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Merge remote-tracking branch 'origin/development' into mesh-order

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Martin Diehl 2021-11-03 07:57:59 +01:00
parent 222116a135 493a0969eb
commit a041551b9f
8 changed files with 148 additions and 157 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit bb73a35f334831eed10d0e293aafea6c0900b7bd
Subproject commit 5a769ec759d9dacc1866c35c6663cd0001e198c5

26
examples/config/Phase_Dislotungsten_W.yaml
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@ -1,26 +0,0 @@
type: dislotungsten
N_sl: [12]
rho_mob_0: [1.0e+9]
rho_dip_0: [1.0]
nu_a: [9.1e+11]
b_sl: [2.72e-10]
Delta_H_kp,0: [2.61154e-19] # 1.63 eV, Delta_H0
tau_Peierls: [2.03e+9]
p_sl: [0.86]
q_sl: [1.69]
h: [2.566e-10]
w: [2.992e-09]
B: [8.3e-5]
D_a: 1.0 # d_edge
# climb (disabled)
D_0: 0.0
Q_cl: 0.0
V_cl: [0.0]
h_sl-sl: [0.009, 0.72, 0.009, 0.05, 0.05, 0.06, 0.09]
a_nonSchmid: [0.938, 0.71, 4.43]

35
examples/config/phase/mechanical/plastic/dislotungsten_W.yaml Normal file
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@ -0,0 +1,35 @@
type: dislotungsten
references:
- D. Cereceda et al.,
International Journal of Plasticity 78:242-265, 2016,
http://dx.doi.org/10.1016/j.ijplas.2015.09.002
- R. Gröger et al.,
Acta Materialia 56(19):5412-5425, 2008,
https://doi.org/10.1016/j.actamat.2008.07.037
output: [Lambda_sl]
N_sl: [12]
b_sl: [2.72e-10]
rho_mob_0: [1.0e+9] # estimated from section 3.2
rho_dip_0: [1.0] # not given
Q_s: [2.61154e-19] # 1.63 eV, Delta_H0
B: [8.3e-5]
omega: [9.1e+11] # nu_0
p_sl: [0.86]
q_sl: [1.69]
tau_Peierls: [2.03e+9]
h: [2.566e-10]
h_sl-sl: [0.009, 0.72, 0.009, 0.05, 0.05, 0.06, 0.09]
w: [2.992e-09] # 11b
# values in Cereceda et al. are high, using parameters from Gröger et al.
a_nonSchmid: [0.0, 0.56, 0.75] # Table 2
# (almost) no annhilation, adjustment needed for simulations beyond the yield point
i_sl: [1] # c, eq. (25)
D: 1.0e+20 # d_g, eq. (25)
D_a: 1.0 # d_edge = D_a*b
# disable climb (not discussed in Cereceda et al.)
D_0: 0.0
f_at: 1
Q_cl: 1.0

2
python/damask/VERSION
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@ -1 +1 @@
v3.0.0-alpha5-29-g84df8b71f
v3.0.0-alpha5-45-g1a558db83

21
python/damask/_orientation.py
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@ -9,27 +9,6 @@ from . import util
from . import tensor
lattice_symmetries = {
'aP': 'triclinic',
'mP': 'monoclinic',
'mS': 'monoclinic',
'oP': 'orthorhombic',
'oS': 'orthorhombic',
'oI': 'orthorhombic',
'oF': 'orthorhombic',
'tP': 'tetragonal',
'tI': 'tetragonal',
'hP': 'hexagonal',
'cP': 'cubic',
'cI': 'cubic',
'cF': 'cubic',
}
_parameter_doc = \
"""
family : {'triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic'}, optional.

4
python/tests/test_Orientation.py
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@ -7,9 +7,9 @@ from damask import Orientation
from damask import Table
from damask import util
from damask import grid_filters
from damask import _orientation
from damask import _crystal
crystal_families = set(_orientation.lattice_symmetries.values())
crystal_families = set(_crystal.lattice_symmetries.values())
@pytest.fixture

212
src/phase_mechanical_plastic_dislotungsten.f90
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@ -24,7 +24,6 @@ submodule(phase:plastic) dislotungsten
tau_Peierls, & !< Peierls stress
!* mobility law parameters
Q_s, & !< activation energy for glide [J]
v_0, & !< dislocation velocity prefactor [m/s]
p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
B, & !< friction coefficient
@ -148,7 +147,7 @@ module function plastic_dislotungsten_init() result(myPlasticity)
else
prm%P_nS_pos = prm%P_sl
prm%P_nS_neg = prm%P_sl
endif
end if
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_as1dFloat('h_sl-sl'), &
phase_lattice(ph))
@ -158,7 +157,6 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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%v_0 = pl%get_as1dFloat('v_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))
@ -189,18 +187,16 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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%v_0 = math_expand(prm%v_0, 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%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%v_0 < 0.0_pReal)) extmsg = trim(extmsg)//' v_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'
@ -209,13 +205,13 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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
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%v_0,prm%p,prm%q,prm%B,prm%h,prm%w,prm%omega, &
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))
endif slipActive
end if slipActive
!--------------------------------------------------------------------------------------------------
! allocate state arrays
@ -258,7 +254,7 @@ module function plastic_dislotungsten_init() result(myPlasticity)
! exit if any parameter is out of range
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(dislotungsten)')
enddo
end do
end function plastic_dislotungsten_init
@ -267,7 +263,7 @@ end function plastic_dislotungsten_init
!> @brief Calculate plastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
Mp,T,ph,en)
Mp,T,ph,en)
real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
real(pReal), dimension(3,3,3,3), intent(out) :: &
@ -287,19 +283,20 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
dot_gamma_pos,dot_gamma_neg, &
ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
associate(prm => param(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)
enddo
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
@ -328,35 +325,36 @@ module subroutine dislotungsten_dotState(Mp,T,ph,en)
dot_rho_dip_climb, &
d_hat
associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph))
call kinetics(Mp,T,ph,en,&
dot_gamma_pos,dot_gamma_neg, &
tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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(:,en) = abs(dot_gamma_pos+dot_gamma_neg)
dot%gamma_sl(:,en) = abs(dot_gamma_pos+dot_gamma_neg)
where(dEq0(tau_pos)) ! ToDo: use avg of +/-
dot_rho_dip_formation = 0.0_pReal
dot_rho_dip_climb = 0.0_pReal
else where
d_hat = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), & ! ToDo: use avg of +/-
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(:,en)/prm%b_sl, &
0.0_pReal, &
prm%dipoleformation)
v_cl = (3.0_pReal*prm%mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*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
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*prm%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(:,en)/prm%b_sl, &
0.0_pReal, &
prm%dipoleformation)
v_cl = (3.0_pReal*prm%mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*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(:,en) = dot%gamma_sl(:,en)/(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(:,en) ! Spontaneous annihilation of 2 edges
dot%rho_dip(:,en) = dot_rho_dip_formation &
- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot%gamma_sl(:,en) & ! Spontaneous annihilation of an edge with a dipole
- dot_rho_dip_climb
dot%rho_mob(:,en) = dot%gamma_sl(:,en)/(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(:,en) ! Spontaneous annihilation of 2 edges
dot%rho_dip(:,en) = dot_rho_dip_formation &
- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot%gamma_sl(:,en) & ! Spontaneous annihilation of an edge with a dipole
- dot_rho_dip_climb
end associate
@ -368,21 +366,22 @@ end subroutine dislotungsten_dotState
!--------------------------------------------------------------------------------------------------
module subroutine dislotungsten_dependentState(ph,en)
integer, intent(in) :: &
integer, intent(in) :: &
ph, &
en
real(pReal), dimension(param(ph)%sum_N_sl) :: &
dislocationSpacing
Lambda_sl_inv
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
dislocationSpacing = sqrt(matmul(prm%forestProjection,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
dst%tau_pass(:,en) = prm%mu*prm%b_sl &
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
dst%Lambda_sl(:,en) = prm%D/(1.0_pReal+prm%D*dislocationSpacing/prm%i_sl)
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
@ -423,7 +422,7 @@ module subroutine plastic_dislotungsten_results(ph,group)
'threshold stress for slip','Pa',prm%systems_sl)
end select
enddo
end do
end associate
@ -456,88 +455,91 @@ pure subroutine kinetics(Mp,T,ph,en, &
ddot_gamma_dtau_neg, &
tau_pos_out, &
tau_neg_out
real(pReal), dimension(param(ph)%sum_N_sl) :: &
StressRatio, &
StressRatio_p,StressRatio_pminus1, &
dvel, vel, &
tau_pos,tau_neg, &
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))
enddo
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
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/(kB*T), &
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
associate(BoltzmannRatio => prm%Q_s/(kB*T), &
dot_gamma_0 => stt%rho_mob(:,en)*prm%b_sl*prm%v_0, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
tau_eff = abs(tau_pos)-dst%tau_pass(:,en)
significantPositiveTau: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
StressRatio = (abs(tau_pos)-dst%tau_pass(:,en))/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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)
vel = prm%h/(t_n + t_k)
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
dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
else where significantPositiveTau
dot_gamma_pos = 0.0_pReal
end where significantPositiveTau
if (present(ddot_gamma_dtau_pos)) then
significantPositiveTau2: where(abs(tau_pos)-dst%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
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)**(prm%p - 1.0_pReal) / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_pos
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
ddot_gamma_dtau_pos = b_rho_half * dvel
else where significantPositiveTau2
ddot_gamma_dtau_pos = 0.0_pReal
end where significantPositiveTau2
end if
ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
else where significantPositiveTau2
ddot_gamma_dtau_pos = 0.0_pReal
end where significantPositiveTau2
endif
tau_eff = abs(tau_neg)-dst%tau_pass(:,en)
significantNegativeTau: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
StressRatio = (abs(tau_neg)-dst%tau_pass(:,en))/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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)
vel = prm%h/(t_n + t_k)
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
dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
else where significantNegativeTau
dot_gamma_neg = 0.0_pReal
end where significantNegativeTau
if (present(ddot_gamma_dtau_neg)) then
significantNegativeTau2: where(abs(tau_neg)-dst%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
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)**(prm%p - 1.0_pReal) / prm%tau_Peierls
dtk = -1.0_pReal * t_k / tau_neg
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
ddot_gamma_dtau_neg = b_rho_half * dvel
else where significantNegativeTau2
ddot_gamma_dtau_neg = 0.0_pReal
end where significantNegativeTau2
end if
ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
else where significantNegativeTau2
ddot_gamma_dtau_neg = 0.0_pReal
end where significantNegativeTau2
end if
end associate
end associate
end associate
end subroutine kinetics

3
src/phase_mechanical_plastic_dislotwin.f90
View File

@ -890,7 +890,8 @@ pure subroutine kinetics_sl(Mp,T,ph,en, &
stressRatio = tau_eff/prm%tau_0
StressRatio_p = stressRatio** prm%p
Q_kB_T = prm%Q_sl/(kB*T)
v_wait_inverse = prm%v_0**(-1.0_pReal) * exp(Q_kB_T*(1.0_pReal-StressRatio_p)** prm%q)
v_wait_inverse = exp(Q_kB_T*(1.0_pReal-StressRatio_p)** prm%q) &
/ prm%v_0
v_run_inverse = prm%B/(tau_eff*prm%b_sl)
dot_gamma_sl = sign(stt%rho_mob(:,en)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau)