Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 55, 4, pp. 1219-1233, Warsaw 2017 DOI: 10.15632/jtam-pl.55.4.1219 EXPERIMENTAL AND NUMERICAL ANALYSIS OF ALUMINUM ALLOY AW5005 BEHAVIOR SUBJECTED TO TENSION AND PERFORATION UNDER DYNAMIC LOADING Amine Bendarma Poznan University of Technology, Institute of Structural Engineering, Poznań, Poland, and Universiapolis, Ecole Polytechnique d’Agadir Bab Al Madina, Qr Tilila, Agadir, Morocco e-mail: b.amine@e-polytechnique.ma Tomasz Jankowiak, Tomasz Łodygowski Poznan University of Technology, Institute of Structural Engineering, Poznań, Poland e-mail: tomasz.jankowiak@put.poznan.pl; tomasz.lodygowski@put.poznan.pl Alexis Rusinek Laboratory of Mechanics, Biomechanics, Polymers and Structures (LaBPS), National Engineering School of Metz (ENIM), Metz, France; e-mail: alexis.rusinek@univ-lorraine.fr Maciej Klósak Universiapolis, Ecole Polytechnique d’Agadir Bab Al Madina, Qr Tilila, Agadir, Morocco, and The International University of Logistics and Transport in Wrocław, Poland e-mail: klosak@e-polytechnique.ma The paper describes mechanical behavior of aluminum alloy AW5005 (EN AW5005) un- der impact loading. The work is focused on tensile tests and the process of perforation of aluminum alloy AW5005 sheets. Experimental, analytical and numerical investigations are carried out to analyse in details the perforation process.Based on these approaches, ballistic properties of the structure impacted by a conical nose shape projectile are studied. Different failure criteria are discussed, coupling numerical and experimental analyses for a wide range of strain rates. Optimization method functions are used to identify the parameters of the failure criteria.Finally, goodcorrelation is obtainedbetween thenumerical and experimental results for both tension and perforation tests. Keywords: aluminum alloy, AW5005, ballistic behavior, failure criterion 1. Introduction In this paper, a study on aluminum alloy AW5005 behavior is reported. This alloy contains nominally 0.8% magnesium and it presents a medium strength, good weldability and good corrosion resistance in marine atmospheres. Themetallurgical state of the aluminum alloy used in thiswork is as received. It has a lower density andan excellent thermal conductivity compared to other aluminum alloys. It is the most commonly used type of aluminum in sheet and plate forms (Kulekci, 2014). The ballistic behavior and resistance of aluminum sheet plates is strongly dependent on the material behavior under dynamic loading. The ballistic properties of the structure are intensely related to thematerial behavior and to the interaction between the projectile and a thin alumi- num target during the perforation process. Therefore, to find expected curves, many dynamic constitutive relations have been studied in several works. For instance, Johnson andCook (1983) proposed a dynamic constitutive relation based on aphenomenological approach.Themodel has 1220 A. Bendarma et al. been often used in impact and perforation problems analysis. Verleysen et al. (2011) investiga- ted the effect of strain rate on the forming behavior of sheet metals and described stress-strain curves of the material using the Johnson-cook model. Erice et al. (2014) presented a coupled elastoplastic-damage constitutive model to simulate the failure behavior of inconel plates. Rusi- nek and Rodŕıguez-Mart́ınez (2009) provided two extensions of the original Rusinek-Klepaczko constitutive relation (Rusinek andKlepaczko, 2001) in order to define the behavior of aluminum alloys at wide ranges of strain rates and temperatures showing a negative strain rate sensitivity. Børvik et al. (2009) studied the influence of amodified Johnson-Cook constitutive relation using numerical simulations of steel plate perforation. Jankowiak et al. (2013) considered perforation of different configurations: mild steel and sandwich plates. The effectiveness of these kinds of structures was checked. The authors also presented the effect of strain rate sensitivity models (Johnson-Cook andRusinek-Klepaczko) on the ballistic curve. Additionally, several effects were considered: strain hardening, yield stress and projectile mass. Based on these results, it was possible to optimize the structure and find the right plate thickness to prevent its perforation. The sandwich configuration containing two sheets of steel is less efficient than amonolithic steel sheet of an equivalent total thickness. It was proven that thickness of the target had an im- portant effect on the ballistic performance. This analysis can be used for the present AW5005 structure optimization. Kpenyigba et al. (2013) and Rusinek et al. (2008) studied the influence of the projectile nose shape (conical, blunt and hemispherical) and the projectile diameter on ballistic properties and failure modes of thin steel targets. In order to simulate the behavior of impacted and perforated structures, the finite elementmethod with an explicit time integration procedure was an effective technique (Kpenyigba et al., 2013; Rusinek et al., 2008; Rusinek and Rodŕıguez-Mart́ınez, 2008; Quinney and Taylor, 1937; Xue and Belytschko, 2010). Numerical simulations, in particular by the FE method, are also effective supplements for theoretical and experimental investigations whichwere carried out to analyze the dynamic behavior of impacted structures. In order to determine mechanical characteristics of the material in quasi-static conditions, tensile tests have been carried out according to the methodology discussed in (Zhong et al., 2016). 2. Experimental approach There are little references about this material, especially concerning mechanical properties of this specific aluminum alloy. However, Kulekci (2014) published that the yield strength is equal to 45MPa and the tensile strength is 110MPa. Additionally, it is described that the elongation of this alloy is close to 15%. In the present paper, a tensile test is used to calibrate thematerial behavior. The specimen is machined from a 1.0mm thickness aluminum sheet. The dimensions of the specimen are presented in Fig. 1. Additionally, the perforation test is used to describe ballistic properties of the material and failure modes for the conical projectile nose shape see Fig. 4. Compression using a sandwich specimen (Zhong et al., 2015) and shear tests (Rusinek and Klepaczko, 2001; Bao and Wierzbicki, 2004) also reports for this material but it is out of scope of this analysis. 2.1. Tensile test Quasi-static uniaxial tensile tests ofAW5005 aluminumhave beenperformedusing a conven- tional hydraulic machine. The dimensions of the flat dumbbell-shaped specimen are shown in Fig. 1 (Zhong et al., 2016). The first part of the specimen is embedded on 40mmwhile the other end of the specimen is fixed to the mobile crosshead. The loading force and the displacement are recorded during the tests for the imposed velocity. Experimental and numerical analysis of aluminum alloy AW5005... 1221 Fig. 1. Dimensions of the tensile specimens Fig. 2. Description of kinematic failure for three selected time points: (a) homogeneous deformation, elastic part, (b) strain localization ε=0.015, (c) shear band before failure ε=0.045, (d) force versus displacement curve for strain rate of 0.001s−1 During the tests, an inclined fracture plane occurs along thickness of the specimens and a shear failure zone is observed along the oblique direction as Fig. 2 shows. The shear fracture is the main failure mode for AW5005 aluminum alloy subjected to quasi-static tension. A camera has been used to investigate the specimen behavior during quasi-static tensile tests. The results are given in Fig. 2 for a strain rate equal to 0.001s−1. A set of perpendicular lines is drawn on the specimen surface with a gap of 2.25mm between them. The tension process is recorded to estimate local deformation along the specimen loaded in tension. The failure process is presen- ted together with the force displacement curve in Fig. 2. The analysis of the three frames A, B and C has allowed one to report the failure development of the specimen. On the frame A, the tensile process starts and the force is increasing together with the displacement. By coupling 1222 A. Bendarma et al. the force and displacementmeasurements obtained using the hydraulicmachine and the displa- cement observed from the camera measurement, the behavior can be defined. After the force reaches the maximum level, the process of tensile plastic strains localization starts as reported on the frame B. Finally, the plastic strain localizes, see the frame C. If the local critical failure strain is reached, a crack is formed and themeasured force decreases to zero. Using local strain measurements, it is observed that the local nominal strains before the failure is close to 0.55 compared to the global strain which equals 0.1. The quasi-static tensile tests are performed for four different strain rates, i.e. 0.001, 0.01, 0.1 and 0.15s−1. The resulting stress-strain curves are presented in Fig. 3. The experimental tests show that there is no strain rate sensitivity for aluminum alloy AW5005 behavior in the range of the strain rate used, but there is a significant difference in terms of ductility. The macroscopic true strains values at failure varies from 0.042 to 0.1. It is also observed that the ductility increases with the strain rate, Fig. 3. It shows that the average yield strength of the AW5005 aluminum is close to 147MPa. Fig. 3. Stress-strain curves for different strain rates at room temperature, aluminumAW5005 2.2. Perforation test This part describes themechanical behavior of aluminumsheets under impact loading.Expe- rimental, analytical and numerical investigations have been carried out to analyze in details the perforation process (Kpenyigba et al., 2013). A wide range of impact velocities from 40 to 180m/s has been covered during the tests. A conical projectile with an angle of 72◦ has 13mm in diameter and the plate is 1.0mm thick. The active part of the specimen during perforation is presented in Fig. 4. The projectile is launched using a pneumatic gas gun, it accelerates in the tube to reach the initial impact velocity V0. Then, the projectile impacts the alumium sheet with partial or complete perforation depending on quantity of kinetic energy delivered to the tested plate. At the end, the residual velocity VR of the projectile is measured after the projectile perforates the plate. Laser sensors are used to measure the initial velocity and a laser barrier for the residual velocities of the projectile during perforation. The projectile massmp is 28g. Thematerial used formachining the projectile ismaraging steel with heat treatment to reach the yield stress of the projectile of 2GPa. Therefore, the projectile is assumed as rigid during the perforation process (Kpenyigba et al., 2013). The results in terms of the ballistic curveVR-V0 are reported inFig. 5a. Experimental and numerical analysis of aluminum alloy AW5005... 1223 Fig. 4. Dimensions of the projectile and target used during perforation tests Fig. 5. (a) Ballistic curve obtained during perforation and determination of ballistic limit, (b) energy absorbed by plate during impact test, determination of failure energy Theresidual velocity of theprojectile canbecalculatedusing the following equationproposed by Recht and Ipson (1963) VR =(V κ 0 −V κ B) 1 κ (2.1) whereV0 is the initial velocity andVB is theballistic velocity. In theabove equation, theconstants VB is equal to 40m/s, and κ is the ballistic curve shape parameter equal to 1.65. The energy absorbed by the plateEd can be calculated using the following equation Ed = mP 2 (V 20 −V 2 R) (2.2) The difference of the initial and residual kinetic energy can be calculated using the experi- mental data, thenbasedon theRecht-Ipson approximation, the energyabsorbedby theplate can be calculated, see Fig. 5b. Using Eq. (2.2), theminimum energy to perforate is 28J (mP =28g and V0 =VB =40m/s). In Fig. 6, for the initial impact velocity of V0 = 85m/s, the failure pattern is presented with four petals for the residual velocity of VR = 66.5m/s. The same failure is observed for V0 = 132.3m/s with VR = 120.2m/s, respectively. The number of petals is equal to 4 in the whole range of impact velocities, i.e. from 40 to 180m/s. A complete description concerning the number of petals depending on the projectile shape and the failure mode was published and discussed in details in (Atkins and Liu, 1998). 1224 A. Bendarma et al. Fig. 6. Experimental observation of failure patterns, V0 =85.3m/s and 132.3m/s 3. Johnson-Cook material model Using experimental tests, the parameters of the Johnson-Cook (JC)model (Johnson andCook, 1983) have been identified and used to simulate tension and perforation tests. The thermo- -viscoplastic behavior of AW5005 aluminum alloy is defined as follows σ=(A+Bεnpl) ( 1+C ln ε̇pl ε̇0 ) (1−T∗ m ) (3.1) where A is the yield stress, B and n are strain hardening coefficients, C is the strain rate sensitivity coefficient, ε̇0 is the strain rate reference value and m is the temperature sensiti- vity parameter. In this work, isothermal conditions are assumed. Therefore, the last term of the JC model related to the non-dimensional temperature T∗ is not considered. All numerical simulations are done at room temperature T =300K. The material constants are obtained by experimental tests. The parameter C has been cal- culated using the presented experimental tests for a quasi-static loading (strain rates from0.001 to 0.15s−1). In this range small strain rates sensitivity has been observed. The optimization using the minimum least square method gives the value of C equal to 0.003. These constants are shown in Table 1. Table 1.Material parameters for the Johnson-Cookmodel A [MPa] B [MPa] n [–] C [–] 147 60 0.9 0.003 In order to define the material behavior completely, a failure criterion was proposed by Johnson andCook (1985).Whenmixedwith their classical constitutive law,Eq. (3.1), it enabled one to reflect failure modes of structures or materials. The Johnson-Cook failure model is applied widely because of the simplicity of formulation. A number of material parameters that are available in literature were provided by Johnson and Holmquist (1989). However, Johnson and Cook only determined the positive range of the stress triaxiality based on some tensile tests and shear tests, and no small or negative values of stress triaxiality were expressed. In order to effectively apply the Johnson-Cook fracturemodel, researchers extended themodel in differentways. Liu et al. (2014) proved that the Johnson-Cook fracturemodel can beused as damage initiation coupledwith damage evolution inmetal cutting simulations. Moreover, the damage evolution combines two different fracture modes effects. In Fig. 7, the progressive damagemodel is used for aluminumalloy. The description includes the elastic partwithE0 (part a-b) and the plasticity range (b-c). The damage initiation with the JCcriterion canbe expressedbyEq. (3.2) (c).Along the line (c-e), thedamage variable evolution grows from 0 to themaximum degradation ratioDmax (d), therefore, stiffness of thematerial is Experimental and numerical analysis of aluminum alloy AW5005... 1225 degraded and reduced to (1−D)E0 whereD is the damage variable andE0 is the initial Young modulus. The damage evolution is described bymesh-independentmeasurements (displacement at failure and damage energy dissipation) in the model. A linear evolution damage rule is used bydefining a value of displacement at failureuf (e). Thus, themaximumdegradation of stiffness as well as themaximumdamage have been taken finally as the failure criterion (d). The element after reaching the failure criterion is deleted from the mesh in simulation. Fig. 7. Schematic representation of tensile test data in stress-displacement space for elastic-plastic materials (ABAQUS, 2011) The Johnson-Cook damage initiation model (Johnson and Cook, 1985; Johnson and Hol- mquist, 1989) describes the strain at damage initiation ε pl D−init including effects of the stress triaxiality, strain rate and temperature, as shown in the following equation ε pl D−init = [d1+d2exp(−d3η)] ( 1+d4 ln ε̇ ε̇0 ) (1+d5T ∗) (3.2) whered1,d2,d3,d4,d5 arematerial parameters,η is the stress triaxiality factor, ε̇0 is the reference strain rate and T∗ is the non-dimensional temperature. The first bracket in Eq. (3.2) concerns the influence of the stress triaxiality factor on the value of strain at damage initiation ε pl D−init. The value of the first bracket decreases as the stress triaxiality factor increases. The second bracket represents the influence of the strain rate on that value, while the third one represents the effect of thermal softening. Table 2. Failure parameters for tension and perforation Tensile test Perforation test Test 1 4 3 4 103 s−1 104 s−1 (0.001s−1) (0.01s−1) (0.1s−1) (0.15s−1) Damage initiation strain ε pl D−init 0.008 0.03 0.08 0.12 0.9 0.96 Displacement at failure uf 0.0008m Max. degradation Dmax 0.6 By using those analytical approaches coupled to experiment results, the failure parameters have been deduced and used in the numerical model for both traction and perforation tests. They are presented in Table 2. The tensile test values are obtained from experiments, whereas the perforation test values are obtained using a numerical analysis and available literature data for similar materials (Jankowiak et al., 2013, 2014; Kpenyigba et al., 2013). The strain rates for perforation tests ε̇ = 1000s−1 and ε̇ = 10000s−1 correspond to initial impact velocities V0 of 120m/s and 180m/s, respectively. Theyhave been observed locally using numerical simulations. 1226 A. Bendarma et al. 4. Numerical approach Numerical models are built using Abaqus/Explicit. The tests using this numerical model are conducted at different strain rates in quasi-static and dynamic conditions with impact velocities up to 180m/s. The shell element type S4Rwith 8 degrees of freedom and 4 nodes with reduced integration (ABAQUS, 2011) have been used. The same element type with the element size of 0.5mm×0.5mmhas been proposed for tension and perforation analysis as presented in Fig. 9a. The effectiveness of such elements for this type of analysis was previously proved by Ambati and Lorenzis (2016), Amiri et al. (2014), Elnasri and Zhao (2016). In order to extend experimental results, some other thickness of the aluminum plate has been added for both tensile and perforation simulations, therefore, thicknesses of 1.0mm and 1.5mm have been used. 4.1. Modelling procedures of tensile and perforation tests In order to verify the Johnson-Cook constitutive and failuremodels, tension and perforation tests have been simulated using Abaqus/Explicit version 6.14. 4.1.1. Tensile test The aim of this numerical analysis has been to reproduce experimental results by checking the observed failuremode.The constitutive parameters have been identified based on the experi- mental tests. The constants are reported inTable 1. The number of elements used formeshing is 16356, and 16731 is the total number of nodes. The distribution of the equivalent plastic strains called PEEQ in Abaqus is presented in Fig. 8b. Fig. 8. Numerical simulation of tensile test, (a) equivalent plastic strain distribution for macroscopic strain equal to ε=0.04, (b) equivalent plastic strain distribution for macroscopic strain ε=0.045 Thenumerical simulations are in agreementwith experimental observationswhere the failure mode is by shearing, see Fig. 2c. Experimental and numerical analysis of aluminum alloy AW5005... 1227 4.1.2. Perforation test The optimal mesh has been obtained using a convergence method (stability of the results withoutmesh dependency). Themesh is denser in the projectile-plate contact zone, thickness of the plate in this area is 1.0mm and the velocity is defined in predefined fields with the range of impact velocities from 40 to 180m/s as conceded in the experiment. This model contains 6048 elements in the central part of impact and 6161 using the same element size (0.5mm×0.5mm). The ballistic curves are reported in the following Section and compared to the experimental results. The interior zone of themodel allows one to initiate the process of crack propagation in a precise way. The projectile behavior has been defined as rigid, because a kinematic coupling constraint (rigid body) has been applied to avoid deformation of the projectile. The friction coefficient is assumed to be equal to 0.2. Fig. 9. Numerical model used during numerical simulations andmesh density distribution: (a) mesh, (b) equivalent plastic strain distribution for macroscopic strain ε A decrease of the number of petals with a nose angle of 72◦ has been observed when the value of failure strain is changed. An analytical model for prediction of the number of petals proposed by Atkins and Liu (1998) has been used and confirmed by FE simulations. 4.2. Failure criterion model 4.3. Model I (Johnson-Cook model) Using values illustrated in Table 2, the parameters are used to identify the Johnson-Cook damage initiation model. The triaxiality dependent part is neglected because the triaxiality in all cases is 1/3. The influence of temperature is also ignored since there is no effect on all strain rates captured by the temperature camera that have been used during the tests. The final equation used to determine the Johnson-Cook damage initiation strain ε pl D−init as a function of strain rates ε̇ corresponding to aluminum alloy is ε pl D−init = [d1] [ 1+d4 ln ε̇ ε̇0 ] (4.1) In order to determine the parameters d1, d4, an algorithm with Matlab optimization using Eq. (4.1) has been developed, and the adopted values are presented in Table 3. 1228 A. Bendarma et al. Fig. 10. Plot of damage initiation strain versus plastic strain rate usingModel I JC), Eq. (4.1) For tensile tests cases 2, 3 and 4, the damage initiation Johnson-Cookmodel gives too high values of the initial damage strain because it is linear in the interval of the strain rate. Finally, the global behavior in space stress-strain is too ductile, therefore, another approach has been proposed. 4.3.1. Failure modeling using optimized Model II Another function has been proposed to better fit the damage initiationmodel. This function (Eq. (4.2)) contains three constants E, F and G to be determined by using an optimization algorithm. The constants are reported in Table 3 ε pl D−init =G exp(E+Fε̇) 1+exp(E+Fε̇) (4.2) As demonstrated in Fig. 11, there is a good correlation between the fitted curve, the expe- rimental and numerical values, however, there is still a bit of miss-match between some points in the middle of the curve. Fig. 11. Plot of damage initiation strain versus plastic strain rate using optimizedModel II, Eq. (4.2) Experimental and numerical analysis of aluminum alloy AW5005... 1229 4.3.2. Failure modeling using Model III Thenext damage initiation criterion (Eq. (4.3)) is definedwith two glued functionswith four constants H, I, J andK. Using an optimization method, a good correlation in a wide range of strain rates is obtained (see Fig. 12) ε pl D−init = { f(ε̇)=H exp(I log10 ε̇) if ε̇¬ ε̇transmition g(ε̇)= J−K exp(log10 ε̇) if ε̇­ ε̇transmition (4.3) The estimated constants are reported in Table 3 with ε̇transmition =1s −1. Table 3.Parameters for failure models Model I (JC) Model II Model III d1 [–] d4 [–] E [–] F [–] G [–] H [–] I [–] J [–] K [–] 0.007 78.722 −0.89 1.13 1.0085 −0.398 1.4523 1.0085 0.6647 Fig. 12. Plot of failure strain versus plastic strain rate using optimizedModel III 5. Comparison of numerical and experimental results 5.1. Tensile test comparisons A comparison has been made between three initiation damage models using test number 3. As it is presented inFig. 13, the best results are obtainedwithModel III. This is why thismodel has been adopted for an other analysis. Initiation damageModel III has been implemented into the numerical model and then com- pared with the experimental data for different strain rates (0.001, 0.01, 0.1 and 0.15s−1). The results are shown in Fig. 14. As it might be seen in Fig. 15, there is a good correlation between the experimental and numerical results. In the case of test 3, the numerical model has demonstrated more ductile behavior at the failure start, whereas for test 4, it has revealed ductility at the terminal phase of failure. 1230 A. Bendarma et al. Fig. 13. Comparison between experimental and numerical curves using 3 failure criteria Fig. 14. Comparison between experimental and numerical curves using optimized initiation damagemodel (Model III) Fig. 15. Numerical result for conical projectile shape, V0 =120m/s, comparison between experiments and simulations 5.2. Perforation test comparison During this study, the samemodel (Model III) has been used to compare the numerical and experimental results in the dynamic field using the perforation process in Abaqus/Explicit with a wide range of impact velocities from 40 to 180m/s and with target thicknesses of 1.0 and Experimental and numerical analysis of aluminum alloy AW5005... 1231 1.5mm. As it is shown in Fig. 15, the number of petals is the same as in the experiments, four petals are observed. It was reported in (Atkins and Liu, 1989; Landkof and Goldsmith, 1985) that the number of petalsN observed duringdynamic perforation coupled to a conical projectile shapewas related to the nose angleφ. In thiswork, one angle (72◦) has been used to analyze the results. In (Kpenyigba et al., 2013) during the analysis of results it was observed that generally the number of petals N decreased when the projectile angle φ/2 increased. Figure 16 contains both the experimental and the numerical results of simulations with the same interval of velocity. Damage initiation criterion Model III has been used to verify the correlation between thenumerical curve and the experiment.There is a good correlation between the experimental and numerical results which adds to the credibility of correctness of the failure criterionmodel. It can be observed that for thicker plates than 1.5mm, the value of the ballistic limit is shifted from 40m/s to 50m/s. Fig. 16. The ballistic curve in experiment and in simulation 6. Conclusions Mechanical characteristics of new aluminum alloy AW5005 have been investigated. The identi- fication of material parameters has been done using the coupling of the simulation and expe- rimental techniques. Additionally, three damage initiation criteria have been used in numerical modelling for both tension and perforation simulations. 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