# UOvar element = document.getElementById("moose-equation-7ea59cc9-5360-4024-a7ef-c1b690307aeb");katex.render("_2", element, {displayMode:false,throwOnError:false}); Hot-Pressing Plasticity Update

Calculates the effective inelastic strain increment required to return the isotropic stress state to a J2 yield surface. This class is intended to be a parent class for classes with specific constitutive models.

note:Activation Possible through Another Model

The functionality in this model can be activated with the input parameter flag has_hotpressing_plasticity in UO2HotPressingCreepUpdate.

## Description

This model accounts for 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 and is referred to as hot-pressing.

The mathematical model of hot-pressing of ceramic UO was described by Rashid et al. (1974), using an analogy of close-packed spherical shells under hydrostatic pressure. The implementation of the hot-pressing model based on the instantaneous plasticity mechanism is describled here. For the details of the hot pressing creep model implementation, see UO2HotPressingCreepUpdate.

In Rashid et al. (1974), yield criterion of UO is described by a modified Mohr-coulomb criterion. Eq. 1 through Eq. 5 summarize the criterion: (1) The incremental plastic strain is given as: (2) where (3) where is the Kronecker delta. The volumetric strain increment is (4) defines a material parameter that relates to the yield stress of 100% UO density. (5) where is the yield stress of UO at initial density , and is the yield stress at 100% UO density. The determination of needs experimental data on the yield stress of UO with different porosities, which is scarce in the literatures. Instead, an approximation is made in the code by using a constant ratio of =0.95. The resultant equation of in Bison is (6)

however is not defined in Rashid et al. (1974). To implement the model in Bison, a new flow rule is used. The yield criterion is formulated as: (7) The effective stress is derived as: (8) The new flow rule used in Bison is provided in following equations. (9) (10)

## Yield Stress Model

The hot-pressing or mechanical densification under instantaneous plastic flow depends on the yield strength of UO, which is currently not available in Bison. A linear hardening material model is used for modeling the yield stress of UO. The yield stress for the linear hardening material is (11) where is the initial yield stress, is the new yield stress (effective stress), is the effective incremental plastic strain, and is the hardening modulus. The incremental effective plastic strain and new yield stress are computed in Bison using a radial return method.

## Example Input Syntax

[./plasticity]
type = UO2HotPressingPlasticityUpdate
block = 1
input_yield_stress = 100e6
input_hardening_modulus = 0
input_hotpressing = true
hotpressing_alpha = 0.0125
model_hotpressing = true
[../]
(test/tests/tensor_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

UO2HotPressingPlasticityUpdate 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

• densityInitial fuel density

C++ Type:double

Description:Initial fuel density

### Required Parameters

• relative_tolerance1e-08Relative convergence tolerance for Newton iteration

Default:1e-08

C++ Type:double

Description:Relative convergence tolerance for Newton iteration

• 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

• 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.

• use_flow_ruleTrueUse modifed flow rule for modified Mohr-Columnb yield function

Default:True

C++ Type:bool

Description:Use modifed flow rule for modified Mohr-Columnb yield function

• model_hotpressingTrueFlag to turn on hot pressing model; equivalent to CreepUO2 when set as false

Default:True

C++ Type:bool

Description:Flag to turn on hot pressing model; equivalent to CreepUO2 when set as false

• input_hardening_modulus0Input UO2 hardening modulus

Default:0

C++ Type:double

Description:Input UO2 hardening modulus

• 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

• hotpressing_alpha0Input hot pressing parameter alpha

Default:0

C++ Type:double

Description:Input hot pressing parameter alpha

• absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

Default:1e-11

C++ Type:double

Description:Absolute convergence tolerance for Newton iteration

• 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

• debug_outputFalseFlag for turn on debug output

Default:False

C++ Type:bool

Description:Flag for turn on debug output

• max_its30Maximum number of Newton iterations

Default:30

C++ Type:unsigned int

Description:Maximum number of Newton iterations

• 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

• input_yield_stress0Input UO2 yield stress

Default:0

C++ Type:double

Description:Input UO2 yield stress

### Optional Parameters

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

Default:effective_plastic_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]