1079 lines
55 KiB
Fortran
1079 lines
55 KiB
Fortran
!--------------------------------------------------------------------------------------------------
|
||
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @brief material subroutine incoprorating dislocation and twinning physics
|
||
!> @details to be done
|
||
!--------------------------------------------------------------------------------------------------
|
||
submodule(constitutive) plastic_dislotwin
|
||
|
||
real(pReal), parameter :: &
|
||
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
|
||
|
||
type :: tParameters
|
||
real(pReal) :: &
|
||
mu = 1.0_pReal, & !< equivalent shear modulus
|
||
nu = 1.0_pReal, & !< equivalent shear Poisson's ratio
|
||
D0 = 1.0_pReal, & !< prefactor for self-diffusion coefficient
|
||
Qsd = 1.0_pReal, & !< activation energy for dislocation climb
|
||
omega = 1.0_pReal, & !< frequency factor for dislocation climb
|
||
D = 1.0_pReal, & !< grain size
|
||
p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
|
||
q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
|
||
CEdgeDipMinDistance = 1.0_pReal, & !<
|
||
i_tw = 1.0_pReal, & !<
|
||
tau_0 = 1.0_pReal, & !< strength due to elements in solid solution
|
||
L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors
|
||
L_tr = 1.0_pReal, & !< Length of trans nuclei in Burgers vectors
|
||
xc_twin = 1.0_pReal, & !< critical distance for formation of twin nucleus
|
||
xc_trans = 1.0_pReal, & !< critical distance for formation of trans nucleus
|
||
V_cs = 1.0_pReal, & !< cross slip volume
|
||
sbResistance = 1.0_pReal, & !< value for shearband resistance
|
||
sbVelocity = 1.0_pReal, & !< value for shearband velocity_0
|
||
E_sb = 1.0_pReal, & !< activation energy for shear bands
|
||
SFE_0K = 1.0_pReal, & !< stacking fault energy at zero K
|
||
dSFE_dT = 1.0_pReal, & !< temperature dependence of stacking fault energy
|
||
gamma_fcc_hex = 1.0_pReal, & !< Free energy difference between austensite and martensite
|
||
i_tr = 1.0_pReal, & !<
|
||
h = 1.0_pReal !< Stack height of hex nucleus
|
||
real(pReal), allocatable, dimension(:) :: &
|
||
b_sl, & !< absolute length of burgers vector [m] for each slip system
|
||
b_tw, & !< absolute length of burgers vector [m] for each twin system
|
||
b_tr, & !< absolute length of burgers vector [m] for each transformation system
|
||
Delta_F,& !< activation energy for glide [J] for each slip system
|
||
v0, & !< dislocation velocity prefactor [m/s] for each slip system
|
||
dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system
|
||
dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system
|
||
t_tw, & !< twin thickness [m] for each twin system
|
||
CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
|
||
t_tr, & !< martensite lamellar thickness [m] for each trans system and instance
|
||
p, & !< p-exponent in glide velocity
|
||
q, & !< q-exponent in glide velocity
|
||
r, & !< r-exponent in twin nucleation rate
|
||
s, & !< s-exponent in trans nucleation rate
|
||
gamma_char, & !< characteristic shear for twins
|
||
B !< drag coefficient
|
||
real(pReal), allocatable, dimension(:,:) :: &
|
||
h_sl_sl, & !<
|
||
h_sl_tw, & !<
|
||
h_tw_tw, & !<
|
||
h_sl_tr, & !<
|
||
h_tr_tr, & !<
|
||
n0_sl, & !< slip system normal
|
||
forestProjection, &
|
||
C66
|
||
real(pReal), allocatable, dimension(:,:,:) :: &
|
||
P_sl, &
|
||
P_tw, &
|
||
P_tr, &
|
||
C66_tw, &
|
||
C66_tr
|
||
integer :: &
|
||
sum_N_sl, & !< total number of active slip system
|
||
sum_N_tw, & !< total number of active twin system
|
||
sum_N_tr !< total number of active transformation system
|
||
integer, allocatable, dimension(:,:) :: &
|
||
fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
|
||
character(len=pStringLen), allocatable, dimension(:) :: &
|
||
output
|
||
logical :: &
|
||
ExtendedDislocations, & !< consider split into partials for climb calculation
|
||
fccTwinTransNucleation, & !< twinning and transformation models are for fcc
|
||
dipoleFormation !< flag indicating consideration of dipole formation
|
||
end type !< container type for internal constitutive parameters
|
||
|
||
type :: tDislotwinState
|
||
real(pReal), dimension(:,:), pointer :: &
|
||
rho_mob, &
|
||
rho_dip, &
|
||
gamma_sl, &
|
||
f_tw, &
|
||
f_tr
|
||
end type tDislotwinState
|
||
|
||
type :: tDislotwinMicrostructure
|
||
real(pReal), dimension(:,:), allocatable :: &
|
||
Lambda_sl, & !< mean free path between 2 obstacles seen by a moving dislocation
|
||
Lambda_tw, & !< mean free path between 2 obstacles seen by a growing twin
|
||
Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite
|
||
tau_pass, &
|
||
tau_hat_tw, &
|
||
tau_hat_tr, &
|
||
V_tw, & !< volume of a new twin
|
||
V_tr, & !< volume of a new martensite disc
|
||
tau_r_tw, & !< stress to bring partials close together (twin)
|
||
tau_r_tr !< stress to bring partials close together (trans)
|
||
end type tDislotwinMicrostructure
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! containers for parameters and state
|
||
type(tParameters), allocatable, dimension(:) :: param
|
||
type(tDislotwinState), allocatable, dimension(:) :: &
|
||
dotState, &
|
||
state
|
||
type(tDislotwinMicrostructure), allocatable, dimension(:) :: dependentState
|
||
|
||
contains
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Perform module initialization.
|
||
!> @details reads in material parameters, allocates arrays, and does sanity checks
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotwin_init
|
||
|
||
integer :: &
|
||
Ninstance, &
|
||
p, i, &
|
||
NipcMyPhase, &
|
||
sizeState, sizeDotState, &
|
||
startIndex, endIndex
|
||
integer, dimension(:), allocatable :: &
|
||
N_sl, N_tw, N_tr
|
||
real(pReal), allocatable, dimension(:) :: &
|
||
rho_mob_0, & !< initial unipolar dislocation density per slip system
|
||
rho_dip_0 !< initial dipole dislocation density per slip system
|
||
character(len=pStringLen) :: &
|
||
extmsg = ''
|
||
|
||
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_LABEL//' init -+>>>'; flush(6)
|
||
|
||
write(6,'(/,a)') ' Ma and Roters, Acta Materialia 52(12):3603–3612, 2004'
|
||
write(6,'(a)') ' https://doi.org/10.1016/j.actamat.2004.04.012'
|
||
|
||
write(6,'(/,a)') ' Roters et al., Computational Materials Science 39:91–95, 2007'
|
||
write(6,'(a)') ' https://doi.org/10.1016/j.commatsci.2006.04.014'
|
||
|
||
write(6,'(/,a)') ' Wong et al., Acta Materialia 118:140–151, 2016'
|
||
write(6,'(a,/)') ' https://doi.org/10.1016/j.actamat.2016.07.032'
|
||
|
||
Ninstance = count(phase_plasticity == PLASTICITY_DISLOTWIN_ID)
|
||
|
||
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
|
||
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
|
||
|
||
allocate(param(Ninstance))
|
||
allocate(state(Ninstance))
|
||
allocate(dotState(Ninstance))
|
||
allocate(dependentState(Ninstance))
|
||
|
||
do p = 1, size(phase_plasticity)
|
||
if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
|
||
associate(prm => param(phase_plasticityInstance(p)), &
|
||
dot => dotState(phase_plasticityInstance(p)), &
|
||
stt => state(phase_plasticityInstance(p)), &
|
||
dst => dependentState(phase_plasticityInstance(p)), &
|
||
config => config_phase(p))
|
||
|
||
prm%output = config%getStrings('(output)', defaultVal=emptyStringArray)
|
||
|
||
! This data is read in already in lattice
|
||
prm%mu = lattice_mu(p)
|
||
prm%nu = lattice_nu(p)
|
||
prm%C66 = lattice_C66(1:6,1:6,p)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! slip related parameters
|
||
N_sl = config%getInts('nslip',defaultVal=emptyIntArray)
|
||
prm%sum_N_sl = sum(abs(N_sl))
|
||
slipActive: if (prm%sum_N_sl > 0) then
|
||
prm%P_sl = lattice_SchmidMatrix_slip(N_sl,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,config%getFloats('interaction_slipslip'), &
|
||
config%getString('lattice_structure'))
|
||
prm%forestProjection = lattice_forestProjection_edge(N_sl,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
prm%forestProjection = transpose(prm%forestProjection)
|
||
|
||
prm%n0_sl = lattice_slip_normal(N_sl,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == lattice_FCC_ID) &
|
||
.and. (N_sl(1) == 12)
|
||
if(prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_FCC_TWINNUCLEATIONSLIPPAIR
|
||
|
||
rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(N_sl))
|
||
rho_dip_0 = config%getFloats('rhoedgedip0',requiredSize=size(N_sl))
|
||
prm%v0 = config%getFloats('v0', requiredSize=size(N_sl))
|
||
prm%b_sl = config%getFloats('slipburgers',requiredSize=size(N_sl))
|
||
prm%Delta_F = config%getFloats('qedge', requiredSize=size(N_sl))
|
||
prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(N_sl))
|
||
prm%p = config%getFloats('p_slip', requiredSize=size(N_sl))
|
||
prm%q = config%getFloats('q_slip', requiredSize=size(N_sl))
|
||
prm%B = config%getFloats('b', requiredSize=size(N_sl), &
|
||
defaultVal=[(0.0_pReal, i=1,size(N_sl))])
|
||
|
||
prm%tau_0 = config%getFloat('solidsolutionstrength')
|
||
prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
|
||
prm%D0 = config%getFloat('d0')
|
||
prm%Qsd = config%getFloat('qsd')
|
||
prm%ExtendedDislocations = config%keyExists('/extend_dislocations/')
|
||
if (prm%ExtendedDislocations) then
|
||
prm%SFE_0K = config%getFloat('sfe_0k')
|
||
prm%dSFE_dT = config%getFloat('dsfe_dt')
|
||
endif
|
||
|
||
prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
|
||
|
||
! multiplication factor according to crystal structure (nearest neighbors bcc vs fcc/hex)
|
||
! details: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
|
||
prm%omega = config%getFloat('omega', defaultVal = 1000.0_pReal) &
|
||
* merge(12.0_pReal,8.0_pReal,any(lattice_structure(p) == [lattice_FCC_ID,lattice_HEX_ID]))
|
||
|
||
! expand: family => system
|
||
rho_mob_0 = math_expand(rho_mob_0, N_sl)
|
||
rho_dip_0 = math_expand(rho_dip_0, N_sl)
|
||
prm%v0 = math_expand(prm%v0, N_sl)
|
||
prm%b_sl = math_expand(prm%b_sl, N_sl)
|
||
prm%Delta_F = math_expand(prm%Delta_F, N_sl)
|
||
prm%CLambdaSlip = math_expand(prm%CLambdaSlip, N_sl)
|
||
prm%p = math_expand(prm%p, N_sl)
|
||
prm%q = math_expand(prm%q, N_sl)
|
||
prm%B = math_expand(prm%B, N_sl)
|
||
|
||
! sanity checks
|
||
if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' D0'
|
||
if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' Qsd'
|
||
if (any(rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
|
||
if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0'
|
||
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
|
||
if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
|
||
if (any(prm%Delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' Delta_F'
|
||
if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//' CLambdaSlip'
|
||
if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B'
|
||
if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//' p'
|
||
if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//' q'
|
||
else slipActive
|
||
rho_mob_0 = emptyRealArray; rho_dip_0 = emptyRealArray
|
||
allocate(prm%b_sl,prm%Delta_F,prm%v0,prm%CLambdaSlip,prm%p,prm%q,prm%B,source=emptyRealArray)
|
||
allocate(prm%forestProjection(0,0),prm%h_sl_sl(0,0))
|
||
endif slipActive
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! twin related parameters
|
||
N_tw = config%getInts('ntwin', defaultVal=emptyIntArray)
|
||
prm%sum_N_tw = sum(abs(N_tw))
|
||
twinActive: if (prm%sum_N_tw > 0) then
|
||
prm%P_tw = lattice_SchmidMatrix_twin(N_tw,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
prm%h_tw_tw = lattice_interaction_TwinByTwin(N_tw,&
|
||
config%getFloats('interaction_twintwin'), &
|
||
config%getString('lattice_structure'))
|
||
|
||
prm%b_tw = config%getFloats('twinburgers', requiredSize=size(N_tw))
|
||
prm%t_tw = config%getFloats('twinsize', requiredSize=size(N_tw))
|
||
prm%r = config%getFloats('r_twin', requiredSize=size(N_tw))
|
||
|
||
prm%xc_twin = config%getFloat('xc_twin')
|
||
prm%L_tw = config%getFloat('l0_twin')
|
||
prm%i_tw = config%getFloat('cmfptwin')
|
||
|
||
prm%gamma_char= lattice_characteristicShear_Twin(N_tw,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
|
||
prm%C66_tw = lattice_C66_twin(N_tw,prm%C66,config%getString('lattice_structure'),&
|
||
config%getFloat('c/a',defaultVal=0.0_pReal))
|
||
|
||
if (.not. prm%fccTwinTransNucleation) then
|
||
prm%dot_N_0_tw = config%getFloats('ndot0_twin')
|
||
prm%dot_N_0_tw = math_expand(prm%dot_N_0_tw,N_tw)
|
||
endif
|
||
|
||
! expand: family => system
|
||
prm%b_tw = math_expand(prm%b_tw,N_tw)
|
||
prm%t_tw = math_expand(prm%t_tw,N_tw)
|
||
prm%r = math_expand(prm%r,N_tw)
|
||
|
||
! sanity checks
|
||
if ( prm%xc_twin < 0.0_pReal) extmsg = trim(extmsg)//' xc_twin'
|
||
if ( prm%L_tw < 0.0_pReal) extmsg = trim(extmsg)//' L_tw'
|
||
if ( prm%i_tw < 0.0_pReal) extmsg = trim(extmsg)//' i_tw'
|
||
if (any(prm%b_tw < 0.0_pReal)) extmsg = trim(extmsg)//' b_tw'
|
||
if (any(prm%t_tw < 0.0_pReal)) extmsg = trim(extmsg)//' t_tw'
|
||
if (any(prm%r < 0.0_pReal)) extmsg = trim(extmsg)//' r'
|
||
if (.not. prm%fccTwinTransNucleation) then
|
||
if (any(prm%dot_N_0_tw < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tw'
|
||
endif
|
||
else twinActive
|
||
allocate(prm%gamma_char,prm%b_tw,prm%dot_N_0_tw,prm%t_tw,prm%r,source=emptyRealArray)
|
||
allocate(prm%h_tw_tw(0,0))
|
||
endif twinActive
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! transformation related parameters
|
||
N_tr = config%getInts('ntrans', defaultVal=emptyIntArray)
|
||
prm%sum_N_tr = sum(abs(N_tr))
|
||
transActive: if (prm%sum_N_tr > 0) then
|
||
prm%b_tr = config%getFloats('transburgers')
|
||
prm%b_tr = math_expand(prm%b_tr,N_tr)
|
||
|
||
prm%h = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%i_tr = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%gamma_fcc_hex = config%getFloat('deltag')
|
||
prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%L_tr = config%getFloat('l0_trans')
|
||
|
||
prm%h_tr_tr = lattice_interaction_TransByTrans(N_tr,config%getFloats('interaction_transtrans'), &
|
||
config%getString('lattice_structure'))
|
||
|
||
prm%C66_tr = lattice_C66_trans(N_tr,prm%C66,config%getString('trans_lattice_structure'), &
|
||
0.0_pReal, &
|
||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
||
config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
||
prm%P_tr = lattice_SchmidMatrix_trans(N_tr,config%getString('trans_lattice_structure'), &
|
||
0.0_pReal, &
|
||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
||
config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
||
if (lattice_structure(p) /= lattice_FCC_ID) then
|
||
prm%dot_N_0_tr = config%getFloats('ndot0_trans')
|
||
prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,N_tr)
|
||
endif
|
||
prm%t_tr = config%getFloats('lamellarsize')
|
||
prm%t_tr = math_expand(prm%t_tr,N_tr)
|
||
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
|
||
prm%s = math_expand(prm%s,N_tr)
|
||
|
||
! sanity checks
|
||
if ( prm%xc_trans < 0.0_pReal) extmsg = trim(extmsg)//' xc_trans'
|
||
if ( prm%L_tr < 0.0_pReal) extmsg = trim(extmsg)//' L_tr'
|
||
if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr'
|
||
if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr'
|
||
if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' s'
|
||
if (lattice_structure(p) /= lattice_FCC_ID) then
|
||
if (any(prm%dot_N_0_tr < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tr'
|
||
endif
|
||
else transActive
|
||
allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyRealArray)
|
||
allocate(prm%h_tr_tr(0,0))
|
||
endif transActive
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! shearband related parameters
|
||
prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
|
||
if (prm%sbVelocity > 0.0_pReal) then
|
||
prm%sbResistance = config%getFloat('shearbandresistance')
|
||
prm%E_sb = config%getFloat('qedgepersbsystem')
|
||
prm%p_sb = config%getFloat('p_shearband')
|
||
prm%q_sb = config%getFloat('q_shearband')
|
||
|
||
! sanity checks
|
||
if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' shearbandresistance'
|
||
if (prm%E_sb < 0.0_pReal) extmsg = trim(extmsg)//' qedgepersbsystem'
|
||
if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_shearband'
|
||
if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_shearband'
|
||
endif
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! parameters required for several mechanisms and their interactions
|
||
if(prm%sum_N_sl + prm%sum_N_tw + prm%sum_N_tw > 0) &
|
||
prm%D = config%getFloat('grainsize')
|
||
|
||
twinOrSlipActive: if (prm%sum_N_tw + prm%sum_N_tr > 0) then
|
||
prm%SFE_0K = config%getFloat('sfe_0k')
|
||
prm%dSFE_dT = config%getFloat('dsfe_dt')
|
||
prm%V_cs = config%getFloat('vcrossslip')
|
||
endif twinOrSlipActive
|
||
|
||
slipAndTwinActive: if (prm%sum_N_sl * prm%sum_N_tw > 0) then
|
||
prm%h_sl_tw = lattice_interaction_SlipByTwin(N_sl,N_tw,&
|
||
config%getFloats('interaction_sliptwin'), &
|
||
config%getString('lattice_structure'))
|
||
if (prm%fccTwinTransNucleation .and. size(N_tw) /= 1) extmsg = trim(extmsg)//' interaction_sliptwin'
|
||
endif slipAndTwinActive
|
||
|
||
slipAndTransActive: if (prm%sum_N_sl * prm%sum_N_tr > 0) then
|
||
prm%h_sl_tr = lattice_interaction_SlipByTrans(N_sl,N_tr,&
|
||
config%getFloats('interaction_sliptrans'), &
|
||
config%getString('lattice_structure'))
|
||
if (prm%fccTwinTransNucleation .and. size(N_tr) /= 1) extmsg = trim(extmsg)//' interaction_sliptrans'
|
||
endif slipAndTransActive
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
|
||
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl &
|
||
+ size(['f_tw']) * prm%sum_N_tw &
|
||
+ size(['f_tr']) * prm%sum_N_tr
|
||
sizeState = sizeDotState
|
||
|
||
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! locally defined state aliases and initialization of state0 and atol
|
||
startIndex = 1
|
||
endIndex = prm%sum_N_sl
|
||
stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rho_mob= spread(rho_mob_0,2,NipcMyPhase)
|
||
dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('atol_rho',defaultVal=1.0_pReal)
|
||
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_rho'
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_sl
|
||
stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rho_dip= spread(rho_dip_0,2,NipcMyPhase)
|
||
dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('atol_rho',defaultVal=1.0_pReal)
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_sl
|
||
stt%gamma_sl=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%gamma_sl=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%atol(startIndex:endIndex) = 1.0e-2_pReal
|
||
! global alias
|
||
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_tw
|
||
stt%f_tw=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%f_tw=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('f_twin',defaultVal=1.0e-7_pReal)
|
||
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_twin'
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_tr
|
||
stt%f_tr=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%f_tr=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('f_trans',defaultVal=1.0e-6_pReal)
|
||
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_trans'
|
||
|
||
allocate(dst%Lambda_sl (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_pass (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(dst%Lambda_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_hat_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_r_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%V_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(dst%Lambda_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_hat_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_r_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%V_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
|
||
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
|
||
|
||
end associate
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! exit if any parameter is out of range
|
||
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOTWIN_LABEL//')')
|
||
|
||
enddo
|
||
|
||
end subroutine plastic_dislotwin_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Return the homogenized elasticity matrix.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
|
||
|
||
real(pReal), dimension(6,6) :: &
|
||
homogenizedC
|
||
integer, intent(in) :: &
|
||
ipc, & !< component-ID of integration point
|
||
ip, & !< integration point
|
||
el !< element
|
||
|
||
integer :: i, &
|
||
of
|
||
real(pReal) :: f_unrotated
|
||
|
||
of = material_phasememberAt(ipc,ip,el)
|
||
associate(prm => param(phase_plasticityInstance(material_phaseAt(ipc,el))),&
|
||
stt => state(phase_plasticityInstance(material_phaseAT(ipc,el))))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
homogenizedC = f_unrotated * prm%C66
|
||
do i=1,prm%sum_N_tw
|
||
homogenizedC = homogenizedC &
|
||
+ stt%f_tw(i,of)*prm%C66_tw(1:6,1:6,i)
|
||
enddo
|
||
do i=1,prm%sum_N_tr
|
||
homogenizedC = homogenizedC &
|
||
+ stt%f_tr(i,of)*prm%C66_tr(1:6,1:6,i)
|
||
enddo
|
||
|
||
end associate
|
||
|
||
end function plastic_dislotwin_homogenizedC
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate plastic velocity gradient and its tangent.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
|
||
|
||
real(pReal), dimension(3,3), intent(out) :: Lp
|
||
real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
|
||
real(pReal), dimension(3,3), intent(in) :: Mp
|
||
integer, intent(in) :: instance,of
|
||
real(pReal), intent(in) :: T
|
||
|
||
integer :: i,k,l,m,n
|
||
real(pReal) :: &
|
||
f_unrotated,StressRatio_p,&
|
||
BoltzmannRatio, &
|
||
ddot_gamma_dtau, &
|
||
tau
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
dot_gamma_sl,ddot_gamma_dtau_slip
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
dot_gamma_twin,ddot_gamma_dtau_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
dot_gamma_tr,ddot_gamma_dtau_trans
|
||
real(pReal):: dot_gamma_sb
|
||
real(pReal), dimension(3,3) :: eigVectors, P_sb
|
||
real(pReal), dimension(3) :: eigValues
|
||
real(pReal), dimension(3,6), parameter :: &
|
||
sb_sComposition = &
|
||
reshape(real([&
|
||
1, 0, 1, &
|
||
1, 0,-1, &
|
||
1, 1, 0, &
|
||
1,-1, 0, &
|
||
0, 1, 1, &
|
||
0, 1,-1 &
|
||
],pReal),[ 3,6]), &
|
||
sb_mComposition = &
|
||
reshape(real([&
|
||
1, 0,-1, &
|
||
1, 0,+1, &
|
||
1,-1, 0, &
|
||
1, 1, 0, &
|
||
0, 1,-1, &
|
||
0, 1, 1 &
|
||
],pReal),[ 3,6])
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
Lp = 0.0_pReal
|
||
dLp_dMp = 0.0_pReal
|
||
|
||
call kinetics_slip(Mp,T,instance,of,dot_gamma_sl,ddot_gamma_dtau_slip)
|
||
slipContribution: do i = 1, prm%sum_N_sl
|
||
Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_slip(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i)
|
||
enddo slipContribution
|
||
|
||
call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin,ddot_gamma_dtau_twin)
|
||
twinContibution: do i = 1, prm%sum_N_tw
|
||
Lp = Lp + dot_gamma_twin(i)*prm%P_tw(1:3,1:3,i)
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_twin(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i)
|
||
enddo twinContibution
|
||
|
||
call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr,ddot_gamma_dtau_trans)
|
||
transContibution: do i = 1, prm%sum_N_tr
|
||
Lp = Lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i)
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_trans(i)* prm%P_tr(k,l,i)*prm%P_tr(m,n,i)
|
||
enddo transContibution
|
||
|
||
Lp = Lp * f_unrotated
|
||
dLp_dMp = dLp_dMp * f_unrotated
|
||
|
||
shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
|
||
|
||
BoltzmannRatio = prm%E_sb/(kB*T)
|
||
call math_eigh33(Mp,eigValues,eigVectors) ! is Mp symmetric by design?
|
||
|
||
do i = 1,6
|
||
P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),&
|
||
matmul(eigVectors,sb_mComposition(1:3,i)))
|
||
tau = math_tensordot(Mp,P_sb)
|
||
|
||
significantShearBandStress: if (abs(tau) > tol_math_check) then
|
||
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%p_sb
|
||
dot_gamma_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1-StressRatio_p)**prm%q_sb), tau)
|
||
ddot_gamma_dtau = abs(dot_gamma_sb)*BoltzmannRatio* prm%p_sb*prm%q_sb/ prm%sbResistance &
|
||
* (abs(tau)/prm%sbResistance)**(prm%p_sb-1.0_pReal) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%q_sb-1.0_pReal)
|
||
|
||
Lp = Lp + dot_gamma_sb * P_sb
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau * P_sb(k,l) * P_sb(m,n)
|
||
endif significantShearBandStress
|
||
enddo
|
||
|
||
endif shearBandingContribution
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate the rate of change of microstructure.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotwin_dotState(Mp,T,instance,of)
|
||
|
||
real(pReal), dimension(3,3), intent(in):: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature at integration point
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
integer :: i
|
||
real(pReal) :: &
|
||
f_unrotated, &
|
||
rho_dip_distance, &
|
||
v_cl, & !< climb velocity
|
||
Gamma, & !< stacking fault energy
|
||
tau, &
|
||
sigma_cl, & !< climb stress
|
||
b_d !< ratio of burgers vector to stacking fault width
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
dot_rho_dip_formation, &
|
||
dot_rho_dip_climb, &
|
||
rho_dip_distance_min, &
|
||
dot_gamma_sl
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
dot_gamma_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
dot_gamma_tr
|
||
|
||
associate(prm => param(instance), stt => state(instance), &
|
||
dot => dotState(instance), dst => dependentState(instance))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
call kinetics_slip(Mp,T,instance,of,dot_gamma_sl)
|
||
dot%gamma_sl(:,of) = abs(dot_gamma_sl)
|
||
|
||
rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl
|
||
|
||
slipState: do i = 1, prm%sum_N_sl
|
||
tau = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
|
||
|
||
significantSlipStress: if (dEq0(tau)) then
|
||
dot_rho_dip_formation(i) = 0.0_pReal
|
||
dot_rho_dip_climb(i) = 0.0_pReal
|
||
else significantSlipStress
|
||
rho_dip_distance = 3.0_pReal*prm%mu*prm%b_sl(i)/(16.0_pReal*PI*abs(tau))
|
||
rho_dip_distance = math_clip(rho_dip_distance, right = dst%Lambda_sl(i,of))
|
||
rho_dip_distance = math_clip(rho_dip_distance, left = rho_dip_distance_min(i))
|
||
|
||
if (prm%dipoleFormation) then
|
||
dot_rho_dip_formation(i) = 2.0_pReal*(rho_dip_distance-rho_dip_distance_min(i))/prm%b_sl(i) &
|
||
* stt%rho_mob(i,of)*abs(dot_gamma_sl(i))
|
||
else
|
||
dot_rho_dip_formation(i) = 0.0_pReal
|
||
endif
|
||
|
||
if (dEq(rho_dip_distance,rho_dip_distance_min(i))) then
|
||
dot_rho_dip_climb(i) = 0.0_pReal
|
||
else
|
||
!@details: Refer: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
|
||
sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i)))
|
||
if (prm%ExtendedDislocations) then
|
||
Gamma = prm%SFE_0K + prm%dSFE_dT * T
|
||
b_d = 24.0_pReal*PI*(1.0_pReal - prm%nu)/(2.0_pReal + prm%nu)* Gamma/(prm%mu*prm%b_sl(i))
|
||
else
|
||
b_d = 1.0_pReal
|
||
endif
|
||
v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Qsd/(kB*T)) &
|
||
* (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal)
|
||
|
||
dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,of) &
|
||
/ (rho_dip_distance-rho_dip_distance_min(i))
|
||
endif
|
||
endif significantSlipStress
|
||
enddo slipState
|
||
|
||
dot%rho_mob(:,of) = abs(dot_gamma_sl)/(prm%b_sl*dst%Lambda_sl(:,of)) &
|
||
- dot_rho_dip_formation &
|
||
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_mob(:,of)*abs(dot_gamma_sl)
|
||
|
||
dot%rho_dip(:,of) = dot_rho_dip_formation &
|
||
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_dip(:,of)*abs(dot_gamma_sl) &
|
||
- dot_rho_dip_climb
|
||
|
||
call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin)
|
||
dot%f_tw(:,of) = f_unrotated*dot_gamma_twin/prm%gamma_char
|
||
|
||
call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr)
|
||
dot%f_tr(:,of) = f_unrotated*dot_gamma_tr
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_dotState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate derived quantities from state.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotwin_dependentState(T,instance,of)
|
||
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), intent(in) :: &
|
||
T
|
||
|
||
real(pReal) :: &
|
||
sumf_twin,Gamma,sumf_trans
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
inv_lambda_sl_sl, & !< 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
||
inv_lambda_sl_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
||
inv_lambda_sl_tr !< 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
inv_lambda_tw_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
||
f_over_t_tw
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite
|
||
f_over_t_tr
|
||
real(pReal), dimension(:), allocatable :: &
|
||
x0
|
||
|
||
|
||
associate(prm => param(instance),&
|
||
stt => state(instance),&
|
||
dst => dependentState(instance))
|
||
|
||
sumf_twin = sum(stt%f_tw(1:prm%sum_N_tw,of))
|
||
sumf_trans = sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
Gamma = prm%SFE_0K + prm%dSFE_dT * T
|
||
|
||
!* rescaled volume fraction for topology
|
||
f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,of)/prm%t_tw ! this is per system ...
|
||
f_over_t_tr = sumf_trans/prm%t_tr ! but this not
|
||
! ToDo ...Physically correct, but naming could be adjusted
|
||
|
||
inv_lambda_sl_sl = sqrt(matmul(prm%forestProjection, &
|
||
stt%rho_mob(:,of)+stt%rho_dip(:,of)))/prm%CLambdaSlip
|
||
|
||
if (prm%sum_N_tw > 0 .and. prm%sum_N_sl > 0) &
|
||
inv_lambda_sl_tw = matmul(prm%h_sl_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
|
||
|
||
inv_lambda_tw_tw = matmul(prm%h_tw_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
|
||
|
||
if (prm%sum_N_tr > 0 .and. prm%sum_N_sl > 0) &
|
||
inv_lambda_sl_tr = matmul(prm%h_sl_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
|
||
|
||
inv_lambda_tr_tr = matmul(prm%h_tr_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
|
||
|
||
if ((prm%sum_N_tw > 0) .or. (prm%sum_N_tr > 0)) then ! ToDo: better logic needed here
|
||
dst%Lambda_sl(:,of) = prm%D &
|
||
/ (1.0_pReal+prm%D*(inv_lambda_sl_sl + inv_lambda_sl_tw + inv_lambda_sl_tr))
|
||
else
|
||
dst%Lambda_sl(:,of) = prm%D &
|
||
/ (1.0_pReal+prm%D*inv_lambda_sl_sl) !!!!!! correct?
|
||
endif
|
||
|
||
dst%Lambda_tw(:,of) = prm%i_tw*prm%D/(1.0_pReal+prm%D*inv_lambda_tw_tw)
|
||
dst%Lambda_tr(:,of) = prm%i_tr*prm%D/(1.0_pReal+prm%D*inv_lambda_tr_tr)
|
||
|
||
!* threshold stress for dislocation motion
|
||
dst%tau_pass(:,of) = prm%mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
|
||
|
||
!* threshold stress for growing twin/martensite
|
||
if(prm%sum_N_tw == prm%sum_N_sl) &
|
||
dst%tau_hat_tw(:,of) = Gamma/(3.0_pReal*prm%b_tw) &
|
||
+ 3.0_pReal*prm%b_tw*prm%mu/(prm%L_tw*prm%b_sl) ! slip burgers here correct?
|
||
if(prm%sum_N_tr == prm%sum_N_sl) &
|
||
dst%tau_hat_tr(:,of) = Gamma/(3.0_pReal*prm%b_tr) &
|
||
+ 3.0_pReal*prm%b_tr*prm%mu/(prm%L_tr*prm%b_sl) & ! slip burgers here correct?
|
||
+ prm%h*prm%gamma_fcc_hex/ (3.0_pReal*prm%b_tr)
|
||
|
||
dst%V_tw(:,of) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,of)**2.0_pReal
|
||
dst%V_tr(:,of) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,of)**2.0_pReal
|
||
|
||
|
||
x0 = prm%mu*prm%b_tw**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip and is the same for twin and trans
|
||
dst%tau_r_tw(:,of) = prm%mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
|
||
|
||
x0 = prm%mu*prm%b_tr**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip
|
||
dst%tau_r_tr(:,of) = prm%mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_dependentState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Write results to HDF5 output file.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotwin_results(instance,group)
|
||
|
||
integer, intent(in) :: instance
|
||
character(len=*), intent(in) :: group
|
||
|
||
integer :: o
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
outputsLoop: do o = 1,size(prm%output)
|
||
select case(trim(prm%output(o)))
|
||
|
||
case('rho_mob')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_mob,'rho_mob',&
|
||
'mobile dislocation density','1/m²')
|
||
case('rho_dip')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip,'rho_dip',&
|
||
'dislocation dipole density''1/m²')
|
||
case('gamma_sl')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma_sl,'gamma_sl',&
|
||
'plastic shear','1')
|
||
case('lambda_sl')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
|
||
'mean free path for slip','m')
|
||
case('tau_pass')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%tau_pass,'tau_pass',&
|
||
'passing stress for slip','Pa')
|
||
|
||
case('f_tw')
|
||
if(prm%sum_N_tw>0) call results_writeDataset(group,stt%f_tw,'f_tw',&
|
||
'twinned volume fraction','m³/m³')
|
||
case('lambda_tw')
|
||
if(prm%sum_N_tw>0) call results_writeDataset(group,dst%Lambda_tw,'Lambda_tw',&
|
||
'mean free path for twinning','m')
|
||
case('tau_hat_tw')
|
||
if(prm%sum_N_tw>0) call results_writeDataset(group,dst%tau_hat_tw,'tau_hat_tw',&
|
||
'threshold stress for twinning','Pa')
|
||
|
||
case('f_tr')
|
||
if(prm%sum_N_tr>0) call results_writeDataset(group,stt%f_tr,'f_tr',&
|
||
'martensite volume fraction','m³/m³')
|
||
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_results
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved
|
||
! stress, and the resolved stress.
|
||
!> @details Derivatives and resolved stress are calculated only optionally.
|
||
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
|
||
! have the optional arguments at the end
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_slip(Mp,T,instance,of, &
|
||
dot_gamma_sl,ddot_gamma_dtau_slip,tau_slip)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(out) :: &
|
||
dot_gamma_sl
|
||
real(pReal), dimension(param(instance)%sum_N_sl), optional, intent(out) :: &
|
||
ddot_gamma_dtau_slip, &
|
||
tau_slip
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
ddot_gamma_dtau
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
tau, &
|
||
stressRatio, &
|
||
StressRatio_p, &
|
||
BoltzmannRatio, &
|
||
v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned)
|
||
v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned)
|
||
dV_wait_inverse_dTau, &
|
||
dV_run_inverse_dTau, &
|
||
dV_dTau, &
|
||
tau_eff !< effective resolved stress
|
||
integer :: i
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_sl
|
||
tau(i) = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
|
||
enddo
|
||
|
||
tau_eff = abs(tau)-dst%tau_pass(:,of)
|
||
|
||
significantStress: where(tau_eff > tol_math_check)
|
||
stressRatio = tau_eff/prm%tau_0
|
||
StressRatio_p = stressRatio** prm%p
|
||
BoltzmannRatio = prm%Delta_F/(kB*T)
|
||
v_wait_inverse = prm%v0**(-1.0_pReal) * exp(BoltzmannRatio*(1.0_pReal-StressRatio_p)** prm%q)
|
||
v_run_inverse = prm%B/(tau_eff*prm%b_sl)
|
||
|
||
dot_gamma_sl = sign(stt%rho_mob(:,of)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau)
|
||
|
||
dV_wait_inverse_dTau = -1.0_pReal * v_wait_inverse * prm%p * prm%q * BoltzmannRatio &
|
||
* (stressRatio**(prm%p-1.0_pReal)) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%q-1.0_pReal) &
|
||
/ prm%tau_0
|
||
dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff
|
||
dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
|
||
/ (v_wait_inverse+v_run_inverse)**2.0_pReal
|
||
ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,of)*prm%b_sl
|
||
else where significantStress
|
||
dot_gamma_sl = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_slip)) ddot_gamma_dtau_slip = ddot_gamma_dtau
|
||
if(present(tau_slip)) tau_slip = tau
|
||
|
||
end subroutine kinetics_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved
|
||
! stress.
|
||
!> @details Derivatives are calculated only optionally.
|
||
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
|
||
! have the optional arguments at the end.
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_twin(Mp,T,dot_gamma_sl,instance,of,&
|
||
dot_gamma_twin,ddot_gamma_dtau_twin)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
|
||
dot_gamma_sl
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_tw), intent(out) :: &
|
||
dot_gamma_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tw), optional, intent(out) :: &
|
||
ddot_gamma_dtau_twin
|
||
|
||
real, dimension(param(instance)%sum_N_tw) :: &
|
||
tau, &
|
||
Ndot0, &
|
||
stressRatio_r, &
|
||
ddot_gamma_dtau
|
||
|
||
integer :: i,s1,s2
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_tw
|
||
tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < dst%tau_r_tw(i,of)) then ! ToDo: correct?
|
||
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
|
||
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
|
||
(prm%L_tw*prm%b_sl(i))*&
|
||
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tw(i,of)-tau(i)))) ! P_ncs
|
||
else
|
||
Ndot0=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0=prm%dot_N_0_tw(i)
|
||
endif isFCC
|
||
enddo
|
||
|
||
significantStress: where(tau > tol_math_check)
|
||
StressRatio_r = (dst%tau_hat_tw(:,of)/tau)**prm%r
|
||
dot_gamma_twin = prm%gamma_char * dst%V_tw(:,of) * Ndot0*exp(-StressRatio_r)
|
||
ddot_gamma_dtau = (dot_gamma_twin*prm%r/tau)*StressRatio_r
|
||
else where significantStress
|
||
dot_gamma_twin = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_twin)) ddot_gamma_dtau_twin = ddot_gamma_dtau
|
||
|
||
end subroutine kinetics_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculate shear rates on transformation systems and their derivatives with respect to
|
||
! resolved stress.
|
||
!> @details Derivatives are calculated only optionally.
|
||
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
|
||
! have the optional arguments at the end.
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_trans(Mp,T,dot_gamma_sl,instance,of,&
|
||
dot_gamma_tr,ddot_gamma_dtau_trans)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
|
||
dot_gamma_sl
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_tr), intent(out) :: &
|
||
dot_gamma_tr
|
||
real(pReal), dimension(param(instance)%sum_N_tr), optional, intent(out) :: &
|
||
ddot_gamma_dtau_trans
|
||
|
||
real, dimension(param(instance)%sum_N_tr) :: &
|
||
tau, &
|
||
Ndot0, &
|
||
stressRatio_s, &
|
||
ddot_gamma_dtau
|
||
|
||
integer :: i,s1,s2
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_tr
|
||
tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < dst%tau_r_tr(i,of)) then ! ToDo: correct?
|
||
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
|
||
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
|
||
(prm%L_tr*prm%b_sl(i))*&
|
||
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tr(i,of)-tau(i)))) ! P_ncs
|
||
else
|
||
Ndot0=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0=prm%dot_N_0_tr(i)
|
||
endif isFCC
|
||
enddo
|
||
|
||
significantStress: where(tau > tol_math_check)
|
||
StressRatio_s = (dst%tau_hat_tr(:,of)/tau)**prm%s
|
||
dot_gamma_tr = dst%V_tr(:,of) * Ndot0*exp(-StressRatio_s)
|
||
ddot_gamma_dtau = (dot_gamma_tr*prm%s/tau)*StressRatio_s
|
||
else where significantStress
|
||
dot_gamma_tr = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_trans)) ddot_gamma_dtau_trans = ddot_gamma_dtau
|
||
|
||
end subroutine kinetics_trans
|
||
|
||
end submodule plastic_dislotwin
|