Compressive Behaviour of Closed-Cell Aluminium Foam at Diﬀerent Strain Rates

materials

Article Compressive Behaviour of Closed-Cell Aluminium Foam at Diﬀerent Strain Rates

Nejc Novak 1,* , Matej Vesenjak 1 , Isabel Duarte 2 , Shigeru Tanaka 3, Kazuyuki Hokamoto 3 , Lovre Krstulovi´c-Opara 4 , Baoqiao Guo 5, Pengwan Chen 5 and Zoran Ren 1

1 Faculty of Mechanical Engineering, University of Maribor, 2000 Maribor, Slovenia; [email protected] (M.V.); [email protected] (Z.R.) 2 Department of Mechanical Engineering, TEMA, University of Aveiro, 3810-193 Aveiro, Portugal; [email protected] 3 Institute of Pulsed Power Science, Kumamoto University, Kumamoto 860-8555, Japan; [email protected] (S.T.); [email protected] (K.H.) 4 Mechanical Engineering and Naval Architecture, Faculty of Electrical Engineering, University of Split, 21000 Split, Croatia; [email protected] 5 State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100811, China; [email protected] (B.G.); [email protected] (P.C.) * Correspondence: [email protected]

Received: 7 November 2019; Accepted: 6 December 2019; Published: 9 December 2019

Abstract: Closed-cell aluminium foams were fabricated and characterised at different strain rates. Quasi-static and high strain rate experimental compression testing was performed using a universal servo-hydraulic testing machine and powder gun. The experimental results show a large influence of strain rate hardening on mechanical properties, which contributes to significant quasi-linear enhancement of energy absorption capabilities at high strain rates. The results of experimental testing were further used for the determination of critical deformation velocities and validation of the proposed computational model. A simple computational model with homogenised crushable foam material model shows good correlation between the experimental and computational results at analysed strain rates. The computational model offers efficient (simple, fast and accurate) analysis of high strain rate deformation behaviour of a closed-cell aluminium foam at different loading velocities.

Keywords: cellular materials; closed-cell aluminium foam; quasi-static; high strain rate; powder gun; computational simulations; crushable foam

1. Introduction Metal foams and cellular structures are being widely studied in different aspects and considered for use in modern applications in engineering, medicine, fashion and others recently [1,2]. They are one of the most promising building materials for future products due to their attractive combination of low density, high energy absorption capability, damping and thermal insulation [3]. Different fabrication procedures were developed in the last decades and most of them are briefly presented in [4]. Their significant cost is still the most important limitation for the mass production of foam and cellular structures. The additive manufacturing technologies are an increasingly powerful tool for fabrication of different types of cellular structures with exactly predefined and controlled geometry on different scales in recent years [5–7]. Some cheaper ways to produce cellular structures with additive manufacturing techniques have been developed recently [8]. Alternatively, a powder metallurgy is already a well-established procedure for the fabrication of closed-cell foams [9,10]. The foams

Materials 2019, 12, 4108; doi:10.3390/ma12244108 www.mdpi.com/journal/materials Materials 2019, 12, 4108 2 of 16 fabricated this way have a characteristic dense material surface layer completely surrounding the inner closed-foam structure. Despite such foams showing a ductile behaviour appropriate for structural applications, this process does not allow for a rigorous control of the cell structure in terms of pore shape and size [4]. This is mainly due to the difficulty of coordination between the mechanisms of metal melting and thermal decomposition of the blowing agent [4]. The problems associated with the quality of these foams and the manufacturing reproducibility has been studied and discussed [11–13]. The metallic foams can be divided into two major groups when considering the morphology of the cells: the open- and the closed-cell foams [7]. The open-cell foams are used for functional applications (e.g., filtration, catalysis, heat transfer and biomedical applications), while closed-cell foams are mostly being used for structural applications, typically as weight-saving and impact-absorbing structures in vehicles. Since this work is concerned only with the closed-cell foams, the following review of work done previously only on this topic is given briefly in the following. The mechanical behaviour of closed-cell aluminium foams was thoroughly characterised under unconstrained and constrained compression loading conditions [14]. The same foams were also inserted in tubes (ex-situ foam filled tubes) and tested under compression and bending loading conditions [15,16]. The powder metallurgy foam fabrication enables also fabrication of closed-cell foams inside the tubes (in-situ foam filled tubes) to achieve increased stiffness by better bonding between the foam filler and the outer tube [17]. The behaviour of closed-cell foams under different loading conditions was also studied in some detail [18], with micro computed tomography (µCT) applied to track the changes of internal structure during the deformation of closed-cell aluminium foam [19]. The influence of the loading velocity up to 150 m/s on the mechanical response of additively manufactured lattice materials [20] and closed-cell aluminium foams [21] was analysed with the Split Hopkinson Pressure Bar (SHPB) apparatus. High strain rate compressive behaviour of aluminium alloy foams was also studied and discussed in [22,23]. Authors in [24] studied the effect of porosity and differences in the deformation pattern of closed-cell aluminium foam under quasi-static and dynamic (SHPB) loading. All mentioned studies point out that the failure modes under quasi-static and dynamic (high strain rate) loading are different. This is attributed to the inertial effect and material strain-rate sensitivity [22,25,26]. The change of the deformation mode and high strain rate hardening was also observed in computational simulations of metallic foams. Mesoscopic computational simulations were performed using µCT scan based geometrical models [24,27]. The Arbitrary Lagrange Eulerian (ALE) method was also applied to take into account the entrapped air inside the closed-cell foam [28]. A cell-based approach also confirmed deformation localisation at higher strain rates [29]. Computational studies of closed-cell aluminium foam and cell-based Voronoi lattice dynamic behaviour showed relationships between the cell geometry and loading rate [30,31]. The behaviour of closed-cell foams can be successfully described by homogenised computational models, i.e., crushable foam material models, which were successfully applied for polymeric, auxetic and aluminium foam core of composite panels under different loading conditions [32–34]. Besides closed-cell foams, similar work was done in the field of open-cell foams in terms of multiaxial loading [35] and impact response [36,37]. All mentioned studies observe that the high strain rate hardening appears above certain (limiting) loading velocity, which is mostly a consequence of inertia effects. An extensive review of dynamic compressive behaviour of cellular materials is given in [38]. As proven many times before, the deformation mode of a given cellular material or structure changes with increasing loading velocity (strain rate). The deformation behaviour of cellular materials at different loading velocities can be in general divided into three deformation modes: homogeneous, transition and shock deformation mode [23,39–41]. These three deformation modes are separated by two critical loading velocities. This work focuses on experimental and computational evaluation of high strain rate behaviour of closed-cell aluminium foam. The results of experiments and validated computational models present the basis for high strain rate deformation and hardening analysis in combination with the analytical Materials 2019, 12, 4108 3 of 16

Materials 2018, 12, x FOR PEER REVIEW 3 of 17 approach. The deformation modes and critical velocities of the closed-cell aluminium foam were determined,analytical approach. evaluated The and deformation are discussed modes herein. and critic Thereal velocities is limited of experimental the closed-cell and aluminium computational foam workwere done determined, in the ﬁeld evaluated of analysis and of the are deformation discussed modes herein. of closed-cellThere is aluminiumlimited experimental foams. Therefore, and thiscomputational work provides work insight done intoin the the field deformation of analysis behaviour of the deformation of interesting modes lightweight of closed-cell materials aluminium which willfoams. be used Therefore, in modern this constructions. work provides insight into the deformation behaviour of interesting lightweight materials which will be used in modern constructions. 2. Fabrication of Specimens and Experimental Methods 2. FabricationThe base closed-cell of Specimens aluminium and Experimental foam was fabricated Methods using the powder metallurgy method [10], whichThe consisted base closed-cell of heating aluminium extruded foamablefoam was precursorfabricated materialusing the placed powder into metallurgy a cylindrical method stainless [10], steelwhich mould consisted in a pre-heatedof heating extruded furnace (MJAmaral,foamable precursor Vale Cambra, material Portugal, placed into Figure a cylindrical1a) at 700 stainless◦C for 12steel min. mould The cavity in a pre-heated of the cylindrical furnace mould(MJAmaral, with Vale inner Cambra, diameter Portugal, of ~25 mm Figure and 1a) length at 700 of  ~150C for mm 12 wasmin. fully The ﬁlledcavity by of the the formedcylindrical liquid mould metallic with foaminner indiameter the process of ~ 25 by mm foaming and length the precursor of ~ 150 mm material was (Figurefully filled1b) with by massthe formed of 61 g andliquid made metallic of aluminium, foam in the silicon process (7 wt.%) by foaming and titanium the precursor hydride (0.5 material wt.%). The(Figure precursor 1b) with material mass wasof 61 prepared g and made by cold of aluminium, isostatic pressing silicon (Schunk(7 wt.%)Sintermetalltechnik and titanium hydride GmbH, (0.5 Gießen,wt.%). The Germany) precursor of the material powder was mixture, prepared followed by cold by isostatic extrusion pressing through (Schunk a horizontal Sintermetalltechnik 25 MN direct extrusionGmbH, Gießen, machine Germany) (Honsel AG,of the Meschede, powder mixture, Germany), followed resulting by extrusion in a rectangular through bar a horizontal of 20 mm 255 MN mm × indirect cross-section extrusion [9 machine]. The mould (Honsel with AG, formed Meschede, foam wasGermany), extracted resulting from the in furnacea rectangular and cooled bar of down 20 mm to room× 5 mm temperature in cross-section after heating[9]. The time.mould The with cylindrical formed foam aluminium was extracted foam (Figure from the1c) furnace was then and removed cooled fromdown the to mould room temperature made of S235JR after carbon heating steel time. (0.17% The cylindrical C, 1.40% Mn, aluminium 0.045% P,foam 0.045% (Figure S, 0.009% 1c) was N) then and cutremoved longitudinally from the to mould six equal made pieces of S235JR to prepare carbon the steel cylindrical (0.17% C, specimens1.40% Mn, 0.045% (Figure P,1d) 0.045% for mechanical S, 0.009% testing.N) and Thecut longitudinally average pore diameterto six equal of pieces the resulting to prepare closed-cell the cylindrical foams isspecimens approximately (Figure 2.65 1d) mmfor (standardmechanical deviation: testing. ~0.87The average mm). The pore specimen’s diameter dataof the are resulting given in closed-cell Table1. foams is approximately 2.65 mm (standard deviation: ~0.87 mm). The specimen’s data are given in Table 1. Table 1. Physical properties of the specimens (standard deviation is given in brackets). Table 1. Physical properties of the specimens (standard deviation is given in brackets). Diameter Length Weight Density Porosity Number of Specimens Diameter Length Weight Density Porosity Number of specimens d [mm] l [mm] m [g] ρ [kg/m3] p [%] Q-S Testing HSR Testing d [mm] l [mm] m [g] ρ [kg/m3] p [%] Q-S testing HSR testing 25.32 (0.15) 23.08 (0.23) 7.9 (0.39) 681 (0.03) 75 5 3 25.32 (0.15) 23.08 (0.23) 7.9 (0.39) 681 (0.03) 75 5 3

FigureFigure 1. 1.The The foaming foaming furnacefurnace ((aa)) andand precursorprecursor materialmaterial (b) used in this work, work, as as well well as as the the visual visual aspectaspect of of the the resulting resulting cylindrical cylindrical aluminium aluminium foam (foamc) and ( thec) and closed-cell the closed-cell foam specimens foam specimens for mechanical for testingmechanical (d). testing (d). Uniaxial compression tests were performed under quasi-static loading conditions using a Uniaxial compression tests were performed under quasi-static loading conditions using a servo- servo-hydraulic INSTRON 8801 testing machine with position controlled cross-head rate of 0.1 mm/s. hydraulic INSTRON 8801 testing machine with position controlled cross-head rate of 0.1 mm/s. The Thetests tests were were carried carried out according out according to the to standard the standard ISO 13314: ISO 13314: 2011 [42]. 2011 In [42order]. In to order reduce to the reduce friction the frictionand thus and minimise thus minimise the support/loa the supportding/loading boundary boundary effects e ﬀonects specim on specimens,ens, the loading the loading plates plates of the of testing machine were lubricated. The engineering stress-strain data were then calculated using the initial specimen’s dimensions from the recorded force-displacement data.

Materials 2019, 12, 4108 4 of 16 the testing machine were lubricated. The engineering stress-strain data were then calculated using the initialMaterials specimen’s 2018, 12, x dimensionsFOR PEER REVIEW from the recorded force-displacement data. 4 of 17 The high strain rate behaviour of closed-cell foams was studied by using a one-stage powder gun whichThe ishigh capable strain ofrate accelerating behaviour of a projectileclosed-cell up foams to velocity was studied of 1.5 by km using/s. The a one-stage projectile powder is, in the gun which is capable of accelerating a projectile up to velocity of 1.5 km/s. The projectile is, in the case of the powder gun, accelerated by the combustion gas of gun powder detonation. This method case of the powder gun, accelerated by the combustion gas of gun powder detonation. This method was already successfully used for the determination of high strain rate behaviour of other cellular was already successfully used for the determination of high strain rate behaviour of other cellular materials including auxetic cellular structures [20,43]. The powder gun device is assembled from two materials including auxetic cellular structures [20,43]. The powder gun device is assembled from two chambers (explosion and target) which are connected with a barrel with an inner diameter of 40 mm. chambers (explosion and target) which are connected with a barrel with an inner diameter of 40 mm. BothBoth chambers chambers are are decompressed decompressed with with thethe vacuumvacuum pumppump to to near near vacuum, vacuum, in in order order to to minimise minimise the the inﬂuenceinfluence of of the the air air resistance resistance during during the the tests.tests. InIn the target chamber, chamber, there there is is an an optical optical observation observation window,window, which which enables enables the the visual visual observation observation ofof thethe deformation procedure, procedure, and and also also an an electrical electrical terminal,terminal, which which enables enables processing processing of of the the signal signal duringduring an impact. The The rigid rigid wall wall and and shock shock are are also also positionedpositioned in in the the target target chamber, chamber, where where the the impactimpact ofof cellular structure structure and and sabot sabot isis happening, happening, and and oﬀersoffers rigid rigid support support during during the the impact impact ofof cellularcellular structure,structure, absorbing absorbing the the energy energy of of the the impacting impacting projectileprojectile afterwards. afterwards. The The projectileprojectile sabotsabot waswas made from polyethylene polyethylene (UHMWPE) (UHMWPE) with with a brass a brass weightweight mounted mounted to to the the front front of of the the sabot sabot asas aa projectileprojectile driver (total (total weight weight of of the the projectile projectile was was about about 180180 g). g). The The closed-cell closed-cell foam foam was was positioned positioned and and glued glued with with epoxy epoxy resin resin to to the the brass brass weightweight (Figure(Figure2 ), which2), which enables enables control control of the of impact the impact velocity. velocity. The The projectile’s projectile’s velocity velocity for for this this testing testing was was set set to to 270 270 m /s, 1 −1 whichm/s, resultedwhich resulted in the engineeringin the engineering strain strain rate of rate approximately of approximately 12,000 12,000 s− . s .

2 cm

FigureFigure 2. 2.Closed-cell Closed-cell foamfoam specimen mounted on on projectile. projectile.

TheThe impact impact velocity velocity and and the the deformation deformation behaviourbehaviour of the closed-cell closed-cell aluminium aluminium foam foam during during impactimpact were were captured captured by the by HPV-1 the HPV-1 high-speed high-speed video camera video (producedcamera (produced by SHIMADZU by SHIMADZU corporation, imagecorporation, capture number:image capture 100, maximum number: 100, resolution: maximum 1 µs). resolution: The mechanical 1 μs). The response mechanical of closed-cell response foams of (impactclosed-cell pressure) foams of the(impact closed-cell pressure) aluminium of the closed-cell foam on the aluminium rigid wall foam was measuredon the rigid with wall the was PVDF gaugemeasured (Piezo with ﬁlm the stress PVDF gauge, gauge PVF2 (Piezo 11-, film 125EK, stress Dynasen), gauge, PVF2 which 11-, was 125EK, already Dynasen), successfully which used was in previousalready experiments successfully [used43]. in previous experiments [43].

3. Experimental3. Experimental Results Results

3.1.3.1. Quasi-Static Quasi-Static Testing Testing TheThe results results of of quasi-static (Q-S) (Q-S) compression compression testing testing in the in form the of form observed of observed engineering engineering stress- stress-strainstrain relationship relationship show show a characteristic a characteristic compressive compressive behaviour behaviour of cellular ofcellular materials, materials, Figure 3. Figure After 3. Afteran initial an initial quasi-linear quasi-linear response, response, the cell the walls cell start walls to startbend toand bend buckle and resulting buckle resultingin the stress in plateau, the stress plateau,which whichis typical is for typical cellular for materials cellular materials[44]. The cell [44 walls]. The begin cell wallsto fracture begin with to fracturefurther deformation with further deformationand the cells and gradually the cells graduallycollapse, collapse,finally leading finally to leading the densification to the densification of the cellular of the cellularstructure. structure. The Theresulting resulting deviation deviation is isa aconsequence consequence of ofthe the aluminium aluminium foam foam density density variation variation throughout throughout the the specimensspecimens (628–713 (628–713 kg kg/m/m3),3), whichwhich stronglystrongly influencesinfluences thethe mechanicalmechanical behaviour. behaviour. Studies Studies have have demonstrateddemonstrated that that these these foams foams develop develop imperfectionsimperfections and structural structural defects defects (e (e.g.,.g., micropores) micropores) during during theirtheir fabrication, fabrication, creating creating weaker weaker regions regions wherewhere thethe foam starts starts to to deform, deform, developing developing one one or ormore more visible deformation bands perpendicular to the loading direction [25,45]. The stiffness of the visible deformation bands perpendicular to the loading direction [25,45]. The stiffness of the specimens specimens increases by increasing the foam density. Also, the plateau region of these specimens is increases by increasing the foam density. Also, the plateau region of these specimens is slightly inclined. slightly inclined. This agrees with our previous results [9,12] for these types of foams. As can be seen from Figure 4, the deformation behaviour is uniform at lower strains, which is followed by crushing in shear planes that are formed in the areas with less stiff cellular structure.

Materials 2019, 12, 4108 5 of 16

This agrees with our previous results [9,12] for these types of foams. As can be seen from Figure4, the Materialsdeformation 2018, 12 behaviour, x FOR PEER is REVIEW uniform at lower strains, which is followed by crushing in shear planes5 thatof 17 Materialsare formed 2018, 12 in, x the FOR areas PEER with REVIEW less stiﬀ cellular structure. 5 of 17 90 90 80 Q-S average 80 Q-S average 70 70 60 60 50 50 40 40 30 30 Engineering Engineering stress[MPa] 20 Engineering Engineering stress[MPa] 20 10 10 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2Engineering 0.3 0.4 strain 0.5 [-] 0.6 0.7 0.8 Engineering strain [-]

Figure 3. Engineering stress-strain relationship of closed-cell aluminium foam under quasi-static Figure 3. Engineering stress-strain relationship of closed-cell aluminium foam under quasi-static Figureloading 3. conditions. Engineering stress-strain relationship of closed-cell aluminium foam under quasi-static loadingloading conditions. conditions.

(a) (b) (c) (a) (b) (c)

1 cm 1 cm (d) (e) (f) (d) (e) (f) Figure 4. DeformationDeformation sequence sequence of of closed-cell closed-cell aluminium aluminium foam foam under under quasi-static quasi-static loading loading conditions. conditions. FigureStrain: 4. ( a Deformation)) 0%; 0%; ( (b)) 12%; 12%; sequence ( c) 24%; of( d )closed-cell 36%; ( e) 48%; aluminium ( f) 60%. foam under quasi-static loading conditions. Strain: (a) 0%; (b) 12%; (c) 24%; (d) 36%; (e) 48%; (f) 60%. 3.2. High Strain Rate Testing 3.2. High Strain Rate Testing The results of high strain rate (HSR) testing in the formform ofof observedobserved engineeringengineering stress-strain relationshipThe results are of shown high instrain Figure rate5 5.. (HSR) Again,Again, testing thethe responseresp in onsethe form isis typicaltypical of observed forfor cellularcellular engineering structuresstructures stress-strain withwith threethree relationshipdistinct didifferencesff erencesare shown due in toto Figure highhigh velocity velocity5. Again, loading:loading: the resp (i)i)onse initial initial is typicalstress peak, for cellular (ii)iii) stress structures oscillations with during three distinctstress plateau differences region, due andand to (iii)highiii) abrupt abrupt velocity densificat densification loading:ion i) (no (noinitial smooth smooth stress transition peak, iii) between stress oscillations the plateau during stress stressregion plateau and densificationdensification region, and region,region, iii) abrupt asas isis densificat usualusual atat quasi-staticquasi-staticion (no smooth loading).loading). transition between the plateau stress region and densification region, as is usual at quasi-static loading).

Materials 2019, 12, 4108 6 of 16 MaterialsMaterials 2018 2018, 12, 12, x, FORx FOR PEER PEER REVIEW REVIEW 6 of6 of 17 17

500500

450450 HSRHSR average average 400400

350350

300300

250250

200200

150150 Engineering Engineering stress[MPa] Engineering Engineering stress[MPa] 100100

5050

0 0 00 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 EngineeringEngineering strain strain [-] [-]

Figure 5. Engineering stress-strain relationship of closed-cell aluminium foam under high strain rate FigureFigure 5. 5. Engineering Engineering stress-strain stress-strain relationship relationship of of closed closed-cell-cell aluminium aluminium foam foam under under high high strain strain rate rate loading conditions. loadingloading conditions. conditions. The deformation pattern captured with a high speed camera is shown on Figure6, where it can TheThe deformation deformation pattern pattern captured captured with with a ahigh high speed speed camera camera is is shown shown on on Figure Figure 6, 6, where where it itcan can be observed that the deformation mode changed to shock mode in comparison to the quasi-static bebe observed observed that that the the deformation deformation mode mode changed changed to to shock shock mode mode in in comparison comparison to to the the quasi-static quasi-static response. Consequently, most of the deformation happens at the impact front between the rigid wall response.response. Consequently, Consequently, most most of of the the deformation deformation ha happensppens at at the the impact impact front front between between the the rigid rigid wall wall and specimen until the specimen is completely compressed. andand specimen specimen until until the the specimen specimen is is completely completely compressed. compressed.

(a()a ) (b()b ) (c()c ) (d()d ) (e()e ) (f()f )

FigureFigureFigure 6. 6.6. Deformation DeformationDeformation sequence sequencesequence of ofof closed-cell closed-cellclosed-cell aluminium aluminiumaluminium foam foamfoam under underunder high highhigh strain strainstrain rate. rate.rate. Strain: Strain:Strain: (a ()a 0%;)) 0%;0%; (b((b)b )18%;) 18%;18%; (c (()cc )36%;) 36%;36%; (d ((d)d )54%;) 54%;54%; (e ((e)e )72%;) 72%;72%; (f ()(f f)90%.) 90%. 90%.

TheTheThe comparison comparisoncomparison between between the the quasi-static quasi-static quasi-static and and and high high high strain strain strain rate rate rate responses responses responses is is shown isshown shown in in Figure inFigure Figure 7. 7. A7 A . significantAsignificant significant strain strain strain rate rate rate hardening hardening hardening effect effect effect can can can be be beobserv observ observededed in in inthe the the case case case of of high high strain strain rate rate loading, loading, which whichwhich isisis mostly mostlymostly the thethe consequence consequenceconsequence of ofof the thethe changed changedchanged deformation deformationdeformation mode modemode and andand micro-inertia micro-inertiamicro-inertia effects. eeffects.ffects. The TheThe change changechange in inin thethethe deformation deformationdeformation mode modemode is isis further furtherfurther analysed analysedanalysed in inin Section SectionSection 4.3. 4.3 4.3. .

Materials 2018, 12, x FOR PEER REVIEW 7 of 17 Materials 2019, 12, 4108 7 of 16

250 Q-S average (strain rate: 0.004 s -1 ) -1 200 HSR average (strain rate: 12,000 s )

150

100 Engineering Engineering stress[MPa] 50

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Engineering strain [-] FigureFigure 7. 7. ComparisonComparison of average quasi-staticquasi-static and and high high strain strain rate rate results results of closed-cell of closed-cell aluminium aluminium foam. foam. 3.3. The Specific Energy Absorption Analysis 3.3. TheThe Specific specific Energy energy Absorption absorption Analysis (SEA) was analysed to evaluate the influence of the strain rateThe hardening. specific energy The SEA absorption was calculated (SEA) bywas dividing analysed the to absorbedevaluate the energy influence (integral of the under strain average rate hardening.stress-strain The curve) SEA bywas crushed calculated mass by and dividing results th fore absorbed both loading energy cases (integral are given under in Table average2. The stress- high strainstrain curve) rate SEAby crushed (evaluated mass at and strains results of for 0.50 both and lo 0.77)ading increased cases are given by 191.7% in Table in comparison2. The high strain to the ratequasi-static SEA (evaluated response at strains at the of strain 0.50 and of 0.77 0.77) (350% increased at strain by 191.7% of 0.50), in comparison which illustrates to the quasi-static significant responseenhancement at the potential strain of in 0.77 the energy(350% at absorption strain of capabilities0.50), which of illustrate tested foamss significant for use inenhancement applications potentialcharacterised in the by energy high strainabsorption rate of capabilities deformation. of tested foams for use in applications characterised by high strain rate of deformation. Table 2. Specific energy absorption of closed-cell aluminium foam at different strain rates.

Table 2. SpecificLoading energy Velocity absorption Regime of closed-cell SEA at 50% aluminium [J/g] foam SEA at different at 77% [J strain/g] rates. LoadingQuasi-static Velocity Regime SEA 13.04at 50% [J/g] SEA at 77% 29.27 [J/g] HighQuasi-static strain rate 58.7413.04 29.27 85.39 High strain rate 58.74 85.39 The evolution of SEA and the discrepancy of all experimental results in the case of quasi-static The evolution of SEA and the discrepancy of all experimental results in the case of quasi-static and high strain rate loading are shown in Figure8a. Quasi-linear increase of SEA in the case of high and high strain rate loading are shown in Figure 8a. Quasi-linear increase of SEA in the case of high strain rate loading can be observed, while in the case of quasi-static loading the increase in the SEA at strain rate loading can be observed, while in the case of quasi-static loading the increase in the SEA larger deformations becomes progressively exponential. The discrepancy of the experimental results is at larger deformations becomes progressively exponential. The discrepancy of the experimental also shown in Figure8a, which is smaller at lower strain rates. Figure8 makes it possible to determine results is also shown in Figure 8a, which is smaller at lower strain rates. Figure 8 makes it possible to the specific energy absorption capabilities of closed-cell aluminium foam at different strains and strain determine the specific energy absorption capabilities of closed-cell aluminium foam at different rates. The comparison in terms of energy absorption between the experimental results and different strains and strain rates. The comparison in terms of energy absorption between the experimental types of cellular metals given in the literature [3] is shown in Figure8b. Good agreement in terms of results and different types of cellular metals given in the literature [3] is shown in Figure 8b. Good deformation energy can be observed for the density of cellular material used in this research. agreement in terms of deformation energy can be observed for the density of cellular material used in this research.

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HSR

Q-S

(a) (b)

Figure 8. (a) TheThe SEASEA evolutionevolution of of closed-cell closed-cell aluminium aluminium foam foam at quasi-staticat quasi-static (Q-S) (Q-S) and and high high strain strain rate rateloading loading (HSR) (HSR) and ( band) comparison (b) comparison of the experimentalof the experimental results with results diff erentwith typesdifferent of cellular types of metals cellular [3]. metals [3]. 4. Computational Simulations 4. Computational Simulations 4.1. Computational Model 4.1. ComputationalThe computational Model model with applied homogenised material model (crushable foam) with volumetric hardening was built in Abaqus Finite Element software, where the explicit solver was used The computational model with applied homogenised material model (crushable foam) with for analysis. The crushable foam model in Abaqus is based on the flow rule, which is non-associated [46]. volumetric hardening was built in Abaqus Finite Element software, where the explicit solver was The tensile hydrostatic stress is kept constant through the deformation process, while the compression used for analysis. The crushable foam model in Abaqus is based on the flow rule, which is non- hydrostatic stress changes due to the densification and collapse of the cellular structure. Crushable foam associated [46]. The tensile hydrostatic stress is kept constant through the deformation process, while material model with volumetric hardening is based on the experimental observation with a significantly the compression hydrostatic stress changes due to the densification and collapse of the cellular different deformation behaviour under the tensile and compression loading conditions. In the case of structure. Crushable foam material model with volumetric hardening is based on the experimental compression loading, the capability of volumetric deformation is much larger due to the buckling of observation with a significantly different deformation behaviour under the tensile and compression struts in the cellular structure [47]. The deformation of crushable foam is by default irreversible, so it loading conditions. In the case of compression loading, the capability of volumetric deformation is can be in most cases treated as plastic deformation. This allows us to define the hardening curve of much larger due to the buckling of struts in the cellular structure [47]. The deformation of crushable the material model only with the values of uniaxial compression loading in respect to uniaxial plastic foam is by default irreversible, so it can be in most cases treated as plastic deformation. This allows deformation. The hardening curve was determined using a genetic optimisation algorithm (OptiMax us to define the hardening curve of the material model only with the values of uniaxial compression software developed at University of Maribor) during the validation procedure [48], with the definition loading in respect to uniaxial plastic deformation. The hardening curve was determined using a of the material parameters provided in Tables3 and4. genetic optimisation algorithm (OptiMax software developed at University of Maribor) during the Axial symmetry with axisymmetric boundary conditions could be applied in the computational validation procedure [48], with the definition of the material parameters provided in Tables 3 and 4. model due to the axial symmetry of the specimens (Figure9). The loading (top) and support (bottom) Axial symmetry with axisymmetric boundary conditions could be applied in the computational plates were modelled with interaction, where all boundary nodes on the top and bottom edge were model due to the axial symmetry of the specimens (Figure 9). The loading (top) and support (bottom) connected to two reference points using kinematic coupling, respectively. Boundary conditions were plates were modelled with interaction, where all boundary nodes on the top and bottom edge were then prescribed to these two reference points. The loading plate was prescribed with a constant velocity connected to two reference points using kinematic coupling, respectively. Boundary conditions were of 1 m/s (quasi-static testing) and 270 m/s (high strain rate testing). The higher computational loading then prescribed to these two reference points. The loading plate was prescribed with a constant velocity in respect to the experimental quasi-static velocity was determined by comparing the reaction velocity of 1 m/s (quasi-static testing) and 270 m/s (high strain rate testing). The higher computational forces at the loading and support plates, which should be identical if there are no inertia effects present. loading velocity in respect to the experimental quasi-static velocity was determined by comparing The support plate has constrained displacement in y-direction and constrained rotation around z-axis, the reaction forces at the loading and support plates, which should be identical if there are no inertia while the loading plate has constrained only the rotation around z-axis. effects present. The support plate has constrained displacement in y-direction and constrained The finite element mesh consists of 299 linear quadrilateral elements (type CAX4R), with average rotation around z-axis, while the loading plate has constrained only the rotation around z-axis. global size of 1 mm. The appropriate size of the finite elements was determined during the convergence The finite element mesh consists of 299 linear quadrilateral elements (type CAX4R), with average study with three different finite element sizes. global size of 1 mm. The appropriate size of the finite elements was determined during the convergence study with three different finite element sizes.

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Loading plate Axisymmetric boundary conditions

Support plate

Figure 9. Mesh and boundary conditions of the axisymmetric computational finite element model. Figure 9. Mesh and boundary conditions of the axisymmetric computational ﬁnite element model.

4.2. Computational Computational Results Results and Comparison with the Experimental Observations The crushable foam constitutive model parameters were determin determineded by using an optimisation algorithm, initially comparing the quasi-static ex experimentperiment and and computational computational responses responses (Figure (Figure 10).10). The material parameters are given in Table 3 3,, wherewhere ρ isis density, density, E is Young’s Young’s modulus, ν is Poisson’s Poisson’s ratio, k isis compressioncompression yield yield stress stress ratio ratio and andkt kist is hydrostatic hydrostatic yield yield stress stress ratio. ratio. After After optimisation optimisation of the of thematerial material parameters, parameters, the same the same material material model model was used wa fors used the high for strainthe high rate strain loading. rate Good loading. agreement Good agreementcan be observed can be for observed both quasi-static for both quasi-static and high strain and high rate testing.strain rate Thus, testing. the computational Thus, the computational model was modelsuccessfully was successfully validated. validated.

Table 3. Parameters for crushable foam material model.

3 3 ρ [kg/m ] ρ [kg/m ] E [MPa]E [MPa] ν [–] ν [–]k [–] kt [–]k [–] kt [–] 681 6815023.8 5023.8 0.110.11 1.53 0.45 1.53 0.45

Table 4. Hardening curve definition. Table 4. Hardening curve definition. Pl. strain [–] 0 0.03 0.12 0.15 0.25 0.42 0.51 0.60 0.9 1.07 1.8 Pl. Strain [–] 0 0.03 0.12 0.15 0.25 0.42 0.51 0.60 0.9 1.07 1.8 Stress [MPa] 11 11.9 15.35 16.12 18.39 20.93 23.05 25.18 29.70 69.82 2100 Stress [MPa] 11 11.9 15.35 16.12 18.39 20.93 23.05 25.18 29.70 69.82 2100 The agreement between the experimental and computational responses is very good at both analysedThe agreementstrain rates between(Figure 10). the experimentalA discrepancy and can computationalbe observed only responses at lower is strains very good of the at HSR both response,analysed strainand only rates the (Figure first stress 10). Apeak discrepancy could not can be beobserved observed in the only computational at lower strains model of the due HSR to initialresponse, boundary and only conditions. the first stress The peak stress could peak not is bea consequence observed in the of computationalcollision in the model experiments due to initial and representsboundary conditions.a typical response The stress of structures peak is a consequence during the initial of collision phase inof thethe experimentsimpact, but does and representsnot affect thea typical global response behaviour of afterwards structures during[20]. the initial phase of the impact, but does not affect the global behaviourAdditionally, afterwards the [20SEA]. capabilities from experimental results and computational simulations wereAdditionally, compared. The the SEA SEA values capabilities from experimental from experimental tests are results given in and Table computational 2, while the simulationsSEA values fromwere compared.computational The simulations SEA values are from 32.19 experimental J/g in the case tests of are Q-S given loading in Table and2 ,95.11 while J/g the in SEA the valuescase of HSRfrom loading. computational This results simulations in 10% areoverestimation 32.19 J/g in theof the case energy of Q-S absorption loading and capabilities 95.11 J/g calculated in the case by of computationalHSR loading.This simulations, results in which 10% overestimation is caused mainly of theby energya discrepancy absorption in the capabilities densification calculated region byin thecomputational case of Q-S simulations,loading and whichdue to isthe caused oscillations mainly (no by filer a discrepancy has been used) in the at densification the plateau stress region region in the incase the of case Q-S of loading HSR loading. and due to the oscillations (no filer has been used) at the plateau stress region in the case of HSR loading.

Materials 2018, 12, x FOR PEER REVIEW 10 of 16 Materials 2019, 12, 4108 10 of 16 Materials 2018, 12, x FOR PEER REVIEW 10 of 17 250 250 250 Q-S average Q-SQ-S average average HSR average 200 HSRQ-S average average 200 HSR average 200 Q-SQ-SHSR computational computational average simulation simulation HSRQ-SQ-S computational computational simulationsimulation simulation 150 150 HSR computational simulation 150

100

100100 Engineering [MPa] stress Engineering

Engineering [MPa] stress Engineering 50 Engineering Engineering stress[MPa] 5050

0 0 00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 000.1 0.10.20.30.40.50.60.70.80.2 Engineering0.3 0.4 strain [0.5-] 0.6 0.7 0.8 EngineeringEngineering strain strain [-][-] Figure 10. Comparison of experimental and computational results of closed-cell aluminium foam Figure 10. Comparison of experimental and computational results of closed-cell aluminium foam behaviourFigure 10. at Comparisonquasi-static (Q of- S)experimental and high strain and rate computational loading (HSR). results of closed-cell aluminium foam behaviour at quasi-static (Q-S) and high strain rate loading (HSR). behaviour at quasi-static (Q-S) and high strain rate loading (HSR). TheThe deformation deformation behaviour behaviour in in the the case case of of quasi quasi-static-static and and high high strain strain rate rate loading loading conditions conditions is is shownshownThe in in Figure Figuredeformation 11 11. .In In the behaviour the case case of of quasi in quasi-static the-static case loadingof loading, quasi-static, a auniform uniform and deformationhigh deformation strain rate of of the loading the specimen specimen conditions can can be be is noted.noted.shown The Thein Figurechange change 11. in in Inthe the the deformation deformation case of quasi-static mode mode can canloading, be be observed observed a uniform in in the thedeformation case case of of high high of strain the strain specimen rate rate loading, loading, can be wherewherenoted. the theThe deformation deformation change in theis is localised localiseddeformation at at the the mode impact impact can front front be obbetween betweenserved loadingin loading the case plate plate of andhigh and specimen. specimen.strain rate This Thisloading, is is a a consequencconsequencewhere the edeformation of of inertia inertia effects e ﬀisects localised and and is is analysedat analysed the impact in in detail detail front in inbetween Section Section loading4.3. 4.3 . plate and specimen. This is a consequence of inertia effects and is analysed in detail in Section 4.3. (a) a)

(b) b)

Figure 11. Equivalent plastic strain (PEEQ) evolution in closed-cell aluminium foam during quasi-static

Figure(a) and 11. high Equivalent strain rate plastic (b) loading strain (strain(PEEQ) increment: evolution 15%).in closed-cell aluminium foam during quasi- staticFigure (a) and11. Equivalenthigh strain plasticrate (b )strain loading (PEEQ) (strain evolution increment: in 15closed-cell%). aluminium foam during quasi- static (a) and high strain rate (b) loading (strain increment: 15%).

Materials 2019 12 Materials 2018, , 12, 4108, x FOR PEER REVIEW 1111 of of 16 17

4.3. High Strain Rate Behaviour Analysis 4.3. High Strain Rate Behaviour Analysis The change of the deformation mode is a consequence of the inertia effect and is triggered at so- The change of the deformation mode is a consequence of the inertia effect and is triggered at called critical velocities. The deformation mode is homogeneous at loading velocities below the first so-called critical velocities. The deformation mode is homogeneous at loading velocities below the critical velocity. A transition deformation mode is observed between the first and the second critical first critical velocity. A transition deformation mode is observed between the first and the second velocity. The deformation mode changes to shock mode above the second critical velocity, and is critical velocity. The deformation mode changes to shock mode above the second critical velocity, and characterised by concentrated deformation at the impact front [40,41,49]. Herein, the critical loading is characterised by concentrated deformation at the impact front [40,41,49]. Herein, the critical loading velocities of the analysed closed-cell aluminium foam were determined from experimental testing velocities of the analysed closed-cell aluminium foam were determined from experimental testing and and computational simulation results, described in the previous section. computational simulation results, described in the previous section. Dynamic deformation behaviour of cellular (porous) materials can be described by several Dynamic deformation behaviour of cellular (porous) materials can be described by several constitutive crushing foam models, which are presented in [38]. The Rigid-Power-Law Hardening constitutive crushing foam models, which are presented in [38]. The Rigid-Power-Law Hardening (R-PLH) model was chosen in this study since it enables high-precision predictions of shock-induced (R-PLH) model was chosen in this study since it enables high-precision predictions of shock-induced stress also in the densification region. The first critical loading velocity can then be obtained as [23]: stress also in the densification region. The first critical loading velocity can then be obtained as [23]: s = ⁄9n+1 K (1) n vcr1 = [σ0/9K] 2 (1) ρ0 where σ0 is the initial yield stress (calculated as average stress between 0.2 and 0.4 of strain), K is wherethe strengthσ0 is the index, initial n yield the strain stress hardening (calculated index as average and ε stressd the densification between 0.2 andstrain. 0.4 The of strain), secondK criticalis the strengthloading index,velocityn the is defined strain hardening as [23]: index and εd the densification strain. The second critical loading velocity is defined as [23]: s n+1 = K 2 (2) v = cr2 εD (2) ρ0

TheThe material material parameters parameters of R-PLH of R-PLH model model (σ0, K, n(σand0, Kε, d)nwere and ﬁttedεd) were according fitted to according the experimental to the dataexperimental from quasi-static data from closed-cell quasi-static aluminium closed-cell foam aluminium compression foam testscompression (Figure 12 tests) and (Figure are given 12) and in Tableare given5 together in Table with 5 computedtogether with critical computed velocities. critic Theal velocities. ﬁtting was The done fitting in MS was Excel done software in MS andExcel nonlinearsoftware GRGand nonlinear solving method GRG solving [50]. method [50].

90 Experimental average 80 R-PLH model 70

40 Stress[MPa] 30

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Strain [-]

FigureFigure 12. 12.The The Rigid-Power-LawRigid-Power-Law Hardening Hardening (R-PLH) (R-PLH) model model ﬁtting fitting to to average average experimental experimental results results of of closed-cellclosed-cell aluminium aluminium foam foam behaviour behaviour under under quasi-static quasi-static loading loading conditions. conditions.

Materials 2019, 12, 4108 12 of 16

Materials 2018Table, 12, 5.x FORMaterial PEER REVIEW parameters and critical loading velocities for closed-cell aluminium foam. 12 of 17

K TablePorosity 5. Materialϕ [–] parametersσ [MPa] and critical loadingn [–] velocitiesε [–] for closed-cellv [m/ s]aluminiumv foam.[m/s] 0 [MPa] d cr1 cr2 Porosity0.75 φ [–] σ0 [MPa] 18.1 K [MPa] 595.7 n 7.7 [–] 0.5εd [–] v 37.5cr1 [m/s] vcr2 46.1 [m/s] 0.75 18.1 595.7 7.7 0.5 37.5 46.1

The parametricparametric computational computational study study of closed-cellof closed-cell aluminium aluminium foam foam behaviour behaviour at diff aterent different loading velocitiesloading velocities (30, 40 and (30, 50 40 m and/s) was 50 m/s) then was performed then performed to evaluate to andevaluate additionally and additionally validate thevalidate developed the computationaldeveloped computational model. Figure model. 13 Figure shows 13 the shows mechanical the mechanical response response of closed-cell of closed-cell aluminium aluminium foam calculatedfoam calculated from from computed computed reaction reaction forces forces on on loading loading (top) (top) and and support (bottom) (bottom) loading loading plates. plates. FigureFigure 1313aa shows the recorded response response at at loading loading ve velocitylocity of of 30 30 m/s m/ s(below (below first first critical critical velocity) velocity) wherewhere responsesresponses at top and bottom loading loading plates plates are are very very similar. similar. This This indicates indicates the the homogeneous homogeneous deformationdeformation mode under quasi-static quasi-static loading loading where where no no significant significant inertia inertia effects effects are are observed, observed, which which isis manifestedmanifested in in similar similar reaction reaction forces forces on on top top and and bottom bottom plates. plates. In the In thecase case of loading of loading velocity velocity of 40 of 40m/s m (Figure/s (Figure 13b), 13b), the the major major discrepancy discrepancy between between the the responses responses is isalready already observ observeded at atlarger larger strains, strains, whilewhile onlyonly aa minorminor discrepancydiscrepancy is is observed observed at at strains strains up up to to 0.6. 0.6. At At a a velocity velocity of of 50 50 m m/s/s (higher (higher than than the secondthe second critical critical velocity) velocity) (Figure (Figure 13c), 13c), the discrepancy the discrepancy between between responses responses on the on bottom the bottom and top and plate top is evenplate moreis even significant. more significant. With further With increase further of incr theease loading of the velocity, loading the velocity, discrepancy the discrepancy is progressively is increasing,progressively which increasing, was clearly which observed was clearly also observed at achieved also velocities at achieved during velocities experiments during (Figureexperiments 11). (Figure 11). 200 200 Top plate 180 180 Top plate Bottom plate 160 160 Bottom plate

140 140

120 120

100 100

80 80

60 60 Engineering Engineering stress[MPa] Engineering Engineering stress[MPa] 40 40

20 20

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Engineering strain [-] Engineering strain [-]

(a) (b) 200

180 Top plate

160 Bottom plate

140

120

100

60 Engineering Engineering stress[MPa] 40

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Engineering strain [-]

(c)

Figure 13. Mechanical response response of of closed-cell closed-cell aluminiu aluminiumm foam foam observed observed on on bottom bottom and and top top plate plate at at didifferentﬀerent loading velocities. a (a) )30 30 m/s, m/s, b ()b 40) 40 m/s m /ands and c) (50c) m/s. 50 m /s.

The changechange inin thethe reaction reaction forces forces is is a consequencea consequence of inertiaof inertia and and internal internal deformation deformation of the of foam,the whichfoam, which is concentrated is concentrated in the in area the ofarea the of impact the impact in the in casethe case of high of high strain strain rate rate loading. loading. This This can can be clearlybe clearly seen seen in Figure in Figure 14, where14, where detailed detailed analysis analysis of eﬀ ofective effective plastic plastic strain strain evolution evolution at diﬀ erentat different loading loading velocities is shown. In the case of loading velocity of 20 m/s (Figure 14a), the effective plastic strain evolution is more or less homogeneous, while in the case of velocities larger than 30 m/s (Figure 14b–d), the effective plastic strain is localised at the impact front.

Materials 2019, 12, 4108 13 of 16 velocities is shown. In the case of loading velocity of 20 m/s (Figure 14a), the eﬀective plastic strain evolution is more or less homogeneous, while in the case of velocities larger than 30 m/s (Figure 14b–d), theMaterials eﬀective 2018, plastic12, x FOR strain PEER REVIEW is localised at the impact front. 13 of 16

(a)

20 m/s

(b)

30 m/s

(c)

40 m/s

(d)

50 m/s

FigureFigure 14. 14.Eﬀ Effectiveective plastic plastic strain strain evolution evolution (PEEQ) (PEEQ) in closed-cell in closed aluminium-cell aluminium foam at foam diﬀerent at different loading velocitiesloading velocities (strain increment: (strain increment: 4%). Loading 4%). Loading velocity: velocity: (a) 20 m (/as;) 20 (b) m/s 30 m; (b/s;) 30 (c) m/s 40 m; (/cs;) 40 (d )m/s 50; m (d/s.) 50 m/s.

Materials 2019, 12, 4108 14 of 16

5. Conclusions Cylindrical closed-cell aluminium foam specimens were fabricated with the powder metallurgy method and subjected to experimental testing under quasi-static and dynamic loading conditions, where significant strain rate hardening was observed. The high strain rate testing was performed at the 1 strain rates above 12,000 s− , which results in shock deformation mode. The analysis of specific energy absorption capabilities has shown that the energy absorption of the aluminium foam is almost 200% larger at higher strain rates (impact) in comparison to quasi-static loading, which should be considered in the design of modern products and structures incorporating closed-cell aluminium foam. A homogenised crushable foam computational model was developed and validated with experimental results. The developed axisymmetric homogenised computational model offers fast, robust and accurate prediction of the mechanical response of closed-cell aluminium foam. The validation of computational models enabled further relevant study of closed-cell aluminium foam behaviour at different strain rates. First, the critical velocities separating different deformation modes (homogeneous, intermediate and shock mode) were determined by using quasi-static experimental data and the Rigid-Power-Law Hardening (R-PLH) model. It was computationally confirmed that the change of the deformation mode appears at the same critical velocities, which were analytically determined. Furthermore, study of the mechanical responses at the loading and support plates was also performed, which proved that the discrepancy between the responses is getting more significant at higher loading velocities above the first critical velocity, where inertia effects are more pronounced. Results presented in this study clearly indicate the advantages of using closed-cell aluminium foam in different dynamic and impact applications, e.g., crashworthiness, ballistic and blast protection, due to the strain rate hardening and strain rate sensitivity. Their excellent energy absorption capabilities allow absorption of more energy at larger strain rates due to the change in the deformation mode and localised deformation. Furthermore, the proposed computational model is efficient (simple, fast and accurate) and offers a possibility to study the behaviour of closed-cell foam in larger composite panels or tubes in possible industrial applications.

Author Contributions: N.N. has participated in writing—original draft preparation, conceptualisation and the planning of experimental testing and computational simulation. M.V. has collaborated in conceptualization of the research, execution of experiments and has contributed to the writing of the manuscript. I.D. provided the material for experimental testing and has contributed to the writing of the manuscript. S.T., K.H., B.G. and P.C. provided the high strain rate experimental facility and collaborate in execution and data analysis of experimental tests. L.K.-O. provided the quasi-static experimental facility and collaborate in execution and data analysis of experimental tests. Z.R. has provided the topic, collaborated in conceptualization and has co-supervised the work carried out by all authors. Funding: This paper is supported by the opening project of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology)-opening project number KFJJ17-03M. The authors also acknowledge the financial support from the Slovenian Research Agency (research core funding No. P2-0063 and bilateral project (Slovenia–Croatia) No. BI-HR/018-19-012). This work was also supported by the projects UID/EMS/00481/2019-FCT and CENTRO-01-0145-FEDER-022083. Conflicts of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be constructed as a potential conflict of interest.

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