!***************************************************** !* 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 ! s0 31e6 ! gdot0 0.001 ! n 20 ! h0 75e6 ! s_sat 63e6 ! w0 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 character(len=64), dimension(:,:), allocatable :: constitutive_j2_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_s0 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_s_sat real(pReal), dimension(:), allocatable :: constitutive_j2_w0 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 integer(pInt), intent(in) :: file integer(pInt), parameter :: maxNchunks = 7 integer(pInt), dimension(1+2*maxNchunks) :: positions integer(pInt) section, maxNinstance, i,j,k,l, output character(len=64) tag character(len=1024) line maxNinstance = count(phase_constitution == constitutive_j2_label) if (maxNinstance == 0) return 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_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_s0(maxNinstance)) ; constitutive_j2_s0 = 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_s_sat(maxNinstance)) ; constitutive_j2_s_sat = 0.0_pReal allocate(constitutive_j2_w0(maxNinstance)) ; constitutive_j2_w0 = 0.0_pReal rewind(file) line = '' section = 0 do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to 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 ('s0') constitutive_j2_s0(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 ('s_sat') constitutive_j2_s_sat(i) = IO_floatValue(line,positions,2) case ('w0') constitutive_j2_w0(i) = IO_floatValue(line,positions,2) case ('taylorfactor') constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2) end select endif enddo 100 do i = 1,maxNinstance ! sanity checks if (constitutive_j2_s0(i) < 0.0_pReal) call IO_error(203) if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(204) if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(205) if (constitutive_j2_h0(i) <= 0.0_pReal) call IO_error(206) if (constitutive_j2_s_sat(i) <= 0.0_pReal) call IO_error(207) if (constitutive_j2_w0(i) <= 0.0_pReal) call IO_error(208) if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(240) enddo do i = 1,maxNinstance constitutive_j2_sizeDotState(i) = 1 constitutive_j2_sizeState(i) = 1 do j = 1,maxval(phase_Noutput) select case(constitutive_j2_output(j,i)) case('flowstress') constitutive_j2_sizePostResults(i) = & constitutive_j2_sizePostResults(i) + 1 case('strainrate') constitutive_j2_sizePostResults(i) = & constitutive_j2_sizePostResults(i) + 1 end select enddo 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(:,:,i) = & math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(:,:,i))) enddo return endsubroutine function constitutive_j2_stateInit(myInstance) !********************************************************************* !* initial microstructural state * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt), intent(in) :: myInstance real(pReal), dimension(1) :: constitutive_j2_stateInit constitutive_j2_stateInit = constitutive_j2_s0(myInstance) return 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 !* Definition of variables 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(:,:,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 subroutine constitutive_j2_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el) !********************************************************************* !* plastic velocity gradient and its tangent * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - Lp : plastic velocity gradient * !* - dLp_dTstar : derivative of Lp (4th-rank tensor) * !********************************************************************* 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 !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i,k,l,m,n real(pReal) Temperature type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(3,3) :: Tstar33 real(pReal), dimension(3,3) :: Lp real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(9,9) :: dLp_dTstar real(pReal) norm_Tstar, squarenorm_Tstar, factor matID = phase_constitutionInstance(material_phase(ipc,ip,el)) Tstar33 = math_Mandel6to33(Tstar_v) squarenorm_Tstar = math_mul6x6(Tstar_v,Tstar_v) norm_Tstar = dsqrt(squarenorm_Tstar) !* Initialization of Lp and dLp_dTstar Lp = 0.0_pReal dLp_dTstar = 0.0_pReal !* for Tstar==0 both Lp and dLp_dTstar are zero (if not n==1) if (norm_Tstar > 0) then !* Calculation of Lp Lp = dsqrt(1.5_pReal)*Tstar33/norm_Tstar*constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* & (dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))**constitutive_j2_n(matID) !* Calculation of the tangent of Lp factor = dsqrt(1.5_pReal)*constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* & (dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)/state(ipc,ip,el)%p(1))**constitutive_j2_n(matID) * & norm_Tstar**(constitutive_j2_n(matID)-1.0_pReal) dLp_dTstar3333 = 0.0_pReal forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dTstar3333(k,l,m,n) = Tstar33(k,l)*Tstar33(m,n) * (constitutive_j2_n(matID)-1.0_pReal)/squarenorm_Tstar forall (k=1:3,l=1:3) & dLp_dTstar3333(k,l,k,l) = dLp_dTstar3333(k,l,k,l) + 1.0_pReal dLp_dTstar = math_Plain3333to99(factor * dLp_dTstar3333) end if return endsubroutine function constitutive_j2_dotState(Tstar_v,Temperature,state,ipc,ip,el) !********************************************************************* !* rate of change of microstructure * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_dotState : evolution of state variable * !********************************************************************* 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 !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID real(pReal) Temperature type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(1) :: constitutive_j2_dotState real(pReal) norm_Tstar matID = phase_constitutionInstance(material_phase(ipc,ip,el)) norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v)) constitutive_j2_dotState = constitutive_j2_h0(matID)*(1.0_pReal-state(ipc,ip,el)%p(1)/constitutive_j2_s_sat(matID))** & constitutive_j2_w0(matID) * & constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* & (dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** & constitutive_j2_n(matID) return endfunction pure function constitutive_j2_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - dt : current time increment * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* 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 !* Definition of variables integer(pInt), intent(in) :: ipc,ip,el real(pReal), intent(in) :: dt,Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state integer(pInt) matID,o,i,c,n real(pReal) norm_Tstar real(pReal), dimension(constitutive_j2_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & constitutive_j2_postResults matID = phase_constitutionInstance(material_phase(ipc,ip,el)) norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v)) c = 0_pInt constitutive_j2_postResults = 0.0_pReal do o = 1,phase_Noutput(material_phase(ipc,ip,el)) select case(constitutive_j2_output(o,matID)) case ('flowstress') constitutive_j2_postResults(c+1) = state(ipc,ip,el)%p(1) c = c + 1 case ('strainrate') constitutive_j2_postResults(c+1) = constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* & (dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** & constitutive_j2_n(matID) c = c + 1 end select enddo return endfunction END MODULE