UO2TensileStrength

Computes the tensile strength of UO2 as a function of grain size, pore size, and porosity.

Description

The UO2TensileStrength material computes the evolving tensile strength of UO $var element = document.getElementById("moose-equation-3967c4ee-2086-416a-b9e3-163baae37c79");katex.render("_2", element, {displayMode:false,throwOnError:false});$ fuel as a function of grain_size, pore_size, and porosity. The fracture stress, $var element = document.getElementById("moose-equation-e7eda5dc-ec19-4c14-bcaa-e64bf51e835f");katex.render("\\sigma_{TS}", element, {displayMode:false,throwOnError:false});$ (MPa) of UO $var element = document.getElementById("moose-equation-5845ebb5-77a8-4f94-9704-d2c9193bc872");katex.render("_2", element, {displayMode:false,throwOnError:false});$ is given by Oguma (1982) as:

$(1)var element = document.getElementById("moose-equation-c993bd36-2f4c-4b9d-b8a1-13b103ade741");katex.render(" \\sigma_{TS}= 626.0 \\exp{\\left(\u22120.057p \\right)} \\left(0.5G + P\\right)^{-0.5}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-73e34784-bbb2-4567-a8e0-4278e50af5f6");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the porosity of the fuel (%), $var element = document.getElementById("moose-equation-0d13b649-e184-43df-86e7-04b8aee1fa4a");katex.render("G", element, {displayMode:false,throwOnError:false});$ is the average grain size ( $var element = document.getElementById("moose-equation-6190058b-4b45-41a7-8104-1e1aa89bf261");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m), and $var element = document.getElementById("moose-equation-ce1be27b-4d54-4984-ab6f-bdf5c60b6fed");katex.render("P", element, {displayMode:false,throwOnError:false});$ is the fabrication pore size ( $var element = document.getElementById("moose-equation-87dd5d90-d2b2-4962-86f9-890f6fce1ee3");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m). The fabrication pore size corresponds to the largest pore size.

According to Oguma (1982), Eq. (1) predicts the UO $var element = document.getElementById("moose-equation-94a022e7-f1b3-455a-86cd-59338a08ca3a");katex.render("_2", element, {displayMode:false,throwOnError:false});$ pellet strength within the approximate ranges of a porosity, $var element = document.getElementById("moose-equation-b5a422ab-8d11-4323-bbfe-1a4b47816024");katex.render("p", element, {displayMode:false,throwOnError:false});$ of 10%, the largest pore size, $var element = document.getElementById("moose-equation-3963b2fc-64a8-4b7e-a992-59fc17055dd9");katex.render("P", element, {displayMode:false,throwOnError:false});$ of 100 $var element = document.getElementById("moose-equation-6073f3d1-4c8c-4f32-be89-8a13aaad8820");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m, and the average grain size, $var element = document.getElementById("moose-equation-12a85e1f-9a30-4c44-bf67-92a81bb540ce");katex.render("G", element, {displayMode:false,throwOnError:false});$ of 80 $var element = document.getElementById("moose-equation-d02507a7-c9d0-4712-a269-d94aea0ea166");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m, to within errors of $var element = document.getElementById("moose-equation-35b112f5-6c64-4d3c-b090-6686981d4c02");katex.render("\\pm", element, {displayMode:false,throwOnError:false});$ 10%.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [uo2_tensile_strength]
    type = UO2TensileStrength<<<{"description": "Computes the tensile strength of UO2 as a function of grain size, pore size, and porosity.", "href": "UO2TensileStrength.html"}>>>
    average_grain_radius<<<{"description": "The postprocessor that holds the mean grain radius of the fuel."}>>> = average_grain_radius
    initial_grain_radius<<<{"description": " The initial grain radius in the fuel (m)."}>>> = 5.0e-6
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
  []
[]

Input Parameters

average_grain_radiusThe postprocessor that holds the mean grain radius of the fuel.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The postprocessor that holds the mean grain radius of the fuel.
initial_grain_radius The initial grain radius in the fuel (m).
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description: The initial grain radius in the fuel (m).

Required Parameters

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.
fabrication_pore_size4e-06The fabrication pore size of the fuel (m).
Default:4e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The fabrication pore size of the fuel (m).

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

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/solid_mechanics/uo2_tensile_strength/ad_uo2_tensile_strength.i)
(test/tests/solid_mechanics/uo2_tensile_strength/uo2_tensile_strength.i)

References

M. Oguma. Microstructure effects on fracture strength of uo2 fuel pellets. Journal of Nuclear Science and Technology, 19(12):1005–1014, 1982. doi:10.1080/18811248.1982.9734249.

@article{OGUMA19821005,
    author = "Oguma, M.",
    title = "Microstructure Effects on Fracture Strength of UO2 Fuel Pellets",
    journal = "Journal of Nuclear Science and Technology",
    volume = "19",
    number = "12",
    pages = "1005-1014",
    year = "1982",
    publisher = "Taylor \& Francis",
    doi = "10.1080/18811248.1982.9734249"
}

(test/tests/solid_mechanics/uo2_tensile_strength/uo2_tensile_strength.i)

# This test confirms the calculation of the fabrication pore size, grain size,
# and porosity dependent tensile strength model for UO2.
# The correlation given by Oguma (1982) as:
#
# sigma_{TS} = 626.0 exp(-0.057p)(0.5G + P)^(-0.5)
#
# where p is the porosity of the fuel (%), G is the grain size (microns), and P
# is the fabrication pore size (microns).
#
# In this test the grain size is evolved using the GrainRadiusAux model which is
# tested elsewhere. The grain size is 2 times the calculated grain radius. Here,
# the grain radius increases as the temperature increases. The temperature is
# linearly increase from 500 K to 2000 K over the simulation duration of 1e6 seconds.
# Similarly, the porosity is linearly increased from 5% to 10% over the duration
# of the simulation. The fabrication pore size is assumed to be the default of
# 4 microns. The calculated tensile strength as at each of the 20 timesteps is
# compared to what the hand calculated tensile strength using Oguma's correlation.
#
#
# average_grain_radius  porosity  temperature         tensile_strength (MPa)
#         (m)             (-)        (K)              BISON        Analytical
#       5.00E-06          0.05       500             156.920        156.920
#       5.00E-06          0.0525     575             154.700        154.700
#       5.00E-06          0.055      650             152.511        152.511
#       5.00E-06          0.0575     725             150.353        150.353
#       5.00E-06          0.06       800             148.226        148.226
#       5.00E-06          0.0625     875             146.129        146.129
#       5.00E-06          0.065      950             144.061        144.061
#       5.00E-06          0.0675    1025             142.023        142.023
#       5.00E-06          0.07      1100             140.013        140.013
#       5.00E-06          0.0725    1175             138.032        138.032
#       5.00E-06          0.075     1250             136.079        136.079
#       5.00E-06          0.0775    1325             134.152        134.152
#       5.00E-06          0.08      1400             132.230        132.230
#       5.02E-06          0.0825    1475             130.248        130.248
#       5.07E-06          0.085     1550             128.025        128.025
#       5.23E-06          0.0875    1625             125.144        125.144
#       5.62E-06          0.09      1700             120.855        120.855
#       6.45E-06          0.0925    1775             114.283        114.283
#       7.98E-06          0.095     1850             105.223        105.223
#       1.04E-05          0.0975    1925              94.702         94.702
#       1.37E-05          0.1       2000              84.169         84.169

[Mesh]
  [line]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Functions]
  [porosity_function]
    type = ParsedFunction
    expression = '0.05 * (1 + t/1e6)'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '500 2000'
  []
[]

[Variables]
  [temperature]
    initial_condition = 500.0
  []
[]

[AuxVariables]
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [grain_radius]
    type = GrainRadiusAux
    variable = grain_radius
    temperature = temperature
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = FunctionDirichletBC
    variable = temperature
    function = temperature_function
    boundary = 'left right'
  []
[]

[Materials]
  [porosity]
    type = GenericFunctionMaterial
    block = 0
    prop_names = 'porosity'
    prop_values = 'porosity_function'
  []
  [uo2_tensile_strength]
    type = UO2TensileStrength
    average_grain_radius = average_grain_radius
    initial_grain_radius = 5.0e-6
    block = 0
  []
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  nl_abs_tol = 1.0e-8
  nl_rel_tol = 1.0e-8
  start_time = 0
  dt = 5e4
  end_time = 1e6
[]

[Postprocessors]
  [average_grain_radius]
    type = ElementAverageValue
    block = 0
    variable = grain_radius
    execute_on = 'initial linear'
  []
  [porosity]
    type = FunctionValuePostprocessor
    function = porosity_function
    execute_on = 'initial linear'
  []
  [tensile_strength]
    type = ElementAverageMaterialProperty
    block = 0
    mat_prop = tensile_strength
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    block = 0
    variable = temperature
    execute_on = 'initial linear'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/uo2_tensile_strength/ad_uo2_tensile_strength.i)

# This test confirms the calculation of the fabrication pore size, grain size,
# and porosity dependent tensile strength model for UO2 using automatic
# differentiation.
# The correlation given by Oguma (1982) as:
#
# sigma_{TS} = 626.0 exp(-0.057p)(0.5G + P)^(-0.5)
#
# where p is the porosity of the fuel (%), G is the grain size (microns), and P
# is the fabrication pore size (microns).
#
# In this test the grain size is evolved using the GrainRadiusAux model which is
# tested elsewhere. The grain size is 2 times the calculated grain radius. Here,
# the grain radius increases as the temperature increases. The temperature is
# linearly increase from 500 K to 2000 K over the simulation duration of 1e6 seconds.
# Similarly, the porosity is linearly increased from 5% to 10% over the duration
# of the simulation. The fabrication pore size is assumed to be the default of
# 4 microns. The calculated tensile strength as at each of the 20 timesteps is
# compared to what the hand calculated tensile strength using Oguma's correlation.
#
#
# average_grain_radius  porosity  temperature         tensile_strength (MPa)
#         (m)             (-)        (K)              BISON        Analytical
#       5.00E-06          0.05       500             156.920        156.920
#       5.00E-06          0.0525     575             154.700        154.700
#       5.00E-06          0.055      650             152.511        152.511
#       5.00E-06          0.0575     725             150.353        150.353
#       5.00E-06          0.06       800             148.226        148.226
#       5.00E-06          0.0625     875             146.129        146.129
#       5.00E-06          0.065      950             144.061        144.061
#       5.00E-06          0.0675    1025             142.023        142.023
#       5.00E-06          0.07      1100             140.013        140.013
#       5.00E-06          0.0725    1175             138.032        138.032
#       5.00E-06          0.075     1250             136.079        136.079
#       5.00E-06          0.0775    1325             134.152        134.152
#       5.00E-06          0.08      1400             132.230        132.230
#       5.02E-06          0.0825    1475             130.248        130.248
#       5.07E-06          0.085     1550             128.025        128.025
#       5.23E-06          0.0875    1625             125.144        125.144
#       5.62E-06          0.09      1700             120.855        120.855
#       6.45E-06          0.0925    1775             114.283        114.283
#       7.98E-06          0.095     1850             105.223        105.223
#       1.04E-05          0.0975    1925              94.702         94.702
#       1.37E-05          0.1       2000              84.169         84.169

[Mesh]
  [line]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Functions]
  [porosity_function]
    type = ParsedFunction
    expression = '0.05 * (1 + t/1e6)'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '500 2000'
  []
[]

[Variables]
  [temperature]
    initial_condition = 500.0
  []
[]

[AuxVariables]
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [grain_radius]
    type = GrainRadiusAux
    variable = grain_radius
    temperature = temperature
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = ADFunctionDirichletBC
    variable = temperature
    function = temperature_function
    boundary = 'left right'
  []
[]

[Materials]
  [porosity]
    type = ADGenericFunctionMaterial
    block = 0
    prop_names = 'porosity'
    prop_values = 'porosity_function'
  []
  [uo2_tensile_strength]
    type = ADUO2TensileStrength
    average_grain_radius = average_grain_radius
    initial_grain_radius = 5.0e-6
    block = 0
  []
  [thermal]
    type = ADHeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  nl_abs_tol = 1.0e-8
  nl_rel_tol = 1.0e-8
  start_time = 0
  dt = 5e4
  end_time = 1e6
[]

[Postprocessors]
  [average_grain_radius]
    type = ElementAverageValue
    block = 0
    variable = grain_radius
    execute_on = 'initial linear'
  []
  [porosity]
    type = FunctionValuePostprocessor
    function = porosity_function
    execute_on = 'initial linear'
  []
  [tensile_strength]
    type = ADElementAverageMaterialProperty
    block = 0
    mat_prop = tensile_strength
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    block = 0
    variable = temperature
    execute_on = 'initial linear'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/uo2_tensile_strength/uo2_tensile_strength.i)

# This test confirms the calculation of the fabrication pore size, grain size,
# and porosity dependent tensile strength model for UO2.
# The correlation given by Oguma (1982) as:
#
# sigma_{TS} = 626.0 exp(-0.057p)(0.5G + P)^(-0.5)
#
# where p is the porosity of the fuel (%), G is the grain size (microns), and P
# is the fabrication pore size (microns).
#
# In this test the grain size is evolved using the GrainRadiusAux model which is
# tested elsewhere. The grain size is 2 times the calculated grain radius. Here,
# the grain radius increases as the temperature increases. The temperature is
# linearly increase from 500 K to 2000 K over the simulation duration of 1e6 seconds.
# Similarly, the porosity is linearly increased from 5% to 10% over the duration
# of the simulation. The fabrication pore size is assumed to be the default of
# 4 microns. The calculated tensile strength as at each of the 20 timesteps is
# compared to what the hand calculated tensile strength using Oguma's correlation.
#
#
# average_grain_radius  porosity  temperature         tensile_strength (MPa)
#         (m)             (-)        (K)              BISON        Analytical
#       5.00E-06          0.05       500             156.920        156.920
#       5.00E-06          0.0525     575             154.700        154.700
#       5.00E-06          0.055      650             152.511        152.511
#       5.00E-06          0.0575     725             150.353        150.353
#       5.00E-06          0.06       800             148.226        148.226
#       5.00E-06          0.0625     875             146.129        146.129
#       5.00E-06          0.065      950             144.061        144.061
#       5.00E-06          0.0675    1025             142.023        142.023
#       5.00E-06          0.07      1100             140.013        140.013
#       5.00E-06          0.0725    1175             138.032        138.032
#       5.00E-06          0.075     1250             136.079        136.079
#       5.00E-06          0.0775    1325             134.152        134.152
#       5.00E-06          0.08      1400             132.230        132.230
#       5.02E-06          0.0825    1475             130.248        130.248
#       5.07E-06          0.085     1550             128.025        128.025
#       5.23E-06          0.0875    1625             125.144        125.144
#       5.62E-06          0.09      1700             120.855        120.855
#       6.45E-06          0.0925    1775             114.283        114.283
#       7.98E-06          0.095     1850             105.223        105.223
#       1.04E-05          0.0975    1925              94.702         94.702
#       1.37E-05          0.1       2000              84.169         84.169

[Mesh]
  [line]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Functions]
  [porosity_function]
    type = ParsedFunction
    expression = '0.05 * (1 + t/1e6)'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '500 2000'
  []
[]

[Variables]
  [temperature]
    initial_condition = 500.0
  []
[]

[AuxVariables]
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [grain_radius]
    type = GrainRadiusAux
    variable = grain_radius
    temperature = temperature
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = FunctionDirichletBC
    variable = temperature
    function = temperature_function
    boundary = 'left right'
  []
[]

[Materials]
  [porosity]
    type = GenericFunctionMaterial
    block = 0
    prop_names = 'porosity'
    prop_values = 'porosity_function'
  []
  [uo2_tensile_strength]
    type = UO2TensileStrength
    average_grain_radius = average_grain_radius
    initial_grain_radius = 5.0e-6
    block = 0
  []
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  nl_abs_tol = 1.0e-8
  nl_rel_tol = 1.0e-8
  start_time = 0
  dt = 5e4
  end_time = 1e6
[]

[Postprocessors]
  [average_grain_radius]
    type = ElementAverageValue
    block = 0
    variable = grain_radius
    execute_on = 'initial linear'
  []
  [porosity]
    type = FunctionValuePostprocessor
    function = porosity_function
    execute_on = 'initial linear'
  []
  [tensile_strength]
    type = ElementAverageMaterialProperty
    block = 0
    mat_prop = tensile_strength
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    block = 0
    variable = temperature
    execute_on = 'initial linear'
  []
[]

[Outputs]
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References