!************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - constitutive equations * !* - parameters definition * !* - orientations * !************************************ MODULE constitutive !*** Include other modules *** use prec, only: pReal,pInt implicit none ! MISSING consistency check after reading 'mattex.mpie' character(len=300), parameter :: mattexFile = 'mattex.mpie' !************************************* !* Definition of material properties * !************************************* !* Physical parameter, attack_frequency != Debye frequency real(pReal), parameter :: attack_frequency = 1.0e10_pReal !* Physical parameter, Boltzmann constant in J/Kelvin real(pReal), parameter :: kB = 1.38e-23_pReal !* Physical parameter, Avogadro number in 1/mol real(pReal), parameter :: avogadro = 6.022e23_pReal !* Physical parameter, Gaz constant in J.mol/Kelvin real(pReal), parameter :: Rgaz = 8.314_pReal !************************************* !* Definition of material properties * !************************************* !* Number of materials integer(pInt) material_maxN !* Lattice structure and number of selected slip or twin systems per material integer(pInt), dimension(:) , allocatable :: material_CrystalStructure integer(pInt), dimension(:) , allocatable :: material_Nslip integer(pInt), dimension(:) , allocatable :: material_Ntwin !* Maximum number of selected slip or twin systems over materials integer(pInt) material_maxNslip integer(pInt) material_maxNtwin !* Elastic constants and matrices real(pReal), dimension(:) , allocatable :: material_C11 real(pReal), dimension(:) , allocatable :: material_C12 real(pReal), dimension(:) , allocatable :: material_C13 real(pReal), dimension(:) , allocatable :: material_C33 real(pReal), dimension(:) , allocatable :: material_C44 real(pReal), dimension(:) , allocatable :: material_Gmod real(pReal), dimension(:,:,:) , allocatable :: material_Cslip_66 real(preal), dimension(:,:,:,:) , allocatable :: material_Ctwin_66 !* Visco-plastic material parameters real(pReal) material_sfe real(pReal), dimension(:) , allocatable :: material_rho0 real(pReal), dimension(:) , allocatable :: material_bg real(pReal), dimension(:) , allocatable :: material_Qedge real(pReal), dimension(:) , allocatable :: material_Qsd real(pReal), dimension(:) , allocatable :: material_D0 real(pReal), dimension(:) , allocatable :: material_GrainSize real(pReal), dimension(:) , allocatable :: material_StackSize real(pReal), dimension(:) , allocatable :: material_ActivationLength real(pReal), dimension(:) , allocatable :: material_TwinSaturation real(pReal), dimension(:) , allocatable :: material_SiteScaling real(pReal), dimension(:) , allocatable :: material_c1 real(pReal), dimension(:) , allocatable :: material_c2 real(pReal), dimension(:) , allocatable :: material_c3 real(pReal), dimension(:) , allocatable :: material_c4 real(pReal), dimension(:) , allocatable :: material_c5 real(pReal), dimension(:) , allocatable :: material_c6 real(pReal), dimension(:) , allocatable :: material_c7 real(pReal), dimension(:) , allocatable :: material_c8 real(pReal), dimension(:) , allocatable :: material_q1 real(pReal), dimension(:) , allocatable :: material_q2 real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff !************************************ !* Definition of texture properties * !************************************ !* Number of textures, maximum number of Gauss and Fiber components integer(pInt) texture_maxN integer(pInt) texture_maxNGauss integer(pInt) texture_maxNFiber !* Textures definition character(len=80), dimension(:), allocatable :: texture_ODFfile character(len=80), dimension(:), allocatable :: texture_symmetry integer(pInt), dimension(:) , allocatable :: texture_Ngrains integer(pInt), dimension(:) , allocatable :: texture_NGauss integer(pInt),dimension(:) , allocatable :: texture_NFiber integer(pInt),dimension(:) , allocatable :: texture_NRandom integer(pInt),dimension(:) , allocatable :: texture_totalNgrains real(pReal), dimension(:,:,:) , allocatable :: texture_Gauss real(pReal), dimension(:,:,:) , allocatable :: texture_Fiber real(pReal), dimension(:,:,:,:), allocatable :: constitutive_EulerAngles !************************************ !* Grains * !************************************ integer(pInt) constitutive_maxNgrains integer(pInt), dimension(:,:) , allocatable :: constitutive_Ngrains integer(pInt), dimension(:,:,:) , allocatable :: constitutive_matID real(pReal), dimension(:,:,:) , allocatable :: constitutive_matVolFrac integer(pInt), dimension(:,:,:) , allocatable :: constitutive_texID real(pReal), dimension(:,:,:) , allocatable :: constitutive_texVolFrac !************************************ !* Kinetics variables * !************************************ real(pReal), dimension(:) , allocatable :: constitutive_tau_slip real(pReal), dimension(:) , allocatable :: constitutive_tau_twin real(pReal), dimension(:) , allocatable :: constitutive_gdot_slip real(pReal), dimension(:) , allocatable :: constitutive_fdot_twin real(pReal), dimension(:) , allocatable :: constitutive_dgdot_dtauslip real(pReal), dimension(:) , allocatable :: constitutive_dfdot_dtautwin real(pReal), dimension(:,:) , allocatable :: constitutive_dfdot_dtauslip real(pReal), dimension(:) , allocatable :: constitutive_locks real(pReal), dimension(:) , allocatable :: constitutive_grainboundaries real(pReal), dimension(:) , allocatable :: constitutive_twinboundaries real(pReal), dimension(:) , allocatable :: constitutive_recovery !************************************ !* State variables * !************************************ integer(pInt) constitutive_maxNstatevars integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nstatevars real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_old real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_new real(pReal), dimension(:) , allocatable :: constitutive_passing_stress real(pReal), dimension(:) , allocatable :: constitutive_jump_width real(pReal), dimension(:) , allocatable :: constitutive_activation_volume real(pReal), dimension(:) , allocatable :: constitutive_rho_m real(pReal), dimension(:) , allocatable :: constitutive_rho_f real(pReal), dimension(:) , allocatable :: constitutive_rho_p real(pReal), dimension(:) , allocatable :: constitutive_g0_slip real(pReal), dimension(:) , allocatable :: constitutive_twin_volume real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_s real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_t real(pReal), dimension(:) , allocatable :: constitutive_twin_mfp !************************************ !* Interaction matrices * !************************************ real(pReal), dimension(:,:,:), allocatable :: constitutive_Pforest real(pReal), dimension(:,:,:), allocatable :: constitutive_Pparallel !************************************ !* Results * !************************************ integer(pInt) constitutive_maxNresults integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults CONTAINS !**************************************** !* - constitutive_Init !* - constitutive_CountSections !* - constitutive_Parse_UnknownPart !* - constitutive_Parse_MaterialPart !* - constitutive_Parse_TexturePart !* - constitutive_Parse_MatTexDat !* - constitutive_Assignment !* - constitutive_HomogenizedC !* - constitutive_Microstructure !* - constitutive_LpAndItsTangent !* - consistutive_DotState !**************************************** subroutine constitutive_Init() !************************************** !* Module initialization * !************************************** call constitutive_Parse_MatTexDat(mattexFile) call constitutive_Assignment() end subroutine subroutine constitutive_CountSections(file,count,part) !********************************************************************* !* This subroutine reads a "part" from the input file until the next * !* part is reached and counts the number of "sections" in the part * !* INPUT: * !* - file : file ID * !* OUTPUT: * !* - part : name of the next "part" * !* - count : number of sections inside the current "part" * !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) part,line,tag integer(pInt) file,count integer(pInt), dimension(3) :: positions count=0 part='' do read(file,'(a80)',END=100) line positions=IO_stringPos(line,1) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then part=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then count=count+1 endif enddo 100 return end subroutine character(len=80) function constitutive_assignNGaussAndFiber(file) !********************************************************************* !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) line,tag integer(pInt) file,section integer(pInt), dimension(3) :: positions constitutive_assignNGaussAndFiber='' section = 0_pInt do read(file,'(a80)',END=100) line positions=IO_stringPos(line,1) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_assignNGaussAndFiber=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 texture_NGauss(section) = 0_pInt texture_NFiber(section) = 0_pInt elseif (tag=='(gauss)') then texture_NGauss(section)=texture_NGauss(section)+1 elseif (tag=='(fiber)') then texture_NFiber(section)=texture_NFiber(section)+1 endif enddo 100 return end function character(len=80) function constitutive_Parse_UnknownPart(file) !********************************************************************* !* read an unknown "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 1 integer(pInt) file integer(pInt), dimension(1+2*maxNchunks) :: positions constitutive_parse_unknownPart='' do read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_Parse_UnknownPart=tag(2:len_trim(tag)-1) exit endif enddo 100 return end function character(len=80) function constitutive_Parse_MaterialPart(file) !********************************************************************* !* This function reads a material "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt,pReal use IO implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 7 integer(pInt) i,file,section integer(pInt), dimension(1+2*maxNchunks) :: positions section = 0 constitutive_parse_materialPart = '' do while(.true.) read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) ! parse leading chunks tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_parse_materialPart=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 else if (section>0) then !$OMP CRITICAL (write2out) select case(tag) case ('lattice_structure') material_CrystalStructure(section)=IO_intValue(line,positions,2) write(6,*) 'lattice_structure', material_CrystalStructure(section) case ('nslip') material_Nslip(section)=IO_intValue(line,positions,2) write(6,*) 'nslip', material_Nslip(section) case ('ntwin') material_Ntwin(section)=IO_intValue(line,positions,2) write(6,*) 'ntwin', material_Ntwin(section) case ('c11') material_C11(section)=IO_floatValue(line,positions,2) write(6,*) 'c11', material_C11(section) case ('c12') material_C12(section)=IO_floatValue(line,positions,2) write(6,*) 'c12', material_C12(section) case ('c13') material_C13(section)=IO_floatValue(line,positions,2) write(6,*) 'c13', material_C13(section) case ('c33') material_C33(section)=IO_floatValue(line,positions,2) write(6,*) 'c33', material_C33(section) case ('c44') material_C44(section)=IO_floatValue(line,positions,2) write(6,*) 'c44', material_C44(section) case ('rho0') material_rho0(section)=IO_floatValue(line,positions,2) write(6,*) 'rho0', material_rho0(section) case ('interaction_coefficients') do i=1,6 material_SlipIntCoeff(i,section)=IO_floatValue(line,positions,i+1) write(6,*) 'interaction_coefficients', material_SlipIntCoeff(i,section) enddo case ('burgers') material_bg(section)=IO_floatValue(line,positions,2) write(6,*) 'burgers', material_bg(section) case ('qedge') material_Qedge(section)=IO_floatValue(line,positions,2) write(6,*) 'Qedge', material_Qedge(section) case ('qsd') material_Qsd(section)=IO_floatValue(line,positions,2) write(6,*) 'Qsd', material_Qsd(section) case ('diff0') material_D0(section)=IO_floatValue(line,positions,2) write(6,*) 'diff0', material_D0(section) case ('grain_size') material_GrainSize(section)=IO_floatValue(line,positions,2) write(6,*) 'grain_size', material_GrainSize(section) case ('stack_size') material_StackSize(section)=IO_floatValue(line,positions,2) write(6,*) 'stack_size', material_StackSize(section) case ('f_sat') material_TwinSaturation(section)=IO_floatValue(line,positions,2) write(6,*) 'twin saturation', material_TwinSaturation(section) case ('site_scaling') material_SiteScaling(section)=IO_floatValue(line,positions,2) write(6,*) 'site_scaling', material_SiteScaling(section) case ('c1') material_c1(section)=IO_floatValue(line,positions,2) write(6,*) 'c1', material_c1(section) case ('c2') material_c2(section)=IO_floatValue(line,positions,2) write(6,*) 'c2', material_c2(section) case ('c3') material_c3(section)=IO_floatValue(line,positions,2) write(6,*) 'c3', material_c3(section) case ('c4') material_c4(section)=IO_floatValue(line,positions,2) write(6,*) 'c4', material_c4(section) case ('c5') material_c5(section)=IO_floatValue(line,positions,2) write(6,*) 'c5', material_c5(section) case ('c6') material_c6(section)=IO_floatValue(line,positions,2) write(6,*) 'c6', material_c6(section) case ('c7') material_c7(section)=IO_floatValue(line,positions,2) write(6,*) 'c7', material_c7(section) case ('c8') material_c8(section)=IO_floatValue(line,positions,2) write(6,*) 'c8', material_c8(section) case ('q1') material_q1(section)=IO_floatValue(line,positions,2) write(6,*) 'q1', material_q1(section) case ('q2') material_q2(section)=IO_floatValue(line,positions,2) write(6,*) 'q2', material_q2(section) end select !$OMP END CRITICAL (write2out) endif endif enddo 100 return end function character(len=80) function constitutive_Parse_TexturePart(file) !********************************************************************* !* This function reads a texture "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt use IO use math, only: inRad implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 13 ! may be more than 10 chunks ..? integer(pInt) file,section,gaussCount,fiberCount,i integer(pInt), dimension(1+2*maxNchunks) :: positions section = 0 gaussCount = 0 fiberCount = 0 constitutive_parse_texturePart = '' do while(.true.) read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) ! parse leading chunks tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_parse_texturePart=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 gaussCount=0 fiberCount=0 else if (section>0) then select case(tag) case ('hybridIA') texture_ODFfile(section)=IO_stringValue(line,positions,2) case ('(gauss)') gaussCount=gaussCount+1 do i=2,10,2 tag=IO_lc(IO_stringValue(line,positions,i)) select case (tag) case('phi1') texture_Gauss(1,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('phi') texture_Gauss(2,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('phi2') texture_Gauss(3,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('scatter') texture_Gauss(4,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('fraction') texture_Gauss(5,gaussCount,section)=IO_floatValue(line,positions,i+1) end select enddo case ('(fiber)') fiberCount=fiberCount+1 do i=2,12,2 tag=IO_lc(IO_stringValue(line,positions,i)) select case (tag) case('alpha1') texture_fiber(1,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('alpha2') texture_fiber(2,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('beta1') texture_fiber(3,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('beta2') texture_fiber(4,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('scatter') texture_fiber(5,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('fraction') texture_fiber(6,fiberCount,section)=IO_floatValue(line,positions,i+1) end select enddo case ('ngrains') texture_Ngrains(section)=IO_intValue(line,positions,2) case ('symmetry') texture_symmetry(section)=IO_stringValue(line,positions,2) end select endif endif enddo 100 return end function subroutine constitutive_Parse_MatTexDat(filename) !********************************************************************* !* This function reads the material and texture input file * !* INPUT: * !* - filename : name of input file * !********************************************************************* use prec, only: pReal,pInt use IO, only: IO_error, IO_open_file use math, only: math_Mandel3333to66, math_Voigt66to3333 use lattice, only: lattice_MaxMaxNslipOfStructure,lattice_MaxMaxNtwinOfStructure implicit none !* Definition of variables character(len=*) filename character(len=80) part,formerPart integer(pInt) sectionCount,i,j,k, fileunit ! set fileunit fileunit=200 !----------------------------- !* First reading: number of materials and textures !----------------------------- !* determine material_maxN and texture_maxN from last respective parts if(IO_open_file(fileunit,filename)==.false.) goto 100 part = '_dummy_' do while (part/='') formerPart = part call constitutive_CountSections(fileunit,sectionCount,part) select case (formerPart) case ('materials') material_maxN = sectionCount case ('textures') texture_maxN = sectionCount end select enddo !* Array allocation allocate(material_CrystalStructure(material_maxN)) ; material_CrystalStructure=0_pInt allocate(material_Nslip(material_maxN)) ; material_Nslip=0_pInt allocate(material_Ntwin(material_maxN)) ; material_Ntwin=0_pInt allocate(material_C11(material_maxN)) ; material_C11=0.0_pReal allocate(material_C12(material_maxN)) ; material_C12=0.0_pReal allocate(material_C13(material_maxN)) ; material_C13=0.0_pReal allocate(material_C33(material_maxN)) ; material_C33=0.0_pReal allocate(material_C44(material_maxN)) ; material_C44=0.0_pReal allocate(material_Gmod(material_maxN)) ; material_Gmod=0.0_pReal allocate(material_Cslip_66(6,6,material_maxN)) ; material_Cslip_66=0.0_pReal allocate(material_Ctwin_66(6,6,lattice_MaxMaxNtwinOfStructure,material_maxN)) ; material_Ctwin_66=0.0_pReal allocate(material_rho0(material_maxN)) ; material_rho0=0.0_pReal allocate(material_SlipIntCoeff(lattice_MaxMaxNslipOfStructure,material_maxN)) ; material_SlipIntCoeff=0.0_pReal allocate(material_bg(material_maxN)) ; material_bg=0.0_pReal allocate(material_Qedge(material_maxN)) ; material_Qedge=0.0_pReal allocate(material_Qsd(material_maxN)) ; material_Qsd=0.0_pReal allocate(material_D0(material_maxN)) ; material_D0=0.0_pReal allocate(material_GrainSize(material_maxN)) ; material_GrainSize=0.0_pReal allocate(material_StackSize(material_maxN)) ; material_StackSize=0.0_pReal allocate(material_ActivationLength(material_maxN)) ; material_ActivationLength=0.0_pReal allocate(material_TwinSaturation(material_maxN)) ; material_TwinSaturation=0.0_pReal allocate(material_SiteScaling(material_maxN)) ; material_SiteScaling=0.0_pReal allocate(material_c1(material_maxN)) ; material_c1=0.0_pReal allocate(material_c2(material_maxN)) ; material_c2=0.0_pReal allocate(material_c3(material_maxN)) ; material_c3=0.0_pReal allocate(material_c4(material_maxN)) ; material_c4=0.0_pReal allocate(material_c5(material_maxN)) ; material_c5=0.0_pReal allocate(material_c6(material_maxN)) ; material_c6=0.0_pReal allocate(material_c7(material_maxN)) ; material_c7=0.0_pReal allocate(material_c8(material_maxN)) ; material_c8=0.0_pReal allocate(material_q1(material_maxN)) ; material_q1=0.0_pReal allocate(material_q2(material_maxN)) ; material_q2=0.0_pReal allocate(texture_ODFfile(texture_maxN)) ; texture_ODFfile='' allocate(texture_Ngrains(texture_maxN)) ; texture_Ngrains=0_pInt allocate(texture_symmetry(texture_maxN)) ; texture_symmetry='' allocate(texture_NGauss(texture_maxN)) ; texture_NGauss=0_pInt allocate(texture_NFiber(texture_maxN)) ; texture_NFiber=0_pInt allocate(texture_NRandom(texture_maxN)) ; texture_NRandom=0_pInt !----------------------------- !* Second reading: number of Gauss and Fiber !----------------------------- rewind(fileunit) part = '_dummy_' do while (part/='') select case (part) case ('textures') part = constitutive_assignNGaussAndFiber(fileunit) case default part = constitutive_Parse_UnknownPart(fileunit) end select enddo !* Array allocation texture_maxNGauss=maxval(texture_NGauss) texture_maxNFiber=maxval(texture_NFiber) allocate(texture_Gauss(5,texture_maxNGauss,texture_maxN)) ; texture_Gauss=0.0_pReal allocate(texture_Fiber(6,texture_maxNFiber,texture_maxN)) ; texture_Fiber=0.0_pReal !----------------------------- !* Third reading: materials and textures are stored !----------------------------- rewind(fileunit) part='_dummy_' do while (part/='') select case (part) case ('materials') part=constitutive_Parse_MaterialPart(fileunit) case ('textures') part=constitutive_Parse_TexturePart(fileunit) case default part=constitutive_Parse_UnknownPart(fileunit) end select enddo close(fileunit) !* Construction of the elasticity matrices do i=1,material_maxN select case (material_CrystalStructure(i)) case(1:2) ! cubic(s) material_Gmod(i)=material_C44(i) forall(k=1:3) forall(j=1:3) material_Cslip_66(k,j,i)=material_C12(i) endforall material_Cslip_66(k,k,i)=material_C11(i) material_Cslip_66(k+3,k+3,i)=material_C44(i) endforall case(3) ! hcp material_Gmod(i)=material_C44(i) !* MISSING: Warning message: C44 in hexagonal structures? material_Cslip_66(1,1,i)=material_C11(i) material_Cslip_66(2,2,i)=material_C11(i) material_Cslip_66(3,3,i)=material_C33(i) material_Cslip_66(1,2,i)=material_C12(i) material_Cslip_66(2,1,i)=material_C12(i) material_Cslip_66(1,3,i)=material_C13(i) material_Cslip_66(3,1,i)=material_C13(i) material_Cslip_66(2,3,i)=material_C13(i) material_Cslip_66(3,2,i)=material_C13(i) material_Cslip_66(4,4,i)=material_C44(i) material_Cslip_66(5,5,i)=material_C44(i) material_Cslip_66(6,6,i)=0.5_pReal*(material_C11(i)-material_C12(i)) end select material_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(material_Cslip_66(:,:,i))) enddo ! MISSING some consistency checks may be..? ! if ODFfile present then set NGauss NFiber =0 return 100 call IO_error(200) ! corrupt materials_textures file end subroutine subroutine constitutive_Assignment() !********************************************************************* !* This subroutine assign material parameters according to ipc,ip,el * !********************************************************************* use prec, only: pReal,pInt use math, only: math_sampleGaussOri,math_sampleFiberOri,math_sampleRandomOri,math_symmetricEulers,math_EulerToR,& math_Mandel3333to66,math_Mandel66to3333 use mesh, only: mesh_NcpElems,FE_Nips,mesh_maxNips,mesh_element use IO, only: IO_hybridIA use lattice, only: lattice_SlipIntType,lattice_sn,lattice_st,lattice_Qtwin,lattice_Sslip_v,lattice_Sslip implicit none !* Definition of variables integer(pInt) e,g,i,j,k,l,m,n,o,p,q,r,s integer(pInt) matID,texID real(pReal) x,y integer(pInt), dimension(:,:,:), allocatable :: hybridIA_population integer(pInt), dimension(texture_maxN) :: Ncomponents,Nsym,multiplicity,ODFmap,sampleCount real(pReal), dimension(3,4*(1+texture_maxNGauss+texture_maxNfiber)) :: Euler real(pReal), dimension(4*(1+texture_maxNGauss+texture_maxNfiber)) :: texVolfrac real(pReal), dimension(texture_maxN) :: sumVolfrac real(pReal), dimension(3,3,3,3) :: C_3333,Ctwin_3333 real(pReal), dimension(3,3) :: Qtwin ! process textures o = 0_pInt ! ODF counter ODFmap = 0_pInt ! blank mapping sampleCount = 0_pInt ! count orientations assigned per texture do texID=1,texture_maxN select case (texture_symmetry(texID)) ! set symmetry factor case ('orthotropic') Nsym(texID) = 4_pInt case ('monoclinic') Nsym(texID) = 2_pInt case default Nsym(texID) = 1_pInt end select if (texture_ODFfile(texID)=='') then ! texture components sumVolfrac(texID) = sum(texture_gauss(5,:,texID))+sum(texture_fiber(6,:,texID)) if (sumVolfrac(texID)<1.0_pReal) texture_NRandom(texID) = 1_pInt ! check whether random component missing Ncomponents(texID) = texture_NGauss(texID)+texture_NFiber(texID)+texture_NRandom(texID) else ! hybrid IA o = o+1 ODFmap(texID) = o ! remember mapping Ncomponents(texID) = 1_pInt ! single "component" endif ! adjust multiplicity and number of grains per IP of components multiplicity(texID) = max(1_pInt,texture_Ngrains(texID)/Ncomponents(texID)/Nsym(texID)) if (mod(texture_Ngrains(texID),Ncomponents(texID)*Nsym(texID)) /= 0_pInt) then texture_Ngrains(texID) = multiplicity(texID)*Ncomponents(texID)*Nsym(texID) !$OMP CRITICAL (write2out) write (6,*) 'changed Ngrains to',texture_Ngrains(texID),' for texture',texID !$OMP END CRITICAL (write2out) endif enddo !* publish globals constitutive_maxNgrains = maxval(texture_Ngrains) material_maxNslip = maxval(material_Nslip) ! max of slip systems among materials present material_maxNtwin = maxval(material_Ntwin) ! max of twin systems among materials present constitutive_maxNstatevars = maxval(material_Nslip) + maxval(material_Ntwin) ! ----------------------------------------------------------------------------------------------------------------------- constitutive_maxNresults = 26_pInt ! ----------------------------------------------------------------------------------------------------------------------- !* calc texture_totalNgrains allocate(texture_totalNgrains(texture_maxN)) ; texture_totalNgrains=0_pInt do i=1,mesh_NcpElems texID = mesh_element(4,i) texture_totalNgrains(texID) = texture_totalNgrains(texID) + FE_Nips(mesh_element(2,i))*texture_Ngrains(texID) enddo ! generate hybridIA samplings for ODFfile textures to later draw from these populations allocate(hybridIA_population(3,maxval(texture_totalNgrains/Nsym,ODFmap /= 0),o)) do texID = 1,texture_maxN if (ODFmap(texID) > 0) & hybridIA_population(:,:,ODFmap(texID)) = IO_hybridIA(texture_totalNgrains(texID)/Nsym(texID),texture_ODFfile(texID)) enddo !* Array allocation allocate(constitutive_Ngrains(mesh_maxNips,mesh_NcpElems)) ; constitutive_Ngrains=0_pInt allocate(constitutive_matID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_matID=0_pInt allocate(constitutive_texID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_texID=0_pInt allocate(constitutive_MatVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_MatVolFrac=0.0_pReal allocate(constitutive_TexVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_TexVolFrac=0.0_pReal allocate(constitutive_EulerAngles(3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_EulerAngles=0.0_pReal allocate(constitutive_Nresults(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nresults=0_pInt allocate(constitutive_Nstatevars(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nstatevars=0_pInt allocate(constitutive_state_old(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) constitutive_state_old=0.0_pReal allocate(constitutive_state_new(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) constitutive_state_new=0.0_pReal allocate(constitutive_Pforest(material_maxNslip,material_maxNslip,material_maxN)) constitutive_Pforest=0.0_pReal allocate(constitutive_Pparallel(material_maxNslip,material_maxNslip,material_maxN)) constitutive_Pparallel=0.0_pReal allocate(constitutive_rho_p(material_maxNslip)) ; constitutive_rho_p=0.0_pReal allocate(constitutive_rho_f(material_maxNslip)) ; constitutive_rho_f=0.0_pReal allocate(constitutive_rho_m(material_maxNslip)) ; constitutive_rho_m=0.0_pReal allocate(constitutive_passing_stress(material_maxNslip)) ; constitutive_passing_stress=0.0_pReal allocate(constitutive_jump_width(material_maxNslip)) ; constitutive_jump_width=0.0_pReal allocate(constitutive_activation_volume(material_maxNslip)) ; constitutive_activation_volume=0.0_pReal allocate(constitutive_g0_slip(material_maxNslip)) ; constitutive_g0_slip=0.0_pReal allocate(constitutive_twin_volume(material_maxNtwin)) ; constitutive_twin_volume=0.0_pReal allocate(constitutive_inv_intertwin_len_s(material_maxNslip)) ; constitutive_inv_intertwin_len_s=0.0_pReal allocate(constitutive_inv_intertwin_len_t(material_maxNtwin)) ; constitutive_inv_intertwin_len_t=0.0_pReal allocate(constitutive_twin_mfp(material_maxNtwin)) ; constitutive_twin_mfp=0.0_pReal allocate(constitutive_tau_slip(material_maxNslip)) ; constitutive_tau_slip=0.0_pReal allocate(constitutive_tau_twin(material_maxNtwin)) ; constitutive_tau_twin=0.0_pReal allocate(constitutive_gdot_slip(material_maxNslip)) ; constitutive_gdot_slip=0.0_pReal allocate(constitutive_fdot_twin(material_maxNtwin)) ; constitutive_fdot_twin=0.0_pReal allocate(constitutive_dgdot_dtauslip(material_maxNslip)) ; constitutive_dgdot_dtauslip=0.0_pReal allocate(constitutive_dfdot_dtautwin(material_maxNtwin)) ; constitutive_dfdot_dtautwin=0.0_pReal allocate(constitutive_dfdot_dtauslip(material_maxNtwin,material_maxNslip)) ; constitutive_dfdot_dtauslip=0.0_pReal allocate(constitutive_locks(material_maxNslip)) ; constitutive_locks=0.0_pReal allocate(constitutive_grainboundaries(material_maxNslip)) ; constitutive_grainboundaries=0.0_pReal allocate(constitutive_twinboundaries(material_maxNslip)) ; constitutive_twinboundaries=0.0_pReal allocate(constitutive_recovery(material_maxNslip)) ; constitutive_locks=0.0_pReal !* Assignment of all grains in all IPs of all cp-elements do e=1,mesh_NcpElems matID=mesh_element(3,e) texID=mesh_element(4,e) do i=1,FE_Nips(mesh_element(2,e)) g = 0_pInt ! grain counter do m = 1,multiplicity(texID) o = 0_pInt ! component counter if (texture_ODFfile(texID)=='') then do k = 1,texture_nGauss(texID) ! *** gauss *** o = o+1 Euler(:,o) = math_sampleGaussOri(texture_Gauss(1:3,k,texID),texture_Gauss(4,k,texID)) texVolFrac(o) = texture_Gauss(5,k,texID) enddo do k = 1,texture_nFiber(texID) ! *** fiber *** o = o+1 Euler(:,o) = math_sampleFiberOri(texture_Fiber(1:2,k,texID),texture_Fiber(3:4,k,texID),texture_Fiber(5,k,texID)) texVolFrac(o) = texture_Fiber(6,k,texID) enddo do k = 1,texture_nRandom(texID) ! *** random *** o = o+1 Euler(:,o) = math_sampleRandomOri() texVolfrac(o) = 1.0_pReal-sumVolfrac(texID) enddo else ! *** hybrid IA *** o = 1 ! only singular orientation, i.e. single "component" Euler(:,o) = hybridIA_population(:,1+sampleCount(texID),ODFmap(texID)) texVolfrac(o) = 1.0_pReal endif if (Nsym(texID) > 1) then ! symmetry generates additional orientations forall (k=1:o) Euler(:,1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = & math_symmetricEulers(texture_symmetry(texID),Euler(:,k)) texVolfrac(1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = texVolfrac(k) end forall endif do s = 1,Nsym(texID)*o ! loop over orientations to be assigned to ip (ex multiplicity) g = g+1 ! next "grain" constitutive_matID(g,i,e) = matID ! copy matID of element constitutive_texID(g,i,e) = texID ! copy texID of element constitutive_MatVolFrac(g,i,e) = 1.0_pReal ! singular material (so far) constitutive_TexVolFrac(g,i,e) = texVolfrac(s)/multiplicity(texID)/Nsym(texID) constitutive_Nstatevars(g,i,e) = material_Nslip(matID) + material_Ntwin(matID)! number of state variables (i.e. tau_c of each slip system) ! ----------------------------------------------------------------------------------------------------------------------- constitutive_Nresults(g,i,e) = 26 ! number of constitutive results output by constitutive_post_results ! ----------------------------------------------------------------------------------------------------------------------- constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation forall (l=1:material_Nslip(matID)) ! initialize state variables constitutive_state_old(l,g,i,e) = material_rho0(matID) constitutive_state_new(l,g,i,e) = material_rho0(matID) end forall enddo ! components sampleCount(texID) = sampleCount(texID)+1 ! next member of hybrid IA population enddo ! multiplicity enddo ! ip enddo ! cp_element !* Construction of the rotated elasticity matrices for twinning do i=1,material_maxN C_3333=math_Mandel66to3333(material_Cslip_66(:,:,i)) do j=1,material_Ntwin(i) Qtwin=lattice_Qtwin(:,:,j,material_CrystalStructure(i)) do k=1,3 do l=1,3 do m=1,3 do n=1,3 Ctwin_3333(k,l,m,n)=0.0_pReal do p=1,3 do q=1,3 do r=1,3 do s=1,3 Ctwin_3333(k,l,m,n)=Ctwin_3333(k,l,m,n)+C_3333(p,q,r,s)*Qtwin(k,p)*Qtwin(l,q)*Qtwin(m,r)*Qtwin(n,s) enddo enddo enddo enddo enddo enddo enddo enddo !* Mapping back to 66-format of the matrices material_Ctwin_66(:,:,j,i) = math_Mandel3333to66(Ctwin_3333) enddo enddo !* Construction of the hardening matrices do i=1,material_maxN !* Iteration over the systems do j=1,material_Nslip(i) do k=1,material_Nslip(i) !* Projection of the dislocation * x=dot_product(lattice_sn(:,j,i),lattice_st(:,k,i)) y=1.0_pReal-x**(2.0_pReal) !* Interaction matrix * constitutive_Pforest(j,k,i)=abs(x)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i) if (y>0.0_pReal) then constitutive_Pparallel(j,k,i)=sqrt(y)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i) else constitutive_Pparallel(j,k,i)=0.0_pReal endif enddo enddo enddo end subroutine function constitutive_HomogenizedC(state,ipc,ip,el) !********************************************************************* !* This function returns the 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 implicit none !* Definition of variables integer(pInt) i,ipc,ip,el integer(pInt) matID real(pReal), dimension(6,6) :: constitutive_homogenizedC real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Homogenization scheme constitutive_homogenizedC = material_Cslip_66(:,:,matID) return end function subroutine constitutive_Microstructure(state,Tp,ipc,ip,el) !********************************************************************* !* This function calculates from state needed variables * !* INPUT: * !* - state : state variables * !* - Tp : temperature * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt use math, only: pi implicit none !* Definition of variables integer(pInt) i,j,ipc,ip,el integer(pInt) matID real(pReal) Tp real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Quantities derived from state - slip !$OMP CRITICAL (evilmatmul) constitutive_rho_f=matmul(constitutive_Pforest (1:material_Nslip(matID),1:material_Nslip(matID),matID),state) constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state) !$OMP END CRITICAL (evilmatmul) do i=1,material_Nslip(matID) constitutive_passing_stress(i) = material_c1(matID)*material_Gmod(matID)*material_bg(matID)*sqrt(constitutive_rho_p(i)) constitutive_jump_width(i) = material_c2(matID)/sqrt(constitutive_rho_f(i)) constitutive_activation_volume(i) = material_c3(matID)*constitutive_jump_width(i)*material_bg(matID)**2.0_pReal constitutive_rho_m(i) = (2.0_pReal*kB*Tp*sqrt(constitutive_rho_p(i)))/& (material_c1(matID)*material_c3(matID)*material_Gmod(matID)*constitutive_jump_width(i)*& material_bg(matID)**3.0_pReal) constitutive_g0_slip(i) = constitutive_rho_m(i)*material_bg(matID)*attack_frequency*constitutive_jump_width(i)*& exp(-material_Qedge(matID)/(kB*Tp)) enddo return end subroutine subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el) !********************************************************************* !* This subroutine contains the constitutive equation for * !* calculating the velocity gradient * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - Tp : temperature * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - Lp : plastic velocity gradient * !* - dLp_dTstar : derivative of Lp (4th-order tensor) * !********************************************************************* use prec, only: pReal,pInt use lattice, only: lattice_Sslip,lattice_Sslip_v use math, only: pi,math_Plain3333to99 implicit none !* Definition of variables integer(pInt) i,j,k,l,m,n,ipc,ip,el integer(pInt) matID real(pReal) Tp real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(3,3) :: Lp,Sslip real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(9,9) :: dLp_dTstar real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,dgdot_dtauslip,tau_slip !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) Lp = 0.0_pReal dLp_dTstar3333 = 0.0_pReal !* Calculation of Lp - slip gdot_slip = 0.0_pReal dgdot_dtauslip = 0.0_pReal do i=1,material_Nslip(matID) Sslip = lattice_Sslip(:,:,i,material_CrystalStructure(matID)) tau_slip(i) = dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID))) if (abs(tau_slip(i)) > constitutive_passing_stress(i)) then gdot_slip(i) = constitutive_g0_slip(i)*sign(1.d0,tau_slip(i))*& sinh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp)) dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(Kb*Tp)*& cosh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp)) endif Lp = Lp + gdot_slip(i) * Sslip enddo write(6,*) 'constitutive_g0_slip' write(6,*) constitutive_g0_slip !* Calculation of the tangent of Lp do i=1,material_Nslip(matID) Sslip = lattice_Sslip(:,:,i,material_CrystalStructure(matID)) forall (k=1:3,l=1:3,m=1:3,n=1:3) dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(i) * Sslip(k,l) * Sslip(m,n) endforall enddo dLp_dTstar = math_Plain3333to99(dLp_dTstar3333) return end subroutine function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el) !********************************************************************* !* This subroutine contains the constitutive equation for * !* calculating rate of change of microstructure * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - Tp : temperature * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_DotState : evolution of state variable * !********************************************************************* use prec, only: pReal,pInt use math, only: pi use lattice, only: lattice_Sslip_v implicit none !* Definition of variables integer(pInt) i,j,ipc,ip,el integer(pInt) matID real(pReal) Tp real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,tau_slip real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: locks,grainboundaries real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: athermal_recovery,thermal_recovery !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) constitutive_dotState = 0.0_pReal !* Dislocation density evolution gdot_slip = 0.0_pReal do i=1,material_Nslip(matID) tau_slip(i) = dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID))) if (abs(tau_slip(i)) > constitutive_passing_stress(i)) then gdot_slip(i) = constitutive_g0_slip(i)*sign(1.d0,tau_slip(i))*& sinh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp)) locks(i) = (sqrt(constitutive_rho_f(i))*abs(gdot_slip(i)))/(material_c4(matID)*material_bg(matID)) grainboundaries(i) = abs(gdot_slip(i))/(material_c5(matID)*material_bg(matID)*material_GrainSize(matID)) athermal_recovery(i) = material_c7(matID)*state(i)*abs(gdot_slip(i)) thermal_recovery(i) = material_c8(matID)*abs(tau_slip(i))*state(i)**2*((material_D0(matID)*material_bg(matID)**3)/& (kB*Tp))*exp(-material_Qsd(matID)/(kB*Tp)) constitutive_dotState(i) = locks(i)+grainboundaries(i)-athermal_recovery(i) !-thermal_recovery(i) endif enddo return end function function constitutive_post_results(Tstar_v,state,Tp,dt,ipc,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - dt : current time increment * !* - Tp : temperature * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !* constitutive_Nresults has to be set accordingly in _Assignment * !********************************************************************* use prec, only: pReal,pInt use lattice, only: lattice_Sslip_v implicit none !* Definition of variables integer(pInt) i,ipc,ip,el integer(pInt) matID real(pReal) Tp,dt real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state,tau_slip,gdot_slip real(pReal), dimension(constitutive_Nresults(ipc,ip,el)) :: constitutive_post_results !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) constitutive_post_results=0.0_pReal !* Output variables if(constitutive_Nresults(ipc,ip,el)==0) return !* Dislocation density evolution do i=1,material_Nslip(matID) tau_slip(i) = dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID))) if (abs(tau_slip(i)) > constitutive_passing_stress(i)) then gdot_slip(i) = constitutive_g0_slip(i)*sign(1.d0,tau_slip(i))*& sinh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp)) endif enddo !* Output variables constitutive_post_results(1) = sum(state(1:material_Nslip(matID))) do i=1,material_Nslip(matID) constitutive_post_results(2+i) = state(i) enddo do i=1,material_Nslip(matID) constitutive_post_results(2+material_Nslip(matID)+i) = constitutive_passing_stress(i) enddo return end function END MODULE