材料模型与状态方程【DOC文档】

1 John-Cook材料本构模型式中，等效塑性应变；s-1的无量纲塑性比，；相对温度，A屈服应力，Pa；B应变硬化系数，Pa；n应变硬化指数；C应变率相关系数；m温度相关系数。表达式的第一项表示对于和（等温状态）时的应力与应变的函数关系；表达式的第二项和第三项分别表示应变和率温度的影响。表 Johnson和Cook给出的值材料硬度(洛氏)密度g/cm3比热J/kg.K熔温KAMPaBMPanCm高导无氧铜F-308.93831356902920.310.0251.09药筒黄铜F-678.5238511891125050.420.0091.68镍200F-798.944617261636480.330.0061.44工业纯铁F-727.8945218111753800.320.0600.55卡彭特电工钢F-837.8945218112903390.400.0550.551006钢F-947.8945218113502750.360.0221.002024-T351铝B-752.778757752654260.340.0151.007039铝B-762.778758773373430.410.0101.004340钢C-307.8347717937925100.260.0141.03S-7钢C-507.75477176315394770.180.0121.00钨合金0.07Ni 0.03FeC-4717.0134172315061700.120.0161.00Du-75TiC-4518.64471473107911200.250.0071.00韩永要弹道学报第16卷第2期rE/GPamA/MPaB/MPaCnmTmelt/KTroom/K93W17.63500.28415061770.0080.121.01450294603钢7.852100.2207921800.0160.121.01520294（断裂破坏时的）应变其中，D1、D2、D3、D4、D5输入参数，s*是压力与有效应力之比，。当破坏参数达到1时，发生破坏。* Hirofumi Iyama, Kousei Takahashi, Takeshi Hinata, Shigeru ItohNumerical Simulation of Aluminum Alloy Forming Using Underwater Shock Wave8th International LS-DYNA Users ConferencerE/GPamA/MPaB/MPaCnmTmelt/KTroom/KA70393373430.010.411.002 Steinberg-Guinan材料本构模型定义材料熔化前的剪切模量p压力，V相对体积，Ec冷压缩能，Em熔化能，R气体常数，A原子量屈服强度如果Em超过Ei，初始塑性应变，当超过，设置等于。材料熔化之后，和G设置为初始值的一半。$ OFHC为高导无氧铜，聚能装药药型罩常用材料*MAT_STEINBERG$ MID R0 G0 SIGO BETA N GAMA SIGM2 8.93 0.477 0.120E-02 36.0 0.450 0.00 0.640E-02$ B BP H F A TMO GAMO SA2.83 2.83 0.377E-03 0.100E-02 63.5 0.179E+04 2.02 1.50$ PC SPALL RP FLAG MMN MMX ECO EC1-9.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00$ EC2 EC3 EC4 EC5 EC6 EC7 EC8 EC90.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN$ EOSID C S1 S2 S3 GAMAO A E02 0.394 1.49 0.00 0.00 2.02 0.470 0.00 $ V01.00M.Katayama, S.Kibe, T.YamamotoNumerical and Experimental Study on the Shaped Charge for Space Debris AssessmentActa Astronauttca Vol.48,No.5-12,pp.363-372,2001/GPa/GPa/GPa/MPa.K-1emaxAluminum27.10.040.484000.271.767-16.692.608e-31.0Copper47.70.120.64360.451.35-17.983.396e-31.0W.H.Lee, J.W.PainterMaterial void-opening computation using particle methodInternational Journal of Impact Engineering 22(1999)1-22二阶状态方程剪切模量G与流体应力Y间的本构关系，系数tungstenaluminumsteelTungsten-copper alloy二阶状态方程A121.674191.18674664.95783232.4562457A214.933380.7629953.68837264.6163216B010.1958273.44476547.47273614.3432909B112.2632341.545057311.5191480.76214541B29.30515150.964296325.52511386.4410793C00.333884370.433816560.394926130.31988993C10.482488610.548734620.528834120.46744784D07.01.53.62.2r019.172.8067.918.983本构关系G01.60.2760.4770.844Ya0.0220.00290.00120.0012b7.7125.03616000n0.130.10.450.26Ymax0.040.00680.00640.0168b1.3757.9713.14465414.739h-0.0001375-0.0067159-0.000377358-0.0008056q1.01.01.01.0f0.0010.0010.0010.001g0.0010.0010.0010.001R0.0000086710.0000083260.00011640.00000663Tme45201220.017901710g0-a0.270.490.520.92a1.41.71.51.53 Mie-Gruneisen状态方程定义压缩材料的压力为定义膨胀材料的压力为其中：C为us-up曲线的截距，体积声速S1、S2、S3是us-up曲线斜率的系数，是Gruneisen 常数，a是的一阶体积修正。Ccm/usS1S2S3g0aE出处铜0.3941.492.020.47水0.16471.921-0.0960.00.352.895e-60.1651.920.1(3)Australia0.1491.791.652.895e-6(1)日本0.1482.56-1.9860.22680.502.895e-60.14891.791.65(4) 日本0.1481.791.65(5) 日本0.14841.790.113.0钨0.3991.241.54铁0.45691.492.170.464340钢0.45781.331.670.43Steel(SS400)0.4581.491.93(5)Aluminum0.53861.3391.97(2)日本POLYRUBBER 8.54000E-021.86500E+00(1)Hirofumi Iyama, Kousei Takahashi, Takeshi Hinata, Shigeru ItohNumerical Simulation of Aluminum Alloy Forming Using Underwater Shock Wave8th International LS-DYNA Users Conference(2)M. Katayama, S. Kibe, T. YamamotoNumerical and Experimental Study on the Shaped Charge for Space Debris AssessmentActa Astronauttca Vol.48,No.5-12,pp.363-372,2001(3)JingPing Lu, Helen Dorsett, David L. KennedySimulation of Aquarium Tests for PBXW-115(AUST)(4)S. Itoh, H. HamashimaDetermination of JWL Parameters from Underwater Explosion Test(5)Katsuhiko Takahashi, Kenji Murata, Akio Torii, Yukio KatoEnhancement of Underwater Shock Wave by Metal Confinement4 多线性多项式状态方程压力由下式定义其中，如果，则设置，。当设置，时，就可以用于符合律状态方程的气体，其中为比热系数。C0C1C2C3C4C5C6E0V0空气0.00.00.00.00.40.40.02.5E-65 空白材料在仿真计算中，水介质的材料模型可以选用空白材料（NULL），通过此材料来避免计算应力、应变。在LS-DYNA中为材料模型9。空白材料模型必须使用状态方程。6 炸药的材料模型在LS-DYNA中，炸药的材料模型一般都选用材料类型8，即MAT_HIGH_EXPLOSIVE_BURN。需要定义的参数有，密度、爆速与C-J爆轰压力等。此种材料类型必须与状态方程一块使用。7 JWL状态方程炸药爆轰产物的状态方程常采用JWL方程。此状态方程通常用于描述高能炸药及爆轰产物，其形式为r/g.cm-3爆速/ms-1A/GPaB/GpaR1R2vE/GJm-3爆压/Gpa文章SEP炸药1.313652.314.301.100.2815.9(1)TNT1.636930373.83.7474.150.90.359.6021(2)371.23.234.150.950.30(3)TNT371.23.234.150.950.30(4)1.658300611.310.654.41.20.328.9(5)pbx95011.8488008.54450.204934.61.350.250.05543(6)PE4BOOSTER1.597900774.0548.6774.8371.0740.849.38124.0(7)SEP1.3169703723.484.591.060.29(8)(1) Hirofumi Iyama, Kousei Takahashi, Takeshi Hinata, Shigeru ItohNumerical Simulation of Aluminum Alloy Forming Using Underwater Shock Wave8th International LS-DYNA Users Conference(2)M.Katayama, S.Kibe, T.YamamotoNumerical and Experimental Study on the Shaped Charge for Space Debris AssessmentActa Astronauttca Vol.48,No.5-12,pp.363-372,2001(3)M.Katayama, S.KibeNumerical Study of the Conical Shaped Charge for Space Debris ImpactInternational Journal of Impact Engineering 26(2001) 357-368(4)Mark Z. Vulitsky, Zvi H. KarniShip Structures Subject to High Explosive Detonation7th International LS-DYNA Users Conference(5)金乾坤等3D Numerical Simulations of Penetration of Oil-Well Perforator into Concrete Targets7th International LS-DYNA Users Conference(6)W.H.Lee, J.W.PainterMaterial void-opening computation using particle methodInternational Journal of Impact Engineering 22(1999)1-22(7)JingPing Lu, Helen Dorsett, David L.KennedySimulation of Aquarium Tests for PBXW-115(AUST)(8)S. Itoh, H. HamashimaDetermination of JWL Parameters from Underwater Explosion Test表 JWL状态方程参数炸药C-J参数JWL状态方程参数密度g/cm3GPamm/sGPam3/m3GPaGPaGPa分子HMXHNSPETN特屈儿TNTTNT基B炸药aCyclotol 77/23H-6Octol 78/22Pentolite压装炸药A-3其它典型炸药C-4注装PBXPBXN-106PBXN-109 PBXN-110PBXN-114PBXN-115压装PBXLX-10-1LX-14-0PBXN-5b1.8911.0001.4001.6501.2601.5001.7701.7301.6301.7171.7541.7601.8211.7001.6501.6501.6011.6341.6601.6721.7111.7821.8651.83542.07.514.421.514.022.033.528.521.029.532.024.034.225.523.530.028.026.022.027.526.012.037.537.09.115.106.347.036.547.458.307.916.937.988.257.478.487.537.368.308.197.847.608.338.155.708.848.8010.504.106.007.457.198.5610.108.207.008.509.2010.309.608.108.008.909.008.2010.208.709.506.0010.5010.202.7402.4682.8812.8042.8312.7882.642.7982.7272.7062.7313.0922.832.782.782.792.8383.23.3713.819.8682.841778.3162.7366.5463.1573.1625.3617.0586.8371.2524.2603.4758.1748.6540.9531.8611.3609.8570.21341950.41122813.0880.7826.17.07110.826.758.87320.1623.2916.9310.673.2317.6789.9248.51313.389.3738.93310.6512.956.1332.710.988.648-13518.3617.240.6430.6581.1631.3491.2671.1520.6990.7741.0451.0821.0751.1431.1671.0330.9761.081.0431.3251.3341.81615.83.4241.2961.2964.205.404.804.556.005.254.404.404.154.24.34.94.54.54.64.44.54.456.005.005.205.004.625.551.001.801.401.351.801.601.201.200.951.11.11.11.21.11.051.21.41.02.01.41.23.51.321.320.300.250.320.350.280.280.250.280.300.340.350.20.380.350.330320.250.380.20.40.30.60.380.38a. B炸药的改进型，RDX/TNT/石蜡 = 64/36/1b. 见LX-10-1炸药的各值，它们是类似的混合炸药James L. ODaniel, Theodor Krauthammer, Kevin L. KoudelaAn UNDEX response validation methodologyInternational Journal of Impact Engineering 27(2002) 919-937Effective orthotropic composite material propertiesrExxEyyEzzmxymyzmxzGxyGyzGxzg/cm3GPaGPaGPaGPaGPaGPaTOP_L1.9420.3920.3910.740.285850.241830.241837.9293.9033.903ALL30_S1.9415.559.84510.130.423380.196220.259566.1343.8433.843MID_L1.9420.5616.9010.670.348390.218590.245338.1013.8843.922$铝 *MAT_JOHNSON_COOK 2 2.77 0.276 3.37E-03 3.43E-03 0.410 0.100E-01 1.00 0.877E+03 300. 0.100E-05 0.875E-05 -9.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN 2 0.5328 1.338 0.00 0.00 2.00 0.00 0.00 0.00 $金属-铜*MAT_JOHNSON_COOK 1 8.96 0.478 1.28 0.340000 0.000000 0.900E-03 0.292E-02 0.310 0.250E-01 1.09 0.136E+04 294. 0.100E-05 0.383E-05 -9.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN 1 0.394 1.49 0.00 0.00 2.02 0.470 0.00 0.00 $炸药*MAT_HIGH_EXPLOSIVE_BURN 2 1.7870001 0.8390000 0.3400000 0.0000000 0.0000000 0.0000000 0.0000000*EOS_JWL 2 5.8140002 6.8010E-2 4.1000000 1.0000000 0.3500000 0.0900000 1.0000000$空气*MAT_NULL 3 1.2250E-3 0.0 17.456E-6 0.0 0.0 0.0 0.0*EOS_LINEAR_POLYNOMIAL 3 0.0 0.0 0.0 0.0 0.40 0.4 0.0 2.5E-6 1.0$水*MAT_NULL 4 1.0 -1.00E-4 1E-6 0.0000000 0.0000000 0.0000000 0.0000000*EOS_GRUNEISEN 4 .14840 1.7900000 .0000000 .0000000 0.110000 3.0000000 .0000000 1.0$ MATERIAL DEFINITIONS $*MAT_HIGH_EXPLOSIVE_BURN 2 1.7870001 0.8390000 0.3400000 0.0000000 0.0000000 0.0000000 0.0000000*EOS_JWL 2 5.8140002 6.8010E-2 4.1000000 1.0000000 0.3500000 0.0900000 1.0000000*INITIAL_DETONATION 2 0.0000000 0.0000000 0.0000000 0.0000000*MAT_NULL 1 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000$水*MAT_010 7 1.000E+00 0.2e-2 0.0 0.000 0.000E-00 2.00 *EOS_GRUNEISEN$水$ EOSID C S1 S2 S3 GAMA0 A E0 6 0.1480 1.79 0 0.0000 1.65 0.0 2.895e-6$ V0 1.0*EOS_GRUNEISEN$水$ EOSID C S1 S2 S3 GAMA0 A E0 15 0.1647 1.921 -0.096 0.0000 0.35 0.0 2.895e-6$ V0 1.0*EOS_GRUNEISEN$水$ EOSID C S1 S2 S3 GAMA0 A E0 1 0.1480 2.56 -1.986 0.2268 0.50 0.0 2.895e-6$ V0 1.0$*MAT_JOHNSON_COOK$钨合金 9 17.6 1.36 3.50 0.286 0.000000 1.806E-02 0.177E-02 0.120 1.600E-02 1.00 1.723E+03 294. 0.100E-05 0.134E-05 -9.0 2.00 0.00 2.00 0.00 0.00 0.00 0.00 $*EOS_GRUNEISEN$钨合金 9 0.399 1.24 0.00 0.00 1.54 0.00 0.00 0.00 $*MAT_PLASTIC_KINEMATIC$树脂 8 1.19 0.780E-01 0.000000 0.800E-03 0.00 1.00 0.00 0.00 2.00 $*MAT_PLASTIC_KINEMATIC$钨合金$ mid ro e pr sigy etan beta 6 1.862E+01 1.170E+00 0.22 1.790E-02 1.0$ src srp fs 0.8$空气*MAT_NULL 4 1.280E-03 0.000E+00 0.000E+00 0.000E+00 0.000E+00*EOS_LINEAR_POLYNOMIAL 4 0.000E-00 1.000E-05 0.000E+00 0.000E+00 0.400 0.400 0.000E+00 0.000E+00 0.000E+00$ *MAT_JOHNSON_COOK $铁 5 7.83000 0.77 7.920E-03 5.10E-03 0.260 0.140E-01 1.03 0.1793E+04 294 0.100E-05 0.477E-05 -9.00E+0 3.00 0.0 0.80 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN $铁 5 0.4569 1.490 0.00 0.00 2.17 0.46 0.00 1.00 $金属-铜*MAT_JOHNSON_COOK 3 8.96 0.478 1.28 0.340000 0.000000 0.900E-03 0.292E-02 0.310 0.250E-01 1.09 0.136E+04 294. 0.100E-05 0.383E-05 -9.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 $金属-铜*EOS_GRUNEISEN 3 0.394 1.49 0.00 0.00 2.02 0.470 0.00 0.00 $Define Steel 4340 *MAT_JOHNSON_COOK 1, 7.8400E+00, 0.759E-00, 2.000E+00, 0.320E+00, 0.000E+00 0.793E-02, 0.510E-02, 2.60E-01, 1.400E-02, 1.030E+00, 1.793E+03, 2.930E+02, 1.000E-05 4.400E-06, 2.000E-02, 2.000E+00, 0.000E+00, 0.80E+00, 2.100E+00, -0.05E+00, 2.000E-03 0.610E+00 *EOS_GRUNEISEN 1, 4.578E-01, 1.330E+00, 0.000E+00, 0.000E+00, 1.670E+00, 0.430E+00, 0.000E+00 1.000E+00 $ SI unit :cm-g-microsecond $ unit conversion factor $ 1 psi=6895 pa, 1 dyn=1e-5 n,1 bar=1e5 pa,1 g/cm*3=0.0361 lb/in*3,1 lb=0.454kg 本参数援引University of Nevada Las Vegas。 *MAT_JOHNSON_COOK 2,8.33,0.51,1.38,0.358.963E-4, 2.9163E-3, 0.31,0.025,1.09,1220,293,1E-54.4E-6,2.4E-3,2.0,0,-0.54,4.89,-3.03,0.0141.12*EOS_GRUNEISEN 2,0.394,1.489,0,0,2.02,0.471.0*MAT_JOHNSON_COOKMIDRO密度G剪切模量E杨氏模量PR泊松系数DTFVP4340STEEL7.840.7592.00.32OFHC COPPER8.331.380.35ABNCMTM熔化温度TR室温EPSO应变率系数4340STEEL0.793E-20.51E-20.260.0141.0317932931E-5OFHC COPPER8.963E-42.9163E-30.310.0251.0912202931E-5CP比热PC失效应力SPALLITD1D2D3D44340STEEL4.4E-60.022.000.82.1-0.050.002OFHC COPPER4.4E-62.4E-3-0.544.89-3.030.014D54340STEEL0.61OFHC COPPER1.12*EOS_GRUNEISENE0SIDCS1S2S3GAMAOAE04340STEEL0.45781.331.670.43OFHC COPPER0.3941.4892.020.47V04340STEEL1.0OFHC COPPER1.0OFHC COPPER 参数援引ANSYS HELP Johnson_Cook Material Model单位：国际单位制OFHC COPPER ansys部分数据来自帮助文件Autodyna and ls-dyna 中john-cook模型参数的对应关系Reference temper -TRSpecific Heat-CPShear Modus-GYield stress-AHarding constant-BHarding exponent-NStrain Rate constant-CThermal softening exponent-MMelting Temperature-TMGRUNEISENParameter C1-CParameter S1-S1Gruneisen Coefficient-GAMAOMIDROGEPRDTFVP含义denistyShear modulusYoungs modulusPoissons Rate类型IFFFFFF缺省值nonenonenonenonenone0.00.0ANSYS8330138e0.35ABNCMTMTREPS0含义meltroom类型FFFFFFFF缺省值none0.00.00.0nonenonenonenoneANSYS89.83e6291.64e60.310.0251.0912003010CPPCSPALLITD1D2D3D4含义Specific heatFailure stress类型FFFFFFF缺省值none0.02.00.00.00.00.00.0ANSYS4400240e6-0.544.89-3.030.014D5含义类型F缺省值0.0ANSYS1.12*MAT_SOIL_AND_FOAM_FAILURE $土壤： 2 1.800E+00 6.400E-04 3.000E-01 3.410E-13 7.030E-07 0.3000000 -6.90E-08 0.000 -1.04e-01 -1.61E-01 -1.91E-01 -2.24E-01 -2.46E-01 -2.71E-01 -2.83E-01 -2.90E-01 -4.00E-01 0 2.000E-04 4.000E-04 6.000E-04 1.200E-03 2.000E-03 4.000E-03 6.000E-03 8.000E-03 4.100E-02 *MAT_HIGH_EXPLOSIVE_BURN $B炸药 1 1.7170000 0.7980000 0.2950000 0.0000000 0.0000000 0.0000000 0.0000000 *EOS_JWL $B炸药 1 5.2420000 7.67800-2 4.2000000 1.1000000 0.3400000 0.0850000 1.0000000 环氧树脂（用作隔板）*MAT_ELASTIC_PLASTIC_HYDRO$ MID R0 G SIGY EH PC FS 3 1.196 2.400E-02 5.000E-04 0.0 -9.00$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00$ EPS9 EPS10 EPS11 EPS12 EPS13 EPS14 EPS15 EPS16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00$ ES1 ES2 ES3 ES4 ES5 ES6 ES7 ES8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00$ ES9 ES10 ES11 ES12 ES13 ES14 ES15 ES16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00*EOS_GRUNEISEN$ EOSID C S1 S2 S3 GAMAO A E0 3 0.1933 3.490 -8.2 9.60 0.61 0.00 0.00 $ V0 1.00*MAT_JOHNSON_COOK $紫铜 2 8.96000 0.46 0.900E-03 2.920E-03 0.310 0.250E-01 1.090.1356E+04 210 0.100E-05 0.383E-05 -9.00E+00 3.00 0.0 3.00 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN $紫铜 2 0.394 1.489 0.00 0.00 2.02 0.47 0.00 1.00 *MAT_JOHNSON_COOK $铁 4 7.83000 0.77 7.920E-03 5.100E-03 0.260 0.140E-01 1.030.1793E+04 294 0.100E-05 0.477E-05 -9.00E+00 3.00 0.0 0.80 0.00 0.00 0.00 0.00 *EOS_GRUNEISEN $铁 4 0.4569 1.490 0.00 0.00 2.17 0.46 0.00 1.00 *MAT_HIGH_EXPLOSIVE_BURN $8701炸药 1 1.8450000 0.8835000 0.3370000 0.0000000 0.0000000 0.0000000 0.0000000 *EOS_JWL $8701炸药 1 8.5450000 0.20493 4.6000000 1.3500000 0.2500000 0.0850000 1.0000000 *MAT_JOHNSON_COOK$钨合金 1 17.6 1.36 3.50 0.284000 0.000000 0.151E-01 0.177E-02 0.120 0.800E-02 1.00 0.145E+04 294. 0.100E-05 0.134E-05 -9.00 3.00 0.00 2.00 0.00 0.00 0.00 0.00 $*EOS_GRUNEISEN$钨