424 lines
12 KiB
Fortran
424 lines
12 KiB
Fortran
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! ---------------------------
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MODULE constitutive
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! ---------------------------
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! *** constitutive equations ***
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use prec, only: pRe,pIn
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implicit none
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! ***************************
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! *** Material parameters ***
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! ***************************
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real(pRe), allocatable :: Cslip_66(:,:,:),Cslip_3333(:,:,:,:,:)
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real(pRe), allocatable :: s0_slip(:),gdot0_slip(:)
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real(pRe), allocatable :: h0(:),w0(:),s_sat(:),q0(:),n_slip(:)
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real(pRe), allocatable :: hardening_matrix(:,:,:)
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character*80, allocatable :: TCfile(:), ODFfile(:)
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real(pRe), parameter :: latent=1.4_pRe
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integer(pIn), parameter :: Nslip(3)
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integer(pIn) Nmats
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real(pRe) sn(3,48,3),sd(3,48,3)
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real(pRe) Sslip(3,48,3,3),Sslip_v(3,48,6)
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! *** Vectors n and d for each fcc slip systems ***
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! MISSING needs to be generalized to fcc and bcc (and hcp?)
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! 1: fcc, 2: bcc, 3: hcp
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! the respective crystal structure has to be defined
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! via material parameter 'crystal_structure' in [material]
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data sd( 1,:)/ 0, 1,-1/ ; data sn( 1,:)/ 1, 1, 1/
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data sd( 2,:)/-1, 0, 1/ ; data sn( 2,:)/ 1, 1, 1/
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data sd( 3,:)/ 1,-1, 0/ ; data sn( 3,:)/ 1, 1, 1/
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data sd( 4,:)/ 0,-1,-1/ ; data sn( 4,:)/-1,-1, 1/
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data sd( 5,:)/ 1, 0, 1/ ; data sn( 5,:)/-1,-1, 1/
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data sd( 6,:)/-1, 1, 0/ ; data sn( 6,:)/-1,-1, 1/
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data sd( 7,:)/ 0,-1, 1/ ; data sn( 7,:)/ 1,-1,-1/
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data sd( 8,:)/-1, 0,-1/ ; data sn( 8,:)/ 1,-1,-1/
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data sd( 9,:)/ 1, 1, 0/ ; data sn( 9,:)/ 1,-1,-1/
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data sd(10,:)/ 0, 1, 1/ ; data sn(10,:)/-1, 1,-1/
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data sd(11,:)/ 1, 0,-1/ ; data sn(11,:)/-1, 1,-1/
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data sd(12,:)/-1,-1, 0/ ; data sn(12,:)/-1, 1,-1/
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contains
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! **************************************
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! *** module Init ***
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! **************************************
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subroutine constitutive_init()
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call constitutive_calc_SchmidM()
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call constitutive_calc_hardeningM()
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call constitutive_parse_materialDat()
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end subroutine
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! **************************************
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! *** Calculation of Schmid matrices ***
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! **************************************
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subroutine constitutive_calc_SchmidM()
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use prec, only: pRe,pIn
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implicit none
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integer(pIn) i,j,k,l
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real(pRe) invNorm
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do j=1,3 ! iterate over crystal system
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do i=1,Nslip(j) ! iterate over slip systems
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do k=1,3
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do l=1,3
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Sslip(j,i,k,l)=sd(j,i,k)*sn(j,i,l)
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enddo
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enddo
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invNorm = dsqrt(1.0_pRe/
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& (sn(j,i,1)**2+sn(j,1,2)**2+sn(j,i,3)**2)/
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& (sd(j,i,1)**2+sd(j,1,2)**2+sd(j,i,3)**2))
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Sslip(j,i,:,:) = Sslip(j,i,:,:)*invNorm
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Sslip_v(j,i,1)=Sslip(j,i,1,1)
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Sslip_v(j,i,2)=Sslip(j,i,2,2)
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Sslip_v(j,i,3)=Sslip(j,i,3,3)
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Sslip_v(j,i,4)=Sslip(j,i,1,2)+Sslip(j,i,2,1)
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Sslip_v(j,i,5)=Sslip(j,i,2,3)+Sslip(j,i,3,2)
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Sslip_v(j,i,6)=Sslip(j,i,1,3)+Sslip(j,i,3,1)
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enddo
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enddo
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end subroutine
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! ****************************************
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! *** Hardening matrix (see Kalidindi) ***
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! ****************************************
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subroutine constitutive_calc_hardeningM()
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use prec, only: pRe,pIn
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implicit none
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integer(pIn) i,j,k,l
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! MISSING iteration over crystal systems
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! PE does not understand the j,k looping
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hardening_matrix=latent
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do i=1,10,3
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do j=1,3
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do k=1,3
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hardening_matrix(i-1+j,i-1+k)=1.0_ZdRe
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enddo
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enddo
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enddo
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! ****************************************
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! *** Reading 'material.mpie' ***
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! ****************************************
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subroutine constitutive_parse_materialDat()
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use prec, only: pRe,pIn
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implicit none
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character*80 line
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integer(pIn) i,j,k,l,positions(4)
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! MISSING: needs to be 2 pass
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! first pass to count Nmats and allocate
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! 2nd pass to read actual parameters
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write(6,*) '## constitutive_parse_materialDat ##'
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write(6,*)
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constitutive_Nmats = 1
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open(200,FILE='material.mpie',ACTION='READ',STATUS='OLD',ERR=100)
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read(200,610,ERR=200,END=200) line
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IF( line(1:1).ne.'[' )THEN
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WRITE(6,*) 'Problem with mat file: no mat. in 1st line'
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ELSE
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WRITE(6,*) 'Reading mat. data'
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DO WHILE( .true. )
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READ(200,610,END=220) line
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IF( line(1:1).eq.'[' )THEN
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constitutive_Nmats = constitutive_Nmats+1
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ELSE
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positions = IO_stringPos(line,2) ! parse 2 parts
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SELECT CASE (IO_stringValue(line,positions,1))
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CASE ('s0_slip')
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s0_slip(mat) = IO_floatValue(line,positions,2)
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CASE ('g0_slip')
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g0_slip(mat) = IO_floatValue(line,positions,2)
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CASE ('n_slip')
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n_slip(mat) = IO_intValue(line,positions,2)
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CASE ('h0')
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h0(mat) = IO_floatValue(line,positions,2)
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CASE ('w0')
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w0(mat) = IO_floatValue(line,positions,2)
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CASE ('tauc_sat')
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tauc_sat(mat) = IO_floatValue(line,positions,2)
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CASE ('C11')
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C11(mat) = IO_floatValue(line,positions,2)
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CASE ('C12')
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C12(mat) = IO_floatValue(line,positions,2)
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CASE ('C44')
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C44(mat) = IO_floatValue(line,positions,2)
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CASE ('TCfile')
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TCfile(mat) = IO_stringValue(line,positions,2)
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CASE ('ODFfile')
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ODFfile(mat) = IO_stringValue(line,positions,2)
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CASE ('Ngrains')
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Ngrains(mat) = IO_intValue(line,positions,2)
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CASE DEFAULT
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WRITE(6,*) 'Unknown mat. parameter ',line
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END IF
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END DO
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END IF
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220 continue
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close(200)
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! ** Defintion of stiffness matrices **
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! MISSING: this needs to be iterated over the materials
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Cslip_66 = 0.0_pRe
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do i=1,3
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do j=1,3
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Cslip_66(i,j) = C12
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enddo
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Cslip_66(i,i) = C11
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Cslip_66(i+3,i+3) = C44
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enddo
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Cslip_3333(:,:,:,:) = math_66to3333(Cslip_66(:,:))
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! *** Transformation to get the MARC order ***
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! *** 11,22,33,12,23,13 ***
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! MISSING this should be outsourced to FEM-spec
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temp=Cslip_66(4,:)
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Cslip_66(4,:)=Cslip_66(6,:)
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Cslip_66(6,:)=Cslip_66(5,:)
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Cslip_66(5,:)=temp
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temp=Cslip_66(:,4)
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Cslip_66(:,4)=2.0d0*Cslip_66(:,6)
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Cslip_66(:,6)=2.0d0*Cslip_66(:,5)
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Cslip_66(:,5)=2.0d0*temp
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! *** Output to MARC output file ***
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write(6,*) 'Material data:'
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write(6,*) 'Slip parameter:(s0_slip,g0_slip,n_slip)'
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write(6,*) s0_slip,g0_slip,n_slip
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write(6,*) 'Slip hardening parameter:(h0,tauc_sat,w0)'
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write(6,*) h0,tauc_sat,w0
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write(6,*) 'Elasticity matrix:'
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write(6,*) Cslip_66(1,:)
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write(6,*) Cslip_66(2,:)
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write(6,*) Cslip_66(3,:)
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write(6,*) Cslip_66(4,:)/2.0d0
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write(6,*) Cslip_66(5,:)/2.0d0
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write(6,*) Cslip_66(6,:)/2.0d0
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write(6,*)
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call flush(6)
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! END OF MISSING mat iterations
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return
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100 call _error(110)
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200 call _error(210)
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end
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subroutine READ_ORIENTATIONS
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!***********************************************************************
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!*** This routine reads orientations from 'orientations.mpie' ***
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!***********************************************************************
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use mpie
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use Zahlendarstellung, only: ZdRe,ZdIn
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implicit none
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! *** Definition of variables ***
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integer(ZdIn) i,j
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! *** Read 'orientations.mpie' file ***
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open(100,FILE='orientations.mpie',ACTION='READ',STATUS='OLD',
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& ERR=100)
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read(100,*,ERR=200,END=200)
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! *** Read number of states, maximum of components over the states ***
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read(100,*,ERR=200,END=200) mpie_nmat,mpie_norimx
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! *** Allocate memory for the arrays ***
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allocate(mpie_mat(mpie_nmat,2+7*mpie_norimx))
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allocate(mpie_cko(mpie_nmat,4:35,3,0:35,2))
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allocate(mpie_ckofile(mpie_nmat,80))
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allocate(mpie_odfmax(mpie_nmat))
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mpie_mat=0.0_ZdRe
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mpie_cko=0.0_ZdRe
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mpie_ckofile=''
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mpie_odfmax=0.0_ZdRe
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! *** Read the different states ***
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do i=1,mpie_nmat
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read(100,*,ERR=200,END=200)
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! *** Number of component and symmetry ***
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read(100,*,ERR=200,END=200) mpie_mat(i,1),mpie_mat(i,2)
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! *** If symmetry = 2, use direct ODF sampling,i.e. read coefficience ***
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if (mpie_mat(i,2)==2_ZdIn) then
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read(100,'(80A)',ERR=200,END=201) mpie_ckofile(i,:)
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201 call mpie_read_ckofile(mpie_cko(i,:,:,:,:),
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& mpie_ckofile(i,:))
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call mpie_odf_max(mpie_cko(i,:,:,:,:),mpie_odfmax(i))
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! *** Set volume fraction to inverse of orientation number for each orientation ***
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do j=1,int(mpie_mat(i,1),ZdIn)
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mpie_mat(i,2+7*j)=1/mpie_mat(i,1)
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enddo
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else
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! *** Read for every component: ***
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! *** gauss: euler angles (phi1, PHI, phi2), dummy, scatter, volume fraction ***
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! *** fiber: alpha1, alpha2, beta1, beta2, scatter, volume fraction ***
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do j=1,int(mpie_mat(i,1),ZdIn)
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read(100,*,ERR=200,END=200) mpie_mat(i,7*j-4),
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& mpie_mat(i,7*j-3),mpie_mat(i,7*j-2),
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& mpie_mat(i,7*j-1),mpie_mat(i,7*j),
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& mpie_mat(i,7*j+1),mpie_mat(i,7*j+2)
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enddo
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endif
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enddo
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close(100)
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! *** Output to MARC output file ***
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write(6,*) 'MPIE Material Routine Ver. 0.1 by L. Hantcherli'
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write(6,*)
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write(6,*) 'Orientations data:'
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write(6,*) 'Number of materials: ', mpie_nmat
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write(6,*) 'Maximum number of components: ', mpie_norimx
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write(6,*)
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do i=1,mpie_nmat
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write(6,*) 'State', i
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if (mpie_mat(i,2)==2_ZdIn) then
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write(6,*) mpie_ckofile(i,:),mpie_mat(i,9),mpie_odfmax(i)
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else
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write(6,*) mpie_mat(i,:)
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endif
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write(6,*)
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enddo
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call flush(6)
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return
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100 call _error(100)
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200 call _error(200)
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end
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subroutine slip_rate (tau_slip,tauc_slip_new,gdot_slip,
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& dgdot_dtaucslip)
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C ********************************************************************
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C Subroutine contains the constitutive equation for the slip
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C rate on each slip system
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C Input: tau_slip : shear stress on each slip system
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C tauc_slip_new : critical shear stress on each slip system
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C Output: gdot_slip : slip rate on each slip system
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C dgdot_dtaucslip: derivative of slip rate on each slip system
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C ********************************************************************
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use mpie
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use Zahlendarstellung
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implicit none
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real(ZdRe) tau_slip(nslip),tauc_slip_new(nslip),
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& gdot_slip(nslip),dgdot_dtaucslip(nslip)
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integer(ZdIn) i
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do i=1,nslip
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gdot_slip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
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& **n_slip*sign(1.0_ZdRe,tau_slip(i))
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dgdot_dtaucslip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
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& **(n_slip-1) *n_slip/tauc_slip_new(i)
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||
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enddo
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||
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|
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||
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|
return
|
||
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|
end
|
||
|
|
|
||
|
|
subroutine hardening (tauc_slip_new,gdot_slip,dtauc_slip)
|
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|
|
C *********************************************************************
|
||
|
|
C Subroutine calculates the increment in critical shear stress due
|
||
|
|
C to plastic deformation on each slip system
|
||
|
|
C Input: tauc_slip_new :critical shear stress needed for slip on each
|
||
|
|
C slip system
|
||
|
|
C gdot_slip :slip rate on each slip system
|
||
|
|
C Output: dtauc_slip :increment of hardening due to slip on each
|
||
|
|
C slip system
|
||
|
|
C Local : selfhr
|
||
|
|
C *********************************************************************
|
||
|
|
use mpie
|
||
|
|
use Zahlendarstellung
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
real(ZdRe) tauc_slip_new(nslip),gdot_slip(nslip),
|
||
|
|
& dtauc_slip(nslip)
|
||
|
|
real(ZdRe) selfhr(nslip)
|
||
|
|
integer(ZdIn) i
|
||
|
|
|
||
|
|
do i=1,nslip
|
||
|
|
selfhr(i)=h0*(1.0_ZdRe-tauc_slip_new(i)/
|
||
|
|
& tauc_sat)**w0
|
||
|
|
& *abs(gdot_slip(i))
|
||
|
|
enddo
|
||
|
|
dtauc_slip=matmul(hardening_matrix,selfhr)
|
||
|
|
|
||
|
|
return
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
subroutine plastic_vel_grad(dt,tau_slip,tauc_slip_new,Lp)
|
||
|
|
C *************************************************************
|
||
|
|
C Subroutine calculates the plastic velocity gradient given the
|
||
|
|
C slip rates
|
||
|
|
C Input: dt : time step
|
||
|
|
C tau_slip : shear stress on each slip system on each
|
||
|
|
C slip system
|
||
|
|
C tauc_slip_new : critical shear stress needed for slip on each
|
||
|
|
C slip system
|
||
|
|
C Output: Lp : plastic velocity gradient
|
||
|
|
C gdot_slip : slip rate on each slip system
|
||
|
|
C *************************************************************
|
||
|
|
use mpie
|
||
|
|
use Zahlendarstellung
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
real(ZdRe) dt,tau_slip(nslip),tauc_slip_new(nslip),
|
||
|
|
& Lp(3,3),gdot_slip(nslip)
|
||
|
|
integer(ZdIn) i
|
||
|
|
|
||
|
|
Lp=0
|
||
|
|
do i=1,nslip
|
||
|
|
gdot_slip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
|
||
|
|
& **n_slip*sign(1.0_ZdRe,tau_slip(i))
|
||
|
|
Lp=Lp+gdot_slip(i)*Sslip(i,:,:)
|
||
|
|
enddo
|
||
|
|
|
||
|
|
return
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
function CPFEM_Cauchy(Estar_v,Fe,C66)
|
||
|
|
C ***************************************************************
|
||
|
|
C Subroutine calculates the cauchy from the elastic strain tensor
|
||
|
|
C Input: Estar_v : elastic strain tensor (in vector form)
|
||
|
|
C Fe : elastic deformation gradient
|
||
|
|
C C66 : Stiffness Tensor
|
||
|
|
C Output: cs : cauchy stress
|
||
|
|
C Local: Tstar_v,Tstar,mm,det
|
||
|
|
C ***************************************************************
|
||
|
|
use math
|
||
|
|
use prec
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
real(pRe) Estar_v(6),Fe(3,3),C66(6,6),CPFEM_Cauchy(6)
|
||
|
|
real(pRe) det,mm(3,3),Tstar(3,3)
|
||
|
|
integer(pIn) i
|
||
|
|
|
||
|
|
det = math_det(Fe)
|
||
|
|
Tstar = math_6to33(matmul(C66,Estar_v))
|
||
|
|
mm=matmul(matmul(Fe,Tstar),transpose(Fe))/det
|
||
|
|
CPFEM_Cauchy = math_33to6(mm)
|
||
|
|
|
||
|
|
return
|
||
|
|
end function
|
||
|
|
|
||
|
|
end module
|