!--------------------------------------------------------------------------------------------------
!> @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
!--------------------------------------------------------------------------------------------------
module plastic_dislotwin
use prec
use debug
use math
use IO
use material
use config
use lattice
use discretization
use results
implicit none
private
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
enum, bind(c)
enumerator :: &
undefined_ID, &
rho_mob_ID, &
rho_dip_ID, &
dot_gamma_sl_ID, &
gamma_sl_ID, &
Lambda_sl_ID, &
resolved_stress_slip_ID, &
tau_pass_ID, &
edge_dipole_distance_ID, &
f_tw_ID, &
Lambda_tw_ID, &
resolved_stress_twin_ID, &
tau_hat_tw_ID, &
f_tr_ID
end enum
type :: tParameters
real(pReal) :: &
mu, &
nu, &
D0, & !< prefactor for self-diffusion coefficient
Qsd, & !< activation energy for dislocation climb
omega, & !< frequency factor for dislocation climb
D, & !< grain size
p_sb, & !< p-exponent in shear band velocity
q_sb, & !< q-exponent in shear band velocity
CEdgeDipMinDistance, & !<
i_tw, & !<
tau_0, & !< strength due to elements in solid solution
L_tw, & !< Length of twin nuclei in Burgers vectors
L_tr, & !< Length of trans nuclei in Burgers vectors
xc_twin, & !< critical distance for formation of twin nucleus
xc_trans, & !< critical distance for formation of trans nucleus
V_cs, & !< cross slip volume
sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
sbVelocity, & !< value for shearband velocity_0
sbQedge, & !< activation energy for shear bands
SFE_0K, & !< stacking fault energy at zero K
dSFE_dT, & !< temperature dependance of stacking fault energy
aTol_rho, & !< absolute tolerance for integration of dislocation density
aTol_f_tw, & !< absolute tolerance for integration of twin volume fraction
aTol_f_tr, & !< absolute tolerance for integration of trans volume fraction
gamma_fcc_hex, & !< Free energy difference between austensite and martensite
i_tr, & !<
h !< Stack height of hex nucleus
real(pReal), dimension(:), allocatable :: &
rho_mob_0, & !< initial unipolar dislocation density per slip system
rho_dip_0, & !< initial dipole dislocation density per slip system
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
atomicVolume, &
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), dimension(:,:), allocatable :: &
h_sl_sl, & !<
h_sl_tw, & !<
h_tw_tw, & !<
h_sl_tr, & !<
h_tr_tr !<
integer, dimension(:,:), allocatable :: &
fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
real(pReal), dimension(:,:), allocatable :: &
n0_sl, & !< slip system normal
forestProjection, &
C66
real(pReal), dimension(:,:,:), allocatable :: &
P_tr, &
P_sl, &
P_tw, &
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, dimension(:), allocatable :: &
N_sl, & !< number of active slip systems for each family
N_tw, & !< number of active twin systems for each family
N_tr !< number of active transformation systems for each family
integer(kind(undefined_ID)), dimension(:), allocatable :: &
outputID !< ID of each post result 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
public :: &
plastic_dislotwin_init, &
plastic_dislotwin_homogenizedC, &
plastic_dislotwin_dependentState, &
plastic_dislotwin_LpAndItsTangent, &
plastic_dislotwin_dotState, &
plastic_dislotwin_results
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_init
integer :: &
Ninstance, &
p, i, &
NipcMyPhase, outputSize, &
sizeState, sizeDotState, &
startIndex, endIndex
integer, dimension(0), parameter :: emptyIntArray = [integer::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
integer(kind(undefined_ID)) :: &
outputID
character(len=pStringLen) :: &
extmsg = ''
character(len=65536), dimension(:), allocatable :: &
outputs
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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%aTol_rho = config%getFloat('atol_rho', defaultVal=0.0_pReal)
prm%aTol_f_tw = config%getFloat('atol_twinfrac', defaultVal=0.0_pReal)
prm%aTol_f_tr = config%getFloat('atol_transfrac', defaultVal=0.0_pReal)
! 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
prm%N_sl = config%getInts('nslip',defaultVal=emptyIntArray)
prm%sum_N_sl = sum(prm%N_sl)
slipActive: if (prm%sum_N_sl > 0) then
prm%P_sl = lattice_SchmidMatrix_slip(prm%N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%h_sl_sl = lattice_interaction_SlipBySlip(prm%N_sl, &
config%getFloats('interaction_slipslip'), &
config%getString('lattice_structure'))
prm%forestProjection = lattice_forestProjection_edge(prm%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(prm%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. (prm%N_sl(1) == 12)
if(prm%fccTwinTransNucleation) &
prm%fcc_twinNucleationSlipPair = lattice_fcc_twinNucleationSlipPair
prm%rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(prm%N_sl))
prm%rho_dip_0 = config%getFloats('rhoedgedip0',requiredSize=size(prm%N_sl))
prm%v0 = config%getFloats('v0', requiredSize=size(prm%N_sl))
prm%b_sl = config%getFloats('slipburgers',requiredSize=size(prm%N_sl))
prm%Delta_F = config%getFloats('qedge', requiredSize=size(prm%N_sl))
prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(prm%N_sl))
prm%p = config%getFloats('p_slip', requiredSize=size(prm%N_sl))
prm%q = config%getFloats('q_slip', requiredSize=size(prm%N_sl))
prm%B = config%getFloats('b', requiredSize=size(prm%N_sl), &
defaultVal=[(0.0_pReal, i=1,size(prm%N_sl))])
prm%tau_0 = config%getFloat('solidsolutionstrength')
prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
prm%D0 = config%getFloat('d0')
prm%Qsd = config%getFloat('qsd')
prm%atomicVolume = config%getFloat('catomicvolume') * prm%b_sl**3.0_pReal
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
! multiplication factor according to crystal structure (nearest neighbors bcc vs fcc/hex)
!@details: Refer: 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, &
lattice_structure(p) == LATTICE_FCC_ID .or. lattice_structure(p) == LATTICE_HEX_ID)
! expand: family => system
prm%rho_mob_0 = math_expand(prm%rho_mob_0, prm%N_sl)
prm%rho_dip_0 = math_expand(prm%rho_dip_0, prm%N_sl)
prm%v0 = math_expand(prm%v0, prm%N_sl)
prm%b_sl = math_expand(prm%b_sl, prm%N_sl)
prm%Delta_F = math_expand(prm%Delta_F, prm%N_sl)
prm%CLambdaSlip = math_expand(prm%CLambdaSlip, prm%N_sl)
prm%p = math_expand(prm%p, prm%N_sl)
prm%q = math_expand(prm%q, prm%N_sl)
prm%B = math_expand(prm%B, prm%N_sl)
prm%atomicVolume = math_expand(prm%atomicVolume,prm%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(prm%rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
if (any(prm%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
allocate(prm%b_sl(0))
endif slipActive
!--------------------------------------------------------------------------------------------------
! twin related parameters
prm%N_tw = config%getInts('ntwin', defaultVal=emptyIntArray)
prm%sum_N_tw = sum(prm%N_tw)
if (prm%sum_N_tw > 0) then
prm%P_tw = lattice_SchmidMatrix_twin(prm%N_tw,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%h_tw_tw = lattice_interaction_TwinByTwin(prm%N_tw,&
config%getFloats('interaction_twintwin'), &
config%getString('lattice_structure'))
prm%b_tw = config%getFloats('twinburgers', requiredSize=size(prm%N_tw))
prm%t_tw = config%getFloats('twinsize', requiredSize=size(prm%N_tw))
prm%r = config%getFloats('r_twin', requiredSize=size(prm%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(prm%N_tw,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%C66_tw = lattice_C66_twin(prm%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,prm%N_tw)
endif
! expand: family => system
prm%b_tw = math_expand(prm%b_tw,prm%N_tw)
prm%t_tw = math_expand(prm%t_tw,prm%N_tw)
prm%r = math_expand(prm%r,prm%N_tw)
else
allocate(prm%gamma_char(0))
allocate(prm%t_tw (0))
allocate(prm%b_tw (0))
allocate(prm%r (0))
allocate(prm%h_tw_tw (0,0))
endif
!--------------------------------------------------------------------------------------------------
! transformation related parameters
prm%N_tr = config%getInts('ntrans', defaultVal=emptyIntArray)
prm%sum_N_tr = sum(prm%N_tr)
if (prm%sum_N_tr > 0) then
prm%b_tr = config%getFloats('transburgers')
prm%b_tr = math_expand(prm%b_tr,prm%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(prm%N_tr,&
config%getFloats('interaction_transtrans'), &
config%getString('lattice_structure'))
prm%C66_tr = lattice_C66_trans(prm%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(prm%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,prm%N_tr)
endif
prm%t_tr = config%getFloats('lamellarsize')
prm%t_tr = math_expand(prm%t_tr,prm%N_tr)
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
prm%s = math_expand(prm%s,prm%N_tr)
else
allocate(prm%t_tr (0))
allocate(prm%b_tr (0))
allocate(prm%s (0))
allocate(prm%h_tr_tr(0,0))
endif
if (sum(prm%N_tw) > 0 .or. 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
if (prm%sum_N_sl > 0 .and. prm%sum_N_tw > 0) then
prm%h_sl_tw = lattice_interaction_SlipByTwin(prm%N_sl,prm%N_tw,&
config%getFloats('interaction_sliptwin'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. prm%sum_N_tw > 12) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if N_tw is [6,6]
endif
if (prm%sum_N_sl > 0 .and. prm%sum_N_tr > 0) then
prm%h_sl_tr = lattice_interaction_SlipByTrans(prm%N_sl,prm%N_tr,&
config%getFloats('interaction_sliptrans'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. prm%sum_N_tr > 12) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if N_tr is [6,6]
endif
!--------------------------------------------------------------------------------------------------
! 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%sbQedge = 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%sbQedge < 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
prm%D = config%getFloat('grainsize')
if (config%keyExists('dipoleformationfactor')) call IO_error(1,ext_msg='use /nodipoleformation/')
prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
!if (Ndot0PerTwinFamily(f,p) < 0.0_pReal) &
! call IO_error(211,el=p,ext_msg='dot_N_0_tw ('//PLASTICITY_DISLOTWIN_label//')')
if (any(prm%atomicVolume <= 0.0_pReal)) &
call IO_error(211,el=p,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%sum_N_tw > 0) then
if (prm%aTol_rho <= 0.0_pReal) &
call IO_error(211,el=p,ext_msg='aTol_rho ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%aTol_f_tw <= 0.0_pReal) &
call IO_error(211,el=p,ext_msg='aTol_f_tw ('//PLASTICITY_DISLOTWIN_label//')')
endif
if (prm%sum_N_tr > 0) then
if (prm%aTol_f_tr <= 0.0_pReal) &
call IO_error(211,el=p,ext_msg='aTol_f_tr ('//PLASTICITY_DISLOTWIN_label//')')
endif
outputs = config%getStrings('(output)', defaultVal=emptyStringArray)
allocate(prm%outputID(0))
do i= 1, size(outputs)
outputID = undefined_ID
select case(outputs(i))
case ('rho_mob')
outputID = merge(rho_mob_ID,undefined_ID,prm%sum_N_sl > 0)
outputSize = prm%sum_N_sl
case ('rho_dip')
outputID = merge(rho_dip_ID,undefined_ID,prm%sum_N_sl > 0)
outputSize = prm%sum_N_sl
case ('gamma_sl')
outputID = merge(gamma_sl_ID,undefined_ID,prm%sum_N_sl > 0)
outputSize = prm%sum_N_sl
case ('lambda_sl')
outputID = merge(Lambda_sl_ID,undefined_ID,prm%sum_N_sl > 0)
outputSize = prm%sum_N_sl
case ('tau_pass')
outputID= merge(tau_pass_ID,undefined_ID,prm%sum_N_sl > 0)
outputSize = prm%sum_N_sl
case ('f_tw')
outputID = merge(f_tw_ID,undefined_ID,prm%sum_N_tw >0)
outputSize = prm%sum_N_tw
case ('lambda_tw')
outputID = merge(Lambda_tw_ID,undefined_ID,prm%sum_N_tw >0)
outputSize = prm%sum_N_tw
case ('tau_hat_tw')
outputID = merge(tau_hat_tw_ID,undefined_ID,prm%sum_N_tw >0)
outputSize = prm%sum_N_tw
case ('f_tr')
outputID = f_tr_ID
outputSize = prm%sum_N_tr
end select
if (outputID /= undefined_ID) then
prm%outputID = [prm%outputID, outputID]
endif
enddo
!--------------------------------------------------------------------------------------------------
! 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, &
prm%sum_N_sl,prm%sum_N_tw,prm%sum_N_tr)
!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1
endIndex = prm%sum_N_sl
stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:)
stt%rho_mob= spread(prm%rho_mob_0,2,NipcMyPhase)
dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:)
stt%rho_dip= spread(prm%rho_dip_0,2,NipcMyPhase)
dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
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)%aTolState(startIndex:endIndex) = 1.0e6_pReal !ToDo: better make optional parameter
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%accumulatedSlip => plasticState(p)%state(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)%aTolState(startIndex:endIndex) = prm%aTol_f_tw
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)%aTolState(startIndex:endIndex) = prm%aTol_f_tr
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
enddo
end subroutine plastic_dislotwin_init
!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
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 calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
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
logical :: error
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
!ToDo: Why do this before shear banding?
Lp = Lp * f_unrotated
dLp_dMp = dLp_dMp * f_unrotated
shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
BoltzmannRatio = prm%sbQedge/(kB*T)
call math_eigenValuesVectorsSym(Mp,eigValues,eigVectors,error)
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_mul33xx33(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
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) * f_unrotated
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) * f_unrotated
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) * f_unrotated
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) * f_unrotated
enddo transContibution
end associate
end subroutine plastic_dislotwin_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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, &
VacancyDiffusion, &
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))
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*T))
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_mul33xx33(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 calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
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 writes results to HDF5 output file
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_results(instance,group)
#if defined(PETSc) || defined(DAMASK_HDF5)
integer, intent(in) :: instance
character(len=*) :: group
integer :: o
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
outputsLoop: do o = 1,size(prm%outputID)
select case(prm%outputID(o))
case (rho_mob_ID)
call results_writeDataset(group,stt%rho_mob,'rho_mob',&
'mobile dislocation density','1/m²')
case (rho_dip_ID)
call results_writeDataset(group,stt%rho_dip,'rho_dip',&
'dislocation dipole density''1/m²')
case (gamma_sl_ID)
call results_writeDataset(group,stt%gamma_sl,'gamma_sl',&
'plastic shear','1')
case (Lambda_sl_ID)
call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
'mean free path for slip','m')
case (tau_pass_ID)
call results_writeDataset(group,dst%tau_pass,'tau_pass',&
'passing stress for slip','Pa')
case (f_tw_ID)
call results_writeDataset(group,stt%f_tw,'f_tw',&
'twinned volume fraction','m³/m³')
case (Lambda_tw_ID)
call results_writeDataset(group,dst%Lambda_tw,'Lambda_tw',&
'mean free path for twinning','m')
case (tau_hat_tw_ID)
call results_writeDataset(group,dst%tau_hat_tw,'tau_hat_tw',&
'threshold stress for twinning','Pa')
case (f_tr_ID)
call results_writeDataset(group,stt%f_tr,'f_tr',&
'martensite volume fraction','m³/m³')
end select
enddo outputsLoop
end associate
#else
integer, intent(in) :: instance
character(len=*) :: group
#endif
end subroutine plastic_dislotwin_results
!--------------------------------------------------------------------------------------------------
!> @brief Shear rates on slip systems, their derivatives with respect to resolved stress and the
! resolved stresss
!> @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_mul33xx33(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 calculates shear rates on twin systems
!--------------------------------------------------------------------------------------------------
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_mul33xx33(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 calculates shear rates on twin systems
!--------------------------------------------------------------------------------------------------
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_mul33xx33(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 module plastic_dislotwin