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DAMASK_EICMD/code/constitutive_j2.f90

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! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##############################################################
!* $Id$
!*****************************************************
!* Module: CONSTITUTIVE_J2 *
!*****************************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!*****************************************************
! [Alu]
! constitution j2
! (output) flowstress
! (output) strainrate
! c11 110.9e9 # (3 C11 + 2 C12 + 2 C44) / 5 ... with C44 = C11-C12 !!
! c12 58.34e9 # (1 C11 + 4 C12 - 1 C44) / 5
! taylorfactor 3
! tau0 31e6
! gdot0 0.001
! n 20
! h0 75e6
! tausat 63e6
! a 2.25
MODULE constitutive_j2
!*** Include other modules ***
use prec, only: pReal,pInt
implicit none
character (len=*), parameter :: constitutive_j2_label = 'j2'
integer(pInt), dimension(:), allocatable :: constitutive_j2_sizeDotState, &
constitutive_j2_sizeState, &
constitutive_j2_sizePostResults
integer(pInt), dimension(:,:), allocatable,target :: constitutive_j2_sizePostResult ! size of each post result output
character(len=64), dimension(:,:), allocatable,target :: constitutive_j2_output ! name of each post result output
real(pReal), dimension(:), allocatable :: constitutive_j2_C11
real(pReal), dimension(:), allocatable :: constitutive_j2_C12
real(pReal), dimension(:,:,:), allocatable :: constitutive_j2_Cslip_66
!* Visco-plastic constitutive_j2 parameters
real(pReal), dimension(:), allocatable :: constitutive_j2_fTaylor
real(pReal), dimension(:), allocatable :: constitutive_j2_tau0
real(pReal), dimension(:), allocatable :: constitutive_j2_gdot0
real(pReal), dimension(:), allocatable :: constitutive_j2_n
real(pReal), dimension(:), allocatable :: constitutive_j2_h0
real(pReal), dimension(:), allocatable :: constitutive_j2_tausat
real(pReal), dimension(:), allocatable :: constitutive_j2_a
real(pReal), dimension(:), allocatable :: constitutive_j2_aTolResistance
CONTAINS
!****************************************
!* - constitutive_j2_init
!* - constitutive_j2_stateInit
!* - constitutive_j2_homogenizedC
!* - constitutive_j2_microstructure
!* - constitutive_j2_LpAndItsTangent
!* - consistutive_j2_dotState
!* - consistutive_j2_postResults
!****************************************
subroutine constitutive_j2_init(file)
!**************************************
!* Module initialization *
!**************************************
use prec, only: pInt, pReal
use math, only: math_Mandel3333to66, math_Voigt66to3333
use IO
use material
use debug, only: debug_verbosity
integer(pInt), intent(in) :: file
integer(pInt), parameter :: maxNchunks = 7
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section, maxNinstance, i,j,k, output, mySize
character(len=64) tag
character(len=1024) line
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '<<<+- constitutive_',trim(constitutive_j2_label),' init -+>>>'
write(6,*) '$Id$'
#include "compilation_info.f90"
!$OMP END CRITICAL (write2out)
maxNinstance = count(phase_constitution == constitutive_j2_label)
if (maxNinstance == 0) return
if (debug_verbosity > 0) then
!$OMP CRITICAL (write2out)
write(6,'(a16,1x,i5)') '# instances:',maxNinstance
write(6,*)
!$OMP END CRITICAL (write2out)
endif
allocate(constitutive_j2_sizeDotState(maxNinstance)) ; constitutive_j2_sizeDotState = 0_pInt
allocate(constitutive_j2_sizeState(maxNinstance)) ; constitutive_j2_sizeState = 0_pInt
allocate(constitutive_j2_sizePostResults(maxNinstance)); constitutive_j2_sizePostResults = 0_pInt
allocate(constitutive_j2_sizePostResult(maxval(phase_Noutput), maxNinstance)); constitutive_j2_sizePostResult = 0_pInt
allocate(constitutive_j2_output(maxval(phase_Noutput), maxNinstance)) ; constitutive_j2_output = ''
allocate(constitutive_j2_C11(maxNinstance)) ; constitutive_j2_C11 = 0.0_pReal
allocate(constitutive_j2_C12(maxNinstance)) ; constitutive_j2_C12 = 0.0_pReal
allocate(constitutive_j2_Cslip_66(6,6,maxNinstance)) ; constitutive_j2_Cslip_66 = 0.0_pReal
allocate(constitutive_j2_fTaylor(maxNinstance)) ; constitutive_j2_fTaylor = 0.0_pReal
allocate(constitutive_j2_tau0(maxNinstance)) ; constitutive_j2_tau0 = 0.0_pReal
allocate(constitutive_j2_gdot0(maxNinstance)) ; constitutive_j2_gdot0 = 0.0_pReal
allocate(constitutive_j2_n(maxNinstance)) ; constitutive_j2_n = 0.0_pReal
allocate(constitutive_j2_h0(maxNinstance)) ; constitutive_j2_h0 = 0.0_pReal
allocate(constitutive_j2_tausat(maxNinstance)) ; constitutive_j2_tausat = 0.0_pReal
allocate(constitutive_j2_a(maxNinstance)) ; constitutive_j2_a = 0.0_pReal
allocate(constitutive_j2_aTolResistance(maxNinstance)) ; constitutive_j2_aTolResistance = 0.0_pReal
rewind(file)
line = ''
section = 0
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
read(file,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(file,'(a1024)',END=100) line
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1
output = 0 ! reset output counter
endif
if (section > 0 .and. phase_constitution(section) == constitutive_j2_label) then ! one of my sections
i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
select case(tag)
case ('(output)')
output = output + 1
constitutive_j2_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
case ('c11')
constitutive_j2_C11(i) = IO_floatValue(line,positions,2)
case ('c12')
constitutive_j2_C12(i) = IO_floatValue(line,positions,2)
case ('tau0')
constitutive_j2_tau0(i) = IO_floatValue(line,positions,2)
case ('gdot0')
constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2)
case ('n')
constitutive_j2_n(i) = IO_floatValue(line,positions,2)
case ('h0')
constitutive_j2_h0(i) = IO_floatValue(line,positions,2)
case ('tausat')
constitutive_j2_tausat(i) = IO_floatValue(line,positions,2)
case ('a', 'w0')
constitutive_j2_a(i) = IO_floatValue(line,positions,2)
case ('taylorfactor')
constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2)
case ('atol_resistance')
constitutive_j2_aTolResistance(i) = IO_floatValue(line,positions,2)
case default
call IO_error(210_pInt,ext_msg=tag)
end select
endif
enddo
100 do i = 1,maxNinstance ! sanity checks
if (constitutive_j2_tau0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='tau0')
if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='gdot0')
if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='n')
if (constitutive_j2_tausat(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='tausat')
if (constitutive_j2_a(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='a')
if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='taylorfactor')
if (constitutive_j2_aTolResistance(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_resistance')
enddo
do i = 1,maxNinstance
do j = 1,maxval(phase_Noutput)
select case(constitutive_j2_output(j,i))
case('flowstress')
mySize = 1_pInt
case('strainrate')
mySize = 1_pInt
case default
call IO_error(212_pInt,ext_msg=constitutive_j2_output(j,i))
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_j2_sizePostResult(j,i) = mySize
constitutive_j2_sizePostResults(i) = &
constitutive_j2_sizePostResults(i) + mySize
endif
enddo
constitutive_j2_sizeDotState(i) = 1
constitutive_j2_sizeState(i) = 1
forall(k=1:3)
forall(j=1:3) &
constitutive_j2_Cslip_66(k,j,i) = constitutive_j2_C12(i)
constitutive_j2_Cslip_66(k,k,i) = constitutive_j2_C11(i)
constitutive_j2_Cslip_66(k+3,k+3,i) = 0.5_pReal*(constitutive_j2_C11(i)-constitutive_j2_C12(i))
end forall
constitutive_j2_Cslip_66(1:6,1:6,i) = &
math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(1:6,1:6,i)))
enddo
return
endsubroutine
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
pure function constitutive_j2_stateInit(myInstance)
use prec, only: pReal,pInt
implicit none
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(1) :: constitutive_j2_stateInit
constitutive_j2_stateInit = constitutive_j2_tau0(myInstance)
return
endfunction
!*********************************************************************
!* relevant microstructural state *
!*********************************************************************
pure function constitutive_j2_aTolState(myInstance)
use prec, only: pReal, &
pInt
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution
!*** output variables
real(pReal), dimension(constitutive_j2_sizeState(myInstance)) :: &
constitutive_j2_aTolState ! relevant state values for the current instance of this constitution
!*** local variables
constitutive_j2_aTolState = constitutive_j2_aTolResistance(myInstance)
endfunction
function constitutive_j2_homogenizedC(state,ipc,ip,el)
!*********************************************************************
!* homogenized elacticity matrix *
!* INPUT: *
!* - state : state variables *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
integer(pInt), intent(in) :: ipc,ip,el
integer(pInt) matID
real(pReal), dimension(6,6) :: constitutive_j2_homogenizedC
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(1:6,1:6,matID)
return
endfunction
subroutine constitutive_j2_microstructure(Temperature,state,ipc,ip,el)
!*********************************************************************
!* calculate derived quantities from state (not used here) *
!* INPUT: *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el, matID
real(pReal) Temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
endsubroutine
!****************************************************************
!* calculates plastic velocity gradient and its tangent *
!****************************************************************
pure subroutine constitutive_j2_LpAndItsTangent(Lp, dLp_dTstar_99, Tstar_dev_v, Temperature, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6, &
math_Mandel6to33, &
math_Plain3333to99
use lattice, only: lattice_Sslip, &
lattice_Sslip_v
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in):: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar_99 ! derivative of Lp with respect to Tstar (9x9 matrix)
!*** local variables ***!
real(pReal), dimension(3,3) :: Tstar_dev_33 ! deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
real(pReal), dimension(3,3,3,3) :: dLp_dTstar_3333 ! derivative of Lp with respect to Tstar as 4th order tensor
real(pReal) gamma_dot, & ! strainrate
norm_Tstar_dev, & ! euclidean norm of Tstar_dev
squarenorm_Tstar_dev ! square of the euclidean norm of Tstar_dev
integer(pInt) matID, &
k, &
l, &
m, &
n
matID = phase_constitutionInstance(material_phase(g,ip,el))
! convert Tstar to matrix and calculate euclidean norm
Tstar_dev_33 = math_Mandel6to33(Tstar_dev_v)
squarenorm_Tstar_dev = math_mul6x6(Tstar_dev_v,Tstar_dev_v)
norm_Tstar_dev = sqrt(squarenorm_Tstar_dev)
! Initialization of Lp and dLp_dTstar
Lp = 0.0_pReal
dLp_dTstar_99 = 0.0_pReal
! for Tstar==0 both Lp and dLp_dTstar are zero (if not n==1)
if (norm_Tstar_dev > 0) then
! Calculation of gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) **constitutive_j2_n(matID)
! Calculation of Lp
Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID)
!* Calculation of the tangent of Lp
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dTstar_3333(k,l,m,n) = (constitutive_j2_n(matID)-1.0_pReal) * Tstar_dev_33(k,l)*Tstar_dev_33(m,n) / squarenorm_Tstar_dev
forall (k=1:3,l=1:3) &
dLp_dTstar_3333(k,l,k,l) = dLp_dTstar_3333(k,l,k,l) + 1.0_pReal
dLp_dTstar_99 = math_Plain3333to99(gamma_dot / constitutive_j2_fTaylor(matID) * dLp_dTstar_3333 / norm_Tstar_dev)
end if
return
endsubroutine
!****************************************************************
!* calculates the rate of change of microstructure *
!****************************************************************
pure function constitutive_j2_dotState(Tstar_v, Temperature, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(1) :: constitutive_j2_dotState ! evolution of state variable
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) gamma_dot, & ! strainrate
hardening, & ! hardening coefficient
norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID
matID = phase_constitutionInstance(material_phase(g,ip,el))
! deviatoric part of 2nd Piola-Kirchhoff stress
Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal
Tstar_dev_v(4:6) = Tstar_v(4:6)
norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
! gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
! hardening coefficient
hardening = constitutive_j2_h0(matID) * &
( 1.0_pReal - state(g,ip,el)%p(1) / constitutive_j2_tausat(matID) ) ** constitutive_j2_a(matID)
! dotState
constitutive_j2_dotState = hardening * gamma_dot
return
endfunction
!****************************************************************
!* calculates the rate of change of temperature *
!****************************************************************
pure function constitutive_j2_dotTemperature(Tstar_v, Temperature, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: pReal,pInt,p_vec
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal) constitutive_j2_dotTemperature ! rate of change of temperature
! calculate dotTemperature
constitutive_j2_dotTemperature = 0.0_pReal
return
endfunction
!*********************************************************************
!* return array of constitutive results *
!*********************************************************************
pure function constitutive_j2_postResults(Tstar_v, Temperature, dt, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance, &
phase_Noutput
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature, &
dt ! current time increment
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(constitutive_j2_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
constitutive_j2_postResults
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID, &
o, &
c
!*** global variables ***!
! constitutive_j2_gdot0
! constitutive_j2_fTaylor
! constitutive_j2_n
matID = phase_constitutionInstance(material_phase(g,ip,el))
! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm
Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal
Tstar_dev_v(4:6) = Tstar_v(4:6)
norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
c = 0_pInt
constitutive_j2_postResults = 0.0_pReal
do o = 1,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_j2_output(o,matID))
case ('flowstress')
constitutive_j2_postResults(c+1) = state(g,ip,el)%p(1)
c = c + 1
case ('strainrate')
constitutive_j2_postResults(c+1) = &
constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
c = c + 1
end select
enddo
return
endfunction
END MODULE
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