From cc6aa1aeba6eaf46276c3f56395b257a1e3f814c Mon Sep 17 00:00:00 2001 From: Luc Hantcherli Date: Tue, 6 Oct 2009 15:19:19 +0000 Subject: [PATCH] Updated constitutive_dislotwin Deleted constitutive_dislobased --- code/constitutive_dislotwin.f90 | 1108 +++++++++++++++++++++++++++++++ 1 file changed, 1108 insertions(+) create mode 100644 code/constitutive_dislotwin.f90 diff --git a/code/constitutive_dislotwin.f90 b/code/constitutive_dislotwin.f90 new file mode 100644 index 000000000..ebb2a266e --- /dev/null +++ b/code/constitutive_dislotwin.f90 @@ -0,0 +1,1108 @@ +!* $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 \ No newline at end of file