810 lines
36 KiB
Fortran
810 lines
36 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief phenomenological crystal plasticity formulation using a powerlaw fitting
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!--------------------------------------------------------------------------------------------------
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submodule(phase:plastic) phenopowerlaw
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use geometry_plastic_nonlocal, only: &
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nCellNeighbors => geometry_plastic_nonlocal_nIPneighbors, &
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IPneighborhood => geometry_plastic_nonlocal_IPneighborhood, &
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IPvolume0 => geometry_plastic_nonlocal_IPvolume0, &
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IParea0 => geometry_plastic_nonlocal_IParea0, &
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IPareaNormal0 => geometry_plastic_nonlocal_IPareaNormal0, &
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geometry_plastic_nonlocal_disable
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type :: tGeometry
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real(pREAL), dimension(:), allocatable :: v_0
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real(pREAL), dimension(:,:), allocatable :: a_0, x_0
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real(pREAL), dimension(:,:,:), allocatable :: n_0
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integer, dimension(:,:,:), allocatable :: IPneighborhood
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end type tGeometry
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type(tGeometry), dimension(:), allocatable :: geom
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type :: tParameters
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real(pREAL), allocatable, dimension(:) :: &
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dot_gamma_0_sl, & !< reference shear strain rate for slip
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dot_gamma_0_tw, & !< reference shear strain rate for twin
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a_sl, &
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n_sl, & !< stress exponent for slip
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n_tw, & !< stress exponent for twin
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xi_inf_sl, & !< maximum critical shear stress for slip
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f_sat_sl_tw, & !< push-up factor for slip saturation due to twinning
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c_1, &
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c_2, &
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c_3, &
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c_4, &
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h_0_sl_sl, & !< reference hardening slip - slip
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h_0_tw_sl, & !< reference hardening twin - slip
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h_0_tw_tw, & !< reference hardening twin - twin
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gamma_char, & !< characteristic shear for twins
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checkstep !< Achal < Checkstep for monte carlo
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real(pREAL), allocatable, dimension(:,:) :: &
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h_sl_sl, & !< slip resistance from slip activity
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h_sl_tw, & !< slip resistance from twin activity
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h_tw_sl, & !< twin resistance from slip activity
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h_tw_tw !< twin resistance from twin activity
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real(pREAL), allocatable, dimension(:,:,:) :: &
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P_sl, &
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P_tw, &
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P_nS_pos, &
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P_nS_neg, &
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CorrespondenceMatrix
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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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character(len=pSTRLEN), allocatable, dimension(:) :: &
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output
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character(len=:), allocatable, dimension(:) :: &
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systems_sl, &
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systems_tw
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logical, allocatable :: &
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discrete_twin
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end type tParameters
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type :: tIndexDotState
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integer, dimension(2) :: &
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xi_sl, &
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xi_tw, &
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gamma_sl, &
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gamma_tw, &
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f_twin
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end type tIndexDotState
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type :: tPhenopowerlawState
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real(pREAL), pointer, dimension(:,:) :: &
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xi_sl, &
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xi_tw, &
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gamma_sl, &
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gamma_tw, &
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f_twin, &
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fmc_twin
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real(pREAL), pointer, dimension(:) :: &
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variant_twin, &
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frozen
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end type tPhenopowerlawState
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!--------------------------------------------------------------------------------------------------
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! containers for parameters, dot state index, and state
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type(tParameters), allocatable, dimension(:) :: param
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type(tIndexDotState), allocatable, dimension(:) :: indexDotState
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type(tPhenopowerlawState), allocatable, dimension(:) :: state, deltastate !Achal added deltastate
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Perform module initialization.
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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module function plastic_phenopowerlaw_init() result(myPlasticity)
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logical, dimension(:), allocatable :: myPlasticity
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integer :: &
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ph, i, o, &
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Nmembers, &
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sizeState, sizeDotState, sizeDeltaState, &
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startIndex, endIndex
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integer, dimension(:), allocatable :: &
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N_sl, & !< number of slip-systems for a given slip family
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N_tw !< number of twin-systems for a given twin family
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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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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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type(tDict), pointer :: &
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phases, &
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phase, &
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mech, &
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pl
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myPlasticity = plastic_active('phenopowerlaw')
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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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phases => config_material%get_dict('phase')
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allocate(geom(phases%length))
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allocate(param(phases%length))
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allocate(indexDotState(phases%length))
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allocate(state(phases%length))
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allocate(deltastate(phases%length))
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extmsg = ''
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do ph = 1, phases%length
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if (.not. myPlasticity(ph)) cycle
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associate(prm => param(ph), stt => state(ph), dlt => deltastate(ph), &
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idx_dot => indexDotState(ph))
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phase => phases%get_dict(ph)
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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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refs = config_listReferences(pl,indent=3)
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if (len(refs) > 0) print'(/,1x,a)', refs
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#if defined (__GFORTRAN__)
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prm%output = output_as1dStr(pl)
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#else
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prm%output = pl%get_as1dStr('output',defaultVal=emptyStrArray)
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#endif
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N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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N_tw = pl%get_as1dInt('N_tw',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(abs(N_sl))
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prm%sum_N_tw = sum(abs(N_tw))
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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slipActive: if (prm%sum_N_sl > 0) then
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prm%dot_gamma_0_sl = math_expand(pl%get_as1dReal('dot_gamma_0_sl',requiredSize=size(N_sl)), N_sl)
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prm%n_sl = math_expand(pl%get_as1dReal('n_sl', requiredSize=size(N_sl)), N_sl)
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prm%a_sl = math_expand(pl%get_as1dReal('a_sl', requiredSize=size(N_sl)), N_sl)
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prm%h_0_sl_sl = math_expand(pl%get_as1dReal('h_0_sl-sl', requiredSize=size(N_sl)), N_sl)
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xi_0_sl = math_expand(pl%get_as1dReal('xi_0_sl', requiredSize=size(N_sl)), N_sl)
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prm%xi_inf_sl = math_expand(pl%get_as1dReal('xi_inf_sl', requiredSize=size(N_sl)), N_sl)
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prm%c_1 = math_expand(pl%get_as1dReal('c_1', requiredSize=size(N_sl), &
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defaultVal=misc_zeros(size(N_sl))), N_sl)
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prm%c_2 = math_expand(pl%get_as1dReal('c_2', requiredSize=size(N_sl), &
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defaultVal=misc_ones(size(N_sl))), N_sl)
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prm%f_sat_sl_tw = math_expand(pl%get_as1dReal('f_sat_sl-tw', requiredSize=size(N_sl), &
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defaultVal=misc_zeros(size(N_sl))), N_sl)
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prm%discrete_twin = pl%get_asBool("discrete_twin", defaultval=.true.)
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prm%h_sl_sl = crystal_interaction_SlipBySlip(N_sl,pl%get_as1dReal('h_sl-sl'),phase_lattice(ph))
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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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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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deallocate(a_nS)
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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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end if
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prm%systems_sl = crystal_labels_slip(N_sl,phase_lattice(ph))
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! sanity checks
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if (any(prm%dot_gamma_0_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' dot_gamma_0_sl'
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if (any(prm%n_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' n_sl'
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if (any(prm%a_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' a_sl'
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if (any(xi_0_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' xi_0_sl'
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if (any(prm%xi_inf_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' xi_inf_sl'
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else slipActive
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xi_0_sl = emptyRealArray
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allocate(prm%dot_gamma_0_sl, &
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prm%a_sl, &
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prm%n_sl, &
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prm%xi_inf_sl, &
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prm%f_sat_sl_tw, &
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prm%c_1, &
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prm%c_2, &
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prm%h_0_sl_sl, &
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source=emptyRealArray)
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allocate(prm%h_sl_sl(0,0))
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end if slipActive
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!--------------------------------------------------------------------------------------------------
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! twin related parameters
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twinActive: if (prm%sum_N_tw > 0) then
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prm%dot_gamma_0_tw = math_expand(pl%get_as1dReal('dot_gamma_0_tw', requiredSize=size(N_tw)), N_tw)
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prm%n_tw = math_expand(pl%get_as1dReal('n_tw', requiredSize=size(N_tw)), N_tw)
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prm%h_0_tw_tw = math_expand(pl%get_as1dReal('h_0_tw-tw', requiredSize=size(N_tw)), N_tw)
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xi_0_tw = math_expand(pl%get_as1dReal('xi_0_tw', requiredSize=size(N_tw)), N_tw)
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prm%c_3 = math_expand(pl%get_as1dReal('c_3', requiredSize=size(N_tw), &
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defaultVal=misc_ones(size(N_tw))), N_tw)
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prm%c_4 = math_expand(pl%get_as1dReal('c_4', requiredSize=size(N_tw), &
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defaultVal=misc_zeros(size(N_tw))), N_tw)
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prm%checkstep = math_expand(pl%get_as1dReal('checkstep', requiredSize=size(N_tw), &
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defaultVal=0.05_pREAL*misc_ones(size(N_tw))), N_tw)
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prm%CorrespondenceMatrix = crystal_CorrespondenceMatrix_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%gamma_char = crystal_characteristicShear_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%h_tw_tw = crystal_interaction_TwinByTwin(N_tw,pl%get_as1dReal('h_tw-tw'),phase_lattice(ph))
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prm%P_tw = crystal_SchmidMatrix_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%systems_tw = crystal_labels_twin(N_tw,phase_lattice(ph))
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! sanity checks
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if (any(prm%dot_gamma_0_tw <= 0.0_pREAL)) extmsg = trim(extmsg)//' dot_gamma_0_tw'
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if (any(prm%n_tw <= 0.0_pREAL)) extmsg = trim(extmsg)//' n_tw'
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if (any(xi_0_tw <= 0.0_pREAL)) extmsg = trim(extmsg)//' xi_0_tw'
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else twinActive
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xi_0_tw = emptyRealArray
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allocate(prm%dot_gamma_0_tw, &
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prm%n_tw, &
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prm%c_3, &
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prm%c_4, &
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prm%gamma_char, &
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prm%h_0_tw_sl, &
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prm%h_0_tw_tw, &
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prm%checkstep, &
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source=emptyRealArray)
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allocate(prm%h_tw_tw(0,0))
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!allocate(prm%CorrespondenceMatrix(0,0,0)) !Achal: this needed or not?
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end if twinActive
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!--------------------------------------------------------------------------------------------------
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! slip-twin related parameters
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slipAndTwinActive: if (prm%sum_N_sl > 0 .and. prm%sum_N_tw > 0) then
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prm%h_0_tw_sl = math_expand(pl%get_as1dReal('h_0_tw-sl',requiredSize=size(N_tw)), N_tw)
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prm%h_sl_tw = crystal_interaction_SlipByTwin(N_sl,N_tw,pl%get_as1dReal('h_sl-tw'),phase_lattice(ph))
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prm%h_tw_sl = crystal_interaction_TwinBySlip(N_tw,N_sl,pl%get_as1dReal('h_tw-sl'),phase_lattice(ph))
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else slipAndTwinActive
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allocate(prm%h_sl_tw(prm%sum_N_sl,prm%sum_N_tw)) ! at least one dimension is 0
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allocate(prm%h_tw_sl(prm%sum_N_tw,prm%sum_N_sl)) ! at least one dimension is 0
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prm%h_0_tw_sl = [(0.0_pREAL,i=1,size(N_tw))]
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end if slipAndTwinActive
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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Nmembers = count(material_ID_phase == ph)
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sizeDotState = size(['xi_sl ','gamma_sl']) * prm%sum_N_sl &
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+ size(['xi_tw ','gamma_tw']) * prm%sum_N_tw &
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+ size(['f_twin ']) * prm%sum_N_tw !Achal
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sizeDeltaState = size(['f_twin ','fmc_twin']) * prm%sum_N_tw & !Achal
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+ size(['variant_twin','frozen '])
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sizeState = size(['xi_sl ','gamma_sl']) * prm%sum_N_sl &
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+ size(['xi_tw ','gamma_tw']) * prm%sum_N_tw &
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+ size(['f_twin ','fmc_twin']) * prm%sum_N_tw & !Achal
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+ size(['variant_twin','frozen '])
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call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,sizeDeltaState)
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deallocate(plasticState(ph)%dotState) ! ToDo: remove dotState completely
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allocate(geom(ph)%v_0(Nmembers))
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allocate(geom(ph)%a_0(nCellNeighbors,Nmembers))
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allocate(geom(ph)%x_0(3,Nmembers))
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allocate(geom(ph)%n_0(3,nCellNeighbors,Nmembers))
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allocate(geom(ph)%IPneighborhood(3,nCellNeighbors,Nmembers))
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call storeGeometry(ph)
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!--------------------------------------------------------------------------------------------------
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! state aliases and initialization
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startIndex = 1
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endIndex = prm%sum_N_sl
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idx_dot%xi_sl = [startIndex,endIndex]
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stt%xi_sl => plasticState(ph)%state(startIndex:endIndex,:)
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stt%xi_sl = spread(xi_0_sl, 2, Nmembers)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_xi',defaultVal=1.0_pREAL)
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if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pREAL)) extmsg = trim(extmsg)//' atol_xi'
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_tw
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idx_dot%xi_tw = [startIndex,endIndex]
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stt%xi_tw => plasticState(ph)%state(startIndex:endIndex,:)
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stt%xi_tw = spread(xi_0_tw, 2, Nmembers)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_xi',defaultVal=1.0_pREAL)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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idx_dot%gamma_sl = [startIndex,endIndex]
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stt%gamma_sl => plasticState(ph)%state(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pREAL)
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if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pREAL)) extmsg = trim(extmsg)//' atol_gamma'
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_tw
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idx_dot%gamma_tw = [startIndex,endIndex]
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stt%gamma_tw => plasticState(ph)%state(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pREAL)
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o = plasticState(ph)%offsetDeltaState
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startIndex = endIndex + 1 ! Achal
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endIndex = endIndex + prm%sum_N_tw ! Achal
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idx_dot%f_twin = [startIndex,endIndex] ! Achal
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stt%f_twin => plasticState(ph)%state(startIndex:endIndex,:) ! Achal
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dlt%f_twin => plasticState(ph)%deltaState(startIndex-o:endIndex-o,:) ! Achal
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pReal)
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startIndex = endIndex + 1
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endIndex = endIndex + 1
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stt%frozen => plasticState(ph)%state(startIndex,:)
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stt%frozen = 0.0_pReal-1.0_pReal
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dlt%frozen => plasticState(ph)%deltaState(startIndex-o,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pReal)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_tw
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stt%fmc_twin => plasticState(ph)%state(startIndex:endIndex,:)
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dlt%fmc_twin => plasticState(ph)%deltaState(startIndex-o:endIndex-o,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pReal)
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startIndex = endIndex + 1
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endIndex = endIndex + 1
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stt%variant_twin => plasticState(ph)%state(startIndex,:)
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stt%variant_twin = 0.0_pReal
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dlt%variant_twin => plasticState(ph)%deltaState(startIndex-o,:)
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plasticState(ph)%atol(startIndex:endIndex) = 0.0_pReal
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end associate
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!--------------------------------------------------------------------------------------------------
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! exit if any parameter is out of range
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if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg))
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end do
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end function plastic_phenopowerlaw_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate plastic velocity gradient and its tangent.
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!> @details assumes that deformation by dislocation glide affects twinned and untwinned volume
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! equally (Taylor assumption). Twinning happens only in untwinned volume
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!--------------------------------------------------------------------------------------------------
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pure module subroutine phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
|
|
|
|
real(pREAL), dimension(3,3), intent(out) :: &
|
|
Lp !< plastic velocity gradient
|
|
real(pREAL), dimension(3,3,3,3), intent(out) :: &
|
|
dLp_dMp !< derivative of Lp with respect to the Mandel stress
|
|
|
|
real(pREAL), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
|
|
integer :: &
|
|
i,k,l,m,n
|
|
real(pREAL), dimension(param(ph)%sum_N_sl) :: &
|
|
dot_gamma_sl,ddot_gamma_dtau_sl
|
|
real(pREAL), dimension(3,3,param(ph)%sum_N_sl) :: &
|
|
P_nS
|
|
real(pREAL), dimension(param(ph)%sum_N_tw) :: &
|
|
dot_gamma_tw,fdot_twin, ddot_gamma_dtau_tw
|
|
|
|
|
|
Lp = 0.0_pREAL
|
|
dLp_dMp = 0.0_pREAL
|
|
|
|
associate(prm => param(ph))
|
|
|
|
call kinetics_sl(Mp,ph,en,dot_gamma_sl,ddot_gamma_dtau_sl)
|
|
P_nS = merge(prm%P_nS_pos,prm%P_nS_neg, spread(spread(dot_gamma_sl,1,3),2,3)>0.0_pREAL) ! faster than 'merge' in loop
|
|
slipSystems: do i = 1, prm%sum_N_sl
|
|
Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
|
|
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
|
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
|
+ ddot_gamma_dtau_sl(i) * prm%P_sl(k,l,i) * P_nS(m,n,i)
|
|
end do slipSystems
|
|
|
|
Discrete_twin: if ( prm%discrete_twin ) then
|
|
call kinetics_tw(Mp,ph,en,dot_gamma_tw,fdot_twin, ddot_gamma_dtau_tw)
|
|
twinSystems: do i = 1, prm%sum_N_tw
|
|
Lp = Lp + dot_gamma_tw(i)*prm%P_tw(1:3,1:3,i)
|
|
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
|
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
|
+ ddot_gamma_dtau_tw(i)*prm%P_tw(k,l,i)*prm%P_tw(m,n,i)
|
|
end do twinSystems
|
|
endif Discrete_twin
|
|
|
|
end associate
|
|
|
|
end subroutine phenopowerlaw_LpAndItsTangent
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Calculate the rate of change of microstructure.
|
|
!--------------------------------------------------------------------------------------------------
|
|
module function phenopowerlaw_dotState(Mp,ph,en) result(dotState)
|
|
|
|
real(pREAL), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
real(pREAL), dimension(plasticState(ph)%sizeDotState) :: &
|
|
dotState
|
|
|
|
real(pREAL) :: &
|
|
sumF
|
|
real(pREAL), dimension(param(ph)%sum_N_sl) :: &
|
|
xi_sl_sat_offset, &
|
|
left_SlipSlip
|
|
|
|
|
|
associate(prm => param(ph), stt => state(ph), &
|
|
dot_xi_sl => dotState(indexDotState(ph)%xi_sl(1):indexDotState(ph)%xi_sl(2)), &
|
|
dot_xi_tw => dotState(indexDotState(ph)%xi_tw(1):indexDotState(ph)%xi_tw(2)), &
|
|
dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)), &
|
|
dot_gamma_tw => dotState(indexDotState(ph)%gamma_tw(1):indexDotState(ph)%gamma_tw(2)), &
|
|
fdot_twin => dotstate(indexDotState(ph)%f_twin(1):indexDotState(ph)%f_twin(2)))
|
|
|
|
call kinetics_sl(Mp,ph,en, dot_gamma_sl)
|
|
call kinetics_tw(Mp,ph,en, dot_gamma_tw, fdot_twin)
|
|
|
|
dot_gamma_sl = abs(dot_gamma_sl)
|
|
sumF = sum(stt%gamma_tw(:,en)/prm%gamma_char)
|
|
|
|
xi_sl_sat_offset = prm%f_sat_sl_tw*sqrt(sumF)
|
|
|
|
left_SlipSlip = sign(abs(1.0_pREAL - stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))**prm%a_sl, &
|
|
1.0_pREAL - stt%xi_sl(:,en) / (prm%xi_inf_sl+xi_sl_sat_offset))
|
|
|
|
dot_xi_sl = prm%h_0_sl_sl * (1.0_pREAL + prm%c_1 * sumF**prm%c_2) &
|
|
* left_SlipSlip &
|
|
* matmul(prm%h_sl_sl,dot_gamma_sl) &
|
|
+ matmul(prm%h_sl_tw,dot_gamma_tw)
|
|
|
|
dot_xi_tw = prm%h_0_tw_sl * sum(stt%gamma_sl(:,en))**prm%c_3 * matmul(prm%h_tw_sl,dot_gamma_sl) &
|
|
+ prm%h_0_tw_tw * sumF **prm%c_4 * matmul(prm%h_tw_tw,dot_gamma_tw)
|
|
|
|
end associate
|
|
|
|
end function phenopowerlaw_dotState
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates (instantaneous) incremental change of microstructure
|
|
!> Satya, Achal
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine plastic_phenopowerlaw_deltaState(ph,en)
|
|
implicit none
|
|
|
|
integer, intent(in)::&
|
|
ph, &
|
|
en
|
|
|
|
logical :: &
|
|
twinJump
|
|
|
|
integer :: &
|
|
twin_var
|
|
|
|
real(pREAL), dimension(3,3) :: &
|
|
deltaFp
|
|
|
|
! These are updated at every strain increment. What should these initilizations be?
|
|
|
|
associate(prm => param(ph), stt => state(ph), dlt => deltastate(ph))
|
|
|
|
twin_var = maxloc(stt%f_twin(:,en),dim=1)
|
|
|
|
call plastic_kinematic_deltaFp(ph,en,twinJump,deltaFp)
|
|
if(twinJump) then
|
|
dlt%f_twin(:,en) = 0.0_pReal - stt%f_twin(:,en)
|
|
dlt%fmc_twin(:,en) = 0.0_pReal - stt%fmc_twin(:,en)
|
|
dlt%frozen(en) = 1.0_pReal - stt%frozen(en)
|
|
dlt%variant_twin(en) = twin_var !- stt%variant_twin(en
|
|
|
|
endif
|
|
|
|
end associate
|
|
|
|
end subroutine plastic_phenopowerlaw_deltaState
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates instantaneous incremental change of kinematics and associated jump state
|
|
!> Satya, Achal
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine plastic_kinematic_deltaFp(ph,en,twinJump,deltaFp)
|
|
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
logical, intent(out) :: &
|
|
twinJump
|
|
real(pREAL), dimension(3,3), intent(out) :: &
|
|
deltaFp
|
|
|
|
integer :: &
|
|
n, & ! neighbor index
|
|
neighbor_e, & ! element index of my neighbor
|
|
neighbor_ip, & ! integration point index of my neighbor
|
|
neighbor_en, &
|
|
neighbor_ph
|
|
|
|
real(pREAL) :: &
|
|
random, &
|
|
nRealNeighbors
|
|
integer :: &
|
|
twin_var, var_growth
|
|
real(pREAL), dimension(param(ph)%sum_N_tw) :: &
|
|
fdot_twin
|
|
real(pREAL), dimension(param(ph)%sum_N_tw) :: &
|
|
tau_tw
|
|
integer :: i
|
|
twinJump = .false.
|
|
deltaFp = math_I3
|
|
|
|
|
|
|
|
associate(prm => param(ph), stt => state(ph), dlt => deltastate(ph))
|
|
|
|
twin_var = maxloc(stt%f_twin(:,en),dim=1)
|
|
|
|
Discrete_twin: if ( prm%discrete_twin ) then
|
|
|
|
Frozen: if(stt%frozen(en)<2.0_pREAL) then
|
|
|
|
call random_number(random)
|
|
|
|
|
|
|
|
do n = 1, ncellneighbors
|
|
neighbor_e = geom(ph)%IPneighborhood(1,n,en) !< Identify neighbor
|
|
|
|
if (any(dNeq(phase_O_0(ph)%data(en)%asQuaternion(),phase_O_0(ph)%data(neighbor_e)%asQuaternion()))) then !< Identify grain boundary elements
|
|
|
|
Ability_Nucleation: if(stt%f_twin(twin_var,en)>(stt%fmc_twin(twin_var,en)+prm%checkstep(twin_var))) then !< Frequency control
|
|
stt%fmc_twin(twin_var,en) = stt%fmc_twin(twin_var,en)+prm%checkstep(twin_var)
|
|
Success_Nucleation: if (random <= stt%f_twin(twin_var,en)) then
|
|
write(6,*)'frozen',stt%frozen(en)
|
|
twinJump = .true.
|
|
deltaFp = prm%CorrespondenceMatrix(:,:,twin_var)
|
|
exit
|
|
endif Success_Nucleation
|
|
endif Ability_Nucleation
|
|
|
|
endif
|
|
|
|
end do
|
|
|
|
NeighborLoop: do n = 1, ncellneighbors
|
|
neighbor_e = geom(ph)%IPneighborhood(1,n,en)
|
|
|
|
if(stt%variant_twin(neighbor_e)>0) then !< Check if neighbor is twinned
|
|
var_growth = stt%variant_twin(neighbor_e)
|
|
exit NeighborLoop
|
|
endif
|
|
|
|
enddo NeighborLoop
|
|
|
|
!Growth_Criteria: if(var_growth>100000.0_pReal) then !< If neighbor twinned,
|
|
! Ability_Growth: if(stt%f_twin(twin_var,en)>(stt%fmc_twin(twin_var,en)+prm%checkstep(twin_var))) then !< Frequency control
|
|
! stt%fmc_twin(twin_var,en) = stt%fmc_twin(twin_var,en)+prm%checkstep(twin_var)
|
|
! Success_Growth: if (random <= stt%f_twin(twin_var,en)) then !< Random sampling
|
|
! write(6,*)'frozen1',stt%frozen(en)
|
|
! twinJump = .true. !< Output flag
|
|
! deltaFp = prm%CorrespondenceMatrix(:,:,twin_var) !< Correspondence Matrix
|
|
! endif Success_Growth
|
|
! endif Ability_Growth
|
|
!endif Growth_Criteria
|
|
|
|
endif Frozen
|
|
|
|
end if Discrete_twin
|
|
end associate
|
|
|
|
end subroutine plastic_kinematic_deltaFp
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Write results to HDF5 output file.
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine plastic_phenopowerlaw_result(ph,group)
|
|
|
|
integer, intent(in) :: ph
|
|
character(len=*), intent(in) :: group
|
|
|
|
integer :: ou
|
|
|
|
|
|
associate(prm => param(ph), stt => state(ph))
|
|
|
|
do ou = 1,size(prm%output)
|
|
|
|
select case(trim(prm%output(ou)))
|
|
|
|
case('xi_sl')
|
|
call result_writeDataset(stt%xi_sl,group,trim(prm%output(ou)), &
|
|
'resistance against plastic slip','Pa',prm%systems_sl)
|
|
case('gamma_sl')
|
|
call result_writeDataset(stt%gamma_sl,group,trim(prm%output(ou)), &
|
|
'plastic shear','1',prm%systems_sl)
|
|
|
|
case('xi_tw')
|
|
call result_writeDataset(stt%xi_tw,group,trim(prm%output(ou)), &
|
|
'resistance against twinning','Pa',prm%systems_tw)
|
|
case('gamma_tw')
|
|
call result_writeDataset(stt%gamma_tw,group,trim(prm%output(ou)), &
|
|
'twinning shear','1',prm%systems_tw)
|
|
|
|
case('f_twin')
|
|
call result_writeDataset(stt%f_twin,group,trim(prm%output(ou)), &
|
|
'volume fraction','1',prm%systems_tw) !Achal
|
|
|
|
case('variant_twin')
|
|
call result_writeDataset(stt%variant_twin,group,trim(prm%output(ou)), &
|
|
'twin variant','1') !Achal
|
|
|
|
case('fbinary_twin')
|
|
call result_writeDataset(stt%frozen,group,trim(prm%output(ou)), &
|
|
'binary twin flag','1') !Achal
|
|
end select
|
|
|
|
end do
|
|
|
|
end associate
|
|
|
|
end subroutine plastic_phenopowerlaw_result
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Calculate shear rates on slip systems and their derivatives with respect to resolved
|
|
! stress.
|
|
!> @details Sign of dot_gamma_sl conveys sense of shear.
|
|
! Derivatives are calculated only optionally, hence, contrary to common convention,
|
|
! here the result (i.e. intent(out)) variables have to be put at the end.
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure subroutine kinetics_sl(Mp,ph,en, &
|
|
dot_gamma_sl,ddot_gamma_dtau_sl)
|
|
|
|
real(pREAL), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
|
|
real(pREAL), dimension(param(ph)%sum_N_sl), intent(out) :: &
|
|
dot_gamma_sl
|
|
real(pREAL), dimension(param(ph)%sum_N_sl), optional, intent(out) :: &
|
|
ddot_gamma_dtau_sl
|
|
|
|
real(pREAL), dimension(param(ph)%sum_N_sl) :: &
|
|
tau_sl_pos, &
|
|
tau_sl_neg
|
|
integer :: i
|
|
|
|
|
|
associate(prm => param(ph), stt => state(ph))
|
|
|
|
tau_sl_pos = [(math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i)),i=1,prm%sum_N_sl)]
|
|
tau_sl_neg = [(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)),i=1,prm%sum_N_sl)]
|
|
|
|
dot_gamma_sl = merge(+1.0_pREAL,-1.0_pREAL, tau_sl_pos>tau_sl_neg) &
|
|
* prm%dot_gamma_0_sl &
|
|
* (max(tau_sl_pos,tau_sl_neg)/stt%xi_sl(:,en))**prm%n_sl
|
|
|
|
if (present(ddot_gamma_dtau_sl)) then
|
|
where(dNeq0(dot_gamma_sl))
|
|
ddot_gamma_dtau_sl = dot_gamma_sl*prm%n_sl/max(tau_sl_pos,tau_sl_neg)
|
|
else where
|
|
ddot_gamma_dtau_sl = 0.0_pREAL
|
|
end where
|
|
end if
|
|
|
|
end associate
|
|
|
|
end subroutine kinetics_sl
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved stress.
|
|
! Twinning is assumed to take place only in an untwinned volume.
|
|
!> @details Derivatives are calculated and returned if corresponding output variables are present in the argument list.
|
|
! NOTE: Contrary to common convention, here the result (i.e. intent(out)) variables have to be put
|
|
! at the end since some of them are optional.
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure subroutine kinetics_tw(Mp,ph,en,&
|
|
dot_gamma_tw, fdot_twin, ddot_gamma_dtau_tw)
|
|
|
|
real(pREAL), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
|
|
real(pREAL), dimension(param(ph)%sum_N_tw), intent(out) :: &
|
|
dot_gamma_tw, fdot_twin
|
|
real(pREAL), dimension(param(ph)%sum_N_tw), intent(out), optional :: &
|
|
ddot_gamma_dtau_tw
|
|
|
|
real(pREAL), dimension(param(ph)%sum_N_tw) :: &
|
|
tau_tw
|
|
integer :: i
|
|
|
|
|
|
associate(prm => param(ph), stt => state(ph), dlt => state(ph))
|
|
|
|
tau_tw = [(math_tensordot(Mp,prm%P_tw(1:3,1:3,i)),i=1,prm%sum_N_tw)]
|
|
|
|
Discrete_twin: if ( prm%discrete_twin ) then
|
|
|
|
where(tau_tw > 0.0_pREAL .and. stt%frozen(en) < 0.9_pReal) ! Achal .and. stt%frozen(en) < 0.9_pReal
|
|
dot_gamma_tw = 0.0_pREAL ! only twin in untwinned volume fraction
|
|
fdot_twin = (0.005_pReal*(abs(tau_tw)/stt%xi_tw(:,en))**prm%n_tw)/prm%gamma_char ! Achal 0.005 is reference slip rate
|
|
else where
|
|
dot_gamma_tw = 0.0_pREAL
|
|
fdot_twin = 0.0_pREAL
|
|
end where
|
|
|
|
else
|
|
where(tau_tw > 0.0_pREAL) ! Achal Unchanged model
|
|
dot_gamma_tw = (1.0_pREAL-sum(stt%gamma_tw(:,en)/prm%gamma_char)) & ! only twin in untwinned volume fraction
|
|
* prm%dot_gamma_0_tw*(tau_tw/stt%xi_tw(:,en))**prm%n_tw
|
|
fdot_twin = 0.0_pREAL ! Achal Unchanged model
|
|
else where
|
|
dot_gamma_tw = 0.0_pREAL
|
|
fdot_twin = 0.0_pREAL
|
|
end where
|
|
|
|
end if Discrete_twin
|
|
|
|
|
|
if (present(ddot_gamma_dtau_tw)) then
|
|
where(dNeq0(dot_gamma_tw))
|
|
ddot_gamma_dtau_tw = dot_gamma_tw*prm%n_tw/tau_tw
|
|
else where
|
|
ddot_gamma_dtau_tw = 0.0_pREAL
|
|
end where
|
|
end if
|
|
|
|
end associate
|
|
|
|
end subroutine kinetics_tw
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine storeGeometry(ph)
|
|
|
|
integer, intent(in) :: ph
|
|
|
|
integer :: ce, nCell
|
|
real(pREAL), dimension(:), allocatable :: v_0
|
|
real(pREAL), dimension(:,:), allocatable :: a_0, x_0
|
|
real(pREAL), dimension(:,:,:), allocatable :: n_0
|
|
integer, dimension(:,:,:), allocatable :: neighborhood
|
|
|
|
|
|
nCell = product(shape(IPVolume0))
|
|
|
|
v_0 = reshape(IPVolume0,[nCell])
|
|
a_0 = reshape(IPArea0,[nCellNeighbors,nCell])
|
|
x_0 = reshape(discretization_IPcoords,[3,nCell])
|
|
n_0 = reshape(IPAreaNormal0,[3,nCellNeighbors,nCell])
|
|
neighborhood = reshape(IPneighborhood,[3,nCellNeighbors,nCell])
|
|
|
|
do ce = 1, size(material_entry_homogenization,1)
|
|
if (material_ID_phase(1,ce) == ph) then
|
|
geom(ph)%v_0(material_entry_phase(1,ce)) = v_0(ce)
|
|
geom(ph)%a_0(:,material_entry_phase(1,ce)) = a_0(:,ce)
|
|
geom(ph)%x_0(:,material_entry_phase(1,ce)) = x_0(:,ce)
|
|
geom(ph)%n_0(:,:,material_entry_phase(1,ce)) = n_0(:,:,ce)
|
|
geom(ph)%IPneighborhood(:,:,material_entry_phase(1,ce)) = neighborhood(:,:,ce)
|
|
end if
|
|
end do
|
|
|
|
end subroutine storeGeometry
|
|
|
|
end submodule phenopowerlaw
|