551 lines
27 KiB
Fortran
551 lines
27 KiB
Fortran
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
|
|||
|
|
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
|
|||
|
|
!> @author David Cereceda, Lawrence Livermore National Laboratory
|
|||
|
|
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
|
|||
|
|
!> @brief crystal plasticity model for bcc metals, especially Tungsten
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
submodule(constitutive:constitutive_plastic) plastic_disloTungsten
|
|||
|
|
|
|||
|
|
real(pReal), parameter :: &
|
|||
|
|
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
|
|||
|
|
|
|||
|
|
type :: tParameters
|
|||
|
|
real(pReal) :: &
|
|||
|
|
D = 1.0_pReal, & !< grain size
|
|||
|
|
mu = 1.0_pReal, & !< equivalent shear modulus
|
|||
|
|
D_0 = 1.0_pReal, & !< prefactor for self-diffusion coefficient
|
|||
|
|
Q_cl = 1.0_pReal !< activation energy for dislocation climb
|
|||
|
|
real(pReal), allocatable, dimension(:) :: &
|
|||
|
|
b_sl, & !< magnitude of burgers vector [m]
|
|||
|
|
D_a, &
|
|||
|
|
i_sl, & !< Adj. parameter for distance between 2 forest dislocations
|
|||
|
|
atomicVolume, & !< factor to calculate atomic volume
|
|||
|
|
tau_0, & !< Peierls stress
|
|||
|
|
!* mobility law parameters
|
|||
|
|
delta_F, & !< activation energy for glide [J]
|
|||
|
|
v0, & !< dislocation velocity prefactor [m/s]
|
|||
|
|
p, & !< p-exponent in glide velocity
|
|||
|
|
q, & !< q-exponent in glide velocity
|
|||
|
|
B, & !< friction coefficient
|
|||
|
|
kink_height, & !< height of the kink pair
|
|||
|
|
w, & !< width of the kink pair
|
|||
|
|
omega !< attempt frequency for kink pair nucleation
|
|||
|
|
real(pReal), allocatable, dimension(:,:) :: &
|
|||
|
|
h_sl_sl, & !< slip resistance from slip activity
|
|||
|
|
forestProjection
|
|||
|
|
real(pReal), allocatable, dimension(:,:,:) :: &
|
|||
|
|
P_sl, &
|
|||
|
|
nonSchmid_pos, &
|
|||
|
|
nonSchmid_neg
|
|||
|
|
integer :: &
|
|||
|
|
sum_N_sl !< total number of active slip system
|
|||
|
|
character(len=pStringLen), allocatable, dimension(:) :: &
|
|||
|
|
output
|
|||
|
|
logical :: &
|
|||
|
|
dipoleFormation !< flag indicating consideration of dipole formation
|
|||
|
|
end type !< container type for internal constitutive parameters
|
|||
|
|
|
|||
|
|
type :: tDisloTungstenState
|
|||
|
|
real(pReal), dimension(:,:), pointer :: &
|
|||
|
|
rho_mob, &
|
|||
|
|
rho_dip, &
|
|||
|
|
gamma_sl
|
|||
|
|
end type tDisloTungstenState
|
|||
|
|
|
|||
|
|
type :: tDisloTungstendependentState
|
|||
|
|
real(pReal), dimension(:,:), allocatable :: &
|
|||
|
|
Lambda_sl, &
|
|||
|
|
threshold_stress
|
|||
|
|
end type tDisloTungstendependentState
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
! containers for parameters and state
|
|||
|
|
type(tParameters), allocatable, dimension(:) :: param
|
|||
|
|
type(tDisloTungstenState), allocatable, dimension(:) :: &
|
|||
|
|
dotState, &
|
|||
|
|
state
|
|||
|
|
type(tDisloTungstendependentState), allocatable, dimension(:) :: dependentState
|
|||
|
|
|
|||
|
|
contains
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Perform module initialization.
|
|||
|
|
!> @details reads in material parameters, allocates arrays, and does sanity checks
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
module function plastic_disloTungsten_init() result(myPlasticity)
|
|||
|
|
|
|||
|
|
logical, dimension(:), allocatable :: myPlasticity
|
|||
|
|
integer :: &
|
|||
|
|
Ninstance, &
|
|||
|
|
p, i, &
|
|||
|
|
NipcMyPhase, &
|
|||
|
|
sizeState, sizeDotState, &
|
|||
|
|
startIndex, endIndex
|
|||
|
|
integer, dimension(:), allocatable :: &
|
|||
|
|
N_sl
|
|||
|
|
real(pReal),dimension(:), allocatable :: &
|
|||
|
|
rho_mob_0, & !< initial dislocation density
|
|||
|
|
rho_dip_0, & !< initial dipole density
|
|||
|
|
a !< non-Schmid coefficients
|
|||
|
|
character(len=pStringLen) :: &
|
|||
|
|
extmsg = ''
|
|||
|
|
class(tNode), pointer :: &
|
|||
|
|
phases, &
|
|||
|
|
phase, &
|
|||
|
|
pl
|
|||
|
|
|
|||
|
|
write(6,'(/,a)') ' <<<+- plastic_disloTungsten init -+>>>'
|
|||
|
|
|
|||
|
|
write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78:242–256, 2016'
|
|||
|
|
write(6,'(a)') ' https://dx.doi.org/10.1016/j.ijplas.2015.09.002'
|
|||
|
|
|
|||
|
|
myPlasticity = plastic_active('disloTungsten')
|
|||
|
|
|
|||
|
|
Ninstance = count(myPlasticity)
|
|||
|
|
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance; flush(6)
|
|||
|
|
if(Ninstance == 0) return
|
|||
|
|
|
|||
|
|
allocate(param(Ninstance))
|
|||
|
|
allocate(state(Ninstance))
|
|||
|
|
allocate(dotState(Ninstance))
|
|||
|
|
allocate(dependentState(Ninstance))
|
|||
|
|
|
|||
|
|
phases => material_root%get('phase')
|
|||
|
|
i = 0
|
|||
|
|
do p = 1, phases%length
|
|||
|
|
phase => phases%get(p)
|
|||
|
|
|
|||
|
|
if(.not. myPlasticity(p)) cycle
|
|||
|
|
i = i + 1
|
|||
|
|
associate(prm => param(i), &
|
|||
|
|
dot => dotState(i), &
|
|||
|
|
stt => state(i), &
|
|||
|
|
dst => dependentState(i))
|
|||
|
|
pl => phase%get('plasticity')
|
|||
|
|
|
|||
|
|
#if defined (__GFORTRAN__)
|
|||
|
|
prm%output = output_asStrings(pl)
|
|||
|
|
#else
|
|||
|
|
prm%output = pl%get_asStrings('output',defaultVal=emptyStringArray)
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
! This data is read in already in lattice
|
|||
|
|
prm%mu = lattice_mu(p)
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
! slip related parameters
|
|||
|
|
N_sl = pl%get_asInts('N_sl',defaultVal=emptyIntArray)
|
|||
|
|
prm%sum_N_sl = sum(abs(N_sl))
|
|||
|
|
slipActive: if (prm%sum_N_sl > 0) then
|
|||
|
|
prm%P_sl = lattice_SchmidMatrix_slip(N_sl,phase%get_asString('lattice'),&
|
|||
|
|
phase%get_asFloat('c/a',defaultVal=0.0_pReal))
|
|||
|
|
|
|||
|
|
if(trim(phase%get_asString('lattice')) == 'bcc') then
|
|||
|
|
a = pl%get_asFloats('nonSchmid_coefficients',defaultVal = emptyRealArray)
|
|||
|
|
prm%nonSchmid_pos = lattice_nonSchmidMatrix(N_sl,a,+1)
|
|||
|
|
prm%nonSchmid_neg = lattice_nonSchmidMatrix(N_sl,a,-1)
|
|||
|
|
else
|
|||
|
|
prm%nonSchmid_pos = prm%P_sl
|
|||
|
|
prm%nonSchmid_neg = prm%P_sl
|
|||
|
|
endif
|
|||
|
|
|
|||
|
|
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_asFloats('h_sl_sl'), &
|
|||
|
|
phase%get_asString('lattice'))
|
|||
|
|
prm%forestProjection = lattice_forestProjection_edge(N_sl,phase%get_asString('lattice'),&
|
|||
|
|
phase%get_asFloat('c/a',defaultVal=0.0_pReal))
|
|||
|
|
prm%forestProjection = transpose(prm%forestProjection)
|
|||
|
|
|
|||
|
|
rho_mob_0 = pl%get_asFloats('rho_mob_0', requiredSize=size(N_sl))
|
|||
|
|
rho_dip_0 = pl%get_asFloats('rho_dip_0', requiredSize=size(N_sl))
|
|||
|
|
prm%v0 = pl%get_asFloats('v_0', requiredSize=size(N_sl))
|
|||
|
|
prm%b_sl = pl%get_asFloats('b_sl', requiredSize=size(N_sl))
|
|||
|
|
prm%delta_F = pl%get_asFloats('Q_s', requiredSize=size(N_sl))
|
|||
|
|
|
|||
|
|
prm%i_sl = pl%get_asFloats('i_sl', requiredSize=size(N_sl))
|
|||
|
|
prm%tau_0 = pl%get_asFloats('tau_peierls', requiredSize=size(N_sl))
|
|||
|
|
prm%p = pl%get_asFloats('p_sl', requiredSize=size(N_sl), &
|
|||
|
|
defaultVal=[(1.0_pReal,i=1,size(N_sl))])
|
|||
|
|
prm%q = pl%get_asFloats('q_sl', requiredSize=size(N_sl), &
|
|||
|
|
defaultVal=[(1.0_pReal,i=1,size(N_sl))])
|
|||
|
|
prm%kink_height = pl%get_asFloats('h', requiredSize=size(N_sl))
|
|||
|
|
prm%w = pl%get_asFloats('w', requiredSize=size(N_sl))
|
|||
|
|
prm%omega = pl%get_asFloats('omega', requiredSize=size(N_sl))
|
|||
|
|
prm%B = pl%get_asFloats('B', requiredSize=size(N_sl))
|
|||
|
|
|
|||
|
|
prm%D = pl%get_asFloat('D')
|
|||
|
|
prm%D_0 = pl%get_asFloat('D_0')
|
|||
|
|
prm%Q_cl = pl%get_asFloat('Q_cl')
|
|||
|
|
prm%atomicVolume = pl%get_asFloat('f_at') * prm%b_sl**3.0_pReal
|
|||
|
|
prm%D_a = pl%get_asFloat('D_a') * prm%b_sl
|
|||
|
|
|
|||
|
|
prm%dipoleformation = pl%get_asBool('dipole_formation_factor', defaultVal = .true.)
|
|||
|
|
|
|||
|
|
! expand: family => system
|
|||
|
|
rho_mob_0 = math_expand(rho_mob_0, N_sl)
|
|||
|
|
rho_dip_0 = math_expand(rho_dip_0, N_sl)
|
|||
|
|
prm%q = math_expand(prm%q, N_sl)
|
|||
|
|
prm%p = math_expand(prm%p, N_sl)
|
|||
|
|
prm%delta_F = math_expand(prm%delta_F, N_sl)
|
|||
|
|
prm%b_sl = math_expand(prm%b_sl, N_sl)
|
|||
|
|
prm%kink_height = math_expand(prm%kink_height, N_sl)
|
|||
|
|
prm%w = math_expand(prm%w, N_sl)
|
|||
|
|
prm%omega = math_expand(prm%omega, N_sl)
|
|||
|
|
prm%tau_0 = math_expand(prm%tau_0, N_sl)
|
|||
|
|
prm%v0 = math_expand(prm%v0, N_sl)
|
|||
|
|
prm%B = math_expand(prm%B, N_sl)
|
|||
|
|
prm%i_sl = math_expand(prm%i_sl, N_sl)
|
|||
|
|
prm%atomicVolume = math_expand(prm%atomicVolume, N_sl)
|
|||
|
|
prm%D_a = math_expand(prm%D_a, N_sl)
|
|||
|
|
|
|||
|
|
! sanity checks
|
|||
|
|
if ( prm%D_0 <= 0.0_pReal) extmsg = trim(extmsg)//' D_0'
|
|||
|
|
if ( prm%Q_cl <= 0.0_pReal) extmsg = trim(extmsg)//' Q_cl'
|
|||
|
|
if (any(rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
|
|||
|
|
if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0'
|
|||
|
|
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v_0'
|
|||
|
|
if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
|
|||
|
|
if (any(prm%delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' Q_s'
|
|||
|
|
if (any(prm%tau_0 < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls'
|
|||
|
|
if (any(prm%D_a <= 0.0_pReal)) extmsg = trim(extmsg)//' D_a or b_sl'
|
|||
|
|
if (any(prm%atomicVolume <= 0.0_pReal)) extmsg = trim(extmsg)//' f_at or b_sl'
|
|||
|
|
|
|||
|
|
else slipActive
|
|||
|
|
rho_mob_0= emptyRealArray; rho_dip_0 = emptyRealArray
|
|||
|
|
allocate(prm%b_sl,prm%D_a,prm%i_sl,prm%atomicVolume,prm%tau_0, &
|
|||
|
|
prm%delta_F,prm%v0,prm%p,prm%q,prm%B,prm%kink_height,prm%w,prm%omega, &
|
|||
|
|
source = emptyRealArray)
|
|||
|
|
allocate(prm%forestProjection(0,0))
|
|||
|
|
allocate(prm%h_sl_sl (0,0))
|
|||
|
|
endif slipActive
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
! allocate state arrays
|
|||
|
|
NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
|
|||
|
|
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl
|
|||
|
|
sizeState = sizeDotState
|
|||
|
|
|
|||
|
|
call constitutive_allocateState(plasticState(p),NipcMyPhase,sizeState,sizeDotState,0)
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
! state aliases and initialization
|
|||
|
|
startIndex = 1
|
|||
|
|
endIndex = prm%sum_N_sl
|
|||
|
|
stt%rho_mob => plasticState(p)%state(startIndex:endIndex,:)
|
|||
|
|
stt%rho_mob = spread(rho_mob_0,2,NipcMyPhase)
|
|||
|
|
dot%rho_mob => plasticState(p)%dotState(startIndex:endIndex,:)
|
|||
|
|
plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
|
|||
|
|
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_rho'
|
|||
|
|
|
|||
|
|
startIndex = endIndex + 1
|
|||
|
|
endIndex = endIndex + prm%sum_N_sl
|
|||
|
|
stt%rho_dip => plasticState(p)%state(startIndex:endIndex,:)
|
|||
|
|
stt%rho_dip = spread(rho_dip_0,2,NipcMyPhase)
|
|||
|
|
dot%rho_dip => plasticState(p)%dotState(startIndex:endIndex,:)
|
|||
|
|
plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
|
|||
|
|
|
|||
|
|
startIndex = endIndex + 1
|
|||
|
|
endIndex = endIndex + prm%sum_N_sl
|
|||
|
|
stt%gamma_sl => plasticState(p)%state(startIndex:endIndex,:)
|
|||
|
|
dot%gamma_sl => plasticState(p)%dotState(startIndex:endIndex,:)
|
|||
|
|
plasticState(p)%atol(startIndex:endIndex) = 1.0e-2_pReal
|
|||
|
|
! global alias
|
|||
|
|
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
|
|||
|
|
|
|||
|
|
allocate(dst%Lambda_sl(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
|
|||
|
|
allocate(dst%threshold_stress(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
|
|||
|
|
|
|||
|
|
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
|
|||
|
|
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
! exit if any parameter is out of range
|
|||
|
|
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(disloTungsten)')
|
|||
|
|
|
|||
|
|
enddo
|
|||
|
|
|
|||
|
|
end function plastic_disloTungsten_init
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Calculate plastic velocity gradient and its tangent.
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
pure module subroutine plastic_disloTungsten_LpAndItsTangent(Lp,dLp_dMp, &
|
|||
|
|
Mp,T,instance,of)
|
|||
|
|
real(pReal), dimension(3,3), intent(out) :: &
|
|||
|
|
Lp !< plastic velocity gradient
|
|||
|
|
real(pReal), dimension(3,3,3,3), intent(out) :: &
|
|||
|
|
dLp_dMp !< derivative of Lp with respect to the Mandel stress
|
|||
|
|
|
|||
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|||
|
|
Mp !< Mandel stress
|
|||
|
|
real(pReal), intent(in) :: &
|
|||
|
|
T !< temperature
|
|||
|
|
integer, intent(in) :: &
|
|||
|
|
instance, &
|
|||
|
|
of
|
|||
|
|
|
|||
|
|
integer :: &
|
|||
|
|
i,k,l,m,n
|
|||
|
|
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
dot_gamma_pos,dot_gamma_neg, &
|
|||
|
|
ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
|
|||
|
|
|
|||
|
|
Lp = 0.0_pReal
|
|||
|
|
dLp_dMp = 0.0_pReal
|
|||
|
|
|
|||
|
|
associate(prm => param(instance))
|
|||
|
|
|
|||
|
|
call kinetics(Mp,T,instance,of,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
|
|||
|
|
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)
|
|||
|
|
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) &
|
|||
|
|
+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%nonSchmid_pos(m,n,i) &
|
|||
|
|
+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%nonSchmid_neg(m,n,i)
|
|||
|
|
enddo
|
|||
|
|
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
end subroutine plastic_disloTungsten_LpAndItsTangent
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Calculate the rate of change of microstructure.
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
module subroutine plastic_disloTungsten_dotState(Mp,T,instance,of)
|
|||
|
|
|
|||
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|||
|
|
Mp !< Mandel stress
|
|||
|
|
real(pReal), intent(in) :: &
|
|||
|
|
T !< temperature
|
|||
|
|
integer, intent(in) :: &
|
|||
|
|
instance, &
|
|||
|
|
of
|
|||
|
|
|
|||
|
|
real(pReal) :: &
|
|||
|
|
VacancyDiffusion
|
|||
|
|
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
gdot_pos, gdot_neg,&
|
|||
|
|
tau_pos,&
|
|||
|
|
tau_neg, &
|
|||
|
|
v_cl, &
|
|||
|
|
dot_rho_dip_formation, &
|
|||
|
|
dot_rho_dip_climb, &
|
|||
|
|
dip_distance
|
|||
|
|
|
|||
|
|
associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
|
|||
|
|
|
|||
|
|
call kinetics(Mp,T,instance,of,&
|
|||
|
|
gdot_pos,gdot_neg, &
|
|||
|
|
tau_pos_out = tau_pos,tau_neg_out = tau_neg)
|
|||
|
|
|
|||
|
|
dot%gamma_sl(:,of) = (gdot_pos+gdot_neg) ! ToDo: needs to be abs
|
|||
|
|
VacancyDiffusion = prm%D_0*exp(-prm%Q_cl/(kB*T))
|
|||
|
|
|
|||
|
|
where(dEq0(tau_pos)) ! ToDo: use avg of pos and neg
|
|||
|
|
dot_rho_dip_formation = 0.0_pReal
|
|||
|
|
dot_rho_dip_climb = 0.0_pReal
|
|||
|
|
else where
|
|||
|
|
dip_distance = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), &
|
|||
|
|
prm%D_a, & ! lower limit
|
|||
|
|
dst%Lambda_sl(:,of)) ! upper limit
|
|||
|
|
dot_rho_dip_formation = merge(2.0_pReal*dip_distance* stt%rho_mob(:,of)*abs(dot%gamma_sl(:,of))/prm%b_sl, & ! ToDo: ignore region of spontaneous annihilation
|
|||
|
|
0.0_pReal, &
|
|||
|
|
prm%dipoleformation)
|
|||
|
|
v_cl = (3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume/(2.0_pReal*pi*kB*T)) &
|
|||
|
|
* (1.0_pReal/(dip_distance+prm%D_a))
|
|||
|
|
dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,of))/(dip_distance-prm%D_a) ! ToDo: Discuss with Franz: Stress dependency?
|
|||
|
|
end where
|
|||
|
|
|
|||
|
|
dot%rho_mob(:,of) = abs(dot%gamma_sl(:,of))/(prm%b_sl*dst%Lambda_sl(:,of)) & ! multiplication
|
|||
|
|
- dot_rho_dip_formation &
|
|||
|
|
- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_mob(:,of)*abs(dot%gamma_sl(:,of)) ! Spontaneous annihilation of 2 single edge dislocations
|
|||
|
|
dot%rho_dip(:,of) = dot_rho_dip_formation &
|
|||
|
|
- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_dip(:,of)*abs(dot%gamma_sl(:,of)) & ! Spontaneous annihilation of a single edge dislocation with a dipole constituent
|
|||
|
|
- dot_rho_dip_climb
|
|||
|
|
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
end subroutine plastic_disloTungsten_dotState
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Calculate derived quantities from state.
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
module subroutine plastic_disloTungsten_dependentState(instance,of)
|
|||
|
|
|
|||
|
|
integer, intent(in) :: &
|
|||
|
|
instance, &
|
|||
|
|
of
|
|||
|
|
|
|||
|
|
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
dislocationSpacing
|
|||
|
|
|
|||
|
|
associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
|
|||
|
|
|
|||
|
|
dislocationSpacing = sqrt(matmul(prm%forestProjection,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
|
|||
|
|
dst%threshold_stress(:,of) = prm%mu*prm%b_sl &
|
|||
|
|
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
|
|||
|
|
|
|||
|
|
dst%Lambda_sl(:,of) = prm%D/(1.0_pReal+prm%D*dislocationSpacing/prm%i_sl)
|
|||
|
|
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
end subroutine plastic_disloTungsten_dependentState
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Write results to HDF5 output file.
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
module subroutine plastic_disloTungsten_results(instance,group)
|
|||
|
|
|
|||
|
|
integer, intent(in) :: instance
|
|||
|
|
character(len=*), intent(in) :: group
|
|||
|
|
|
|||
|
|
integer :: o
|
|||
|
|
|
|||
|
|
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
|||
|
|
outputsLoop: do o = 1,size(prm%output)
|
|||
|
|
select case(trim(prm%output(o)))
|
|||
|
|
case('rho_mob')
|
|||
|
|
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_mob,trim(prm%output(o)), &
|
|||
|
|
'mobile dislocation density','1/m²')
|
|||
|
|
case('rho_dip')
|
|||
|
|
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip,trim(prm%output(o)), &
|
|||
|
|
'dislocation dipole density''1/m²')
|
|||
|
|
case('gamma_sl')
|
|||
|
|
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma_sl,trim(prm%output(o)), &
|
|||
|
|
'plastic shear','1')
|
|||
|
|
case('Lambda_sl')
|
|||
|
|
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%Lambda_sl,trim(prm%output(o)), &
|
|||
|
|
'mean free path for slip','m')
|
|||
|
|
case('tau_pass')
|
|||
|
|
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%threshold_stress,trim(prm%output(o)), &
|
|||
|
|
'threshold stress for slip','Pa')
|
|||
|
|
end select
|
|||
|
|
enddo outputsLoop
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
end subroutine plastic_disloTungsten_results
|
|||
|
|
|
|||
|
|
|
|||
|
|
!--------------------------------------------------------------------------------------------------
|
|||
|
|
!> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved
|
|||
|
|
! stress, and the resolved stress.
|
|||
|
|
!> @details Derivatives and resolved stress are calculated only optionally.
|
|||
|
|
! 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(Mp,T,instance,of, &
|
|||
|
|
dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out)
|
|||
|
|
|
|||
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|||
|
|
Mp !< Mandel stress
|
|||
|
|
real(pReal), intent(in) :: &
|
|||
|
|
T !< temperature
|
|||
|
|
integer, intent(in) :: &
|
|||
|
|
instance, &
|
|||
|
|
of
|
|||
|
|
|
|||
|
|
real(pReal), intent(out), dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
dot_gamma_pos, &
|
|||
|
|
dot_gamma_neg
|
|||
|
|
real(pReal), intent(out), optional, dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
ddot_gamma_dtau_pos, &
|
|||
|
|
ddot_gamma_dtau_neg, &
|
|||
|
|
tau_pos_out, &
|
|||
|
|
tau_neg_out
|
|||
|
|
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
|||
|
|
StressRatio, &
|
|||
|
|
StressRatio_p,StressRatio_pminus1, &
|
|||
|
|
dvel, vel, &
|
|||
|
|
tau_pos,tau_neg, &
|
|||
|
|
t_n, t_k, dtk,dtn, &
|
|||
|
|
needsGoodName ! ToDo: @Karo: any idea?
|
|||
|
|
integer :: j
|
|||
|
|
|
|||
|
|
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
|||
|
|
|
|||
|
|
do j = 1, prm%sum_N_sl
|
|||
|
|
tau_pos(j) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,j))
|
|||
|
|
tau_neg(j) = math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,j))
|
|||
|
|
enddo
|
|||
|
|
|
|||
|
|
|
|||
|
|
if (present(tau_pos_out)) tau_pos_out = tau_pos
|
|||
|
|
if (present(tau_neg_out)) tau_neg_out = tau_neg
|
|||
|
|
|
|||
|
|
associate(BoltzmannRatio => prm%delta_F/(kB*T), &
|
|||
|
|
dot_gamma_0 => stt%rho_mob(:,of)*prm%b_sl*prm%v0, &
|
|||
|
|
effectiveLength => dst%Lambda_sl(:,of) - prm%w)
|
|||
|
|
|
|||
|
|
significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
|
|||
|
|
StressRatio = (abs(tau_pos)-dst%threshold_stress(:,of))/prm%tau_0
|
|||
|
|
StressRatio_p = StressRatio** prm%p
|
|||
|
|
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
|
|||
|
|
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
|
|||
|
|
|
|||
|
|
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
|
|||
|
|
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
|
|||
|
|
|
|||
|
|
vel = prm%kink_height/(t_n + t_k)
|
|||
|
|
|
|||
|
|
dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
|
|||
|
|
else where significantPositiveTau
|
|||
|
|
dot_gamma_pos = 0.0_pReal
|
|||
|
|
end where significantPositiveTau
|
|||
|
|
|
|||
|
|
if (present(ddot_gamma_dtau_pos)) then
|
|||
|
|
significantPositiveTau2: where(abs(tau_pos)-dst%threshold_stress(:,of) > 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)**(prm%p - 1.0_pReal) / prm%tau_0
|
|||
|
|
dtk = -1.0_pReal * t_k / tau_pos
|
|||
|
|
|
|||
|
|
dvel = -1.0_pReal * prm%kink_height * (dtk + dtn) / (t_n + t_k)**2.0_pReal
|
|||
|
|
|
|||
|
|
ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
|
|||
|
|
else where significantPositiveTau2
|
|||
|
|
ddot_gamma_dtau_pos = 0.0_pReal
|
|||
|
|
end where significantPositiveTau2
|
|||
|
|
endif
|
|||
|
|
|
|||
|
|
significantNegativeTau: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check)
|
|||
|
|
StressRatio = (abs(tau_neg)-dst%threshold_stress(:,of))/prm%tau_0
|
|||
|
|
StressRatio_p = StressRatio** prm%p
|
|||
|
|
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
|
|||
|
|
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
|
|||
|
|
|
|||
|
|
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
|
|||
|
|
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
|
|||
|
|
|
|||
|
|
vel = prm%kink_height/(t_n + t_k)
|
|||
|
|
|
|||
|
|
dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
|
|||
|
|
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%threshold_stress(:,of) > 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)**(prm%p - 1.0_pReal) / prm%tau_0
|
|||
|
|
dtk = -1.0_pReal * t_k / tau_neg
|
|||
|
|
|
|||
|
|
dvel = -1.0_pReal * prm%kink_height * (dtk + dtn) / (t_n + t_k)**2.0_pReal
|
|||
|
|
|
|||
|
|
ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
|
|||
|
|
else where significantNegativeTau2
|
|||
|
|
ddot_gamma_dtau_neg = 0.0_pReal
|
|||
|
|
end where significantNegativeTau2
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
end associate
|
|||
|
|
end associate
|
|||
|
|
|
|||
|
|
end subroutine kinetics
|
|||
|
|
|
|||
|
|
end submodule plastic_disloTungsten
|