FeCrAlCreepUpdate

Computes 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 FeCrAl alloys is calculated by the FeCrAlCreepUpdate model. Seven alloy options exist including the commercial alloys Kanthal APMT, MA956, PM2000, and Fecralloy as well as the Oak Ridge National Laboratory alloys C06M, C35M, and C36M. This model must be run in conjunction with ComputeMultipleInelasticStress.

Thermal Creep of APMT, PM2000, C06M, and C36M

No specific thermal creep model exists for these alloys. However, the FeCrAl handbook has reported a creep law generalized for all alloys given by:

$var element = document.getElementById("moose-equation-2a4768e1-d754-4de1-892d-b9d1110e09fc");katex.render(" \\dot{\\epsilon} = 2.0849 \\times 10^{-43} \\sigma^{7.1} \\exp \\left(-\\frac{39208.6}{T}\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3d94eb4f-f4f9-43b2-a29c-976b7e9b5887");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the effectives tress in Pa and $var element = document.getElementById("moose-equation-f7096823-b6f3-41d4-b6f2-cc2c30fa3aaf");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K.

Thermal Creep of MA956

The thermal creep rate of MA956 is calculated by a Norton creep law as proposed by Seiler et al. (2011): $var element = document.getElementById("moose-equation-8e5ee164-2df6-4f5f-bcbd-3734be05bf1f");katex.render("\\dot{\\epsilon} =\\underbrace{A_0 \\cdot \\text{exp}\\left(\\alpha T\\right) \\cdot \\text{exp}\\left(-\\frac{Q}{RT}\\right)}_\\text{A} \\cdot \\sigma^n", element, {displayMode:true,throwOnError:false});$ where Q is the activation energy, n is the creep exponent and $var element = document.getElementById("moose-equation-a0a7cabd-f238-4b96-8c7d-aca6c5df3741");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ 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 $var element = document.getElementById("moose-equation-23337b76-fa92-493a-8840-10f5bb50d907");katex.render("\\sigma_{c1}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-038d2824-0e06-415b-a43b-a129caef4abc");katex.render("\\sigma_{c2}", element, {displayMode:false,throwOnError:false});$ . 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 $var element = document.getElementById("moose-equation-5694551c-6c2c-449a-9a23-22e7de3cb798");katex.render(" \\sigma_{c1} = \\left(\\frac{A_1}{A_2}\\right)^{\\frac{1}{n_2 - n_1}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-e98ef384-6186-45db-96cb-9001208b4d65");katex.render("A_1(A_0, Q, \\alpha, R, T)", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-c25b86b3-1419-47e6-8be6-16909ed996f7");katex.render("n_1", element, {displayMode:false,throwOnError:false});$ are parameters in the range $var element = document.getElementById("moose-equation-fb558b4f-439f-44e5-bbaf-8bfb8e4fa5b2");katex.render("\\sigma < \\sigma_{c1}", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-f5657038-3bf4-4e11-8fcc-2da38e49802b");katex.render("A_2(A_0, Q, \\alpha, R, T)", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-00e02fdc-a1e6-4708-a863-d30410542b58");katex.render("n_2", element, {displayMode:false,throwOnError:false});$ are parameters in the range $var element = document.getElementById("moose-equation-31c12390-2754-4c01-8a6d-ad8d19ff0f4a");katex.render("\\sigma_{c1} < \\sigma < \\sigma_{c2}", element, {displayMode:false,throwOnError:false});$ , 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)

	$var element = document.getElementById("moose-equation-333aa080-1c49-4e3b-ae2a-8ded5f268a1f");katex.render("A_0", element, {displayMode:false,throwOnError:false});$ (MPa $var element = document.getElementById("moose-equation-9d7ea9e2-5c88-4a7b-b78f-a9c3f8a100a6");katex.render("^{-n}", element, {displayMode:false,throwOnError:false});$ s $var element = document.getElementById("moose-equation-dabb7151-a07a-4758-bc47-11029cc6b26c");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )	n (-)	Q (kJ/mol)	$var element = document.getElementById("moose-equation-40e68c67-5fa8-456e-ba21-057184577645");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ (K $var element = document.getElementById("moose-equation-bb7eac78-58ad-4dd3-a611-71a1635e645b");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )
$var element = document.getElementById("moose-equation-2a75081f-7ed6-4ff6-bab9-648de9a6daf3");katex.render("\\sigma < \\sigma_{c1}", element, {displayMode:false,throwOnError:false});$	11.3e-6	4.9827	453	0.0
$var element = document.getElementById("moose-equation-e4f15b46-6984-48d6-96ac-51d852b24857");katex.render("\\sigma_{c1} < \\sigma < \\sigma_{c2}", element, {displayMode:false,throwOnError:false});$		41.0	453	0.1
$var element = document.getElementById("moose-equation-e91116a0-c76b-401c-998a-8fe1b5442c06");katex.render("\\sigma > \\sigma_{c2}", element, {displayMode:false,throwOnError:false});$	11.9e-6	5.2911	486	-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. $var element = document.getElementById("moose-equation-553d191e-fac1-4d93-8bda-219d1235d506");katex.render(" \\dot{\\epsilon} = 5.96\\times 10^{-27} {\\sigma}^{5.5} \\text{exp} \\left(-\\frac{47136}{T}\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-2d96befc-565b-4b3c-9de2-bb043f80b5b0");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ 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 $var element = document.getElementById("moose-equation-e0774d8f-61ba-4275-b2ee-be30ca68fb9d");katex.render(" \\dot{\\epsilon} = 2.89\\times 10^{-36} {\\sigma}^{5.5} \\text{exp} \\left(-\\frac{29709}{T}\\right)", element, {displayMode:true,throwOnError:false});$ while above 873.15 K, the correlation proposed by Saunders et al. (1997) for Fecralloy is employed. $var element = document.getElementById("moose-equation-04f37037-dfd1-4c57-acb0-aaf6e0be7795");katex.render("\\dot{\\epsilon}", element, {displayMode:false,throwOnError:false});$ is the creep rate (s $var element = document.getElementById("moose-equation-6c71e087-b5a2-4c1f-ba2f-1c50eb064cef");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-4dbf08b5-12f5-46a3-9afe-a15550c5a76d");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ the effective stress (Pa) and T (K) is the temperature.

Irradiation Creep

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 $var element = document.getElementById("moose-equation-8e49d774-caf2-4bdf-a78b-bb81f3f59cff");katex.render("5\\times 10^{-6}", element, {displayMode:false,throwOnError:false});$ per MPa per dpa. Utilizing the following conversion factor: $var element = document.getElementById("moose-equation-90646acc-fb42-4259-9576-9b0cb4c2ebda");katex.render("1\\times 10^{25}", element, {displayMode:false,throwOnError:false});$ n/m $var element = document.getElementById("moose-equation-cba4aa4e-70ac-43f2-8512-7646edff4842");katex.render("^2", element, {displayMode:false,throwOnError:false});$ = 0.9 dpa, a correlation for irradiation creep can be derived. $var element = document.getElementById("moose-equation-4f25eef5-6333-4dbf-a09b-ef509027c28b");katex.render(" \\dot{\\epsilon} = 4.5\\times 10^{-31}\\sigma \\phi", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-1aca934f-8e7e-4113-b3f1-aa0e85f7d94b");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the effective stress in MPa and $var element = document.getElementById("moose-equation-4f6040eb-b7dc-4494-879b-c98ded12f562");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ is the fast neutron flux in n/m $var element = document.getElementById("moose-equation-cba21446-9e3d-4884-ba42-d41a8e9865e3");katex.render("^2", element, {displayMode:false,throwOnError:false});$ -s.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [fecralcreep]
    type = FeCrAlCreepUpdate<<<{"description": "Computes the thermal and irradiation creep behavior of FeCrAl cladding alloys.  This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "FeCrAlCreepUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temp
    fast_neutron_flux<<<{"description": "The fast neutron flux"}>>> = fast_neutron_flux
    fecral_material_type<<<{"description": "The FeCrAl alloy being used for the cladding material. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY"}>>> = C35M
    model_irradiation_creep<<<{"description": "Set true to activate irradiation induced creep"}>>> = true
    model_thermal_creep<<<{"description": "Set true to activate steady state thermal creep"}>>> = false
  []
[]

FeCrAlCreepUpdate 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."}>>> = 'fecralcreep'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
  []
[]

Input Parameters

fecral_material_typeThe FeCrAl alloy being used for the cladding material. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY
C++ Type:MooseEnum
Options:APMT, C06M, C35M, C36M, MA956, PM2000, FECRALLOY
Controllable:No
Description:The FeCrAl alloy being used for the cladding material. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY

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
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.
fast_neutron_fluxThe fast neutron flux
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The fast neutron flux
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.
model_irradiation_creepTrueSet true to activate irradiation induced creep
Default:True
C++ Type:bool
Controllable:No
Description:Set true to activate irradiation induced creep
model_thermal_creepTrueSet true to activate steady state thermal creep
Default:True
C++ Type:bool
Controllable:No
Description:Set true to activate steady state thermal creep
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
temperatureThe coupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled temperature (K)
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

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
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
Description:Scale factor to be applied to the thermal creep stress exponent. Used for calibration and sensitivity studies.

Advanced: Scaling Factors 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_creep_strainName of the material property that stores the effective inelastic strain
Default:effective_creep_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

(test/tests/solid_mechanics/fecral_creep/irradiation_creep.i)
(test/tests/solid_mechanics/fecral_creep/C35M.i)
(test/tests/solid_mechanics/fecral_creep/fecralloy.i)
(test/tests/solid_mechanics/fecral_creep/handbook.i)
(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)
(test/tests/solid_mechanics/fecral_creep/MA956.i)
(test/tests/solid_mechanics/fecral_creep/creep_dt.i)

References

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, 48:189–200, 1997.

@ARTICLE{saunders1997,
    author = "Saunders, S. R. J. and Evans, H. E. and Li, M. and Gohil, D. D. and Osgerby, S.",
    title = "Oxidation Growth Stresses in an Alumina-Forming Ferritic Steel Measured by Creep Deflection",
    journal = "Oxidation of Metals",
    year = "1997",
    volume = "48",
    pages = "189-200"
}

P. Seiler, M. Bäker, and J. Rösler. Variation of creep properties and interfacial roughness in thermal barrier coating systems. Advanced Ceramic Coatings and Materials for Extreme Environments, 32:129–136, 2011.

@ARTICLE{seiler2011,
    author = {Seiler, P. and B\"{a}ker, M. and R\"{o}sler, J.},
    title = "Variation of creep properties and interfacial roughness in thermal barrier coating systems",
    journal = "{A}dvanced {C}eramic {C}oatings and {M}aterials for {E}xtreme {E}nvironments",
    year = "2011",
    volume = "32",
    pages = "129-136"
}

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.

@techreport{terrani_et_al_2016,
    author = "Terrani, K. A. and Karlsen, T. M. and Yamamoto, Y.",
    title = "Input Correlations for Irradiation Creep of {FeCrAl} and {SiC} Based on In-Pile {Halden} Test Results",
    institution = "{ORNL}",
    year = "2016",
    month = "May",
    number = "ORNL/TM-2016/191"
}

(test/tests/solid_mechanics/fecral_creep/irradiation_creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the irradiation creep model for FeCrAl alloys. For this test
#  MA956 is used as the FeCrAl alloy.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress a constant temperature of 300.0 K and a constant flux of 1e18
#  n/m^2-s. Results are taken from different times in the simulation: 40, 60, 90
#  and 110 seconds.  The creep rate predicted by BISON is compared to the
#  analytical solution for these stresses and fluxes.
#
#    Time (s)    Von Mises Stress     Analytical Creep       BISON Creep
#                     (MPa)             Rate (s^-1)          Rate (s^-1)
#
#       40           70.8737            3.18932e-11         3.18932e-11
#       60           60.9280            2.74176e-11         2.74176e-11
#       90           44.8406            2.01783e-11         2.01783e-11
#      110           34.1167            1.53525e-11         1.53525e-11
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]

  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []

[]

[AuxVariables]

  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 35 60 85 110'
    y = '0 90 75.25 62.50 48.75 35'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]


[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 1
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temperature_bc]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fecral_material_type = C35M
    model_irradiation_creep = true
    model_thermal_creep = false
  []

  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []

[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
[]

(test/tests/solid_mechanics/fecral_creep/irradiation_creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the irradiation creep model for FeCrAl alloys. For this test
#  MA956 is used as the FeCrAl alloy.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress a constant temperature of 300.0 K and a constant flux of 1e18
#  n/m^2-s. Results are taken from different times in the simulation: 40, 60, 90
#  and 110 seconds.  The creep rate predicted by BISON is compared to the
#  analytical solution for these stresses and fluxes.
#
#    Time (s)    Von Mises Stress     Analytical Creep       BISON Creep
#                     (MPa)             Rate (s^-1)          Rate (s^-1)
#
#       40           70.8737            3.18932e-11         3.18932e-11
#       60           60.9280            2.74176e-11         2.74176e-11
#       90           44.8406            2.01783e-11         2.01783e-11
#      110           34.1167            1.53525e-11         1.53525e-11
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]

  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []

[]

[AuxVariables]

  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 35 60 85 110'
    y = '0 90 75.25 62.50 48.75 35'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]


[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 1
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temperature_bc]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fecral_material_type = C35M
    model_irradiation_creep = true
    model_thermal_creep = false
  []

  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []

[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
[]

(test/tests/solid_mechanics/fecral_creep/irradiation_creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the irradiation creep model for FeCrAl alloys. For this test
#  MA956 is used as the FeCrAl alloy.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress a constant temperature of 300.0 K and a constant flux of 1e18
#  n/m^2-s. Results are taken from different times in the simulation: 40, 60, 90
#  and 110 seconds.  The creep rate predicted by BISON is compared to the
#  analytical solution for these stresses and fluxes.
#
#    Time (s)    Von Mises Stress     Analytical Creep       BISON Creep
#                     (MPa)             Rate (s^-1)          Rate (s^-1)
#
#       40           70.8737            3.18932e-11         3.18932e-11
#       60           60.9280            2.74176e-11         2.74176e-11
#       90           44.8406            2.01783e-11         2.01783e-11
#      110           34.1167            1.53525e-11         1.53525e-11
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]

  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []

[]

[AuxVariables]

  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 35 60 85 110'
    y = '0 90 75.25 62.50 48.75 35'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]


[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 1
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temperature_bc]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fecral_material_type = C35M
    model_irradiation_creep = true
    model_thermal_creep = false
  []

  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []

[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
[]

(test/tests/solid_mechanics/fecral_creep/C35M.i)

#--------------------------------------------------------------------------------
#  This test verify the implementation of the thermal creep model that has been
#  added to BISON for C35M. The model was taken from Terrani et al., 2016,
#  ORNL/TM-2016/191. This model applies at temperatures under 873 K.
#  The correlation for the creep rate is:
#
#  e_dot = 2.89e-36 * sigma^(5.5) * exp(-29709 / T)                      (s^-1)
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress at 623.15 K.  Results are taken from different times in the
#  simulation: 40, 60, 90 and 110 seconds. The creep rate predicted by BISON is
#  compared to the analytical solution for these stresses.
#
#    Time (s)    Von Mises Stress     Analytical Creep       BISON Creep
#                     (MPa)             Rate (s^-1)          Rate (s^-1)
#
#       40           25.3431            3.61061e-16          3.61061e-16
#       60           29.2424            7.93276e-16          7.93276e-16
#       90           35.0915            2.16255e-15          2.16255e-15
#      110           38.9911            3.86067e-15          3.86067e-15
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 110'
    y = '0 20 40'
  []
  [temperature_function]
    type = PiecewiseLinear
    x='0 10'
    y='300 623.15'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]


[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []

  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fecral_material_type = C35M
    model_irradiation_creep = false
    model_thermal_creep = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250.0
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
  [avg_clad_temp]
    type = ElementAverageValue
    block = 1
    variable = temp
    execute_on = 'initial linear'
  []
[]

(test/tests/solid_mechanics/fecral_creep/fecralloy.i)

#--------------------------------------------------------------------------------
#  This tests the thermal creep model that has been added to BISON for Fecralloy.
#  The model from Saunders et. al, 1997 has been incorporated.  The
#  model is of a Norton Law form with a Arrhenius law for the constant in the form
#
#  e_dot = 5.96e-27 * sigma^(5.5) * exp(-47136 / T)
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress at 973.15 K.  Results are taken from different times in the
#  simulation: 40, 60, 90 and 110 seconds.  The creep rate predicted by BISON is
#  compared to the analytical solution for these stresses.
#
#    Time (s)    Von Mises Stress     Analytical Creep       BISON Creep
#                     (MPa)             Rate (s^-1)          Rate (s^-1)
#
#       40           25.4650             3.34906e-7           3.34906e-7
#       60           29.5002             7.19650e-7           7.19650e-7
#       90           35.5898             1.93256e-6           1.93256e-6
#      110           39.6183             3.44707e-6           3.44707e-6
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 110'
    y = '0 20 40'
  []
  [temperature_function]
    type = PiecewiseLinear
    x='0 10'
    y='300 973.15'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]


[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fecral_material_type = FECRALLOY
    model_irradiation_creep = false
    model_thermal_creep = true
  []

  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7150
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []

[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
  [avg_clad_temp]
    type = ElementAverageValue
    block = 1
    variable = temp
    execute_on = 'initial linear'
  []
[]

(test/tests/solid_mechanics/fecral_creep/handbook.i)

#--------------------------------------------------------------------------------
#  This test verifies the implementation of the thermal creep model that has been
#  added to BISON for general FeCrAl alloys from the FeCrAl Handbook:
#
#  K. G. Field, M. A. Snead, Y. Yamamoto, and K. A. Terrani, "Handbook on the
#  Material Properties of FeCrAl Alloys for Nuclear Power Production Applications,
#  Technical Report ORNL/TM-2017/186, 2017.
#
# The correlation is a generic model that is applicable to the following FeCrAl
# alloys available in BISON: Kanthal APMT, PM2000, C06M, and C36M. The correlation
# is given by:
#
#  e_dot = 2.0849e-43 * sigma^(7.1) * exp(-39208.6 /T)                (s^-1)
#
#  where sigma is the Von Mises stress in Pa. In this test a
#  uniaxial specimen is pulled in the axial direction by
#  a constant stress of 40 MPa under varying temperatures.
#  Results are taken from different times in the
#  simulation: 2e5, 4e5, 6e5, 8e5 and 1e6 seconds. The creep rate predicted by
#  BISON is compared to the analytical solution for these conditions.
#
#    Time (s)     Temperature     Analytical Creep       BISON Creep
#                     (K)            Rate (s^-1)          Rate (s^-1)
#
#      2e5            440            3.92222e-28         3.92222e-28
#      4e5            580            8.60904e-19         8.60904e-19
#      6e5            720            4.40151e-13         4.40151e-13
#      8e5            860            3.11616e-9          3.11616e-9
#      1e6           1000            1.84346e-6          1.84346e-6
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]


[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_function]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '300 1000.0'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -4e7
    []
  []
  [bottom_fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = 'bottom top front back left right'
    function = temperature_function
    preset = false
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecral_creep'
  []
  [fecral_creep]
    type = FeCrAlCreepUpdate
    fecral_material_type = C06M
    model_irradiation_creep = false
    temperature = temp
  []
  [density]
    type = StrainAdjustedDensity
    strain_free_density = 1.0
  []
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0e6
    specific_heat = 1.0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 1e6

  dt = 1e4
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
  []
  [temperature]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  displacements = 'disp_x disp_y'
  patch_size = 10 # For contact algorithm
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = uo2_fecral_smeared.e
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 293.0
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_inner_wall = 5
    clad_outer_wall = 2
    clad_top = 3
    clad_bottom = 1
    pellet_exteriors = 8
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_hoop]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [mass_gain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 2.5e4 2.5e4'
    scale_factor = 1
  []

  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []

  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
    scale_factor = 15.5e6
  []

  [mass_flux_func]
    type = PiecewiseLinear
    x = '-200 0  1e8'
    y = '3800. 3800. 3800.'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
  [clad]
    block = clad
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []

  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = pellet_type_1
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 81
    num_axial = 11
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = pellet_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [creep_strain_hoop]
    type = RankTwoScalarAux
    rank_two_tensor = creep_strain
    variable = creep_strain_hoop
    scalar_type = HoopStress
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate
    property = creep_rate
    execute_on = timestep_end
    block = clad
  []
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 2
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 2
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    normal_smoothing_distance = 0.1
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles
    gas_released = fis_gas_released
    contact_pressure = contact_pressure
    quadrature = true
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []

  [no_y_clad_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []

  [no_y_fuel_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1020
    value = 0.0
  []

  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = pressure_ramp
    []
  []

  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []

[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = pressure_ramp # Pa
    inlet_massflux = mass_flux_func # kg/m^2-sec
    rod_diameter = 9.5e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
    oxide_thickness = oxide_thickness
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    temperature = temp
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet_type_1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [elastic_stress]
    type = ComputeSmearedCrackingStress
    block = pellet_type_1
    cracking_stress = 1.68e8
    inelastic_models = 'fuel_creep'
    softening_models = exponential_softening
    shear_retention_factor = 0.1
    max_stress_correction = 0
    cracked_elasticity_type = DIAGONAL
    output_properties = crack_damage
    outputs = exodus
  []
  [exponential_softening]
    type = ExponentialSoftening
  []
  [fuel_creep]
    type = UO2CreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    temperature = temp
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMATPROEigenstrain
    block = pellet_type_1
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [clad_thermal]
    type = FeCrAlThermal
    material = C35M
    block = clad
    temperature = temp
  []
  [clad_elasticity_tensor] # isotropic elasticity tensor for Zry cladding
    type = FeCrAlElasticityTensor
    temperature = temp
    fecral_material_type = C35M
    block = clad
  []
  [clad_stress] # stress update class to govern the return mapping algorithm for creep
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_creep clad_plasticity'
    block = clad
  []
  [clad_creep]
    type = FeCrAlCreepUpdate
    block = clad
    temperature = temp
    fecral_material_type = C35M
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
    max_inelastic_increment = 1e-4
  []
  [thermal_expansion]
    type = FeCrAlThermalExpansionEigenstrain
    block = clad
    temperature = temp
    fecral_material_type = C35M
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = clad
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = clad_volumetric_strain
  []
  [clad_plasticity]
    type = FeCrAlPlasticityUpdate
    block = clad
    hardening_constant = 2.5e9
    temperature = temp
    yield_stress = 500.0
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 7250.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []

  [failure_criterion]
    type = FeCrAlCladdingFailure
    boundary = '2 5'
    hoop_stress = hoop_stress
    failure_criterion = UTS
    temperature = temp
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = PWR
    boundary = 2
  []
[]

[Dampers]
  [limitT]
    type = BoundingValueNodalDamper
    max_value = 3200.0
    min_value = 293.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its = 100
  l_tol = 8e-3

  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 1e8

  dtmax = 1e5
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 5e5
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2.0
    timestep_limiting_postprocessor = material_timestep
  []

  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []

  [avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temp
  []

  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
  []

  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []

  [_dt]
    type = TimestepSize
  []

  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []

  [alhr_input]
    type = FunctionValuePostprocessor
    function = power_history
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet_type_1
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [mass_gain]
    type = ElementExtremeValue
    block = clad
    variable = mass_gain
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = clad
  []
[]

[Outputs]
  perf_graph = true
  time_step_interval =  1
  exodus = true
  csv = true
  print_linear_residuals = true
  color = false

  [console]
    type = Console
    max_rows = 25
  []
[]

(test/tests/solid_mechanics/fecral_creep/MA956.i)

#--------------------------------------------------------------------------------
#  This tests the secondary creep model that has been added to BISON for INCOLOY
#  MA956. The model from Seiler et al., 2011  has been incorporated.  The
#  model is of the following form:
#
#  e_dot = A_0 * exp(alpha * T) * exp(-Q / (R * T)) * sigma^(n)
#         \_______________________________________/
#                           A
#
#  where A_0, alpha, Q and n are dependent upon the stress.  The table below
#  gives the values of these parameters
#
#                                    A_0           n        Q          alpha
#                               [MPa^-n*s^-1]     [-]    [kJ/mol]      [K^-1]
# -------------------------------------------------------------------------------
#  sigma < sigma_c1                78.978       4.9827     453          0.0
#  sigma_c1 < sigma < sigma_c2   3.466e-124      41.0      453          0.1
#  sigma > sigma_c2               8.68e16       5.2911     486         -0.0122
# ------------------------------------------------------------------------------
#
#  where sigma_c1 and sigma_c2 are calculated via the following:
#
#  sigma_c1 = (A_1 / A_2)^(1 / (n_2 - n_1)
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a varying stress at varying temperatures. Results are taken from different
#  times in the simulation: 40, 60, 90 and 110 seconds.  The creep rate predicted
#  by BISON is compared to the analytical solution for these stresses and temperatures.
#
#    Time (s)   Von Mises Stress   Temp     Analytical Creep       BISON Creep
#                    (MPa)          (K)       Rate (s^-1)          Rate (s^-1)
#
#       40         71.6538       681.945      3.23313e-24          3.23313e-24
#       60         610.928       936.575      3.90916e-15          3.90916e-15
#       90         44.8430       1318.52      1.7659e-8            1.76590e-8
#      110         34.4078       1573.15      3.48813e-6           3.47777e-6
#
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]

  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300.0
  []

[]

[AuxVariables]

  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 110'
    y = '0 90 35'
  []
  [temperature_function]
    type = PiecewiseLinear
    x='0 10  110'
    y='300 300 1573.15'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
[]


[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fecral_material_type = MA956
    model_irradiation_creep = false
    model_thermal_creep = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = ' lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_tol      = 1e-8
  start_time = 0.0
  end_time   = 110

  dt = 10
  dtmin = 10
[]

[Outputs]
  exodus = true
  [console]
    type = Console
    execute_on = 'timestep_end failed nonlinear linear'
  []
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
  [avg_clad_temp]
    type = ElementAverageValue
    block = 1
    variable = temp
    execute_on = 'initial linear'
  []
[]

(test/tests/solid_mechanics/fecral_creep/creep_dt.i)

#--------------------------------------------------------------------------------
#  This test is checks that the iteration adapative timestepper automatically
#  takes the limiting timestep calculated by the creep rate if it is smaller
#  then the timestep automatically calculated by the timestepper using the
#  the iteration adaptive process.  This verifies that the mechanism to Limit
#  timestep based upon the creep behavior is being as expected.
#
#  A uniaxial specimen is pulled in the axial direction by a varying stress at
#  a constant temperature of 300.0 K and a constant flux of 1e25 n/m^2-s.
#
#  The maximum creep rate allowed is set to 1e-4 in the material model FeCralCreepUpdate.
#  When the creep rate exceeds this value of the next timestep is limited to
#  1e-4/creep_rate.
#
#  In this simulation at t=10 s the limiting timestep is found to be 0.215321 s.
# Since this value is lower than the timestep of 1 s set by the timestepper
#  using the iteration adaptive process the timestep is set to the limited
#  value based upon creep of 0.24691358.
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = uniaxial_specimen_rz.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [vonmises]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  [pressure_pull]
    type = PiecewiseLinear
    x = '0 10 11'
    y = '0 90 90'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    execute_on = timestep_end
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  []
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 1
    factor = 1e25
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [top_surface]
    type = Pressure
    boundary = 2
    factor =   1e6
    function = pressure_pull
    variable = disp_y
  []
  [bottom_fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 4
    value = 0.0
  []
  [bottom_fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  []
  [temperature_bc]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
    block = 1
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'fecralcreep'
    block = 1
  []
  [fecralcreep]
    type = FeCrAlCreepUpdate
    block = 1
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fecral_material_type = C35M
    model_irradiation_creep = true
    model_thermal_creep = false
    max_inelastic_increment = 1.e-4
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 7250
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100

  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 11

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    timestep_limiting_postprocessor = material_timestep
  []
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [creep_rate]
    type = ElementalVariableValue
    elementid = 0
    variable = creep_rate_aux
  []
  [vonmises]
    type = ElementalVariableValue
    elementid = 0
    variable = vonmises
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = 1
  []
[]

Description
Thermal Creep of APMT , PM 2000 , C 06 M , and C 36 M
Thermal Creep of MA 956
Thermal Creep of Fecralloy
Thermal Creep of C 35 M
Irradiation Creep
Example Input Syntax
Input Parameters
Input Files
References