of the above-mentioned two material shells under detonation of the explosive, the fracture morphology of the recovered fragments was characterized. As shown in Fig. 6, there were typical optical images of fragments after 45Cr shell blasting. From the top view, it can be seen that the fragments mainly exhibit a long strip characteristic with a length of 40-50 mm, and the surface color of fracture is black, confirming the oxidation in air under the high-temperature and high-pressure effect of detonation. From the side and front views, clear sliding shear surfaces were formed after the shell is broken, with an angle of approximately 45° or 135° to the radial direction of the shell. At the same time, a flow-like structure with obvious orientation can be observed on the shear surface, indicating that the dominant fracture mode is shear fracture caused by the expansion of adiabatic shear bands (ASBs) from the inner surface.

For the HCSiMn shell, the typical fragment morphology images were shown in Fig. 7. On the contrary, the size (length of 20-30 mm) and aspect ratio of the formed fragments were smaller than those of the 45Cr shell, which is consistent with the conclusion in subsection 3.1 that the HCSiMn shell has better fragmentation. At the outer surface of shell, obvious crack formation can be observed, which is distributed along the axial direction of the shell, but has not yet extended throughout the entire thickness direction. Furthermore, it was found that the fracture morphology was mostly irregular, and although a few shear slip surfaces were formed by shear force, most of the fractures exhibit brittle fracture characteristics, indicating that the tensile-shear fracture mode dominates the fracture process for HCSiMn shell. From the above, as the plastic toughness of the material increases, the fracture mode of the shell might gradually change from tensile-shear fracture to pure shear fracture, which can also be achieved by different heat treatment processes on the same material [22].

In addition, for both 45Cr and HCSiMn shells, grooving on the outer surface of shell effectively controlled the quality and shape of the fragments, making the typical fragments had regular shape and mass, as shown in Fig. 8. These grooves can be considered as prefabricated weak points on the shell, and detonation tensile waves were preferentially formed and superimposed in the grooves [33], forming large tensile stresses to break the shell. Therefore, the shell was more likely to fracture along the edge of the diamond grooves, which helps to improve shell fragmentation, although it cannot be guaranteed that all fragments are of the same shape and size.

Further observation of the microscopic fracture morphology of the 45Cr shell fragment was carried out using the SEM, as shown in Fig. 9. Firstly, the cracks formed on the outer surface of the shell were usually close to the edge of the shear slip surface (Fig. 9(a)) and propagated axially (Fig. 9(b)), suggesting that the cracks propagate primarily due to the movement of the internal sliding surfaces, eventually resulting in the fracture of shell. Secondly, due to the better plasticity and toughness of the 45Cr shell, the softening and plastic deformation of the shell at high temperatures could promote the formation of adiabatic shear bands at the local inner surface [2], leading to formation of flow-like structure, as characterized in Figs. 9(c) and 9(d). Notably, its alignment was not always consistently in the radial direction, also influenced by the location of the detonation point and shell thickness direction [23].

Different from the cases for 45Cr shell, microcracks damage zone consisting of numerous small axial cracks were observed on the surface of the fragments for HCSiMn shell (Fig. 10(a)). The formation, nucleation, and continuous propagation of the microcracks created the main crack (Fig. 10(b)), which penetrated the shell radially, causing laminar tearing of the surrounding shell in the radially outward direction (Fig. 10(c)). Furthermore, the fracture surface indicated a typical tensile brittle fracture feature, as evidenced by the absence of any apparent plastic deformation flow (Fig. 10(d)). Crack propagation always adhered to the principle of minimizing energy consumption [34], irrespective of the fracture mode. Nonetheless, the higher hardness and brittleness of HCSiMn shell meant that the plastic deformation experienced is inadequate to facilitate the development of adiabatic shear bands. According to the unloading wave theory and Taylor shell fracture criterion [1,5], once a crack appears, the stress at both ends of the crack is released, and microcracks on the outer shell surface gradually propagated inward under the action of circumferential tensile stress. This process eventually caused the stress at the inner surface to unload to zero, ultimately resulting in shell failure. Therefore, the formation and development of microcrack damage zone on outer surface of the HCSiMn shell was crucial for its better fragmentation.

From the microscopic view, the formed microcrack damage zones were closely related to the metallographic structure of the steel. Since the main microfracture mode of the shell at high detonation strain rates is dominated by intergranular fracture [24], cracks propagate and interact mainly along grain boundaries, ultimately leading to the formation of fragments. Therefore, there may be a positive correlation between the microscopic average grain size (d) and the characteristic mass (m) of the macroscopic fragments (d f m) [4], that is, the smaller d, the more grain boundaries there are, the higher the probability of crack intersection and convergence, so more fragments are formed after fracture and the smaller the average fragment mass and m, so it is necessary to pay attention to the differences in grain size and metallographic structure between two materials, which can be observed under a metallographic microscope by adopting the grain boundary corrosion method [4], as shown in Fig. 11.

According to the morphology characteristics and heat treatment process, the metallographic structure of 45Cr steel was corresponded to tempered troostite (Fig. 11(a)), where the ferrite basically maintains the original martensite morphology (bar like), while the precipitation of alloy carbides can be difficult to distinguish. However, after tempering at a higher temperature of 600 °C, the tempered sorbite structure was formed for the HCSiMn steel where ferrite has lost its original bar like morphology characteristics due to the recrystallization process (Fig. 11(b)), and a large number of spherical alloy carbide particles (enlarged SEM image) can be observed on the substrate. The formation of such carbide particle was found to be closely related to the fragment fracture process [23], that is the flow-like plastic characteristics of fracture surface was less obvious with the increasing of the number of spherical carbide particles.

To further demonstrate the influence of microstructure on the macroscopic fragmentation process of the shell, the metallographic characteristics of the cross-section of the recovered fragments were analyzed as shown in Fig. 12. For the 45Cr shell (Fig. 12(a)), the fracture cross-section showed a clear intergranular fracture pattern, indicating that cracks are more likely to propagate along grain boundaries, resulting in a positive correlation between the μ and d. For the HCSiMn shell (Fig. 12(b)), there are obvious microcracks distributed throughout the fracture cross-section and it can be seen from the crack propagation tip that they tend to propagate along the distribution of carbide particles. The schematic diagram in Figs. 12(c) and 12(d) show the fragmentation process of the shell influenced by the steel microstructures. The fragments characteristic mass of 45Cr steel mainly depended on its own grain size (greater than HCSiMn steel) due to the microscopic intergranular fracture. As the fact that HCSiMn steel is a high carbon steel and contains a large amount of alloying elements, its solid solution with the steel or the formation of carbides can inhibit grain growth during the heat treatment process [35], playing a role in refining grains and reducing the characteristic mass of formed fragments after blasting. Meanwhile, the precipitated carbide particles belong to the hard and brittle phase [36], which acts as the weak point of fragmentation under the high strain rate of detonation. Their dispersed distribution in the substrate can play a "pinning" effect, causing fracture microcracks to preferentially generate and expand along the carbide boundary, which is equivalent to further reducing the size of the broken grain and improving the fragility of the shell. In particular, carbide precipitation after high-temperature tempering was also accompanied by martensite decomposition, leading to an increase in steel plasticity and toughness [22], which to some extent compensates for the increase in brittleness caused by carbide precipitation, especially for the same type of steel, and has a more complex effect on fragmentation.

3.3. Quantitative assessment of projectile's comprehensive damage power by using HCSiMn steel

The high-velocity fragments produced by the metallic cylindrical shell were the important damage elements for killing active troops and lightly armored targets. Here, theoretical analysis is combined to quantitatively assess the shell material influence on the comprehensive damage power of the projectile. The power field formed by fragments was reflected in the form of a power data set [37,38], which not only considers the distribution of fragment quantity-mass, but also considers the characteristic parameters of fragment flying velocity. The final fracture velocity of the shell, corresponding to the initial velocity at which fragments are formed, can be predicted using the Gurney formula [13]. It is usually related to the explosive parameters and charge ratio (explosive mass/shell mass), but has weak correlation with the fracture mode [39]. Research has shown that as the yield strength of the shell material increases, the shell fracture time advances and the maximum expansion speed decreases. Therefore, the modified Gurney formula by considering the material strength correction was adopted to describe the initial velocity of fragments (v0) which can be approximately equal to shell maximum expansion speed [40].

... (4)

where the D is the detonation velocity, η is the ratio of explosive mass to shell mass, ε₀ is the strain rate under quasi-static condition and in the Johnson Cook model ε₀ = 1 s^-1, δ is the shell thickness, δ_s is the yield strength, ρ_c is the shell mass density.

It can be calculated that the v_o = 1213 m/s for 45Cr shell after expansion and fracture, while for HCSiMn shell, the v_o = 1177 m/s due to its higher δ_s. The flying process of fragments was affected by air resistance, and their speed decays exponentially with distance (x) as follow [41]:

... (5)

... (6)

where a is the velocity attenuation coefficient, C_D is the aerodynamic drag coefficient, ρ_a is the air density, S is the fragment windward area (S = φm^2/3, φ is the fragment shape coefficient), and m is the fragment characteristic mass.

Based on the fragment morphology in Figs. 6 and 7, considering the influence of an irregular rectangular fragment shape on the C_D and φ (C_D of 1.5, φ of 3.6) and substituting the associated parameters into Eq. (6), it is calculated that α = 0.0176 for the 45Cr fragment, and α = 0.0234 for the HCSiMn fragment. The velocity and mass of the fragment were the key parameters determining its penetration into the target. When attacking personnel targets, the energy standard for fragments to kill the human body can be selected as E = 78.4 J [42]. Based on the kinetic energy formula (0:5mv² = E) and velocity curve, the critical fragment mass for killing personnel targets (m_c1) can be obtained, as shown in Fig. 13(a). When attacking lightly armored vehicle targets which can be equivalent to 12 mm thick Q235 steel plates [43], Huang et al. provided the formula for the ultimate penetration velocity (v_m) under forward penetration conditions as follows [44]:

... (7)

where a and b were experimental fitting parameters, which are 4.62 and 0.71, respectively; h is the thickness of the target plate (12 mm), d is the geometric diameter of the fragment, ρ_t is the target plate density, ρ_c is the shell density, δ_t is the strength limit of the target plate.

By substituting the related parameters and v_x into Eq. (7), the critical fragment diameter can be obtained, and the critical fragment mass for damaging light armored vehicle targets (m_c2) can be further estimated, as shown in Fig. 13(b). Due to the fact that the velocity of HCSiMn fragments is slightly less than that of 45Cr at the same distance, the critical fragment mass for damaging target was essentially greater than that of 45Cr fragments.

Fragments with a mass greater than or equal to the critical fragment mass are effective fragments that can cause damage to the target. To focus mainly on the effect of different μ on the performance of the projectile, we fix Ʌ at 0.5 to regress the Weibull distribution to the well-known Mott distribution. The fitted characteristic mass parameter of μ = 2.02 g for the 45Cr shell, the μ = 0.86 g for the HCSiMn shell, so that effective fragments at different distances can be described by Eq. (3), as shown in Figs. 13(c) and 13(d). It can be seen that within the conventional killing range (<60 m), selecting HCSiMn shell significantly increases the number of fragments that cause effective damage to personnel targets as compared to the 45Cr shell, while the number of fragments that cause damage to light armored vehicles decreases more rapidly with distance than the 45Cr shell.

Furthermore, according to the Shapiro formula [45], the fragment scattering angle can be obtained to be approximately 8.2°. Therefore, after calculating the fragment scattering area, the effective fragment density at different distances can be obtained, as shown in Fig. 14. Taking the characteristic radius with an effective fragment density of 2 piece/m2 as the killing power radius against light armored vehicle targets [42], the killing power radius of the test projectile made by 45Cr shell and HCSiMn shell against light armored vehicle targets were R₁ = 10.85 m and R₁' = 10.21 m, respectively. It can be seen that using the HCSiMn shell with higher hardness and brittleness reduces the killing power of light armored vehicle targets by only about 6%.

The damage probability (P(r)) of fragments to personnel targets is determined by the kinetic energy and quantity of fragments, and is also reflected in the effective fragment density distribution. Using Eq. (8) as the damage law model [43], the P(r) of two types of projectiles at different distances to personnel targets can be obtained (Fig. 15).

P(r) = 1 - e^-ε(r)Sp (8)

where ε(r) is the effective fragment distribution density (Fig. 14), Sp is target vulnerable area, and 0.75 m² is taken for the standing posture of the personnel.

According to the definition of dense killing radius [43]: the probability of damage for the 45Cr and HCSiMn projectiles is 0.492, and the damage radius (i.e. dense killing radius) is R₂ = 24.13 m and R₂ = 30.41 m, respectively. Therefore, the use of the HCSiMn shell effectively enhanced the damage power to personnel targets by about 26%, mainly due to the formation of more dense small fragments after fragmentatio.

It was worth noting that the quantitative assessment of the damage power of the two types of projectiles in this section was mainly based on theoretical calculations, and their respective absolute values still need further correction from experimental results. However, the relative values of results can quantitatively compare the influence of shell materials on the damage power, which is of great scientific significance for designing high fragmentation explosive projectile.

4. Conclusions In this paper, the influence of 45Cr and HCSiMn steel materials on projectile fragmentation was investigated mainly by fragments recovery experiments under static explosive loading. Based on Weibull and Mott theories, the quantity-mass distribution of fragments formed by the two materials and under different groove conditions (h = 0/1/2 mm) was analyzed. By characterizing the fracture morphology and metallographic structure, the microscopic mechanisms of material properties affecting the fracture mode and macroscopic fragmentation were revealed. In addition, the effect of the shell material on the damage performance of the projectile was quantitatively assessed. The results were as follows.

(1) Driven by RDX based aluminum containing explosive, the number of small fragments (<4 g) formed by expansion and fragmentation of the natural shell of HCSiMn is 154% greater than that of the 45Cr shell, and the quantity-mass distribution characteristics can be accurately described by Weibull theory: The better fragmentation of HCSiMn steel shell was reflected in its smaller μ of 0.57 g, which also aggravates the distribution uniformity of fragments as smaller Ʌ of 0.45. The grooves on the outer surface can further increase the fragmentation and reduce μ, while the effect of the grooves on Ʌ was not significant.

(2) The expansion fracture of the 45Cr shell was dominated by the shear fracture process, and the adiabatic shear from the inner surface induced the formation of a slip surface at an angle of 45° to the radial direction of the shell; the expansion fracture of the HCSiMn shell exhibited more brittle tensile fracture characteristics, and its high fragmentation under detonation is closely related to the formation of microcrack damage zones on the outer surface of the shell. Microscopically, the shell expansion and fracture process are affected by the metallographic structure: the tempered troostite structure of 45Cr basically retains the martensitic morphology of the original larger grain size (d). The intergranular fracture at high strain rates affected the fracture process of the steel shell, so that μ is positively correlated with d; Whereas HCSiMn is a high-carbon and high-alloy steel, the tempered sorbite structure after heat treatment has finer grains, which is beneficial for reducing μ. At the same time, the numerous dispersed spherical alloy carbide particles in the steel substrate can exert a "pinning" effect on the grains, making it easier for cracks to nucleate and propagate along the particle boundary, further improving shell fragmentation.

(3) By taking into account the influence of projectile material properties on fragment velocity, quantity and mass distribution, the effective fragment density distribution causing damage to personnel and light armored vehicle targets can be determined by theoretical calculations. The HCSiMn material projectile has a higher fragmentation, which can increase the dense killing radius of personnel targets by about 26%, while the killing radius of light armored vehicles is only slightly reduced by 6%. This result has important technical application prospects for the development of high fragmentation warheads.

CRediT authorship contribution statement

Kang Wang: Conceptualization, Investigation, Data curation, Writing e original draft. Peng Chen: Project administration, Supervision, Writing e review & editing. Xingyun Sun: Validation, Writing e review & editing. Yufeng Liu: Methodology, Supervision. Jiayu Meng: Data curation, Writing e review & editing. Xiaoyuan Li: Visualization, Writing e review & editing. Xiongwei Zheng: Data curation, Writing e review & editing. Chuan Xiao: Project administration, Supervision, Writing e 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.

Acknowledgments

This work was funded by the National Natural Science Foundation of China (Grant Nos. 12302444 and 12202349).

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ARTICLE INFO

Article history:

Received 7 December 2023

Received in revised form 22 January 2024

Accepted 22 February 2024

Available online 28 February 2024

Peer review under responsibility of China Ordnance Society

Footnote

** Corresponding author.

** Corresponding author.

E-;mail addresses: [email protected] (P. Chen), [email protected] (C. Xiao).

References

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