!* $Id: constitutive_dislotwin.f90 412 2009-09-18 15:37:14Z MPIE\c.kords $ !************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - constitutive equations * !* - parameters definition * !* - orientations * !************************************ ! [TWIP steel FeMnC] ! C11 175.0e9 # elastic constants in Pa ! C12 115.0e9 ! C44 135.0e9 ! lattice_structure fcc ! Nslip 12 ! Ntwin 12 ! constitution dislotwin ! (output) dislocationdensity ! (output) shearrate_slip ! (output) mfp_slip # mean free path ! (output) resolvedstress_slip ! (output) resistance_slip # passing stress ! (output) volumefraction ! (output) shearrate_twin ! (output) mfp_twin # mean free path ! (output) resolvedstress_twin ! (output) resistance_twin # "nucleation barrier" ! ### dislocation density-based constitutive parameters ### ! burgers 2.56e-10 # Burgers vector [m] ! Qedge 5.5e-19 # Activation energy for dislocation glide [J/K] (0.5*G*b^3) ! grainsize 2.0e-5 # Average grain size [m] ! stacksize 5.0e-8 # Twin stack mean thickness [m] ! interaction_slipslip 1.0 2.2 3.0 1.6 3.8 4.5 # Dislocation interaction coefficients ! interaction_sliptwin 0.0 1.0 # Dislocation interaction coefficients ! interaction_twintwin 0.0 1.0 # Dislocation interaction coefficients ! # dislocation glide ! rho0 2.5e12 # Initial dislocation density [m/m³] ! Cmfpslip 1.0 # Adjustable parameter controlling dislocation mean free path ! Cactivolume 1.0 # Adjustable parameter controlling activation volume ! Cthresholdslip 0.1 # Adjustable parameter controlling threshold stress for dislocation motion ! Cstorage 0.02 # Adjustable parameter controlling dislocation storage ! Carecovery 15.0 # Adjustable parameter controlling athermal recovery ! # mechanical twinning ! Ndot0 0.0 # Number of potential twin source per volume per time [1/m³.s] ! fmax 1.0 # Maximum admissible twin volume fraction ! Cmfptwin 1.0 # Adjustable parameter controlling twin mean free path ! Cthresholdtwin 1.0 # Adjustable parameter controlling threshold stress for deformation twinning MODULE constitutive_dislotwin !*** Include other modules *** use prec, only: pReal,pInt implicit none character (len=*), parameter :: constitutive_dislotwin_label = 'dislotwin' integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_sizeDotState, & constitutive_dislotwin_sizeState, & constitutive_dislotwin_sizePostResults integer(pInt), dimension(:,:), allocatable,target :: constitutive_dislotwin_sizePostResult character(len=64), dimension(:,:), allocatable,target :: constitutive_dislotwin_output character(len=32), dimension(:), allocatable :: constitutive_dislotwin_structureName integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_structure, & constitutive_dislotwin_totalNslip, & constitutive_dislotwin_totalNtwin integer(pInt), dimension(:,:), allocatable :: constitutive_dislotwin_Nslip, & constitutive_dislotwin_Ntwin, & constitutive_dislotwin_slipFamily, & constitutive_dislotwin_twinFamily real(pReal), dimension(:), allocatable :: constitutive_dislotwin_CoverA, & constitutive_dislotwin_C11, & constitutive_dislotwin_C12, & constitutive_dislotwin_C13, & constitutive_dislotwin_C33, & constitutive_dislotwin_C44, & constitutive_dislotwin_Gmod real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_Cslip_66 real(pReal), dimension(:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_66 real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_dislotwin_Cslip_3333 real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_3333 real(pReal), dimension(:,:), allocatable :: constitutive_dislotwin_rho0, & constitutive_dislotwin_Burgers, & constitutive_dislotwin_Qedge, & constitutive_dislotwin_stacksize, & constitutive_dislotwin_Ndot0, & constitutive_dislotwin_interaction_slipslip, & constitutive_dislotwin_interaction_sliptwin, & constitutive_dislotwin_interaction_twinslip, & constitutive_dislotwin_interaction_twintwin real(pReal), dimension(:), allocatable :: constitutive_dislotwin_grainsize, & constitutive_dislotwin_fmax, & constitutive_dislotwin_Cmfpslip, & constitutive_dislotwin_Cmfptwin, & constitutive_dislotwin_Cthresholdslip, & constitutive_dislotwin_Cthresholdtwin, & constitutive_dislotwin_Cactivolume, & constitutive_dislotwin_Carecovery, & constitutive_dislotwin_Cstorage real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_parall_interaction, & constitutive_dislotwin_forest_interaction, & constitutive_dislotwin_hardeningMatrix_sliptwin, & constitutive_dislotwin_hardeningMatrix_twinslip, & constitutive_dislotwin_hardeningMatrix_twintwin !************************************* !* Definition of material properties * !************************************* !* Physical parameter, attack_frequency != Debye frequency real(pReal), parameter :: attack_frequency = 1.0e10_pReal !* Physical parameter, Boltzmann constant in J/Kelvin real(pReal), parameter :: kB = 1.38e-23_pReal !* Physical parameter, Avogadro number in 1/mol real(pReal), parameter :: avogadro = 6.022e23_pReal !* Physical parameter, Gas constant in J.mol/Kelvin real(pReal), parameter :: Rgas = 8.314_pReal CONTAINS !**************************************** !* - constitutive_init !* - constitutive_stateInit !* - constitutive_homogenizedC !* - constitutive_microstructure !* - constitutive_LpAndItsTangent !* - consistutive_dotState !* - constitutive_dotTemperature !* - consistutive_postResults !**************************************** subroutine constitutive_dislotwin_init(file) !************************************** !* Module initialization * !************************************** use prec, only: pInt,pReal use math, only: math_Mandel3333to66,math_Voigt66to3333,math_mul3x3 use IO use material use lattice integer(pInt), intent(in) :: file integer(pInt), parameter :: maxNchunks = 21 integer(pInt), dimension(1+2*maxNchunks) :: positions integer(pInt) section,maxNinstance,i,j,k,l,m,n,o,p,q,r,s,output,mySize character(len=64) tag character(len=1024) line real(pReal) x,y write(6,*) write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_dislotwin_label,' init -+>>>' write(6,*) '$Id: constitutive_dislotwin.f90 412 2009-09-18 15:37:14Z MPIE\c.kords $' write(6,*) maxNinstance = count(phase_constitution == constitutive_dislotwin_label) if (maxNinstance == 0) return allocate(constitutive_dislotwin_sizeDotState(maxNinstance)) ; constitutive_dislotwin_sizeDotState = 0_pInt allocate(constitutive_dislotwin_sizeState(maxNinstance)) ; constitutive_dislotwin_sizeState = 0_pInt allocate(constitutive_dislotwin_sizePostResults(maxNinstance)) ; constitutive_dislotwin_sizePostResults = 0_pInt allocate(constitutive_dislotwin_sizePostResult(maxval(phase_Noutput), & maxNinstance)) ; constitutive_dislotwin_sizePostResult = 0_pInt allocate(constitutive_dislotwin_output(maxval(phase_Noutput), & maxNinstance)) ; constitutive_dislotwin_output = '' allocate(constitutive_dislotwin_structureName(maxNinstance)) ; constitutive_dislotwin_structureName = '' allocate(constitutive_dislotwin_structure(maxNinstance)) ; constitutive_dislotwin_structure = 0_pInt allocate(constitutive_dislotwin_Nslip(lattice_maxNslipFamily,& maxNinstance)) ; constitutive_dislotwin_Nslip = 0_pInt allocate(constitutive_dislotwin_Ntwin(lattice_maxNtwinFamily,& maxNinstance)) ; constitutive_dislotwin_Ntwin = 0_pInt allocate(constitutive_dislotwin_slipFamily(lattice_maxNslip,& maxNinstance)) ; constitutive_dislotwin_slipFamily = 0_pInt allocate(constitutive_dislotwin_twinFamily(lattice_maxNtwin,& maxNinstance)) ; constitutive_dislotwin_twinFamily = 0_pInt allocate(constitutive_dislotwin_totalNslip(maxNinstance)) ; constitutive_dislotwin_totalNslip = 0_pInt allocate(constitutive_dislotwin_totalNtwin(maxNinstance)) ; constitutive_dislotwin_totalNtwin = 0_pInt allocate(constitutive_dislotwin_CoverA(maxNinstance)) ; constitutive_dislotwin_CoverA = 0.0_pReal allocate(constitutive_dislotwin_C11(maxNinstance)) ; constitutive_dislotwin_C11 = 0.0_pReal allocate(constitutive_dislotwin_C12(maxNinstance)) ; constitutive_dislotwin_C12 = 0.0_pReal allocate(constitutive_dislotwin_C13(maxNinstance)) ; constitutive_dislotwin_C13 = 0.0_pReal allocate(constitutive_dislotwin_C33(maxNinstance)) ; constitutive_dislotwin_C33 = 0.0_pReal allocate(constitutive_dislotwin_C44(maxNinstance)) ; constitutive_dislotwin_C44 = 0.0_pReal allocate(constitutive_dislotwin_Gmod(maxNinstance)) ; constitutive_dislotwin_Gmod = 0.0_pReal allocate(constitutive_dislotwin_Cslip_66(6,6,maxNinstance)) ; constitutive_dislotwin_Cslip_66 = 0.0_pReal allocate(constitutive_dislotwin_Cslip_3333(3,3,3,3,maxNinstance)) ; constitutive_dislotwin_Cslip_3333 = 0.0_pReal allocate(constitutive_dislotwin_rho0(lattice_maxNslipFamily, & maxNinstance)) ; constitutive_dislotwin_rho0 = 0.0_pReal allocate(constitutive_dislotwin_Burgers(lattice_maxNslipFamily, & maxNinstance)) ; constitutive_dislotwin_Burgers = 0.0_pReal allocate(constitutive_dislotwin_Qedge(lattice_maxNslipFamily, & maxNinstance)) ; constitutive_dislotwin_Qedge = 0.0_pReal allocate(constitutive_dislotwin_grainsize(maxNinstance)) ; constitutive_dislotwin_grainsize = 0.0_pReal allocate(constitutive_dislotwin_stacksize(lattice_maxNtwinFamily, & maxNinstance)) ; constitutive_dislotwin_stacksize = 0.0_pReal allocate(constitutive_dislotwin_fmax(maxNinstance)) ; constitutive_dislotwin_fmax = 0.0_pReal allocate(constitutive_dislotwin_Ndot0(lattice_maxNtwinFamily, & maxNinstance)) ; constitutive_dislotwin_Ndot0 = 0.0_pReal allocate(constitutive_dislotwin_Cmfpslip(maxNinstance)) ; constitutive_dislotwin_Cmfpslip = 0.0_pReal allocate(constitutive_dislotwin_Cmfptwin(maxNinstance)) ; constitutive_dislotwin_Cmfptwin = 0.0_pReal allocate(constitutive_dislotwin_Cthresholdslip(maxNinstance)) ; constitutive_dislotwin_Cthresholdslip = 0.0_pReal allocate(constitutive_dislotwin_Cthresholdtwin(maxNinstance)) ; constitutive_dislotwin_Cthresholdtwin = 0.0_pReal allocate(constitutive_dislotwin_Cactivolume(maxNinstance)) ; constitutive_dislotwin_Cactivolume = 0.0_pReal allocate(constitutive_dislotwin_Carecovery(maxNinstance)) ; constitutive_dislotwin_Carecovery = 0.0_pReal allocate(constitutive_dislotwin_Cstorage(maxNinstance)) ; constitutive_dislotwin_Cstorage = 0.0_pReal allocate(constitutive_dislotwin_interaction_slipslip(lattice_maxNinteraction,& maxNinstance)) ; constitutive_dislotwin_interaction_slipslip = 0.0_pReal allocate(constitutive_dislotwin_interaction_sliptwin(lattice_maxNinteraction,& maxNinstance)) ; constitutive_dislotwin_interaction_sliptwin = 0.0_pReal allocate(constitutive_dislotwin_interaction_twinslip(lattice_maxNinteraction,& maxNinstance)) ; constitutive_dislotwin_interaction_twinslip = 0.0_pReal allocate(constitutive_dislotwin_interaction_twintwin(lattice_maxNinteraction,& maxNinstance)) ; constitutive_dislotwin_interaction_twintwin = 0.0_pReal rewind(file) line = '' section = 0 do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to read(file,'(a1024)',END=100) line enddo do ! read thru sections of phase part read(file,'(a1024)',END=100) line if (IO_isBlank(line)) cycle ! skip empty lines if (IO_getTag(line,'<','>') /= '') exit ! stop at next part if (IO_getTag(line,'[',']') /= '') then ! next section section = section + 1 output = 0 ! reset output counter endif if (section > 0 .and. phase_constitution(section) == constitutive_dislotwin_label) then ! one of my sections i = phase_constitutionInstance(section) ! which instance of my constitution is present phase positions = IO_stringPos(line,maxNchunks) tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key select case(tag) case ('(output)') output = output + 1 constitutive_dislotwin_output(output,i) = IO_lc(IO_stringValue(line,positions,2)) case ('lattice_structure') constitutive_dislotwin_structureName(i) = IO_lc(IO_stringValue(line,positions,2)) case ('covera_ratio') constitutive_dislotwin_CoverA(i) = IO_floatValue(line,positions,2) case ('c11') constitutive_dislotwin_C11(i) = IO_floatValue(line,positions,2) case ('c12') constitutive_dislotwin_C12(i) = IO_floatValue(line,positions,2) case ('c13') constitutive_dislotwin_C13(i) = IO_floatValue(line,positions,2) case ('c33') constitutive_dislotwin_C33(i) = IO_floatValue(line,positions,2) case ('c44') constitutive_dislotwin_C44(i) = IO_floatValue(line,positions,2) case ('nslip') forall (j = 1:lattice_maxNslipFamily) constitutive_dislotwin_Nslip(j,i) = IO_intValue(line,positions,1+j) case ('ntwin') forall (j = 1:lattice_maxNtwinFamily) constitutive_dislotwin_Ntwin(j,i) = IO_intValue(line,positions,1+j) case ('rho0') forall (j = 1:lattice_maxNslipFamily) constitutive_dislotwin_rho0(j,i) = IO_floatValue(line,positions,1+j) case ('burgers') forall (j = 1:lattice_maxNslipFamily) constitutive_dislotwin_Burgers(j,i) = IO_floatValue(line,positions,1+j) case ('qedge') forall (j = 1:lattice_maxNslipFamily) constitutive_dislotwin_Qedge(j,i) = IO_floatValue(line,positions,1+j) case ('grainsize') constitutive_dislotwin_grainsize(i) = IO_floatValue(line,positions,2) case ('stacksize') forall (j = 1:lattice_maxNtwinFamily) constitutive_dislotwin_stacksize(j,i) = IO_floatValue(line,positions,1+j) case ('fmax') constitutive_dislotwin_fmax(i) = IO_floatValue(line,positions,2) case ('ndot0') forall (j = 1:lattice_maxNtwinFamily) constitutive_dislotwin_Ndot0(j,i) = IO_floatValue(line,positions,1+j) case ('cmfpslip') constitutive_dislotwin_Cmfpslip(i) = IO_floatValue(line,positions,2) case ('cmfptwin') constitutive_dislotwin_Cmfptwin(i) = IO_floatValue(line,positions,2) case ('cthresholdslip') constitutive_dislotwin_Cthresholdslip(i) = IO_floatValue(line,positions,2) case ('cthresholdtwin') constitutive_dislotwin_Cthresholdtwin(i) = IO_floatValue(line,positions,2) case ('cactivolume') constitutive_dislotwin_Cactivolume(i) = IO_floatValue(line,positions,2) case ('carecovery') constitutive_dislotwin_Carecovery(i) = IO_floatValue(line,positions,2) case ('cstorage') constitutive_dislotwin_Cstorage(i) = IO_floatValue(line,positions,2) case ('interaction_slipslip') forall (j = 1:lattice_maxNinteraction) & constitutive_dislotwin_interaction_slipslip(j,i) = IO_floatValue(line,positions,1+j) case ('interaction_sliptwin') forall (j = 1:lattice_maxNinteraction) & constitutive_dislotwin_interaction_sliptwin(j,i) = IO_floatValue(line,positions,1+j) case ('interaction_twinslip') forall (j = 1:lattice_maxNinteraction) & constitutive_dislotwin_interaction_twinslip(j,i) = IO_floatValue(line,positions,1+j) case ('interaction_twintwin') forall (j = 1:lattice_maxNinteraction) & constitutive_dislotwin_interaction_twintwin(j,i) = IO_floatValue(line,positions,1+j) end select endif enddo 100 do i = 1,maxNinstance constitutive_dislotwin_structure(i) = lattice_initializeStructure(constitutive_dislotwin_structureName(i), & constitutive_dislotwin_CoverA(i)) constitutive_dislotwin_Nslip(:,i) = min(lattice_NslipSystem(:,constitutive_dislotwin_structure(i)),& constitutive_dislotwin_Nslip(:,i)) constitutive_dislotwin_Ntwin(:,i) = min(lattice_NtwinSystem(:,constitutive_dislotwin_structure(i)),& constitutive_dislotwin_Ntwin(:,i)) constitutive_dislotwin_totalNslip(i) = sum(constitutive_dislotwin_Nslip(:,i)) constitutive_dislotwin_totalNtwin(i) = sum(constitutive_dislotwin_Ntwin(:,i)) ! sanity checks (still under construction) if (constitutive_dislotwin_structure(i) < 1 .or. & ! sanity checks constitutive_dislotwin_structure(i) > 3) call IO_error(205) if (any(constitutive_dislotwin_rho0(:,i) < 0.0_pReal)) call IO_error(220) if (any(constitutive_dislotwin_Burgers(:,i) <= 0.0_pReal .and. & constitutive_dislotwin_Nslip(:,i) > 0)) call IO_error(221) if (any(constitutive_dislotwin_Qedge(:,i) <= 0.0_pReal .and. & constitutive_dislotwin_Nslip(:,i) > 0)) call IO_error(222) enddo allocate(constitutive_dislotwin_parall_interaction(maxval(constitutive_dislotwin_totalNslip),& maxval(constitutive_dislotwin_totalNslip),& maxNinstance)) allocate(constitutive_dislotwin_forest_interaction(maxval(constitutive_dislotwin_totalNslip),& maxval(constitutive_dislotwin_totalNslip),& maxNinstance)) allocate(constitutive_dislotwin_hardeningMatrix_sliptwin(maxval(constitutive_dislotwin_totalNslip),& maxval(constitutive_dislotwin_totalNtwin),& maxNinstance)) allocate(constitutive_dislotwin_hardeningMatrix_twinslip(maxval(constitutive_dislotwin_totalNtwin),& maxval(constitutive_dislotwin_totalNslip),& maxNinstance)) allocate(constitutive_dislotwin_hardeningMatrix_twintwin(maxval(constitutive_dislotwin_totalNtwin),& maxval(constitutive_dislotwin_totalNtwin),& maxNinstance)) constitutive_dislotwin_parall_interaction = 0.0_pReal constitutive_dislotwin_forest_interaction = 0.0_pReal constitutive_dislotwin_hardeningMatrix_sliptwin = 0.0_pReal constitutive_dislotwin_hardeningMatrix_twinslip = 0.0_pReal constitutive_dislotwin_hardeningMatrix_twintwin = 0.0_pReal allocate(constitutive_dislotwin_Ctwin_66(6,6,maxval(constitutive_dislotwin_totalNtwin),maxNinstance)) constitutive_dislotwin_Ctwin_66 = 0.0_pReal allocate(constitutive_dislotwin_Ctwin_3333(3,3,3,3,maxval(constitutive_dislotwin_totalNtwin),maxNinstance)) constitutive_dislotwin_Ctwin_3333 = 0.0_pReal do i = 1,maxNinstance do j = 1,maxval(phase_Noutput) select case(constitutive_dislotwin_output(j,i)) case('dislocationdensity', & 'shearrate_slip', & 'mfp_slip', & 'resolvedstress_slip', & 'resistance_slip' & ) mySize = constitutive_dislotwin_totalNslip(i) case('volumefraction', & 'shearrate_twin', & 'mfp_twin', & 'resolvedstress_twin', & 'resistance_twin' & ) mySize = constitutive_dislotwin_totalNtwin(i) case default mySize = 0_pInt end select if (mySize > 0_pInt) then ! any meaningful output found constitutive_dislotwin_sizePostResult(j,i) = mySize constitutive_dislotwin_sizePostResults(i) = constitutive_dislotwin_sizePostResults(i) + mySize endif enddo constitutive_dislotwin_sizeDotState(i) = constitutive_dislotwin_totalNslip(i) + constitutive_dislotwin_totalNtwin(i) constitutive_dislotwin_sizeState(i) = 10*constitutive_dislotwin_totalNslip(i) + 5*constitutive_dislotwin_totalNtwin(i) constitutive_dislotwin_Gmod(i) = constitutive_dislotwin_C44(i) select case (constitutive_dislotwin_structure(i)) case(1:2) ! cubic(s) forall(k=1:3) forall(j=1:3) & constitutive_dislotwin_Cslip_66(k,j,i) = constitutive_dislotwin_C12(i) constitutive_dislotwin_Cslip_66(k,k,i) = constitutive_dislotwin_C11(i) constitutive_dislotwin_Cslip_66(k+3,k+3,i) = constitutive_dislotwin_C44(i) end forall case(3:) ! all hex constitutive_dislotwin_Cslip_66(1,1,i) = constitutive_dislotwin_C11(i) constitutive_dislotwin_Cslip_66(2,2,i) = constitutive_dislotwin_C11(i) constitutive_dislotwin_Cslip_66(3,3,i) = constitutive_dislotwin_C33(i) constitutive_dislotwin_Cslip_66(1,2,i) = constitutive_dislotwin_C12(i) constitutive_dislotwin_Cslip_66(2,1,i) = constitutive_dislotwin_C12(i) constitutive_dislotwin_Cslip_66(1,3,i) = constitutive_dislotwin_C13(i) constitutive_dislotwin_Cslip_66(3,1,i) = constitutive_dislotwin_C13(i) constitutive_dislotwin_Cslip_66(2,3,i) = constitutive_dislotwin_C13(i) constitutive_dislotwin_Cslip_66(3,2,i) = constitutive_dislotwin_C13(i) constitutive_dislotwin_Cslip_66(4,4,i) = constitutive_dislotwin_C44(i) constitutive_dislotwin_Cslip_66(5,5,i) = constitutive_dislotwin_C44(i) constitutive_dislotwin_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_dislotwin_C11(i)- & constitutive_dislotwin_C12(i)) end select constitutive_dislotwin_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_dislotwin_Cslip_66(:,:,i))) constitutive_dislotwin_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_dislotwin_Cslip_66(:,:,i)) !* Inverse lookup of my slip system family l = 0_pInt do j = 1,lattice_maxNslipFamily do k = 1,constitutive_dislotwin_Nslip(j,i) l = l + 1 constitutive_dislotwin_slipFamily(l,i) = j enddo; enddo !* Inverse lookup of my twin system family l = 0_pInt do j = 1,lattice_maxNtwinFamily do k = 1,constitutive_dislotwin_Ntwin(j,i) l = l + 1 constitutive_dislotwin_twinFamily(l,i) = j enddo; enddo !* Construction of the twin elasticity matrices do j=1,lattice_maxNtwinFamily do k=1,constitutive_dislotwin_Ntwin(j,i) do l=1,3 ; do m=1,3 ; do n=1,3 ; do o=1,3 ; do p=1,3 ; do q=1,3 ; do r=1,3 ; do s=1,3 constitutive_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1,i))+k,i) = & constitutive_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1,i))+k,i) + & constitutive_dislotwin_Cslip_3333(p,q,r,s,i)*& lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k,constitutive_dislotwin_structure(i))* & lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k,constitutive_dislotwin_structure(i))* & lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k,constitutive_dislotwin_structure(i))* & lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k,constitutive_dislotwin_structure(i)) enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo constitutive_dislotwin_Ctwin_66(:,:,k,i) = math_Mandel3333to66(constitutive_dislotwin_Ctwin_3333(:,:,:,:,k,i)) enddo enddo !* Construction of the hardening matrices !* Iteration over the systems do j=1,lattice_maxNslipFamily do k=1,constitutive_dislotwin_Nslip(j,i) do l=1,lattice_maxNslipFamily do m=1,constitutive_dislotwin_Nslip(l,i) !* Projection of the dislocation * x = math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & constitutive_dislotwin_structure(i)), & lattice_st(:,sum(lattice_NslipSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i))) y = 1.0_pReal-x**(2.0_pReal) !* Interaction matrix * constitutive_dislotwin_forest_interaction(sum(constitutive_dislotwin_Nslip(1:j-1,i))+k, & sum(constitutive_dislotwin_Nslip(1:l-1,i))+m,i) = & abs(x)*constitutive_dislotwin_interaction_slipslip(lattice_interactionSlipSlip( & sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & sum(lattice_NslipSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i)),i) if (y>0.0_pReal) & constitutive_dislotwin_parall_interaction(sum(constitutive_dislotwin_Nslip(1:j-1,i))+k, & sum(constitutive_dislotwin_Nslip(1:l-1,i))+m,i) = & sqrt(y)*constitutive_dislotwin_interaction_slipslip(lattice_interactionSlipSlip( & sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & sum(lattice_NslipSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i)),i) enddo; enddo; enddo; enddo do j=1,lattice_maxNslipFamily do k=1,constitutive_dislotwin_Nslip(j,i) do l=1,lattice_maxNtwinFamily do m=1,constitutive_dislotwin_Ntwin(l,i) constitutive_dislotwin_hardeningMatrix_sliptwin(sum(constitutive_dislotwin_Nslip(1:j-1,i))+k,& sum(constitutive_dislotwin_Ntwin(1:l-1,i))+m,i) = & constitutive_dislotwin_interaction_sliptwin(lattice_interactionSlipTwin( & sum(lattice_NslipSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & sum(lattice_NtwinSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i)),i) enddo; enddo; enddo; enddo do j=1,lattice_maxNtwinFamily do k=1,constitutive_dislotwin_Ntwin(j,i) do l=1,lattice_maxNslipFamily do m=1,constitutive_dislotwin_Nslip(l,i) constitutive_dislotwin_hardeningMatrix_twinslip(sum(constitutive_dislotwin_Ntwin(1:j-1,i))+k,& sum(constitutive_dislotwin_Nslip(1:l-1,i))+m,i) = & constitutive_dislotwin_interaction_twinslip(lattice_interactionTwinSlip( & sum(lattice_NtwinSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & sum(lattice_NslipSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i)),i) enddo; enddo; enddo; enddo do j=1,lattice_maxNtwinFamily do k=1,constitutive_dislotwin_Ntwin(j,i) do l=1,lattice_maxNtwinFamily do m=1,constitutive_dislotwin_Ntwin(l,i) constitutive_dislotwin_hardeningMatrix_twintwin(sum(constitutive_dislotwin_Ntwin(1:j-1,i))+k,& sum(constitutive_dislotwin_Ntwin(1:l-1,i))+m,i) = & constitutive_dislotwin_interaction_twintwin(lattice_interactionTwinTwin( & sum(lattice_NtwinSystem(1:j-1,constitutive_dislotwin_structure(i)))+k, & sum(lattice_NtwinSystem(1:l-1,constitutive_dislotwin_structure(i)))+m, & constitutive_dislotwin_structure(i)), i ) enddo; enddo; enddo; enddo enddo return end subroutine function constitutive_dislotwin_stateInit(myInstance) !********************************************************************* !* initial microstructural state * !********************************************************************* use prec, only: pReal,pInt use lattice, only: lattice_maxNslipFamily,lattice_maxNtwinFamily implicit none !* Definition of variables integer(pInt), intent(in) :: myInstance integer(pInt) i real(pReal), dimension(constitutive_dislotwin_sizeState(myInstance)) :: constitutive_dislotwin_stateInit constitutive_dislotwin_stateInit = 0.0_pReal do i = 1,lattice_maxNslipFamily constitutive_dislotwin_stateInit(1+sum(constitutive_dislotwin_Nslip(1:i-1,myInstance)) : & sum(constitutive_dislotwin_Nslip(1:i ,myInstance))) = & constitutive_dislotwin_rho0(i,myInstance) enddo return end function !********************************************************************* !* relevant microstructural state * !********************************************************************* pure function constitutive_dislotwin_relevantState(myInstance) use prec, only: pReal, & pInt implicit none !*** input variables integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution !*** output variables real(pReal), dimension(constitutive_dislotwin_sizeState(myInstance)) :: & constitutive_dislotwin_relevantState ! relevant state values for the current instance of this constitution !*** local variables constitutive_dislotwin_relevantState = 1.0e-200_pReal endfunction function constitutive_dislotwin_homogenizedC(state,ipc,ip,el) !********************************************************************* !* calculates homogenized elacticity matrix * !* - state : microstructure quantities * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt,p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance implicit none !* Definition of variables integer(pInt), intent(in) :: ipc,ip,el integer(pInt) matID,ns,nt,i real(pReal) sumf real(pReal), dimension(6,6) :: constitutive_dislotwin_homogenizedC type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state !* Shortened notation matID = phase_constitutionInstance(material_phase(ipc,ip,el)) ns = constitutive_dislotwin_totalNslip(matID) nt = constitutive_dislotwin_totalNtwin(matID) !* Total twin volume fraction sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0 !* Homogenized elasticity matrix constitutive_dislotwin_homogenizedC = (1.0_pReal-sumf)*constitutive_dislotwin_Cslip_66(:,:,matID) do i=1,nt constitutive_dislotwin_homogenizedC = constitutive_dislotwin_homogenizedC + & state(ipc,ip,el)%p(ns+i)*constitutive_dislotwin_Ctwin_66(:,:,i,matID) enddo return end function subroutine constitutive_dislotwin_microstructure(Temperature,state,ipc,ip,el) !********************************************************************* !* calculates quantities characterizing the microstructure * !* - Temperature : temperature * !* - state : microstructure quantities * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: pi use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance use lattice, only: lattice_interactionSlipTwin,lattice_interactionTwinTwin implicit none !* Definition of variables integer(pInt), intent(in) :: ipc,ip,el integer(pInt) matID,ns,nt,i real(pReal) Temperature,sumf real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: fOverStacksize type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state !* Shortened notation matID = phase_constitutionInstance(material_phase(ipc,ip,el)) ns = constitutive_dislotwin_totalNslip(matID) nt = constitutive_dislotwin_totalNtwin(matID) !* State: 1 : ns rho_ssd !* State: ns+1 : ns+nt f !* State: ns+nt+1 : 2*ns+nt rho_forest !* State: 2*ns+nt+1 : 3*ns+nt rho_parallel !* State: 3*ns+nt+1 : 4*ns+nt 1/lambda_slip !* State: 4*ns+nt+1 : 5*ns+nt 1/lambda_sliptwin !* State: 5*ns+nt+1 : 5*ns+2*nt 1/lambda_twin !* State: 5*ns+2*nt+1 : 6*ns+2*nt mfp_slip !* State: 6*ns+2*nt+1 : 6*ns+3*nt mfp_twin !* State: 6*ns+3*nt+1 : 7*ns+3*nt threshold_stress_slip !* State: 7*ns+3*nt+1 : 7*ns+4*nt threshold_stress_twin !* State: 7*ns+4*nt+1 : 8*ns+4*nt activation volume !* State: 8*ns+4*nt+1 : 8*ns+5*nt twin volume !* State: 8*ns+5*nt+1 : 9*ns+5*nt rho_mobile !* State: 9*ns+5*nt+1 : 10*ns+5*nt initial shear rate !* Total twin volume fraction sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0 !* rescaled twin volume fraction for topology forall (i = 1:nt) & fOverStacksize(i) = state(ipc,ip,el)%p(ns+i)/constitutive_dislotwin_stacksize(constitutive_dislotwin_twinFamily(i,matID),matID) !* Forest and parallel dislocation densities !$OMP CRITICAL (evilmatmul) state(ipc,ip,el)%p((ns+nt+1):(2*ns+nt)) = & matmul(constitutive_dislotwin_forest_interaction(1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns)) state(ipc,ip,el)%p((2*ns+nt+1):(3*ns+nt)) = & matmul(constitutive_dislotwin_parall_interaction(1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns)) !$OMP END CRITICAL (evilmatmul) !* 1/mean free distance between 2 forest dislocations seen by a moving dislocation forall (i=1:ns) state(ipc,ip,el)%p(3*ns+nt+i) = sqrt(state(ipc,ip,el)%p(ns+nt+i)) !* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation !$OMP CRITICAL (evilmatmul) state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = 0.0_pReal if (nt > 0_pInt) state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = & matmul(constitutive_dislotwin_hardeningMatrix_sliptwin(1:ns,1:nt,matID),fOverStacksize(1:nt))/& (2.0_pReal*(1.0_pReal-sumf)) !$OMP END CRITICAL (evilmatmul) !* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin !$OMP CRITICAL (evilmatmul) if (nt > 0_pInt) state(ipc,ip,el)%p((5*ns+nt+1):(5*ns+2*nt)) = & matmul(constitutive_dislotwin_hardeningMatrix_twintwin(1:nt,1:nt,matID),fOverStacksize(1:nt))/& (2.0_pReal*(1.0_pReal-sumf)) !$OMP END CRITICAL (evilmatmul) !* mean free path between 2 obstacles seen by a moving dislocation do i=1,ns if (nt > 0_pInt) then state(ipc,ip,el)%p(5*ns+2*nt+i) = (constitutive_dislotwin_Cmfpslip(matID)*constitutive_dislotwin_grainsize(matID))/& (1.0_pReal+constitutive_dislotwin_grainsize(matID)*& (state(ipc,ip,el)%p(3*ns+nt+i)+state(ipc,ip,el)%p(4*ns+nt+i))) else state(ipc,ip,el)%p(5*ns+i) = (constitutive_dislotwin_Cmfpslip(matID)*constitutive_dislotwin_grainsize(matID))/& (1.0_pReal+constitutive_dislotwin_grainsize(matID)*(state(ipc,ip,el)%p(3*ns+i))) endif enddo !* mean free path between 2 obstacles seen by a growing twin forall (i=1:nt) & state(ipc,ip,el)%p(6*ns+2*nt+i) = (constitutive_dislotwin_Cmfptwin(matID)*constitutive_dislotwin_grainsize(matID))/& (1.0_pReal+constitutive_dislotwin_grainsize(matID)*state(ipc,ip,el)%p(5*ns+nt+i)) !* threshold stress for dislocation motion forall (i=1:ns) & state(ipc,ip,el)%p(6*ns+3*nt+i) = constitutive_dislotwin_Cthresholdslip(matID)*& constitutive_dislotwin_Burgers(constitutive_dislotwin_slipFamily(i,matID),matID)*& constitutive_dislotwin_Gmod(matID)*sqrt(state(ipc,ip,el)%p(2*ns+nt+i)) !* threshold stress for growing twin forall (i=1:nt) & state(ipc,ip,el)%p(7*ns+3*nt+i) = constitutive_dislotwin_Cthresholdtwin(matID)*(sqrt(3.0_pReal)/3.0_pReal)*(& (0.0002_pReal*Temperature-0.0396_pReal)/constitutive_dislotwin_Burgers(constitutive_dislotwin_slipFamily(i,matID),matID)+& (constitutive_dislotwin_Burgers(constitutive_dislotwin_slipFamily(i,matID),matID)*& constitutive_dislotwin_Gmod(matID))/state(ipc,ip,el)%p(5*ns+2*nt+i)) !* activation volume for dislocation glide forall (i=1:ns) & state(ipc,ip,el)%p(7*ns+4*nt+i) = constitutive_dislotwin_Cactivolume(matID)*& constitutive_dislotwin_Burgers(constitutive_dislotwin_slipFamily(i,matID),matID)**2*state(ipc,ip,el)%p(5*ns+2*nt+i) !* final twin volume after growth forall (i=1:nt) & state(ipc,ip,el)%p(8*ns+4*nt+i) = (pi/6.0_pReal)*& constitutive_dislotwin_stacksize(constitutive_dislotwin_twinFamily(i,matID),matID)*& state(ipc,ip,el)%p(6*ns+2*nt+i)*state(ipc,ip,el)%p(6*ns+2*nt+i) !* mobile dislocation densities forall (i=1:ns) & state(ipc,ip,el)%p(8*ns+5*nt+i) = (2.0_pReal*kB*Temperature*state(ipc,ip,el)%p(2*ns+nt+i))/& (state(ipc,ip,el)%p(6*ns+3*nt+i)*state(ipc,ip,el)%p(7*ns+4*nt+i)) !* initial shear rate for slip forall (i=1:ns) & state(ipc,ip,el)%p(9*ns+5*nt+i) = state(ipc,ip,el)%p(8*ns+5*nt+i)*& constitutive_dislotwin_Burgers(constitutive_dislotwin_slipFamily(i,matID),matID)*& attack_frequency*state(ipc,ip,el)%p(5*ns+2*nt+i)*& exp(-constitutive_dislotwin_Qedge(constitutive_dislotwin_slipFamily(i,matID),matID)/& ! -------------------- (kB*Temperature)) end subroutine subroutine constitutive_dislotwin_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el) !********************************************************************* !* calculates plastic velocity gradient and its tangent * !* INPUT: * !* - Temperature : temperature * !* - state : microstructure quantities * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - Lp : plastic velocity gradient * !* - dLp_dTstar : derivative of Lp (4th-rank tensor) * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: math_Plain3333to99 use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,structID,ns,nt,f,i,j,k,l,m,n,index_myFamily real(pReal) Temperature,sumf type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(3,3) :: Lp real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(9,9) :: dLp_dTstar real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & gdot_slip,dgdot_dtauslip,tau_slip real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & gdot_twin,dgdot_dtautwin,tau_twin !* Shortened notation matID = phase_constitutionInstance(material_phase(ipc,ip,el)) structID = constitutive_dislotwin_structure(matID) ns = constitutive_dislotwin_totalNslip(matID) nt = constitutive_dislotwin_totalNtwin(matID) !* Total twin volume fraction sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0 Lp = 0.0_pReal dLp_dTstar3333 = 0.0_pReal dLp_dTstar = 0.0_pReal !* Dislocation glide part gdot_slip = 0.0_pReal dgdot_dtauslip = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Nslip(f,matID) ! process each (active) slip system in family j = j+1_pInt !* Calculation of Lp tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID)) if ( abs(tau_slip(j)) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then gdot_slip(j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau_slip(j))*& sinh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)) dgdot_dtauslip(j) = (state(ipc,ip,el)%p(9*ns+5*nt+j)*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)*& cosh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)) endif Lp = Lp + (1.0_pReal - sumf)*gdot_slip(j)*lattice_Sslip(:,:,index_myFamily+i,structID) !* Calculation of the tangent of Lp forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*lattice_Sslip(k,l,index_myFamily+i,structID) & *lattice_Sslip(m,n,index_myFamily+i,structID) enddo enddo !* Mechanical twinning part gdot_twin = 0.0_pReal dgdot_dtautwin = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all slip families index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Ntwin(f,matID) ! process each (active) slip system in family j = j+1_pInt !* Calculation of Lp tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID)) if ( tau_twin(j) > 0.0_pReal ) then gdot_twin(j) = (constitutive_dislotwin_fmax(matID) - sumf)*lattice_shearTwin(index_myFamily+i,structID)*& state(ipc,ip,el)%p(8*ns+4*nt+j)*constitutive_dislotwin_Ndot0(f,matID)*& exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau_twin(j))**10.0_pReal) dgdot_dtautwin(j) = (gdot_twin(j)*10.0_pReal*state(ipc,ip,el)%p(7*ns+3*nt+j)**10.0_pReal)/(tau_twin(j)**11.0_pReal) endif Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,structID) !* Calculation of the tangent of Lp forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + dgdot_dtautwin(j)*lattice_Stwin(k,l,index_myFamily+i,structID) & *lattice_Stwin(m,n,index_myFamily+i,structID) enddo enddo dLp_dTstar = math_Plain3333to99(dLp_dTstar3333) return end subroutine function constitutive_dislotwin_dotState(Tstar_v,Temperature,state,ipc,ip,el) !********************************************************************* !* rate of change of microstructure * !* INPUT: * !* - Temperature : temperature * !* - state : microstructure quantities * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_dotState : evolution of state variable * !********************************************************************* use prec, only: pReal,pInt,p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,structID,ns,nt,f,i,j,k,index_myFamily real(pReal) Temperature,sumf type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & gdot_slip,tau_slip,storage,arecovery real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & gdot_twin,tau_twin real(pReal), dimension(constitutive_dislotwin_sizeDotState(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & constitutive_dislotwin_dotState !* Shortened notation matID = phase_constitutionInstance(material_phase(ipc,ip,el)) structID = constitutive_dislotwin_structure(matID) ns = constitutive_dislotwin_totalNslip(matID) nt = constitutive_dislotwin_totalNtwin(matID) !* Total twin volume fraction sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0 constitutive_dislotwin_dotState = 0.0_pReal !* Dislocation density evolution gdot_slip = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Nslip(f,matID) ! process each (active) slip system in family j = j+1_pInt !* Calculation of Lp tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID)) if ( abs(tau_slip(j)) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then gdot_slip(j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau_slip(j))* & sinh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)) storage(j) = (constitutive_dislotwin_Cstorage(matID)*abs(gdot_slip(j)))/& (constitutive_dislotwin_Burgers(f,matID)*state(ipc,ip,el)%p(5*ns+2*nt+j)) arecovery(j) = constitutive_dislotwin_Carecovery(matID)*state(ipc,ip,el)%p(j)*abs(gdot_slip(j)) constitutive_dislotwin_dotState(j) = storage(j) - arecovery(j) endif enddo enddo !* Twin volume fraction evolution gdot_twin = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all twin families index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Ntwin(f,matID) ! process each (active) twin system in family j = j+1_pInt !* Calculation of Lp tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID)) if ( tau_twin(j) > 0.0_pReal ) & constitutive_dislotwin_dotState(ns+j) = (constitutive_dislotwin_fmax(matID) - sumf)* & lattice_shearTwin(index_myFamily+i,structID)*state(ipc,ip,el)%p(8*ns+4*nt+j)*constitutive_dislotwin_Ndot0(f,matID)*& exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau_twin(j))**10.0_pReal) enddo enddo return end function function constitutive_dislotwin_dotTemperature(Tstar_v,Temperature,state,ipc,ip,el) !********************************************************************* !* rate of change of microstructure * !* INPUT: * !* - Temperature : temperature * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_dotTemperature : evolution of Temperature * !********************************************************************* use prec, only: pReal,pInt,p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains implicit none !* Definition of variables integer(pInt) ipc,ip,el real(pReal) Temperature type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal) constitutive_dislotwin_dotTemperature constitutive_dislotwin_dotTemperature = 0.0_pReal return end function pure function constitutive_dislotwin_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Temperature : temperature * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - dt : current time increment * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt,p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput use lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Definition of variables integer(pInt), intent(in) :: ipc,ip,el real(pReal), intent(in) :: dt,Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state integer(pInt) matID,structID,ns,nt,f,o,i,c,j,index_myFamily real(pReal) sumf,tau real(pReal), dimension(constitutive_dislotwin_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & constitutive_dislotwin_postResults !* Shortened notation matID = phase_constitutionInstance(material_phase(ipc,ip,el)) structID = constitutive_dislotwin_structure(matID) ns = constitutive_dislotwin_totalNslip(matID) nt = constitutive_dislotwin_totalNtwin(matID) !* Total twin volume fraction sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0 !* Required output c = 0_pInt constitutive_dislotwin_postResults = 0.0_pReal do o = 1,phase_Noutput(material_phase(ipc,ip,el)) select case(constitutive_dislotwin_output(o,matID)) case ('dislocationdensity') constitutive_dislotwin_postResults(c+1:c+ns) = state(ipc,ip,el)%p(1:ns) c = c + ns case ('shearrate_slip') j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Nslip(f,matID) ! process each (active) slip system in family j = j + 1_pInt tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID)) if ( abs(tau) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then constitutive_dislotwin_postResults(c+j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau)* & sinh(((abs(tau)-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)) else constitutive_dislotwin_postResults(c+j) = 0.0_pReal endif enddo ; enddo c = c + ns case ('mfp_slip') constitutive_dislotwin_postResults(c+1:c+ns) = state(ipc,ip,el)%p((5*ns+2*nt+1):(6*ns+2*nt)) c = c + ns case ('resolvedstress_slip') j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Nslip(f,matID) ! process each (active) slip system in family j = j + 1_pInt constitutive_dislotwin_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID)) enddo; enddo c = c + ns case ('resistance_slip') constitutive_dislotwin_postResults(c+1:c+ns) = state(ipc,ip,el)%p((6*ns+3*nt+1):(7*ns+3*nt)) c = c + ns case ('volumefraction') constitutive_dislotwin_postResults(c+1:c+nt) = state(ipc,ip,el)%p((ns+1):(ns+nt)) c = c + nt case ('shearrate_twin') if (nt > 0_pInt) then j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all slip families index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Ntwin(f,matID) ! process each (active) slip system in family j = j + 1_pInt tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID)) if ( tau > 0.0_pReal ) then constitutive_dislotwin_postResults(c+j) = (constitutive_dislotwin_fmax(matID) - sumf)* & lattice_shearTwin(index_myFamily+i,structID)*state(ipc,ip,el)%p(8*ns+4*nt+j)* & constitutive_dislotwin_Ndot0(f,matID)*exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau)**10.0_pReal) else constitutive_dislotwin_postResults(c+j) = 0.0_pReal endif enddo ; enddo endif c = c + nt case ('mfp_twin') constitutive_dislotwin_postResults(c+1:c+nt) = state(ipc,ip,el)%p((6*ns+2*nt+1):(6*ns+3*nt)) c = c + nt case ('resolvedstress_twin') if (nt > 0_pInt) then j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all slip families index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family do i = 1,constitutive_dislotwin_Ntwin(f,matID) ! process each (active) slip system in family j = j + 1_pInt constitutive_dislotwin_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID)) enddo; enddo endif c = c + nt case ('resistance_twin') constitutive_dislotwin_postResults(c+1:c+nt) = state(ipc,ip,el)%p((7*ns+3*nt+1):(7*ns+4*nt)) c = c + nt end select enddo return end function END MODULE