DAMASK_EICMD/src/plastic_disloUCLA.f90

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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author David Cereceda, Lawrence Livermore National Laboratory
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief crystal plasticity model for bcc metals, especially Tungsten
!--------------------------------------------------------------------------------------------------
module plastic_disloUCLA
use prec
use debug
use math
use IO
use material
use config
use lattice
use discretization
use results
implicit none
private
integer, dimension(:,:), allocatable, target, public :: &
plastic_disloUCLA_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_disloUCLA_output !< name of each post result output
real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
enum, bind(c)
enumerator :: &
undefined_ID, &
rho_mob_ID, &
rho_dip_ID, &
dot_gamma_sl_ID, &
gamma_sl_ID, &
Lambda_sl_ID, &
thresholdstress_ID
end enum
type, private :: tParameters
real(pReal) :: &
aTol_rho, &
D, & !< grain size
mu, &
D_0, & !< prefactor for self-diffusion coefficient
Q_cl !< activation energy for dislocation climb
real(pReal), dimension(:), allocatable :: &
rho_mob_0, & !< initial dislocation density
rho_dip_0, & !< initial dipole density
b_sl, & !< magnitude of burgers vector [m]
nonSchmidCoeff, &
D_a, &
i_sl, & !< Adj. parameter for distance between 2 forest dislocations
atomicVolume, &
tau_0, &
!* mobility law parameters
delta_F, & !< activation energy for glide [J]
v0, & !< dislocation velocity prefactor [m/s]
p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
B, & !< friction coefficient
kink_height, & !< height of the kink pair
w, & !< width of the kink pair
omega !< attempt frequency for kink pair nucleation
real(pReal), dimension(:,:), allocatable :: &
h_sl_sl, & !< slip resistance from slip activity
forestProjectionEdge
real(pReal), dimension(:,:,:), allocatable :: &
Schmid, &
nonSchmid_pos, &
nonSchmid_neg
integer :: &
sum_N_sl !< total number of active slip system
integer, dimension(:), allocatable :: &
N_sl !< number of active slip systems for each family
integer(kind(undefined_ID)), dimension(:),allocatable :: &
outputID !< ID of each post result output
logical :: &
dipoleFormation !< flag indicating consideration of dipole formation
end type !< container type for internal constitutive parameters
type, private :: tDisloUCLAState
real(pReal), dimension(:,:), pointer :: &
rho_mob, &
rho_dip, &
gamma_sl
end type tDisloUCLAState
type, private :: tDisloUCLAdependentState
real(pReal), dimension(:,:), allocatable :: &
Lambda_sl, &
threshold_stress
end type tDisloUCLAdependentState
!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:), private :: param
type(tDisloUCLAState), allocatable, dimension(:), private :: &
dotState, &
state
type(tDisloUCLAdependentState), allocatable, dimension(:), private :: dependentState
public :: &
plastic_disloUCLA_init, &
plastic_disloUCLA_dependentState, &
plastic_disloUCLA_LpAndItsTangent, &
plastic_disloUCLA_dotState, &
plastic_disloUCLA_postResults, &
plastic_disloUCLA_results
private :: &
kinetics
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_init()
integer :: &
Ninstance, &
p, i, &
NipcMyPhase, &
sizeState, sizeDotState, &
startIndex, endIndex
integer, dimension(0), parameter :: emptyIntArray = [integer::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
integer(kind(undefined_ID)) :: &
outputID
character(len=pStringLen) :: &
extmsg = ''
character(len=65536), dimension(:), allocatable :: &
outputs
write(6,'(/,a)') ' <<<+- plastic_'//PLASTICITY_DISLOUCLA_label//' init -+>>>'
write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78:242256, 2016'
write(6,'(a)') ' https://dx.doi.org/10.1016/j.ijplas.2015.09.002'
Ninstance = count(phase_plasticity == PLASTICITY_DISLOUCLA_ID)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),Ninstance),source=0)
allocate(plastic_disloUCLA_output(maxval(phase_Noutput),Ninstance))
plastic_disloUCLA_output = ''
allocate(param(Ninstance))
allocate(state(Ninstance))
allocate(dotState(Ninstance))
allocate(dependentState(Ninstance))
do p = 1, size(phase_plasticity)
if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_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))
!--------------------------------------------------------------------------------------------------
! optional parameters that need to be defined
prm%mu = lattice_mu(p)
prm%aTol_rho = config%getFloat('atol_rho')
! sanity checks
if (prm%aTol_rho <= 0.0_pReal) extmsg = trim(extmsg)//' atol_rho'
!--------------------------------------------------------------------------------------------------
! slip related parameters
prm%N_sl = config%getInts('nslip',defaultVal=emptyIntArray)
prm%sum_N_sl = sum(prm%N_sl)
slipActive: if (prm%sum_N_sl > 0) then
prm%Schmid = lattice_SchmidMatrix_slip(prm%N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
if(trim(config%getString('lattice_structure')) == 'bcc') then
prm%nonSchmidCoeff = config%getFloats('nonschmid_coefficients',&
defaultVal = emptyRealArray)
prm%nonSchmid_pos = lattice_nonSchmidMatrix(prm%N_sl,prm%nonSchmidCoeff,+1)
prm%nonSchmid_neg = lattice_nonSchmidMatrix(prm%N_sl,prm%nonSchmidCoeff,-1)
else
allocate(prm%nonSchmidCoeff(0))
prm%nonSchmid_pos = prm%Schmid
prm%nonSchmid_neg = prm%Schmid
endif
prm%h_sl_sl = lattice_interaction_SlipBySlip(prm%N_sl, &
config%getFloats('interaction_slipslip'), &
config%getString('lattice_structure'))
prm%forestProjectionEdge = lattice_forestProjection_edge(prm%N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%forestProjectionEdge = transpose(prm%forestProjectionEdge)
prm%rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(prm%N_sl))
prm%rho_dip_0 = config%getFloats('rhoedgedip0', requiredSize=size(prm%N_sl))
prm%v0 = config%getFloats('v0', requiredSize=size(prm%N_sl))
prm%b_sl = config%getFloats('slipburgers', requiredSize=size(prm%N_sl))
prm%delta_F = config%getFloats('qedge', requiredSize=size(prm%N_sl))
prm%i_sl = config%getFloats('clambdaslip', requiredSize=size(prm%N_sl))
prm%tau_0 = config%getFloats('tau_peierls', requiredSize=size(prm%N_sl))
prm%p = config%getFloats('p_slip', requiredSize=size(prm%N_sl), &
defaultVal=[(1.0_pReal,i=1,size(prm%N_sl))])
prm%q = config%getFloats('q_slip', requiredSize=size(prm%N_sl), &
defaultVal=[(1.0_pReal,i=1,size(prm%N_sl))])
prm%kink_height = config%getFloats('kink_height', requiredSize=size(prm%N_sl))
prm%w = config%getFloats('kink_width', requiredSize=size(prm%N_sl))
prm%omega = config%getFloats('omega', requiredSize=size(prm%N_sl))
prm%B = config%getFloats('friction_coeff', requiredSize=size(prm%N_sl))
prm%D = config%getFloat('grainsize')
prm%D_0 = config%getFloat('d0')
prm%Q_cl = config%getFloat('qsd')
prm%atomicVolume = config%getFloat('catomicvolume') * prm%b_sl**3.0_pReal
prm%D_a = config%getFloat('cedgedipmindistance') * prm%b_sl
prm%dipoleformation = config%getFloat('dipoleformationfactor') > 0.0_pReal !should be on by default, ToDo: change to /key/-type key
! expand: family => system
prm%rho_mob_0 = math_expand(prm%rho_mob_0, prm%N_sl)
prm%rho_dip_0 = math_expand(prm%rho_dip_0, prm%N_sl)
prm%q = math_expand(prm%q, prm%N_sl)
prm%p = math_expand(prm%p, prm%N_sl)
prm%delta_F = math_expand(prm%delta_F, prm%N_sl)
prm%b_sl = math_expand(prm%b_sl, prm%N_sl)
prm%kink_height = math_expand(prm%kink_height, prm%N_sl)
prm%w = math_expand(prm%w, prm%N_sl)
prm%omega = math_expand(prm%omega, prm%N_sl)
prm%tau_0 = math_expand(prm%tau_0, prm%N_sl)
prm%v0 = math_expand(prm%v0, prm%N_sl)
prm%B = math_expand(prm%B, prm%N_sl)
prm%i_sl = math_expand(prm%i_sl, prm%N_sl)
prm%atomicVolume = math_expand(prm%atomicVolume, prm%N_sl)
prm%D_a = math_expand(prm%D_a, prm%N_sl)
! sanity checks
if ( prm%D_0 <= 0.0_pReal) extmsg = trim(extmsg)//' D_0'
if ( prm%Q_cl <= 0.0_pReal) extmsg = trim(extmsg)//' Q_cl'
if (any(prm%rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedge0'
if (any(prm%rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedgedip0'
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' slipb_sl'
if (any(prm%delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' qedge'
if (any(prm%tau_0 < 0.0_pReal)) extmsg = trim(extmsg)//' tau_0'
if (any(prm%D_a <= 0.0_pReal)) extmsg = trim(extmsg)//' cedgedipmindistance or slipb_sl'
if (any(prm%atomicVolume <= 0.0_pReal)) extmsg = trim(extmsg)//' catomicvolume or slipb_sl'
else slipActive
allocate(prm%rho_mob_0(0))
allocate(prm%rho_dip_0(0))
endif slipActive
!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') &
call IO_error(211,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOUCLA_label//')')
!--------------------------------------------------------------------------------------------------
! output pararameters
outputs = config%getStrings('(output)',defaultVal=emptyStringArray)
allocate(prm%outputID(0))
do i=1, size(outputs)
outputID = undefined_ID
select case(trim(outputs(i)))
case ('edge_density')
outputID = merge(rho_mob_ID,undefined_ID,prm%sum_N_sl>0)
case ('dipole_density')
outputID = merge(rho_dip_ID,undefined_ID,prm%sum_N_sl>0)
case ('shear_rate','shearrate','shear_rate_slip','shearrate_slip')
outputID = merge(dot_gamma_sl_ID,undefined_ID,prm%sum_N_sl>0)
case ('accumulated_shear','accumulatedshear','accumulated_shear_slip')
outputID = merge(gamma_sl_ID,undefined_ID,prm%sum_N_sl>0)
case ('mfp','mfp_slip')
outputID = merge(Lambda_sl_ID,undefined_ID,prm%sum_N_sl>0)
case ('threshold_stress','threshold_stress_slip')
outputID = merge(thresholdstress_ID,undefined_ID,prm%sum_N_sl>0)
end select
if (outputID /= undefined_ID) then
plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i)
plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = prm%sum_N_sl
prm%outputID = [prm%outputID, outputID]
endif
enddo
!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl
sizeState = sizeDotState
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0, &
prm%sum_N_sl,0,0)
plasticState(p)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p)))
!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1
endIndex = prm%sum_N_sl
stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:)
stt%rho_mob= spread(prm%rho_mob_0,2,NipcMyPhase)
dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:)
stt%rho_dip= spread(prm%rho_dip_0,2,NipcMyPhase)
dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%gamma_sl=>plasticState(p)%state(startIndex:endIndex,:)
dot%gamma_sl=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal ! Don't use for convergence check
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:)
allocate(dst%Lambda_sl(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
allocate(dst%threshold_stress(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
end associate
enddo
end subroutine plastic_disloUCLA_init
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
pure subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp, &
Mp,T,instance,of)
real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
real(pReal), dimension(3,3,3,3), intent(out) :: &
dLp_dMp !< derivative of Lp with respect to the Mandel stress
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
integer :: &
i,k,l,m,n
real(pReal), dimension(param(instance)%sum_N_sl) :: &
dot_gamma_pos,dot_gamma_neg, &
ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
associate(prm => param(instance))
call kinetics(Mp,T,instance,of,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
do i = 1, prm%sum_N_sl
Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%Schmid(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_pos(i) * prm%Schmid(k,l,i) * prm%nonSchmid_pos(m,n,i) &
+ ddot_gamma_dtau_neg(i) * prm%Schmid(k,l,i) * prm%nonSchmid_neg(m,n,i)
enddo
end associate
end subroutine plastic_disloUCLA_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_dotState(Mp,T,instance,of)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
real(pReal) :: &
VacancyDiffusion
real(pReal), dimension(param(instance)%sum_N_sl) :: &
gdot_pos, gdot_neg,&
tau_pos,&
tau_neg, &
v_cl, &
dot_rho_dip_formation, &
dot_rho_dip_climb, &
dip_distance
associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
call kinetics(Mp,T,instance,of,&
gdot_pos,gdot_neg, &
tau_pos_out = tau_pos,tau_neg_out = tau_neg)
dot%gamma_sl(:,of) = (gdot_pos+gdot_neg) ! ToDo: needs to be abs
VacancyDiffusion = prm%D_0*exp(-prm%Q_cl/(kB*T))
where(dEq0(tau_pos)) ! ToDo: use avg of pos and neg
dot_rho_dip_formation = 0.0_pReal
dot_rho_dip_climb = 0.0_pReal
else where
dip_distance = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), &
prm%D_a, & ! lower limit
dst%Lambda_sl(:,of)) ! upper limit
dot_rho_dip_formation = merge(2.0_pReal*dip_distance* stt%rho_mob(:,of)*abs(dot%gamma_sl(:,of))/prm%b_sl, & ! ToDo: ignore region of spontaneous annihilation
0.0_pReal, &
prm%dipoleformation)
v_cl = (3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume/(2.0_pReal*pi*kB*T)) &
* (1.0_pReal/(dip_distance+prm%D_a))
dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,of))/(dip_distance-prm%D_a) ! ToDo: Discuss with Franz: Stress dependency?
end where
dot%rho_mob(:,of) = abs(dot%gamma_sl(:,of))/(prm%b_sl*dst%Lambda_sl(:,of)) & ! multiplication
- dot_rho_dip_formation &
- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_mob(:,of)*abs(dot%gamma_sl(:,of)) ! Spontaneous annihilation of 2 single edge dislocations
dot%rho_dip(:,of) = dot_rho_dip_formation &
- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_dip(:,of)*abs(dot%gamma_sl(:,of)) & ! Spontaneous annihilation of a single edge dislocation with a dipole constituent
- dot_rho_dip_climb
end associate
end subroutine plastic_disloUCLA_dotState
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_dependentState(instance,of)
integer, intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%sum_N_sl) :: &
dislocationSpacing
associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
dislocationSpacing = sqrt(matmul(prm%forestProjectionEdge, &
stt%rho_mob(:,of)+stt%rho_dip(:,of)))
dst%threshold_stress(:,of) = prm%mu*prm%b_sl &
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
dst%Lambda_sl(:,of) = prm%D/(1.0_pReal+prm%D*dislocationSpacing/prm%i_sl)
end associate
end subroutine plastic_disloUCLA_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_disloUCLA_postResults(Mp,T,instance,of) result(postResults)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
real(pReal), dimension(sum(plastic_disloUCLA_sizePostResult(:,instance))) :: &
postResults
integer :: &
o,c
real(pReal), dimension(param(instance)%sum_N_sl) :: &
gdot_pos,gdot_neg
c = 0
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
outputsLoop: do o = 1,size(prm%outputID)
select case(prm%outputID(o))
case (rho_mob_ID)
postResults(c+1:c+prm%sum_N_sl) = stt%rho_mob(1:prm%sum_N_sl,of)
case (rho_dip_ID)
postResults(c+1:c+prm%sum_N_sl) = stt%rho_dip(1:prm%sum_N_sl,of)
case (dot_gamma_sl_ID)
call kinetics(Mp,T,instance,of,gdot_pos,gdot_neg)
postResults(c+1:c+prm%sum_N_sl) = gdot_pos + gdot_neg
case (gamma_sl_ID)
postResults(c+1:c+prm%sum_N_sl) = stt%gamma_sl(1:prm%sum_N_sl, of)
case (Lambda_sl_ID)
postResults(c+1:c+prm%sum_N_sl) = dst%Lambda_sl(1:prm%sum_N_sl, of)
case (thresholdstress_ID)
postResults(c+1:c+prm%sum_N_sl) = dst%threshold_stress(1:prm%sum_N_sl,of)
end select
c = c + prm%sum_N_sl
enddo outputsLoop
end associate
end function plastic_disloUCLA_postResults
!--------------------------------------------------------------------------------------------------
!> @brief writes results to HDF5 output file
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_results(instance,group)
#if defined(PETSc) || defined(DAMASK_HDF5)
integer, intent(in) :: instance
character(len=*), intent(in) :: group
integer :: o
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
outputsLoop: do o = 1,size(prm%outputID)
select case(prm%outputID(o))
case (rho_mob_ID)
call results_writeDataset(group,stt%rho_mob,'rho_mob',&
'mobile dislocation density','1/m²')
case (rho_dip_ID)
call results_writeDataset(group,stt%rho_dip,'rho_dip',&
'dislocation dipole density''1/m²')
case (dot_gamma_sl_ID)
call results_writeDataset(group,stt%gamma_sl,'dot_gamma_sl',&
'plastic shear','1')
case (Lambda_sl_ID)
call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
'mean free path for slip','m')
case (thresholdstress_ID)
call results_writeDataset(group,dst%threshold_stress,'tau_pass',&
'threshold stress for slip','Pa')
end select
enddo outputsLoop
end associate
#else
integer, intent(in) :: instance
character(len=*), intent(in) :: group
#endif
end subroutine plastic_disloUCLA_results
!--------------------------------------------------------------------------------------------------
!> @brief Shear rates on slip systems, their derivatives with respect to resolved stress and the
! resolved stresss
!> @details Derivatives and resolved stress are calculated only optionally.
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics(Mp,T,instance,of, &
dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
real(pReal), intent(out), dimension(param(instance)%sum_N_sl) :: &
dot_gamma_pos, &
dot_gamma_neg
real(pReal), intent(out), optional, dimension(param(instance)%sum_N_sl) :: &
ddot_gamma_dtau_pos, &
ddot_gamma_dtau_neg, &
tau_pos_out, &
tau_neg_out
real(pReal), dimension(param(instance)%sum_N_sl) :: &
StressRatio, &
StressRatio_p,StressRatio_pminus1, &
dvel, vel, &
tau_pos,tau_neg, &
t_n, t_k, dtk,dtn, &
needsGoodName ! ToDo: @Karo: any idea?
integer :: j
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
do j = 1, prm%sum_N_sl
tau_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j))
tau_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
enddo
if (present(tau_pos_out)) tau_pos_out = tau_pos
if (present(tau_neg_out)) tau_neg_out = tau_neg
associate(BoltzmannRatio => prm%delta_F/(kB*T), &
dot_gamma_0 => stt%rho_mob(:,of)*prm%b_sl*prm%v0, &
effectiveLength => dst%Lambda_sl(:,of) - prm%w)
significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
StressRatio = (abs(tau_pos)-dst%threshold_stress(:,of))/prm%tau_0
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
vel = prm%kink_height/(t_n + t_k)
dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
else where significantPositiveTau
dot_gamma_pos = 0.0_pReal
end where significantPositiveTau
if (present(ddot_gamma_dtau_pos)) then
significantPositiveTau2: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_0
dtk = -1.0_pReal * t_k / tau_pos
dvel = -1.0_pReal * prm%kink_height * (dtk + dtn) / (t_n + t_k)**2.0_pReal
ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
else where significantPositiveTau2
ddot_gamma_dtau_pos = 0.0_pReal
end where significantPositiveTau2
endif
significantNegativeTau: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check)
StressRatio = (abs(tau_neg)-dst%threshold_stress(:,of))/prm%tau_0
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
vel = prm%kink_height/(t_n + t_k)
dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
else where significantNegativeTau
dot_gamma_neg = 0.0_pReal
end where significantNegativeTau
if (present(ddot_gamma_dtau_neg)) then
significantNegativeTau2: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check)
dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_0
dtk = -1.0_pReal * t_k / tau_neg
dvel = -1.0_pReal * prm%kink_height * (dtk + dtn) / (t_n + t_k)**2.0_pReal
ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
else where significantNegativeTau2
ddot_gamma_dtau_neg = 0.0_pReal
end where significantNegativeTau2
end if
end associate
end associate
end subroutine kinetics
end module plastic_disloUCLA