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
!--------------------------------------------------------------------------------------------------
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module plastic_disloUCLA
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:,:), allocatable, target, public :: &
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plastic_disloUCLA_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_disloUCLA_output !< name of each post result output
real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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enum, bind(c)
enumerator :: &
undefined_ID, &
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rho_ID, &
rhoDip_ID, &
shearrate_ID, &
accumulatedshear_ID, &
mfp_ID, &
thresholdstress_ID, &
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dipoledistance_ID
end enum
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type, private :: tParameters
real(pReal) :: &
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aTolRho, &
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grainSize, &
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SolidSolutionStrength, & !< Strength due to elements in solid solution
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mu, &
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D0, & !< prefactor for self-diffusion coefficient
Qsd !< activation energy for dislocation climb
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real(pReal), allocatable, dimension(:) :: &
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rho0, & !< initial edge dislocation density
rhoDip0, & !< initial edge dipole density
burgers, & !< absolute length of burgers vector [m]
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nonSchmidCoeff, &
minDipDistance, &
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CLambda, & !< Adj. parameter for distance between 2 forest dislocations
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atomicVolume, &
tau_Peierls, &
tau0, &
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!* mobility law parameters
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H0kp, & !< activation energy for glide [J]
v0, & !< dislocation velocity prefactor [m/s]
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p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
B, & !< friction coefficient
kink_height, & !< height of the kink pair
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w, & !< width of the kink pair
omega !< attempt frequency for kink pair nucleation
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real(pReal), allocatable, dimension(:,:) :: &
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interaction_SlipSlip, & !< slip resistance from slip activity
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forestProjectionEdge
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real(pReal), allocatable, dimension(:,:,:) :: &
Schmid_slip, &
Schmid_twin, &
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
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logical :: &
dipoleformation
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end type !< container type for internal constitutive parameters
type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance)
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type, private :: tDisloUCLAState
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real(pReal), pointer, dimension(:,:) :: &
rhoEdge, &
rhoEdgeDip, &
accshear_slip
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end type
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type, private :: tDisloUCLAdependentState
real(pReal), allocatable, dimension(:,:) :: &
mfp, &
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dislocationSpacing, &
threshold_stress
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end type tDisloUCLAdependentState
type(tDisloUCLAState ), allocatable, dimension(:), private :: &
dotState, &
state
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type(tDisloUCLAdependentState), allocatable, dimension(:), private :: &
dependentState
public :: &
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plastic_disloUCLA_init, &
plastic_disloUCLA_dependentState, &
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plastic_disloUCLA_LpAndItsTangent, &
plastic_disloUCLA_dotState, &
plastic_disloUCLA_postResults
private :: &
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kinetics
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_init()
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
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use prec, only: &
pStringLen
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_mul3x3, &
math_expand
use IO, only: &
IO_error, &
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IO_timeStamp
use material, only: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
material_allocatePlasticState, &
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PLASTICITY_DISLOUCLA_label, &
PLASTICITY_DISLOUCLA_ID, &
material_phase, &
plasticState
use config, only: &
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MATERIAL_partPhase, &
config_phase
use lattice
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implicit none
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integer(pInt) :: &
index_myFamily, index_otherFamily, &
f,j,k,o, &
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Ninstance, &
p, i, &
NipcMyPhase, outputSize, &
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sizeState, sizeDotState, &
startIndex, endIndex
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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)::]
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integer(kind(undefined_ID)) :: &
outputID
character(len=pStringLen) :: &
structure = '',&
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'
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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"
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Ninstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
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write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
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allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt)
allocate(plastic_disloUCLA_output(maxval(phase_Noutput),Ninstance))
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plastic_disloUCLA_output = ''
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allocate(param(Ninstance))
allocate(state(Ninstance))
allocate(dotState(Ninstance))
allocate(dependentState(Ninstance))
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do p = 1_pInt, size(phase_plasticityInstance)
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if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle
associate(prm => param(phase_plasticityInstance(p)), &
dot => dotState(phase_plasticityInstance(p)), &
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stt => state(phase_plasticityInstance(p)), &
dst => dependentState(phase_plasticityInstance(p)), &
config => config_phase(p))
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structure = config%getString('lattice_structure')
!--------------------------------------------------------------------------------------------------
! optional parameters that need to be defined
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prm%mu = lattice_mu(p)
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prm%aTolRho = config%getFloat('atol_rho')
! sanity checks
if (prm%aTolRho <= 0.0_pReal) extmsg = trim(extmsg)//' atol_rho'
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!--------------------------------------------------------------------------------------------------
! slip related parameters
prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray)
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prm%totalNslip = sum(prm%Nslip)
slipActive: if (prm%totalNslip > 0_pInt) then
prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,structure(1:3),&
config%getFloat('c/a',defaultVal=0.0_pReal))
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if(structure=='bcc') then
prm%nonSchmidCoeff = config%getFloats('nonschmid_coefficients',&
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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_slip
prm%nonSchmid_neg = prm%Schmid_slip
endif
prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, &
config%getFloats('interaction_slipslip'), &
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structure(1:3))
prm%rho0 = config%getFloats('rhoedge0', requiredShape=shape(prm%Nslip))
prm%rhoDip0 = config%getFloats('rhoedgedip0', requiredShape=shape(prm%Nslip))
prm%v0 = config%getFloats('v0', requiredShape=shape(prm%Nslip))
prm%burgers = config%getFloats('slipburgers', requiredShape=shape(prm%Nslip))
prm%H0kp = config%getFloats('qedge', requiredShape=shape(prm%Nslip))
prm%clambda = config%getFloats('clambdaslip', requiredShape=shape(prm%Nslip))
prm%tau_Peierls = config%getFloats('tau_peierls', requiredShape=shape(prm%Nslip)) ! ToDo: Deprecated
prm%p = config%getFloats('p_slip', requiredShape=shape(prm%Nslip), &
defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%q = config%getFloats('q_slip', requiredShape=shape(prm%Nslip), &
defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%kink_height = config%getFloats('kink_height', requiredShape=shape(prm%Nslip))
prm%w = config%getFloats('kink_width', requiredShape=shape(prm%Nslip))
prm%omega = config%getFloats('omega', requiredShape=shape(prm%Nslip))
prm%B = config%getFloats('friction_coeff', requiredShape=shape(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/-key
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! expand: family => system
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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)
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prm%w = math_expand(prm%w, prm%Nslip)
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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)
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prm%tau0 = prm%tau_peierls + prm%SolidSolutionStrength
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! sanity checks
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 ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' d0'
if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' qsd'
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!if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')')
else slipActive
allocate(prm%rho0(0))
allocate(prm%rhoDip0(0))
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endif slipActive
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!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') &
call IO_error(211_pInt,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOUCLA_label//')')
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!--------------------------------------------------------------------------------------------------
! output pararameters
outputs = config%getStrings('(output)',defaultVal=emptyStringArray)
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allocate(prm%outputID(0))
do i=1_pInt, size(outputs)
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outputID = undefined_ID
outputSize = prm%totalNslip
select case(trim(outputs(i)))
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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)
case ('edge_dipole_distance')
outputID = merge(dipoleDistance_ID,undefined_ID,prm%totalNslip>0_pInt)
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end select
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if (outputID /= undefined_ID) then
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plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i)
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plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
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prm%outputID = [prm%outputID, outputID]
endif
end do
!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phase==p)
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sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * prm%totalNslip
sizeState = sizeDotState
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call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, &
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prm%totalNslip,0_pInt,0_pInt)
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plasticState(p)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p)))
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allocate(prm%forestProjectionEdge(prm%totalNslip,prm%totalNslip),source = 0.0_pReal)
i = 0_pInt
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)
i = i + 1_pInt
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)
prm%forestProjectionEdge(index_myFamily+j,index_otherFamily+k) = &
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)))
enddo; enddo
enddo slipSystemsLoop
enddo mySlipFamilies
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!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1_pInt
endIndex = prm%totalNslip
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stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
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stt%rhoEdge= spread(prm%rho0,2,NipcMyPhase)
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dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
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startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
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stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
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stt%rhoEdgeDip= spread(prm%rhoDip0,2,NipcMyPhase)
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dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
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startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
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stt%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
dot%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1e6_pReal
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:)
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allocate(dst%mfp(prm%totalNslip,NipcMyPhase), source=0.0_pReal)
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allocate(dst%dislocationSpacing(prm%totalNslip,NipcMyPhase),source=0.0_pReal)
allocate(dst%threshold_stress(prm%totalNslip,NipcMyPhase), source=0.0_pReal)
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plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
end associate
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enddo
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end subroutine plastic_disloUCLA_init
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_dependentState(instance,of)
implicit none
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integer(pInt), intent(in) :: instance, of
integer(pInt) :: &
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i
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associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
forall (i = 1_pInt:prm%totalNslip)
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dst%dislocationSpacing(i,of) = sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
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prm%forestProjectionEdge(:,i)))
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dst%threshold_stress(i,of) = prm%mu*prm%burgers(i) &
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* sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
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prm%interaction_SlipSlip(i,:)))
end forall
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dst%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*dst%dislocationSpacing(:,of)/prm%Clambda)
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dst%dislocationSpacing(:,of) = dst%mfp(:,of) ! ToDo: Hack to recover wrong behavior for the moment
end associate
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end subroutine plastic_disloUCLA_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
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pure subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of)
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implicit none
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real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
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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) :: &
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Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
integer(pInt) :: &
i,k,l,m,n
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real(pReal), dimension(param(instance)%totalNslip) :: &
dgdot_dtauslip_pos,dgdot_dtauslip_neg, &
gdot_slip_pos,gdot_slip_neg
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
associate(prm => param(instance))
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call kinetics(Mp,Temperature,instance,of,gdot_slip_pos,gdot_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg)
slipSystems: do i = 1_pInt, prm%totalNslip
Lp = Lp + (gdot_slip_pos(i)+gdot_slip_neg(i))*prm%Schmid_slip(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_dtauslip_pos(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_pos(m,n,i) &
+ dgdot_dtauslip_neg(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_neg(m,n,i)
enddo slipSystems
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end associate
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end subroutine plastic_disloUCLA_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of)
use prec, only: &
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tol_math_check, &
dEq0
use math, only: &
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PI, &
math_clip
implicit none
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real(pReal), dimension(3,3), intent(in):: &
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Mp !< Mandel stress
real(pReal), intent(in) :: &
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temperature !< temperature
integer(pInt), intent(in) :: &
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instance, of
real(pReal) :: &
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VacancyDiffusion
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real(pReal), dimension(param(instance)%totalNslip) :: &
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gdot_slip_pos, gdot_slip_neg,&
tau_slip_pos,&
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tau_slip_neg, &
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DotRhoDipFormation, ClimbVelocity, EdgeDipDistance, &
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DotRhoEdgeDipClimb
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associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
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call kinetics(Mp,Temperature,instance,of,&
gdot_slip_pos,gdot_slip_neg, &
tau_slip_pos1 = tau_slip_pos,tau_slip_neg1 = tau_slip_neg)
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dot%accshear_slip(:,of) = (gdot_slip_pos+gdot_slip_neg) ! ToDo: needs to be abs
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VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
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where(dEq0(tau_slip_pos)) ! ToDo: use avg of pos and neg
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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_slip_pos)), &
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prm%minDipDistance, & ! lower limit
dst%mfp(:,of)) ! upper limit
DotRhoDipFormation = merge(((2.0_pReal*EdgeDipDistance)/prm%burgers)* stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)), & ! ToDo: ignore region of spontaneous annihilation
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0.0_pReal, &
prm%dipoleformation)
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ClimbVelocity = (3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume/(2.0_pReal*pi*kB*Temperature)) &
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* (1.0_pReal/(EdgeDipDistance+prm%minDipDistance))
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DotRhoEdgeDipClimb = (4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(:,of))/(EdgeDipDistance-prm%minDipDistance) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot%rhoEdge(:,of) = abs(dot%accshear_slip(:,of))/(prm%burgers*dst%mfp(:,of)) & ! multiplication
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- DotRhoDipFormation &
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- (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)) !* Spontaneous annihilation of 2 single edge dislocations
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dot%rhoEdgeDip(:,of) = DotRhoDipFormation &
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- (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdgeDip(:,of)*abs(dot%accshear_slip(:,of)) & !* Spontaneous annihilation of a single edge dislocation with a dipole constituent
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- DotRhoEdgeDipClimb
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end associate
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end subroutine plastic_disloUCLA_dotState
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!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
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function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postResults)
use prec, only: &
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dEq, dNeq0
use math, only: &
PI, &
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math_mul33xx33
implicit none
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
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temperature !< temperature
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integer(pInt), intent(in) :: &
instance, &
of
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real(pReal), dimension(sum(plastic_disloUCLA_sizePostResult(:,instance))) :: &
postResults
integer(pInt) :: &
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o,c,i
real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_slip_pos,gdot_slip_neg
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c = 0_pInt
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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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)
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case (shearrate_ID)
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call kinetics(Mp,Temperature,instance,of,gdot_slip_pos,gdot_slip_neg)
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postResults(c+1:c+prm%totalNslip) = gdot_slip_pos + gdot_slip_neg
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case (accumulatedshear_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip, of)
case (mfp_ID)
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postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp(1_pInt:prm%totalNslip, of)
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case (thresholdstress_ID)
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postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress(1_pInt:prm%totalNslip,of)
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case (dipoleDistance_ID) ! ToDo: Discuss required changes with Franz
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do i = 1_pInt, prm%totalNslip
if (dNeq0(abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))) then
postResults(c+i) = (3.0_pReal*prm%mu*prm%burgers(i)) &
/ (16.0_pReal*pi*abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))
else
postResults(c+i) = huge(1.0_pReal)
endif
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postResults(c+i)=min(postResults(c+i),dst%mfp(i,of))
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enddo
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end select
c = c + prm%totalNslip
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enddo outputsLoop
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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
!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics(Mp,Temperature,instance,of, &
gdot_slip_pos,gdot_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg,tau_slip_pos1,tau_slip_neg1)
use prec, only: &
tol_math_check, &
dEq, dNeq0
use math, only: &
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PI, &
math_mul33xx33
implicit none
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
real(pReal), intent(in) :: &
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temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), intent(out), dimension(param(instance)%totalNslip) :: &
gdot_slip_pos, &
gdot_slip_neg
real(pReal), intent(out), optional, dimension(param(instance)%totalNslip) :: &
dgdot_dtauslip_pos, &
dgdot_dtauslip_neg, &
tau_slip_pos1, &
tau_slip_neg1
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real(pReal), dimension(param(instance)%totalNslip) :: &
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StressRatio, &
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StressRatio_p,StressRatio_pminus1, &
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dvel_slip, vel_slip, &
tau_slip_pos,tau_slip_neg, &
needsGoodName ! ToDo: @Karo: any idea?
integer(pInt) :: j
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do j = 1_pInt, prm%totalNslip
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tau_slip_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j))
tau_slip_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
enddo
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if (present(tau_slip_pos1)) tau_slip_pos1 = tau_slip_pos
if (present(tau_slip_neg1)) tau_slip_neg1 = tau_slip_neg
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associate(BoltzmannRatio => prm%H0kp/(kB*Temperature), &
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DotGamma0 => stt%rhoEdge(:,of)*prm%burgers*prm%v0, &
effectiveLength => dst%mfp(:,of) - prm%w)
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significantPositiveTau: where(abs(tau_slip_pos)-dst%threshold_stress(:,of) > tol_math_check)
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StressRatio = (abs(tau_slip_pos)-dst%threshold_stress(:,of))/prm%tau0
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StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
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vel_slip = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega &
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* effectiveLength * tau_slip_pos * needsGoodName &
/ ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_slip_pos &
+ prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName &
)
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gdot_slip_pos = DotGamma0 * sign(vel_slip,tau_slip_pos) * 0.5_pReal
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else where significantPositiveTau
gdot_slip_pos = 0.0_pReal
end where significantPositiveTau
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if (present(dgdot_dtauslip_pos)) then
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significantPositiveTau2: where(abs(tau_slip_pos)-dst%threshold_stress(:,of) > tol_math_check)
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dvel_slip = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength &
* ( &
(needsGoodName + tau_slip_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_slip_pos &
+ prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName &
) &
- tau_slip_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_slip_pos &
+ prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal
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dgdot_dtauslip_pos = DotGamma0 * dvel_slip* 0.5_pReal
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else where significantPositiveTau2
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dgdot_dtauslip_pos = 0.0_pReal
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end where significantPositiveTau2
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endif
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significantNegativeTau: where(abs(tau_slip_neg)-dst%threshold_stress(:,of) > tol_math_check)
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StressRatio = (abs(tau_slip_neg)-dst%threshold_stress(:,of))/prm%tau0
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StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
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vel_slip = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega &
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* effectiveLength * tau_slip_neg * needsGoodName &
/ ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_slip_neg &
+ prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName &
)
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gdot_slip_neg = DotGamma0 * sign(vel_slip,tau_slip_neg) * 0.5_pReal
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else where significantNegativeTau
gdot_slip_neg = 0.0_pReal
end where significantNegativeTau
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if (present(dgdot_dtauslip_neg)) then
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significantNegativeTau2: where(abs(tau_slip_neg)-dst%threshold_stress(:,of) > tol_math_check)
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dvel_slip = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength &
* ( &
(needsGoodName + tau_slip_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_slip_neg &
+ prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName &
) &
- tau_slip_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_slip_neg &
+ prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal
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dgdot_dtauslip_neg = DotGamma0 * dvel_slip * 0.5_pReal
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else where significantNegativeTau2
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dgdot_dtauslip_neg = 0.0_pReal
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end where significantNegativeTau2
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end if
end associate
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end associate
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end subroutine kinetics
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end module plastic_disloUCLA