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
commit
1d2bbc8cd9
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@ -17,17 +17,17 @@ 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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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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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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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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@ -40,14 +40,13 @@ submodule(phase:plastic) dislotwin
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Q_sl,& !< activation energy for glide [J] for each slip system
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v_0, & !< dislocation velocity prefactor [m/s] for each slip system
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dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system
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dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system
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t_tw, & !< twin thickness [m] for each twin system
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i_sl, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
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t_tr, & !< martensite lamellar thickness [m] for each trans system
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p, & !< p-exponent in glide velocity
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q, & !< q-exponent in glide velocity
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r, & !< r-exponent in twin nucleation rate
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s, & !< s-exponent in trans nucleation rate
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r, & !< exponent in twin nucleation rate
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s, & !< exponent in trans nucleation rate
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tau_0, & !< strength due to elements in solid solution
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gamma_char, & !< characteristic shear for twins
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B, & !< drag coefficient
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@ -102,11 +101,7 @@ submodule(phase:plastic) dislotwin
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Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite
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tau_pass, & !< threshold stress for slip
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tau_hat_tw, & !< threshold stress for twinning
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tau_hat_tr, & !< threshold stress for transformation
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V_tw, & !< volume of a new twin
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V_tr, & !< volume of a new martensite disc
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tau_r_tw, & !< stress to bring partials close together (twin)
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tau_r_tr !< stress to bring partials close together (trans)
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tau_hat_tr !< threshold stress for transformation
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end type tDislotwinDependentState
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!--------------------------------------------------------------------------------------------------
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@ -153,10 +148,10 @@ module function plastic_dislotwin_init() result(myPlasticity)
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print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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print'(/,1x,a)', 'A. Ma and F. Roters, Acta Materialia 52(12):3603–3612, 2004'
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print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2004.04.012'//IO_EOL
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print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2004.04.012'
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print'(/,1x,a)', 'F. Roters et al., Computational Materials Science 39:91–95, 2007'
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print'( 1x,a)', 'https://doi.org/10.1016/j.commatsci.2006.04.014'//IO_EOL
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print'( 1x,a)', 'https://doi.org/10.1016/j.commatsci.2006.04.014'
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print'(/,1x,a)', 'S.L. Wong et al., Acta Materialia 118:140–151, 2016'
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print'( 1x,a)', 'https://doi.org/10.1016/j.actamat.2016.07.032'
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@ -306,10 +301,10 @@ module function plastic_dislotwin_init() result(myPlasticity)
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prm%b_tr = pl%get_as1dFloat('b_tr')
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prm%b_tr = math_expand(prm%b_tr,prm%N_tr)
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prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%i_tr = pl%get_asFloat('i_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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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%x_c_tr = pl%get_asFloat('x_c_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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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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prm%a_cF = pl%get_asFloat('a_cF', defaultVal=0.0_pReal)
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@ -324,10 +319,6 @@ module function plastic_dislotwin_init() result(myPlasticity)
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prm%a_cI, &
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prm%a_cF)
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if (phase_lattice(ph) /= 'cF') then
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prm%dot_N_0_tr = pl%get_as1dFloat('dot_N_0_tr')
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prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,prm%N_tr)
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endif
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prm%t_tr = pl%get_as1dFloat('t_tr')
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prm%t_tr = math_expand(prm%t_tr,prm%N_tr)
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prm%s = pl%get_as1dFloat('p_tr',defaultVal=[0.0_pReal])
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@ -339,11 +330,8 @@ module function plastic_dislotwin_init() result(myPlasticity)
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if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr'
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if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr'
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if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' p_tr'
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if (phase_lattice(ph) /= 'cF') then
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if (any(prm%dot_N_0_tr < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tr'
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end if
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else transActive
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allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyRealArray)
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allocate(prm%s,prm%b_tr,prm%t_tr,source=emptyRealArray)
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allocate(prm%h_tr_tr(0,0))
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end if transActive
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@ -443,13 +431,9 @@ module function plastic_dislotwin_init() result(myPlasticity)
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allocate(dst%Lambda_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
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allocate(dst%tau_hat_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
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allocate(dst%tau_r_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
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allocate(dst%V_tw (prm%sum_N_tw,Nmembers),source=0.0_pReal)
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allocate(dst%Lambda_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
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allocate(dst%tau_hat_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
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allocate(dst%tau_r_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
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allocate(dst%V_tr (prm%sum_N_tr,Nmembers),source=0.0_pReal)
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end associate
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@ -656,12 +640,14 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
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dot_gamma_tr
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real(pReal) :: &
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mu, &
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nu
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nu, &
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Gamma
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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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@ -689,8 +675,7 @@ module subroutine dislotwin_dotState(Mp,T,ph,en)
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else
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! Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
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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) &
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* (prm%Gamma_sf(1) + prm%Gamma_sf(2) * T) / (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 / (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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@ -742,8 +727,6 @@ 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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@ -756,7 +739,7 @@ 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
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Gamma = prm%Gamma_sf(1) + prm%Gamma_sf(2) * (T-prm%T_ref)
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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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@ -786,16 +769,6 @@ module subroutine dislotwin_dependentState(T,ph,en)
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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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dst%V_tw(:,en) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,en)**2
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dst%V_tr(:,en) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,en)**2
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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
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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)
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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
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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)
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end associate
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end subroutine dislotwin_dependentState
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@ -959,48 +932,68 @@ 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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Ndot0, &
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stressRatio_r, &
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ddot_gamma_dtau
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integer :: i,s1,s2
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real :: &
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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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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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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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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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s1=prm%fcc_twinNucleationSlipPair(1,i)
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s2=prm%fcc_twinNucleationSlipPair(2,i)
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if (tau(i) < dst%tau_r_tw(i,en)) then ! ToDo: correct?
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Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,en)+stt%rho_dip(s2,en))+&
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abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,en)+stt%rho_dip(s1,en)))/&
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(prm%L_tw*prm%b_sl(i))*&
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(1.0_pReal-exp(-prm%V_cs/(K_B*T)*(dst%tau_r_tw(i,en)-tau(i))))
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else
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Ndot0=0.0_pReal
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end if
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else isFCC
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Ndot0=prm%dot_N_0_tw(i)
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end if isFCC
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end do
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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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significantStress: where(tau > tol_math_check)
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StressRatio_r = (dst%tau_hat_tw(:,en)/tau)**prm%r
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dot_gamma_tw = prm%gamma_char * dst%V_tw(:,en) * Ndot0*exp(-StressRatio_r)
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ddot_gamma_dtau = (dot_gamma_tw*prm%r/tau)*StressRatio_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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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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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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P = exp(-(dst%tau_hat_tw(i,en)/tau)**prm%r(i))
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dP_dTau = prm%r(i) * (dst%tau_hat_tw(i,en)/tau)**prm%r(i)/tau * P
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s = prm%fcc_twinNucleationSlipPair(1:2,i)
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dot_N_0 = sum(abs(dot_gamma_sl(s(2:1:-1)))*(stt%rho_mob(s,en)+stt%rho_dip(s,en))) &
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/ (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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V = PI/4.0_pReal*dst%Lambda_tw(i,en)**2*prm%t_tw(i)
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dot_gamma_tw(i) = V*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) = V*dot_N_0*(P*dP_ncs_dtau + P_ncs*dP_dtau)
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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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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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@ -1029,47 +1022,53 @@ 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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tau, &
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Ndot0, &
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stressRatio_s, &
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ddot_gamma_dtau
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integer :: i,s1,s2
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real :: &
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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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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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associate(prm => param(ph), stt => state(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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do i = 1, prm%sum_N_tr
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tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
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isFCC: if (prm%fccTwinTransNucleation) then
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s1=prm%fcc_twinNucleationSlipPair(1,i)
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||||
s2=prm%fcc_twinNucleationSlipPair(2,i)
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if (tau(i) < dst%tau_r_tr(i,en)) then ! ToDo: correct?
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||||
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)
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||||
end if isFCC
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||||
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
|
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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
|
||||
|
||||
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
|
||||
|
|
|
|||
|
|
@ -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, &
|
||||
|
|
|
|||
Loading…
Reference in New Issue