adapted dislotungsten; does not converge with large(r) coefficients...
This commit is contained in:
Philip Eisenlohr
parent
715bc1bb83
commit
dd3d5483d6
2
PRIVATE
2
PRIVATE
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@ -1 +1 @@
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Subproject commit b4a2af3be9551e267a10554b1692a81b935882fd
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Subproject commit 4125c71c17a7f876b9766c52f0d7ca7d5e8110a5
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@ -92,8 +92,9 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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real(pREAL),dimension(:), allocatable :: &
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f_edge, & !< edge character fraction of total dislocation density
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rho_mob_0, & !< initial dislocation density
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rho_dip_0, & !< initial dipole density
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a !< non-Schmid coefficients
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rho_dip_0 !< initial dipole density
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real(pREAL), dimension(:,:), allocatable :: &
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a_nS !< non-Schmid coefficients
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character(len=:), allocatable :: &
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refs, &
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extmsg
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@ -153,12 +154,14 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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prm%P_sl = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
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if (phase_lattice(ph) == 'cI') then
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a = pl%get_as1dReal('a_nonSchmid_110',defaultVal = emptyRealArray)
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prm%P_nS_pos = crystal_nonSchmidMatrix(N_sl,a,+1)
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prm%P_nS_neg = crystal_nonSchmidMatrix(N_sl,a,-1)
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allocate(a_nS(3,size(pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray))))
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a_nS(1,:) = pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray)
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prm%P_nS_pos = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=+1)
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prm%P_nS_neg = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=-1)
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deallocate(a_nS)
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else
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prm%P_nS_pos = prm%P_sl
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prm%P_nS_neg = prm%P_sl
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prm%P_nS_pos = +prm%P_sl
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prm%P_nS_neg = -prm%P_sl
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end if
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prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal=.false.)
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@ -280,9 +283,9 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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Lp !< plastic velocity gradient
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real(pREAL), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pREAL), dimension(3,3), intent(in) :: &
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real(pREAL), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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integer, intent(in) :: &
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ph, &
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en
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@ -291,8 +294,7 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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real(pREAL) :: &
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T !< temperature
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_pos,dot_gamma_neg, &
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ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
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dot_gamma, ddot_gamma_dtau
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T = thermal_T(ph,en)
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@ -301,13 +303,14 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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associate(prm => param(ph))
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call kinetics(Mp,T,ph,en,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
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call kinetics(Mp,T,ph,en, dot_gamma,ddot_gamma_dtau)
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do i = 1, prm%sum_N_sl
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Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%P_sl(1:3,1:3,i)
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Lp = Lp + dot_gamma(i)*prm%P_sl(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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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) &
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+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i)
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+ ddot_gamma_dtau(i) * prm%P_sl(k,l,i) &
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* merge(prm%P_nS_pos(m,n,i), &
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prm%P_nS_neg(m,n,i), dot_gamma(i)>0.0_pREAL)
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end do
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end associate
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@ -329,52 +332,50 @@ module function dislotungsten_dotState(Mp,ph,en) result(dotState)
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dotState
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_pos, dot_gamma_neg,&
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tau_pos,&
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tau_neg, &
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tau_eff, &
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v_cl, &
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dot_rho_dip_formation, &
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dot_rho_dip_climb, &
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d_hat
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real(pREAL) :: &
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mu, T
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mu, nu, T
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), &
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dot_rho_mob => dotState(indexDotState(ph)%rho_mob(1):indexDotState(ph)%rho_mob(2)), &
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dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
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dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
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dot_gamma => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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T = thermal_T(ph,en)
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call kinetics(Mp,T,ph,en,&
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dot_gamma_pos,dot_gamma_neg, &
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tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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dot_gamma, tau = tau_eff)
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dot_gamma_sl = abs(dot_gamma_pos+dot_gamma_neg)
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dot_gamma = abs(dot_gamma)
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where(dEq0((tau_pos+tau_neg)*0.5_pREAL))
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where(dEq0(dot_gamma))
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dot_rho_dip_formation = 0.0_pREAL
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dot_rho_dip_climb = 0.0_pREAL
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else where
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d_hat = math_clip(3.0_pREAL*mu*prm%b_sl/(16.0_pREAL*PI*abs(tau_pos+tau_neg)*0.5_pREAL), &
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prm%d_caron, & ! lower limit
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dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pREAL*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot_gamma_sl/prm%b_sl, &
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d_hat = math_clip(mu*prm%b_sl/(8.0_pREAL*PI*(1.0_pREAL-nu)*tau_eff), &
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left = prm%d_caron, & ! lower limit
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right = dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(dot_gamma * 2.0_pREAL*(d_hat-prm%d_caron)/prm%b_sl * stt%rho_mob(:,en), &
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0.0_pREAL, &
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prm%dipoleformation)
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v_cl = (3.0_pREAL*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(TAU*K_B*T)) &
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v_cl = (3.0_pREAL*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(2.0_pREAL*PI*K_B*T)) &
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* (1.0_pREAL/(d_hat+prm%d_caron))
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dot_rho_dip_climb = (4.0_pREAL*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot_rho_mob = dot_gamma_sl/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- (2.0_pREAL*prm%d_caron)/prm%b_sl*stt%rho_mob(:,en)*dot_gamma_sl ! Spontaneous annihilation of 2 edges
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dot_rho_mob = dot_gamma / (prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_mob(:,en) ! spontaneous annihilation of 2 edges
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dot_rho_dip = dot_rho_dip_formation &
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- (2.0_pREAL*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot_gamma_sl & ! Spontaneous annihilation of an edge with a dipole
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- dot_rho_dip_climb
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- dot_rho_dip_climb &
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- dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_dip(:,en) ! spontaneous annihilation of an edge with a dipole
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end associate
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@ -457,51 +458,44 @@ end subroutine plastic_dislotungsten_result
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! at the end since some of them are optional.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics(Mp,T,ph,en, &
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dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out)
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dot_gamma,ddot_gamma_dtau,tau)
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real(pREAL), dimension(3,3), intent(in) :: &
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real(pREAL), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pREAL), intent(in) :: &
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real(pREAL), intent(in) :: &
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T !< temperature
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integer, intent(in) :: &
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integer, intent(in) :: &
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ph, &
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en
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real(pREAL), intent(out), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_pos, &
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dot_gamma_neg
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real(pREAL), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
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ddot_gamma_dtau_pos, &
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ddot_gamma_dtau_neg, &
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tau_pos_out, &
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tau_neg_out
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real(pREAL), dimension(param(ph)%sum_N_sl), intent(out) :: &
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dot_gamma
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real(pREAL), dimension(param(ph)%sum_N_sl), optional, intent(out) :: &
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ddot_gamma_dtau, &
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tau
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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StressRatio, &
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StressRatio_p,StressRatio_pminus1, &
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dvel, &
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tau_pos, tau_neg, tau_eff, &
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t_n, t_k, dtk,dtn
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integer :: j
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t_n,t_k, dtk,dtn
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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 j = 1, prm%sum_N_sl
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tau_pos(j) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,j))
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tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j))
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end do
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tau_pos = [(math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i)),i=1,prm%sum_N_sl)]
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tau_neg = [(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)),i=1,prm%sum_N_sl)]
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tau_eff = math_clip(merge(tau_pos,tau_neg, tau_pos>tau_neg) - dst%tau_pass(:,en),left = 0.0_pREAL)
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if (present(tau_pos_out)) tau_pos_out = tau_pos
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if (present(tau_neg_out)) tau_neg_out = tau_neg
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if (present(tau)) tau = tau_eff
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associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
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b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pREAL, &
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b_rho => stt%rho_mob(:,en) * prm%b_sl, &
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effectiveLength => dst%Lambda_sl(:,en) - prm%w)
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tau_eff = abs(tau_pos)-dst%tau_pass(:,en)
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significantPositiveTau: where(tau_eff > tol_math_check)
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where(tau_eff > tol_math_check)
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StressRatio = tau_eff/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL)
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@ -510,53 +504,21 @@ pure subroutine kinetics(Mp,T,ph,en, &
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/ (prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14)
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dot_gamma_pos = b_rho_half * sign(prm%h/(t_n + t_k),tau_pos)
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else where significantPositiveTau
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dot_gamma_pos = 0.0_pREAL
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end where significantPositiveTau
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dot_gamma = b_rho * prm%h/(t_n + t_k) * merge(+1.0_pREAL,-1.0_pREAL, tau_pos>tau_neg)
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else where
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dot_gamma = 0.0_pREAL
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end where
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if (present(ddot_gamma_dtau_pos)) then
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significantPositiveTau2: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
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if (present(ddot_gamma_dtau)) then
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where(tau_eff > tol_math_check)
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dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) &
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* StressRatio_pminus1 / prm%tau_Peierls
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dtk = -1.0_pREAL * t_k / tau_pos
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dtk = -1.0_pREAL * t_k / tau_eff
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dvel = -1.0_pREAL * prm%h * (dtk + dtn) / (t_n + t_k)**2
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ddot_gamma_dtau_pos = b_rho_half * dvel
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else where significantPositiveTau2
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ddot_gamma_dtau_pos = 0.0_pREAL
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end where significantPositiveTau2
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end if
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tau_eff = abs(tau_neg)-dst%tau_pass(:,en)
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significantNegativeTau: where(tau_eff > tol_math_check)
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StressRatio = tau_eff/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL)
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t_n = prm%b_sl*exp(BoltzmannRatio*(1.0_pREAL-StressRatio_p) ** prm%q) &
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/ (prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14)
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dot_gamma_neg = b_rho_half * sign(prm%h/(t_n + t_k),tau_neg)
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else where significantNegativeTau
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dot_gamma_neg = 0.0_pREAL
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end where significantNegativeTau
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if (present(ddot_gamma_dtau_neg)) then
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significantNegativeTau2: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
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dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) &
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* StressRatio_pminus1 / prm%tau_Peierls
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dtk = -1.0_pREAL * t_k / tau_neg
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dvel = -1.0_pREAL * prm%h * (dtk + dtn) / (t_n + t_k)**2
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ddot_gamma_dtau_neg = b_rho_half * dvel
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else where significantNegativeTau2
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ddot_gamma_dtau_neg = 0.0_pREAL
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end where significantNegativeTau2
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ddot_gamma_dtau = -1.0_pREAL * dot_gamma * (dtn + dtk) / (t_n + t_k)
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else where
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ddot_gamma_dtau = 0.0_pREAL
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end where
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end if
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end associate
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