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DAMASK_EICMD
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tidied up the Schmid matrix calculations. 

added internal check against dilatation in Schmid matrices.
This commit is contained in:
Philip Eisenlohr 2012-10-12 17:59:50 +00:00
parent b20c612e25
commit 82a13af474
1 changed files with 65 additions and 69 deletions
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134
code/lattice.f90
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@ -487,31 +487,31 @@ module lattice
2, -1, -1, 0, 0, 0, 0, 1, &
-1, 2, -1, 0, 0, 0, 0, 1, &
-1, -1, 2, 0, 0, 0, 0, 1, &
! 1st type prismatic systems <1120>{1010} (independent of c/a-ratio)
! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio)
2, -1, -1, 0, 0, 1, -1, 0, &
-1, 2, -1, 0, -1, 0, 1, 0, &
-1, -1, 2, 0, 1, -1, 0, 0, &
! 1st type 1st order pyramidal systems <1120>{1011} -- plane normals depend on the c/a-ratio
! 1st type 1st order pyramidal systems <11.0>{10.1} -- plane normals depend on the c/a-ratio
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, &
1, -2, 1, 0, 1, 0, -1, 1, &
! pyramidal system: c+a slip <2113>{1011} -- plane normals depend on the c/a-ratio
-1, 2, -1, 3, 0, 1, -1, 1, &
1, 1, -2, 3, 0, 1, -1, 1, &
-2, 1, 1, 3, -1, 1, 0, 1, &
-1, 2, -1, 3, -1, 1, 0, 1, &
-1, -1, 2, 3, -1, 0, 1, 1, &
-2, 1, 1, 3, -1, 0, 1, 1, &
1, -2, 1, 3, 0, -1, 1, 1, &
-1, -1, 2, 3, 0, -1, 1, 1, &
2, -1, -1, 3, 1, -1, 0, 1, &
1, -2, 1, 3, 1, -1, 0, 1, &
1, 1, -2, 3, 1, 0, -1, 1, &
2, -1, -1, 3, 1, 0, -1, 1, &
! pyramidal system: c+a slip <11-2-3>{11-22} -- as for hexagonal Ice (Castelnau et al 1996, similar to twin system found below)
! pyramidal system: c+a slip <-21.-3>{-10.1} -- plane normals depend on the c/a-ratio
-1, 2, -1, -3, 0, 1, -1, 1, &
1, 1, -2, -3, 0, 1, -1, 1, &
-2, 1, 1, -3, -1, 1, 0, 1, &
-1, 2, -1, -3, -1, 1, 0, 1, &
-1, -1, 2, -3, -1, 0, 1, 1, &
-2, 1, 1, -3, -1, 0, 1, 1, &
1, -2, 1, -3, 0, -1, 1, 1, &
-1, -1, 2, -3, 0, -1, 1, 1, &
2, -1, -1, -3, 1, -1, 0, 1, &
1, -2, 1, -3, 1, -1, 0, 1, &
1, 1, -2, -3, 1, 0, -1, 1, &
2, -1, -1, -3, 1, 0, -1, 1, &
! pyramidal system: c+a slip <11.-3>{11.2} -- as for hexagonal Ice (Castelnau et al 1996, similar to twin system found below)
2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
1, 1, -2, -3, 1, 1, -2, 2, & ! not sorted, just copied from twin system
-1, 2, -1, -3, -1, 2, -1, 2, &
@ -836,7 +836,8 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
use prec, only: pReal,pInt
use math, only: math_vectorproduct, &
math_tensorproduct, &
math_mul3x3, &
math_norm3, &
math_trace33, &
math_symmetric33, &
math_Mandel33to6, &
math_axisAngleToR, &
@ -853,8 +854,6 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
tn = 0.0_pReal, &
tt = 0.0_pReal
real(pReal), dimension(lattice_maxNtwin) :: ts = 0.0_pReal
real(pReal), dimension(3) :: hex_d = 0.0_pReal, &
hex_n = 0.0_pReal
integer(pInt), dimension(lattice_maxNslipFamily) :: myNslipSystem = 0_pInt
integer(pInt), dimension(lattice_maxNtwinFamily) :: myNtwinSystem = 0_pInt
integer(pInt) :: i,myNslip,myNtwin,myStructure = 0_pInt
@ -872,16 +871,14 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
lattice_fcc_Nstructure = lattice_fcc_Nstructure + 1_pInt ! count fcc instances
if (lattice_fcc_Nstructure == 1_pInt) then ! me is first fcc structure
processMe = .true.
do i = 1_pInt,myNslip ! calculate slip system vectors
sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)/sqrt(math_mul3x3(lattice_fcc_systemSlip(1:3,i),lattice_fcc_systemSlip(1:3,i)))
sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)/sqrt(math_mul3x3(lattice_fcc_systemSlip(4:6,i),lattice_fcc_systemSlip(4:6,i)))
st(1:3,i) = math_vectorproduct(sd(1:3,i),sn(1:3,i))
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)
sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)
enddo
do i = 1_pInt,myNtwin ! calculate twin system vectors and (assign) shears
td(1:3,i) = lattice_fcc_systemTwin(1:3,i)/sqrt(math_mul3x3(lattice_fcc_systemTwin(1:3,i),lattice_fcc_systemTwin(1:3,i)))
tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)/sqrt(math_mul3x3(lattice_fcc_systemTwin(4:6,i),lattice_fcc_systemTwin(4:6,i)))
tt(1:3,i) = math_vectorproduct(td(1:3,i),tn(1:3,i))
ts(i) = lattice_fcc_shearTwin(i)
do i = 1_pInt,myNtwin ! assign twin system vectors and shears
td(1:3,i) = lattice_fcc_systemTwin(1:3,i)
tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
ts(i) = lattice_fcc_shearTwin(i)
enddo
interactionSlipSlip => lattice_fcc_interactionSlipSlip
interactionSlipTwin => lattice_fcc_interactionSlipTwin
@ -898,16 +895,14 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
lattice_bcc_Nstructure = lattice_bcc_Nstructure + 1_pInt ! count bcc instances
if (lattice_bcc_Nstructure == 1_pInt) then ! me is first bcc structure
processMe = .true.
do i = 1_pInt,myNslip ! calculate slip system vectors
sd(1:3,i) = lattice_bcc_systemSlip(1:3,i)/sqrt(math_mul3x3(lattice_bcc_systemSlip(1:3,i),lattice_bcc_systemSlip(1:3,i)))
sn(1:3,i) = lattice_bcc_systemSlip(4:6,i)/sqrt(math_mul3x3(lattice_bcc_systemSlip(4:6,i),lattice_bcc_systemSlip(4:6,i)))
st(1:3,i) = math_vectorproduct(sd(1:3,i),sn(1:3,i))
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1:3,i) = lattice_bcc_systemSlip(1:3,i)
sn(1:3,i) = lattice_bcc_systemSlip(4:6,i)
enddo
do i = 1_pInt,myNtwin ! calculate twin system vectors and (assign) shears
td(1:3,i) = lattice_bcc_systemTwin(1:3,i)/sqrt(math_mul3x3(lattice_bcc_systemTwin(1:3,i),lattice_bcc_systemTwin(1:3,i)))
tn(1:3,i) = lattice_bcc_systemTwin(4:6,i)/sqrt(math_mul3x3(lattice_bcc_systemTwin(4:6,i),lattice_bcc_systemTwin(4:6,i)))
tt(1:3,i) = math_vectorproduct(td(1:3,i),tn(1:3,i))
ts(i) = lattice_bcc_shearTwin(i)
do i = 1_pInt,myNtwin ! assign twin system vectors and shears
td(1:3,i) = lattice_bcc_systemTwin(1:3,i)
tn(1:3,i) = lattice_bcc_systemTwin(4:6,i)
ts(i) = lattice_bcc_shearTwin(i)
enddo
interactionSlipSlip => lattice_bcc_interactionSlipSlip
interactionSlipTwin => lattice_bcc_interactionSlipTwin
@ -926,30 +921,22 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
processMe = .true.
! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexgonal system (a, b, c)
do i = 1_pInt,myNslip
hex_d(1) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
hex_d(2) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*(0.5_pReal*sqrt(3.0_pReal))
hex_d(3) = lattice_hex_systemSlip(4,i)*CoverA
hex_n(1) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
hex_n(2) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal)
hex_n(3) = lattice_hex_systemSlip(8,i)/CoverA
sd(1:3,i) = hex_d/sqrt(math_mul3x3(hex_d,hex_d))
sn(1:3,i) = hex_n/sqrt(math_mul3x3(hex_n,hex_n))
st(1:3,i) = math_vectorproduct(sd(1:3,i),sn(1:3,i))
sd(1,i) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*(0.5_pReal*sqrt(3.0_pReal))
sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA
sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal)
sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA
enddo
do i = 1_pInt,myNtwin
hex_d(1) = lattice_hex_systemTwin(1,i)*1.5_pReal
hex_d(2) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*(0.5_pReal*sqrt(3.0_pReal))
hex_d(3) = lattice_hex_systemTwin(4,i)*CoverA
hex_n(1) = lattice_hex_systemTwin(5,i)
hex_n(2) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal)
hex_n(3) = lattice_hex_systemTwin(8,i)/CoverA
td(1,i) = lattice_hex_systemTwin(1,i)*1.5_pReal
td(2,i) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*(0.5_pReal*sqrt(3.0_pReal))
td(3,i) = lattice_hex_systemTwin(4,i)*CoverA
tn(1,i) = lattice_hex_systemTwin(5,i)
tn(2,i) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal)
tn(3,i) = lattice_hex_systemTwin(8,i)/CoverA
td(1:3,i) = hex_d/sqrt(math_mul3x3(hex_d,hex_d))
tn(1:3,i) = hex_n/sqrt(math_mul3x3(hex_n,hex_n))
tt(1:3,i) = math_vectorproduct(td(1:3,i),tn(1:3,i))
select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29
select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29
case (1_pInt) ! {10.2}<-10.1>
ts(i) = (3.0_pReal-CoverA*CoverA)/sqrt(3.0_pReal)/CoverA
case (2_pInt) ! {11.2}<11.-3>
@ -970,22 +957,31 @@ integer(pInt) function lattice_initializeStructure(struct,CoverA)
if (processMe) then
if (myStructure > lattice_Nstructure) &
call IO_error(666_pInt,0_pInt,0_pInt,0_pInt,'structure index too large') ! check for memory leakage
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
lattice_sd(1:3,i,myStructure) = sd(1:3,i)
lattice_st(1:3,i,myStructure) = st(1:3,i)
lattice_sn(1:3,i,myStructure) = sn(1:3,i)
lattice_Sslip(1:3,1:3,i,myStructure) = math_tensorproduct(sd(1:3,i),sn(1:3,i))
call IO_error(666_pInt,myStructure,ext_msg = 'structure index out of bounds') ! check for memory leakage
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
lattice_sd(1:3,i,myStructure) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector
lattice_sn(1:3,i,myStructure) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
lattice_st(1:3,i,myStructure) = math_vectorproduct(lattice_sd(1:3,i,myStructure), &
lattice_sn(1:3,i,myStructure))
lattice_Sslip(1:3,1:3,i,myStructure) = math_tensorproduct(lattice_sd(1:3,i,myStructure), &
lattice_sn(1:3,i,myStructure))
lattice_Sslip_v(1:6,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,i,myStructure)))
if (abs(math_trace33(lattice_Sslip(1:3,1:3,i,myStructure))) > 1.0e-8) &
call IO_error(0_pInt,myStructure,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix')
endif
enddo
do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure
lattice_td(1:3,i,myStructure) = td(1:3,i)
lattice_tt(1:3,i,myStructure) = tt(1:3,i)
lattice_tn(1:3,i,myStructure) = tn(1:3,i)
lattice_Stwin(1:3,1:3,i,myStructure) = math_tensorproduct(td(1:3,i),tn(1:3,i))
lattice_td(1:3,i,myStructure) = td(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector
lattice_tn(1:3,i,myStructure) = tn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
lattice_tt(1:3,i,myStructure) = math_vectorproduct(lattice_td(1:3,i,myStructure), &
lattice_tn(1:3,i,myStructure))
lattice_Stwin(1:3,1:3,i,myStructure) = math_tensorproduct(lattice_td(1:3,i,myStructure), &
lattice_tn(1:3,i,myStructure))
lattice_Stwin_v(1:6,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myStructure)))
lattice_Qtwin(1:3,1:3,i,myStructure) = math_AxisAngleToR(tn(1:3,i),180.0_pReal*inRad)
lattice_Qtwin(1:3,1:3,i,myStructure) = math_AxisAngleToR(tn(1:3,i),180.0_pReal*INRAD)
lattice_shearTwin(i,myStructure) = ts(i)
if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myStructure))) > 1.0e-8) &
call IO_error(0_pInt,myStructure,i,0_pInt,ext_msg = 'dilatational twin Schmid matrix')
enddo
lattice_NslipSystem(1:lattice_maxNslipFamily,myStructure) = myNslipSystem ! number of slip systems in each family
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myStructure) = myNtwinSystem ! number of twin systems in each family