材料模型与状态方程

John-Cook材料本构模型

式中，£P一一等效塑性应变:

7P

£----&)=1.0的无量纲塑性比，S=二一;

T—T

7’——相对温度，T*=-------3—

T-T

'meltxroom

A----屈服应力，Pa；

B一一应变硬化系数，Pa：

n一一应变硬化指数；

C一一应变率相关系数：

m一一温度相关系数。

表达式的第一项(A+8£”)表示对干©'=1.0和7"=()(等温状态)时的应力与应变的函数关系；表达式的第二项

(1+Cln/)和第三项(1-Tw)分别表示应变利率温度的影响。

表Johnson和Cook给出的值

硬度密度比热熔温AB

材料nCm

(洛氏)g/cn?J/kg.KKMPaMPa

高导无氧铜F-308.93831356902920.310.0251.09

药筒黄铜F-678.5238511891125050.420.0091.68

锲200F-798.944617261636480.330.0061.44

工业纯铁F-727.8945218111753800.320.0600.55

卡彭特电工钢F-837.8945218112903390.400.0550.55

1006钢F-947.8945218113502750.360.0221.00

2024-T35I铝B-752.778757752654260.340.0151.00

7039铝B-762.778758773373430.410.0101.00

4340钢C-307.8347717937925100.260.0141.03

S-7钢C-507.75477176315394770.180.0121.00

钓合金

C-4717.0134172315061700.120.0161.00

0.07NiO.OSFe

Du-75TiC-4518.64471473107911200.250.0071.00

群永要《弹道学报》第16卷第2期

PE/GPaA/MPaB/MPaCnmTm"KTrvom/K

93W17.63500.28415061770.0080.121.01450294

603钢7.852100.2207921800.0160.121.01520294

(断裂破坏时的)应变

其中，Di、D2、6、DKDs输入参数，o*是压力与有效应力之比，a=p/o-e(f.o

兰破坏参数D=y——到达।时，发生破坏。

1tHirofumiIyama,KouseiTakahashi.TakeshiHinata.ShigeruItoh.NumericalSimulationofA1uminum.AlloyForming

UsingUnderwaterShockWave.8"InternationalLS-DYNAUsersConference

PE/GPaA/MPaB/MPaCnmTmEKTnH.,n/K

A70393373430.010.411.00

2Steinherg-Guinan材料本构模型

定义材料熔化前的剪切模量

p-----压力，V------相对体枳，Ec------冷压缩能，Em------熔化能

?=巫，R——气体常数，A——原子量

A

屉服强度

如果Em超过Ei,

y；---初始塑性应变，

当〃超过设置〃等于巴“。

材料熔化之后，by和G设置为初始值的一半.

$OFHC为高导无氧铜，聚能装药药型罩常用材料*MAT_STEINBERG$MIDROGOSIGOBETANGAMASIGM28.930.477

0.120E-0236.00.4500.000.640E-02$BBPHFATMOGAMOSA2.832.830.377E-030.100E-0263.50.179E+042.02

1.50$PCSPALLRPFLAGMMNMMXECOECI-9.003.000.000.000.000.000.000.00$EC2EC3EC4EC5EC6EC7EC8

EC90.000.000.000.000.000.000.000.00*EOS_GRUNEISEN$EOSIDCSIS2S3GAMAOAE020.3941.490.000.00

2.020.4700.00$V01.00

M.Katayama,S.Kibe,T.Yamamoto.NumericalandExperimentalStudyontheShapedChargeforSpaceDebris

Assessment.ActaAstronauttcaVol.48,No.5-12,pp.363-372,2001

/GPa/GPa/GPa/MPa.K-1Cniax

Aluminum27.10.040.484000.271.767-16.692.608e-31.0

Copper47.70.120.64360.451.35-17.983.396c-31.0

W.H.Lee.J.W.Painter.Materialvoid-openingcomputationusingparticlemethod.InternationalJournalofImpac:Engineering

22(1999)1-22

二阶状态方程

翦切模量G与流体应力Y间的本构关系

痣(1+网”Lx，&(x)=Eo(x)+3R"),

(1一x)

。二20。-。)-!，E^=[P{x}dx-3R'TAD,喂蚪

D\1-A)

系数tungstenaluminumsteelTungsten-copperalloy

二Ai21.674191.18674664.95783232.4562457

阶A214.933380.7629953.68837264.6163216

状Bo10.1958273.44476547.47273614.3432909

态Bi12.2632341.545057311.5191480.76214541

方

B29.30515150.964296325.52511386.4410793

程Co0.333884370.433816560.394926130.31988993

Cl0.482488610.548734620.528834120.46744784

Do7.01.53.62.2

po19.172.8067.918.983

Go1.60.2760.4770.844

Ya0.0220.00290.00120.0012

B7.7125.03616000

n0.130.10.450.26

Ymax0.040.00680.00640.0168

b1.3757.9713.14465414.739

h-0.0001375-0.0067159-0.000377358-0.0008056

本构关系

q1.01.01.01.0

f0.0010.0()10.0010.0()1

g0.0010.0010.0010.001

R'0.0000086710.0000083260.00011640.00000663

Tmc45201220.017901710

y（）-a0.270.490.520.92

a1.41.71.51.5

3Mie-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曲线的裁距，体积声速

Si、S2、S3是u、-Up曲线斜率的系数，九是Gruneisen常数，//=//＞（）—1»a是，（）的一阶体积修正。

C出处

SiS2S3YoaE

cm/us

铜0.3941.492.020.47

0.16471.921-0.0960.00.352.895e-6

0.1651.920.1(3)AustraIia

0.1491.791.652.895e-6⑴日本

水0.1482.56-1.9860.22680.502.895e-6

0.14891.791.65（4）日本

0.1481.791.65（5）日本

0.14841.790.113.0

铝0.3991.241.54

铁0.45691.492.170.46

4340钢0.45781.331.670.43

Steel(SS400)0.4581.491.93(5)

Aluminum0.53861.3391.97⑵日本

POLYRUBBER8.54000E-021.865OOE+OO

(l)HirofumiIyama,KouseiTakahashi,TakeshiHinata,ShigeruItoh.NumericalSimulationofA1uminumAlloyForming

UsingUnderwaterShockWave.8"'[nternationalLS-DYNAUsersConference

(2)M.Katayama,S.Kibe,T.Yamamoto.NumericalandExperimentalStudyontheShapedChargeforSpaceDebris

Assessment.ActaAstronauttcaVol.48,No.5-12,pp.363-372,2001

(3)JingPingLu.HelenDorsett.DavidL.Kennedy.SimulationofAquariumTestsforPBXW-115(AUST)

(4)S.Itoh,H.Hamashima.DeterminationofJWLParametersfromUnderwaterExplosionTest

15)KatsuhikoTakahashi,KenjiMurata,AkioTorii.YukioKato.EnhancpmentofUnderwaterShockWavphyMptal

Confinement

4多线性多项式状态方程

压力由下式定义

其中，〃二夕/夕0-1,如果4<0,那么设置。2〃2=0,C(y=0o

当设置C()=C[=G=。3=。6=0，G=。5=7-1时，就可以用于符合/律状态方程的气体，其中/为

比热系数。

coClC2C3C4C5C6E0VO

空气0.00.00.00.00.40.40.02.5E-6

5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),通过此材料来防止计算应力、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，炸药的材料模型一股都选用材料类型8,即MAT」nGH_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。

7JWL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

爆速ABE爆压文

PRiR2GJ

信J/ms'1/GPa/Gpa/GJm-3/Gpa章

SEP炸药1.313652.314301.100.2815.9(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)

pbx950l1.8488008.54450.204934.61.350.250.05543(6)

PE4

1.597900774.0548.6774.8371.0740.849.38124.0(7)

BOOSTER

SEP1.3169703723.484.591.060.29(8)

(1)HirofumiIyama,KousciTakahashi.TakeshiHinata,ShigeruItoh.NumericalSimulationofAluminumAlloyForming

UsingUnderwaterShockWave.8"'InternationalLS-DYNAUsersConference

(2)M.Katayama,S.Kibe,T.Yamamoto.NumericalandExperimentalStudyontheShapedChargeforSpaceDebris

Assessment.ActaAstronauttcaVol.48,No.5-12,pp.363-372,2001

(3)M.Katayama,S.Kibe.NumericalStudyoftheConicalShapedChargeforSpaceDebrisImpact.International

JournalofImpactEngineering26(2001)357-358

(4)MarkZ.Vulitsky.ZviH.Kami.ShipStructuresSubjecttoHighExplosiveDetonation.7InternaticnalLS-DYNA

UsersConference

⑸金乾坤等.3DNumericalSimulationsofPenetrationofOil-UellPerforatorintoConcreteTargets.7"

InternationalLS-DYNAUsersConference

(6)W.H.Lee,J.W.Painter.Materialvoid-openingcomputationusingparticlemethod.InternationalJournalofImpactEngineering

22(1999)1-22

(7)JingPingLu.HelenDorsett.DavidL.Kennedy.SimulationofAquariumTestsforPBXW-l15(Al-ST)

(8)S.Itoh,H.Hamashima.DeterminationofJW1.ParametersfromUnderwaterExplosionTest

表JWL状态方程参数

C-J参数JWL状态方程参数

密度PDEoABC

炸药33

g/cmGPamm/t>sGPamVmGPaGPaGPa%R2(O

分子

黑

778377—o&4330

.50.

HMX421O16.1.08o.

Z4.50225844025

HNS0.56.•o.

乃

2610歌368.766.7u.638.03532

60.5435J5•o.

514700468.873u494..580o.35

(x)2I.JS3S•

455721700o.2

77湍6n6,608

701419252•

PETN7302Z.00&6235.J236.29n525.,20o.28

56..4.•os.

63035611Q93oJ994,02025

107.4.

3&.1&O2.6458S.31267744,I50•2

2520L.0o4.95o.8

特屈儿LZ2.7983731.645o.3

2000.283n0

2.727.7。

TNT2.706

2

TNT基2.731I

3

253.092522z678o821

鹿4.

2.834.910.34

B炸药a39Z.6049924o754.

2.783S.035

27518131434.2

Cyclotol77/23.0。2.780.2

&.54..51

H-634.210.307461338167S0.38

4..4.

9.6湍090.35

Ociol78/2225.554973o334.

253OL..3337.6,050.33

Pentolite3.588996032

压装炸药2

1.650

A-3oz3

,60130..308.907961110.6508

9.00

其它典型炸药14

J8.20

910.20z838625

C-4288.70.o.

9.50o.

注装PBX8.09.1o.

86.004.452

2。7.4570,38

-6.00.Q0o.

PBXN-1066Z.7&.134

2。01o.2

-50.5.00

PBXN-109275.6395.201o.4

8.工2112

PBXN-11061.J35.003.4

2。513..2

PBXN-114z

1。03.3718.5.3

PBXN-115.73.81932.6

6232

玉装PBX

3z55o362964.5538

84o.5.o.

LX-IO-13zo2o86887.2429638

80o.,841o.

LX-14-()

PBXN-511

a.B炸药的改良型，RDX/TNT/石蜡=64/36/1

b.见LX-10-1炸药的各值，它们是类似的混合炸药

JamesL.O'Daniel.TlieodorKrauthammer.KevinL.Koudela.AnUNDEXresponsevalidationmethodology.International

JournalofImpactEngineering27(2002)919-937

Effectiveorthotropiccompositematerialproperties

PExxEyyEzz[ixynyz^xzGxyGyzGxz

g/cm3GPaGPaGPaGPaGPaGPa

TOP_L1.9420.3920.3910.740.285850.24183C.241837.9293.9033.903

ALL30_S1.9415.559.84510.130.423380.19622C.259566.1343.8433.843

M1D_L1.9420.5616.9010.670.348390.21859C.245338.1013.8843.922

S铝

*MAT_JOHNSON_COOK

22.770.276

3.37E-U33.43E-U3U.4100.1(JUfc-01l.(X)0.877E-HJ330().0.I00E-U5

0.875E-05-9.003.000.000.000.000.0()0.00

0.00

*EOS_GRUNEISEN

20.53281.3380.000.002.000.000.00

0.00

S金属-铜

*MAT_JOHNSON_COOK

18.960.4781.280.3400000.000000

0.900E-030.292E-020.3100.250E-011.090.I36E+04294.0.100E-05

0.383E-05-9.003.000.000.000.000.000.00

0.00

*EOS_GRUNEISEN

10.3941.490.(X)0.002.020.4700.00

0.00

$炸药

*MAT_HIGH_EXPLOSIVE_BURN

21.78700()10.83900000.34000000.00000000.00000000.00000000.0000(X)0

♦EOSJWL

25.8140(X)26.8010E-24.10000001.000(X)000.35000000.09000091.0000000

$空气

*MAT_NULL

31,2250E-30.0I7.456E-60.00.00.00.0

♦EOS.LINEAICPOLYNOMIAL

30.00.00.00.00.400.40.0

2.5E-61.0

3水

♦MAT_NULL

41.0-1.00E-4IE-60.00000000.00000000.00000000.0000000

♦EOS.GRUNEISEN

4.148401.7900000.0000000.00000000.1100003.0000300.0000000

1.0

sMATERIALDEFINITIONS

s$$s$$s$$s$$s$$s$$$$$$$$$$$$$$$$$$$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$$s$

s

*MAT_HIGH_EXPLOSIVE_BURN

21.7870(X)10.8390(X)00.3400(X)00.00000000.0(X)00000.00000()0O.()(XX)O()O

*EOS_JWL

25.81400026.801OE-24.10000001.00000000.35000000.09000031.0000000

*INITIAL_DETONATION

20.00000000.00000000.00000000.0000000

♦MAT_NULL

I1.00000000.00000000.00000000.00000000.0000000O.OOOOCXJO0.0000000

S水

*MAT_010

71.000E+000.2e-20.0O.UUOO.OOUh-OO2.00

*EOS_GRUNEISEN

S水

$EOSIDCSIS2S3GAMAOA

60.14801.7900.00001.650.02.895e-6

SVO

1.()

♦EOS_GRUNEISEN

S水

sEOSIDCSIS2S3GAMAOAEO

150.16471.921-0.0960.00000.350.02.895e-6

SVO

1.0

*EOS_GRUNEISEN

3水

$EOSIDCSIS2S3GAMAOAEO

0.14802.56-1.9860.22680.500.02.895e-6

SVO

1.0

S

*MATJOHNSON.CWK

S铝合金

917.61.363.500.2860.000000

1.806E-020.177E-020.1201.600E-021.001.723E+03294.0.100E-05

0J34E-O5-9.O2.000.002.000.000.000.00

0.00

S

*EOS_GRUNEISEN

S铝合金

90.3991.240.000.001.540.000.00

0.00

s

*MAT_PLASTIC_KINEMATIC

$树脂

81.19O.78OE-O10.0000000.800E-030.001.00

0.000.002.00

S

*MAT_PLAST1C_KINEMAT1C

$铝合金

Smidprsigycianbcm

61.862E+011.170E+000.22I.790E-02i.O

srcsrpfs

0.8

S

$空气

♦MATNULL

41.280E-030.000E+00O.OOOE+OOO.OOOE+OO0.000E+00

*EOS_LINEAR_POLYNOM1AL

4O.OOOE-OO1.0O0E-05O.OOOE+OOO.OOOE+OO0.4000.4000.000E+00

O.OOOE+OOO.OOOE+OO

$

S

♦MATJOHNSONCOOK

57.830000.77

7.92OE-O35.1OE-O30.2600.140E-011.030.1793E+042940.100E-05

0.477E-05-9.00E+03.000.00.800.000.000.00

0.0()

*EOS_GRUNEISEN

S铁

50.45691.4900.000.(X)2.170.460.0()

1.00

S金属-铜

*MAT_JOHNSON_COOK

38.960.4781.280.3400000.000000

0.900E-030.292E-020.3100.250E-011.090.I36E+04294.0.100E-05

0.383E-05-9.003.000.000.000.000.000.00

0.00

S金属-铜

*EOS_GRUNEISEN

30.3941.490.000.002.020.4700.00

0.00

$DefineSteel4340

*MAT_JOF^SON_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,

4.400E-06,2.000E-02,2.000E+00,0.000E+00,0.80E+00,2.100E+00,-0.05E+00,

0.610E+00

*EOS_GRUNEISEN

1,4.578E-01,1.330E+00,0.OOOE+OO,0.000E+00,1.670E+00,0.430E+00,0.000E+00

l.UOUE+UU

$SIunit:cm-g-microsecond

Sunitconversionfactor

S1psi=6895pa,1dyn=le-5n,1bar=le5pa,1g/cm**3=0.0361lb/in**3,1lb=0.454kg

本参数援引UniversityofNevadaLasVegas»

*MAT_JOHNSON_COOK

2,8.33,0.51,1.38,0.35

8.963E42.9163E-3,0.31.0.025J.09.1220,293.1E-5

4.4E-6,2.4E-3,2.0,0,-0.54,4.89,-3.03,0.014

1.12

*EOS_GRUNEISEN

2,0.394,1.489,0,0,2,02,0.47

1.0

*MAT_JOHNSON_COOK

ROGEPR

MID