# Zircaloy Hayes Thermal and Hoppe Irradiation Creep

Calculates the secondary thermal Hayes and Kassner secondary creep and the Hoope irradiation creep for Zircaloy cladding. This material must be run in conjunction with ComputeMultipleInelasticStress.

## Description

Hayes-Kassner secondary thermal creep and Hoppe secondary irradiation creep are both calculated in this class, ZryCreepHayesHoppeUpdate. This material is not suitable for use in high temperatures, such as under LOCA conditions, and primary creep is not integrated with the secondary creep.

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

## Thermal Creep in Standard Operating Conditions

The standard operating temperature thermal creep model used to calculate the secondary thermal creep with a power-law model is based on the work of Hayes and Kassner (2006). Hayes and Kassner found that zircaloy creep rate can be described with a conventional five-power creep law, as described in the review by Kassner and PÃ©rez-Prado (2000).

### Hayes-Kassner Secondary Thermal Creep

The secondary thermal creep strain rate equation implemented in Bison is (1) where is the effective thermal creep rate (1/s), is the effective (Mises) stress (Pa), is the activation energy (J/mol), is the universal gas constant (J/mol-K), is the temperature (K), is the shear modulus (Pa), and and are material constants.

The shear modulus value is taken directly from the elasticity tensor within Bison. Hayes and Kassner (2006) specify a creep law power (n) of 5. A value for is not reported in Hayes and Kassner (2006); however, based on experimental data presented in that paper, an approximate value of = 3.14 10 (1/s) was computed based on the relationship for the diffusion given in Moon et al. (2006); this value is used in Bison.

### Primary Thermal Creep

Primary creep is not implemented for use with the Hayes-Kassner thermal creep model.

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: (2) where is the effective irradiation creep rate (1/s), is the fast neutron flux (n/m-s), is the effective (Mises) stress (MPa), and , , and are material constants. The material constant values = 3.557 10, = 0.85, and = 1.0 are for stress relief annealed zircaloy.

note

The original Hoppe formulation is given in terms of circumferential stress, whereas the relation implemented in Bison assumes an effective (Mises) stress.

## Example Input Syntax


[./zrycreep]
type = ZryCreepHayesHoppeUpdate
temperature = temp
fast_neutron_flux = fast_neutron_flux
model_thermal_creep = true
[../]

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


[./stress]
type = ComputeMultipleInelasticStress
tangent_operator = elastic
inelastic_models = 'zrycreep'
[../]

## Input 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

• temperatureThe coupled temperature (K)

C++ Type:std::vector

Description:The coupled temperature (K)

• 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

• 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

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

• 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

### 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

• 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

• 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. T. A. Hayes and M. Kassner. Creep of zirconium and zirconium alloys. Metallurgical and Materials Transactions A, 37A:2389â€“2396, 2006.[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, 157â€“172. Avignon, France, April 21-24, 1991.[BibTeX]
3. ME Kassner and M-T PÃ©rez-Prado. Five-power-law creep in single phase metals and alloys. Progress in Materials Science, 45(1):1â€“102, 2000.[BibTeX]
4. J.H. Moon, P.E. Cantonwine, K.R. Anderson, S. Karthikeyan, and M.J. Mills. Characterization and modeling of creep mechanisms in zircaloy-4. Journal of Nuclear Materials, 353(3):177 – 189, 2006. doi:10.1016/j.jnucmat.2006.01.023.[BibTeX]