contains lattice structure definitions including Schmid matrices for slip, twin, trans, More...

Data Types
interface	lattice_forestprojection_edge

interface	lattice_forestprojection_screw

Enumerations
enum	{ lattice_undefined_id }

Functions/Subroutines
subroutine, public	lattice_init
	Module initialization. More...

real(preal) function, dimension(sum(ntwin)), public	lattice_characteristicshear_twin (Ntwin, structure, CoverA)
	Characteristic shear for twinning. More...

real(preal) function, dimension(6, 6, sum(ntwin)), public	lattice_c66_twin (Ntwin, C66, structure, CoverA)
	Rotated elasticity matrices for twinning in 66-vector notation. More...

real(preal) function, dimension(6, 6, sum(ntrans)), public	lattice_c66_trans (Ntrans, C_parent66, structure_target, cOverA_trans, a_bcc, a_fcc)
	Rotated elasticity matrices for transformation in 66-vector notation. More...

real(preal) function, dimension(1:3, 1:3, sum(nslip)), public	lattice_nonschmidmatrix (Nslip, nonSchmidCoefficients, sense)
	Non-schmid projections for bcc with up to 6 coefficients. More...

real(preal) function, dimension(sum(nslip), sum(nslip)), public	lattice_interaction_slipbyslip (Nslip, interactionValues, structure)
	Slip-slip interaction matrix details only active slip systems are considered. More...

real(preal) function, dimension(sum(ntwin), sum(ntwin)), public	lattice_interaction_twinbytwin (Ntwin, interactionValues, structure)
	Twin-twin interaction matrix details only active twin systems are considered. More...

real(preal) function, dimension(sum(ntrans), sum(ntrans)), public	lattice_interaction_transbytrans (Ntrans, interactionValues, structure)
	Trans-trans interaction matrix details only active trans systems are considered. More...

real(preal) function, dimension(sum(nslip), sum(ntwin)), public	lattice_interaction_slipbytwin (Nslip, Ntwin, interactionValues, structure)
	Slip-twin interaction matrix details only active slip and twin systems are considered. More...

real(preal) function, dimension(sum(nslip), sum(ntrans)), public	lattice_interaction_slipbytrans (Nslip, Ntrans, interactionValues, structure)
	Slip-trans interaction matrix details only active slip and trans systems are considered. More...

real(preal) function, dimension(sum(ntwin), sum(nslip)), public	lattice_interaction_twinbyslip (Ntwin, Nslip, interactionValues, structure)
	Twin-slip interaction matrix details only active twin and slip systems are considered. More...

real(preal) function, dimension(3, 3, sum(nslip)), public	lattice_schmidmatrix_slip (Nslip, structure, cOverA)
	Schmid matrix for slip details only active slip systems are considered. More...

real(preal) function, dimension(3, 3, sum(ntwin)), public	lattice_schmidmatrix_twin (Ntwin, structure, cOverA)
	Schmid matrix for twinning details only active twin systems are considered. More...

real(preal) function, dimension(3, 3, sum(ntrans)), public	lattice_schmidmatrix_trans (Ntrans, structure_target, cOverA, a_bcc, a_fcc)
	Schmid matrix for twinning details only active twin systems are considered. More...

real(preal) function, dimension(3, 3, 3, sum(ncleavage)), public	lattice_schmidmatrix_cleavage (Ncleavage, structure, cOverA)
	Schmid matrix for cleavage details only active cleavage systems are considered. More...

real(preal) function, dimension(3, sum(nslip)), public	lattice_slip_direction (Nslip, structure, cOverA)
	Slip direction of slip systems (\|\| b) More...

real(preal) function, dimension(3, sum(nslip)), public	lattice_slip_normal (Nslip, structure, cOverA)
	Normal direction of slip systems (\|\| n) More...

real(preal) function, dimension(3, sum(nslip)), public	lattice_slip_transverse (Nslip, structure, cOverA)
	Transverse direction of slip systems ( \|\| t = b x n) More...

character(len=:) function, dimension(:), allocatable, public	lattice_labels_slip (Nslip, structure)
	Labels for slip systems details only active slip systems are considered. More...

real(preal) function, dimension(3, 3), public	lattice_applylatticesymmetry33 (T, structure)
	Return 3x3 tensor with symmetry according to given crystal structure. More...

real(preal) function, dimension(6, 6)	applylatticesymmetryc66 (C66, structure)
	Return stiffness matrix in 6x6 notation with symmetry according to given crystal structure. More...

character(len=:) function, dimension(:), allocatable, public	lattice_labels_twin (Ntwin, structure)
	Labels for twin systems details only active twin systems are considered. More...

real(preal) function, dimension(sum(nslip), sum(nslip))	slipprojection_transverse (Nslip, structure, cOverA)
	Projection of the transverse direction onto the slip plane. More...

real(preal) function, dimension(sum(nslip), sum(nslip))	slipprojection_direction (Nslip, structure, cOverA)
	Projection of the slip direction onto the slip plane. More...

real(preal) function, dimension(3, 3, sum(nslip))	coordinatesystem_slip (Nslip, structure, cOverA)
	build a local coordinate system on slip systems More...

real(preal) function, dimension(sum(reacting_used), sum(acting_used))	buildinteraction (reacting_used, acting_used, reacting_max, acting_max, values, matrix)
	Populate reduced interaction matrix. More...

real(preal) function, dimension(3, 3, sum(active))	buildcoordinatesystem (active, potential, system, structure, cOverA)
	Build a local coordinate system on slip, twin, trans, cleavage systems. More...

subroutine	buildtransformationsystem (Q, S, Ntrans, cOverA, a_fcc, a_bcc)
	Helper function to define transformation systems. More...

character(len=:) function, dimension(:), allocatable	getlabels (active, potential, system)
	select active systems as strings More...

real(preal) function	equivalent_nu (C, assumption)
	Equivalent Poisson's ratio (ν) More...

real(preal) function	equivalent_mu (C, assumption)
	Equivalent shear modulus (μ) More...

subroutine	unittest
	check correctness of some lattice functions More...

Variables
integer, dimension(2), parameter	fcc_nslipsystem = [12, 6]

integer, dimension(1), parameter	fcc_ntwinsystem = [12]

integer, dimension(1), parameter	fcc_ntranssystem = [12]

integer, dimension(1), parameter	fcc_ncleavagesystem = [3]

integer, parameter	fcc_nslip = sum(FCC_NSLIPSYSTEM)
	total # of slip systems for fcc More...

integer, parameter	fcc_ntwin = sum(FCC_NTWINSYSTEM)
	total # of twin systems for fcc More...

integer, parameter	fcc_ntrans = sum(FCC_NTRANSSYSTEM)
	total # of transformation systems for fcc More...

integer, parameter	fcc_ncleavage = sum(FCC_NCLEAVAGESYSTEM)
	total # of cleavage systems for fcc More...

real(preal), dimension(3+3, fcc_nslip), parameter	fcc_systemslip = reshape(real([ 0, 1,-1, 1, 1, 1, -1, 0, 1, 1, 1, 1, 1,-1, 0, 1, 1, 1, 0,-1,-1, -1,-1, 1, 1, 0, 1, -1,-1, 1, -1, 1, 0, -1,-1, 1, 0,-1, 1, 1,-1,-1, -1, 0,-1, 1,-1,-1, 1, 1, 0, 1,-1,-1, 0, 1, 1, -1, 1,-1, 1, 0,-1, -1, 1,-1, -1,-1, 0, -1, 1,-1, 1, 1, 0, 1,-1, 0, 1,-1, 0, 1, 1, 0, 1, 0, 1, 1, 0,-1, 1, 0,-1, 1, 0, 1, 0, 1, 1, 0, 1,-1, 0, 1,-1, 0, 1, 1 ], pReal), shape(FCC_SYSTEMSLIP))
	Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli. More...

real(preal), dimension(3+3, fcc_ntwin), parameter	fcc_systemtwin = reshape(real( [ -2, 1, 1, 1, 1, 1, 1,-2, 1, 1, 1, 1, 1, 1,-2, 1, 1, 1, 2,-1, 1, -1,-1, 1, -1, 2, 1, -1,-1, 1, -1,-1,-2, -1,-1, 1, -2,-1,-1, 1,-1,-1, 1, 2,-1, 1,-1,-1, 1,-1, 2, 1,-1,-1, 2, 1,-1, -1, 1,-1, -1,-2,-1, -1, 1,-1, -1, 1, 2, -1, 1,-1 ], pReal), shape(FCC_SYSTEMTWIN))
	Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli. More...

integer, dimension(2, fcc_ntwin), parameter, public	lattice_fcc_twinnucleationslippair = reshape( [ 2,3, 1,3, 1,2, 5,6, 4,6, 4,5, 8,9, 7,9, 7,8, 11,12, 10,12, 10,11 ], shape(lattice_FCC_TWINNUCLEATIONSLIPPAIR))

real(preal), dimension(3+3, fcc_ncleavage), parameter	fcc_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(FCC_SYSTEMCLEAVAGE))

integer, dimension(2), parameter	bcc_nslipsystem = [12, 12]

integer, dimension(1), parameter	bcc_ntwinsystem = [12]

integer, dimension(1), parameter	bcc_ncleavagesystem = [3]

integer, parameter	bcc_nslip = sum(BCC_NSLIPSYSTEM)
	total # of slip systems for bcc More...

integer, parameter	bcc_ntwin = sum(BCC_NTWINSYSTEM)
	total # of twin systems for bcc More...

integer, parameter	bcc_ncleavage = sum(BCC_NCLEAVAGESYSTEM)
	total # of cleavage systems for bcc More...

real(preal), dimension(3+3, bcc_nslip), parameter	bcc_systemslip = reshape(real([ 1,-1, 1, 0, 1, 1, -1,-1, 1, 0, 1, 1, 1, 1, 1, 0,-1, 1, -1, 1, 1, 0,-1, 1, -1, 1, 1, 1, 0, 1, -1,-1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 1, 1,-1, 1, -1, 0, 1, -1, 1, 1, 1, 1, 0, -1, 1,-1, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 1,-1, -1, 1, 0, -1, 1, 1, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1,-1, 2,-1, 1, 1,-1, 1, 2, 1,-1, 1,-1, 1, 1, 2, 1, 1, 1,-1, -1, 2, 1, 1, 1, 1, 1,-2, 1, -1, 1, 1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1,-1, 1, -1, 1, 2, -1, 1, 1, 1,-1, 2, 1, 1, 1, 1, 1,-2 ], pReal), shape(BCC_SYSTEMSLIP))

real(preal), dimension(3+3, bcc_ntwin), parameter	bcc_systemtwin = reshape(real([ -1, 1, 1, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1,-1, 2,-1, 1, 1,-1, 1, 2, 1,-1, 1,-1, 1, 1, 2, 1, 1, 1,-1, -1, 2, 1, 1, 1, 1, 1,-2, 1, -1, 1, 1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1,-1, 1, -1, 1, 2, -1, 1, 1, 1,-1, 2, 1, 1, 1, 1, 1,-2 ], pReal), shape(BCC_SYSTEMTWIN))

real(preal), dimension(3+3, bcc_ncleavage), parameter	bcc_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(BCC_SYSTEMCLEAVAGE))

integer, dimension(6), parameter	hex_nslipsystem = [3, 3, 3, 6, 12, 6]

integer, dimension(4), parameter	hex_ntwinsystem = [6, 6, 6, 6]

integer, parameter	hex_nslip = sum(HEX_NSLIPSYSTEM)
	total # of slip systems for hex More...

integer, parameter	hex_ntwin = sum(HEX_NTWINSYSTEM)
	total # of twin systems for hex More...

real(preal), dimension(4+4, hex_nslip), parameter	hex_systemslip = reshape(real([ 2, -1, -1, 0, 0, 0, 0, 1, -1, 2, -1, 0, 0, 0, 0, 1, -1, -1, 2, 0, 0, 0, 0, 1, 2, -1, -1, 0, 0, 1, -1, 0, -1, 2, -1, 0, -1, 0, 1, 0, -1, -1, 2, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, 1, -2, 0, 0, -1, 1, 0, -2, 1, 1, 0, 1, 0, -1, 0, 1, -2, 1, 0, -1, 2, -1, 0, 1, 0, -1, 1, -2, 1, 1, 0, 0, 1, -1, 1, -1, -1, 2, 0, -1, 1, 0, 1, 1, -2, 1, 0, -1, 0, 1, 1, 2, -1, -1, 0, 0, -1, 1, 1, 1, 1, -2, 0, 1, -1, 0, 1, -2, 1, 1, 3, 1, 0, -1, 1, -1, -1, 2, 3, 1, 0, -1, 1, -1, -1, 2, 3, 0, 1, -1, 1, 1, -2, 1, 3, 0, 1, -1, 1, 1, -2, 1, 3, -1, 1, 0, 1, 2, -1, -1, 3, -1, 1, 0, 1, 2, -1, -1, 3, -1, 0, 1, 1, 1, 1, -2, 3, -1, 0, 1, 1, 1, 1, -2, 3, 0, -1, 1, 1, -1, 2, -1, 3, 0, -1, 1, 1, -1, 2, -1, 3, 1, -1, 0, 1, -2, 1, 1, 3, 1, -1, 0, 1, -1, -1, 2, 3, 1, 1, -2, 2, 1, -2, 1, 3, -1, 2, -1, 2, 2, -1, -1, 3, -2, 1, 1, 2, 1, 1, -2, 3, -1, -1, 2, 2, -1, 2, -1, 3, 1, -2, 1, 2, -2, 1, 1, 3, 2, -1, -1, 2 ], pReal), shape(HEX_SYSTEMSLIP))
	slip systems for hex, sorted by P. Eisenlohr CCW around `starting next to a_1 axis` More...

real(preal), dimension(4+4, hex_ntwin), parameter	hex_systemtwin = reshape(real([ -1, 0, 1, 1, 1, 0, -1, 2, 0, -1, 1, 1, 0, 1, -1, 2, 1, -1, 0, 1, -1, 1, 0, 2, 1, 0, -1, 1, -1, 0, 1, 2, 0, 1, -1, 1, 0, -1, 1, 2, -1, 1, 0, 1, 1, -1, 0, 2, -1, -1, 2, 6, 1, 1, -2, 1, 1, -2, 1, 6, -1, 2, -1, 1, 2, -1, -1, 6, -2, 1, 1, 1, 1, 1, -2, 6, -1, -1, 2, 1, -1, 2, -1, 6, 1, -2, 1, 1, -2, 1, 1, 6, 2, -1, -1, 1, 1, 0, -1, -2, 1, 0, -1, 1, 0, 1, -1, -2, 0, 1, -1, 1, -1, 1, 0, -2, -1, 1, 0, 1, -1, 0, 1, -2, -1, 0, 1, 1, 0, -1, 1, -2, 0, -1, 1, 1, 1, -1, 0, -2, 1, -1, 0, 1, 1, 1, -2, -3, 1, 1, -2, 2, -1, 2, -1, -3, -1, 2, -1, 2, -2, 1, 1, -3, -2, 1, 1, 2, -1, -1, 2, -3, -1, -1, 2, 2, 1, -2, 1, -3, 1, -2, 1, 2, 2, -1, -1, -3, 2, -1, -1, 2 ], pReal), shape(HEX_SYSTEMTWIN))
	twin systems for hex, sorted by P. Eisenlohr CCW around `starting next to a_1 axis` More...

integer, dimension(13), parameter	bct_nslipsystem = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ]

integer, parameter	bct_nslip = sum(BCT_NSLIPSYSTEM)
	total # of slip systems for bct More...

real(preal), dimension(3+3, bct_nslip), parameter	bct_systemslip = reshape(real([ 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1,-1, 1, 1, 1, 0, 1,-1,-1, 1, 1, 0, -1,-1,-1, -1, 1, 0, -1,-1, 1, -1, 1, 0, 1, -1, 0, 1, 1, 0, 1, 1, 0, 1,-1, 0, 0, 1, 1, 1, 0, 0, 0,-1, 1, 1, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 1, 1, 0,-1,-1, 0,-1, 1, -1, 0,-1, -1, 0, 1, 1, 0,-1, 1, 0, 1, 1,-1, 1, 0, 1, 1, 1, 1,-1, 0, 1, 1, 1, 1, 1, 0, 1,-1, -1, 1, 1, 0, 1,-1, 1,-1,-1, 1, 0, 1, -1,-1, 1, 1, 0, 1, 1, 1, 1, 1, 0,-1, 1,-1, 1, 1, 0,-1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1,-1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,-1, 0, 1,-1, 2, 1, 1, 0,-1,-1, 2,-1, 1, 1, 0,-1, 1, 2, 1, -1, 0,-1, -1, 2, 1, 0, 1,-1, -2, 1, 1, 0,-1,-1, -2,-1, 1, -1, 0,-1, -1,-2, 1, 1, 0,-1, 1,-2, 1, -1, 1, 1, 2, 1, 1, -1,-1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1, -1,-1, 1, -1, 2, 1, 1, 1, 1, -2, 1, 1, 1,-1, 1, -2,-1, 1, -1, 1, 1, -1,-2, 1, 1, 1, 1, 1,-2, 1 ], pReal), shape(BCT_SYSTEMSLIP))
	slip systems for bct sorted by Bieler More...

integer, dimension(3), parameter	ort_ncleavagesystem = [1, 1, 1]

integer, parameter	ort_ncleavage = sum(ORT_NCLEAVAGESYSTEM)
	total # of cleavage systems for ortho More...

real(preal), dimension(3+3, ort_ncleavage), parameter	ort_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(ORT_SYSTEMCLEAVAGE))

@, public	lattice_iso_id

@, public	lattice_fcc_id

@, public	lattice_bcc_id

@, public	lattice_bct_id

@, public	lattice_hex_id

@, public	lattice_ort_id

real(preal), dimension(:), allocatable, public, protected	lattice_mu

real(preal), dimension(:), allocatable, public, protected	lattice_nu

real(preal), dimension(:), allocatable, public, protected	lattice_damagemobility

real(preal), dimension(:), allocatable, public, protected	lattice_massdensity

real(preal), dimension(:), allocatable, public, protected	lattice_specificheat

real(preal), dimension(:,:,:), allocatable, public, protected	lattice_c66

real(preal), dimension(:,:,:), allocatable, public, protected	lattice_thermalconductivity

real(preal), dimension(:,:,:), allocatable, public, protected	lattice_damagediffusion

integer(kind(lattice_undefined_id)), dimension(:), allocatable, public, protected	lattice_structure

Detailed Description

contains lattice structure definitions including Schmid matrices for slip, twin, trans,

Author: Franz Roters, Max-Planck-Institut für Eisenforschung GmbH; Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH; Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH; Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH

Enumeration Type Documentation

◆ anonymous enum

anonymous enum

private

Enumerator
lattice_undefined_id

Definition at line 388 of file lattice.f90.

Function/Subroutine Documentation

◆ applylatticesymmetryc66()

real(preal) function, dimension(6,6) lattice::applylatticesymmetryc66	(	real(preal), dimension(6,6), intent(in)	C66,
		character(len=*), intent(in)	structure
	)

private

Return stiffness matrix in 6x6 notation with symmetry according to given crystal structure.

J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962

Definition at line 1730 of file lattice.f90.

References io::io_error().

Referenced by lattice_c66_trans(), lattice_init(), and unittest().

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◆ buildcoordinatesystem()

real(preal) function, dimension(3,3,sum(active)) lattice::buildcoordinatesystem	(	integer, dimension(:), intent(in)	active,
		integer, dimension(:), intent(in)	potential,
		real(preal), dimension(:,:), intent(in)	system,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

private

Build a local coordinate system on slip, twin, trans, cleavage systems.

Order: Direction, plane (normal), and common perpendicular

Parameters

[in]	potential	# of potential systems per family
[in]	structure	lattice structure

Parameters

active # of active systems per family

Definition at line 1987 of file lattice.f90.

References io::io_error(), and math::math_cross().

Referenced by coordinatesystem_slip(), lattice_c66_twin(), lattice_nonschmidmatrix(), lattice_schmidmatrix_cleavage(), lattice_schmidmatrix_slip(), lattice_schmidmatrix_twin(), and unittest().

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◆ buildinteraction()

real(preal) function, dimension(sum(reacting_used),sum(acting_used)) lattice::buildinteraction	(	integer, dimension(:), intent(in)	reacting_used,
		integer, dimension(:), intent(in)	acting_used,
		integer, dimension(:), intent(in)	reacting_max,
		integer, dimension(:), intent(in)	acting_max,
		real(preal), dimension(:), intent(in)	values,
		integer, dimension(:,:), intent(in)	matrix
	)

private

Populate reduced interaction matrix.

Parameters

[in]	acting_max	max # of acting systems per family for given lattice
[in]	values	interaction values
[in]	matrix	interaction types

Parameters

reacting_used	# of reacting systems per family as specified in material.config
acting_used	# of acting systems per family as specified in material.config
reacting_max	max # of reacting systems per family for given lattice

Definition at line 1943 of file lattice.f90.

References io::io_error().

Referenced by lattice_interaction_slipbyslip(), lattice_interaction_slipbytrans(), lattice_interaction_slipbytwin(), lattice_interaction_transbytrans(), lattice_interaction_twinbyslip(), and lattice_interaction_twinbytwin().

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◆ buildtransformationsystem()

subroutine lattice::buildtransformationsystem	(	real(preal), dimension(3,3,sum(ntrans)), intent(out)	Q,
		real(preal), dimension(3,3,sum(ntrans)), intent(out)	S,
		integer, dimension(:), intent(in)	Ntrans,
		real(preal), intent(in)	cOverA,
		real(preal), intent(in)	a_fcc,
		real(preal), intent(in)	a_bcc
	)

private

Helper function to define transformation systems.

Parameters

[out]	s	Eigendeformation tensor for phase transformation
[in]	a_fcc	lattice parameter a for parent fcc structure

Parameters

Q	Total rotation: Q = R*B
cOverA	c/a for target hex structure
a_bcc	lattice parameter a for target bcc structure

Definition at line 2058 of file lattice.f90.

References prec::deq0(), io::io_error(), math::math_cross(), math::math_i3, and math::math_outer().

Referenced by lattice_c66_trans(), and lattice_schmidmatrix_trans().

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◆ coordinatesystem_slip()

real(preal) function, dimension(3,3,sum(nslip)) lattice::coordinatesystem_slip	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

private

build a local coordinate system on slip systems

Order: Direction, plane (normal), and common perpendicular

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1900 of file lattice.f90.

References bcc_nslipsystem, bcc_systemslip, bct_nslipsystem, bct_systemslip, buildcoordinatesystem(), fcc_nslipsystem, fcc_systemslip, hex_nslipsystem, hex_systemslip, and io::io_error().

Referenced by lattice_slip_direction(), lattice_slip_normal(), and lattice_slip_transverse().

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◆ equivalent_mu()

real(preal) function lattice::equivalent_mu	(	real(preal), dimension(6,6), intent(in)	C,
		character(len=*), intent(in)	assumption
	)

private

Equivalent shear modulus (μ)

https://doi.org/10.1143/JPSJ.20.635

Parameters

[in]	c	Stiffness tensor (Voigt notation)
[in]	assumption	Assumption ('Voigt' = isostrain, 'Reuss' = isostress)

Definition at line 2271 of file lattice.f90.

References io::io_error(), io::io_lc(), and math::math_invert().

Referenced by equivalent_nu(), lattice_init(), and unittest().

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◆ equivalent_nu()

real(preal) function lattice::equivalent_nu	(	real(preal), dimension(6,6), intent(in)	C,
		character(len=*), intent(in)	assumption
	)

private

Equivalent Poisson's ratio (ν)

https://doi.org/10.1143/JPSJ.20.635

Parameters

[in]	c	Stiffness tensor (Voigt notation)
[in]	assumption	Assumption ('Voigt' = isostrain, 'Reuss' = isostress)

Definition at line 2239 of file lattice.f90.

References equivalent_mu(), io::io_error(), io::io_lc(), and math::math_invert().

Referenced by lattice_init(), and unittest().

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◆ getlabels()

character(len=:) function, dimension(:), allocatable lattice::getlabels	(	integer, dimension(:), intent(in)	active,
		integer, dimension(:), intent(in)	potential,
		real(preal), dimension(:,:), intent(in)	system
	)

private

select active systems as strings

Parameters

[in] potential # of potential systems per family

Parameters

active # of active systems per family

Definition at line 2182 of file lattice.f90.

Referenced by lattice_labels_slip(), and lattice_labels_twin().

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◆ lattice_applylatticesymmetry33()

real(preal) function, dimension(3,3), public lattice::lattice_applylatticesymmetry33	(	real(preal), dimension(3,3), intent(in)	T,
		character(len=*), intent(in)	structure
	)

Return 3x3 tensor with symmetry according to given crystal structure.

Definition at line 1692 of file lattice.f90.

References io::io_error().

Referenced by kinematics_thermal_expansion::kinematics_thermal_expansion_init(), and lattice_init().

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◆ lattice_c66_trans()

real(preal) function, dimension(6,6,sum(ntrans)), public lattice::lattice_c66_trans	(	integer, dimension(:), intent(in)	Ntrans,
		real(preal), dimension(6,6), intent(in)	C_parent66,
		character(len=*), intent(in)	structure_target,
		real(preal)	cOverA_trans,
		real(preal)	a_bcc,
		real(preal)	a_fcc
	)

Rotated elasticity matrices for transformation in 66-vector notation.

Parameters

[in]	ntrans	number of active twin systems per family
[in]	structure_target	lattice structure

Definition at line 665 of file lattice.f90.

References applylatticesymmetryc66(), buildtransformationsystem(), io::io_error(), and prec::tol_math_check.

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◆ lattice_c66_twin()

real(preal) function, dimension(6,6,sum(ntwin)), public lattice::lattice_c66_twin	(	integer, dimension(:), intent(in)	Ntwin,
		real(preal), dimension(6,6), intent(in)	C66,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	CoverA
	)

Rotated elasticity matrices for twinning in 66-vector notation.

Parameters

[in]	ntwin	number of active twin systems per family
[in]	structure	lattice structure
[in]	c66	unrotated parent stiffness matrix
[in]	covera	c/a ratio

Definition at line 624 of file lattice.f90.

References bcc_nslipsystem, bcc_systemtwin, buildcoordinatesystem(), fcc_nslipsystem, fcc_systemtwin, hex_nslipsystem, hex_systemtwin, io::io_error(), and math::pi.

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◆ lattice_characteristicshear_twin()

real(preal) function, dimension(sum(ntwin)), public lattice::lattice_characteristicshear_twin	(	integer, dimension(:), intent(in)	Ntwin,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	CoverA
	)

Characteristic shear for twinning.

Parameters

[in]	ntwin	number of active twin systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 547 of file lattice.f90.

References hex_ntwin, hex_ntwinsystem, and io::io_error().

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◆ lattice_init()

subroutine, public lattice::lattice_init

Module initialization.

Definition at line 457 of file lattice.f90.

References applylatticesymmetryc66(), config::config_phase, equivalent_mu(), equivalent_nu(), io::io_error(), lattice_applylatticesymmetry33(), lattice_bcc_id, lattice_bct_id, lattice_c66, lattice_damagediffusion, lattice_damagemobility, lattice_fcc_id, lattice_hex_id, lattice_iso_id, lattice_massdensity, lattice_mu, lattice_nu, lattice_ort_id, lattice_specificheat, lattice_structure, lattice_thermalconductivity, lattice_undefined_id, math::math_sym3333to66(), math::math_voigt66to3333(), prec::tol_math_check, and io::unittest().

Referenced by cpfem2::cpfem_initall().

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◆ lattice_interaction_slipbyslip()

real(preal) function, dimension(sum(nslip),sum(nslip)), public lattice::lattice_interaction_slipbyslip	(	integer, dimension(:), intent(in)	Nslip,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Slip-slip interaction matrix details only active slip systems are considered.

Parameters

[in]	nslip	number of active slip systems per family
[in]	interactionvalues	values for slip-slip interaction
[in]	structure	lattice structure

Definition at line 775 of file lattice.f90.

References bcc_nslipsystem, bct_nslipsystem, buildinteraction(), fcc_nslipsystem, hex_nslipsystem, and io::io_error().

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◆ lattice_interaction_slipbytrans()

real(preal) function, dimension(sum(nslip),sum(ntrans)), public lattice::lattice_interaction_slipbytrans	(	integer, dimension(:), intent(in)	Nslip,
		integer, dimension(:), intent(in)	Ntrans,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Slip-trans interaction matrix details only active slip and trans systems are considered.

Parameters

[in]	ntrans	number of active trans systems per family
[in]	interactionvalues	values for slip-trans interaction
[in]	structure	lattice structure (parent crystal)

Parameters

Nslip number of active slip systems per family

Definition at line 1281 of file lattice.f90.

References buildinteraction(), fcc_nslipsystem, fcc_ntranssystem, and io::io_error().

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◆ lattice_interaction_slipbytwin()

real(preal) function, dimension(sum(nslip),sum(ntwin)), public lattice::lattice_interaction_slipbytwin	(	integer, dimension(:), intent(in)	Nslip,
		integer, dimension(:), intent(in)	Ntwin,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Slip-twin interaction matrix details only active slip and twin systems are considered.

Parameters

[in]	ntwin	number of active twin systems per family
[in]	interactionvalues	values for slip-twin interaction
[in]	structure	lattice structure

Parameters

Nslip number of active slip systems per family

Definition at line 1141 of file lattice.f90.

References bcc_nslipsystem, bcc_ntwinsystem, buildinteraction(), fcc_nslipsystem, fcc_ntwinsystem, hex_nslipsystem, hex_ntwinsystem, and io::io_error().

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◆ lattice_interaction_transbytrans()

real(preal) function, dimension(sum(ntrans),sum(ntrans)), public lattice::lattice_interaction_transbytrans	(	integer, dimension(:), intent(in)	Ntrans,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Trans-trans interaction matrix details only active trans systems are considered.

Parameters

[in]	ntrans	number of active trans systems per family
[in]	interactionvalues	values for trans-trans interaction
[in]	structure	lattice structure (parent crystal)

Definition at line 1096 of file lattice.f90.

References buildinteraction(), fcc_ntranssystem, and io::io_error().

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◆ lattice_interaction_twinbyslip()

real(preal) function, dimension(sum(ntwin),sum(nslip)), public lattice::lattice_interaction_twinbyslip	(	integer, dimension(:), intent(in)	Ntwin,
		integer, dimension(:), intent(in)	Nslip,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Twin-slip interaction matrix details only active twin and slip systems are considered.

Parameters

[in]	nslip	number of active slip systems per family
[in]	interactionvalues	values for twin-twin interaction
[in]	structure	lattice structure

Parameters

Ntwin number of active twin systems per family

Definition at line 1337 of file lattice.f90.

References bcc_nslipsystem, bcc_ntwinsystem, buildinteraction(), fcc_nslipsystem, fcc_ntwinsystem, hex_nslipsystem, hex_ntwinsystem, and io::io_error().

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◆ lattice_interaction_twinbytwin()

real(preal) function, dimension(sum(ntwin),sum(ntwin)), public lattice::lattice_interaction_twinbytwin	(	integer, dimension(:), intent(in)	Ntwin,
		real(preal), dimension(:), intent(in)	interactionValues,
		character(len=*), intent(in)	structure
	)

Twin-twin interaction matrix details only active twin systems are considered.

Parameters

[in]	ntwin	number of active twin systems per family
[in]	interactionvalues	values for twin-twin interaction
[in]	structure	lattice structure

Definition at line 995 of file lattice.f90.

References bcc_ntwinsystem, buildinteraction(), fcc_ntwinsystem, hex_ntwinsystem, and io::io_error().

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◆ lattice_labels_slip()

character(len=:) function, dimension(:), allocatable, public lattice::lattice_labels_slip	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure
	)

Labels for slip systems details only active slip systems are considered.

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure

Definition at line 1649 of file lattice.f90.

References bcc_nslipsystem, bcc_systemslip, bct_nslipsystem, bct_systemslip, fcc_nslipsystem, fcc_systemslip, getlabels(), hex_nslipsystem, hex_systemslip, and io::io_error().

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◆ lattice_labels_twin()

character(len=:) function, dimension(:), allocatable, public lattice::lattice_labels_twin	(	integer, dimension(:), intent(in)	Ntwin,
		character(len=*), intent(in)	structure
	)

Labels for twin systems details only active twin systems are considered.

Parameters

[in]	ntwin	number of active slip systems per family
[in]	structure	lattice structure

Definition at line 1811 of file lattice.f90.

References bcc_ntwinsystem, bcc_systemtwin, fcc_ntwinsystem, fcc_systemtwin, getlabels(), hex_ntwinsystem, hex_systemtwin, and io::io_error().

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◆ lattice_nonschmidmatrix()

real(preal) function, dimension(1:3,1:3,sum(nslip)), public lattice::lattice_nonschmidmatrix	(	integer, dimension(:), intent(in)	Nslip,
		real(preal), dimension(:), intent(in)	nonSchmidCoefficients,
		integer, intent(in)	sense
	)

Non-schmid projections for bcc with up to 6 coefficients.

Parameters

[in]	nslip	number of active slip systems per family
[in]	nonschmidcoefficients	non-Schmid coefficients for projections
[in]	sense	sense (-1,+1)

Definition at line 728 of file lattice.f90.

References bcc_nslipsystem, bcc_systemslip, buildcoordinatesystem(), io::io_error(), lattice_schmidmatrix_slip(), math::math_cross(), math::math_outer(), and prec::preal.

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◆ lattice_schmidmatrix_cleavage()

real(preal) function, dimension(3,3,3,sum(ncleavage)), public lattice::lattice_schmidmatrix_cleavage	(	integer, dimension(:), intent(in)	Ncleavage,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Schmid matrix for cleavage details only active cleavage systems are considered.

Parameters

[in]	ncleavage	number of active cleavage systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1546 of file lattice.f90.

References bcc_ncleavagesystem, bcc_systemcleavage, buildcoordinatesystem(), fcc_ncleavagesystem, fcc_systemcleavage, io::io_error(), math::math_outer(), ort_ncleavagesystem, and ort_systemcleavage.

Referenced by kinematics_cleavage_opening::kinematics_cleavage_opening_init(), and source_damage_anisobrittle::source_damage_anisobrittle_init().

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◆ lattice_schmidmatrix_slip()

real(preal) function, dimension(3,3,sum(nslip)), public lattice::lattice_schmidmatrix_slip	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Schmid matrix for slip details only active slip systems are considered.

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure

Definition at line 1415 of file lattice.f90.

References bcc_nslipsystem, bcc_systemslip, bct_nslipsystem, bct_systemslip, buildcoordinatesystem(), fcc_nslipsystem, fcc_systemslip, hex_nslipsystem, hex_systemslip, io::io_error(), math::math_outer(), math::math_trace33(), and prec::tol_math_check.

Referenced by lattice_nonschmidmatrix().

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◆ lattice_schmidmatrix_trans()

real(preal) function, dimension(3,3,sum(ntrans)), public lattice::lattice_schmidmatrix_trans	(	integer, dimension(:), intent(in)	Ntrans,
		character(len=*), intent(in)	structure_target,
		real(preal), intent(in)	cOverA,
		real(preal)	a_bcc,
		real(preal)	a_fcc
	)

Schmid matrix for twinning details only active twin systems are considered.

Parameters

[in]	ntrans	number of active twin systems per family
[in]	structure_target	lattice structure
[in]	covera	c/a ratio

Definition at line 1516 of file lattice.f90.

References buildtransformationsystem(), and io::io_error().

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◆ lattice_schmidmatrix_twin()

real(preal) function, dimension(3,3,sum(ntwin)), public lattice::lattice_schmidmatrix_twin	(	integer, dimension(:), intent(in)	Ntwin,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Schmid matrix for twinning details only active twin systems are considered.

Parameters

[in]	ntwin	number of active twin systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1467 of file lattice.f90.

References bcc_ntwinsystem, bcc_systemtwin, buildcoordinatesystem(), fcc_ntwinsystem, fcc_systemtwin, hex_ntwinsystem, hex_systemtwin, io::io_error(), math::math_outer(), math::math_trace33(), and prec::tol_math_check.

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◆ lattice_slip_direction()

real(preal) function, dimension(3,sum(nslip)), public lattice::lattice_slip_direction	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Slip direction of slip systems (|| b)

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1594 of file lattice.f90.

References coordinatesystem_slip().

Referenced by kinematics_slipplane_opening::kinematics_slipplane_opening_init(), and slipprojection_direction().

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◆ lattice_slip_normal()

real(preal) function, dimension(3,sum(nslip)), public lattice::lattice_slip_normal	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Normal direction of slip systems (|| n)

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1612 of file lattice.f90.

References coordinatesystem_slip().

Referenced by kinematics_slipplane_opening::kinematics_slipplane_opening_init(), slipprojection_direction(), and slipprojection_transverse().

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◆ lattice_slip_transverse()

real(preal) function, dimension(3,sum(nslip)), public lattice::lattice_slip_transverse	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

Transverse direction of slip systems ( || t = b x n)

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1630 of file lattice.f90.

References coordinatesystem_slip().

Referenced by kinematics_slipplane_opening::kinematics_slipplane_opening_init(), and slipprojection_transverse().

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◆ slipprojection_direction()

real(preal) function, dimension(sum(nslip),sum(nslip)) lattice::slipprojection_direction	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

private

Projection of the slip direction onto the slip plane.

: This projection is used to calculate forest hardening for screw dislocations

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1876 of file lattice.f90.

References lattice_slip_direction(), lattice_slip_normal(), and math::math_inner().

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◆ slipprojection_transverse()

real(preal) function, dimension(sum(nslip),sum(nslip)) lattice::slipprojection_transverse	(	integer, dimension(:), intent(in)	Nslip,
		character(len=*), intent(in)	structure,
		real(preal), intent(in)	cOverA
	)

private

Projection of the transverse direction onto the slip plane.

: This projection is used to calculate forest hardening for edge dislocations

Parameters

[in]	nslip	number of active slip systems per family
[in]	structure	lattice structure
[in]	covera	c/a ratio

Definition at line 1852 of file lattice.f90.

References lattice_slip_normal(), lattice_slip_transverse(), and math::math_inner().

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◆ unittest()

subroutine lattice::unittest

private

check correctness of some lattice functions

Definition at line 2299 of file lattice.f90.

References applylatticesymmetryc66(), buildcoordinatesystem(), prec::dneq(), equivalent_mu(), equivalent_nu(), io::io_error(), and math::math_i3.

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Variable Documentation

◆ bcc_ncleavage

integer, parameter lattice::bcc_ncleavage = sum(BCC_NCLEAVAGESYSTEM)

private

total # of cleavage systems for bcc

Definition at line 125 of file lattice.f90.

◆ bcc_ncleavagesystem

integer, dimension(1), parameter lattice::bcc_ncleavagesystem = [3]

private

of cleavage systems per family for bcc

Definition at line 122 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

◆ bcc_nslip

integer, parameter lattice::bcc_nslip = sum(BCC_NSLIPSYSTEM)

private

total # of slip systems for bcc

Definition at line 125 of file lattice.f90.

◆ bcc_nslipsystem

integer, dimension(2), parameter lattice::bcc_nslipsystem = [12, 12]

private

of slip systems per family for bcc

Definition at line 116 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_c66_twin(), lattice_interaction_slipbyslip(), lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_labels_slip(), lattice_nonschmidmatrix(), and lattice_schmidmatrix_slip().

◆ bcc_ntwin

integer, parameter lattice::bcc_ntwin = sum(BCC_NTWINSYSTEM)

private

total # of twin systems for bcc

Definition at line 125 of file lattice.f90.

◆ bcc_ntwinsystem

integer, dimension(1), parameter lattice::bcc_ntwinsystem = [12]

private

of twin systems per family for bcc

Definition at line 119 of file lattice.f90.

Referenced by lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_interaction_twinbytwin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ bcc_systemcleavage

real(preal), dimension(3+3,bcc_ncleavage), parameter lattice::bcc_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(BCC_SYSTEMCLEAVAGE))

private

Definition at line 184 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

◆ bcc_systemslip

real(preal), dimension(3+3,bcc_nslip), parameter lattice::bcc_systemslip = reshape(real([ 1,-1, 1, 0, 1, 1, -1,-1, 1, 0, 1, 1, 1, 1, 1, 0,-1, 1, -1, 1, 1, 0,-1, 1, -1, 1, 1, 1, 0, 1, -1,-1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 1, 1,-1, 1, -1, 0, 1, -1, 1, 1, 1, 1, 0, -1, 1,-1, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 1,-1, -1, 1, 0, -1, 1, 1, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1,-1, 2,-1, 1, 1,-1, 1, 2, 1,-1, 1,-1, 1, 1, 2, 1, 1, 1,-1, -1, 2, 1, 1, 1, 1, 1,-2, 1, -1, 1, 1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1,-1, 1, -1, 1, 2, -1, 1, 1, 1,-1, 2, 1, 1, 1, 1, 1,-2 ], pReal), shape(BCC_SYSTEMSLIP))

private

Definition at line 136 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_labels_slip(), lattice_nonschmidmatrix(), and lattice_schmidmatrix_slip().

◆ bcc_systemtwin

real(preal), dimension(3+3,bcc_ntwin), parameter lattice::bcc_systemtwin = reshape(real([ -1, 1, 1, 2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1,-1, 2,-1, 1, 1,-1, 1, 2, 1,-1, 1,-1, 1, 1, 2, 1, 1, 1,-1, -1, 2, 1, 1, 1, 1, 1,-2, 1, -1, 1, 1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1,-1, 1, -1, 1, 2, -1, 1, 1, 1,-1, 2, 1, 1, 1, 1, 1,-2 ], pReal), shape(BCC_SYSTEMTWIN))

private

Definition at line 167 of file lattice.f90.

Referenced by lattice_c66_twin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ bct_nslip

integer, parameter lattice::bct_nslip = sum(BCT_NSLIPSYSTEM)

private

total # of slip systems for bct

Definition at line 290 of file lattice.f90.

◆ bct_nslipsystem

integer, dimension(13), parameter lattice::bct_nslipsystem = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ]

private

of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009

Definition at line 287 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_interaction_slipbyslip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ bct_systemslip

real(preal), dimension(3+3,bct_nslip), parameter lattice::bct_systemslip = reshape(real([ 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1,-1, 1, 1, 1, 0, 1,-1,-1, 1, 1, 0, -1,-1,-1, -1, 1, 0, -1,-1, 1, -1, 1, 0, 1, -1, 0, 1, 1, 0, 1, 1, 0, 1,-1, 0, 0, 1, 1, 1, 0, 0, 0,-1, 1, 1, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 1, 1, 0,-1,-1, 0,-1, 1, -1, 0,-1, -1, 0, 1, 1, 0,-1, 1, 0, 1, 1,-1, 1, 0, 1, 1, 1, 1,-1, 0, 1, 1, 1, 1, 1, 0, 1,-1, -1, 1, 1, 0, 1,-1, 1,-1,-1, 1, 0, 1, -1,-1, 1, 1, 0, 1, 1, 1, 1, 1, 0,-1, 1,-1, 1, 1, 0,-1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1,-1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,-1, 0, 1,-1, 2, 1, 1, 0,-1,-1, 2,-1, 1, 1, 0,-1, 1, 2, 1, -1, 0,-1, -1, 2, 1, 0, 1,-1, -2, 1, 1, 0,-1,-1, -2,-1, 1, -1, 0,-1, -1,-2, 1, 1, 0,-1, 1,-2, 1, -1, 1, 1, 2, 1, 1, -1,-1, 1, 2,-1, 1, 1,-1, 1, 1, 2, 1, -1,-1, 1, -1, 2, 1, 1, 1, 1, -2, 1, 1, 1,-1, 1, -2,-1, 1, -1, 1, 1, -1,-2, 1, 1, 1, 1, 1,-2, 1 ], pReal), shape(BCT_SYSTEMSLIP))

private

slip systems for bct sorted by Bieler

Definition at line 297 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ fcc_ncleavage

integer, parameter lattice::fcc_ncleavage = sum(FCC_NCLEAVAGESYSTEM)

private

total # of cleavage systems for fcc

Definition at line 37 of file lattice.f90.

◆ fcc_ncleavagesystem

integer, dimension(1), parameter lattice::fcc_ncleavagesystem = [3]

private

of cleavage systems per family for fcc

Definition at line 34 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

◆ fcc_nslip

integer, parameter lattice::fcc_nslip = sum(FCC_NSLIPSYSTEM)

private

total # of slip systems for fcc

Definition at line 37 of file lattice.f90.

◆ fcc_nslipsystem

integer, dimension(2), parameter lattice::fcc_nslipsystem = [12, 6]

private

of slip systems per family for fcc

Definition at line 25 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_c66_twin(), lattice_interaction_slipbyslip(), lattice_interaction_slipbytrans(), lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ fcc_ntrans

integer, parameter lattice::fcc_ntrans = sum(FCC_NTRANSSYSTEM)

private

total # of transformation systems for fcc

Definition at line 37 of file lattice.f90.

◆ fcc_ntranssystem

integer, dimension(1), parameter lattice::fcc_ntranssystem = [12]

private

of transformation systems per family for fcc

Definition at line 31 of file lattice.f90.

Referenced by lattice_interaction_slipbytrans(), and lattice_interaction_transbytrans().

◆ fcc_ntwin

integer, parameter lattice::fcc_ntwin = sum(FCC_NTWINSYSTEM)

private

total # of twin systems for fcc

Definition at line 37 of file lattice.f90.

◆ fcc_ntwinsystem

integer, dimension(1), parameter lattice::fcc_ntwinsystem = [12]

private

of twin systems per family for fcc

Definition at line 28 of file lattice.f90.

Referenced by lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_interaction_twinbytwin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ fcc_systemcleavage

real(preal), dimension(3+3,fcc_ncleavage), parameter lattice::fcc_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(FCC_SYSTEMCLEAVAGE))

private

Definition at line 106 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

◆ fcc_systemslip

real(preal), dimension(3+3,fcc_nslip), parameter lattice::fcc_systemslip = reshape(real([ 0, 1,-1, 1, 1, 1, -1, 0, 1, 1, 1, 1, 1,-1, 0, 1, 1, 1, 0,-1,-1, -1,-1, 1, 1, 0, 1, -1,-1, 1, -1, 1, 0, -1,-1, 1, 0,-1, 1, 1,-1,-1, -1, 0,-1, 1,-1,-1, 1, 1, 0, 1,-1,-1, 0, 1, 1, -1, 1,-1, 1, 0,-1, -1, 1,-1, -1,-1, 0, -1, 1,-1, 1, 1, 0, 1,-1, 0, 1,-1, 0, 1, 1, 0, 1, 0, 1, 1, 0,-1, 1, 0,-1, 1, 0, 1, 0, 1, 1, 0, 1,-1, 0, 1,-1, 0, 1, 1 ], pReal), shape(FCC_SYSTEMSLIP))

private

Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli.

Definition at line 50 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ fcc_systemtwin

real(preal), dimension(3+3,fcc_ntwin), parameter lattice::fcc_systemtwin = reshape(real( [ -2, 1, 1, 1, 1, 1, 1,-2, 1, 1, 1, 1, 1, 1,-2, 1, 1, 1, 2,-1, 1, -1,-1, 1, -1, 2, 1, -1,-1, 1, -1,-1,-2, -1,-1, 1, -2,-1,-1, 1,-1,-1, 1, 2,-1, 1,-1,-1, 1,-1, 2, 1,-1,-1, 2, 1,-1, -1, 1,-1, -1,-2,-1, -1, 1,-1, -1, 1, 2, -1, 1,-1 ], pReal), shape(FCC_SYSTEMTWIN))

private

Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli.

Definition at line 74 of file lattice.f90.

Referenced by lattice_c66_twin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ hex_nslip

integer, parameter lattice::hex_nslip = sum(HEX_NSLIPSYSTEM)

private

total # of slip systems for hex

Definition at line 200 of file lattice.f90.

◆ hex_nslipsystem

integer, dimension(6), parameter lattice::hex_nslipsystem = [3, 3, 3, 6, 12, 6]

private

of slip systems per family for hex

Definition at line 194 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_c66_twin(), lattice_interaction_slipbyslip(), lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ hex_ntwin

integer, parameter lattice::hex_ntwin = sum(HEX_NTWINSYSTEM)

private

total # of twin systems for hex

Definition at line 200 of file lattice.f90.

Referenced by lattice_characteristicshear_twin().

◆ hex_ntwinsystem

integer, dimension(4), parameter lattice::hex_ntwinsystem = [6, 6, 6, 6]

private

of slip systems per family for hex

Definition at line 197 of file lattice.f90.

Referenced by lattice_characteristicshear_twin(), lattice_interaction_slipbytwin(), lattice_interaction_twinbyslip(), lattice_interaction_twinbytwin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ hex_systemslip

real(preal), dimension(4+4,hex_nslip), parameter lattice::hex_systemslip = reshape(real([ 2, -1, -1, 0, 0, 0, 0, 1, -1, 2, -1, 0, 0, 0, 0, 1, -1, -1, 2, 0, 0, 0, 0, 1, 2, -1, -1, 0, 0, 1, -1, 0, -1, 2, -1, 0, -1, 0, 1, 0, -1, -1, 2, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, 1, -2, 0, 0, -1, 1, 0, -2, 1, 1, 0, 1, 0, -1, 0, 1, -2, 1, 0, -1, 2, -1, 0, 1, 0, -1, 1, -2, 1, 1, 0, 0, 1, -1, 1, -1, -1, 2, 0, -1, 1, 0, 1, 1, -2, 1, 0, -1, 0, 1, 1, 2, -1, -1, 0, 0, -1, 1, 1, 1, 1, -2, 0, 1, -1, 0, 1, -2, 1, 1, 3, 1, 0, -1, 1, -1, -1, 2, 3, 1, 0, -1, 1, -1, -1, 2, 3, 0, 1, -1, 1, 1, -2, 1, 3, 0, 1, -1, 1, 1, -2, 1, 3, -1, 1, 0, 1, 2, -1, -1, 3, -1, 1, 0, 1, 2, -1, -1, 3, -1, 0, 1, 1, 1, 1, -2, 3, -1, 0, 1, 1, 1, 1, -2, 3, 0, -1, 1, 1, -1, 2, -1, 3, 0, -1, 1, 1, -1, 2, -1, 3, 1, -1, 0, 1, -2, 1, 1, 3, 1, -1, 0, 1, -1, -1, 2, 3, 1, 1, -2, 2, 1, -2, 1, 3, -1, 2, -1, 2, 2, -1, -1, 3, -2, 1, 1, 2, 1, 1, -2, 3, -1, -1, 2, 2, -1, 2, -1, 3, 1, -2, 1, 2, -2, 1, 1, 3, 2, -1, -1, 2 ], pReal), shape(HEX_SYSTEMSLIP))

private

slip systems for hex, sorted by P. Eisenlohr CCW around starting next to a_1 axis

Definition at line 209 of file lattice.f90.

Referenced by coordinatesystem_slip(), lattice_labels_slip(), and lattice_schmidmatrix_slip().

◆ hex_systemtwin

real(preal), dimension(4+4,hex_ntwin), parameter lattice::hex_systemtwin = reshape(real([ -1, 0, 1, 1, 1, 0, -1, 2, 0, -1, 1, 1, 0, 1, -1, 2, 1, -1, 0, 1, -1, 1, 0, 2, 1, 0, -1, 1, -1, 0, 1, 2, 0, 1, -1, 1, 0, -1, 1, 2, -1, 1, 0, 1, 1, -1, 0, 2, -1, -1, 2, 6, 1, 1, -2, 1, 1, -2, 1, 6, -1, 2, -1, 1, 2, -1, -1, 6, -2, 1, 1, 1, 1, 1, -2, 6, -1, -1, 2, 1, -1, 2, -1, 6, 1, -2, 1, 1, -2, 1, 1, 6, 2, -1, -1, 1, 1, 0, -1, -2, 1, 0, -1, 1, 0, 1, -1, -2, 0, 1, -1, 1, -1, 1, 0, -2, -1, 1, 0, 1, -1, 0, 1, -2, -1, 0, 1, 1, 0, -1, 1, -2, 0, -1, 1, 1, 1, -1, 0, -2, 1, -1, 0, 1, 1, 1, -2, -3, 1, 1, -2, 2, -1, 2, -1, -3, -1, 2, -1, 2, -2, 1, 1, -3, -2, 1, 1, 2, -1, -1, 2, -3, -1, -1, 2, 2, 1, -2, 1, -3, 1, -2, 1, 2, 2, -1, -1, -3, 2, -1, -1, 2 ], pReal), shape(HEX_SYSTEMTWIN))

private

twin systems for hex, sorted by P. Eisenlohr CCW around starting next to a_1 axis

Definition at line 253 of file lattice.f90.

Referenced by lattice_c66_twin(), lattice_labels_twin(), and lattice_schmidmatrix_twin().

◆ lattice_bcc_id

@, public lattice::lattice_bcc_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_bct_id

@, public lattice::lattice_bct_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_c66

real(preal), dimension(:,:,:), allocatable, public, protected lattice::lattice_c66

Definition at line 404 of file lattice.f90.

Referenced by constitutive::constitutive_homogenizedc(), and lattice_init().

◆ lattice_damagediffusion

real(preal), dimension(:,:,:), allocatable, public, protected lattice::lattice_damagediffusion

Definition at line 404 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_damagemobility

real(preal), dimension(:), allocatable, public, protected lattice::lattice_damagemobility

Definition at line 399 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_fcc_id

@, public lattice::lattice_fcc_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_fcc_twinnucleationslippair

integer, dimension(2,fcc_ntwin), parameter, public lattice::lattice_fcc_twinnucleationslippair = reshape( [ 2,3, 1,3, 1,2, 5,6, 4,6, 4,5, 8,9, 7,9, 7,8, 11,12, 10,12, 10,11 ], shape(lattice_FCC_TWINNUCLEATIONSLIPPAIR))

Definition at line 90 of file lattice.f90.

◆ lattice_hex_id

@, public lattice::lattice_hex_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_iso_id

@, public lattice::lattice_iso_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_massdensity

real(preal), dimension(:), allocatable, public, protected lattice::lattice_massdensity

Definition at line 399 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_mu

real(preal), dimension(:), allocatable, public, protected lattice::lattice_mu

Definition at line 399 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_nu

real(preal), dimension(:), allocatable, public, protected lattice::lattice_nu

Definition at line 399 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_ort_id

@, public lattice::lattice_ort_id

Definition at line 395 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_specificheat

real(preal), dimension(:), allocatable, public, protected lattice::lattice_specificheat

Definition at line 399 of file lattice.f90.

Referenced by lattice_init().

◆ lattice_structure

integer(kind(lattice_undefined_id)), dimension(:), allocatable, public, protected lattice::lattice_structure

Definition at line 408 of file lattice.f90.

Referenced by crystallite::crystallite_results(), and lattice_init().

◆ lattice_thermalconductivity

real(preal), dimension(:,:,:), allocatable, public, protected lattice::lattice_thermalconductivity

Definition at line 404 of file lattice.f90.

Referenced by lattice_init().

◆ ort_ncleavage

integer, parameter lattice::ort_ncleavage = sum(ORT_NCLEAVAGESYSTEM)

private

total # of cleavage systems for ortho

Definition at line 372 of file lattice.f90.

◆ ort_ncleavagesystem

integer, dimension(3), parameter lattice::ort_ncleavagesystem = [1, 1, 1]

private

of cleavage systems per family for ortho

Definition at line 369 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

◆ ort_systemcleavage

real(preal), dimension(3+3,ort_ncleavage), parameter lattice::ort_systemcleavage = reshape(real([ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1 ], pReal), shape(ORT_SYSTEMCLEAVAGE))

private

Definition at line 379 of file lattice.f90.

Referenced by lattice_schmidmatrix_cleavage().

Data Types

Enumerations

Functions/Subroutines

Variables

Detailed Description

Enumeration Type Documentation

◆ anonymous enum

Function/Subroutine Documentation

◆ applylatticesymmetryc66()

◆ buildcoordinatesystem()

◆ buildinteraction()

◆ buildtransformationsystem()

◆ coordinatesystem_slip()

◆ equivalent_mu()

◆ equivalent_nu()

◆ getlabels()

◆ lattice_applylatticesymmetry33()

◆ lattice_c66_trans()

◆ lattice_c66_twin()

◆ lattice_characteristicshear_twin()

◆ lattice_init()

◆ lattice_interaction_slipbyslip()

◆ lattice_interaction_slipbytrans()

◆ lattice_interaction_slipbytwin()

◆ lattice_interaction_transbytrans()

◆ lattice_interaction_twinbyslip()

◆ lattice_interaction_twinbytwin()

◆ lattice_labels_slip()

◆ lattice_labels_twin()

◆ lattice_nonschmidmatrix()

◆ lattice_schmidmatrix_cleavage()

◆ lattice_schmidmatrix_slip()

◆ lattice_schmidmatrix_trans()

◆ lattice_schmidmatrix_twin()

◆ lattice_slip_direction()

◆ lattice_slip_normal()

◆ lattice_slip_transverse()

◆ slipprojection_direction()

◆ slipprojection_transverse()

◆ unittest()

Variable Documentation

◆ bcc_ncleavage

◆ bcc_ncleavagesystem

of cleavage systems per family for bcc

◆ bcc_nslip

◆ bcc_nslipsystem

of slip systems per family for bcc

◆ bcc_ntwin

◆ bcc_ntwinsystem

of twin systems per family for bcc

◆ bcc_systemcleavage

◆ bcc_systemslip

◆ bcc_systemtwin

◆ bct_nslip

◆ bct_nslipsystem

of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009

◆ bct_systemslip

◆ fcc_ncleavage

◆ fcc_ncleavagesystem

of cleavage systems per family for fcc

◆ fcc_nslip

◆ fcc_nslipsystem

of slip systems per family for fcc

◆ fcc_ntrans

◆ fcc_ntranssystem

of transformation systems per family for fcc

◆ fcc_ntwin

◆ fcc_ntwinsystem

of twin systems per family for fcc

◆ fcc_systemcleavage

◆ fcc_systemslip

◆ fcc_systemtwin

◆ hex_nslip

◆ hex_nslipsystem

of slip systems per family for hex

◆ hex_ntwin

◆ hex_ntwinsystem

of slip systems per family for hex

◆ hex_systemslip

◆ hex_systemtwin