# Creep MOX

Calculates the thermal and irradiation creep of MOX fuel

warning:Deprecated Solid Mechanics Material

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

## Description

The CreepMOX material calculates the thermal and irradiation creep for MOX fuel. The creep model for MOX is a combined model from MATPRO Allison et al. (1993) and Guerin Guerin (1985). Experimental data used by MATPRO for MOX cover indeed a range of temperature above 1500 K, so that the proposed model accounts essentially for thermal creep. In Guerin (1985), Guerin provides an semi-empirical law for MOX irradiation creep, hired from Milet's experiments, whose results have been published in Milet and Piconi (1983). MATPRO provides a time-dependant multiplier which allows to account for primary and secondary creep. Thus the creep model for MOX implemented in Bison is given by: (1) with the steady state creep rate being defined as (2) where T is the Temperature (K), is the effective stress (Pa), is the fission rate (), is the grain size (), and is the concentration in weight percent. and, in SI units, the parameters for Eq. 1 and Eq. 2 are given in Table 1.

Table 1: Parameters used in the MOX Creep Model

Model ExpressionParameter Value

Figure 1 shows a comparison between creep models implemented in Bison for UO and MOX. The time origin for primary creep is updated in Bison when the stress rate is greater than a value specified by the user. Two successive time origins cannot be closer than 5 times the characteristic time of transient creep.

Figure 1: Comparison of creep rates for MOX and UO. The creep rate for MOX is higher than that of UO.

## Example Input Syntax

[./creep]
type = CreepMOX
block = 0
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
temp = temp
fission_rate = fission_rate
youngs_modulus = 2.e11
poissons_ratio = .345
Pu_content = 7
thermal_expansion = 0.0
formulation = Nonlinear3D
[../]
(test/tests/creep_mox/creepMOX_test.i)

## Input Parameters

• densityInitial fuel density

C++ Type:double

Description:Initial fuel density

### Required Parameters

• constitutive_modelConstitutiveModel to use (optional)

C++ Type:std::string

Description:ConstitutiveModel to use (optional)

• cracking_stress0The stress threshold beyond which cracking occurs. Must be positive.

Default:0

C++ Type:double

Description:The stress threshold beyond which cracking occurs. Must be positive.

• store_stress_olderFalseParameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

Default:False

C++ Type:bool

Description:Parameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

• cracking_releaseabruptThe cracking release type. Choices are abrupt (default) and exponential.

Default:abrupt

C++ Type:std::string

Description:The cracking release type. Choices are abrupt (default) and exponential.

• bulk_modulusThe bulk modulus for the material.

C++ Type:double

Description:The bulk modulus for the material.

• Pu_content7content of PuO2, in weight percent

Default:7

C++ Type:double

Description:content of PuO2, in weight percent

• formulationElement formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

C++ Type:MooseEnum

Description:Element formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

• cracking_beta1The coefficient used in the exponetional model.

Default:1

C++ Type:double

Description:The coefficient used in the exponetional model.

• compute_InteractionIntegralFalseWhether to compute the Interaction Integral.

Default:False

C++ Type:bool

Description:Whether to compute the Interaction Integral.

• thermal_expansion_reference_temperatureReference temperature for mean thermal expansion function.

C++ Type:double

Description:Reference temperature for mean thermal expansion function.

• stress_free_temperatureThe stress-free temperature. If not specified, the initial temperature is used.

C++ Type:double

Description:The stress-free temperature. If not specified, the initial temperature is used.

• youngs_modulusYoung's modulus of the material.

C++ Type:double

Description:Young's modulus of the material.

• initial_stressThe initial stress tensor (xx, yy, zz, xy, yz, zx)

C++ Type:std::vector

Description:The initial stress tensor (xx, yy, zz, xy, yz, zx)

• poissons_ratioPoisson's ratio for the material.

C++ Type:double

Description:Poisson's ratio for the material.

• compute_methodThe method used in the stress calculation.

C++ Type:MooseEnum

Description:The method used in the stress calculation.

• increment_calculationRashidApproxThe algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

Default:RashidApprox

C++ Type:std::string

Description:The algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

• strain_zzThe zz strain

C++ Type:std::vector

Description:The zz strain

• volumetric_locking_correctionTrueSet to false to turn off volumetric locking correction

Default:True

C++ Type:bool

Description:Set to false to turn off volumetric locking correction

• output_iteration_infoFalseSet true to output sub-newton iteration information

Default:False

C++ Type:bool

Description:Set true to output sub-newton iteration information

• 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

• youngs_modulus_functionYoung's modulus as a function of temperature.

C++ Type:FunctionName

Description:Young's modulus as a function of temperature.

• active_crack_planesPlanes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

C++ Type:std::vector

Description:Planes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

• disp_zThe z displacement

C++ Type:std::vector

Description:The z displacement

• disp_yThe y displacement

C++ Type:std::vector

Description:The y displacement

• cracking_residual_stress0The fraction of the cracking stress allowed to be maintained following a crack.

Default:0

C++ Type:double

Description:The fraction of the cracking stress allowed to be maintained following a crack.

• shear_modulusThe shear modulus of the material.

C++ Type:double

Description:The shear modulus of the material.

• scalar_strain_zzThe zz strain (scalar variable)

C++ Type:std::vector

Description:The zz strain (scalar variable)

• disp_rThe r displacement

C++ Type:std::vector

Description:The r displacement

• appended_property_nameName appended to material properties to make them unique

C++ Type:std::string

Description:Name appended to material properties to make them unique

• cracking_stress_functionThe cracking stress as a function of time and location

C++ Type:FunctionName

Description:The cracking stress as a function of time and location

• outputThe reporting postprocessor to use for the max_iterations value.

C++ Type:PostprocessorName

Description:The reporting postprocessor to use for the max_iterations value.

• poissons_ratio_functionPoisson's ratio as a function of temperature.

C++ Type:FunctionName

Description:Poisson's ratio as a function of temperature.

• dep_matl_propsNames of material properties this material depends on.

C++ Type:std::vector

Description:Names of material properties this material depends on.

• thermal_expansion_function_typeType of thermal expansion function. Choices are: instantaneous mean

C++ Type:MooseEnum

Description:Type of thermal expansion function. Choices are: instantaneous mean

• large_strainFalseWhether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

Default:False

C++ Type:bool

Description:Whether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

• transient_stress_rate50stress rate limit which activates transient creep

Default:50

C++ Type:double

Description:stress rate limit which activates transient creep

Default:1e-05

C++ Type:double

• 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

• fission_rateCoupled fission rate

C++ Type:std::vector

Description:Coupled fission rate

• max_its10Maximum number of sub-newton iterations

Default:10

C++ Type:unsigned int

Description:Maximum number of sub-newton iterations

• cracking_neg_fractionThe fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

C++ Type:double

Description:The fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

• thermal_expansion_functionThermal expansion coefficient as a function of temperature.

C++ Type:FunctionName

Description:Thermal expansion coefficient as a function of temperature.

• compute_JIntegralFalseWhether to compute the J Integral.

Default:False

C++ Type:bool

Description:Whether to compute the J Integral.

• max_cracks3The maximum number of cracks allowed at a material point.

Default:3

C++ Type:unsigned int

Description:The maximum number of cracks allowed at a material point.

• thermal_expansionThe thermal expansion coefficient.

C++ Type:double

Description:The thermal expansion coefficient.

• disp_xThe x displacement

C++ Type:std::vector

Description:The x displacement

• absolute_tolerance1e-20Absolute convergence tolerance for sub-newtion iteration

Default:1e-20

C++ Type:double

Description:Absolute convergence tolerance for sub-newtion iteration

• relative_tolerance1e-05Relative convergence tolerance for sub-newtion iteration

Default:1e-05

C++ Type:double

Description:Relative convergence tolerance for sub-newtion iteration

• 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

• lambdaLame's first parameter for the material.

C++ Type:double

Description:Lame's first parameter for the material.

### 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. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPROâ€“A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]
2. Y. Guerin. Mechanical-behaviour of nuclear fuel under irradiation. Annales de chimie - science des materiaux, 10:405â€“414, 1985.[BibTeX]
3. C. Milet and C. Piconi. Fluage en pile de l'oxyde mixte uo2-puo2. Journal of Nuclear Materials, 116:196â€“199, 1983.[BibTeX]