Zircaloy Limback-Andersson Thermal and Hoppe Irradiation Creep

Calculates the Limback-Andersson thermal primary and secondary creep and the Hoppe irradiation creep for Zircaloy cladding. This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

Secondary Hoppe irradiation creep and Limback-Andersson secondary and primary thermal creep are both calculated in this single class, ZryCreepLimbackHoppeUpdate, and thermal creep does not account for phase changes present at higher temperatures, such as those temperatures occurring under loss-of-coolant accident (LOCA) conditions. This material, which must be run in conjunction with ComputeMultipleInelasticStress calculates the inelastic creep strain, the elastic strain, and the resulting stress for zircaloy materials.

note:LOCA Creep a Separate Material Model

To model the zircaloy cladding in temperatures above 700K, the specific LOCA Zry creep model, ZryCreepLOCAErbacherLimbackHoppeUpdate should be used in the input file.

The contributions to creep from irradiation, primary, and thermal secondary creep are summed at each iteration.

Irradiation Creep

Irradiation-induced creep of cladding materials is based on an empirical model developed by Hoppe (1991) that relates the creep rate to the current fast neutron flux and stress. The specific relation implemented is: (1) where is the effective irradiation creep rate (1/s), is the fast neutron flux , is the effective (Mises) stress (MPa), and , , and are material constants. The material constants , , and are shown in the table for different cladding materials. Note that the original Hoppe formulation is given in terms of circumferential stress, whereas the relation implemented in Bison assumes an effective (von Mises) stress.

Table 1: Irradiation Creep Zircaloy Material Constants

Clad Type
stress relief annealed (Zr2 or Zr4)
recrystallization annealed (Zr2)
partially recrystallization annealed (Zr2)
stress relief annealed ZIRLO

The constants used in the irradiation creep model depend on the material selected as an input parameter.

Thermal Creep in Standard Operating Conditions

The Limback-Andersson model includes both primary and secondary creep; primary creep can be important as part of power changes when the load on the cladding changes relatively suddenly.

Limback-Andersson Secondary Thermal Creep

Secondary thermal creep rate in the Limback-Andersson model is given as the Matsuo (1987) model where the creep rate (hr) is (2) where the constants , , and are shown in the table below for the different cladding materials, is the temperature (K), = 65 (dimensionless), = 8.314 (J/mol/K), = 0.56 (dimensionless), = 1.4 10 ((n/cm)), and = 1.3 (dimensionless).

Based on the Limback model, a new model for ZIRLO was developed by adjusting some parameters to fit data on ZIRLO material using (Foster et al., 2008; Quecedo et al., 2009; Seok et al., 2011).

Table 2: Standard Thermal Creep Zircaloy Material Constants

Clad TypeA (K/MPa/hr)Q (kJ/mol)n
stress relief annealed (Zr2 or Zr4)
recrystallization annealed (Zr2)
partially recrystallization annealed (Zr2)
stress relief annealed ZIRLO

Note that is a function of effective stress: (3)

Primary Creep from Limback-Andersson

The primary thermal creep rate is calculated as a non zero value when the secondary thermal creep rate is greater than zero while the primary creep strain is below the saturation value. Within these bounds, the primary thermal creep rate is calculated as (4) where = 52 (dimensionless) and is a time constant type variable defined as: (5) where is the saturated primary creep strain and is the steady state creep rate: the sum of the secondary thermal and irradiation creep rates.

The primary saturated strain, , can be determined by either the Matsuo model or Limback's modified Matsuo model, (Matsuo, 1987). The Limback modified model, given below, is used as the default method to calculate primary thermal creep strain. (6)

Table 3: Parameters for the Eqn Eq. 6

Model ParameterParameter Value
(dimensionless)
(dimensionless)

Both primary creep strain and secondary thermal creep strain are saved as independent material properties, primary_creep_strain and thermal_secondary_creep_strain; these material properties can be saved to the output file through the use of AuxKernels to individually examine these components of the creep strain.

Total Zircaloy Creep Strain

Total creep strain is the combination of the primary and secondary creep strains: (7)

Example Input Syntax


[./zry_creep]
  type = ZryCreepLimbackHoppeUpdate
  temperature = temp
  fast_neutron_fluence = fast_neutron_fluence
  fast_neutron_flux = fast_neutron_flux
  model_primary_creep = true
[../]
(test/tests/tensor_mechanics/zry_creep/primary_creep_limback_rz_tm.i)

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


[./stress]
  type = ComputeMultipleInelasticStress
  tangent_operator = elastic
  inelastic_models = 'zry_creep'
[../]
(test/tests/tensor_mechanics/zry_creep/primary_creep_limback_rz_tm.i)

Input Parameters

  • fast_neutron_fluenceThe fast neutron fluence

    C++ Type:std::vector

    Description:The fast neutron fluence

  • 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

  • initial_fast_fluence0The initial fast neutron fluence

    Default:0

    C++ Type:double

    Description:The initial fast neutron fluence

  • 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.

  • outputThe reporting postprocessor to use for the max_iterations value.

    C++ Type:PostprocessorName

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

  • model_thermal_creepTrueSet true to activate steady state thermal creep

    Default:True

    C++ Type:bool

    Description:Set true to activate steady state thermal creep

  • max_its30Maximum number of Newton iterations

    Default:30

    C++ Type:unsigned int

    Description:Maximum number of Newton iterations

  • model_primary_creepTrueSet true to activate primary creep

    Default:True

    C++ Type:bool

    Description:Set true to activate primary creep

  • zircaloy_material_typestress_relief_annealedType of zircaloy material properties to use in calculating creep. Choices are: stress_relief_annealed recrystalization_annealed partial_recrystallization_annealed zirlo

    Default:stress_relief_annealed

    C++ Type:MooseEnum

    Description:Type of zircaloy material properties to use in calculating creep. Choices are: stress_relief_annealed recrystalization_annealed partial_recrystallization_annealed zirlo

  • 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

  • model_irradiation_creepTrueSet true to activate irradiation induced creep

    Default:True

    C++ Type:bool

    Description:Set true to activate irradiation induced creep

  • fast_neutron_fluxThe fast neutron flux

    C++ Type:std::vector

    Description:The fast neutron flux

  • relative_tolerance1e-08Relative convergence tolerance for Newton iteration

    Default:1e-08

    C++ Type:double

    Description:Relative convergence tolerance for Newton iteration

  • 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

  • max_creep_increment0.001Maximum creep strain increment allowed by accuracy time step criterion

    Default:0.001

    C++ Type:double

    Description:Maximum creep strain increment allowed by accuracy time step criterion

  • 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

  • temperatureThe coupled temperature (K)

    C++ Type:std::vector

    Description:The coupled temperature (K)

Optional Parameters

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

    Default:effective_creep_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

Advanced Parameters

  • creeprate_scale_factor1scaling factor for total creep rate. Used for calibration and sensitivity studies

    Default:1

    C++ Type:double

    Description:scaling factor for total creep rate. Used for calibration and sensitivity studies

Advanced: Scaling Factors Parameters

  • 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

Outputs Parameters

Input Files

Child Objects

References

  1. J.P. Foster, H.K. Yueh, and R.J. Comstock. Zirloâ„¢ cladding improvement. Journal of ASTM International, 2008.[BibTeX]
  2. N. E. Hoppe. Engineering model for zircaloy creep and growth. In Proceedings of the ANS-ENS International Topical Meeting on LWR Fuel Performance, 157–172. Avignon, France, April 21-24, 1991.[BibTeX]
  3. Y. Matsuo. Thermal creep of zircaloy-4 cladding under internal pressure. Journal of Nuclear Science and Technology, 24(2):111–119, February 1987.[BibTeX]
  4. M. Quecedo, M. Lloret, J.M. Conde, C. Alejano, J.A. Gago, and F.J. Fernandez. Results of thermal creep test on highly irradiated zirloâ„¢. Nuclear Engineering and Technology, 41(2):179–186, 2009.[BibTeX]
  5. C.S. Seok, B. Marple, Y.J. Song, S. Gollapudi, I. Charit, and K.L. Murty. High temperature deformation characteristics of zirloâ„¢ tubing via ring-creep and burst tests. Nuclear Engineering and Design, 241:599–602, 2011.[BibTeX]