!************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - constitutive equations * !* - parameters definition * !* - orientations * !************************************ ! [Alu] ! constitution dislobased ! (output) dislodensity ! (output) rateofshear ! lattice_structure 1 ! Nslip 12 ! ! c11 106.75e9 ! c12 60.41e9 ! c44 28.34e9 ! ! burgers 2.86e-10 # Burgers vector [m] ! Qedge 3e-19 # Activation energy for dislocation glide [J/K] (0.5*G*b^3) ! Qsd 2.4e-19 # Activation energy for self diffusion [J/K] (gamma-iron) ! diff0 1e-3 # prefactor vacancy diffusion coeffficent (gamma-iron) ! interaction_coefficients 1.0 2.2 3.0 1.6 3.8 4.5 # Dislocation interaction coefficients ! ! rho0 6.0e12 # Initial dislocation density [m/m^3] ! ! c1 0.1 # Passing stress adjustment ! c2 2.0 # Jump width adjustment ! c3 1.0 # Activation volume adjustment ! c4 50.0 # Average slip distance adjustment for lock formation ! c7 8.0 # Athermal recovery adjustment ! c8 1.0e10 # Thermal recovery adjustment (plays no role for me) MODULE constitutive_dislobased !*** Include other modules *** use prec, only: pReal,pInt implicit none character (len=*), parameter :: constitutive_dislobased_label = 'dislobased' integer(pInt), dimension(:), allocatable :: constitutive_dislobased_sizeDotState, & constitutive_dislobased_sizeState, & constitutive_dislobased_sizePostResults integer(pInt), dimension(:,:), allocatable,target :: constitutive_dislobased_sizePostResult ! size of each post result output character(len=64), dimension(:,:), allocatable,target :: constitutive_dislobased_output ! name of each post result output character(len=32), dimension(:), allocatable :: constitutive_dislobased_structureName integer(pInt), dimension(:), allocatable :: constitutive_dislobased_structure integer(pInt), dimension(:), allocatable :: constitutive_dislobased_Nslip real(pReal), dimension(:), allocatable :: constitutive_dislobased_C11 real(pReal), dimension(:), allocatable :: constitutive_dislobased_C12 real(pReal), dimension(:), allocatable :: constitutive_dislobased_C13 real(pReal), dimension(:), allocatable :: constitutive_dislobased_C33 real(pReal), dimension(:), allocatable :: constitutive_dislobased_C44 real(pReal), dimension(:), allocatable :: constitutive_dislobased_Gmod real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Cslip_66 !* Visco-plastic constitutive_phenomenological parameters real(pReal), dimension(:), allocatable :: constitutive_dislobased_rho0 real(pReal), dimension(:), allocatable :: constitutive_dislobased_bg real(pReal), dimension(:), allocatable :: constitutive_dislobased_Qedge real(pReal), dimension(:), allocatable :: constitutive_dislobased_Qsd real(pReal), dimension(:), allocatable :: constitutive_dislobased_D0 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c1 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c2 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c3 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c4 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c5 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c6 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c7 real(pReal), dimension(:), allocatable :: constitutive_dislobased_c8 real(pReal), dimension(:), allocatable :: constitutive_dislobased_CoverA real(pReal), dimension(:,:), allocatable :: constitutive_dislobased_SlipIntCoeff real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iparallel real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iforest !************************************* !* 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, Gas constant in J.mol/Kelvin real(pReal), parameter :: Rgaz = 8.314_pReal CONTAINS !**************************************** !* - constitutive_init !* - constitutive_homogenizedC !* - constitutive_microstructure !* - constitutive_LpAndItsTangent !* - consistutive_dotState !* - consistutive_postResults !**************************************** subroutine constitutive_dislobased_init(file) !************************************** !* Module initialization * !************************************** use prec, only: pInt, pReal use math, only: math_Mandel3333to66, math_Voigt66to3333, math_mul3x3 use IO use material use lattice, only: lattice_sn, lattice_st, lattice_interactionSlipSlip, lattice_initializeStructure 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, mySize character(len=64) tag character(len=1024) line real(pReal) x,y write(6,*) write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_dislobased_label,' init -+>>>' write(6,*) maxNinstance = count(phase_constitution == constitutive_dislobased_label) if (maxNinstance == 0) return allocate(constitutive_dislobased_sizeDotState(maxNinstance)) ; constitutive_dislobased_sizeDotState = 0_pInt allocate(constitutive_dislobased_sizeState(maxNinstance)) ; constitutive_dislobased_sizeState = 0_pInt allocate(constitutive_dislobased_sizePostResults(maxNinstance)); constitutive_dislobased_sizePostResults = 0_pInt allocate(constitutive_dislobased_sizePostResult(maxval(phase_Noutput), & maxNinstance)) ; constitutive_dislobased_sizePostResult = 0_pInt allocate(constitutive_dislobased_output(maxval(phase_Noutput), & maxNinstance)) ; constitutive_dislobased_output = '' allocate(constitutive_dislobased_structureName(maxNinstance)) ; constitutive_dislobased_structureName = '' allocate(constitutive_dislobased_structure(maxNinstance)) ; constitutive_dislobased_structure = 0_pInt allocate(constitutive_dislobased_Nslip(maxNinstance)) ; constitutive_dislobased_Nslip = 0_pInt allocate(constitutive_dislobased_C11(maxNinstance)) ; constitutive_dislobased_C11 = 0.0_pReal allocate(constitutive_dislobased_C12(maxNinstance)) ; constitutive_dislobased_C12 = 0.0_pReal allocate(constitutive_dislobased_C13(maxNinstance)) ; constitutive_dislobased_C13 = 0.0_pReal allocate(constitutive_dislobased_C33(maxNinstance)) ; constitutive_dislobased_C33 = 0.0_pReal allocate(constitutive_dislobased_C44(maxNinstance)) ; constitutive_dislobased_C44 = 0.0_pReal allocate(constitutive_dislobased_Gmod(maxNinstance)) ; constitutive_dislobased_Gmod = 0.0_pReal allocate(constitutive_dislobased_Cslip_66(6,6,maxNinstance)) ; constitutive_dislobased_Cslip_66 = 0.0_pReal allocate(constitutive_dislobased_rho0(maxNinstance)) ; constitutive_dislobased_rho0 = 0.0_pReal allocate(constitutive_dislobased_bg(maxNinstance)) ; constitutive_dislobased_bg = 0.0_pReal allocate(constitutive_dislobased_Qedge(maxNinstance)) ; constitutive_dislobased_Qedge = 0.0_pReal allocate(constitutive_dislobased_Qsd(maxNinstance)) ; constitutive_dislobased_Qsd = 0.0_pReal allocate(constitutive_dislobased_D0(maxNinstance)) ; constitutive_dislobased_D0 = 0.0_pReal allocate(constitutive_dislobased_c1(maxNinstance)) ; constitutive_dislobased_c1 = 0.0_pReal allocate(constitutive_dislobased_c2(maxNinstance)) ; constitutive_dislobased_c2 = 0.0_pReal allocate(constitutive_dislobased_c3(maxNinstance)) ; constitutive_dislobased_c3 = 0.0_pReal allocate(constitutive_dislobased_c4(maxNinstance)) ; constitutive_dislobased_c4 = 0.0_pReal allocate(constitutive_dislobased_c5(maxNinstance)) ; constitutive_dislobased_c5 = 0.0_pReal allocate(constitutive_dislobased_c6(maxNinstance)) ; constitutive_dislobased_c6 = 0.0_pReal allocate(constitutive_dislobased_c7(maxNinstance)) ; constitutive_dislobased_c7 = 0.0_pReal allocate(constitutive_dislobased_c8(maxNinstance)) ; constitutive_dislobased_c8 = 0.0_pReal allocate(constitutive_dislobased_CoverA(maxNinstance)) ; constitutive_dislobased_CoverA = 0.0_pReal allocate(constitutive_dislobased_SlipIntCoeff(6,maxNinstance)) ; constitutive_dislobased_SlipIntCoeff = 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_dislobased_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_dislobased_output(output,i) = IO_lc(IO_stringValue(line,positions,2)) case ('lattice_structure') constitutive_dislobased_structureName(i) = IO_lc(IO_stringValue(line,positions,2)) case ('covera_ratio') constitutive_dislobased_CoverA(i) = IO_floatValue(line,positions,2) case ('nslip') constitutive_dislobased_Nslip(i) = IO_intValue(line,positions,2) case ('c11') constitutive_dislobased_C11(i) = IO_floatValue(line,positions,2) case ('c12') constitutive_dislobased_C12(i) = IO_floatValue(line,positions,2) case ('c13') constitutive_dislobased_C13(i) = IO_floatValue(line,positions,2) case ('c33') constitutive_dislobased_C33(i) = IO_floatValue(line,positions,2) case ('c44') constitutive_dislobased_C44(i) = IO_floatValue(line,positions,2) case ('rho0') constitutive_dislobased_rho0(i) = IO_floatValue(line,positions,2) case ('burgers') constitutive_dislobased_bg(i) = IO_floatValue(line,positions,2) case ('qedge') constitutive_dislobased_Qedge(i) = IO_floatValue(line,positions,2) case ('qsd') constitutive_dislobased_Qsd(i) = IO_floatValue(line,positions,2) case ('diff0') constitutive_dislobased_D0(i) = IO_floatValue(line,positions,2) case ('c1') constitutive_dislobased_c1(i) = IO_floatValue(line,positions,2) case ('c2') constitutive_dislobased_c2(i) = IO_floatValue(line,positions,2) case ('c3') constitutive_dislobased_c3(i) = IO_floatValue(line,positions,2) case ('c4') constitutive_dislobased_c4(i) = IO_floatValue(line,positions,2) case ('c5') constitutive_dislobased_c5(i) = IO_floatValue(line,positions,2) case ('c6') constitutive_dislobased_c6(i) = IO_floatValue(line,positions,2) case ('c7') constitutive_dislobased_c7(i) = IO_floatValue(line,positions,2) case ('c8') constitutive_dislobased_c8(i) = IO_floatValue(line,positions,2) case ('interaction_coefficients') forall (j=1:6) & constitutive_dislobased_SlipIntCoeff(j,i) = IO_floatValue(line,positions,1+j) end select endif enddo 100 do i = 1,maxNinstance constitutive_dislobased_structure(i) = lattice_initializeStructure(constitutive_dislobased_structureName(i), & constitutive_dislobased_CoverA(i)) ! sanity checks if (constitutive_dislobased_structure(i) < 1) call IO_error(205) if (constitutive_dislobased_rho0(i) < 0.0_pReal) call IO_error(220) if (constitutive_dislobased_bg(i) <= 0.0_pReal) call IO_error(221) if (constitutive_dislobased_Qedge(i) <= 0.0_pReal) call IO_error(222) if (constitutive_dislobased_Qsd(i) <= 0.0_pReal) call IO_error(223) if (constitutive_dislobased_D0(i) <= 0.0_pReal) call IO_error(224) if (constitutive_dislobased_Nslip(i) < 1) call IO_error(225) enddo allocate(constitutive_dislobased_Iparallel(maxval(constitutive_dislobased_Nslip),& maxval(constitutive_dislobased_Nslip),& maxNinstance)) allocate(constitutive_dislobased_Iforest(maxval(constitutive_dislobased_Nslip),& maxval(constitutive_dislobased_Nslip),& maxNinstance)) do i = 1,maxNinstance do j = 1,maxval(phase_Noutput) select case(constitutive_dislobased_output(j,i)) case('dislodensity') mySize = constitutive_dislobased_Nslip(i) case('rateofshear') mySize = constitutive_dislobased_Nslip(i) case default mySize = 0_pInt end select if (mySize > 0_pInt) then ! any meaningful output found constitutive_dislobased_sizePostResult(j,i) = mySize constitutive_dislobased_sizePostResults(i) = & constitutive_dislobased_sizePostResults(i) + mySize endif enddo constitutive_dislobased_sizeDotState(i) = constitutive_dislobased_Nslip(i) constitutive_dislobased_sizeState(i) = 8*constitutive_dislobased_Nslip(i) constitutive_dislobased_Gmod(i) = constitutive_dislobased_C44(i) select case (constitutive_dislobased_structure(i)) case(1:2) ! cubic(s) forall(k=1:3) forall(j=1:3) & constitutive_dislobased_Cslip_66(k,j,i) = constitutive_dislobased_C12(i) constitutive_dislobased_Cslip_66(k,k,i) = constitutive_dislobased_C11(i) constitutive_dislobased_Cslip_66(k+3,k+3,i) = constitutive_dislobased_C44(i) end forall case(3:) ! all hex constitutive_dislobased_Cslip_66(1,1,i) = constitutive_dislobased_C11(i) constitutive_dislobased_Cslip_66(2,2,i) = constitutive_dislobased_C11(i) constitutive_dislobased_Cslip_66(3,3,i) = constitutive_dislobased_C33(i) constitutive_dislobased_Cslip_66(1,2,i) = constitutive_dislobased_C12(i) constitutive_dislobased_Cslip_66(2,1,i) = constitutive_dislobased_C12(i) constitutive_dislobased_Cslip_66(1,3,i) = constitutive_dislobased_C13(i) constitutive_dislobased_Cslip_66(3,1,i) = constitutive_dislobased_C13(i) constitutive_dislobased_Cslip_66(2,3,i) = constitutive_dislobased_C13(i) constitutive_dislobased_Cslip_66(3,2,i) = constitutive_dislobased_C13(i) constitutive_dislobased_Cslip_66(4,4,i) = constitutive_dislobased_C44(i) constitutive_dislobased_Cslip_66(5,5,i) = constitutive_dislobased_C44(i) constitutive_dislobased_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_dislobased_C11(i)- & constitutive_dislobased_C12(i)) end select constitutive_dislobased_Cslip_66(:,:,i) = & math_Mandel3333to66(math_Voigt66to3333(constitutive_dislobased_Cslip_66(:,:,i))) !* Construction of the hardening matrices !* Iteration over the systems do j = 1,constitutive_dislobased_Nslip(i) do k = 1,constitutive_dislobased_Nslip(i) !* Projection of the dislocation * x = math_mul3x3(lattice_sn(:,j,i),lattice_st(:,k,i)) y = 1.0_pReal-x**(2.0_pReal) !* Interaction matrix * constitutive_dislobased_Iforest(j,k,i) = abs(x)*& constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i) if (y>0.0_pReal) & constitutive_dislobased_Iparallel(j,k,i) = sqrt(y)*& constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i) enddo enddo enddo return end subroutine function constitutive_dislobased_stateInit(myInstance) !********************************************************************* !* initial microstructural state * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt), intent(in) :: myInstance real(pReal), dimension(constitutive_dislobased_Nslip(myInstance)) :: constitutive_dislobased_stateInit constitutive_dislobased_stateInit = constitutive_dislobased_rho0(myInstance) return end function function constitutive_dislobased_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_dislobased_homogenizedC type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state matID = phase_constitutionInstance(material_phase(ipc,ip,el)) constitutive_dislobased_homogenizedC = constitutive_dislobased_Cslip_66(:,:,matID) return end function subroutine constitutive_dislobased_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,n,i real(pReal) Temperature type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state matID = phase_constitutionInstance(material_phase(ipc,ip,el)) n = constitutive_dislobased_Nslip(matID) !* Quantities derived from state - slip !* State: 1 : n rho !* n+1 : 2n rho_f !* 2n+1 : 3n rho_p !* 3n+1 : 4n passing stress !* 4n+1 : 5n jump width !* 5n+1 : 6n activation volume !* 6n+1 : 7n rho_m !* 7n+1 : 8n g0_slip !$OMP CRITICAL (evilmatmul) state(ipc,ip,el)%p((n+1):(2*n)) = matmul(constitutive_dislobased_Iforest (1:n,1:n,matID),state(ipc,ip,el)%p(1:n)) state(ipc,ip,el)%p((2*n+1):(3*n)) = matmul(constitutive_dislobased_Iparallel(1:n,1:n,matID),state(ipc,ip,el)%p(1:n)) !$OMP END CRITICAL (evilmatmul) do i=1,n state(ipc,ip,el)%p(3*n+i) = & constitutive_dislobased_c1(matID)*constitutive_dislobased_Gmod(matID)*& constitutive_dislobased_bg(matID)*sqrt(state(ipc,ip,el)%p(2*n+i)) state(ipc,ip,el)%p(4*n+i) = & constitutive_dislobased_c2(matID)/sqrt(state(ipc,ip,el)%p(n+i)) state(ipc,ip,el)%p(5*n+i) = & constitutive_dislobased_c3(matID)*state(ipc,ip,el)%p(4*n+i)*constitutive_dislobased_bg(matID)**2.0_pReal state(ipc,ip,el)%p(6*n+i) = & (2.0_pReal*kB*Temperature*sqrt(state(ipc,ip,el)%p(2*n+i)))/& (constitutive_dislobased_c1(matID)*constitutive_dislobased_c3(matID)*constitutive_dislobased_Gmod(matID)*& state(ipc,ip,el)%p(4*n+i)*constitutive_dislobased_bg(matID)**3.0_pReal) state(ipc,ip,el)%p(7*n+i) = & state(ipc,ip,el)%p(6*n+i)*constitutive_dislobased_bg(matID)*attack_frequency*state(ipc,ip,el)%p(4*n+i)*& exp(-constitutive_dislobased_Qedge(matID)/(kB*Temperature)) enddo end subroutine subroutine constitutive_dislobased_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_Plain3333to99, math_mul6x6 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) :: Lp real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(9,9) :: dLp_dTstar real(pReal), dimension(constitutive_dislobased_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & gdot_slip,dgdot_dtauslip,tau_slip matID = phase_constitutionInstance(material_phase(ipc,ip,el)) n = constitutive_dislobased_Nslip(matID) !* Calculation of Lp Lp = 0.0_pReal gdot_slip = 0.0_pReal do i = 1,constitutive_dislobased_Nslip(matID) tau_slip(i) = math_mul6x6(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID))) if ((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))>0) & gdot_slip(i) = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip(i))*& sinh(((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)) Lp = Lp + gdot_slip(i)*lattice_Sslip(:,:,i,constitutive_dislobased_structure(matID)) enddo !* Calculation of the tangent of Lp dLp_dTstar3333 = 0.0_pReal dLp_dTstar = 0.0_pReal dgdot_dtauslip = 0.0_pReal do i = 1,constitutive_dislobased_Nslip(matID) if ((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))>0) & dgdot_dtauslip(i) = (state(ipc,ip,el)%p(7*n+i)*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)*& cosh(((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)) 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)*lattice_Sslip(k,l,i,constitutive_dislobased_structure(matID))* & lattice_Sslip(m,n,i,constitutive_dislobased_structure(matID)) enddo dLp_dTstar = math_Plain3333to99(dLp_dTstar3333) return end subroutine function constitutive_dislobased_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 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,i,n real(pReal) Temperature,tau_slip,gdot_slip,locks,athermal_recovery,thermal_recovery type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_dislobased_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & constitutive_dislobased_dotState matID = phase_constitutionInstance(material_phase(ipc,ip,el)) n = constitutive_dislobased_Nslip(matID) !* Dislocation density evolution constitutive_dislobased_dotState = 0.0_pReal do i = 1,n tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID))) if (abs(tau_slip) > state(ipc,ip,el)%p(3*n+i)) then gdot_slip = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip)*& sinh(((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)) locks = (sqrt(state(ipc,ip,el)%p(n+i))*abs(gdot_slip))/& (constitutive_dislobased_c4(matID)*constitutive_dislobased_bg(matID)) athermal_recovery = constitutive_dislobased_c7(matID)*state(ipc,ip,el)%p(i)*abs(gdot_slip) !thermal_recovery = constitutive_dislobased_c8(matID)*abs(tau_slip)*state(ipc,ip,el)%p(i)**(2.0_pReal)*& ! ((constitutive_dislobased_D0(matID)*constitutive_dislobased_bg(matID)**(3.0_pReal))/& ! (kB*Temperature))*exp(-constitutive_dislobased_Qsd(matID)/(kB*Temperature)) constitutive_dislobased_dotState(i) = locks - athermal_recovery endif enddo return end function !**************************************************************** !* calculates the rate of change of temperature * !**************************************************************** pure function constitutive_dislobased_dotTemperature(Tstar_v,Temperature,state,ipc,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):: ipc, & ! 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_dislobased_dotTemperature ! rate of change of temparature ! calculate dotTemperature constitutive_dislobased_dotTemperature = 0.0_pReal return endfunction pure function constitutive_dislobased_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) tau_slip, active_rate real(pReal), dimension(constitutive_dislobased_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: & constitutive_dislobased_postResults matID = phase_constitutionInstance(material_phase(ipc,ip,el)) n = constitutive_dislobased_Nslip(matID) c = 0_pInt constitutive_dislobased_postResults = 0.0_pReal do o = 1,phase_Noutput(material_phase(ipc,ip,el)) select case(constitutive_dislobased_output(o,matID)) case ('dislodensity') constitutive_dislobased_postResults(c+1:c+n) = state(ipc,ip,el)%p(1:n) c = c + n case ('rateofshear') do i = 1,n tau_slip = math_mul6x6(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID))) if ((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))>0) then constitutive_dislobased_postResults(c+i) = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip)*& sinh(((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)) else constitutive_dislobased_postResults(c+i) = 0.0_pReal endif enddo c = c + n end select enddo return end function END MODULE