# FeCrAl Thermal and Irradiation Creep Update

Calculates the thermal and irradiation creep behavior of FeCrAl cladding alloys. This material must be run in conjunction with ComputeMultipleInelasticStress.

## Description

Thermal and irradiation creep of the FeCrAl alloys MA956, Fecralloy and C35M are calculated by the FeCrAlCreepUpdate model. It is important to note that if this model is used with the FeCrAl alloys APMT and PM2000 only irradiation creep will be calculated because no thermal creep correlations currently exist for these alloys. This model must be run in conjunction with ComputeMultipleInelasticStress.

### Thermal Creep of MA956

The thermal creep rate of MA956 is calculated by a Norton creep law as proposed by Seiler et al. (2011): (1) where Q is the activation energy, n is the creep exponent and an additional factor. The creep behavior of MA956 is characterized by three regimes with independent sets of creep parameters. The transition from one regime to another takes place at the critical stress and . These critical stresses are calculated during the simulation by equating two equations with the different creep parameters in the two regimes. For example the first critical stress is defined as (2) where and are parameters in the range , and and are parameters in the range , respectively. Table 1 below lists the creep parameters of MA956 for the various stress regimes.

Table 1: Creep parameters of MA956 Seiler et al. (2011)

(MPas)n (-)Q (kJ/mol) (K)
11.3e-64.98274530.0
41.04530.1
11.9e-65.2911486-0.0122

### Thermal Creep of Fecralloy

The model for thermal creep of Fecralloy is in the form of a Norton creep law as proposed by Saunders et al. (1997). The coefficient in the Norton law is in the form of an Arrhenius equation. (3) where is the effective stress in Pa and T is the temperature in K.

### Thermal Creep of C35M

The model for thermal creep of C35M is in the form of a Norton creep law. As proposed by Terrani et al. (2016), below 873.15 K the following correlation for thermal creep is adopted (4) while above 873.15 K, the correlation proposed by Saunders et al. (1997) for Fecralloy is employed. is the creep rate (s), the effective stress (Pa) and T (K) is the temperature.

The model incorporated into Bison for irradiation creep of FeCrAl alloys is taken from Terrani et al. (2016). The coefficient for irradiation creep recommended is per MPa per dpa. Utilizing the following conversion factor: n/m = 0.9 dpa, a correlation for irradiation creep can be derived. (5) where is the effective stress in MPa and is the fast neutron flux in n/m-s.

## Example Input Syntax


[./fecralcreep]
type = FeCrAlCreepUpdate
block = 1
temperature = temp
fast_neutron_flux = fast_neutron_flux
fecral_material_type = C35M
model_thermal_creep = false
[../]

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


[./stress]
type = ComputeMultipleInelasticStress
tangent_operator = elastic
inelastic_models = 'fecralcreep'
block = 1
[../]

## Input Parameters

• fecral_material_typeThe FeCrAl alloy being used for the cladding material. Choices are: APMT MA956 PM2000 FECRALLOY C35M

C++ Type:MooseEnum

Description:The FeCrAl alloy being used for the cladding material. Choices are: APMT MA956 PM2000 FECRALLOY C35M

### 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

• 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.

• max_its30Maximum number of Newton iterations

Default:30

C++ Type:unsigned int

Description:Maximum number of Newton iterations

• 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

• model_thermal_creepTrueSet true to activate steady state thermal creep

Default:True

C++ Type:bool

Description:Set true to activate steady state thermal creep

• 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

• activation_energy_scale_factor1Scale factor to be applied to the thermal creep activation energy. Used for calibration and sensitivity studies.

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal creep activation energy. Used for calibration and sensitivity studies.

• exponential_constant_scale_factor1Scale factor to be applied to the thermal creep exponential constant in the MA956 model. Used for calibration and sensitivity studies.

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal creep exponential constant in the MA956 model. Used for calibration and sensitivity studies.

• irradiation_creep_scale_factor1Scale factor to be applied to irradiation creep strain rate. Used for calibration and sensitivity studies.

Default:1

C++ Type:double

Description:Scale factor to be applied to irradiation creep strain rate. Used for calibration and sensitivity studies.

• pre_exponential_scale_factor1Scale factor to be applied to the thermal creep exponential prefactor. Used for calibration and sensitivity studies.

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal creep exponential prefactor. Used for calibration and sensitivity studies.

• stress_exponent_scale_factor1Scale factor to be applied to the thermal creep stress exponent. Used for calibration and sensitivity studies.

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal creep stress exponent. Used for calibration and sensitivity studies.

• 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

• 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. S. R. J. Saunders, H. E. Evans, M. Li, D. D. Gohil, and S. Osgerby. Oxidation growth stresses in an alumina-forming ferritic steel measured by creep deflection. Oxidation of Metals, 48:189â€“200, 1997.[BibTeX]
2. P. Seiler, M. BÃ¤ker, and J. RÃ¶sler. Variation of creep properties and interfacial roughness in thermal barrier coating systems. Advanced Ceramic Coatings and Materials for Extreme Environments, 32:129â€“136, 2011.[BibTeX]
3. K. A. Terrani, T. M. Karlsen, and Y. Yamamoto. Input correlations for irradiation creep of FeCrAl and SiC based on in-pile Halden test results. Technical Report ORNL/TM-2016/191, ORNL, May 2016.[BibTeX]