calculation of shear modulus for cubic crystals can be simplifieid, tests added for different crystal symmetries

This commit is contained in:
Sharan Roongta 2022-11-12 00:03:30 +01:00 committed by Sharan
parent 1264d8dfc1
commit 8b5fa37428
9 changed files with 119 additions and 48 deletions

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@ -9,7 +9,7 @@ phase:
lattice: cF
mechanical:
output: [F, P, F_e, F_p, L_p, O]
elastic: {type: Hooke, C_11: 106.75e+9, C_12: 60.41e+9, C_44: 28.34e+9, modulus_type: 'Voigt'}
elastic: {type: Hooke, C_11: 106.75e+9, C_12: 60.41e+9, C_44: 28.34e+9}
plastic:
type: phenopowerlaw
N_sl: [12]

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@ -9,6 +9,7 @@
submodule(homogenization:mechanical) RGC
use rotations
use lattice
use phase
type :: tParameters
integer, dimension(:), allocatable :: &
@ -652,9 +653,9 @@ module function RGC_updateState(P,F,avgF,dt,dPdF,ce) result(doneAndHappy)
real(pReal), dimension(6,6) :: C
C = phase_homogenizedC66(material_phaseID(co,ce),material_phaseEntry(co,ce)) ! damage not included!
equivalentMu = lattice_equivalent_mu(C,'voigt')
equivalentMu = lattice_isotropic_mu(C,'voigt',phase_lattice_structure(co,ce))
end function equivalentMu

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@ -376,8 +376,8 @@ module lattice
public :: &
lattice_init, &
lattice_equivalent_nu, &
lattice_equivalent_mu, &
lattice_isotropic_nu, &
lattice_isotropic_mu, &
lattice_symmetrize_33, &
lattice_symmetrize_C66, &
lattice_SchmidMatrix_slip, &
@ -2149,10 +2149,11 @@ end function getlabels
!> @brief Equivalent Poisson's ratio (ν)
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
pure function lattice_equivalent_nu(C,assumption) result(nu)
pure function lattice_isotropic_nu(C,assumption,lattice) result(nu)
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=5), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
character(len=2), intent(in) :: lattice
real(pReal) :: nu
real(pReal) :: K, mu
@ -2172,20 +2173,22 @@ pure function lattice_equivalent_nu(C,assumption) result(nu)
error stop 'invalid assumption'
end if
mu = lattice_equivalent_mu(C,assumption)
mu = lattice_isotropic_mu(C,assumption,lattice)
nu = (1.5_pReal*K-mu)/(3.0_pReal*K+mu)
end function lattice_equivalent_nu
end function lattice_isotropic_nu
!--------------------------------------------------------------------------------------------------
!> @brief Equivalent shear modulus (μ)
!> @details https://doi.org/10.1143/JPSJ.20.635
!> @details Nonlinear Mechanics of Crystals 10.1007/978-94-007-0350-6, pp 563
!--------------------------------------------------------------------------------------------------
pure function lattice_equivalent_mu(C,assumption) result(mu)
pure function lattice_isotropic_mu(C,assumption,lattice) result(mu)
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=5), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
character(len=2), intent(in) :: lattice
real(pReal) :: mu
logical :: error
@ -2193,18 +2196,32 @@ pure function lattice_equivalent_mu(C,assumption) result(mu)
if (IO_lc(assumption) == 'voigt') then
mu = (1.0_pReal*(C(1,1)+C(2,2)+C(3,3)) -1.0_pReal*(C(1,2)+C(2,3)+C(1,3)) +3.0_pReal*(C(4,4)+C(5,5)+C(6,6))) &
/ 15.0_pReal
select case(lattice)
case('cF','cI')
mu = ( C(1,1) - C(1,2) + C(4,4)*3.0_pReal) / 5.0_pReal
case default
mu = ( C(1,1)+C(2,2)+C(3,3) &
-(C(1,2)+C(2,3)+C(1,3)) &
+(C(4,4)+C(5,5)+C(6,6)) * 3.0_pReal &
) / 15.0_pReal
end select
elseif (IO_lc(assumption) == 'reuss') then
call math_invert(S,error,C)
if (error) error stop 'matrix inversion failed'
mu = 15.0_pReal &
/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
select case(lattice)
case('cF','cI')
mu = 1.0_pReal &
/ ((4.0_pReal/(5.0_pReal * (C(1,1)-C(1,2)))) + (3.0_pReal/(5.0_pReal*C(4,4))))
case default
call math_invert(S,error,C)
if (error) error stop 'matrix inversion failed'
mu = 15.0_pReal &
/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
end select
else
error stop 'invalid assumption'
end if
end function lattice_equivalent_mu
end function lattice_isotropic_mu
!--------------------------------------------------------------------------------------------------
@ -2270,16 +2287,42 @@ subroutine selfTest
call random_number(C)
C(1,1) = C(1,1) + C(1,2) + 0.1_pReal
C(1,3) = C(1,2)
C(3,3) = C(1,1)
C(4,4) = 0.5_pReal * (C(1,1) - C(1,2))
C = lattice_symmetrize_C66(C,'cI')
if (dNeq(C(4,4),lattice_equivalent_mu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_mu/voigt'
if (dNeq(C(4,4),lattice_equivalent_mu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_mu/reuss'
C(6,6) = C(4,4)
C_cI = lattice_symmetrize_C66(C,'cI')
if (dNeq(C_cI(4,4),lattice_isotropic_mu(C_cI,'voigt','cI'),1.0e-12_pReal)) error stop 'isotropic_mu/cI/voigt'
if (dNeq(C_cI(4,4),lattice_isotropic_mu(C_cI,'reuss','cI'),1.0e-12_pReal)) error stop 'isotropic_mu/cI/reuss'
lambda = C_cI(1,2)
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_cI,'voigt','cI')), &
lattice_isotropic_nu(C_cI,'voigt','cI'),1.0e-12_pReal)) error stop 'isotropic_nu/cI/voigt'
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_cI,'reuss','cI')), &
lattice_isotropic_nu(C_cI,'reuss','cI'),1.0e-12_pReal)) error stop 'isotropic_nu/cI/reuss'
C_hP = lattice_symmetrize_C66(C,'hP')
if (dNeq(C(4,4),lattice_isotropic_mu(C_hP,'voigt','hP'),1.0e-12_pReal)) error stop 'isotropic_mu/hP/voigt'
if (dNeq(C(4,4),lattice_isotropic_mu(C_hP,'reuss','hP'),1.0e-12_pReal)) error stop 'isotropic_mu/hP/reuss'
lambda = C_hP(1,2)
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_hP,'voigt','hP')), &
lattice_isotropic_nu(C_hP,'voigt','hP'),1.0e-12_pReal)) error stop 'isotropic_nu/hP/voigt'
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_hP,'reuss','hP')), &
lattice_isotropic_nu(C_hP,'reuss','hP'),1.0e-12_pReal)) error stop 'isotropic_nu/hP/reuss'
C_tI = lattice_symmetrize_C66(C,'tI')
if (dNeq(C(6,6),lattice_isotropic_mu(C_tI,'voigt','tI'),1.0e-12_pReal)) error stop 'isotropic_mu/tI/voigt'
if (dNeq(C(6,6),lattice_isotropic_mu(C_tI,'reuss','tI'),1.0e-12_pReal)) error stop 'isotropic_mu/tI/reuss'
lambda = C_tI(1,2)
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_tI,'voigt','tI')), &
lattice_isotropic_nu(C_tI,'voigt','tI'),1.0e-12_pReal)) error stop 'isotropic_nu/tI/voigt'
if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_tI,'reuss','tI')), &
lattice_isotropic_nu(C_tI,'reuss','tI'),1.0e-12_pReal)) error stop 'isotropic_nu/tI/reuss'
lambda = C(1,2)
if (dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'voigt')), &
lattice_equivalent_nu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_nu/voigt'
if (dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'reuss')), &
lattice_equivalent_nu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_nu/reuss'
end subroutine selfTest

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@ -347,6 +347,7 @@ module phase
phase_K_T, &
phase_mu_phi, &
phase_mu_T, &
phase_lattice_structure, &
phase_results, &
phase_allocateState, &
phase_forward, &
@ -434,6 +435,20 @@ subroutine phase_init
end subroutine phase_init
!--------------------------------------------------------------------------------------------------
!> @brief Get lattice structure for a given phase
!--------------------------------------------------------------------------------------------------
function phase_lattice_structure(co,ce) result(lattice)
integer, intent(in) :: co, ce
character(len=2) :: lattice
lattice = phase_lattice(material_phaseID(co,ce))
end function phase_lattice_structure
!--------------------------------------------------------------------------------------------------
!> @brief Allocate the components of the state structure for a given phase
!--------------------------------------------------------------------------------------------------

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@ -169,14 +169,16 @@ submodule(phase) mechanical
integer, intent(in) :: ph, en
end function elastic_C66
pure module function elastic_mu(ph,en) result(mu)
pure module function elastic_mu(ph,en,isotropic_bound) result(mu)
real(pReal) :: mu
integer, intent(in) :: ph, en
character(len=5), intent(in) :: isotropic_bound
end function elastic_mu
pure module function elastic_nu(ph,en) result(nu)
pure module function elastic_nu(ph,en,isotropic_bound) result(nu)
real(pReal) :: nu
integer, intent(in) :: ph, en
character(len=5), intent(in) :: isotropic_bound
end function elastic_nu
end interface

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@ -8,7 +8,6 @@ submodule(phase:mechanical) elastic
C_33, &
C_44, &
C_66
character(len=pStringLen) :: modulus_type
end type tParameters
type(tParameters), allocatable, dimension(:) :: param
@ -58,8 +57,6 @@ module subroutine elastic_init(phases)
if (phase_lattice(ph) == 'tI') &
prm%C_66 = polynomial(elastic%asDict(),'C_66','T')
prm%modulus_type=elastic%get_asString('modulus_type',defaultVal='Voigt')
end associate
end do
@ -105,17 +102,18 @@ end function elastic_C66
!--------------------------------------------------------------------------------------------------
!> @brief return shear modulus
!--------------------------------------------------------------------------------------------------
pure module function elastic_mu(ph,en) result(mu)
pure module function elastic_mu(ph,en,isotropic_bound) result(mu)
integer, intent(in) :: &
ph, &
en
character(len=5), intent(in) :: isotropic_bound
real(pReal) :: &
mu
associate(prm => param(ph))
mu = lattice_equivalent_mu(elastic_C66(ph,en),prm%modulus_type)
mu = lattice_isotropic_mu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
end associate
@ -125,17 +123,18 @@ end function elastic_mu
!--------------------------------------------------------------------------------------------------
!> @brief return Poisson ratio
!--------------------------------------------------------------------------------------------------
pure module function elastic_nu(ph,en) result(nu)
pure module function elastic_nu(ph,en,isotropic_bound) result(nu)
integer, intent(in) :: &
ph, &
en
character(len=5), intent(in) :: isotropic_bound
real(pReal) :: &
nu
associate(prm => param(ph))
nu = lattice_equivalent_nu(elastic_C66(ph,en),prm%modulus_type)
nu = lattice_isotropic_nu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
end associate

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@ -35,6 +35,8 @@ submodule(phase:plastic) dislotungsten
P_nS_neg
integer :: &
sum_N_sl !< total number of active slip system
character(len=5) :: &
isotropic_bound
character(len=pStringLen), allocatable, dimension(:) :: &
output
logical :: &
@ -131,6 +133,8 @@ module function plastic_dislotungsten_init() result(myPlasticity)
prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
#endif
prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
!--------------------------------------------------------------------------------------------------
! slip related parameters
N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
@ -333,7 +337,7 @@ module function dislotungsten_dotState(Mp,ph,en) result(dotState)
dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
mu = elastic_mu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
T = thermal_T(ph,en)
call kinetics(Mp,T,ph,en,&
@ -384,7 +388,7 @@ module subroutine dislotungsten_dependentState(ph,en)
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
dst%tau_pass(:,en) = elastic_mu(ph,en)*prm%b_sl &
dst%tau_pass(:,en) = elastic_mu(ph,en,prm%isotropic_bound)*prm%b_sl &
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
Lambda_sl_inv = 1.0_pReal/prm%D &

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@ -74,6 +74,8 @@ submodule(phase:plastic) dislotwin
fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
character(len=:), allocatable :: &
lattice_tr
character(len=5) :: &
isotropic_bound
character(len=pStringLen), allocatable, dimension(:) :: &
output
logical :: &
@ -186,6 +188,8 @@ module function plastic_dislotwin_init() result(myPlasticity)
prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
#endif
prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
!--------------------------------------------------------------------------------------------------
! slip related parameters
N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
@ -644,8 +648,8 @@ module function dislotwin_dotState(Mp,ph,en) result(dotState)
dot_f_tw => dotState(indexDotState(ph)%f_tw(1):indexDotState(ph)%f_tw(2)), &
dot_f_tr => dotState(indexDotState(ph)%f_tr(1):indexDotState(ph)%f_tr(2)))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
T = thermal_T(ph,en)
f_matrix = 1.0_pReal &
@ -732,7 +736,7 @@ module subroutine dislotwin_dependentState(ph,en)
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
mu = elastic_mu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
sumf_tw = sum(stt%f_tw(1:prm%sum_N_tw,en))
sumf_tr = sum(stt%f_tr(1:prm%sum_N_tr,en))
@ -930,8 +934,8 @@ pure subroutine kinetics_tw(Mp,T,abs_dot_gamma_sl,ph,en,&
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
Gamma_sf = prm%Gamma_sf%at(T)
tau_hat = 3.0_pReal*prm%b_tw(1)*mu/prm%L_tw &
@ -1006,8 +1010,8 @@ pure subroutine kinetics_tr(Mp,T,abs_dot_gamma_sl,ph,en,&
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
Gamma_sf = prm%Gamma_sf%at(T)
tau_hat = 3.0_pReal*prm%b_tr(1)*mu/prm%L_tr &

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@ -115,6 +115,8 @@ submodule(phase:plastic) nonlocal
sum_N_sl = 0
integer, dimension(:), allocatable :: &
colinearSystem !< colinear system to the active slip system (only valid for fcc!)
character(len=5) :: &
isotropic_bound
character(len=pStringLen), dimension(:), allocatable :: &
output
logical :: &
@ -241,6 +243,7 @@ module function plastic_nonlocal_init() result(myPlasticity)
prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
#endif
prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
prm%atol_rho = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
ini%N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
@ -609,8 +612,8 @@ module subroutine nonlocal_dependentState(ph, en)
associate(prm => param(ph),dst => dependentState(ph), stt => state(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
rho = getRho(ph,en)
stt%rho_forest(:,en) = matmul(prm%forestProjection_Edge, sum(abs(rho(:,edg)),2)) &
@ -880,8 +883,8 @@ module subroutine plastic_nonlocal_deltaState(Mp,ph,en)
associate(prm => param(ph),dst => dependentState(ph),del => deltaState(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
!*** shortcut to state variables
forall (s = 1:prm%sum_N_sl, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),en)
@ -994,8 +997,8 @@ module subroutine nonlocal_dotState(Mp,timestep, &
associate(prm => param(ph), dst => dependentState(ph), dot => dotState(ph), stt => state(ph))
mu = elastic_mu(ph,en)
nu = elastic_nu(ph,en)
mu = elastic_mu(ph,en,prm%isotropic_bound)
nu = elastic_nu(ph,en,prm%isotropic_bound)
Temperature = thermal_T(ph,en)
tau = 0.0_pReal