04球形闭孔泡沫金属材料力学行为研究.pdf

1、 30 4 2009 M 8 % 8 CH INESE JOU RNAL OF SOLID M ECHAN ICS Vol. 30 No. 4August 2009o d *尚艳军1 null 卢天健1* null 陈常青2( 1 Y v t ? t b , d 4 + , y y d h k T 1 , = z . N , y 9 1 / null M w L , C 4 O , o d d + M / f w # ? p , 4 . T V , ? z E K 9 T .1 o M null o d , Z ( FCC) , K s ,1 F , f 0null M “ “ p a ! F

2、 / ? Z 7 C B ? . (null d ? K s , M 1 “ . Demiry 1 3 E 8 7 d S y y s , F N / , y M ,7 O y vl 9 M . 1 ? z . S 0 14 1 o 8 y d ? K s , Z z r T .Y , d h # d e d d # q e M Y , d d# q / C d + , d # q h d V C o o d , 7 d # q h d V C H d . d # q a d d C ,y 7 - 16 . M 7 , “ - o 8 . o d h . d H d # q h , D 17

3、o d d # q h*S E $ 9 “ ( 2006CB601202) , S E / ? Z 9 “ ( 2006AA03Z519 ) , S E 1 S “ ( 10572111,10632060) S E null 111 9 “ ( B06024) .2008null05null11 l 1 , 2009null06null25 l .Y T . null null T el: 029null82665600, null null Tax: 029null82665937, null null Enullmail: tjlu m ail. xjtu. edu. cn. d o d

4、% 4 . N $ , K s ,y % 4 F 4 W 1 “ , M W G 1 “ , y f . , o ( o ) d h 7 Z k , i | k T K 9 T 1 s .1null Z Z K o d (n m 1) , L ! “ v l o d .m H l,o d r. m o o M MH , r | K v r / l= 2/ 4. r / l 2/ 4 H , d M 7 d . d , # K r/ l d o d M d # q sY :null*nulls= l3 - 16nullr 3/ 3l3 null ( 1)Px = 1- null*nulls =1

5、6nullr 33l3 ( 2)1. 2null H H q % 4 9 , | aH H q 9 T V L 1 o . V A S L = B 8 V , H H q , 9 T ? VL = 4 ? 10, 19null21 . m 2 , i ( , v+ ) , B ( , v - ) . :x v+i = x v-i , null x v+j = x v-j , null x v+k = x v-k ! l ( 3) i j k, x v+m x v-m ( m= i, j , k) H v+ v- U S . , H H q V Y V /T F Z H :uv+i - uv-i

6、 = ij ( x v+j - x v-j ) , null i, j = 1, 2, 3 ( 4) S v+ v- M H ,uv+i uv-i v + v- M s , x v+j x v-j v + v- U S , ij 4 M s . K 9 H ,F Z T Y V F 4 , 7 4 M ij , “ V Y V F 1 F ? .m 2null H H q H M Fig. 2 null M atched nodes for periodic boundary conditions1. 3null K 9 L 8 ( C3D8R) m 1 U , s h s .9 | % 8

7、( h ) f E s=70. 3 GPa, 1 !s= 0. 345. s o d / Y H , Mises#326# % 8 null null null null null null null null null null null null null null null null null 2009 M 30 y 5 _ 0( 5) 0= E s 0, 0= 0. 1%, n= 0. 2.2null d h L L d h 2 v 1, q 5 F 4 , 8 ? E ! . h F C , k “ L M F . T “ j 25mm % 25 mm % 50 mm, d j (

8、1null3) mm, k“ K 7 d j . d h L MT S k , M ; d ( M “ d ARAMIS . h k “ h W , / h V p B Y p ( PT FE Pow der Spray) h _ L Y .L V | M F a e Z T , q 0. 01 m m/ s F ,K M k “ 80% , ARAMIS “ d k “ V M _ M _ M . d h V f E 1 ! V , f E w L | q . 1! ; d ( M “ d _ a: _ M 1 . d h y d h nullM w L . V A , M d h null

9、 M w L A Y . “ M h l , null M w L ? 3 /M :L | q v h l , f h l ; h l , K v M 9 F .3.1null m 4 K 9 k o d ( f Ea 1 !)M W G 1 “ ,m Bt T . L 1 , f E T B B ) . V w L E ? C , K 9 T V /#327# 4 null null null null null null null null null null + : null o d T 0 V U :EE s= 0. 86 null*nulls2+ 0. 13 null*nulls(

10、6)!= 1+ 15. 078(null* / nulls)1+ 51. 306(null* / nulls) ( 7)7 k T w L E V r T :EE s= 0. 95 null*nulls2+ 0. 14 null*nulls( 8)! M v f / , V Z f 11 GibsonnullAshby , k T . M f / Z % M v 1 , N H GibsonnullAshby ? z ? . D 15 7 a d Z K s , T S = ( 0. 5) , S = ( 0. 5) z , S = ( d z ? . m 4( b) V A 1 M M v

11、, GibsonnullAshby E s , 1 M .m T 9 V , K T L T z .3. 2null 3. 2.1null o d y d o d / Y , d o d y d h y d h i B t J . 6 ? C , S 0 14 1 9 k T M B . Chen 10 Y V K s ) = Vor onoi + , d o d y d L = , B s . y N , T / Y L = i l . o d 1 F / #328# % 8 null null null null null null null null null null null nul

12、l null null null null null 2009 M 30 (m 6) . 1 F y 0 K = 33 /11 S/ T , I n F y 0 s Y 2a1( % )a0. 5a0( % )a- 1a( ( 11= 0 % ) , B F y 0 , i % f . ChennullLu 24 + + M Q , ? z E k 7 d d M 25 ,7 O u s M M , L L = . ChennullLu , + null + M l null / :null2= 2e + 22m ( 16)null 2 = 2e + 2v2 ( 17) e M ises r

13、, m ( , e r M , v 8 M , , 1 ! % ,1 “ / :2= 9( 1- 2!)2( 1+ !) ( 18)N , ChennullLu f l / :%= null2+ %1 (null , m ) - Y(null ) = 0 ( 19) f %1(null , m) d o d % ( K = ( )a % ( K= 1)a % ( K = 0) F F ( K = - 1) / M Y , + null M w L n m 7 U . V m V ? C , F f / L + , ChennullLu B 1 + .Y V w L E , V s Y % a

14、% / + null+ M f T :m 7 null F + null+ M w LFig. 7 null The characteristic stressnullstrain curvesalong different loading paths#329# 4 null null null null null null null null null null + : null o d nullhc = - 4. 7278e- null / 0. 00044- 6. 7422e- null / 0. 07467+ 11. 3520( 20)nullhl = - 4. 5684e- null

15、 / 0. 00041- 2. 8747e- null / 0. 02542+ 7. 2976( 21)nulluc = - 3. 9771e- null / 0. 00037 - 4. 0451e- null / 0. 05963 + 7. 9552( 22)nullunullt = - 3. 8622e- null / 0. 00035- 4. 5541e- null / 0. 05013+ 8. 3405( 23) f o d , f T / :%= null2 + A (null ) m+ B(null ) 2m + C(null ) 3m- Y(null ) = 0( 24)T V

16、- 9 T .Y V F f w L E T T ( 20)null( 23) , V f %. p / :null2hc - nullhc / null2hc /2 - null3hc /3null2ht nullht / null2ht / 2 null3ht /3null2uc - nulluc / j , 1, , E B . o d d # q h J . S S ( B) , 2004, 47( 5) : 407null413.( Zou Yi, He Deping, Jiang Jiaqiao. New type ofspherical pore Al alloy foam wi

17、th low porosity andhigh strength J . Science in China, Series B, 2004, 47( 5) : 407null413. ( in Chinese) ) 18 null , 1, . h 8 o 3 J . S S ( B) , 2005, 35 ( 3) : 212null219. ( Shang Jintang, H e Deping. Spherical foam growth in Al alloymelt J . Science in China, Series B, 2005, 35 ( 3) :212null219.

18、( in Chinese) ) 19 null Laroussi M , Sab K, Alaoui A. Foam mechanics: nonnulllinear response of an elastic 3Dnull periodic microstrucnullture J . Int ernational Journal of Solids and Strucnulltures, 2002, 39: 3599null3623. 20 null Roberts A P, Garboczi E J. Elastic properties of monulldel random thr

19、eenulldimensional opennullcell solids J .Journal of the M echanics and Physics of Solids,2002, 50: 33null55. 21 null Li K, Gao X L, Subhash G. Effects of cell shape andcell wall thickness variations on the elast ic propertiesof tw onulldimensional cellular solids J . InternationalJournal of Solids a

20、nd Structures, 2005, 42:1777null1795. 22 null Deshpande V S, Fleck N A. M ultinullaxial yield behaviorof polymer foams J . Acta M aterialia, 2001, 49:1859null1866. 23 null Deshpande V S, Fleck N A. Isotropic constitutivemodels for metallic foams J . Journal of the M enullchanics and Physics of Solid

21、s, 2000, 48: 1253null1283. 24 null Chen C, Lu T J. A phenomenological framew ork ofconstitut ive modeling for incompressible and comnullpressible elastonullplastic solids J . Int ernational Journullnal of Solids and Structures, 2000, 37: 7769null7786. 25 null = , , f , . h 1 “ L J . , 2004, 36:673nu

22、ll679. ( Wang Erheng, Yu Jilin, Wang Fei, SunLiang. A theoretical and experimental study on thequasinullst atic constitut ive model of aluminum foams J . Acta M echanica Sinica, 2004, 36: 673null679. ( inChinese) ) 26 null Gurson A L. Continuum t heory of ductile rupture byvoid nucleation and growth

23、: Part 1nullYield criteria andflow rules for porous ductile media J . Journal ofEngineering M at erials and Technology, 1977, 99( 2) :2null15.THEMECHANICALBEHAVIORSOFCLOSEDnullCELLALUMINUMnullALLOYFOAMSWITHSPHERICALPORESYanjun Shang 1 null null T ianjian Lu1 null null Changqing Chen2( 1 M OE K ey L

24、aboratory f or Streng th and Vibration, School of Aerosp ace, X i an J iaotong University , X i an, 710049)( 2 School of Aerospace , A M L , Tsing hua University, Beij ing, 100084)Abstractnull Facenullcentered cubic unit cell model is em ployed to investigate the m acroscopic elastonullpalsticbehavi

25、ors of closednullcell foam s w ith spher ical pores. T he dependence of the elastic constants and yieldstrength of the foams on the relative density are calculated and are found to agree w ith the exper im ental renullsults. T he str essnullstrain cur ves under proportional triaxial loadings are als

26、o simulated. They are then used todeterm ine the material param eters in a phenomenological elastoplastic m odel. T he sonulldeter mined phenomenullnological model is found to be able to predict the num er ically calculated characteristic stressnullstrain curves,w ith good agr eement achieved.Keywordsnull closednullcell foams, spherical pores, facenullcentered cubic unit cell model, finite element analynullsis, proportional loading, stress potential#332# % 8 null null null null null null null null null null null null null null null null null 2009 M 30