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correct calculation of tangent. 

thanks to Seyedamirhossein Motaman (RWTH Aachen) for reporting
This commit is contained in:
Martin Diehl 2022-01-01 11:37:04 +01:00
parent e678b231d9
commit 770cf33667
1 changed files with 64 additions and 52 deletions
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100
src/phase_mechanical_plastic_dislotwin.f90
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@ -17,8 +17,8 @@ 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
@ -731,8 +731,6 @@ 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
@ -941,16 +939,15 @@ 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) :: &
tau, &
dot_N_0, &
ratio_tau_r, &
ddot_gamma_dtau
real :: & real :: &
ratio_tau_s, &
tau, tau_r, &
dot_N_0, &
x0, & x0, &
tau_r, &
Gamma, & Gamma, &
mu, nu mu, nu, &
P_ncs, dP_ncs_dtau, &
P, dP_dtau
integer, dimension(2) :: & integer, dimension(2) :: &
s s
integer :: i integer :: i
@ -958,41 +955,53 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph)) associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
isFCC: if (prm%fccTwinTransNucleation) then
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) Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
do i = 1, prm%sum_N_tw do i = 1, prm%sum_N_tw
tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i)) tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
isFCC: if (prm%fccTwinTransNucleation) then x0 = mu*prm%b_tw(i)**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, the Burgers vector for slip is used
x0 = mu*prm%b_tw(i)**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
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) 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)
if (tau(i) < tau_r) then ! ToDo: correct?
if (tau > tol_math_check .and. tau < tau_r) then
ratio_tau_s = (dst%tau_hat_tw(i,en)/tau)**prm%r(i)
P = exp(-ratio_tau_s)
dP_dTau = prm%r(i) * ratio_tau_s/tau * P
s=prm%fcc_twinNucleationSlipPair(1:2,i) s=prm%fcc_twinNucleationSlipPair(1:2,i)
dot_N_0(i)=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+& dot_N_0=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+&
abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/& abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/(prm%L_tw*prm%b_sl(i))
(prm%L_tw*prm%b_sl(i))*(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau(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)
dot_gamma_tw(i) = dst%V_tw(i,en)*dot_N_0*P_ncs*P
if (present(ddot_gamma_dtau_tw)) &
ddot_gamma_dtau_tw(i) = dst%V_tw(i,en)*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
else else
dot_N_0(i)=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
dot_N_0(i)=prm%dot_N_0_tw(i)
end if isFCC
end do end do
significantStress: where(tau > tol_math_check) else isFCC
ratio_tau_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) * dot_N_0*exp(-ratio_tau_r) error stop 'not implemented'
ddot_gamma_dtau = (dot_gamma_tw*prm%r/tau)*ratio_tau_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
@ -1021,15 +1030,15 @@ 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) :: &
ddot_gamma_dtau
real :: & real :: &
ratio_tau_s, & ratio_tau_s, &
tau, tau_r, & tau, tau_r, &
dot_N_0, & dot_N_0, &
x0, & x0, &
Gamma, & Gamma, &
mu, nu mu, nu, &
P_ncs, dP_ncs_dtau, &
P, dP_dtau
integer, dimension(2) :: & integer, dimension(2) :: &
s s
integer :: i integer :: i
@ -1043,29 +1052,32 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
do i = 1, prm%sum_N_tr do i = 1, prm%sum_N_tr
tau = math_tensordot(Mp,prm%P_tr(1:3,1:3,i)) tau = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
x0 = mu*prm%b_tr(i)**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 x0 = mu*prm%b_tr(i)**2/(Gamma*8.0_pReal*PI)*(2.0_pReal+nu)/(1.0_pReal-nu) ! ToDo: In the paper, the Burgers vector for slip is used
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) 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)
if (tau > tol_math_check .and. tau < tau_r) then
if (tau > tol_math_check .and. tau < tau_r) then
ratio_tau_s = (dst%tau_hat_tr(i,en)/tau)**prm%s(i) ratio_tau_s = (dst%tau_hat_tr(i,en)/tau)**prm%s(i)
P = exp(-ratio_tau_s)
dP_dTau = prm%s(i) * ratio_tau_s/tau * P
s=prm%fcc_twinNucleationSlipPair(1:2,i) s=prm%fcc_twinNucleationSlipPair(1:2,i)
dot_N_0=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+& dot_N_0=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+&
abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/& abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/(prm%L_tr*prm%b_sl(i))
(prm%L_tr*prm%b_sl(i))*(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau)))
dot_gamma_tr(i) = dst%V_tr(i,en) * dot_N_0*exp(-ratio_tau_s) P_ncs = 1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau))
ddot_gamma_dtau(i) = (dot_gamma_tr(i)*prm%s(i)/tau)*ratio_tau_s dP_ncs_dtau = prm%V_cs / (K_B * T) * (P_ncs - 1.0_pReal)
dot_gamma_tr(i) = dst%V_tr(i,en)*dot_N_0*P_ncs*P
if (present(ddot_gamma_dtau_tr)) &
ddot_gamma_dtau_tr(i) = dst%V_tr(i,en)*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
else else
dot_gamma_tr(i) = 0.0_pReal dot_gamma_tr(i) = 0.0_pReal
ddot_gamma_dtau(i) = 0.0_pReal if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr(i) = 0.0_pReal
end if end if
end do end do
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