second order expansion of temperature-dependent variables
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Martin Diehl
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e7a999ffb1
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@ -25,14 +25,14 @@ submodule(phase:plastic) dislotwin
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xi_sb = 1.0_pReal, & !< value for shearband resistance
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v_sb = 1.0_pReal, & !< value for shearband velocity_0
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E_sb = 1.0_pReal, & !< activation energy for shear bands
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delta_G = 1.0_pReal, & !< free energy difference between austensite and martensite
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i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
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h = 1.0_pReal, & !< stack height of hex nucleus
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T_ref = T_ROOM, &
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a_cI = 1.0_pReal, &
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a_cF = 1.0_pReal
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real(pReal), dimension(2) :: &
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Gamma_sf = 0.0_pReal
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real(pReal), dimension(3) :: &
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Gamma_sf = 0.0_pReal, & !< stacking fault energy
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Delta_G = 0.0_pReal !< free energy difference between austensite and martensite
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real(pReal), allocatable, dimension(:) :: &
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b_sl, & !< absolute length of Burgers vector [m] for each slip system
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b_tw, & !< absolute length of Burgers vector [m] for each twin system
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@ -303,7 +303,9 @@ module function plastic_dislotwin_init() result(myPlasticity)
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prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: This is not optional!
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prm%i_tr = pl%get_asFloat('i_tr', defaultVal=0.0_pReal) ! ToDo: This is not optional!
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prm%delta_G = pl%get_asFloat('delta_G')
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prm%Delta_G(1) = pl%get_asFloat('Delta_G')
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prm%Delta_G(2) = pl%get_asFloat('Delta_G,T', defaultVal=0.0_pReal)
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prm%Delta_G(3) = pl%get_asFloat('Delta_G,T^2',defaultVal=0.0_pReal)
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prm%x_c_tr = pl%get_asFloat('x_c_tr', defaultVal=0.0_pReal) ! ToDo: This is not optional!
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prm%L_tr = pl%get_asFloat('L_tr')
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prm%a_cI = pl%get_asFloat('a_cI', defaultVal=0.0_pReal)
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@ -363,6 +365,7 @@ module function plastic_dislotwin_init() result(myPlasticity)
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prm%T_ref = pl%get_asFloat('T_ref')
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prm%Gamma_sf(1) = pl%get_asFloat('Gamma_sf')
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prm%Gamma_sf(2) = pl%get_asFloat('Gamma_sf,T',defaultVal=0.0_pReal)
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prm%Gamma_sf(3) = pl%get_asFloat('Gamma_sf,T^2',defaultVal=0.0_pReal)
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end if
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slipAndTwinActive: if (prm%sum_N_sl * prm%sum_N_tw > 0) then
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@ -559,7 +562,7 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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+ ddot_gamma_dtau_sl(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i)
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end do slipContribution
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call kinetics_tw(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tw,ddot_gamma_dtau_tw)
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if (prm%sum_N_tw > 0) call kinetics_tw(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tw,ddot_gamma_dtau_tw)
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twinContibution: do i = 1, prm%sum_N_tw
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Lp = Lp + dot_gamma_tw(i)*prm%P_tw(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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@ -567,7 +570,7 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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+ ddot_gamma_dtau_tw(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i)
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end do twinContibution
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call kinetics_tr(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tr,ddot_gamma_dtau_tr)
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if (prm%sum_N_tr > 0) call kinetics_tr(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tr,ddot_gamma_dtau_tr)
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transContibution: do i = 1, prm%sum_N_tr
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Lp = Lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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@ -641,13 +644,12 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
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real(pReal) :: &
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mu, &
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nu, &
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Gamma
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Gamma_sf
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associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph))
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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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f_matrix = 1.0_pReal &
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- sum(stt%f_tw(1:prm%sum_N_tw,en)) &
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@ -674,8 +676,11 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
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dot_rho_dip_climb(i) = 0.0_pReal
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else
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! Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
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Gamma_sf = prm%Gamma_sf(1) &
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+ prm%Gamma_sf(2) * (T-prm%T_ref) &
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+ prm%Gamma_sf(3) * (T-prm%T_ref)**2
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sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i)))
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b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) * Gamma / (mu*prm%b_sl(i)), &
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b_d = merge(24.0_pReal*PI*(1.0_pReal - nu)/(2.0_pReal + nu) * Gamma_sf / (mu*prm%b_sl(i)), &
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1.0_pReal, &
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prm%ExtendedDislocations)
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v_cl = 2.0_pReal*prm%omega*b_d**2*exp(-prm%Q_cl/(K_B*T)) &
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@ -695,10 +700,10 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
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- 2.0_pReal*prm%d_caron/prm%b_sl * stt%rho_dip(:,en)*abs(dot_gamma_sl) &
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- dot_rho_dip_climb
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call kinetics_tw(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tw)
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if (prm%sum_N_tw > 0) call kinetics_tw(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tw)
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dot%f_tw(:,en) = f_matrix*dot_gamma_tw/prm%gamma_char
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call kinetics_tr(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tr)
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if (prm%sum_N_tr > 0) call kinetics_tr(Mp,T,dot_gamma_sl,ph,en,dot_gamma_tr)
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dot%f_tr(:,en) = f_matrix*dot_gamma_tr
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end associate
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@ -718,7 +723,8 @@ module subroutine dislotwin_dependentState(T,ph,en)
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T
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real(pReal) :: &
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sumf_tw,Gamma,sumf_tr
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Gamma_sf, Delta_G, &
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sumf_tw, sumf_tr
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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inv_lambda_sl
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real(pReal), dimension(param(ph)%sum_N_tw) :: &
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@ -739,7 +745,12 @@ module subroutine dislotwin_dependentState(T,ph,en)
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sumf_tw = sum(stt%f_tw(1:prm%sum_N_tw,en))
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sumf_tr = sum(stt%f_tr(1:prm%sum_N_tr,en))
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Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
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Gamma_sf = prm%Gamma_sf(1) &
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+ prm%Gamma_sf(2) * (T-prm%T_ref) &
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+ prm%Gamma_sf(3) * (T-prm%T_ref)**2
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Delta_G = prm%Delta_G(1) &
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+ prm%Delta_G(2) * (T-prm%T_ref) &
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+ prm%Delta_G(3) * (T-prm%T_ref)**2
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!* rescaled volume fraction for topology
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f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,en)/prm%t_tw ! this is per system ...
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@ -763,11 +774,11 @@ module subroutine dislotwin_dependentState(T,ph,en)
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dst%tau_pass(:,en) = mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
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!* threshold stress for growing twin/martensite
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dst%tau_hat_tw(:,en) = Gamma/(3.0_pReal*prm%b_tw) &
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dst%tau_hat_tw(:,en) = Gamma_sf/(3.0_pReal*prm%b_tw) &
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+ 3.0_pReal*prm%b_tw*mu/(prm%L_tw*prm%b_tw)
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dst%tau_hat_tr(:,en) = Gamma/(3.0_pReal*prm%b_tr) &
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dst%tau_hat_tr(:,en) = Gamma_sf/(3.0_pReal*prm%b_tr) &
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+ 3.0_pReal*prm%b_tr*mu/(prm%L_tr*prm%b_tr) &
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+ prm%h*prm%delta_G/(3.0_pReal*prm%b_tr)
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+ prm%h*Delta_G/(3.0_pReal*prm%b_tr)
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end associate
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@ -936,7 +947,7 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
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tau, tau_r, &
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dot_N_0, &
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x0, V, &
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Gamma, &
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Gamma_sf, &
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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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@ -950,11 +961,13 @@ pure subroutine kinetics_tw(Mp,T,dot_gamma_sl,ph,en,&
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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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Gamma_sf = prm%Gamma_sf(1) &
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+ prm%Gamma_sf(2) * (T-prm%T_ref) &
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+ prm%Gamma_sf(3) * (T-prm%T_ref)**2
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do i = 1, prm%sum_N_tw
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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*(2.0_pReal+nu)/(Gamma*8.0_pReal*PI*(1.0_pReal-nu)) ! ToDo: In the paper, the Burgers vector for slip is used
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x0 = mu*prm%b_tw(i)**2*(2.0_pReal+nu)/(Gamma_sf*8.0_pReal*PI*(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) ! ToDo: In the paper, the Burgers vector for slip is used
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if (tau > tol_math_check .and. tau < tau_r) then
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@ -1026,7 +1039,7 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
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tau, tau_r, &
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dot_N_0, &
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x0, V, &
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Gamma, &
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Gamma_sf, &
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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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@ -1039,11 +1052,13 @@ pure subroutine kinetics_tr(Mp,T,dot_gamma_sl,ph,en,&
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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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Gamma_sf = prm%Gamma_sf(1) &
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+ prm%Gamma_sf(2) * (T-prm%T_ref) &
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+ prm%Gamma_sf(3) * (T-prm%T_ref)**2
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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*(2.0_pReal+nu)/(Gamma*8.0_pReal*PI*(1.0_pReal-nu)) ! ToDo: In the paper, the Burgers vector for slip is used
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x0 = mu*prm%b_tr(i)**2*(2.0_pReal+nu)/(Gamma_sf*8.0_pReal*PI*(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) ! ToDo: In the paper, the Burgers vector for slip is used
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if (tau > tol_math_check .and. tau < tau_r) then
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