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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 typing import Sequence, Union, TextIO
import numpy as np
import matplotlib as mpl
if os.name == 'posix' and 'DISPLAY' not in os.environ:
@ -17,9 +16,9 @@ from PIL import Image
from . import util
from . import Table
_eps = 216./24389.
_kappa = 24389./27.
_ref_white = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65
_EPS = 216./24389.
_KAPPA = 24389./27.
_REF_WHITE = np.array([.95047, 1.00000, 1.08883]) # Observer = 2, Illuminant = D65
# ToDo (if needed)
# - support alpha channel (paraview/ASCII/input)
@ -522,10 +521,10 @@ class Colormap(mpl.colors.ListedColormap):
f_z = (lab[0]+16.)/116. - lab[2]/200.
return np.array([
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,
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)
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,
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)
@staticmethod
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
"""
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.)
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.)
return np.array([
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
!--------------------------------------------------------------------------------------------------
#include "parallelization.f90"
#include "constants.f90"
#include "IO.f90"
#include "YAML_types.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
use prec
use constants
use math
use rotations
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)))
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(1,1,2) = 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)
if (any(phase_lattice(p) == ['hP','tI'])) then
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)
end if
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)))
Li = dot_T * ( &
prm%A(1:3,1:3,1)*(T - prm%T_ref)**0 & ! constant 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(1:3,1:3,1) & ! constant 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
) / &
(1.0_pReal &
+ prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1. &
+ prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2. &
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3. &
+ 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 / 2.0_pReal &
+ prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3.0_pReal &
)
end associate
dLi_dTstar = 0.0_pReal

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

7
src/phase_mechanical_plastic_dislotungsten.f90
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@ -7,9 +7,6 @@
!--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotungsten
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters
real(pReal) :: &
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, &
0.0_pReal, &
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))
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
@ -475,7 +472,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
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), &
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)

17
src/phase_mechanical_plastic_dislotwin.f90
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@ -9,9 +9,6 @@
!--------------------------------------------------------------------------------------------------
submodule(phase:plastic) dislotwin
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
type :: tParameters
real(pReal) :: &
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
i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
h = 1.0_pReal, & !< Stack height of hex nucleus
T_ref = 0.0_pReal, &
T_ref = T_ROOM, &
a_cI = 1.0_pReal, &
a_cF = 1.0_pReal
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
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?
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)), &
1.0_pReal, &
prm%ExtendedDislocations)
v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Q_cl/(kB*T)) &
* (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal)
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/(K_B*T)) - 1.0_pReal)
dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,en) &
/ (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)
stressRatio = tau_eff/prm%tau_0
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) &
/ prm%v_0
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))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(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
Ndot0=0.0_pReal
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))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
(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
Ndot0=0.0_pReal
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
real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
! storage order of dislocation types
integer, dimension(*), parameter :: &
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
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 &
/ (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)) &
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) &
@ -1671,9 +1668,9 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
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)
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), &
0.0_pReal, &
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
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
tSolidSolution = 1.0_pReal / prm%nu_a &
* exp(prm%Q_sol / (kB * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * T) &
* 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 / (K_B * T) &
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), &
0.0_pReal, &
tauEff < criticalStress_S)