function to calculate nonSchmid matrix
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Martin Diehl
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103b46ecbb
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@ -2081,6 +2081,7 @@ pure function lattice_qDisorientation(Q1, Q2, struct)
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end function lattice_qDisorientation
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function lattice_C66_twin(Ntwin,C66,structure,CoverA)
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use IO, only: &
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IO_error
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@ -2221,31 +2222,48 @@ function lattice_C66_trans(Ntrans,C66_parent,structure_parent,cOverA_parent, &
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end function
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!function lattice_nonSchmidMatrix
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! coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_BCC_SYSTEMSLIP,pInt),structure)
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!
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! do i = 1_pInt,myNslip ! assign slip system vectors
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! direction = coordinateSystem(1:3,1,i)
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! normal = coordinateSystem(1:3,1,i)
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! ! "np" and "nn" according to Gröger_etal2008, Acta Materialia 56 (2008) 5412–5425, table 1 (corresponds to their "n1" for positive and negative slip direction respectively)
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! np = math_mul33x3(math_axisAngleToR(sdU,+60.0_pReal*INRAD), normal)
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! ! Schmid matrices with non-Schmid contributions according to Koester_etal2012, Acta Materialia 60 (2012) 3894–3901, eq. (17) ("n1" is replaced by either "np" or "nn" according to either positive or negative slip direction)
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! nonSchmidMatrix_pos(1:3,1:3,1,i) = math_tensorproduct33(direction, np)
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! nonSchmidMatrix_pos(1:3,1:3,2,i) = math_tensorproduct33(math_crossproduct(normal, direction), normal)
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! nonSchmidMatrix_pos(1:3,1:3,3,i) = math_tensorproduct33(math_crossproduct(np, direction), np)
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! nonSchmidMatrix_pos(1:3,1:3,4,i) = math_tensorproduct33(normal, normal)
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! nonSchmidMatrix_pos(1:3,1:3,5,i) = math_tensorproduct33(math_crossproduct(normal, direction), math_crossproduct(normal, direction))
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! nonSchmidMatrix_pos(1:3,1:3,6,i) = math_tensorproduct33(direction, direction)
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!
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! nn = math_mul33x3(math_axisAngleToR(-sdU,60.0_pReal*INRAD), normal)
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! sns(1:3,1:3,2,1,i) = math_tensorproduct33(-sdU, nn)
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! sns(1:3,1:3,2,2,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), snU)
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! sns(1:3,1:3,2,3,i) = math_tensorproduct33(math_crossproduct(nn, -sdU), nn)
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! sns(1:3,1:3,2,4,i) = math_tensorproduct33(snU, snU)
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! sns(1:3,1:3,2,5,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), math_crossproduct(snU, -sdU))
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! sns(1:3,1:3,2,6,i) = math_tensorproduct33(-sdU, -sdU)
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! enddo
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!end function lattice_nonSchmidMatrix
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! ! "np" and "nn" according to Gröger_etal2008, Acta Materialia 56 (2008) 5412–5425, table 1 (corresponds to their "n1" for positive and negative slip direction respectively)
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function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix)
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use math, only: &
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INRAD, &
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math_tensorproduct33, &
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math_crossproduct, &
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math_mul33x3, &
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math_axisAngleToR
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implicit none
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integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family
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real(pReal), dimension(6), intent(in) :: nonSchmidCoefficients
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integer(pInt), intent(in) :: sense !< sense (-1,+1)
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real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix
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real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem
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real(pReal), dimension(:), allocatable :: direction
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real(pReal), dimension(:), allocatable :: normal,np
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integer(pInt) :: i
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if (abs(sense) /= 1_pInt) write(6,*) 'mist'
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coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_BCC_SYSTEMSLIP,pInt),'bcc')
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coordinateSystem(1:3,1,sum(Nslip)) = coordinateSystem(1:3,1,sum(Nslip)) *real(sense,pReal)
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nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'bcc')
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do i = 1_pInt,sum(Nslip)
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direction = coordinateSystem(1:3,1,i)
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normal = coordinateSystem(1:3,2,i)
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np = math_mul33x3(math_axisAngleToR(+direction,60.0_pReal*INRAD), normal)
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nonSchmidMatrix(1:3,1:3,i) &
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= nonSchmidMatrix(1:3,1:3,i) &
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+ nonSchmidCoefficients(1) * math_tensorproduct33(direction, np) &
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+ nonSchmidCoefficients(2) * math_tensorproduct33(math_crossproduct(normal, direction), normal) &
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+ nonSchmidCoefficients(3) * math_tensorproduct33(math_crossproduct(np, direction), np) &
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+ nonSchmidCoefficients(4) * math_tensorproduct33(normal, normal) &
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+ nonSchmidCoefficients(5) * math_tensorproduct33(math_crossproduct(normal, direction), &
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math_crossproduct(normal, normal)) &
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+ nonSchmidCoefficients(6) * math_tensorproduct33(direction, direction)
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enddo
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end function lattice_nonSchmidMatrix
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!--------------------------------------------------------------------------------------------------
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!> @brief Populates reduced slip-slip interaction matrix
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@ -2376,7 +2394,7 @@ end function lattice_interactionSlipTwin2
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!--------------------------------------------------------------------------------------------------
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!> @brief Populates reduced slip-twin interaction matrix
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!> @brief Populates reduced twin-slip interaction matrix
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!> ToDo: prefix "2" needed as long as deprecated array lattice_interactionTwinTwin exists
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!--------------------------------------------------------------------------------------------------
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function lattice_interactionTwinSlip2(Ntwin,Nslip,interactionValues,structure)
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