! 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 . ! !############################################################## !* $Id$ !***************************************************** !* 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 use prec, only: pReal,pInt implicit none private character (len=*), parameter, public :: constitutive_j2_label = 'j2' integer(pInt), dimension(:), allocatable, public :: & constitutive_j2_sizeDotState, & constitutive_j2_sizeState, & constitutive_j2_sizePostResults integer(pInt), dimension(:,:), allocatable, target, public :: & constitutive_j2_sizePostResult ! size of each post result output character(len=64), dimension(:,:), allocatable, target, public :: & constitutive_j2_output ! name of each post result output integer(pInt), dimension(:), allocatable, private :: & constitutive_j2_Noutput real(pReal), dimension(:), allocatable, private ::& constitutive_j2_C11, & constitutive_j2_C12 real(pReal), dimension(:,:,:), allocatable, private :: & constitutive_j2_Cslip_66 !* Visco-plastic constitutive_j2 parameters real(pReal), dimension(:), allocatable, private :: & constitutive_j2_fTaylor, & constitutive_j2_tau0, & constitutive_j2_gdot0, & constitutive_j2_n, & constitutive_j2_h0, & constitutive_j2_tausat, & constitutive_j2_a, & constitutive_j2_aTolResistance public :: constitutive_j2_init, & constitutive_j2_stateInit, & constitutive_j2_aTolState, & constitutive_j2_homogenizedC, & constitutive_j2_microstructure, & constitutive_j2_LpAndItsTangent, & constitutive_j2_dotState, & constitutive_j2_dotTemperature, & constitutive_j2_postResults contains subroutine constitutive_j2_init(myFile) !************************************** !* Module initialization * !************************************** use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use math, only: math_Mandel3333to66, math_Voigt66to3333 use IO use material use debug, only: debug_what, & debug_constitutive, & debug_levelBasic implicit none integer(pInt), intent(in) :: myFile integer(pInt), parameter :: maxNchunks = 7_pInt integer(pInt), dimension(1_pInt+2_pInt*maxNchunks) :: positions integer(pInt) :: section = 0_pInt, maxNinstance, i,j,k, 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 = int(count(phase_constitution == constitutive_j2_label),pInt) if (maxNinstance == 0_pInt) return if (iand(debug_what(debug_constitutive),debug_levelBasic) /= 0_pInt) 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_Noutput(maxNinstance)) constitutive_j2_Noutput = 0_pInt 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(myFile) do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to read(myFile,'(a1024)',END=100) line enddo do ! read thru sections of phase part read(myFile,'(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_pInt ! advance section counter cycle endif if (section > 0_pInt .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_pInt)) ! extract key select case(tag) case ('constitution') cycle case ('(output)') constitutive_j2_Noutput(i) = constitutive_j2_Noutput(i) + 1_pInt constitutive_j2_output(constitutive_j2_Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt)) case ('c11') constitutive_j2_C11(i) = IO_floatValue(line,positions,2_pInt) case ('c12') constitutive_j2_C12(i) = IO_floatValue(line,positions,2_pInt) case ('tau0') constitutive_j2_tau0(i) = IO_floatValue(line,positions,2_pInt) case ('gdot0') constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2_pInt) case ('n') constitutive_j2_n(i) = IO_floatValue(line,positions,2_pInt) case ('h0') constitutive_j2_h0(i) = IO_floatValue(line,positions,2_pInt) case ('tausat') constitutive_j2_tausat(i) = IO_floatValue(line,positions,2_pInt) case ('a', 'w0') constitutive_j2_a(i) = IO_floatValue(line,positions,2_pInt) case ('taylorfactor') constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2_pInt) case ('atol_resistance') constitutive_j2_aTolResistance(i) = IO_floatValue(line,positions,2_pInt) case default call IO_error(210_pInt,ext_msg=tag) end select endif enddo 100 do i = 1_pInt,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_pInt,maxNinstance do j = 1_pInt,constitutive_j2_Noutput(i) 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_pInt constitutive_j2_sizeState(i) = 1_pInt forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) constitutive_j2_Cslip_66(k,j,i) = constitutive_j2_C12(i) end forall 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 end subroutine constitutive_j2_init !********************************************************************* !* initial microstructural state * !********************************************************************* pure function constitutive_j2_stateInit(myInstance) implicit none integer(pInt), intent(in) :: myInstance real(pReal), dimension(1) :: constitutive_j2_stateInit constitutive_j2_stateInit = constitutive_j2_tau0(myInstance) end function constitutive_j2_stateInit !********************************************************************* !* relevant microstructural state * !********************************************************************* pure function constitutive_j2_aTolState(myInstance) 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 constitutive_j2_aTolState = constitutive_j2_aTolResistance(myInstance) end function constitutive_j2_aTolState 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: 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) end function constitutive_j2_homogenizedC 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: 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)) end subroutine constitutive_j2_microstructure !**************************************************************** !* 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: p_vec use math, only: math_mul6x6, & math_Mandel6to33, & math_Plain3333to99 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_pInt) 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_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & 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_pInt:3_pInt,l=1_pInt:3_pInt) & 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 end subroutine constitutive_j2_LpAndItsTangent !**************************************************************** !* 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: p_vec use math, only: math_mul6x6 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 end function constitutive_j2_dotState !**************************************************************** !* 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: p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains 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 end function constitutive_j2_dotTemperature !********************************************************************* !* 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: p_vec use math, only: math_mul6x6 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_pInt,phase_Noutput(material_phase(g,ip,el)) select case(constitutive_j2_output(o,matID)) case ('flowstress') constitutive_j2_postResults(c+1_pInt) = state(g,ip,el)%p(1) c = c + 1_pInt case ('strainrate') constitutive_j2_postResults(c+1_pInt) = & 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_pInt end select enddo end function constitutive_j2_postResults end module constitutive_j2