DAMASK_EICMD/src/plastic_dislotwin.f90

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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
!--------------------------------------------------------------------------------------------------
module plastic_dislotwin
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:,:), allocatable, target, public :: &
plastic_dislotwin_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_dislotwin_output !< name of each post result output
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real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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! START: Do something here
real(pReal), dimension(:,:), allocatable, private :: &
tau_r_twin, & !< stress to bring partial close together for each twin system and instance
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tau_r_trans !< stress to bring partial close together for each trans system and instance
real(pReal), dimension(:,:,:), allocatable, private :: &
forestProjectionEdge, & !< matrix of forest projections of edge dislocations for each instance
projectionMatrix_Trans !< matrix for projection of slip system shear on fault band (twin) systems for each instance
real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
sbSv
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! END: Do something here
enum, bind(c)
enumerator :: undefined_ID, &
edge_density_ID, &
dipole_density_ID, &
shear_rate_slip_ID, &
accumulated_shear_slip_ID, &
mfp_slip_ID, &
resolved_stress_slip_ID, &
threshold_stress_slip_ID, &
edge_dipole_distance_ID, &
stress_exponent_ID, &
twin_fraction_ID, &
shear_rate_twin_ID, &
accumulated_shear_twin_ID, &
mfp_twin_ID, &
resolved_stress_twin_ID, &
threshold_stress_twin_ID, &
resolved_stress_shearband_ID, &
shear_rate_shearband_ID, &
sb_eigenvalues_ID, &
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sb_eigenvectors_ID, &
stress_trans_fraction_ID, &
strain_trans_fraction_ID, &
trans_fraction_ID
end enum
type,private :: tParameters
integer(kind(undefined_ID)), dimension(:), allocatable, private :: &
outputID !< ID of each post result output
real(pReal) :: &
CAtomicVolume, & !< atomic volume in Bugers vector unit
D0, & !< prefactor for self-diffusion coefficient
Qsd, & !< activation energy for dislocation climb
GrainSize, & !<grain size
pShearBand, & !< p-exponent in shear band velocity
qShearBand, & !< q-exponent in shear band velocity
MaxTwinFraction, & !<max allowed total twin volume fraction
CEdgeDipMinDistance, & !<
Cmfptwin, & !<
Cthresholdtwin, & !<
SolidSolutionStrength, & !<strength due to elements in solid solution
L0_twin, & !< Length of twin nuclei in Burgers vectors
L0_trans, & !< Length of trans nuclei in Burgers vectors
xc_twin, & !< critical distance for formation of twin nucleus
xc_trans, & !< critical distance for formation of trans nucleus
VcrossSlip, & !< cross slip volume
sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
sbVelocity, & !< value for shearband velocity_0
sbQedge, & !< value for shearband systems Qedge
SFE_0K, & !< stacking fault energy at zero K
dSFE_dT, & !< temperature dependance of stacking fault energy
dipoleFormationFactor, & !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
aTolRho, & !< absolute tolerance for integration of dislocation density
aTolTwinFrac, & !< absolute tolerance for integration of twin volume fraction
aTolTransFrac, & !< absolute tolerance for integration of trans volume fraction
deltaG, & !< Free energy difference between austensite and martensite
Cmfptrans, & !<
Cthresholdtrans, & !<
transStackHeight !< Stack height of hex nucleus
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integer(pInt), private :: &
totalNslip, & !< number of active slip systems for each family and instance
totalNtwin, & !< number of active twin systems for each family and instance
totalNtrans !< number of active transformation systems for each family and instance
integer(pInt), dimension(:), allocatable, private :: &
Nslip, & !< number of active slip systems for each family and instance
Ntwin, & !< number of active twin systems for each family and instance
Ntrans !< number of active transformation systems for each family and instance
real(pReal), dimension(:), allocatable, private :: &
rho0, & !< initial unipolar dislocation density per slip system
rhoDip0, & !< initial dipole dislocation density per slip system
burgers_slip, & !< absolute length of burgers vector [m] for each slip systems
burgers_twin, & !< absolute length of burgers vector [m] for each slip systems
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burgers_trans, & !< absolute length of burgers vector [m] for each twin family and instance
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Qedge,& !< activation energy for glide [J] for each slip system and instance
v0, & !dislocation velocity prefactor [m/s] for each slip system and instance
tau_peierls,& !< Peierls stress [Pa] for each family and instance
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Ndot0_twin, & !< twin nucleation rate [1/m³s] for each twin system and instance
Ndot0_trans, & !< trans nucleation rate [1/m³s] for each trans system and instance
twinsize, & !< twin thickness [m] for each twin system and instance
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CLambdaSlipPerSlipSystem, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
lamellarsizePerTransSystem, & !< martensite lamellar thickness [m] for each trans system and instance
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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
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shear_twin !< characteristic shear for twins
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real(pReal), dimension(:,:), allocatable, private :: &
interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type and instance
interaction_SlipTwin, & !< coefficients for slip-twin interaction for each interaction type and instance
interaction_TwinSlip, & !< coefficients for twin-slip interaction for each interaction type and instance
interaction_TwinTwin, & !< coefficients for twin-twin interaction for each interaction type and instance
interaction_SlipTrans, & !< coefficients for slip-trans interaction for each interaction type and instance
interaction_TransSlip, & !< coefficients for trans-slip interaction for each interaction type and instance
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interaction_TransTrans !< coefficients for trans-trans interaction for each interaction type and instance
integer(pInt), dimension(:,:), allocatable, private :: &
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fcc_twinNucleationSlipPair
real(pReal), dimension(:,:,:), allocatable :: &
Schmid_trans, &
Schmid_slip, &
Schmid_twin
real(pReal), dimension(:,:,:), allocatable, private :: &
Ctwin66, &
Ctrans66
end type
type(tParameters), dimension(:), allocatable, private,target :: param !< containers of constitutive parameters (len Ninstance)
type, private :: tDislotwinState
real(pReal), pointer, dimension(:,:) :: &
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rhoEdge, &
rhoEdgeDip, &
accshear_slip, &
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twinFraction, &
accshear_twin, &
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stressTransFraction, &
strainTransFraction , &
invLambdaSlip, &
invLambdaSlipTwin, &
invLambdaTwin, &
invLambdaSlipTrans, &
invLambdaTrans, &
mfp_slip, &
mfp_twin, &
mfp_trans, &
threshold_stress_slip, &
threshold_stress_twin, &
threshold_stress_trans, &
twinVolume, &
martensiteVolume
end type
type(tDislotwinState), allocatable, dimension(:), private :: &
state, &
dotState
public :: &
plastic_dislotwin_init, &
plastic_dislotwin_homogenizedC, &
plastic_dislotwin_microstructure, &
plastic_dislotwin_LpAndItsTangent, &
plastic_dislotwin_dotState, &
plastic_dislotwin_postResults
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_init(fileUnit)
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
use prec, only: &
dEq0, &
dNeq0, &
dNeq
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333, &
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math_mul3x3, &
math_expand,&
pi
use mesh, only: &
mesh_maxNips, &
mesh_NcpElems
use IO, only: &
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IO_warning, &
IO_error, &
IO_timeStamp
use material, only: &
homogenization_maxNgrains, &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
PLASTICITY_DISLOTWIN_label, &
PLASTICITY_DISLOTWIN_ID, &
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material_phase, &
plasticState
use config, only: &
MATERIAL_partPhase, &
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config_phase
use lattice
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use numerics,only: &
numerics_integrator
implicit none
integer(pInt), intent(in) :: fileUnit
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integer(pInt) :: maxNinstance,&
f,instance,j,i,k,l,m,n,o,p,q,r,s,p1, &
offset_slip, index_myFamily, index_otherFamily, &
startIndex, endIndex, outputSize
integer(pInt) :: sizeState, sizeDotState, sizeDeltaState
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integer(pInt) :: NofMyPhase
integer(kind(undefined_ID)) outputID
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real(pReal), dimension(:,:,:,:,:), allocatable :: &
Ctwin3333, & !< twin elasticity matrix
Ctrans3333 !< trans elasticity matrix
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real(pReal), allocatable, dimension(:) :: &
invLambdaSlip0,&
MeanFreePathSlip0,&
MeanFreePathTrans0,&
MeanFreePathTwin0,&
tauSlipThreshold0,&
TwinVolume0,&
MartensiteVolume0
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real(pReal), allocatable, dimension(:,:) :: temp1,temp2,temp3
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character(len=65536) :: &
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tag = ''
character(len=65536), dimension(:), allocatable :: outputs
integer(pInt), dimension(0), parameter :: emptyInt = [integer(pInt)::]
real(pReal), dimension(0), parameter :: emptyReal = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyString = [character(len=65536)::]
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type(tParameters),pointer :: prm
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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write(6,'(/,a)') ' A. Ma and F. Roters, Acta Materialia, 52(12):36033612, 2004'
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write(6,'(a)') ' https://doi.org/10.1016/j.actamat.2004.04.012'
write(6,'(/,a)') ' F.Roters et al., Computational Materials Science, 39:9195, 2007'
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write(6,'(a)') ' https://doi.org/10.1016/j.commatsci.2006.04.014'
write(6,'(/,a)') ' Wong et al., Acta Materialia, 118:140151, 2016'
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write(6,'(a,/)') ' https://doi.org/10.1016/j.actamat.2016.07.032'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOTWIN_ID),pInt)
if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
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allocate(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
allocate(plastic_dislotwin_output(maxval(phase_Noutput),maxNinstance))
plastic_dislotwin_output = ''
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allocate(param(maxNinstance))
allocate(state(maxNinstance))
allocate(dotState(maxNinstance))
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allocate(sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), source=0.0_pReal)
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do p = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
instance = phase_plasticityInstance(p)
prm => param(instance)
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prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyInt)
if (size(prm%Nslip) > count(lattice_NslipSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
if (any(lattice_NslipSystem(1:size(prm%Nslip),p)-prm%Nslip < 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
if (any(prm%Nslip < 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
prm%totalNslip = sum(prm%Nslip)
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if (prm%totalNslip > 0_pInt) then
prm%rho0 = config_phase(p)%getFloats('rhoedge0')
prm%rhoDip0 = config_phase(p)%getFloats('rhoedgedip0')
prm%burgers_slip = config_phase(p)%getFloats('slipburgers')
if (size(prm%burgers_slip) /= size(prm%Nslip)) call IO_error(150_pInt,ext_msg='slipburgers')
prm%burgers_slip = math_expand(prm%burgers_slip,prm%Nslip)
prm%Qedge = config_phase(p)%getFloats('qedge')
prm%Qedge = math_expand(prm%Qedge,prm%Nslip)
prm%v0 = config_phase(p)%getFloats('v0')
prm%v0 = math_expand(prm%v0,prm%Nslip)
prm%interaction_SlipSlip = spread(config_phase(p)%getFloats('interaction_slipslip'),2,1)
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prm%CEdgeDipMinDistance = config_phase(p)%getFloat('cedgedipmindistance')
prm%CLambdaSlipPerSlipSystem = config_phase(p)%getFloats('clambdaslip')
prm%CLambdaSlipPerSlipSystem= math_expand(prm%CLambdaSlipPerSlipSystem,prm%Nslip)
prm%tau_peierls = config_phase(p)%getFloats('tau_peierls',defaultVal=[0.0_pReal])
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prm%p = config_phase(p)%getFloats('p_slip')
prm%q = config_phase(p)%getFloats('q_slip')
endif
prm%Ntwin = config_phase(p)%getInts('ntwin', defaultVal=emptyInt)
if (size(prm%Ntwin) > count(lattice_NtwinSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
if (any(lattice_NtwinSystem(1:size(prm%Ntwin),p)-prm%Ntwin < 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
if (any(prm%Ntwin < 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
prm%totalNtwin = sum(prm%Ntwin)
if (prm%totalNtwin > 0_pInt) then
prm%burgers_twin = config_phase(p)%getFloats('twinburgers')
prm%burgers_twin = math_expand(prm%burgers_twin,prm%Ntwin)
prm%xc_twin = config_phase(p)%getFloat('xc_twin')
prm%Cthresholdtwin = config_phase(p)%getFloat('cthresholdtwin', defaultVal=0.0_pReal)
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prm%Cmfptwin = config_phase(p)%getFloat('cmfptwin', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%interaction_TwinTwin = spread(config_phase(p)%getFloats('interaction_twintwin'),2,1)
if (lattice_structure(p) /= LATTICE_fcc_ID) then
prm%Ndot0_twin = config_phase(p)%getFloats('ndot0_twin')
prm%Ndot0_twin = math_expand(prm%Ndot0_twin,prm%Ntwin)
endif
prm%twinsize = config_phase(p)%getFloats('twinsize')
prm%twinsize= math_expand(prm%twinsize,prm%Ntwin)
prm%r = config_phase(p)%getFloats('r_twin')
prm%r = math_expand(prm%r,prm%Ntwin)
prm%L0_twin = config_phase(p)%getFloat('l0_twin')
endif
prm%Ntrans = config_phase(p)%getInts('ntrans', defaultVal=emptyInt)
prm%totalNtrans = sum(prm%Ntrans)
!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
if (prm%totalNtrans > 0_pInt) then
prm%burgers_trans = config_phase(p)%getFloats('transburgers')
prm%burgers_trans = math_expand(prm%burgers_trans,prm%Ntrans)
prm%Cthresholdtrans = config_phase(p)%getFloat('cthresholdtrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%transStackHeight = config_phase(p)%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%Cmfptrans = config_phase(p)%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%deltaG = config_phase(p)%getFloat('deltag')
prm%xc_trans = config_phase(p)%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%L0_trans = config_phase(p)%getFloat('l0_trans')
prm%interaction_TransTrans = spread(config_phase(p)%getFloats('interaction_transtrans'),2,1)
if (lattice_structure(p) /= LATTICE_fcc_ID) then
prm%Ndot0_trans = config_phase(p)%getFloats('ndot0_trans')
prm%Ndot0_trans = math_expand(prm%Ndot0_trans,prm%Ntrans)
endif
prm%lamellarsizePerTransSystem = config_phase(p)%getFloats('lamellarsize')
prm%lamellarsizePerTransSystem = math_expand(prm%lamellarsizePerTransSystem,prm%Ntrans)
prm%s = config_phase(p)%getFloats('s_trans',defaultVal=[0.0_pReal])
endif
if (sum(prm%Ntwin) > 0_pInt .or. sum(prm%Ntrans) > 0_pInt) then
prm%SFE_0K = config_phase(p)%getFloat('sfe_0k')
prm%dSFE_dT = config_phase(p)%getFloat('dsfe_dt')
prm%VcrossSlip = config_phase(p)%getFloat('vcrossslip')
endif
if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then
prm%interaction_SlipTwin = spread(config_phase(p)%getFloats('interaction_sliptwin'),2,1)
prm%interaction_TwinSlip = spread(config_phase(p)%getFloats('interaction_twinslip'),2,1)
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prm%p = math_expand(prm%p,prm%Nslip)
prm%q = math_expand(prm%q,prm%Nslip)
prm%tau_peierls = math_expand(prm%tau_peierls,prm%Nslip)
endif
if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then
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prm%interaction_TransSlip = spread(config_phase(p)%getFloats('interaction_transslip'),2,1)
prm%interaction_SlipTrans = spread(config_phase(p)%getFloats('interaction_sliptrans'),2,1)
endif
prm%aTolRho = config_phase(p)%getFloat('atol_rho', defaultVal=0.0_pReal)
prm%aTolTwinFrac = config_phase(p)%getFloat('atol_twinfrac', defaultVal=0.0_pReal)
prm%aTolTransFrac = config_phase(p)%getFloat('atol_transfrac', defaultVal=0.0_pReal)
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prm%CAtomicVolume = config_phase(p)%getFloat('catomicvolume')
prm%GrainSize = config_phase(p)%getFloat('grainsize')
prm%MaxTwinFraction = config_phase(p)%getFloat('maxtwinfraction') ! ToDo: only used in postResults
prm%D0 = config_phase(p)%getFloat('d0')
prm%Qsd = config_phase(p)%getFloat('qsd')
prm%SolidSolutionStrength = config_phase(p)%getFloat('solidsolutionstrength')
prm%dipoleFormationFactor= config_phase(p)%getFloat('dipoleformationfactor', defaultVal=1.0_pReal) ! ToDo: How to handle that???
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prm%sbVelocity = config_phase(p)%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
if (prm%sbVelocity > 0.0_pReal) then
prm%sbResistance = config_phase(p)%getFloat('shearbandresistance')
prm%sbQedge = config_phase(p)%getFloat('qedgepersbsystem')
prm%pShearBand = config_phase(p)%getFloat('p_shearband')
prm%qShearBand = config_phase(p)%getFloat('q_shearband')
endif
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outputs = config_phase(p)%getStrings('(output)', defaultVal=emptyString)
allocate(prm%outputID(0))
do i= 1_pInt, size(outputs)
outputID = undefined_ID
select case(outputs(i))
case ('edge_density')
outputID = edge_density_ID
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outputSize = prm%totalNslip
case ('dipole_density')
outputID = dipole_density_ID
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outputSize = prm%totalNslip
case ('shear_rate_slip','shearrate_slip')
outputID = shear_rate_slip_ID
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outputSize = prm%totalNslip
case ('accumulated_shear_slip')
outputID = accumulated_shear_slip_ID
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outputSize = prm%totalNslip
case ('mfp_slip')
outputID = mfp_slip_ID
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outputSize = prm%totalNslip
case ('resolved_stress_slip')
outputID = resolved_stress_slip_ID
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outputSize = prm%totalNslip
case ('threshold_stress_slip')
outputID= threshold_stress_slip_ID
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outputSize = prm%totalNslip
case ('edge_dipole_distance')
outputID = edge_dipole_distance_ID
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outputSize = prm%totalNslip
case ('stress_exponent')
outputID = stress_exponent_ID
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outputSize = prm%totalNslip
case ('twin_fraction')
outputID = twin_fraction_ID
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outputSize = prm%totalNtwin
case ('shear_rate_twin','shearrate_twin')
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outputID = shear_rate_twin_ID
outputSize = prm%totalNtwin
case ('accumulated_shear_twin')
outputID = accumulated_shear_twin_ID
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outputSize = prm%totalNtwin
case ('mfp_twin')
outputID = mfp_twin_ID
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outputSize = prm%totalNtwin
case ('resolved_stress_twin')
outputID = resolved_stress_twin_ID
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outputSize = prm%totalNtwin
case ('threshold_stress_twin')
outputID = threshold_stress_twin_ID
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outputSize = prm%totalNtwin
case ('resolved_stress_shearband')
outputID = resolved_stress_shearband_ID
outputSize = 6_pInt
case ('shear_rate_shearband','shearrate_shearband')
outputID = shear_rate_shearband_ID
outputSize = 6_pInt
case ('stress_trans_fraction')
outputID = stress_trans_fraction_ID
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outputSize = prm%totalNtrans
case ('strain_trans_fraction')
outputID = strain_trans_fraction_ID
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outputSize = prm%totalNtrans
case ('trans_fraction','total_trans_fraction')
outputID = trans_fraction_ID
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outputSize = prm%totalNtrans
end select
if (outputID /= undefined_ID) then
plastic_dislotwin_output(i,instance) = outputs(i)
plastic_dislotwin_sizePostResult(i,instance) = outputSize
prm%outputID = [prm%outputID , outputID]
endif
enddo
do f = 1_pInt,lattice_maxNslipFamily
! if (rhoEdge0(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOTWIN_label//')')
! if (rhoEdgeDip0(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOTWIN_label//')')
! if (burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOTWIN_label//')')
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!if (v0PerSlipFamily(f,instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOTWIN_label//')')
!if (prm%tau_peierlsPerSlipFamily(f) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOTWIN_label//')')
enddo
do f = 1_pInt,lattice_maxNtwinFamily
! if (burgersPerTwinFamily(f,instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='twinburgers ('//PLASTICITY_DISLOTWIN_label//')')
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!if (Ndot0PerTwinFamily(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='ndot0_twin ('//PLASTICITY_DISLOTWIN_label//')')
enddo
if (prm%CAtomicVolume <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%D0 <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%Qsd <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOTWIN_label//')')
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if (prm%totalNtwin > 0_pInt) then
if (dEq0(prm%SFE_0K) .and. &
dEq0(prm%dSFE_dT) .and. &
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lattice_structure(p) == LATTICE_fcc_ID) &
call IO_error(211_pInt,el=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%aTolRho <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%aTolTwinFrac <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOTWIN_label//')')
endif
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if (prm%totalNtrans > 0_pInt) then
if (dEq0(prm%SFE_0K) .and. &
dEq0(prm%dSFE_dT) .and. &
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lattice_structure(p) == LATTICE_fcc_ID) &
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call IO_error(211_pInt,el=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%aTolTransFrac <= 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='aTolTransFrac ('//PLASTICITY_DISLOTWIN_label//')')
endif
!if (prm%sbResistance < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='sbResistance ('//PLASTICITY_DISLOTWIN_label//')')
!if (prm%sbVelocity < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='sbVelocity ('//PLASTICITY_DISLOTWIN_label//')')
!if (prm%sbVelocity > 0.0_pReal .and. &
! prm%pShearBand <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='pShearBand ('//PLASTICITY_DISLOTWIN_label//')')
if (dNeq0(prm%dipoleFormationFactor) .and. &
dNeq(prm%dipoleFormationFactor, 1.0_pReal)) &
call IO_error(211_pInt,el=instance,ext_msg='dipoleFormationFactor ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%sbVelocity > 0.0_pReal .and. &
prm%qShearBand <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='qShearBand ('//PLASTICITY_DISLOTWIN_label//')')
enddo
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! ToDo: this works only for one instance!
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allocate(forestProjectionEdge(prm%totalNslip,prm%totalNslip,maxNinstance), source=0.0_pReal)
allocate(projectionMatrix_Trans(prm%totalNtrans,prm%totalNslip,maxNinstance), source=0.0_pReal)
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initializeInstances: do p = 1_pInt, size(phase_plasticity)
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if (phase_plasticity(p) /= PLASTICITY_dislotwin_ID) cycle
NofMyPhase=count(material_phase==p)
instance = phase_plasticityInstance(p)
prm => param(instance)
!--------------------------------------------------------------------------------------------------
! allocate state arrays
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sizeDotState = int(size(['rho ','rhoDip ','accshearslip']),pInt) * prm%totalNslip &
+ int(size(['twinFraction','accsheartwin']),pInt) * prm%totalNtwin &
+ int(size(['stressTransFraction','strainTransFraction']),pInt) * prm%totalNtrans
sizeDeltaState = 0_pInt
sizeState = sizeDotState &
+ int(size(['invLambdaSlip ','invLambdaSlipTwin ','invLambdaSlipTrans',&
'meanFreePathSlip ','tauSlipThreshold ']),pInt) * prm%totalNslip &
+ int(size(['invLambdaTwin ','meanFreePathTwin','tauTwinThreshold',&
'twinVolume ']),pInt) * prm%totalNtwin &
+ int(size(['invLambdaTrans ','meanFreePathTrans','tauTransThreshold', &
'martensiteVolume ']),pInt) * prm%totalNtrans
plasticState(p)%sizeState = sizeState
plasticState(p)%sizeDotState = sizeDotState
plasticState(p)%sizeDeltaState = sizeDeltaState
plasticState(p)%sizePostResults = sum(plastic_dislotwin_sizePostResult(:,instance))
plasticState(p)%nSlip = prm%totalNslip
plasticState(p)%nTwin = prm%totalNtwin
plasticState(p)%nTrans= prm%totalNtrans
allocate(plasticState(p)%aTolState (sizeState), source=0.0_pReal)
allocate(plasticState(p)%state0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%partionedState0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%subState0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%state (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%deltaState (sizeDeltaState,NofMyPhase), source=0.0_pReal)
if (any(numerics_integrator == 1_pInt)) then
allocate(plasticState(p)%previousDotState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(p)%previousDotState2 (sizeDotState,NofMyPhase), source=0.0_pReal)
endif
if (any(numerics_integrator == 4_pInt)) &
allocate(plasticState(p)%RK4dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
if (any(numerics_integrator == 5_pInt)) &
allocate(plasticState(p)%RKCK45dotState (6,sizeDotState,NofMyPhase),source=0.0_pReal)
offset_slip = 2_pInt*plasticState(p)%nslip
plasticState(p)%slipRate => &
plasticState(p)%dotState(offset_slip+1:offset_slip+plasticState(p)%nslip,1:NofMyPhase)
plasticState(p)%accumulatedSlip => &
plasticState(p)%state (offset_slip+1:offset_slip+plasticState(p)%nslip,1:NofMyPhase)
allocate(temp1(prm%totalNslip,prm%totalNslip), source =0.0_pReal)
allocate(temp2(prm%totalNslip,prm%totalNtwin), source =0.0_pReal)
allocate(temp3(prm%totalNslip,prm%totalNtrans),source =0.0_pReal)
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allocate(prm%Schmid_slip(3,3,prm%totalNslip),source = 0.0_pReal)
i = 0_pInt
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mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1)
index_myFamily = sum(prm%Nslip(1:f-1_pInt))
slipSystemsLoop: do j = 1_pInt,prm%Nslip(f)
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i = i + 1_pInt
prm%Schmid_slip(1:3,1:3,i) = lattice_Sslip(1:3,1:3,1,sum(lattice_Nslipsystem(1:f-1,p))+j,p)
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do o = 1_pInt, size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = &
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,p))+j,p), &
lattice_st(:,sum(lattice_NslipSystem(1:o-1,p))+k,p)))
temp1(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_SlipSlip(lattice_interactionSlipSlip( &
sum(lattice_NslipSystem(1:f-1,p))+j, &
sum(lattice_NslipSystem(1:o-1,p))+k, &
p),1 )
enddo; enddo
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do o = 1_pInt,size(prm%Ntwin,1)
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
do k = 1_pInt,prm%Ntwin(o) ! loop over (active) systems in other family (twin)
temp2(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_SlipTwin(lattice_interactionSlipTwin( &
sum(lattice_NslipSystem(1:f-1_pInt,p))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, &
p),1 )
enddo; enddo
do o = 1_pInt,size(prm%Ntrans,1)
index_otherFamily = sum(prm%Ntrans(1:o-1_pInt))
do k = 1_pInt,prm%Ntrans(o) ! loop over (active) systems in other family (trans)
temp3(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_SlipTrans(lattice_interactionSlipTrans( &
sum(lattice_NslipSystem(1:f-1_pInt,p))+j, &
sum(lattice_NtransSystem(1:o-1_pInt,p))+k, &
p),1 )
enddo; enddo
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enddo slipSystemsLoop
enddo mySlipFamilies
prm%interaction_SlipSlip = temp1; deallocate(temp1)
prm%interaction_SlipTwin = temp2; deallocate(temp2)
prm%interaction_SlipTrans = temp3; deallocate(temp3)
allocate(temp1(prm%totalNtwin,prm%totalNslip), source =0.0_pReal)
allocate(temp2(prm%totalNtwin,prm%totalNtwin), source =0.0_pReal)
allocate(prm%Ctwin66(6,6,prm%totalNtwin), source=0.0_pReal)
if (allocated(Ctwin3333)) deallocate(Ctwin3333)
allocate(Ctwin3333(3,3,3,3,prm%totalNtwin), source=0.0_pReal)
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allocate(prm%Schmid_twin(3,3,prm%totalNtwin),source = 0.0_pReal)
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if (lattice_structure(p) == LATTICE_fcc_ID) &
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allocate(prm%fcc_twinNucleationSlipPair(2,prm%totalNtwin),source = 0_pInt)
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allocate(prm%shear_twin(prm%totalNtwin),source = 0.0_pReal)
i = 0_pInt
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twinFamiliesLoop: do f = 1_pInt, size(prm%Ntwin,1)
index_myFamily = sum(prm%Ntwin(1:f-1_pInt)) ! index in truncated twin system list
twinSystemsLoop: do j = 1_pInt,prm%Ntwin(f)
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i = i + 1_pInt
prm%Schmid_twin(1:3,1:3,i) = lattice_Stwin(1:3,1:3,sum(lattice_NTwinsystem(1:f-1,p))+j,p)
prm%shear_twin(i) = lattice_shearTwin(sum(lattice_Ntwinsystem(1:f-1,p))+j,p)
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if (lattice_structure(p) == LATTICE_fcc_ID) prm%fcc_twinNucleationSlipPair(1:2,i) = &
lattice_fcc_twinNucleationSlipPair(1:2,sum(lattice_Ntwinsystem(1:f-1,p))+j)
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!* Rotate twin elasticity matrices
index_otherFamily = sum(lattice_NtwinSystem(1:f-1_pInt,p)) ! index in full lattice twin list
do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt; do o = 1_pInt,3_pInt
do p1 = 1_pInt,3_pInt; do q = 1_pInt,3_pInt; do r = 1_pInt,3_pInt; do s = 1_pInt,3_pInt
Ctwin3333(l,m,n,o,index_myFamily+j) = &
Ctwin3333(l,m,n,o,index_myFamily+j) + &
lattice_C3333(p1,q,r,s,p) * &
lattice_Qtwin(l,p1,index_otherFamily+j,p) * &
lattice_Qtwin(m,q,index_otherFamily+j,p) * &
lattice_Qtwin(n,r,index_otherFamily+j,p) * &
lattice_Qtwin(o,s,index_otherFamily+j,p)
enddo; enddo; enddo; enddo
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enddo; enddo; enddo; enddo
prm%Ctwin66(1:6,1:6,index_myFamily+j) = &
math_Mandel3333to66(Ctwin3333(1:3,1:3,1:3,1:3,index_myFamily+j))
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!* Interaction matrices
do o = 1_pInt,size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
temp1(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TwinSlip(lattice_interactionTwinSlip( &
sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, &
sum(lattice_NslipSystem(1:o-1_pInt,p))+k, &
p),1 )
enddo; enddo
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do o = 1_pInt,size(prm%Ntwin,1)
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
do k = 1_pInt,prm%Ntwin(o) ! loop over (active) systems in other family (twin)
temp2(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TwinTwin(lattice_interactionTwinTwin( &
sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, &
p),1 )
enddo; enddo
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enddo twinSystemsLoop
enddo twinFamiliesLoop
prm%interaction_TwinSlip = temp1; deallocate(temp1)
prm%interaction_TwinTwin = temp2; deallocate(temp2)
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allocate(temp1(prm%totalNtrans,prm%totalNslip), source =0.0_pReal)
allocate(temp2(prm%totalNtrans,prm%totalNtrans), source =0.0_pReal)
allocate(prm%Ctrans66(6,6,prm%totalNtrans) ,source=0.0_pReal)
if (allocated(Ctrans3333)) deallocate(Ctrans3333)
allocate(Ctrans3333(3,3,3,3,prm%totalNtrans), source=0.0_pReal)
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allocate(prm%Schmid_trans(3,3,prm%totalNtrans),source = 0.0_pReal)
i = 0_pInt
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transFamiliesLoop: do f = 1_pInt,size(prm%Ntrans,1)
index_myFamily = sum(prm%Ntrans(1:f-1_pInt)) ! index in truncated trans system list
transSystemsLoop: do j = 1_pInt,prm%Ntrans(f)
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i = i + 1_pInt
prm%Schmid_trans(1:3,1:3,i) = lattice_Strans(1:3,1:3,sum(lattice_Ntranssystem(1:f-1,p))+j,p)
index_otherFamily = sum(lattice_NtransSystem(1:f-1_pInt,p)) ! index in full lattice trans list
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do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt; do o = 1_pInt,3_pInt
do p1 = 1_pInt,3_pInt; do q = 1_pInt,3_pInt; do r = 1_pInt,3_pInt; do s = 1_pInt,3_pInt
Ctrans3333(l,m,n,o,index_myFamily+j) = &
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Ctrans3333(l,m,n,o,index_myFamily+j) + &
lattice_trans_C3333(p1,q,r,s,p) * &
lattice_Qtrans(l,p1,index_otherFamily+j,p) * &
lattice_Qtrans(m,q,index_otherFamily+j,p) * &
lattice_Qtrans(n,r,index_otherFamily+j,p) * &
lattice_Qtrans(o,s,index_otherFamily+j,p)
enddo; enddo; enddo; enddo
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enddo; enddo; enddo; enddo
prm%Ctrans66(1:6,1:6,index_myFamily+j) = &
math_Mandel3333to66(Ctrans3333(1:3,1:3,1:3,1:3,index_myFamily+j))
!* Interaction matrices
do o = 1_pInt,size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
temp1(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TransSlip(lattice_interactionTransSlip( &
sum(lattice_NtransSystem(1:f-1_pInt,p))+j, &
sum(lattice_NslipSystem(1:o-1_pInt,p))+k, &
p) ,1 )
enddo; enddo
do o = 1_pInt,size(prm%Ntrans,1)
index_otherFamily = sum(prm%Ntrans(1:o-1_pInt))
do k = 1_pInt,prm%Ntrans(o) ! loop over (active) systems in other family (trans)
temp2(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TransTrans(lattice_interactionTransTrans( &
sum(lattice_NtransSystem(1:f-1_pInt,p))+j, &
sum(lattice_NtransSystem(1:o-1_pInt,p))+k, &
p),1 )
enddo; enddo
!* Projection matrices for shear from slip systems to fault-band (twin) systems for strain-induced martensite nucleation
! select case(trans_lattice_structure(p))
! case (LATTICE_bcc_ID)
! do o = 1_pInt,sum(prm%Ntrans,1)
! index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
! do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (trans)
! temp3(index_myFamily+j,index_otherFamily+k) = &
! lattice_projectionTrans( sum(lattice_NtransSystem(1:f-1,p))+j, &
! sum(lattice_NslipSystem(1:o-1,p))+k, p)
! enddo; enddo
! end select
enddo transSystemsLoop
enddo transFamiliesLoop
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prm%interaction_TransSlip = temp1; deallocate(temp1)
prm%interaction_TransTrans = temp2; deallocate(temp2)
startIndex=1_pInt
endIndex=prm%totalNslip
state(instance)%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(prm%rho0,prm%Nslip),2,NofMyPhase)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(prm%rhoDip0,prm%Nslip),2,NofMyPhase)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%twinFraction=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%twinFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%accshear_twin=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%accshear_twin=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%stressTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%stressTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%strainTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%strainTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%invLambdaSlip=>plasticState(p)%state(startIndex:endIndex,:)
invLambdaSlip0 = spread(0.0_pReal,1,prm%totalNslip)
forall (i = 1_pInt:prm%totalNslip) &
invLambdaSlip0(i) = sqrt(dot_product(math_expand(prm%rho0,prm%Nslip)+ &
math_expand(prm%rhoDip0,prm%Nslip),forestProjectionEdge(1:prm%totalNslip,i,instance)))/ &
prm%CLambdaSlipPerSlipSystem(i)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(invLambdaSlip0,prm%Nslip),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%invLambdaSlipTwin=>plasticState(p)%state(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%invLambdaTwin=>plasticState(p)%state(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%invLambdaSlipTrans=>plasticState(p)%state(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%invLambdaTrans=>plasticState(p)%state(startIndex:endIndex,:)
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%mfp_slip=>plasticState(p)%state(startIndex:endIndex,:)
MeanFreePathSlip0 = prm%GrainSize/(1.0_pReal+invLambdaSlip0*prm%GrainSize)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(MeanFreePathSlip0,prm%Nslip),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%mfp_twin=>plasticState(p)%state(startIndex:endIndex,:)
MeanFreePathTwin0 = spread(prm%GrainSize,1,prm%totalNtwin)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(MeanFreePathTwin0,prm%Ntwin),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%mfp_trans=>plasticState(p)%state(startIndex:endIndex,:)
MeanFreePathTrans0 = spread(prm%GrainSize,1,prm%totalNtrans)
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(MeanFreePathTrans0,prm%Ntrans),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNslip
state(instance)%threshold_stress_slip=>plasticState(p)%state(startIndex:endIndex,:)
tauSlipThreshold0 = spread(0.0_pReal,1,prm%totalNslip)
forall (i = 1_pInt:prm%totalNslip) tauSlipThreshold0(i) = &
lattice_mu(p)*prm%burgers_slip(i) * &
sqrt(dot_product(math_expand(prm%rho0 + prm%rhoDip0,prm%Nslip),&
prm%interaction_SlipSlip(i,1:prm%totalNslip)))
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(tauSlipThreshold0,prm%Nslip),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%threshold_stress_twin=>plasticState(p)%state(startIndex:endIndex,:)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%threshold_stress_trans=>plasticState(p)%state(startIndex:endIndex,:)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtwin
state(instance)%twinVolume=>plasticState(p)%state(startIndex:endIndex,:)
TwinVolume0= spread(0.0_pReal,1,prm%totalNtwin)
forall (i = 1_pInt:prm%totalNtwin) TwinVolume0(i) = &
(PI/4.0_pReal)*prm%twinsize(i)*MeanFreePathTwin0(i)**2.0_pReal
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(TwinVolume0,prm%Ntwin),2, NofMyPhase)
startIndex=endIndex+1
endIndex=endIndex+prm%totalNtrans
state(instance)%martensiteVolume=>plasticState(p)%state(startIndex:endIndex,:)
MartensiteVolume0= spread(0.0_pReal,1,prm%totalNtrans)
forall (i = 1_pInt:prm%totalNtrans) MartensiteVolume0(i) = &
(PI/4.0_pReal)*prm%lamellarsizePerTransSystem(i)*MeanFreePathTrans0(i)**2.0_pReal
plasticState(p)%state0(startIndex:endIndex,:) = &
spread(math_expand(MartensiteVolume0,prm%Ntrans),2, NofMyPhase)
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enddo initializeInstances
! ToDo: this should be stored somewhere else. Works only for the whole instance!!
! ToDo: prm%totalNtwin should be the maximum over all totalNtwins!
allocate(tau_r_twin(prm%totalNtwin, maxNinstance), source=0.0_pReal)
allocate(tau_r_trans(prm%totalNtrans, maxNinstance), source=0.0_pReal)
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end subroutine plastic_dislotwin_init
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!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
function plastic_dislotwin_homogenizedC(ipc,ip,el)
use material, only: &
phase_plasticityInstance, &
phaseAt, phasememberAt
use lattice, only: &
lattice_C66
implicit none
real(pReal), dimension(6,6) :: &
plastic_dislotwin_homogenizedC
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(tParameters) :: prm
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type(tDislotwinState) :: stt
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integer(pInt) :: instance,i, &
ph, &
of
real(pReal) :: sumf, sumftr
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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associate( prm => param(instance), stt =>state(instance))
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!* Total twin volume fraction
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sumf = sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
!* Total transformed volume fraction
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sumftr = sum(stt%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
!* Homogenized elasticity matrix
plastic_dislotwin_homogenizedC = (1.0_pReal-sumf-sumftr)*lattice_C66(1:6,1:6,ph)
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do i=1_pInt,prm%totalNtwin
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
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+ stt%twinFraction(i,of)*prm%Ctwin66(1:6,1:6,i)
enddo
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do i=1_pInt,prm%totalNtrans
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
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+ (stt%stressTransFraction(i,of) + stt%strainTransFraction(i,of))*&
prm%Ctrans66(1:6,1:6,i)
enddo
end associate
end function plastic_dislotwin_homogenizedC
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_microstructure(temperature,ipc,ip,el)
use math, only: &
pi
use material, only: &
material_phase, &
phase_plasticityInstance, &
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plasticState, &
phaseAt, phasememberAt
use lattice, only: &
lattice_mu, &
lattice_nu
implicit none
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in) :: &
temperature !< temperature at IP
integer(pInt) :: &
instance, &
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s, &
ph, &
of
real(pReal) :: &
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sumf,sfe,sumftr
real(pReal), dimension(:), allocatable :: &
x0, &
fOverStacksize, &
ftransOverLamellarSize
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type(tParameters) :: prm !< parameters of present instance
type(tDislotwinState) :: stt !< state of present instance
of = phasememberAt(ipc,ip,el)
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ph = material_phase(ipc,ip,el)
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associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
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sumf = sum(stt%twinFraction(1:prm%totalNtwin,of))
sumftr = sum(stt%stressTransFraction(1:prm%totalNtrans,of)) &
+ sum(stt%strainTransFraction(1:prm%totalNtrans,of))
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sfe = prm%SFE_0K + prm%dSFE_dT * Temperature
!* rescaled volume fraction for topology
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fOverStacksize = stt%twinFraction(1_pInt:prm%totalNtwin,of)/prm%twinsize
ftransOverLamellarSize = sumftr /prm%lamellarsizePerTransSystem
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
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forall (s = 1_pInt:prm%totalNslip) &
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stt%invLambdaSlip(s,of) = &
sqrt(dot_product((stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)),&
forestProjectionEdge(1:prm%totalNslip,s,instance)))/prm%CLambdaSlipPerSlipSystem(s)
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
!$OMP CRITICAL (evilmatmul)
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if (prm%totalNtwin > 0_pInt .and. prm%totalNslip > 0_pInt) &
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stt%invLambdaSlipTwin(1_pInt:prm%totalNslip,of) = &
matmul(prm%interaction_SlipTwin,fOverStacksize)/(1.0_pReal-sumf)
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!ToDo: needed? if (prm%totalNtwin > 0_pInt) &
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stt%invLambdaTwin(1_pInt:prm%totalNtwin,of) = &
matmul(prm%interaction_TwinTwin,fOverStacksize)/(1.0_pReal-sumf)
!* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
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if (prm%totalNtrans > 0_pInt .and. prm%totalNslip > 0_pInt) &
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stt%invLambdaSlipTrans(1_pInt:prm%totalNslip,of) = &
matmul(prm%interaction_SlipTrans,ftransOverLamellarSize)/(1.0_pReal-sumftr)
!* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
!ToDo: needed? if (prm%totalNtrans > 0_pInt) &
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stt%invLambdaTrans(1_pInt:prm%totalNtrans,of) = &
matmul(prm%interaction_TransTrans,ftransOverLamellarSize)/(1.0_pReal-sumftr)
!$OMP END CRITICAL (evilmatmul)
!* mean free path between 2 obstacles seen by a moving dislocation
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do s = 1_pInt,prm%totalNslip
if ((prm%totalNtwin > 0_pInt) .or. (prm%totalNtrans > 0_pInt)) then ! ToDo: This is too simplified
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stt%mfp_slip(s,of) = &
prm%GrainSize/(1.0_pReal+prm%GrainSize*&
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(stt%invLambdaSlip(s,of) + stt%invLambdaSlipTwin(s,of) + stt%invLambdaSlipTrans(s,of)))
else
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stt%mfp_slip(s,of) = &
prm%GrainSize/&
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(1.0_pReal+prm%GrainSize*(stt%invLambdaSlip(s,of))) !!!!!! correct?
endif
enddo
!* mean free path between 2 obstacles seen by a growing twin/martensite
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stt%mfp_twin(:,of) = prm%Cmfptwin*prm%GrainSize/ (1.0_pReal+prm%GrainSize*stt%invLambdaTwin(:,of))
stt%mfp_trans(:,of) = prm%Cmfptrans*prm%GrainSize/(1.0_pReal+prm%GrainSize*stt%invLambdaTrans(:,of))
!* threshold stress for dislocation motion
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forall (s = 1_pInt:prm%totalNslip) stt%threshold_stress_slip(s,of) = &
lattice_mu(ph)*prm%burgers_slip(s)*&
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sqrt(dot_product(stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of),&
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prm%interaction_SlipSlip(s,1:prm%totalNslip)))
!* threshold stress for growing twin/martensite
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stt%threshold_stress_twin(:,of) = prm%Cthresholdtwin* &
(sfe/(3.0_pReal*prm%burgers_twin)+ 3.0_pReal*prm%burgers_twin*lattice_mu(ph)/ &
(prm%L0_twin*prm%burgers_slip)) ! slip burgers here correct?
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stt%threshold_stress_trans(:,of) = prm%Cthresholdtrans* &
(sfe/(3.0_pReal*prm%burgers_trans) + 3.0_pReal*prm%burgers_trans*lattice_mu(ph)/&
(prm%L0_trans*prm%burgers_slip) + prm%transStackHeight*prm%deltaG/ (3.0_pReal*prm%burgers_trans) )
! final volume after growth
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stt%twinVolume(:,of) = (PI/4.0_pReal)*prm%twinsize*stt%mfp_twin(:,of)**2.0_pReal
stt%martensiteVolume(:,of) = (PI/4.0_pReal)*prm%lamellarsizePerTransSystem*stt%mfp_trans(:,of)**2.0_pReal
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!ToDo: MD: This does not work for non-isothermal simulations!!!!!
!* equilibrium separation of partial dislocations (twin)
x0 = lattice_mu(ph)*prm%burgers_twin**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+lattice_nu(ph))/(1.0_pReal-lattice_nu(ph))
tau_r_twin(:,instance)= lattice_mu(ph)*prm%burgers_twin/(2.0_pReal*PI)*&
(1/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
!* equilibrium separation of partial dislocations (trans)
x0 = lattice_mu(ph)*prm%burgers_trans**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+lattice_nu(ph))/(1.0_pReal-lattice_nu(ph))
tau_r_trans(:,instance)= lattice_mu(ph)*prm%burgers_trans/(2.0_pReal*PI)*&
(1/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
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end associate
end subroutine plastic_dislotwin_microstructure
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
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tol_math_check, &
dNeq0
use math, only: &
math_Plain3333to99, &
math_Mandel6to33, &
math_Mandel33to6, &
math_eigenValuesVectorsSym, &
math_tensorproduct33, &
math_symmetric33, &
math_mul33xx33, &
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math_mul33x3
use material, only: &
material_phase, &
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plasticState, &
phase_plasticityInstance, &
phaseAt, phasememberAt
use lattice, only: &
lattice_structure, &
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LATTICE_fcc_ID
implicit none
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
real(pReal), dimension(3,3), intent(out) :: Lp
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99
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integer(pInt) :: ph,of,j,k,l,m,n,s1,s2,instance
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real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,&
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StressRatio_r,BoltzmannRatio,Ndot0_twin,stressRatio, &
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Ndot0_trans,StressRatio_s, &
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dgdot_dtau, &
tau
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real(pReal), dimension(3,3,3,3) :: dLp_dS
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real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
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gdot_slip
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real(pReal):: gdot_sb,gdot_twin,gdot_trans
real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix
real(pReal), dimension(3) :: eigValues, sb_s, sb_m
logical :: error
real(pReal), dimension(3,6), parameter :: &
sb_sComposition = &
reshape(real([&
1, 0, 1, &
1, 0,-1, &
1, 1, 0, &
1,-1, 0, &
0, 1, 1, &
0, 1,-1 &
],pReal),[ 3,6]), &
sb_mComposition = &
reshape(real([&
1, 0,-1, &
1, 0,+1, &
1,-1, 0, &
1, 1, 0, &
0, 1,-1, &
0, 1, 1 &
],pReal),[ 3,6])
real(pReal), dimension(3,3) :: &
S !< Second-Piola Kirchhoff stress
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type(tParameters) :: prm !< parameters of present instance
type(tDislotwinState) :: ste !< state of present instance
of = phasememberAt(ipc,ip,el)
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ph = material_phase(ipc,ip,el)
instance = phase_plasticityInstance(ph)
associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
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sumf = sum(stt%twinFraction(1:prm%totalNtwin,of))
sumftr = sum(stt%stressTransFraction(1:prm%totalNtrans,of)) &
+ sum(stt%strainTransFraction(1:prm%totalNtrans,of))
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Lp = 0.0_pReal
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dLp_dS = 0.0_pReal
S = math_Mandel6to33(Tstar_v)
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slipContribution: do j = 1_pInt, prm%totalNslip
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tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
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significantSlipStress: if((abs(tau)-stt%threshold_stress_slip(j,of)) > tol_math_check) then
stressRatio = ((abs(tau)- stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+prm%tau_peierls(j)))
StressRatio_p = stressRatio** prm%p(j)
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StressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal) ! ToDo: no very helpful
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BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
gdot_slip(j) = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j) &
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* sign(exp(-BoltzmannRatio*(1-StressRatio_p)** prm%q(j)), tau)
dgdot_dtau = abs(gdot_slip(j))*BoltzmannRatio*prm%p(j) * prm%q(j) &
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/ (prm%SolidSolutionStrength+prm%tau_peierls(j)) &
* StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal)
Lp = Lp + gdot_slip(j)*prm%Schmid_slip(1:3,1:3,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtau * prm%Schmid_slip(k,l,j) * prm%Schmid_slip(m,n,j)
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else significantSlipStress
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gdot_slip(j) = 0.0_pReal
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endif significantSlipStress
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enddo slipContribution
!ToDo: Why do this before shear banding?
Lp = Lp * (1.0_pReal - sumf - sumftr)
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dLp_dS = dLp_dS * (1.0_pReal - sumf - sumftr)
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shearBanding: if(dNeq0(prm%sbVelocity)) then
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
call math_eigenValuesVectorsSym(S,eigValues,eigVectors,error)
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do j = 1_pInt,6_pInt
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j))
sb_m = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_mComposition(1:3,j))
sb_Smatrix = math_tensorproduct33(sb_s,sb_m)
sbSv(1:6,j,ipc,ip,el) = math_Mandel33to6(math_symmetric33(sb_Smatrix))
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tau = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el))
!* Stress ratios
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if (abs(tau) < tol_math_check) then
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StressRatio_p = 0.0_pReal
StressRatio_pminus1 = 0.0_pReal
else
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StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand
StressRatio_pminus1 = (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal)
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endif
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gdot_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand), tau)
dgdot_dtau = ((abs(gdot_sb)*BoltzmannRatio* prm%pShearBand*prm%qShearBand)/ prm%sbResistance) &
* StressRatio_pminus1*(1_pInt-StressRatio_p)**(prm%qShearBand-1.0_pReal)
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Lp = Lp + gdot_sb*sb_Smatrix
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
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dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
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+ dgdot_dtau * sb_Smatrix(k,l) * sb_Smatrix(m,n)
enddo
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endif shearBanding
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twinContibution: do j = 1_pInt, prm%totalNtwin
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tau = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,j))
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significantTwinStress: if (tau > tol_math_check) then
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StressRatio_r = (stt%threshold_stress_twin(j,of)/tau)**prm%r(j)
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isFCCtwin: if (lattice_structure(ph) == LATTICE_FCC_ID) then
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s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j)
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if (tau < tau_r_twin(j,instance)) then
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Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+& !!!!! correct?
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
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(prm%L0_twin*prm%burgers_slip(j))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
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(tau_r_twin(j,instance)-tau)))
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else
Ndot0_twin=0.0_pReal
end if
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else isFCCtwin
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Ndot0_twin=prm%Ndot0_twin(j)
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endif isFCCtwin
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gdot_twin = (1.0_pReal-sumf-sumftr)* prm%shear_twin(j) * stt%twinVolume(j,of) &
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* Ndot0_twin*exp(-StressRatio_r)
dgdot_dtau = ((gdot_twin*prm%r(j))/tau)*StressRatio_r
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Lp = Lp + gdot_twin*prm%Schmid_twin(1:3,1:3,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtau* prm%Schmid_twin(k,l,j)*prm%Schmid_twin(m,n,j)
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endif significantTwinStress
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enddo twinContibution
transConstribution: do j = 1_pInt, prm%totalNtrans
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tau = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j))
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significantTransStress: if (tau > tol_math_check) then
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StressRatio_s = (stt%threshold_stress_trans(j,of)/tau)**prm%s(j)
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isFCCtrans: if (lattice_structure(ph) == LATTICE_FCC_ID) then
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s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j)
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if (tau < tau_r_trans(j,instance)) then
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Ndot0_trans=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+& !!!!! correct?
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
(prm%L0_trans*prm%burgers_slip(j))*&
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(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*(tau_r_trans(j,instance)-tau)))
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else
Ndot0_trans=0.0_pReal
end if
else isFCCtrans
Ndot0_trans=prm%Ndot0_trans(j)
endif isFCCtrans
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gdot_trans = (1.0_pReal-sumf-sumftr)* stt%martensiteVolume(j,of) &
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* Ndot0_trans*exp(-StressRatio_s)
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dgdot_dtau = ((gdot_trans*prm%s(j))/tau)*StressRatio_s
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Lp = Lp + gdot_trans*prm%Schmid_trans(1:3,1:3,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtau * prm%Schmid_trans(k,l,j)* prm%Schmid_trans(m,n,j)
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endif significantTransStress
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enddo transConstribution
end associate
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dLp_dTstar99 = math_Plain3333to99(dLp_dS)
end subroutine plastic_dislotwin_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
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use prec, only: &
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tol_math_check, &
dEq0
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use math, only: &
math_mul33xx33, &
math_Mandel6to33, &
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pi
use material, only: &
material_phase, &
phase_plasticityInstance, &
plasticState, &
phaseAt, phasememberAt
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use lattice, only: &
lattice_mu, &
lattice_structure, &
LATTICE_fcc_ID
implicit none
real(pReal), dimension(6), intent(in):: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
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integer(pInt) :: instance,j,s1,s2, &
ph, &
of
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real(pReal) :: sumf,sumftr,StressRatio_p,BoltzmannRatio,&
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EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,&
Ndot0_trans,StressRatio_s,EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, &
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DotRhoDipFormation,DotRhoMultiplication,DotRhoEdgeEdgeAnnihilation, &
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tau
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real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
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gdot_slip
real(pReal), dimension(3,3) :: &
S !< Second-Piola Kirchhoff stress
type(tParameters) :: prm
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type(tDislotwinState) :: stt, dst
!* Shortened notation
of = phasememberAt(ipc,ip,el)
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ph = material_phase(ipc,ip,el)
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S = math_Mandel6to33(Tstar_v)
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plasticState(ph)%dotState(:,of) = 0.0_pReal
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associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))), &
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))), &
dst => dotstate(phase_plasticityInstance(material_phase(ipc,ip,el))))
sumf = sum(stt%twinFraction(1_pInt:prm%totalNtwin,of))
sumftr = sum(stt%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
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slipState: do j = 1_pInt, prm%totalNslip
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tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
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significantSlipStress1: if((abs(tau)-stt%threshold_stress_slip(j,of)) > tol_math_check) then
stressRatio =((abs(tau)- stt%threshold_stress_slip(j,of))/&
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(prm%SolidSolutionStrength+prm%tau_peierls(j)))
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StressRatio_p = stressRatio** prm%p(j)
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BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
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gdot_slip(j) = stt%rhoEdge(j,of)*prm%burgers_slip(j)*prm%v0(j) &
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* sign(exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%q(j)),tau)
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else significantSlipStress1
gdot_slip(j) = 0.0_pReal
endif significantSlipStress1
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DotRhoMultiplication = abs(gdot_slip(j))/(prm%burgers_slip(j)*stt%mfp_slip(j,of))
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EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip(j)
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significantSlipStress2: if (dEq0(tau)) then
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DotRhoDipFormation = 0.0_pReal
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else significantSlipStress2
EdgeDipDistance = (3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j))/&
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(16.0_pReal*PI*abs(tau))
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if (EdgeDipDistance>stt%mfp_slip(j,of)) EdgeDipDistance=stt%mfp_slip(j,of)
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if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
DotRhoDipFormation = ((2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance))/prm%burgers_slip(j))*&
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stt%rhoEdge(j,of)*abs(gdot_slip(j))*prm%dipoleFormationFactor
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endif significantSlipStress2
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!* Spontaneous annihilation of 2 single edge dislocations
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DotRhoEdgeEdgeAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j))*&
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stt%rhoEdge(j,of)*abs(gdot_slip(j))
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!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
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DotRhoEdgeDipAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j)) &
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* stt%rhoEdgeDip(j,of)*abs(gdot_slip(j))
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!* Dislocation dipole climb
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AtomicVolume = prm%CAtomicVolume*prm%burgers_slip(j)**(3.0_pReal) ! no need to calculate this over and over again
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
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if (dEq0(tau)) then
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DotRhoEdgeDipClimb = 0.0_pReal
else
if (dEq0(EdgeDipDistance-EdgeDipMinDistance)) then
DotRhoEdgeDipClimb = 0.0_pReal
else
ClimbVelocity = 3.0_pReal*lattice_mu(ph)*VacancyDiffusion*AtomicVolume/ &
(2.0_pReal*pi*kB*Temperature*(EdgeDipDistance+EdgeDipMinDistance))
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DotRhoEdgeDipClimb = 4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(j,of)/ &
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(EdgeDipDistance-EdgeDipMinDistance)
endif
endif
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dst%rhoEdge(j,of) = DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
dst%rhoEdgeDip(j,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
dst%accshear_slip(j,of) = abs(gdot_slip(j))
enddo slipState
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twinState: do j = 1_pInt, prm%totalNtwin
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tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
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significantTwinStress: if (tau > tol_math_check) then
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StressRatio_r = (stt%threshold_stress_twin(j,of)/tau)**prm%r(j)
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isFCCtwin: if (lattice_structure(ph) == LATTICE_FCC_ID) then
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s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j)
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if (tau < tau_r_twin(j,instance)) then
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Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
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(prm%L0_twin*prm%burgers_slip(j))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
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(tau_r_twin(j,instance)-tau)))
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else
Ndot0_twin=0.0_pReal
end if
else isFCCtwin
Ndot0_twin=prm%Ndot0_twin(j)
endif isFCCtwin
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dst%twinFraction(j,of) = (1.0_pReal-sumf-sumftr)*&
stt%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
dst%accshear_twin(j,of) = dst%twinFraction(j,of) * prm%shear_twin(j)
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endif significantTwinStress
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enddo twinState
transState: do j = 1_pInt, prm%totalNtrans
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tau = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j))
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significantTransStress: if (tau > tol_math_check) then
StressRatio_s = (stt%threshold_stress_trans(j,of)/tau)**prm%s(j)
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isFCCtrans: if (lattice_structure(ph) == LATTICE_FCC_ID) then
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s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j)
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if (tau < tau_r_trans(j,instance)) then
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Ndot0_trans=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
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(prm%L0_trans*prm%burgers_slip(j))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
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(tau_r_trans(j,instance)-tau)))
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else
Ndot0_trans=0.0_pReal
end if
else isFCCtrans
Ndot0_trans=prm%Ndot0_trans(j)
endif isFCCtrans
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dst%strainTransFraction(j,of) = (1.0_pReal-sumf-sumftr)*&
stt%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
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!* Dotstate for accumulated shear due to transformation
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!dst%accshear_trans(j,of) = dst%strainTransFraction(j,of) * &
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! lattice_sheartrans(index_myfamily+i,ph)
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endif significantTransStress
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enddo transState
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end associate
end subroutine plastic_dislotwin_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
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function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el) result(postResults)
use prec, only: &
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tol_math_check, &
dEq0
use math, only: &
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PI, &
math_mul33xx33, &
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math_Mandel6to33
use material, only: &
material_phase, &
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plasticState, &
phase_plasticityInstance,&
phaseAt, phasememberAt
use lattice, only: &
lattice_mu, &
lattice_structure, &
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LATTICE_fcc_ID
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
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real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: &
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postResults
integer(pInt) :: &
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instance,&
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o,c,j,&
s1,s2, &
ph, &
of
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real(pReal) :: sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,Ndot0_twin,dgdot_dtauslip, &
stressRatio
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real(preal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
gdot_slip
real(pReal), dimension(3,3) :: &
S !< Second-Piola Kirchhoff stress
type(tParameters) :: prm
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type(tDislotwinState) :: stt
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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S = math_Mandel6to33(Tstar_v)
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associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))), &
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
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sumf = sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
c = 0_pInt
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postResults = 0.0_pReal
do o = 1_pInt,size(prm%outputID)
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select case(prm%outputID(o))
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case (edge_density_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (dipole_density_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (shear_rate_slip_ID)
do j = 1_pInt, prm%totalNslip
tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
if((abs(tau)-stt%threshold_stress_slip(j,of)) > tol_math_check) then
stressRatio = ((abs(tau)-stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+&
prm%tau_peierls(j)))
StressRatio_p = stressRatio** prm%p(j)
StressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
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postResults(c+j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
prm%q(j))*sign(1.0_pReal,tau)
else
postResults(c+j) = 0.0_pReal
endif
enddo
c = c + prm%totalNslip
case (accumulated_shear_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (mfp_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%mfp_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (resolved_stress_slip_ID)
do j = 1_pInt, prm%totalNslip
postResults(c+j) = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
enddo
c = c + prm%totalNslip
case (threshold_stress_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%threshold_stress_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (edge_dipole_distance_ID)
do j = 1_pInt, prm%totalNslip
postResults(c+j) = (3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j)) &
/ (16.0_pReal*PI*abs(math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))))
postResults(c+j)=min(postResults(c+j),stt%mfp_slip(j,of))
! postResults(c+j)=max(postResults(c+j),&
! plasticState(ph)%state(4*ns+2*nt+2*nr+j, of))
enddo
c = c + prm%totalNslip
case (resolved_stress_shearband_ID)
do j = 1_pInt,6_pInt ! loop over all shearband families
postResults(c+j) = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el))
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enddo
c = c + 6_pInt
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case (shear_rate_shearband_ID)
do j = 1_pInt,6_pInt ! loop over all shearbands
tau = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el))
if (abs(tau) < tol_math_check) then
StressRatio_p = 0.0_pReal
StressRatio_pminus1 = 0.0_pReal
else
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand
StressRatio_pminus1 = (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal)
endif
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
DotGamma0 = prm%sbVelocity
postResults(c+j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand)*&
sign(1.0_pReal,tau)
enddo
c = c + 6_pInt
case (twin_fraction_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = stt%twinFraction(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (shear_rate_twin_ID)
do j = 1_pInt, prm%totalNslip
tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
if((abs(tau)-stt%threshold_stress_slip(j,of)) > tol_math_check) then
StressRatio_p = ((abs(tau)-stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+&
prm%tau_peierls(j)))&
**prm%p(j)
StressRatio_pminus1 = ((abs(tau)-stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+&
prm%tau_peierls(j)))&
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**(prm%p(j)-1.0_pReal)
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
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gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
prm%q(j))*sign(1.0_pReal,tau)
else
gdot_slip(j) = 0.0_pReal
endif
enddo
do j = 1_pInt, prm%totalNtwin
tau = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,j))
if ( tau > 0.0_pReal ) then
select case(lattice_structure(ph))
case (LATTICE_fcc_ID)
s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j)
if (tau < tau_r_twin(j,instance)) then
Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
(prm%L0_twin* prm%burgers_slip(j))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)* (tau_r_twin(j,instance)-tau)))
else
Ndot0_twin=0.0_pReal
end if
case default
Ndot0_twin=prm%Ndot0_twin(j)
end select
StressRatio_r = (stt%threshold_stress_twin(j,of)/tau) **prm%r(j)
postResults(c+j) = (prm%MaxTwinFraction-sumf)*prm%shear_twin(j) &
* stt%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
endif
enddo
c = c + prm%totalNtwin
case (accumulated_shear_twin_ID)
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postResults(c+1_pInt:c+prm%totalNtwin) = stt%accshear_twin(1_pInt:prm%totalNtwin,of)
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c = c + prm%totalNtwin
case (mfp_twin_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = stt%mfp_twin(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (resolved_stress_twin_ID)
do j = 1_pInt, prm%totalNtwin
postResults(c+j) = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,j))
enddo
c = c + prm%totalNtwin
case (threshold_stress_twin_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = stt%threshold_stress_twin(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (stress_exponent_ID)
do j = 1_pInt, prm%totalNslip
tau = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
if((abs(tau)-stt%threshold_stress_slip(j,of)) > tol_math_check) then
StressRatio_p = ((abs(tau)-stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+&
prm%tau_peierls(j)))&
**prm%p(j)
StressRatio_pminus1 = ((abs(tau)-stt%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+&
prm%tau_peierls(j)))&
**(prm%p(j)-1.0_pReal)
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
prm%q(j))*sign(1.0_pReal,tau)
dgdot_dtauslip = abs(gdot_slip(j))*BoltzmannRatio*prm%p(j) *prm%q(j)/&
(prm%SolidSolutionStrength+ prm%tau_peierls(j))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal)
else
gdot_slip(j) = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
endif
postResults(c+j) = merge(0.0_pReal,(tau/gdot_slip(j))*dgdot_dtauslip,dEq0(gdot_slip(j)))
enddo
c = c + prm%totalNslip
case (stress_trans_fraction_ID)
postResults(c+1_pInt:c+prm%totalNtrans) = &
stt%stressTransFraction(1_pInt:prm%totalNtrans,of)
c = c + prm%totalNtrans
case (strain_trans_fraction_ID)
postResults(c+1_pInt:c+prm%totalNtrans) = stt%strainTransFraction(1_pInt:prm%totalNtrans,of)
c = c + prm%totalNtrans
case (trans_fraction_ID) !ToDo: deprecated
postResults(c+1_pInt:c+prm%totalNtrans) = stt%stressTransFraction(1_pInt:prm%totalNtrans,of) &
+ stt%strainTransFraction(1_pInt:prm%totalNtrans,of)
c = c + prm%totalNtrans
end select
enddo
end associate
end function plastic_dislotwin_postResults
end module plastic_dislotwin