Modeling of Aluminum Foams for Impact Absorption in Multilayer Structures

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#$% 96 47 79 ;< 4 + 6 7 9:..0 +./ +,*,,./ 0 / 4 04,,./ 0 / / * +=> @7 +>A B.; 4 9 D EF G4 =9 C 0.0 4 9C0B ABAQUS A@ 6 7 9 :4 ;< :=> KLJ 9=J; / =./, I0 4 @ EF H =B 0 0 0 EF 9Q R', P0 9=D @ 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. Y 0 @,:A @ 9 9 4 =/.0 4 E0 A@ 4 '; @ B C @ ` =: 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 o0 7 9 9= A 9C Ansys Autodyn A@ _ GL [, 9 X0 P D B C n m ` :_=. @ 7 9=9 : 9 7 9 6 ` 9V W A [] 9=@ GJLJ L0 D0 / BL0 @ @ gf C BL0 @ D V W [6] _= 9C0B ABAQUS _ A@ 4 '; =./C m B m ` _ 4 '; @ < _= _ GL.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., _= 9Q @.6 ).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/ :('

` 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./ +,* BL0 @ w C 9C0B, E0 @ [] _= 9 I0 9V W @ H.4 @ _= C 9_ A ;< V W.0 Y 0 ABAQUS _ A@ V _= 9AL [] _= V W _= Hi_=.0 4 9C0B 4 '; @ < C @ 0^ HV 9 H HV 9.0 4 E0._= 4J0 4 @ ( 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/ ().[] 0 4 0 AL cd BV X;.6 ρ B0. 6/9 BV AL P @ 40 V 4 9C0B @.4 0/6 BV @.0 Y 9 9/ 9' L 0 0 4 9C 9 _ B 4 cd, [] =..0 4 Y 9/ : 9 9' @ :: _, 9D0 0 9C D 7 @ 9/ :=> H ' Y 0 P0 D 9/ 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 9C0B @ 9/ m ;< V W m.0 4 ` [] n m S= 9C0D tf L_, C ELJ 9=C<. Y E0 +.G < D C 4 9Q @ D @.=.4 4 v X0 = Y u= @L, ( 6 @ = 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 < H @ 0 B < _ @ <.4 WD. : : < @ : 9=Ra,.0 4. W y` A : T : 0 C @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 0 9.0 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.0 4... ;R',, 9=@ 9C0B Plastic Poisson s Ratio Compression Yield Stress Ratio Plateau Stress 4

9b< ; K00 e9_< [] 7 R>7 7 6SA H 7 HSS = D EF, X A 0 9 9= cd 4.0 4 s B, +,*..0./ I7DI A6. ;F H 7 N; [] 7 @ 6.7 #$% 6<./ TA. *@ 770 00 0/ (kg/m³).6 (GPa) 0 B 0 [] A7 ;< TA. *@ 900 0 0/ 400 (kg/m³).6 (GPa)0 B 0 (MPa) vl : 0^ 9C0B 9 [, X0 B C.0 4 E0 : q / 0 E0 G 0^ < C A 0 9C0B 9 9 G Y [, 0^ Y.[] 0 4 : : o TU 4 0^ G4 x σ = A + B :C 0 gp = s : 9 0^ ( n ɺ ε ) ( m ε + C ln θˆ ) ɺ ε 0 ( + ˆ θ ) p ɺ ε ε f = d + d exp d d4 ln + d q ε 0 ɺ o 0 (4) W 0 A 4 : T~ 0^ : ε 4 C B A t, : o n εɺ 0 () (4) : T~ 0^ : o ɺ ε 4 A V 9 θˆ B` 9 C 9= q H. : / p < 4J0 X; m 4 : ε f ω = ( ε / ε f ) C ω 0^ : _ 4 9= d d CA : V [, 4 XJ B.4 ` =D o C 4 4 () W Hi_=.4 / ε f X0 B 9=T X; (4) B, ().[] 0 BV 0 4 s E0 9 [, B_P ABAQUS _ A@ 9C0B @.= HighSpeed Steel 9.4 =/ 4 9C @ cd B, 60 LF _Y = _ D G Y 9C 4, ( D G) u{ C L _ w.4 Y m A _Y H 9: 4 7 (CDR) 0 9V 0 : = @_ 44 0 _ 46 9 =_ H V X v/4 vn @ 9=9 @ _ { =B hw0.4 _ 4 446 607 A) =B 0 _0 H zw0 4 ` G.4 9'Y 9 ` gf (D G +,* 6 6$A 6...0./ +PQ;@ *@ BL0 4 / F 0 0/ 0/ D0 (kg/m ).6 (MPa) vl : v : 0 (GPa)0 B ;<4 ++7 +,* A@ C < :4 =9 ;< :=> G4 @6 @0 B g< :4 9C0B ` 9 D EF C ELJ 9=J; @ g<.4 Gb v= 4 0 EF C 9 0 9 EF ^P v/4 vn, E0 w,.= A 9AL @ 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 _) 0 4 0 LF B C @6 I` `.(4 s B @6 < 9 m =@, Partition D Stress (Standard Hexahedral Linear)

.= / @ 9, 9 H 0 _ 0 D C 4 : 9Q R',, @ L_P O#0 6 @6 +7 6..0./ 6 I W;,. H Y 0/9 9=9 7 _ 9 C CA : _. A 4 =/.0 4 / 6 G4 @ B, 4 B0. 400 B 9 : / H6 H ' 0 B0. 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. * 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. 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. A, H _P 9=: D 4 9 0 4 7 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 H @6 +7 (9) *@A +7(B0A) 6 *@A +7 7 6.7,A H%> +I W;,. 4 H Y 0/0 O#0 6 J; 9AL @ C 9 @ 9 H @,.0 4 N 0 9 9= H L @ : tc G4.4 @L / @ 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 =/.4 @ 9 7 G4 W_= 9=: A @ J; _= 0 R', @ D P g0 H G 4 A 94 g0 9 =_ :A Hi_=.0 9 @, G 9 EF C (V G_ =D0, GY @, :A = H J; (K ).0 I 9: 6 +7 ;F *@ @, D0 (kg) / /94 / /96 /6 /4 : / _ (MPa) 400 4 9 4 J; 0 (mm) 7 J; @ (mm) 6 4 0 J; 9 (mm) 70 9 B @ @0 @6 vn v/4 (R) +7P, 4 @ C 9_ ;< V W 4 _ A@ 4 '; @ gf / =./ S< TU 0 9 0.4 9C0B ABAQUS 7 6 D0 H6 ' @ 9Q R', @ 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 9 @ C 9 B_< := Hi_= =: := _ :`. E (0) 4 6 A7 ;< ;A 0A,,J I 7 H 4 +7 (9). +7(B0A) @ J; v/4 vn 9=9 =/ G4.0 4 7 L 4 X 4 X =9 H : / 4 @0 9=9 0 9=: C 0 B0..4 _ @6 7

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