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!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH
!> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine incoprorating dislocation and twinning physics
!> @details to be done
!--------------------------------------------------------------------------------------------------
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submodule ( constitutive : constitutive_plastic ) plastic_dislotwin
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real ( pReal ) , parameter :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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type :: tParameters
real ( pReal ) :: &
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mu = 1.0_pReal , & !< equivalent shear modulus
nu = 1.0_pReal , & !< equivalent shear Poisson's ratio
D0 = 1.0_pReal , & !< prefactor for self-diffusion coefficient
Qsd = 1.0_pReal , & !< activation energy for dislocation climb
omega = 1.0_pReal , & !< frequency factor for dislocation climb
D = 1.0_pReal , & !< grain size
p_sb = 1.0_pReal , & !< p-exponent in shear band velocity
q_sb = 1.0_pReal , & !< q-exponent in shear band velocity
CEdgeDipMinDistance = 1.0_pReal , & !<
i_tw = 1.0_pReal , & !<
tau_0 = 1.0_pReal , & !< strength due to elements in solid solution
L_tw = 1.0_pReal , & !< Length of twin nuclei in Burgers vectors
L_tr = 1.0_pReal , & !< Length of trans nuclei in Burgers vectors
xc_twin = 1.0_pReal , & !< critical distance for formation of twin nucleus
xc_trans = 1.0_pReal , & !< critical distance for formation of trans nucleus
V_cs = 1.0_pReal , & !< cross slip volume
sbResistance = 1.0_pReal , & !< value for shearband resistance
sbVelocity = 1.0_pReal , & !< value for shearband velocity_0
E_sb = 1.0_pReal , & !< activation energy for shear bands
SFE_0K = 1.0_pReal , & !< stacking fault energy at zero K
dSFE_dT = 1.0_pReal , & !< temperature dependence of stacking fault energy
gamma_fcc_hex = 1.0_pReal , & !< Free energy difference between austensite and martensite
i_tr = 1.0_pReal , & !<
h = 1.0_pReal !< Stack height of hex nucleus
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real ( pReal ) , allocatable , dimension ( : ) :: &
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b_sl , & !< absolute length of burgers vector [m] for each slip system
b_tw , & !< absolute length of burgers vector [m] for each twin system
b_tr , & !< absolute length of burgers vector [m] for each transformation system
Delta_F , & !< activation energy for glide [J] for each slip system
v0 , & !< dislocation velocity prefactor [m/s] for each slip system
dot_N_0_tw , & !< twin nucleation rate [1/m³s] for each twin system
dot_N_0_tr , & !< trans nucleation rate [1/m³s] for each trans system
t_tw , & !< twin thickness [m] for each twin system
CLambdaSlip , & !< Adj. parameter for distance between 2 forest dislocations for each slip system
t_tr , & !< martensite lamellar thickness [m] for each trans system and instance
p , & !< p-exponent in glide velocity
q , & !< q-exponent in glide velocity
r , & !< r-exponent in twin nucleation rate
s , & !< s-exponent in trans nucleation rate
gamma_char , & !< characteristic shear for twins
B !< drag coefficient
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real ( pReal ) , allocatable , dimension ( : , : ) :: &
h_sl_sl , & !<
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h_sl_tw , & !<
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h_tw_tw , & !<
h_sl_tr , & !<
h_tr_tr , & !<
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n0_sl , & !< slip system normal
forestProjection , &
C66
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real ( pReal ) , allocatable , dimension ( : , : , : ) :: &
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P_sl , &
P_tw , &
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P_tr , &
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C66_tw , &
C66_tr
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integer :: &
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sum_N_sl , & !< total number of active slip system
sum_N_tw , & !< total number of active twin system
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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
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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
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type :: tDislotwinState
real ( pReal ) , dimension ( : , : ) , pointer :: &
rho_mob , &
rho_dip , &
gamma_sl , &
f_tw , &
f_tr
end type tDislotwinState
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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
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!--------------------------------------------------------------------------------------------------
! containers for parameters and state
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type ( tParameters ) , allocatable , dimension ( : ) :: param
type ( tDislotwinState ) , allocatable , dimension ( : ) :: &
dotState , &
state
type ( tDislotwinMicrostructure ) , allocatable , dimension ( : ) :: dependentState
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Perform module initialization.
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!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_init
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integer :: &
Ninstance , &
p , i , &
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NipcMyPhase , &
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sizeState , sizeDotState , &
startIndex , endIndex
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integer , dimension ( : ) , allocatable :: &
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N_sl , N_tw , N_tr
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real ( pReal ) , allocatable , dimension ( : ) :: &
rho_mob_0 , & !< initial unipolar dislocation density per slip system
rho_dip_0 !< initial dipole dislocation density per slip system
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character ( len = pStringLen ) :: &
extmsg = ''
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write ( 6 , '(/,a)' ) ' <<<+- constitutive_' / / PLASTICITY_DISLOTWIN_LABEL / / ' init -+>>>'
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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'
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Ninstance = count ( phase_plasticity == PLASTICITY_DISLOTWIN_ID )
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write ( 6 , '(a16,1x,i5,/)' ) '# instances:' , Ninstance ; flush ( 6 )
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allocate ( param ( Ninstance ) )
allocate ( state ( Ninstance ) )
allocate ( dotState ( Ninstance ) )
allocate ( dependentState ( Ninstance ) )
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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 ) )
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prm % output = config % getStrings ( '(output)' , defaultVal = emptyStringArray )
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! This data is read in already in lattice
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prm % mu = lattice_mu ( p )
prm % nu = lattice_nu ( p )
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prm % C66 = lattice_C66 ( 1 : 6 , 1 : 6 , p )
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!--------------------------------------------------------------------------------------------------
! slip related parameters
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N_sl = config % getInts ( 'nslip' , defaultVal = emptyIntArray )
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prm % sum_N_sl = sum ( abs ( N_sl ) )
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slipActive : if ( prm % sum_N_sl > 0 ) then
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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' ) , &
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config % getString ( 'lattice_structure' ) )
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prm % forestProjection = lattice_forestProjection_edge ( N_sl , config % getString ( 'lattice_structure' ) , &
config % getFloat ( 'c/a' , defaultVal = 0.0_pReal ) )
prm % forestProjection = transpose ( prm % forestProjection )
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prm % n0_sl = lattice_slip_normal ( N_sl , config % getString ( 'lattice_structure' ) , &
config % getFloat ( 'c/a' , defaultVal = 0.0_pReal ) )
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prm % fccTwinTransNucleation = merge ( . true . , . false . , lattice_structure ( p ) == lattice_FCC_ID ) &
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. and . ( N_sl ( 1 ) == 12 )
if ( prm % fccTwinTransNucleation ) prm % fcc_twinNucleationSlipPair = lattice_FCC_TWINNUCLEATIONSLIPPAIR
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rho_mob_0 = config % getFloats ( 'rhoedge0' , requiredSize = size ( N_sl ) )
rho_dip_0 = config % getFloats ( 'rhoedgedip0' , requiredSize = size ( N_sl ) )
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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 ) ) ] )
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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
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prm % SFE_0K = config % getFloat ( 'sfe_0k' )
prm % dSFE_dT = config % getFloat ( 'dsfe_dt' )
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endif
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prm % dipoleformation = . not . config % keyExists ( '/nodipoleformation/' )
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! multiplication factor according to crystal structure (nearest neighbors bcc vs fcc/hex)
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! details: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
prm % omega = config % getFloat ( 'omega' , defaultVal = 100 0.0_pReal ) &
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* merge ( 1 2.0_pReal , 8.0_pReal , any ( lattice_structure ( p ) == [ lattice_FCC_ID , lattice_HEX_ID ] ) )
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! expand: family => system
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rho_mob_0 = math_expand ( rho_mob_0 , N_sl )
rho_dip_0 = math_expand ( rho_dip_0 , N_sl )
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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 )
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! sanity checks
if ( prm % D0 < = 0.0_pReal ) extmsg = trim ( extmsg ) / / ' D0'
if ( prm % Qsd < = 0.0_pReal ) extmsg = trim ( extmsg ) / / ' Qsd'
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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'
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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
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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 ) )
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endif slipActive
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!--------------------------------------------------------------------------------------------------
! twin related parameters
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N_tw = config % getInts ( 'ntwin' , defaultVal = emptyIntArray )
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prm % sum_N_tw = sum ( abs ( N_tw ) )
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twinActive : if ( prm % sum_N_tw > 0 ) then
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prm % P_tw = lattice_SchmidMatrix_twin ( N_tw , config % getString ( 'lattice_structure' ) , &
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config % getFloat ( 'c/a' , defaultVal = 0.0_pReal ) )
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prm % h_tw_tw = lattice_interaction_TwinByTwin ( N_tw , &
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config % getFloats ( 'interaction_twintwin' ) , &
config % getString ( 'lattice_structure' ) )
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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 ) )
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prm % xc_twin = config % getFloat ( 'xc_twin' )
prm % L_tw = config % getFloat ( 'l0_twin' )
prm % i_tw = config % getFloat ( 'cmfptwin' )
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prm % gamma_char = lattice_characteristicShear_Twin ( N_tw , config % getString ( 'lattice_structure' ) , &
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config % getFloat ( 'c/a' , defaultVal = 0.0_pReal ) )
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prm % C66_tw = lattice_C66_twin ( N_tw , prm % C66 , config % getString ( 'lattice_structure' ) , &
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config % getFloat ( 'c/a' , defaultVal = 0.0_pReal ) )
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if ( . not . prm % fccTwinTransNucleation ) then
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prm % dot_N_0_tw = config % getFloats ( 'ndot0_twin' )
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prm % dot_N_0_tw = math_expand ( prm % dot_N_0_tw , N_tw )
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endif
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! expand: family => system
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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 )
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! 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
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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
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!--------------------------------------------------------------------------------------------------
! transformation related parameters
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N_tr = config % getInts ( 'ntrans' , defaultVal = emptyIntArray )
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prm % sum_N_tr = sum ( abs ( N_tr ) )
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transActive : if ( prm % sum_N_tr > 0 ) then
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prm % b_tr = config % getFloats ( 'transburgers' )
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prm % b_tr = math_expand ( prm % b_tr , N_tr )
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prm % h = config % getFloat ( 'transstackheight' , defaultVal = 0.0_pReal ) ! ToDo: How to handle that???
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prm % i_tr = config % getFloat ( 'cmfptrans' , defaultVal = 0.0_pReal ) ! ToDo: How to handle that???
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prm % gamma_fcc_hex = config % getFloat ( 'deltag' )
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prm % xc_trans = config % getFloat ( 'xc_trans' , defaultVal = 0.0_pReal ) ! ToDo: How to handle that???
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prm % L_tr = config % getFloat ( 'l0_trans' )
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prm % h_tr_tr = lattice_interaction_TransByTrans ( N_tr , config % getFloats ( 'interaction_transtrans' ) , &
config % getString ( 'lattice_structure' ) )
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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 ) )
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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 ) )
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if ( lattice_structure ( p ) / = lattice_FCC_ID ) then
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prm % dot_N_0_tr = config % getFloats ( 'ndot0_trans' )
prm % dot_N_0_tr = math_expand ( prm % dot_N_0_tr , N_tr )
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endif
prm % t_tr = config % getFloats ( 'lamellarsize' )
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prm % t_tr = math_expand ( prm % t_tr , N_tr )
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prm % s = config % getFloats ( 's_trans' , defaultVal = [ 0.0_pReal ] )
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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
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else transActive
allocate ( prm % s , prm % b_tr , prm % t_tr , prm % dot_N_0_tr , source = emptyRealArray )
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allocate ( prm % h_tr_tr ( 0 , 0 ) )
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endif transActive
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!--------------------------------------------------------------------------------------------------
! shearband related parameters
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prm % sbVelocity = config % getFloat ( 'shearbandvelocity' , defaultVal = 0.0_pReal )
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if ( prm % sbVelocity > 0.0_pReal ) then
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prm % sbResistance = config % getFloat ( 'shearbandresistance' )
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prm % E_sb = config % getFloat ( 'qedgepersbsystem' )
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prm % p_sb = config % getFloat ( 'p_shearband' )
prm % q_sb = config % getFloat ( 'q_shearband' )
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! sanity checks
if ( prm % sbResistance < 0.0_pReal ) extmsg = trim ( extmsg ) / / ' shearbandresistance'
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if ( prm % E_sb < 0.0_pReal ) extmsg = trim ( extmsg ) / / ' qedgepersbsystem'
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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
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!--------------------------------------------------------------------------------------------------
! 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
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!--------------------------------------------------------------------------------------------------
! allocate state arrays
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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
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call material_allocateState ( plasticState ( p ) , NipcMyPhase , sizeState , sizeDotState , 0 )
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!--------------------------------------------------------------------------------------------------
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! locally defined state aliases and initialization of state0 and atol
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startIndex = 1
endIndex = prm % sum_N_sl
stt % rho_mob = > plasticState ( p ) % state ( startIndex : endIndex , : )
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stt % rho_mob = spread ( rho_mob_0 , 2 , NipcMyPhase )
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dot % rho_mob = > plasticState ( p ) % dotState ( startIndex : endIndex , : )
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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'
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startIndex = endIndex + 1
endIndex = endIndex + prm % sum_N_sl
stt % rho_dip = > plasticState ( p ) % state ( startIndex : endIndex , : )
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stt % rho_dip = spread ( rho_dip_0 , 2 , NipcMyPhase )
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dot % rho_dip = > plasticState ( p ) % dotState ( startIndex : endIndex , : )
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plasticState ( p ) % atol ( startIndex : endIndex ) = config % getFloat ( 'atol_rho' , defaultVal = 1.0_pReal )
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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 , : )
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plasticState ( p ) % atol ( startIndex : endIndex ) = 1.0e-2_pReal
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! global alias
plasticState ( p ) % slipRate = > plasticState ( p ) % dotState ( startIndex : endIndex , : )
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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 , : )
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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'
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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 , : )
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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'
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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 )
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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 )
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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 )
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plasticState ( p ) % state0 = plasticState ( p ) % state ! ToDo: this could be done centrally
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end associate
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!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if ( extmsg / = '' ) call IO_error ( 211 , ext_msg = trim ( extmsg ) / / '(' / / PLASTICITY_DISLOTWIN_LABEL / / ')' )
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enddo
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end subroutine plastic_dislotwin_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Return the homogenized elasticity matrix.
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!--------------------------------------------------------------------------------------------------
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module function plastic_dislotwin_homogenizedC ( ipc , ip , el ) result ( homogenizedC )
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real ( pReal ) , dimension ( 6 , 6 ) :: &
homogenizedC
integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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integer :: i , &
of
real ( pReal ) :: f_unrotated
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of = material_phasememberAt ( ipc , ip , el )
associate ( prm = > param ( phase_plasticityInstance ( material_phaseAt ( ipc , el ) ) ) , &
stt = > state ( phase_plasticityInstance ( material_phaseAT ( ipc , el ) ) ) )
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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 ) )
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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
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end associate
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end function plastic_dislotwin_homogenizedC
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate plastic velocity gradient and its tangent.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_LpAndItsTangent ( Lp , dLp_dMp , Mp , T , instance , of )
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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
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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 ) :: &
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dot_gamma_sl , ddot_gamma_dtau_slip
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real ( pReal ) , dimension ( param ( instance ) % sum_N_tw ) :: &
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dot_gamma_twin , ddot_gamma_dtau_twin
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real ( pReal ) , dimension ( param ( instance ) % sum_N_tr ) :: &
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dot_gamma_tr , ddot_gamma_dtau_trans
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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 ] )
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associate ( prm = > param ( instance ) , stt = > state ( instance ) )
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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 ) )
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
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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
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call kinetics_twin ( Mp , T , dot_gamma_sl , instance , of , dot_gamma_twin , ddot_gamma_dtau_twin )
twinContibution : do i = 1 , prm % sum_N_tw
Lp = Lp + dot_gamma_twin ( i ) * prm % P_tw ( 1 : 3 , 1 : 3 , i )
forall ( k = 1 : 3 , l = 1 : 3 , m = 1 : 3 , n = 1 : 3 ) &
dLp_dMp ( k , l , m , n ) = dLp_dMp ( k , l , m , n ) &
+ ddot_gamma_dtau_twin ( i ) * prm % P_tw ( k , l , i ) * prm % P_tw ( m , n , i )
enddo twinContibution
call kinetics_trans ( Mp , T , dot_gamma_sl , instance , of , dot_gamma_tr , ddot_gamma_dtau_trans )
transContibution : do i = 1 , prm % sum_N_tr
Lp = Lp + dot_gamma_tr ( i ) * prm % P_tr ( 1 : 3 , 1 : 3 , i )
forall ( k = 1 : 3 , l = 1 : 3 , m = 1 : 3 , n = 1 : 3 ) &
dLp_dMp ( k , l , m , n ) = dLp_dMp ( k , l , m , n ) &
+ ddot_gamma_dtau_trans ( i ) * prm % P_tr ( k , l , i ) * prm % P_tr ( m , n , i )
enddo transContibution
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Lp = Lp * f_unrotated
dLp_dMp = dLp_dMp * f_unrotated
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shearBandingContribution : if ( dNeq0 ( prm % sbVelocity ) ) then
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BoltzmannRatio = prm % E_sb / ( kB * T )
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call math_eigh33 ( eigValues , eigVectors , Mp ) ! is Mp symmetric by design?
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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 ) ) )
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tau = math_tensordot ( Mp , P_sb )
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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 )
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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
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endif shearBandingContribution
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end associate
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end subroutine plastic_dislotwin_LpAndItsTangent
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate the rate of change of microstructure.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_dotState ( Mp , T , instance , of )
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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 , &
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v_cl , & !< climb velocity
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Gamma , & !< stacking fault energy
tau , &
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sigma_cl , & !< climb stress
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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
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associate ( prm = > param ( instance ) , stt = > state ( instance ) , &
dot = > dotState ( instance ) , dst = > dependentState ( instance ) )
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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 ) )
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call kinetics_slip ( Mp , T , instance , of , dot_gamma_sl )
dot % gamma_sl ( : , of ) = abs ( dot_gamma_sl )
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rho_dip_distance_min = prm % CEdgeDipMinDistance * prm % b_sl
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slipState : do i = 1 , prm % sum_N_sl
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tau = math_tensordot ( Mp , prm % P_sl ( 1 : 3 , 1 : 3 , i ) )
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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 ) / ( 1 6.0_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 ) ) )
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if ( prm % ExtendedDislocations ) then
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Gamma = prm % SFE_0K + prm % dSFE_dT * T
b_d = 2 4.0_pReal * PI * ( 1.0_pReal - prm % nu ) / ( 2.0_pReal + prm % nu ) * Gamma / ( prm % mu * prm % b_sl ( i ) )
else
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b_d = 1.0_pReal
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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 )
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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
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end associate
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end subroutine plastic_dislotwin_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate derived quantities from state.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_dependentState ( T , instance , of )
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integer , intent ( in ) :: &
instance , &
of
real ( pReal ) , intent ( in ) :: &
T
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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
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associate ( prm = > param ( instance ) , &
stt = > state ( instance ) , &
dst = > dependentState ( instance ) )
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sumf_twin = sum ( stt % f_tw ( 1 : prm % sum_N_tw , of ) )
sumf_trans = sum ( stt % f_tr ( 1 : prm % sum_N_tr , of ) )
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Gamma = prm % SFE_0K + prm % dSFE_dT * T
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!* rescaled volume fraction for topology
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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
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inv_lambda_sl_sl = sqrt ( matmul ( prm % forestProjection , &
stt % rho_mob ( : , of ) + stt % rho_dip ( : , of ) ) ) / prm % CLambdaSlip
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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 )
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inv_lambda_tw_tw = matmul ( prm % h_tw_tw , f_over_t_tw ) / ( 1.0_pReal - sumf_twin )
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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 )
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inv_lambda_tr_tr = matmul ( prm % h_tr_tr , f_over_t_tr ) / ( 1.0_pReal - sumf_trans )
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if ( ( prm % sum_N_tw > 0 ) . or . ( prm % sum_N_tr > 0 ) ) then ! ToDo: better logic needed here
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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
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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 )
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!* 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 ) ) )
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!* 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?
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+ prm % h * prm % gamma_fcc_hex / ( 3.0_pReal * prm % b_tr )
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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
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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
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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 )
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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
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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 )
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end associate
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end subroutine plastic_dislotwin_dependentState
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!--------------------------------------------------------------------------------------------------
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!> @brief Write results to HDF5 output file.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_results ( instance , group )
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integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
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integer :: o
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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' , &
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'dislocation dipole density' , '1/m²' )
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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' )
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end select
enddo outputsLoop
end associate
end subroutine plastic_dislotwin_results
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved
! stress, and the resolved stress.
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!> @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
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_slip ( Mp , T , instance , of , &
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dot_gamma_sl , ddot_gamma_dtau_slip , tau_slip )
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
real ( pReal ) , intent ( in ) :: &
T !< temperature
integer , intent ( in ) :: &
instance , &
of
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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
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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
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integer :: i
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associate ( prm = > param ( instance ) , stt = > state ( instance ) , dst = > dependentState ( instance ) )
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do i = 1 , prm % sum_N_sl
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tau ( i ) = math_tensordot ( Mp , prm % P_sl ( 1 : 3 , 1 : 3 , i ) )
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enddo
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tau_eff = abs ( tau ) - dst % tau_pass ( : , of )
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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 )
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dot_gamma_sl = sign ( stt % rho_mob ( : , of ) * prm % b_sl / ( v_wait_inverse + v_run_inverse ) , tau )
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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
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end associate
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if ( present ( ddot_gamma_dtau_slip ) ) ddot_gamma_dtau_slip = ddot_gamma_dtau
if ( present ( tau_slip ) ) tau_slip = tau
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end subroutine kinetics_slip
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!--------------------------------------------------------------------------------------------------
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!> @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.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_twin ( Mp , T , dot_gamma_sl , instance , of , &
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dot_gamma_twin , ddot_gamma_dtau_twin )
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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
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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
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real , dimension ( param ( instance ) % sum_N_tw ) :: &
tau , &
Ndot0 , &
stressRatio_r , &
ddot_gamma_dtau
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integer :: i , s1 , s2
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associate ( prm = > param ( instance ) , stt = > state ( instance ) , dst = > dependentState ( instance ) )
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do i = 1 , prm % sum_N_tw
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tau ( i ) = math_tensordot ( Mp , prm % P_tw ( 1 : 3 , 1 : 3 , i ) )
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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
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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
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end associate
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if ( present ( ddot_gamma_dtau_twin ) ) ddot_gamma_dtau_twin = ddot_gamma_dtau
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end subroutine kinetics_twin
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!--------------------------------------------------------------------------------------------------
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!> @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.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_trans ( Mp , T , dot_gamma_sl , instance , of , &
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dot_gamma_tr , ddot_gamma_dtau_trans )
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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
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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
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real , dimension ( param ( instance ) % sum_N_tr ) :: &
tau , &
Ndot0 , &
stressRatio_s , &
ddot_gamma_dtau
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integer :: i , s1 , s2
associate ( prm = > param ( instance ) , stt = > state ( instance ) , dst = > dependentState ( instance ) )
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do i = 1 , prm % sum_N_tr
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tau ( i ) = math_tensordot ( Mp , prm % P_tr ( 1 : 3 , 1 : 3 , i ) )
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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
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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
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end associate
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if ( present ( ddot_gamma_dtau_trans ) ) ddot_gamma_dtau_trans = ddot_gamma_dtau
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end subroutine kinetics_trans
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end submodule plastic_dislotwin