DAMASK_EICMD/src/phase_mechanical_plastic_di...

556 lines
25 KiB
Fortran
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

!--------------------------------------------------------------------------------------------------
!> @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
!--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotungsten
type :: tParameters
real(pReal) :: &
D = 1.0_pReal, & !< grain size
D_0 = 1.0_pReal, & !< prefactor for self-diffusion coefficient
Q_cl = 1.0_pReal !< activation energy for dislocation climb
real(pReal), allocatable, dimension(:) :: &
b_sl, & !< magnitude of Burgers vector [m]
d_caron, & !< distance of spontaneous annhihilation
i_sl, & !< Adj. parameter for distance between 2 forest dislocations
f_at, & !< factor to calculate atomic volume
tau_Peierls, & !< Peierls stress
!* mobility law parameters
Q_s, & !< activation energy for glide [J]
p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
B, & !< friction coefficient
h, & !< height of the kink pair
w, & !< width of the kink pair
omega !< attempt frequency for kink pair nucleation
real(pReal), allocatable, dimension(:,:) :: &
h_sl_sl, & !< slip resistance from slip activity
forestProjection
real(pReal), allocatable, dimension(:,:,:) :: &
P_sl, &
P_nS_pos, &
P_nS_neg
integer :: &
sum_N_sl !< total number of active slip system
character(len=pStringLen), allocatable, dimension(:) :: &
output
logical :: &
dipoleFormation !< flag indicating consideration of dipole formation
character(len=:), allocatable, dimension(:) :: &
systems_sl
end type tParameters !< container type for internal constitutive parameters
type :: tIndexDotState
integer, dimension(2) :: &
rho_mob, &
rho_dip, &
gamma_sl
end type tIndexDotState
type :: tDislotungstenState
real(pReal), dimension(:,:), pointer :: &
rho_mob, &
rho_dip, &
gamma_sl
end type tDislotungstenState
type :: tDislotungstenDependentState
real(pReal), dimension(:,:), allocatable :: &
Lambda_sl, &
tau_pass
end type tDislotungstenDependentState
!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:) :: param
type(tIndexDotState), allocatable, dimension(:) :: indexDotState
type(tDisloTungstenState), allocatable, dimension(:) :: state
type(tDisloTungstenDependentState), allocatable, dimension(:) :: dependentState
contains
!--------------------------------------------------------------------------------------------------
!> @brief Perform module initialization.
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
module function plastic_dislotungsten_init() result(myPlasticity)
logical, dimension(:), allocatable :: myPlasticity
integer :: &
ph, &
Nmembers, &
sizeState, sizeDotState, &
startIndex, endIndex
integer, dimension(:), allocatable :: &
N_sl
real(pReal),dimension(:), allocatable :: &
rho_mob_0, & !< initial dislocation density
rho_dip_0, & !< initial dipole density
a !< non-Schmid coefficients
character(len=pStringLen) :: &
extmsg = ''
type(tDict), pointer :: &
phases, &
phase, &
mech, &
pl
myPlasticity = plastic_active('dislotungsten')
if (count(myPlasticity) == 0) return
print'(/,1x,a)', '<<<+- phase:mechanical:plastic:dislotungsten init -+>>>'
print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
print'(/,1x,a)', 'D. Cereceda et al., International Journal of Plasticity 78:242256, 2016'
print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2015.09.002'
phases => config_material%get_dict('phase')
allocate(param(phases%length))
allocate(indexDotState(phases%length))
allocate(state(phases%length))
allocate(dependentState(phases%length))
do ph = 1, phases%length
if (.not. myPlasticity(ph)) cycle
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), &
idx_dot => indexDotState(ph))
phase => phases%get_dict(ph)
mech => phase%get_dict('mechanical')
pl => mech%get_dict('plastic')
#if defined (__GFORTRAN__)
prm%output = output_as1dString(pl)
#else
prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
#endif
!--------------------------------------------------------------------------------------------------
! slip related parameters
N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
prm%sum_N_sl = sum(abs(N_sl))
slipActive: if (prm%sum_N_sl > 0) then
prm%systems_sl = lattice_labels_slip(N_sl,phase_lattice(ph))
prm%P_sl = lattice_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
if (phase_lattice(ph) == 'cI') then
a = pl%get_as1dFloat('a_nonSchmid',defaultVal = emptyRealArray)
prm%P_nS_pos = lattice_nonSchmidMatrix(N_sl,a,+1)
prm%P_nS_neg = lattice_nonSchmidMatrix(N_sl,a,-1)
else
prm%P_nS_pos = prm%P_sl
prm%P_nS_neg = prm%P_sl
end if
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_as1dFloat('h_sl-sl'), &
phase_lattice(ph))
prm%forestProjection = lattice_forestProjection_edge(N_sl,phase_lattice(ph),&
phase_cOverA(ph))
prm%forestProjection = transpose(prm%forestProjection)
rho_mob_0 = pl%get_as1dFloat('rho_mob_0', requiredSize=size(N_sl))
rho_dip_0 = pl%get_as1dFloat('rho_dip_0', requiredSize=size(N_sl))
prm%b_sl = pl%get_as1dFloat('b_sl', requiredSize=size(N_sl))
prm%Q_s = pl%get_as1dFloat('Q_s', requiredSize=size(N_sl))
prm%i_sl = pl%get_as1dFloat('i_sl', requiredSize=size(N_sl))
prm%tau_Peierls = pl%get_as1dFloat('tau_Peierls', requiredSize=size(N_sl))
prm%p = pl%get_as1dFloat('p_sl', requiredSize=size(N_sl))
prm%q = pl%get_as1dFloat('q_sl', requiredSize=size(N_sl))
prm%h = pl%get_as1dFloat('h', requiredSize=size(N_sl))
prm%w = pl%get_as1dFloat('w', requiredSize=size(N_sl))
prm%omega = pl%get_as1dFloat('omega', requiredSize=size(N_sl))
prm%B = pl%get_as1dFloat('B', requiredSize=size(N_sl))
prm%D = pl%get_asFloat('D')
prm%D_0 = pl%get_asFloat('D_0')
prm%Q_cl = pl%get_asFloat('Q_cl')
prm%f_at = pl%get_asFloat('f_at') * prm%b_sl**3
prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal = .false.)
! expand: family => system
rho_mob_0 = math_expand(rho_mob_0, N_sl)
rho_dip_0 = math_expand(rho_dip_0, N_sl)
prm%q = math_expand(prm%q, N_sl)
prm%p = math_expand(prm%p, N_sl)
prm%Q_s = math_expand(prm%Q_s, N_sl)
prm%b_sl = math_expand(prm%b_sl, N_sl)
prm%h = math_expand(prm%h, N_sl)
prm%w = math_expand(prm%w, N_sl)
prm%omega = math_expand(prm%omega, N_sl)
prm%tau_Peierls = math_expand(prm%tau_Peierls, N_sl)
prm%B = math_expand(prm%B, N_sl)
prm%i_sl = math_expand(prm%i_sl, N_sl)
prm%f_at = math_expand(prm%f_at, N_sl)
prm%d_caron = pl%get_asFloat('D_a') * prm%b_sl
! sanity checks
if ( prm%D_0 < 0.0_pReal) extmsg = trim(extmsg)//' D_0'
if ( prm%Q_cl <= 0.0_pReal) extmsg = trim(extmsg)//' Q_cl'
if (any(rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0'
if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
if (any(prm%Q_s <= 0.0_pReal)) extmsg = trim(extmsg)//' Q_s'
if (any(prm%tau_Peierls < 0.0_pReal)) extmsg = trim(extmsg)//' tau_Peierls'
if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B'
if (any(prm%d_caron < 0.0_pReal)) extmsg = trim(extmsg)//' d_caron(D_a,b_sl)'
if (any(prm%f_at <= 0.0_pReal)) extmsg = trim(extmsg)//' f_at or b_sl'
else slipActive
rho_mob_0 = emptyRealArray; rho_dip_0 = emptyRealArray
allocate(prm%b_sl,prm%d_caron,prm%i_sl,prm%f_at,prm%tau_Peierls, &
prm%Q_s,prm%p,prm%q,prm%B,prm%h,prm%w,prm%omega, &
source = emptyRealArray)
allocate(prm%forestProjection(0,0))
allocate(prm%h_sl_sl (0,0))
end if slipActive
!--------------------------------------------------------------------------------------------------
! allocate state arrays
Nmembers = count(material_phaseID == ph)
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl
sizeState = sizeDotState
call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,0)
deallocate(plasticState(ph)%dotState) ! ToDo: remove dotState completely
!--------------------------------------------------------------------------------------------------
! state aliases and initialization
startIndex = 1
endIndex = prm%sum_N_sl
idx_dot%rho_mob = [startIndex,endIndex]
stt%rho_mob => plasticState(ph)%state(startIndex:endIndex,:)
stt%rho_mob = spread(rho_mob_0,2,Nmembers)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_rho'
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
idx_dot%rho_dip = [startIndex,endIndex]
stt%rho_dip => plasticState(ph)%state(startIndex:endIndex,:)
stt%rho_dip = spread(rho_dip_0,2,Nmembers)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
idx_dot%gamma_sl = [startIndex,endIndex]
stt%gamma_sl => plasticState(ph)%state(startIndex:endIndex,:)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_gamma',defaultVal=1.0e-6_pReal)
if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_gamma'
allocate(dst%Lambda_sl(prm%sum_N_sl,Nmembers), source=0.0_pReal)
allocate(dst%tau_pass(prm%sum_N_sl,Nmembers), source=0.0_pReal)
end associate
!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg))
end do
end function plastic_dislotungsten_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculate plastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
Mp,ph,en)
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
integer, intent(in) :: &
ph, &
en
integer :: &
i,k,l,m,n
real(pReal) :: &
T !< temperature
real(pReal), dimension(param(ph)%sum_N_sl) :: &
dot_gamma_pos,dot_gamma_neg, &
ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
T = thermal_T(ph,en)
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
associate(prm => param(ph))
call kinetics(Mp,T,ph,en,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
do i = 1, prm%sum_N_sl
Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%P_sl(1:3,1:3,i)
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) &
+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i)
end do
end associate
end subroutine dislotungsten_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief Calculate the rate of change of microstructure.
!--------------------------------------------------------------------------------------------------
module function dislotungsten_dotState(Mp,ph,en) result(dotState)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
integer, intent(in) :: &
ph, &
en
real(pReal), dimension(plasticState(ph)%sizeDotState) :: &
dotState
real(pReal), dimension(param(ph)%sum_N_sl) :: &
dot_gamma_pos, dot_gamma_neg,&
tau_pos,&
tau_neg, &
v_cl, &
dot_rho_dip_formation, &
dot_rho_dip_climb, &
d_hat
real(pReal) :: &
mu, T
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), &
dot_rho_mob => dotState(indexDotState(ph)%rho_mob(1):indexDotState(ph)%rho_mob(2)), &
dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
mu = elastic_mu(ph,en)
T = thermal_T(ph,en)
call kinetics(Mp,T,ph,en,&
dot_gamma_pos,dot_gamma_neg, &
tau_pos_out = tau_pos,tau_neg_out = tau_neg)
dot_gamma_sl = abs(dot_gamma_pos+dot_gamma_neg)
where(dEq0((tau_pos+tau_neg)*0.5_pReal))
dot_rho_dip_formation = 0.0_pReal
dot_rho_dip_climb = 0.0_pReal
else where
d_hat = math_clip(3.0_pReal*mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos+tau_neg)*0.5_pReal), &
prm%d_caron, & ! lower limit
dst%Lambda_sl(:,en)) ! upper limit
dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot_gamma_sl/prm%b_sl, &
0.0_pReal, &
prm%dipoleformation)
v_cl = (3.0_pReal*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(TAU*K_B*T)) &
* (1.0_pReal/(d_hat+prm%d_caron))
dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
end where
dot_rho_mob = dot_gamma_sl/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
- dot_rho_dip_formation &
- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_mob(:,en)*dot_gamma_sl ! Spontaneous annihilation of 2 edges
dot_rho_dip = dot_rho_dip_formation &
- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot_gamma_sl & ! Spontaneous annihilation of an edge with a dipole
- dot_rho_dip_climb
end associate
end function dislotungsten_dotState
!--------------------------------------------------------------------------------------------------
!> @brief Calculate derived quantities from state.
!--------------------------------------------------------------------------------------------------
module subroutine dislotungsten_dependentState(ph,en)
integer, intent(in) :: &
ph, &
en
real(pReal), dimension(param(ph)%sum_N_sl) :: &
Lambda_sl_inv
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
dst%tau_pass(:,en) = elastic_mu(ph,en)*prm%b_sl &
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
Lambda_sl_inv = 1.0_pReal/prm%D &
+ sqrt(matmul(prm%forestProjection,stt%rho_mob(:,en)+stt%rho_dip(:,en)))/prm%i_sl
dst%Lambda_sl(:,en) = Lambda_sl_inv**(-1.0_pReal)
end associate
end subroutine dislotungsten_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief Write results to HDF5 output file.
!--------------------------------------------------------------------------------------------------
module subroutine plastic_dislotungsten_results(ph,group)
integer, intent(in) :: ph
character(len=*), intent(in) :: group
integer :: ou
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
do ou = 1,size(prm%output)
select case(trim(prm%output(ou)))
case('rho_mob')
call results_writeDataset(stt%rho_mob,group,trim(prm%output(ou)), &
'mobile dislocation density','1/m²',prm%systems_sl)
case('rho_dip')
call results_writeDataset(stt%rho_dip,group,trim(prm%output(ou)), &
'dislocation dipole density','1/m²',prm%systems_sl)
case('gamma_sl')
call results_writeDataset(stt%gamma_sl,group,trim(prm%output(ou)), &
'plastic shear','1',prm%systems_sl)
case('Lambda_sl')
call results_writeDataset(dst%Lambda_sl,group,trim(prm%output(ou)), &
'mean free path for slip','m',prm%systems_sl)
case('tau_pass')
call results_writeDataset(dst%tau_pass,group,trim(prm%output(ou)), &
'threshold stress for slip','Pa',prm%systems_sl)
end select
end do
end associate
end subroutine plastic_dislotungsten_results
!--------------------------------------------------------------------------------------------------
!> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved
! stress, and the resolved stress.
!> @details Derivatives and resolved stress are calculated only optionally.
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics(Mp,T,ph,en, &
dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
ph, &
en
real(pReal), intent(out), dimension(param(ph)%sum_N_sl) :: &
dot_gamma_pos, &
dot_gamma_neg
real(pReal), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
ddot_gamma_dtau_pos, &
ddot_gamma_dtau_neg, &
tau_pos_out, &
tau_neg_out
real(pReal), dimension(param(ph)%sum_N_sl) :: &
StressRatio, &
StressRatio_p,StressRatio_pminus1, &
dvel, &
tau_pos, tau_neg, tau_eff, &
t_n, t_k, dtk,dtn
integer :: j
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
do j = 1, prm%sum_N_sl
tau_pos(j) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,j))
tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j))
end do
if (present(tau_pos_out)) tau_pos_out = tau_pos
if (present(tau_neg_out)) tau_neg_out = tau_neg
associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
tau_eff = abs(tau_pos)-dst%tau_pass(:,en)
significantPositiveTau: where(tau_eff > tol_math_check)
StressRatio = tau_eff/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
t_n = prm%b_sl*exp(BoltzmannRatio*(1.0_pReal-StressRatio_p) ** prm%q) &
/ (prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_eff) ! corrected eq. (14)
dot_gamma_pos = b_rho_half * sign(prm%h/(t_n + t_k),tau_pos)
else where significantPositiveTau
dot_gamma_pos = 0.0_pReal
end where significantPositiveTau
if (present(ddot_gamma_dtau_pos)) then
significantPositiveTau2: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
* StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_pos
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
ddot_gamma_dtau_pos = b_rho_half * dvel
else where significantPositiveTau2
ddot_gamma_dtau_pos = 0.0_pReal
end where significantPositiveTau2
end if
tau_eff = abs(tau_neg)-dst%tau_pass(:,en)
significantNegativeTau: where(tau_eff > tol_math_check)
StressRatio = tau_eff/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
t_n = prm%b_sl*exp(BoltzmannRatio*(1.0_pReal-StressRatio_p) ** prm%q) &
/ (prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_eff) ! corrected eq. (14)
dot_gamma_neg = b_rho_half * sign(prm%h/(t_n + t_k),tau_neg)
else where significantNegativeTau
dot_gamma_neg = 0.0_pReal
end where significantNegativeTau
if (present(ddot_gamma_dtau_neg)) then
significantNegativeTau2: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
* StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_neg
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
ddot_gamma_dtau_neg = b_rho_half * dvel
else where significantNegativeTau2
ddot_gamma_dtau_neg = 0.0_pReal
end where significantNegativeTau2
end if
end associate
end associate
end subroutine kinetics
end submodule dislotungsten