# Experimental and Numerical Simulation to Validate Critical Perforation Velocity on a Flat Plate Aluminium Alloy 6061

Authors: Bharosh Kumar Yadav; Mehdi Jahangiri; Dalbir Singh
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Aluminium 6061 (Al6061) alloy, which is known as commercial alloy, is massively used in aviation and automobile industries. Therefore, research on Al6061 alloy is gaining significance among scientists and researchers all over the world as it provides light weight, high strength and stiffness, high impact, and corrosion resistance in engineering applications. The comprehensive analysis of mechanical behavior under large stress-strain deformation responses of the alloy is studied over a wide range of strain-rates such as 1 × 10−3 s−1, 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1 under room temperature to elevated temperatures of 100°C and 200°C. In this regard, this study aims to evaluate the Johnson–Cook strength and fracture constants utilizing the Johnson–Cook constitutive model equations. Furthermore, the evaluated constant parameters have been used to perform numerical simulation analysis utilizing ABAQUS/CAE software. According to the study’s findings, the critical perforation velocity was found to be 70 ms−1 when a flat-nosed bullet (45 mm length and 12 mm diameter) made of stainless steel weighing 50 grams was fired normally to the center of a square plate specimen of Al6061 alloy. The specimen of the square flat plate was prepared with side 205 mm and 2 mm thickness (205 × 205 × 2 mm3). A good correlation for critical perforation velocity of experimental acquisition data and numerical simulation results has been found. These findings increase the knowledge of the material’s response application to the high-velocity impact that can be used in arms-ammunition, aviation, marine, automobile, and home appliances.


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## Body

## 1. Introduction

### 1.1. Background

Aluminium 6061 alloy is one of the commercial aluminum alloys being massively used in aerospace and automobile industries; it is a versatile heat treatable extruded alloy with medium to high strength capabilities. The typical application for aluminium alloy includes Aircraft and Aerospace components, Marine fittings, Transport, Bicycle frames, Vehicle rims, Camera lenses, Driveshaft, Electrical fittings and connectors, Brake components, Valves, Couplings, etc. [1, 2]. Researchers are working to develop materials that have light weight, high strength and stiffness, high impact, and corrosion resistance as they are widely used in structural application. Al6061 alloy is used as structural components in the aerospace, aeronautical, marine, and automobile industries. Al6061-T6 increases high toughness and weldability and found more application potential [3–5].


### 1.2. Literature Review

A few recent studies reported on the mechanical strength and fracture behavior application to high-velocity bullet impact on aluminum 6061 alloys. Some of the relevant research is discussed in the following section.Due to rapid simultaneous advancement in hardware technologies as well as in mechanics and material modeling during the last decades, engineers are nowadays able to analyze complex structures undergoing static and dynamic loading conditions in many engineering disciplines. In addition, high strain-rate deformations such as dynamic and high-velocity impact have increasing importance in industrial applications. Complex thermo-mechanical processes and numerical solution procedures such as the finite element method for solving strongly coupled mechanical and thermal boundary-value problems practices are gaining significantly in engineering fields [6–13]. Rathore et al. studied numerical simulation for Aluminium alloy 6060 to predict fracture behavior under the high-velocity impact of the flat-faced rigid circular projectile and the comparative effect has been studied in the range of 100 m/s, 150 m/s, and 250 m/s. They found plugging behavior and material experience shear-type deformation projectile impacting at high velocity [14]. Rai et al. performed ballistic impact on aluminium 5083-H116 plate numerically with Johnson Cook plastic model and their study was verified by hand calculations and engineering judgment. They conclude the Johnson Cook failure model was not able to capture scabbing phenomena, eventually ballistic resistance was overestimated in numerical simulation [15]. Senthil and Iqbal predict superior layer of armour steel, mild steel, and aluminum 7075-T651 alloy against 7.62 AP projectile, and the behavior was predicted by incorporating the Johnson Cook model [16]. Borvik et al. studied experimentally and numerically normal and oblique impact of 20 mm thick AA6082-T4 aluminium plates and the material parameters were identified utilizing the Johnson–Cook model [17]. Xiao et al. performed ballistic resistance of double layered 2024-T351 aluminium alloy plate against blunt projectiles and the modeling was carried out in ABAQUS/Explicit utilizing Johnson Cook plastic model [18]. Santha Rao and Shashank Simhadri proposed an improvement mechanism of aluminium alloy 5083 composites with hybrid reinforcement particles through friction stir process [19]. Bala et al. studied the bullet impact behavior of bamboo wall panels and found bamcrete panels have depth bullet penetration and energy absorption capacity compared to RCC [20]. Wu et al. performed anti-blast properties of 6063-T5 aluminium alloy with circular tube coated with polyurea elastomer and they conclude that polyurea cannot be directly applied. Mechanical performance of polyurea materials was studied while performing Quasi-static compression and tensile experiments [21]. Bagwe et al. studied numerical analysis of armour steel and aluminium alloy impacted by armour-piercing bullet and their ballistic performances were compared using ANSYS and the material model was developed utilizing the Johnson–Cook material model [22]. Several studies worldwide have been carried out on various materials and their performance-development techniques to meet the engineering requirement [23–31]. This leads to increasing demand for accurate, robust, and efficient numerical models to analyze the mechanical response of engineering structures under dynamic loading conditions.


### 1.3. Research Gap

From the available literature, there is minimal information regarding the critical velocity application essentially to evaluate perforation to ensure the reliability of the helmet impact of the soldier. According to the author’s knowledge, it is found that none of the researchers focused on the comprehensive analysis of mechanical behavior of plastic strength, fracture, numerical analysis, and experimental application to high-velocity bullet impact. Thus, this research work aims to increase the knowledge of material’s response application to the high-velocity impact that can be used in arms-ammunition, aviation, marine, automobile, and home appliances.


### 1.4. Research Objective

With the massive use and importance of Al6061 alloy, this research has been focused to elaborate on the detailed material behavior and comparative analysis has been carried out. The following are the main objectives of this study:(i)
To evaluate the comprehensive analysis of mechanical behavior under large stress-strain deformation and failure responses of the Al6061 alloy over a wide range of strain-rates such as 1 × 10−3 s−1, 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1 under room temperature to an elevated temperature 100°C and 200°C, respectively.(ii)
To determine the Johnson–Cook strength and fracture constants of an Al6061 alloy utilizing the Johnson–Cook constitutive model equation.(iii)
To determine the critical perforation velocity of an Al6061 alloy flat plate, when the bullet is fired with flat-nosed normal to the center of the plate.(iv)
To validate critical perforation velocity with the comparisons of a high-velocity bullet impact experimental acquisition results with ABAQUS/CAE numerical simulation results.


### 1.5. Novelty of the Study

The novelty of the study includes comprehensive mechanical behavior, evaluation of Johnson–Cook strength, fracture constants, and critical perforation velocity of 2 mm thickness of Al6061 alloy. OriginPro-V2017 software was used to obtain Johnson–Cook constants and ABAQUS/CAE to model the impact and analyze critical perforation velocity. Moreover, the numerical simulation has been compared with the experimental results to validate the critical perforation velocity. To the best of our knowledge, this is the first attempt in the literature.


### 1.6. Organization of the Study

The organization of the study is ordered as follows: Section1 presents the Al6061 alloy background and literature which supports the ideas of the proposed research. As a result of the theory of machines in Section 2, an adequate theory of Split Hopkinson Pressure Bar is discussed and some relevant research in the literature has been reported that the Johnson–Cook model equation benefits accuracy and reliability compared to other model equations in the determination of Johnson–Cook strength and fracture constants. Also, a detailed experimental setup of high-velocity bullet impact is covered in the same section. Section 3 presents the method of sample preparation and method to determine Johnson–Cook strength and fracture parameters. The obtained constant parameters have been used to perform numerical simulation analysis utilizing ABAQUS/CAE software. In Section 4, to contribute to a fair comparative study, the results and observations were carried out to compare numerical simulation results with experimental results for the validation. Finally, Section 5 reports the main conclusions and recommendations.


## 1.1. Background

Aluminium 6061 alloy is one of the commercial aluminum alloys being massively used in aerospace and automobile industries; it is a versatile heat treatable extruded alloy with medium to high strength capabilities. The typical application for aluminium alloy includes Aircraft and Aerospace components, Marine fittings, Transport, Bicycle frames, Vehicle rims, Camera lenses, Driveshaft, Electrical fittings and connectors, Brake components, Valves, Couplings, etc. [1, 2]. Researchers are working to develop materials that have light weight, high strength and stiffness, high impact, and corrosion resistance as they are widely used in structural application. Al6061 alloy is used as structural components in the aerospace, aeronautical, marine, and automobile industries. Al6061-T6 increases high toughness and weldability and found more application potential [3–5].


## 1.2. Literature Review

A few recent studies reported on the mechanical strength and fracture behavior application to high-velocity bullet impact on aluminum 6061 alloys. Some of the relevant research is discussed in the following section.Due to rapid simultaneous advancement in hardware technologies as well as in mechanics and material modeling during the last decades, engineers are nowadays able to analyze complex structures undergoing static and dynamic loading conditions in many engineering disciplines. In addition, high strain-rate deformations such as dynamic and high-velocity impact have increasing importance in industrial applications. Complex thermo-mechanical processes and numerical solution procedures such as the finite element method for solving strongly coupled mechanical and thermal boundary-value problems practices are gaining significantly in engineering fields [6–13]. Rathore et al. studied numerical simulation for Aluminium alloy 6060 to predict fracture behavior under the high-velocity impact of the flat-faced rigid circular projectile and the comparative effect has been studied in the range of 100 m/s, 150 m/s, and 250 m/s. They found plugging behavior and material experience shear-type deformation projectile impacting at high velocity [14]. Rai et al. performed ballistic impact on aluminium 5083-H116 plate numerically with Johnson Cook plastic model and their study was verified by hand calculations and engineering judgment. They conclude the Johnson Cook failure model was not able to capture scabbing phenomena, eventually ballistic resistance was overestimated in numerical simulation [15]. Senthil and Iqbal predict superior layer of armour steel, mild steel, and aluminum 7075-T651 alloy against 7.62 AP projectile, and the behavior was predicted by incorporating the Johnson Cook model [16]. Borvik et al. studied experimentally and numerically normal and oblique impact of 20 mm thick AA6082-T4 aluminium plates and the material parameters were identified utilizing the Johnson–Cook model [17]. Xiao et al. performed ballistic resistance of double layered 2024-T351 aluminium alloy plate against blunt projectiles and the modeling was carried out in ABAQUS/Explicit utilizing Johnson Cook plastic model [18]. Santha Rao and Shashank Simhadri proposed an improvement mechanism of aluminium alloy 5083 composites with hybrid reinforcement particles through friction stir process [19]. Bala et al. studied the bullet impact behavior of bamboo wall panels and found bamcrete panels have depth bullet penetration and energy absorption capacity compared to RCC [20]. Wu et al. performed anti-blast properties of 6063-T5 aluminium alloy with circular tube coated with polyurea elastomer and they conclude that polyurea cannot be directly applied. Mechanical performance of polyurea materials was studied while performing Quasi-static compression and tensile experiments [21]. Bagwe et al. studied numerical analysis of armour steel and aluminium alloy impacted by armour-piercing bullet and their ballistic performances were compared using ANSYS and the material model was developed utilizing the Johnson–Cook material model [22]. Several studies worldwide have been carried out on various materials and their performance-development techniques to meet the engineering requirement [23–31]. This leads to increasing demand for accurate, robust, and efficient numerical models to analyze the mechanical response of engineering structures under dynamic loading conditions.


## 1.3. Research Gap

From the available literature, there is minimal information regarding the critical velocity application essentially to evaluate perforation to ensure the reliability of the helmet impact of the soldier. According to the author’s knowledge, it is found that none of the researchers focused on the comprehensive analysis of mechanical behavior of plastic strength, fracture, numerical analysis, and experimental application to high-velocity bullet impact. Thus, this research work aims to increase the knowledge of material’s response application to the high-velocity impact that can be used in arms-ammunition, aviation, marine, automobile, and home appliances.


## 1.4. Research Objective

With the massive use and importance of Al6061 alloy, this research has been focused to elaborate on the detailed material behavior and comparative analysis has been carried out. The following are the main objectives of this study:(i)
To evaluate the comprehensive analysis of mechanical behavior under large stress-strain deformation and failure responses of the Al6061 alloy over a wide range of strain-rates such as 1 × 10−3 s−1, 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1 under room temperature to an elevated temperature 100°C and 200°C, respectively.(ii)
To determine the Johnson–Cook strength and fracture constants of an Al6061 alloy utilizing the Johnson–Cook constitutive model equation.(iii)
To determine the critical perforation velocity of an Al6061 alloy flat plate, when the bullet is fired with flat-nosed normal to the center of the plate.(iv)
To validate critical perforation velocity with the comparisons of a high-velocity bullet impact experimental acquisition results with ABAQUS/CAE numerical simulation results.


## 1.5. Novelty of the Study

The novelty of the study includes comprehensive mechanical behavior, evaluation of Johnson–Cook strength, fracture constants, and critical perforation velocity of 2 mm thickness of Al6061 alloy. OriginPro-V2017 software was used to obtain Johnson–Cook constants and ABAQUS/CAE to model the impact and analyze critical perforation velocity. Moreover, the numerical simulation has been compared with the experimental results to validate the critical perforation velocity. To the best of our knowledge, this is the first attempt in the literature.


## 1.6. Organization of the Study

The organization of the study is ordered as follows: Section1 presents the Al6061 alloy background and literature which supports the ideas of the proposed research. As a result of the theory of machines in Section 2, an adequate theory of Split Hopkinson Pressure Bar is discussed and some relevant research in the literature has been reported that the Johnson–Cook model equation benefits accuracy and reliability compared to other model equations in the determination of Johnson–Cook strength and fracture constants. Also, a detailed experimental setup of high-velocity bullet impact is covered in the same section. Section 3 presents the method of sample preparation and method to determine Johnson–Cook strength and fracture parameters. The obtained constant parameters have been used to perform numerical simulation analysis utilizing ABAQUS/CAE software. In Section 4, to contribute to a fair comparative study, the results and observations were carried out to compare numerical simulation results with experimental results for the validation. Finally, Section 5 reports the main conclusions and recommendations.


## 2. Johnson–Cook Model and High-Velocity Impact

### 2.1. Theory of the Split Hopkinson Pressure Bar (SHPB)

In 1913, Bertram Hopkinson introduced a technique to measure the peak pressure developed during a high strain-rate deformation event. A Kolsky bar, also widely known as a Split Hopkinson Pressure Bar (SHPB) [32], consists of two long slender bars that are closely sandwiched to a short cylindrical specimen between them. By striking the end of one bar, a compressive stress wave shall be generated and will immediately traverse across the stricken bar and reach at one end of the specimen. The wave shall be partially reflected and transverse back to the impact end. The remainder of the wave shall then go through the specimen and into the second bar causing the irresponsible plastic deformation on the specimen. It can be observed that the reflected and transmitted waves are proportional to the specimen’s strain-rate and stress, respectively. The specimen stain can be determined by integrating the strain-rate [33–35]. By monitoring the strains in the two bars, the specimen stress-strain properties can be calculated out which is depicted in Figure 1.Figure 1
Schematic of the SHPB machine.


#### 2.1.1. SHPB 3 Assumptions

(a)
One-Dimensional Stress Wave Assumption. The bar's cross-section must be kept flat, with a uniform distribution of axial stresses solely in the section. Therefore, the motion variable in the bar includes the displacement (u), the particle velocity (V), the stress (σ), and strain (ε) as a function of the axial coordinate x and the time (t). It concludes that the diameter of the bar be sufficiently small relative to its length so that the lateral inertia effect can be ignored.(b)
Stress-Strain Independent Assumption. The stress of the bar is only a single-valued function of the strain, i.e., the strain-rate effect of the bar is ignored.(c)
Strain Distribution of the Specimen along the Length of Uniform. During the loading process, the internal stress and strain of the specimen are evenly distributed in the longitudinal directions. The average strain of the whole specimen in the length is approximated as the strain in the specimen, i.e., the length of the specimen be sufficiently short and the time of passage of the stress wave through the specimen much less than the width of the loading pulse leaving the specimen in a uniformly compressed state.The transmission of deformation energy in the specimen as a transmitted wave and the remaining energy will be reflected in the form of a reflective wave. During the deformation process, the pulse signal is recorded by a strain gauge which is attached at the middle of both the rods, and strain-rate, stress, and strain felt by the specimen during the experiment can be evaluated. The average engineering stress on the specimen can be calculated using the following formula [36]:(1)σst=P1t+P2t2As,where P1t and P2t are the pressure of the rods and As is the initial cross-sectional area of the specimen. Assume that the pressure bar's Young's modulus, velocity, and cross-sectional area are E, C0, and Ao of the incident wave εIt and transmitted wave εRt, respectively.According to Wang Li-li, elastic wave for one dimension stress [37].(2)P1t=EA0εIt+εRt,(3)P2t=EA0εTt.Substituting (2) and (3) in equation (1) can be written as follows: (4)σst=12EA0AsEIt+ERt+ETt.The strain-rate in the specimen is given by(5)εs˙t=V1t−V2tIs,where V1t and V2t are the particles end face velocity of the incident and transmitted bar and Is is the original length of the specimen. Furthermore, it can be written as follows:(6)V1t=C0ε1t−ε2t,(7)V2t=C0εTt.Substituting (5) and (6) in (4) can be written as follows: (8)ε˙st=C0IsεIt−εRt−εTt.Integrating (7) will give the average engineering strain as follows:(9)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.Thus, summarizing the SHPB three assumptions can be further simplified as follows:(10)σst=12EA0AsεIt−εRt−εTt,(11)ε˙st=C0IsεIt−εRt−εTt,(12)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.The stress uniformity of the specimen is assumed to beP1t=P2t, and εIt+εRt=εTt. The SHPB is the most commonly used experimental technique for the determination of the dynamic compressive behavior of the materials at higher strain-rates such as 1 × 103s−1, 2 × 103s−1, and 3 × 103s−1. The striker bar is fired at high speed to collide with the incident bar creating an incident strain pulse (εI), which propagates along the bar until it reaches the specimen. At that point, acoustic impedance mismatches between bar and specimen materials, resulting in a portion of the pulse reflecting along the incident bar producing a strain (εR); during the process some of the pulses are transmitted through the specimen and into the transmitter bar with strain (εT). The engineering stress (σ¯), strain-rate (ε˙), and strain (ε) experienced by the specimen can be further simplified from equations (9), (10), and (11) as follows:(13)σst=EA0As.εTt,ε˙st=2C0Is.εRt,εst=2C0Is∫0tεRtdt.Hence, engineering stress and strain transformed to calculate true stress and true strain of the sample during the experiment is given by(14)σ¯=σ1+ε,ε¯=log1+ε.


### 2.2. Johnson–Cook Constitutive Equation

Johnson and Cook’s model was developed during the 1980s to study the impact, ballistic penetration, and explosive detonation problems. A constitutive model is primarily intended for computations, and it is recognized that more complicated models can describe the material behavior accurately. The constitutive equation developed by Johnson–Cook also known as Johnson and Cook model carried out to evaluate the high rate of deformation during the simulation. The model has proven to be very popular and has been used extensively in national laboratories, military laboratories, and private industry to study material behaviors under conditions of large strain and a wide range of strain-rates and temperatures [38, 39].There are many computer codes and constitutive models depicted in Table1 for the analysis accounting for large strains, high strain-rates, and thermal softening, which can generalize strength and fracture mechanism [40–43].Table 1
Types of constitutive equations.
AuthorsEquationParametersLudwik (1909)σ=σ0+Kεnσ0, K, n = constantsHolloman (1945)σ=KεnK,n = constantsSwift (1952)σ=Kε1+εnK,n = constantsε1 = pre-deformationVoce (1948)σ=σ0−σ0−σ1exp−nεσ0,σ1,n = constantTome et al. (1984)σ=σ0+σ1+θ1ε1−expθ0ε/σ1σ0=yield stressσ1=dσ/dε = constantsθ0andθ1 = workhard. coef.Ludwingson (1971)σ=K1εn1+expK2+n2εK1, K2, n1, n2 = constantsGladman et al. (1970)σ=σ0+K1lnε+K2εσ0,K1, K2 = constantsEl-Magd and Troost (1997)σ=Kεnε˙/ε˙0mK, n, m, ε˙0 = constantsEl-Magd (1997)σ=K1K2+εn+ηε˙exp−βT−T0/TmK1, K1, n, η, β= constantsReiff et al. (1986)σ=K1+K2ε˙/ε1m+K3εK1, K2,K3, m = constantsJohnson and cook (1983)σ=A+Bεpn1+Clogε˙∗1−T∗mA, B, n, C, m = constantsCowper Symondsσy=σ0+βEpεeffp1+ε˙p/D1/pD, P = constantsσy = initial yield strengthEp=plastic hardening modulusZerilli and Armstrong (1987)σ=σ0+K1ε˙0/ε˙−K3T+K2/e−K4εn+K5d−1/2σ0,K1,K2,K3,K4,K5,n,ε˙0 = constantsThe context of dynamic modeling requires the generalized constitutive equations which can describe the rate-dependent inelastic behavior of metals as functions of strains, strain-rates, and temperature. Due to simplicity and good results in high dynamic regions, many numerical simulations literature is based on the Johnson–Cook material model [44–46].


#### 2.2.1. Johnson–Cook Strength Model

The JC model consists of two parts. The first part describes material plastic flow stress that varies with strain, strain-rate, and temperatures. According to Johnson and Cook, the model for the Von Mises flow stress,σ, is expressed as [44](15)σ=A+Bεpn1+Clogε˙∗1−T∗m,where A, B, C, n, and m are material constants and are evaluated from an empirical fit of flow stress (as a function of strain, strain-rate, and temperatures).Whereεp is the equivalent plastic strain, ε˙∗=ε⋅/ε0 is the dimensionless plastic strain-rate for ε0˙=1s−1 considered as reference strain-rate. And, T∗=T−Troom/Tmelt−Troom is nondimensional homologous temperature, where T is the absolute temperature, Troom is the room temperature, and Tmelt is the material melting temperature of the Al6061 alloy.The first bracket of (14) represents the isothermal stress which is a function of strain ε0˙=1s−1 (reference strain-rate for convenience). The second bracket denotes the strain-rate effect and the third bracket accounts for the thermal effects.


#### 2.2.2. Johnson–Cook Fracture Model

The second part describes the fracture model intended to show the relative effect of various parameters. It also attempts to account for path dependency by accumulating damage as the deformation proceeds. For high-rate deformation problems, it is assumed that an arbitrary percentage of the plastic work done during deformation produces heat in the deforming of the material. For most of the materials, 90–100% of the plastic work is dissipated as heat in the material [47]. Therefore, the temperature used in the above (14) is derived from the increase in temperature according to the following expressions [46]:(16)ΔT=αρc∫σεdε,where ΔT is the temperature increase, α is the % of plastic work transformed into heat, c is the heat capacity, and ρ is the density.Fracture in the Johnson–Cook material model is derived from the following cumulative damage law as Refs. [46, 48(17)D=∑Δεεf,where Δε is the increment of equivalent plastic strain which occurs during an integration cycle, and εf is the equivalent strain to fracture under the current conditions of strain-rate, temperature, pressure, and equivalent stress. Fracture is then allowed to occur when D = 1.0, for constant values of the variables (σ∗,ε∗˙,T∗), and for σ∗≤1.5.The general expression for the strain at fracture is given by Ref. [46]:(18)εf=D1+D2expD3σ∗1+D4logε∗˙1+D5T∗.The dimensionless pressure-stress ratio is defined asσ∗=σm/σ¯, where σm is the average of the three normal stresses, and σ¯ is the Von Mises equivalent stress. The dimensional strain-rate (ε∗˙) and homologous temperature (T∗) are identical to those used in the Johnson–Cook strength model, and (17) D1,D2,D3,D4&D5 are the fracture constants. The expression in the first set of a bracket in (17) supports the hydrostatic tension pressure and triaxiality formation during the failure deformation path of Al6061 alloy during the experimental tension tests in three different notched specimens. The second set of bracket represents the effect of strain-rate, and the third set of bracket gives information about the effect of temperatures.(1) Triaxiality Stress. The stress state is often a complex stress state, which is the collection of two and more than two basic deformations shown in Figure 2. To describe this complex stress state, the stress triaxiality follows the following expressions [49]:(19)Rσ=σmσe=σ1+σ2+σ3/31/2σ1−σ22+σ2−σ32+σ3−σ42,where σ1,σ2,σ3,σm,andσe are expressed as three principal stresses, hydrostatic pressure, and von Mises equivalent stress, respectively. The stress triaxiality is a dimensionless parameter, which reflects the degree of the constraint of the plastic deformation capacity of the material. The fracture mechanism of the Al6061 alloy material during the experiment is dominated by pore expansion and polymerization, leading to the local shear band and leading transformation. Uniaxial tensile (pull-up) stress triaxiality is 1/3, for uniaxial compression, stress triaxiality is −1/3 and for pure torsion, the stress triaxiality is 0.Figure 2
Triaxial stress in the notched specimen.Bridgman found a method for finding the true stress-strain relation assuming uniform strain distribution in the notched section and the stress equation of the specimen is presented as [48](20)dσrrdr+σzz−σrrρ+σrr−σθθr=Assuming the notched curve is an arc, then the stress component of the notched specimen is given as(21)σrr=σθθ=σelog1+a2−r22aR,σzz=σe1+log1+a2−r22aR.According to the definition of stress triaxiality, the formula of stress triaxiality and equivalent failure strain can be obtained as [50](22)Rσ=13+log1+a2−r22aR,εf=2loga0a,where a and R are minimum cross-sectional radius and radius of the notched radius, respectively, r is the distance to the center of the cross-sectional, a0 is the initial radius of the smallest cross-section, and εf is the equivalent failure strain. The value of the triaxiality of stress is maximum at the smallest cross-section (i.e., r = 0).(23)Rσmaxx=13+log1+a02R0.


### 2.3. Experimental Setup of High-Velocity Bullet Impact

The bullet impact over flat Al6061 alloy was carried out utilizing the high-velocity bullet impact experimental setup to determine the critical perforation velocity. The working principle of the experimental setup is described in this section and the schematic of the experimental setup is shown in Figure3.Figure 3
Schematic diagram of high-velocity bullet impact.A pneumatic gas gun is equipped with an air compressor in which air is compressed into the desired pressure and the bullet propels forward when the pressure valve is activated. The system consists of a 78 mm bore compressed air gun with a supporting compressor, instrumentation, and control system. The compressor system pumps air into the storage tank, and the air storage tank used for driving the gun is shown in Figure4.Figure 4
Air compressor with a driving tank system.The bullet was held inside a wood sabot such that the sabot was trapped by a steel stopper reaching the end of the barrel allowing the bullet to continue its flight without any velocity loss as shown in Figure5.Figure 5
Sabot wooden stopper.


#### 2.3.1. Target Description

The square aluminum plate (205 × 205 × 2 mm3) was sandwiched between 2 and 2 steel frames and 2–2 plastic layer frames, front and back. The steel frame and target specimen plate assembly were rigidly attached with support structure connected nut-bolts as shown in Figure 6.Figure 6
The Sandwich structure with support.


#### 2.3.2. Velocity and Orientation Measurements

The velocity of the bullet was measured utilizing the projectile time-of-flight technique in which two helium or neon laser beams are placed at the known distance across the muzzle of the sabot stripper and the target shown in Figure7. The distance between the laser beams and the elapsed time were used to calculate the velocity.Figure 7
Velocity measurement setup before impact.


#### 2.3.3. Data Acquisition

As the bullet impact over the flat plate process was very short, 3–4 ms, the high-speed data acquisition recorder was carried out to collect the strain data using super dynamic strain gauges and sensors. The schematic of the data acquisition setup is shown in Figure8.Figure 8
Schematic of the data acquisition process.


#### 2.3.4. Measurement of Strains

The strain gauge was fixed at the back surface of the target plate to get the strain-time history during the bullet impact process. Three strain gauges were tightly stuck, i.e., bonded with glue to the target plate according to the pattern in which the center of the target was coinciding, as shown in Figure9. The sensing element of the strain gauge was made of copper-nickel foil and works on the principle of resistance change. The strain measurement system frequency response was set to 10 MHz with strain gauges recording strains and voltage measuring in the range of 0–20000 µε, and ±5 V, respectively.Figure 9
Strain gauges on the target specimen and real bullet.


## 2.1. Theory of the Split Hopkinson Pressure Bar (SHPB)

In 1913, Bertram Hopkinson introduced a technique to measure the peak pressure developed during a high strain-rate deformation event. A Kolsky bar, also widely known as a Split Hopkinson Pressure Bar (SHPB) [32], consists of two long slender bars that are closely sandwiched to a short cylindrical specimen between them. By striking the end of one bar, a compressive stress wave shall be generated and will immediately traverse across the stricken bar and reach at one end of the specimen. The wave shall be partially reflected and transverse back to the impact end. The remainder of the wave shall then go through the specimen and into the second bar causing the irresponsible plastic deformation on the specimen. It can be observed that the reflected and transmitted waves are proportional to the specimen’s strain-rate and stress, respectively. The specimen stain can be determined by integrating the strain-rate [33–35]. By monitoring the strains in the two bars, the specimen stress-strain properties can be calculated out which is depicted in Figure 1.Figure 1
Schematic of the SHPB machine.


### 2.1.1. SHPB 3 Assumptions

(a)
One-Dimensional Stress Wave Assumption. The bar's cross-section must be kept flat, with a uniform distribution of axial stresses solely in the section. Therefore, the motion variable in the bar includes the displacement (u), the particle velocity (V), the stress (σ), and strain (ε) as a function of the axial coordinate x and the time (t). It concludes that the diameter of the bar be sufficiently small relative to its length so that the lateral inertia effect can be ignored.(b)
Stress-Strain Independent Assumption. The stress of the bar is only a single-valued function of the strain, i.e., the strain-rate effect of the bar is ignored.(c)
Strain Distribution of the Specimen along the Length of Uniform. During the loading process, the internal stress and strain of the specimen are evenly distributed in the longitudinal directions. The average strain of the whole specimen in the length is approximated as the strain in the specimen, i.e., the length of the specimen be sufficiently short and the time of passage of the stress wave through the specimen much less than the width of the loading pulse leaving the specimen in a uniformly compressed state.The transmission of deformation energy in the specimen as a transmitted wave and the remaining energy will be reflected in the form of a reflective wave. During the deformation process, the pulse signal is recorded by a strain gauge which is attached at the middle of both the rods, and strain-rate, stress, and strain felt by the specimen during the experiment can be evaluated. The average engineering stress on the specimen can be calculated using the following formula [36]:(1)σst=P1t+P2t2As,where P1t and P2t are the pressure of the rods and As is the initial cross-sectional area of the specimen. Assume that the pressure bar's Young's modulus, velocity, and cross-sectional area are E, C0, and Ao of the incident wave εIt and transmitted wave εRt, respectively.According to Wang Li-li, elastic wave for one dimension stress [37].(2)P1t=EA0εIt+εRt,(3)P2t=EA0εTt.Substituting (2) and (3) in equation (1) can be written as follows: (4)σst=12EA0AsEIt+ERt+ETt.The strain-rate in the specimen is given by(5)εs˙t=V1t−V2tIs,where V1t and V2t are the particles end face velocity of the incident and transmitted bar and Is is the original length of the specimen. Furthermore, it can be written as follows:(6)V1t=C0ε1t−ε2t,(7)V2t=C0εTt.Substituting (5) and (6) in (4) can be written as follows: (8)ε˙st=C0IsεIt−εRt−εTt.Integrating (7) will give the average engineering strain as follows:(9)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.Thus, summarizing the SHPB three assumptions can be further simplified as follows:(10)σst=12EA0AsεIt−εRt−εTt,(11)ε˙st=C0IsεIt−εRt−εTt,(12)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.The stress uniformity of the specimen is assumed to beP1t=P2t, and εIt+εRt=εTt. The SHPB is the most commonly used experimental technique for the determination of the dynamic compressive behavior of the materials at higher strain-rates such as 1 × 103s−1, 2 × 103s−1, and 3 × 103s−1. The striker bar is fired at high speed to collide with the incident bar creating an incident strain pulse (εI), which propagates along the bar until it reaches the specimen. At that point, acoustic impedance mismatches between bar and specimen materials, resulting in a portion of the pulse reflecting along the incident bar producing a strain (εR); during the process some of the pulses are transmitted through the specimen and into the transmitter bar with strain (εT). The engineering stress (σ¯), strain-rate (ε˙), and strain (ε) experienced by the specimen can be further simplified from equations (9), (10), and (11) as follows:(13)σst=EA0As.εTt,ε˙st=2C0Is.εRt,εst=2C0Is∫0tεRtdt.Hence, engineering stress and strain transformed to calculate true stress and true strain of the sample during the experiment is given by(14)σ¯=σ1+ε,ε¯=log1+ε.


## 2.1.1. SHPB 3 Assumptions

(a)
One-Dimensional Stress Wave Assumption. The bar's cross-section must be kept flat, with a uniform distribution of axial stresses solely in the section. Therefore, the motion variable in the bar includes the displacement (u), the particle velocity (V), the stress (σ), and strain (ε) as a function of the axial coordinate x and the time (t). It concludes that the diameter of the bar be sufficiently small relative to its length so that the lateral inertia effect can be ignored.(b)
Stress-Strain Independent Assumption. The stress of the bar is only a single-valued function of the strain, i.e., the strain-rate effect of the bar is ignored.(c)
Strain Distribution of the Specimen along the Length of Uniform. During the loading process, the internal stress and strain of the specimen are evenly distributed in the longitudinal directions. The average strain of the whole specimen in the length is approximated as the strain in the specimen, i.e., the length of the specimen be sufficiently short and the time of passage of the stress wave through the specimen much less than the width of the loading pulse leaving the specimen in a uniformly compressed state.The transmission of deformation energy in the specimen as a transmitted wave and the remaining energy will be reflected in the form of a reflective wave. During the deformation process, the pulse signal is recorded by a strain gauge which is attached at the middle of both the rods, and strain-rate, stress, and strain felt by the specimen during the experiment can be evaluated. The average engineering stress on the specimen can be calculated using the following formula [36]:(1)σst=P1t+P2t2As,where P1t and P2t are the pressure of the rods and As is the initial cross-sectional area of the specimen. Assume that the pressure bar's Young's modulus, velocity, and cross-sectional area are E, C0, and Ao of the incident wave εIt and transmitted wave εRt, respectively.According to Wang Li-li, elastic wave for one dimension stress [37].(2)P1t=EA0εIt+εRt,(3)P2t=EA0εTt.Substituting (2) and (3) in equation (1) can be written as follows: (4)σst=12EA0AsEIt+ERt+ETt.The strain-rate in the specimen is given by(5)εs˙t=V1t−V2tIs,where V1t and V2t are the particles end face velocity of the incident and transmitted bar and Is is the original length of the specimen. Furthermore, it can be written as follows:(6)V1t=C0ε1t−ε2t,(7)V2t=C0εTt.Substituting (5) and (6) in (4) can be written as follows: (8)ε˙st=C0IsεIt−εRt−εTt.Integrating (7) will give the average engineering strain as follows:(9)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.Thus, summarizing the SHPB three assumptions can be further simplified as follows:(10)σst=12EA0AsεIt−εRt−εTt,(11)ε˙st=C0IsεIt−εRt−εTt,(12)εst=C0Is∫0t∫0tεIt−εRt−εTtdt.The stress uniformity of the specimen is assumed to beP1t=P2t, and εIt+εRt=εTt. The SHPB is the most commonly used experimental technique for the determination of the dynamic compressive behavior of the materials at higher strain-rates such as 1 × 103s−1, 2 × 103s−1, and 3 × 103s−1. The striker bar is fired at high speed to collide with the incident bar creating an incident strain pulse (εI), which propagates along the bar until it reaches the specimen. At that point, acoustic impedance mismatches between bar and specimen materials, resulting in a portion of the pulse reflecting along the incident bar producing a strain (εR); during the process some of the pulses are transmitted through the specimen and into the transmitter bar with strain (εT). The engineering stress (σ¯), strain-rate (ε˙), and strain (ε) experienced by the specimen can be further simplified from equations (9), (10), and (11) as follows:(13)σst=EA0As.εTt,ε˙st=2C0Is.εRt,εst=2C0Is∫0tεRtdt.Hence, engineering stress and strain transformed to calculate true stress and true strain of the sample during the experiment is given by(14)σ¯=σ1+ε,ε¯=log1+ε.


## 2.2. Johnson–Cook Constitutive Equation

Johnson and Cook’s model was developed during the 1980s to study the impact, ballistic penetration, and explosive detonation problems. A constitutive model is primarily intended for computations, and it is recognized that more complicated models can describe the material behavior accurately. The constitutive equation developed by Johnson–Cook also known as Johnson and Cook model carried out to evaluate the high rate of deformation during the simulation. The model has proven to be very popular and has been used extensively in national laboratories, military laboratories, and private industry to study material behaviors under conditions of large strain and a wide range of strain-rates and temperatures [38, 39].There are many computer codes and constitutive models depicted in Table1 for the analysis accounting for large strains, high strain-rates, and thermal softening, which can generalize strength and fracture mechanism [40–43].Table 1
Types of constitutive equations.
AuthorsEquationParametersLudwik (1909)σ=σ0+Kεnσ0, K, n = constantsHolloman (1945)σ=KεnK,n = constantsSwift (1952)σ=Kε1+εnK,n = constantsε1 = pre-deformationVoce (1948)σ=σ0−σ0−σ1exp−nεσ0,σ1,n = constantTome et al. (1984)σ=σ0+σ1+θ1ε1−expθ0ε/σ1σ0=yield stressσ1=dσ/dε = constantsθ0andθ1 = workhard. coef.Ludwingson (1971)σ=K1εn1+expK2+n2εK1, K2, n1, n2 = constantsGladman et al. (1970)σ=σ0+K1lnε+K2εσ0,K1, K2 = constantsEl-Magd and Troost (1997)σ=Kεnε˙/ε˙0mK, n, m, ε˙0 = constantsEl-Magd (1997)σ=K1K2+εn+ηε˙exp−βT−T0/TmK1, K1, n, η, β= constantsReiff et al. (1986)σ=K1+K2ε˙/ε1m+K3εK1, K2,K3, m = constantsJohnson and cook (1983)σ=A+Bεpn1+Clogε˙∗1−T∗mA, B, n, C, m = constantsCowper Symondsσy=σ0+βEpεeffp1+ε˙p/D1/pD, P = constantsσy = initial yield strengthEp=plastic hardening modulusZerilli and Armstrong (1987)σ=σ0+K1ε˙0/ε˙−K3T+K2/e−K4εn+K5d−1/2σ0,K1,K2,K3,K4,K5,n,ε˙0 = constantsThe context of dynamic modeling requires the generalized constitutive equations which can describe the rate-dependent inelastic behavior of metals as functions of strains, strain-rates, and temperature. Due to simplicity and good results in high dynamic regions, many numerical simulations literature is based on the Johnson–Cook material model [44–46].


### 2.2.1. Johnson–Cook Strength Model

The JC model consists of two parts. The first part describes material plastic flow stress that varies with strain, strain-rate, and temperatures. According to Johnson and Cook, the model for the Von Mises flow stress,σ, is expressed as [44](15)σ=A+Bεpn1+Clogε˙∗1−T∗m,where A, B, C, n, and m are material constants and are evaluated from an empirical fit of flow stress (as a function of strain, strain-rate, and temperatures).Whereεp is the equivalent plastic strain, ε˙∗=ε⋅/ε0 is the dimensionless plastic strain-rate for ε0˙=1s−1 considered as reference strain-rate. And, T∗=T−Troom/Tmelt−Troom is nondimensional homologous temperature, where T is the absolute temperature, Troom is the room temperature, and Tmelt is the material melting temperature of the Al6061 alloy.The first bracket of (14) represents the isothermal stress which is a function of strain ε0˙=1s−1 (reference strain-rate for convenience). The second bracket denotes the strain-rate effect and the third bracket accounts for the thermal effects.


### 2.2.2. Johnson–Cook Fracture Model

The second part describes the fracture model intended to show the relative effect of various parameters. It also attempts to account for path dependency by accumulating damage as the deformation proceeds. For high-rate deformation problems, it is assumed that an arbitrary percentage of the plastic work done during deformation produces heat in the deforming of the material. For most of the materials, 90–100% of the plastic work is dissipated as heat in the material [47]. Therefore, the temperature used in the above (14) is derived from the increase in temperature according to the following expressions [46]:(16)ΔT=αρc∫σεdε,where ΔT is the temperature increase, α is the % of plastic work transformed into heat, c is the heat capacity, and ρ is the density.Fracture in the Johnson–Cook material model is derived from the following cumulative damage law as Refs. [46, 48(17)D=∑Δεεf,where Δε is the increment of equivalent plastic strain which occurs during an integration cycle, and εf is the equivalent strain to fracture under the current conditions of strain-rate, temperature, pressure, and equivalent stress. Fracture is then allowed to occur when D = 1.0, for constant values of the variables (σ∗,ε∗˙,T∗), and for σ∗≤1.5.The general expression for the strain at fracture is given by Ref. [46]:(18)εf=D1+D2expD3σ∗1+D4logε∗˙1+D5T∗.The dimensionless pressure-stress ratio is defined asσ∗=σm/σ¯, where σm is the average of the three normal stresses, and σ¯ is the Von Mises equivalent stress. The dimensional strain-rate (ε∗˙) and homologous temperature (T∗) are identical to those used in the Johnson–Cook strength model, and (17) D1,D2,D3,D4&D5 are the fracture constants. The expression in the first set of a bracket in (17) supports the hydrostatic tension pressure and triaxiality formation during the failure deformation path of Al6061 alloy during the experimental tension tests in three different notched specimens. The second set of bracket represents the effect of strain-rate, and the third set of bracket gives information about the effect of temperatures.(1) Triaxiality Stress. The stress state is often a complex stress state, which is the collection of two and more than two basic deformations shown in Figure 2. To describe this complex stress state, the stress triaxiality follows the following expressions [49]:(19)Rσ=σmσe=σ1+σ2+σ3/31/2σ1−σ22+σ2−σ32+σ3−σ42,where σ1,σ2,σ3,σm,andσe are expressed as three principal stresses, hydrostatic pressure, and von Mises equivalent stress, respectively. The stress triaxiality is a dimensionless parameter, which reflects the degree of the constraint of the plastic deformation capacity of the material. The fracture mechanism of the Al6061 alloy material during the experiment is dominated by pore expansion and polymerization, leading to the local shear band and leading transformation. Uniaxial tensile (pull-up) stress triaxiality is 1/3, for uniaxial compression, stress triaxiality is −1/3 and for pure torsion, the stress triaxiality is 0.Figure 2
Triaxial stress in the notched specimen.Bridgman found a method for finding the true stress-strain relation assuming uniform strain distribution in the notched section and the stress equation of the specimen is presented as [48](20)dσrrdr+σzz−σrrρ+σrr−σθθr=Assuming the notched curve is an arc, then the stress component of the notched specimen is given as(21)σrr=σθθ=σelog1+a2−r22aR,σzz=σe1+log1+a2−r22aR.According to the definition of stress triaxiality, the formula of stress triaxiality and equivalent failure strain can be obtained as [50](22)Rσ=13+log1+a2−r22aR,εf=2loga0a,where a and R are minimum cross-sectional radius and radius of the notched radius, respectively, r is the distance to the center of the cross-sectional, a0 is the initial radius of the smallest cross-section, and εf is the equivalent failure strain. The value of the triaxiality of stress is maximum at the smallest cross-section (i.e., r = 0).(23)Rσmaxx=13+log1+a02R0.


## 2.2.1. Johnson–Cook Strength Model

The JC model consists of two parts. The first part describes material plastic flow stress that varies with strain, strain-rate, and temperatures. According to Johnson and Cook, the model for the Von Mises flow stress,σ, is expressed as [44](15)σ=A+Bεpn1+Clogε˙∗1−T∗m,where A, B, C, n, and m are material constants and are evaluated from an empirical fit of flow stress (as a function of strain, strain-rate, and temperatures).Whereεp is the equivalent plastic strain, ε˙∗=ε⋅/ε0 is the dimensionless plastic strain-rate for ε0˙=1s−1 considered as reference strain-rate. And, T∗=T−Troom/Tmelt−Troom is nondimensional homologous temperature, where T is the absolute temperature, Troom is the room temperature, and Tmelt is the material melting temperature of the Al6061 alloy.The first bracket of (14) represents the isothermal stress which is a function of strain ε0˙=1s−1 (reference strain-rate for convenience). The second bracket denotes the strain-rate effect and the third bracket accounts for the thermal effects.


## 2.2.2. Johnson–Cook Fracture Model

The second part describes the fracture model intended to show the relative effect of various parameters. It also attempts to account for path dependency by accumulating damage as the deformation proceeds. For high-rate deformation problems, it is assumed that an arbitrary percentage of the plastic work done during deformation produces heat in the deforming of the material. For most of the materials, 90–100% of the plastic work is dissipated as heat in the material [47]. Therefore, the temperature used in the above (14) is derived from the increase in temperature according to the following expressions [46]:(16)ΔT=αρc∫σεdε,where ΔT is the temperature increase, α is the % of plastic work transformed into heat, c is the heat capacity, and ρ is the density.Fracture in the Johnson–Cook material model is derived from the following cumulative damage law as Refs. [46, 48(17)D=∑Δεεf,where Δε is the increment of equivalent plastic strain which occurs during an integration cycle, and εf is the equivalent strain to fracture under the current conditions of strain-rate, temperature, pressure, and equivalent stress. Fracture is then allowed to occur when D = 1.0, for constant values of the variables (σ∗,ε∗˙,T∗), and for σ∗≤1.5.The general expression for the strain at fracture is given by Ref. [46]:(18)εf=D1+D2expD3σ∗1+D4logε∗˙1+D5T∗.The dimensionless pressure-stress ratio is defined asσ∗=σm/σ¯, where σm is the average of the three normal stresses, and σ¯ is the Von Mises equivalent stress. The dimensional strain-rate (ε∗˙) and homologous temperature (T∗) are identical to those used in the Johnson–Cook strength model, and (17) D1,D2,D3,D4&D5 are the fracture constants. The expression in the first set of a bracket in (17) supports the hydrostatic tension pressure and triaxiality formation during the failure deformation path of Al6061 alloy during the experimental tension tests in three different notched specimens. The second set of bracket represents the effect of strain-rate, and the third set of bracket gives information about the effect of temperatures.(1) Triaxiality Stress. The stress state is often a complex stress state, which is the collection of two and more than two basic deformations shown in Figure 2. To describe this complex stress state, the stress triaxiality follows the following expressions [49]:(19)Rσ=σmσe=σ1+σ2+σ3/31/2σ1−σ22+σ2−σ32+σ3−σ42,where σ1,σ2,σ3,σm,andσe are expressed as three principal stresses, hydrostatic pressure, and von Mises equivalent stress, respectively. The stress triaxiality is a dimensionless parameter, which reflects the degree of the constraint of the plastic deformation capacity of the material. The fracture mechanism of the Al6061 alloy material during the experiment is dominated by pore expansion and polymerization, leading to the local shear band and leading transformation. Uniaxial tensile (pull-up) stress triaxiality is 1/3, for uniaxial compression, stress triaxiality is −1/3 and for pure torsion, the stress triaxiality is 0.Figure 2
Triaxial stress in the notched specimen.Bridgman found a method for finding the true stress-strain relation assuming uniform strain distribution in the notched section and the stress equation of the specimen is presented as [48](20)dσrrdr+σzz−σrrρ+σrr−σθθr=Assuming the notched curve is an arc, then the stress component of the notched specimen is given as(21)σrr=σθθ=σelog1+a2−r22aR,σzz=σe1+log1+a2−r22aR.According to the definition of stress triaxiality, the formula of stress triaxiality and equivalent failure strain can be obtained as [50](22)Rσ=13+log1+a2−r22aR,εf=2loga0a,where a and R are minimum cross-sectional radius and radius of the notched radius, respectively, r is the distance to the center of the cross-sectional, a0 is the initial radius of the smallest cross-section, and εf is the equivalent failure strain. The value of the triaxiality of stress is maximum at the smallest cross-section (i.e., r = 0).(23)Rσmaxx=13+log1+a02R0.


## 2.3. Experimental Setup of High-Velocity Bullet Impact

The bullet impact over flat Al6061 alloy was carried out utilizing the high-velocity bullet impact experimental setup to determine the critical perforation velocity. The working principle of the experimental setup is described in this section and the schematic of the experimental setup is shown in Figure3.Figure 3
Schematic diagram of high-velocity bullet impact.A pneumatic gas gun is equipped with an air compressor in which air is compressed into the desired pressure and the bullet propels forward when the pressure valve is activated. The system consists of a 78 mm bore compressed air gun with a supporting compressor, instrumentation, and control system. The compressor system pumps air into the storage tank, and the air storage tank used for driving the gun is shown in Figure4.Figure 4
Air compressor with a driving tank system.The bullet was held inside a wood sabot such that the sabot was trapped by a steel stopper reaching the end of the barrel allowing the bullet to continue its flight without any velocity loss as shown in Figure5.Figure 5
Sabot wooden stopper.


### 2.3.1. Target Description

The square aluminum plate (205 × 205 × 2 mm3) was sandwiched between 2 and 2 steel frames and 2–2 plastic layer frames, front and back. The steel frame and target specimen plate assembly were rigidly attached with support structure connected nut-bolts as shown in Figure 6.Figure 6
The Sandwich structure with support.


### 2.3.2. Velocity and Orientation Measurements

The velocity of the bullet was measured utilizing the projectile time-of-flight technique in which two helium or neon laser beams are placed at the known distance across the muzzle of the sabot stripper and the target shown in Figure7. The distance between the laser beams and the elapsed time were used to calculate the velocity.Figure 7
Velocity measurement setup before impact.


### 2.3.3. Data Acquisition

As the bullet impact over the flat plate process was very short, 3–4 ms, the high-speed data acquisition recorder was carried out to collect the strain data using super dynamic strain gauges and sensors. The schematic of the data acquisition setup is shown in Figure8.Figure 8
Schematic of the data acquisition process.


### 2.3.4. Measurement of Strains

The strain gauge was fixed at the back surface of the target plate to get the strain-time history during the bullet impact process. Three strain gauges were tightly stuck, i.e., bonded with glue to the target plate according to the pattern in which the center of the target was coinciding, as shown in Figure9. The sensing element of the strain gauge was made of copper-nickel foil and works on the principle of resistance change. The strain measurement system frequency response was set to 10 MHz with strain gauges recording strains and voltage measuring in the range of 0–20000 µε, and ±5 V, respectively.Figure 9
Strain gauges on the target specimen and real bullet.


## 2.3.1. Target Description

The square aluminum plate (205 × 205 × 2 mm3) was sandwiched between 2 and 2 steel frames and 2–2 plastic layer frames, front and back. The steel frame and target specimen plate assembly were rigidly attached with support structure connected nut-bolts as shown in Figure 6.Figure 6
The Sandwich structure with support.


## 2.3.2. Velocity and Orientation Measurements

The velocity of the bullet was measured utilizing the projectile time-of-flight technique in which two helium or neon laser beams are placed at the known distance across the muzzle of the sabot stripper and the target shown in Figure7. The distance between the laser beams and the elapsed time were used to calculate the velocity.Figure 7
Velocity measurement setup before impact.


## 2.3.3. Data Acquisition

As the bullet impact over the flat plate process was very short, 3–4 ms, the high-speed data acquisition recorder was carried out to collect the strain data using super dynamic strain gauges and sensors. The schematic of the data acquisition setup is shown in Figure8.Figure 8
Schematic of the data acquisition process.


## 2.3.4. Measurement of Strains

The strain gauge was fixed at the back surface of the target plate to get the strain-time history during the bullet impact process. Three strain gauges were tightly stuck, i.e., bonded with glue to the target plate according to the pattern in which the center of the target was coinciding, as shown in Figure9. The sensing element of the strain gauge was made of copper-nickel foil and works on the principle of resistance change. The strain measurement system frequency response was set to 10 MHz with strain gauges recording strains and voltage measuring in the range of 0–20000 µε, and ±5 V, respectively.Figure 9
Strain gauges on the target specimen and real bullet.


## 3. Methodology

The detailed methodology to validate the critical perforation velocity of the Al6061 alloy is illustrated in Figure10.Figure 10
Flowchart illustrating the methodology.


### 3.1. Sample Preparation

To conduct the research, the various samples of Al6061 alloy were prepared to study comprehensive mechanical behavior. The quasi-static, quasi-dynamics, and high-velocity bullet impact tests were performed under a wide range of strain-rates as well as at elevated temperatures. Accordingly, experimental machines have been utilized to perform this research.


#### 3.1.1. Quasi-Static

(1) Tensile Test. DNS-100 electronic universal testing machine shown in Figure 11 was utilized to determine the tensile mechanical behavior of Al6061 alloy at three different temperatures such as room temperature 20°C, and elevated temperatures at 100°C and 200°C, respectively.Figure 11
DNS100 tensile testing machine.For that, the smooth specimen of diameter 5.0 mm, and three different notched specimens (notched diameter 1.5 mm, 2.0 mm, and 2.5 mm) were prepared, which are depicted in Figure12, respectively. Mechanical behaviors of smooth and notched specimens have been studied experimentally, which are presented in Figures 13 and 14 of the appendix, respectively. To calculate failure strain during the tensile process, the data were recorded with the help of a high-speed camera for precise accuracy.Figure 12
Tensile test of Al6061 alloy for smooth and notched specimens.Figure 13
Notched specimens’ mechanical response at three different temperatures. (a) Notched specimen with radii 1.5 mm. (b) Notched specimen with radii 2.0 mm. (c) Notched specimen with radii 2.5 mm.
(a)(b)(c)Figure 14
Tensile response of smooth and notched specimen under reference strain-rate (ε˙) = 10−3/s. (a) Smooth and notched specimen at 20°C. (b) Smooth and notched specimen at 100°C. (c) Smooth and notched specimen at 200°C.
(a)(b)(c)(2) Torsion Test. A dog-bone shape sample was prepared Φ5.7 × 14 mm for the torsion rate and twisting ability of the Al6061 alloy and the test was performed utilizing the computer-controlled DHW 1000 strain-rate machine, which is shown inFigure 15. The torsional response of the specimen is presented in Figure 16 of the appendix.Figure 15
DHW1000 torsion test machine and Dog-bone Al6061 alloy sample.Figure 16
Torsional response. Quasi-static torsion test at reference strain-rate (10−3/s).


#### 3.1.2. Quasi-Dynamic

(1) Split-Hopkinson Pressure Bar (SHPB). SHPB experimental setup was chosen for the compression test of Al6061 alloy and samples were prepared to maintain good polishing at both the ends whose dimension was made intentionally Φ5 × 5 mm before the experiment, which is shown in Figure 17. Figure 18 of the appendix presents the compression experimental behavior of the specimen at strain-rates of 1000/s, 2000/s, and 3000/s at room temperature to an elevated temperature of 100°C and 200°C, respectively.Figure 17
SHPB experimental setup and compression sample.Figure 18
Compression tests. (a) Compression response at20°C under three strain-rates (ε˙). (b) Compression response at 100°C under three strain-rates (ε˙). (c) Compression response at 200°C under three strain-rates (ε˙).
(a)(b)(c)(2) Split-Hopkinson Tension Bar (SHTB). The development of a method to test material to be in tension under high strain-rates (later called Split Hopkinson Tension Bar, SHTB) was introduced a decade later after the SHPB [51, 52]. The progress in using SHTB was very slow due to difficulties inherent in sample design, load application, and data interpretation. Many arrangements have been used to apply a tension pulse to the specimen. The differences between them are inherent in the load application, sample design, and bars arrangements. To perform tension tests in the Al6061 alloy, the experimental setup was reconfigured. The SHTB tension experimental specimen size was manufactured Φ3 × 5 mm, which is shown in Figure 19.Figure 19
SHTB experimental setup and tension sample.While performing this experimental test, proper alignment and positioning of the sample with grips are the most important because mismatch might create traction in pulse, impedance, and reflections in wave propagation. The specimen was necessary to fix at both the ends of the incident and transmitted bars and strain gauge transmits the generated tension traction pulse to the computer when a longer bolt head with input bar is used to drive a hollow tube striker with the same inner diameter and area. The tension responses of the specimen have been studied and experimental tests have been presented in Figure20 of the appendix.Figure 20
Tension tests. (a) Tension response at20°C under three strain-rates (ε˙). (b) Tension response at 100°C under three strain-rates (ε˙). (c) Tension response at 200°C under three strain-rates (ε˙).
(a)(b)(c)


#### 3.1.3. High-Velocity Bullet Impact

A cylindrical blunt-nosed bullet (45 mm length and 12 mm diameter) weighing 0.05 kg made of stainless steel is fired normally to the center of the Al6061 alloy specimen (205 × 205 × 2 mm3) to predict the critical perforation velocity. The strain gauge is fixed on the backside of the specimen at three different locations. One at the center of the impact region and two lateral sides apart from its exact center 40 mm. The nomenclature was done as (4, 3), (0, 5) for the two lateral sides while (2, 1) for the center impact region as shown in Figure 9. The strain pulse along the X- and Y-axis is monitored and stored in a computer-controlled data acquisition system.


### 3.2. Determination of Johnson–Cook Constant Parameters

#### 3.2.1. Johnson–Cook Strength Parameters

During the tension test, reference strain-rate (ε˙) of 10−3/s was carried out for smooth (radius 5.0 mm) and notched specimen (radii of 1.5 mm, 2.0 mm, 2.5 mm) to evaluate true stress-strain curve plotted under room temperature (20°C), and at elevated temperatures of 100°C and 200°C, respectively, to observe the material behavior of Al6061 alloy. An isolated furnace split-tube of 20 cm was utilized to maintain the elevated temperatures 100°C and 200°C to the specimen for observing the actual material behavior. Pure torsion and fracture morphology under reference strain-rate have been studied in this work. Similarly, compression behaviors of Al6061 alloy have been studied dynamically with temperature variant in which 3 dynamic strain-rates (ε˙) (1000/s, 2000/s, and 3000/s) were carried out at room temperature (20°C) to elevated temperatures of 100°C and 200°C, respectively.(1) Determination of A, B, and n. Quasi-static experimental test of a smooth specimen whose radius was 5.0 mm carried out the tensile test at reference strain-rate (ε˙) of 10−3/s under three different temperatures at room temperature (20°C) to elevated temperature 100°C and 200°C. Under this condition, equation (18) becomes(24)σ=A+Bεpn.At reference strain-rate, true plastic stress-strain curves are plotted and the plastic strain was calculated by subtracting the elastic strain from the total strain. The average stress-strain value was calculated, as shown in Table2, and the average plastic Johnson Cook parameters were evaluated using the graph fitting methods utilizing OriginPro V2017 software, which is shown in Figure 21.Table 2
Obtained values ofA, B, and n.
SNJohnson–Cook strength parameterAverage obtained fitted values1A3182B3953n0.73707Figure 21
Average fitting values ofA, B, and n.Substituting the values ofA, B, and n in (24) becomes(25)A+Bεpn=318+395εp0.73707.(2) Determination of C. Compression test of the Al6061 alloy shown in Figure 17 whose dimension Φ5 × 5 mm carried out at room temperature of 20°C under three dynamic strain-rates (ε˙) of 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1, respectively. Under this condition, the Johnson–Cook constitutive model (14) becomes(26)σA=1+Clogε˙∗.Then, from the experimental data, plastic strain, true strain, andσ/A values were evaluated. The value of C was obtained utilizing the graph fitting methods which were 0.01224, as shown in Figure 22.Figure 22
Average fitting value ofC.(3) Determination of m. Quasi-static tensile tests were performed on smooth specimen shown in Figure12 whose radius was 5.0 mm at reference strain-rate of (ε˙) of 1 × 10−3 s−1 carried out at three different temperatures such as 20°C, 100°C, and 200°C, respectively, and (14) becomes: (27)σA=1−T∗m.The average true plastic stress and strain were evaluated from the obtained experimental data at three different temperatures. The average value ofm of 1.77019 was obtained utilizing the graph fitting methods, as shown in Figure 23.Figure 23
Average fitting value ofm.The Johnson–Cook plastic constants were evaluated utilizing the graph fitting methods of the Al6061 alloy which is depicted in Table3.Table 3
Johnson–Cook plastic constants of Al6061 alloy.
ConstantsABnCmAl6061 alloy318.22599395.368690.737070.012241.77019


#### 3.2.2. Johnson–Cook Fracture Parameters

From this experimental test research of Al6061 alloy (R0: 1.5 mm, 2.0 mm, and 2.5 mm) notched specimens, their corresponding stress triaxiality have been calculated as 0.6248, 0.5724, and 0.5289, respectively.(1) Determination of D1, D2, and D3. Tension tests of the smooth specimen (radius 5.0 mm), notched specimen (radii 1.5 mm, 2.0 mm, and 2.5 mm), and torsion tests of the dog-bone specimen (radius 5.7 mm and length 14 mm) were carried out at room temperature of 20°C and reference strain-rate (ε˙) of 1 × 10−3 s−1. Tables 4–8of the appendix presents the determination of failure strain and stress triaxiality under the reference strain-rate. Under this state, we may write (17) as(28)εf=D1+D2expD3σ∗.Table 4
Notched radii = 1.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/40=2log1.325σ∗=1/3+log1+2.18/2×1.52.εf=2log53/42=2log1.2619047σ∗=1/3+log1+2.26/2×1.53.εf=2log53/41=2log1.292682926σ∗=1/3+log1+2.22/2×1.5Table 5
Notched radii = 2.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/36=2log1.5σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5552.εf=2log53/41=2log1.2126829σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5553.εf=2log53/42=2log1.28571426σ∗=1/3+log1+2.22/2×2.0=1/3+log1.555Table 6
Notched radii = 2.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log53/40=2log1.325σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4442.εf=2log53/41=2log1.29268293σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4443.εf=2log53/42=2log1.26190476σ∗=1/3+log1+2.22/2×2.5=1/3+log1.444Table 7
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log119/81=2log1.4691358σ∗=1/3+log1+5.0/2×5.0=1/3+log1.52.εf=2log121/93=2log1.30107527σ∗=1/3+log1+5.0/2×5.0=1/3+log1.53.εf=2log119/80=2log1.4875σ∗=1/3+log1+5.0/2×5.0=1/3+log1.5Table 8
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=rf/3Stress triaxialityσ∗=01.εf=5.7∗610.5312271∗3.14/1.7320508∗180∗13.74σ∗=02.εf=5.7∗804.486958440488∗3.14/1.7320508∗180∗13.76σ∗=03.εf=5.7∗593.179758867875∗3.14/1.7320508∗180∗13.88σ∗=0Then, the fracture strain (εf) and triaxiality state of stress (σ∗) were evaluated using the high-speed camera from the experimental tension tests results of the smooth, notched specimen and torsion tests using dog-bone specimen under reference strain-rate represented by substitute (28). Average fitting values of Johnson–Cook constants of D1, D2 , and D3 are 0.08196, 2.27659, and F02D1.81322, respectively, as shown in Figure 24.(29)εf=0.08196+2.27659∗exp−1.81322∗−13.Figure 24
Average fitting values ofD1, D2, and D3.(2) Determination of D4. The smooth specimen shown in Figure 12 carried out dynamic tensile tests under three different strain-rates (ε˙) of 1 × 10−3 s−1, 2 × 10−3 s−1, and 3 × 10−3 s−1 at room temperature (20°C). The fracture process was recorded by a high-speed camera and the calculation of average failure strain under three strain-rates were calculated as 0.8497, 0.6767, and 0.9458, respectively, as shown in Figure 25. Table 9 of the appendix presents the calculation of average failure strain under strain-rates of 1000/s, 2000/s, and 3000/s, respectively. The average graph fitting value of D4 is −0.07239 then equation (21) can be written as follows:(30)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙.Figure 25
Average fitting values ofD4.Table 9
Radius = 3.0 mm and length = 5.0 mm at20°C under different strain-rate ε˙:1×103/s,2×103/s,3×103/s, respectively.
SNFailure strainεf=2logd/dfStrain-ratesε˙1.εf=2×log105/68εf=2×log104/68Avg.εf=0.8497663881000/s2.εf=2×log105/75εf=2×log104/75Avg.εf=0.6767980432000/s3.εf=2×log104/64εf=2×log103/65Avg.εf=0.9458495343000/s(3) Determination of D5. The smooth specimen shown in Figure 12 performed tensile tests under reference strain rate (ε˙) 1 × 10−3 s−1 at room temperature (20°C) to elevated temperatures 100°C and 200°C, respectively. The fracture process was recorded by a high-speed camera. The average graph fitting value of D5 is –0.00626 which is shown in Figure 26. Table 10 of the appendix presents the calculations of failure strains at three different temperatures. The Johnson–Cook fracture (20) can be written as(31)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙+1−0.00626.Figure 26
Average fitting value ofD5.Table 10
Failure strain–Temperatures.
SNFailure strainεfTemperatures1.0.7941937170.5263821050.79413971720°C2.0.7133498880.8677291650.747932882100°C3.0.8925742050.8677291650.818946259200°CThe Johnson–Cook fracture constants were evaluated using the graph fitting methods of the Al6061 alloy, which are depicted in Table11.Table 11
Johnson–Cook fracture constant of Al 6061 alloy.
ConstantsD1D2D3D4D5Al60610.081962.27659−1.81322−0.07239−0.00626


### 3.3. Numerical Simulations

The finite element software ABAQUS/CAE was utilized to model the bullet impact and the corresponding numerical simulations. The cylindrical bullet was deployed to impact over a square plate of Al6061 alloy. Several impact simulations were carried out to determine the critical perforation velocity when the bullet projected normal to the square flat specimen. The Johnson–Cook plastic and fracture constants were evaluated using OriginPro-V2017.


#### 3.3.1. Modeling of Bullet and Al6061 Alloy Plate

The blunt-nosed cylindrical bullet was assigned all the material properties of stainless steel. The evaluated Johnson–Cook constant parameters were assigned for the Al6061 alloy specimen. The 50-gram bullet’s length 50 mm and diameter 12 mm projected normal to the center of the specimen (205 × 205 × 2 mm3). The design, modeling, and simulation were carried out using ABAQUS/CAE software. Several impacts have been carried out to determine the critical perforation velocity. The sensitivity of element size was carried out and appropriate sizes were assigned in the geometry, which is presented in Figure 27. The boundary condition was set to the outer facing four edges of the plate, wherein A, B, and C of the flat plate and their element size were assigned as 3 × 2, 2 × 2, and 3 × 3, respectively. The total number of nodes and elements of the messed specimen were 36975 & 28896, while the central impact regions were 19945 & 15376. The critical perforation velocity was found to be 70 ms−1 when a rigid steel bullet was fired normally to the center of the flat plate.Figure 27
Al6061 flat plate with a stainless steel bullet.


## 3.1. Sample Preparation

To conduct the research, the various samples of Al6061 alloy were prepared to study comprehensive mechanical behavior. The quasi-static, quasi-dynamics, and high-velocity bullet impact tests were performed under a wide range of strain-rates as well as at elevated temperatures. Accordingly, experimental machines have been utilized to perform this research.


### 3.1.1. Quasi-Static

(1) Tensile Test. DNS-100 electronic universal testing machine shown in Figure 11 was utilized to determine the tensile mechanical behavior of Al6061 alloy at three different temperatures such as room temperature 20°C, and elevated temperatures at 100°C and 200°C, respectively.Figure 11
DNS100 tensile testing machine.For that, the smooth specimen of diameter 5.0 mm, and three different notched specimens (notched diameter 1.5 mm, 2.0 mm, and 2.5 mm) were prepared, which are depicted in Figure12, respectively. Mechanical behaviors of smooth and notched specimens have been studied experimentally, which are presented in Figures 13 and 14 of the appendix, respectively. To calculate failure strain during the tensile process, the data were recorded with the help of a high-speed camera for precise accuracy.Figure 12
Tensile test of Al6061 alloy for smooth and notched specimens.Figure 13
Notched specimens’ mechanical response at three different temperatures. (a) Notched specimen with radii 1.5 mm. (b) Notched specimen with radii 2.0 mm. (c) Notched specimen with radii 2.5 mm.
(a)(b)(c)Figure 14
Tensile response of smooth and notched specimen under reference strain-rate (ε˙) = 10−3/s. (a) Smooth and notched specimen at 20°C. (b) Smooth and notched specimen at 100°C. (c) Smooth and notched specimen at 200°C.
(a)(b)(c)(2) Torsion Test. A dog-bone shape sample was prepared Φ5.7 × 14 mm for the torsion rate and twisting ability of the Al6061 alloy and the test was performed utilizing the computer-controlled DHW 1000 strain-rate machine, which is shown inFigure 15. The torsional response of the specimen is presented in Figure 16 of the appendix.Figure 15
DHW1000 torsion test machine and Dog-bone Al6061 alloy sample.Figure 16
Torsional response. Quasi-static torsion test at reference strain-rate (10−3/s).


### 3.1.2. Quasi-Dynamic

(1) Split-Hopkinson Pressure Bar (SHPB). SHPB experimental setup was chosen for the compression test of Al6061 alloy and samples were prepared to maintain good polishing at both the ends whose dimension was made intentionally Φ5 × 5 mm before the experiment, which is shown in Figure 17. Figure 18 of the appendix presents the compression experimental behavior of the specimen at strain-rates of 1000/s, 2000/s, and 3000/s at room temperature to an elevated temperature of 100°C and 200°C, respectively.Figure 17
SHPB experimental setup and compression sample.Figure 18
Compression tests. (a) Compression response at20°C under three strain-rates (ε˙). (b) Compression response at 100°C under three strain-rates (ε˙). (c) Compression response at 200°C under three strain-rates (ε˙).
(a)(b)(c)(2) Split-Hopkinson Tension Bar (SHTB). The development of a method to test material to be in tension under high strain-rates (later called Split Hopkinson Tension Bar, SHTB) was introduced a decade later after the SHPB [51, 52]. The progress in using SHTB was very slow due to difficulties inherent in sample design, load application, and data interpretation. Many arrangements have been used to apply a tension pulse to the specimen. The differences between them are inherent in the load application, sample design, and bars arrangements. To perform tension tests in the Al6061 alloy, the experimental setup was reconfigured. The SHTB tension experimental specimen size was manufactured Φ3 × 5 mm, which is shown in Figure 19.Figure 19
SHTB experimental setup and tension sample.While performing this experimental test, proper alignment and positioning of the sample with grips are the most important because mismatch might create traction in pulse, impedance, and reflections in wave propagation. The specimen was necessary to fix at both the ends of the incident and transmitted bars and strain gauge transmits the generated tension traction pulse to the computer when a longer bolt head with input bar is used to drive a hollow tube striker with the same inner diameter and area. The tension responses of the specimen have been studied and experimental tests have been presented in Figure20 of the appendix.Figure 20
Tension tests. (a) Tension response at20°C under three strain-rates (ε˙). (b) Tension response at 100°C under three strain-rates (ε˙). (c) Tension response at 200°C under three strain-rates (ε˙).
(a)(b)(c)


### 3.1.3. High-Velocity Bullet Impact

A cylindrical blunt-nosed bullet (45 mm length and 12 mm diameter) weighing 0.05 kg made of stainless steel is fired normally to the center of the Al6061 alloy specimen (205 × 205 × 2 mm3) to predict the critical perforation velocity. The strain gauge is fixed on the backside of the specimen at three different locations. One at the center of the impact region and two lateral sides apart from its exact center 40 mm. The nomenclature was done as (4, 3), (0, 5) for the two lateral sides while (2, 1) for the center impact region as shown in Figure 9. The strain pulse along the X- and Y-axis is monitored and stored in a computer-controlled data acquisition system.


## 3.1.1. Quasi-Static

(1) Tensile Test. DNS-100 electronic universal testing machine shown in Figure 11 was utilized to determine the tensile mechanical behavior of Al6061 alloy at three different temperatures such as room temperature 20°C, and elevated temperatures at 100°C and 200°C, respectively.Figure 11
DNS100 tensile testing machine.For that, the smooth specimen of diameter 5.0 mm, and three different notched specimens (notched diameter 1.5 mm, 2.0 mm, and 2.5 mm) were prepared, which are depicted in Figure12, respectively. Mechanical behaviors of smooth and notched specimens have been studied experimentally, which are presented in Figures 13 and 14 of the appendix, respectively. To calculate failure strain during the tensile process, the data were recorded with the help of a high-speed camera for precise accuracy.Figure 12
Tensile test of Al6061 alloy for smooth and notched specimens.Figure 13
Notched specimens’ mechanical response at three different temperatures. (a) Notched specimen with radii 1.5 mm. (b) Notched specimen with radii 2.0 mm. (c) Notched specimen with radii 2.5 mm.
(a)(b)(c)Figure 14
Tensile response of smooth and notched specimen under reference strain-rate (ε˙) = 10−3/s. (a) Smooth and notched specimen at 20°C. (b) Smooth and notched specimen at 100°C. (c) Smooth and notched specimen at 200°C.
(a)(b)(c)(2) Torsion Test. A dog-bone shape sample was prepared Φ5.7 × 14 mm for the torsion rate and twisting ability of the Al6061 alloy and the test was performed utilizing the computer-controlled DHW 1000 strain-rate machine, which is shown inFigure 15. The torsional response of the specimen is presented in Figure 16 of the appendix.Figure 15
DHW1000 torsion test machine and Dog-bone Al6061 alloy sample.Figure 16
Torsional response. Quasi-static torsion test at reference strain-rate (10−3/s).


## 3.1.2. Quasi-Dynamic

(1) Split-Hopkinson Pressure Bar (SHPB). SHPB experimental setup was chosen for the compression test of Al6061 alloy and samples were prepared to maintain good polishing at both the ends whose dimension was made intentionally Φ5 × 5 mm before the experiment, which is shown in Figure 17. Figure 18 of the appendix presents the compression experimental behavior of the specimen at strain-rates of 1000/s, 2000/s, and 3000/s at room temperature to an elevated temperature of 100°C and 200°C, respectively.Figure 17
SHPB experimental setup and compression sample.Figure 18
Compression tests. (a) Compression response at20°C under three strain-rates (ε˙). (b) Compression response at 100°C under three strain-rates (ε˙). (c) Compression response at 200°C under three strain-rates (ε˙).
(a)(b)(c)(2) Split-Hopkinson Tension Bar (SHTB). The development of a method to test material to be in tension under high strain-rates (later called Split Hopkinson Tension Bar, SHTB) was introduced a decade later after the SHPB [51, 52]. The progress in using SHTB was very slow due to difficulties inherent in sample design, load application, and data interpretation. Many arrangements have been used to apply a tension pulse to the specimen. The differences between them are inherent in the load application, sample design, and bars arrangements. To perform tension tests in the Al6061 alloy, the experimental setup was reconfigured. The SHTB tension experimental specimen size was manufactured Φ3 × 5 mm, which is shown in Figure 19.Figure 19
SHTB experimental setup and tension sample.While performing this experimental test, proper alignment and positioning of the sample with grips are the most important because mismatch might create traction in pulse, impedance, and reflections in wave propagation. The specimen was necessary to fix at both the ends of the incident and transmitted bars and strain gauge transmits the generated tension traction pulse to the computer when a longer bolt head with input bar is used to drive a hollow tube striker with the same inner diameter and area. The tension responses of the specimen have been studied and experimental tests have been presented in Figure20 of the appendix.Figure 20
Tension tests. (a) Tension response at20°C under three strain-rates (ε˙). (b) Tension response at 100°C under three strain-rates (ε˙). (c) Tension response at 200°C under three strain-rates (ε˙).
(a)(b)(c)


## 3.1.3. High-Velocity Bullet Impact

A cylindrical blunt-nosed bullet (45 mm length and 12 mm diameter) weighing 0.05 kg made of stainless steel is fired normally to the center of the Al6061 alloy specimen (205 × 205 × 2 mm3) to predict the critical perforation velocity. The strain gauge is fixed on the backside of the specimen at three different locations. One at the center of the impact region and two lateral sides apart from its exact center 40 mm. The nomenclature was done as (4, 3), (0, 5) for the two lateral sides while (2, 1) for the center impact region as shown in Figure 9. The strain pulse along the X- and Y-axis is monitored and stored in a computer-controlled data acquisition system.


## 3.2. Determination of Johnson–Cook Constant Parameters

### 3.2.1. Johnson–Cook Strength Parameters

During the tension test, reference strain-rate (ε˙) of 10−3/s was carried out for smooth (radius 5.0 mm) and notched specimen (radii of 1.5 mm, 2.0 mm, 2.5 mm) to evaluate true stress-strain curve plotted under room temperature (20°C), and at elevated temperatures of 100°C and 200°C, respectively, to observe the material behavior of Al6061 alloy. An isolated furnace split-tube of 20 cm was utilized to maintain the elevated temperatures 100°C and 200°C to the specimen for observing the actual material behavior. Pure torsion and fracture morphology under reference strain-rate have been studied in this work. Similarly, compression behaviors of Al6061 alloy have been studied dynamically with temperature variant in which 3 dynamic strain-rates (ε˙) (1000/s, 2000/s, and 3000/s) were carried out at room temperature (20°C) to elevated temperatures of 100°C and 200°C, respectively.(1) Determination of A, B, and n. Quasi-static experimental test of a smooth specimen whose radius was 5.0 mm carried out the tensile test at reference strain-rate (ε˙) of 10−3/s under three different temperatures at room temperature (20°C) to elevated temperature 100°C and 200°C. Under this condition, equation (18) becomes(24)σ=A+Bεpn.At reference strain-rate, true plastic stress-strain curves are plotted and the plastic strain was calculated by subtracting the elastic strain from the total strain. The average stress-strain value was calculated, as shown in Table2, and the average plastic Johnson Cook parameters were evaluated using the graph fitting methods utilizing OriginPro V2017 software, which is shown in Figure 21.Table 2
Obtained values ofA, B, and n.
SNJohnson–Cook strength parameterAverage obtained fitted values1A3182B3953n0.73707Figure 21
Average fitting values ofA, B, and n.Substituting the values ofA, B, and n in (24) becomes(25)A+Bεpn=318+395εp0.73707.(2) Determination of C. Compression test of the Al6061 alloy shown in Figure 17 whose dimension Φ5 × 5 mm carried out at room temperature of 20°C under three dynamic strain-rates (ε˙) of 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1, respectively. Under this condition, the Johnson–Cook constitutive model (14) becomes(26)σA=1+Clogε˙∗.Then, from the experimental data, plastic strain, true strain, andσ/A values were evaluated. The value of C was obtained utilizing the graph fitting methods which were 0.01224, as shown in Figure 22.Figure 22
Average fitting value ofC.(3) Determination of m. Quasi-static tensile tests were performed on smooth specimen shown in Figure12 whose radius was 5.0 mm at reference strain-rate of (ε˙) of 1 × 10−3 s−1 carried out at three different temperatures such as 20°C, 100°C, and 200°C, respectively, and (14) becomes: (27)σA=1−T∗m.The average true plastic stress and strain were evaluated from the obtained experimental data at three different temperatures. The average value ofm of 1.77019 was obtained utilizing the graph fitting methods, as shown in Figure 23.Figure 23
Average fitting value ofm.The Johnson–Cook plastic constants were evaluated utilizing the graph fitting methods of the Al6061 alloy which is depicted in Table3.Table 3
Johnson–Cook plastic constants of Al6061 alloy.
ConstantsABnCmAl6061 alloy318.22599395.368690.737070.012241.77019


### 3.2.2. Johnson–Cook Fracture Parameters

From this experimental test research of Al6061 alloy (R0: 1.5 mm, 2.0 mm, and 2.5 mm) notched specimens, their corresponding stress triaxiality have been calculated as 0.6248, 0.5724, and 0.5289, respectively.(1) Determination of D1, D2, and D3. Tension tests of the smooth specimen (radius 5.0 mm), notched specimen (radii 1.5 mm, 2.0 mm, and 2.5 mm), and torsion tests of the dog-bone specimen (radius 5.7 mm and length 14 mm) were carried out at room temperature of 20°C and reference strain-rate (ε˙) of 1 × 10−3 s−1. Tables 4–8of the appendix presents the determination of failure strain and stress triaxiality under the reference strain-rate. Under this state, we may write (17) as(28)εf=D1+D2expD3σ∗.Table 4
Notched radii = 1.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/40=2log1.325σ∗=1/3+log1+2.18/2×1.52.εf=2log53/42=2log1.2619047σ∗=1/3+log1+2.26/2×1.53.εf=2log53/41=2log1.292682926σ∗=1/3+log1+2.22/2×1.5Table 5
Notched radii = 2.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/36=2log1.5σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5552.εf=2log53/41=2log1.2126829σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5553.εf=2log53/42=2log1.28571426σ∗=1/3+log1+2.22/2×2.0=1/3+log1.555Table 6
Notched radii = 2.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log53/40=2log1.325σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4442.εf=2log53/41=2log1.29268293σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4443.εf=2log53/42=2log1.26190476σ∗=1/3+log1+2.22/2×2.5=1/3+log1.444Table 7
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log119/81=2log1.4691358σ∗=1/3+log1+5.0/2×5.0=1/3+log1.52.εf=2log121/93=2log1.30107527σ∗=1/3+log1+5.0/2×5.0=1/3+log1.53.εf=2log119/80=2log1.4875σ∗=1/3+log1+5.0/2×5.0=1/3+log1.5Table 8
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=rf/3Stress triaxialityσ∗=01.εf=5.7∗610.5312271∗3.14/1.7320508∗180∗13.74σ∗=02.εf=5.7∗804.486958440488∗3.14/1.7320508∗180∗13.76σ∗=03.εf=5.7∗593.179758867875∗3.14/1.7320508∗180∗13.88σ∗=0Then, the fracture strain (εf) and triaxiality state of stress (σ∗) were evaluated using the high-speed camera from the experimental tension tests results of the smooth, notched specimen and torsion tests using dog-bone specimen under reference strain-rate represented by substitute (28). Average fitting values of Johnson–Cook constants of D1, D2 , and D3 are 0.08196, 2.27659, and F02D1.81322, respectively, as shown in Figure 24.(29)εf=0.08196+2.27659∗exp−1.81322∗−13.Figure 24
Average fitting values ofD1, D2, and D3.(2) Determination of D4. The smooth specimen shown in Figure 12 carried out dynamic tensile tests under three different strain-rates (ε˙) of 1 × 10−3 s−1, 2 × 10−3 s−1, and 3 × 10−3 s−1 at room temperature (20°C). The fracture process was recorded by a high-speed camera and the calculation of average failure strain under three strain-rates were calculated as 0.8497, 0.6767, and 0.9458, respectively, as shown in Figure 25. Table 9 of the appendix presents the calculation of average failure strain under strain-rates of 1000/s, 2000/s, and 3000/s, respectively. The average graph fitting value of D4 is −0.07239 then equation (21) can be written as follows:(30)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙.Figure 25
Average fitting values ofD4.Table 9
Radius = 3.0 mm and length = 5.0 mm at20°C under different strain-rate ε˙:1×103/s,2×103/s,3×103/s, respectively.
SNFailure strainεf=2logd/dfStrain-ratesε˙1.εf=2×log105/68εf=2×log104/68Avg.εf=0.8497663881000/s2.εf=2×log105/75εf=2×log104/75Avg.εf=0.6767980432000/s3.εf=2×log104/64εf=2×log103/65Avg.εf=0.9458495343000/s(3) Determination of D5. The smooth specimen shown in Figure 12 performed tensile tests under reference strain rate (ε˙) 1 × 10−3 s−1 at room temperature (20°C) to elevated temperatures 100°C and 200°C, respectively. The fracture process was recorded by a high-speed camera. The average graph fitting value of D5 is –0.00626 which is shown in Figure 26. Table 10 of the appendix presents the calculations of failure strains at three different temperatures. The Johnson–Cook fracture (20) can be written as(31)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙+1−0.00626.Figure 26
Average fitting value ofD5.Table 10
Failure strain–Temperatures.
SNFailure strainεfTemperatures1.0.7941937170.5263821050.79413971720°C2.0.7133498880.8677291650.747932882100°C3.0.8925742050.8677291650.818946259200°CThe Johnson–Cook fracture constants were evaluated using the graph fitting methods of the Al6061 alloy, which are depicted in Table11.Table 11
Johnson–Cook fracture constant of Al 6061 alloy.
ConstantsD1D2D3D4D5Al60610.081962.27659−1.81322−0.07239−0.00626


## 3.2.1. Johnson–Cook Strength Parameters

During the tension test, reference strain-rate (ε˙) of 10−3/s was carried out for smooth (radius 5.0 mm) and notched specimen (radii of 1.5 mm, 2.0 mm, 2.5 mm) to evaluate true stress-strain curve plotted under room temperature (20°C), and at elevated temperatures of 100°C and 200°C, respectively, to observe the material behavior of Al6061 alloy. An isolated furnace split-tube of 20 cm was utilized to maintain the elevated temperatures 100°C and 200°C to the specimen for observing the actual material behavior. Pure torsion and fracture morphology under reference strain-rate have been studied in this work. Similarly, compression behaviors of Al6061 alloy have been studied dynamically with temperature variant in which 3 dynamic strain-rates (ε˙) (1000/s, 2000/s, and 3000/s) were carried out at room temperature (20°C) to elevated temperatures of 100°C and 200°C, respectively.(1) Determination of A, B, and n. Quasi-static experimental test of a smooth specimen whose radius was 5.0 mm carried out the tensile test at reference strain-rate (ε˙) of 10−3/s under three different temperatures at room temperature (20°C) to elevated temperature 100°C and 200°C. Under this condition, equation (18) becomes(24)σ=A+Bεpn.At reference strain-rate, true plastic stress-strain curves are plotted and the plastic strain was calculated by subtracting the elastic strain from the total strain. The average stress-strain value was calculated, as shown in Table2, and the average plastic Johnson Cook parameters were evaluated using the graph fitting methods utilizing OriginPro V2017 software, which is shown in Figure 21.Table 2
Obtained values ofA, B, and n.
SNJohnson–Cook strength parameterAverage obtained fitted values1A3182B3953n0.73707Figure 21
Average fitting values ofA, B, and n.Substituting the values ofA, B, and n in (24) becomes(25)A+Bεpn=318+395εp0.73707.(2) Determination of C. Compression test of the Al6061 alloy shown in Figure 17 whose dimension Φ5 × 5 mm carried out at room temperature of 20°C under three dynamic strain-rates (ε˙) of 1 × 103 s−1, 2 × 103 s−1, and 3 × 103 s−1, respectively. Under this condition, the Johnson–Cook constitutive model (14) becomes(26)σA=1+Clogε˙∗.Then, from the experimental data, plastic strain, true strain, andσ/A values were evaluated. The value of C was obtained utilizing the graph fitting methods which were 0.01224, as shown in Figure 22.Figure 22
Average fitting value ofC.(3) Determination of m. Quasi-static tensile tests were performed on smooth specimen shown in Figure12 whose radius was 5.0 mm at reference strain-rate of (ε˙) of 1 × 10−3 s−1 carried out at three different temperatures such as 20°C, 100°C, and 200°C, respectively, and (14) becomes: (27)σA=1−T∗m.The average true plastic stress and strain were evaluated from the obtained experimental data at three different temperatures. The average value ofm of 1.77019 was obtained utilizing the graph fitting methods, as shown in Figure 23.Figure 23
Average fitting value ofm.The Johnson–Cook plastic constants were evaluated utilizing the graph fitting methods of the Al6061 alloy which is depicted in Table3.Table 3
Johnson–Cook plastic constants of Al6061 alloy.
ConstantsABnCmAl6061 alloy318.22599395.368690.737070.012241.77019


## 3.2.2. Johnson–Cook Fracture Parameters

From this experimental test research of Al6061 alloy (R0: 1.5 mm, 2.0 mm, and 2.5 mm) notched specimens, their corresponding stress triaxiality have been calculated as 0.6248, 0.5724, and 0.5289, respectively.(1) Determination of D1, D2, and D3. Tension tests of the smooth specimen (radius 5.0 mm), notched specimen (radii 1.5 mm, 2.0 mm, and 2.5 mm), and torsion tests of the dog-bone specimen (radius 5.7 mm and length 14 mm) were carried out at room temperature of 20°C and reference strain-rate (ε˙) of 1 × 10−3 s−1. Tables 4–8of the appendix presents the determination of failure strain and stress triaxiality under the reference strain-rate. Under this state, we may write (17) as(28)εf=D1+D2expD3σ∗.Table 4
Notched radii = 1.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/40=2log1.325σ∗=1/3+log1+2.18/2×1.52.εf=2log53/42=2log1.2619047σ∗=1/3+log1+2.26/2×1.53.εf=2log53/41=2log1.292682926σ∗=1/3+log1+2.22/2×1.5Table 5
Notched radii = 2.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log54/36=2log1.5σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5552.εf=2log53/41=2log1.2126829σ∗=1/3+log1+2.22/2×2.0=1/3+log1.5553.εf=2log53/42=2log1.28571426σ∗=1/3+log1+2.22/2×2.0=1/3+log1.555Table 6
Notched radii = 2.5 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log53/40=2log1.325σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4442.εf=2log53/41=2log1.29268293σ∗=1/3+log1+2.22/2×2.5=1/3+log1.4443.εf=2log53/42=2log1.26190476σ∗=1/3+log1+2.22/2×2.5=1/3+log1.444Table 7
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=2logd/dfStress triaxialityσ∗=1/3+log1+a/2R1.εf=2log119/81=2log1.4691358σ∗=1/3+log1+5.0/2×5.0=1/3+log1.52.εf=2log121/93=2log1.30107527σ∗=1/3+log1+5.0/2×5.0=1/3+log1.53.εf=2log119/80=2log1.4875σ∗=1/3+log1+5.0/2×5.0=1/3+log1.5Table 8
Radii = 5.0 mm at20°C under reference strain-rate ε˙:1×10−3/s.
SNFailure strainεf=rf/3Stress triaxialityσ∗=01.εf=5.7∗610.5312271∗3.14/1.7320508∗180∗13.74σ∗=02.εf=5.7∗804.486958440488∗3.14/1.7320508∗180∗13.76σ∗=03.εf=5.7∗593.179758867875∗3.14/1.7320508∗180∗13.88σ∗=0Then, the fracture strain (εf) and triaxiality state of stress (σ∗) were evaluated using the high-speed camera from the experimental tension tests results of the smooth, notched specimen and torsion tests using dog-bone specimen under reference strain-rate represented by substitute (28). Average fitting values of Johnson–Cook constants of D1, D2 , and D3 are 0.08196, 2.27659, and F02D1.81322, respectively, as shown in Figure 24.(29)εf=0.08196+2.27659∗exp−1.81322∗−13.Figure 24
Average fitting values ofD1, D2, and D3.(2) Determination of D4. The smooth specimen shown in Figure 12 carried out dynamic tensile tests under three different strain-rates (ε˙) of 1 × 10−3 s−1, 2 × 10−3 s−1, and 3 × 10−3 s−1 at room temperature (20°C). The fracture process was recorded by a high-speed camera and the calculation of average failure strain under three strain-rates were calculated as 0.8497, 0.6767, and 0.9458, respectively, as shown in Figure 25. Table 9 of the appendix presents the calculation of average failure strain under strain-rates of 1000/s, 2000/s, and 3000/s, respectively. The average graph fitting value of D4 is −0.07239 then equation (21) can be written as follows:(30)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙.Figure 25
Average fitting values ofD4.Table 9
Radius = 3.0 mm and length = 5.0 mm at20°C under different strain-rate ε˙:1×103/s,2×103/s,3×103/s, respectively.
SNFailure strainεf=2logd/dfStrain-ratesε˙1.εf=2×log105/68εf=2×log104/68Avg.εf=0.8497663881000/s2.εf=2×log105/75εf=2×log104/75Avg.εf=0.6767980432000/s3.εf=2×log104/64εf=2×log103/65Avg.εf=0.9458495343000/s(3) Determination of D5. The smooth specimen shown in Figure 12 performed tensile tests under reference strain rate (ε˙) 1 × 10−3 s−1 at room temperature (20°C) to elevated temperatures 100°C and 200°C, respectively. The fracture process was recorded by a high-speed camera. The average graph fitting value of D5 is –0.00626 which is shown in Figure 26. Table 10 of the appendix presents the calculations of failure strains at three different temperatures. The Johnson–Cook fracture (20) can be written as(31)εf=0.08196+2.27659∗exp−1.81322∗−131+−0.07239logε∗˙+1−0.00626.Figure 26
Average fitting value ofD5.Table 10
Failure strain–Temperatures.
SNFailure strainεfTemperatures1.0.7941937170.5263821050.79413971720°C2.0.7133498880.8677291650.747932882100°C3.0.8925742050.8677291650.818946259200°CThe Johnson–Cook fracture constants were evaluated using the graph fitting methods of the Al6061 alloy, which are depicted in Table11.Table 11
Johnson–Cook fracture constant of Al 6061 alloy.
ConstantsD1D2D3D4D5Al60610.081962.27659−1.81322−0.07239−0.00626


## 3.3. Numerical Simulations

The finite element software ABAQUS/CAE was utilized to model the bullet impact and the corresponding numerical simulations. The cylindrical bullet was deployed to impact over a square plate of Al6061 alloy. Several impact simulations were carried out to determine the critical perforation velocity when the bullet projected normal to the square flat specimen. The Johnson–Cook plastic and fracture constants were evaluated using OriginPro-V2017.


### 3.3.1. Modeling of Bullet and Al6061 Alloy Plate

The blunt-nosed cylindrical bullet was assigned all the material properties of stainless steel. The evaluated Johnson–Cook constant parameters were assigned for the Al6061 alloy specimen. The 50-gram bullet’s length 50 mm and diameter 12 mm projected normal to the center of the specimen (205 × 205 × 2 mm3). The design, modeling, and simulation were carried out using ABAQUS/CAE software. Several impacts have been carried out to determine the critical perforation velocity. The sensitivity of element size was carried out and appropriate sizes were assigned in the geometry, which is presented in Figure 27. The boundary condition was set to the outer facing four edges of the plate, wherein A, B, and C of the flat plate and their element size were assigned as 3 × 2, 2 × 2, and 3 × 3, respectively. The total number of nodes and elements of the messed specimen were 36975 & 28896, while the central impact regions were 19945 & 15376. The critical perforation velocity was found to be 70 ms−1 when a rigid steel bullet was fired normally to the center of the flat plate.Figure 27
Al6061 flat plate with a stainless steel bullet.


## 3.3.1. Modeling of Bullet and Al6061 Alloy Plate

The blunt-nosed cylindrical bullet was assigned all the material properties of stainless steel. The evaluated Johnson–Cook constant parameters were assigned for the Al6061 alloy specimen. The 50-gram bullet’s length 50 mm and diameter 12 mm projected normal to the center of the specimen (205 × 205 × 2 mm3). The design, modeling, and simulation were carried out using ABAQUS/CAE software. Several impacts have been carried out to determine the critical perforation velocity. The sensitivity of element size was carried out and appropriate sizes were assigned in the geometry, which is presented in Figure 27. The boundary condition was set to the outer facing four edges of the plate, wherein A, B, and C of the flat plate and their element size were assigned as 3 × 2, 2 × 2, and 3 × 3, respectively. The total number of nodes and elements of the messed specimen were 36975 & 28896, while the central impact regions were 19945 & 15376. The critical perforation velocity was found to be 70 ms−1 when a rigid steel bullet was fired normally to the center of the flat plate.Figure 27
Al6061 flat plate with a stainless steel bullet.


## 4. Results and Observations

### 4.1. Numerical Simulation Results

The finite element software ABAQUS/CAE was utilized to model and the numerical simulations were carried out for bullet impact. The cylindrical bullet was deployed to impact normal to the center of a square plate Al6061 alloy. Several bullet impact simulations were carried out to find the critical perforation velocity of the specimen. The Johnson–Cook’s plastic and fracture constants were evaluated and justified material properties before running the numerical simulation. The critical perforation velocity was found to be 70 ms−1 and impact scenarios are shown in Figure 28.Figure 28
Critical perforation velocity.Two unit-cells with element numbers 9288 and 1172 at a distance of 40 mm from the central element with number 9264 facing the X‐ and Y‐axis, respectively, are chosen for numerical simulation. The strain gauges were fixed at three places, 40 mm far from the impact center facing the X‐ and Y‐axis, respectively, during the experimental tests to compare impact behavior numerically. The true strain was much higher when a bullet was fired with 70 ms−1 and the strain produced was 0.00525 and 0.00325, respectively, on X-axis and Y-axis during the 2 µs time of impact, which is shown in Figure 29.Figure 29
Strain produced at 70 ms−1.


### 4.2. Experimental Results

The Al60601 alloy of the square flat plate specimen (205 × 205 × 2 mm3) was prepared. The cylindrical blunt-nosed stainless steel bullet weighing 0.05 kg was fired normally to the center of the specimen to predict the critical perforation velocity of the plate under a high-velocity impact. Three strain gauges at three different locations on the specimen were fixed, one at the exact center and two lateral sides at a distance of 40 mm far from the center facing X- and Y-axis, respectively, with the help of glue. The nomenclature was done such that (4, 3), (0, 5) for lateral sides, and (1, 2) for the central location, respectively. The critical perforation velocity of the bullet was found to be 70 ms−1 experimentally in which the bullet got trapped/suspended on the Al6061 alloy flat plate, which is shown in Figure 30.Figure 30
Critical perforation velocity.


### 4.3. Comparison of Bullet Impact Experiment and Numerical Simulation Results

In this section, numerical simulations were compared with experimental results at three different velocities such as 60 ms−1, 65 ms−1, and 70 ms−1, respectively, as depicted in Figure 31. The experimental results and numerical simulation results show very good agreement with each other. The velocity of 70 ms−1 was found to be the critical perforation velocity and was validated with iSIGHT experimental tests.Figure 31
iSIGHT comparison of experimental results with numerical simulation results.
(a)(b)(c)


## 4.1. Numerical Simulation Results

The finite element software ABAQUS/CAE was utilized to model and the numerical simulations were carried out for bullet impact. The cylindrical bullet was deployed to impact normal to the center of a square plate Al6061 alloy. Several bullet impact simulations were carried out to find the critical perforation velocity of the specimen. The Johnson–Cook’s plastic and fracture constants were evaluated and justified material properties before running the numerical simulation. The critical perforation velocity was found to be 70 ms−1 and impact scenarios are shown in Figure 28.Figure 28
Critical perforation velocity.Two unit-cells with element numbers 9288 and 1172 at a distance of 40 mm from the central element with number 9264 facing the X‐ and Y‐axis, respectively, are chosen for numerical simulation. The strain gauges were fixed at three places, 40 mm far from the impact center facing the X‐ and Y‐axis, respectively, during the experimental tests to compare impact behavior numerically. The true strain was much higher when a bullet was fired with 70 ms−1 and the strain produced was 0.00525 and 0.00325, respectively, on X-axis and Y-axis during the 2 µs time of impact, which is shown in Figure 29.Figure 29
Strain produced at 70 ms−1.


## 4.2. Experimental Results

The Al60601 alloy of the square flat plate specimen (205 × 205 × 2 mm3) was prepared. The cylindrical blunt-nosed stainless steel bullet weighing 0.05 kg was fired normally to the center of the specimen to predict the critical perforation velocity of the plate under a high-velocity impact. Three strain gauges at three different locations on the specimen were fixed, one at the exact center and two lateral sides at a distance of 40 mm far from the center facing X- and Y-axis, respectively, with the help of glue. The nomenclature was done such that (4, 3), (0, 5) for lateral sides, and (1, 2) for the central location, respectively. The critical perforation velocity of the bullet was found to be 70 ms−1 experimentally in which the bullet got trapped/suspended on the Al6061 alloy flat plate, which is shown in Figure 30.Figure 30
Critical perforation velocity.


## 4.3. Comparison of Bullet Impact Experiment and Numerical Simulation Results

In this section, numerical simulations were compared with experimental results at three different velocities such as 60 ms−1, 65 ms−1, and 70 ms−1, respectively, as depicted in Figure 31. The experimental results and numerical simulation results show very good agreement with each other. The velocity of 70 ms−1 was found to be the critical perforation velocity and was validated with iSIGHT experimental tests.Figure 31
iSIGHT comparison of experimental results with numerical simulation results.
(a)(b)(c)


## 5. Conclusions and Future Works

The study was focused to validate critical perforation velocity numerically and experimentally. The following are the significant findings of the present study:(1)
The experimental results conclude that when the temperature and strain-rates increases, the yield and flow stress of Al6061 alloy also increase.(2)
The Johnson–Cook strength and fracture constants are evaluated of an Al6061 alloy utilizing Johnson–Cook constitutive model equation, which is obtained as follows: (i) strength constants such asA, B, n, C, and m are 318.22599, 395.36869, 0.73707, 0.01224, and 1.77019, respectively. (ii) fracture constants such as D1, D2, D3, D4, and D5 are 0.08196, 2.27659, −1.81322, −0.07239, and −0.00626, respectively.(3)
Based on the experimental and numerical simulation results, the critical perforation velocity of stainless steel bullet impact is found to be 70 ms−1.(4)
The study results are expected to provide safety limits to the manufacturer assessing the impact-crashworthiness of 2 mm Al6061 alloy in aviation, marine, automobile, or defense fields.(5)
The Al6061 alloy may be accepted for future application where light-weight, moderate impact, good strength, and corrosion resistance are required.Further study is needed to evaluate the Al6061 alloy responses when impacted with a certain angle and with a hemispherical nosed bullet.



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*Source: 3707200-2022-02-24.xml*