# Volumetric Swelling for Uvar element = document.getElementById("moose-equation-9cd6c545-69b8-4d44-a7ad-0344ddba297c");katex.render("_3", element, {displayMode:false,throwOnError:false});Sivar element = document.getElementById("moose-equation-8d70d0dc-0406-4466-b05e-75f19c9998b9");katex.render("_2", element, {displayMode:false,throwOnError:false});

Computes a volumetric strain to account for solid and gaseous swelling and densification in U3Si2 fuel

warning:Deprecated Solid Mechanics Material

The functionality of this solid mechanics material is being replaced in the TensorMechanics system by U3Si2VolumetricSwellingEigenstrain.

## Description

The VSwellingU3Si2 model computes a volumetric strain to account for solid and gaseous swelling and densification in USi fuel.

Since the data for USi is limited, an empirical expression for the swelling of USi was determined using data from figure 3 of M. R. Finlay (2004). The swelling of fuel particles was calculated by Finlay using the results of miniplate irradiation tests. To convert Finlay's data (fission density) to FIMA, a value of 10.735 g/cm was used as the heavy metal density, equivalent to 95% theoretical heavy metal density. Based on Finlay's data the volumetric strain can be written as a function of burnup: (1) where is the volumetric strain at a given burnup Bu. The burnup is in units of FIMA. The quadratic equation for the total volumetric strain is then decoupled into its solid and gaseous components. The solid swelling is a linear function of burnup based upon the data of Hofman and Ryu (1989) using the same conversion procedure from fission density to burnup given above: (2) which results in a gaseous swelling contribution given by the following quadratic function of burnup: (3)

USi is expected to experience densification similar to UO. Thus, the fuel densification can be calculated using the ESCORE empirical model (Rashid et al., 2004) given by: (4) where is the densification strain, is the total densification that can occur (given as a fraction of theoretical density), is the burnup, and is the burnup at which densification is complete. The parameter is dependent on temperature: (5) Note that in Eq. 5 the temperature variable, , is given in Celcius.

## Example Input Syntax


[./volume_swelling]
type = VSwellingU3Si2
block = '1 2 3 4 5 6 7'
temp = temp
burnup = burnup
complete_burnup = 10
gas_swelling_type = STANDARD
save_densification = true
save_solid_swell = true
[../]
(test/tests/VSwellingU3Si2/VSwellingU3Si2_test.i)

## Input Parameters

• densityInitial fuel density

C++ Type:double

Description:Initial fuel density

### Required Parameters

• 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.

• tempCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

• initial_porosity0.05Initial fuel porosity (/)

Default:0.05

C++ Type:double

Description:Initial fuel porosity (/)

• save_solid_swellFalseShould the solid swelling be saved in a material property

Default:False

C++ Type:bool

Description:Should the solid swelling be saved in a material property

• complete_burnup5The burnup at which densification is complete input in units of MWd/kgU

Default:5

C++ Type:double

Description:The burnup at which densification is complete input in units of MWd/kgU

• gas_factor1Scale factor on the gaseous swelling of the fuel

Default:1

C++ Type:double

Description:Scale factor on the gaseous swelling of the fuel

• total_densification0.01The densification that will occur given as a fraction of theoretical density

Default:0.01

C++ Type:double

Description:The densification that will occur given as a fraction of theoretical density

• 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

• save_densificationFalseShould the densification be saved in a material property

Default:False

C++ Type:bool

Description:Should the densification be saved in a material property

• 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

• gas_swelling_typeSTANDARDUse gaseous swelling from U3SI2FG or STANDARD

Default:STANDARD

C++ Type:MooseEnum

Description:Use gaseous swelling from U3SI2FG or STANDARD

• burnup_functionBurnup function

C++ Type:BurnupFunctionName

Description:Burnup function

• burnupCoupled Burnup

C++ Type:std::vector

Description:Coupled Burnup

• solid_factor1Scale factor on the solid swelling of the fuel

Default:1

C++ Type:double

Description:Scale factor on the solid swelling of the fuel

### 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. G. L. Hofman and W. S. Ryu. Detailed Analysis of Uranium Silicide Dispersion Fuel Swelling. Technical Report CONF-8909141â€“10, Argonne National Laboratory, 1989.[BibTeX]
2. J.L Snelgrove M. R. Finlay, G. L. Hofman. Irradiation behaviour of uranium silicide compounds. Journal of Nuclear Materials, 325:118–128, 2004.[BibTeX]
3. Y Rashid, R Dunham, and R Montgomery. Fuel Analysis and Licensing Code: FALCON MOD01. Technical Report, Electric Power Research Institute, December 2004.[BibTeX]