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Merge branch 'dynamic-C' into 'development' 

temperature dependend elastic constants.

See merge request damask/DAMASK!465
This commit is contained in:
Philip Eisenlohr 2021-11-26 21:41:36 +00:00
parent d52a14f74f 2fbe34497e
commit f32a788614
10 changed files with 110 additions and 58 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit 76bb51348de75207d483d369628670e5ae51dca9 Subproject commit bc6de828cc4ee9c941b37113ca49fcf51abd3512

19
python/damask/_colormap.py
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@ -5,7 +5,6 @@ import colorsys
from pathlib import Path from pathlib import Path
from typing import Sequence, Union, TextIO from typing import Sequence, Union, TextIO
import numpy as np import numpy as np
import matplotlib as mpl import matplotlib as mpl
if os.name == 'posix' and 'DISPLAY' not in os.environ: if os.name == 'posix' and 'DISPLAY' not in os.environ:
@ -17,9 +16,9 @@ from PIL import Image
from . import util from . import util
from . import Table from . import Table
_eps = 216./24389. _EPS = 216./24389.
_kappa = 24389./27. _KAPPA = 24389./27.
_ref_white = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65 _REF_WHITE = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65
# ToDo (if needed) # ToDo (if needed)
# - support alpha channel (paraview/ASCII/input) # - support alpha channel (paraview/ASCII/input)
@ -522,10 +521,10 @@ class Colormap(mpl.colors.ListedColormap):
f_z = (lab[0]+16.)/116. - lab[2]/200. f_z = (lab[0]+16.)/116. - lab[2]/200.
return np.array([ return np.array([
f_x**3. if f_x**3. > _eps else (116.*f_x-16.)/_kappa, f_x**3. if f_x**3. > _EPS else (116.*f_x-16.)/_KAPPA,
((lab[0]+16.)/116.)**3 if lab[0]>_kappa*_eps else lab[0]/_kappa, ((lab[0]+16.)/116.)**3 if lab[0]>_KAPPA*_EPS else lab[0]/_KAPPA,
f_z**3. if f_z**3. > _eps else (116.*f_z-16.)/_kappa f_z**3. if f_z**3. > _EPS else (116.*f_z-16.)/_KAPPA
])*(ref_white if ref_white is not None else _ref_white) ])*(ref_white if ref_white is not None else _REF_WHITE)
@staticmethod @staticmethod
def _xyz2lab(xyz: np.ndarray, ref_white: np.ndarray = None) -> np.ndarray: def _xyz2lab(xyz: np.ndarray, ref_white: np.ndarray = None) -> np.ndarray:
@ -537,8 +536,8 @@ class Colormap(mpl.colors.ListedColormap):
http://www.brucelindbloom.com/index.html?Eqn_Lab_to_XYZ.html http://www.brucelindbloom.com/index.html?Eqn_Lab_to_XYZ.html
""" """
ref_white = ref_white if ref_white is not None else _ref_white ref_white = ref_white if ref_white is not None else _REF_WHITE
f = np.where(xyz/ref_white > _eps,(xyz/ref_white)**(1./3.),(_kappa*xyz/ref_white+16.)/116.) f = np.where(xyz/ref_white > _EPS,(xyz/ref_white)**(1./3.),(_KAPPA*xyz/ref_white+16.)/116.)
return np.array([ return np.array([
116.0 * f[1] - 16.0, 116.0 * f[1] - 16.0,

1
src/commercialFEM_fileList.f90
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@ -4,6 +4,7 @@
!> @details List of files needed by MSC.Marc !> @details List of files needed by MSC.Marc
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
#include "parallelization.f90" #include "parallelization.f90"
#include "constants.f90"
#include "IO.f90" #include "IO.f90"
#include "YAML_types.f90" #include "YAML_types.f90"
#include "YAML_parse.f90" #include "YAML_parse.f90"

15
src/constants.f90 Normal file
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@ -0,0 +1,15 @@
!--------------------------------------------------------------------------------------------------
!> @author Martin Diehl, KU Leuven
!> @brief physical constants
!--------------------------------------------------------------------------------------------------
module constants
use prec
implicit none
public
real(pReal), parameter :: &
T_ROOM = 300.0_pReal, & !< Room temperature in K
K_B = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
end module constants

1
src/phase.f90
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@ -5,6 +5,7 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
module phase module phase
use prec use prec
use constants
use math use math
use rotations use rotations
use IO use IO

18
src/phase_mechanical_eigen_thermalexpansion.f90
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@ -58,14 +58,14 @@ module function thermalexpansion_init(kinematics_length) result(myKinematics)
associate(prm => param(kinematics_thermal_expansion_instance(p))) associate(prm => param(kinematics_thermal_expansion_instance(p)))
kinematic_type => kinematics%get(k) kinematic_type => kinematics%get(k)
prm%T_ref = kinematic_type%get_asFloat('T_ref', defaultVal=0.0_pReal) prm%T_ref = kinematic_type%get_asFloat('T_ref', defaultVal=T_ROOM)
prm%A(1,1,1) = kinematic_type%get_asFloat('A_11') prm%A(1,1,1) = kinematic_type%get_asFloat('A_11')
prm%A(1,1,2) = kinematic_type%get_asFloat('A_11,T',defaultVal=0.0_pReal) prm%A(1,1,2) = kinematic_type%get_asFloat('A_11,T', defaultVal=0.0_pReal)
prm%A(1,1,3) = kinematic_type%get_asFloat('A_11,T^2',defaultVal=0.0_pReal) prm%A(1,1,3) = kinematic_type%get_asFloat('A_11,T^2',defaultVal=0.0_pReal)
if (any(phase_lattice(p) == ['hP','tI'])) then if (any(phase_lattice(p) == ['hP','tI'])) then
prm%A(3,3,1) = kinematic_type%get_asFloat('A_33') prm%A(3,3,1) = kinematic_type%get_asFloat('A_33')
prm%A(3,3,2) = kinematic_type%get_asFloat('A_33,T',defaultVal=0.0_pReal) prm%A(3,3,2) = kinematic_type%get_asFloat('A_33,T', defaultVal=0.0_pReal)
prm%A(3,3,3) = kinematic_type%get_asFloat('A_33,T^2',defaultVal=0.0_pReal) prm%A(3,3,3) = kinematic_type%get_asFloat('A_33,T^2',defaultVal=0.0_pReal)
end if end if
do i=1, size(prm%A,3) do i=1, size(prm%A,3)
@ -98,14 +98,14 @@ module subroutine thermalexpansion_LiAndItsTangent(Li, dLi_dTstar, ph,me)
associate(prm => param(kinematics_thermal_expansion_instance(ph))) associate(prm => param(kinematics_thermal_expansion_instance(ph)))
Li = dot_T * ( & Li = dot_T * ( &
prm%A(1:3,1:3,1)*(T - prm%T_ref)**0 & ! constant coefficient prm%A(1:3,1:3,1) & ! constant coefficient
+ prm%A(1:3,1:3,2)*(T - prm%T_ref)**1 & ! linear coefficient + prm%A(1:3,1:3,2)*(T - prm%T_ref)**1 & ! linear coefficient
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**2 & ! quadratic coefficient + prm%A(1:3,1:3,3)*(T - prm%T_ref)**2 & ! quadratic coefficient
) / & ) / &
(1.0_pReal & (1.0_pReal &
+ prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1. & + prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1.0_pReal &
+ prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2. & + prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2.0_pReal &
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3. & + prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3.0_pReal &
) )
end associate end associate
dLi_dTstar = 0.0_pReal dLi_dTstar = 0.0_pReal

73
src/phase_mechanical_elastic.f90
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@ -1,13 +1,15 @@
submodule(phase:mechanical) elastic submodule(phase:mechanical) elastic
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal),dimension(3) :: &
C_11 = 0.0_pReal, & C_11 = 0.0_pReal, &
C_12 = 0.0_pReal, & C_12 = 0.0_pReal, &
C_13 = 0.0_pReal, & C_13 = 0.0_pReal, &
C_33 = 0.0_pReal, & C_33 = 0.0_pReal, &
C_44 = 0.0_pReal, & C_44 = 0.0_pReal, &
C_66 = 0.0_pReal C_66 = 0.0_pReal
real(pReal) :: &
T_ref
end type tParameters end type tParameters
type(tParameters), allocatable, dimension(:) :: param type(tParameters), allocatable, dimension(:) :: param
@ -28,7 +30,7 @@ module subroutine elastic_init(phases)
phase, & phase, &
mech, & mech, &
elastic elastic
logical :: thermal_active
print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>' print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>'
print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>' print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>'
@ -45,15 +47,35 @@ module subroutine elastic_init(phases)
associate(prm => param(ph)) associate(prm => param(ph))
prm%C_11 = elastic%get_asFloat('C_11') prm%T_ref = elastic%get_asFloat('T_ref', defaultVal=T_ROOM)
prm%C_12 = elastic%get_asFloat('C_12')
prm%C_44 = elastic%get_asFloat('C_44')
prm%C_11(1) = elastic%get_asFloat('C_11')
prm%C_11(2) = elastic%get_asFloat('C_11,T', defaultVal=0.0_pReal)
prm%C_11(3) = elastic%get_asFloat('C_11,T^2',defaultVal=0.0_pReal)
prm%C_12(1) = elastic%get_asFloat('C_12')
prm%C_12(2) = elastic%get_asFloat('C_12,T', defaultVal=0.0_pReal)
prm%C_12(3) = elastic%get_asFloat('C_12,T^2',defaultVal=0.0_pReal)
prm%C_44(1) = elastic%get_asFloat('C_44')
prm%C_44(2) = elastic%get_asFloat('C_44,T', defaultVal=0.0_pReal)
prm%C_44(3) = elastic%get_asFloat('C_44,T^2',defaultVal=0.0_pReal)
if (any(phase_lattice(ph) == ['hP','tI'])) then if (any(phase_lattice(ph) == ['hP','tI'])) then
prm%C_13 = elastic%get_asFloat('C_13') prm%C_13(1) = elastic%get_asFloat('C_13')
prm%C_33 = elastic%get_asFloat('C_33') prm%C_13(2) = elastic%get_asFloat('C_13,T', defaultVal=0.0_pReal)
prm%C_13(3) = elastic%get_asFloat('C_13,T^2',defaultVal=0.0_pReal)
prm%C_33(1) = elastic%get_asFloat('C_33')
prm%C_33(2) = elastic%get_asFloat('C_33,T', defaultVal=0.0_pReal)
prm%C_33(3) = elastic%get_asFloat('C_33,T^2',defaultVal=0.0_pReal)
end if
if (phase_lattice(ph) == 'tI') then
prm%C_66(1) = elastic%get_asFloat('C_66')
prm%C_66(2) = elastic%get_asFloat('C_66,T', defaultVal=0.0_pReal)
prm%C_66(3) = elastic%get_asFloat('C_66,T^2',defaultVal=0.0_pReal)
end if end if
if (phase_lattice(ph) == 'tI') prm%C_66 = elastic%get_asFloat('C_66')
end associate end associate
end do end do
@ -69,21 +91,44 @@ module function elastic_C66(ph,en) result(C66)
integer, intent(in) :: & integer, intent(in) :: &
ph, & ph, &
en en
real(pReal), dimension(6,6) :: C66 real(pReal), dimension(6,6) :: C66
real(pReal) :: T
associate(prm => param(ph)) associate(prm => param(ph))
C66 = 0.0_pReal C66 = 0.0_pReal
C66(1,1) = prm%C_11 T = thermal_T(ph,en)
C66(1,2) = prm%C_12
C66(4,4) = prm%C_44 C66(1,1) = prm%C_11(1) &
+ prm%C_11(2)*(T - prm%T_ref)**1 &
+ prm%C_11(3)*(T - prm%T_ref)**2
C66(1,2) = prm%C_12(1) &
+ prm%C_12(2)*(T - prm%T_ref)**1 &
+ prm%C_12(3)*(T - prm%T_ref)**2
C66(4,4) = prm%C_44(1) &
+ prm%C_44(2)*(T - prm%T_ref)**1 &
+ prm%C_44(3)*(T - prm%T_ref)**2
if (any(phase_lattice(ph) == ['hP','tI'])) then if (any(phase_lattice(ph) == ['hP','tI'])) then
C66(1,3) = prm%C_13 C66(1,3) = prm%C_13(1) &
C66(3,3) = prm%C_33 + prm%C_13(2)*(T - prm%T_ref)**1 &
+ prm%C_13(3)*(T - prm%T_ref)**2
C66(3,3) = prm%C_33(1) &
+ prm%C_33(2)*(T - prm%T_ref)**1 &
+ prm%C_33(3)*(T - prm%T_ref)**2
end if end if
if (phase_lattice(ph) == 'tI') C66(6,6) = prm%C_66 if (phase_lattice(ph) == 'tI') then
C66(6,6) = prm%C_66(1) &
+ prm%C_66(2)*(T - prm%T_ref)**1 &
+ prm%C_66(3)*(T - prm%T_ref)**2
end if
C66 = lattice_symmetrize_C66(C66,phase_lattice(ph)) C66 = lattice_symmetrize_C66(C66,phase_lattice(ph))

7
src/phase_mechanical_plastic_dislotungsten.f90
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@ -7,9 +7,6 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotungsten submodule(phase:plastic) dislotungsten
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal) :: &
D = 1.0_pReal, & !< grain size D = 1.0_pReal, & !< grain size
@ -344,7 +341,7 @@ module subroutine dislotungsten_dotState(Mp,T,ph,en)
dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, & 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, & 0.0_pReal, &
prm%dipoleformation) prm%dipoleformation)
v_cl = (3.0_pReal*mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*T)) & v_cl = (3.0_pReal*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(2.0_pReal*PI*K_B*T)) &
* (1.0_pReal/(d_hat+prm%d_caron)) * (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? 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 end where
@ -475,7 +472,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
if (present(tau_pos_out)) tau_pos_out = tau_pos if (present(tau_pos_out)) tau_pos_out = tau_pos
if (present(tau_neg_out)) tau_neg_out = tau_neg if (present(tau_neg_out)) tau_neg_out = tau_neg
associate(BoltzmannRatio => prm%Q_s/(kB*T), & associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, & b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w) effectiveLength => dst%Lambda_sl(:,en) - prm%w)

17
src/phase_mechanical_plastic_dislotwin.f90
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@ -9,9 +9,6 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotwin submodule(phase:plastic) dislotwin
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters type :: tParameters
real(pReal) :: & real(pReal) :: &
Q_cl = 1.0_pReal, & !< activation energy for dislocation climb Q_cl = 1.0_pReal, & !< activation energy for dislocation climb
@ -31,7 +28,7 @@ submodule(phase:plastic) dislotwin
delta_G = 1.0_pReal, & !< Free energy difference between austensite and martensite delta_G = 1.0_pReal, & !< Free energy difference between austensite and martensite
i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
h = 1.0_pReal, & !< Stack height of hex nucleus h = 1.0_pReal, & !< Stack height of hex nucleus
T_ref = 0.0_pReal, & T_ref = T_ROOM, &
a_cI = 1.0_pReal, & a_cI = 1.0_pReal, &
a_cF = 1.0_pReal a_cF = 1.0_pReal
real(pReal), dimension(2) :: & real(pReal), dimension(2) :: &
@ -597,7 +594,7 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,ph,en)
shearBandingContribution: if (dNeq0(prm%v_sb)) then shearBandingContribution: if (dNeq0(prm%v_sb)) then
E_kB_T = prm%E_sb/(kB*T) E_kB_T = prm%E_sb/(K_B*T)
call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design? call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design?
do i = 1,6 do i = 1,6
@ -694,8 +691,8 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
* (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (mu*prm%b_sl(i)), & * (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (mu*prm%b_sl(i)), &
1.0_pReal, & 1.0_pReal, &
prm%ExtendedDislocations) prm%ExtendedDislocations)
v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Q_cl/(kB*T)) & v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Q_cl/(K_B*T)) &
* (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal) * (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(K_B*T)) - 1.0_pReal)
dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,en) & dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,en) &
/ (d_hat-prm%d_caron(i)) / (d_hat-prm%d_caron(i))
@ -907,7 +904,7 @@ pure subroutine kinetics_sl(Mp,T,ph,en, &
significantStress: where(tau_eff > tol_math_check) significantStress: where(tau_eff > tol_math_check)
stressRatio = tau_eff/prm%tau_0 stressRatio = tau_eff/prm%tau_0
StressRatio_p = stressRatio** prm%p StressRatio_p = stressRatio** prm%p
Q_kB_T = prm%Q_sl/(kB*T) Q_kB_T = prm%Q_sl/(K_B*T)
v_wait_inverse = 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 / prm%v_0
v_run_inverse = prm%B/(tau_eff*prm%b_sl) v_run_inverse = prm%B/(tau_eff*prm%b_sl)
@ -980,7 +977,7 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+& Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(prm%L_tw*prm%b_sl(i))*& (prm%L_tw*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tw(i,en)-tau(i)))) (1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tw(i,en)-tau(i))))
else else
Ndot0=0.0_pReal Ndot0=0.0_pReal
end if end if
@ -1049,7 +1046,7 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+& Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(prm%L_tr*prm%b_sl(i))*& (prm%L_tr*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tr(i,en)-tau(i)))) (1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tr(i,en)-tau(i))))
else else
Ndot0=0.0_pReal Ndot0=0.0_pReal
end if end if

15
src/phase_mechanical_plastic_nonlocal.f90
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@ -19,9 +19,6 @@ submodule(phase:plastic) nonlocal
type(tGeometry), dimension(:), allocatable :: geom type(tGeometry), dimension(:), allocatable :: geom
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
! storage order of dislocation types ! storage order of dislocation types
integer, dimension(*), parameter :: & integer, dimension(*), parameter :: &
sgl = [1,2,3,4,5,6,7,8] !< signed (single) sgl = [1,2,3,4,5,6,7,8] !< signed (single)
@ -1094,9 +1091,9 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
! thermally activated annihilation of edge dipoles by climb ! thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal rhoDotThermalAnnihilation = 0.0_pReal
D_SD = prm%D_0 * exp(-prm%Q_cl / (kB * Temperature)) ! eq. 3.53 D_SD = prm%D_0 * exp(-prm%Q_cl / (K_B * Temperature)) ! eq. 3.53
v_climb = D_SD * mu * prm%V_at & v_climb = D_SD * mu * prm%V_at &
/ (PI * (1.0_pReal-nu) * (dUpper(:,1) + dLower(:,1)) * kB * Temperature) ! eq. 3.54 / (PI * (1.0_pReal-nu) * (dUpper(:,1) + dLower(:,1)) * K_B * Temperature) ! eq. 3.54
forall (s = 1:prm%sum_N_sl, dUpper(s,1) > dLower(s,1)) & forall (s = 1:prm%sum_N_sl, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * v_climb(s) / (dUpper(s,1) - dLower(s,1)), & rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * v_climb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) & - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
@ -1671,9 +1668,9 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
activationEnergy_P = criticalStress_P * activationVolume_P activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
tPeierls = 1.0_pReal / prm%nu_a & tPeierls = 1.0_pReal / prm%nu_a &
* exp(activationEnergy_P / (kB * T) & * exp(activationEnergy_P / (K_B * T) &
* (1.0_pReal - tauRel_P**prm%p)**prm%q) * (1.0_pReal - tauRel_P**prm%p)**prm%q)
dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (kB * T) & dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (K_B * T) &
* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), & * (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), &
0.0_pReal, & 0.0_pReal, &
tauEff < criticalStress_P) tauEff < criticalStress_P)
@ -1685,8 +1682,8 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
criticalStress_S = prm%Q_sol / activationVolume_S criticalStress_S = prm%Q_sol / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
tSolidSolution = 1.0_pReal / prm%nu_a & tSolidSolution = 1.0_pReal / prm%nu_a &
* exp(prm%Q_sol / (kB * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q) * exp(prm%Q_sol / (K_B * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * T) & dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (K_B * T) &
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), & * (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), &
0.0_pReal, & 0.0_pReal, &
tauEff < criticalStress_S) tauEff < criticalStress_S)