Energy absorption and impact response of ballistic resistance laminate

Zainab Shakir Radeef; Adnan A. Hussein; Zainab Talib Abid; Mahmood Shakir Naser

doi:10.1515/eng-2024-0027

Article Open Access

Energy absorption and impact response of ballistic resistance laminate

Zainab Shakir Radeef , Adnan A. Hussein , Zainab Talib Abid and Mahmood Shakir Naser

Published/Copyright: June 25, 2024

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From the journal Open Engineering Volume 14 Issue 1

Abstract

High-speed impact performance has significantly expanded over the past few decades. The target response based on the impact conditions has been more difficult to visualise and evaluate. In this article, Ansys model analysis has been used to measure, visualise, and predict the projectile and target responses of Kevlar^® (K) and Ramie^® textile-reinforced unsaturated polyester resin (UP) matrix. The laminate thickness threshold was detected experimentally based on the highest stress intensity factor and energy release rates. Furthermore, tensile strength and bending of the laminate were found. The impact conditions have a significant impact on the target response; thus, an explicit dynamic analysis was used to visualise the impact response based on the number of target fixed supports (FSs). Two FS (2 FS) target absorbs 11% more energy than four FS (4 FS) target. Additionally, the target size has a major effect on the projectile and laminate responses, and a successful arrest of the projectile was detected in both cases. The smallest targets with 2 FS have the highest and wider response, where a successful change in the projectile trajectory was obtained.

Keywords: ansys; impact; combat armour; Kevlar; Ramie; ballistic laminates; model analysis

1 Introduction

In continuous progress, various combat armours have been developed and captured incredible attention by researchers due to society’s urgent effort for protection. Upon impact and penetration, a projectile’s trajectory depends on several factors, including bullet shape, velocity, orientation, target composition, and target initial conditions (i.e. fixed supports [FSs]). This study conducted an experimental and analytical study and the results revealed significant values that were rarely addressed previously. An investigation was conducted to analyse the tensile strength, fracture toughness, and bending properties of polyester (KUP) and Rami-reinforced unsaturated polyester (RUP). In addition, the study highlighted the difference in energy absorption and structural response based on the initial boundary conditions of a rectangular target (20 × 10 cm²). Boundary conditions have a significant impact on the structural response; therefore, two fixed supports (2 FS) and four fixed supports (4 FS) were utilised to investigate the response or mode morphologies. Analytical methods were used to capture the response of the target and bullet, as it was not possible to visualise the entire collision event. The panel’s area, geometry [1], volume, properties, and boundary conditions [2] should be considered thoroughly by the designers. The successful design of armour is realised when considering post-response mode shapes after impact. The structural response was studied by Li et al.; where a curvature target with 4 FS was subject to bomb blasts and explosions. The results from this study show that plate curvature has a profound effect on blast mitigation. As the radius of curvature decreases (becomes more sharply curved), the area of plastic deformation decreases [3]. The initial bullet velocity has been measured using a high-speed camera or piezoelectric accelerometer sensors [4,5,6]. The orientation and deformation of the bullet are also still hard to see; nevertheless, it is a more difficult part of the data to quantify precisely. Due to the difficulty of visualising the impact response and comprehending the influence of boundary conditions on wave propagation and distribution, it is fairly challenging to record the wave’s propagation and capture the structural response at the perforation moment [7]. Conversely, the bullet’s dynamic energy and remanent energy were evaluated, and the visibility of the bullet’s direction remains challenging. The target was struck by a 9 mm projectile at velocities ranging from 100 to 600 m/s. Model analyses for the textile-reinforced polymer targets, tensile strength, and fracture toughness were developed. Measuring the fracture toughness assists in ascertaining the minimal thickness required to verify the complete arrest of the threats. It is an important property that affects the response behaviour of the laminates [8,9,10,11,12]. The radial and tangential stress and the plastic bending were the main deformation parameters that were adopted to estimate the ballistic behaviour of any composite laminates [13,14,15,16]. The target response with a honeycomb front layer and a Kevlar-29 composite backing layer was discovered, and the ballistic performance of such targets has a significant response. The fracture was contained inside the confines of the cell walls, which prevented the stress wave from spreading [17]. Explicit dynamic finite-element analysis was carried out on auxetic sandwich composite body armour consisting of three bonded panels; the front panel consisted of aluminium alloy, followed by a movable and discrete sandwich core, and silicon carbide (SiC) for the back panel. The movement of discretely sandwiched cells resulted in better energy absorption and local deformation; as a result, the ballistic limit improved, allowing for the safe usage of armour up to a velocity of 400 m/s [18]. The structure response plays a critical role in preventing and limiting the deformation; hence, the fibre-reinforced polymer simulation is attractively studied. Mostly, the fabric composites are synthesised from Kevlar, polymers, bio-fibre, fibreglass, and carbon fibre, and they also include functional piezoelectric composite fibres [19]. It was demonstrated that plant fibres and Kevlar-reinforced epoxy were highly effective in absorbing the energy, reducing blast effects, and enhancing fragmentation resistance [20,21]. Tough materials are incapable of quickly forming cracks, which makes metals extremely resistant to breaking under stress and have a sizable zone of plastic deformation. Therefore, in this work, the optimal thickness of KUP and RUP was studied, and the stress intensity factor (SIF), strain energy release, and critical crack length were determined. The toughness has a direct influence on the structural response [8,9,10,11,12]. Despite the localised damage caused by a projectile, the composites maintained a reasonable load-bearing capacity even after penetration by a projectile [22]. In the investigation of a mullite matrix reinforced with NdPO₄-coated mullite woven fibre mats using the Chevron notches technique, it was found that the critical SIF (K _Ic) of the fibres was in the range of 1.8–3.3 MPa m^1/2, such value is in line with the range that is limited by the standard materials selection chart [23].

Researchers examined the distortion of the projectiles and the role of the target’s toughness. The findings indicate that after striking a variety of composite laminates, the projectile could deform slightly. The impactor shape has a severe penetration effect where the dissipated energy of the bullet increases extraordinarily, and local penetration damage was observed in the conical impactor [24]. To comprehend the failure mode and damage phenomena, the damage level and toughness of ultrahigh-molecular-weight thermoplastic components have been investigated. The load-carrying capacity and absorbed energy were measured. More elastic and plastic deformation mechanisms could aid in enhancing the structural response [25].

Randjbaran et al. predicted the bullet velocity, target thickness, damaged size, and the behaviour of the target responses of inclined targets. The greatest increases in impact resistance can be obtained analytically by increasing the angles of targets by 26%. This will improve the impact of mechanical properties [26].

The increasing number of laminate layers yields increasing friction between the impactor and targets [27,28]. Further research on the structural response with proof textile and a hierarchical Steiner tree structure is still proposed [29].

Finite-element simulations were used to analyse and measure the performance of various ballistic laminate architectures. Findings from these simulations, when compared to experimental data, demonstrated a reasonably accurate description of the numerical models’ analysis [30]. Modal analysis and simulation proposed for designing woven-reinforced polymer laminates are quite difficult to build [7]. The radial and tangential stress and the plastic bending were adopted to estimate the ballistic behaviour of any composite laminates [13,14,15,16]. The numerical predictions aligned with the actual data in terms of both residual velocity and damage morphology. The analytical model was used to detect the ballistic limits, enabling the evaluation of panels over a range of thicknesses from 4.5 to 14.5 mm [16,31], as well as the laminate fabric’s orientation. Accordingly, the designed laminates from KUP and RUP were aligned in layers with textile orientations of 45° and 90°, respectively. Corresponding to the work introduced by the research groups, it emphasised the significance of fibre orientation and revealed the effects of the fibre angle. The laminates composed of layers with angles of 0°, 90°, and 45° exhibited superior resistance against ballistic impact compared to other angle combinations. Therefore, it is advantageous to evenly distribute the different layer angles to enhance the impact resistance of laminates [24,32] and the deformation of projectiles [33]. The outlines of this article are drawn in the flow chart as given in Figure 1.

Figure 1

Simulated parameters.

Upon the impact, the energy is distributed longitudinally and transversely in the laminates, and then the waves reflect instantaneously towards the impact point [34]. There is still room to explore the laminate response and comprehend the mechanisms of wave propagation. Determine the fracture toughness and then strain energy release rate, define the mechanical parameters in the linear elastic region, compute bending using Ansys, and simulate fibres and textiles using the material design system (MDS). The nonlinear, anisotropic, and asymmetric features of fibre-reinforced composites were taken into consideration when doing the three-dimensional (3D) impact analysis of the laminated and braided composites.

2 Theory

When the impact occurs at a high speed, the laminates deform in a certain mode-shape, and the generated wave propagates and transfers towards the boundaries longitudinally and transversally, causing sinusoidal oscillation of the laminate structure. The deformed and strained waves rapidly travel at sound speed towards the edges of the structure and then bounce back to the point of impact due to the response behaviour of the structure. This study highlights the generation of two distinct types of directional waves: longitudinal waves and transverse waves. The longitudinal wave denotes the vibration that travels parallel to the target plane and travels towards the boundaries of the laminate (i.e. target edges). Subsequently, the wave changes its direction and either terminates or regenerates with different energy and mode shapes. This analytical representation of the longitudinal wave is comprehensively explored, and the mathematical expression of this phenomenon is given as follows:

(1) ( x , t ) = y 0 cos w t − x c ,

where y represents the displacement of the point propagated by a sound wave, x is the distance between the point and wave source, t denotes the elapsed time, y ₀ represents the amplitude of the oscillations, c is the speed of the wave, and w is the angular frequency of the wave. The transverse wave appears as transferred, fluctuating waves of the structure and is expressed by

(2) S ( p , t ) = A u sin t − ( p − o ) d v T + ∅ ,

where A _u describes the amplitude or strength of the wave, T defines its period, v indicates the speed of propagation, and φ its phase at o where p and o are fixed points. Each of these parameters is a real number. d represents the propagation direction (a vector with unit length). The total deformation solution provides a good visualisation of the scalar total deformation vector for the three-component deformation A _X, A _Y, A _Z, then it is given as

(3) A = A X 2 + A Y 2 + A Z 2 .

Here, A _X, A _Y, and A _Z are the directional deformations. At the impact point, a local deformation develops, and the projectile is arrested by the pulled fabric of the first layer, where this layer is pulled further than the layers behind. The SIF is expressed as follows:

(4) K IC = − ∫ v 0 Q i , j [ σ kI ε kj aux δ ij − σ kj aux U k , j − σ kj U k , j aux ] d V / ∫ S 0 δ Q n d S ,

where σ ij , ε ij , and U i denote the stress, strain, and displacement, respectively. σ ij aux , ε ij aux , and U i are the stress, strain, and displacement of the auxiliary field, and q _i represents the crack-extension vector. The bullet’s kinetic energy dissipates to form two main waves: a longitudinal wave that moves in-plane (moves the fabric outward and parallel to the fabric axis) and a wave with a transverse direction that represents the movement out-of-plane of the fabric composite or laminate. The equation employed to determine the transverse wave speed c (Equation (5)), while the transverse wave deforms the laminates vertically to generate an out-of-plane movement is presented in Equation (6)

(5) c = E ρ ,

(6) U = c ( ε ( 1 + ε ) − ε ,

where E is the material’s Young’s modulus (GPa), c is the longitudinal wave speed (m/s), ρ is the material’s mass density (kg/mm³), and ε is the strain in the fibre. The kinetic energy absorbed by the plate is one of the common metrics used to assess the ballistic performance of body armour. The ogival projectile used in this study has an estimated mass of 7 g and an impact velocity in the range of 200–600 m/s

(7) KE = 1 2 m ( v s 2 − v r 2 ) ,

where m denotes the projectile’s mass, v _s denotes its striking speed, and v _r is the residual speed.

3 Modal analysis

An analytical model was employed to capture the impact and structural deformation. A ballistic impact-induced deformation of the composite was quantified by measuring the dynamic energy and remanent energy of the projectile. A fabricated projectile (9 mm) stroked the target at a velocity range of 100–600 m/s. The construction of modal analysis and simulation of textile-reinforced polymer targets is fairly challenging; thus, the tensile and fracture toughness models were built to determine the minimum thickness that verifies the full arrest of the threats.

3.1 Design of woven composite

The mechanical behaviour of different composite materials has always been one of the most attractive topics to model. Many academics have concentrated on modelling textile materials because of their unique structures. This study used the MDS to simulate fibre and fabric, define the mechanical properties in the linear elastic region, evaluate fracture toughness, then strain energy release rate, and calculate bending using an Ansys Workbench. Finite-element modelling of the composite fabrics assists in realising homogenous microstructure properties of the composites where the fibre volume fraction and yarn volume fraction are taken into consideration. This tool is integrated with the material properties database. Accordingly, Kevlar laminate (KUP) and Ramie laminate (RUP) were modelled, and the model geometry consisted of two types of representative volume elements (RVE): one for unidirectional (UD) fibres and another for fabrics. To generate homogenised characteristics, a material designer tool is used to modernise the design of woven composites. This tool can model any composite material at a microscale. The software collects averaged material data for the linear elastic stiffness of KUP–RUP laminates, which can then be used in subsequence simulations. First, the selected geometrical type was UD fibre distribution; it was selected to configure a hexagonal unit cell with a fibre volume fraction and a fibre diameter of 0.5 and 20 µm, respectively. The characteristics of the composite components are listed in Table 1, which includes the attributes accessible in the Ansys engineering materials database.

Table 1

Single-unit cell characteristics

Design parameters	Ramie	Kevlar	Polyester
Weaving types	Plain	Plain	N/A
Fibre volume fraction	0.325	0.55	N/A
Yarn fibre volume fraction	0.65	0.80	N/A
Fibre-oriented angle (degree)	90	45	N/A
Yarn spacing (mm)	1	0.5	N/A
Fabric thickness	0.2	0.2	N/A
Density (kg/m³)	1500	1256	1200
Poisson’s ratio	0.3	0.44	0.33
Yield strength (GPa)	0.086	3	3.2
Yong modulus (GPa)	9.5	62	0.276
Tensile ultimate (MPa)	86	85.9	310

The RUP weaved yarn has an orientation angle of 90°, whereas the KUP matrix yarn angle is oriented toward 45°. Ansys Material Designer, a tool within Ansys Mechanical, aids in the optimisation of microstructures and the homogenisation of material properties for intricate materials and composites. The first stage of design was creating the fibre polymer unit cell. The second stage involves the fabrication of the textile design. The finite-element analysis was used to ascertain the mechanical characteristics of KUP and RUP composite. Figure 2 shows the composite properties that have been simulated. Consequently, the mechanical characteristics, fracture toughness, and impact parameters were simulated. The finite-element solution provides precise values for calculating the mechanical properties of the KUP and RUP composites, as shown in Table 2.

Figure 2

Fabric simulation model: (a) UD fibre unit design, (b) defined mesh and yarn orientation of simulated Kevlar versus raw Kevlar fabric, and (c) defined mesh and yarn orientation of simulated Ramie fabric versus Raw Ramie fabric.

Table 2

Mechanical properties of fabrics designed by Ansys materials design model

Property	Kevlar woven-UP	Ramie woven-UP
Poisson’s ratio (at 0 shear angle)	0.383-_{XY direction}	0.323-_{XY direction}
	0.375-_{YZ direction}	0.350-_{YZ direction}
	0.375-_{XZ direction}	0.323-_{XZ direction}
Young’s modulus (GPa)	4.474-_{X direction}	6.642-_{X direction}
	4.474-_{Y direction}	5.858-_{Y direction}
	4.443-_{Z direction}	5.858-_{Z direction}
Shear strength (GPa)	1.642-_{XY direction}	2.204-_{XY direction}
	1.615-_{YZ direction}	2.170-_{YZ direction}
	1.615-_{XZ direction}	2.204-_{XZ direction}

The 3D woven fabric is created using a traditional weaving technique that involves intertwining two sets of yarns at right angles: the warp yarns at 0° and the weft yarns at 90°. Whereas the Kevlar textile was aligned at a 45° angle to the reference of the Ramie textile, which is woven with weft and warp yarns at 0° and 90°.

3.2 Tensile test and model

The mechanical properties of KUP were examined to determine its elasticity and strength by adopting the composite ASTM D638 standard method; the dimensions and meshing modal of the sample are given Figure 3(a), and the experimental results were compared with the analytical tensile strength results. The explicit dynamics model is built using nodes 154,377 and elements 128,642. Young’s modulus of the KUP–RUP composite was measured to be 4.487 GPa, and its maximum tensile strength was found to be around 70 MPa. These values are within the range specified by conventional material selection charts and previous experimental research [35]. The deviation between the experimental and analytical results was around 4%, which presents a good degree of comparability, as shown in Figure 3(a).

Figure 3

Theoretical and experimental comparison: (a) analytical modal and schematic drawing and (b) stress–strain test.

To determine the optimal thickness of RUP with considering the strength of the laminates and the fabrication cost, the mechanical properties were detected analytically with different thicknesses of Kevlar laminate and Ramie laminate. The (1K/5R) denotes 1 mm of KUP laminate to 5 mm of RUP. The mechanical properties of 3K/3R that were detected experimentally are provided in Table 3. It is obvious that 3K/3R laminate has a high strain rate and excellent toughness.

Table 3

Mechanical properties of 3K/3R laminates

Load at maximum tension strain (kN)	Tensile extension at maximum tensile strain (mm)	Tensile stress at maximum tensile strain (GPa)	Young’s modulus (GPa)	Energy at maximum tensile stress (J)
12.628	9.082	0.0756	4.487	70.668

It was found that 6 mm of Kevlar laminates showed an excellent stress strength variant of 70% than Ramie laminates strength. KUP–RUP laminates with equivalent thickness (i.e. 3 mm) were selected due to their comparable strength properties and cost effect. Figure 4 illustrates the tensile strength of KUP–RUP laminates with varying thicknesses, specifically laminates with thicknesses of 2K/4R, 3K/3R/4K/2R, and 5K/1R.

Figure 4

Simulated tensile strength of KUP/RUP laminates for different thicknesses of Kevlar and Ramie polyester matrices. The thickness of 3K/3R is the optimal tensile properties.

Therefore, the thickness that underwent further examination and study is 3K/3R, which is considered to be the most suitable.

3.3 Fracture toughness experimental work and modal analysis

Regarding the fracture toughness model, a pre-defined crack using smart crack growth assumptions that support 3D crack growth in compact tension mode (Mode I) was considered. The sample model is based on using quadratic tetrahedron limit (solid 18) elements. In addition, the static structural model was designed to calculate the SIFs and J-integrals for detecting the optimal thickness of KUP and RUP laminates. The fracture calculation parameters were adopted from the ASTM E833 (liner elastic plane strain conditions) standard. Finally, the fracture toughness and tensile tests were investigated analytically and compared with the experimental data. The fracture toughness represents the material’s resistance to crack propagation. The laminate-thickness in-plan stress is preferred for combat amour because of its high capacity to withstand rupture and failure at the amour edges (laminate sides). The compact tension model is illustrated in Figure 5(a). The schematic depiction of the tensile sample and compact tension is illustrated in Figure 5(b).

Figure 5

Compact tension sample: (a) analysis model and (b) schematic drawing.

Unsaturated polyester resin (UPR) and Kevlar are inorganic substances that adhere well to one another, whereas Ramie also has extradentary adhesion to UPR. The sample was fabricated according to the Fracture Toughness Strander ASTM E833 for composite fibre laminates [24]. The experimental setup and sample size for the flexural test are shown in Figure 6(b), and the flexural strength is shown in relation to the deformation. The maximum flexural stress obtained was 81 MPa, accompanied by severe bending deformation exceeding 55 mm. Despite the considerable bending of the sample, an extremely slight delamination between the fabric layers occurred. It was seen that the 3K/3R material can withstand the bending load force without crack propagation where this is the most important design factor to consider for ballistic laminates.

Figure 6

Three-point flexural test of 3K/3R: (a) experimental setup and bending deformation, (b) deformed sample and schematic drawing, and (c) bending stress and the flexural deformation.

Additionally, KUP–RUP has anisotropic properties, and to detect the bending stiffness of such laminates separately, four samples underwent a three-point bending (flexure test) to obtain average results. This test can reveal information about a material or composite’s structural integrity and mechanical qualities by revealing how it responds to bending stress. The standard test methods were strictly adhered to for measuring the fracture toughness of the laminate’s sides (structure boundaries). It should be noted that the laminates are composed of three distinct components, K-R-UP, each having significant differences in their mechanical properties.

Compared with other laminates, flexural strength measurements for KUP laminates with thicknesses up to 3 mm showed values between 40 and 50 MPa [36], and KUP laminates up to 3 mm thick showed values of 40–50 MPa. This indicates that optimising the flexural characteristics resulting from the presence of RUP yields a result that is equivalent to the experimental findings and the standard materials chart [23,37]. The current topic dives into the importance of detecting the thickness of the laminate and how it affects resistance to fracture, as well as the effect on energy absorption. In this research, estimation of the critical thickness threshold in laminate was achieved by evaluating the stress intensity parameters and the fracture propagation. Figure 7 represents the SIFs for KUP and RUP, which are calculated depending on laminate thicknesses. The Ansys results for the fracture parameters are illustrated in Table 4.

Figure 7

The SIF of different target thicknesses: (a) Kevlar-polyester and (b) Ramie-polyester laminates.

Table 4

Fracture toughness modal parameters of KUP and RUP laminates

Material	Fracture force F _max (N)	Fracture toughness K _Ic (MPa √m)	Strain energy release rate J-integral (J/m²)	Critical crack length (mm)
KUP	570	4.5	935	4
RUP	170	1.53	142	2.8

The determined parameters of fracture toughness and strain energy release rate were compared with the standard materials selection chart [23]. It is important to notice that the Kevlar-polyester laminate exhibited the highest SIFs at a thickness of 2 mm the crack needs high stress and energy to propagate accordingly the prepared KUP laminate shows stable withstand the threats. However, any subsequent increase in thickness resulted in a progressive decrease in SIFs, except for the layer that is 1 mm thick.

Similarly, RUP with a thickness that represents the ideal threshold due to its high fracture resistance, elastic strength, impact energy absorption, and the best design cost-effect. In thick laminates, the stress field ahead of the crack has the lowest SIF value, meaning the field has the lowest elastic stress and energy strain rate (i.e. minimum strain energy density field). The analytical methodology is more cost-effective and time-consuming than producing pre-cracked structural components before testing. In these experimental tests, a pre-cracked compact tension specimen CT is used. The economised finite-element approach was used in conjunction with the ANSYS workbench 22 R1 software for predicting fracture toughness, as shown in Figure 7.

Kevlar laminates had the highest SIF and higher J-integral rates compared to Ramie laminates. The blue trace represents the K _Ic of the KUP at the force of 550 N and the J-integral of the RUP; the red trace illustrates the K _Ic of the RUP. Stable crack growth length occurs and extends linearly until it exceeds the critical limits. This was followed by the observation of a nonlinear plastic fracture and the subsequent growth of an unstable crack. KUP exhibits a higher release of strain energy compared to RUP due to the inherent ductility of Kevlar fabrics, as given in Figure 8. In the initial stage of crack extension, the matrix of UP experiences failure, followed by the deformation of Kevlar fibres and the resistance to crack propagation. Conversely, laminated fabrics composed of Ramie and UP exhibit failure at a lower rate of strain energy; the determined values coincide with the standard materials selection chart [24]. Composite laminates of KUP with a maximum thickness of up to 1 mm exhibit a higher critical SIF. The maximum critical stress intensity of RUP is observed at a 4 mm thickness. The average thickness of 3 mm is selected for both laminates (KUP and RUP).

Figure 8

Critical SIF of KUP and RUP laminates versus the laminates thickness.

3.4 Ballistic limits analysis

The experimental and numerical results of the ballistic test are presented in this section along with a thorough analysis of the modal designed with 51,098 nodes and 24,678 elements. Two models have been analysed based on the number of fixed supports of the laminate: 2 FS and 4 FS. Following a collision, transverse and longitudinal waves propagate outward until they approach the nearest end of fixed support. After that, the waves transfer continuously reflecting back and forth between the stimulated point and the boundary until vanishing. Ballistic test results revealed that the laminates effectively stopped the bullets without full penetration. The energy absorption of 3K/3R laminate was determined and the percentage error based on the practical results was 5%. The energy absorption of laminates and time history are illustrated in Figure 9(a). It was selected to capture the defamation in two 2 FS and 4 FS; the z-axis is the direction of the fired bullet. The impact velocity of the 9 mm FMJ bullet was modelled using an initial velocity (100–600 m/s) specified by the NIJ standard [38]. The absorption of energy will be governed by impact velocity, material properties, and boundary conditions where the targets experience cyclic elastic strain (equivalent to von Mises strain) levels that might reach their highest value by increasing the fixed supports, as shown in Figure 9(b); at a bullet velocity of 100 m/s, the elastic strain with 4 FS is higher and that causes significant damage of the composite upon a time, a similar behaviour was detected at higher velocities.

Figure 9

(a) Ballistic limits of 3K/3R (4 FS) laminates experimental and analytical. (b) Maximum elastic strain of bullets at a velocity of 100 m/s.

The acquired mode shape of the laminates depends on the bullet velocity. Intense deformation is shown in the laminates that impact at velocities of 300–600 m/s. The laminates exhibit enhanced mobility, enabling them to move in tandem with the projectile, resulting in the formation of extensive fluctuating bending zones. This phenomenon leads to an increase in energy dissipation and the generation of substantial transverse waves. Figure 10 demonstrates a small increase in energy absorption of the 2 FS laminate as the bullet velocity increases. This is attributed to the mobility of the free sides, which move with the projectile and absorb its kinetic energy.

Figure 10

Disparity in energy absorption.

A substantial difference in energy absorption was seen when considering the number of fixed supports, particularly at velocities of up to 400 m/s. The rate of energy absorption in the 2 FS condition is 11% higher than in the 4 FS condition.

It is important to note that projectile velocity can be halted or redirected away from the target, and this depends entirely on the transverse and longitudinal waves. The waves fluctuated. The energy absorbed by the 4 FS laminates may decrease because some of this energy is transmitted to the projectile that is trapped inside the laminate, as shown in Figure 11.

Figure 11

Perforation of targets based on their boundary conditions.

By utilising analytical methods, it is possible to map the trajectory of a fired bullet and analyse the velocity history profile. When the target fixed supports are 4 FS, at the impact moment, the velocity of the bullet drops to zero faster than the 2 FS condition; hence, laminates with 2 FS move freely and are pulled up by the projectile before any perforation occurs. During the impact moment, the bullet successfully perforates the target, partially causing a collapse in its kinetic energy. However, the bullet retains potential energy, which allows it to recover its capability to perforate the laminate, as illustrated in Figure 11. The size of the targets has a significant effect on the response time of laminates since smaller targets result in shorter travel times and greater internal frequencies of targets.

Following the impact, the structure yields a response that ejects the bullet outside the target, but the rate of ejection decreases as the size of the target increases. At the smallest size of the target, there is a fast response of laminate, causing the bullet to eject instantaneously. In Figure 12(a), the bullet ejects from 4 FS laminates at a velocity of up to 100 m/s, whereas the ejection velocity of 2 FS was up to 150 m/s. The fact behind that is the response speed and mode shape. The findings indicated that decreasing the laminate size to 2 FS resulted in increased responsiveness and an extended absorption duration. The bullet velocity profile of 2 FS and targets of different sizes is depicted in Figure 12(b).

Figure 12

Bullet velocity based on the fixed supports of different target sizes: (a) 24 FS and (b) 2 FS.

The acceleration of the bullet alters the trajectory backwards. Impact perforation was compared analytically and experimentally, as shown in Figure 13(a); in addition, the resistance to multi-impact of laminate is presented in Figure 12(b), where this result was determined in the Faculty of Engineering Lab/University Putra Malaysia [39].

Figure 13

Optimisation of total deformation of bullets and laminates with considering the number of fixed supports (a) 2 FS laminate and (b) 4 FS laminate.

In contrast, it was confirmed that the bullet could change direction and orientation using 2FS and 4 FS; in addition, the total deformation could be concentrated on the bullet using 4 FS, as given in Figure 13(b), which shows high deformation concentrated of the bullet after impact.

Throughout the perforation, the bullet alters its trajectory backwards. Impact perforation was compared analytically in Figure 14(a), and a similar perforation thickness was determined compared with the experiment sample. The KUP–RUP showed high resistance and good withstanding against threats. This result was determined in the Faculty of Engineering Lab/University Putra Malaysia [39].

Figure 14

Ballistic resistance laminate: (a) analysis model for bullet perforation, (b) cross section to impacted laminate, and (c) multisport impact of KUP–RUP laminate [39].

4 Conclusion

The ballistic limit and energy absorption of laminates at high-velocity impact events were investigated. The target was struck by a projectile with a velocity range of 100–600 m/s. Increasing the thickness of KUP laminate yields ideal ballistic resistance since its fracture toughness is 0.75% higher compared to that of RUP laminate. Young’s modulus of 3K/3R is 4.487 GPa. The deviation between the experimental tensile strength and analytical results was around 4%, which presents a good degree of comparability. A flexural test was conducted to determine the flexural rigidity of the laminate. Furthermore, the findings indicated that a laminate thickness of at least 6 mm effectively arrested the bullet, resulting in little observable damage. KUP–RUP’s ballistic limit matched the second and IIIA of NIJ standards.

The second objective of this study is to determine how the number of fixed supports influences the response of the laminate and the projectile. Two distinct response mechanisms were recognised depending on the fixed support conditions (i.e. 2 FS and 4 FS): utilising 2 FS results in projectile ejection, whereas utilising 4 FS increases the laminate rigidity and deformation of the projectile. The energy absorption of the analytical results differed by 5% from the detection attained experimentally.

The dimensions of the laminate significantly impact the structural response, and according to the findings, the smaller targets exhibit a greater and broader response.

Use extra-supported laminate with a thickness of 8 mm, especially when using 2 FS laminates, to achieve the highest level of protective safety and prevent any potential damage from the local bending and defragments occurring at the impact point. Finally, the article explored the possibility of using the structural response to alter the path of a projectile. Nevertheless, further empirical investigations are necessary to ascertain the optimal target volume and boundary conditions.

zina_engi@yahoo.com

Acknowledgement

The authors’ deepest appreciation goes out to all UPM employees and instructors in mechanical laboratories who helped them advance their professional development. In addition, the authors would like to acknowledge the Iraqi Ministry of Higher Education for their assistance.

Funding information: Authors state no funding involved.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results and approved the final version of the manuscript. ZSR is the corresponding author who contributed to the investigation and writing of the manuscript. AAH and ZTA contributed to the analytical work using ASYS 2022R1 and funding acquisition. MSN assisted in providing writing, reviewing, and editing services.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: Most datasets generated and analysed in this study are comprised in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

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Received: 2024-02-09

Revised: 2024-03-16

Accepted: 2024-04-10

Published Online: 2024-06-25

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2024-0027

Keywords for this article

ansys; impact; combat armour; Kevlar; Ramie; ballistic laminates; model analysis

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