!-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @brief contains lattice structure definitions including Schmid matrices for slip, twin, trans, ! and cleavage as well as interaction among the various systems !-------------------------------------------------------------------------------------------------- module lattice use prec use IO use config use math implicit none private ! BEGIN DEPRECATED integer, parameter, public :: & LATTICE_maxNcleavageFamily = 3 !< max # of transformation system families over lattice structures integer, allocatable, dimension(:,:), protected, public :: & lattice_NcleavageSystem !< total # of transformation systems in each family real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: & lattice_Scleavage !< Schmid matrices for cleavage systems ! END DEPRECATED !-------------------------------------------------------------------------------------------------- ! face centered cubic integer, dimension(2), parameter :: & LATTICE_FCC_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for fcc integer, dimension(1), parameter :: & LATTICE_FCC_NTWINSYSTEM = [12] !< # of twin systems per family for fcc integer, dimension(1), parameter :: & LATTICE_FCC_NTRANSSYSTEM = [12] !< # of transformation systems per family for fcc integer, dimension(2), parameter :: & LATTICE_FCC_NCLEAVAGESYSTEM = [3, 4] !< # of cleavage systems per family for fcc integer, parameter :: & LATTICE_FCC_NSLIP = sum(LATTICE_FCC_NSLIPSYSTEM), & !< total # of slip systems for fcc LATTICE_FCC_NTWIN = sum(LATTICE_FCC_NTWINSYSTEM), & !< total # of twin systems for fcc LATTICE_FCC_NTRANS = sum(LATTICE_FCC_NTRANSSYSTEM), & !< total # of transformation systems for fcc LATTICE_FCC_NCLEAVAGE = sum(LATTICE_FCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for fcc real(pReal), dimension(3+3,LATTICE_FCC_NSLIP), parameter :: & LATTICE_FCC_SYSTEMSLIP = reshape(real([& ! Slip direction Plane normal ! SCHMID-BOAS notation 0, 1,-1, 1, 1, 1, & ! B2 -1, 0, 1, 1, 1, 1, & ! B4 1,-1, 0, 1, 1, 1, & ! B5 0,-1,-1, -1,-1, 1, & ! C1 1, 0, 1, -1,-1, 1, & ! C3 -1, 1, 0, -1,-1, 1, & ! C5 0,-1, 1, 1,-1,-1, & ! A2 -1, 0,-1, 1,-1,-1, & ! A3 1, 1, 0, 1,-1,-1, & ! A6 0, 1, 1, -1, 1,-1, & ! D1 1, 0,-1, -1, 1,-1, & ! D4 -1,-1, 0, -1, 1,-1, & ! D6 ! Slip system <110>{110} 1, 1, 0, 1,-1, 0, & 1,-1, 0, 1, 1, 0, & 1, 0, 1, 1, 0,-1, & 1, 0,-1, 1, 0, 1, & 0, 1, 1, 0, 1,-1, & 0, 1,-1, 0, 1, 1 & ],pReal),shape(LATTICE_FCC_SYSTEMSLIP)) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli character(len=*), dimension(2), parameter :: LATTICE_FCC_SLIPFAMILY_NAME = & ['<0 1 -1>{1 1 1}', & '<0 1 -1>{0 1 1}'] real(pReal), dimension(3+3,LATTICE_FCC_NTWIN), parameter :: & LATTICE_FCC_SYSTEMTWIN = reshape(real( [& -2, 1, 1, 1, 1, 1, & 1,-2, 1, 1, 1, 1, & 1, 1,-2, 1, 1, 1, & 2,-1, 1, -1,-1, 1, & -1, 2, 1, -1,-1, 1, & -1,-1,-2, -1,-1, 1, & -2,-1,-1, 1,-1,-1, & 1, 2,-1, 1,-1,-1, & 1,-1, 2, 1,-1,-1, & 2, 1,-1, -1, 1,-1, & -1,-2,-1, -1, 1,-1, & -1, 1, 2, -1, 1,-1 & ],pReal),shape(LATTICE_FCC_SYSTEMTWIN)) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli character(len=*), dimension(1), parameter :: LATTICE_FCC_TWINFAMILY_NAME = & ['<-2 1 1>{1 1 1}'] integer, dimension(2,LATTICE_FCC_NTWIN), parameter, public :: & LATTICE_FCC_TWINNUCLEATIONSLIPPAIR = reshape( [& 2,3, & 1,3, & 1,2, & 5,6, & 4,6, & 4,5, & 8,9, & 7,9, & 7,8, & 11,12, & 10,12, & 10,11 & ],shape(LATTICE_FCC_TWINNUCLEATIONSLIPPAIR)) real(pReal), dimension(3+3,LATTICE_FCC_NCLEAVAGE), parameter :: & LATTICE_FCC_SYSTEMCLEAVAGE = reshape(real([& ! Cleavage direction Plane normal 0, 1, 0, 1, 0, 0, & 0, 0, 1, 0, 1, 0, & 1, 0, 0, 0, 0, 1, & 0, 1,-1, 1, 1, 1, & 0,-1,-1, -1,-1, 1, & -1, 0,-1, 1,-1,-1, & 0, 1, 1, -1, 1,-1 & ],pReal),shape(LATTICE_FCC_SYSTEMCLEAVAGE)) !-------------------------------------------------------------------------------------------------- ! body centered cubic integer, dimension(2), parameter :: & LATTICE_BCC_NSLIPSYSTEM = [12, 12] !< # of slip systems per family for bcc integer, dimension(1), parameter :: & LATTICE_BCC_NTWINSYSTEM = [12] !< # of twin systems per family for bcc integer, dimension(2), parameter :: & LATTICE_BCC_NCLEAVAGESYSTEM = [3, 6] !< # of cleavage systems per family for bcc integer, parameter :: & LATTICE_BCC_NSLIP = sum(LATTICE_BCC_NSLIPSYSTEM), & !< total # of slip systems for bcc LATTICE_BCC_NTWIN = sum(LATTICE_BCC_NTWINSYSTEM), & !< total # of twin systems for bcc LATTICE_BCC_NCLEAVAGE = sum(LATTICE_BCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for bcc real(pReal), dimension(3+3,LATTICE_BCC_NSLIP), parameter :: & LATTICE_BCC_SYSTEMSLIP = reshape(real([& ! Slip direction Plane normal ! Slip system <111>{110} 1,-1, 1, 0, 1, 1, & -1,-1, 1, 0, 1, 1, & 1, 1, 1, 0,-1, 1, & -1, 1, 1, 0,-1, 1, & -1, 1, 1, 1, 0, 1, & -1,-1, 1, 1, 0, 1, & 1, 1, 1, -1, 0, 1, & 1,-1, 1, -1, 0, 1, & -1, 1, 1, 1, 1, 0, & -1, 1,-1, 1, 1, 0, & 1, 1, 1, -1, 1, 0, & 1, 1,-1, -1, 1, 0, & ! Slip system <111>{112} -1, 1, 1, 2, 1, 1, & 1, 1, 1, -2, 1, 1, & 1, 1,-1, 2,-1, 1, & 1,-1, 1, 2, 1,-1, & 1,-1, 1, 1, 2, 1, & 1, 1,-1, -1, 2, 1, & 1, 1, 1, 1,-2, 1, & -1, 1, 1, 1, 2,-1, & 1, 1,-1, 1, 1, 2, & 1,-1, 1, -1, 1, 2, & -1, 1, 1, 1,-1, 2, & 1, 1, 1, 1, 1,-2 & ],pReal),shape(LATTICE_BCC_SYSTEMSLIP)) character(len=*), dimension(2), parameter :: LATTICE_BCC_SLIPFAMILY_NAME = & ['<1 -1 1>{0 1 1}', & '<1 -1 1>{2 1 1}'] real(pReal), dimension(3+3,LATTICE_BCC_NTWIN), parameter :: & LATTICE_BCC_SYSTEMTWIN = reshape(real([& ! Twin system <111>{112} -1, 1, 1, 2, 1, 1, & 1, 1, 1, -2, 1, 1, & 1, 1,-1, 2,-1, 1, & 1,-1, 1, 2, 1,-1, & 1,-1, 1, 1, 2, 1, & 1, 1,-1, -1, 2, 1, & 1, 1, 1, 1,-2, 1, & -1, 1, 1, 1, 2,-1, & 1, 1,-1, 1, 1, 2, & 1,-1, 1, -1, 1, 2, & -1, 1, 1, 1,-1, 2, & 1, 1, 1, 1, 1,-2 & ],pReal),shape(LATTICE_BCC_SYSTEMTWIN)) character(len=*), dimension(1), parameter :: LATTICE_BCC_TWINFAMILY_NAME = & ['<1 1 1>{2 1 1}'] real(pReal), dimension(3+3,LATTICE_BCC_NCLEAVAGE), parameter :: & LATTICE_BCC_SYSTEMCLEAVAGE = reshape(real([& ! Cleavage direction Plane normal 0, 1, 0, 1, 0, 0, & 0, 0, 1, 0, 1, 0, & 1, 0, 0, 0, 0, 1, & 1,-1, 1, 0, 1, 1, & 1, 1, 1, 0,-1, 1, & -1, 1, 1, 1, 0, 1, & 1, 1, 1, -1, 0, 1, & -1, 1, 1, 1, 1, 0, & 1, 1, 1, -1, 1, 0 & ],pReal),shape(LATTICE_BCC_SYSTEMCLEAVAGE)) !-------------------------------------------------------------------------------------------------- ! hexagonal integer, dimension(6), parameter :: & LATTICE_HEX_NSLIPSYSTEM = [3, 3, 3, 6, 12, 6] !< # of slip systems per family for hex integer, dimension(4), parameter :: & LATTICE_HEX_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hex integer, dimension(1), parameter :: & LATTICE_HEX_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for hex integer, parameter :: & LATTICE_HEX_NSLIP = sum(LATTICE_HEX_NSLIPSYSTEM), & !< total # of slip systems for hex LATTICE_HEX_NTWIN = sum(LATTICE_HEX_NTWINSYSTEM), & !< total # of twin systems for hex LATTICE_HEX_NCLEAVAGE = sum(LATTICE_HEX_NCLEAVAGESYSTEM) !< total # of cleavage systems for hex real(pReal), dimension(4+4,LATTICE_HEX_NSLIP), parameter :: & LATTICE_HEX_SYSTEMSLIP = reshape(real([& ! Slip direction Plane normal ! Basal systems <11.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base)) 2, -1, -1, 0, 0, 0, 0, 1, & -1, 2, -1, 0, 0, 0, 0, 1, & -1, -1, 2, 0, 0, 0, 0, 1, & ! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio) 2, -1, -1, 0, 0, 1, -1, 0, & -1, 2, -1, 0, -1, 0, 1, 0, & -1, -1, 2, 0, 1, -1, 0, 0, & ! 2nd type prismatic systems <10.0>{11.0} -- a slip; plane normals independent of c/a-ratio 0, 1, -1, 0, 2, -1, -1, 0, & -1, 0, 1, 0, -1, 2, -1, 0, & 1, -1, 0, 0, -1, -1, 2, 0, & ! 1st type 1st order pyramidal systems <11.0>{-11.1} -- plane normals depend on the c/a-ratio 2, -1, -1, 0, 0, 1, -1, 1, & -1, 2, -1, 0, -1, 0, 1, 1, & -1, -1, 2, 0, 1, -1, 0, 1, & 1, 1, -2, 0, -1, 1, 0, 1, & -2, 1, 1, 0, 0, -1, 1, 1, & 1, -2, 1, 0, 1, 0, -1, 1, & ! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the c/a-ratio 2, -1, -1, 3, -1, 1, 0, 1, & 1, -2, 1, 3, -1, 1, 0, 1, & -1, -1, 2, 3, 1, 0, -1, 1, & -2, 1, 1, 3, 1, 0, -1, 1, & -1, 2, -1, 3, 0, -1, 1, 1, & 1, 1, -2, 3, 0, -1, 1, 1, & -2, 1, 1, 3, 1, -1, 0, 1, & -1, 2, -1, 3, 1, -1, 0, 1, & 1, 1, -2, 3, -1, 0, 1, 1, & 2, -1, -1, 3, -1, 0, 1, 1, & 1, -2, 1, 3, 0, 1, -1, 1, & -1, -1, 2, 3, 0, 1, -1, 1, & ! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below) 2, -1, -1, 3, -2, 1, 1, 2, & ! sorted according to similar twin system -1, 2, -1, 3, 1, -2, 1, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a) -1, -1, 2, 3, 1, 1, -2, 2, & -2, 1, 1, 3, 2, -1, -1, 2, & 1, -2, 1, 3, -1, 2, -1, 2, & 1, 1, -2, 3, -1, -1, 2, 2 & ],pReal),shape(LATTICE_HEX_SYSTEMSLIP)) !< slip systems for hex sorted by A. Alankar & P. Eisenlohr character(len=*), dimension(6), parameter :: LATTICE_HEX_SLIPFAMILY_NAME = & ['<1 1 . 1>{0 0 . 1} ', & '<1 1 . 1>{1 0 . 0} ', & '<1 0 . 0>{1 1 . 0} ', & '<1 1 . 0>{-1 1 . 1} ', & '<1 1 . 3>{-1 0 . 1} ', & '<1 1 . 3>{-1 -1 . 2}'] real(pReal), dimension(4+4,LATTICE_HEX_NTWIN), parameter :: & LATTICE_HEX_SYSTEMTWIN = reshape(real([& ! Compression or Tension =f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981) 1, -1, 0, 1, -1, 1, 0, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a) -1, 0, 1, 1, 1, 0, -1, 2, & 0, 1, -1, 1, 0, -1, 1, 2, & -1, 1, 0, 1, 1, -1, 0, 2, & 1, 0, -1, 1, -1, 0, 1, 2, & 0, -1, 1, 1, 0, 1, -1, 2, & ! 2, -1, -1, 6, -2, 1, 1, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a) -1, 2, -1, 6, 1, -2, 1, 1, & -1, -1, 2, 6, 1, 1, -2, 1, & -2, 1, 1, 6, 2, -1, -1, 1, & 1, -2, 1, 6, -1, 2, -1, 1, & 1, 1, -2, 6, -1, -1, 2, 1, & ! -1, 1, 0, -2, -1, 1, 0, 1, & !! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) 1, 0, -1, -2, 1, 0, -1, 1, & 0, -1, 1, -2, 0, -1, 1, 1, & 1, -1, 0, -2, 1, -1, 0, 1, & -1, 0, 1, -2, -1, 0, 1, 1, & 0, 1, -1, -2, 0, 1, -1, 1, & ! 2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a) -1, 2, -1, -3, -1, 2, -1, 2, & -1, -1, 2, -3, -1, -1, 2, 2, & -2, 1, 1, -3, -2, 1, 1, 2, & 1, -2, 1, -3, 1, -2, 1, 2, & 1, 1, -2, -3, 1, 1, -2, 2 & ],pReal),shape(LATTICE_HEX_SYSTEMTWIN)) !< twin systems for hex, order follows Prof. Tom Bieler's scheme character(len=*), dimension(4), parameter :: LATTICE_HEX_TWINFAMILY_NAME = & ['<-1 0 . 1>{1 0 . 2} ', & '<1 1 . 6>{-1 -1 . 1}', & '<1 0 . -2>{1 0 . 1} ', & '<1 1 . -3>{1 1 . 2} '] real(pReal), dimension(4+4,LATTICE_HEX_NCLEAVAGE), parameter :: & LATTICE_HEX_SYSTEMCLEAVAGE = reshape(real([& ! Cleavage direction Plane normal 2,-1,-1, 0, 0, 0, 0, 1, & 0, 0, 0, 1, 2,-1,-1, 0, & 0, 0, 0, 1, 0, 1,-1, 0 & ],pReal),shape(LATTICE_HEX_SYSTEMCLEAVAGE)) !-------------------------------------------------------------------------------------------------- ! body centered tetragonal integer, dimension(13), parameter :: & LATTICE_BCT_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009 integer, parameter :: & LATTICE_BCT_NSLIP = sum(LATTICE_BCT_NSLIPSYSTEM) !< total # of slip systems for bct real(pReal), dimension(3+3,LATTICE_BCT_NSLIP), parameter :: & LATTICE_BCT_SYSTEMSLIP = reshape(real([& ! Slip direction Plane normal ! Slip family 1 {100)<001] (Bravais notation {hkl) @brief Module initialization !-------------------------------------------------------------------------------------------------- subroutine lattice_init integer :: Nphases character(len=65536) :: & tag = '' integer :: i,p real(pReal), dimension(:), allocatable :: & temp, & CoverA !< c/a ratio for low symmetry type lattice write(6,'(/,a)') ' <<<+- lattice init -+>>>' Nphases = size(config_phase) allocate(lattice_structure(Nphases),source = LATTICE_undefined_ID) allocate(lattice_C66(6,6,Nphases), source=0.0_pReal) allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal) allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients allocate(lattice_thermalConductivity33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_damageDiffusion33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_damageMobility ( Nphases), source=0.0_pReal) allocate(lattice_massDensity ( Nphases), source=0.0_pReal) allocate(lattice_specificHeat ( Nphases), source=0.0_pReal) allocate(lattice_referenceTemperature ( Nphases), source=300.0_pReal) allocate(lattice_mu(Nphases), source=0.0_pReal) allocate(lattice_nu(Nphases), source=0.0_pReal) allocate(lattice_Scleavage(3,3,3,lattice_maxNcleavage,Nphases),source=0.0_pReal) allocate(lattice_NcleavageSystem(lattice_maxNcleavageFamily,Nphases),source=0) allocate(CoverA(Nphases),source=0.0_pReal) do p = 1, size(config_phase) tag = config_phase(p)%getString('lattice_structure') select case(trim(tag(1:3))) case('iso') lattice_structure(p) = LATTICE_iso_ID case('fcc') lattice_structure(p) = LATTICE_fcc_ID case('bcc') lattice_structure(p) = LATTICE_bcc_ID case('hex') lattice_structure(p) = LATTICE_hex_ID case('bct') lattice_structure(p) = LATTICE_bct_ID case('ort') lattice_structure(p) = LATTICE_ort_ID end select lattice_C66(1,1,p) = config_phase(p)%getFloat('c11',defaultVal=0.0_pReal) lattice_C66(1,2,p) = config_phase(p)%getFloat('c12',defaultVal=0.0_pReal) lattice_C66(1,3,p) = config_phase(p)%getFloat('c13',defaultVal=0.0_pReal) lattice_C66(2,2,p) = config_phase(p)%getFloat('c22',defaultVal=0.0_pReal) lattice_C66(2,3,p) = config_phase(p)%getFloat('c23',defaultVal=0.0_pReal) lattice_C66(3,3,p) = config_phase(p)%getFloat('c33',defaultVal=0.0_pReal) lattice_C66(4,4,p) = config_phase(p)%getFloat('c44',defaultVal=0.0_pReal) lattice_C66(5,5,p) = config_phase(p)%getFloat('c55',defaultVal=0.0_pReal) lattice_C66(6,6,p) = config_phase(p)%getFloat('c66',defaultVal=0.0_pReal) CoverA(p) = config_phase(p)%getFloat('c/a',defaultVal=0.0_pReal) lattice_thermalConductivity33(1,1,p) = config_phase(p)%getFloat('thermal_conductivity11',defaultVal=0.0_pReal) lattice_thermalConductivity33(2,2,p) = config_phase(p)%getFloat('thermal_conductivity22',defaultVal=0.0_pReal) lattice_thermalConductivity33(3,3,p) = config_phase(p)%getFloat('thermal_conductivity33',defaultVal=0.0_pReal) temp = config_phase(p)%getFloats('thermal_expansion11',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(1,1,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion22',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(2,2,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion33',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(3,3,1:size(temp),p) = temp lattice_specificHeat(p) = config_phase(p)%getFloat( 'specific_heat',defaultVal=0.0_pReal) lattice_massDensity(p) = config_phase(p)%getFloat( 'mass_density',defaultVal=0.0_pReal) lattice_referenceTemperature(p) = config_phase(p)%getFloat( 'reference_temperature',defaultVal=0.0_pReal) lattice_DamageDiffusion33(1,1,p) = config_phase(p)%getFloat( 'damage_diffusion11',defaultVal=0.0_pReal) lattice_DamageDiffusion33(2,2,p) = config_phase(p)%getFloat( 'damage_diffusion22',defaultVal=0.0_pReal) lattice_DamageDiffusion33(3,3,p) = config_phase(p)%getFloat( 'damage_diffusion33',defaultVal=0.0_pReal) lattice_DamageMobility(p) = config_phase(p)%getFloat( 'damage_mobility',defaultVal=0.0_pReal) enddo do i = 1,Nphases if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) & .and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(131,el=i) ! checking physical significance of c/a if ((CoverA(i) > 2.0_pReal) & .and. lattice_structure(i) == LATTICE_bct_ID) call IO_error(131,el=i) ! checking physical significance of c/a call lattice_initializeStructure(i, CoverA(i)) enddo end subroutine lattice_init !-------------------------------------------------------------------------------------------------- !> @brief !!!!!!!DEPRECTATED!!!!!! !-------------------------------------------------------------------------------------------------- subroutine lattice_initializeStructure(myPhase,CoverA) integer, intent(in) :: myPhase real(pReal), intent(in) :: & CoverA integer :: & i, & myNcleavage lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),& lattice_C66(1:6,1:6,myPhase)) lattice_mu(myPhase) = 0.2_pReal *( lattice_C66(1,1,myPhase) & - lattice_C66(1,2,myPhase) & + 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 lattice_nu(myPhase) = ( lattice_C66(1,1,myPhase) & + 4.0_pReal*lattice_C66(1,2,myPhase) & - 2.0_pReal*lattice_C66(4,4,myPhase)) & /( 4.0_pReal*lattice_C66(1,1,myPhase) & + 6.0_pReal*lattice_C66(1,2,myPhase) & + 2.0_pReal*lattice_C66(4,4,myPhase))! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt lattice_C66(1:6,1:6,myPhase) = math_sym3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel-weighting do i = 1, 6 if (abs(lattice_C66(i,i,myPhase)) @brief Symmetrizes stiffness matrix according to lattice type !> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962 !-------------------------------------------------------------------------------------------------- pure function lattice_symmetrizeC66(struct,C66) integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(6,6), intent(in) :: C66 real(pReal), dimension(6,6) :: lattice_symmetrizeC66 integer :: j,k lattice_symmetrizeC66 = 0.0_pReal select case(struct) case (LATTICE_iso_ID) do k=1,3 forall(j=1:3) lattice_symmetrizeC66(k,j) = C66(1,2) lattice_symmetrizeC66(k,k) = C66(1,1) lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2)) enddo case (LATTICE_fcc_ID,LATTICE_bcc_ID) do k=1,3 forall(j=1:3) lattice_symmetrizeC66(k,j) = C66(1,2) lattice_symmetrizeC66(k,k) = C66(1,1) lattice_symmetrizeC66(k+3,k+3) = C66(4,4) enddo case (LATTICE_hex_ID) lattice_symmetrizeC66(1,1) = C66(1,1) lattice_symmetrizeC66(2,2) = C66(1,1) lattice_symmetrizeC66(3,3) = C66(3,3) lattice_symmetrizeC66(1,2) = C66(1,2) lattice_symmetrizeC66(2,1) = C66(1,2) lattice_symmetrizeC66(1,3) = C66(1,3) lattice_symmetrizeC66(3,1) = C66(1,3) lattice_symmetrizeC66(2,3) = C66(1,3) lattice_symmetrizeC66(3,2) = C66(1,3) lattice_symmetrizeC66(4,4) = C66(4,4) lattice_symmetrizeC66(5,5) = C66(4,4) lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2)) case (LATTICE_ort_ID) lattice_symmetrizeC66(1,1) = C66(1,1) lattice_symmetrizeC66(2,2) = C66(2,2) lattice_symmetrizeC66(3,3) = C66(3,3) lattice_symmetrizeC66(1,2) = C66(1,2) lattice_symmetrizeC66(2,1) = C66(1,2) lattice_symmetrizeC66(1,3) = C66(1,3) lattice_symmetrizeC66(3,1) = C66(1,3) lattice_symmetrizeC66(2,3) = C66(2,3) lattice_symmetrizeC66(3,2) = C66(2,3) lattice_symmetrizeC66(4,4) = C66(4,4) lattice_symmetrizeC66(5,5) = C66(5,5) lattice_symmetrizeC66(6,6) = C66(6,6) case (LATTICE_bct_ID) lattice_symmetrizeC66(1,1) = C66(1,1) lattice_symmetrizeC66(2,2) = C66(1,1) lattice_symmetrizeC66(3,3) = C66(3,3) lattice_symmetrizeC66(1,2) = C66(1,2) lattice_symmetrizeC66(2,1) = C66(1,2) lattice_symmetrizeC66(1,3) = C66(1,3) lattice_symmetrizeC66(3,1) = C66(1,3) lattice_symmetrizeC66(2,3) = C66(1,3) lattice_symmetrizeC66(3,2) = C66(1,3) lattice_symmetrizeC66(4,4) = C66(4,4) lattice_symmetrizeC66(5,5) = C66(4,4) lattice_symmetrizeC66(6,6) = C66(6,6) case default lattice_symmetrizeC66 = C66 end select end function lattice_symmetrizeC66 !-------------------------------------------------------------------------------------------------- !> @brief Symmetrizes 2nd order tensor according to lattice type !-------------------------------------------------------------------------------------------------- pure function lattice_symmetrize33(struct,T33) integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(3,3), intent(in) :: T33 real(pReal), dimension(3,3) :: lattice_symmetrize33 integer :: k lattice_symmetrize33 = 0.0_pReal select case(struct) case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID) do k=1,3 lattice_symmetrize33(k,k) = T33(1,1) enddo case (LATTICE_hex_ID) lattice_symmetrize33(1,1) = T33(1,1) lattice_symmetrize33(2,2) = T33(1,1) lattice_symmetrize33(3,3) = T33(3,3) case (LATTICE_ort_ID,lattice_bct_ID) lattice_symmetrize33(1,1) = T33(1,1) lattice_symmetrize33(2,2) = T33(2,2) lattice_symmetrize33(3,3) = T33(3,3) case default lattice_symmetrize33 = T33 end select end function lattice_symmetrize33 !-------------------------------------------------------------------------------------------------- !> @brief figures whether unit quat falls into stereographic standard triangle !-------------------------------------------------------------------------------------------------- logical pure function lattice_qInSST(Q, struct) real(pReal), dimension(4), intent(in) :: Q ! orientation integer(kind(LATTICE_undefined_ID)), intent(in) :: struct ! lattice structure real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q Rodrig = math_qToRodrig(Q) if (any(IEEE_is_NaN(Rodrig))) then lattice_qInSST = .false. else select case (struct) case (LATTICE_bcc_ID,LATTICE_fcc_ID) lattice_qInSST = Rodrig(1) > Rodrig(2) .and. & Rodrig(2) > Rodrig(3) .and. & Rodrig(3) > 0.0_pReal case (LATTICE_hex_ID) lattice_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. & Rodrig(2) > 0.0_pReal .and. & Rodrig(3) > 0.0_pReal case default lattice_qInSST = .true. end select endif end function lattice_qInSST !-------------------------------------------------------------------------------------------------- !> @brief calculates the disorientation for 2 unit quaternions !-------------------------------------------------------------------------------------------------- pure function lattice_qDisorientation(Q1, Q2, struct) real(pReal), dimension(4) :: lattice_qDisorientation real(pReal), dimension(4), intent(in) :: & Q1, & !< 1st orientation Q2 !< 2nd orientation integer(kind(LATTICE_undefined_ID)), optional, intent(in) :: & !< if given, symmetries between the two orientation will be considered struct real(pReal), dimension(4) :: dQ,dQsymA,mis integer :: i,j,k,s,symmetry integer(kind(LATTICE_undefined_ID)) :: myStruct integer, dimension(2), parameter :: & NsymOperations = [24,12] real(pReal), dimension(4,36), parameter :: & symOperations = reshape([& 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations 0.0_pReal, 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), & ! 2-fold symmetry 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), & 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, & 0.0_pReal, 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), -1.0_pReal/sqrt(2.0_pReal), & 0.0_pReal, -1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), & 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), -1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, & 0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry -0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & 0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & -0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & 0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & -0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & 0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & -0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & -1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 0.0_pReal, & 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, & 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & -1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, & 1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), & 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, & -1.0_pReal/sqrt(2.0_pReal), 0.0_pReal, 0.0_pReal, 1.0_pReal/sqrt(2.0_pReal), & ! 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & 0.0_pReal, 0.5_pReal, 2.0_pReal/sqrt(3.0_pReal), 0.0_pReal, & 0.0_pReal, -0.5_pReal, 2.0_pReal/sqrt(3.0_pReal), 0.0_pReal, & 0.0_pReal, 2.0_pReal/sqrt(3.0_pReal), 0.5_pReal, 0.0_pReal, & 0.0_pReal, -2.0_pReal/sqrt(3.0_pReal), 0.5_pReal, 0.0_pReal, & 2.0_pReal/sqrt(3.0_pReal), 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry -2.0_pReal/sqrt(3.0_pReal), 0.0_pReal, 0.0_pReal, 0.5_pReal, & 0.5_pReal, 0.0_pReal, 0.0_pReal, 2.0_pReal/sqrt(3.0_pReal), & -0.5_pReal, 0.0_pReal, 0.0_pReal, 2.0_pReal/sqrt(3.0_pReal), & 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal & ],[4,36]) !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36 !-------------------------------------------------------------------------------------------------- ! check if a structure with known symmetries is given if (present(struct)) then myStruct = struct select case (struct) case(LATTICE_fcc_ID,LATTICE_bcc_ID) symmetry = 1 case(LATTICE_hex_ID) symmetry = 2 case default symmetry = 0 end select else symmetry = 0 myStruct = LATTICE_undefined_ID endif !-------------------------------------------------------------------------------------------------- ! calculate misorientation, for cubic and hexagonal structure find symmetries dQ = math_qMul(math_qConj(Q1),Q2) lattice_qDisorientation = dQ select case(symmetry) case (1,2) s = sum(NsymOperations(1:symmetry-1)) do i = 1,2 dQ = math_qConj(dQ) ! switch order of "from -- to" do j = 1,NsymOperations(symmetry) ! run through first crystal's symmetries dQsymA = math_qMul(symOperations(1:4,s+j),dQ) ! apply sym do k = 1,NsymOperations(symmetry) ! run through 2nd crystal's symmetries mis = math_qMul(dQsymA,symOperations(1:4,s+k)) ! apply sym if (mis(1) < 0.0_pReal) & ! want positive angle mis = -mis if (mis(1)-lattice_qDisorientation(1) > -tol_math_check & .and. lattice_qInSST(mis,LATTICE_undefined_ID)) lattice_qDisorientation = mis ! found better one enddo; enddo; enddo case (0) if (lattice_qDisorientation(1) < 0.0_pReal) lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg end select end function lattice_qDisorientation !-------------------------------------------------------------------------------------------------- !> @brief Characteristic shear for twinning !-------------------------------------------------------------------------------------------------- function lattice_characteristicShear_Twin(Ntwin,structure,CoverA) result(characteristicShear) integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(sum(Ntwin)) :: characteristicShear integer :: & a, & !< index of active system c, & !< index in complete system list mf, & !< index of my family ms !< index of my system in current family integer, dimension(LATTICE_HEX_NTWIN), parameter :: & HEX_SHEARTWIN = reshape( [& 1, & ! <-10.1>{10.2} 1, & 1, & 1, & 1, & 1, & 2, & ! <11.6>{-1-1.1} 2, & 2, & 2, & 2, & 2, & 3, & ! <10.-2>{10.1} 3, & 3, & 3, & 3, & 3, & 4, & ! <11.-3>{11.2} 4, & 4, & 4, & 4, & 4 & ],[LATTICE_HEX_NTWIN]) ! indicator to formulas below if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure)) a = 0 myFamilies: do mf = 1,size(Ntwin,1) mySystems: do ms = 1,Ntwin(mf) a = a + 1 select case(structure(1:3)) case('fcc','bcc') characteristicShear(a) = 0.5_pReal*sqrt(2.0_pReal) case('hex') if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) & call IO_error(131,ext_msg='lattice_characteristicShear_Twin') c = sum(LATTICE_HEX_NTWINSYSTEM(1:mf-1))+ms select case(HEX_SHEARTWIN(c)) ! from Christian & Mahajan 1995 p.29 case (1) ! <-10.1>{10.2} characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA case (2) ! <11.6>{-1-1.1} characteristicShear(a) = 1.0_pReal/cOverA case (3) ! <10.-2>{10.1} characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA case (4) ! <11.-3>{11.2} characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA end select case default call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure)) end select enddo mySystems enddo myFamilies end function lattice_characteristicShear_Twin !-------------------------------------------------------------------------------------------------- !> @brief Rotated elasticity matrices for twinning in 66-vector notation !-------------------------------------------------------------------------------------------------- function lattice_C66_twin(Ntwin,C66,structure,CoverA) integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(6,6), intent(in) :: C66 !< unrotated parent stiffness matrix real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(6,6,sum(Ntwin)) :: lattice_C66_twin real(pReal),dimension(3,3,sum(Ntwin)) :: coordinateSystem real(pReal), dimension(3,3) :: R integer :: i if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure)) select case(structure(1:3)) case('fcc') coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_FCC_NSLIPSYSTEM,LATTICE_FCC_SYSTEMTWIN,& trim(structure),0.0_pReal) case('bcc') coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_BCC_NSLIPSYSTEM,LATTICE_BCC_SYSTEMTWIN,& trim(structure),0.0_pReal) case('hex') coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_HEX_NSLIPSYSTEM,LATTICE_HEX_SYSTEMTWIN,& 'hex',cOverA) case default call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure)) end select do i = 1, sum(Ntwin) R = math_axisAngleToR(coordinateSystem(1:3,2,i), PI) ! ToDo: Why always 180 deg? lattice_C66_twin(1:6,1:6,i) = math_sym3333to66(math_rotate_forward3333(math_66toSym3333(C66),R)) enddo end function lattice_C66_twin !-------------------------------------------------------------------------------------------------- !> @brief Rotated elasticity matrices for transformation in 66-vector notation !-------------------------------------------------------------------------------------------------- function lattice_C66_trans(Ntrans,C_parent66,structure_target, & CoverA_trans,a_bcc,a_fcc) integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family character(len=*), intent(in) :: structure_target !< lattice structure real(pReal), dimension(6,6), intent(in) :: C_parent66 real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans real(pReal), dimension(6,6) :: C_bar66, C_target_unrotated66 real(pReal), dimension(3,3,3,3) :: C_target_unrotated real(pReal), dimension(3,3,sum(Ntrans)) :: Q,S real(pReal) :: a_bcc, a_fcc, CoverA_trans integer :: i if (len_trim(structure_target) /= 3) & call IO_error(137,ext_msg='lattice_C66_trans (target): '//trim(structure_target)) !ToDo: add checks for CoverA_trans,a_fcc,a_bcc !-------------------------------------------------------------------------------------------------- ! elasticity matrix of the target phase in cube orientation if (structure_target(1:3) == 'hex') then C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal C_bar66(1,2) = (C_parent66(1,1) + 5.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/6.0_pReal C_bar66(3,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) + 4.0_pReal*C_parent66(4,4))/3.0_pReal C_bar66(1,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/3.0_pReal C_bar66(4,4) = (C_parent66(1,1) - C_parent66(1,2) + C_parent66(4,4))/3.0_pReal C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal)) C_target_unrotated66 = 0.0_pReal C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4) C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4) C_target_unrotated66(1,3) = C_bar66(1,3) C_target_unrotated66(3,3) = C_bar66(3,3) C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2))) C_target_unrotated66 = lattice_symmetrizeC66(LATTICE_HEX_ID,C_target_unrotated66) elseif (structure_target(1:3) == 'bcc') then C_target_unrotated66 = C_parent66 else call IO_error(137,ext_msg='lattice_C66_trans (target): '//trim(structure_target)) endif do i = 1, 6 if (abs(C_target_unrotated66(i,i)) @brief Non-schmid projections for bcc with up to 6 coefficients ! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17) ! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1 !-------------------------------------------------------------------------------------------------- function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family real(pReal), dimension(:), intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections integer, intent(in) :: sense !< sense (-1,+1) real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem !< coordinate system of slip system real(pReal), dimension(:), allocatable :: direction, normal, np integer :: i if (abs(sense) /= 1) call IO_error(0,ext_msg='lattice_nonSchmidMatrix') coordinateSystem = buildCoordinateSystem(Nslip,LATTICE_BCC_NSLIPSYSTEM,LATTICE_BCC_SYSTEMSLIP,& 'bcc',0.0_pReal) coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip)) *real(sense,pReal) ! convert unidirectional coordinate system nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'bcc',0.0_pReal) ! Schmid contribution do i = 1,sum(Nslip) direction = coordinateSystem(1:3,1,i) normal = coordinateSystem(1:3,2,i) np = matmul(math_axisAngleToR(direction,60.0_pReal*INRAD), normal) if (size(nonSchmidCoefficients)>0) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(1) * math_outer(direction, np) if (size(nonSchmidCoefficients)>1) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(2) * math_outer(math_cross(normal, direction), normal) if (size(nonSchmidCoefficients)>2) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(3) * math_outer(math_cross(np, direction), np) if (size(nonSchmidCoefficients)>3) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(4) * math_outer(normal, normal) if (size(nonSchmidCoefficients)>4) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(5) * math_outer(math_cross(normal, direction), & math_cross(normal, direction)) if (size(nonSchmidCoefficients)>5) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(6) * math_outer(direction, direction) enddo end function lattice_nonSchmidMatrix !-------------------------------------------------------------------------------------------------- !> @brief Slip-slip interaction matrix !> details only active slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipBySlip(Nslip,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-slip interaction character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Nslip),sum(Nslip)) :: interactionMatrix integer, dimension(:), allocatable :: NslipMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NSLIP), parameter :: & FCC_INTERACTIONSLIPSLIP = reshape( [& 1, 2, 2, 4, 6, 5, 3, 5, 5, 4, 5, 6, 9,10, 9,10,11,12, & ! -----> acting 2, 1, 2, 6, 4, 5, 5, 4, 6, 5, 3, 5, 9,10,11,12, 9,10, & ! | 2, 2, 1, 5, 5, 3, 5, 6, 4, 6, 5, 4, 11,12, 9,10, 9,10, & ! | 4, 6, 5, 1, 2, 2, 4, 5, 6, 3, 5, 5, 9,10,10, 9,12,11, & ! v 6, 4, 5, 2, 1, 2, 5, 3, 5, 5, 4, 6, 9,10,12,11,10, 9, & ! reacting 5, 5, 3, 2, 2, 1, 6, 5, 4, 5, 6, 4, 11,12,10, 9,10, 9, & 3, 5, 5, 4, 5, 6, 1, 2, 2, 4, 6, 5, 10, 9,10, 9,11,12, & 5, 4, 6, 5, 3, 5, 2, 1, 2, 6, 4, 5, 10, 9,12,11, 9,10, & 5, 6, 4, 6, 5, 4, 2, 2, 1, 5, 5, 3, 12,11,10, 9, 9,10, & 4, 5, 6, 3, 5, 5, 4, 6, 5, 1, 2, 2, 10, 9, 9,10,12,11, & 5, 3, 5, 5, 4, 6, 6, 4, 5, 2, 1, 2, 10, 9,11,12,10, 9, & 6, 5, 4, 5, 6, 4, 5, 5, 3, 2, 2, 1, 12,11, 9,10,10, 9, & 9, 9,11, 9, 9,11,10,10,12,10,10,12, 1, 7, 8, 8, 8, 8, & 10,10,12,10,10,12, 9, 9,11, 9, 9,11, 7, 1, 8, 8, 8, 8, & 9,11, 9,10,12,10,10,12,10, 9,11, 9, 8, 8, 1, 7, 8, 8, & 10,12,10, 9,11, 9, 9,11, 9,10,12,10, 8, 8, 7, 1, 8, 8, & 11, 9, 9,12,10,10,11, 9, 9,12,10,10, 8, 8, 8, 8, 1, 7, & 12,10,10,11, 9, 9,12,10,10,11, 9, 9, 8, 8, 8, 8, 7, 1 & ],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for fcc !< 1: self interaction !< 2: coplanar interaction !< 3: collinear interaction !< 4: Hirth locks !< 5: glissile junctions !< 6: Lomer locks !< 7: crossing (similar to Hirth locks in <110>{111} for two {110} planes) !< 8: similar to Lomer locks in <110>{111} for two {110} planes !< 9: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane !<10: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane !<11: crossing btw one {110} and one {111} plane !<12: collinear btw one {110} and one {111} plane integer, dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NSLIP), parameter :: & BCC_INTERACTIONSLIPSLIP = reshape( [& 1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! -----> acting 2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! | 6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! | 6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v 5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & ! reacting 4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, & 4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, & 3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, & 4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, & 3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, & 5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, & 4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, & ! 6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, & 4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, & 3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, & 3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, & 4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, & 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, & 4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, & 3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, & 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 & ],shape(BCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377 !< 1: self interaction !< 2: coplanar interaction !< 3: collinear interaction !< 4: mixed-asymmetrical junction !< 5: mixed-symmetrical junction !< 6: edge junction integer, dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NSLIP), parameter :: & HEX_INTERACTIONSLIPSLIP = reshape( [& 1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! -----> acting 2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | 2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | ! ! v 6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! reacting 6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & 6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! 12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & ! 20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & ! 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, & ! 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 & ],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for hex (onion peel naming scheme) integer, dimension(LATTICE_BCT_NSLIP,LATTICE_BCT_NSLIP), parameter :: & BCT_INTERACTIONSLIPSLIP = reshape( [& 1, 2, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! -----> acting 2, 1, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! | ! | 6, 6, 4, 5, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! v 6, 6, 5, 4, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! reacting ! 12, 12, 11, 11, 9, 10, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, & 12, 12, 11, 11, 10, 9, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, & ! 20, 20, 19, 19, 18, 18, 16, 17, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, & 20, 20, 19, 19, 18, 18, 17, 16, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, & 20, 20, 19, 19, 18, 18, 17, 17, 16, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, & 20, 20, 19, 19, 18, 18, 17, 17, 17, 16, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, & ! 30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 25, 26, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, & 30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 26, 25, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, & ! 42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 36, 37, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, & 42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 36, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, & 42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 36, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, & 42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 37, 36, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, & ! 56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 49, 50, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, & 56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 50, 49, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, & ! 72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 64, 65, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, & 72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 65, 64, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, & ! 90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 81, 82, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, & 90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 81, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, & 90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 81, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, & 90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 82, 81, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, & ! 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 100,101,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,100,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,100,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,100,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,100,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,100,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,100,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & 110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,101,100, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, & ! 132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, & 132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 121, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, & 132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 121, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, & 132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 121, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, & ! 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 144,145,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,144,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,144,145,145,145,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,144,145,145,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,144,145,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,144,145,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,144,145, 168,168,168,168,168,168,168,168, & 156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,145,144, 168,168,168,168,168,168,168,168, & ! 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,169,170,170,170,170,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,169,170,170,170,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,169,170,170,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,170,169,170,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, & 182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 & ],shape(BCT_INTERACTIONSLIPSLIP)) if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure)) select case(structure(1:3)) case('fcc') interactionTypes = FCC_INTERACTIONSLIPSLIP NslipMax = LATTICE_FCC_NSLIPSYSTEM case('bcc') interactionTypes = BCC_INTERACTIONSLIPSLIP NslipMax = LATTICE_BCC_NSLIPSYSTEM case('hex') interactionTypes = HEX_INTERACTIONSLIPSLIP NslipMax = LATTICE_HEX_NSLIPSYSTEM case('bct') interactionTypes = BCT_INTERACTIONSLIPSLIP NslipMax = LATTICE_BCT_NSLIPSYSTEM case default call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes) end function lattice_interaction_SlipBySlip !-------------------------------------------------------------------------------------------------- !> @brief Twin-twin interaction matrix !> details only active twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TwinByTwin(Ntwin,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Ntwin),sum(Ntwin)) :: interactionMatrix integer, dimension(:), allocatable :: NtwinMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NTWIN), parameter :: & FCC_INTERACTIONTWINTWIN = reshape( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 2,2,2,1,1,1,2,2,2,2,2,2, & ! v 2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting 2,2,2,1,1,1,2,2,2,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1 & ],shape(FCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for fcc integer, dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NTWIN), parameter :: & BCC_INTERACTIONTWINTWIN = reshape( [& 1,3,3,3,3,3,3,2,3,3,2,3, & ! -----> acting 3,1,3,3,3,3,2,3,3,3,3,2, & ! | 3,3,1,3,3,2,3,3,2,3,3,3, & ! | 3,3,3,1,2,3,3,3,3,2,3,3, & ! v 3,3,3,2,1,3,3,3,3,2,3,3, & ! reacting 3,3,2,3,3,1,3,3,2,3,3,3, & 3,2,3,3,3,3,1,3,3,3,3,2, & 2,3,3,3,3,3,3,1,3,3,2,3, & 3,3,2,3,3,2,3,3,1,3,3,3, & 3,3,3,2,2,3,3,3,3,1,3,3, & 2,3,3,3,3,3,3,2,3,3,1,3, & 3,2,3,3,3,3,2,3,3,3,3,1 & ],shape(BCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for bcc !< 1: self interaction !< 2: collinear interaction !< 3: other interaction integer, dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NTWIN), parameter :: & HEX_INTERACTIONTWINTWIN = reshape( [& 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! 6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & ! 12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, & ! 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 & ],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure)) select case(structure(1:3)) case('fcc') interactionTypes = FCC_INTERACTIONTWINTWIN NtwinMax = LATTICE_FCC_NTWINSYSTEM case('bcc') interactionTypes = BCC_INTERACTIONTWINTWIN NtwinMax = LATTICE_BCC_NTWINSYSTEM case('hex') interactionTypes = HEX_INTERACTIONTWINTWIN NtwinMax = LATTICE_HEX_NTWINSYSTEM case default call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure)) end select interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes) end function lattice_interaction_TwinByTwin !-------------------------------------------------------------------------------------------------- !> @brief Trans-trans interaction matrix !> details only active trans systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TransByTrans(Ntrans,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Ntrans !< number of active trans systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for trans-trans interaction character(len=*), intent(in) :: structure !< lattice structure (parent crystal) real(pReal), dimension(sum(Ntrans),sum(Ntrans)) :: interactionMatrix integer, dimension(:), allocatable :: NtransMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NTRANS,LATTICE_FCC_NTRANS), parameter :: & FCC_INTERACTIONTRANSTRANS = reshape( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 2,2,2,1,1,1,2,2,2,2,2,2, & ! v 2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting 2,2,2,1,1,1,2,2,2,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1 & ],shape(FCC_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for fcc if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure)) if(structure(1:3) == 'fcc') then interactionTypes = FCC_INTERACTIONTRANSTRANS NtransMax = LATTICE_FCC_NTRANSSYSTEM else call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure)) end if interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes) end function lattice_interaction_TransByTrans !-------------------------------------------------------------------------------------------------- !> @brief Slip-twin interaction matrix !> details only active slip and twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family Ntwin !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-twin interaction character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Nslip),sum(Ntwin)) :: interactionMatrix integer, dimension(:), allocatable :: NslipMax, & NtwinMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NSLIP), parameter :: & FCC_INTERACTIONSLIPTWIN = reshape( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> twin (acting) 1,1,1,3,3,3,3,3,3,2,2,2, & ! | 1,1,1,2,2,2,3,3,3,3,3,3, & ! | 3,3,3,1,1,1,3,3,3,2,2,2, & ! v 3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting) 2,2,2,1,1,1,3,3,3,3,3,3, & 2,2,2,3,3,3,1,1,1,3,3,3, & 3,3,3,2,2,2,1,1,1,3,3,3, & 3,3,3,3,3,3,1,1,1,2,2,2, & 3,3,3,2,2,2,3,3,3,1,1,1, & 2,2,2,3,3,3,3,3,3,1,1,1, & 3,3,3,3,3,3,2,2,2,1,1,1, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4 & ],shape(FCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for fcc !< 1: coplanar interaction !< 2: screw trace between slip system and twin habit plane (easy cross slip) !< 3: other interaction integer, dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NSLIP), parameter :: & BCC_INTERACTIONSLIPTWIN = reshape( [& 3,3,3,2,2,3,3,3,3,2,3,3, & ! -----> twin (acting) 3,3,2,3,3,2,3,3,2,3,3,3, & ! | 3,2,3,3,3,3,2,3,3,3,3,2, & ! | 2,3,3,3,3,3,3,2,3,3,2,3, & ! v 2,3,3,3,3,3,3,2,3,3,2,3, & ! slip (reacting) 3,3,2,3,3,2,3,3,2,3,3,3, & 3,2,3,3,3,3,2,3,3,3,3,2, & 3,3,3,2,2,3,3,3,3,2,3,3, & 2,3,3,3,3,3,3,2,3,3,2,3, & 3,3,3,2,2,3,3,3,3,2,3,3, & 3,2,3,3,3,3,2,3,3,3,3,2, & 3,3,2,3,3,2,3,3,2,3,3,3, & ! 1,3,3,3,3,3,3,2,3,3,2,3, & 3,1,3,3,3,3,2,3,3,3,3,2, & 3,3,1,3,3,2,3,3,2,3,3,3, & 3,3,3,1,2,3,3,3,3,2,3,3, & 3,3,3,2,1,3,3,3,3,2,3,3, & 3,3,2,3,3,1,3,3,2,3,3,3, & 3,2,3,3,3,3,1,3,3,3,3,2, & 2,3,3,3,3,3,3,1,3,3,2,3, & 3,3,2,3,3,2,3,3,1,3,3,3, & 3,3,3,2,2,3,3,3,3,1,3,3, & 2,3,3,3,3,3,3,2,3,3,1,3, & 3,2,3,3,3,3,2,3,3,3,3,1 & ],shape(BCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for bcc !< 1: coplanar interaction !< 2: screw trace between slip system and twin habit plane (easy cross slip) !< 3: other interaction integer, dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NSLIP), parameter :: & HEX_INTERACTIONSLIPTWIN = reshape( [& 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! ----> twin (acting) 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | ! v 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip (reacting) 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & ! 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & ! 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & ! 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 & ! ],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure)) select case(structure(1:3)) case('fcc') interactionTypes = FCC_INTERACTIONSLIPTWIN NslipMax = LATTICE_FCC_NSLIPSYSTEM NtwinMax = LATTICE_FCC_NTWINSYSTEM case('bcc') interactionTypes = BCC_INTERACTIONSLIPTWIN NslipMax = LATTICE_BCC_NSLIPSYSTEM NtwinMax = LATTICE_BCC_NTWINSYSTEM case('hex') interactionTypes = HEX_INTERACTIONSLIPTWIN NslipMax = LATTICE_HEX_NSLIPSYSTEM NtwinMax = LATTICE_HEX_NTWINSYSTEM case default call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes) end function lattice_interaction_SlipByTwin !-------------------------------------------------------------------------------------------------- !> @brief Slip-trans interaction matrix !> details only active slip and trans systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family Ntrans !< number of active trans systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-trans interaction character(len=*), intent(in) :: structure !< lattice structure (parent crystal) real(pReal), dimension(sum(Nslip),sum(Ntrans)) :: interactionMatrix integer, dimension(:), allocatable :: NslipMax, & NtransMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NTRANS,LATTICE_FCC_NSLIP), parameter :: & FCC_INTERACTIONSLIPTRANS = reshape( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> trans (acting) 1,1,1,3,3,3,3,3,3,2,2,2, & ! | 1,1,1,2,2,2,3,3,3,3,3,3, & ! | 3,3,3,1,1,1,3,3,3,2,2,2, & ! v 3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting) 2,2,2,1,1,1,3,3,3,3,3,3, & 2,2,2,3,3,3,1,1,1,3,3,3, & 3,3,3,2,2,2,1,1,1,3,3,3, & 3,3,3,3,3,3,1,1,1,2,2,2, & 3,3,3,2,2,2,3,3,3,1,1,1, & 2,2,2,3,3,3,3,3,3,1,1,1, & 3,3,3,3,3,3,2,2,2,1,1,1, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4, & 4,4,4,4,4,4,4,4,4,4,4,4 & ],shape(FCC_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for fcc if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure)) select case(structure(1:3)) case('fcc') interactionTypes = FCC_INTERACTIONSLIPTRANS NslipMax = LATTICE_FCC_NSLIPSYSTEM NtransMax = LATTICE_FCC_NTRANSSYSTEM case default call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes) end function lattice_interaction_SlipByTrans !-------------------------------------------------------------------------------------------------- !> @brief Twin-slip interaction matrix !> details only active twin and slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,structure) result(interactionMatrix) integer, dimension(:), intent(in) :: Ntwin, & !< number of active twin systems per family Nslip !< number of active slip systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Ntwin),sum(Nslip)) :: interactionMatrix integer, dimension(:), allocatable :: NtwinMax, & NslipMax integer, dimension(:,:), allocatable :: interactionTypes integer, dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NTWIN), parameter :: & FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc integer, dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NTWIN), parameter :: & BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc integer, dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NTWIN), parameter :: & HEX_INTERACTIONTWINSLIP = reshape( [& 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! ----> slip (acting) 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin (reacting) 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & ! 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & ! 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 & ],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure)) select case(structure(1:3)) case('fcc') interactionTypes = FCC_INTERACTIONTWINSLIP NtwinMax = LATTICE_FCC_NTWINSYSTEM NslipMax = LATTICE_FCC_NSLIPSYSTEM case('bcc') interactionTypes = BCC_INTERACTIONTWINSLIP NtwinMax = LATTICE_BCC_NTWINSYSTEM NslipMax = LATTICE_BCC_NSLIPSYSTEM case('hex') interactionTypes = HEX_INTERACTIONTWINSLIP NtwinMax = LATTICE_HEX_NTWINSYSTEM NslipMax = LATTICE_HEX_NSLIPSYSTEM case default call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure)) end select interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes) end function lattice_interaction_TwinBySlip !-------------------------------------------------------------------------------------------------- !> @brief Schmid matrix for slip !> details only active slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA real(pReal), dimension(3,3,sum(Nslip)) :: SchmidMatrix real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem real(pReal), dimension(:,:), allocatable :: slipSystems integer, dimension(:), allocatable :: NslipMax integer :: i if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure)) select case(structure(1:3)) case('fcc') NslipMax = LATTICE_FCC_NSLIPSYSTEM slipSystems = LATTICE_FCC_SYSTEMSLIP case('bcc') NslipMax = LATTICE_BCC_NSLIPSYSTEM slipSystems = LATTICE_BCC_SYSTEMSLIP case('hex') NslipMax = LATTICE_HEX_NSLIPSYSTEM slipSystems = LATTICE_HEX_SYSTEMSLIP case('bct') NslipMax = LATTICE_BCT_NSLIPSYSTEM slipSystems = LATTICE_BCT_SYSTEMSLIP case default call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure)) end select if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) & call IO_error(145,ext_msg='Nslip '//trim(structure)) if (any(Nslip < 0)) & call IO_error(144,ext_msg='Nslip '//trim(structure)) coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA) do i = 1, sum(Nslip) SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) & call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for slip') enddo end function lattice_SchmidMatrix_slip !-------------------------------------------------------------------------------------------------- !> @brief Schmid matrix for twinning !> details only active twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_twin(Ntwin,structure,cOverA) result(SchmidMatrix) integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,3,sum(Ntwin)) :: SchmidMatrix real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem real(pReal), dimension(:,:), allocatable :: twinSystems integer, dimension(:), allocatable :: NtwinMax integer :: i if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure)) select case(structure(1:3)) case('fcc') NtwinMax = LATTICE_FCC_NTWINSYSTEM twinSystems = LATTICE_FCC_SYSTEMTWIN case('bcc') NtwinMax = LATTICE_BCC_NTWINSYSTEM twinSystems = LATTICE_BCC_SYSTEMTWIN case('hex') NtwinMax = LATTICE_HEX_NTWINSYSTEM twinSystems = LATTICE_HEX_SYSTEMTWIN case default call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure)) end select if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) & call IO_error(145,ext_msg='Ntwin '//trim(structure)) if (any(Ntwin < 0)) & call IO_error(144,ext_msg='Ntwin '//trim(structure)) coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,structure,cOverA) do i = 1, sum(Ntwin) SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) & call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for twin') enddo end function lattice_SchmidMatrix_twin !-------------------------------------------------------------------------------------------------- !> @brief Schmid matrix for twinning !> details only active twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_trans(Ntrans,structure_target,cOverA,a_bcc,a_fcc) result(SchmidMatrix) integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family real(pReal), intent(in) :: cOverA !< c/a ratio character(len=*), intent(in) :: structure_target !< lattice structure real(pReal), dimension(3,3,sum(Ntrans)) :: SchmidMatrix real(pReal), dimension(3,3,sum(Ntrans)):: devNull real(pReal) :: a_bcc, a_fcc if (len_trim(structure_target) /= 3) & call IO_error(137,ext_msg='lattice_SchmidMatrix_trans (target): '//trim(structure_target)) if (structure_target(1:3) /= 'bcc' .and. structure_target(1:3) /= 'hex') & call IO_error(137,ext_msg='lattice_SchmidMatrix_trans (target): '//trim(structure_target)) !ToDo: add checks for CoverA_trans,a_fcc,a_bcc call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA,a_fcc,a_bcc) end function lattice_SchmidMatrix_trans !-------------------------------------------------------------------------------------------------- !> @brief Schmid matrix for cleavage !> details only active cleavage systems are considered !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_cleavage(Ncleavage,structure,cOverA) result(SchmidMatrix) integer, dimension(:), intent(in) :: Ncleavage !< number of active cleavage systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,3,3,sum(Ncleavage)) :: SchmidMatrix real(pReal), dimension(3,3,sum(Ncleavage)) :: coordinateSystem real(pReal), dimension(:,:), allocatable :: cleavageSystems integer, dimension(:), allocatable :: NcleavageMax integer :: i if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure)) select case(structure(1:3)) case('iso') NcleavageMax = LATTICE_ISO_NCLEAVAGESYSTEM cleavageSystems = LATTICE_ISO_SYSTEMCLEAVAGE case('ort') NcleavageMax = LATTICE_ORT_NCLEAVAGESYSTEM cleavageSystems = LATTICE_ORT_SYSTEMCLEAVAGE case('fcc') NcleavageMax = LATTICE_FCC_NCLEAVAGESYSTEM cleavageSystems = LATTICE_FCC_SYSTEMCLEAVAGE case('bcc') NcleavageMax = LATTICE_BCC_NCLEAVAGESYSTEM cleavageSystems = LATTICE_BCC_SYSTEMCLEAVAGE case('hex') NcleavageMax = LATTICE_HEX_NCLEAVAGESYSTEM cleavageSystems = LATTICE_HEX_SYSTEMCLEAVAGE case default call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure)) end select if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0)) & call IO_error(145,ext_msg='Ncleavage '//trim(structure)) if (any(Ncleavage < 0)) & call IO_error(144,ext_msg='Ncleavage '//trim(structure)) coordinateSystem = buildCoordinateSystem(Ncleavage,NcleavageMax,cleavageSystems,structure,cOverA) do i = 1, sum(Ncleavage) SchmidMatrix(1:3,1:3,1,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) SchmidMatrix(1:3,1:3,2,i) = math_outer(coordinateSystem(1:3,3,i),coordinateSystem(1:3,2,i)) SchmidMatrix(1:3,1:3,3,i) = math_outer(coordinateSystem(1:3,2,i),coordinateSystem(1:3,2,i)) enddo end function lattice_SchmidMatrix_cleavage !-------------------------------------------------------------------------------------------------- !> @brief Slip direction of slip systems (|| b) !-------------------------------------------------------------------------------------------------- function lattice_slip_direction(Nslip,structure,cOverA) result(d) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,sum(Nslip)) :: d real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA) d = coordinateSystem(1:3,1,1:sum(Nslip)) end function lattice_slip_direction !-------------------------------------------------------------------------------------------------- !> @brief Normal direction of slip systems (|| n) !-------------------------------------------------------------------------------------------------- function lattice_slip_normal(Nslip,structure,cOverA) result(n) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,sum(Nslip)) :: n real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA) n = coordinateSystem(1:3,2,1:sum(Nslip)) end function lattice_slip_normal !-------------------------------------------------------------------------------------------------- !> @brief Transverse direction of slip systems ( || t = b x n) !-------------------------------------------------------------------------------------------------- function lattice_slip_transverse(Nslip,structure,cOverA) result(t) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,sum(Nslip)) :: t real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA) t = coordinateSystem(1:3,3,1:sum(Nslip)) end function lattice_slip_transverse !-------------------------------------------------------------------------------------------------- !> @brief Projection of the transverse direction onto the slip plane !> @details: This projection is used to calculate forest hardening for edge dislocations !-------------------------------------------------------------------------------------------------- function slipProjection_transverse(Nslip,structure,cOverA) result(projection) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem integer :: i, j coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA) do i=1, sum(Nslip); do j=1, sum(Nslip) projection(i,j) = abs(math_inner(coordinateSystem(1:3,2,i),coordinateSystem(1:3,3,j))) enddo; enddo end function slipProjection_transverse !-------------------------------------------------------------------------------------------------- !> @brief Projection of the slip direction onto the slip plane !> @details: This projection is used to calculate forest hardening for screw dislocations !-------------------------------------------------------------------------------------------------- function slipProjection_direction(Nslip,structure,cOverA) result(projection) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem integer :: i, j coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA) do i=1, sum(Nslip); do j=1, sum(Nslip) projection(i,j) = abs(math_inner(coordinateSystem(1:3,2,i),coordinateSystem(1:3,1,j))) enddo; enddo end function slipProjection_direction !-------------------------------------------------------------------------------------------------- !> @brief build a local coordinate system on slip systems !> @details Order: Direction, plane (normal), and common perpendicular !-------------------------------------------------------------------------------------------------- function coordinateSystem_slip(Nslip,structure,cOverA) result(coordinateSystem) integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem real(pReal), dimension(:,:), allocatable :: slipSystems integer, dimension(:), allocatable :: NslipMax if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure)) select case(structure(1:3)) case('fcc') NslipMax = LATTICE_FCC_NSLIPSYSTEM slipSystems = LATTICE_FCC_SYSTEMSLIP case('bcc') NslipMax = LATTICE_BCC_NSLIPSYSTEM slipSystems = LATTICE_BCC_SYSTEMSLIP case('hex') NslipMax = LATTICE_HEX_NSLIPSYSTEM slipSystems = LATTICE_HEX_SYSTEMSLIP case('bct') NslipMax = LATTICE_BCT_NSLIPSYSTEM slipSystems = LATTICE_BCT_SYSTEMSLIP case default call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure)) end select if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) & call IO_error(145,ext_msg='Nslip '//trim(structure)) if (any(Nslip < 0)) & call IO_error(144,ext_msg='Nslip '//trim(structure)) coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA) end function coordinateSystem_slip !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced interaction matrix !-------------------------------------------------------------------------------------------------- function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix) integer, dimension(:), intent(in) :: & reacting_used, & !< # of reacting systems per family as specified in material.config acting_used, & !< # of acting systems per family as specified in material.config reacting_max, & !< max # of reacting systems per family for given lattice acting_max !< max # of acting systems per family for given lattice real(pReal), dimension(:), intent(in) :: values !< interaction values integer, dimension(:,:), intent(in) :: matrix !< interaction types real(pReal), dimension(sum(reacting_used),sum(acting_used)) :: buildInteraction integer :: & acting_family_index, acting_family, acting_system, & reacting_family_index, reacting_family, reacting_system, & i,j,k,l do acting_family = 1,size(acting_used,1) acting_family_index = sum(acting_used(1:acting_family-1)) do acting_system = 1,acting_used(acting_family) do reacting_family = 1,size(reacting_used,1) reacting_family_index = sum(reacting_used(1:reacting_family-1)) do reacting_system = 1,reacting_used(reacting_family) i = sum( acting_max(1: acting_family-1)) + acting_system j = sum(reacting_max(1:reacting_family-1)) + reacting_system k = acting_family_index + acting_system l = reacting_family_index + reacting_system if (matrix(i,j) > size(values)) call IO_error(138,ext_msg='buildInteraction') buildInteraction(l,k) = values(matrix(i,j)) enddo; enddo enddo; enddo end function buildInteraction !-------------------------------------------------------------------------------------------------- !> @brief build a local coordinate system on slip, twin, trans, cleavage systems !> @details Order: Direction, plane (normal), and common perpendicular !-------------------------------------------------------------------------------------------------- function buildCoordinateSystem(active,complete,system,structure,cOverA) integer, dimension(:), intent(in) :: & active, & complete real(pReal), dimension(:,:), intent(in) :: & system character(len=*), intent(in) :: & structure !< lattice structure real(pReal), intent(in) :: & cOverA real(pReal), dimension(3,3,sum(active)) :: & buildCoordinateSystem real(pReal), dimension(3) :: & direction, normal integer :: & a, & !< index of active system c, & !< index in complete system matrix f, & !< index of my family s !< index of my system in current family if (len_trim(structure) /= 3) & call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure)) if (trim(structure(1:3)) == 'bct' .and. cOverA > 2.0_pReal) & call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure)) if (trim(structure(1:3)) == 'hex' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) & call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure)) a = 0 activeFamilies: do f = 1,size(active,1) activeSystems: do s = 1,active(f) a = a + 1 c = sum(complete(1:f-1))+s select case(trim(structure(1:3))) case ('fcc','bcc','iso','ort','bct') direction = system(1:3,c) normal = system(4:6,c) case ('hex') direction = [ system(1,c)*1.5_pReal, & (system(1,c)+2.0_pReal*system(2,c))*sqrt(0.75_pReal), & system(4,c)*cOverA ] ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]) normal = [ system(5,c), & (system(5,c)+2.0_pReal*system(6,c))/sqrt(3.0_pReal), & system(8,c)/cOverA ] ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) case default call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure)) end select buildCoordinateSystem(1:3,1,a) = direction/norm2(direction) buildCoordinateSystem(1:3,2,a) = normal/norm2(normal) buildCoordinateSystem(1:3,3,a) = math_cross(buildCoordinateSystem(1:3,1,a),& buildCoordinateSystem(1:3,2,a)) enddo activeSystems enddo activeFamilies end function buildCoordinateSystem !-------------------------------------------------------------------------------------------------- !> @brief Helper function to define transformation systems ! Needed to calculate Schmid matrix and rotated stiffness matrices. ! @details: set c/a = 0.0 for fcc -> bcc transformation ! set a_bcc = 0.0 for fcc -> hex transformation !-------------------------------------------------------------------------------------------------- subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc) integer, dimension(:), intent(in) :: & Ntrans real(pReal), dimension(3,3,sum(Ntrans)), intent(out) :: & Q, & !< Total rotation: Q = R*B S !< Eigendeformation tensor for phase transformation real(pReal), intent(in) :: & cOverA, & !< c/a for target hex structure a_bcc, & !< lattice parameter a for target bcc structure a_fcc !< lattice parameter a for parent fcc structure real(pReal), dimension(3,3) :: & R, & !< Pitsch rotation U, & !< Bain deformation B, & !< Rotation of fcc to Bain coordinate system ss, sd real(pReal), dimension(3) :: & x, y, z integer :: & i real(pReal), dimension(3+3,LATTICE_FCC_NTRANS), parameter :: & LATTICE_FCCTOHEX_SYSTEMTRANS = reshape(real( [& -2, 1, 1, 1, 1, 1, & 1,-2, 1, 1, 1, 1, & 1, 1,-2, 1, 1, 1, & 2,-1, 1, -1,-1, 1, & -1, 2, 1, -1,-1, 1, & -1,-1,-2, -1,-1, 1, & -2,-1,-1, 1,-1,-1, & 1, 2,-1, 1,-1,-1, & 1,-1, 2, 1,-1,-1, & 2, 1,-1, -1, 1,-1, & -1,-2,-1, -1, 1,-1, & -1, 1, 2, -1, 1,-1 & ],pReal),shape(LATTICE_FCCTOHEX_SYSTEMTRANS)) real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter :: & LATTICE_FCCTOBCC_SYSTEMTRANS = reshape([& 0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3) 0.0, 1.0, 0.0, -10.26, & 0.0, 0.0, 1.0, 10.26, & 0.0, 0.0, 1.0, -10.26, & 1.0, 0.0, 0.0, 10.26, & 1.0, 0.0, 0.0, -10.26, & 0.0, 0.0, 1.0, 10.26, & 0.0, 0.0, 1.0, -10.26, & 1.0, 0.0, 0.0, 10.26, & 1.0, 0.0, 0.0, -10.26, & 0.0, 1.0, 0.0, 10.26, & 0.0, 1.0, 0.0, -10.26 & ],shape(LATTICE_FCCTOBCC_SYSTEMTRANS)) integer, dimension(9,LATTICE_fcc_Ntrans), parameter :: & LATTICE_FCCTOBCC_BAINVARIANT = reshape( [& 1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3) 1, 0, 0, 0, 1, 0, 0, 0, 1, & 1, 0, 0, 0, 1, 0, 0, 0, 1, & 1, 0, 0, 0, 1, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0 & ],shape(LATTICE_FCCTOBCC_BAINVARIANT)) real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter :: & LATTICE_FCCTOBCC_BAINROT = reshape([& 1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant 1.0, 0.0, 0.0, 45.0, & 1.0, 0.0, 0.0, 45.0, & 1.0, 0.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0 & ],shape(LATTICE_FCCTOBCC_BAINROT)) if (size(Ntrans) < 1 .or. size(Ntrans) > 1) & call IO_error(0) !ToDo: define error if (a_bcc > 0.0_pReal .and. dEq0(cOverA)) then ! fcc -> bcc transformation do i = 1,sum(Ntrans) R = math_axisAngleToR(lattice_fccTobcc_systemTrans(1:3,i), & lattice_fccTobcc_systemTrans(4,i)*INRAD) B = math_axisAngleToR(lattice_fccTobcc_bainRot(1:3,i), & lattice_fccTobcc_bainRot(4,i)*INRAD) x = real(LATTICE_fccTobcc_bainVariant(1:3,i),pReal) y = real(LATTICE_fccTobcc_bainVariant(4:6,i),pReal) z = real(LATTICE_fccTobcc_bainVariant(7:9,i),pReal) U = (a_bcc/a_fcc)*math_outer(x,x) & + (a_bcc/a_fcc)*math_outer(y,y) * sqrt(2.0_pReal) & + (a_bcc/a_fcc)*math_outer(z,z) * sqrt(2.0_pReal) Q(1:3,1:3,i) = matmul(R,B) S(1:3,1:3,i) = matmul(R,U) - MATH_I3 enddo elseif (cOverA > 0.0_pReal .and. dEq0(a_bcc)) then ! fcc -> hex transformation ss = MATH_I3 sd = MATH_I3 ss(1,3) = sqrt(2.0_pReal)/4.0_pReal if (cOverA > 1.0_pReal .and. cOverA < 2.0_pReal) & sd(3,3) = cOverA/sqrt(8.0_pReal/3.0_pReal) do i = 1,sum(Ntrans) x = lattice_fccTohex_systemTrans(1:3,i)/norm2(lattice_fccTohex_systemTrans(1:3,i)) z = lattice_fccTohex_systemTrans(4:6,i)/norm2(lattice_fccTohex_systemTrans(4:6,i)) y = -math_cross(x,z) Q(1:3,1,i) = x Q(1:3,2,i) = y Q(1:3,3,i) = z S(1:3,1:3,i) = matmul(Q(1:3,1:3,i), matmul(matmul(sd,ss), transpose(Q(1:3,1:3,i)))) - MATH_I3 ! ToDo: This is of interest for the Schmid matrix only enddo else call IO_error(0) !ToDo: define error endif end subroutine buildTransformationSystem end module lattice