FeCrAlCladdingFailure

A failure model for FeCrAl cladding. Four failure criteria exist including ultimate tensile strength, Tresca criterion, an Idaho National Laboratory developed criterion and an University of Tennessee developed criterion.

Description

The model FeCrAlCladdingFailure determines whether or not FeCrAl claddings have failed based upon a chosen criterion. There are four options available to choose from in this model:

Ultimate Tensile Strength Criterion

For the UTS criterion the hoop stress is compared to the UTS of the material. For FeCrAl alloys the UTS is calculated as a function of temperature based upon the data of Yamamoto et al. (2015) as shown in Table 1. Yamamoto et al. (2015)`s data only covers temperatures ranging from 300 to $var element = document.getElementById("moose-equation-ff3e98a1-7a8e-49e0-8376-38ab94d6db59");katex.render("\\sim", element, {displayMode:false,throwOnError:false});$ 1000 K. Based on research by Yano et al. (2016) on other ferritic and martensitic steels, there are distinct temperature dependent regions (low, mid, high) of the ultimate tensile strength (UTS). In the low temperature region the UTS drops relatively slowly with increasing temperature. In the midrange temperatures there is a rapid decrease in the UTS as temperature increases. The high temperature region results in a slow reduction of the UTS to approximately zero at the melting point. Using these observations on other alloys, an additional data point of a UTS of zero was added to Yamamoto's data at the melting point of FeCrAl alloys (1773 K). The minimum UTS is used if the temperature is outside the temperature bounds presented here. For example if the temperature is 280 K the UTS is taken as 569.475 MPa.

Table 1: Value of FeCrAl Ultimate Tensile Strength as a Function of Temperature

Temperature (K)	Ultimate Tensile Strength (MPa)
294.738	569.475
551.495	543.205
644.048	527.023
829.850	288.826
1011.95	65.373
1773.00	0.0

Tresca Criterion

In the well known Tresca failure criterion if the maximum shear stress exceeds one half of the yield stress the material is considered failed. According to Boresi and Schmidt (2003) the maximum shear stress is determined from the principal stresses. The maximum shear stress is the largest value of the following three quantities: $var element = document.getElementById("moose-equation-cd8f9201-a9e6-4bd7-a72d-96b256bc35e2");katex.render(" \\tau_{1} = \\frac{\\lvert \\sigma_{2} - \\sigma_{3} \\rvert}{2}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-096c60dd-8f5c-4997-a960-ffad030a5f48");katex.render("\\tau_{2} = \\frac{\\lvert \\sigma_{3} - \\sigma_{1} \\rvert}{2}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-50fe6421-0821-4b22-8de5-e40314b2e1d5");katex.render("\\tau_{3} = \\frac{\\lvert \\sigma_{1} - \\sigma_{2} \\rvert}{2}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f251d757-9df1-49a9-8687-f4adad5df7fd");katex.render("\\sigma_{1}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-96568973-ca66-4fa7-8fb2-b4d7088ca18a");katex.render("\\sigma_{2}", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-36f72371-9ca5-4c6a-9285-d0d7fd6b1b73");katex.render("\\sigma_{3}", element, {displayMode:false,throwOnError:false});$ are the max, mid, and min prinicipal stresses respectively.

Idaho National Laboratory Criterion

The INL model for failure of FeCrAl alloys is based upon the experimental work of Massey et al. (2016). It was found that the UTS and Tresca criteria described above do not accurately predict the failure observed in Massey et al. (2016)'s experiments. Therefore, in the absence of other burst data for FeCrAl, it is argued that the data can be used directly to develop a failure criterion. In particular, data from Massey et al. (2016) relative to the B135Y alloy, which is a 13Cr-5Al first-generation FeCrAl alloy developed at Oak Ridge National Laboratory (ORNL) Pint and Baldesberger (2018) and Pint et al. (2020), were used in the development of this failure criterion.

The developed failure model is a burst stress ( $var element = document.getElementById("moose-equation-f95b75b5-2b02-4018-81b7-8376e78c6a9f");katex.render("\\sigma_{burst}", element, {displayMode:false,throwOnError:false});$ ) that varies as a function of temperature. The experimental data can be visualized as hoop stress as a function of temperature. Using a least squares methodology a best fit to the experimental data is performed to obtain a correlation for burst stress as an exponential function of temperature. Below 796.8 K the UTS is used as the burst stress. Therefore, the combined equation is given by: $var element = document.getElementById("moose-equation-0f542913-7e4c-4664-bd72-8f9600ec8fab");katex.render(" \\sigma_{burst} = \\begin{cases} \\text{UTS}, & \\text{for } T \\leq 796.8~\\text{K}\\\\ 28440.98 \\exp \\left(-0.005588T \\right), & \\text{for } T > 796.8~\\text{K} \\end{cases}", element, {displayMode:true,throwOnError:false});$ Further details of the derivation of the above model can be found in Gamble et al. (2017).

University of Tennessee Criterion

The UTK model for failure of FeCrAl cladding is based on the experimental data from LOCA testing of C26M FeCrAl claddings performed in ORNL's Severe Accident Test Station Pint and Baldesberger (2018) and Pint et al. (2020). C26M is a Fe-12Cr-6Al-2Mo-0.2Si-0.03Y alloy developed at ORNL and under irradiation in a lead test rod in the Edwin I. Hatch commercial nuclear power plant since 2018 (Rebak, 2018). Experimental data for the burst hoop stress of the C26M claddings as a function of temperature were fitted to derive the criterion (Sweet and Wirth, 2020). The burst stress reaches zero at $var element = document.getElementById("moose-equation-86095c54-b3ce-45c9-9194-48264a741c79");katex.render("\\approx", element, {displayMode:false,throwOnError:false});$ 1550 K, based-on the high temperature performance of stainless steels, which lose much of their strength before the alloy reaches the melting temperature (Sweet and Wirth, 2020). Below 829.4 K the UTS is used as the burst stress. The equation for the burst stress reads: $var element = document.getElementById("moose-equation-d77289cc-2b36-407d-a0f1-1b8969daf09c");katex.render(" \\sigma_{burst} = \\begin{cases} \\text{UTS}, & \\text{for } T \\leq 829.4~\\text{K}\\\\ 9750.0 \\exp \\left(-0.00419T \\right) -14.7, & \\text{for } T > 829.4~\\text{K} \\end{cases}", element, {displayMode:true,throwOnError:false});$

Experimental data for burst hoop stress vs. temperature of FeCrAl alloys and corresponding failure criteria from INL and UTK are illustrated in Figure 1. The UTK failure criterion tends to be less conservative than the INL criterion, consistent with the higher strength of the C26M FeCrAl alloy compared to the first-generation B135Y alloy.

Figure 1: Experimental data for burst stress vs. temperature of FeCrAl alloys B135Y (Massey et al., 2016) and C26M (Pint et al., 2020) and corresponding failure criteria from INL (Gamble et al., 2017) and UTK (Sweet and Wirth, 2020).

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [failure_fecral]
    type = FeCrAlCladdingFailure<<<{"description": "A failure model for FeCrAl cladding. Four failure criteria exist including ultimate tensile strength, Tresca criterion, an Idaho National Laboratory developed criterion and an University of Tennessee developed criterion.", "href": "FeCrAlCladdingFailure.html"}>>>
    temperature<<<{"description": "Temperature in cladding (K)"}>>> = temp
    hoop_stress<<<{"description": "Hoop stress in cladding (Pa)"}>>> = hoop_stress
    failure_criterion<<<{"description": "The criterion selected for failure of the material. Default is Ultimate Tensile Strength."}>>> = INL
  []
[]

Input Parameters

temperatureTemperature in cladding (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature in cladding (K)

Required Parameters

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
burst_stress_scale_factor1Scaling factor on the burst stress.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor on the burst stress.
comparedless_equalOptions for variable _compared_ to criteria: greater_than greater_equal less_equal less_than
Default:less_equal
C++ Type:MooseEnum
Options:greater_than, greater_equal, less_equal, less_than
Controllable:No
Description:Options for variable _compared_ to criteria: greater_than greater_equal less_equal less_than
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_criteria0Numerical value providing criteria value.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Numerical value providing criteria value.
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.
failure_criterionUTSThe criterion selected for failure of the material. Default is Ultimate Tensile Strength.
Default:UTS
C++ Type:MooseEnum
Options:UTS, TRESCA, INL, UTK
Controllable:No
Description:The criterion selected for failure of the material. Default is Ultimate Tensile Strength.
function_criteriaFunction name providing criteria value.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function name providing criteria value.
hoop_stressHoop stress in cladding (Pa)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Hoop stress in cladding (Pa)
max_principal_stressMax principal stress (Pa)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Max principal stress (Pa)
mid_principal_stressMid principal stress (Pa)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Mid principal stress (Pa)
min_principal_stressMin principal stress (Pa)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Min principal stress (Pa)
variable_checkVariable name which is compared to criteria. Example: Var < 0, true=failed
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable name which is compared to criteria. Example: Var < 0, true=failed

Optional Parameters

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.
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
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

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_failure/fecral_failure_inl.i)
(test/tests/solid_mechanics/fecral_failure/fecral_failure_utk.i)
(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)
(test/tests/solid_mechanics/fecral_failure/fecral_failure_uts.i)
(test/tests/solid_mechanics/fecral_failure/fecral_failure_tresca.i)

References

A. P. Boresi and R. J. Schmidt. Advanced Mechanics of Materials, 6th Edition. John Wiley & Sons, Inc., 2003.

K.A. Gamble, T. Barani, D. Pizzocri, J.D. Hales, K.A. Terrani, and G. Pastore. An investigation of FeCrAl cladding behavior under normal operating and loss of coolant conditions. Journal of Nuclear Materials, 491:55–66, 2017. doi:10.1016/j.jnucmat.2017.04.039.

@article{GAMBLE201755,
    author = "Gamble, K.A. and Barani, T. and Pizzocri, D. and Hales, J.D. and Terrani, K.A. and Pastore, G.",
    title = "An investigation of {FeCrAl} cladding behavior under normal operating and loss of coolant conditions",
    journal = "Journal of Nuclear Materials",
    volume = "491",
    pages = "55-66",
    year = "2017",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2017.04.039"
}

Caleb P. Massey, Kurt A. Terrani, Sebastien N. Dryepondt, and Bruce A. Pint. Cladding burst behavior of Fe-based alloys under LOCA. Journal of Nuclear Materials, 470():128–138, 2016. URL: http://www.sciencedirect.com/science/article/pii/S0022311515303871, doi:http://dx.doi.org/10.1016/j.jnucmat.2015.12.018.

@article{Massey2016128,
    author = "Massey, Caleb P. and Terrani, Kurt A. and Dryepondt, Sebastien N. and Pint, Bruce A.",
    title = "Cladding burst behavior of {F}e-based alloys under {LOCA}",
    journal = "Journal of Nuclear Materials",
    volume = "470",
    number = "",
    pages = "128-138",
    year = "2016",
    note = "",
    issn = "0022-3115",
    doi = "http://dx.doi.org/10.1016/j.jnucmat.2015.12.018",
    url = "http://www.sciencedirect.com/science/article/pii/S0022311515303871"
}

B. A. Pint and L. A. Baldesberger. Steam Oxidation and Burst Testing in the Severe Accident Test Station. Technical Report ORNL/LTR-2018/527, Oak Ridge National Laboratory, 2018.

@TechReport{Pint2018,
    author = "Pint, B. A. and Baldesberger, L. A.",
    title = "{Steam Oxidation and Burst Testing in the Severe Accident Test Station}",
    year = "2018",
    institution = "Oak Ridge National Laboratory",
    number = "ORNL/LTR-2018/527"
}

B. A. Pint, L. A. Baldesberger, and K. A. Kane. Steam oxidation, burst and critical heat flux testing of commercial FeCrAl cladding. In J.H. Jackson et al., editor, Proc. of the 19th International Conference on Environmental Degradation of Materials in Nuclear Power Systems - Water Reactors, 311–319. Boston, MA, United States, August 2020. ANS.

@INPROCEEDINGS{Pint2019,
    Author = "Pint, B. A. and Baldesberger, L. A. and Kane, K. A.",
    editor = "et al., J.H. Jackson",
    Title = "{Steam oxidation, burst and critical heat flux testing of commercial FeCrAl cladding}",
    BookTitle = "Proc. of the 19th International Conference on Environmental Degradation of Materials in Nuclear Power Systems - Water Reactors",
    Pages = "311-319",
    publisher = "ANS",
    address = "Boston, MA, United States",
    year = "2020",
    month = "August"
}

R. B. Rebak. Beneficial Oxidation Resistance of FeCrAl Alloys for Accident Tolerant Fuel Cladding. In The European Corrosion Congress (EUROCORR). Krakow, Poland, September 2018.

@INPROCEEDINGS{Rebak2018,
    Author = "Rebak, R. B.",
    Title = "{Beneficial Oxidation Resistance of FeCrAl Alloys for Accident Tolerant Fuel Cladding}",
    BookTitle = "The European Corrosion Congress (EUROCORR)",
    address = "Krakow, Poland",
    year = "2018",
    month = "September"
}

R. T. Sweet and B. D. Wirth. BISON analysis of Accident Tolerant Fuel clad concepts during normal operation and LOCA conditions. In CASL Virtual Meeting, 157–160. ANS, November 2020.

@INPROCEEDINGS{Sweet2020,
    Author = "Sweet, R. T. and Wirth, B. D.",
    Title = "{BISON analysis of Accident Tolerant Fuel clad concepts during normal operation and LOCA conditions}",
    BookTitle = "CASL Virtual Meeting",
    publisher = "ANS",
    Pages = "157-160",
    year = "2020",
    month = "November"
}

Y. Yamamoto, B.A. Pint, K.A. Terrani, K.G. Field, Y. Yang, and L.L. Snead. Development and property evaluation of nuclear grade wrought FeCrAl fuel cladding for light water reactors. Journal of Nuclear Materials, 467:703–716, 2015.

@article{yamamoto2015,
    author = "Yamamoto, Y. and Pint, B.A. and Terrani, K.A. and Field, K.G. and Yang, Y. and Snead, L.L.",
    title = "{Development and property evaluation of nuclear grade wrought FeCrAl fuel cladding for light water reactors}",
    journal = "Journal of Nuclear Materials",
    volume = "467",
    pages = "703-716",
    year = "2015"
}

Y. Yano, T. Tanno, Y. Sekio, H. Oka, S. Ohtsuka, T. Uwaba, and T. Kaito. Tensile properties and hardness of two types of 11cr-ferritic/martensitic steel after aging up to 45,000 h. Nuclear Materials and Energy, 000:1–7, 2016.

@article{yano2016,
    author = "Yano, Y. and Tanno, T. and Sekio, Y. and Oka, H. and Ohtsuka, S. and Uwaba, T. and Kaito, T.",
    title = "Tensile properties and hardness of two types of 11Cr-ferritic/martensitic steel after aging up to 45,000 h",
    journal = "Nuclear Materials and Energy",
    volume = "000",
    pages = "1-7",
    year = "2016"
}

(test/tests/solid_mechanics/fecral_failure/fecral_failure_inl.i)

# The FeCrAlCladding Failure model determines whether the clad has failed based
# upon one of four criteria:
#
# 1: Ultimate Tensile Strength
# 2: Tresca Criterion
# 3: Idaho National Laboratory developed Criterion
# 4: University of Tennessee developed Criterion
#
# This input file tests the Idaho National Laboratory (INL) criterion.  There are four
# thin tubes at different temperatures. The temperatures of the tubes are 300, 700,
# 900, and 1100 K respectively. The tubes are loaded on their internal surface
# with a pressure of 10 MPa.
#
# For the INL criterion the hoop stress is compared to the a burst stress that
# is a funciton of temperature.  The model depends on the temperature regime such that:
#
# sigma_burst = Ultimate Tensile Strength for T <= 796.8 K
# sigma_burst = 28440.98 * exp(-0.005588*T) for T > 796.8 K
#
# If the hoop stress is greater than the sigma_burst, the FeCrAl clad is said to
# have failed. Due to the applied internal pressure the hoop stress is 118.13 MPa.
# The only tube to fail is the tube at 1100 K as its sigma_burst is 60.8728 MPa.
#
#  Temperature (K)  Burst Stress (MPa)      Hoop Stress (MPa)       Failed?
#       300             568.9366                 118.13               NO
#       700             455.2929                 118.13               NO
#       900             186.1190                 118.13               NO
#      1100              60.8728                 118.13              YES
#

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst]
    order = CONSTANT
    family = MONOMIAL
  []

  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [inner_pressure]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e6 10e6'
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
  []

  [burst]
    type = MaterialRealAux
    variable = burst
    property = failed
  []
  [burst_stress]
    type = MaterialRealAux
    variable = burst_stress
    property = burst_stress
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [Pressure]
    [inner_pressure]
      boundary = '2 6 10 14'
      function = inner_pressure
    []
  []

  [y_bottom_top]
    type = DirichletBC
    boundary = '1 3 5 7 9 11 13 15'
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4'
  []

  [failure_fecral]
    type = FeCrAlCladdingFailure
    temperature = temp
    hoop_stress = hoop_stress
    failure_criterion = INL
  []

  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    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-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_failure/fecral_failure_inl.i)

# The FeCrAlCladding Failure model determines whether the clad has failed based
# upon one of four criteria:
#
# 1: Ultimate Tensile Strength
# 2: Tresca Criterion
# 3: Idaho National Laboratory developed Criterion
# 4: University of Tennessee developed Criterion
#
# This input file tests the Idaho National Laboratory (INL) criterion.  There are four
# thin tubes at different temperatures. The temperatures of the tubes are 300, 700,
# 900, and 1100 K respectively. The tubes are loaded on their internal surface
# with a pressure of 10 MPa.
#
# For the INL criterion the hoop stress is compared to the a burst stress that
# is a funciton of temperature.  The model depends on the temperature regime such that:
#
# sigma_burst = Ultimate Tensile Strength for T <= 796.8 K
# sigma_burst = 28440.98 * exp(-0.005588*T) for T > 796.8 K
#
# If the hoop stress is greater than the sigma_burst, the FeCrAl clad is said to
# have failed. Due to the applied internal pressure the hoop stress is 118.13 MPa.
# The only tube to fail is the tube at 1100 K as its sigma_burst is 60.8728 MPa.
#
#  Temperature (K)  Burst Stress (MPa)      Hoop Stress (MPa)       Failed?
#       300             568.9366                 118.13               NO
#       700             455.2929                 118.13               NO
#       900             186.1190                 118.13               NO
#      1100              60.8728                 118.13              YES
#

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst]
    order = CONSTANT
    family = MONOMIAL
  []

  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [inner_pressure]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e6 10e6'
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
  []

  [burst]
    type = MaterialRealAux
    variable = burst
    property = failed
  []
  [burst_stress]
    type = MaterialRealAux
    variable = burst_stress
    property = burst_stress
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [Pressure]
    [inner_pressure]
      boundary = '2 6 10 14'
      function = inner_pressure
    []
  []

  [y_bottom_top]
    type = DirichletBC
    boundary = '1 3 5 7 9 11 13 15'
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4'
  []

  [failure_fecral]
    type = FeCrAlCladdingFailure
    temperature = temp
    hoop_stress = hoop_stress
    failure_criterion = INL
  []

  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    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-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_failure/fecral_failure_utk.i)

# The FeCrAlCladding Failure model determines whether the clad has failed based
# upon one of four criteria:
#
# 1: Ultimate Tensile Strength
# 2: Tresca Criterion
# 3: Idaho National Laboratory developed Criterion
# 4: University of Tennessee developed Criterion
#
# This input file tests the University of Tennessee (UTK) criterion.  There are
# four thin tubes at different temperatures. The temperatures of the tubes are
# 300, 700, 900, and 1100 K respectively. The tubes are loaded on their internal
# surface with a pressure of 10 MPa.
#
# For the UTK criterion the hoop stress is compared to the a burst stress that is
# a function of temperature.  The expression for the burst stress (in MPa) is:
#
# sigma_burst = Ultimate Tensile Strength for T <= 829.4 K
# sigma_burst = 9750 * exp(-0.00419*T) - 14.7 for T > 829.4 K
#
# If the hoop stress is greater than the sigma_burst, the FeCrAl clad is said to
# have failed. Due to the applied internal pressure the hoop stress is 118.13 MPa.
# The only tube to fail is the tube at 1100 K as its sigma_burst is 82.4273 MPa.
#
#  Temperature (K)  Burst Stress (MPa)      Hoop Stress (MPa)       Failed?
#       300             568.9366                 118.13               NO
#       700             455.2929                 118.13               NO
#       900             209.8330                 118.13               NO
#      1100              82.4273                 118.13              YES
#

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst]
    order = CONSTANT
    family = MONOMIAL
  []

  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [inner_pressure]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e6 10e6'
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
  []

  [burst]
    type = MaterialRealAux
    variable = burst
    property = failed
  []
  [burst_stress]
    type = MaterialRealAux
    variable = burst_stress
    property = burst_stress
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [Pressure]
    [inner_pressure]
      boundary = '2 6 10 14'
      function = inner_pressure
    []
  []

  [y_bottom_top]
    type = DirichletBC
    boundary = '1 3 5 7 9 11 13 15'
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4'
  []

  [failure_fecral]
    type = FeCrAlCladdingFailure
    temperature = temp
    hoop_stress = hoop_stress
    failure_criterion = UTK
  []

  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    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-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1
  dt = 0.1
[]

[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_failure/fecral_failure_uts.i)

# The FeCrAlCladding Failure model determines whether the clad has failed based
# upon one of four criteria:
#
# 1: Ultimate Tensile Strength
# 2: Tresca Criterion
# 3: Idaho National Laboratory developed Criterion
# 4: University of Tennessee developed Criterion
#
# This input file tests the Ultimate Tensile Strength (UTS) criterion.  There are four
# thin tubes at different temperatures. The temperatures of the tubes are 300, 700,
# 900, and 1100 K respectively. The tubes are loaded on their internal surface
# with a pressure of 10 MPa.
#
# For the Ultimate Tensile Strength criterion the hoop stress is compared to the
# UTS calculated based upon the UTS function set internally to the FeCrAlFailure
# model. If the hoop stress is greater than the UTS, the FeCrAl clad is said to
# have failed. Due to the applied internal pressure the hoop stress is 118.3 MPa.
# The only tube to fail is the tube at 1100 K as its UTS is 57.8096 MPa.
#
#  Temperature (K)  Burst Stress (MPa)      Hoop Stress (MPa)       Failed?
#       300             568.9366                118.13                NO
#       700             455.2929                118.13                NO
#       900             202.7457                118.13                NO
#      1100              57.8096                118.13               YES

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst]
    order = CONSTANT
    family = MONOMIAL
  []

  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    decomposition_method = EigenSolution
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [inner_pressure]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e6 10e6'
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
  []

  [burst]
    type = MaterialRealAux
    variable = burst
    property = failed
  []
  [burst_stress]
    type = MaterialRealAux
    variable = burst_stress
    property = burst_stress
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [Pressure]
    [inner_pressure]
      boundary = '2 6 10 14'
      function = inner_pressure
    []
  []

  [y_bottom_top]
    type = DirichletBC
    boundary = '1 3 5 7 9 11 13 15'
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4'
  []

  [failure_fecral]
    type = FeCrAlCladdingFailure
    temperature = temp
    hoop_stress = hoop_stress
    failure_criterion = UTS
  []

  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    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-8
  nl_abs_tol = 1e-10
  l_tol = 1e-8

  start_time = 0.0
  end_time = 1
  dt = 0.1
[]

[Outputs]
  file_base = fecral_failure_uts_eigen_out
  exodus = true
[]

(test/tests/solid_mechanics/fecral_failure/fecral_failure_tresca.i)

# The FeCrAlCladding Failure model determines whether the clad has failed based
# upon one of four criteria:
#
# 1: Ultimate Tensile Strength
# 2: Tresca Criterion
# 3: Idaho National Laboratory developed Criterion
# 4: University of Tennessee developed Criterion
#
# This input file tests the Tresca criterion.  There are four thin tubes at
# different temperatures. The temperatures of the tubes are 300, 700, 900, and
# 1100 K respectively. The tubes are loaded on their internal surface with a
# pressure of 10 MPa.
#
# For the Tresca criterion the maximum shear stress is compared to the half of the
# yield stress (YS) calculated based upon the YS function set internally to the
# FeCrAlPlasticityUpdate model. If the maximum shear stress is greater than the
# YS, the FeCrAl clad is said to have failed. Due to the applied internal pressure
# maximum shear stress is 61.4386 MPa.
# The only tube to fail is the tube at 1100 K as half of its YS is 29.5461 MPa.
#
#  Temperature (K)  Burst Stress (MPa)      Max Shear Stress (MPa)       Failed?
#       300             221.0023                 61.4386                   NO
#       700             136.5982                 61.4386                   NO
#       900              80.2588                 61.4386                   NO
#      1100              29.5461                 61.4386                  YES
#

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst]
    order = CONSTANT
    family = MONOMIAL
  []

  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [burst_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [min_principal_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [mid_principal_stress]
    order = CONSTANT
    family = MONOMIAL
  []

  [max_principal_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [inner_pressure]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e6 10e6'
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
  []

  [burst]
    type = MaterialRealAux
    variable = burst
    property = failed
  []
  [burst_stress]
    type = MaterialRealAux
    variable = burst_stress
    property = burst_stress
  []
  [min_princial_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = min_principal_stress
    scalar_type = MinPrincipal
  []
  [mid_princial_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = mid_principal_stress
    scalar_type = MidPrincipal
  []
  [max_princial_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = max_principal_stress
    scalar_type = MaxPrincipal
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [Pressure]
    [inner_pressure]
      boundary = '2 6 10 14'
      function = inner_pressure
    []
  []

  [y_bottom_top]
    type = DirichletBC
    boundary = '1 3 5 7 9 11 13 15'
    variable = disp_y
    value = 0.0
  []
[]

[Materials]

  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4'
  []

  # For this test the plasticity model is only included to have access to the yield stress function. ComputeRadialReturnStress is not used in this test.
  [fecral_plasticity]
    type = FeCrAlPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    yield_stress = 1e6 #should be ignored
    hardening_constant = 0.0
  []
  [failure_fecral]
    type = FeCrAlCladdingFailure
    temperature = temp
    min_principal_stress = min_principal_stress
    mid_principal_stress = mid_principal_stress
    max_principal_stress = max_principal_stress
    failure_criterion = TRESCA
  []

  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    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-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References