Modeling of Aluminum Foams for Impact Absorption in Multilayer Structures

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Myrtle Young
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1 #$% ;< :..0 +./ +,*,,./ 0 / 4 04,,./ 0 / / * +>A B.; 4 9 D EF G4 =9 C C0B ABAQUS A@ :4 ;< :=> KLJ 9=J; / =./, I0 EF H =B EF 9Q R', P0 S< TU 4 V W =9 H OJ/ P0 9 D.0 4 N 9C0B 9 4 E0 ( D EF) 0^ 9C0B 9 [, X0 B C =/.0 4 E0 A@ 4 B ` =: H / _P 9=: _ ^P 4 A :` 0 EF _P 9=: R', 9F /4.0 := 0 C D0. : 9Q Ra, 4 [, X0 B 9AL@ :+D +CA@ Modeling of Aluminum Foams for Impact Absorption in Multilayer Structures R. Hesari S. Y. Ahmadi Brooghani Department of Mechanical Engineering, University of Birjand, Birjand, Iran Department of Mechanical Engineering, University of Birjand, Birjand, Iran Abstract In this study metal foams are simulated by their mechanical properties with continuum mechanics model. To do so, six multi layered armors were simulated. Three armors consisted of steel/ceramic ates with different thicknesses and other armors had a layered aluminum foam between their layers. A bullet with specified velocity was collided to armors and the JohnsonCook model was used for the steel ate and bullet and the crushable foam model was used for aluminum foam. The results of the present research showed that the multi layered armor with aluminum foam (.4 percent overweight) reduced the stress in ceramic ate more than 0 times compared to armors without aluminum foam. Keywords: Metal Foam, JohnsonCook, Crushable Foam, Energy Absorbent, Plateau Stress. [4] AL. : B _ : 4 o = A 9C Ansys Autodyn A@ _ GL [, 9 X0 P D B C n m ` 7 9=9 : ` 9V W A [] 9=@ GJLJ L0 D0 gf C D V W [6] _= 9C0B ABAQUS _ A@ 4 '; =./C m B m ` _ 4 < _= _ : q pp. 9AL 9=@ : 9C0B 4 D V W [7], 9 4 9C _n< 4J0._= 4J0 < `._=e VY B GF< m _ ; R', 4 b cd G F 9AL 9=@ 9=D0 9AL 9=@ cd., _= ).6 AL cd E< 9AL =E< C) =E< 04 J ( AL 9AL gf gv W D.[]. e (= E< C :0C h4 9AL 9=@ cd W L D TU 0 [] _= ji B C.D (0 ) 7 D0 0^ 9C0B 9 [, X0 [, : B E0 6k._ 9C0B 9 XJ D 6 C KLJ 9=J; D V W [] :_= n m ` 7 (H 0 ) D _ ( 4 9C _ Crushable foam 4 Crushable Foam with Isotropic Hardening (CIH) Crushable Foam with Volumetric Hardening (CVH) Relative Density JohnsonCook * rh_hesari@yahoo.com: 94/0/ 0 : 9/07/ :('

2 ` A ` 9AL EF. P 0 v` X0 C D C 4 : C 9C G}) 9=P0 D g<.[] 9L, D EF I0 4 : q ( L D =[ 0 0 F H 4 KV; X0 =[ H., := R', 9Q 9=Ra, C E0 '.4.[0] 4 T~D C 4 [4..0./ +,* w C 9C0B, [] _= 9 I0 9V _= C 9_ A ;< V W.0 Y 0 ABAQUS _ A@ V _= 9AL [] _= V W _= Hi_=.0 4 9C0B 4 < 0^ HV 9 H HV E0._= 4J0 ( ν p ) 0^ 0 ` HV C < 7 EF y` H.6 9=@ 9 ` N 9 EF ` A V W H.[] 4 : 4 C _Y H 9..0 GY 0^ 0, 0 9/ vl K = ( υ p ).[] 4 0, A 9AL 9=@ 0 B ;< V W E foam = A. E Al. ρ 0 B E Al 0/ ().[] AL cd BV X;.6 ρ B0. 6/9 BV AL 40 V 4 0/6 Y 9 9/ 9' L C 9 _ B 4 cd, [] =..0 4 Y 9/ : 9 :: _, 9D0 0 9C D 9/ :=> H ' Y 0 P0 D 9/ 9 :: _ C A ` [] t, n m 9C0B m 0 4 E0 A ().(G4) 0 4 n._= 4J0 B. s _n< 4J0 B VY < A 9=@ C E0 n0 ;< V W.= GL _= 9Q R', 9 E0, GD ;< V W 4 9/ m ;< V W m.0 4 ` [] n m S= 9C0D tf L_, C ELJ 9=C<. Y E0 +.G < D C 4 4 v X0 = Y ( = G/ 9=BL0 9= C D ' = H,.4.J 9Q Y v= Gb v= 94 D0 I` :J KLJ 9= : 4 _ 4 =/ G4,.[9] 4 B_P :0< 0 9 9AL@ :: gx < 0 B < <.4 WD. : : : 9=Ra,.0 4. W y` A : T : 0 <. < _= 0 =BL0 4 { :: ID B 9Q 9Q 9=Ra, 0^ 4 [0] +J/ +./ 6 I7DI A6. H N;A O/# ++7.[0] 4 F Y 0 H 9/ pp w; H. G` D n 9=BL0 _P gf < H 9Q R', A H/ zw y` C 7 9=D0 9 m B_V 9 :4C gf Gb 0 (AL) ` D EF _V D H4 E 0 9 H ;R',, 9=@ 9C0B Plastic Poisson s Ratio Compression Yield Stress Ratio Plateau Stress 4

3 9b< ; K00 e9_< [] 7 R>7 7 6SA H 7 HSS = D EF, X A 0 9 9= cd s B, +,*..0./ I7DI A6. ;F H 7 N; [] 6.7 #$% 6<./ TA. *@ / (kg/m³).6 (GPa) 0 B 0 [] A7 ;< TA. *@ / 400 (kg/m³).6 (GPa)0 B 0 (MPa) vl : 0^ 9C0B 9 [, X0 B C.0 4 E0 : q / 0 E0 G 0^ < C A 0 9C0B 9 9 G Y [, 0^ Y.[] 0 4 : : o TU 4 0^ G4 x σ = A + B :C 0 gp = s : 9 0^ ( n ɺ ε ) ( m ε + C ln θˆ ) ɺ ε 0 ( + ˆ θ ) p ɺ ε ε f = d + d exp d d4 ln + d q ε 0 ɺ o 0 (4) W 0 A 4 : T~ 0^ : ε 4 C B A t, : o n εɺ 0 () (4) : T~ 0^ : o ɺ ε 4 A V 9 θˆ B` 9 C 9= q H. : / p < 4J0 X; m 4 : ε f ω = ( ε / ε f ) C ω 0^ : _ 4 9= d d CA : V [, 4 XJ B.4 ` =D o C 4 4 () W Hi_=.4 / ε f X0 B 9=T X; (4) B, ().[] 0 BV 0 4 s E0 9 [, B_P ABAQUS _ A@ HighSpeed Steel 9.4 =/ 4 cd B, 60 LF _Y = _ D G Y 9C 4, ( D G) u{ C L _ w.4 Y m A _Y H 9: 4 7 (CDR) 0 9V 0 : 44 0 _ 46 9 =_ H V X v/4 _ { =B hw0.4 _ A) =B 0 _0 H zw0 4 ` G.4 9'Y 9 ` gf (D G +,* 6 6$A / +PQ;@ *@ BL0 4 / F 0 0/ 0/ D0 (kg/m ).6 (MPa) vl : v : 0 (GPa)0 B ;< ,* A@ C < :4 =9 ;< B g< :4 9C0B ` 9 D EF C ELJ g<.4 Gb v= 4 0 EF C EF ^P v/4 vn, E0 w,.= A 9=9 9 G_P i, A = 9C0B P0 7.4 RJ 4 E0 6 0= V. D =9 T 40 A C E0 9C00,.4 =/ G4 A V _) LF B I` `.(4 s < 9 m =@, Partition D Stress (Standard Hexahedral Linear)

$400 0 vl : 9C0BV =[ n X0 =D @ A @ 9 4 0 4 _P 9=:, GY := X0 ` =: H / 9W 0 4 0 / < 0 := 0 C : B 9 D0 C @ < 0 0 B0. `, A H { C.$ 0 :A A 4 y^_p ; :A A ; B_P C (K ).0 [] 7 @ 6<./ +A7 U.D.

$V# @ N; 0 V W 0 0 V W H i 9=.4 KLJ 9 H6 D C 9C L 9=J; X 0 9 4 7 L 00 A =B gef ƒp.4 _ D C GF< 9=: 9Q R', 0,.0.0 Y 0 < _ 0 C A, HA) 0 J; 9 _ H D zw0 G` { C ( E< B< gan H/ C < H 4 A 9 g< _ C.$

4 .= 9, 9 H 0 _ 0 D C 4 : 9Q L_P O# / 6 I W;,. H Y 0/9 9=9 7 _ 9 C CA : _. A 4 =/.0 4 / 6 B, 4 B B 9 : / H6 H ' 0 B vl : 9C0BV =[ n X _P 9=:, GY := X0 ` =: H / 9W / < 0 := 0 C : B 9 D0 < 0 0 B0. `, A H { C.0 :A A 4 y^_p ; :A A ; B_P C (K ).0 [] 6<./ +A7 U.D. * R;A7 4 *@ (MPa) 9 (MPa) 0/04 0/070 /7 0/4 0/0 0 0/000 0/ 79 4 A B n m d d d d 4 d ( εɺ0 ) t, : o 4 n, (HL) Ra 9 (HL) B` 9 (J/kg.K) >9. N; 0 V W 0 0 V W H i 9=.4 KLJ 9 H6 D C 9C L 9=J; X L 00 A =B gef ƒp.4 _ D C GF< 9=: 9Q R', 0,.0.0 Y 0 < _ 0 C A, HA) 0 J; 9 _ H D zw0 G` { C ( E< B< gan H/ C < H 4 A 9 g< _ C. A, H _P 9=: D T L gf G gf =9 _. C X`P G D C C H { D C =: H/ 4 =/ 4 G4., 0 EF D < G` 9=_... ;R',, 9=@ 9C0B (R) 6 A7 ;< ;A 0A,,J I 6 +7 (9) *@A +7(B0A) 6 *@A ,A H%> +I W;,. 4 H Y 0/0 O#0 6 J; C 9 4 N 0 9 9= H : tc C 6

$9b< ; K00 e9_< 6 A7 ;< ;A 0A,,J I H \] @ \ ++7 J; : R', W G 9` B, 4 s 4 9C0B 9=9 @, = w =.0 9 9 C X @6 @0 9=9 @ J; C J; 0 9 0 4 E0 (L 6) @ 9, 9 J; :A H v,.0 @6 @09= 9 / 6@, :A pp 0 9 9= 4 =/.$

5 9b< ; K00 e9_< 6 A7 ;< ;A 0A,,J I H \ ++7 J; : R', W G 9` B, 4 s 4 9C0B = w = J; C J; E0 (L 9, 9 J; :A 9 / 6@, :A pp 0 9 9= G4 W_= 9=: J; _= 0 D P g0 H G 4 A 94 g0 9 =_ :A Hi_=.0 G 9 EF C (V G_ =D0, :A = H J; (K ).0 I 9: 6 +7 ;F D0 (kg) / /94 / /96 /6 /4 : / _ (MPa) J; 0 (mm) 7 (mm) J; 9 (mm) 70 @6 vn v/4 (R) +7P, C 9_ ;< V W 4 _ A@ 4 gf / =./ S< TU C0B ABAQUS 7 6 D0 H6 9Q 40 P0 9 D C GF< 9=:.4 Y Hi_=. 0 D =D0 H T [, X0 B C P0 9=D 9C0B 9 m. E0 0^ 9C0B 9 : 0 ;< V W C C : 0 Y _ GL _ 9/ 9' C GF< m. 9AL 9=@ 9/ m 4 =/ ` n m 4 9C.4 A. 0 Y 7 6 C 9 B_< := Hi_= =: := _ :`. E (0) 4 6 A7 ;< ;A 0A,,J I 7 H 4 +7 (9). J; v/4 vn 9=9 =/ G L 4 X 4 X =9 H : / 9=9 0 9=: C 0 B0..4 7

6 A,9C D09=( V W; 9b< 0 / AL 9=@.9,./ [0] [] Yan W., Durif E., Yamada Y., Wen C. Crushing Simulation of FoamFilled Aluminum Tubes. Materials Transactions, Vol. 4, No. 7, pp. 90 to 906, 007. [] SIMULIA, Abaqus Analysis User's Manual. Providence RI: Dassault Systemes, 0. [] Panigrahi, S.K., Das, K., Ballistic impact analyses of triangular corrugated ates filled with foam core, Advances in Computational Design,Vol., No., pp. 94, 06. 9=: 4 C 9 =9 0 < 0 _P =/ 0 _P 9=: 94 g D0 =: / 4 H_= 0 9 9D0 L 6 J; 9 9D0 ` D0 C Hi_= 4 / '.4. 9=D0 C _ 0 L 4 J; := _ B0. 0 A / :A pp L.4 0 [, X0 B C / gv W, < 0^ 9C0B 9 LY Hi_= 4 E0 9AL 9=@ 9C0B 9 4 _ ( _ A 9AL 9=@ ; R', 7 ' 0 4 ` =./C m 0 9C0B 9 ;< V W 9=( C E0 s n m A n X0 P0 D.=... ;R',, 9=@ 9C0B WA7 [] Ashby M.F., Evans, A.G., Fleck N.A., Gibson L.J., Hutchinson, J.W., Wadley, H.N.G. Metal foams: a design guide. Butterworth Heinemann, Massachusetts, Boston, 000. [] Vanichayangkuranont T., Maneeratana K., Chollacoop N., Numerical Simulations of Level A Ballistic Impact on Ceramic/Steel Armor. The 0th Conference of Mechanical Engineering Network of Thailand, Nakhon Ratchasima, Thailand, 006. [] Pechoucek P., Rolc, S., Buchar J. Fragment Simulating Projectile Penetration into Layered Targets. Engineering Mechanics, Vol., No. /6, pp. 6, 0. [4] Flis L., Numerical Simulation of Ballistic Impact on 0GHMBA Steel Armor, Scientific Journal of Polish Naval Academy, pp., 00. [] Gama B.A., Bogetti T.A., Fink B.K., Yu C.J., Claar T.D., Eifert H.H., Gallespie Jr. J.W. Aluminum Foam Integral Armor: A New Dimension in Armor Design. Composite Structures, Vol., pp. 9, 00. [6] Moo Ryu K., Young An, J., Cho W. S., Yoo Y. C., Kim H. S. Mechanical Modeling of AlMg Alloy OpenCell Foams, Materials Transactions, Vol. 46, No., pp. 6 6, 00. [7] Tita V., Caliri Junior M. F., Numerical Simulation of Anisotropic Polymeric Foams, Latin American Journal of Solids and Structures, 9, pp. 9 79, 0. [] Abravi M.S., Malekjafarian M., Golestanipour M., Amini Mashhadi H., Sadrnezhaad S.K. Investigation of SiC and CaCO on Compressive Properties of Aluminum Foam. 7th International Conference on Porous Metals and Metallic Foams, pp. 994, 0. [9] Yu C.J., Eifert H.H., Hall I.W., Franz R., Leighton K. Feasibility Study on Deformation Energy Absorption of Metal Foams at High Strain Rates, Fraunhofer Resource Center, Newark, Delaware, USA, 99.

Introduction to Engineering Materials ENGR2000. Dr. Coates

Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed