1 # 1 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/constitutive_plastic_dislotwin.f90"
4 # 1 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/constitutive_plastic_dislotwin.f90"
16 real(pReal),
parameter :: &
29 cedgedipmindistance = 1.0_preal, &
34 xc_twin = 1.0_preal, &
35 xc_trans = 1.0_preal, &
37 sbresistance = 1.0_preal, &
38 sbvelocity = 1.0_preal, &
41 dsfe_dt = 1.0_preal, &
42 gamma_fcc_hex = 1.0_preal, &
45 real(pReal),
allocatable,
dimension(:) :: &
46 b_sl, & !< absolute length of burgers vector [m] for each slip system
47 b_tw, & !< absolute length of burgers vector [m] for each twin system
48 b_tr, & !< absolute length of burgers vector [m] for each transformation system
49 Delta_F,& !< activation energy for glide [J] for each slip system
50 v0, & !< dislocation velocity prefactor [m/s] for each slip system
51 dot_N_0_tw, & !< twin nucleation rate [1/m s] 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
!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%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
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 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
³s] for each twin system
52 dot_N_0_tr, & !< trans nucleation rate [1/m s] 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
!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%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
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 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
³s] for each trans system
53 t_tw, & !< twin thickness [m] for each twin system
54 CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
55 t_tr, & !< martensite lamellar thickness [m] for each trans system and instance
56 p, & !< p-exponent in glide velocity
57 q, & !< q-exponent in glide velocity
58 r, & !< r-exponent in twin nucleation rate
59 s, & !< s-exponent in trans nucleation rate
60 gamma_char, & !< characteristic shear for twins
62 real(pReal),
allocatable,
dimension(:,:) :: &
68 n0_sl, & !< slip system normal
71 real(pReal),
allocatable,
dimension(:,:,:) :: &
78 sum_N_sl, & !< total number of active slip system
79 sum_N_tw, & !< total number of active twin system
81 integer,
allocatable,
dimension(:,:) :: &
82 fcc_twinNucleationSlipPair
83 character(len=pStringLen),
allocatable,
dimension(:) :: &
86 ExtendedDislocations, & !< consider split into partials for climb calculation
87 fccTwinTransNucleation, & !< twinning and transformation models are for fcc
91 type :: tdislotwinstate
92 real(pReal),
dimension(:,:),
pointer :: &
98 end type tdislotwinstate
100 type :: tdislotwinmicrostructure
101 real(pReal),
dimension(:,:),
allocatable :: &
102 Lambda_sl, & !< mean free path between 2 obstacles seen by a moving dislocation
103 Lambda_tw, & !< mean free path between 2 obstacles seen by a growing twin
104 Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite
108 V_tw, & !< volume of a new twin
109 V_tr, & !< volume of a new martensite disc
110 tau_r_tw, & !< stress to bring partials close together (twin)
112 end type tdislotwinmicrostructure
116 type(tParameters),
allocatable,
dimension(:) :: param
117 type(tDislotwinState),
allocatable,
dimension(:) :: &
120 type(tDislotwinMicrostructure),
allocatable,
dimension(:) :: dependentState
129 module subroutine plastic_dislotwin_init
135 sizeState, sizeDotState, &
137 integer,
dimension(:),
allocatable :: &
139 real(pReal),
allocatable,
dimension(:) :: &
140 rho_mob_0, & !< initial unipolar dislocation density per slip system
142 character(len=pStringLen) :: &
145 write(6,
'(/,a)')
' <<<+- constitutive_'//plasticity_dislotwin_label//
' init -+>>>';
flush(6)
147 write(6,
'(/,a)')
' Ma and Roters, Acta Materialia 52(12):3603–3612, 2004'
148 write(6,
'(a)')
' https://doi.org/10.1016/j.actamat.2004.04.012'
150 write(6,
'(/,a)')
' Roters et al., Computational Materials Science 39:91–95, 2007'
151 write(6,
'(a)')
' https://doi.org/10.1016/j.commatsci.2006.04.014'
153 write(6,
'(/,a)')
' Wong et al., Acta Materialia 118:140–151, 2016'
154 write(6,
'(a,/)')
' https://doi.org/10.1016/j.actamat.2016.07.032'
156 ninstance = count(phase_plasticity == plasticity_dislotwin_id)
158 if (iand(debug_level(debug_constitutive),debug_levelbasic) /= 0) &
159 write(6,
'(a16,1x,i5,/)')
'# instances:',ninstance
161 allocate(param(ninstance))
162 allocate(state(ninstance))
163 allocate(dotstate(ninstance))
164 allocate(dependentstate(ninstance))
166 do p = 1,
size(phase_plasticity)
167 if (phase_plasticity(p) /= plasticity_dislotwin_id) cycle
168 associate(prm => param(phase_plasticityinstance(p)), &
169 dot => dotstate(phase_plasticityinstance(p)), &
170 stt => state(phase_plasticityinstance(p)), &
171 dst => dependentstate(phase_plasticityinstance(p)), &
172 config => config_phase(p))
174 prm%output =
config%getStrings(
'(output)', defaultval=emptystringarray)
177 prm%mu = lattice_mu(p)
178 prm%nu = lattice_nu(p)
179 prm%C66 = lattice_c66(1:6,1:6,p)
183 n_sl =
config%getInts(
'nslip',defaultval=emptyintarray)
184 prm%sum_N_sl = sum(abs(n_sl))
185 slipactive:
if (prm%sum_N_sl > 0)
then
186 prm%P_sl = lattice_schmidmatrix_slip(n_sl,
config%getString(
'lattice_structure'),&
187 config%getFloat(
'c/a',defaultval=0.0_preal))
188 prm%h_sl_sl = lattice_interaction_slipbyslip(n_sl,
config%getFloats(
'interaction_slipslip'), &
189 config%getString(
'lattice_structure'))
190 prm%forestProjection = lattice_forestprojection_edge(n_sl,
config%getString(
'lattice_structure'),&
191 config%getFloat(
'c/a',defaultval=0.0_preal))
192 prm%forestProjection = transpose(prm%forestProjection)
194 prm%n0_sl = lattice_slip_normal(n_sl,
config%getString(
'lattice_structure'),&
195 config%getFloat(
'c/a',defaultval=0.0_preal))
196 prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == lattice_fcc_id) &
197 .and. (n_sl(1) == 12)
198 if(prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_fcc_twinnucleationslippair
200 rho_mob_0 =
config%getFloats(
'rhoedge0', requiredsize=
size(n_sl))
201 rho_dip_0 =
config%getFloats(
'rhoedgedip0',requiredsize=
size(n_sl))
202 prm%v0 =
config%getFloats(
'v0', requiredsize=
size(n_sl))
203 prm%b_sl =
config%getFloats(
'slipburgers',requiredsize=
size(n_sl))
204 prm%Delta_F =
config%getFloats(
'qedge', requiredsize=
size(n_sl))
205 prm%CLambdaSlip =
config%getFloats(
'clambdaslip',requiredsize=
size(n_sl))
206 prm%p =
config%getFloats(
'p_slip', requiredsize=
size(n_sl))
207 prm%q =
config%getFloats(
'q_slip', requiredsize=
size(n_sl))
208 prm%B =
config%getFloats(
'b', requiredsize=
size(n_sl), &
209 defaultval=[(0.0_preal, i=1,
size(n_sl))])
211 prm%tau_0 =
config%getFloat(
'solidsolutionstrength')
212 prm%CEdgeDipMinDistance =
config%getFloat(
'cedgedipmindistance')
213 prm%D0 =
config%getFloat(
'd0')
214 prm%Qsd =
config%getFloat(
'qsd')
215 prm%ExtendedDislocations =
config%keyExists(
'/extend_dislocations/')
216 if (prm%ExtendedDislocations)
then
217 prm%SFE_0K =
config%getFloat(
'sfe_0k')
218 prm%dSFE_dT =
config%getFloat(
'dsfe_dt')
221 prm%dipoleformation = .not.
config%keyExists(
'/nodipoleformation/')
225 prm%omega =
config%getFloat(
'omega', defaultval = 1000.0_preal) &
226 * merge(12.0_preal,8.0_preal,any(lattice_structure(p) == [lattice_fcc_id,lattice_hex_id]))
229 rho_mob_0 = math_expand(rho_mob_0, n_sl)
230 rho_dip_0 = math_expand(rho_dip_0, n_sl)
231 prm%v0 = math_expand(prm%v0, n_sl)
232 prm%b_sl = math_expand(prm%b_sl, n_sl)
233 prm%Delta_F = math_expand(prm%Delta_F, n_sl)
234 prm%CLambdaSlip = math_expand(prm%CLambdaSlip, n_sl)
235 prm%p = math_expand(prm%p, n_sl)
236 prm%q = math_expand(prm%q, n_sl)
237 prm%B = math_expand(prm%B, n_sl)
240 if ( prm%D0 <= 0.0_preal) extmsg = trim(extmsg)//
' D0'
241 if ( prm%Qsd <= 0.0_preal) extmsg = trim(extmsg)//
' Qsd'
242 if (any(rho_mob_0 < 0.0_preal)) extmsg = trim(extmsg)//
' rho_mob_0'
243 if (any(rho_dip_0 < 0.0_preal)) extmsg = trim(extmsg)//
' rho_dip_0'
244 if (any(prm%v0 < 0.0_preal)) extmsg = trim(extmsg)//
' v0'
245 if (any(prm%b_sl <= 0.0_preal)) extmsg = trim(extmsg)//
' b_sl'
246 if (any(prm%Delta_F <= 0.0_preal)) extmsg = trim(extmsg)//
' Delta_F'
247 if (any(prm%CLambdaSlip <= 0.0_preal)) extmsg = trim(extmsg)//
' CLambdaSlip'
248 if (any(prm%B < 0.0_preal)) extmsg = trim(extmsg)//
' B'
249 if (any(prm%p<=0.0_preal .or. prm%p>1.0_preal)) extmsg = trim(extmsg)//
' p'
250 if (any(prm%q< 1.0_preal .or. prm%q>2.0_preal)) extmsg = trim(extmsg)//
' q'
252 rho_mob_0 = emptyrealarray; rho_dip_0 = emptyrealarray
253 allocate(prm%b_sl,prm%Delta_F,prm%v0,prm%CLambdaSlip,prm%p,prm%q,prm%B,source=emptyrealarray)
254 allocate(prm%forestProjection(0,0),prm%h_sl_sl(0,0))
259 n_tw =
config%getInts(
'ntwin', defaultval=emptyintarray)
260 prm%sum_N_tw = sum(abs(n_tw))
261 twinactive:
if (prm%sum_N_tw > 0)
then
262 prm%P_tw = lattice_schmidmatrix_twin(n_tw,
config%getString(
'lattice_structure'),&
263 config%getFloat(
'c/a',defaultval=0.0_preal))
264 prm%h_tw_tw = lattice_interaction_twinbytwin(n_tw,&
265 config%getFloats(
'interaction_twintwin'), &
266 config%getString(
'lattice_structure'))
268 prm%b_tw =
config%getFloats(
'twinburgers', requiredsize=
size(n_tw))
269 prm%t_tw =
config%getFloats(
'twinsize', requiredsize=
size(n_tw))
270 prm%r =
config%getFloats(
'r_twin', requiredsize=
size(n_tw))
272 prm%xc_twin =
config%getFloat(
'xc_twin')
273 prm%L_tw =
config%getFloat(
'l0_twin')
274 prm%i_tw =
config%getFloat(
'cmfptwin')
276 prm%gamma_char= lattice_characteristicshear_twin(n_tw,
config%getString(
'lattice_structure'),&
277 config%getFloat(
'c/a',defaultval=0.0_preal))
279 prm%C66_tw = lattice_c66_twin(n_tw,prm%C66,
config%getString(
'lattice_structure'),&
280 config%getFloat(
'c/a',defaultval=0.0_preal))
282 if (.not. prm%fccTwinTransNucleation)
then
283 prm%dot_N_0_tw =
config%getFloats(
'ndot0_twin')
284 prm%dot_N_0_tw = math_expand(prm%dot_N_0_tw,n_tw)
288 prm%b_tw = math_expand(prm%b_tw,n_tw)
289 prm%t_tw = math_expand(prm%t_tw,n_tw)
290 prm%r = math_expand(prm%r,n_tw)
293 if ( prm%xc_twin < 0.0_preal) extmsg = trim(extmsg)//
' xc_twin'
294 if ( prm%L_tw < 0.0_preal) extmsg = trim(extmsg)//
' L_tw'
295 if ( prm%i_tw < 0.0_preal) extmsg = trim(extmsg)//
' i_tw'
296 if (any(prm%b_tw < 0.0_preal)) extmsg = trim(extmsg)//
' b_tw'
297 if (any(prm%t_tw < 0.0_preal)) extmsg = trim(extmsg)//
' t_tw'
298 if (any(prm%r < 0.0_preal)) extmsg = trim(extmsg)//
' r'
299 if (.not. prm%fccTwinTransNucleation)
then
300 if (any(prm%dot_N_0_tw < 0.0_preal)) extmsg = trim(extmsg)//
' dot_N_0_tw'
303 allocate(prm%gamma_char,prm%b_tw,prm%dot_N_0_tw,prm%t_tw,prm%r,source=emptyrealarray)
304 allocate(prm%h_tw_tw(0,0))
309 n_tr =
config%getInts(
'ntrans', defaultval=emptyintarray)
310 prm%sum_N_tr = sum(abs(n_tr))
311 transactive:
if (prm%sum_N_tr > 0)
then
312 prm%b_tr =
config%getFloats(
'transburgers')
313 prm%b_tr = math_expand(prm%b_tr,n_tr)
315 prm%h =
config%getFloat(
'transstackheight', defaultval=0.0_preal)
316 prm%i_tr =
config%getFloat(
'cmfptrans', defaultval=0.0_preal)
317 prm%gamma_fcc_hex =
config%getFloat(
'deltag')
318 prm%xc_trans =
config%getFloat(
'xc_trans', defaultval=0.0_preal)
319 prm%L_tr =
config%getFloat(
'l0_trans')
321 prm%h_tr_tr = lattice_interaction_transbytrans(n_tr,
config%getFloats(
'interaction_transtrans'), &
322 config%getString(
'lattice_structure'))
324 prm%C66_tr = lattice_c66_trans(n_tr,prm%C66,
config%getString(
'trans_lattice_structure'), &
326 config%getFloat(
'a_bcc', defaultval=0.0_preal), &
327 config%getFloat(
'a_fcc', defaultval=0.0_preal))
329 prm%P_tr = lattice_schmidmatrix_trans(n_tr,
config%getString(
'trans_lattice_structure'), &
331 config%getFloat(
'a_bcc', defaultval=0.0_preal), &
332 config%getFloat(
'a_fcc', defaultval=0.0_preal))
334 if (lattice_structure(p) /= lattice_fcc_id)
then
335 prm%dot_N_0_tr =
config%getFloats(
'ndot0_trans')
336 prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,n_tr)
338 prm%t_tr =
config%getFloats(
'lamellarsize')
339 prm%t_tr = math_expand(prm%t_tr,n_tr)
340 prm%s =
config%getFloats(
's_trans',defaultval=[0.0_preal])
341 prm%s = math_expand(prm%s,n_tr)
344 if ( prm%xc_trans < 0.0_preal) extmsg = trim(extmsg)//
' xc_trans'
345 if ( prm%L_tr < 0.0_preal) extmsg = trim(extmsg)//
' L_tr'
346 if ( prm%i_tr < 0.0_preal) extmsg = trim(extmsg)//
' i_tr'
347 if (any(prm%t_tr < 0.0_preal)) extmsg = trim(extmsg)//
' t_tr'
348 if (any(prm%s < 0.0_preal)) extmsg = trim(extmsg)//
' s'
349 if (lattice_structure(p) /= lattice_fcc_id)
then
350 if (any(prm%dot_N_0_tr < 0.0_preal)) extmsg = trim(extmsg)//
' dot_N_0_tr'
353 allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyrealarray)
354 allocate(prm%h_tr_tr(0,0))
359 prm%sbVelocity =
config%getFloat(
'shearbandvelocity',defaultval=0.0_preal)
360 if (prm%sbVelocity > 0.0_preal)
then
361 prm%sbResistance =
config%getFloat(
'shearbandresistance')
362 prm%E_sb =
config%getFloat(
'qedgepersbsystem')
363 prm%p_sb =
config%getFloat(
'p_shearband')
364 prm%q_sb =
config%getFloat(
'q_shearband')
367 if (prm%sbResistance < 0.0_preal) extmsg = trim(extmsg)//
' shearbandresistance'
368 if (prm%E_sb < 0.0_preal) extmsg = trim(extmsg)//
' qedgepersbsystem'
369 if (prm%p_sb <= 0.0_preal) extmsg = trim(extmsg)//
' p_shearband'
370 if (prm%q_sb <= 0.0_preal) extmsg = trim(extmsg)//
' q_shearband'
375 if(prm%sum_N_sl + prm%sum_N_tw + prm%sum_N_tw > 0) &
376 prm%D =
config%getFloat(
'grainsize')
378 twinorslipactive:
if (prm%sum_N_tw + prm%sum_N_tr > 0)
then
379 prm%SFE_0K =
config%getFloat(
'sfe_0k')
380 prm%dSFE_dT =
config%getFloat(
'dsfe_dt')
381 prm%V_cs =
config%getFloat(
'vcrossslip')
382 endif twinorslipactive
384 slipandtwinactive:
if (prm%sum_N_sl * prm%sum_N_tw > 0)
then
385 prm%h_sl_tw = lattice_interaction_slipbytwin(n_sl,n_tw,&
386 config%getFloats(
'interaction_sliptwin'), &
387 config%getString(
'lattice_structure'))
388 if (prm%fccTwinTransNucleation .and.
size(n_tw) /= 1) extmsg = trim(extmsg)//
' interaction_sliptwin'
389 endif slipandtwinactive
391 slipandtransactive:
if (prm%sum_N_sl * prm%sum_N_tr > 0)
then
392 prm%h_sl_tr = lattice_interaction_slipbytrans(n_sl,n_tr,&
393 config%getFloats(
'interaction_sliptrans'), &
394 config%getString(
'lattice_structure'))
395 if (prm%fccTwinTransNucleation .and.
size(n_tr) /= 1) extmsg = trim(extmsg)//
' interaction_sliptrans'
396 endif slipandtransactive
400 nipcmyphase = count(material_phaseat == p) * discretization_nip
401 sizedotstate =
size([
'rho_mob ',
'rho_dip ',
'gamma_sl']) * prm%sum_N_sl &
402 +
size([
'f_tw']) * prm%sum_N_tw &
403 +
size([
'f_tr']) * prm%sum_N_tr
404 sizestate = sizedotstate
406 call material_allocateplasticstate(p,nipcmyphase,sizestate,sizedotstate,0)
411 endindex = prm%sum_N_sl
412 stt%rho_mob=>plasticstate(p)%state(startindex:endindex,:)
413 stt%rho_mob= spread(rho_mob_0,2,nipcmyphase)
414 dot%rho_mob=>plasticstate(p)%dotState(startindex:endindex,:)
415 plasticstate(p)%atol(startindex:endindex) =
config%getFloat(
'atol_rho',defaultval=1.0_preal)
416 if (any(plasticstate(p)%atol(startindex:endindex) < 0.0_preal)) extmsg = trim(extmsg)//
' atol_rho'
418 startindex = endindex + 1
419 endindex = endindex + prm%sum_N_sl
420 stt%rho_dip=>plasticstate(p)%state(startindex:endindex,:)
421 stt%rho_dip= spread(rho_dip_0,2,nipcmyphase)
422 dot%rho_dip=>plasticstate(p)%dotState(startindex:endindex,:)
423 plasticstate(p)%atol(startindex:endindex) =
config%getFloat(
'atol_rho',defaultval=1.0_preal)
425 startindex = endindex + 1
426 endindex = endindex + prm%sum_N_sl
427 stt%gamma_sl=>plasticstate(p)%state(startindex:endindex,:)
428 dot%gamma_sl=>plasticstate(p)%dotState(startindex:endindex,:)
429 plasticstate(p)%atol(startindex:endindex) = 1.0e-2_preal
431 plasticstate(p)%slipRate => plasticstate(p)%dotState(startindex:endindex,:)
433 startindex = endindex + 1
434 endindex = endindex + prm%sum_N_tw
435 stt%f_tw=>plasticstate(p)%state(startindex:endindex,:)
436 dot%f_tw=>plasticstate(p)%dotState(startindex:endindex,:)
437 plasticstate(p)%atol(startindex:endindex) =
config%getFloat(
'f_twin',defaultval=1.0e-7_preal)
438 if (any(plasticstate(p)%atol(startindex:endindex) < 0.0_preal)) extmsg = trim(extmsg)//
' f_twin'
440 startindex = endindex + 1
441 endindex = endindex + prm%sum_N_tr
442 stt%f_tr=>plasticstate(p)%state(startindex:endindex,:)
443 dot%f_tr=>plasticstate(p)%dotState(startindex:endindex,:)
444 plasticstate(p)%atol(startindex:endindex) =
config%getFloat(
'f_trans',defaultval=1.0e-6_preal)
445 if (any(plasticstate(p)%atol(startindex:endindex) < 0.0_preal)) extmsg = trim(extmsg)//
' f_trans'
447 allocate(dst%Lambda_sl (prm%sum_N_sl,nipcmyphase),source=0.0_preal)
448 allocate(dst%tau_pass (prm%sum_N_sl,nipcmyphase),source=0.0_preal)
450 allocate(dst%Lambda_tw (prm%sum_N_tw,nipcmyphase),source=0.0_preal)
451 allocate(dst%tau_hat_tw (prm%sum_N_tw,nipcmyphase),source=0.0_preal)
452 allocate(dst%tau_r_tw (prm%sum_N_tw,nipcmyphase),source=0.0_preal)
453 allocate(dst%V_tw (prm%sum_N_tw,nipcmyphase),source=0.0_preal)
455 allocate(dst%Lambda_tr (prm%sum_N_tr,nipcmyphase),source=0.0_preal)
456 allocate(dst%tau_hat_tr (prm%sum_N_tr,nipcmyphase),source=0.0_preal)
457 allocate(dst%tau_r_tr (prm%sum_N_tr,nipcmyphase),source=0.0_preal)
458 allocate(dst%V_tr (prm%sum_N_tr,nipcmyphase),source=0.0_preal)
460 plasticstate(p)%state0 = plasticstate(p)%state
466 if (extmsg /=
'')
call io_error(211,ext_msg=trim(extmsg)//
'('//plasticity_dislotwin_label//
')')
470 end subroutine plastic_dislotwin_init
476 module function plastic_dislotwin_homogenizedc(ipc,ip,el) result(homogenizedc)
478 real(pReal),
dimension(6,6) :: &
480 integer,
intent(in) :: &
481 ipc, & !< component-ID of integration point
482 ip, & !< integration point
487 real(pReal) :: f_unrotated
489 of = material_phasememberat(ipc,ip,el)
490 associate(prm => param(phase_plasticityinstance(material_phaseat(ipc,el))),&
491 stt => state(phase_plasticityinstance(material_phaseat(ipc,el))))
493 f_unrotated = 1.0_preal &
494 - sum(stt%f_tw(1:prm%sum_N_tw,of)) &
495 - sum(stt%f_tr(1:prm%sum_N_tr,of))
497 homogenizedc = f_unrotated * prm%C66
499 homogenizedc = homogenizedc &
500 + stt%f_tw(i,of)*prm%C66_tw(1:6,1:6,i)
503 homogenizedc = homogenizedc &
504 + stt%f_tr(i,of)*prm%C66_tr(1:6,1:6,i)
509 end function plastic_dislotwin_homogenizedc
515 module subroutine plastic_dislotwin_lpanditstangent(lp,dlp_dmp,mp,t,instance,of)
517 real(pReal),
dimension(3,3),
intent(out) :: Lp
518 real(pReal),
dimension(3,3,3,3),
intent(out) :: dLp_dMp
519 real(pReal),
dimension(3,3),
intent(in) :: Mp
520 integer,
intent(in) :: instance,of
521 real(pReal),
intent(in) :: T
525 f_unrotated,StressRatio_p,&
529 real(pReal),
dimension(param(instance)%sum_N_sl) :: &
530 dot_gamma_sl,ddot_gamma_dtau_slip
531 real(pReal),
dimension(param(instance)%sum_N_tw) :: &
532 dot_gamma_twin,ddot_gamma_dtau_twin
533 real(pReal),
dimension(param(instance)%sum_N_tr) :: &
534 dot_gamma_tr,ddot_gamma_dtau_trans
535 real(pReal):: dot_gamma_sb
536 real(pReal),
dimension(3,3) :: eigVectors, P_sb
537 real(pReal),
dimension(3) :: eigValues
538 real(pReal),
dimension(3,6),
parameter :: &
558 associate(prm => param(instance), stt => state(instance))
560 f_unrotated = 1.0_preal &
561 - sum(stt%f_tw(1:prm%sum_N_tw,of)) &
562 - sum(stt%f_tr(1:prm%sum_N_tr,of))
567 call kinetics_slip(mp,t,instance,of,dot_gamma_sl,ddot_gamma_dtau_slip)
568 slipcontribution:
do i = 1, prm%sum_N_sl
569 lp = lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
570 forall (k=1:3,l=1:3,m=1:3,n=1:3) &
571 dlp_dmp(k,l,m,n) = dlp_dmp(k,l,m,n) &
572 + ddot_gamma_dtau_slip(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i)
573 enddo slipcontribution
576 lp = lp * f_unrotated
577 dlp_dmp = dlp_dmp * f_unrotated
579 shearbandingcontribution:
if(dneq0(prm%sbVelocity))
then
581 boltzmannratio = prm%E_sb/(kb*t)
582 call math_eigh33(mp,eigvalues,eigvectors)
585 p_sb = 0.5_preal * math_outer(matmul(eigvectors,sb_scomposition(1:3,i)),&
586 matmul(eigvectors,sb_mcomposition(1:3,i)))
587 tau = math_tensordot(mp,p_sb)
589 significantshearbandstress:
if (abs(tau) > tol_math_check)
then
590 stressratio_p = (abs(tau)/prm%sbResistance)**prm%p_sb
591 dot_gamma_sb = sign(prm%sbVelocity*exp(-boltzmannratio*(1-stressratio_p)**prm%q_sb), tau)
592 ddot_gamma_dtau = abs(dot_gamma_sb)*boltzmannratio* prm%p_sb*prm%q_sb/ prm%sbResistance &
593 * (abs(tau)/prm%sbResistance)**(prm%p_sb-1.0_preal) &
594 * (1.0_preal-stressratio_p)**(prm%q_sb-1.0_preal)
596 lp = lp + dot_gamma_sb * p_sb
597 forall (k=1:3,l=1:3,m=1:3,n=1:3) &
598 dlp_dmp(k,l,m,n) = dlp_dmp(k,l,m,n) &
599 + ddot_gamma_dtau * p_sb(k,l) * p_sb(m,n)
600 endif significantshearbandstress
603 endif shearbandingcontribution
605 call kinetics_twin(mp,t,dot_gamma_sl,instance,of,dot_gamma_twin,ddot_gamma_dtau_twin)
606 twincontibution:
do i = 1, prm%sum_N_tw
607 lp = lp + dot_gamma_twin(i)*prm%P_tw(1:3,1:3,i) * f_unrotated
608 forall (k=1:3,l=1:3,m=1:3,n=1:3) &
609 dlp_dmp(k,l,m,n) = dlp_dmp(k,l,m,n) &
610 + ddot_gamma_dtau_twin(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i) * f_unrotated
611 enddo twincontibution
613 call kinetics_trans(mp,t,dot_gamma_sl,instance,of,dot_gamma_tr,ddot_gamma_dtau_trans)
614 transcontibution:
do i = 1, prm%sum_N_tr
615 lp = lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i) * f_unrotated
616 forall (k=1:3,l=1:3,m=1:3,n=1:3) &
617 dlp_dmp(k,l,m,n) = dlp_dmp(k,l,m,n) &
618 + ddot_gamma_dtau_trans(i)* prm%P_tr(k,l,i)*prm%P_tr(m,n,i) * f_unrotated
619 enddo transcontibution
624 end subroutine plastic_dislotwin_lpanditstangent
630 module subroutine plastic_dislotwin_dotstate(mp,t,instance,of)
632 real(pReal),
dimension(3,3),
intent(in):: &
634 real(pReal),
intent(in) :: &
636 integer,
intent(in) :: &
644 v_cl, & !< climb velocity
645 Gamma, & !< stacking fault energy
647 sigma_cl, & !< climb stress
649 real(pReal),
dimension(param(instance)%sum_N_sl) :: &
650 dot_rho_dip_formation, &
652 rho_dip_distance_min, &
654 real(pReal),
dimension(param(instance)%sum_N_tw) :: &
656 real(pReal),
dimension(param(instance)%sum_N_tr) :: &
659 associate(prm => param(instance), stt => state(instance), &
660 dot => dotstate(instance), dst => dependentstate(instance))
662 f_unrotated = 1.0_preal &
663 - sum(stt%f_tw(1:prm%sum_N_tw,of)) &
664 - sum(stt%f_tr(1:prm%sum_N_tr,of))
666 call kinetics_slip(mp,t,instance,of,dot_gamma_sl)
667 dot%gamma_sl(:,of) = abs(dot_gamma_sl)
669 rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl
671 slipstate:
do i = 1, prm%sum_N_sl
672 tau = math_tensordot(mp,prm%P_sl(1:3,1:3,i))
674 significantslipstress:
if (deq0(tau))
then
675 dot_rho_dip_formation(i) = 0.0_preal
676 dot_rho_dip_climb(i) = 0.0_preal
677 else significantslipstress
678 rho_dip_distance = 3.0_preal*prm%mu*prm%b_sl(i)/(16.0_preal*pi*abs(tau))
679 rho_dip_distance = math_clip(rho_dip_distance, right = dst%Lambda_sl(i,of))
680 rho_dip_distance = math_clip(rho_dip_distance, left = rho_dip_distance_min(i))
682 if (prm%dipoleFormation)
then
683 dot_rho_dip_formation(i) = 2.0_preal*(rho_dip_distance-rho_dip_distance_min(i))/prm%b_sl(i) &
684 * stt%rho_mob(i,of)*abs(dot_gamma_sl(i))
686 dot_rho_dip_formation(i) = 0.0_preal
689 if (deq(rho_dip_distance,rho_dip_distance_min(i)))
then
690 dot_rho_dip_climb(i) = 0.0_preal
693 sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(mp,prm%n0_sl(1:3,i)))
694 if (prm%ExtendedDislocations)
then
695 gamma = prm%SFE_0K + prm%dSFE_dT * t
696 b_d = 24.0_preal*pi*(1.0_preal - prm%nu)/(2.0_preal + prm%nu)* gamma/(prm%mu*prm%b_sl(i))
700 v_cl = 2.0_preal*prm%omega*b_d**2.0_preal*exp(-prm%Qsd/(kb*t)) &
701 * (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_preal/(kb*t)) - 1.0_preal)
703 dot_rho_dip_climb(i) = 4.0_preal*v_cl*stt%rho_dip(i,of) &
704 / (rho_dip_distance-rho_dip_distance_min(i))
706 endif significantslipstress
709 dot%rho_mob(:,of) = abs(dot_gamma_sl)/(prm%b_sl*dst%Lambda_sl(:,of)) &
710 - dot_rho_dip_formation &
711 - 2.0_preal*rho_dip_distance_min/prm%b_sl * stt%rho_mob(:,of)*abs(dot_gamma_sl)
713 dot%rho_dip(:,of) = dot_rho_dip_formation &
714 - 2.0_preal*rho_dip_distance_min/prm%b_sl * stt%rho_dip(:,of)*abs(dot_gamma_sl) &
717 call kinetics_twin(mp,t,dot_gamma_sl,instance,of,dot_gamma_twin)
718 dot%f_tw(:,of) = f_unrotated*dot_gamma_twin/prm%gamma_char
720 call kinetics_trans(mp,t,dot_gamma_sl,instance,of,dot_gamma_tr)
721 dot%f_tr(:,of) = f_unrotated*dot_gamma_tr
725 end subroutine plastic_dislotwin_dotstate
731 module subroutine plastic_dislotwin_dependentstate(t,instance,of)
733 integer,
intent(in) :: &
736 real(pReal),
intent(in) :: &
740 sumf_twin,Gamma,sumf_trans
741 real(pReal),
dimension(param(instance)%sum_N_sl) :: &
742 inv_lambda_sl_sl, & !< 1/mean free distance between 2 forest dislocations seen by a moving dislocation
743 inv_lambda_sl_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
745 real(pReal),
dimension(param(instance)%sum_N_tw) :: &
746 inv_lambda_tw_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
748 real(pReal),
dimension(param(instance)%sum_N_tr) :: &
749 inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite
751 real(pReal),
dimension(:),
allocatable :: &
755 associate(prm => param(instance),&
756 stt => state(instance),&
757 dst => dependentstate(instance))
759 sumf_twin = sum(stt%f_tw(1:prm%sum_N_tw,of))
760 sumf_trans = sum(stt%f_tr(1:prm%sum_N_tr,of))
762 gamma = prm%SFE_0K + prm%dSFE_dT * t
765 f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,of)/prm%t_tw
766 f_over_t_tr = sumf_trans/prm%t_tr
769 inv_lambda_sl_sl = sqrt(matmul(prm%forestProjection, &
770 stt%rho_mob(:,of)+stt%rho_dip(:,of)))/prm%CLambdaSlip
772 if (prm%sum_N_tw > 0 .and. prm%sum_N_sl > 0) &
773 inv_lambda_sl_tw = matmul(prm%h_sl_tw,f_over_t_tw)/(1.0_preal-sumf_twin)
775 inv_lambda_tw_tw = matmul(prm%h_tw_tw,f_over_t_tw)/(1.0_preal-sumf_twin)
777 if (prm%sum_N_tr > 0 .and. prm%sum_N_sl > 0) &
778 inv_lambda_sl_tr = matmul(prm%h_sl_tr,f_over_t_tr)/(1.0_preal-sumf_trans)
780 inv_lambda_tr_tr = matmul(prm%h_tr_tr,f_over_t_tr)/(1.0_preal-sumf_trans)
782 if ((prm%sum_N_tw > 0) .or. (prm%sum_N_tr > 0))
then
783 dst%Lambda_sl(:,of) = prm%D &
784 / (1.0_preal+prm%D*(inv_lambda_sl_sl + inv_lambda_sl_tw + inv_lambda_sl_tr))
786 dst%Lambda_sl(:,of) = prm%D &
787 / (1.0_preal+prm%D*inv_lambda_sl_sl)
790 dst%Lambda_tw(:,of) = prm%i_tw*prm%D/(1.0_preal+prm%D*inv_lambda_tw_tw)
791 dst%Lambda_tr(:,of) = prm%i_tr*prm%D/(1.0_preal+prm%D*inv_lambda_tr_tr)
794 dst%tau_pass(:,of) = prm%mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
797 if(prm%sum_N_tw == prm%sum_N_sl) &
798 dst%tau_hat_tw(:,of) = gamma/(3.0_preal*prm%b_tw) &
799 + 3.0_preal*prm%b_tw*prm%mu/(prm%L_tw*prm%b_sl)
800 if(prm%sum_N_tr == prm%sum_N_sl) &
801 dst%tau_hat_tr(:,of) = gamma/(3.0_preal*prm%b_tr) &
802 + 3.0_preal*prm%b_tr*prm%mu/(prm%L_tr*prm%b_sl) &
803 + prm%h*prm%gamma_fcc_hex/ (3.0_preal*prm%b_tr)
805 dst%V_tw(:,of) = (pi/4.0_preal)*prm%t_tw*dst%Lambda_tw(:,of)**2.0_preal
806 dst%V_tr(:,of) = (pi/4.0_preal)*prm%t_tr*dst%Lambda_tr(:,of)**2.0_preal
809 x0 = prm%mu*prm%b_tw**2.0_preal/(gamma*8.0_preal*pi)*(2.0_preal+prm%nu)/(1.0_preal-prm%nu)
810 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)
812 x0 = prm%mu*prm%b_tr**2.0_preal/(gamma*8.0_preal*pi)*(2.0_preal+prm%nu)/(1.0_preal-prm%nu)
813 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)
817 end subroutine plastic_dislotwin_dependentstate
823 module subroutine plastic_dislotwin_results(instance,group)
825 integer,
intent(in) :: instance
826 character(len=*),
intent(in) :: group
830 associate(prm => param(instance), stt => state(instance), dst => dependentstate(instance))
831 outputsloop:
do o = 1,
size(prm%output)
832 select case(trim(prm%output(o)))
835 if(prm%sum_N_sl>0)
call results_writedataset(group,stt%rho_mob,
'rho_mob',&
836 'mobile dislocation density',
'1/m²')
838 if(prm%sum_N_sl>0)
call results_writedataset(group,stt%rho_dip,
'rho_dip',&
839 'dislocation dipole density''1/m²')
841 if(prm%sum_N_sl>0)
call results_writedataset(group,stt%gamma_sl,
'gamma_sl',&
844 if(prm%sum_N_sl>0)
call results_writedataset(group,dst%Lambda_sl,
'Lambda_sl',&
845 'mean free path for slip',
'm')
847 if(prm%sum_N_sl>0)
call results_writedataset(group,dst%tau_pass,
'tau_pass',&
848 'passing stress for slip',
'Pa')
851 if(prm%sum_N_tw>0)
call results_writedataset(group,stt%f_tw,
'f_tw',&
852 'twinned volume fraction',
'm³/m³')
854 if(prm%sum_N_tw>0)
call results_writedataset(group,dst%Lambda_tw,
'Lambda_tw',&
855 'mean free path for twinning',
'm')
857 if(prm%sum_N_tw>0)
call results_writedataset(group,dst%tau_hat_tw,
'tau_hat_tw',&
858 'threshold stress for twinning',
'Pa')
861 if(prm%sum_N_tr>0)
call results_writedataset(group,stt%f_tr,
'f_tr',&
862 'martensite volume fraction',
'm³/m³')
868 end subroutine plastic_dislotwin_results
878 pure subroutine kinetics_slip(Mp,T,instance,of, &
879 dot_gamma_sl,ddot_gamma_dtau_slip,tau_slip)
881 real(pReal),
dimension(3,3),
intent(in) :: &
883 real(pReal),
intent(in) :: &
885 integer,
intent(in) :: &
889 real(pReal),
dimension(param(instance)%sum_N_sl),
intent(out) :: &
891 real(pReal),
dimension(param(instance)%sum_N_sl),
optional,
intent(out) :: &
892 ddot_gamma_dtau_slip, &
894 real(pReal),
dimension(param(instance)%sum_N_sl) :: &
897 real(pReal),
dimension(param(instance)%sum_N_sl) :: &
902 v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned)
903 v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned)
904 dV_wait_inverse_dTau, &
905 dV_run_inverse_dTau, &
910 associate(prm => param(instance), stt => state(instance), dst => dependentstate(instance))
912 do i = 1, prm%sum_N_sl
913 tau(i) = math_tensordot(mp,prm%P_sl(1:3,1:3,i))
916 tau_eff = abs(tau)-dst%tau_pass(:,of)
918 significantstress:
where(tau_eff > tol_math_check)
919 stressratio = tau_eff/prm%tau_0
920 stressratio_p = stressratio** prm%p
921 boltzmannratio = prm%Delta_F/(kb*t)
922 v_wait_inverse = prm%v0**(-1.0_preal) * exp(boltzmannratio*(1.0_preal-stressratio_p)** prm%q)
923 v_run_inverse = prm%B/(tau_eff*prm%b_sl)
925 dot_gamma_sl = sign(stt%rho_mob(:,of)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau)
927 dv_wait_inverse_dtau = -1.0_preal * v_wait_inverse * prm%p * prm%q * boltzmannratio &
928 * (stressratio**(prm%p-1.0_preal)) &
929 * (1.0_preal-stressratio_p)**(prm%q-1.0_preal) &
931 dv_run_inverse_dtau = -1.0_preal * v_run_inverse/tau_eff
932 dv_dtau = -1.0_preal * (dv_wait_inverse_dtau+dv_run_inverse_dtau) &
933 / (v_wait_inverse+v_run_inverse)**2.0_preal
934 ddot_gamma_dtau = dv_dtau*stt%rho_mob(:,of)*prm%b_sl
935 else where significantstress
936 dot_gamma_sl = 0.0_preal
937 ddot_gamma_dtau = 0.0_preal
938 end where significantstress
942 if(
present(ddot_gamma_dtau_slip)) ddot_gamma_dtau_slip = ddot_gamma_dtau
943 if(
present(tau_slip)) tau_slip = tau
945 end subroutine kinetics_slip
955 pure subroutine kinetics_twin(Mp,T,dot_gamma_sl,instance,of,&
956 dot_gamma_twin,ddot_gamma_dtau_twin)
958 real(pReal),
dimension(3,3),
intent(in) :: &
960 real(pReal),
intent(in) :: &
962 integer,
intent(in) :: &
965 real(pReal),
dimension(param(instance)%sum_N_sl),
intent(in) :: &
968 real(pReal),
dimension(param(instance)%sum_N_tw),
intent(out) :: &
970 real(pReal),
dimension(param(instance)%sum_N_tw),
optional,
intent(out) :: &
973 real,
dimension(param(instance)%sum_N_tw) :: &
981 associate(prm => param(instance), stt => state(instance), dst => dependentstate(instance))
983 do i = 1, prm%sum_N_tw
984 tau(i) = math_tensordot(mp,prm%P_tw(1:3,1:3,i))
985 isfcc:
if (prm%fccTwinTransNucleation)
then
986 s1=prm%fcc_twinNucleationSlipPair(1,i)
987 s2=prm%fcc_twinNucleationSlipPair(2,i)
988 if (tau(i) < dst%tau_r_tw(i,of))
then
989 ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
990 abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/&
991 (prm%L_tw*prm%b_sl(i))*&
992 (1.0_preal-exp(-prm%V_cs/(kb*t)*(dst%tau_r_tw(i,of)-tau(i))))
997 ndot0=prm%dot_N_0_tw(i)
1001 significantstress:
where(tau > tol_math_check)
1002 stressratio_r = (dst%tau_hat_tw(:,of)/tau)**prm%r
1003 dot_gamma_twin = prm%gamma_char * dst%V_tw(:,of) * ndot0*exp(-stressratio_r)
1004 ddot_gamma_dtau = (dot_gamma_twin*prm%r/tau)*stressratio_r
1005 else where significantstress
1006 dot_gamma_twin = 0.0_preal
1007 ddot_gamma_dtau = 0.0_preal
1008 end where significantstress
1012 if(
present(ddot_gamma_dtau_twin)) ddot_gamma_dtau_twin = ddot_gamma_dtau
1014 end subroutine kinetics_twin
1024 pure subroutine kinetics_trans(Mp,T,dot_gamma_sl,instance,of,&
1025 dot_gamma_tr,ddot_gamma_dtau_trans)
1027 real(pReal),
dimension(3,3),
intent(in) :: &
1029 real(pReal),
intent(in) :: &
1031 integer,
intent(in) :: &
1034 real(pReal),
dimension(param(instance)%sum_N_sl),
intent(in) :: &
1037 real(pReal),
dimension(param(instance)%sum_N_tr),
intent(out) :: &
1039 real(pReal),
dimension(param(instance)%sum_N_tr),
optional,
intent(out) :: &
1040 ddot_gamma_dtau_trans
1042 real,
dimension(param(instance)%sum_N_tr) :: &
1049 associate(prm => param(instance), stt => state(instance), dst => dependentstate(instance))
1051 do i = 1, prm%sum_N_tr
1052 tau(i) = math_tensordot(mp,prm%P_tr(1:3,1:3,i))
1053 isfcc:
if (prm%fccTwinTransNucleation)
then
1054 s1=prm%fcc_twinNucleationSlipPair(1,i)
1055 s2=prm%fcc_twinNucleationSlipPair(2,i)
1056 if (tau(i) < dst%tau_r_tr(i,of))
then
1057 ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
1058 abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/&
1059 (prm%L_tr*prm%b_sl(i))*&
1060 (1.0_preal-exp(-prm%V_cs/(kb*t)*(dst%tau_r_tr(i,of)-tau(i))))
1065 ndot0=prm%dot_N_0_tr(i)
1069 significantstress:
where(tau > tol_math_check)
1070 stressratio_s = (dst%tau_hat_tr(:,of)/tau)**prm%s
1071 dot_gamma_tr = dst%V_tr(:,of) * ndot0*exp(-stressratio_s)
1072 ddot_gamma_dtau = (dot_gamma_tr*prm%s/tau)*stressratio_s
1073 else where significantstress
1074 dot_gamma_tr = 0.0_preal
1075 ddot_gamma_dtau = 0.0_preal
1076 end where significantstress
1080 if(
present(ddot_gamma_dtau_trans)) ddot_gamma_dtau_trans = ddot_gamma_dtau
1082 end subroutine kinetics_trans
1084 end submodule plastic_dislotwin
1.8.17