A new formulation for predicting the perforation of ballistic impacts in concrete

Uma nova formulação para previsão da perfuração de impactos balísticos em concreto

Abstract

This work presents a model for determining the depth of projectile perforation based on the RBL formula for ballistic impact, validated with microconcrete specimens made with Portland cement and coarse aggregate of granite and basalt. The model was validated with 7.62 x 51 mm FMJ (Full Metal Jacketed) ammunition on specimens with 5 cm of diameter and a height variation of 5.00 - 10.00 cm The transformation of kinetic energy into heat was found to be one of the forms of energy release. Experimental results showed that the calculation model proposed here predicts penetration depth values closer to the experimental values than current models, which is favorable for the safety.

Keywords:
concrete constitutive model; Ballistic impact; Microconcrete

Resumo

Este trabalho apresenta um modelo para determinar a profundidade da penetração de um projetil baseado sobre a formula RBL para impactos balísticos, validados com corpos de prova de microconcreto feito em cimento Portland, agregados de granitos grossos e basalto. O modelo foi validado com munição FMJ (revestido totalmente de metal) de 7,62 x 51 mm sobre corpos de prova de 5 cm de diâmetro e alturas variando entre 5 a 10 cm. Foi possível determinar que uma das formas de liberação de energia ocorreu a través da energia cinética em calor. Os resultados experimentais mostram que o modelo calculado aqui predisse valores de profundidade de penetração mais próximos aos valores experimentais usados nos modelos atuais, das quais são favoráveis para a segurança.

Palavras-chave:
Modelo constitutive de concreto; Impacto balístico; Microconcreto

Introduction

Concrete is widely used in civil construction, with many applications that utilize its inherent qualities. Its use as a ballistic protection material is valid, as it has been used by military and civil engineers for many years in the construction of protective structures, such as bunkers, wooded houses and lockers in order to resist impacts of explosives. Several studies have demonstrated the effectiveness of concrete in this application, with good results as reported in many studies (Chen et al., 2023; Gao; Kong; Fang, 2023; Xin et al., 2023; Sun et al. 2021; Rajput; Iqbal; Gupta, 2018; Tu; Lu, 2010; Li et al., 2005; Teng et al., 2005). However, the mechanical forces of penetration and perforation of concrete are more complex than in metals, due to its distinct behavior under compressive and tensile forces. Therefore, the study of concrete as a ballistic protection material must consider these complex forces during impact (Rajput; Iqbal, 2017; Abdel-Kader; Fouda, 2014; Wu; Chen; Zhang, 2015). Besides, many studies also describe the complex interplay of factors involved in the reactions of concrete to impact, such as the combination of inertia effects, material loading speed, and the form of energy propagation.

Concrete is a composite material, composed of a variety of heterogeneous materials. When subjected to dynamic loads, it undergoes catastrophic fracture, with multiple fragmentation and pulverization. The process starts with the initial elastic response of the material, followed by plastic flow, micro- and macro-crack formation, fragmentation, and finally rupture (Grote; Park; Zhou, 2001).

Zielinski and Reinhardt (1982) found that the uniaxial-generated tensile impact strength of microconcrete and common concrete is greater than that of mortar. This can be explained by the interruption of cracks by coarse aggregate particles, which are harder and denser than the matrix. The crack interruption increases the amount of energy absorbed in the fracture process. Ozbek et al. (2013) observed that cracks in concrete form parallel to the loading axis, followed by shear cones below the aggregates. They also observed that the fracture does not only occur in the cement paste, but also propagates through the aggregates. Micallef et al. (2014) and Du, Jin and Ma (2014) found that shear mechanisms generally govern the behavior of reinforced concrete structures subjected to localized impact loads. Garcia-Avila, Porta Nova and Rabiei (2014) described how the impact face material can decelerate, degrade, and erode the projectile.

Polanco-Loria et al. (2008) reported that modeling and formulations can be used to describe the effect of loading on concrete by projectiles. Li et al. (2005) reviewed a number of formulations that have been used to try to understand the effect of projectiles impact, with the goal of predicting damage and perforation depth.

The continuous improvement of weapons and projectiles has required the constant development of materials and protective structures for the protection of human life, as shown in the studies by Andraskar, Tiwari and Goel (2022) and Wu et al. (2020).

Firearms that were once used for hunting and warfare are now commonly used by criminals and terrorists. This has led to a need for improved protection for civilians, including their homes, buildings, and guardhouses. Several authors have studied the use of large-caliber weapons, such as the 7.62 x 51 mm, in attacks against these structures (Iqbal et al., 2023; Dresch et al., 2021; Choudhary et al., 2020; Chao et al., 2019; Polla et al., 2019).

For that reason, in this study is propose and evaluate a new model of the United States Army Corps of Arms (ACA) formulation for microconcrete with impacts of 7.62 mm projectiles on concrete specimens confined with basalt or granite as aggregate, and assesses its interferences.

Proposed analytical structural model

The adapted formula (Equation 1) from the Ballistics Research Laboratory (LRB) of the ACA, cited by Li et al. (2005), is the most widely used security prediction model:

$\frac{x}{d}=\frac{1.33\times 10^{-3}}{\sqrt{f_c}}\left(\frac{M}{d^3}\right)d^{0.2}{V}_0^{1.33}$ Eq. 1

Several authors have used this formula as a basis for their models (Wu; Chen; Zhang, 2015; Ben-Dor; Dubinsky; Elperinet, 2009; Vossoughi et al., 2007).

The kinetic energy of a 7.62 mm rifle shot is almost constant, as its mass is the same in all shots and the speed will be between 800 to 850 m/s. This energy (E) directly influences the projectile's penetration. In the modification proposed in the present study, the initial kinetic energy (E) is introduced into the square root of Equation 1 and divided by the material strength.

This hypothesis is plausible because material strength is inversely proportional to penetration, and material strength (f) and impact energy (E) are associated factors.

This formulation raises the velocity variation (V₀) to 1.33 instead of squaring it (2). This reduces the direct influence of the velocity factor, thus emphasizing the initial energy term (E). This also considers the pressure loss on impact to the medium that is not absorbed in the bulkhead system. In this new proposal, the term √fc in Equation 1 is replaced by √E/f_c.

The numerical factor of Equation 1 (1.33 x 10^-3) was altered by incorporating the minimum thickness of scabbing displacement, where hs/d = 2x/d.

Therefore, the final protection value of the plate against scattering or subsequent detachment of fragments from the face opposite to the trip can be predicted without the need for a second calculation.

The effective perforation will be e/d = 1.3x/d.

The new factor will be incorporated into the final value of the formula, which will be determine the minimum thickness of the plate required to stop the projectile without the displacement.

The factor contained in the proposed new formula is the result of multiplying the existing constants from previous modifications (2 x 1.3 = 2.6).

Taking into account an initial factor with a safety range of 15% to cover the resistance variation of the same slab of the same material due to the heterogeneities of the concrete, we have 2.6 x 1.15 = 2.99. Therefore, the final constant is suggested to be 3.0.

Equation 2 presents the proposed modeling, called "Vicente Lima":

$\frac{x}{d}=\frac{3.00\times 10^{-2}}{\sqrt{E/f_c}}\left(\frac{M}{d^3}\right)d^{0.2}{V}_0^{1.33}$ Eq. 2

Experimental procedures

Experimental tests were conducted to characterize the material under study and validate the Vicente Lima model in real-world settings.

Compression test

Concrete based on Portland cement composite with the addition of granulated blast furnace slag (CPII-E-40 RS), manufactured by MIZU SA, was dosed with proportions of gravel of zero grade (granite or basalt) for production of specimens for the tests. The volume of gravel was kept constant as a reference, and the same washed sand, commercialized in the region, from the Guandu River (Rio de Janeiro - RJ - Brazil), was used for all samples (Figure 1).

The specimens were molded with dimensions of ( 5 cm of diameter and height of 5 cm for the preliminary ballistic impact tests (two specimens), as shown by RAJPUT et al. (2018), and ( 5 cm of diameter and height of 10 cm for the ballistic impact resistance tests (two copies) and compressive strength (three copies), as suggested by Rajput and Iqbal (2017), see Figure 2. Micro-concrete was used to prevent the wall effect from occurring during molding due to the low ratio of mold size to maximum aggregate dimension.

The compressive strength test on specimens of ( 5 cm x 10 cm were conducted in accordance with the recommendations of NBR 5739 (ABNT, 2018). The results are presented in Table 1.

Gabet, Malécot and Daudeville (2008) worked with fine aggregate concretes with a maximum aggregate diameter of 8 mm, and achieved results close to 30 MPa. This demonstrates that the type of aggregate influences the strength of concrete, as also shown by other studies (Gao et al., 2020; Kazemian; Rooholamini; Hassani, 2019; Werner; Thienel; Kustermann, 2013; Pacheco-Torgal et al., 2007; Donza; Cabrera; Irassar, 2002).

Ballistic impact

Ballistics tests were conducted at the Army Assessment Center - CAEx (Rio de Janeiro - RJ - Brazil), in the Test Line for Small Arms - Line IV, with 7.62 x 51 FMJ (Full Metallic Jacket) projectiles with a mass of 9.8 g and a shooting stand, according to the experimental setup shown in Figure 3. The shielding system's protection level against ballistic impact, according to NBR 15000 (ABNT, 2020), is presented in Table 2.

Figure 1 -
Coarse aggregate, gravel grade 0# (zero) (a) Granite and (b) Basalt

Figure 2 -
(A) Molds used; (B) Cylindrical specimens ((5 cm x 5 cm) and ((5 cm x 10 cm); e (C) Specimens in wet curing in drinking water for 28 days

Table 1 -
Compressive strength test specimens in Ø5 x 10cm

Compressive strength test (MPa) 28 days
Specimens	Aggregate
	Granite	Basalt
	19.86	36.87
	35.60	35.24
	25.46	37.89
Average	26.98	36.67
Standart deviation	7.98	1.34

Figure 3 -
Stand, side view (Line IV-CAEx)

Table 2 -
Ammunition used in ballistics tests: level and type

Level	Ammunition	Mass of the Projectile (g)	V0 (m/s)	Impact Energy (J)
III	7.62 x 51FMJ (.308 - Winchester)	9.8 ± 0.1	838 ± 15	3.406

• Source: NBR 15000 (ABNT, 2020).
• Note: FMJ - Full Metal Jacketed.

The confinement and anchoring system for the specimens was created using the cylindrical specimen molding forms. These consist of a cylindrical body cut along its generatrix, with a thread at the lower end. To resist the expansion effort of the concrete, the cylindrical body has a steel clamp with a nut and lock nut welded to it, which is closed by a steel T-bolt. Two of these pieces were joined together by a steel sleeve, with the addition of a 1 mm thick aluminum sheet at the front end (Figure 4).

A device with a height of 20 cm and an internal diameter of 5 cm was used for specimens (CP) with two different heights, 5 and 10 cm. The device is similar to that used by Zhang et al. (2019), and square plates with a side of 5 cm have also been used in the literature (Fabris et al., 2020). The specimens were confined in the molds themselves to better understand the reaction of the materials to the impact of the projectile and its shock wave.

The PCs were anchored to the ballistic test fixture, which had a metal plate with good resistance to perforation as the bottom shield (see Figure 5). Test results are shown in Table 3 and 4.

Although all (5 x 5 cm CPs failed to retain the projectile, the anchoring mechanism of the system was found to be valid. In the reference plate, it was observed that concrete strength did not influence the result due to the low thickness of the CP. However, the type of aggregate, with different grain formats, helped to minimize the damage caused to the plate.

Granite has a more rounded shape with a rougher surface, while basalt has a lamellar shape with a smoother surface. This difference in grain shape was reflected in the damage to the reference plates at the bottom of the CPs. The granite CPs did not suffer visible damage, while the basalt CPs had the mark of the projectile's collision well defined.

The tests with (5 x 10 cm CPs were anchored on the device, as shown in the results in Table 4. Figure 6 shows that the confinement system resisted the impact of the projectile and retained the test specimen inside. The confinement form remained in good condition.

The loss of mass is proportional to the perforation, as shown in Table 4. The reason for this behavior is because the specific kinetic energy (initial kinetic energy of the projectile per unit of concrete compressive strength) is proportional to both the loss of mass and perforation. This means that we can use the specific kinetic energy to obtain a reference value constant for the loss of mass and the perforation. The penetration depth is calculated from the initial and final height difference of the CP.

Comparison of the analytical model with the experimental result

Figure 7 shows a graph comparing the actual impact effect, the LRB formula (Equation 1), and the Vicente Lima formula. The specific kinetic energy is plotted on the x-axis, relative to the material's resistance, and the perforation reached by the projectile or expected is plotted on the y-axis.

Use numerical simulations to validate or predict the response of the impacted object (Kamran; Iqbal, 2022; Wang; Guo; Hou, 2022; Rajput; Iqbal; Bhargava, 2017; Morales-Alonso et al., 2015; Jinzhu et al., 2013; Park; Yoo; Chungb, 2005).

The input data on the ordinate axis, using the relationship between strength and impact energy, highlights a common behavior among the materials, with the formation of groups by type of materials. This makes the visualization of depth evident for each group. In addition, it reduces distortions in energy variation and compensates for the resistance of the material used, which is provided by the average.

Table 5 shows that the adaptation of the original formula led to results that were closer to the depth generated by the impact for the two aggregates. The values of the empirical formulas were compared to the real value, and the negative values are more favorable as a safety factor, with a predicted penetration that is greater than the actual penetration.

Figure 4 -
(a) Parts of the containment device; (b) Assembled device; e (c) Sample confined in the device

Figure 5 -
Bulkhead with (5 x 5cm (diameter x height) specimen, before and after shooting to the left and right, respectively. The projectile mark can be observed on the concrete set on the plate

Table 3 -
Mass loss of (5 x 5 cm concrete specimens after impact test

Specimen	Initial Mass (g)	Final Mass (g)	Initial Height (cm)	Final Height (cm)	Velocity (m/s)	Impact Energy (J)	NP
Basalt	244.34	0.00	5.20	0.00	836.00	3424.59	PC
	254.62	0.00	5.15	0.00	829.00	3367.48	PC
Granite	236.50	0.00	5.00	0.00	842.00	3473.92	PC
	230.28	0.00	5.20	0.00	838.00	3440.99	PC

• Note: NP: Drilling Level; and
• PC: Full Penetration.

Table 4 -
Mass loss of (5 x 10 cm concrete specimens after impact test

Specimen	Initial Mass (g)	Final Mass (g)	Initial Height (cm)	Final Height (cm)	Velocity (m/s)	Impact Energy (J)	NP
Basalt	443.11	209.19	10.14	4.52	839.00	3449.21	PP
	448.29	213.68	10.13	4.38	837.00	3432.79	PP
Granite	443.48	221.34	9.96	5.77	833.00	3400.06	PP
	443.42	218.26	9.86	5.75	835.00	3416.40	PP

• Note: NP: Drilling Level; and
• PP: Partial Penetration.

Figure 6 -
Specimen inside the mold after firing

Figure 7 -
The relationship between specific kinetic energy and compressive strength can be used to predict penetration depth (*5.00 cm height)

Table 5 -
Penetration results, simulations, and percentage difference

Real and Calculated penetration (cm)
Specimen	Real	RLB	%	V. Lima	%
Basalt	5.62	4.31	23.39%	6.06	-7.89%
	5.75	4.29	25.36%	6.06	-5.37%
Granite	4.19	4.97	18.65%	5.19	-23.84%
	4.11	4.99	21.35%	5.19	-26.35%
Basalt*	5.20	4.28	17.60%	6.06	-16.47%
	5.15	4.24	17.72%	6.04	-17.27%
Granite*	5.00	5.04	-0.86%	5.21	-4.14%
	5.20	5.01	-3.63%	5.20	0.19%

As shown in Table 5, the Vicente Lima formula predicts a minimum final thickness of the protection layer with a good safety margin. All results were higher than the real impact values, which is favorable for security and defense. When compared to the RLB formula (Equation 1), these values provide a comfortable safety value and a dimension that is much closer to the real impact, allowing for a better design of the protection bulkhead.

Conclusion

The restructuring of the values of the original LRB formula (1941) from the US Army Weapon Corps provided a better dimensioning of the impact damage in terms of actual depth for microconcrete. It also presented a better penetration value and a safety factor already included in the prediction of the minimum plate thickness.

From the results of the impact tests, we can conclude that the height of 5 cm specimens did not resist the impact, as predicted by the new formulation. The heights of 10 cm specimens were able to stop the projectile and retain part of its body. In this case, the influence of the safety factor is clear, as the remaining part is greater than the CP forecast and the calculated value.

The concrete strength does not directly correlate with the damage caused, but the aggregate type is more significant. This is evident in the Vicente Lima formula, which better approximates the real results for granite aggregate.

The type of aggregate has a direct influence on the resistance and rupture models. Granitic aggregates, which are rougher and rounder, tend to conical rupture, while basaltic aggregates, which are more lamellar, tend to planar rupture.

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Edited by

Editor:

Marcelo Henrique Farias de Medeiros

Editoras de seção:

Ercília Hitomi Hirota e Juliana Parise Baldauf

Publication Dates

• Publication in this collection
  19 Apr 2024
• Date of issue
  2024

History

• Received
  15 May 2023
• Accepted
  14 Aug 2023