U10MoThermalExpansionEigenstrain

Computes eigenstrain due to thermal expansion in U-10Mo

Description

U10MoThermalExpansionEigenstrain computes the the thermal expansion behavior of U-10Mo alloys. Bison offers seven modeling options:

  1. The Rest option is taken from Rest et al. (2006) for the computation of coefficient of thermal expansion (CTE), is the CTE (K):

(1) where is the temperature (K). This correlation is considered valid in the temperature range 298–873 K.

commentnote:Mean or instantaneous CTE

Rest et al. (2006) used both mean and instantaneous measured data for the CTE to develop Eq. (1). There is no clear definition whether this model is developed for mean or instantaneous CTE. It's assumed that the model represents the mean CTE based on the discussion in Rabin et al. (2020).

  1. The Burkes option is one of the recommended models in Rabin et al. (2020). The data points for the mean CTE of unirradiated U-10Mo are tabulated in Table 1. The actual data points are reported by Burkes et al. (2010) in the temperature range 200–800C.

  2. The BurkesFit option is a model for the best-fit line to the data reported by Burkes et al. (2010) in Table 1. The mean CTE of unirradiated U-10Mo, is

where is the temperature (C). This model is considered valid in the temperature range 200–800C.

  1. The Saller option is from Rabin et al. (2020). The data points for the mean CTE of unirradiated U-10Mo are tabulated in Table 1. The actual data points are reported by Saller et al. (1956) in the temperature range 200–600C.

  2. The BurkesSallerAvg option is from Rabin et al. (2020). The data points for the mean CTE of unirradiated U-10Mo are tabulated in Table 1 as an average of data reported by Burkes et al. (2010) and Saller et al. (1956).

Table 1: Mean CTE of unirradiated U-10Mo, the actual data points are reported by Burkes et al. (2010) and Saller et al. (1956). Here, the room temperature is 21C.

Temperature (C)Burkes, CTE (1/C)Saller, CTE (1/C)Average, CTE (1/C)
21–10011.811.511.7
21–20012.611.812.4
21–30014.112.413.7
21–40016.112.715.2
21–50016.413.015.6
21–60016.613.515.8
21–70016.7—16.7
21–80017.2—17.2

  1. The Beghi option is a model for the best-line to the data reported by Konobeevsky (1958) and Saller et al. (1956). The mean CTE of U-10Mo, is given by Beghi (1968) as:

where is the temperature (C). This correlation is considered valid in the temperature range 20–500C.

  1. The McGeary option is based on the average CTE reported by Bostrom et al. (1955) for U-10Mo alloys. This correlation is considered valid in the temperature range 100–400C.

Figure 1 compares the Bison predictions using aforementioned seven models from a regression test (test/tests/solid_mechanics/u10mo_eigenstrains/thermal_expansion/test.i). In this test, a single (1x1x1) block is exposed to a time varying temperature ramped from 300 K to 1200 K over 1 s in ten time steps. Since the block is only loaded thermally, the thermal strain corresponds to the total strain.

Figure 1: In this test, a single (1x1x1) block is exposed to a time varying temperature ramped from 300 K to 1200 K over 1 s in ten time steps. Since the block is only loaded thermally, the thermal strain corresponds to the total strain.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [thermal_eigenstrain]
    type = U10MoThermalExpansionEigenstrain<<<{"description": "Computes eigenstrain due to thermal expansion in U-10Mo", "href": "U10MoThermalExpansionEigenstrain.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    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."}>>> = thermal_eigenstrain
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 298
    model_option<<<{"description": "The modeling options for the compuation of U-10Mo thermal expansion eigenstrain are: Rest Burkes BurkesFit Saller BurkesSallerAvg Beghi McGeary"}>>> = Rest
  []
[]
(test/tests/solid_mechanics/u10mo_eigenstrains/thermal_expansion/test.i)

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.

  • stress_free_temperatureReference temperature at which there is no thermal expansion for thermal eigenstrain calculation

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation

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.

  • mean_thermal_expansion_coefficient_nameName of the mean coefficient of thermal expansion.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the mean coefficient of thermal expansion.

  • model_optionRestThe modeling options for the compuation of U-10Mo thermal expansion eigenstrain are: Rest Burkes BurkesFit Saller BurkesSallerAvg Beghi McGeary

    Default:Rest

    C++ Type:MooseEnum

    Options:Rest, Burkes, BurkesFit, Saller, BurkesSallerAvg, Beghi, McGeary

    Controllable:No

    Description:The modeling options for the compuation of U-10Mo thermal expansion eigenstrain are: Rest Burkes BurkesFit Saller BurkesSallerAvg Beghi McGeary

  • temperatureCoupled temperature

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Coupled temperature

  • use_old_temperatureFalseFlag to optionally use the temperature value from the previous timestep.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Flag to optionally use the temperature value from the previous timestep.

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

  • thermal_expansion_scale_factor1Scalar multiplier to apply to thermal expansion. Used for sensitivity studies and debugging.

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Scalar multiplier to apply to thermal expansion. Used for sensitivity studies and debugging.

  • 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

References

  1. G. Beghi. Gamma phase uranium-molybdenum fuel alloys. Technical Report EUR-4053e, European Atomic Energy Community - EURATOM, Brussels, 1968.[BibTeX]
  2. W. A. Bostrom, M. W. Burkart, E. K. Halteman, R. D. Leggett, R. K. McGeary, and T. R. Padden. Development and properties of uranium-base alloys corrosion resistant in high-temperature water, part i., alloys without protective cladding. Technical Report WAPD-127, Westinghouse Electric Corp. Atomic Power Div., Pittsburgh, 1955. doi:10.2172/4339248.[BibTeX]
  3. D. E. Burkes, G. S. Mickum, and D. M. Wachs. Thermophysical properties of U-10Mo alloy. Technical Report INL/EXT-10-19373, Idaho National Laboratory, Idaho Falls, ID (United States), 10 2010.[BibTeX]
  4. S. T. Konobeevsky. Some physical properties of uranium, plutonium, and their alloys. In Proceedings of the 2nd UN International Conference on the Peaceful Uses of Atomic Energy, number P/2230. 1958.[BibTeX]
  5. B. Rabin, M. Meyer, J. Cole, I. Glagolenko, W. Jones, J-F. Jue, D. Keiser Jr, C. Miller, G. Moore, H. Ozaltun, F. Rice, A. Robinson, J. Smith, D. Wachs, W. Williams, N. Woolstenhulme, G. Hofman, and Y. Kim. Preliminary report on U-Mo monolithic fuel for research reactors. Technical Report INL EXT-17-40975, Idaho National Laboratory, 4 2020.[BibTeX]
  6. J. Rest, Y. S. Kim, G. L. Hofman, M. K. Meyer, and S. L. Hayes. U-Mo Fuels Handbook Version 1.0. Technical Report ANL-09/31, Argonne National Laboratory, Argonne, Illinois, June 2006. doi:10.2172/1335129.[BibTeX]
  7. H. A. Saller, R. F. Dickerson, and W. E. Murr. Uranium alloys for high temperature application. Technical Report BMI-1098, Battelle Memorial Institute, Columbus, Ohio, 6 1956. URL: https://www.osti.gov/servlets/purl/4330099, doi:10.2172/4330099.[BibTeX]