# Minor Actinide MOX Fuel Thermal Expansion Eigenstrain

Calculates eigenstrain due to isotropic thermal expansion in MA-MOX fuel using JNM 469 (2016) 223-227 correlations

## Description

MA-MOX, or minor actinide bearing mixed oxide fuel, is modeled in Bison as a function of oxygen to metal ratio in the fuel and of temperature, (Kato et al., 2011). The MA-MOX correlations used in this material model were developed by Kato et al. (2016). It is important to note that the correlation currently implemented in Bison is for Pu. (1) where is the temperature (K) and is the stress free temperature thermal expansion strain. The value of the coefficients ( through ) depend on the Oxygen-to-Metal ratio in the fuel and are given in Table 1.

Table 1: Thermal Expansion Coefficient Values as a Function of Oxygen-to-Metal Ratio

Oxygen to Metal RatioThermal Expansion CoefficientCoefficient Value
2.00-0.002869
9.44e-6
2.90e-10
4.10e-13
-------------------------------------------------------------------------
1.99-0.002915
9.60e-6
2.65e-10
4.20e-13
-------------------------------------------------------------------------
1.98-0.002950
9.72e-6
2.55e-10
4.35e-13
-------------------------------------------------------------------------
1.97-0.002990
9.85e-6
2.50e-10
4.50e-13

## Example Input Syntax


[./thermal_expansion]
type = MAMOXThermalExpansionEigenstrain
temperature = temperature
stress_free_temperature = 300.0
eigenstrain_name = thermal_expansion
[../]
(test/tests/tensor_mechanics/mamox_mechanics/thermal_expansion.i)

The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting in the Tensor Mechanics Master Action is shown below:


[Modules]
[./TensorMechanics]
[./Master]
[./all]
strain = SMALL
incremental = true
eigenstrain_names = 'thermal_expansion'
generate_output = 'strain_yy strain_xx strain_zz'
[../]
[../]
[../]
[]
(test/tests/tensor_mechanics/mamox_mechanics/thermal_expansion.i)

## Input Parameters

• oxygen_to_metal_ratioDeviation from stoichiometry. Options are 2.00, 1.99, 1.98 and 1.97

C++ Type:double

Description:Deviation from stoichiometry. Options are 2.00, 1.99, 1.98 and 1.97

• stress_free_temperatureStress free temperature (does not produce thermal expansion stress) for thermal eigenstrain calculation; set as the initial temperature if value is not specified for the fuel

C++ Type:double

Description:Stress free temperature (does not produce thermal expansion stress) for thermal eigenstrain calculation; set as the initial temperature if value is not specified for the fuel

• temperatureCoupled temperature

C++ Type:std::vector

Description:Coupled temperature

• 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

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.

### Required Parameters

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

• 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

Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• 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

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.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• 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 computeSubdomainProperties() 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

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 computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

## References

1. M. Kato, Y. Ikusawa, T. Sunaoshi, A. Nelson, and K. McClellan. Thermal expansion measurement of $(U,Pu)O_2-x$ in oxygen partial pressure-controlled atmosphere. Journal of Nuclear Materials, 469:223â€“227, 2016.[BibTeX]
2. M. Kato, K. Maeda, T. Ozawa, M. Kashimura, and Y. Kihara. Physical properties and irradiation behavior analysis of Np- and Am-bearing MOX fuels. Journal of Nuclear Science and Technology, 48:646â€“653, 2011.[BibTeX]