adapted phenopowerlaw
This commit is contained in:
Philip Eisenlohr
parent
4de21b5f86
commit
2a88285088
2
PRIVATE
2
PRIVATE
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@ -1 +1 @@
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Subproject commit ed4e161d4302852a31c59a1d1d9b11d49f1a5427
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Subproject commit b4a2af3be9551e267a10554b1692a81b935882fd
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@ -1395,17 +1395,26 @@ end function crystal_interaction_TwinBySlip
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!--------------------------------------------------------------------------------------------------
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!> @brief Schmid matrix for slip
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!> details only active slip systems are considered
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! Non-schmid projections for cI with up to 6 coefficients
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! https://doi.org/10.1016/j.actamat.2012.03.053, eq. (17)
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! https://doi.org/10.1016/j.actamat.2008.07.037, table 1
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!--------------------------------------------------------------------------------------------------
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function crystal_SchmidMatrix_slip(Nslip,lattice,cOverA) result(SchmidMatrix)
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function crystal_SchmidMatrix_slip(Nslip,lattice,cOverA,nonSchmidCoefficients,sense) result(SchmidMatrix)
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integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
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character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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real(pREAL), intent(in) :: cOverA
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real(pREAL), dimension(:,:), optional, intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections
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integer, optional, intent(in) :: sense !< sense (-1,+1)
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real(pREAL), dimension(3,3,sum(Nslip)) :: SchmidMatrix
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real(pREAL), dimension(3,3,sum(Nslip)) :: coordinateSystem
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real(pREAL), dimension(:,:), allocatable :: slipSystems
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integer, dimension(:), allocatable :: NslipMax
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integer, dimension(:), allocatable :: slipFamily
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real(pREAL), dimension(3) :: direction, normal, np
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real(pREAL), dimension(:), allocatable :: coeff
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type(tRotation) :: R
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integer :: i
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select case(lattice)
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@ -1431,12 +1440,37 @@ function crystal_SchmidMatrix_slip(Nslip,lattice,cOverA) result(SchmidMatrix)
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if (any(Nslip < 0)) &
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call IO_error(144,ext_msg='Nslip '//trim(lattice))
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slipFamily = math_expand([(i, i=1,size(Nslip))],Nslip)
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coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,lattice,cOverA)
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if (present(sense)) then
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if (abs(sense) /= 1) error stop 'neither +1 nor -1 sense in crystal_SchmidMatrix_slip'
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coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip)) * real(sense,pREAL)
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end if
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do i = 1, sum(Nslip)
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SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
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do i = 1,sum(Nslip)
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direction = coordinateSystem(1:3,1,i)
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normal = coordinateSystem(1:3,2,i)
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SchmidMatrix(1:3,1:3,i) = math_outer(direction,normal)
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if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
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error stop 'dilatational Schmid matrix for slip'
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if (present(nonSchmidCoefficients)) then
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select case(lattice)
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case('cI')
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coeff = nonSchmidCoefficients(slipFamily(i),:)
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call R%fromAxisAngle([direction,60.0_pREAL],degrees=.true.,P=1)
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np = R%rotate(normal)
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SchmidMatrix(1:3,1:3,i) = SchmidMatrix(1:3,1:3,i) &
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+ coeff(1) * math_outer(direction, np) &
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+ coeff(2) * math_outer(math_cross(normal, direction), normal) &
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+ coeff(3) * math_outer(math_cross(np, direction), np) &
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+ coeff(4) * math_outer(normal, normal) &
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+ coeff(5) * math_outer(math_cross(normal, direction), &
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math_cross(normal, direction)) &
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+ coeff(6) * math_outer(direction, direction)
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end select
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end if
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end do
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end function crystal_SchmidMatrix_slip
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@ -36,8 +36,6 @@ submodule(phase:plastic) phenopowerlaw
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integer :: &
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sum_N_sl, & !< total number of active slip system
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sum_N_tw !< total number of active twin systems
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logical :: &
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nonSchmidActive = .false.
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character(len=pSTRLEN), allocatable, dimension(:) :: &
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output
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character(len=:), allocatable, dimension(:) :: &
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@ -89,8 +87,9 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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real(pREAL), dimension(:), allocatable :: &
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xi_0_sl, & !< initial critical shear stress for slip
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xi_0_tw, & !< initial critical shear stress for twin
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a, & !< non-Schmid coefficients
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ones
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real(pREAL), dimension(:,:), allocatable :: &
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a_nS !< non-Schmid coefficients
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character(len=:), allocatable :: &
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refs, &
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extmsg
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@ -105,7 +104,7 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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if (count(myPlasticity) == 0) return
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print'(/,1x,a)', '<<<+- phase:mechanical:plastic:phenopowerlaw init -+>>>'
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print'(/,1x,a,1x,i0)', '# phases:',count(myPlasticity); flush(IO_STDOUT)
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print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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phases => config_material%get_dict('phase')
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@ -124,7 +123,7 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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mech => phase%get_dict('mechanical')
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pl => mech%get_dict('plastic')
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print'(/,1x,a,1x,i0,a)', 'phase',ph,': '//phases%key(ph)
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print'(/,1x,a,i0,a)', 'phase ',ph,': '//phases%key(ph)
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refs = config_listReferences(pl,indent=3)
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if (len(refs) > 0) print'(/,1x,a)', refs
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@ -160,13 +159,13 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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prm%P_sl = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
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if (phase_lattice(ph) == 'cI') then
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a = pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray)
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if (size(a) > 0) prm%nonSchmidActive = .true.
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prm%P_nS_pos = crystal_nonSchmidMatrix(N_sl,a,+1)
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prm%P_nS_neg = crystal_nonSchmidMatrix(N_sl,a,-1)
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allocate(a_nS(3,size(pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray))),source=0.0_pREAL)
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a_nS(1,:) = pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray)
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prm%P_nS_pos = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=+1)
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prm%P_nS_neg = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=-1)
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else
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prm%P_nS_pos = prm%P_sl
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prm%P_nS_neg = prm%P_sl
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prm%P_nS_pos = +prm%P_sl
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prm%P_nS_neg = -prm%P_sl
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end if
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prm%systems_sl = crystal_labels_slip(N_sl,phase_lattice(ph))
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@ -312,8 +311,7 @@ pure module subroutine phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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integer :: &
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i,k,l,m,n
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_sl_pos,dot_gamma_sl_neg, &
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ddot_gamma_dtau_sl_pos,ddot_gamma_dtau_sl_neg
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dot_gamma_sl,ddot_gamma_dtau_sl
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real(pREAL), dimension(param(ph)%sum_N_tw) :: &
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dot_gamma_tw,ddot_gamma_dtau_tw
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@ -322,13 +320,14 @@ pure module subroutine phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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associate(prm => param(ph))
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call kinetics_sl(Mp,ph,en,dot_gamma_sl_pos,dot_gamma_sl_neg,ddot_gamma_dtau_sl_pos,ddot_gamma_dtau_sl_neg)
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call kinetics_sl(Mp,ph,en,dot_gamma_sl,ddot_gamma_dtau_sl)
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slipSystems: do i = 1, prm%sum_N_sl
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Lp = Lp + (dot_gamma_sl_pos(i)+dot_gamma_sl_neg(i))*prm%P_sl(1:3,1:3,i)
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Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ ddot_gamma_dtau_sl_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) &
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+ ddot_gamma_dtau_sl_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i)
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+ ddot_gamma_dtau_sl(i) * prm%P_sl(k,l,i) &
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* merge(prm%P_nS_pos(m,n,i), &
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prm%P_nS_neg(m,n,i), dot_gamma_sl(i)>0.0_pREAL)
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end do slipSystems
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call kinetics_tw(Mp,ph,en,dot_gamma_tw,ddot_gamma_dtau_tw)
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@ -370,23 +369,23 @@ module function phenopowerlaw_dotState(Mp,ph,en) result(dotState)
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dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)), &
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dot_gamma_tw => dotState(indexDotState(ph)%gamma_tw(1):indexDotState(ph)%gamma_tw(2)))
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call kinetics_sl(Mp,ph,en, dot_gamma_sl_pos,dot_gamma_sl_neg)
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dot_gamma_sl = abs(dot_gamma_sl_pos+dot_gamma_sl_neg)
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call kinetics_sl(Mp,ph,en, dot_gamma_sl)
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call kinetics_tw(Mp,ph,en, dot_gamma_tw)
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dot_gamma_sl = abs(dot_gamma_sl)
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sumF = sum(stt%gamma_tw(:,en)/prm%gamma_char)
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xi_sl_sat_offset = prm%f_sat_sl_tw*sqrt(sumF)
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left_SlipSlip = sign(abs(1.0_pREAL-stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))**prm%a_sl, &
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1.0_pREAL-stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))
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left_SlipSlip = sign(abs(1.0_pREAL - stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))**prm%a_sl, &
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1.0_pREAL - stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))
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dot_xi_sl = prm%h_0_sl_sl * (1.0_pREAL + prm%c_1 * sumF**prm%c_2) &
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* left_SlipSlip * matmul(prm%h_sl_sl,dot_gamma_sl) &
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* left_SlipSlip &
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* matmul(prm%h_sl_sl,dot_gamma_sl) &
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+ matmul(prm%h_sl_tw,dot_gamma_tw)
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dot_xi_tw = prm%h_0_tw_sl * sum(stt%gamma_sl(:,en))**prm%c_3 &
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* matmul(prm%h_tw_sl,dot_gamma_sl) &
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+ prm%h_0_tw_tw * sumF**prm%c_4 * matmul(prm%h_tw_tw,dot_gamma_tw)
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dot_xi_tw = prm%h_0_tw_sl * sum(stt%gamma_sl(:,en))**prm%c_3 * matmul(prm%h_tw_sl,dot_gamma_sl) &
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+ prm%h_0_tw_tw * sumF **prm%c_4 * matmul(prm%h_tw_tw,dot_gamma_tw)
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end associate
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@ -436,12 +435,12 @@ end subroutine plastic_phenopowerlaw_result
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on slip systems and their derivatives with respect to resolved
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! stress.
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!> @details Derivatives are calculated only optionally.
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! NOTE: Contrary to common convention, here the result (i.e. intent(out)) variables have to be put
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! at the end since some of them are optional.
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!> @details Sign of dot_gamma_sl conveys sense of shear.
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! Derivatives are calculated only optionally, hence, contrary to common convention,
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! here the result (i.e. intent(out)) variables have to be put at the end.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_sl(Mp,ph,en, &
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dot_gamma_sl_pos,dot_gamma_sl_neg,ddot_gamma_dtau_sl_pos,ddot_gamma_dtau_sl_neg)
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dot_gamma_sl,ddot_gamma_dtau_sl)
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real(pREAL), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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@ -449,12 +448,10 @@ pure subroutine kinetics_sl(Mp,ph,en, &
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ph, &
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en
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real(pREAL), intent(out), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_sl_pos, &
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dot_gamma_sl_neg
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real(pREAL), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
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ddot_gamma_dtau_sl_pos, &
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ddot_gamma_dtau_sl_neg
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real(pREAL), dimension(param(ph)%sum_N_sl), intent(out) :: &
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dot_gamma_sl
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real(pREAL), dimension(param(ph)%sum_N_sl), optional, intent(out) :: &
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ddot_gamma_dtau_sl
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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tau_sl_pos, &
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@ -463,38 +460,18 @@ pure subroutine kinetics_sl(Mp,ph,en, &
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associate(prm => param(ph), stt => state(ph))
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do i = 1, prm%sum_N_sl
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tau_sl_pos(i) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i))
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tau_sl_neg(i) = merge(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)), &
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0.0_pREAL, prm%nonSchmidActive)
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end do
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tau_sl_pos = [(math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i)),i=1,prm%sum_N_sl)]
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tau_sl_neg = [(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)),i=1,prm%sum_N_sl)]
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where(dNeq0(tau_sl_pos))
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dot_gamma_sl_pos = prm%dot_gamma_0_sl * merge(0.5_pREAL,1.0_pREAL, prm%nonSchmidActive) & ! 1/2 if non-Schmid active
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* sign(abs(tau_sl_pos/stt%xi_sl(:,en))**prm%n_sl, tau_sl_pos)
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else where
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dot_gamma_sl_pos = 0.0_pREAL
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end where
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dot_gamma_sl = merge(+1.0_pREAL,-1.0_pREAL, tau_sl_pos>tau_sl_neg) &
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* prm%dot_gamma_0_sl &
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* (merge(tau_sl_pos,tau_sl_neg, tau_sl_pos>tau_sl_neg)/stt%xi_sl(:,en))**prm%n_sl
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where(dNeq0(tau_sl_neg))
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dot_gamma_sl_neg = prm%dot_gamma_0_sl * 0.5_pREAL & ! only used if non-Schmid active, always 1/2
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* sign(abs(tau_sl_neg/stt%xi_sl(:,en))**prm%n_sl, tau_sl_neg)
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if (present(ddot_gamma_dtau_sl)) then
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where(dNeq0(dot_gamma_sl))
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ddot_gamma_dtau_sl = dot_gamma_sl*prm%n_sl/merge(tau_sl_pos,tau_sl_neg, tau_sl_pos>tau_sl_neg)
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else where
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dot_gamma_sl_neg = 0.0_pREAL
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end where
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if (present(ddot_gamma_dtau_sl_pos)) then
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where(dNeq0(dot_gamma_sl_pos))
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ddot_gamma_dtau_sl_pos = dot_gamma_sl_pos*prm%n_sl/tau_sl_pos
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else where
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ddot_gamma_dtau_sl_pos = 0.0_pREAL
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end where
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end if
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if (present(ddot_gamma_dtau_sl_neg)) then
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where(dNeq0(dot_gamma_sl_neg))
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ddot_gamma_dtau_sl_neg = dot_gamma_sl_neg*prm%n_sl/tau_sl_neg
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else where
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ddot_gamma_dtau_sl_neg = 0.0_pREAL
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ddot_gamma_dtau_sl = 0.0_pREAL
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end where
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end if
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@ -504,8 +481,8 @@ end subroutine kinetics_sl
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved
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! stress. Twinning is assumed to take place only in an untwinned volume.
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!> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved stress.
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! Twinning is assumed to take place only in an untwinned volume.
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!> @details Derivatives are calculated and returned if corresponding output variables are present in the argument list.
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! NOTE: Contrary to common convention, here the result (i.e. intent(out)) variables have to be put
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! at the end since some of them are optional.
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@ -535,7 +512,7 @@ pure subroutine kinetics_tw(Mp,ph,en,&
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where(tau_tw > 0.0_pREAL)
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dot_gamma_tw = (1.0_pREAL-sum(stt%gamma_tw(:,en)/prm%gamma_char)) & ! only twin in untwinned volume fraction
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* prm%dot_gamma_0_tw*(abs(tau_tw)/stt%xi_tw(:,en))**prm%n_tw
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* prm%dot_gamma_0_tw*(tau_tw/stt%xi_tw(:,en))**prm%n_tw
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else where
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dot_gamma_tw = 0.0_pREAL
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end where
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