斜冲击界面动力学研究.pdf-道客多多

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2、, 4 Bz ? , 0(2)L* =L*c (P/2- A0)(P/2- A0c) A A0cL*c A A0c(3)T: L( t)r “ ; t HW; vn( t)#Dn( t)sYE_ #E_M; A0 S (V ); C1aC2 ,Vr “ HW 6/ qb “L*c#A0c r 1 , XD9) b,Z(2)#(3) r “ Amonton pb Y L ,Z( 2) VBL=C1Qtc0dvndt1vnn1dt dDn/dt 0, L 0(4)T: n1an2 , tcatf V+ HWb E_ p = p( Dn,dDn/ dt, vn, dvn/dt, ,) (5)yNZ(

3、4)Vrr “ L VG E_ bB4 W. J. Stronge3 , 4 B“9 , Y 8| M_ # ?bN , !L= 0.18( ),9 A. D. Lewis 8 (Tb 7, W. J. Stronge3/N H,Ai LHq, ,yN, 3 AJ ? , VBs s ,9 ?G “ 0by7 | ,r “ !9 Z T E L 4 V# S G b105 2 v M:| 3 E_Y (8$E_F H, S f ? 3M,F9F H, 8 8 7 S? 3 MbE_F9F H, u9,( ) Mb M 7 S / ( pm = 1.07Y 1.1Y (6)T: Ye %( )

4、y b( ) M H,J u s ( bW,H, ( pm = H = 2. 8Y 3Y (7)T:Hb V ,$r ohF H, ( pmX$D. Tabor 11V UpmY =23 1+ ln13EYar (8)T: a( ; E f bZ(8)V pm a/ r9F7V1.1Y9F3YbJ. R. Matthews12X I n F,TV , TZ(8)YG M 9,9 VbyN | , E_YVrp = n4/ 5(5mv20n/4)1/5Pr p t* (19)m dvdt = F t t*Fcos( A+ B) - LFsin(A+ B) t t* (20)F =Pa21p t

5、t*A1sin( C- A) + A2cosCp t t* (21)a1 = r2- y2A= arctan(v/ u)B= arcsin ( a1 - rsinA)2+ ( r - y - r(1- cosA)21/22rC= arcsin r - y - r(1- cosA)/2rsinBA1 = r2arcsin( a21- y2tan2A/ r) - ( a21 - y2tan2A)( r2 - a21+ y2tan2A)A2 = a21arccos(ytanA/ a1) - ytanA a21- y2tan2Am1 r o v| + mFig.1 Geometric shape of

6、 the oblique impact of ahardsphere of radius r at avelocity v against aductile solidT: t*| VB+ H Y,t t*H, o J V M(; 9 t* V a bA1#A2sYm1 j2j3#j2j1 O bZ(21)pZ( 9a)( 9b) ,Z(19)#(20)LZ(2)#(3) bZ(17) (21)F (9a)(9b)a( 2)a(3)#(10)a(11)(12) (16) VRunga-KuttaE pb SHqt= 0, x( 0) = 0, y(0) = r, u(0) =v0cosA0,v

7、(0)= v0sinA0, L(0) = 0, v0, A0 S #b5 L Z(12)V U RY M#M q9F79F,7 67/bXi 107 2 v M:| Z + MaM q#f bM q H, /1“R= R0+ BEn (22)T: R0 S y Y; nF ; B bG. R. Johnson204 /ZR= (R0+ BEn)(1+ cln E#E#0) (1- T* m1) = R0 # Rd (23)T* = T - TrTm- Tr(24)Rd = (1+ BR0 En) (1+ cln E#E#0)(1- T* m1) (25)T:TrR0;Tm ; E#0= 1.0

8、s- 1; cam1 bJohnson-CookZX$Wb R0aBacanam1X$ b y | #Johnson-Cook1“I. M. Hutchings19 L Ebm2 3sY r= 4. 75mm o 200m/s| VPH2.35GPa H,Q aQ A0Mbm9V U LTbm4 m2 3 Sm2 4.75mm o200m/ s a| VPH= 2.35GPaB“ L, 9 Q M LT1 Fig.2 Comparison between calculated and experimentalvariation of the rebound velocitywith the i

9、nitialimpact anglefor a steel sphere of 4.75mm radiusat a velocityof 200m/s impinging obliquely ontoa steel plate of 2. 35GPa quasi staticVPHm3 4.75mm o200m/s a| VPH= 2.35GPaB“ L, 9 Q M LT1 Fig.3 Comparison between calculated and experimentalvariation of the rebound angle with the initial impactangl

10、efor a steel sphere of 4.75mm radiusat a velocity of 200m/s impinging obliquely ontoasteel plate of 2.35GPa quasi static VPH108 I 22 V1 3m2am3#m4 wL Z(2)a(3)(23) Table 1 Parameters in Eqs.(2), (3)and(23) usedto produce curves in Fig.2 Fig. 3 andFig.4C1 C2 L*c A0c R0/G1a B/G1a n c m11. 0 1. 0 0.1798

11、52.0 0.79220 0.51020 0.2620 0. 01420 1.0320m4 m2m30b f ,9 ( uLaRaRdapd#p HWtMFig.4 Calculated variations of L, R, Rd, pd andp in the contact region with timefor initialimpact angleof 30b in theFig.2 Fig.3 30b H, 9 ( ur “ La RaZ(25)V URdaZ(13)V Upd#E_ p HWMb9 /V1bm2 3 Vn, y | V | Y,Q #Q ,1 LTb 7i IZ(

12、2)#(3) r“ rb1r “ , |5 ) b| , T-M1 5, b6 1.4 B| ,N 4:( 1)r “ ) V# S f b(2) E_Y I n(aMK#9#MaM qr (b(3) I n VM,(MaM qaM ( , X 9 t 4b2.Johnson-CookZ | ,I. M. Hutchings19| L E,9 Q aQ M LT1 Bb ID: 1 Bhushan B. Contact Mechanics of Rough Surfaces in Tribology: Single Asperity contactJ . Appl Mech Rev, 1996

13、, 49( 5):275) 298. 2 Feeny B, Guran A,Hinrichs N , et al. A Historical Review on Dry Friction and Stick-slip PhenomenaJ . Appl Mech Rev ,1998, 51( 5): 321) 341. 3 StrongeW J. Planar Impact of Rough Compliant Bodies J .Int J Impact Engng,1994,15( 4): 435- 450. 4 Pfeiffer F, Glocker C. Impacts withFri

14、ctionA . Procof 1995 Design EngineeringTech ConfC.1995, 3(suppl) : 171) 180. 5 Sundararajan G. The EnergyAbsorbed duringtheObliqueImpact of aHard Ball Against DuctileTarget MaterialsJ . Int J Im-pact Engng, 1990, 9(3): 343) 358. 6 Ko PL. The Significance of Shear and Normal Force Components on TubeW

15、ear due to Fretting and Periodic Impacting J.Wear, 1985, 106: 261) 281. 7 Maw N, Barber J R, Fawcett J N. TheOblique Impact of ElasticSpheres J .Wear, 1976, 38: 101- 114. 8 Lewis A D, Rogers R J. Experimental and Numerical Study of Forces during Oblique Impact J .J Sound213) 234. 11 Tabor D. Indenta

16、tion Hardness and Its Measurement: Some Cautionary CommentsA . Blau P J, Lawn B R. MicroindentationTechniques in Materials Science and Engineering C .Philadelphia:ASTM,1986. 129- 159. 12 Matthews J R. Indentation Hardness and Hot PressingJ .ActaMet,1980, 28:311) 318. 13 Hertz H. Uber dieBeruhrung Fe

17、ster ElastischeKorperUndUber dieHarte (onthe Contact of Rigid Elastic Solids and on Hard-ness) A . Verhandlungen des Vereins zur Beforderung des GewerbefleissesM . Leipzig:s.n. . 1882. 14 Tabor D. Hardness of MetalsM.Oxford: Clarendon Press, 1951. 15 Hutchings IM. Strain RateEffects in Microparticle

18、 Impact J . J Phys D: Appl Phys, 1977, 10:L179) L184. 16 Hutchings IM, LevyA V. Thermal Effects in theErosion of DuctileMatelsJ .Wear,1989, 131: 105) 121. 17 Oden J T, Martins J A C.Models and Computational Methods in for Dynamic Friction PhenomenaJ. Comput Methods in ApplMech and Eng, 1985,52:527)

19、634. 18 Rabier P, Martins JA C, Oden J T. Existence andLocal Uniqueness of Solutions to Contact Problems in Elasticitywith Nonlin-earFriction LawsJ . Int J Eng Sci,1986,24: 1755) 1768. 19 Hutchings IM, Macmillan N H, Rickerby D G. Further Studies of theObliqueImpact of aHard SphereAgainst a DuctileS

20、olidJ . Int JMech Sci, 1981, 23: 639) 646. 20 Johnson G R, Cook W H.A ConstitutiveModel and Data forMetals Subjected toLarge Strains, High Strain-rates andHighTem-peraturesA. Proc17th Int Nat Symposium on BallisticsC. 1983.541) 547.On Interface Dynamics with Applications to Oblique ImpactCHEN Da-nian, YU Yu-ying, YIN Zh-i hua, SHEN Xiong-wei( Mechanics oblique impact; effective impact friction coefficient; constitute equation110 I 22

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