常见材料参数

1、输入参数：copper:1. Johnson - Cook material model:density: 8330 kg/m3young s modulus: 138000 MPaPoisson s ratio: 0.35-A: 89.63 MPa-B: 291.64 Mpa-C: 0.025n: 0.31m: 1.09melting temp: 1200 Croom temp: 30 Cspecific heat: 4400 J/kg CGruneisen EOS:C: 0.394-S1:1.489S2: 0.0S3: 0.0-y0 : 2.02-A: 0.47 2. Johnson -

2、Cook material modeldensity: 8330 kg/m3young s modulus: 138000 MPaPoisson s ratio: 0.35A: 90 MPaB: 680 MPaC: 0.044n: 0.9m: 2melting temp: 1200 Croom temp: 30 Cspecific heat: 4400 J/kg CInternational Journal of Impact Engineering 30 (2004) 593 - 615Load spreading and penetration resistance of layered

3、structuresa numerical studyJ.R. Robbins a 1? J.L. Dingab *, Y.M. GuptaacTabic Density longitudinal) (Cl)? and shear (C) wave speeds for the male rials,in. the numerical) simuLationSiC6061 AluminuniRH A sicclHardened 4340 sLcelPM MAP 堕,Em)2.7047.B2?Q (km s)n.ih6.485.845.M2.72Cs fkm /s)7.743.193.15?.i

4、5.36Tabic 2Material parameters for JobnsonCook model606 Alum mumRHA steelHardened 4340 sledPM MAf?Jp pG G/A- /A-0.32410.79221.5100.06480.11380.5100.62740.000.420260.161.00.0020.0140.006().0I./4o o.pppG G GA1E昭ro74&73 I8.52 26?58534.29o Q 5nThe Johnson - Holmquist model 16 used to describe the SiCTub

5、lc 3MaLcria.ll paramcLcrs for Johnson-HolmquList Modelp p p p pn G G G G G X /I.- yl. /f /A- /I. 均法，民巴65 5 8 5 4 620&4.9911 &2elQ4EA2a%0.004J .040.0052200.00.0JC.5DP (GPa)王明洋文章中有一些岩石和混凝土的参数DE报口号DE95001416题名CTH analyses of steel rod penetration into aluminum and concrete targets with comparisons to e

6、xperimental data作者 Kmetyk, L. N. Yarrington, P.机构 Sandia National Labs., Albuquerque, NM.SAND-94-1498Table 221. Material Properties Used in CTH Analyses for Ogival-Nosed Rods Penetrating 7075-T651 Aluminum TargetsPropertyPenetrator (Steel)Target (AluminumDensity, p (gm/cm3)8.022.70Sound speed, Cs (c

7、m/s)4.610 x1055.380 X105Us Up slope, S1.731.337Gruneisen coefficient, r1.672.100Specific heat, Cv (erg/gm-eV)5.34xl0i1.02X1011Poissons ratio, v0.30.33Yield stress, Y (dynes/cm2)17.2x10，Johnson-Cook model constantsA (dynes/cm2)4.48x10B (dynes/cm2)2.95x10$C (dynes/cm2)0n0.39205Tm (eV)0.0668Pfrac (djme

8、s/cm2)-35x10-5x10s*Table 3.2.1. Material Properties Used in CTH Analyses for Hemispherical-Nosed Rods Penetrating 6061-T651 Aluminum TargetsPropertyPenetrator(Steel)Target (AluminumDensity, p (gm/cm3)8.022.70Sound speed, C$ (cm/s)4.61x105538x10sU$ 玖 slope, S1.731,33 了Gruneisen coefficient, F1.672.10

9、0Specific heat, Cv (erg/gm-eV)5.34x101。1.02xl0iiPoissons ratio, v0,30.33Yield stress, Y (dynes/cm2)17.2xl()9Johnson-Cook model constantsA (dynes/cm2)2.76x109B (dynes/cm2)0.92x109C (dynes/cm2)0n0,2591Tm (eV)0.0792Pfrac (dynes/cm2)-35 x10s-5xl09Table 4.2A. hUteriAl Prapcitieg 1W ib CTH Analyx of Ogivd

10、-Nftjcd Ro(k P*相Hili理40M?3 Cancrelft Tm警匡PropertyPenctralof (St)Itrget (CouctcLc)Dmsity, p (gm/cm5)&畛点Sflund jpeed,心时&)610 x10*g - UpSL?aGru质咐 (XiefEriHiL F Spcdfix: h&at, Cv (erg/gm-cV)1.675,3。炉ixid11PoissaDs ratio.站0-3Yield stress, V ggjM1)17,2x10Johnson-muikL oaDstUnts T (dynes/cmJJ急景1伊pt dynesfa

11、n3IX静pj (dynes/cm2)Txl护li (tlyncB/cmsj部邮la (dU/cmf)4-亦1伊5a (dynea/cm1)4.510焚(dues/cm2)1 K 10flf% iclyEes/cm勺0.6网*1x10fi (dyncs/cms)4xltf3 (dyuM/cm1)0Ka，(4ynEs/cmE-l0B0p* (dyEies/majD(7 (dynea/cm21.25m10i:(dyMs/rm1-35xlQxltf6International Journal of Impact Engineering 27 (2002) 807 -835Behind-the-arm

12、or debris analysisG. Yossifon, A.L. Yarin*Table 1M ate rial and geometrical characLerijiLics of the projccti k and LarsteLProjpctikTarget (RH心MassNp闾LengthL (mm )Diameter D ( mm )Etensity 丹(g/cm1)Yield stressY (MPa)Elongation 们)Thickns H ( mm )Vickers hardness (HV)62 S1202017.1?14601C703 30-抑|hc prc

13、jjectile and targel wcic modclcJ ns isolmpic clastk pktslic niiilcniils. The von Mises tensik How stress. Y, wits expressed uccording ! I Die .li)h nson-Cook mockl lis: = M4 号闩I + Cln/l - T(|5)Tabte .2Material modeTs parameters3ParametersUnitsRHAWSAStrength corastant for Y = A + .Bc|l + ClErl 厂呵AMPa

14、911460BMPa510177界0.260.12C0.0140.0161.031.0Therrna! prrtiesDensitypg/cm37.8317.13Specific heatCpJ/kgK4777Reference tempera ture Ttc-300300Melting temperatu.ire179317.23E!aic p啊政Bulk modulus一KGPa159278Shear modulus一GGPa77145Failure properiiesMaximum tensite strain to faillure一身、40%10%Fracture toughne

15、ssK&XIPaiTi12807021 The material! properties for RHA are taken from 17, and those for WSA are taken from 18.hThe strength model constants for RHA cor respond to 4340 steel of Ref. 1 7 having static yield strsts of 792 MPaand hardness of 30 RC. The measured RH A hardness is 345 H V (sse Table 1)、or c

16、quivateinitly 35 RC. In order to conrect the yield stress according to the difference in the hairdns values we make use of the foHowing conversiora equation 19: BHN = 1.979|Tensile StrengthffeQ + 11.24.1 7 Johnson GR, Cook WH. Fractum chanicteristics. of three nietaU subjected to various strains, st

17、rain rates, ternpeniLyrK and prewtures. Eng Fract Meeh 19S5;21:3 48 (4340 Steel)1 8 Johnson GR, Cook WH. A constitutive model and du La for metals subjected to Large stmms, high strain rates and high temperaturffi. 7th Intenaticinal Symposium cm Ballistics, The Hague, The Netherlands, 19S3 (Tungsten

18、 Alloy (7%Ni, 3%Fe)19 Anckson CE? Morris BL* Littlefield DL. A penetration mechanics dLabaM. Tgas, US: S.R.L San Antcmio, 1992.International Journal of Impact Engineering 27 (2002) 37 -64Perforation of 12mm thick steel plates by 20mm diameter projectiles with flat, hemispherical and conical noses Pa

19、rt II: numerical simulationsT. B_rvika,*, O.S. Hopperstada, T. Berstadb, M. LangsethJohnson-Cook material modelIdble 1Mate rial const ants for We Id ox 4()。E sice 3tkistic constants and density Yield stress and strain hardening St min rate hardeningDam age cvDlutionEGPap (kg m初AM&)Bn知m %)CAj2(H)。一 3

20、378504900.735x l(1A0.0114顷)()Adiabatic heating and lemperEiture softeningFradurc stiiiin constantsCp (.I kgK)7.VI K7th (K)而(K)BlDiLh 也452().91.1 x lL1S00叫3u 一归0.07051.732-().54 -5 ULi J R ., Yu J L, Wei Z G. Influence of specimen geometry on adiabatic shear instability of tungsten heavy alloys. Inte

21、rnational Journal of Impact Engineering 2003, (28): 303-314.A two-dimensional axis-symmetric adiabatic model is introduced in the simulations and the Johnson - Cook model is employed to describe the thermo-viscoplastic behavior of the material.tungsten heavy alloys (WHA) are currently basic material

22、s for kinetic energy penetratorThe rate-dependent thermo-viscoplastic model of Johnson - Cook 7 is used for numerical simulation7 =.4 11广)E),(I)wlicrc A, 8、h, C and /n aiv iiiLilurici tonsl etuis.尚 is llic ruJuruiitc sliLtiii ritlc. T* = T TrTr. 7m is llic 】n 妃ling luiipurLtlLiru ol llic iiiiilcriLt

23、. itucl Tr llic rcluruiicu lumper ill Lire.11 iS LiSSLLUlUll lllLil llU uJlcfl ol llULil tOllllLKlioil IS lCguclLibu SO till： rUSpOUSC IS LilliLibLilit. 丁ILLS liu Icxii luuipcrLil Lire isc depends on llic woik ol deloriiuilioii by()t dT = 0.9rr 出;-(2)According to Yadav and Raincsh S, wc choos-c = IO

24、-4 s-. A = 1093 MPa, B = 1270MPa. C = 18.8 x IO-3, h = 0一史，m = 0.7S, Tm = 1S50K. Tr = 293 K. c =134 J.脂 K一 ituil (I = 18,600 kg/ni3.International Journal of Impact Engineering 28 (2003) 1077 - 1106Square aluminum tubes subjected to oblique loadingA. Reyes*, M. Langseth, O.S. Hopperstadmaterial model

25、 103 in LS-DYNA:Table 2Mechanical properties (based on the engineering stress-strain curves) for each temper and thicknessTemperh (m m)g mtn2)n,； i mm2)E (N/mm2)T4l.W867758 9002.47867761 60()3.3475593004部7215655 9()0T6L9220()22361 10()2.462()323158 3003352()622762 3()()4.3919621761 SOOTEible 5Materi

26、al constants for temper T4ParameterTemper T4h = 1.9 mmh = 2.5 mmh = 33 mmh = 4.4 mm(MPa)77 775.6363.0365.77Qi (MP&)10.646.94124.63J8Qi (MPa)139.5139.29.62128.0Cl3887320714.813135c13.7413.77368914.171.01.()1.01.0TEible 6Material constants for temper T6ParameterTemper T6ft = 1.9 mmh = 2.5 mmh = 3.4 mm

27、h = 4.4 mmn0 (MPa)123.0153.8139.748.6Qa ( MPei)76.0567.5566.4346.61Q2 (MPa)58.1249.115L5449.58Cl433715.7643933135c17.29274418.5621.6().()1.()LO1.()International Journal of Impact Engineering 28 (2003) 377 - 390Plate perforation by eroding rod projectiles$D.J. Gee*the Johnson - Cook 11 model.Tublc JJ

28、ohnson Cook consli Lull vc m ode I con jiLan ts-A (GPa)B (GPa)CrM (eV)ProjectileJ.?500.06JJ0.J4S5Plait0.79220.5095C.0J40.26J.0?0.J545International Journal of Impact Engineering () -Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles experimental studyTore BArvika,b,*, Ari

29、ld H. Clausena, Odd Sture Hopperstada, Magnus Langsethfracture model of Johnson and Cook 30,31,Table JMalcria.ll consLanLs. for a 25 mm Lhick AA5Q&3H1 16 plate in the rolling direction of the material)E GPaVP曲向A |MPtiBMPaA. |L1C也702700J 675960.551J().001O.fi59JJ IJ 顿Kn*|K 玲IK孔IKm6血n9J0(.).92.? x89?2

30、9?0.026 J0.26?-03490.J47J6.fiSee Clausen ei al. 8 and Biirvik et aL |33 for details and notation.International Journal of Impact Engineering 28 (2003) 1017 -1035The adaptive and erosive numerical modelling of confined boron carbide subjected to large-scale dynamic loadings with element conversion to

31、 undeformable meshless particlesM.G Cottrella,*, J. Yub, D.R.J. OwenaTable 1Matcriall paramcLcrsi. for boron carbide wwzd in.Johnson HnTinnqLLbi* mcxicl |6ParameterNotationValue usedInitial den血y (kgnV25JOEkislic bulk modulus (MPa)K - K2.WC00CoefL For 2nd degree term in EOS (XfPa)Al-59?,000CoefL For

32、 3rd degree Lenn in EOS (MPa)K?2,fi00,000Elas.tie shear modul!iis (MPa)C197,000HugonioL elastic limit (MPa)HEL19,000Intact reng th coctficicniA0.927IniacL strength cxponcni.V0.67Strain rale cocfUicicnl (s 1)C0.005F rac lured st reng th coc fHeie n tB0.70Fractured strength exponentM0.K5Normalised max

33、Lniu.m fractured jitrengthf”iCM 且0.20Norrnial!iM：d maximum ini act st reng th。皿直UnlimitedDamage cocflicicnLZ)J0.00 JDamage exponentZ)20.50Bulk ing factorJ .00Maximum tcnxilc strength (MPa)项Tublc 2Malcrial parameters (or inngslcn alloy and jjtecl used in Johnson Cooks model J 2 and the Mie Griincistn

34、 equation ofataifi 】3ParameterNotationTu.ngs.tcn 2Steel |HDensity (kgm 3)PnJ7,(t00Tfi.OElas.tie bulk mcxluliLis (MPa)K286,000J 59,000Elasllic bulk wave vc loci Uy (ms-)如耳一Slope in Ls versus. Up diagramJ. 2?7Grunciscn cocfticicntrJ.SlElastic shear moduliis (MPa)GJ 60,000踞。Static yield Dim讯(MPii)AJ 50

35、6792Strain hardening modulins. (MPa)BJ77510Strain hardening exponentfl0.J20.26Strain rate coctficicnlc0.0J60.0J4Thermal xoftcning exponentJ.00J.0?Initial reference Lcmpcraturc (K)J.00Specific heat capacity (J kg-1 K-1)GJ?4477Melting tempera Lure (K)LnriLJ 7 2.179?Energy con vcrs-ion coefficien t (%)

36、f9090$Gee D J. Plate perforation by eroding rod projectiles. International Journal of Impact Engineering, 2003,(28)： 377-390.tungsten-alloy cylindrical rod projectiles. Steel plateTable JJohnson Cook consLitutivc model constanisA (GPa)B (GPa)Cz?Th 5ProjcElilcJ.?500.06JJ0.14R5Pllitc0.79 220.50950.014

37、0.261.03C.J545International Journal of Impact Engineering 27 (2002) 807 -835Behind-the-armor debris analysisG. Yossifon, A.L. Yarin*The projectile and target were modeled as isotropic elastic plastic materials. The von Mises tensile flow stress, Y; was expressed according to the Johnson-Cook model a

38、s:F = A + Bl + L In 有 l -，Table 2MiLei il itode!parameLersParameLersUniLsRtAWSAStirength ccnsLants for Y A | 厂 Is广|l - IAy：6b1460RMan1.26i. ：2c0?：il6/ItL.i3LJIThermal pnr)/心丫标Density “弱7.H317.13Specific healJ.kp.K47：171Jeference LemperaLbre 7 国K和I300M el i nji te ni perat Lre 丁 meJtKL723咿pir 做Bulk i

39、nodulus- K顷27HShear modulusG-I -I145Maximum Letuile strain to failure j：f44)%U炀Fracture toughnessMPa in口HO70Ihe tinaLeri 出 pro percies 命 r JiA ite La ken rrom |I7, mnd hose for are a ken from |H).“The stretijith nnxiel mtimtatits for 此iA correspond to 处邳 steel of 17： havinii static yield stress cf 7

40、2 MPii and hardness of 3i RC. The meajiLred JiA hardness 点 345 V (see Table li. or eqiiiiiler：ly 35 RC. In order to correct the yield scress accord in 侦 tc he dirTerence m he tiardness Mues we itgKe use cf Lhe rallbirig cotiversibn equalicm (19): BHN = 1.979fTetisile SLretigLh(f | 11.24.Internationa

41、l Journal of Impact Engineering 25, (2001) 703J714Tungsten long-rod penetration into con ned cylinders of boroncarbide at and above ordnance velocitiesL. Westerling*, P. Lundberg, B. LundbergFor boron carbide, JohnsonHolmquists constitutive model 16 was used with yield stress 歹=(1 D)a-(p,E)+where D3

42、0,1 is the damage parameter, _ the yield stress of the intact material (D0) and is the yield stress of the fully damaged material (D1). These yield stresses are functions of the hydrostatic pressure p and the strain rate _ . The constitutive parameters are dened in the appendix, and their values, al

43、so due to JohnsonHolmquist 16, are given in Table 1. For tungsten and steel use was made of MieGruK neisen and linear equations of state, respectively, andTable 1Pajatnetcrs for boron CLirbide used in Johtisoti-Hobiiqujsts modeParameterNotauaiiValues in 16Values used inAUTODYNDensity (kg m3)Po251025

44、10Bulk modulus (GPaK = K,233233CoelT. for 2tid degree term in EOS (G Pa|匕-593-59；CoelT. for Nrd degree ter tn in EOS i G Pll I&28002800Shear modulus (GPa)G197197Hugaiiiot elastic limit i HELl iGPll 1HELE.iEllcclive stress al HEL (GPajHl 115.44Pressure at HEL (GPa)Pimi8.71Volumetric strain at HELAh i

45、0.0408Intact strength coellicientA0.9270.9637Intact strength exponentV0.670.67Strain rate coellicientC0.0050.005Fracture strength coellicient80700.7311FRicture strength exponentM0.850.85Mdxitmnn fracture slrenylh0.202045Damage coellicient0.0010.001Damage exponent0.50.5Bulking factorE1.01.0Tensile st

46、rength (GPa)0.260.26JohnsonCooks constitutive model 17 with yield stress)(】-(法J)where _ is plastic strain,is plastic strain rate, 1 is temperature, and A, B, C, m, n, 1_and 1_ are parameters. Values of the parameters were obtained from the material library in AUTODYN and are given in Table 2. These

47、values can also be found in 17,18. The density of tungsten, however, was obtained from the supplier.Table 2PiiRitnetcjs for tungsten and steelPiiRitnetejblDtillLDnTungstenSteelDensity (ky.m H*17600Bulk modulus (GPalK159Bulk sound speed ijn/s)4D2Slope in I vcjsiis I. p didyjajns1.237Griincjscn coelli

48、cientr1.54Shear modulusG160S1.8Stalic yield jmit (GPa)A1.5060.72Strain hardctiiny Jiiodulus (GPajBD.l 770.51Sin hardctiiny exponcnlnD.120.26Strain rate coeRicientcMl 60.014PldSlic stfdiji rate thjeshold i 1/s)Bpii1.01.0TlierniLil softejiin exponentm1.01.瞠Reference letnpcjatiuc iK)T3iXiSpecilic heat

49、Kl134477Mcltiny tempcfLilure (Kl1723E韩永要，赵国志,李向东，方 清.长管体垂直侵彻半无限均质靶板的数值模拟.弹道 学报，第16卷第2期2004年6月33-36计算对象为93钨合金管侵彻半无限厚某装甲钢靶板，材料的计算参数如表1,其中管 体参数来自于文献3 ,4 .由于所研究问题具有对称性,本文中管体和靶板均取原型 的1/2.管体长度为70 mm，外径分别为10 mm和12 mm 2组，内外径比从0.1到0.9之 间变化;靶板为55 mm X55 mm X 110 mm的长方体.计算过程中忽略热能损失.表1材料参数材料E.- GPa.J/MPa5/MPaCm

50、丁 y K93 W17. 53500. 23415061770. 0080. 121.01450294603钢7. S52100. 2207921800. 0160. 121.01520294Cottrel M G. The adaptive and erosive numerical modelling of confined boron carbide subjected to large scale dynamic loadings with element conversion to undeformable meshes particlesJ . International Engi

51、neering of Impact , 2003 ,28 :1017 - 1035Charles E A. On the hydrodynamic approximation for long rod penetrationJ . International Engineering of Impact , 1999 ,22 :23 - 43欧阳春，赵国志，杜中华,李文彬.弹丸垂直侵彻钢筋混凝土介质的工程解析模型.第24 卷，第3期爆炸与冲击,2004弹、靶参数取自文献3 ，其中弹丸口径2 a = 76. 2mm，弹头弧形半径S = 114. 3mm , 弹质量m =519kg。混凝土材料参数:

52、E = 31. 5GPa ,p = 2240kg/ m3，单轴无约束抗压 强度/ = 35MPa ,抗剪强度Y =95MPa ,锁变压缩体积应变 3= 0. 04。钢筋材料参数:Es =200GPa ,p s = 7850kg/ m3，屈服应力O s =500MPa。张迪3 1,林逸汉1,曹菊珍2混凝土靶体计及压实效应的球腔动态膨胀模型和 侵彻计算.计算力学学报第21卷第4期2004年8月对混凝土靶体Ho lmqu ist T J三段模型和Go ld V M密实模型的数值计算使用了以 下数据：E = 35. 7 GPa, M= 0. 2, Y = 0. 048 GPaK= 0. 63,拉伸强度/ = 0.