notation as in paper

This commit is contained in:
Martin Diehl 2021-07-21 15:03:28 +02:00
parent b2e94974ca
commit 8259cb3cdc
2 changed files with 93 additions and 104 deletions

View File

@ -18,6 +18,8 @@ submodule(phase:plastic) kinehardening
h_inf_b, & !< asymptotic hardening rate of back stress for each slip
xi_inf_f, &
xi_inf_b
real(pReal), allocatable, dimension(:,:) :: &
h_sl_sl !< slip resistance from slip activity
real(pReal), allocatable, dimension(:,:,:) :: &
P, &
nonSchmid_pos, &
@ -122,7 +124,7 @@ module function plastic_kinehardening_init() result(myPlasticity)
prm%nonSchmid_pos = prm%P
prm%nonSchmid_neg = prm%P
endif
prm%interaction_SlipSlip = lattice_interaction_SlipBySlip(N_sl, &
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl, &
pl%get_as1dFloat('h_sl-sl'), &
phase%get_asString('lattice'))
@ -158,7 +160,7 @@ module function plastic_kinehardening_init() result(myPlasticity)
else slipActive
xi_0 = emptyRealArray
allocate(prm%xi_inf_f,prm%xi_inf_b,prm%h_0_f,prm%h_inf_f,prm%h_0_b,prm%h_inf_b,source=emptyRealArray)
allocate(prm%interaction_SlipSlip(0,0))
allocate(prm%h_sl_sl(0,0))
endif slipActive
!--------------------------------------------------------------------------------------------------
@ -288,7 +290,7 @@ module subroutine plastic_kinehardening_dotState(Mp,ph,en)
sumGamma = sum(stt%accshear(:,en))
dot%crss(:,en) = matmul(prm%interaction_SlipSlip,dot%accshear(:,en)) &
dot%crss(:,en) = matmul(prm%h_sl_sl,dot%accshear(:,en)) &
* ( prm%h_inf_f &
+ (prm%h_0_f - prm%h_inf_f + prm%h_0_f*prm%h_inf_f*sumGamma/prm%xi_inf_f) &
* exp(-sumGamma*prm%h_0_f/prm%xi_inf_f) &

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@ -46,10 +46,10 @@ submodule(phase:plastic) phenopowerlaw
type :: tPhenopowerlawState
real(pReal), pointer, dimension(:,:) :: &
xi_slip, &
xi_twin, &
gamma_slip, &
gamma_twin
xi_sl, &
xi_tw, &
gamma_sl, &
gamma_tw
end type tPhenopowerlawState
!--------------------------------------------------------------------------------------------------
@ -235,30 +235,30 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
! state aliases and initialization
startIndex = 1
endIndex = prm%sum_N_sl
stt%xi_slip => plasticState(ph)%state (startIndex:endIndex,:)
stt%xi_slip = spread(xi_0_sl, 2, Nmembers)
dot%xi_slip => plasticState(ph)%dotState(startIndex:endIndex,:)
stt%xi_sl => plasticState(ph)%state (startIndex:endIndex,:)
stt%xi_sl = spread(xi_0_sl, 2, Nmembers)
dot%xi_sl => plasticState(ph)%dotState(startIndex:endIndex,:)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal)
if(any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_xi'
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_tw
stt%xi_twin => plasticState(ph)%state (startIndex:endIndex,:)
stt%xi_twin = spread(xi_0_tw, 2, Nmembers)
dot%xi_twin => plasticState(ph)%dotState(startIndex:endIndex,:)
stt%xi_tw => plasticState(ph)%state (startIndex:endIndex,:)
stt%xi_tw = spread(xi_0_tw, 2, Nmembers)
dot%xi_tw => plasticState(ph)%dotState(startIndex:endIndex,:)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal)
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%gamma_slip => plasticState(ph)%state (startIndex:endIndex,:)
dot%gamma_slip => plasticState(ph)%dotState(startIndex:endIndex,:)
stt%gamma_sl => plasticState(ph)%state (startIndex:endIndex,:)
dot%gamma_sl => plasticState(ph)%dotState(startIndex:endIndex,:)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_gamma',defaultVal=1.0e-6_pReal)
if(any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_gamma'
startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_tw
stt%gamma_twin => plasticState(ph)%state (startIndex:endIndex,:)
dot%gamma_twin => plasticState(ph)%dotState(startIndex:endIndex,:)
stt%gamma_tw => plasticState(ph)%state (startIndex:endIndex,:)
dot%gamma_tw => plasticState(ph)%dotState(startIndex:endIndex,:)
plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_gamma',defaultVal=1.0e-6_pReal)
end associate
@ -293,28 +293,28 @@ pure module subroutine phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
integer :: &
i,k,l,m,n
real(pReal), dimension(param(ph)%sum_N_sl) :: &
gdot_slip_pos,gdot_slip_neg, &
gdot_sl_pos,gdot_sl_neg, &
dgdot_dtauslip_pos,dgdot_dtauslip_neg
real(pReal), dimension(param(ph)%sum_N_tw) :: &
gdot_twin,dgdot_dtautwin
gdot_tw,dgdot_dtautwin
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
associate(prm => param(ph))
call kinetics_slip(Mp,ph,en,gdot_slip_pos,gdot_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg)
call kinetics_sl(Mp,ph,en,gdot_sl_pos,gdot_sl_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg)
slipSystems: do i = 1, prm%sum_N_sl
Lp = Lp + (gdot_slip_pos(i)+gdot_slip_neg(i))*prm%P_sl(1:3,1:3,i)
Lp = Lp + (gdot_sl_pos(i)+gdot_sl_neg(i))*prm%P_sl(1:3,1:3,i)
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) &
+ dgdot_dtauslip_pos(i) * prm%P_sl(k,l,i) * prm%nonSchmid_pos(m,n,i) &
+ dgdot_dtauslip_neg(i) * prm%P_sl(k,l,i) * prm%nonSchmid_neg(m,n,i)
enddo slipSystems
call kinetics_twin(Mp,ph,en,gdot_twin,dgdot_dtautwin)
call kinetics_tw(Mp,ph,en,gdot_tw,dgdot_dtautwin)
twinSystems: do i = 1, prm%sum_N_tw
Lp = Lp + gdot_twin(i)*prm%P_tw(1:3,1:3,i)
Lp = Lp + gdot_tw(i)*prm%P_tw(1:3,1:3,i)
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) &
+ dgdot_dtautwin(i)*prm%P_tw(k,l,i)*prm%P_tw(m,n,i)
@ -337,46 +337,33 @@ module subroutine phenopowerlaw_dotState(Mp,ph,en)
en
real(pReal) :: &
c_SlipSlip,c_TwinSlip,c_TwinTwin, &
xi_slip_sat_offset,&
sumGamma,sumF
xi_sl_sat_offset,&
sumF
real(pReal), dimension(param(ph)%sum_N_sl) :: &
left_SlipSlip,right_SlipSlip, &
gdot_slip_pos,gdot_slip_neg
gdot_sl_pos,gdot_sl_neg, &
right_SlipSlip
associate(prm => param(ph), stt => state(ph), &
dot => dotState(ph))
sumGamma = sum(stt%gamma_slip(:,en))
sumF = sum(stt%gamma_twin(:,en)/prm%gamma_char)
associate(prm => param(ph), stt => state(ph), dot => dotState(ph))
!--------------------------------------------------------------------------------------------------
! system-independent (nonlinear) prefactors to M_Xx (X influenced by x) matrices
c_SlipSlip = prm%h_0_sl_sl * (1.0_pReal + prm%c_1*sumF** prm%c_2)
c_TwinSlip = prm%h_0_tw_sl * sumGamma**prm%c_3
c_TwinTwin = prm%h_0_tw_tw * sumF**prm%c_4
call kinetics_sl(Mp,ph,en,gdot_sl_pos,gdot_sl_neg)
dot%gamma_sl(:,en) = abs(gdot_sl_pos+gdot_sl_neg)
call kinetics_tw(Mp,ph,en,dot%gamma_tw(:,en))
!--------------------------------------------------------------------------------------------------
! calculate left and right vectors
left_SlipSlip = 1.0_pReal + prm%h_int
xi_slip_sat_offset = prm%f_sat_sl_tw*sqrt(sumF)
right_SlipSlip = sign(abs(1.0_pReal-stt%xi_slip(:,en) / (prm%xi_inf_sl+xi_slip_sat_offset)) **prm%a_sl, &
1.0_pReal-stt%xi_slip(:,en) / (prm%xi_inf_sl+xi_slip_sat_offset))
!--------------------------------------------------------------------------------------------------
! shear rates
call kinetics_slip(Mp,ph,en,gdot_slip_pos,gdot_slip_neg)
dot%gamma_slip(:,en) = abs(gdot_slip_pos+gdot_slip_neg)
call kinetics_twin(Mp,ph,en,dot%gamma_twin(:,en))
sumF = sum(stt%gamma_tw(:,en)/prm%gamma_char)
xi_sl_sat_offset = prm%f_sat_sl_tw*sqrt(sumF)
right_SlipSlip = sign(abs(1.0_pReal-stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset)) **prm%a_sl, &
1.0_pReal-stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))
!--------------------------------------------------------------------------------------------------
! hardening
dot%xi_slip(:,en) = c_SlipSlip * left_SlipSlip * &
matmul(prm%h_sl_sl,dot%gamma_slip(:,en)*right_SlipSlip) &
+ matmul(prm%h_sl_tw,dot%gamma_twin(:,en))
dot%xi_sl(:,en) = prm%h_0_sl_sl * (1.0_pReal + prm%c_1*sumF** prm%c_2) * (1.0_pReal + prm%h_int) &
* matmul(prm%h_sl_sl,dot%gamma_sl(:,en)*right_SlipSlip) &
+ matmul(prm%h_sl_tw,dot%gamma_tw(:,en))
dot%xi_tw(:,en) = prm%h_0_tw_sl * sum(stt%gamma_sl(:,en))**prm%c_3 &
* matmul(prm%h_tw_sl,dot%gamma_sl(:,en)) &
+ prm%h_0_tw_tw * sumF**prm%c_4 * matmul(prm%h_tw_tw,dot%gamma_tw(:,en))
dot%xi_twin(:,en) = c_TwinSlip * matmul(prm%h_tw_sl,dot%gamma_slip(:,en)) &
+ c_TwinTwin * matmul(prm%h_tw_tw,dot%gamma_twin(:,en))
end associate
end subroutine phenopowerlaw_dotState
@ -397,17 +384,17 @@ module subroutine plastic_phenopowerlaw_results(ph,group)
select case(trim(prm%output(o)))
case('xi_sl')
if(prm%sum_N_sl>0) call results_writeDataset(stt%xi_slip,group,trim(prm%output(o)), &
if(prm%sum_N_sl>0) call results_writeDataset(stt%xi_sl,group,trim(prm%output(o)), &
'resistance against plastic slip','Pa')
case('gamma_sl')
if(prm%sum_N_sl>0) call results_writeDataset(stt%gamma_slip,group,trim(prm%output(o)), &
if(prm%sum_N_sl>0) call results_writeDataset(stt%gamma_sl,group,trim(prm%output(o)), &
'plastic shear','1')
case('xi_tw')
if(prm%sum_N_tw>0) call results_writeDataset(stt%xi_twin,group,trim(prm%output(o)), &
if(prm%sum_N_tw>0) call results_writeDataset(stt%xi_tw,group,trim(prm%output(o)), &
'resistance against twinning','Pa')
case('gamma_tw')
if(prm%sum_N_tw>0) call results_writeDataset(stt%gamma_twin,group,trim(prm%output(o)), &
if(prm%sum_N_tw>0) call results_writeDataset(stt%gamma_tw,group,trim(prm%output(o)), &
'twinning shear','1')
end select
@ -424,8 +411,8 @@ end subroutine plastic_phenopowerlaw_results
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end.
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics_slip(Mp,ph,en, &
gdot_slip_pos,gdot_slip_neg,dgdot_dtau_slip_pos,dgdot_dtau_slip_neg)
pure subroutine kinetics_sl(Mp,ph,en, &
gdot_sl_pos,gdot_sl_neg,dgdot_dtau_sl_pos,dgdot_dtau_sl_neg)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
@ -434,56 +421,56 @@ pure subroutine kinetics_slip(Mp,ph,en, &
en
real(pReal), intent(out), dimension(param(ph)%sum_N_sl) :: &
gdot_slip_pos, &
gdot_slip_neg
gdot_sl_pos, &
gdot_sl_neg
real(pReal), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
dgdot_dtau_slip_pos, &
dgdot_dtau_slip_neg
dgdot_dtau_sl_pos, &
dgdot_dtau_sl_neg
real(pReal), dimension(param(ph)%sum_N_sl) :: &
tau_slip_pos, &
tau_slip_neg
tau_sl_pos, &
tau_sl_neg
integer :: i
associate(prm => param(ph), stt => state(ph))
do i = 1, prm%sum_N_sl
tau_slip_pos(i) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,i))
tau_slip_neg(i) = merge(math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,i)), &
tau_sl_pos(i) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,i))
tau_sl_neg(i) = merge(math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,i)), &
0.0_pReal, prm%nonSchmidActive)
enddo
where(dNeq0(tau_slip_pos))
gdot_slip_pos = prm%dot_gamma_0_sl * merge(0.5_pReal,1.0_pReal, prm%nonSchmidActive) & ! 1/2 if non-Schmid active
* sign(abs(tau_slip_pos/stt%xi_slip(:,en))**prm%n_sl, tau_slip_pos)
where(dNeq0(tau_sl_pos))
gdot_sl_pos = prm%dot_gamma_0_sl * merge(0.5_pReal,1.0_pReal, prm%nonSchmidActive) & ! 1/2 if non-Schmid active
* sign(abs(tau_sl_pos/stt%xi_sl(:,en))**prm%n_sl, tau_sl_pos)
else where
gdot_slip_pos = 0.0_pReal
gdot_sl_pos = 0.0_pReal
end where
where(dNeq0(tau_slip_neg))
gdot_slip_neg = prm%dot_gamma_0_sl * 0.5_pReal & ! only used if non-Schmid active, always 1/2
* sign(abs(tau_slip_neg/stt%xi_slip(:,en))**prm%n_sl, tau_slip_neg)
where(dNeq0(tau_sl_neg))
gdot_sl_neg = prm%dot_gamma_0_sl * 0.5_pReal & ! only used if non-Schmid active, always 1/2
* sign(abs(tau_sl_neg/stt%xi_sl(:,en))**prm%n_sl, tau_sl_neg)
else where
gdot_slip_neg = 0.0_pReal
gdot_sl_neg = 0.0_pReal
end where
if (present(dgdot_dtau_slip_pos)) then
where(dNeq0(gdot_slip_pos))
dgdot_dtau_slip_pos = gdot_slip_pos*prm%n_sl/tau_slip_pos
if (present(dgdot_dtau_sl_pos)) then
where(dNeq0(gdot_sl_pos))
dgdot_dtau_sl_pos = gdot_sl_pos*prm%n_sl/tau_sl_pos
else where
dgdot_dtau_slip_pos = 0.0_pReal
dgdot_dtau_sl_pos = 0.0_pReal
end where
endif
if (present(dgdot_dtau_slip_neg)) then
where(dNeq0(gdot_slip_neg))
dgdot_dtau_slip_neg = gdot_slip_neg*prm%n_sl/tau_slip_neg
if (present(dgdot_dtau_sl_neg)) then
where(dNeq0(gdot_sl_neg))
dgdot_dtau_sl_neg = gdot_sl_neg*prm%n_sl/tau_sl_neg
else where
dgdot_dtau_slip_neg = 0.0_pReal
dgdot_dtau_sl_neg = 0.0_pReal
end where
endif
end associate
end subroutine kinetics_slip
end subroutine kinetics_sl
!--------------------------------------------------------------------------------------------------
@ -493,8 +480,8 @@ end subroutine kinetics_slip
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end.
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics_twin(Mp,ph,en,&
gdot_twin,dgdot_dtau_twin)
pure subroutine kinetics_tw(Mp,ph,en,&
gdot_tw,dgdot_dtau_tw)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
@ -503,37 +490,37 @@ pure subroutine kinetics_twin(Mp,ph,en,&
en
real(pReal), dimension(param(ph)%sum_N_tw), intent(out) :: &
gdot_twin
gdot_tw
real(pReal), dimension(param(ph)%sum_N_tw), intent(out), optional :: &
dgdot_dtau_twin
dgdot_dtau_tw
real(pReal), dimension(param(ph)%sum_N_tw) :: &
tau_twin
tau_tw
integer :: i
associate(prm => param(ph), stt => state(ph))
do i = 1, prm%sum_N_tw
tau_twin(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
tau_tw(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
enddo
where(tau_twin > 0.0_pReal)
gdot_twin = (1.0_pReal-sum(stt%gamma_twin(:,en)/prm%gamma_char)) & ! only twin in untwinned volume fraction
* prm%dot_gamma_0_tw*(abs(tau_twin)/stt%xi_twin(:,en))**prm%n_tw
where(tau_tw > 0.0_pReal)
gdot_tw = (1.0_pReal-sum(stt%gamma_tw(:,en)/prm%gamma_char)) & ! only twin in untwinned volume fraction
* prm%dot_gamma_0_tw*(abs(tau_tw)/stt%xi_tw(:,en))**prm%n_tw
else where
gdot_twin = 0.0_pReal
gdot_tw = 0.0_pReal
end where
if (present(dgdot_dtau_twin)) then
where(dNeq0(gdot_twin))
dgdot_dtau_twin = gdot_twin*prm%n_tw/tau_twin
if (present(dgdot_dtau_tw)) then
where(dNeq0(gdot_tw))
dgdot_dtau_tw = gdot_tw*prm%n_tw/tau_tw
else where
dgdot_dtau_twin = 0.0_pReal
dgdot_dtau_tw = 0.0_pReal
end where
endif
end associate
end subroutine kinetics_twin
end subroutine kinetics_tw
end submodule phenopowerlaw