From 06ed8c817726f0883995d9d79420f5aaaabe8898 Mon Sep 17 00:00:00 2001 From: Christoph Kords Date: Tue, 23 Jun 2009 10:39:29 +0000 Subject: [PATCH] corrected the constitutive law for j2-plasticity in Lp and its tangent and dotState. --- trunk/constitutive_j2.f90 | 380 +++++++++++++++++++++++--------------- trunk/material.config | 4 +- 2 files changed, 236 insertions(+), 148 deletions(-) diff --git a/trunk/constitutive_j2.f90 b/trunk/constitutive_j2.f90 index 1dd57dc30..b745bb431 100644 --- a/trunk/constitutive_j2.f90 +++ b/trunk/constitutive_j2.f90 @@ -14,11 +14,11 @@ ! 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 +! tau0 31e6 ! gdot0 0.001 ! n 20 ! h0 75e6 -! s_sat 63e6 +! tau_sat 63e6 ! w0 2.25 MODULE constitutive_j2 @@ -38,11 +38,11 @@ MODULE constitutive_j2 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_tau0 real(pReal), dimension(:), allocatable :: constitutive_j2_gdot0 real(pReal), dimension(:), allocatable :: constitutive_j2_n real(pReal), dimension(:), allocatable :: constitutive_j2_h0 - real(pReal), dimension(:), allocatable :: constitutive_j2_s_sat + real(pReal), dimension(:), allocatable :: constitutive_j2_tau_sat real(pReal), dimension(:), allocatable :: constitutive_j2_w0 @@ -85,11 +85,11 @@ subroutine constitutive_j2_init(file) 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_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_s_sat(maxNinstance)) ; constitutive_j2_s_sat = 0.0_pReal + allocate(constitutive_j2_tau_sat(maxNinstance)) ; constitutive_j2_tau_sat = 0.0_pReal allocate(constitutive_j2_w0(maxNinstance)) ; constitutive_j2_w0 = 0.0_pReal rewind(file) @@ -120,16 +120,16 @@ subroutine constitutive_j2_init(file) 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 ('tau0') + constitutive_j2_tau0(i) = IO_floatValue(line,positions,2) case ('gdot0') constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2) case ('n') constitutive_j2_n(i) = IO_floatValue(line,positions,2) case ('h0') constitutive_j2_h0(i) = IO_floatValue(line,positions,2) - case ('s_sat') - constitutive_j2_s_sat(i) = IO_floatValue(line,positions,2) + case ('tau_sat') + constitutive_j2_tau_sat(i) = IO_floatValue(line,positions,2) case ('w0') constitutive_j2_w0(i) = IO_floatValue(line,positions,2) case ('taylorfactor') @@ -139,11 +139,11 @@ subroutine constitutive_j2_init(file) enddo 100 do i = 1,maxNinstance ! sanity checks - if (constitutive_j2_s0(i) < 0.0_pReal) call IO_error(203) + if (constitutive_j2_tau0(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_tau_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 @@ -179,20 +179,31 @@ subroutine constitutive_j2_init(file) endsubroutine -function constitutive_j2_stateInit(myInstance) !********************************************************************* !* initial microstructural state * !********************************************************************* - use prec, only: pReal,pInt - implicit none +pure function constitutive_j2_stateInit(myInstance) + + !*** variables and functions from other modules ***! + use prec, only: pReal,pInt + + implicit none + + !*** input variables ***! + integer(pInt), intent(in) :: myInstance + + !*** output variables ***! + real(pReal), dimension(1) :: constitutive_j2_stateInit + + !*** local variables ***! + + !*** global variables ***! + ! constitutive_j2_tau0 -!* Definition of variables - integer(pInt), intent(in) :: myInstance - real(pReal), dimension(1) :: constitutive_j2_stateInit + + constitutive_j2_stateInit = constitutive_j2_tau0(myInstance) - constitutive_j2_stateInit = constitutive_j2_s0(myInstance) - - return + return endfunction @@ -248,156 +259,233 @@ subroutine constitutive_j2_microstructure(Temperature,state,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 +!**************************************************************** +!* calculates plastic velocity gradient and its tangent * +!**************************************************************** +pure subroutine constitutive_j2_LpAndItsTangent(Lp, dLp_dTstar_99, Tstar_dev_v, Temperature, state, g, ip, el) - implicit none + !*** variables and functions from other modules ***! + use prec, only: pReal, & + pInt, & + p_vec + use math, only: math_mul6x6, & + math_Mandel6to33, & + math_Plain3333to99, & + math_spectral1 + use lattice, only: lattice_Sslip, & + lattice_Sslip_v + use mesh, only: mesh_NcpElems, & + mesh_maxNips + use material, only: homogenization_maxNgrains, & + material_phase, & + phase_constitutionInstance -!* 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 + 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 + + !*** global variables ***! + ! constitutive_j2_gdot0 + ! constitutive_j2_fTaylor + ! constitutive_j2_n + - matID = phase_constitutionInstance(material_phase(ipc,ip,el)) + matID = phase_constitutionInstance(material_phase(g,ip,el)) - Tstar33 = math_Mandel6to33(Tstar_v) - squarenorm_Tstar = math_mul6x6(Tstar_v,Tstar_v) - norm_Tstar = dsqrt(squarenorm_Tstar) + ! 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 = dsqrt(squarenorm_Tstar_dev) -!* Initialization of Lp and dLp_dTstar - Lp = 0.0_pReal - dLp_dTstar = 0.0_pReal + ! 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 > 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) + ! for Tstar==0 both Lp and dLp_dTstar are zero (if not n==1) + if (norm_Tstar_dev > 0) then + + ! Calculation of gamma_dot + gamma_dot = constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev & + / &!--------------------------------------------------- + (constitutive_j2_fTaylor(matID) * state(g,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 + ! Calculation of Lp + Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID) + + !* Calculation of the tangent of Lp + forall (k=1:3,l=1:3,m=1:3,n=1:3) & + dLp_dTstar_3333(k,l,m,n) = (constitutive_j2_n(matID)-1.0_pReal) * Tstar_dev_33(k,l)*Tstar_dev_33(m,n) / squarenorm_Tstar_dev + forall (k=1:3,l=1:3) & + dLp_dTstar_3333(k,l,k,l) = dLp_dTstar_3333(k,l,k,l) + 1.0_pReal + dLp_dTstar_99 = math_Plain3333to99(gamma_dot / constitutive_j2_fTaylor(matID) * dLp_dTstar_3333 / norm_Tstar_dev) + end if + + return endsubroutine -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 +!**************************************************************** +!* calculates the rate of change of microstructure * +!**************************************************************** +pure function constitutive_j2_dotState(Tstar_v, Temperature, state, g, ip, el) -!* 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 + !*** variables and functions from other modules ***! + use prec, only: pReal, & + pInt, & + p_vec + use math, only: math_mul6x6 + use lattice, only: lattice_Sslip_v + use mesh, only: mesh_NcpElems, & + mesh_maxNips + use material, only: homogenization_maxNgrains, & + material_phase, & + phase_constitutionInstance + + implicit none - matID = phase_constitutionInstance(material_phase(ipc,ip,el)) + !*** 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 - 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) + !*** global variables ***! + ! constitutive_j2_gdot0 + ! constitutive_j2_fTaylor + ! constitutive_j2_n + ! constitutive_j2_h0 + ! constitutive_j2_tau_sat + ! constitutive_j2_w0 + + matID = phase_constitutionInstance(material_phase(g,ip,el)) - return + ! caclulate deviatoric part of 2nd Piola-Kirchhoff stress + Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3_pReal + Tstar_dev_v(4:6) = Tstar_v(4:6) + + norm_Tstar_dev = dsqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v)) + + ! Calculation of gamma_dot + gamma_dot = constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev & + / &!--------------------------------------------------- + (constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID) + + ! calculate hardening coefficient + hardening = constitutive_j2_h0(matID) * & + ( 1.0_pReal - state(g,ip,el)%p(1) / constitutive_j2_tau_sat(matID) ) ** constitutive_j2_w0(matID) + + ! finally calculate dotState + constitutive_j2_dotState = hardening * gamma_dot + + 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 +pure function constitutive_j2_postResults(Tstar_v, Temperature, dt, state, g, ip, el) -!* 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 +!*** variables and functions from other modules ***! + use prec, only: pReal, & + pInt, & + p_vec + use math, only: math_mul6x6 + use lattice, only: lattice_Sslip_v + use mesh, only: mesh_NcpElems, & + mesh_maxNips + use material, only: homogenization_maxNgrains, & + material_phase, & + phase_constitutionInstance, & + phase_Noutput - 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 + implicit none - 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 + !*** 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_pReal + Tstar_dev_v(4:6) = Tstar_v(4:6) + norm_Tstar_dev = dsqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v)) + + c = 0_pInt + constitutive_j2_postResults = 0.0_pReal + + do o = 1,phase_Noutput(material_phase(g,ip,el)) + select case(constitutive_j2_output(o,matID)) + case ('flowstress') + constitutive_j2_postResults(c+1) = state(g,ip,el)%p(1) + c = c + 1 + case ('strainrate') + constitutive_j2_postResults(c+1) = & + constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev & + / &!--------------------------------------------------- + (constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID) + c = c + 1 + end select + enddo return diff --git a/trunk/material.config b/trunk/material.config index c846521df..f35cd1cfd 100644 --- a/trunk/material.config +++ b/trunk/material.config @@ -41,11 +41,11 @@ c12 58.34e9 (output) flowstress (output) strainrate taylorfactor 3 -s0 31e6 +tau0 31e6 gdot0 0.001 n 20 h0 75e6 -s_sat 63e6 +tau_sat 63e6 w0 2.25 constitution phenomenological