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polishing

This commit is contained in:
Martin Diehl 2018-12-04 22:30:07 +01:00
parent a34e27cfcd
commit 9caa91ee14
2 changed files with 190 additions and 208 deletions
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2
src/constitutive.f90
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@ -425,7 +425,7 @@ subroutine constitutive_microstructure(orientations, Fe, Fp, ipc, ip, el)
case (PLASTICITY_DISLOUCLA_ID) plasticityType case (PLASTICITY_DISLOUCLA_ID) plasticityType
of = phasememberAt(ipc,ip,el) of = phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phase(ipc,ip,el)) instance = phase_plasticityInstance(material_phase(ipc,ip,el))
call plastic_disloUCLA_dependentState(temperature(ho)%p(tme),instance,of) call plastic_disloUCLA_dependentState(instance,of)
case (PLASTICITY_NONLOCAL_ID) plasticityType case (PLASTICITY_NONLOCAL_ID) plasticityType
call plastic_nonlocal_microstructure (Fe,Fp,ip,el) call plastic_nonlocal_microstructure (Fe,Fp,ip,el)
end select plasticityType end select plasticityType

396
src/plastic_disloUCLA.f90
View File

@ -29,7 +29,7 @@ module plastic_disloUCLA
real(pReal), dimension(:,:,:), allocatable, private :: & real(pReal), dimension(:,:,:), allocatable, private :: &
plastic_disloUCLA_forestProjectionEdge !< matrix of forest projections of edge dislocations for each instance plastic_disloUCLA_forestProjectionEdge !< matrix of forest projections of edge dislocations for each instance
enum, bind(c) enum, bind(c)
enumerator :: undefined_ID, & enumerator :: undefined_ID, &
rho_ID, & rho_ID, &
rhoDip_ID, & rhoDip_ID, &
@ -59,13 +59,13 @@ module plastic_disloUCLA
v0, & !< dislocation velocity prefactor [m/s] for each family and instance v0, & !< dislocation velocity prefactor [m/s] for each family and instance
CLambda, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance CLambda, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
p, & !< p-exponent in glide velocity p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity q, & !< q-exponent in glide velocity
!* mobility law parameters !* mobility law parameters
kink_height, & !< height of the kink pair kink_height, & !< height of the kink pair
kink_width, & !< width of the kink pair kink_width, & !< width of the kink pair
omega, & !< attempt frequency for kink pair nucleation omega, & !< attempt frequency for kink pair nucleation
viscosity, & !< friction coeff. B (kMC) viscosity, & !< friction coeff. B (kMC)
!* !*
tau_Peierls, & tau_Peierls, &
nonSchmidCoeff, & nonSchmidCoeff, &
atomicVolume, & atomicVolume, &
@ -88,28 +88,28 @@ module plastic_disloUCLA
end type !< container type for internal constitutive parameters end type !< container type for internal constitutive parameters
type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance) type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance)
type, private :: tDisloUCLAState type, private :: tDisloUCLAState
real(pReal), pointer, dimension(:,:) :: & real(pReal), pointer, dimension(:,:) :: &
rhoEdge, & rhoEdge, &
rhoEdgeDip, & rhoEdgeDip, &
accshear_slip, & accshear_slip, &
whole whole
end type end type
type, private :: tDisloUCLAMicrostructure type, private :: tDisloUCLAdependentState
real(pReal), allocatable, dimension(:,:) :: & real(pReal), allocatable, dimension(:,:) :: &
mfp, & mfp, &
threshold_stress threshold_stress
end type tDisloUCLAMicrostructure end type tDisloUCLAdependentState
type(tDisloUCLAState ), allocatable, dimension(:), private :: & type(tDisloUCLAState ), allocatable, dimension(:), private :: &
state, & state, &
dotState dotState
type(tDisloUCLAMicrostructure), allocatable, dimension(:), private :: & type(tDisloUCLAdependentState), allocatable, dimension(:), private :: &
microstructure dependentState
public :: & public :: &
plastic_disloUCLA_init, & plastic_disloUCLA_init, &
plastic_disloUCLA_dependentState, & plastic_disloUCLA_dependentState, &
@ -156,15 +156,15 @@ subroutine plastic_disloUCLA_init()
MATERIAL_partPhase, & MATERIAL_partPhase, &
config_phase config_phase
use lattice use lattice
implicit none implicit none
integer(pInt) :: maxNinstance,& integer(pInt) :: maxNinstance,&
f,instance,j,k,o, i, & f,j,k,o, i, &
outputSize, phase, & outputSize, &
offset_slip, index_myFamily, index_otherFamily, & offset_slip, index_myFamily, index_otherFamily, &
startIndex, endIndex, p startIndex, endIndex, p, &
integer(pInt) :: sizeState, sizeDotState sizeState, sizeDotState, &
integer(pInt) :: NofMyPhase NofMyPhase
character(len=65536) :: & character(len=65536) :: &
structure = '' structure = ''
character(len=65536), dimension(:), allocatable :: outputs character(len=65536), dimension(:), allocatable :: outputs
@ -172,16 +172,16 @@ subroutine plastic_disloUCLA_init()
integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::] integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::] real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::] character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOUCLA_label//' init -+>>>' write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOUCLA_label//' init -+>>>'
write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78, 2016, 242-256' 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,'(/,a)') ' http://dx.doi.org/10.1016/j.ijplas.2015.09.002'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp() write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90" #include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt) maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt)
if (maxNinstance == 0_pInt) return if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) & if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
@ -192,19 +192,19 @@ subroutine plastic_disloUCLA_init()
allocate(plastic_disloUCLA_totalNslip(maxNinstance), source=0_pInt) allocate(plastic_disloUCLA_totalNslip(maxNinstance), source=0_pInt)
allocate(param(maxNinstance)) allocate(param(maxNinstance))
allocate(state(maxNinstance)) allocate(state(maxNinstance))
allocate(dotState(maxNinstance)) allocate(dotState(maxNinstance))
allocate(microstructure(maxNinstance)) allocate(dependentState(maxNinstance))
do p = 1_pInt, size(phase_plasticityInstance) do p = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle
associate(prm => param(phase_plasticityInstance(p)), & associate(prm => param(phase_plasticityInstance(p)), &
dot => dotState(phase_plasticityInstance(p)), & dot => dotState(phase_plasticityInstance(p)), &
stt => state(phase_plasticityInstance(p)), & stt => state(phase_plasticityInstance(p)), &
mse => microstructure(phase_plasticityInstance(p))) dst => dependentState(phase_plasticityInstance(p)))
structure = config_phase(p)%getString('lattice_structure') structure = config_phase(p)%getString('lattice_structure')
prm%mu = lattice_mu(p) prm%mu = lattice_mu(p)
@ -273,9 +273,8 @@ do p = 1_pInt, size(phase_plasticityInstance)
prm%clambda = math_expand(prm%clambda, prm%Nslip) prm%clambda = math_expand(prm%clambda, prm%Nslip)
prm%atomicVolume = math_expand(prm%atomicVolume, prm%Nslip) prm%atomicVolume = math_expand(prm%atomicVolume, prm%Nslip)
prm%minDipDistance = math_expand(prm%minDipDistance, prm%Nslip) prm%minDipDistance = math_expand(prm%minDipDistance, prm%Nslip)
instance = phase_plasticityInstance(p) plastic_disloUCLA_totalNslip(phase_plasticityInstance(p)) = prm%totalNslip
plastic_disloUCLA_totalNslip(instance) = prm%totalNslip
!if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) & !if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')')
! if (prm%D0 <= 0.0_pReal) & ! if (prm%D0 <= 0.0_pReal) &
@ -283,61 +282,10 @@ do p = 1_pInt, size(phase_plasticityInstance)
! if (plastic_disloUCLA_Qsd(instance) <= 0.0_pReal) & ! if (plastic_disloUCLA_Qsd(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOUCLA_label//')')
! if (plastic_disloUCLA_aTolRho(instance) <= 0.0_pReal) & ! if (plastic_disloUCLA_aTolRho(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOUCLA_label//')')
!if (plastic_disloUCLA_rhoEdge0(f,instance) < 0.0_pReal) &
else slipActive
allocate(prm%rho0(0))
allocate(prm%rhoDip0(0))
endif slipActive
#if defined(__GFORTRAN__)
outputs = ['GfortranBug86277']
outputs = config_phase(p)%getStrings('(output)',defaultVal=outputs)
if (outputs(1) == 'GfortranBug86277') outputs = emptyStringArray
#else
outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray)
#endif
allocate(prm%outputID(0))
do i = 1_pInt, size(outputs)
outputID = undefined_ID
outputSize = prm%totalNslip
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 ('resolved_stress','resolved_stress_slip')
outputID = merge(resolvedstress_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)
case ('stress_exponent')
outputID = merge(stressexponent_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)) = outputSize
prm%outputID = [prm%outputID, outputID]
endif
enddo
!if (plastic_disloUCLA_rhoEdge0(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOUCLA_label//')')
!if (plastic_disloUCLA_rhoEdgeDip0(f,instance) < 0.0_pReal) & !if (plastic_disloUCLA_rhoEdgeDip0(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOUCLA_label//')')
!if (plastic_disloUCLA_burgersPerSlipFamily(f,instance) <= 0.0_pReal) & !if (plastic_disloUCLA_burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOUCLA_label//')')
@ -346,55 +294,101 @@ do p = 1_pInt, size(phase_plasticityInstance)
!if (plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) & !if (plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOUCLA_label//')') ! call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOUCLA_label//')')
phase = p
NofMyPhase=count(material_phase==phase) else slipActive
instance = phase_plasticityInstance(phase) allocate(prm%rho0(0))
allocate(prm%rhoDip0(0))
endif slipActive
#if defined(__GFORTRAN__)
outputs = ['GfortranBug86277']
outputs = config_phase(p)%getStrings('(output)',defaultVal=outputs)
if (outputs(1) == 'GfortranBug86277') outputs = emptyStringArray
#else
outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray)
#endif
allocate(prm%outputID(0))
do i = 1_pInt, size(outputs)
outputID = undefined_ID
outputSize = prm%totalNslip
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 ('resolved_stress','resolved_stress_slip')
outputID = merge(resolvedstress_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)
case ('stress_exponent')
outputID = merge(stressexponent_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)) = outputSize
prm%outputID = [prm%outputID, outputID]
endif
enddo
NofMyPhase=count(material_phase==p)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! allocate state arrays ! allocate state arrays
sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * prm%totalNslip sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * prm%totalNslip
sizeState = sizeDotState sizeState = sizeDotState
call material_allocatePlasticState(phase,NofMyPhase,sizeState,sizeDotState,0_pInt, & call material_allocatePlasticState(p,NofMyPhase,sizeState,sizeDotState,0_pInt, &
prm%totalNslip,0_pInt,0_pInt) prm%totalNslip,0_pInt,0_pInt)
plasticState(phase)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p))) plasticState(p)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p)))
offset_slip = 2_pInt*plasticState(phase)%nSlip offset_slip = 2_pInt*plasticState(p)%nSlip
plasticState(phase)%slipRate => & plasticState(p)%slipRate => &
plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase) plasticState(p)%dotState(offset_slip+1:offset_slip+plasticState(p)%nSlip,1:NofMyPhase)
plasticState(phase)%accumulatedSlip => & plasticState(p)%accumulatedSlip => &
plasticState(phase)%state (offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase) plasticState(p)%state (offset_slip+1:offset_slip+plasticState(p)%nSlip,1:NofMyPhase)
startIndex=1_pInt
endIndex=prm%totalNslip
stt%rhoEdge=>plasticState(phase)%state(startIndex:endIndex,:)
stt%rhoEdge= spread(prm%rho0,2,NofMyPhase)
dotState(instance)%rhoEdge=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex=endIndex+1_pInt startIndex=1_pInt
endIndex=endIndex+prm%totalNslip endIndex=prm%totalNslip
stt%rhoEdgeDip=>plasticState(phase)%state(startIndex:endIndex,:) stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
stt%rhoEdgeDip= spread(prm%rhoDip0,2,NofMyPhase) stt%rhoEdge= spread(prm%rho0,2,NofMyPhase)
dotState(instance)%rhoEdgeDip=>plasticState(phase)%dotState(startIndex:endIndex,:) dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex=endIndex+1_pInt startIndex=endIndex+1_pInt
endIndex=endIndex+prm%totalNslip endIndex=endIndex+prm%totalNslip
stt%accshear_slip=>plasticState(phase)%state(startIndex:endIndex,:) stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:) stt%rhoEdgeDip= spread(prm%rhoDip0,2,NofMyPhase)
plasticState(p)%aTolState(startIndex:endIndex) = 1e6_pReal dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
dotState(instance)%whole => plasticState(phase)%dotState startIndex=endIndex+1_pInt
endIndex=endIndex+prm%totalNslip
stt%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
dot%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1e6_pReal
dot%whole => plasticState(p)%dotState
allocate(mse%mfp(prm%totalNslip,NofMyPhase),source=0.0_pReal) allocate(dst%mfp(prm%totalNslip,NofMyPhase),source=0.0_pReal)
allocate(mse%threshold_stress(prm%totalNslip,NofMyPhase),source=0.0_pReal) allocate(dst%threshold_stress(prm%totalNslip,NofMyPhase),source=0.0_pReal)
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
end associate end associate
enddo enddo
@ -404,63 +398,60 @@ do p = 1_pInt, size(phase_plasticityInstance)
maxval(plastic_disloUCLA_totalNslip),maxNinstance), & maxval(plastic_disloUCLA_totalNslip),maxNinstance), &
source=0.0_pReal) source=0.0_pReal)
do p = 1_pInt, size(phase_plasticityInstance) do p = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle
associate(prm => param(phase_plasticityInstance(p)), & associate(prm => param(phase_plasticityInstance(p)), &
dot => dotState(phase_plasticityInstance(p)), & dot => dotState(phase_plasticityInstance(p)), &
stt => state(phase_plasticityInstance(p)), & stt => state(phase_plasticityInstance(p)), &
mse => microstructure(phase_plasticityInstance(p))) dst => dependentState(phase_plasticityInstance(p)))
mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1) mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1)
index_myFamily = sum(prm%Nslip(1:f-1_pInt)) ! index in truncated slip system list index_myFamily = sum(prm%Nslip(1:f-1_pInt)) ! index in truncated slip system list
mySlipSystems: do j = 1_pInt,prm%Nslip(f) mySlipSystems: do j = 1_pInt,prm%Nslip(f)
!* Calculation of forest projections for edge dislocations !* Calculation of forest projections for edge dislocations
otherSlipFamilies: do o = 1_pInt,size(prm%Nslip,1) otherSlipFamilies: do o = 1_pInt,size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt)) index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
otherSlipSystems: do k = 1_pInt,prm%Nslip(o) otherSlipSystems: do k = 1_pInt,prm%Nslip(o)
plastic_disloUCLA_forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = & plastic_disloUCLA_forestProjectionEdge(index_myFamily+j,index_otherFamily+k,phase_plasticityInstance(p)) = &
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,p))+j,p), & 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))) lattice_st(:,sum(lattice_NslipSystem(1:o-1,p))+k,p)))
enddo otherSlipSystems; enddo otherSlipFamilies enddo otherSlipSystems; enddo otherSlipFamilies
enddo mySlipSystems enddo mySlipSystems
enddo mySlipFamilies enddo mySlipFamilies
end associate end associate
enddo enddo
end subroutine plastic_disloUCLA_init end subroutine plastic_disloUCLA_init
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state !> @brief calculates derived quantities from state
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_dependentState(temperature,instance,of) subroutine plastic_disloUCLA_dependentState(instance,of)
implicit none implicit none
integer(pInt), intent(in) :: instance, of integer(pInt), intent(in) :: instance, of
real(pReal), intent(in) :: &
temperature !< temperature at IP
integer(pInt) :: & integer(pInt) :: &
s i
real(pReal), dimension(param(instance)%totalNslip) :: & real(pReal), dimension(param(instance)%totalNslip) :: &
invLambdaSlip ! 1/mean free distance between 2 forest dislocations seen by a moving dislocation invLambdaSlip ! 1/mean free distance between 2 forest dislocations seen by a moving dislocation
associate(prm => param(instance), stt => state(instance),mse => microstructure(instance)) associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
forall (s = 1_pInt:prm%totalNslip) &
invLambdaSlip(s) = sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
plastic_disloUCLA_forestProjectionEdge(:,s,instance))) &
/ prm%Clambda(s)
mse%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*invLambdaSlip)
forall (s = 1_pInt:prm%totalNslip) & forall (i = 1_pInt:prm%totalNslip)
mse%threshold_stress(s,of) = prm%mu*prm%burgers(s) & invLambdaSlip(i) = sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
plastic_disloUCLA_forestProjectionEdge(:,i,instance))) &
/ prm%Clambda(i)
dst%threshold_stress(i,of) = prm%mu*prm%burgers(i) &
* sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), & * sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), &
prm%interaction_SlipSlip(s,:))) prm%interaction_SlipSlip(i,:)))
end forall
dst%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*invLambdaSlip)
end associate end associate
@ -471,7 +462,7 @@ end subroutine plastic_disloUCLA_dependentState
!> @brief calculates plastic velocity gradient and its tangent !> @brief calculates plastic velocity gradient and its tangent
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of) subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of)
implicit none implicit none
integer(pInt), intent(in) :: instance, of integer(pInt), intent(in) :: instance, of
real(pReal), intent(in) :: Temperature real(pReal), intent(in) :: Temperature
@ -483,13 +474,13 @@ subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,
real(pReal), dimension(param(instance)%totalNslip) :: & real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_slip_pos,gdot_slip_neg,tau_slip_pos,tau_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg gdot_slip_pos,gdot_slip_neg,tau_slip_pos,tau_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg
associate(prm => param(instance)) associate(prm => param(instance))
Lp = 0.0_pReal Lp = 0.0_pReal
dLp_dMp = 0.0_pReal dLp_dMp = 0.0_pReal
call kinetics(Mp,Temperature,instance,of, & call kinetics(Mp,Temperature,instance,of, &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg) gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
slipSystems: do i = 1_pInt, prm%totalNslip 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) Lp = Lp + (gdot_slip_pos(i)+gdot_slip_neg(i))*prm%Schmid_slip(1:3,1:3,i)
@ -534,24 +525,24 @@ subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of)
dgdot_dtauslip_neg,dgdot_dtauslip_pos,DotRhoDipFormation, ClimbVelocity, EdgeDipDistance, & dgdot_dtauslip_neg,dgdot_dtauslip_pos,DotRhoDipFormation, ClimbVelocity, EdgeDipDistance, &
DotRhoEdgeDipClimb DotRhoEdgeDipClimb
associate(prm => param(instance), stt => state(instance),dot => dotState(instance), mse => microstructure(instance)) associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
call kinetics(Mp,Temperature,instance,of, & call kinetics(Mp,Temperature,instance,of, &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg) gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
dot%whole(:,of) = 0.0_pReal dot%whole(:,of) = 0.0_pReal
dot%accshear_slip(:,of) = (gdot_slip_pos+gdot_slip_neg)*0.5_pReal dot%accshear_slip(:,of) = (gdot_slip_pos+gdot_slip_neg)*0.5_pReal
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature)) VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
where(dEq0(tau_slip_pos)) where(dEq0(tau_slip_pos))
EdgeDipDistance = mse%mfp(:,of) !ToDo MD@FR: correct? was not handled properly before EdgeDipDistance = dst%mfp(:,of) !ToDo MD@FR: correct? was not handled properly before
DotRhoDipFormation = 0.0_pReal DotRhoDipFormation = 0.0_pReal
DotRhoEdgeDipClimb = 0.0_pReal DotRhoEdgeDipClimb = 0.0_pReal
else where else where
EdgeDipDistance = math_clip((3.0_pReal*prm%mu*prm%burgers)/(16.0_pReal*PI*abs(tau_slip_pos)), & EdgeDipDistance = math_clip((3.0_pReal*prm%mu*prm%burgers)/(16.0_pReal*PI*abs(tau_slip_pos)), &
prm%minDipDistance, & ! lower limit prm%minDipDistance, & ! lower limit
mse%mfp(:,of)) ! upper limit dst%mfp(:,of)) ! upper limit
DotRhoDipFormation = merge(((2.0_pReal*EdgeDipDistance)/prm%burgers)* stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)), & DotRhoDipFormation = merge(((2.0_pReal*EdgeDipDistance)/prm%burgers)* stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)), &
0.0_pReal, & 0.0_pReal, &
prm%dipoleformation) prm%dipoleformation)
@ -560,7 +551,7 @@ subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of)
DotRhoEdgeDipClimb = (4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(:,of))/(EdgeDipDistance-prm%minDipDistance) DotRhoEdgeDipClimb = (4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(:,of))/(EdgeDipDistance-prm%minDipDistance)
end where end where
dot%rhoEdge(:,of) = abs(dot%accshear_slip(:,of))/(prm%burgers*mse%mfp(:,of)) & ! multiplication dot%rhoEdge(:,of) = abs(dot%accshear_slip(:,of))/(prm%burgers*dst%mfp(:,of)) & ! multiplication
- DotRhoDipFormation & - DotRhoDipFormation &
- ((2.0_pReal*prm%minDipDistance)/prm%burgers)*stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)) !* Spontaneous annihilation of 2 single edge dislocations - ((2.0_pReal*prm%minDipDistance)/prm%burgers)*stt%rhoEdge(:,of)*abs(dot%accshear_slip(:,of)) !* Spontaneous annihilation of 2 single edge dislocations
@ -569,10 +560,10 @@ subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of)
- DotRhoEdgeDipClimb - DotRhoEdgeDipClimb
end associate end associate
end subroutine plastic_disloUCLA_dotState end subroutine plastic_disloUCLA_dotState
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results !> @brief return array of constitutive results
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -601,7 +592,7 @@ function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postRe
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos, & gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos, &
gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
associate( prm => param(instance), stt => state(instance), mse => microstructure(instance)) associate( prm => param(instance), stt => state(instance), dst => dependentState(instance))
postResults = 0.0_pReal postResults = 0.0_pReal
c = 0_pInt c = 0_pInt
@ -614,7 +605,7 @@ function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postRe
case (rhoDip_ID) case (rhoDip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of) postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
case (shearrate_ID,stressexponent_ID) case (shearrate_ID,stressexponent_ID)
call kinetics(Mp,Temperature,instance,of, & call kinetics(Mp,Temperature,instance,of, &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg) gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
if (prm%outputID(o) == shearrate_ID) then if (prm%outputID(o) == shearrate_ID) then
@ -631,13 +622,13 @@ function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postRe
case (accumulatedshear_ID) case (accumulatedshear_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip, of) postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip, of)
case (mfp_ID) case (mfp_ID)
postResults(c+1_pInt:c+prm%totalNslip) = mse%mfp(1_pInt:prm%totalNslip, of) postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp(1_pInt:prm%totalNslip, of)
case (resolvedstress_ID) case (resolvedstress_ID)
do i = 1_pInt, prm%totalNslip do i = 1_pInt, prm%totalNslip
postResults(c+i) =math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i)) postResults(c+i) =math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))
enddo enddo
case (thresholdstress_ID) case (thresholdstress_ID)
postResults(c+1_pInt:c+prm%totalNslip) = mse%threshold_stress(1_pInt:prm%totalNslip,of) postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress(1_pInt:prm%totalNslip,of)
case (dipoleDistance_ID) case (dipoleDistance_ID)
do i = 1_pInt, prm%totalNslip do i = 1_pInt, prm%totalNslip
if (dNeq0(abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))) then if (dNeq0(abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))) then
@ -646,7 +637,7 @@ function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postRe
else else
postResults(c+i) = huge(1.0_pReal) postResults(c+i) = huge(1.0_pReal)
endif endif
postResults(c+i)=min(postResults(c+i),mse%mfp(i,of)) postResults(c+i)=min(postResults(c+i),dst%mfp(i,of))
enddo enddo
end select end select
@ -684,50 +675,45 @@ instance,of
dvel_slip, vel_slip dvel_slip, vel_slip
real(pReal), intent(out), dimension(plastic_disloUCLA_totalNslip(instance)) :: & real(pReal), intent(out), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
associate(prm => param(instance), stt => state(instance),mse => microstructure(instance))
gdot_slip_pos = 0.0_pReal gdot_slip_pos = 0.0_pReal
gdot_slip_neg = 0.0_pReal gdot_slip_neg = 0.0_pReal
dgdot_dtauslip_pos = 0.0_pReal dgdot_dtauslip_pos = 0.0_pReal
dgdot_dtauslip_neg = 0.0_pReal dgdot_dtauslip_neg = 0.0_pReal
associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
do j = 1_pInt, prm%totalNslip do j = 1_pInt, prm%totalNslip
!* Boltzmann ratio
BoltzmannRatio = prm%H0kp(j)/(kB*Temperature) BoltzmannRatio = prm%H0kp(j)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers(j)*prm%v0(j) DotGamma0 = stt%rhoEdge(j,of)*prm%burgers(j)*prm%v0(j)
!* Resolved shear stress on slip system
tau_slip_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j)) 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)) tau_slip_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
significantPositiveTau: if((abs(tau_slip_pos(j))-mse%threshold_stress(j, of)) > tol_math_check) then significantPositiveTau: if((abs(tau_slip_pos(j))-dst%threshold_stress(j, of)) > tol_math_check) then
!* Stress ratio
stressRatio = ((abs(tau_slip_pos(j))-mse%threshold_stress(j, of))/& stressRatio = ((abs(tau_slip_pos(j))-dst%threshold_stress(j, of)) &
(prm%solidSolutionStrength+& / (prm%solidSolutionStrength+prm%tau_Peierls(j)))
prm%tau_Peierls(j)))
stressRatio_p = stressRatio** prm%p(j) stressRatio_p = stressRatio** prm%p(j)
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal) stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*prm%burgers(j) & vel_slip = 2.0_pReal*prm%burgers(j) * prm%kink_height(j) * prm%omega(j) &
* prm%kink_height(j) * prm%omega(j) & * ( dst%mfp(j,of) - prm%kink_width(j) ) &
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
* (tau_slip_pos(j) & * (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
/ ( & / ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) & 2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
) )
gdot_slip_pos(j) = DotGamma0 * sign(vel_slip,tau_slip_pos(j))
!* Derivatives of shear rates
dvel_slip = & gdot_slip_pos(j) = DotGamma0 * sign(vel_slip,tau_slip_pos(j))
2.0_pReal*prm%burgers(j) &
* prm%kink_height(j) * prm%omega(j) & dvel_slip = 2.0_pReal*prm%burgers(j) * prm%kink_height(j) * prm%omega(j) &
* ( mse%mfp(j,of) - prm%kink_width(j) ) & * ( dst%mfp(j,of) - prm%kink_width(j) ) &
* ( & * ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & (exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
+ tau_slip_pos(j) & + tau_slip_pos(j) &
@ -739,14 +725,14 @@ instance,of
) & ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) & * (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
) & ) &
- (tau_slip_pos(j) & - (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) & * (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& * (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
*BoltzmannRatio*prm%p(j)& *BoltzmannRatio*prm%p(j)&
*prm%q(j)/& *prm%q(j)/&
@ -758,7 +744,7 @@ instance,of
( & ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) & 2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
)**2.0_pReal & )**2.0_pReal &
) )
@ -768,63 +754,59 @@ instance,of
endif significantPositiveTau endif significantPositiveTau
significantNegativeTau: if((abs(tau_slip_neg(j))-mse%threshold_stress(j, of)) > tol_math_check) then significantNegativeTau: if((abs(tau_slip_neg(j))-dst%threshold_stress(j, of)) > tol_math_check) then
!* Stress ratios
stressRatio = ((abs(tau_slip_neg(j))-mse%threshold_stress(j, of))/& stressRatio = ((abs(tau_slip_neg(j))-dst%threshold_stress(j, of)) &
(prm%solidSolutionStrength+& / (prm%solidSolutionStrength+prm%tau_Peierls(j)))
prm%tau_Peierls(j)))
stressRatio_p = stressRatio** prm%p(j) stressRatio_p = stressRatio** prm%p(j)
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal) stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*prm%burgers(j) & vel_slip = 2.0_pReal*prm%burgers(j) * prm%kink_height(j) * prm%omega(j) &
* prm%kink_height(j) * prm%omega(j) & * ( dst%mfp(j,of) - prm%kink_width(j) ) &
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
* (tau_slip_neg(j) & * (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
/ ( & / ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) & 2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
) )
gdot_slip_neg(j) = DotGamma0 * sign(vel_slip,tau_slip_neg(j)) gdot_slip_neg(j) = DotGamma0 * sign(vel_slip,tau_slip_neg(j))
!* Derivatives of shear rates
dvel_slip = & dvel_slip = 2.0_pReal*prm%burgers(j) * prm%kink_height(j) * prm%omega(j) &
2.0_pReal*prm%burgers(j) & * ( dst%mfp(j,of) - prm%kink_width(j) ) &
* prm%kink_height(j) * prm%omega(j) &
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
* ( & * ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & (exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
+ tau_slip_neg(j) & + tau_slip_neg(j) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& * (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
*BoltzmannRatio*prm%p(j)& *BoltzmannRatio*prm%p(j)&
*prm%q(j)/& *prm%q(j)/&
(prm%solidSolutionStrength+prm%tau_Peierls(j))*& (prm%solidSolutionStrength+prm%tau_Peierls(j))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) & StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) &
) & ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) & * (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
) & ) &
- (tau_slip_neg(j) & - (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) & * (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& * (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
*BoltzmannRatio*prm%p(j)& *BoltzmannRatio*prm%p(j)&
*prm%q(j)/& *prm%q(j)/&
(prm%solidSolutionStrength+prm%tau_Peierls(j))*& (prm%solidSolutionStrength+prm%tau_Peierls(j))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )& StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )&
) & ) &
) & ) &
/ ( & / ( &
( & ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) & 2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * prm%B(j) & + prm%omega(j) * prm%B(j) &
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) & *(( dst%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) & * exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
)**2.0_pReal & )**2.0_pReal &
) )