# UOvar element = document.getElementById("moose-equation-0083a778-8dad-43a0-8765-92d750e42a95");katex.render("_2", element, {displayMode:false,throwOnError:false}); Hot-Pressing Creep Update

Calculates the secondary thermal and irradiation creep for UO2 LWR fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.

## Description

This model accounts for creep and, if selected, instantaneous plastic flow surrounding pores in ceramic UO2 fuel pellet, which under pressure, can reduce pore volume and consequently reduce fuel porosity and increase fuel density. This is a densification mechanism of UO fuel under compressive stresses, which contributes to fuel densification in addition to the irradiation induced densification. Such mechanical densification process is more pronounced at high temperatures with high creep rate or plastic deformations, and it is also referred to as hot-pressing.

The mathematical model of hot-pressing of ceramic UO was described by Rashid et al. (1974). By using an analogy of close-packed spherical shells in infinite media under hydrostatic compression, model on the stress-induced densification based on the mechanism of instantaneous plasticity and creep was derived. This section describes the implementation of the hot-pressing model based on the mechanisms of creep as follows. For the details of the instantaneous plasticity model implementation, see UO2HotPressingPlasticityUpdate.

Creep is modeling with a power-law form (1) The tangential creep rate of porous media, with density , at the pore surface is given as in Rashid et al. (1974). (2) And, the volumetric creep rate is (3) Hot-pressing parameter is defined as (4) where the hydrostatic pressure (Pa), is the exponent in the power law creep equation, is the leading coefficient in the power law creep equation, is the fractional density (dimensionless), is the creep rate, and the subscripts and represent tangential and volumetric components respectively.

Figure 1: Hot-pressing parameter vs. fractional density

This material parameter is used in the hot-pressing model for the volumetric creep of UO. The creep of UO involves several mechanisms, and in their mathematical descriptions, different exponent could be used for the different mechanisms. The volumetric creep strain implemented in Bison code is assumed to be the combination of all the creep strains together. From Eq. 4, the hot-pressing parameter depends on the fuel density. With the increase of fuel density, the parameter would be reduced; when fractional density approaches 1.0, the parameter approaches zero, and the densification would essentially be terminated, i.e., the volumetric creep strain rate in Eq. 3 becomes zero. A plot of the hot-pressing parameter versus initial density at different is shown in Figure 1.

## Example Input Syntax


[./hotpressing]
type = UO2HotPressingCreepUpdate
block = 1
base_name = hp
temperature = temp
input_hotpressing = true
hotpressing_nu = 0.01
fission_rate = fission_rate
oxygen_to_metal_ratio = 2.0
a7 = 3.72264e-35
q3 = 2617
[../]
(test/tests/tensor_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

UO2HotPressingCreepUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:


type = ComputeMultipleInelasticStress
tangent_operator = elastic
inelastic_models = 'creep hotpressing plasticity'
block = 1
max_iterations = 30
relative_tolerance = 1e-7
absolute_tolerance = 1e-7
[../]
(test/tests/tensor_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

## Input Parameters

• temperatureCoupled temperature

C++ Type:std::vector

Description:Coupled temperature

• densityInitial fuel density

C++ Type:double

Description:Initial fuel density

### Required Parameters

• matpro_poissons_ratioFalseFlag for using MATPRO to compute Poisson's ratio

Default:False

C++ Type:bool

Description:Flag for using MATPRO to compute Poisson's ratio

• acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

Default:10

C++ Type:double

Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

• input_hotpressingFalseFlag for using input hot pressing parameter

Default:False

C++ Type:bool

Description:Flag for using input hot pressing parameter

• debug_outputFalseFlag for turn on debug output

Default:False

C++ Type:bool

Description:Flag for turn on debug output

• burnup_functionBurnup function

C++ Type:BurnupFunctionName

Description:Burnup function

• input_hardening_modulus0Input UO2 hardening modulus

Default:0

C++ Type:double

Description:Input UO2 hardening modulus

• q30Activation energy for irradiation creep, divided by gas constant (1/K)

Default:0

C++ Type:double

Description:Activation energy for irradiation creep, divided by gas constant (1/K)

• matpro_thermal_expansionFalseFlag for using MATPRO to compute the thermal expansion coefficient

Default:False

C++ Type:bool

Description:Flag for using MATPRO to compute the thermal expansion coefficient

• 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

• oxygen_to_metal_ratio2Oxygen to metal ratio

Default:2

C++ Type:double

Description:Oxygen to metal ratio

• matpro_youngs_modulusFalseFlag for using MATPRO to compute Young's modulus

Default:False

C++ Type:bool

Description:Flag for using MATPRO to compute Young's modulus

• a77.78e-37Coefficient on irradiation creep term

Default:7.78e-37

C++ Type:double

• max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step

Default:0.0001

C++ Type:double

Description:The maximum inelastic strain increment allowed in a time step

• abs_error1e-06Absolute error in the iteration loop to compute trial pressure

Default:1e-06

C++ Type:double

Description:Absolute error in the iteration loop to compute trial pressure

Default:1e-05

C++ Type:double

• rel_error0.001Relative error in the iteration loop to computer trial pressure

Default:0.001

C++ Type:double

Description:Relative error in the iteration loop to computer trial pressure

• has_hotpressing_plasticityFalseFlag to turn on instantaneous plasticity model

Default:False

C++ Type:bool

Description:Flag to turn on instantaneous plasticity model

• base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

C++ Type:std::string

Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

• fission_rateCoupled fission rate

C++ Type:std::vector

Description:Coupled fission rate

• po2_fraction0Weight fraction of PO2

Default:0

C++ Type:double

Description:Weight fraction of PO2

• max_its30Maximum number of Newton iterations

Default:30

C++ Type:unsigned int

Description:Maximum number of Newton iterations

• hotpressing_nu0Input hot pressing parameter

Default:0

C++ Type:double

Description:Input hot pressing parameter

• 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

• absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

Default:1e-11

C++ Type:double

Description:Absolute convergence tolerance for Newton iteration

• max_iteration1000Maximum iteration number

Default:1000

C++ Type:int

Description:Maximum iteration number

• relative_tolerance1e-08Relative convergence tolerance for Newton iteration

Default:1e-08

C++ Type:double

Description:Relative convergence tolerance for Newton iteration

• burnupCoupled burnup

C++ Type:std::vector

Description:Coupled burnup

### Optional Parameters

• effective_inelastic_strain_nameeffective_hotpressing_strainName of the material property that stores the effective inelastic strain

Default:effective_hotpressing_strain

C++ Type:std::string

Description:Name of the material property that stores the effective inelastic strain

• 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

• internal_solve_output_onon_errorWhen to output internal Newton solve information

Default:on_error

C++ Type:MooseEnum

Description:When to output internal Newton solve information

• internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.

Default:False

C++ Type:bool

Description:Set true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.

### Debug Parameters

• 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. Y. R. Rashid, H. T. Tang, and E. B. Johansson. Mathematical treatment of hot pressing of reactor fuel. Nuclear Engineering Design, 29:1–6, 1974.[BibTeX]