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adapted dislotungsten; does not converge with large(r) coefficients...

This commit is contained in:
Philip Eisenlohr 2023-09-15 21:20:55 -04:00
parent 715bc1bb83
commit dd3d5483d6
2 changed files with 64 additions and 102 deletions
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2
PRIVATE

@ -1 +1 @@
Subproject commit b4a2af3be9551e267a10554b1692a81b935882fd Subproject commit 4125c71c17a7f876b9766c52f0d7ca7d5e8110a5

164
src/phase_mechanical_plastic_dislotungsten.f90
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@ -92,8 +92,9 @@ module function plastic_dislotungsten_init() result(myPlasticity)
real(pREAL),dimension(:), allocatable :: & real(pREAL),dimension(:), allocatable :: &
f_edge, & !< edge character fraction of total dislocation density f_edge, & !< edge character fraction of total dislocation density
rho_mob_0, & !< initial dislocation density rho_mob_0, & !< initial dislocation density
rho_dip_0, & !< initial dipole density rho_dip_0 !< initial dipole density
a !< non-Schmid coefficients real(pREAL), dimension(:,:), allocatable :: &
a_nS !< non-Schmid coefficients
character(len=:), allocatable :: & character(len=:), allocatable :: &
refs, & refs, &
extmsg extmsg
@ -153,12 +154,14 @@ module function plastic_dislotungsten_init() result(myPlasticity)
prm%P_sl = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph)) prm%P_sl = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
if (phase_lattice(ph) == 'cI') then if (phase_lattice(ph) == 'cI') then
a = pl%get_as1dReal('a_nonSchmid_110',defaultVal = emptyRealArray) allocate(a_nS(3,size(pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray))))
prm%P_nS_pos = crystal_nonSchmidMatrix(N_sl,a,+1) a_nS(1,:) = pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray)
prm%P_nS_neg = crystal_nonSchmidMatrix(N_sl,a,-1) prm%P_nS_pos = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=+1)
prm%P_nS_neg = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=-1)
deallocate(a_nS)
else else
prm%P_nS_pos = prm%P_sl prm%P_nS_pos = +prm%P_sl
prm%P_nS_neg = prm%P_sl prm%P_nS_neg = -prm%P_sl
end if end if
prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal=.false.) prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal=.false.)
@ -280,9 +283,9 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
Lp !< plastic velocity gradient Lp !< plastic velocity gradient
real(pREAL), dimension(3,3,3,3), intent(out) :: & real(pREAL), dimension(3,3,3,3), intent(out) :: &
dLp_dMp !< derivative of Lp with respect to the Mandel stress dLp_dMp !< derivative of Lp with respect to the Mandel stress
real(pREAL), dimension(3,3), intent(in) :: & real(pREAL), dimension(3,3), intent(in) :: &
Mp !< Mandel stress Mp !< Mandel stress
integer, intent(in) :: & integer, intent(in) :: &
ph, & ph, &
en en
@ -291,8 +294,7 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
real(pREAL) :: & real(pREAL) :: &
T !< temperature T !< temperature
real(pREAL), dimension(param(ph)%sum_N_sl) :: & real(pREAL), dimension(param(ph)%sum_N_sl) :: &
dot_gamma_pos,dot_gamma_neg, & dot_gamma, ddot_gamma_dtau
ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
T = thermal_T(ph,en) T = thermal_T(ph,en)
@ -301,13 +303,14 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
associate(prm => param(ph)) associate(prm => param(ph))
call kinetics(Mp,T,ph,en,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg) call kinetics(Mp,T,ph,en, dot_gamma,ddot_gamma_dtau)
do i = 1, prm%sum_N_sl do i = 1, prm%sum_N_sl
Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%P_sl(1:3,1:3,i) Lp = Lp + dot_gamma(i)*prm%P_sl(1:3,1:3,i)
forall (k=1:3,l=1:3,m=1:3,n=1:3) & forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) & dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) & + ddot_gamma_dtau(i) * prm%P_sl(k,l,i) &
+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i) * merge(prm%P_nS_pos(m,n,i), &
prm%P_nS_neg(m,n,i), dot_gamma(i)>0.0_pREAL)
end do end do
end associate end associate
@ -329,52 +332,50 @@ module function dislotungsten_dotState(Mp,ph,en) result(dotState)
dotState dotState
real(pREAL), dimension(param(ph)%sum_N_sl) :: & real(pREAL), dimension(param(ph)%sum_N_sl) :: &
dot_gamma_pos, dot_gamma_neg,& tau_eff, &
tau_pos,&
tau_neg, &
v_cl, & v_cl, &
dot_rho_dip_formation, & dot_rho_dip_formation, &
dot_rho_dip_climb, & dot_rho_dip_climb, &
d_hat d_hat
real(pREAL) :: & real(pREAL) :: &
mu, T mu, nu, T
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), & associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), &
dot_rho_mob => dotState(indexDotState(ph)%rho_mob(1):indexDotState(ph)%rho_mob(2)), & dot_rho_mob => dotState(indexDotState(ph)%rho_mob(1):indexDotState(ph)%rho_mob(2)), &
dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), & dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2))) dot_gamma => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
mu = elastic_mu(ph,en,prm%isotropic_bound) mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
T = thermal_T(ph,en) T = thermal_T(ph,en)
call kinetics(Mp,T,ph,en,& call kinetics(Mp,T,ph,en,&
dot_gamma_pos,dot_gamma_neg, & dot_gamma, tau = tau_eff)
tau_pos_out = tau_pos,tau_neg_out = tau_neg)
dot_gamma_sl = abs(dot_gamma_pos+dot_gamma_neg) dot_gamma = abs(dot_gamma)
where(dEq0((tau_pos+tau_neg)*0.5_pREAL)) where(dEq0(dot_gamma))
dot_rho_dip_formation = 0.0_pREAL dot_rho_dip_formation = 0.0_pREAL
dot_rho_dip_climb = 0.0_pREAL dot_rho_dip_climb = 0.0_pREAL
else where else where
d_hat = math_clip(3.0_pREAL*mu*prm%b_sl/(16.0_pREAL*PI*abs(tau_pos+tau_neg)*0.5_pREAL), & d_hat = math_clip(mu*prm%b_sl/(8.0_pREAL*PI*(1.0_pREAL-nu)*tau_eff), &
prm%d_caron, & ! lower limit left = prm%d_caron, & ! lower limit
dst%Lambda_sl(:,en)) ! upper limit right = dst%Lambda_sl(:,en)) ! upper limit
dot_rho_dip_formation = merge(2.0_pREAL*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot_gamma_sl/prm%b_sl, & dot_rho_dip_formation = merge(dot_gamma * 2.0_pREAL*(d_hat-prm%d_caron)/prm%b_sl * stt%rho_mob(:,en), &
0.0_pREAL, & 0.0_pREAL, &
prm%dipoleformation) prm%dipoleformation)
v_cl = (3.0_pREAL*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(TAU*K_B*T)) & 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)) &
* (1.0_pREAL/(d_hat+prm%d_caron)) * (1.0_pREAL/(d_hat+prm%d_caron))
dot_rho_dip_climb = (4.0_pREAL*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency? dot_rho_dip_climb = (4.0_pREAL*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
end where end where
dot_rho_mob = dot_gamma_sl/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication dot_rho_mob = dot_gamma / (prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
- dot_rho_dip_formation & - dot_rho_dip_formation &
- (2.0_pREAL*prm%d_caron)/prm%b_sl*stt%rho_mob(:,en)*dot_gamma_sl ! Spontaneous annihilation of 2 edges - dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_mob(:,en) ! spontaneous annihilation of 2 edges
dot_rho_dip = dot_rho_dip_formation & dot_rho_dip = dot_rho_dip_formation &
- (2.0_pREAL*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot_gamma_sl & ! Spontaneous annihilation of an edge with a dipole - dot_rho_dip_climb &
- dot_rho_dip_climb - dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_dip(:,en) ! spontaneous annihilation of an edge with a dipole
end associate end associate
@ -457,51 +458,44 @@ end subroutine plastic_dislotungsten_result
! at the end since some of them are optional. ! at the end since some of them are optional.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure subroutine kinetics(Mp,T,ph,en, & pure subroutine kinetics(Mp,T,ph,en, &
dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out) dot_gamma,ddot_gamma_dtau,tau)
real(pREAL), dimension(3,3), intent(in) :: & real(pREAL), dimension(3,3), intent(in) :: &
Mp !< Mandel stress Mp !< Mandel stress
real(pREAL), intent(in) :: & real(pREAL), intent(in) :: &
T !< temperature T !< temperature
integer, intent(in) :: & integer, intent(in) :: &
ph, & ph, &
en en
real(pREAL), intent(out), dimension(param(ph)%sum_N_sl) :: & real(pREAL), dimension(param(ph)%sum_N_sl), intent(out) :: &
dot_gamma_pos, & dot_gamma
dot_gamma_neg real(pREAL), dimension(param(ph)%sum_N_sl), optional, intent(out) :: &
real(pREAL), intent(out), optional, dimension(param(ph)%sum_N_sl) :: & ddot_gamma_dtau, &
ddot_gamma_dtau_pos, & tau
ddot_gamma_dtau_neg, &
tau_pos_out, &
tau_neg_out
real(pREAL), dimension(param(ph)%sum_N_sl) :: & real(pREAL), dimension(param(ph)%sum_N_sl) :: &
StressRatio, & StressRatio, &
StressRatio_p,StressRatio_pminus1, & StressRatio_p,StressRatio_pminus1, &
dvel, &
tau_pos, tau_neg, tau_eff, & tau_pos, tau_neg, tau_eff, &
t_n, t_k, dtk,dtn t_n,t_k, dtk,dtn
integer :: j integer :: i
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph)) associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
do j = 1, prm%sum_N_sl tau_pos = [(math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i)),i=1,prm%sum_N_sl)]
tau_pos(j) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,j)) tau_neg = [(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)),i=1,prm%sum_N_sl)]
tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j)) tau_eff = math_clip(merge(tau_pos,tau_neg, tau_pos>tau_neg) - dst%tau_pass(:,en),left = 0.0_pREAL)
end do
if (present(tau_pos_out)) tau_pos_out = tau_pos if (present(tau)) tau = tau_eff
if (present(tau_neg_out)) tau_neg_out = tau_neg
associate(BoltzmannRatio => prm%Q_s/(K_B*T), & associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pREAL, & b_rho => stt%rho_mob(:,en) * prm%b_sl, &
effectiveLength => dst%Lambda_sl(:,en) - prm%w) effectiveLength => dst%Lambda_sl(:,en) - prm%w)
tau_eff = abs(tau_pos)-dst%tau_pass(:,en)
significantPositiveTau: where(tau_eff > tol_math_check) where(tau_eff > tol_math_check)
StressRatio = tau_eff/prm%tau_Peierls StressRatio = tau_eff/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL) StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL)
@ -510,53 +504,21 @@ pure subroutine kinetics(Mp,T,ph,en, &
/ (prm%omega*effectiveLength) / (prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14) t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14)
dot_gamma_pos = b_rho_half * sign(prm%h/(t_n + t_k),tau_pos) dot_gamma = b_rho * prm%h/(t_n + t_k) * merge(+1.0_pREAL,-1.0_pREAL, tau_pos>tau_neg)
else where significantPositiveTau else where
dot_gamma_pos = 0.0_pREAL dot_gamma = 0.0_pREAL
end where significantPositiveTau end where
if (present(ddot_gamma_dtau_pos)) then if (present(ddot_gamma_dtau)) then
significantPositiveTau2: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check) where(tau_eff > tol_math_check)
dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) & dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) &
* StressRatio_pminus1 / prm%tau_Peierls * StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pREAL * t_k / tau_pos dtk = -1.0_pREAL * t_k / tau_eff
dvel = -1.0_pREAL * prm%h * (dtk + dtn) / (t_n + t_k)**2 ddot_gamma_dtau = -1.0_pREAL * dot_gamma * (dtn + dtk) / (t_n + t_k)
else where
ddot_gamma_dtau_pos = b_rho_half * dvel ddot_gamma_dtau = 0.0_pREAL
else where significantPositiveTau2 end where
ddot_gamma_dtau_pos = 0.0_pREAL
end where significantPositiveTau2
end if
tau_eff = abs(tau_neg)-dst%tau_pass(:,en)
significantNegativeTau: where(tau_eff > tol_math_check)
StressRatio = tau_eff/prm%tau_Peierls
StressRatio_p = StressRatio** prm%p
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL)
t_n = prm%b_sl*exp(BoltzmannRatio*(1.0_pREAL-StressRatio_p) ** prm%q) &
/ (prm%omega*effectiveLength)
t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14)
dot_gamma_neg = b_rho_half * sign(prm%h/(t_n + t_k),tau_neg)
else where significantNegativeTau
dot_gamma_neg = 0.0_pREAL
end where significantNegativeTau
if (present(ddot_gamma_dtau_neg)) then
significantNegativeTau2: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) &
* StressRatio_pminus1 / prm%tau_Peierls
dtk = -1.0_pREAL * t_k / tau_neg
dvel = -1.0_pREAL * prm%h * (dtk + dtn) / (t_n + t_k)**2
ddot_gamma_dtau_neg = b_rho_half * dvel
else where significantNegativeTau2
ddot_gamma_dtau_neg = 0.0_pREAL
end where significantNegativeTau2
end if end if
end associate end associate