464 lines
18 KiB
Fortran
464 lines
18 KiB
Fortran
!--------------------------------------------------------------------------------------------------
|
||
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
|
||
!> @brief material subroutine for isotropic plasticity
|
||
!> @details Isotropic Plasticity which resembles the phenopowerlaw plasticity without
|
||
!! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an
|
||
!! untextured polycrystal
|
||
!--------------------------------------------------------------------------------------------------
|
||
module plastic_isotropic
|
||
use prec
|
||
use debug
|
||
use math
|
||
use IO
|
||
use material
|
||
use config
|
||
use discretization
|
||
use results
|
||
|
||
implicit none
|
||
private
|
||
|
||
integer, dimension(:,:), allocatable, target, public :: &
|
||
plastic_isotropic_sizePostResult !< size of each post result output
|
||
character(len=64), dimension(:,:), allocatable, target, public :: &
|
||
plastic_isotropic_output !< name of each post result output
|
||
|
||
enum, bind(c)
|
||
enumerator :: &
|
||
undefined_ID, &
|
||
xi_ID, &
|
||
dot_gamma_ID
|
||
end enum
|
||
|
||
type :: tParameters
|
||
real(pReal) :: &
|
||
M, & !< Taylor factor
|
||
xi_0, & !< initial critical stress
|
||
dot_gamma_0, & !< reference strain rate
|
||
n, & !< stress exponent
|
||
h0, &
|
||
h_ln, &
|
||
xi_inf, & !< maximum critical stress
|
||
a, &
|
||
c_1, &
|
||
c_4, &
|
||
c_3, &
|
||
c_2, &
|
||
aTol_xi, &
|
||
aTol_gamma
|
||
integer :: &
|
||
of_debug = 0
|
||
integer(kind(undefined_ID)), allocatable, dimension(:) :: &
|
||
outputID
|
||
logical :: &
|
||
dilatation
|
||
end type tParameters
|
||
|
||
type :: tIsotropicState
|
||
real(pReal), pointer, dimension(:) :: &
|
||
xi, &
|
||
gamma
|
||
end type tIsotropicState
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! containers for parameters and state
|
||
type(tParameters), allocatable, dimension(:) :: param
|
||
type(tIsotropicState), allocatable, dimension(:) :: &
|
||
dotState, &
|
||
state
|
||
|
||
public :: &
|
||
plastic_isotropic_init, &
|
||
plastic_isotropic_LpAndItsTangent, &
|
||
plastic_isotropic_LiAndItsTangent, &
|
||
plastic_isotropic_dotState, &
|
||
plastic_isotropic_postResults, &
|
||
plastic_isotropic_results
|
||
|
||
contains
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief module initialization
|
||
!> @details reads in material parameters, allocates arrays, and does sanity checks
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_isotropic_init
|
||
|
||
integer :: &
|
||
Ninstance, &
|
||
p, i, &
|
||
NipcMyPhase, &
|
||
sizeState, sizeDotState
|
||
|
||
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
|
||
|
||
integer(kind(undefined_ID)) :: &
|
||
outputID
|
||
|
||
character(len=pStringLen) :: &
|
||
extmsg = ''
|
||
character(len=65536), dimension(:), allocatable :: &
|
||
outputs
|
||
|
||
write(6,'(/,a)') ' <<<+- plastic_'//PLASTICITY_ISOTROPIC_label//' init -+>>>'
|
||
|
||
write(6,'(/,a)') ' Maiti and Eisenlohr, Scripta Materialia 145:37–40, 2018'
|
||
write(6,'(a)') ' https://doi.org/10.1016/j.scriptamat.2017.09.047'
|
||
|
||
Ninstance = count(phase_plasticity == PLASTICITY_ISOTROPIC_ID)
|
||
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
|
||
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
|
||
|
||
allocate(plastic_isotropic_sizePostResult(maxval(phase_Noutput),Ninstance),source=0)
|
||
allocate(plastic_isotropic_output(maxval(phase_Noutput),Ninstance))
|
||
plastic_isotropic_output = ''
|
||
|
||
allocate(param(Ninstance))
|
||
allocate(state(Ninstance))
|
||
allocate(dotState(Ninstance))
|
||
|
||
do p = 1, size(phase_plasticity)
|
||
if (phase_plasticity(p) /= PLASTICITY_ISOTROPIC_ID) cycle
|
||
associate(prm => param(phase_plasticityInstance(p)), &
|
||
dot => dotState(phase_plasticityInstance(p)), &
|
||
stt => state(phase_plasticityInstance(p)), &
|
||
config => config_phase(p))
|
||
|
||
#ifdef DEBUG
|
||
if (p==material_phaseAt(debug_g,debug_e)) &
|
||
prm%of_debug = material_phasememberAt(debug_g,debug_i,debug_e)
|
||
#endif
|
||
|
||
prm%xi_0 = config%getFloat('tau0')
|
||
prm%xi_inf = config%getFloat('tausat')
|
||
prm%dot_gamma_0 = config%getFloat('gdot0')
|
||
prm%n = config%getFloat('n')
|
||
prm%h0 = config%getFloat('h0')
|
||
prm%M = config%getFloat('m')
|
||
prm%h_ln = config%getFloat('h0_slopelnrate', defaultVal=0.0_pReal)
|
||
prm%c_1 = config%getFloat('tausat_sinhfita',defaultVal=0.0_pReal)
|
||
prm%c_4 = config%getFloat('tausat_sinhfitb',defaultVal=0.0_pReal)
|
||
prm%c_3 = config%getFloat('tausat_sinhfitc',defaultVal=0.0_pReal)
|
||
prm%c_2 = config%getFloat('tausat_sinhfitd',defaultVal=0.0_pReal)
|
||
prm%a = config%getFloat('a')
|
||
prm%aTol_xi = config%getFloat('atol_flowstress',defaultVal=1.0_pReal)
|
||
prm%aTol_gamma = config%getFloat('atol_shear', defaultVal=1.0e-6_pReal)
|
||
|
||
prm%dilatation = config%keyExists('/dilatation/')
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! sanity checks
|
||
extmsg = ''
|
||
if (prm%aTol_gamma <= 0.0_pReal) extmsg = trim(extmsg)//' aTol_gamma'
|
||
if (prm%xi_0 < 0.0_pReal) extmsg = trim(extmsg)//' xi_0'
|
||
if (prm%dot_gamma_0 <= 0.0_pReal) extmsg = trim(extmsg)//' dot_gamma_0'
|
||
if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' n'
|
||
if (prm%a <= 0.0_pReal) extmsg = trim(extmsg)//' a'
|
||
if (prm%M <= 0.0_pReal) extmsg = trim(extmsg)//' m'
|
||
if (prm%aTol_xi <= 0.0_pReal) extmsg = trim(extmsg)//' atol_xi'
|
||
if (prm%aTol_gamma <= 0.0_pReal) extmsg = trim(extmsg)//' atol_shear'
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! exit if any parameter is out of range
|
||
if (extmsg /= '') &
|
||
call IO_error(211,ext_msg=trim(extmsg)//'('//PLASTICITY_ISOTROPIC_label//')')
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! output pararameters
|
||
outputs = config%getStrings('(output)',defaultVal=emptyStringArray)
|
||
allocate(prm%outputID(0))
|
||
do i=1, size(outputs)
|
||
outputID = undefined_ID
|
||
select case(outputs(i))
|
||
|
||
case ('flowstress')
|
||
outputID = xi_ID
|
||
case ('strainrate')
|
||
outputID = dot_gamma_ID
|
||
|
||
end select
|
||
|
||
if (outputID /= undefined_ID) then
|
||
plastic_isotropic_output(i,phase_plasticityInstance(p)) = outputs(i)
|
||
plastic_isotropic_sizePostResult(i,phase_plasticityInstance(p)) = 1
|
||
prm%outputID = [prm%outputID, outputID]
|
||
endif
|
||
|
||
enddo
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
|
||
sizeDotState = size(['xi ','accumulated_shear'])
|
||
sizeState = sizeDotState
|
||
|
||
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0, &
|
||
1,0,0)
|
||
plasticState(p)%sizePostResults = sum(plastic_isotropic_sizePostResult(:,phase_plasticityInstance(p)))
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! locally defined state aliases and initialization of state0 and aTolState
|
||
stt%xi => plasticState(p)%state (1,:)
|
||
stt%xi = prm%xi_0
|
||
dot%xi => plasticState(p)%dotState(1,:)
|
||
plasticState(p)%aTolState(1) = prm%aTol_xi
|
||
|
||
stt%gamma => plasticState(p)%state (2,:)
|
||
dot%gamma => plasticState(p)%dotState(2,:)
|
||
plasticState(p)%aTolState(2) = prm%aTol_gamma
|
||
! global alias
|
||
plasticState(p)%slipRate => plasticState(p)%dotState(2:2,:)
|
||
plasticState(p)%accumulatedSlip => plasticState(p)%state (2:2,:)
|
||
|
||
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
|
||
|
||
end associate
|
||
|
||
enddo
|
||
|
||
end subroutine plastic_isotropic_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates plastic velocity gradient and its tangent
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,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
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(3,3) :: &
|
||
Mp_dev !< deviatoric part of the Mandel stress
|
||
real(pReal) :: &
|
||
dot_gamma, & !< strainrate
|
||
norm_Mp_dev, & !< norm of the deviatoric part of the Mandel stress
|
||
squarenorm_Mp_dev !< square of the norm of the deviatoric part of the Mandel stress
|
||
integer :: &
|
||
k, l, m, n
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
|
||
Mp_dev = math_deviatoric33(Mp)
|
||
squarenorm_Mp_dev = math_mul33xx33(Mp_dev,Mp_dev)
|
||
norm_Mp_dev = sqrt(squarenorm_Mp_dev)
|
||
|
||
if (norm_Mp_dev > 0.0_pReal) then
|
||
dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp_dev/(prm%M*stt%xi(of))) **prm%n
|
||
|
||
Lp = dot_gamma/prm%M * Mp_dev/norm_Mp_dev
|
||
#ifdef DEBUG
|
||
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0 &
|
||
.and. (of == prm%of_debug .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0)) then
|
||
write(6,'(/,a,/,3(12x,3(f12.4,1x)/))') '<< CONST isotropic >> Tstar (dev) / MPa', &
|
||
transpose(Mp_dev)*1.0e-6_pReal
|
||
write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> norm Tstar / MPa', norm_Mp_dev*1.0e-6_pReal
|
||
write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> gdot', dot_gamma
|
||
end if
|
||
#endif
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = (prm%n-1.0_pReal) * Mp_dev(k,l)*Mp_dev(m,n) / squarenorm_Mp_dev
|
||
forall (k=1:3,l=1:3) &
|
||
dLp_dMp(k,l,k,l) = dLp_dMp(k,l,k,l) + 1.0_pReal
|
||
forall (k=1:3,m=1:3) &
|
||
dLp_dMp(k,k,m,m) = dLp_dMp(k,k,m,m) - 1.0_pReal/3.0_pReal
|
||
dLp_dMp = dot_gamma / prm%M * dLp_dMp / norm_Mp_dev
|
||
else
|
||
Lp = 0.0_pReal
|
||
dLp_dMp = 0.0_pReal
|
||
end if
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_isotropic_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates plastic velocity gradient and its tangent
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,instance,of)
|
||
|
||
real(pReal), dimension(3,3), intent(out) :: &
|
||
Li !< inleastic velocity gradient
|
||
real(pReal), dimension(3,3,3,3), intent(out) :: &
|
||
dLi_dMi !< derivative of Li with respect to the Mandel stress
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mi !< Mandel stress
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(3,3) :: &
|
||
Mi_sph !< spherical part of the Mandel stress
|
||
real(pReal) :: &
|
||
dot_gamma, & !< shear rate
|
||
tr !< pressure
|
||
integer :: &
|
||
k, l, m, n
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
|
||
tr=math_trace33(math_spherical33(Mi))
|
||
|
||
if (prm%dilatation .and. abs(tr) > 0.0_pReal) then ! no stress or J2 plasticity --> Li and its derivative are zero
|
||
Li = math_I3 &
|
||
* prm%dot_gamma_0/prm%M * (3.0_pReal*prm%M*stt%xi(of))**(-prm%n) &
|
||
* tr * abs(tr)**(prm%n-1.0_pReal)
|
||
|
||
#ifdef DEBUG
|
||
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0 &
|
||
.and. (of == prm%of_debug .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0)) then
|
||
write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> pressure / MPa', tr/3.0_pReal*1.0e-6_pReal
|
||
write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> gdot', prm%dot_gamma_0 * (3.0_pReal*prm%M*stt%xi(of))**(-prm%n) &
|
||
* tr * abs(tr)**(prm%n-1.0_pReal)
|
||
end if
|
||
#endif
|
||
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLi_dMi(k,l,m,n) = n / tr * Li(k,l) * math_I3(m,n)
|
||
|
||
else
|
||
Li = 0.0_pReal
|
||
dLi_dMi = 0.0_pReal
|
||
endif
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_isotropic_LiAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_isotropic_dotState(Mp,instance,of)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal) :: &
|
||
dot_gamma, & !< strainrate
|
||
xi_inf_star, & !< saturation xi
|
||
norm_Mp !< norm of the (deviatoric) Mandel stress
|
||
|
||
associate(prm => param(instance), stt => state(instance), dot => dotState(instance))
|
||
|
||
if (prm%dilatation) then
|
||
norm_Mp = sqrt(math_mul33xx33(Mp,Mp))
|
||
else
|
||
norm_Mp = sqrt(math_mul33xx33(math_deviatoric33(Mp),math_deviatoric33(Mp)))
|
||
endif
|
||
|
||
dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp /(prm%M*stt%xi(of))) **prm%n
|
||
|
||
if (dot_gamma > 1e-12_pReal) then
|
||
if (dEq0(prm%c_1)) then
|
||
xi_inf_star = prm%xi_inf
|
||
else
|
||
xi_inf_star = prm%xi_inf &
|
||
+ asinh( (dot_gamma / prm%c_1)**(1.0_pReal / prm%c_2))**(1.0_pReal / prm%c_3) &
|
||
/ prm%c_4 * (dot_gamma / prm%dot_gamma_0)**(1.0_pReal / prm%n)
|
||
endif
|
||
dot%xi(of) = dot_gamma &
|
||
* ( prm%h0 + prm%h_ln * log(dot_gamma) ) &
|
||
* abs( 1.0_pReal - stt%xi(of)/xi_inf_star )**prm%a &
|
||
* sign(1.0_pReal, 1.0_pReal - stt%xi(of)/xi_inf_star)
|
||
else
|
||
dot%xi(of) = 0.0_pReal
|
||
endif
|
||
|
||
dot%gamma(of) = dot_gamma ! ToDo: not really used
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_isotropic_dotState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief return array of constitutive results
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_isotropic_postResults(Mp,instance,of) result(postResults)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(sum(plastic_isotropic_sizePostResult(:,instance))) :: &
|
||
postResults
|
||
|
||
real(pReal) :: &
|
||
norm_Mp !< norm of the Mandel stress
|
||
integer :: &
|
||
o,c
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
|
||
if (prm%dilatation) then
|
||
norm_Mp = sqrt(math_mul33xx33(Mp,Mp))
|
||
else
|
||
norm_Mp = sqrt(math_mul33xx33(math_deviatoric33(Mp),math_deviatoric33(Mp)))
|
||
endif
|
||
|
||
c = 0
|
||
|
||
outputsLoop: do o = 1,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
|
||
case (xi_ID)
|
||
postResults(c+1) = stt%xi(of)
|
||
c = c + 1
|
||
case (dot_gamma_ID)
|
||
postResults(c+1) = prm%dot_gamma_0 &
|
||
* (sqrt(1.5_pReal) * norm_Mp /(prm%M * stt%xi(of)))**prm%n
|
||
c = c + 1
|
||
|
||
end select
|
||
enddo outputsLoop
|
||
|
||
end associate
|
||
|
||
end function plastic_isotropic_postResults
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief writes results to HDF5 output file
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_isotropic_results(instance,group)
|
||
#if defined(PETSc) || defined(DAMASKHDF5)
|
||
|
||
integer, intent(in) :: instance
|
||
character(len=*), intent(in) :: group
|
||
|
||
integer :: o
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
outputsLoop: do o = 1,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
case (xi_ID)
|
||
call results_writeDataset(group,stt%xi,'xi','resistance against plastic flow','Pa')
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
#else
|
||
integer, intent(in) :: instance
|
||
character(len=*) :: group
|
||
#endif
|
||
|
||
end subroutine plastic_isotropic_results
|
||
|
||
|
||
end module plastic_isotropic
|