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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, only: &
pReal, &
pInt
implicit none
private
integer(pInt), 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_ID, &
rhoDip_ID, &
shearrate_ID, &
accumulatedshear_ID, &
mfp_ID, &
thresholdstress_ID
end enum
type, private :: tParameters
real(pReal) :: &
aTolRho, &
grainSize, &
SolidSolutionStrength, & !< Strength due to elements in solid solution
mu, &
D0, & !< prefactor for self-diffusion coefficient
Qsd !< activation energy for dislocation climb
real(pReal), allocatable, dimension(:) :: &
rho0, & !< initial edge dislocation density
rhoDip0, & !< initial edge dipole density
burgers, & !< absolute length of burgers vector [m]
nonSchmidCoeff, &
minDipDistance, &
CLambda, & !< Adj. parameter for distance between 2 forest dislocations
atomicVolume, &
tau_Peierls, &
tau0, &
!* mobility law parameters
H0kp, & !< 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), allocatable, dimension(:,:) :: &
interaction_SlipSlip, & !< slip resistance from slip activity
forestProjectionEdge
real(pReal), allocatable, dimension(:,:,:) :: &
Schmid, &
nonSchmid_pos, &
nonSchmid_neg
integer(pInt) :: &
totalNslip !< total number of active slip system
integer(pInt), allocatable, dimension(:) :: &
Nslip !< number of active slip systems for each family
integer(kind(undefined_ID)), allocatable, dimension(:) :: &
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), pointer, dimension(:,:) :: &
rhoEdge, &
rhoEdgeDip, &
accshear
end type tDisloUCLAState
type, private :: tDisloUCLAdependentState
real(pReal), allocatable, dimension(:,:) :: &
mfp, &
dislocationSpacing, &
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
private :: &
kinetics
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_init()
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
use prec, only: &
pStringLen
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_expand
use IO, only: &
IO_error, &
IO_timeStamp
use material, only: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
material_allocatePlasticState, &
PLASTICITY_DISLOUCLA_label, &
PLASTICITY_DISLOUCLA_ID, &
material_phase, &
plasticState
use config, only: &
MATERIAL_partPhase, &
config_phase
use lattice
implicit none
integer(pInt) :: &
Ninstance, &
p, i, &
NipcMyPhase, &
sizeState, sizeDotState, &
startIndex, endIndex
integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
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, 2016, 242-256'
write(6,'(/,a)') ' http://dx.doi.org/10.1016/j.ijplas.2015.09.002'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
Ninstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt)
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_pInt, 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%aTolRho = config%getFloat('atol_rho')
! sanity checks
if (prm%aTolRho <= 0.0_pReal) extmsg = trim(extmsg)//' atol_rho'
!--------------------------------------------------------------------------------------------------
! slip related parameters
prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray)
prm%totalNslip = sum(prm%Nslip)
slipActive: if (prm%totalNslip > 0_pInt) then
prm%Schmid = lattice_SchmidMatrix_slip(prm%Nslip,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%Nslip,prm%nonSchmidCoeff,+1_pInt)
prm%nonSchmid_neg = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,-1_pInt)
else
prm%nonSchmid_pos = prm%Schmid
prm%nonSchmid_neg = prm%Schmid
endif
prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, &
config%getFloats('interaction_slipslip'), &
config%getString('lattice_structure'))
prm%forestProjectionEdge = lattice_forestProjection(prm%Nslip,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%rho0 = config%getFloats('rhoedge0', requiredSize=size(prm%Nslip))
prm%rhoDip0 = config%getFloats('rhoedgedip0', requiredSize=size(prm%Nslip))
prm%v0 = config%getFloats('v0', requiredSize=size(prm%Nslip))
prm%burgers = config%getFloats('slipburgers', requiredSize=size(prm%Nslip))
prm%H0kp = config%getFloats('qedge', requiredSize=size(prm%Nslip))
prm%clambda = config%getFloats('clambdaslip', requiredSize=size(prm%Nslip))
prm%tau_Peierls = config%getFloats('tau_peierls', requiredSize=size(prm%Nslip)) ! ToDo: Deprecated
prm%p = config%getFloats('p_slip', requiredSize=size(prm%Nslip), &
defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%q = config%getFloats('q_slip', requiredSize=size(prm%Nslip), &
defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%kink_height = config%getFloats('kink_height', requiredSize=size(prm%Nslip))
prm%w = config%getFloats('kink_width', requiredSize=size(prm%Nslip))
prm%omega = config%getFloats('omega', requiredSize=size(prm%Nslip))
prm%B = config%getFloats('friction_coeff', requiredSize=size(prm%Nslip))
prm%SolidSolutionStrength = config%getFloat('solidsolutionstrength') ! ToDo: Deprecated
prm%grainSize = config%getFloat('grainsize')
prm%D0 = config%getFloat('d0')
prm%Qsd = config%getFloat('qsd')
prm%atomicVolume = config%getFloat('catomicvolume') * prm%burgers**3.0_pReal
prm%minDipDistance = config%getFloat('cedgedipmindistance') * prm%burgers
prm%dipoleformation = config%getFloat('dipoleformationfactor') > 0.0_pReal !should be on by default, ToDo: change to /key/-type key
! expand: family => system
prm%rho0 = math_expand(prm%rho0, prm%Nslip)
prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip)
prm%q = math_expand(prm%q, prm%Nslip)
prm%p = math_expand(prm%p, prm%Nslip)
prm%H0kp = math_expand(prm%H0kp, prm%Nslip)
prm%burgers = math_expand(prm%burgers, prm%Nslip)
prm%kink_height = math_expand(prm%kink_height, prm%Nslip)
prm%w = math_expand(prm%w, prm%Nslip)
prm%omega = math_expand(prm%omega, prm%Nslip)
prm%tau_Peierls = math_expand(prm%tau_Peierls, prm%Nslip)
prm%v0 = math_expand(prm%v0, prm%Nslip)
prm%B = math_expand(prm%B, prm%Nslip)
prm%clambda = math_expand(prm%clambda, prm%Nslip)
prm%atomicVolume = math_expand(prm%atomicVolume, prm%Nslip)
prm%minDipDistance = math_expand(prm%minDipDistance, prm%Nslip)
prm%tau0 = prm%tau_peierls + prm%SolidSolutionStrength
! sanity checks
if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' d0'
if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' qsd'
if (any(prm%rho0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedge0'
if (any(prm%rhoDip0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedgedip0'
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
if (any(prm%burgers <= 0.0_pReal)) extmsg = trim(extmsg)//' slipburgers'
if (any(prm%H0kp <= 0.0_pReal)) extmsg = trim(extmsg)//' qedge'
if (any(prm%tau_peierls < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls'
if (any(prm%minDipDistance <= 0.0_pReal)) extmsg = trim(extmsg)//' cedgedipmindistance or slipburgers'
if (any(prm%atomicVolume <= 0.0_pReal)) extmsg = trim(extmsg)//' catomicvolume or slipburgers'
else slipActive
allocate(prm%rho0(0))
allocate(prm%rhoDip0(0))
endif slipActive
!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') &
call IO_error(211_pInt,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOUCLA_label//')')
!--------------------------------------------------------------------------------------------------
! output pararameters
outputs = config%getStrings('(output)',defaultVal=emptyStringArray)
allocate(prm%outputID(0))
do i=1_pInt, size(outputs)
outputID = undefined_ID
select case(trim(outputs(i)))
case ('edge_density')
outputID = merge(rho_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('dipole_density')
outputID = merge(rhoDip_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('shear_rate','shearrate','shear_rate_slip','shearrate_slip')
outputID = merge(shearrate_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('accumulated_shear','accumulatedshear','accumulated_shear_slip')
outputID = merge(accumulatedshear_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('mfp','mfp_slip')
outputID = merge(mfp_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('threshold_stress','threshold_stress_slip')
outputID = merge(thresholdstress_ID,undefined_ID,prm%totalNslip>0_pInt)
end select
if (outputID /= undefined_ID) then
plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i)
plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = prm%totalNslip
prm%outputID = [prm%outputID, outputID]
endif
enddo
!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phase == p)
sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * prm%totalNslip
sizeState = sizeDotState
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, &
prm%totalNslip,0_pInt,0_pInt)
plasticState(p)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p)))
!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1_pInt
endIndex = prm%totalNslip
stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
stt%rhoEdge= spread(prm%rho0,2,NipcMyPhase)
dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
stt%rhoEdgeDip= spread(prm%rhoDip0,2,NipcMyPhase)
dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
stt%accshear=>plasticState(p)%state(startIndex:endIndex,:)
dot%accshear=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal !ToDo: better make optional parameter
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:)
allocate(dst%mfp(prm%totalNslip,NipcMyPhase), source=0.0_pReal)
allocate(dst%dislocationSpacing(prm%totalNslip,NipcMyPhase),source=0.0_pReal)
allocate(dst%threshold_stress(prm%totalNslip,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,Temperature,instance,of)
implicit none
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) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
integer(pInt) :: &
i,k,l,m,n
real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_pos,gdot_neg, &
dgdot_dtau_pos,dgdot_dtau_neg
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
associate(prm => param(instance))
call kinetics(Mp,Temperature,instance,of,gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg)
do i = 1_pInt, prm%totalNslip
Lp = Lp + (gdot_pos(i)+gdot_neg(i))*prm%Schmid(1:3,1:3,i)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtau_pos(i) * prm%Schmid(k,l,i) * prm%nonSchmid_pos(m,n,i) &
+ dgdot_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,Temperature,instance,of)
use prec, only: &
tol_math_check, &
dEq0
use math, only: &
PI, &
math_clip
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal) :: &
VacancyDiffusion
real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_pos, gdot_neg,&
tau_pos,&
tau_neg, &
DotRhoDipFormation, ClimbVelocity, EdgeDipDistance, &
DotRhoEdgeDipClimb
associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
call kinetics(Mp,Temperature,instance,of,&
gdot_pos,gdot_neg, &
tau_pos1 = tau_pos,tau_neg1 = tau_neg)
dot%accshear(:,of) = (gdot_pos+gdot_neg) ! ToDo: needs to be abs
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
where(dEq0(tau_pos)) ! ToDo: use avg of pos and neg
DotRhoDipFormation = 0.0_pReal
DotRhoEdgeDipClimb = 0.0_pReal
else where
EdgeDipDistance = math_clip((3.0_pReal*prm%mu*prm%burgers)/(16.0_pReal*PI*abs(tau_pos)), &
prm%minDipDistance, & ! lower limit
dst%mfp(:,of)) ! upper limit
DotRhoDipFormation = merge(((2.0_pReal*EdgeDipDistance)/prm%burgers)* stt%rhoEdge(:,of)*abs(dot%accshear(:,of)), & ! ToDo: ignore region of spontaneous annihilation
0.0_pReal, &
prm%dipoleformation)
ClimbVelocity = (3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume/(2.0_pReal*pi*kB*Temperature)) &
* (1.0_pReal/(EdgeDipDistance+prm%minDipDistance))
DotRhoEdgeDipClimb = (4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(:,of))/(EdgeDipDistance-prm%minDipDistance) ! ToDo: Discuss with Franz: Stress dependency?
end where
dot%rhoEdge(:,of) = abs(dot%accshear(:,of))/(prm%burgers*dst%mfp(:,of)) & ! multiplication
- DotRhoDipFormation &
- (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdge(:,of)*abs(dot%accshear(:,of)) !* Spontaneous annihilation of 2 single edge dislocations
dot%rhoEdgeDip(:,of) = DotRhoDipFormation &
- (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdgeDip(:,of)*abs(dot%accshear(:,of)) & !* Spontaneous annihilation of a single edge dislocation with a dipole constituent
- DotRhoEdgeDipClimb
end associate
end subroutine plastic_disloUCLA_dotState
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_dependentState(instance,of)
implicit none
integer(pInt), intent(in) :: &
instance, &
of
integer(pInt) :: &
i
associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
forall (i = 1_pInt:prm%totalNslip)
dst%dislocationSpacing(i,of) = sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
prm%forestProjectionEdge(:,i)))
dst%threshold_stress(i,of) = prm%mu*prm%burgers(i) &
* sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
prm%interaction_SlipSlip(i,:)))
end forall
dst%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*dst%dislocationSpacing(:,of)/prm%Clambda)
dst%dislocationSpacing(:,of) = dst%mfp(:,of) ! ToDo: Hack to recover wrong behavior for the moment
end associate
end subroutine plastic_disloUCLA_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postResults)
use prec, only: &
dEq, dNeq0
use math, only: &
PI, &
math_mul33xx33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), dimension(sum(plastic_disloUCLA_sizePostResult(:,instance))) :: &
postResults
integer(pInt) :: &
o,c,i
real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_pos,gdot_neg
c = 0_pInt
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
outputsLoop: do o = 1_pInt,size(prm%outputID)
select case(prm%outputID(o))
case (rho_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of)
case (rhoDip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
case (shearrate_ID)
call kinetics(Mp,Temperature,instance,of,gdot_pos,gdot_neg)
postResults(c+1:c+prm%totalNslip) = gdot_pos + gdot_neg
case (accumulatedshear_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear(1_pInt:prm%totalNslip, of)
case (mfp_ID)
postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp(1_pInt:prm%totalNslip, of)
case (thresholdstress_ID)
postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress(1_pInt:prm%totalNslip,of)
end select
c = c + prm%totalNslip
enddo outputsLoop
end associate
end function plastic_disloUCLA_postResults
!--------------------------------------------------------------------------------------------------
!> @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,Temperature,instance,of, &
gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg,tau_pos1,tau_neg1)
use prec, only: &
tol_math_check, &
dEq, dNeq0
use math, only: &
PI, &
math_mul33xx33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), intent(out), dimension(param(instance)%totalNslip) :: &
gdot_pos, &
gdot_neg
real(pReal), intent(out), optional, dimension(param(instance)%totalNslip) :: &
dgdot_dtau_pos, &
dgdot_dtau_neg, &
tau_pos1, &
tau_neg1
real(pReal), dimension(param(instance)%totalNslip) :: &
StressRatio, &
StressRatio_p,StressRatio_pminus1, &
dvel, vel, &
tau_pos,tau_neg, &
needsGoodName ! ToDo: @Karo: any idea?
integer(pInt) :: j
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
do j = 1_pInt, prm%totalNslip
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_pos1)) tau_pos1 = tau_pos
if (present(tau_neg1)) tau_neg1 = tau_neg
associate(BoltzmannRatio => prm%H0kp/(kB*Temperature), &
DotGamma0 => stt%rhoEdge(:,of)*prm%burgers*prm%v0, &
effectiveLength => dst%mfp(:,of) - prm%w)
significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
StressRatio = (abs(tau_pos)-dst%threshold_stress(:,of))/prm%tau0
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
vel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega &
* effectiveLength * tau_pos * needsGoodName &
/ ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_pos &
+ prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName &
)
gdot_pos = DotGamma0 * sign(vel,tau_pos) * 0.5_pReal
else where significantPositiveTau
gdot_pos = 0.0_pReal
end where significantPositiveTau
if (present(dgdot_dtau_pos)) then
significantPositiveTau2: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
dvel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength &
* ( &
(needsGoodName + tau_pos * abs(needsGoodName)*BoltzmannRatio*prm%p &
* prm%q/prm%tau0 &
* StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) &
) &
* ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_pos &
+ prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName &
) &
- tau_pos * needsGoodName * (2.0_pReal*prm%burgers**2.0_pReal &
+ prm%omega * prm%B *effectiveLength **2.0_pReal&
* (abs(needsGoodName)*BoltzmannRatio*prm%p *prm%q/prm%tau0 &
*StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) )&
) &
) &
/(2.0_pReal*prm%burgers**2.0_pReal*tau_pos &
+ prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal
dgdot_dtau_pos = DotGamma0 * dvel* 0.5_pReal
else where significantPositiveTau2
dgdot_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%tau0
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
vel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega &
* effectiveLength * tau_neg * needsGoodName &
/ ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_neg &
+ prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName &
)
gdot_neg = DotGamma0 * sign(vel,tau_neg) * 0.5_pReal
else where significantNegativeTau
gdot_neg = 0.0_pReal
end where significantNegativeTau
if (present(dgdot_dtau_neg)) then
significantNegativeTau2: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check)
dvel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength &
* ( &
(needsGoodName + tau_neg * abs(needsGoodName)*BoltzmannRatio*prm%p &
* prm%q/prm%tau0 &
* StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) &
) &
* ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_neg &
+ prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName &
) &
- tau_neg * needsGoodName * (2.0_pReal*prm%burgers**2.0_pReal &
+ prm%omega * prm%B *effectiveLength **2.0_pReal&
* (abs(needsGoodName)*BoltzmannRatio*prm%p *prm%q/prm%tau0 &
*StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) )&
) &
) &
/(2.0_pReal*prm%burgers**2.0_pReal*tau_neg &
+ prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal
dgdot_dtau_neg = DotGamma0 * dvel * 0.5_pReal
else where significantNegativeTau2
dgdot_dtau_neg = 0.0_pReal
end where significantNegativeTau2
end if
end associate
end associate
end subroutine kinetics
end module plastic_disloUCLA
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