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thermal expansion coefficient alpha = a + b(T-T_0) + c(T-T_0)^2

This commit is contained in:
Philip Eisenlohr 2018-02-25 14:14:03 -05:00
parent a901a81ba8
commit bc998846ab
2 changed files with 45 additions and 25 deletions
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21
src/kinematics_thermal_expansion.f90
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@ -174,8 +174,12 @@ pure function kinematics_thermal_expansion_initialStrain(ipc, ip, el)
offset = thermalMapping(homog)%p(ip,el)
kinematics_thermal_expansion_initialStrain = &
(temperature(homog)%p(offset) - lattice_referenceTemperature(phase)) * &
lattice_thermalExpansion33(1:3,1:3,phase)
(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**1 / 1. * &
lattice_thermalExpansion33(1:3,1:3,1,phase) + & ! constant coefficient
(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**2 / 2. * &
lattice_thermalExpansion33(1:3,1:3,2,phase) + & ! linear coefficient
(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**3 / 3. * &
lattice_thermalExpansion33(1:3,1:3,3,phase) ! quadratic coefficient
end function kinematics_thermal_expansion_initialStrain
@ -215,9 +219,16 @@ subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar3333, ipc,
TDot = temperatureRate(homog)%p(offset)
TRef = lattice_referenceTemperature(phase)
Li = TDot* &
lattice_thermalExpansion33(1:3,1:3,phase)/ &
(1.0_pReal + lattice_thermalExpansion33(1:3,1:3,phase)*(T - TRef))
Li = TDot * ( &
lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**0 & ! constant coefficient
+ lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**1 & ! linear coefficient
+ lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**2 & ! quadratic coefficient
) / &
(1.0_pReal \
+ lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**1 / 1. &
+ lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**2 / 2. &
+ lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**3 / 3. &
)
dLi_dTstar3333 = 0.0_pReal
end subroutine kinematics_thermal_expansion_LiAndItsTangent

23
src/lattice.f90
View File

@ -1082,9 +1082,10 @@ module lattice
lattice_nu, &
lattice_trans_mu, &
lattice_trans_nu
real(pReal), dimension(:,:,:,:), allocatable, public, protected :: & ! with higher-order parameters (e.g. temperature-dependent)
lattice_thermalExpansion33
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_thermalConductivity33, &
lattice_thermalExpansion33, &
lattice_damageDiffusion33, &
lattice_vacancyfluxDiffusion33, &
lattice_vacancyfluxMobility33, &
@ -1380,8 +1381,8 @@ subroutine lattice_init
allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal)
allocate(lattice_trans_C66(6,6,Nphases), source=0.0_pReal)
allocate(lattice_trans_C3333(3,3,3,3,Nphases), source=0.0_pReal)
allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients
allocate(lattice_thermalConductivity33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_thermalExpansion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_damageDiffusion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_vacancyfluxDiffusion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_vacancyfluxMobility33 (3,3,Nphases), source=0.0_pReal)
@ -1545,11 +1546,17 @@ subroutine lattice_init
case ('thermal_conductivity33')
lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_expansion11')
lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(1,1,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('thermal_expansion22')
lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(2,2,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('thermal_expansion33')
lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(3,3,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('specific_heat')
lattice_specificHeat(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyformationenergy')
@ -1756,10 +1763,12 @@ subroutine lattice_initializeStructure(myPhase,CoverA,CoverA_trans,a_fcc,a_bcc)
end select
end select
forall (i = 1_pInt:3_pInt) &
lattice_thermalExpansion33 (1:3,1:3,i,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalExpansion33 (1:3,1:3,i,myPhase))
lattice_thermalConductivity33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalConductivity33 (1:3,1:3,myPhase))
lattice_thermalExpansion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalExpansion33(1:3,1:3,myPhase))
lattice_DamageDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_DamageDiffusion33 (1:3,1:3,myPhase))
lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&