ZryPlasticityUpdate

Computes the plastic strain as a function of strain rate for Zircaloy cladding. Note: This material must be run in conjunction with both ComputeMultipleInelasticStress and ZryElasticityTensor.

Description

ZryPlasticityUpdate calculates the plastic strain for zircaloy cladding materials as a function of temperature, fluence, strain rate, material cold work factor, and as-recieved oxygen concentration. This material, which must be run in conjunction with ComputeMultipleInelasticStress calculates the plastic strain, the elastic strain, and the resulting stress for zircaloy materials. This material should also be used with the ZryElasticityTensor material.

After yield, the stress-strain relationship follows a power law model where K is the strength coefficient, n is the strain hardening exponent, m is the strain rate exponent and is the strain rate. Note that the total strain ( ) is used in the above expression.

The yield stress ( ) is calculated as the non-zero intersection of the power law hardening equation and Hooke's law and is given by In this analytical model, the Young's modulus, E, is a function of temperature of the cladding, fast neutron fluence, cold work factor and oxygen concentration. The Young's modulus is calculated using the MATPRO material model CELMOD in ZryElasticityTensor.

warningwarning

The Young's modulus calculation is completed in the ZryElasticityTensor class; therefore, it is imperative to use ZryElasticityTensor with the MATPRO options set to true (matpro_youngs_modulus = true and matpro_poissons_ratio = true) when using ZryPlasticityUpdate for the simulation to produce accurate results.

Because this class uses the J2 radial return mapping algorithm, the stress after yield needs to be written in terms of the plastic strain () instead of the total strain (). This formulation can be achieved by in the von Mises stress space by substituting for the elastic strain. Then the stress-plastic strain relation after yield can be written as The hardening modulus can then be obtained as

This material contains two model options to calculate the constants used in the power law plasticity equation: the default PNNL model is based on the report from Geelhood et al. (2008), and a second MATPRO model based on EPRI's Pre-SW Falcon Version 31 code.

PNNL Model

The correlations for the plasticity power law hardening relations in this model are taken from Geelhood et al. (2008). The strength coefficient, K, strain hardening exponent, n, and strain rate exponent, m, are functions of the cladding temperature, fast neutron fluence, fast neutron flux and cold work factor. To account for the effect of annealing, the MATPRO material model CANEAL is used correct the cold work factor and fast neutron fluence. The reader is referred to Sections 2.2, 2.3, and 2.4 of Geelhood et al. (2008) for the specific equations: these equations are piecewise in both temperature and fluence.

MATPRO Model

This model option uses MATPRO equations to find the strength coefficient, K, strain hardening exponent, n, and strain rate exponent, m, as a function of the cladding temperature, fast neutron fluence, fast neutron flux and cold work factor, similar to Allison et al. (1993). Note that a fixed strain rate of 1e-3 m/s is used in this model.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [zry_plasticity]
    type = ZryPlasticityUpdate<<<{"description": "Computes the plastic strain as a function of strain rate for Zircaloy cladding. Note: This material must be run in conjunction with both ComputeMultipleInelasticStress and ZryElasticityTensor.", "href": "ZryPlasticityUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    fast_neutron_flux<<<{"description": "The fast neutron flux"}>>> = fast_neutron_flux
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    initial_fast_fluence<<<{"description": "Initial fast fluence to be used with the MATPRO model."}>>> = 1.0e22
    temperature<<<{"description": "Temperature of the cladding (K)"}>>> = temp
    cold_work_factor<<<{"description": "cold work factor - between 0.0 and 0.75"}>>> = 0.01
    plasticity_model_type<<<{"description": "The type of correlation to use to calculate the elastic constants for the ziracloy cladding. Choices are: PNNL MATPRO"}>>> = MATPRO
  []
[]
(test/tests/solid_mechanics/zry_plasticity/clad_yield_stress_model_rz_rev1.i)

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

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [stress]
    type = ComputeMultipleInelasticStress<<<{"description": "Compute state (stress and internal parameters such as plastic strains and internal parameters) using an iterative process.  Combinations of creep models and plastic models may be used.", "href": "../ComputeMultipleInelasticStress.html"}>>>
    tangent_operator<<<{"description": "Type of tangent operator to return.  'elastic': return the elasticity tensor.  'nonlinear': return the full, general consistent tangent operator."}>>> = elastic
    inelastic_models<<<{"description": "The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second."}>>> = 'zry_plasticity'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
  []
[]
(test/tests/solid_mechanics/zry_plasticity/clad_yield_stress_model_rz_rev1.i)

This class uses the MATPRO relations for the elasticity tensor constants to calculate the yield stress, therefore, the input file must also include the elasticity tensor class, ZryElasticityTensor, as shown below:

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [zry_elasticity_tensor]
    type = ZryElasticityTensor<<<{"description": "Either provides constant elasticity constants for Zircaloy cladding or calculates the Young's modulus and Poisson's ratio for Zircaloy cladding using MATPRO relations as a function of temperature and fast neutron fluence.", "href": "ZryElasticityTensor.html"}>>>
    matpro_poissons_ratio<<<{"description": "Flag for using MATPRO to compute Poisson's ratio"}>>> = true
    matpro_youngs_modulus<<<{"description": "Flag for using MATPRO to compute Young's modulus"}>>> = true
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    cold_work_factor<<<{"description": "cold work factor - between 0.0 and 0.75"}>>> = 0.01
    initial_fast_fluence<<<{"description": "The initial fast neutron fluence"}>>> = 1.0e22
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
  []
[]
(test/tests/solid_mechanics/zry_plasticity/clad_yield_stress_model_rz_rev1.i)

Input Parameters

  • fast_neutron_fluenceThe fast neutron fluence

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The fast neutron fluence

  • fast_neutron_fluxThe fast neutron flux

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The fast neutron flux

  • temperatureTemperature of the cladding (K)

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Temperature of the cladding (K)

Required Parameters

  • absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

    Default:1e-11

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Absolute convergence tolerance for Newton iteration

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

    Default:10

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

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

  • adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.

  • automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether to use automatic differentiation to compute the derivative.

  • 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

    Controllable:No

    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.

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object applies

  • cold_work_factor0cold work factor - between 0.0 and 0.75

    Default:0

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:cold work factor - between 0.0 and 0.75

  • 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 computeQpProperties() 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

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

  • initial_fast_fluence0Initial fast fluence to be used with the MATPRO model.

    Default:0

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Initial fast fluence to be used with the MATPRO model.

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

    Default:0.0001

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

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

  • maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.

    Default:25

    C++ Type:unsigned int

    Controllable:No

    Description:The maximum number of substeps allowed before cutting the time step.

  • oxygen_concentration0Average oxygen concentration excluding oxide layer - average oxygen concentration of as received cladding (Kg O2/ Kg Zr)

    Default:0

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Average oxygen concentration excluding oxide layer - average oxygen concentration of as received cladding (Kg O2/ Kg Zr)

  • plasticity_model_typePNNLThe type of correlation to use to calculate the elastic constants for the ziracloy cladding. Choices are: PNNL MATPRO

    Default:PNNL

    C++ Type:MooseEnum

    Options:PNNL, MATPRO

    Controllable:No

    Description:The type of correlation to use to calculate the elastic constants for the ziracloy cladding. Choices are: PNNL MATPRO

  • relative_tolerance1e-08Relative convergence tolerance for Newton iteration

    Default:1e-08

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Relative convergence tolerance for Newton iteration

  • strain_rateFixed strain rate value

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Fixed strain rate value

  • use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.

  • use_substeppingNONEWhether and how to use substepping

    Default:NONE

    C++ Type:MooseEnum

    Options:NONE, ERROR_BASED, INCREMENT_BASED

    Controllable:No

    Description:Whether and how to use substepping

  • zircaloy_alloy_type4Type of Ziracloy alloy to be used: Zircaloy-2 or -4

    Default:4

    C++ Type:unsigned int

    Controllable:No

    Description:Type of Ziracloy alloy to be used: Zircaloy-2 or -4

Optional Parameters

  • apply_strainTrueFlag to apply strain. Used for testing.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Flag to apply strain. Used for testing.

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

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

    Default:effective_plastic_strain

    C++ Type:std::string

    Controllable:No

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:The seed for the master random number generator

  • substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps

    Default:0.1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps

  • 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

    Controllable:No

    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.

Advanced Parameters

  • 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

    Controllable:No

    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.

  • internal_solve_output_onon_errorWhen to output internal Newton solve information

    Default:on_error

    C++ Type:MooseEnum

    Options:never, on_error, always

    Controllable:No

    Description:When to output internal Newton solve information

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<std::string>

    Controllable:No

    Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

  • outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object

    Default:none

    C++ Type:std::vector<OutputName>

    Controllable:No

    Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

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: MATPRO-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. K.J. Geelhood, C.E. Beyer, and W.G. Luscher. PNNL Stress/Strain correlation for Zircaloy. Technical Report PNNL-17700, Pacific Northwest National Laboratory, 2008.[BibTeX]