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Research Papers

# Response of Steel Fiber Reinforced Cementitious Composite Panels Subjected to Extreme Loading ConditionsOPEN ACCESS

[+] Author and Article Information
Amar Prakash

CSIR-Structural Engineering Research Centre,
Taramani,
Chennai 600113, India
e-mail: amar@serc.res.in

S. M. Srinivasan

Department of Applied Mechanics,
Chennai 600036, India
e-mail: mssiva@iitm.ac.in

A. Rama Mohan Rao

CSIR-Structural Engineering Research Centre,
Taramani,
Chennai 600113, India
e-mail: arm@serc.res.in

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 10, 2016; final manuscript received December 16, 2016; published online February 9, 2017. Assoc. Editor: Taehyo Park.

J. Eng. Mater. Technol 139(2), 021019 (Feb 09, 2017) (7 pages) Paper No: MATS-16-1178; doi: 10.1115/1.4035705 History: Received June 10, 2016; Revised December 16, 2016

## Abstract

Application of steel fiber reinforced cementitious composites (SFRCC) in the construction of protective structures against extreme loading conditions, such as high-velocity impact and blasts, is an active area of research. It is a challenging task to capture the material behavior under such harsh conditions where strain rate of loading exceeds beyond 104 s−1. In this paper, an effort is made to simulate numerically the multihits of short projectiles on SFRCC panels. A total of 90 numbers of SFRCC panels consist of various core layer materials, thicknesses, fiber volumes, and angle of obliquity, are tested under high-velocity impacts of short projectiles. In numerical simulations, the boundary conditions and impact loading sequence are maintained, similar to that used during impact tests. In order to carry out a realistic numerical simulation, in-service munitions and ammunitions are used. The numerical response is found to corroborate with experimental results. It is observed that, if two consecutive hits are made within a distance of ten times the diameter of the projectile, then it is considered a case of multihit, else, it is considered as single hit case. The damage contours based on effective plastic strain are found to correlate with impact-tested SFRCC panels.

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## Introduction

Response of cementitious composites subjected to extreme loadings, such as high-velocity impact and blast, has been investigated extensively for both civilian and military structures [1,2]. Resistance to high-velocity impact of short projectile requires uniform distribution of toughness and strength within the target structure. The homogeneity in strength and toughness of panels can be improved by the inclusion of discrete steel fibers to the cementitious matrix like plain concrete and slurry as reported by Naaman and Homrich [3].

In recent years, increasing trends of usage of different types of fibers in the construction of protective structures [4,5] are observed. The experimental and computational works done related to these new fiber composite materials are limited compared to plain or reinforced concrete studies. Hence, it is felt necessary to understand the behavior of steelfiber composite panels under short projectile impacts, which create harsh environmental conditions for keeping structural integrity of the panels intact. There are two ways to achieve this, i.e., either by conducting adequate number of experiments under the impact loading or by the introduction of advanced simulation techniques using appropriate constitutive material models.

Prediction of behavior of SFRCC panels under short projectile impacts through actual tests is often beyond affordability [6]. Because the experimental investigations on the high-velocity impact behavior of SFRCC panels demand manpower, materials resource, and financial investment. In addition to this, measurement of many output parameters, namely, projectile velocity, strains, accelerations, and pressure, etc., within the target panel at critical location needs sophisticated instrumentations. Hence, it is difficult to conduct real tests more frequently to study the effects of various influential parameters on the impact behavior of structural members. However, due to the availability of advanced computational power, it has now become possible to numerically simulate highly nonlinear dynamic problems like high-velocity impact. Owing to these advancements in computational power, the determination of impact resistance of fiber composite protective structures has not only become faster but also simplified too. It has also become convenient to conduct parametric studies, to investigate effects of various design parameters like material strengths, geometry of target, and projectile, etc., on the performance of target panels.

Local impact effects in concrete target structures have been studied [7], and multistage perforation formulations were proposed. The angle of backside cone surface in targets predicted based on proposed formulae was found to match well with experimental results. Huang et al. [8] numerically simulated the perforation of reinforced concrete targets. High-velocity impact of fragments on reinforced concrete slab has been modeled using LS-DYNA and is reported in Ref. [9]. Evaluation of damage in concrete plate under high-velocity impacts has been investigated [10]. Mechanism of cratering and scabbing was explained through numerical simulations. Cotsovos and Pavbric [11] explained apparent strength gain at high strain rate loading. Numerical simulations have also been conducted for oblique impacts [12], and results were compared well with experimental results. Both experimental and numerical investigations have been conducted [13] on high-performance fiber-reinforced cement-based composites subjected to impact loading using LS-DYNA. Numerical and experimental results were found in good agreement. Effect of steel and other fibers has been presented on impact resistance using both experimental and numerical investigations.

Numerical parametric studies have been performed [14,15] with explicit computational tool using a steel projectile impacting on a concrete target. The study concluded that the residual strength and the criterion for erosion influence the depth of penetration. By increasing the residual strength of material and the criterion for erosion, the depth of penetration is decreased. Wang et al. [16] studied both experimentally and numerically the effect of fiber inclusion in steel fiber reinforced concrete (SFRC). They have found that the elastic–plastic hydrodynamic model is effective for characterizing principal features of SFRC, especially postyield damage softening behavior. Constitutive models for concrete were evaluated [17] for fiber composites under dynamic loading. They have proposed a material model based concrete damage model with modified parameters for dynamic behavior of fiber composite materials. Luccioni et al. [18] proposed a simple homogenized approach based on a modified mixture theory. The fibers bond–slip behavior was automatically derived from concrete properties and fibers geometry or it can be alternatively obtained from pull out tests. Comparisons with other numerical approaches modeling SFRC as an equivalent homogeneous material have been demonstrated by them. In the existing literature, the authors could not find any information on the damage assessment in SFRCC panels subjected to multi-impacts; most of the researches [1922] conducted are limited to the visual inspection for crater size on the surface and depth of penetration along with mentioning the cracking available on panels. Most of the investigations on the impact resistance of cementitious panels concluded based on visual observations under single hit.

From the brief review of literature on numerical simulations of high-velocity impact resistance of SFRCC panels, it is evident that there is need to study the behavior of such panels under harsh conditions. The harsh conditions are likely to occur when a target panel is subjected to multihits of short projectiles. Therefore, efforts are made to simulate high-velocity impacts of short projectiles on steel fiber reinforced cementitious composite panels with various fiber volume fractions 0%, 2%, 4%, 6%, 8%, and 10%; various thicknesses 50, 60, 75, 90, and 100 mm; and layer configurations SIFCON-SIFCON-SIFCON (SSS), SIFCON-latex modified concrete-SIFCON, SIFCON-wiremesh layers-SIFCON, SIFCON-concrete-SIFCON, SIFCON-rubber mat-SIFCON, mortar-mortar-mortar, etc., as well [23,24]. However, results for SFRCC panels with 10% fiber only are highlighted in this paper. The study reported here in this paper is a part of comprehensive experimental and numerical investigations carried out by Amar Prakash [24].

## Materials and Mix Proportions

The materials used in preparing cementitious composite panels include steel fibers, cement, fine aggregates, super plasticizers, etc. The details related to these materials and their proportions are furnished in Table 1.

The high-velocity impact tests are carried out on SFRCC panels with varied fiber volume fractions. The fiber volume fractions vf are varied between 0% (no fiber), 2%, 4%, 6%, 8%, and 10%, while maintaining the same mix proportion of cement–sand slurry in all the specimens tested. The material quantities used for cement and sand slurry as per design mix are given in Table 2 for one batch of mix, considering the concrete mixer capacity (that is 50 kg load).

## Experiments on SFRCC Specimens and Panels

###### Casting and Curing of Control Specimens.

Considering the guidelines of ACI 544, the dry cement and fine aggregate are mixed for 1 min in a wheel-mounted concrete mixer of capacity 50 kg. The mixing is continued for another minute while adding 80% of water. Finally, the 100 ml super plasticizer is mixed with remaining 20% of water and it is also added to the mix. The mixing is continued for three more minutes to prepare the flowable cement–sand slurry. Fibers weighed as per the specified volume fractions are placed in specimen molds in layers alternating with cement–sand slurry.

For each fiber volume fraction, six numbers of cylinders of size 100 mm in diameter and 200 mm long and six numbers of cubes of size 100 mm and 150 mm are prepared for uniaxial compressive strength test, density, and sound velocity measurements. For flexure tests, prism specimens of size 100 mm × 100 mm × 500 mm for each fiber volume fraction and, for uniaxial tensile strength tests, 25 mm thick standard dogbone specimens are prepared. All the prepared specimens are demolded after 24 h and kept under water in the tank for 28 days for curing. Based on the standard laboratory tests on the specimens with different fiber volumes, the mechanical properties obtained are furnished in Table 3.

A fabricated steel mold with four partitions was used, which facilitates to cast four panels of size 300 × 300 × 100 mm size at a time as shown in Fig. 1.

In order to prepare the SFRCC panels, cement–sand slurry with designed mix proportions is prepared using pan type mixer and poured in to the steel molds up to 5 mm thick level. Steel fibers are distributed randomly over the slurry layer within the steel mold and compacted manually with steel tamping rods, so that entire fibers get embedded in slurry layer. To achieve a uniform fiber distribution across the panel thickness of 100 mm, the fibers are spread in about 18 layers. In order to achieve uniform fiber distribution in each layer, the orientations of fiber changed in alternate layers. For changing the orientation of fibers within each layer, varying hand stroke directions are used while placing the fibers. This process of slurry pouring and the steel fibers placement continued alternatively till the desired thickness of panel was attained.

###### High-Velocity Impact Tests on SFRCC Panels.

In order to have a realistic assessment of impact performances of the panels, in-service munitions (INSAS rifle and AK-47 rifle) and ammunitions (5.56 mm and 7.62 mm caliber projectiles) are used. The impact tests are conducted in reasonably controlled conditions. The distance of shooting point is kept 25 m away from the target panels, primarily from safety consideration, so that no fragment after spalling can hit back the shooter and aiming becomes easier. Another reason for this distance was to avoid drop in muzzle velocity, because far-off target distance may cause a drop in the muzzle velocity of projectile. Hence, the distance of shooting point is maintained at 25 m for all the tests carried out. In addition to this, in-service weapon and ammunitions, time of tests and boundary conditions, support stand, etc., are not changed during impact testing of the panels. For assessment of performance under the high-velocity impact, five types of SFRCC panels are prepared with different lay-up sequences. Among them, results corresponding to the SSS type (which consists of the layers of slurry infiltrated fiber concrete (SIFCON)) are considered in this paper.

Based on records of the 25 actual rounds of both calibers, the mean and standard deviations of projectile velocities in meter per second are determined statistically for 5.56 mm caliber projectile as 891(mean)±11.52(standard deviation) and similarly for 7.62 mm caliber projectile as 721(mean)±14.21(standard deviation). Accordingly, the corresponding kinetic energies of the 5.56 mm and 7.62 mm caliber projectile are calculated as 1.7 kJ and 2.2 kJ, respectively. The thicknesses of projectile's jacket are considered as 0.70 mm and 1.5 mm for 5.56 mm and 7.62 mm caliber projectiles, respectively. The core for 5.56 mm was made of lead (soft material), whereas for 7.62 mm projectile, the core is made of steel (hard material).

The panels with 2%, 4%, 6%, 8%, and 10% having a thickness of 100 mm were tested under single hit as well as multihits. It was found that a minimum of 2% fiber content can resist the 7.62 mm projectile, however, the severe cracking through thickness makes it vulnerable to use under multihit situations. However, 6% with 100 mm is adequate for multihit of 7.62 mm projectile. Due to restriction of space only, 10% fiber volume case is considered in this paper (more details are available in thesis [24]).

## Numerical Simulation

A Lagrangian approach based finite element (FE) model using eight-noded solid elements is developed for both target panel and projectiles. The homogenized properties of the cementitious composite material as per laboratory tests are adopted. Appropriate boundary conditions, contacts, and interaction were assigned between various parts of the FE model.

###### Material Model for SFRCC: The Modified RHT Model.

The Riedel, Hiermaier, and Thoma (RHT) model [25,26] for cementitious composite materials is adopted with slight modification in damage constants to capture the effect of fiber addition on postpeak behavior. In this model, the behavior of cementitious materials under high strain rate loading is expressed in terms of three stress limit surfaces, namely, initial yield surface, failure surface, and residual friction surface. During impact, these surfaces account for reduction in strength along different meridians; thus, it is a combination of plasticity and shear damage models. The failure surface, i.e., the ultimate strength of the fiber-reinforced composite material, is formed from material parameters including the compressive, tensile, and shear strength. When the stress reaches the failure surface, a parameterized damage model governs the evolution of damage driven by plastic strain, which in turn represents the postfailure stress limit surface by interpolating between the initial yield surface and the failure surface and residual surface.

When a target panel made of fiber-reinforced cementitious composite material is subjected to high strain rate loading, the material undergoes a very complex stress state. Most of the constitutive laws use the plastic flow rules in stress space differentiating between hydrostatic and deviatoric components [27,28]. During impact analysis, the loading function takes account of these two parts of stress. For lower pressure zone, deviatoric part is used, whereas for high-pressure zone hydrostatic part is used, as the effect of deviatoric stress is insignificant. The strain rate effects are taken into account as per CEB 1990 guidelines [29]. For ductile materials of projectiles well known, Johnson–Cook model is used, and available input parameters in the literature [30] are used. In many of the real life situations, the SFRCC panels are subjected to multihits in majority of situations. Therefore, in order to investigate responses of SFRCC panels under multihit situation, numerical simulation studies are carried out in this paper. In view of this, the SFRCC panels are subjected to a sequence of three hits, simulating exactly the multihit tests carried out experimentally.

In order to simulate test conditions in the numerical simulations, a time delay up to 200 μs is set between two consecutive hits. This time delay is set to give sufficient time gap between two consecutive hits in order to allow complete dissipation of kinetic energy due to the previous hit. The multihit locations on the panel are determined based on the experiments conducted earlier [23]. It is important to note that the autodyn code [31] takes care of the damage state of materials due to previous hits. Hence, no need to modify any damage parameter after each hit. In order to investigate the internal damage state of the panels with the current numerical simulations and also to distinguish the single hit situation from multihit situation based on the conditions laid down earlier, it is decided to conduct detailed three-dimensional (3D) finite element analysis using autodyn code [31]. In order to capture the behavior of porous material like SFRCC, P-alpha equation of state is used. The two-stage pressure–density behavior under high strain rate loading is shown in Fig. 2. Initial slope indicates elastic path due to stiffness of pore walls, then with increased pressure pore wall structure collapses and elastic plastic path represents this. Eventually, when all the pores get closed, it takes further pressure and follows elastic path again.

###### Damage Accumulation in Riedel, Hiermaier, and Thoma Model.

As mentioned earlier, once cementitious material begins to harden or soften the damage factor, D is used to determine the value of the current strength surface. The value of D lies between 0 and 1, which indicate two extremes that is no damage of material and fully damaged material in tension, respectively. The damage factor is defined as Display Formula

(1)$D=∑Δεpεf$

where $Δεp$ is the accumulated plastic strain, and $εf$ is the failure strain given by Display Formula

(2)$εf=D1(pfc′−pspallfc′)D2$

D1 and D2 are the user-input material constants. The default values for D1 and D2 are given as 0.04 and 1.0, respectively. Damage causes a reduction in strength. Hence, the strength is modified by shifting the surface from an initial surface to a current damaged one. During softening, it is interpolated between the limit and residual surfaces as described in Ref. [27].

###### Modifications to Model Fiber-Reinforced Cementitious Composite.

RHT model provides scaling effect, hence only few critical inputs are only needed. The rest of the parameter can be determined according to scaling. However, this model is developed primarily to simulate the behavior of plain concrete, and hence, default values do not provide satisfactory response for fiber-reinforced composites. In view of this, suitable modifications are incorporated in RHT model in order to simulate the behavior of steel fiber reinforced cementitious composite material. The inclusion of fibers to cementitious concrete or matrix results in improved postcracking behavior. Hence, the main difference between material models used for plain concrete and steel fiber reinforced composite material is the failure description on tension. Due to the enhanced ductility of fiber-reinforced materials, the crack control ability and energy absorption capacity increase, which result in increased impact resistance. Apart from using the experimentally obtained compressive, tensile, and derived shear strength values, the failure strain εf is also increased accordingly to match numerical responses with experimental investigations. Due to this increase in failure strain, value of damage D gets reduced as can be realized from Eq. (1). Hence, the critical value of D1 parameter in Eq. (2) is obtained by conducting a separate parametric study on D1 between 0.02 and 0.1, and it is found that the value of 0.06 provides impact responses of SFRCC panels (having fiber volume more than or equal to 4%) closer to the experimental results. Hence, for the fiber contents above 4%, the value of coefficient D1 is proposed as 0.06 instead of the default 0.04. Due to this modification, the behavior of fiber-reinforced cementitious composites is modeled reasonably well, for volume fractions of hooked end steel fiber, more than or equal to 4% by volume. For lesser fiber volumes than 4%, the default value as 0.04 found to be suitable. The material properties used in the modified RHT model are provided in detail [24,32].

###### Time Integration Scheme Used for Solution.

In this paper, to solve nonlinear dynamic problem like high-velocity impact, explicit time integration is used. Advantage of using explicit time integration is that for a lumped mass system, the global stiffness matrix is bypassed and integration is performed elementwise. Hence, this results in a very efficient scheme, and it does not require updating of the global stiffness matrix. Wave propagation codes are usually designed to treat problems with submillisecond loading and response times, where steep stress gradients or shockwaves are present. The solution process using explicit time integration starts by determining nodal velocities from initial conditions. From the velocities, the nodal displacements are computed. From the known velocity and displacements, the strain rates, strains, stresses, pressures, and nodal forces are computed. After that, the solution advances one time step. The new velocities and displacements are determined from the old ones and solution continues as explained above, and it continues till the desired time limit is reached. The detailed description about the explicit time integration and computational cycle is provided in Ref. [33].

###### Issue Involved With Lagrangian Code.

One of the important issues of large distortions is associated with all the Lagrange codes. Because of very high strain rate loading, the grid distorts severely with the material, and element size tends to zero. The time step is based on the size of the smallest element in the grid; hence, as element size tends to zero, the time step also tends to zero. In this vicious cycle, lots of computational cycles are wasted to make only a little progress.

During the high-velocity impact analysis, the Lagrangian cells near the contact point can usually get distorted beyond acceptable limits and affects the progress of the numerical computation. Erosion technique is a numerical mechanism for the automatic removal of elements during a simulation. In this method, the severely distorted elements are removed before they become inverted. However, the mass is redistributed to the adjacent nodes and inertia is maintained. In this way, the time step should remain reasonably large and solution can continue till the desired end time. The numerical simulations carried out in the present study are based on Lagrangian approach. Since hexahedral elements are used together with single point integration, hourglass modes of deformation can develop. Hence, important measure to avoid the hourglassing is taken, that is, a set of corrective forces are added to the solutions. The addition of these forces does not affect the momentum balance, but specific internal energy gets slightly changed. The entire scheme has been implemented in the autodyn [31]. This seeks to inhibit high-frequency hourglass oscillations while having negligible effect on the longer term global deformations.

###### Numerical Responses.

The results obtained based on the numerical simulations are discussed as follows in Fig. 3. The damage contours obtained for a typical multihit situation on the SFRCC panel with 7.62 mm projectile are compared with the experimental results, and the details are presented in Fig. 3.

It is observed that, if the impact distance between two hits is beyond ten times the caliber diameter of projectile, the damage zones remain separated both internally (subsurface) and externally as shown in Fig. 3. However, if the impact distance is less than ten times the diameter of projectile, the damage zones are found to be overlapped internally as well as on the surface as shown in Fig. 3(c). Hence, it can be inferred from this observation that the multiple hits on the SFRCC panels within ten times the caliber diameter will be considered as the multihit cases, otherwise it can be considered as single hit.

It can be observed from Fig. 4 that the damage contours obtained from the numerical simulation studies carried out on SSS type panel having 10% fiber volumes fraction are compared with the actual damage zone obtained through experiments. It can also be observed from the sectional details shown in Fig. 4(c) that the subsurface damage zones for multiple hits within ten times the 5.56 mm projectile diameter get merged similar to the experimental observations shown in Fig. 4(d).

The depth of penetrations and crater diameters obtained for SFRCC panels having 10% fiber volume fractions is compared with the experimental results and details that are furnished in Table 4. The depth of penetration is considered here as the maximum depth inside the crater tunnel (after removal of debris of jacket and core if any) normal to front face as typically shown in Fig. 5.

It can be observed that the maximum variation in the crater diameter is found to be 12.38%. Similarly, the maximum variation in depth of penetration (DOP) is found to be 6.5%. The dissipation of kinetic energies separately for projectile's core and jacket during each hit is shown in Fig. 6. Similar multihit studies are carried out on SFRCC (SSS) panel with 7.62 mm projectile as well.

The depth of penetrations and crater diameters obtained for SFRCC panel with 10% fiber volume are compared with the experimental results, and details are furnished in Table 5 for 7.62 mm caliber projectiles.

It is observed that the shape of craters on the front face of the tested SFRCC panels matches well with the damage contours obtained numerically as shown in Figs. 7(a) and 7(b). It can be observed that the maximum variation in the crater diameter is found to be 8.39%. Similarly, the maximum variation in DOP is found to be 11.3%. The dissipation of kinetic energy during each hit is shown in Fig. 7(c). This indicates that the FE model and material models adopted for the numerical simulations exhibit reliable solutions to the multihit problem.

Comparison of overlapping internal damage zones for the SFRCC actual panel after cutting and that obtained through numerical simulation is shown in Fig. 8. The damage contours are found to be similar as the marked damage zone in the dissected panel along the dashed line.

## Summary and Observations

In this paper, numerical simulation of multihits of short projectiles on SFRCC panels is presented. Based on the numerical simulation and high-velocity impact tests, the following observations are made:

• It is found that the RHT model with suitable modification in damage constants simulates postpeak behavior of SFRCC correctly.

• It is observed that for 5.56 mm caliber projectile, the maximum variation in the crater diameter is found to be 12.38%. Similarly, the maximum variation in DOP is found to be 6.5%. Whereas, in the case of 7.62 mm caliber projectile, the maximum variation in the crater diameter is found to be 8.39% and maximum variation in DOP is found to be 11.3%.

• Numerical simulation of multihit situations is carried out by providing a preset time delay such that the entire kinetic energy of projectile gets dissipated.

• It is found that, if the distance between two consecutive hits is more than ten times the diameter of the projectile, the hit is considered as single hit.

## Acknowledgements

This paper is being published with the kind permission of the Director, CSIR-SERC. The help rendered by colleagues from Shock and Vibration Group at the CSIR-SERC is highly acknowledged.

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## References

Tai, Y. S. , 2009, “ Flat Ended Projectile Penetrating Ultra-High Strength Concrete Plate Target,” Theor. Appl. Fract. Mech., 51(2), pp. 117–128.
Zhou, X. Q. , and Hao, H. , 2009, “ Mesoscale Modelling and Analysis of Damage and Fragmentation of Concrete Slab Under Contact Detonation,” Int. J. Impact Eng., 36(12), pp. 1315–1326.
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## Figures

Fig. 1

Plan and cross section of SFRCC panels: (a) SFRCC panel and (b) cross sections at A–A

Fig. 8

Comparison of internal damage (along the dashed line in Fig. 7) under multi-impact of 7.62 mm projectile

Fig. 6

Kinetic energy variation during multihits of 5.56 mm projectile

Fig. 2

P-alpha equation of state (relation between pressure and density)

Fig. 7

SFRCC panel (10% fiber Vf) after three hits of 7.62 mm projectile: (a) tested panel, (b) damage contours, and (c) kinetic energy dissipation

Fig. 3

Responses of numerical simulation of multihit cases on SFRCC panels with 10% fiber volume subjected to impact of 7.62 mm caliber projectile: (a) after first hit at center, (b) after second hit, (c) after third hit, (d) section at dotted line, and (e) section at dashed line

Fig. 4

Comparison of damage in SSS type panel under multihits of 5.56 mm projectile: (a) damage contours for front face, (b) front view of tested panel, (c) damage contours for the section at dotted lines, and (d) actual panel after cutting along dashed line

Fig. 5

Typical terminology used for the measurement of damaged SFRCC panels

## Tables

Table 3 Material properties with varying fiber volume fractions
Table 2 Quantities of materials used for cement sand slurry
Table 1 Materials used and mix proportions for SFRCC
Table 4 Comparison of numerical simulation of multihit and experimental results for 5.56 mm projectile
Table 5 Comparison of numerical simulation of multihit and experimental results for 7.62 mm projectile

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