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Merge branch 'dislotwin-fix-tangent' into 'development' 

corrected tangent calculation for twinning and transformation

See merge request damask/DAMASK!492
This commit is contained in:
Franz Roters 2022-01-17 07:57:51 +00:00
parent f4979c6314 1140625b12
commit 1d2bbc8cd9
2 changed files with 111 additions and 113 deletions
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209
src/phase_mechanical_plastic_dislotwin.f90
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@ -17,17 +17,17 @@ submodule(phase:plastic) dislotwin
p_sb = 1.0_pReal, & !< p-exponent in shear band velocity p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
q_sb = 1.0_pReal, & !< q-exponent in shear band velocity q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning
L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors L_tw = 1.0_pReal, & !< length of twin nuclei in Burgers vectors: TODO unit should be meters
L_tr = 1.0_pReal, & !< Length of trans nuclei in Burgers vectors L_tr = 1.0_pReal, & !< length of trans nuclei in Burgers vectors: TODO unit should be meters
x_c_tw = 1.0_pReal, & !< critical distance for formation of twin nucleus x_c_tw = 1.0_pReal, & !< critical distance for formation of twin nucleus
x_c_tr = 1.0_pReal, & !< critical distance for formation of trans nucleus x_c_tr = 1.0_pReal, & !< critical distance for formation of trans nucleus
V_cs = 1.0_pReal, & !< cross slip volume V_cs = 1.0_pReal, & !< cross slip volume
xi_sb = 1.0_pReal, & !< value for shearband resistance xi_sb = 1.0_pReal, & !< value for shearband resistance
v_sb = 1.0_pReal, & !< value for shearband velocity_0 v_sb = 1.0_pReal, & !< value for shearband velocity_0
E_sb = 1.0_pReal, & !< activation energy for shear bands E_sb = 1.0_pReal, & !< activation energy for shear bands
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 = T_ROOM, & T_ref = T_ROOM, &
a_cI = 1.0_pReal, & a_cI = 1.0_pReal, &
a_cF = 1.0_pReal a_cF = 1.0_pReal
@ -40,14 +40,13 @@ submodule(phase:plastic) dislotwin
Q_sl,& !< activation energy for glide [J] for each slip system Q_sl,& !< activation energy for glide [J] for each slip system
v_0, & !< dislocation velocity prefactor [m/s] for each slip system v_0, & !< dislocation velocity prefactor [m/s] for each slip system
dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system
dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system
t_tw, & !< twin thickness [m] for each twin system t_tw, & !< twin thickness [m] for each twin system
i_sl, & !< Adj. parameter for distance between 2 forest dislocations for each slip system i_sl, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
t_tr, & !< martensite lamellar thickness [m] for each trans system t_tr, & !< martensite lamellar thickness [m] for each trans system
p, & !< p-exponent in glide velocity p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity q, & !< q-exponent in glide velocity
r, & !< r-exponent in twin nucleation rate r, & !< exponent in twin nucleation rate
s, & !< s-exponent in trans nucleation rate s, & !< exponent in trans nucleation rate
tau_0, & !< strength due to elements in solid solution tau_0, & !< strength due to elements in solid solution
gamma_char, & !< characteristic shear for twins gamma_char, & !< characteristic shear for twins
B, & !< drag coefficient B, & !< drag coefficient
@ -102,11 +101,7 @@ submodule(phase:plastic) dislotwin
Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite
tau_pass, & !< threshold stress for slip tau_pass, & !< threshold stress for slip
tau_hat_tw, & !< threshold stress for twinning tau_hat_tw, & !< threshold stress for twinning
tau_hat_tr, & !< threshold stress for transformation tau_hat_tr !< threshold stress for transformation
V_tw, & !< volume of a new twin
V_tr, & !< volume of a new martensite disc
tau_r_tw, & !< stress to bring partials close together (twin)
tau_r_tr !< stress to bring partials close together (trans)
end type tDislotwinDependentState end type tDislotwinDependentState
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -153,10 +148,10 @@ module function plastic_dislotwin_init() result(myPlasticity)
print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT) print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
print'(/,1x,a)', 'A. Ma and F. Roters, Acta Materialia 52(12):3603–3612, 2004' print'(/,1x,a)', 'A. Ma and F. Roters, Acta Materialia 52(12):3603–3612, 2004'
print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2004.04.012'//IO_EOL print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2004.04.012'
print'(/,1x,a)', 'F. Roters et al., Computational Materials Science 39:91–95, 2007' print'(/,1x,a)', 'F. Roters et al., Computational Materials Science 39:91–95, 2007'
print'( 1x,a)', 'https://doi.org/10.1016/j.commatsci.2006.04.014'//IO_EOL print'( 1x,a)', 'https://doi.org/10.1016/j.commatsci.2006.04.014'
print'(/,1x,a)', 'S.L. Wong et al., Acta Materialia 118:140–151, 2016' print'(/,1x,a)', 'S.L. Wong et al., Acta Materialia 118:140–151, 2016'
print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2016.07.032' print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2016.07.032'
@ -306,10 +301,10 @@ module function plastic_dislotwin_init() result(myPlasticity)
prm%b_tr = pl%get_as1dFloat('b_tr') prm%b_tr = pl%get_as1dFloat('b_tr')
prm%b_tr = math_expand(prm%b_tr,prm%N_tr) prm%b_tr = math_expand(prm%b_tr,prm%N_tr)
prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: This is not optional!
prm%i_tr = pl%get_asFloat('i_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%i_tr = pl%get_asFloat('i_tr', defaultVal=0.0_pReal) ! ToDo: This is not optional!
prm%delta_G = pl%get_asFloat('delta_G') prm%delta_G = pl%get_asFloat('delta_G')
prm%x_c_tr = pl%get_asFloat('x_c_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%x_c_tr = pl%get_asFloat('x_c_tr', defaultVal=0.0_pReal) ! ToDo: This is not optional!
prm%L_tr = pl%get_asFloat('L_tr') prm%L_tr = pl%get_asFloat('L_tr')
prm%a_cI = pl%get_asFloat('a_cI', defaultVal=0.0_pReal) prm%a_cI = pl%get_asFloat('a_cI', defaultVal=0.0_pReal)
prm%a_cF = pl%get_asFloat('a_cF', defaultVal=0.0_pReal) prm%a_cF = pl%get_asFloat('a_cF', defaultVal=0.0_pReal)
@ -324,10 +319,6 @@ module function plastic_dislotwin_init() result(myPlasticity)
prm%a_cI, & prm%a_cI, &
prm%a_cF) prm%a_cF)
if (phase_lattice(ph) /= 'cF') then
prm%dot_N_0_tr = pl%get_as1dFloat('dot_N_0_tr')
prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,prm%N_tr)
endif
prm%t_tr = pl%get_as1dFloat('t_tr') prm%t_tr = pl%get_as1dFloat('t_tr')
prm%t_tr = math_expand(prm%t_tr,prm%N_tr) prm%t_tr = math_expand(prm%t_tr,prm%N_tr)
prm%s = pl%get_as1dFloat('p_tr',defaultVal=[0.0_pReal]) prm%s = pl%get_as1dFloat('p_tr',defaultVal=[0.0_pReal])
@ -339,11 +330,8 @@ module function plastic_dislotwin_init() result(myPlasticity)
if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr' if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr'
if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr' if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr'
if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' p_tr' if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' p_tr'
if (phase_lattice(ph) /= 'cF') then
if (any(prm%dot_N_0_tr < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tr'
end if
else transActive else transActive
allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyRealArray) allocate(prm%s,prm%b_tr,prm%t_tr,source=emptyRealArray)
allocate(prm%h_tr_tr(0,0)) allocate(prm%h_tr_tr(0,0))
end if transActive end if transActive
@ -443,13 +431,9 @@ module function plastic_dislotwin_init() result(myPlasticity)
allocate(dst%Lambda_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal) allocate(dst%Lambda_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
allocate(dst%tau_hat_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal) allocate(dst%tau_hat_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
allocate(dst%tau_r_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
allocate(dst%V_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
allocate(dst%Lambda_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal) allocate(dst%Lambda_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
allocate(dst%tau_hat_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal) allocate(dst%tau_hat_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
allocate(dst%tau_r_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
allocate(dst%V_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
end associate end associate
@ -656,12 +640,14 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
dot_gamma_tr dot_gamma_tr
real(pReal) :: & real(pReal) :: &
mu, & mu, &
nu nu, &
Gamma
associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph)) associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph))
mu = elastic_mu(ph,en) mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en) nu = elastic_nu(ph,en)
Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
f_matrix = 1.0_pReal & f_matrix = 1.0_pReal &
- sum(stt%f_tw(1:prm%sum_N_tw,en)) & - sum(stt%f_tw(1:prm%sum_N_tw,en)) &
@ -689,8 +675,7 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
else else
! Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981 ! Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i))) sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i)))
b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) & b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) * Gamma / (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*exp(-prm%Q_cl/(K_B*T)) & v_cl = 2.0_pReal*prm%omega*b_d**2*exp(-prm%Q_cl/(K_B*T)) &
@ -742,8 +727,6 @@ module subroutine dislotwin_dependentState(T,ph,en)
real(pReal), dimension(param(ph)%sum_N_tr) :: & real(pReal), dimension(param(ph)%sum_N_tr) :: &
inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite
f_over_t_tr f_over_t_tr
real(pReal), dimension(:), allocatable :: &
x0
real(pReal) :: & real(pReal) :: &
mu, & mu, &
nu nu
@ -756,7 +739,7 @@ module subroutine dislotwin_dependentState(T,ph,en)
sumf_tw = sum(stt%f_tw(1:prm%sum_N_tw,en)) sumf_tw = sum(stt%f_tw(1:prm%sum_N_tw,en))
sumf_tr = sum(stt%f_tr(1:prm%sum_N_tr,en)) sumf_tr = sum(stt%f_tr(1:prm%sum_N_tr,en))
Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * T Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
!* rescaled volume fraction for topology !* rescaled volume fraction for topology
f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,en)/prm%t_tw ! this is per system ... f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,en)/prm%t_tw ! this is per system ...
@ -786,16 +769,6 @@ module subroutine dislotwin_dependentState(T,ph,en)
+ 3.0_pReal*prm%b_tr*mu/(prm%L_tr*prm%b_tr) & + 3.0_pReal*prm%b_tr*mu/(prm%L_tr*prm%b_tr) &
+ prm%h*prm%delta_G/(3.0_pReal*prm%b_tr) + prm%h*prm%delta_G/(3.0_pReal*prm%b_tr)
dst%V_tw(:,en) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,en)**2
dst%V_tr(:,en) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,en)**2
x0 = mu*prm%b_tw**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip
dst%tau_r_tw(:,en) = mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tw)+cos(pi/3.0_pReal)/x0)
x0 = mu*prm%b_tr**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, this is the Burgers vector for slip
dst%tau_r_tr(:,en) = mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tr)+cos(pi/3.0_pReal)/x0)
end associate end associate
end subroutine dislotwin_dependentState end subroutine dislotwin_dependentState
@ -959,48 +932,68 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
real(pReal), dimension(param(ph)%sum_N_tw), optional, intent(out) :: & real(pReal), dimension(param(ph)%sum_N_tw), optional, intent(out) :: &
ddot_gamma_dtau_tw ddot_gamma_dtau_tw
real, dimension(param(ph)%sum_N_tw) :: & real :: &
tau, & tau, tau_r, &
Ndot0, & dot_N_0, &
stressRatio_r, & x0, V, &
ddot_gamma_dtau Gamma, &
mu, nu, &
integer :: i,s1,s2 P_ncs, dP_ncs_dtau, &
P, dP_dtau
integer, dimension(2) :: &
s
integer :: i
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph)) associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
do i = 1, prm%sum_N_tw
tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
isFCC: if (prm%fccTwinTransNucleation) then isFCC: if (prm%fccTwinTransNucleation) then
s1=prm%fcc_twinNucleationSlipPair(1,i) mu = elastic_mu(ph,en)
s2=prm%fcc_twinNucleationSlipPair(2,i) nu = elastic_nu(ph,en)
if (tau(i) < dst%tau_r_tw(i,en)) then ! ToDo: correct? Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
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)))/& do i = 1, prm%sum_N_tw
(prm%L_tw*prm%b_sl(i))*& tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tw(i,en)-tau(i)))) x0 = mu*prm%b_tw(i)**2*(2.0_pReal+nu)/(Gamma*8.0_pReal*PI*(1.0_pReal-nu)) ! ToDo: In the paper, the Burgers vector for slip is used
tau_r = mu*prm%b_tw(i)/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tw)+cos(PI/3.0_pReal)/x0) ! ToDo: In the paper, the Burgers vector for slip is used
if (tau > tol_math_check .and. tau < tau_r) then
P = exp(-(dst%tau_hat_tw(i,en)/tau)**prm%r(i))
dP_dTau = prm%r(i) * (dst%tau_hat_tw(i,en)/tau)**prm%r(i)/tau * P
s = prm%fcc_twinNucleationSlipPair(1:2,i)
dot_N_0 = sum(abs(dot_gamma_sl(s(2:1:-1)))*(stt%rho_mob(s,en)+stt%rho_dip(s,en))) &
/ (prm%L_tw*prm%b_sl(i))
P_ncs = 1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau))
dP_ncs_dtau = prm%V_cs / (K_B * T) * (P_ncs - 1.0_pReal)
V = PI/4.0_pReal*dst%Lambda_tw(i,en)**2*prm%t_tw(i)
dot_gamma_tw(i) = V*dot_N_0*P_ncs*P
if (present(ddot_gamma_dtau_tw)) &
ddot_gamma_dtau_tw(i) = V*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
else else
Ndot0=0.0_pReal dot_gamma_tw(i) = 0.0_pReal
if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
end if end if
else isFCC
Ndot0=prm%dot_N_0_tw(i)
end if isFCC
end do end do
significantStress: where(tau > tol_math_check) else isFCC
StressRatio_r = (dst%tau_hat_tw(:,en)/tau)**prm%r do i = 1, prm%sum_N_tw
dot_gamma_tw = prm%gamma_char * dst%V_tw(:,en) * Ndot0*exp(-StressRatio_r) error stop 'not implemented'
ddot_gamma_dtau = (dot_gamma_tw*prm%r/tau)*StressRatio_r tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
else where significantStress if (tau > tol_math_check) then
dot_gamma_tw = 0.0_pReal dot_gamma_tw(i) = 0.0_pReal
ddot_gamma_dtau = 0.0_pReal if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
end where significantStress else
dot_gamma_tw(i) = 0.0_pReal
if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
end if
end do
end if isFCC
end associate end associate
if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw = ddot_gamma_dtau
end subroutine kinetics_tw end subroutine kinetics_tw
@ -1029,47 +1022,53 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
real(pReal), dimension(param(ph)%sum_N_tr), optional, intent(out) :: & real(pReal), dimension(param(ph)%sum_N_tr), optional, intent(out) :: &
ddot_gamma_dtau_tr ddot_gamma_dtau_tr
real, dimension(param(ph)%sum_N_tr) :: & real :: &
tau, & tau, tau_r, &
Ndot0, & dot_N_0, &
stressRatio_s, & x0, V, &
ddot_gamma_dtau Gamma, &
integer :: i,s1,s2 mu, nu, &
P_ncs, dP_ncs_dtau, &
P, dP_dtau
integer, dimension(2) :: &
s
integer :: i
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph)) associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
do i = 1, prm%sum_N_tr do i = 1, prm%sum_N_tr
tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i)) tau = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
isFCC: if (prm%fccTwinTransNucleation) then x0 = mu*prm%b_tr(i)**2*(2.0_pReal+nu)/(Gamma*8.0_pReal*PI*(1.0_pReal-nu)) ! ToDo: In the paper, the Burgers vector for slip is used
s1=prm%fcc_twinNucleationSlipPair(1,i) tau_r = mu*prm%b_tr(i)/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%x_c_tr)+cos(PI/3.0_pReal)/x0) ! ToDo: In the paper, the Burgers vector for slip is used
s2=prm%fcc_twinNucleationSlipPair(2,i)
if (tau(i) < dst%tau_r_tr(i,en)) then ! ToDo: correct? if (tau > tol_math_check .and. tau < tau_r) then
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+& P = exp(-(dst%tau_hat_tr(i,en)/tau)**prm%s(i))
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/& dP_dTau = prm%s(i) * (dst%tau_hat_tr(i,en)/tau)**prm%s(i)/tau * P
(prm%L_tr*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tr(i,en)-tau(i)))) s = prm%fcc_twinNucleationSlipPair(1:2,i)
dot_N_0 = sum(abs(dot_gamma_sl(s(2:1:-1)))*(stt%rho_mob(s,en)+stt%rho_dip(s,en))) &
/ (prm%L_tr*prm%b_sl(i))
P_ncs = 1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau))
dP_ncs_dtau = prm%V_cs / (K_B * T) * (P_ncs - 1.0_pReal)
V = PI/4.0_pReal*dst%Lambda_tr(i,en)**2*prm%t_tr(i)
dot_gamma_tr(i) = V*dot_N_0*P_ncs*P
if (present(ddot_gamma_dtau_tr)) &
ddot_gamma_dtau_tr(i) = V*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
else else
Ndot0=0.0_pReal dot_gamma_tr(i) = 0.0_pReal
if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr(i) = 0.0_pReal
end if end if
else isFCC
Ndot0=prm%dot_N_0_tr(i)
end if isFCC
end do end do
significantStress: where(tau > tol_math_check)
StressRatio_s = (dst%tau_hat_tr(:,en)/tau)**prm%s
dot_gamma_tr = dst%V_tr(:,en) * Ndot0*exp(-StressRatio_s)
ddot_gamma_dtau = (dot_gamma_tr*prm%s/tau)*StressRatio_s
else where significantStress
dot_gamma_tr = 0.0_pReal
ddot_gamma_dtau = 0.0_pReal
end where significantStress
end associate end associate
if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr = ddot_gamma_dtau
end subroutine kinetics_tr end subroutine kinetics_tr
end submodule dislotwin end submodule dislotwin

3
src/phase_mechanical_plastic_nonlocal.f90
View File

@ -203,7 +203,7 @@ module function plastic_nonlocal_init() result(myPlasticity)
print'(/,a,i0)', ' # phases: ',Ninstances; flush(IO_STDOUT) print'(/,a,i0)', ' # phases: ',Ninstances; flush(IO_STDOUT)
print'(/,1x,a)', 'C. Reuber et al., Acta Materialia 71:333–348, 2014' print'(/,1x,a)', 'C. Reuber et al., Acta Materialia 71:333–348, 2014'
print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2014.03.012'//IO_EOL print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2014.03.012'
print'(/,1x,a)', 'C. Kords, Dissertation RWTH Aachen, 2014' print'(/,1x,a)', 'C. Kords, Dissertation RWTH Aachen, 2014'
print'( 1x,a)', 'http://publications.rwth-aachen.de/record/229993' print'( 1x,a)', 'http://publications.rwth-aachen.de/record/229993'
@ -1570,7 +1570,6 @@ subroutine stateInit(ini,phase,Nentries)
upto, & upto, &
s s
real(pReal), dimension(2) :: & real(pReal), dimension(2) :: &
noise, &
rnd rnd
real(pReal) :: & real(pReal) :: &
meanDensity, & meanDensity, &