!-------------------------------------------------------------------------------------------------- !> @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, only: & pReal, & pInt implicit none private ! BEGIN DEPRECATED integer(pInt), parameter, public :: & LATTICE_maxNslipFamily = 13_pInt, & !< max # of slip system families over lattice structures LATTICE_maxNcleavageFamily = 3_pInt !< max # of transformation system families over lattice structures integer(pInt), allocatable, dimension(:,:), protected, public :: & lattice_NslipSystem, & !< total # of slip systems in each family lattice_NcleavageSystem !< total # of transformation systems in each family real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: & lattice_Scleavage !< Schmid matrices for cleavage systems real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_sn, & !< normal direction of slip system lattice_st, & !< sd x sn lattice_sd !< slip direction of slip system ! END DEPRECATED !-------------------------------------------------------------------------------------------------- ! face centered cubic integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, private :: & LATTICE_FCC_NSLIPSYSTEM = int([12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],pInt) !< # of slip systems per family for fcc integer(pInt), dimension(1), parameter, private :: & LATTICE_FCC_NTWINSYSTEM = int([12],pInt) !< # of twin systems per family for fcc integer(pInt), dimension(1), parameter, private :: & LATTICE_FCC_NTRANSSYSTEM = int([12],pInt) !< # of transformation systems per family for fcc integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, private :: & LATTICE_FCC_NCLEAVAGESYSTEM = int([3, 4, 0],pInt) !< # of cleavage systems per family for fcc integer(pInt), parameter, private :: & 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, private :: & 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, private :: 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, private :: & 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, private :: LATTICE_FCC_TWINFAMILY_NAME = & ['<-2 1 1>{1 1 1}'] integer(pInt), dimension(2_pInt,LATTICE_FCC_NTWIN), parameter, public :: & LATTICE_FCC_TWINNUCLEATIONSLIPPAIR = reshape(int( [& 2,3, & 1,3, & 1,2, & 5,6, & 4,6, & 4,5, & 8,9, & 7,9, & 7,8, & 11,12, & 10,12, & 10,11 & ],pInt),shape(LATTICE_FCC_TWINNUCLEATIONSLIPPAIR)) real(pReal), dimension(3+3,LATTICE_fcc_Ncleavage), parameter, private :: & 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(pInt), dimension(LATTICE_maxNslipFamily), parameter, private :: & LATTICE_BCC_NSLIPSYSTEM = int([ 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], pInt) !< # of slip systems per family for bcc integer(pInt), dimension(1), parameter, private :: & LATTICE_BCC_NTWINSYSTEM = int([12], pInt) !< # of twin systems per family for bcc integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, private :: & LATTICE_bcc_NcleavageSystem = int([3, 6, 0],pInt) !< # of cleavage systems per family for bcc integer(pInt), parameter, private :: & 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, private :: & 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, private :: 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, private :: & 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, private :: LATTICE_BCC_TWINFAMILY_NAME = & ['<1 1 1>{2 1 1}'] real(pReal), dimension(3+3,LATTICE_bcc_Ncleavage), parameter, private :: & 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(pInt), dimension(LATTICE_maxNslipFamily), parameter, private :: & LATTICE_HEX_NSLIPSYSTEM = int([ 3, 3, 3, 6, 12, 6, 0, 0, 0, 0, 0, 0, 0],pInt) !< # of slip systems per family for hex integer(pInt), dimension(4), parameter, private :: & LATTICE_HEX_NTWINSYSTEM = int([ 6, 6, 6, 6],pInt) !< # of slip systems per family for hex integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, private :: & LATTICE_hex_NcleavageSystem = int([3, 0, 0],pInt) !< # of cleavage systems per family for hex integer(pInt), parameter, private :: & 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, private :: & 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, private :: 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, private :: & 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, private :: 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, private :: & 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(pInt), dimension(LATTICE_maxNslipFamily), parameter, private :: & LATTICE_bct_NslipSystem = int([2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ],pInt) !< # of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009 integer(pInt), parameter, private :: & LATTICE_bct_Nslip = sum(lattice_bct_NslipSystem) !< total # of slip systems for bct real(pReal), dimension(3+3,LATTICE_bct_Nslip), parameter, private :: & LATTICE_bct_systemSlip = reshape(real([& ! Slip direction Plane normal ! Slip family 1 {100)<001] (Bravais notation {hkl) @brief Module initialization !-------------------------------------------------------------------------------------------------- subroutine lattice_init use IO, only: & IO_error use config, only: & config_phase implicit none integer(pInt) :: Nphases character(len=65536) :: & tag = '' integer(pInt) :: 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(trans_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_NslipSystem(lattice_maxNslipFamily,Nphases),source=0_pInt) allocate(lattice_Scleavage(3,3,3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_NcleavageSystem(lattice_maxNcleavageFamily,Nphases),source=0_pInt) allocate(CoverA(Nphases),source=0.0_pReal) allocate(lattice_sd(3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_st(3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_sn(3,lattice_maxNslip,Nphases),source=0.0_pReal) do p = 1, size(config_phase) tag = config_phase(p)%getString('lattice_structure') select case(trim(tag)) case('iso','isotropic') lattice_structure(p) = LATTICE_iso_ID case('fcc') lattice_structure(p) = LATTICE_fcc_ID case('bcc') lattice_structure(p) = LATTICE_bcc_ID case('hex','hexagonal') lattice_structure(p) = LATTICE_hex_ID case('bct') lattice_structure(p) = LATTICE_bct_ID case('ort','orthorhombic') lattice_structure(p) = LATTICE_ort_ID end select tag = 'undefined' tag = config_phase(p)%getString('trans_lattice_structure',defaultVal=tag) select case(trim(tag)) case('bcc') trans_lattice_structure(p) = LATTICE_bcc_ID case('hex','hexagonal') trans_lattice_structure(p) = LATTICE_hex_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_pInt,Nphases if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) & .and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(131_pInt,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_pInt,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) use prec, only: & tol_math_check use math, only: & math_mul33x33, & math_sym3333to66, & math_Voigt66to3333, & math_crossproduct use IO, only: & IO_error implicit none integer(pInt), intent(in) :: myPhase real(pReal), intent(in) :: & CoverA real(pReal), dimension(3,lattice_maxNslip) :: & sd, sn integer(pInt) :: & j, i, & myNslip, 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_pInt, 6_pInt if (abs(lattice_C66(i,i,myPhase))[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)] sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*& 0.5_pReal*sqrt(3.0_pReal) sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal) sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA enddo !-------------------------------------------------------------------------------------------------- ! bct case (LATTICE_bct_ID) myNslip = lattice_bct_Nslip lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_bct_NslipSystem do i = 1_pInt,myNslip ! assign slip system vectors sd(1:2,i) = lattice_bct_systemSlip(1:2,i) sd(3,i) = lattice_bct_systemSlip(3,i)*CoverA sn(1:2,i) = lattice_bct_systemSlip(4:5,i) sn(3,i) = lattice_bct_systemSlip(6,i)/CoverA enddo !-------------------------------------------------------------------------------------------------- ! orthorhombic (no crystal plasticity) case (LATTICE_ort_ID) myNcleavage = lattice_ort_Ncleavage lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_ort_NcleavageSystem lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = & lattice_SchmidMatrix_cleavage(lattice_ort_NcleavageSystem,'ort',covera) !-------------------------------------------------------------------------------------------------- ! isotropic (no crystal plasticity) case (LATTICE_iso_ID) myNcleavage = lattice_iso_Ncleavage lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_iso_NcleavageSystem lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = & lattice_SchmidMatrix_cleavage(lattice_iso_NcleavageSystem,'iso',covera) !-------------------------------------------------------------------------------------------------- ! something went wrong case default call IO_error(130_pInt,ext_msg='lattice_initializeStructure') end select do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure lattice_sd(1:3,i,myPhase) = sd(1:3,i)/norm2(sd(1:3,i)) ! make unit vector lattice_sn(1:3,i,myPhase) = sn(1:3,i)/norm2(sn(1:3,i)) ! make unit vector lattice_st(1:3,i,myPhase) = math_crossproduct(lattice_sd(1:3,i,myPhase),lattice_sn(1:3,i,myPhase)) enddo end subroutine lattice_initializeStructure !-------------------------------------------------------------------------------------------------- !> @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) implicit none integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(6,6), intent(in) :: C66 real(pReal), dimension(6,6) :: lattice_symmetrizeC66 integer(pInt) :: j,k lattice_symmetrizeC66 = 0.0_pReal select case(struct) case (LATTICE_iso_ID) forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) 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)) end forall case (LATTICE_fcc_ID,LATTICE_bcc_ID) forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2) lattice_symmetrizeC66(k,k) = C66(1,1) lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4) end forall 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) implicit none integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(3,3), intent(in) :: T33 real(pReal), dimension(3,3) :: lattice_symmetrize33 integer(pInt) :: k lattice_symmetrize33 = 0.0_pReal select case(struct) case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID) forall(k=1_pInt:3_pInt) lattice_symmetrize33(k,k) = T33(1,1) 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) use, intrinsic :: & IEEE_arithmetic use math, only: & math_qToRodrig implicit none 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) use prec, only: & tol_math_check use math, only: & math_qMul, & math_qConj implicit none 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(pInt) :: i,j,k,s,symmetry integer(kind(LATTICE_undefined_ID)) :: myStruct integer(pInt), dimension(2), parameter :: & NsymOperations = [24_pInt,12_pInt] 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_pInt case(LATTICE_hex_ID) symmetry = 2_pInt case default symmetry = 0_pInt end select else symmetry = 0_pInt 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_pInt,2_pInt) s = sum(NsymOperations(1:symmetry-1_pInt)) do i = 1_pInt,2_pInt dQ = math_qConj(dQ) ! switch order of "from -- to" do j = 1_pInt,NsymOperations(symmetry) ! run through first crystal's symmetries dQsymA = math_qMul(symOperations(1:4,s+j),dQ) ! apply sym do k = 1_pInt,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_pInt) 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) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=3), intent(in) :: structure !< lattice structure real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(sum(Ntwin)) :: characteristicShear integer(pInt) :: & 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(pInt), dimension(LATTICE_HEX_NTWIN), parameter :: & HEX_SHEARTWIN = reshape(int( [& 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 & ],pInt),[LATTICE_HEX_NTWIN]) ! indicator to formulas below if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_characteristicShear_Twin: '//trim(structure)) a = 0_pInt myFamilies: do mf = 1_pInt,size(Ntwin,1) mySystems: do ms = 1_pInt,Ntwin(mf) a = a + 1_pInt 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_pInt,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_pInt) ! <-10.1>{10.2} characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA case (2_pInt) ! <11.6>{-1-1.1} characteristicShear(a) = 1.0_pReal/cOverA case (3_pInt) ! <10.-2>{10.1} characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA case (4_pInt) ! <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_pInt,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) use IO, only: & IO_error use math, only: & INRAD, & math_axisAngleToR, & math_sym3333to66, & math_66toSym3333, & math_rotate_forward3333 implicit none integer(pInt), 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(pInt) :: i if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,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_pInt,ext_msg='lattice_C66_twin: '//trim(structure)) end select do i = 1, sum(Ntwin) R = math_axisAngleToR(coordinateSystem(1:3,2,i), 180.0_pReal * INRAD) ! 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 !> ToDo: Completely untested and incomplete and undocumented !-------------------------------------------------------------------------------------------------- function lattice_C66_trans(Ntrans,C_parent66,structure_target, & CoverA_trans,a_bcc,a_fcc) use prec, only: & tol_math_check use IO, only: & IO_error use math, only: & INRAD, & MATH_I3, & math_axisAngleToR, & math_sym3333to66, & math_66toSym3333, & math_rotate_forward3333, & math_mul33x33, & math_tensorproduct33, & math_crossproduct implicit none integer(pInt), 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) :: C_bar66, C_target_unrotated66 real(pReal), dimension(3,3,3,3) :: C_target_unrotated real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans real(pReal), dimension(3,3,sum(Ntrans)) :: Q,S real(pReal) :: a_bcc, a_fcc, CoverA_trans integer(pInt) :: i if (len_trim(structure_target) /= 3_pInt) & call IO_error(137_pInt,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_pInt,ext_msg='lattice_C66_trans (target): '//trim(structure_target)) endif do i = 1_pInt, 6_pInt 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) use IO, only: & IO_error use math, only: & INRAD, & math_tensorproduct33, & math_crossproduct, & math_mul33x3, & math_axisAngleToR implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family real(pReal), dimension(:), intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections integer(pInt), 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(pInt) :: i if (abs(sense) /= 1_pInt) call IO_error(0_pInt,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_pInt,sum(Nslip) direction = coordinateSystem(1:3,1,i) normal = coordinateSystem(1:3,2,i) np = math_mul33x3(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_tensorproduct33(direction, np) if (size(nonSchmidCoefficients)>1) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(2) * math_tensorproduct33(math_crossproduct(normal, direction), normal) if (size(nonSchmidCoefficients)>2) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(3) * math_tensorproduct33(math_crossproduct(np, direction), np) if (size(nonSchmidCoefficients)>3) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(4) * math_tensorproduct33(normal, normal) if (size(nonSchmidCoefficients)>4) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(5) * math_tensorproduct33(math_crossproduct(normal, direction), & math_crossproduct(normal, direction)) if (size(nonSchmidCoefficients)>5) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(6) * math_tensorproduct33(direction, direction) enddo end function lattice_nonSchmidMatrix !-------------------------------------------------------------------------------------------------- !> @brief Slip-slip interaction matrix !> details only active slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipSlip(Nslip,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NslipMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NSLIP), parameter :: & FCC_INTERACTIONSLIPSLIP = reshape(int( [& 1, 2, 2, 4, 6, 5, 3, 5, 5, 4, 5, 6, 9,10, 9,10,11,12, & ! ---> slip 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 slip 6, 4, 5, 2, 1, 2, 5, 3, 5, 5, 4, 6, 9,10,12,11,10, 9, & 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 & ],pInt),shape(FCC_INTERACTIONSLIPSLIP),order=[2,1]) !< 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(pInt), dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NSLIP), parameter :: & BCC_INTERACTIONSLIPSLIP = reshape(int( [& 1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! ---> slip 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 slip 5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & 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 & ],pInt),shape(BCC_INTERACTIONSLIPSLIP),order=[2,1]) !< 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(pInt), dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NSLIP), parameter :: & HEX_INTERACTIONSLIPSLIP = reshape(int( [& 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, & ! ---> slip 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 slip 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, & 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 & ],pInt),shape(HEX_INTERACTIONSLIPSLIP),order=[2,1]) !< Slip--slip interaction types for hex (onion peel naming scheme) integer(pInt), dimension(LATTICE_BCT_NSLIP,LATTICE_BCT_NSLIP), parameter :: & BCT_INTERACTIONSLIPSLIP = reshape(int( [& 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, & 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, & 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, & ! 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 & ],pInt),shape(BCT_INTERACTIONSLIPSLIP),order=[2,1]) if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_SlipSlip: '//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_pInt,ext_msg='lattice_interaction_SlipSlip: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes) end function lattice_interaction_SlipSlip !-------------------------------------------------------------------------------------------------- !> @brief Twin-twin interaction matrix !> details only active twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TwinTwin(Ntwin,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NtwinMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NTWIN), parameter :: & FCC_INTERACTIONTWINTWIN = reshape(int( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin 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 twin 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, & 2,2,2,2,2,2,1,1,1,2,2,2, & 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 & ],pInt),shape(FCC_INTERACTIONTWINTWIN),order=[2,1]) !< Twin-twin interaction types for fcc integer(pInt), dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NTWIN), parameter :: & BCC_INTERACTIONTWINTWIN = reshape(int( [& 1,3,3,3,3,3,3,2,3,3,2,3, & ! ---> twin 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 twin 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 & ],pInt),shape(BCC_INTERACTIONTWINTWIN),order=[2,1]) !< Twin-twin interaction types for bcc !< 1: self interaction !< 2: collinear interaction !< 3: other interaction integer(pInt), dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NTWIN), parameter :: & HEX_INTERACTIONTWINTWIN = reshape(int( [& 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! ---> twin 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 twin 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & 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 & ],pInt),shape(HEX_INTERACTIONTWINTWIN),order=[2,1]) !< Twin-twin interaction types for hex if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_TwinTwin: '//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_pInt,ext_msg='lattice_interaction_TwinTwin: '//trim(structure)) end select interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes) end function lattice_interaction_TwinTwin !-------------------------------------------------------------------------------------------------- !> @brief Trans-trans interaction matrix !> details only active trans systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TransTrans(Ntrans,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NtransMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NTRANS,LATTICE_FCC_NTRANS), parameter :: & FCC_INTERACTIONTRANSTRANS = reshape(int( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> trans 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 trans 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, & 2,2,2,2,2,2,1,1,1,2,2,2, & 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 & ],pInt),shape(FCC_INTERACTIONTRANSTRANS),order=[2,1]) !< Trans-trans interaction types for fcc if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_TransTrans: '//trim(structure)) if(structure(1:3) == 'fcc') then interactionTypes = FCC_INTERACTIONTRANSTRANS NtransMax = LATTICE_FCC_NTRANSSYSTEM else call IO_error(137_pInt,ext_msg='lattice_interaction_TransTrans: '//trim(structure)) end if interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes) end function lattice_interaction_TransTrans !-------------------------------------------------------------------------------------------------- !> @brief Slip-twin interaction matrix !> details only active slip and twin systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipTwin(Nslip,Ntwin,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NslipMax, & NtwinMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NTWIN), parameter :: & FCC_INTERACTIONSLIPTWIN = reshape(int( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin 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 slip 3,3,3,1,1,1,2,2,2,3,3,3, & 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 & ],pInt),shape(FCC_INTERACTIONSLIPTWIN),order=[2,1]) !< 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(pInt), dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NTWIN), parameter :: & BCC_INTERACTIONSLIPTWIN = reshape(int( [& 3,3,3,2,2,3,3,3,3,2,3,3, & ! ---> twin 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 slip 2,3,3,3,3,3,3,2,3,3,2,3, & 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 & ],pInt),shape(BCC_INTERACTIONSLIPTWIN),order=[2,1]) !< 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(pInt), dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NTWIN), parameter :: & HEX_INTERACTIONSLIPTWIN = reshape(int( [& 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 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 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 & ! ],pInt),shape(HEX_INTERACTIONSLIPTWIN),order=[2,1]) !< Slip-twin interaction types for hex if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_SlipTwin: '//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_pInt,ext_msg='lattice_interaction_SlipTwin: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes) end function lattice_interaction_SlipTwin !-------------------------------------------------------------------------------------------------- !> @brief Slip-trans interaction matrix !> details only active slip and trans systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_SlipTrans(Nslip,Ntrans,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NslipMax, & NtransMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NSLIP,LATTICE_fcc_Ntrans), parameter :: & FCC_INTERACTIONSLIPTRANS = reshape(int( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> trans 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 slip 3,3,3,1,1,1,2,2,2,3,3,3, & 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 & ],pInt),shape(FCC_INTERACTIONSLIPTRANS),order=[2,1]) !< Slip-trans interaction types for fcc if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_SlipTrans: '//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_pInt,ext_msg='lattice_interaction_SlipTrans: '//trim(structure)) end select interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes) end function lattice_interaction_SlipTrans !-------------------------------------------------------------------------------------------------- !> @brief Twin-slip interaction matrix !> details only active twin and slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_interaction_TwinSlip(Ntwin,Nslip,interactionValues,structure) result(interactionMatrix) use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NtwinMax, & NslipMax integer(pInt), dimension(:,:), allocatable :: interactionTypes integer(pInt), dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NSLIP), parameter :: & FCC_INTERACTIONTWINSLIP = 1_pInt !< Twin-Slip interaction types for fcc integer(pInt), dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NSLIP), parameter :: & BCC_INTERACTIONTWINSLIP = 1_pInt !< Twin-slip interaction types for bcc integer(pInt), dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NSLIP), parameter :: & HEX_INTERACTIONTWINSLIP = reshape(int( [& 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 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 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 & ],pInt),shape(HEX_INTERACTIONTWINSLIP),order=[2,1]) !< Twin-twin interaction types for hex if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_interaction_TwinSlip: '//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_pInt,ext_msg='lattice_interaction_TwinSlip: '//trim(structure)) end select interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes) end function lattice_interaction_TwinSlip !-------------------------------------------------------------------------------------------------- !> @brief Schmid matrix for slip !> details only active slip systems are considered !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix) use prec, only: & tol_math_check use IO, only: & IO_error use math, only: & math_trace33, & math_tensorproduct33 implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NslipMax integer(pInt) :: i if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,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_pInt,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure)) end select if (any(NslipMax(1:size(Nslip)) - Nslip < 0_pInt)) & call IO_error(145_pInt,ext_msg='Nslip '//trim(structure)) if (any(Nslip < 0_pInt)) & call IO_error(144_pInt,ext_msg='Nslip '//trim(structure)) coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA) do i = 1, sum(Nslip) SchmidMatrix(1:3,1:3,i) = math_tensorproduct33(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_pInt,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) use prec, only: & tol_math_check use IO, only: & IO_error use math, only: & math_trace33, & math_tensorproduct33 implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NtwinMax integer(pInt) :: i if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,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_pInt,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure)) end select if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntwin '//trim(structure)) if (any(Ntwin < 0_pInt)) & call IO_error(144_pInt,ext_msg='Ntwin '//trim(structure)) coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,structure,cOverA) do i = 1, sum(Ntwin) SchmidMatrix(1:3,1:3,i) = math_tensorproduct33(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_pInt,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) use prec, only: & tol_math_check use IO, only: & IO_error use math, only: & math_trace33, & math_tensorproduct33 implicit none integer(pInt), dimension(:), intent(in) :: Ntrans !< number of active twin systems per family real(pReal), intent(in) :: cOverA !< c/a ratio real(pReal), dimension(3,3,sum(Ntrans)) :: SchmidMatrix character(len=*), intent(in) :: & structure_target !< lattice structure real(pReal), dimension(3,3,sum(Ntrans)) :: devNull real(pReal) :: a_bcc, a_fcc if (len_trim(structure_target) /= 3_pInt) & call IO_error(137_pInt,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_pInt,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) use math, only: & math_tensorproduct33 use IO, only: & IO_error implicit none integer(pInt), 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(pInt), dimension(:), allocatable :: NcleavageMax integer(pInt) :: i if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,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_pInt,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure)) end select if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ncleavage '//trim(structure)) if (any(Ncleavage < 0_pInt)) & call IO_error(144_pInt,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_tensorproduct33(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) SchmidMatrix(1:3,1:3,2,i) = math_tensorproduct33(coordinateSystem(1:3,3,i),coordinateSystem(1:3,2,i)) SchmidMatrix(1:3,1:3,3,i) = math_tensorproduct33(coordinateSystem(1:3,2,i),coordinateSystem(1:3,2,i)) enddo end function lattice_SchmidMatrix_cleavage !-------------------------------------------------------------------------------------------------- !> @brief Forest projection (for edge dislocations) !-------------------------------------------------------------------------------------------------- function lattice_forestProjection(Nslip,structure,cOverA) result(projection) use math, only: & math_mul3x3 use IO, only: & IO_error implicit none integer(pInt), 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 real(pReal), dimension(:,:), allocatable :: slipSystems integer(pInt), dimension(:), allocatable :: NslipMax integer(pInt) :: i, j if (len_trim(structure) /= 3_pInt) & call IO_error(137_pInt,ext_msg='lattice_forestProjection: '//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_pInt,ext_msg='lattice_forestProjection: '//trim(structure)) end select if (any(NslipMax(1:size(Nslip)) - Nslip < 0_pInt)) & call IO_error(145_pInt,ext_msg='Nslip '//trim(structure)) if (any(Nslip < 0_pInt)) & call IO_error(144_pInt,ext_msg='Nslip '//trim(structure)) coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA) do i=1_pInt, sum(Nslip); do j=1_pInt, sum(Nslip) projection(i,j) = abs(math_mul3x3(coordinateSystem(1:3,2,i),coordinateSystem(1:3,3,j))) enddo; enddo end function lattice_forestProjection !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced interaction matrix !-------------------------------------------------------------------------------------------------- function buildInteraction(activeA,activeB,maxA,maxB,values,matrix) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: & activeA, & !< number of active systems as specified in material.config activeB, & !< number of active systems as specified in material.config maxA, & !< number of maximum available systems maxB !< number of maximum available systems real(pReal), dimension(:), intent(in) :: values !< interaction values integer(pInt), dimension(:,:), intent(in) :: matrix !< complete interaction matrix real(pReal), dimension(sum(activeA),sum(activeB)) :: buildInteraction integer(pInt) :: & index_myFamily, index_otherFamily, & mf, ms, of, os myFamilies: do mf = 1_pInt,size(activeA,1) index_myFamily = sum(activeA(1:mf-1_pInt)) mySystems: do ms = 1_pInt,activeA(mf) otherFamilies: do of = 1_pInt,size(activeB,1) index_otherFamily = sum(activeB(1:of-1_pInt)) otherSystems: do os = 1_pInt,activeB(of) if(matrix(sum(maxA(1:mf-1))+ms, sum(maxB(1:of-1))+os) > size(values)) & call IO_error(138,ext_msg='buildInteraction') buildInteraction(index_myFamily+ms,index_otherFamily+os) = & values(matrix(sum(maxA(1:mf-1))+ms, sum(maxB(1:of-1))+os)) enddo otherSystems; enddo otherFamilies; enddo mySystems;enddo myFamilies end function buildInteraction !-------------------------------------------------------------------------------------------------- !> @brief build a local coordinate system in a slip, twin, trans, cleavage system !> @details Order: Direction, plane (normal), and common perpendicular !-------------------------------------------------------------------------------------------------- function buildCoordinateSystem(active,complete,system,structure,cOverA) use IO, only: & IO_error use math, only: & math_crossproduct implicit none integer(pInt), 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(pInt) :: & 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_pInt) & call IO_error(137_pInt,ext_msg='buildCoordinateSystem: '//trim(structure)) if (trim(structure(1:3)) == 'bct' .and. cOverA > 2.0_pReal) & call IO_error(131_pInt,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_pInt,ext_msg='buildCoordinateSystem:'//trim(structure)) a = 0_pInt activeFamilies: do f = 1_pInt,size(active,1) activeSystems: do s = 1_pInt,active(f) a = a + 1_pInt 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_pInt,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_crossproduct(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) use prec, only: & dEq0 use math, only: & math_crossproduct, & math_tensorproduct33, & math_mul33x33, & math_mul33x3, & math_axisAngleToR, & INRAD, & MATH_I3 use IO, only: & IO_error implicit none integer(pInt), 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(pInt) :: & 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(pInt), dimension(9,LATTICE_fcc_Ntrans), parameter :: & LATTICE_FCCTOBCC_BAINVARIANT = reshape(int( [& 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 & ],pInt),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_pInt .or. size(Ntrans) > 1_pInt) print*, 'mist' ! ToDo if (a_bcc > 0.0_pReal .and. dEq0(cOverA)) then ! fcc -> bcc transformation do i = 1_pInt,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_tensorproduct33(x,x) & + (a_bcc/a_fcc)*math_tensorproduct33(y,y) * sqrt(2.0_pReal) & + (a_bcc/a_fcc)*math_tensorproduct33(z,z) * sqrt(2.0_pReal) Q(1:3,1:3,i) = math_mul33x33(R,B) S(1:3,1:3,i) = math_mul33x33(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_pInt,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_crossproduct(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) = math_mul33x33(Q(1:3,1:3,i), math_mul33x33(math_mul33x33(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_pInt) !ToDo: define error endif end subroutine buildTransformationSystem end module lattice