diff --git a/src/phase_mechanical_plastic_dislotwin.f90 b/src/phase_mechanical_plastic_dislotwin.f90 index 78681fa24..bc6fb0ee6 100644 --- a/src/phase_mechanical_plastic_dislotwin.f90 +++ b/src/phase_mechanical_plastic_dislotwin.f90 @@ -17,17 +17,17 @@ submodule(phase:plastic) dislotwin p_sb = 1.0_pReal, & !< p-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 - L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors - L_tr = 1.0_pReal, & !< Length of trans 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: TODO unit should be meters 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 V_cs = 1.0_pReal, & !< cross slip volume xi_sb = 1.0_pReal, & !< value for shearband resistance v_sb = 1.0_pReal, & !< value for shearband velocity_0 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 - h = 1.0_pReal, & !< Stack height of hex nucleus + h = 1.0_pReal, & !< stack height of hex nucleus T_ref = T_ROOM, & a_cI = 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 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_tr, & !< trans nucleation rate [1/m³s] for each trans system t_tw, & !< twin thickness [m] for each twin 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 p, & !< p-exponent in glide velocity q, & !< q-exponent in glide velocity - r, & !< r-exponent in twin nucleation rate - s, & !< s-exponent in trans nucleation rate + r, & !< exponent in twin nucleation rate + s, & !< exponent in trans nucleation rate tau_0, & !< strength due to elements in solid solution gamma_char, & !< characteristic shear for twins B, & !< drag coefficient @@ -102,11 +101,7 @@ submodule(phase:plastic) dislotwin Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite tau_pass, & !< threshold stress for slip tau_hat_tw, & !< threshold stress for twinning - 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) + tau_hat_tr !< threshold stress for transformation end type tDislotwinDependentState !-------------------------------------------------------------------------------------------------- @@ -153,10 +148,10 @@ module function plastic_dislotwin_init() result(myPlasticity) 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)', '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)', '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)', '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 = math_expand(prm%b_tr,prm%N_tr) - prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: How to handle that??? - prm%i_tr = pl%get_asFloat('i_tr', 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: This is not optional! 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%a_cI = pl%get_asFloat('a_cI', 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_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 = math_expand(prm%t_tr,prm%N_tr) 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 (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 (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 - 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)) 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%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%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 @@ -656,12 +640,14 @@ module subroutine dislotwin_dotState(Mp,T,ph,en) dot_gamma_tr real(pReal) :: & mu, & - nu + nu, & + Gamma associate(prm => param(ph), stt => state(ph), dot => dotState(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) f_matrix = 1.0_pReal & - sum(stt%f_tw(1:prm%sum_N_tw,en)) & @@ -689,8 +675,7 @@ module subroutine dislotwin_dotState(Mp,T,ph,en) else ! 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))) - b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) & - * (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (mu*prm%b_sl(i)), & + b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) * Gamma / (mu*prm%b_sl(i)), & 1.0_pReal, & prm%ExtendedDislocations) 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) :: & inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite f_over_t_tr - real(pReal), dimension(:), allocatable :: & - x0 real(pReal) :: & mu, & 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_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 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) & + 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 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) :: & ddot_gamma_dtau_tw - real, dimension(param(ph)%sum_N_tw) :: & - tau, & - Ndot0, & - stressRatio_r, & - ddot_gamma_dtau - - integer :: i,s1,s2 + real :: & + tau, tau_r, & + dot_N_0, & + x0, V, & + Gamma, & + 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)) - 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 - s1=prm%fcc_twinNucleationSlipPair(1,i) - s2=prm%fcc_twinNucleationSlipPair(2,i) - if (tau(i) < dst%tau_r_tw(i,en)) then ! ToDo: correct? - 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/(K_B*T)*(dst%tau_r_tw(i,en)-tau(i)))) - else - Ndot0=0.0_pReal - end if - else isFCC - Ndot0=prm%dot_N_0_tw(i) - end if isFCC - end do + isFCC: if (prm%fccTwinTransNucleation) then + mu = elastic_mu(ph,en) + nu = elastic_nu(ph,en) + Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref) - significantStress: where(tau > tol_math_check) - StressRatio_r = (dst%tau_hat_tw(:,en)/tau)**prm%r - dot_gamma_tw = prm%gamma_char * dst%V_tw(:,en) * Ndot0*exp(-StressRatio_r) - ddot_gamma_dtau = (dot_gamma_tw*prm%r/tau)*StressRatio_r - else where significantStress - dot_gamma_tw = 0.0_pReal - ddot_gamma_dtau = 0.0_pReal - end where significantStress + do i = 1, prm%sum_N_tw + tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,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 + 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 + + else isFCC + do i = 1, prm%sum_N_tw + error stop 'not implemented' + tau = math_tensordot(Mp,prm%P_tw(1:3,1:3,i)) + if (tau > tol_math_check) then + dot_gamma_tw(i) = 0.0_pReal + if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw(i) = 0.0_pReal + 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 - if (present(ddot_gamma_dtau_tw)) ddot_gamma_dtau_tw = ddot_gamma_dtau - 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) :: & ddot_gamma_dtau_tr - real, dimension(param(ph)%sum_N_tr) :: & - tau, & - Ndot0, & - stressRatio_s, & - ddot_gamma_dtau - integer :: i,s1,s2 + real :: & + tau, tau_r, & + dot_N_0, & + x0, V, & + Gamma, & + 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)) + 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 - tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i)) - isFCC: if (prm%fccTwinTransNucleation) then - s1=prm%fcc_twinNucleationSlipPair(1,i) - s2=prm%fcc_twinNucleationSlipPair(2,i) - if (tau(i) < dst%tau_r_tr(i,en)) then ! ToDo: correct? - 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/(K_B*T)*(dst%tau_r_tr(i,en)-tau(i)))) - else - Ndot0=0.0_pReal - end if - else isFCC - Ndot0=prm%dot_N_0_tr(i) - end if isFCC + tau = math_tensordot(Mp,prm%P_tr(1:3,1:3,i)) + 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 + 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 + + if (tau > tol_math_check .and. tau < tau_r) then + P = exp(-(dst%tau_hat_tr(i,en)/tau)**prm%s(i)) + dP_dTau = prm%s(i) * (dst%tau_hat_tr(i,en)/tau)**prm%s(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_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 + dot_gamma_tr(i) = 0.0_pReal + if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr(i) = 0.0_pReal + end if 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 - if (present(ddot_gamma_dtau_tr)) ddot_gamma_dtau_tr = ddot_gamma_dtau - end subroutine kinetics_tr end submodule dislotwin diff --git a/src/phase_mechanical_plastic_nonlocal.f90 b/src/phase_mechanical_plastic_nonlocal.f90 index 7118055fe..1715af2d9 100644 --- a/src/phase_mechanical_plastic_nonlocal.f90 +++ b/src/phase_mechanical_plastic_nonlocal.f90 @@ -203,7 +203,7 @@ module function plastic_nonlocal_init() result(myPlasticity) print'(/,a,i0)', ' # phases: ',Ninstances; flush(IO_STDOUT) 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)', 'http://publications.rwth-aachen.de/record/229993' @@ -1570,7 +1570,6 @@ subroutine stateInit(ini,phase,Nentries) upto, & s real(pReal), dimension(2) :: & - noise, & rnd real(pReal) :: & meanDensity, &