correct calculation of tangent.
thanks to Seyedamirhossein Motaman (RWTH Aachen) for reporting
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Martin Diehl
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e678b231d9
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770cf33667
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@ -17,8 +17,8 @@ submodule(phase:plastic) dislotwin
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p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
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q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
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i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning
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L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors
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L_tr = 1.0_pReal, & !< Length of trans nuclei in Burgers vectors
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L_tw = 1.0_pReal, & !< length of twin nuclei in Burgers vectors: TODO unit should be meters
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L_tr = 1.0_pReal, & !< length of trans nuclei in Burgers vectors: TODO unit should be meters
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x_c_tw = 1.0_pReal, & !< critical distance for formation of twin nucleus
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x_c_tr = 1.0_pReal, & !< critical distance for formation of trans nucleus
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V_cs = 1.0_pReal, & !< cross slip volume
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@ -731,8 +731,6 @@ module subroutine dislotwin_dependentState(T,ph,en)
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real(pReal), dimension(param(ph)%sum_N_tr) :: &
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inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite
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f_over_t_tr
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real(pReal), dimension(:), allocatable :: &
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x0
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real(pReal) :: &
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mu, &
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nu
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@ -941,16 +939,15 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
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real(pReal), dimension(param(ph)%sum_N_tw), optional, intent(out) :: &
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ddot_gamma_dtau_tw
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real, dimension(param(ph)%sum_N_tw) :: &
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tau, &
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dot_N_0, &
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ratio_tau_r, &
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ddot_gamma_dtau
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real :: &
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ratio_tau_s, &
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tau, tau_r, &
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dot_N_0, &
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x0, &
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tau_r, &
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Gamma, &
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mu, nu
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mu, nu, &
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P_ncs, dP_ncs_dtau, &
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P, dP_dtau
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integer, dimension(2) :: &
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s
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integer :: i
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@ -958,41 +955,53 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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isFCC: if (prm%fccTwinTransNucleation) then
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mu = elastic_mu(ph,en)
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nu = elastic_nu(ph,en)
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Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
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do i = 1, prm%sum_N_tw
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tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
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isFCC: if (prm%fccTwinTransNucleation) then
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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
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tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
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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
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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)
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if (tau(i) < tau_r) then ! ToDo: correct?
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if (tau > tol_math_check .and. tau < tau_r) then
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ratio_tau_s = (dst%tau_hat_tw(i,en)/tau)**prm%r(i)
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P = exp(-ratio_tau_s)
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dP_dTau = prm%r(i) * ratio_tau_s/tau * P
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s=prm%fcc_twinNucleationSlipPair(1:2,i)
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dot_N_0(i)=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+&
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abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/&
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(prm%L_tw*prm%b_sl(i))*(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau(i))))
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dot_N_0=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+&
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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))
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P_ncs = 1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau))
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dP_ncs_dtau = prm%V_cs / (K_B * T) * (P_ncs - 1.0_pReal)
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dot_gamma_tw(i) = dst%V_tw(i,en)*dot_N_0*P_ncs*P
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if (present(ddot_gamma_dtau_tw)) &
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ddot_gamma_dtau_tw(i) = dst%V_tw(i,en)*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
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else
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dot_N_0(i)=0.0_pReal
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dot_gamma_tw(i) = 0.0_pReal
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if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
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end if
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else isFCC
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dot_N_0(i)=prm%dot_N_0_tw(i)
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end if isFCC
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end do
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significantStress: where(tau > tol_math_check)
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ratio_tau_r = (dst%tau_hat_tw(:,en)/tau)**prm%r
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dot_gamma_tw = prm%gamma_char * dst%V_tw(:,en) * dot_N_0*exp(-ratio_tau_r)
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ddot_gamma_dtau = (dot_gamma_tw*prm%r/tau)*ratio_tau_r
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else where significantStress
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dot_gamma_tw = 0.0_pReal
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ddot_gamma_dtau = 0.0_pReal
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end where significantStress
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else isFCC
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do i = 1, prm%sum_N_tw
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error stop 'not implemented'
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tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
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if (tau > tol_math_check) then
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dot_gamma_tw(i) = 0.0_pReal
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if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
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else
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dot_gamma_tw(i) = 0.0_pReal
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if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal
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end if
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end do
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end if isFCC
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end associate
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if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw = ddot_gamma_dtau
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end subroutine kinetics_tw
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@ -1021,15 +1030,15 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
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real(pReal), dimension(param(ph)%sum_N_tr), optional, intent(out) :: &
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ddot_gamma_dtau_tr
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real, dimension(param(ph)%sum_N_tr) :: &
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ddot_gamma_dtau
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real :: &
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ratio_tau_s, &
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tau, tau_r, &
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dot_N_0, &
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x0, &
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Gamma, &
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mu, nu
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mu, nu, &
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P_ncs, dP_ncs_dtau, &
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P, dP_dtau
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integer, dimension(2) :: &
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s
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integer :: i
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@ -1043,29 +1052,32 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
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do i = 1, prm%sum_N_tr
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tau = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
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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
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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
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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)
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if (tau > tol_math_check .and. tau < tau_r) then
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if (tau > tol_math_check .and. tau < tau_r) then
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ratio_tau_s = (dst%tau_hat_tr(i,en)/tau)**prm%s(i)
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P = exp(-ratio_tau_s)
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dP_dTau = prm%s(i) * ratio_tau_s/tau * P
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s=prm%fcc_twinNucleationSlipPair(1:2,i)
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dot_N_0=(abs(dot_gamma_sl(s(1)))*(stt%rho_mob(s(2),en)+stt%rho_dip(s(2),en))+&
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abs(dot_gamma_sl(s(2)))*(stt%rho_mob(s(1),en)+stt%rho_dip(s(1),en)))/&
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(prm%L_tr*prm%b_sl(i))*(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau)))
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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))
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dot_gamma_tr(i) = dst%V_tr(i,en) * dot_N_0*exp(-ratio_tau_s)
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ddot_gamma_dtau(i) = (dot_gamma_tr(i)*prm%s(i)/tau)*ratio_tau_s
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P_ncs = 1.0_pReal-exp(-prm%V_cs/(K_B*T)*(tau_r-tau))
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dP_ncs_dtau = prm%V_cs / (K_B * T) * (P_ncs - 1.0_pReal)
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dot_gamma_tr(i) = dst%V_tr(i,en)*dot_N_0*P_ncs*P
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if (present(ddot_gamma_dtau_tr)) &
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ddot_gamma_dtau_tr(i) = dst%V_tr(i,en)*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
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else
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dot_gamma_tr(i) = 0.0_pReal
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ddot_gamma_dtau(i) = 0.0_pReal
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if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr(i) = 0.0_pReal
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end if
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end do
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end associate
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if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr = ddot_gamma_dtau
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end subroutine kinetics_tr
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end submodule dislotwin
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