Experimental and numerical studies of fragmentation shells filled with advanced HMX-plastic explosive compared to various explosive charges

The wide usage of TNT as a main charge for fragmentation shells has been eliminated due to its lower performance and exudation on the fuze thread and relevant safety measures inconvenience. These disadvantages have not become accepted anymore due to the desired safety requirements and the limited efficiency of the TNT, especially when different new explosives are introduced into researches. This research studies the fragmentation calculations of the 120 mm high explosive shell when its is loaded with different explosives rather than TNT. Different explosives have been used in the current research include the melt cast compositions such as Octol and composition B, a cast cured composition based on RDX with HTPB polymer matrix and the plastic explosive composition HMX-silicone. The fingerprint of the fragmentation pattern of each shell loaded with different explosive has been obtained using Autodyn smooth particle hydrodynamic (SPH) algorithm, whose numerical model has been validated with previous measurements using TNT explosive. Based on obtained numerical estimates, the HMX-silicone explosive has been proposed to replace the traditional TNT explosive material. This explosive has been then manufactured and casted into the studied 120 mm shell, where the experimental field pit test was established to collect, separate and analyse the resultant fragments. Current calculations and experimental results showed that the shell loaded by composition HMX-silicone produced the highest fragmentation velocities (i.e. 1.5 times that of TNT) and the largest number of fragments (i.e. 2.7 times that of TNT) with lower masses, which will be recommended for our next production stages instead of the traditional TNT.


Introduction
The dual effect of the mortar 120 mm high explosive (HE) round includes both the massive fragments distribution and the blast load evolved from the detonation of the main explosive charge in the bomblet containing about 2.25 kg TNT (Elshenawy et al. 2019). When the volume of the expanded casing of the fragmented warhead exceeds 3.24 times that of the initial mortar volume, casing cracks begin to propagate causing the fracture of the fragmented body, which expands forming clouds of various sized fragments (Meyers 1994;Zecevic et al. 2004).
Several studies and researches have been conducted on the fragmentation pattern of this ammunition to assess the fragments number, mass and their initial velocities (Kong et al. 2013). Zhao et al. (2020) studied the fragmentation of steel projectile using underwater setup test to conclude the mass distribution of the produced fragments. Zecevic et al. (2011) concluded the variation of the fragments' mass and their distribution for different years of the bomblet body production. The preliminary design analysis of the mortar ammunition is very crucial because it saves the cost of field testings' that are necessary to evaluate such design.
The mortar bomblet in general can produce large number of random various sized fragments and masses based on initial warhead design and type of the used masses of explosives and casing materials (Elshenawy et al. 2019). Catovic and Kljuno (2021) applied a new model to estimate the lethal area of artillery projectiles filled by HEs. The mass distribution of fragments obtained from the detonation of 1 3 different shells loaded with cast cured composition based on HMX was studied by Arnold and Rottenkolber (2008).
Limited numbers of researches in literature have discussed the effect of the explosive types on the fragmentation pattern. Murphy et al. (1997) have briefly summarized the effect of explosive type on the two shaped charges loaded with Comp. A5 and LX-19 explosives. Minor difference of 2% related to the penetration depth was concluded, whereas significant variation within fragmentation analysis have been found when these two explosives were tested experimentally. Dunnin et al. (2005) studied the effect of using three different thermobaric explosive charges instead of composition C4 baseline charge and the relevant accompanied fragmentation pattern. Experimental test results showed that thermobaric charges exhibited no observed difference in both fragments mass and their relevant velocities because the secondary burning reaction of magnesium or aluminium with atmospheric oxygen was found to begin after the fragments have been accelerated and become out of range of effect. Chen et al. (2014) have implemented the powerful explosive JO8 based on (HMX/Binder, 95/5 wt%) during the study of the effect of shell thickness of the produced fragment velocity and relevant masses. They found that using lower metal to explosive mass ratio results in faster fragments, lower mass and large number of fragments and vice versa.
TNT and composition B (mixture of RDX and TNT) are the most usable explosives for filling the fragmentation warheads due to the cast-ability of these explosives (Mishra et al. 2017). In addition, composition B has several applications and mostly used as more powerful explosive than TNT (Becuwe and Delclos 1993). The sensitivity and explosive properties of several explosives were compared with the traditional TNT (Elbeih and Zeman 2014). Dinitroanisole (DNAN) and 3-nitro-1,2,4-triazol-5-one (NTO) have been studied as a melt cast explosive to replace TNT in several applications (Trzciński et al. 2014;Hussein et al. 2021Hussein et al. , 2017. High performance melt cast composition named Octol (HMX-TNT composition) were studied in literature . Several low sensitive explosives were tested and compared with TNT compositions (Abd-Elghany et al. 2017Elbeih et al. 2017). The explosive properties of cast cured compositions based on RDX and its performance as explosive filler for shaped charges were also investigated (Elshenawy et al. 2016Elbeih et al. 2018). On the other side, the efficiency and characteristics of plastic explosives for civilian and military applications were investigated in several researches (Jitea et al. 2019).
Applications of different explosives types for filling mortar projectiles instead of TNT especially plastic explosives are not available in literature. In the current research work, the 120 mm HE mortar projectile, which has a total mass of 12.6 kg, of which the TNT explosive load 2.25 kg (Zecevic et al. 2011), is loaded with different explosive charges instead of TNT. The studied explosives are Octol (75 wt% HMX and 25% TNT), Composition B (comp. B), and cast cured composition based on RDX bonded by HTPB polymer matrix in addition to advance HMX-plastic explosive based on silicone matrix. The explosive performance in this mortar ammunition is based on the fragment mass and its velocity as well as the total number of produced fragments. Assessment of these output data is performed using extensive Autodyn hydrodynamic SPH algorithm for this fragmentation bomblet, whereas the blast wave generated from these explosives will not be studied in the current paper.

Fragmentation analysis
Unlike traditional shaped charge, the 120 mm mortar canister/projectile has a thick wall confinement in order to produce massive fragments in order to achieve large penetration depth into different shelters and fortifications due to high kinetic energy of these fragments and also to achieve human causalities. The material that is used in the fabrication of the 120 mm mortar body is Steel 9189VP (JAS) (Zecevic et al. 2011).
Held (Carleone 1993) has conducted an experimental approach to represent the fragments mass distribution-their number according to: where M(n)-mass of fragments of number of fragments greater than n, M o is the total mass of fragments, B and λexperimental constants, which are specific for every explosive charge loading. In order to determine the values of B and λ, it is feasible to take a logarithm of Eq. (1) so that using a logarithmic scale, the point of intersection n = 1, or log n = 0, will give constant B directly on the ordinate axis, whereas the exponent λ will be determined directly from the slope of straight line: The fragment velocity; V f for each slice can be estimated according to a generalized Gurney formula (Dynamics et al. 1990): where,

√
2E is the Gurney constant of the used explosive, M is the mass of the steel casing layer within a certain slice, C is the mass of the explosive layer within the slice, r is the efficiency factor due to rarefaction waves from the sides (0 < r < 1), d is the efficiency factor due to detonation mach stem effects (d ≥ 1), and g is the efficiency factor due to the gas leakage when casing breaks up (0 < g ≤ 1). The Gurney constant ( √ 2E ) can be approximately estimated by √ 2E = 0.338D , where D is the detonation velocity (Keshavarz and Semnani 2006). The initial fragment velocity is much affected by the traveling distance due to the air resistance, which accounts for the velocity decrease or the fragment retardation velocity (Dynamics et al. 1990): where m is the fragment mass, c w is the dimensionless drag coefficient depending on the fragment type, ρ is the density of the air, A is the average presented fragment area.

Hydrocode autodyn modeling
A numerical hydrocode is a computer program that uses a combination of finite difference and continuum mechanics to solve dynamic problems that occur in a very short time scale (Century Dynamics 2003). AUTODYN hydrocode is based on momentum, mass, and energy conservation equations, where the material can be defined by its strength model (A. Team 1997) and its equation of state (EOS).
In the current research, the AUTODYN hydrocode is used to further investigate the bomblet fragmentation pattern and distribution. The fragmentation calculations in Autodyn are performed using SPH (Smooth particle hydrodynamics) solver, or meshless free solver.

SPH fragmentation simulation
Unlike standard mesh based techniques such as Euler and Lagrange, Smooth particle hydrodynamics (SPH) has proved efficiency when dealing with fragmentation phenomena. It has some advantages such as avoiding problems associated with the traditional Lagrangian technique such as mesh tangling and overlapping at large deformations. Besides, it exhibits fast, accurate and efficient model for different materials exhibiting fragmentation. In SPH solver, the differential equations uses interpolation functions to give a "Kernel estimate" of the field variables at each interpolation point by evaluating the integrals as sums over the neighboring interpolation points known as SPH nodes (Fairlie et al. 1998).
Using this technique, the Bomblet fragmentation model has been established for 120 mm HE projectile including explosive charge, steel casing and detonation algorithm logic is also assigned for the explosive charge load. The Lagrangian solver is selected for the explosive charge and fuze material, while the SPH model is chosen for the steel casing to calculate the fragmentation mass distribution. The chosen particle size for the charge casing is 1 mm. Smaller SPH sizes lower than 1 mm have been tried and found to have a very low time-step calculation cycles lower than 10-7 ms and therefore consumes extraordinary CPU calculation time with divergent solution. Fragmentation HTML file is obtained when the SPH cycles are finished. The HTML file is used for fragmentation analysis for the studied projectile.

Materials modeling
The bomblet body fragment's material was modeled as steel 1006 with shock EOS and Johnson-Cook strength model. It was found that the shock Hugoniot values of shock velocity (U) and the material velocity behind the shock (u p ) can be fitted to a straight line (A. Team 1997): where C o is the sound speed in the material, and s is a constant giving the slope of shock velocity-particle velocity relationship. This equation is valid up to twice the initial sound speed C o and shock pressures as much as 100 GPa (A. Team 1997). The Mie-Gruneisen EOS based on the shock Hugoniot is expressed as: where Γ is the Gruneisen Gamma coefficient and equals to B o ∕(1 + ) , where B o is a constant, Γρ = Γ o ρ o = constant is assumed, and ρ is the density. p H and e H are the Hugoniot pressure and energy, respectively, given by: where μ = (ρ/ρo) − 1 is the compressibility. The relevant mechanical properties of these materials are obtained from Autodyn library and listed in Table 2.
The Johnson cook constitutive model is suitable for modeling materials subjected to large strains, high strain-rates at high temperatures. This model defines the dynamic yield stress Y (Johnson and Cook 1983) as: where A is the yield strength, B is the hardening constant, εp is the effective plastic strain, n is the hardening exponent, C is the strain-rate constant and m is the thermal exponent constant, ̇ * p is the normalized effective plastic strain-rate, and T melt is the melting temperature and T H is the homologous temperature, that can be calculated by Johnson and Cook (1983): The constants in these expressions were determined by means of material tests over a wide range of temperatures and strain-rates. The values of these constants in Eq. (9) for the case material are listed in Table 1.
The equation of state (EOS) for the used HE is "Jones Wilkins Lee" (JWL) equation (Baudin and Serradeill 2010), i.e. (10) where p is the pressure, v is the relative volume (1/ρ), A, B, r 1 , r 2 and ω are constants. E is the specific internal energy per unit mass. The values of these constants for the explosive materials have been determined either from dynamic test experiments or the cylinder expansion test (Lee et al. 1968;Tarver et al. 1996). Jafari et al. have presented different improved methods to determine the detonation performance of ideal and non-ideal explosive compositions (Jafari et al. 2021;Jafari and Keshavarz 2017;Keshavarz et al. 2020). In this study, the values of the above mentioned constants are available in the Autodyn material library of and listed in Table 2 for the studied explosive materials.

Mesh sensitivity analysis
There is no doubt that the shape and the mesh density of the numerical model have significant effect on the numerical calculations' results. Generally, simulations with fine meshes are required to guarantee more accurate solution in spite of having longer time duration when compared to coarse meshing models. When the SPH particle size is considered within the mesh sensitivity study, its relevant impact on the simulation results may become significant. In order to investigate the mesh sensitivity during the numerical fragment analysis, different five mesh densities were suggested for the SPH casing material, while both the Lagrangian explosive and fuze's meshes remain unchanged. Uniform SPH packing particle sizes of 1, 2, 3, 4 and 5 are selected for casing material. On the other hand, the time consumption for each numerical simulation is recorded until the entire steel casing is fragmented and the steel fragments acquire their stable flight speed. Figure 1 shows subsequent  8.16 × 10 6 8.34 × 10 6 9.74 × 10 6 9.87 × 10 6 1.00 × 10 7 C-J pressure (kPa) (Elbeih et al. 2013) 19.5 × 10 6 2.01 × 10 7 2.95 × 10 7 27.8 × 10 6 2.74 × 10 7 detonation stages at different times from the moment of detonation. Figure 2 shows the five different casings with different meshes with the relevant consumed time; whereas Fig. 3 shows the fragment velocity profile along the bomblet height using different mesh sizes. It can be observed that the velocity curves of the different studied five mesh sizes have identical shape at the beginning and at the end, whereas the difference among the five SPH particle sizes become significant at the middle of casing height. Figure 3 shows a convergent behaviour of the fragment velocity towards the finest SPH of packing size 1. We could not do any further numerical model with SPH particle size smaller than 1 because it generates extraordinary very small time-step as small as 10 -9 ns, which gives unsteady divergent solution, which lasts very long time duration without reaching a reasonable fragment velocity. The time consumption for each numerical model listed below Fig. 2 shows the cost of the fine SPH particle size from time consumption point of view. The SPH particle size of 1 takes about more than twice that of the SPH particle size of 2. On the other hand, the coarse SPH particle size of 5 having total number of nodes of 2764 takes only three hours calculations but the maximum deviation in the calculated produced fragment velocity is 381 m/s, which means 30% increase in the fragment velocity compared to the SPH particle size of 1. This is unacceptable result especially when the fragment speed is considered for comparison between the studied explosives. Generally, the SPH particle size of 1 having 358,321 total nodes of the steel casing with total time consumption of 95 h is selected Fig. 1 Sample of the SPH fragmentation at different times from the detonation moment Fig. 2 The five different SPH packing sizes for fragmentation casings with the relevant consumed time for mesh sensitivity analysis and applied to all numerical fragmentation analysis because of its accepted accuracy and affordable time consumption.

Preparation of HMX-silicone filling charge
Advanced plastic explosive based on HMX-silicone has been prepared, in which HMX is a product of Eurenco Company, France. It has two different mean particle sizes (250 µm and 32 µm). Silicone matrix (silicone-binder) was used to incorporate the explosive crystals and prepare a plastic explosive. Silicone polymer (Wacker AK40000) was used in this study. A vacuum vertical mixer was used to prepare the plastic explosive. A mixture of the two grades of HMX (2:1 ratio of 250 and 32 µm respectively) was mixed with the silicone matrix in the mixer for one hour at temperature 40 °C. The prepared HMX-silicone plastic explosive contains 91wt% of HMX and 9wt% of silicone matrix. The obtained HMXsilicone was fabricated as cylinders of 22 mm diameter using extruder.

Measurement of HMX-silicone detonation velocity
EXPLOMET-FO-2000 multichannel test apparatus obtained from KONTINITRO AG was used to measure the detonation velocity of the HMX-silicone explosive. The explosive charge was fabricated as cylinders with length of 250 mm and diameter of 22 mm. Two optical fibre optics have been inserted in the charges with 150 mm distance between them with 50 mm distance from the two ends of the charge as shown in Fig. 4. Plain detonator was used to initiate the charge without boaster. Three samples were tested to obtain good precision with maximum difference 69 m/s. The obtained detonation velocity was listed in Table 2.

Sensitivities measurements
The sensitivity of HMX-silicone in comparison with the other explosives against impact and friction stimuli were measured using BAM impact sensitivity instrument (Suceska 1995) via dropping 2 and 5 kg weight hammers and BAM friction test apparatus using the Probit analysis (Finney 1971). The results of these tests are reported in Table 3.

Experimental fragmentation pit test
In order to static fire the bomblet fragmentation body, the steel bomb body was prepared for fragmentation testing. The steel body was filled manually with 2.6 kg of the plastic explosive HMX-silicone.
The filled steel body was inserted into sand filled steel canister of thickness 2 mm, whereas the second layer is compacted Alumina powder of 2 m radius surrounding the central steel canister. The purpose of these layers is to soft recover the steel fragments generated from the explosion process. The explosive charge is detonated using an electric detonator located in the upper side of the bomblet in the place of the fuze as shown in Fig. 5. After the detonation of the charge, the sand and alumina are sieved to separate and

Autodyn fragmentation validation
To validate the used Autodyn SPH calculation algorithm for the fragmentation calculations, a complete setup of the 120 mm bomblet has been constructed suing SPH of size 1 mm. after chemical reaction of TNT explosive materials, post processing analysis output file is obtained. This output HTML file contains the entire fragmentation analysis containing masses, velocities and dimensions of the generated fragments. Figure 6 shows the subsequent detonation stages of the bomblet showing the expansion and crack propagation of the generation of the body fragments at different times from the start time of the bomblet detonation. Figure 7 shows the relation between fragment number and relevant mass in comparison to Held's calculation obtained from Zecevic et al. (2011). The first part of Fig. 7 shows an identical behaviors between the SPH calculations and both estimations based on the Held's analysis and the experimental testing, but on the other hand there is a little shift between discussed results when the mass of fragments fall below 8 g, which showed lower number of fragments using SPH in comparing with experimental and previous calculations. The extensive data of the TNT fragmentation calculations have been assembled and used in further analysis for the determination of the constant B and λ average according to Eq. (2). Figure 8 shows a linear relation between the logarithmic masses and cumulative fragment numbers. The best fit  interpolation shows a quite accurate linear relation of an error less than 0.1% especially when the very small masses of fragments lower than 1 g were neglected. The values of the constants B and λ were approximated and found to be

Fragmentation patterns calculations for different explosives
The same steps used for TNT bomblet were followed with the entire explosives for the calculated fragmentation analysis using the same number of SPH elements used globally. The different characteristic Gurney velocity for each explosive gives different fragment velocity, whereas the explosive internal energy for the studied eight explosives showed a big variation in the fragment numbers. Figure 9 shows the dependence of the average maximum fragment velocity of the studied explosives on its detonation velocity. TNT, which has the lowest detonation velocity, exhibited the lowest fragment velocity, whereas the powerful HMXsilicone showed the maximum fragment velocity exceeding 1920 m/s with corresponding decrease in the fragment mass. The fragments obtained from the HMX-silicone explosive was found to be 2.71 times that of the baseline TNT explosive material. Table 4 lists the relative number of fragments and the relevant maximum fragment velocity for the selected explosives with respect to TNT baseline explosive. Figure 10 shows the relation between fragment velocity and the characteristic ρ o D 2 for the different explosives. Velocity of the resultant fragments confirm the fact of different energy explosives, exhibits different velocities and therefore different injury criteria for the selected explosives are expected. Figure 11 presents clearly the graduation of the fragment velocity along the bomblet axis from the nose to its rear. Offset lines means scaled velocity at different places from the bomblet fuze due to the variation in the explosive/ metal mass ratios.

Sensitivities results
The combination between impact and friction sensitivities of the used explosive charges are presented in Fig. 12. Comp B and Octol have very close w.r.t. impact and friction sensitivities. This result is logic as the two compositions are based on TNT and both the pure RDX and HMX have close results of sensitivities. Comp B and Octol correlate with the pure TNT as shown in Fig. 11. Also the cast cured PBX Fig. 9 The relation between detonation velocity and average maximum fragment velocity Table 4 The constants λ and β, the relative number of fragments and the maximum fragment velocity for the studied explosives * The relative number of fragments is calculated with respect to the baseline TNT explosive material  (RDX-HTPB) has lower impact and friction sensitivities than the melt cast explosives (comp B and Octol) and correlate with them. It is obvious that the HTPB polymer matrix decreased the sensitivity of RDX to a range lower than the melt cast explosives. The advanced plastic explosive HMXsilicone has friction sensitivity in the same range of both Comp B and Octol; while it has lower impact sensitivity. It is clear that the silicone polymer significantly decreased the impact sensitivity of HMX. HMX-silicone has impact sensitivity lower than all the studied compositions except the pure TNT, while its friction sensitivity is in the same range of the melt cast explosive compositions. These results encouraged our research team to suggest the HMX-silicone as a filling explosive for the steel bomb fragmentation body.

The pit test result
After the bomblet charge containing HMX-silicone explosive has been detonated inside the sand and alumina confinements, the sand and alumina have been collected and sieved in order to retireve the generated fragments, which will be used for further fragment analysis. The generated fragments were then assembled, categorized, separated, counted and weighted according to their masses. The total recovered mass was found to be 72% of the initial mass. This ratio is comparable to those obtained by Koch and Estermann (2004), which did not exceed 75% of the total initial mass or 88% as per Abdallah (2012). The reason behind losing about 28% of the recovered mass is that the separation of fragments have been performed manually by sieving without electro-magenet technology, which may have significant effect on the recovered percentage and fragment loss due to expected human error. Briefly, a very large number of tiny fragments below 1 g have been observed but neglected. On the other hand, fragment masses above 300 g were collecetd and abondant during the fragment estimation analysis. A sample of the recovered fragments is shown in Fig. 13; whereas the numerical fragmentation pattern of the HMX-silicone explosive calculated using SPH algorithm with the experimental recovered fragments' mass and number are shown together in Fig. 14. Unfortunately, the collected fragments' groups are limited to few groups shown clearly in Fig. 14 for the purpose of illustration and proof of the conceptual design acceptance. Besides, the absence of the flash X-ray system is compensated with the validated SPH numerical model, which shows feasibility of the proposed new explosive charge filler (HMX-silicone) instead of the traditional TNT.

Conclusions
Theoretical study including numerical calculations have been carried out using Autodyn SPH algorithm for 120 mm shell loaded with various explosives. The selected model was first validated and verified using previous field testing and analysis for similar shell filled with TNT explosive. Various patterns of normal fragmentation distributions were obtained when different explosives were tested numerically, through which HMX-silicone was chosen for its higher efficiency and accepted reasonable sensitivity. This sensitivity results proved that the advanced plastic explosive (HMX-silicone) has impact sensitivity lower than all the studied compositions except the pure TNT, while its friction sensitivity is in the same range of the melt cast explosive compositions. In addition, it was found that the proposed HMX-silicone explosive charge has a significant effect on the resultant normal fragment pattern including fragment number, its mass and velocity. The plastic explosive HMX-silicone was found to produce the largest number of fragments (i.e. 2.7 times fragment number of the TNT) with the smallest masses and the largest average fragment speed (i.e. 1.5 times that of the TNT). As a result, the research team suggests this powerful explosive to replace the traditional TNT due to its higher performance and reasonable accepted sensitivity.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Conflict of 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.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.