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单晶塑性

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SUBROUTINE UMAT(stress,statev,ddsdde,sse,spd,scd,

1 rpl, ddsddt, drplde, drpldt,

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

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

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

c WRITE (6,*) '

c NOTE: MODIFICATIONS TO *UMAT FOR ABAQUS VERSION 5.3 (14 APR '94)

c (1) The list of variables above defining the *UMAT subroutine,

c and the first (standard) block of variables dimensioned below,

c have variable names added compared to earlier ABAQUS versions.

c (2) The statement: include 'aba_param.inc' must be added as below.

c (3) As of version 5.3, ABAQUS files use double precision only.

c The file aba_param.inc has a line "implicit real*8" and, since

c it is included in the main subroutine, it will define the variables

c there as double precision. But other subroutines still need the

c definition "implicit real*8" since there may be variables that are

c not passed to them through the list or common block.

c (4) This is current as of version 5.6 of ABAQUS.

c (5) Note added by J. W. Kysar (4 November 1997). This UMAT has been

c modified to keep track of the cumulative shear strain in each

c individual slip system. This information is needed to correct an

c error in the implementation of the Bassani and Wu hardening law.

c Any line of code which has been added or modified is preceded

c immediately by a line beginning CFIXA and succeeded by a line

c beginning CFIXB. Any comment line added or modified will begin

c with CFIX.

c The hardening law by Bassani and Wu was implemented incorrectly.

c This law is a function of both hyperbolic secant squared and hyperbolic

c tangent. However, the arguments of sech and tanh are related to the *total*

c slip on individual slip systems. Formerly, the UMAT implemented this

c hardening law by using the *current* slip on each slip system. Therein

c lay the problem. The UMAT did not restrict the current slip to be a

c positive value. So when a slip with a negative sign was encountered, the

c term containing tanh led to a negative hardening rate (since tanh is an

c odd function).

c The UMAT has been fixed by adding state variables to keep track of the

c *total* slip on each slip system by integrating up the absolute value

C----- Variables:

C STRESS -- stresses (INPUT & OUTPUT)

C Cauchy stresses for finite deformation

C STATEV -- solution dependent state variables (INPUT & OUTPUT)

C DDSDDE -- Jacobian matrix (OUTPUT)

C----- Variables passed in for information:

C STRAN -- strains

C logarithmic strain for finite deformation

C (actually, integral of the symmetric part of velocity

C gradient with respect to time)

C DSTRAN -- increments of strains

C CMNAME -- name given in the *MATERIAL option

C NDI -- number of direct stress components

C NSHR -- number of engineering shear stress components

C NTENS -- NDI+NSHR

C NSTATV -- number of solution dependent state variables (as

C defined in the *DEPVAR option)

C PROPS -- material constants entered in the *USER MATERIAL

C option

C NPROPS -- number of material constants

C----- This subroutine provides the plastic constitutive relation of

C single crystals for finite element code ABAQUS. The plastic slip

C of single crystal obeys the Schmid law. The program gives the

C choice of small deformation theory and theory of finite rotation

C and finite strain.

C The strain increment is composed of elastic part and plastic

C part. The elastic strain increment corresponds to lattice

C stretching, the plastic part is the sum over all slip systems of

C plastic slip. The shear strain increment for each slip system is

C assumed a function of the ratio of corresponding resolved shear

C stress over current strength, and of the time step. The resolved

C shear stress is the double product of stress tensor with the slip

C deformation tensor (Schmid factor), and the increment of current

C strength is related to shear strain increments over all slip

C systems through self- and latent-hardening functions.

C----- The implicit integration method proposed by Peirce, Shih and

C Needleman (1984) is used here. The subroutine provides an option

C of iteration to solve stresses and solution dependent state

CHARACTER*8 CMNAME

EXTERNAL F

dimension stress(ntens),statev(nstatv),

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

2 stran(ntens),dstran(ntens),time(2),predef(1),dpred(1),

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

DIMENSION ISPDIR(3), ISPNOR(3), NSLIP(3),

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

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

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

5 FSLIP(ND), DFDXSP(ND), DDEMSD(6,ND),

6 H(ND,ND), DDGDDE(ND,6),

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

8 DGAMMA(ND), DTAUSP(ND), DGSLIP(ND),

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

DIMENSION FSLIP1(ND), STRES1(6), GAMMA1(ND), TAUSP1(ND),

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

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

4 DSPNRO(3,ND), DSPDRO(3,ND),

5 DHDGDG(ND,ND)

C----- NSLIP -- number of slip systems in each set

C----- SLPDIR -- slip directions (unit vectors in the initial state)

C----- SLPNOR -- normals to slip planes (unit normals in the initial

C state)

C----- SLPDEF -- slip deformation tensors (Schmid factors)

C SLPDEF(1,i) -- SLPDIR(1,i)*SLPNOR(1,i)

C SLPDEF(2,i) -- SLPDIR(2,i)*SLPNOR(2,i)

C SLPDEF(3,i) -- SLPDIR(3,i)*SLPNOR(3,i)

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

C SLPDIR(2,i)*SLPNOR(1,i)

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

C SLPDIR(3,i)*SLPNOR(1,i)

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

C SLPDIR(3,i)*SLPNOR(2,i)

C where index i corresponds to the ith slip system

C----- SLPSPN -- slip spin tensors (only needed for finite rotation)

C SLPSPN(1,i) -- [SLPDIR(1,i)*SLPNOR(2,i)-

C SLPDIR(2,i)*SLPNOR(1,i)]/2

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

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