最新黄永刚单晶塑性有限元umat子程序.docx

最新黄永刚单晶塑性有限元umat子程序.docx

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最新黄永刚单晶塑性有限元umat子程序

SUBROUTINEUMAT（stress,statev,ddsdde,sse,spd,scd,

1rpl,ddsddt,drplde,drpldt,

2stran,dstran,time,dtime,temp,dtemp,predef,dpred,cmname,

3ndi,nshr,ntens,nstatv,props,nprops,coords,drot,pnewdt,

4celent,dfgrd0,dfgrd1,noel,npt,layer,kspt,kstep,kinc）

cWRITE（6,*）'

cNOTE:

MODIFICATIONSTO*UMATFORABAQUSVERSION5.3（14APR'94）

c

c

（1）Thelistofvariablesabovedefiningthe*UMATsubroutine,

candthefirst（standard）blockofvariablesdimensionedbelow,

chavevariablenamesaddedcomparedtoearlierABAQUSversions.

c

c

（2）Thestatement:

include'aba_param.inc'mustbeaddedasbelow.

c

c（3）Asofversion5.3,ABAQUSfilesusedoubleprecisiononly.

cThefileaba_param.inchasaline"implicitreal*8"and,since

citisincludedinthemainsubroutine,itwilldefinethevariables

cthereasdoubleprecision.Butothersubroutinesstillneedthe

cdefinition"implicitreal*8"sincetheremaybevariablesthatare

cnotpassedtothemthroughthelistorcommonblock.

c

c（4）Thisiscurrentasofversion5.6ofABAQUS.

c

c（5）NoteaddedbyJ.W.Kysar（4November1997）.ThisUMAThasbeen

cmodifiedtokeeptrackofthecumulativeshearstrainineach

cindividualslipsystem.Thisinformationisneededtocorrectan

cerrorintheimplementationoftheBassaniandWuhardeninglaw.

cAnylineofcodewhichhasbeenaddedormodifiedispreceded

cimmediatelybyalinebeginningCFIXAandsucceededbyaline

cbeginningCFIXB.Anycommentlineaddedormodifiedwillbegin

cwithCFIX.

c

cThehardeninglawbyBassaniandWuwasimplementedincorrectly.

cThislawisafunctionofbothhyperbolicsecantsquaredandhyperbolic

ctangent.However,theargumentsofsechandtanharerelatedtothe*total*

csliponindividualslipsystems.Formerly,theUMATimplementedthis

chardeninglawbyusingthe*current*sliponeachslipsystem.Therein

claytheproblem.TheUMATdidnotrestrictthecurrentsliptobea

cpositivevalue.Sowhenaslipwithanegativesignwasencountered,the

ctermcontainingtanhledtoanegativehardeningrate（sincetanhisan

coddfunction）.

cTheUMAThasbeenfixedbyaddingstatevariablestokeeptrackofthe

c*total*sliponeachslipsystembyintegratinguptheabsolutevalue

cofslipratesforeachindividualslipsystem.These"solutiondependent

cvariables"areavailableforpostprocessing.Theonlyrequiredchange

cintheinputfileisthattheDEPVARcommandmustbechanged.

c

C-----UsesingleprecisiononCrayby

C

（1）deletingthestatement"IMPLICIT*8（A-H,O-Z）";

C

（2）changing"REAL*8FUNCTION"to"FUNCTION";

C（3）changingdoubleprecisionfunctionsDSIGNtoSIGN.

C

C-----Subroutines:

C

CROTATION--formingrotationmatrix,i.e.thedirection

Ccosinesofcubiccrystal[100],[010]and[001]

Cdirectionsinglobalsystemattheinitial

Cstate

C

CSLIPSYS--calculatingnumberofslipsystems,unit

Cvectorsinslipdirectionsandunitnormalsto

Cslipplanesinacubiccrystalattheinitial

Cstate

C

CGSLPINIT--calculatinginitialvalueofcurrentstrengths

Catinitialstate

C

CSTRAINRATE--basedoncurrentvaluesofresolvedshear

Cstressesandcurrentstrength,calculating

Cshearstrain-ratesinslipsystems

C

CLATENTHARDEN--formingself-andlatent-hardeningmatrix

C

CITERATION--generatingarraysfortheNewton-Rhapson

Citeration

C

CLUDCMP--LUdecomposition

C

CLUBKSB--linearequationsolverbasedonLU

Cdecompositionmethod（mustcallLUDCMPfirst）

C-----Functionsubprogram:

CF--shearstrain-ratesinslipsystems

C-----Variables:

C

CSTRESS--stresses（INPUT&OUTPUT）

CCauchystressesforfinitedeformation

CSTATEV--solutiondependentstatevariables（INPUT&OUTPUT）

CDDSDDE--Jacobianmatrix（OUTPUT）

C-----Variablespassedinforinformation:

C

CSTRAN--strains

Clogarithmicstrainforfinitedeformation

C（actually,integralofthesymmetricpartofvelocity

Cgradientwithrespecttotime）

CDSTRAN--incrementsofstrains

CCMNAME--namegiveninthe*MATERIALoption

CNDI--numberofdirectstresscomponents

CNSHR--numberofengineeringshearstresscomponents

CNTENS--NDI+NSHR

CNSTATV--numberofsolutiondependentstatevariables（as

Cdefinedinthe*DEPVARoption）

CPROPS--materialconstantsenteredinthe*USERMATERIAL

Coption

CNPROPS--numberofmaterialconstants

C

C-----Thissubroutineprovidestheplasticconstitutiverelationof

CsinglecrystalsforfiniteelementcodeABAQUS.Theplasticslip

CofsinglecrystalobeystheSchmidlaw.Theprogramgivesthe

Cchoiceofsmalldeformationtheoryandtheoryoffiniterotation

Candfinitestrain.

CThestrainincrementiscomposedofelasticpartandplastic

Cpart.Theelasticstrainincrementcorrespondstolattice

Cstretching,theplasticpartisthesumoverallslipsystemsof

Cplasticslip.Theshearstrainincrementforeachslipsystemis

Cassumedafunctionoftheratioofcorrespondingresolvedshear

Cstressovercurrentstrength,andofthetimestep.Theresolved

Cshearstressisthedoubleproductofstresstensorwiththeslip

Cdeformationtensor（Schmidfactor）,andtheincrementofcurrent

Cstrengthisrelatedtoshearstrainincrementsoverallslip

Csystemsthroughself-andlatent-hardeningfunctions.

C-----TheimplicitintegrationmethodproposedbyPeirce,Shihand

CNeedleman（1984）isusedhere.Thesubroutineprovidesanoption

Cofiterationtosolvestressesandsolutiondependentstate

Cvariableswithineachincrement.

C-----ThepresentprogramisforasingleCUBICcrystal.However,

Cthiscodecanbegeneralizedforothercrystals（e.g.HCP,

CTetragonal,Orthotropic,etc.）.OnlysubroutinesROTATIONand

CSLIPSYSneedtobemodifiedtoincludetheeffectofcrystal

Caspectratio.

C

C-----Importantnotice:

C

C

（1）ThenumberofstatevariablesNSTATVmustbelargerthan（or

CFIXequalto）TEN（10）timesthetotalnumberofslipsystemsin

Callsets,NSLPTL,plusFIVE（5）

CFIXNSTATV>=10*NSLPTL+5

CDenotesasaslipdirectionandmasnormaltoaslipplane.

CHere（s,-m）,（-s,m）and（-s,-m）areNOTconsidered

Cindependentof（s,m）.Thenumberofslipsystemsineachset

Ccouldbeeither6,12,24or48foracubiccrystal,e.g.12

Cfor{110}<111>.

C

CUserswhoneedmoreparameterstocharacterizethe

Cconstitutivelawofsinglecrystal,e.g.theframework

CproposedbyZarka,shouldmakeNSTATVlargerthan（orequal

Cto）thenumberofthoseparametersNPARMTplusninetimes

Cthetotalnumberofslipsystems,NSLPTL,plusfive

CFIXNSTATV>=NPARMT+10*NSLPTL+5

C

C

（2）Thetangentstiffnessmatrixingeneralisnotsymmetricif

Clatenthardeningisconsidered.Usersmustdeclare"UNSYMM"

Cintheinputfile,atthe*USERMATERIALcard.

C

PARAMETER（ND=150）

C-----TheparameterNDdeterminesthedimensionsofthearraysin

Cthissubroutine.Thecurrentchoice150isaupperboundfora

Ccubiccrystalwithuptothreesetsofslipsystemsactivated.

CUsersmayreducetheparameterNDtoanynumberaslongaslarger

Cthanorequaltothetotalnumberofslipsystemsinallsets.

CForexample,if{110}<111>istheonlysetofslipsystem

Cpotentiallyactivated,NDcouldbetakenastwelve（12）.

c

include'aba_param.inc'

c

CHARACTER*8CMNAME

EXTERNALF

dimensionstress（ntens）,statev（nstatv）,

1ddsdde（ntens,ntens）,ddsddt（ntens）,drplde（ntens）,

2stran（ntens）,dstran（ntens）,time

（2）,predef

（1）,dpred

（1）,

3props（nprops）,coords（3）,drot（3,3）,dfgrd0（3,3）,dfgrd1（3,3）

DIMENSIONISPDIR（3）,ISPNOR（3）,NSLIP（3）,

2SLPDIR（3,ND）,SLPNOR（3,ND）,SLPDEF（6,ND）,

3SLPSPN（3,ND）,DSPDIR（3,ND）,DSPNOR（3,ND）,

4DLOCAL（6,6）,D（6,6）,ROTD（6,6）,ROTATE（3,3）,

5FSLIP（ND）,DFDXSP（ND）,DDEMSD（6,ND）,

6H（ND,ND）,DDGDDE（ND,6）,

7DSTRES（6）,DELATS（6）,DSPIN（3）,DVGRAD（3,3）,

8DGAMMA（ND）,DTAUSP（ND）,DGSLIP（ND）,

9WORKST（ND,ND）,INDX（ND）,TERM（3,3）,TRM0（3,3）,ITRM（3）

DIMENSIONFSLIP1（ND）,STRES1（6）,GAMMA1（ND）,TAUSP1（ND）,

2GSLP1（ND）,SPNOR1（3,ND）,SPDIR1（3,ND）,DDSDE1（6,6）,

3DSOLD（6）,DGAMOD（ND）,DTAUOD（ND）,DGSPOD（ND）,

4DSPNRO（3,ND）,DSPDRO（3,ND）,

5DHDGDG（ND,ND）

C-----NSLIP--numberofslipsystemsineachset

C-----SLPDIR--slipdirections（unitvectorsintheinitialstate）

C-----SLPNOR--normalstoslipplanes（unitnormalsintheinitial

Cstate）

C-----SLPDEF--slipdeformationtensors（Schmidfactors）

CSLPDEF（1,i）--SLPDIR（1,i）*SLPNOR（1,i）

CSLPDEF（2,i）--SLPDIR（2,i）*SLPNOR（2,i）

CSLPDEF（3,i）--SLPDIR（3,i）*SLPNOR（3,i）

CSLPDEF（4,i）--SLPDIR（1,i）*SLPNOR（2,i）+

CSLPDIR（2,i）*SLPNOR（1,i）

CSLPDEF（5,i）--SLPDIR（1,i）*SLPNOR（3,i）+

CSLPDIR（3,i）*SLPNOR（1,i）

CSLPDEF（6,i）--SLPDIR（2,i）*SLPNOR（3,i）+

CSLPDIR（3,i）*SLPNOR（2,i）

Cwhereindexicorrespondstotheithslipsystem

C-----SLPSPN--slipspintensors（onlyneededforfiniterotation）

CSLPSPN（1,i）--[SLPDIR（1,i）*SLPNOR（2,i）-

CSLPDIR（2,i）*SLPNOR（1,i）]/2

CSLPSPN（2,i）--[SLPDIR（3,i）*SLPNOR（1,i）-

CSLPDIR（1,i）*SLPNOR（3,i）]/2

CSLPSPN（3,i）--[SLPDIR（2,i）*SLPNOR（3,i）-

CSLPDIR（3,i）*SLPNOR（2,i）]/2

Cwhereindexicorrespondstotheithslipsystem

C-----DSPDIR--incrementsofslipdirections

C-----DSPNOR--incrementsofnormalstoslipplanes

C

C-----DLOCAL--elasticmatrixinlocalcubiccrystalsystem

C-----D--elasticmatrixinglobalsystem

C-----ROTD--rotationmatrixtransformingDLOCALtoD

C

C-----ROTATE--rotationmatrix,directioncosinesof[100],[010]

Cand[001]ofcubiccrystalinglobalsystem

C

C-----FSLIP--shearstrain-ratesinslipsystems

C-----DFDXSP--derivativesofFSLIPw.r.tx=TAUSLP/GSLIP,where

CTAUSLPistheresolvedshearstressandGSLIPi