195 lines
9.3 KiB
Fortran
195 lines
9.3 KiB
Fortran
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!************************************
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!* Module: CRYSTAL *
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!************************************
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!* contains: *
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!* - Crystal structure definition *
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!* - Slip system definition *
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!* - Schmid matrices calculation *
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!************************************
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MODULE crystal
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!*** Include other modules ***
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use prec, only: pReal,pInt
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implicit none
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!************************************
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!* Crystal structures *
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!************************************
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!* Number of crystal structures (1-FCC,2-BCC,3-HCP)
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integer(pInt), parameter :: crystal_MaxCrystalStructure = 3
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!* Total number of slip systems per crystal structure
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!* (as to be changed according the definition of slip systems)
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integer(pInt), dimension(crystal_MaxCrystalStructure), parameter :: crystal_MaxNslipOfStructure = &
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reshape((/12,48,12/),(/crystal_MaxCrystalStructure/))
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!* Maximum number of slip systems over crystal structures
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integer(pInt), parameter :: crystal_MaxMaxNslipOfStructure = 48
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!* Slip direction, slip normales and Schmid matrices
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real(pReal), dimension(3,3,crystal_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: crystal_Sslip
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real(pReal), dimension(6,crystal_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: crystal_Sslip_v
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real(pReal), dimension(3,crystal_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: crystal_sn
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real(pReal), dimension(3,crystal_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: crystal_sd
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!*** Slip systems for FCC structures (1) ***
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!* System {111}<110> Sort according Eisenlohr&Hantcherli
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data crystal_sd(:, 1,1)/ 0, 1,-1/ ; data crystal_sn(:, 1,1)/ 1, 1, 1/
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data crystal_sd(:, 2,1)/-1, 0, 1/ ; data crystal_sn(:, 2,1)/ 1, 1, 1/
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data crystal_sd(:, 3,1)/ 1,-1, 0/ ; data crystal_sn(:, 3,1)/ 1, 1, 1/
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data crystal_sd(:, 4,1)/ 0,-1,-1/ ; data crystal_sn(:, 4,1)/-1,-1, 1/
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data crystal_sd(:, 5,1)/ 1, 0, 1/ ; data crystal_sn(:, 5,1)/-1,-1, 1/
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data crystal_sd(:, 6,1)/-1, 1, 0/ ; data crystal_sn(:, 6,1)/-1,-1, 1/
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data crystal_sd(:, 7,1)/ 0,-1, 1/ ; data crystal_sn(:, 7,1)/ 1,-1,-1/
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data crystal_sd(:, 8,1)/-1, 0,-1/ ; data crystal_sn(:, 8,1)/ 1,-1,-1/
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data crystal_sd(:, 9,1)/ 1, 1, 0/ ; data crystal_sn(:, 9,1)/ 1,-1,-1/
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data crystal_sd(:,10,1)/ 0, 1, 1/ ; data crystal_sn(:,10,1)/-1, 1,-1/
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data crystal_sd(:,11,1)/ 1, 0,-1/ ; data crystal_sn(:,11,1)/-1, 1,-1/
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data crystal_sd(:,12,1)/-1,-1, 0/ ; data crystal_sn(:,12,1)/-1, 1,-1/
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!*** Slip systems for BCC structures (2) ***
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!* System {110}<111>
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!* Sort?
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data crystal_sd(:, 1,2)/ 1,-1, 1/ ; data crystal_sn(:, 1,2)/ 0, 1, 1/
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data crystal_sd(:, 2,2)/-1,-1, 1/ ; data crystal_sn(:, 2,2)/ 0, 1, 1/
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data crystal_sd(:, 3,2)/ 1, 1, 1/ ; data crystal_sn(:, 3,2)/ 0,-1, 1/
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data crystal_sd(:, 4,2)/-1, 1, 1/ ; data crystal_sn(:, 4,2)/ 0,-1, 1/
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data crystal_sd(:, 5,2)/-1, 1, 1/ ; data crystal_sn(:, 5,2)/ 1, 0, 1/
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data crystal_sd(:, 6,2)/-1,-1, 1/ ; data crystal_sn(:, 6,2)/ 1, 0, 1/
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data crystal_sd(:, 7,2)/ 1, 1, 1/ ; data crystal_sn(:, 7,2)/-1, 0, 1/
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data crystal_sd(:, 8,2)/ 1,-1, 1/ ; data crystal_sn(:, 8,2)/-1, 0, 1/
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data crystal_sd(:, 9,2)/-1, 1, 1/ ; data crystal_sn(:, 9,2)/ 1, 1, 0/
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data crystal_sd(:,10,2)/-1, 1,-1/ ; data crystal_sn(:,10,2)/ 1, 1, 0/
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data crystal_sd(:,11,2)/ 1, 1, 1/ ; data crystal_sn(:,11,2)/-1, 1, 0/
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data crystal_sd(:,12,2)/ 1, 1,-1/ ; data crystal_sn(:,12,2)/-1, 1, 0/
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!* System {112}<111>
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!* Sort?
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data crystal_sd(:,13,2)/-1, 1, 1/ ; data crystal_sn(:,13,2)/ 2, 1, 1/
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data crystal_sd(:,14,2)/ 1, 1, 1/ ; data crystal_sn(:,14,2)/-2, 1, 1/
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data crystal_sd(:,15,2)/ 1, 1,-1/ ; data crystal_sn(:,15,2)/ 2,-1, 1/
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data crystal_sd(:,16,2)/ 1,-1, 1/ ; data crystal_sn(:,16,2)/ 2, 1,-1/
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data crystal_sd(:,17,2)/ 1,-1, 1/ ; data crystal_sn(:,17,2)/ 1, 2, 1/
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data crystal_sd(:,18,2)/ 1, 1,-1/ ; data crystal_sn(:,18,2)/-1, 2, 1/
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data crystal_sd(:,19,2)/ 1, 1, 1/ ; data crystal_sn(:,19,2)/ 1,-2, 1/
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data crystal_sd(:,20,2)/-1, 1, 1/ ; data crystal_sn(:,20,2)/ 1, 2,-1/
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data crystal_sd(:,21,2)/ 1, 1,-1/ ; data crystal_sn(:,21,2)/ 1, 1, 2/
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data crystal_sd(:,22,2)/ 1,-1, 1/ ; data crystal_sn(:,22,2)/-1, 1, 2/
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data crystal_sd(:,23,2)/-1, 1, 1/ ; data crystal_sn(:,23,2)/ 1,-1, 2/
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data crystal_sd(:,24,2)/ 1, 1, 1/ ; data crystal_sn(:,24,2)/ 1, 1,-2/
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!* System {123}<111>
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!* Sort?
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data crystal_sd(:,25,2)/ 1, 1,-1/ ; data crystal_sn(:,25,2)/ 1, 2, 3/
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data crystal_sd(:,26,2)/ 1,-1, 1/ ; data crystal_sn(:,26,2)/-1, 2, 3/
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data crystal_sd(:,27,2)/-1, 1, 1/ ; data crystal_sn(:,27,2)/ 1,-2, 3/
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data crystal_sd(:,28,2)/ 1, 1, 1/ ; data crystal_sn(:,28,2)/ 1, 2,-3/
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data crystal_sd(:,29,2)/ 1,-1, 1/ ; data crystal_sn(:,29,2)/ 1, 3, 2/
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data crystal_sd(:,30,2)/ 1, 1,-1/ ; data crystal_sn(:,30,2)/-1, 3, 2/
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data crystal_sd(:,31,2)/ 1, 1, 1/ ; data crystal_sn(:,31,2)/ 1,-3, 2/
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data crystal_sd(:,32,2)/-1, 1, 1/ ; data crystal_sn(:,32,2)/ 1, 3,-2/
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data crystal_sd(:,33,2)/ 1, 1,-1/ ; data crystal_sn(:,33,2)/ 2, 1, 3/
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data crystal_sd(:,34,2)/ 1,-1, 1/ ; data crystal_sn(:,34,2)/-2, 1, 3/
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data crystal_sd(:,35,2)/-1, 1, 1/ ; data crystal_sn(:,35,2)/ 2,-1, 3/
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data crystal_sd(:,36,2)/ 1, 1, 1/ ; data crystal_sn(:,36,2)/ 2, 1,-3/
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data crystal_sd(:,37,2)/ 1,-1, 1/ ; data crystal_sn(:,37,2)/ 2, 3, 1/
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data crystal_sd(:,38,2)/ 1, 1,-1/ ; data crystal_sn(:,38,2)/-2, 3, 1/
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data crystal_sd(:,39,2)/ 1, 1, 1/ ; data crystal_sn(:,39,2)/ 2,-3, 1/
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data crystal_sd(:,40,2)/-1, 1, 1/ ; data crystal_sn(:,40,2)/ 2, 3,-1/
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data crystal_sd(:,41,2)/-1, 1, 1/ ; data crystal_sn(:,41,2)/ 3, 1, 2/
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data crystal_sd(:,42,2)/ 1, 1, 1/ ; data crystal_sn(:,42,2)/-3, 1, 2/
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data crystal_sd(:,43,2)/ 1, 1,-1/ ; data crystal_sn(:,43,2)/ 3,-1, 2/
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data crystal_sd(:,44,2)/ 1,-1, 1/ ; data crystal_sn(:,44,2)/ 3, 1,-2/
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data crystal_sd(:,45,2)/-1, 1, 1/ ; data crystal_sn(:,45,2)/ 3, 2, 1/
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data crystal_sd(:,46,2)/ 1, 1, 1/ ; data crystal_sn(:,46,2)/-3, 2, 1/
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data crystal_sd(:,47,2)/ 1, 1,-1/ ; data crystal_sn(:,47,2)/ 3,-2, 1/
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data crystal_sd(:,48,2)/ 1,-1, 1/ ; data crystal_sn(:,48,2)/ 3, 2,-1/
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!*** Slip systems for HCP structures (3) ***
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!* Basal systems {0001}<1120> (independent of c/a-ratio)
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!* 1- (0 0 0 1)[-2 1 1 0]
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!* 2- (0 0 0 1)[ 1 -2 1 0]
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!* 3- (0 0 0 1)[ 1 1 -2 0]
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!* Plane (hkil)->(hkl)
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!* Direction [uvtw]->[(u-t) (v-t) w]
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!* Automatical transformation from Bravais to Miller
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!* not done for the moment
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!* Sort?
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data crystal_sd(:, 1,3)/-1, 0, 0/ ; data crystal_sn(:, 1,3)/ 0, 0, 1/
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data crystal_sd(:, 2,3)/ 0,-1, 0/ ; data crystal_sn(:, 2,3)/ 0, 0, 1/
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data crystal_sd(:, 3,3)/ 1, 1, 0/ ; data crystal_sn(:, 3,3)/ 0, 0, 1/
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!* 1st type prismatic systems {1010}<1120> (independent of c/a-ratio)
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!* 1- ( 0 1 -1 0)[-2 1 1 0]
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!* 2- ( 1 0 -1 0)[ 1 -2 1 0]
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!* 3- (-1 1 0 0)[ 1 1 -2 0]
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!* Sort?
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data crystal_sd(:, 4,3)/-1, 0, 0/ ; data crystal_sn(:, 4,3)/ 0, 1, 0/
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data crystal_sd(:, 5,3)/ 0,-1, 0/ ; data crystal_sn(:, 5,3)/ 1, 0, 0/
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data crystal_sd(:, 6,3)/ 1, 1, 0/ ; data crystal_sn(:, 6,3)/-1, 1, 0/
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!* 1st type 1st order pyramidal systems {1011}<1120>
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!* plane normales depend on the c/a-ratio
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!* 1- ( 0 -1 1 1)[-2 1 1 0]
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!* 2- ( 0 1 -1 1)[-2 1 1 0]
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!* 3- (-1 0 1 1)[ 1 -2 1 0]
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!* 4- ( 1 0 -1 1)[ 1 -2 1 0]
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!* 5- (-1 1 0 1)[ 1 1 -2 0]
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!* 6- ( 1 -1 0 1)[ 1 1 -2 0]
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!* Sort?
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data crystal_sd(:, 7,3)/-1, 0, 0/ ; data crystal_sn(:, 7,3)/ 0,-1, 1/
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data crystal_sd(:, 8,3)/ 0,-1, 0/ ; data crystal_sn(:, 8,3)/ 0, 1, 1/
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data crystal_sd(:, 9,3)/ 1, 1, 0/ ; data crystal_sn(:, 9,3)/-1, 0, 1/
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data crystal_sd(:,10,3)/-1, 0, 0/ ; data crystal_sn(:,10,3)/ 1, 0, 1/
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data crystal_sd(:,11,3)/ 0,-1, 0/ ; data crystal_sn(:,11,3)/-1, 1, 1/
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data crystal_sd(:,12,3)/ 1, 1, 0/ ; data crystal_sn(:,12,3)/ 1,-1, 1/
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CONTAINS
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!****************************************
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!* - crystal_Init
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!* - crystal_SchmidMatrices
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!****************************************
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subroutine crystal_Init()
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!**************************************
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!* Module initialization *
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!**************************************
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call crystal_SchmidMatrices()
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end subroutine
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subroutine crystal_SchmidMatrices()
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!**************************************
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!* Calculation of Schmid matrices *
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!**************************************
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use prec, only: pReal,pInt
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implicit none
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!* Definition of variables
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integer(pInt) i,j,k,l
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real(pReal) invNorm
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!* Iteration over the crystal structures
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do l=1,3
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!* Iteration over the systems
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do k=1,crystal_MaxNslipOfStructure(l)
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!* Defintion of Schmid matrix
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forall (i=1:3,j=1:3)
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crystal_Sslip(i,j,k,l)=crystal_sd(i,k,l)*crystal_sn(j,k,l)
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endforall
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!* Normalization of Schmid matrix
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invNorm=dsqrt(1.0_pReal/((crystal_sn(1,k,l)**2+crystal_sn(2,k,l)**2+crystal_sn(3,k,l)**2)*&
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(crystal_sd(1,k,l)**2+crystal_sd(2,k,l)**2+crystal_sd(3,k,l)**2)))
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crystal_Sslip(:,:,k,l)=crystal_Sslip(:,:,k,l)*invNorm
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!* Vectorization of normalized Schmid matrix
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crystal_Sslip_v(1,k,l)=crystal_Sslip(1,1,k,l)
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crystal_Sslip_v(2,k,l)=crystal_Sslip(2,2,k,l)
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crystal_Sslip_v(3,k,l)=crystal_Sslip(3,3,k,l)
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!* be compatible with Mandel notation of Tstar
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crystal_Sslip_v(4,k,l)=(crystal_Sslip(1,2,k,l)+crystal_Sslip(2,1,k,l))/dsqrt(2.0_pReal)
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crystal_Sslip_v(5,k,l)=(crystal_Sslip(2,3,k,l)+crystal_Sslip(3,2,k,l))/dsqrt(2.0_pReal)
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crystal_Sslip_v(6,k,l)=(crystal_Sslip(1,3,k,l)+crystal_Sslip(3,1,k,l))/dsqrt(2.0_pReal)
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enddo
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enddo
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end subroutine
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END MODULE
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