# UPuZr Elasticity Tensor

Calculates the Young's modulus and Poisson's ratio for UPuZr fuel based on supplied fractions of Pu and Zr

## Description

Due to the redistribution of zirconium in the fuel, and the need to model both U-Zr and U-Pu-Zr fuel, correlations included in UPuZrElasticityTensor must be applicable to any concentration of plutonium or zirconium. Unfortunately, the available models for the elastic properties of U-Pu-Zr alloys are generally incomplete. Regardless, some correlations can be made given the sparse data, as described in IFR Property Evaluation Working Group (1988).

The correlation for Young's modulus can be derived using data from U-11Pu-6.3Zr cast fuel pins as: (1) where = 1.6 10 MPa is the Young's modulus for pure U at the reference temperature of 588 K, is the fractional porosity, is the zirconium weight fraction, is the plutonium weight fraction, is the temperature in K, and = 1405 K is the melting temperature of pure uranium. is the Young's modulus degradation factor due to porosity, and is typically 1.2.

The correlation for Poisson's ratio can be derived from the U-Zr correlation as: (2) where =0.24 is the Poisson's ratio of pure U at the reference temperature of 588 K. is the Poissons' ratio degradation factor due to porosity, and is typically 0.8.

## Example Input Syntax

[./elasticity_tensor]
type = UPuZrElasticityTensor
block = 0
temperature = temp
X_Pu = X_Pu
X_Zr = X_Zr
porosity = porosity
[../]
(test/tests/tensor_mechanics/upuzr_elasticity_tensor/upuzr_calc_moduli.i)

## Input Parameters

• temperatureCoupled temperature

C++ Type:std::vector

Description:Coupled temperature

### Required Parameters

• A_U0.238029Atomic weight of uranium [kg/mol]

Default:0.238029

C++ Type:double

Description:Atomic weight of uranium [kg/mol]

• 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.

• elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.

C++ Type:FunctionName

Description:Optional function to use as a scalar prefactor on the elasticity tensor.

• 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

• X_ZrCoupled zirconium atom fraction

C++ Type:std::vector

Description:Coupled zirconium atom fraction

• youngs_degredation_factor1.2Degredation factor for Youngs Modulus due to porosity. Degredation is calculed by (1 - factor * porosity) * E

Default:1.2

C++ Type:double

Description:Degredation factor for Youngs Modulus due to porosity. Degredation is calculed by (1 - factor * porosity) * E

• X_PuCoupled plutonium atom fraction

C++ Type:std::vector

Description:Coupled plutonium atom fraction

• save_moduliFalseFlag to save Young's modulus and Poisson's ratio to a material property

Default:False

C++ Type:bool

Description:Flag to save Young's modulus and Poisson's ratio to a material property

• porosity0Porosity material property name

Default:0

C++ Type:MaterialPropertyName

Description:Porosity material property name

• 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

• poissons_degredation_factor0.8Degrediation factor for Poissons ratio. Degredation is calculaed by (1 - factor * porosity) * nu

Default:0.8

C++ Type:double

Description:Degrediation factor for Poissons ratio. Degredation is calculaed by (1 - factor * porosity) * nu

• A_Zr0.091224Atomic weight of zirconium [kg/mol]

Default:0.091224

C++ Type:double

Description:Atomic weight of zirconium [kg/mol]

• A_Pu0.244Atomic weight of plutonium [kg/mol]

Default:0.244

C++ Type:double

Description:Atomic weight of plutonium [kg/mol]

• 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

### 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. Compiled by: IFR Property Evaluation Working Group. Metallic fuels handbook. Argonne National Laboratory, June 1988.[BibTeX]