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Calibration (Prismatic slip) of the new dislocation density based CPFE model for single crystal alpha-Ti (Titanmod). Formulated edge and screw dislocations mobilities in presence of kink pairs. Updated comments. The model shows the plateau in stress evolution in prismatic orientation which is observed in experiments.

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Alankar Alankar 2010-07-15 07:16:15 +00:00
parent 49926d5d66
commit 60decea760
1 changed files with 185 additions and 141 deletions
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322
code/constitutive_titanmod.f90
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@ -52,53 +52,53 @@ real(pReal), dimension(:), allocatable :: constitutive_titanmod_
constitutive_titanmod_CAtomicVolume, & ! atomic volume in Bugers vector unit constitutive_titanmod_CAtomicVolume, & ! atomic volume in Bugers vector unit
constitutive_titanmod_D0, & ! prefactor for self-diffusion coefficient constitutive_titanmod_D0, & ! prefactor for self-diffusion coefficient
constitutive_titanmod_Qsd, & ! activation energy for dislocation climb constitutive_titanmod_Qsd, & ! activation energy for dislocation climb
constitutive_titanmod_GrainSize, & ! grain size constitutive_titanmod_GrainSize, & ! grain size - Not being used
constitutive_titanmod_MaxTwinFraction, & ! maximum allowed total twin volume fraction constitutive_titanmod_MaxTwinFraction, & ! maximum allowed total twin volume fraction
constitutive_titanmod_r, & ! r-exponent in twin nucleation rate constitutive_titanmod_r, & ! r-exponent in twin nucleation rate
constitutive_titanmod_CEdgeDipMinDistance, & ! constitutive_titanmod_CEdgeDipMinDistance, & ! Not being used
constitutive_titanmod_Cmfptwin, & ! constitutive_titanmod_Cmfptwin, & ! Not being used
constitutive_titanmod_Cthresholdtwin, & ! constitutive_titanmod_Cthresholdtwin, & ! Not being used
constitutive_titanmod_relevantRho ! dislocation density considered relevant constitutive_titanmod_relevantRho ! dislocation density considered relevant
real(pReal), dimension(:,:,:), allocatable :: constitutive_titanmod_Cslip_66 ! elasticity matrix in Mandel notation for each instance real(pReal), dimension(:,:,:), allocatable :: constitutive_titanmod_Cslip_66 ! elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_66 ! twin elasticity matrix in Mandel notation for each instance real(pReal), dimension(:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_66 ! twin elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_titanmod_Cslip_3333 ! elasticity matrix for each instance real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_titanmod_Cslip_3333 ! elasticity matrix for each instance
real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_3333 ! twin elasticity matrix for each instance real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_3333 ! twin elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable :: constitutive_titanmod_rho_edge0, & ! initial edge dislocation density per slip system for each family and instance real(pReal), dimension(:,:), allocatable :: constitutive_titanmod_rho_edge0, & ! initial edge dislocation density per slip system for each family and instance
constitutive_titanmod_rho_screw0, & ! initial edge dipole density per slip system for each family and instance constitutive_titanmod_rho_screw0, & ! initial screw dislocation density per slip system for each family and instance
constitutive_titanmod_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each slip family and instance constitutive_titanmod_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each slip family and instance
constitutive_titanmod_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance constitutive_titanmod_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
constitutive_titanmod_burgersPerTwinFamily, & ! absolute length of burgers vector [m] for each twin family and instance constitutive_titanmod_burgersPerTwinFamily, & ! absolute length of burgers vector [m] for each twin family and instance
constitutive_titanmod_burgersPerTwinSystem, & ! absolute length of burgers vector [m] for each twin system and instance constitutive_titanmod_burgersPerTwinSystem, & ! absolute length of burgers vector [m] for each twin system and instance
constitutive_titanmod_f0_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_f0_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance
constitutive_titanmod_f0_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_f0_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance
constitutive_titanmod_tau0e_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_tau0e_PerSlipFamily, & ! Initial yield stress edge dislocations per slip family
constitutive_titanmod_tau0e_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_tau0e_PerSlipSystem, & ! Initial yield stress edge dislocations per slip system
constitutive_titanmod_tau0s_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_tau0s_PerSlipFamily, & ! Initial yield stress screw dislocations per slip family
constitutive_titanmod_tau0s_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_tau0s_PerSlipSystem, & ! Initial yield stress screw dislocations per slip system
constitutive_titanmod_capre_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_capre_PerSlipFamily, & ! Capture radii for edge dislocations per slip family
constitutive_titanmod_capre_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_capre_PerSlipSystem, & ! Capture radii for edge dislocations per slip system
constitutive_titanmod_caprs_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_caprs_PerSlipFamily, & ! Capture radii for screw dislocations per slip family
constitutive_titanmod_caprs_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_caprs_PerSlipSystem, & ! Capture radii for screw dislocations per slip system
constitutive_titanmod_pe_PerSlipFamily, & ! p-exponent in glide velocity constitutive_titanmod_pe_PerSlipFamily, & ! p-exponent in glide velocity
constitutive_titanmod_ps_PerSlipFamily, & ! p-exponent in glide velocity constitutive_titanmod_ps_PerSlipFamily, & ! p-exponent in glide velocity
constitutive_titanmod_qe_PerSlipFamily, & ! q-exponent in glide velocity constitutive_titanmod_qe_PerSlipFamily, & ! q-exponent in glide velocity
constitutive_titanmod_qs_PerSlipFamily, & ! q-exponent in glide velocity constitutive_titanmod_qs_PerSlipFamily, & ! q-exponent in glide velocity
constitutive_titanmod_pe_PerSlipSystem, & ! p-exponent in glide velocity constitutive_titanmod_pe_PerSlipSystem, & ! p-exponent in glide velocity
constitutive_titanmod_ps_PerSlipSystem, & ! p-exponent in glide velocity constitutive_titanmod_ps_PerSlipSystem, & ! p-exponent in glide velocity
constitutive_titanmod_qe_PerSlipSystem, & ! q-exponent in glide velocity constitutive_titanmod_qe_PerSlipSystem, & ! q-exponent in glide velocity
constitutive_titanmod_qs_PerSlipSystem, & ! q-exponent in glide velocity constitutive_titanmod_qs_PerSlipSystem, & ! q-exponent in glide velocity
constitutive_titanmod_v0e_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance constitutive_titanmod_v0e_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0e_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance constitutive_titanmod_v0e_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_v0s_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance constitutive_titanmod_v0s_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0s_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance constitutive_titanmod_v0s_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_Ndot0PerTwinFamily, & ! twin nucleation rate [1/m³s] for each twin family and instance constitutive_titanmod_Ndot0PerTwinFamily, & ! twin nucleation rate [1/m³s] for each twin family and instance
constitutive_titanmod_Ndot0PerTwinSystem, & ! twin nucleation rate [1/m³s] for each twin system and instance constitutive_titanmod_Ndot0PerTwinSystem, & ! twin nucleation rate [1/m³s] for each twin system and instance
constitutive_titanmod_twinsizePerTwinFamily, & ! twin thickness [m] for each twin family and instance constitutive_titanmod_twinsizePerTwinFamily, & ! twin thickness [m] for each twin family and instance
constitutive_titanmod_twinsizePerTwinSystem, & ! twin thickness [m] for each twin system and instance constitutive_titanmod_twinsizePerTwinSystem, & ! twin thickness [m] for each twin system and instance
constitutive_titanmod_CeLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance constitutive_titanmod_CeLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_CeLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance constitutive_titanmod_CeLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_titanmod_CsLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance constitutive_titanmod_CsLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_CsLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance constitutive_titanmod_CsLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_titanmod_interactionSlipSlip, & ! coefficients for slip-slip interaction for each interaction type and instance constitutive_titanmod_interactionSlipSlip, & ! coefficients for slip-slip interaction for each interaction type and instance
constitutive_titanmod_interactionSlipTwin, & ! coefficients for slip-twin interaction for each interaction type and instance constitutive_titanmod_interactionSlipTwin, & ! coefficients for slip-twin interaction for each interaction type and instance
constitutive_titanmod_interactionTwinSlip, & ! coefficients for twin-slip interaction for each interaction type and instance constitutive_titanmod_interactionTwinSlip, & ! coefficients for twin-slip interaction for each interaction type and instance
@ -252,6 +252,10 @@ constitutive_titanmod_Ndot0PerTwinFamily = 0.0_pReal
constitutive_titanmod_twinsizePerTwinFamily = 0.0_pReal constitutive_titanmod_twinsizePerTwinFamily = 0.0_pReal
constitutive_titanmod_CeLambdaSlipPerSlipFamily = 0.0_pReal constitutive_titanmod_CeLambdaSlipPerSlipFamily = 0.0_pReal
constitutive_titanmod_CsLambdaSlipPerSlipFamily = 0.0_pReal constitutive_titanmod_CsLambdaSlipPerSlipFamily = 0.0_pReal
constitutive_titanmod_pe_PerSlipFamily = 0.0_pReal
constitutive_titanmod_ps_PerSlipFamily = 0.0_pReal
constitutive_titanmod_qe_PerSlipFamily = 0.0_pReal
constitutive_titanmod_qs_PerSlipFamily = 0.0_pReal
allocate(constitutive_titanmod_interactionSlipSlip(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
allocate(constitutive_titanmod_interactionSlipTwin(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionSlipTwin(lattice_maxNinteraction,maxNinstance))
allocate(constitutive_titanmod_interactionTwinSlip(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionTwinSlip(lattice_maxNinteraction,maxNinstance))
@ -297,39 +301,44 @@ do ! read thru sections of
write(6,*) tag write(6,*) tag
case ('c11') case ('c11')
constitutive_titanmod_C11(i) = IO_floatValue(line,positions,2) constitutive_titanmod_C11(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag,constitutive_titanmod_C11(i)
case ('c12') case ('c12')
constitutive_titanmod_C12(i) = IO_floatValue(line,positions,2) constitutive_titanmod_C12(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag,constitutive_titanmod_C12(i)
case ('c13') case ('c13')
constitutive_titanmod_C13(i) = IO_floatValue(line,positions,2) constitutive_titanmod_C13(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag,constitutive_titanmod_C13(i)
case ('c33') case ('c33')
constitutive_titanmod_C33(i) = IO_floatValue(line,positions,2) constitutive_titanmod_C33(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag,constitutive_titanmod_C33(i)
case ('c44') case ('c44')
constitutive_titanmod_C44(i) = IO_floatValue(line,positions,2) constitutive_titanmod_C44(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag,constitutive_titanmod_C44(i)
case ('nslip') case ('nslip')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_Nslip(j,i) = IO_intValue(line,positions,1+j) constitutive_titanmod_Nslip(j,i) = IO_intValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_Nslip(1,i),constitutive_titanmod_Nslip(2,i),constitutive_titanmod_Nslip(3,i), &
constitutive_titanmod_Nslip(4,i)
case ('ntwin') case ('ntwin')
forall (j = 1:lattice_maxNtwinFamily) & forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_Ntwin(j,i) = IO_intValue(line,positions,1+j) constitutive_titanmod_Ntwin(j,i) = IO_intValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_Ntwin(1,i),constitutive_titanmod_Ntwin(2,i),constitutive_titanmod_Ntwin(3,i), &
constitutive_titanmod_Ntwin(4,i)
case ('rho_edge0') case ('rho_edge0')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_rho_edge0(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_rho_edge0(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_rho_edge0(1,i),constitutive_titanmod_rho_edge0(2,i), &
constitutive_titanmod_rho_edge0(3,i), constitutive_titanmod_rho_edge0(4,i)
case ('rho_screw0') case ('rho_screw0')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_rho_screw0(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_rho_screw0(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_rho_screw0(1,i),constitutive_titanmod_rho_screw0(2,i), &
constitutive_titanmod_rho_screw0(3,i), constitutive_titanmod_rho_screw0(4,i)
case ('slipburgers') case ('slipburgers')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_burgersPerSlipFamily(1,i),constitutive_titanmod_burgersPerSlipFamily(2,i), &
constitutive_titanmod_burgersPerSlipFamily(3,i), constitutive_titanmod_burgersPerSlipFamily(4,i)
case ('twinburgers') case ('twinburgers')
forall (j = 1:lattice_maxNtwinFamily) & forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
@ -337,31 +346,38 @@ do ! read thru sections of
case ('f0') case ('f0')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_f0_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_f0_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_f0_PerSlipFamily(1,i),constitutive_titanmod_f0_PerSlipFamily(2,i), &
constitutive_titanmod_f0_PerSlipFamily(3,i), constitutive_titanmod_f0_PerSlipFamily(4,i)
case ('tau0e') case ('tau0e')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_tau0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_tau0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_tau0e_PerSlipFamily(1,i),constitutive_titanmod_tau0e_PerSlipFamily(2,i), &
constitutive_titanmod_tau0e_PerSlipFamily(3,i), constitutive_titanmod_tau0e_PerSlipFamily(4,i)
case ('tau0s') case ('tau0s')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_tau0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_tau0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_tau0s_PerSlipFamily(1,i),constitutive_titanmod_tau0s_PerSlipFamily(2,i), &
constitutive_titanmod_tau0s_PerSlipFamily(3,i), constitutive_titanmod_tau0s_PerSlipFamily(4,i)
case ('capre') case ('capre')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_capre_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_capre_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_capre_PerSlipFamily(1,i),constitutive_titanmod_capre_PerSlipFamily(2,i), &
constitutive_titanmod_capre_PerSlipFamily(3,i), constitutive_titanmod_capre_PerSlipFamily(4,i)
case ('caprs') case ('caprs')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_caprs_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_caprs_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_caprs_PerSlipFamily(1,i),constitutive_titanmod_caprs_PerSlipFamily(2,i), &
constitutive_titanmod_caprs_PerSlipFamily(3,i), constitutive_titanmod_caprs_PerSlipFamily(4,i)
case ('v0e') case ('v0e')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_v0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_v0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_v0e_PerSlipFamily(1,i),constitutive_titanmod_v0e_PerSlipFamily(2,i), &
constitutive_titanmod_v0e_PerSlipFamily(3,i), constitutive_titanmod_v0e_PerSlipFamily(4,i)
case ('v0s') case ('v0s')
forall (j = 1:lattice_maxNslipFamily) & forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_v0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_v0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag write(6,*) tag,constitutive_titanmod_v0s_PerSlipFamily(1,i),constitutive_titanmod_v0s_PerSlipFamily(2,i), &
constitutive_titanmod_v0s_PerSlipFamily(3,i), constitutive_titanmod_v0s_PerSlipFamily(4,i)
case ('ndot0') case ('ndot0')
forall (j = 1:lattice_maxNtwinFamily) & forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_Ndot0PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j) constitutive_titanmod_Ndot0PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
@ -385,17 +401,25 @@ do ! read thru sections of
constitutive_titanmod_MaxTwinFraction(i) = IO_floatValue(line,positions,2) constitutive_titanmod_MaxTwinFraction(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag
case ('pe') case ('pe')
constitutive_titanmod_pe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) forall (j = 1:lattice_maxNslipFamily) &
write(6,*) tag constitutive_titanmod_pe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_pe_PerSlipFamily(1,i),constitutive_titanmod_pe_PerSlipFamily(2,i), &
constitutive_titanmod_pe_PerSlipFamily(3,i), constitutive_titanmod_pe_PerSlipFamily(4,i),i
case ('ps') case ('ps')
constitutive_titanmod_ps_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) forall (j = 1:lattice_maxNslipFamily) &
write(6,*) tag constitutive_titanmod_ps_PerSlipFamily(j,i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_ps_PerSlipFamily(1,i),constitutive_titanmod_ps_PerSlipFamily(2,i), &
constitutive_titanmod_ps_PerSlipFamily(3,i), constitutive_titanmod_ps_PerSlipFamily(4,i),i
case ('qe') case ('qe')
constitutive_titanmod_qe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) forall (j = 1:lattice_maxNslipFamily) &
write(6,*) tag constitutive_titanmod_qe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_qe_PerSlipFamily(1,i),constitutive_titanmod_qe_PerSlipFamily(2,i), &
constitutive_titanmod_qe_PerSlipFamily(3,i), constitutive_titanmod_qe_PerSlipFamily(4,i),i
case ('qs') case ('qs')
constitutive_titanmod_qs_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) forall (j = 1:lattice_maxNslipFamily) &
write(6,*) tag constitutive_titanmod_qs_PerSlipFamily(j,i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_qs_PerSlipFamily(1,i),constitutive_titanmod_qs_PerSlipFamily(2,i), &
constitutive_titanmod_qs_PerSlipFamily(3,i), constitutive_titanmod_qs_PerSlipFamily(4,i),i
case ('rexponent') case ('rexponent')
constitutive_titanmod_r(i) = IO_floatValue(line,positions,2) constitutive_titanmod_r(i) = IO_floatValue(line,positions,2)
write(6,*) tag write(6,*) tag
@ -1068,40 +1092,81 @@ do f = 1,lattice_maxNslipFamily ! loop over all
!************************************************* !*************************************************
!* Stress ratio for edge !* Stress ratio for edge
StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))>0.0_pReal) then
StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ &
constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance) constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance)
else
StressRatio_edge_p=0.0_pReal
endif
!* Stress ratio for screw !* Stress ratio for screw
if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))>0.0_pReal) then
StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ & StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ &
constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance) constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance)
else
StressRatio_screw_p=0.0_pReal
endif
!* Stress ratio for edge p minus1 !* Stress ratio for edge p minus1
if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))>0.0_pReal) then
StressRatio_edge_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & StressRatio_edge_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ &
constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1) constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1)
else
StressRatio_edge_pminus1=0.0_pReal
endif
!* Stress ratio for screw p minus1 !* Stress ratio for screw p minus1
if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))>0.0_pReal) then
StressRatio_screw_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ & StressRatio_screw_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ &
constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1) constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1)
else
StressRatio_screw_pminus1=0.0_pReal
endif
!* Boltzmann ratio !* Boltzmann ratio
BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(f,myInstance)/(kB*Temperature) BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature)
!* Initial shear rates !* Initial shear rates
DotGamma0 = & DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*& constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*2.0_pReal*(state(g,ip,el)%p(j)*&
constitutive_titanmod_v0e_PerSlipSystem(j,myInstance) + constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)+state(g,ip,el)%p(ns+j)* &
constitutive_titanmod_v0e_PerSlipSystem(j,myInstance))
!* Shear rates due to slip !* Shear rates due to slip
gdot_slip(j) = state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(j,myInstance)* & gdot_slip(j) = constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*2.0_pReal*(state(g,ip,el)%p(j)* &
constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** & constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** &
constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* sign(1.0_pReal,tau_slip(j)) constitutive_titanmod_qe_PerSlipSystem(j,myInstance))+state(g,ip,el)%p(ns+j)* &
constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_screw_p)** &
constitutive_titanmod_qs_PerSlipSystem(j,myInstance)))* sign(1.0_pReal,tau_slip(j))
!* Derivatives of shear rates !* Derivatives of shear rates
dgdot_dtauslip(j) = & dgdot_dtauslip(j) = &
((abs(gdot_slip(j))*BoltzmannRatio*& 2.0_pReal* &
constitutive_titanmod_pe_PerSlipSystem(j,myInstance)*constitutive_titanmod_qe_PerSlipSystem(j,myInstance))/ & ( &
state(g,ip,el)%p(5*ns+3*nt+j))*& ( &
StressRatio_edge_pminus1*(1-StressRatio_edge_p)**(constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal) ( &
( &
abs(gdot_slip(j)) &
*BoltzmannRatio*&
constitutive_titanmod_pe_PerSlipSystem(j,myInstance)* &
constitutive_titanmod_qe_PerSlipSystem(j,myInstance) &
)/ &
constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance) &
)*&
StressRatio_edge_pminus1*(1-StressRatio_edge_p)** &
(constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal) &
) + &
( &
( &
(abs(gdot_slip(j))*BoltzmannRatio*&
constitutive_titanmod_ps_PerSlipSystem(j,myInstance)* &
constitutive_titanmod_qs_PerSlipSystem(j,myInstance) &
)/ &
constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance) &
)*&
StressRatio_screw_pminus1*(1-StressRatio_screw_p)**(constitutive_titanmod_qs_PerSlipSystem(j,myInstance)-1.0_pReal) &
) &
)
!************************************************* !*************************************************
!* Plastic velocity gradient for dislocation glide !* Plastic velocity gradient for dislocation glide
@ -1239,25 +1304,43 @@ forall (s = 1:ns) &
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratio for edge !* Stress ratio for edge
StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j)) > 0.0_pReal) then
StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ &
constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))** constitutive_titanmod_pe_PerSlipSystem(j,myInstance) constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))** constitutive_titanmod_pe_PerSlipSystem(j,myInstance)
else
StressRatio_edge_p=0.0_pReal
endif
!* Stress ratio for screw !* Stress ratio for screw
StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j)) > 0.0_pReal) then
StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ &
constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_ps_PerSlipSystem(j,myInstance) constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_ps_PerSlipSystem(j,myInstance)
!* Boltzmann ratio else
BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(s,myInstance)/(kB*Temperature) StressRatio_screw_p=0.0_pReal
endif
if (tau_slip(j) == 0.0_pReal) then !* Boltzmann ratio
edge_velocity(j) = 0.0_pReal BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature)
screw_velocity(j) = 0.0_pReal
else ! if (tau_slip(j) == 0.0_pReal) then
! edge_velocity(j) = 0.0_pReal
! screw_velocity(j) = 0.0_pReal
! else
edge_velocity(j) =constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** & edge_velocity(j) =constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** &
constitutive_titanmod_qe_PerSlipSystem(j,myInstance)) constitutive_titanmod_qe_PerSlipSystem(j,myInstance))
screw_velocity(j) =constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_screw_p)** & screw_velocity(j) =constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_screw_p)** &
constitutive_titanmod_qs_PerSlipSystem(j,myInstance)) constitutive_titanmod_qs_PerSlipSystem(j,myInstance))
endif ! endif
! write(6,*) 'edge_segment(j) ',edge_segment(j)
! write(6,*) 'screw_segment(j) ',screw_segment(j)
! write(6,*) 'tau_slip(j) ',tau_slip(j)
! write(6,*) 'Temperature ',Temperature
! write(6,*) 'kB ',kB
! write(6,*) 'constitutive_titanmod_f0_PerSlipSystem(j,myInstance) ',constitutive_titanmod_f0_PerSlipSystem(j,myInstance)
! write(6,*) 'StressRatio_edge_p',StressRatio_edge_p,j
! write(6,*) 'StressRatio_screw_p',StressRatio_screw_p,j
! write(6,*) 'edge_velocity(j)',edge_velocity(j),j
! write(6,*) 'screw_velocity(j)',screw_velocity(j),j
!* Multiplication of edge dislocations !* Multiplication of edge dislocations
DotRhoEdgeGeneration(j) = 4.0_pReal*(state(g,ip,el)%p(ns+j)*screw_velocity(j)/screw_segment(j)) DotRhoEdgeGeneration(j) = 4.0_pReal*(state(g,ip,el)%p(ns+j)*screw_velocity(j)/screw_segment(j))
!* Multiplication of screw dislocations !* Multiplication of screw dislocations
@ -1279,6 +1362,11 @@ forall (s = 1:ns) &
constitutive_titanmod_dotState(ns+j) = & constitutive_titanmod_dotState(ns+j) = &
DotRhoScrewGeneration(j)+DotRhoScrewAnnihilation(j) DotRhoScrewGeneration(j)+DotRhoScrewAnnihilation(j)
! write(6,*) 'DotRhoEdgeGeneration(j)',DotRhoEdgeGeneration(j)
! write(6,*) 'DotRhoScrewGeneration(j)',DotRhoScrewGeneration(j)
! write(6,*) 'DotRhoEdgeAnnihilation(j)',DotRhoEdgeAnnihilation(j)
! write(6,*) 'DotRhoScrewAnnihilation(j)',DotRhoScrewAnnihilation(j)
enddo enddo
enddo enddo
@ -1300,7 +1388,6 @@ do f = 1,lattice_maxNtwinFamily ! loop over all
(constitutive_titanmod_MaxTwinFraction(myInstance)-sumf)*& (constitutive_titanmod_MaxTwinFraction(myInstance)-sumf)*&
state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r) state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r)
endif endif
enddo enddo
enddo enddo
@ -1426,34 +1513,31 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* & DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* &
sign(1.0_pReal,tau) sign(1.0_pReal,tau)
enddo ; enddo enddo ; enddo
! invLambdaSlipe', &
! 'invLambdaSlips', &
! 'etauSlipThreshold', &
! 'stauSlipThreshold', &
! 'invLambdaSlipTwin
c = c + ns c = c + ns
case ('mfp_slip') case ('edgesegment')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((4*ns+2*nt+1):(5*ns+2*nt)) constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((4*ns+2*nt+1):(5*ns+2*nt))
c = c + ns c = c + ns
case ('resolved_stress_slip') case ('screwsegment')
j = 0_pInt j = 0_pInt
do f = 1,lattice_maxNslipFamily ! loop over all slip families do f = 1,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure))
do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family do i = 1,constitutive_titanmod_Nslip(f,myInstance)
j = j + 1_pInt j = j + 1_pInt
constitutive_titanmod_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) constitutive_titanmod_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
enddo; enddo enddo; enddo
c = c + ns c = c + ns
case ('threshold_stress_slip') case ('edgeresistance')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((5*ns+3*nt+1):(6*ns+3*nt)) constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((5*ns+3*nt+1):(6*ns+3*nt))
c = c + ns c = c + ns
case ('edge_dipole_distance') case ('screwresistance')
j = 0_pInt constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+3*nt))
do f = 1,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_titanmod_postResults(c+j) = &
(3.0_pReal*constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(f,myInstance))/&
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))))
constitutive_titanmod_postResults(c+j) = min(constitutive_titanmod_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j))
! constitutive_titanmod_postResults(c+j) = max(constitutive_titanmod_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j))
enddo; enddo
c = c + ns c = c + ns
case ('twin_fraction') case ('twin_fraction')
constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((2*ns+1):(2*ns+nt)) constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((2*ns+1):(2*ns+nt))
@ -1461,9 +1545,9 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
case ('shear_rate_twin') case ('shear_rate_twin')
if (nt > 0_pInt) then if (nt > 0_pInt) then
j = 0_pInt j = 0_pInt
do f = 1,lattice_maxNtwinFamily ! loop over all twin families do f = 1,lattice_maxNtwinFamily
index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure))
do i = 1,constitutive_titanmod_Ntwin(f,myInstance) ! process each (active) twin system in family do i = 1,constitutive_titanmod_Ntwin(f,myInstance)
j = j + 1_pInt j = j + 1_pInt
!* Resolved shear stress on twin system !* Resolved shear stress on twin system
@ -1498,46 +1582,6 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
case ('threshold_stress_twin') case ('threshold_stress_twin')
constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+4*nt)) constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+4*nt))
c = c + nt c = c + nt
case ('stress_exponent')
j = 0_pInt
do f = 1,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_p = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance)
StressRatio_pminus1 = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))** &
(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(f,myInstance)* &
constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)
!* Shear rates due to slip
gdot_slip = &
DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* &
sign(1.0_pReal,tau)
!* Derivatives of shear rates
dgdot_dtauslip = &
((abs(gdot_slip)*BoltzmannRatio*&
constitutive_titanmod_pe_PerSlipSystem(j,myInstance)*constitutive_titanmod_qe_PerSlipSystem(j,myInstance))/ &
state(g,ip,el)%p(5*ns+3*nt+j))*&
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal)
!* Stress exponent
if (gdot_slip==0.0_pReal) then
constitutive_titanmod_postResults(c+j) = 0.0_pReal
else
constitutive_titanmod_postResults(c+j) = (tau/gdot_slip)*dgdot_dtauslip
endif
enddo ; enddo
c = c + ns
end select end select
enddo enddo