PyCQuadraticFitIrradiationEigenstrain

Computes irradiation-induced dimensional changes for PyC from a quadratic fit of PyC swelling data for BAF=1.036 at 600 and 1050 C.

Description

A second set of strain rates were used in Collin (2014) to compute irradiation-induced dimensional changes of the PyC layers. The strain rates are obtained at a given temperature by extrapolation between the following radial ( $var element = document.getElementById("moose-equation-94620162-6ef6-4aed-9fb3-deac696600df");katex.render("\\dot{\\varepsilon_r}", element, {displayMode:false,throwOnError:false});$ ) and tangential ( $var element = document.getElementById("moose-equation-9c2a79f0-7c46-48f8-9a6a-73e1a4b8e2e3");katex.render("\\dot{\\varepsilon_t}", element, {displayMode:false,throwOnError:false});$ ) strain rates:

$var element = document.getElementById("moose-equation-9a74d394-dd69-4c95-bdf3-5b0984d7a8b4");katex.render(" \\dot{\\varepsilon_r} = \\frac{1}{100} \\left(-1.044 + 0.306\\phi \\right) \\quad \\textrm{at} \\quad \\textrm{600\\degree{C}}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-8df51853-b96f-445d-8509-dccc82d6c55b");katex.render(" \\dot{\\varepsilon_r} = \\frac{1}{100} \\left(-1.145 + 0.560\\phi\\right) \\quad \\textrm{at} \\quad \\textrm{1050\\degree{C}}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-749739f1-1c89-4a31-bf88-c581bf8b8a09");katex.render(" \\dot{\\varepsilon_t} = \\frac{1}{100} \\left(-1.276 + 0.282\\phi \\right) \\quad \\textrm{at} \\quad \\textrm{600\\degree{C}}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-7fa21736-ef92-413f-a728-ab72333a9cad");katex.render(" \\dot{\\varepsilon_t} = \\frac{1}{100} \\left(-1.493 + 0.278\\phi\\right) \\quad \\textrm{at} \\quad \\textrm{1050\\degree{C}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-717edc86-64da-4a28-8995-4361ef716d3d");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ (10 $var element = document.getElementById("moose-equation-82008a5b-59f5-4a11-b258-827ce7cb5735");katex.render("^{25}", element, {displayMode:false,throwOnError:false});$ n/m $var element = document.getElementById("moose-equation-8a125910-4135-404e-8c18-95246f4498b5");katex.render("^{2}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-a03bfe9b-2b98-443b-8d12-1a6f6af588d6");katex.render("E>", element, {displayMode:false,throwOnError:false});$ 0.18 MeV) is the fast neutron fluence.

Automatic differentiation is available using ADPyCQuadraticFitIrradiationEigenstrain.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [irradiation_strain]
    type = PyCQuadraticFitIrradiationEigenstrain<<<{"description": "Computes irradiation-induced dimensional changes for PyC from a quadratic fit of PyC swelling data for BAF=1.036 at 600 and 1050 C.", "href": "PyCQuadraticFitIrradiationEigenstrain.html"}>>>
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = IIDC_strain
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
  []
[]

Input Parameters

eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
flux_conversion_factorConvert fast neutron flux E>0.10 to E>0.18 MeV
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Convert fast neutron flux E>0.10 to E>0.18 MeV
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
disp_ppX0The reporting postprocessor for particle displacement x-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement x-axis
disp_ppY0The reporting postprocessor for particle displacement y-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement y-axis
disp_ppZ0The reporting postprocessor for particle displacement z-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement z-axis
fast_neutron_fluencefast_neutron_fluenceCoupled fast (E>0.10 MeV) neutron fluence (n/m^2)
Default:fast_neutron_fluence
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Coupled fast (E>0.10 MeV) neutron fluence (n/m^2)
particle_center0 0 0Center of particle
Default:0 0 0
C++ Type:libMesh::Point
Controllable:No
Description:Center of particle

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

irradiation_eigenstrain_scale_factor1Scale factor for PyC IIDC
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scale factor for PyC IIDC

Advanced: Scaling Factors Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/triso/pyc_eigenstrains/irradiation_strain/ad_test_quadratic_fit.i)
(test/tests/triso/pyc_eigenstrains/irradiation_strain/test_quadratic_fit.i)

References

Blaise P. Collin. Modeling and analysis of UN TRISO fuel for LWR application using the PARFUME code. Journal of Nuclear Materials, 451(1):65–77, 2014. URL: https://www.sciencedirect.com/science/article/pii/S0022311514001573, doi:https://doi.org/10.1016/j.jnucmat.2014.03.032.

@article{Collin2014UN,
    author = "Collin, Blaise P.",
    title = "Modeling and analysis of {UN TRISO} fuel for {LWR} application using the {PARFUME} code",
    journal = "Journal of Nuclear Materials",
    volume = "451",
    number = "1",
    pages = "65-77",
    year = "2014",
    issn = "0022-3115",
    doi = "https://doi.org/10.1016/j.jnucmat.2014.03.032",
    url = "https://www.sciencedirect.com/science/article/pii/S0022311514001573"
}

(test/tests/triso/pyc_eigenstrains/irradiation_strain/test_quadratic_fit.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
  execute_on = 'initial timestep_end'
  particle_center = '0 0 0'
  flux_conversion_factor = 0.85
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.499
    xmax = 0.500
    ymin = -0.001
    ymax = 0.001
    zmin = -0.001
    zmax = 0.001
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 1373.15
  []
[]

[Functions]
  [fluence_function]
    type = PiecewiseLinear
    x = '0    1e2    1e6'
    y = '0 1.5e23 7.5e25'
  []
  [BAF_function]
    type = PiecewiseLinear
    x = '   0    1e4'
    y = '1.05  1.182'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [perm_PyC]
    strain = FINITE
    eigenstrain_names = 'IIDC_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
  []
[]

[BCs]
  [no_z_all]
    type = DirichletBC
    variable = disp_z
    boundary = 'front'
    value = 0
  []
  [no_y_all]
    type = DirichletBC
    variable = disp_y
    boundary = 'top'
    value = 0
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  []
[]

[Materials]
 [fluence]
   type = GenericFunctionMaterial
   prop_values = fluence_function
   prop_names = fast_neutron_fluence
 []
 [BAF]
   type = GenericFunctionMaterial
   prop_values = BAF_function
   prop_names = BAF
 []
 [normal_vectors_triso]
   type = NormalVectorsTRISO
 []
 [irradiation_strain]
   type = PyCQuadraticFitIrradiationEigenstrain
   eigenstrain_name = IIDC_strain
   temperature = temperature
 []
 [thermal_expansion]
   type = ComputeThermalExpansionEigenstrain
   temperature = temperature
   thermal_expansion_coeff = 10e-6
   stress_free_temperature = 300.0
   eigenstrain_name = thermal_eigenstrain
 []
 [stress]
   type = ComputeFiniteStrainElasticStress
 []
 [elasticity_tensor]
   type = ComputeIsotropicElasticityTensor
   youngs_modulus = 1e6
   poissons_ratio = 0.3
 []
 [thermal]
   type = GenericConstantMaterial
   # The recommended property values for PyC. See TRISO documentation page
   prop_names = 'density specific_heat thermal_conductivity'
   prop_values = '1900.0 720.0 4.0'
 []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'
  l_max_its = 50
  l_tol = 1e-2
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  start_time = 0.0
  end_time = 1e4
  num_steps = 140
  dt = 1e2
[]

[Postprocessors]
 [temperature]
   type = ElementExtremeValue
   value_type = 'max'
   variable = temperature
 []
 [disp_x_max]
   type = NodalExtremeValue
   boundary = 'left'
   value_type = 'max'
   variable = disp_x
 []
 [disp_y_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_y
 []
 [disp_z_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_z
 []
 [radial_IIDC_strain]
   type = ElementAverageMaterialProperty
   mat_prop = radial_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [tangential_IIDC_strain]
   type = ElementAverageMaterialProperty
   mat_prop = tangential_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [fast_neutron_fluence]
   type = ElementAverageMaterialProperty
   mat_prop = fast_neutron_fluence
   execute_on = 'initial timestep_end'
 []
[]

[Outputs]
  csv = true
[]

(test/tests/triso/pyc_eigenstrains/irradiation_strain/ad_test_quadratic_fit.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
  execute_on = 'initial timestep_end'
  particle_center = '0 0 0'
  flux_conversion_factor = 0.85
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.499
    xmax = 0.500
    ymin = -0.001
    ymax = 0.001
    zmin = -0.001
    zmax = 0.001
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 1373.15
  []
[]

[Functions]
  [fluence_function]
    type = PiecewiseLinear
    x = '0    1e2    1e6'
    y = '0 1.5e23 7.5e25'
  []
  [BAF_function]
    type = PiecewiseLinear
    x = '   0    1e4'
    y = '1.05  1.182'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [perm_PyC]
    strain = FINITE
    add_variables = true
    eigenstrain_names = 'IIDC_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    use_automatic_differentiation = true
  []
[]

[BCs]
  [no_z_all]
    type = ADDirichletBC
    variable = disp_z
    boundary = 'front'
    value = 0
  []
  [no_y_all]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'top'
    value = 0
  []
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  []
[]

[Materials]
 [fluence]
   type = ADGenericFunctionMaterial
   prop_values = fluence_function
   prop_names = fast_neutron_fluence
 []
 [BAF]
   type = ADGenericFunctionMaterial
   prop_values = BAF_function
   prop_names = BAF
 []
 [normal_vectors_triso]
   type = NormalVectorsTRISO
 []
 [irradiation_strain]
   type = ADPyCQuadraticFitIrradiationEigenstrain
   eigenstrain_name = IIDC_strain
   temperature = temperature
 []
 [thermal_expansion]
   type = ADComputeThermalExpansionEigenstrain
   temperature = temperature
   thermal_expansion_coeff = 10e-6
   stress_free_temperature = 300.0
   eigenstrain_name = thermal_eigenstrain
 []
 [stress]
   type = ADComputeFiniteStrainElasticStress
 []
 [elasticity_tensor]
   type = ADComputeIsotropicElasticityTensor
   youngs_modulus = 1e6
   poissons_ratio = 0.3
 []
 [thermal]
   type = ADGenericConstantMaterial
   # The recommended property values for PyC. See TRISO documentation page
   prop_names = 'density specific_heat thermal_conductivity'
   prop_values = '1900.0 720.0 4.0'
 []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'
  l_max_its = 50
  l_tol = 1e-2
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  start_time = 0.0
  end_time = 1e4
  num_steps = 140
  dt = 1e2
[]

[Postprocessors]
 [temperature]
   type = ElementExtremeValue
   value_type = 'max'
   variable = temperature
 []
 [disp_x_max]
   type = NodalExtremeValue
   boundary = 'left'
   value_type = 'max'
   variable = disp_x
 []
 [disp_y_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_y
 []
 [disp_z_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_z
 []
 [radial_IIDC_strain]
   type = ADElementAverageMaterialProperty
   mat_prop = radial_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [tangential_IIDC_strain]
   type = ADElementAverageMaterialProperty
   mat_prop = tangential_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [fast_neutron_fluence]
   type = ADElementAverageMaterialProperty
   mat_prop = fast_neutron_fluence
   execute_on = 'initial timestep_end'
 []
[]

[Outputs]
  csv = true
[]

(test/tests/triso/pyc_eigenstrains/irradiation_strain/test_quadratic_fit.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
  execute_on = 'initial timestep_end'
  particle_center = '0 0 0'
  flux_conversion_factor = 0.85
[]

[Mesh]
  [cube]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.499
    xmax = 0.500
    ymin = -0.001
    ymax = 0.001
    zmin = -0.001
    zmax = 0.001
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 1373.15
  []
[]

[Functions]
  [fluence_function]
    type = PiecewiseLinear
    x = '0    1e2    1e6'
    y = '0 1.5e23 7.5e25'
  []
  [BAF_function]
    type = PiecewiseLinear
    x = '   0    1e4'
    y = '1.05  1.182'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [perm_PyC]
    strain = FINITE
    eigenstrain_names = 'IIDC_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
  []
[]

[BCs]
  [no_z_all]
    type = DirichletBC
    variable = disp_z
    boundary = 'front'
    value = 0
  []
  [no_y_all]
    type = DirichletBC
    variable = disp_y
    boundary = 'top'
    value = 0
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  []
[]

[Materials]
 [fluence]
   type = GenericFunctionMaterial
   prop_values = fluence_function
   prop_names = fast_neutron_fluence
 []
 [BAF]
   type = GenericFunctionMaterial
   prop_values = BAF_function
   prop_names = BAF
 []
 [normal_vectors_triso]
   type = NormalVectorsTRISO
 []
 [irradiation_strain]
   type = PyCQuadraticFitIrradiationEigenstrain
   eigenstrain_name = IIDC_strain
   temperature = temperature
 []
 [thermal_expansion]
   type = ComputeThermalExpansionEigenstrain
   temperature = temperature
   thermal_expansion_coeff = 10e-6
   stress_free_temperature = 300.0
   eigenstrain_name = thermal_eigenstrain
 []
 [stress]
   type = ComputeFiniteStrainElasticStress
 []
 [elasticity_tensor]
   type = ComputeIsotropicElasticityTensor
   youngs_modulus = 1e6
   poissons_ratio = 0.3
 []
 [thermal]
   type = GenericConstantMaterial
   # The recommended property values for PyC. See TRISO documentation page
   prop_names = 'density specific_heat thermal_conductivity'
   prop_values = '1900.0 720.0 4.0'
 []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'
  l_max_its = 50
  l_tol = 1e-2
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  start_time = 0.0
  end_time = 1e4
  num_steps = 140
  dt = 1e2
[]

[Postprocessors]
 [temperature]
   type = ElementExtremeValue
   value_type = 'max'
   variable = temperature
 []
 [disp_x_max]
   type = NodalExtremeValue
   boundary = 'left'
   value_type = 'max'
   variable = disp_x
 []
 [disp_y_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_y
 []
 [disp_z_max]
   type = NodalExtremeValue
   value_type = 'max'
   variable = disp_z
 []
 [radial_IIDC_strain]
   type = ElementAverageMaterialProperty
   mat_prop = radial_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [tangential_IIDC_strain]
   type = ElementAverageMaterialProperty
   mat_prop = tangential_IIDC_strain
   execute_on = 'initial timestep_end'
 []
 [fast_neutron_fluence]
   type = ElementAverageMaterialProperty
   mat_prop = fast_neutron_fluence
   execute_on = 'initial timestep_end'
 []
[]

[Outputs]
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References