FeCrAlThermalExpansionEigenstrain

Computes the eigenstrain due to thermal expansion using a function that describes the mean thermal expansion as a function of temperature. The function is calculated internally based upon the FeCrAl alloy of interest.

Description

The FeCrAlThermalExpansionEigenstrain model computes the eigenstrain due to thermal expansion FeCrAl alloys. Seven alloys are available to choose from including the commercial alloys Kanthal APMT, Incoloy MA956, Plansee PM2000, and Fecralloy as well as the Oak Ridge National Laboratory alloys C06M, C35M, and C36M.

For Kanthal APMT, C06M, C35M, and C36M, the FeCrAl handbook (Field et al., 2018) provides a correlation for the instantaneous thermal expansion coefficient. This correlation is given by:

$(1)var element = document.getElementById("moose-equation-74bb2f8b-51cb-4217-bb58-97427f9f8ef0");katex.render(" \\alpha = 1.0 \\times 10^{-6} \\left(A_1 T^3 + A_2 T^2 + A_3 T + A_4\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4a672408-d9cc-4585-acb7-e8f33603c0b0");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ is the instantaneous thermal expansion coefficient $var element = document.getElementById("moose-equation-813fd538-5947-4cf0-b59b-648ebe3eb79b");katex.render("A_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-9f649a81-5334-432f-949b-e83389b6d40d");katex.render("A_2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-849f8e1c-7e84-437e-aeca-890c88229304");katex.render("A_3", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-4dc56d44-a811-4844-af7c-9ecb865c6e7c");katex.render("A_4", element, {displayMode:false,throwOnError:false});$ are fitting constants, and $var element = document.getElementById("moose-equation-9d849abc-d4be-43ad-a20a-4ce479cf7fff");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K. The fitting coefficients are tabulated in Table 1.

Table 1: Coefficients for instantaneous thermal expansion function

Alloy	$var element = document.getElementById("moose-equation-d43ac34b-9431-48a1-b566-9746245b40de");katex.render("A_1", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-2715a0bb-4089-4435-85ec-7a115f586781");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-2824cbb8-e7b5-4d91-a837-1fc3282271f5");katex.render("^{-10}", element, {displayMode:false,throwOnError:false});$ )	$var element = document.getElementById("moose-equation-ab1f77d5-ed8d-4f98-b75a-a180926cedc3");katex.render("A_2", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-0d022acf-510c-45d9-aa69-b76f3d34fa32");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-a0b478ac-a830-4688-bd76-b276daff141c");katex.render("^{-7}", element, {displayMode:false,throwOnError:false});$ )	$var element = document.getElementById("moose-equation-93314982-c8c5-4a03-ad85-bb191bdbe7d2");katex.render("A_3", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-76c5ee33-e682-4ff4-a8e5-6f4f7ee1e75c");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-974f982d-da54-47b5-b34b-2acdb6169c1a");katex.render("^{-3}", element, {displayMode:false,throwOnError:false});$ )	$var element = document.getElementById("moose-equation-00f125b2-a977-43e1-aa4f-8606cd61195f");katex.render("A_4", element, {displayMode:false,throwOnError:false});$
\|Kanthal APMT	1.771	9.558	1.937	10.27
\|C06M	10.74	-21.36	4.694	10.03
\|C35M	9.095	-17.46	4.530	9.810
\|C36M	3.079	2.719	2.535	10.56

The values provided in the literature for the coefficient of thermal expansion (CTE) of MA956, PM2000 and Fecralloy are provided as mean thermal expansion values with a reference temperature of 293.15 K. The method of Niffenegger and Reichlin (2012) is employed to convert the mean thermal expansion values tabulated below into instantaneous values. The methodology described by Niffenegger and Reichlin (2012) is described in detail on the page for ComputeMeanThermalExpansionFunctionEigenstrain in MOOSE.

Table 2: The mean CTE as a function of temperature for MA956 (Corporation, 2004)

Temperature ( $var element = document.getElementById("moose-equation-f297bd53-2045-4a12-84c9-9770efb1abe5");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C)	CTE (m/m-K) $var element = document.getElementById("moose-equation-cbe0601d-feec-4f55-8377-7b26d87aa53b");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-ec04c7f9-9ef3-4a21-a29c-a019af6122c3");katex.render("^{-6}", element, {displayMode:false,throwOnError:false});$
100	11.3
200	11.6
300	11.9
400	12.3
500	12.7
600	13.0
700	13.4
800	13.9
900	14.4
1000	14.9
1100	15.5

Table 3: The mean CTE as a function of temperature for PM2000 (MatWeb, 2014)

Temperature ( $var element = document.getElementById("moose-equation-dace1e1e-1fda-4bdf-8aa7-cd64078ed01b");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C)	CTE (m/m-K) $var element = document.getElementById("moose-equation-15782764-f00e-4ea8-b2b4-978944b4ca77");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-a56caf78-7bfe-4e1c-90a1-65f2db032562");katex.render("^{-6}", element, {displayMode:false,throwOnError:false});$
100	12.4
250	13.1
500	14.7
1000	15.4

Table 4: The mean CTE as a function of temperature for Fecralloy (MatWeb, 2014)

Temperature ( $var element = document.getElementById("moose-equation-24f67ef4-948a-4cd9-995d-3f6cc71b2af5");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C)	CTE (m/m-K) $var element = document.getElementById("moose-equation-9c78b05e-861a-46cd-a194-f9caab9826ff");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-25c64c38-5226-42d6-867d-dfd7bcc0aa91");katex.render("^{-6}", element, {displayMode:false,throwOnError:false});$
250	11.0
500	12.0
1000	15.0

Range of Applicability and Uncertainty

The temperature range over which the models for the thermal expansion coefficient is valid depends upon the material analyzed. For Kanthal APMT, C06M, C35M, and C36M the correlation is valid from 293 K to 1500 K. The piecewise linear data is valid from 293.15 K to 1373.15 K for MA956, 293.15 K to 1273.15 K for PM2000, and 293.15 K to 1273.15 K for Fecralloy.

The experimental data for the instantaneous thermal expansion coefficient of Kanthal APMT, C06M, C35M, and C36M was obtained from four measurements: two in the rolling and transverse directions respectively. The mean of these four measurements represent the data point provided in the Handbook with the error bars representing one standard deviation. Examining all of the alloys and excluding the room temperature measurement (since the reference temperature of the material is also room temperature), the uncertainty in the thermal expansion coefficient ranges from 3% to 4% over the temperature range of applicability. For 95% confidence two standard deviations is required. Therefore, the uncertainty is multiplied by two resulting in the uncertainty of the model being 8% over the temperature range of applicability.

Uncertainty in the the experimental data for MA956, PM2000, and Fecralloy is not provided, but based upon the uncertainty in the measurements for Kanthal APMT and the laboratory optimized alloys, a temperature independent uncertainty of 8% on the thermal expansion coefficient is recommended for conservatism.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain<<<{"description": "Computes the eigenstrain due to thermal expansion using a function that describes the mean thermal expansion as a function of temperature. The function is calculated internally based upon the FeCrAl alloy of interest.", "href": "FeCrAlThermalExpansionEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    fecral_material_type<<<{"description": "The FeCrAl alloy being used for the cladding. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY"}>>> = APMT
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = eigenstrain_APMT
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 300
  []
[]

The eigenstrain name must also be passed to the strain calculator, as shown below:

[Physics<<<{"href": "../../../syntax/Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../../syntax/Physics/SolidMechanics/index.html"}>>>]
    [QuasiStatic<<<{"href": "../../../syntax/Physics/SolidMechanics/QuasiStatic/index.html"}>>>]
      [APMT]
        block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = 1
        strain<<<{"description": "Strain formulation"}>>> = finite
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = eigenstrain_APMT
      []
      [MA956]
        block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = 2
        strain<<<{"description": "Strain formulation"}>>> = finite
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = eigenstrain_MA956
      []
    []
  []
[]

Input Parameters

eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
stress_free_temperatureReference temperature at which there is no thermal expansion for thermal eigenstrain calculation
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation

Required Parameters

base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
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
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_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.
fecral_material_typeAPMTThe FeCrAl alloy being used for the cladding. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY
Default:APMT
C++ Type:MooseEnum
Options:APMT, C06M, C35M, C36M, MA956, PM2000, FECRALLOY
Controllable:No
Description:The FeCrAl alloy being used for the cladding. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY
mean_thermal_expansion_coefficient_nameName of the mean coefficient of thermal expansion.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the mean coefficient of thermal expansion.
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

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

cte_scale_factor1Scale factor to be applied to the thermal expansion coefficient. 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 expansion coefficient. Used for calibration and sensitivity studies

Advanced: Scaling Factors 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_eigenstrains/fecral_thermal_expansion/PM2000_Fecralloy.i)
(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C35M.i)
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C36M.i)
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C06M.i)

References

Special Metals Corporation. Special Metals Incoloy alloy MA956. www.specialmetals.com/documents/Incoloy+alloy+MA956.pdf, 2004.

@MISC{ma956_2004,
    author = "Corporation, Special Metals",
    title = "{Special Metals Incoloy alloy MA956}",
    howpublished = "www.specialmetals.com/documents/Incoloy+alloy+MA956.pdf",
    year = "2004"
}

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/SPR-2018/905 Rev. 1, Oak Ridge National Laboratory, 2018.

@TECHREPORT{fecral_handbook,
    author = "Field, K. G. and Snead, M. A. and Yamamoto, Y. and Terrani, K. A.",
    title = "Handbook on the Material Properties of FeCrAl Alloys for Nuclear Power Production Applications",
    institution = "Oak Ridge National Laboratory",
    number = "ORNL/SPR-2018/905 Rev. 1",
    year = "2018"
}

MatWeb. Resistalloy International Fecralloy Electrical Resistance Steel. http://www.matweb.com/search/datasheet.aspx?MatGUID=c2427c6297594858bedac2a4e5981d2f, 2014.

@MISC{fecralloy_matweb,
    author = "MatWeb",
    title = "{Resistalloy International Fecralloy Electrical Resistance Steel}",
    howpublished = "http://www.matweb.com/search/datasheet.aspx?MatGUID=c2427c6297594858bedac2a4e5981d2f",
    year = "2014"
}

MatWeb. Schwarzkopf Plansee PM 2000. http://www.matweb.com/search/datasheet.aspx?matguid=21e9ec9a0de24b47bcf69ab11c375567, 2014.

@MISC{pm2000_matweb,
    author = "MatWeb",
    title = "{Schwarzkopf Plansee PM 2000}",
    howpublished = "http://www.matweb.com/search/datasheet.aspx?matguid=21e9ec9a0de24b47bcf69ab11c375567",
    year = "2014"
}

M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in finite element calculations. Nuclear Engineering and Design, 243:356–359, 2012.

@article{niffenegger2012,
    author = "Niffenegger, M. and Reichlin, K.",
    title = "The proper use of thermal expansion coefficients in finite element calculations",
    journal = "Nuclear Engineering and Design",
    volume = "243",
    pages = "356-359",
    year = "2012"
}

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)

# This tests the thermal expansion coefficient function for both
# APMT and MA956 FeCrAl alloys.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s. Block one is treated as APMT and block two as
# MA956. The thermal strain is calculated by using the method of:
#
# M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in
# finite element calculations. Nuclear Engineering and Design, 243:356-359, Feb. 2012.
#
# for MA956 because the thermal expansions are given as mean values.
#
# The analytical and BISON calculations of displacement is shown below for the
# two materials. The calculation is done using finite strain formulation.
#
#                       APMT                               MA956
#            ------------------------------------------------------------------
#  Temp      BISON Disp.    Analytical Disp.     BISON Disp.   Analytical Disp.
#  (K)          (m)              (m)                (m)              (m)
#  300           0                0                 0                 0
#  420       1.333321e-3      1.333321e-3       1.374670e-3      1.374670e-3
#  540       2.709371e-3      2.709371e-3       2.839372e-3      2.839372e-3
#  660       4.132522e-3      4.132522e-3       4.424986e-3      4.424986e-3
#  780       5.607399e-3      5.607399e-3       6.133877e-3      6.133877e-3
#  900       7.138883e-3      7.138883e-3       7.907337e-3      7.907337e-3
#  1020      8.732114e-3      8.732114e-3       9.880418e-3      9.880418e-3
#  1140      1.039249e-2      1.039249e-2       1.204799e-2      1.204799e-2
#  1260      1.212570e-2      1.212570e-2       1.436627e-2      1.436627e-2
#  1380      1.393768e-2      1.393768e-2       1.690892e-2      1.690892e-2
#  1500      1.583466e-2      1.583466e-2       1.880200e-2      1.880200e-2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 'blocks.e'
  []
[]

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [APMT]
    block = 1
    strain = finite
    eigenstrain_names = eigenstrain_APMT
  []
  [MA956]
    block = 2
    strain = finite
    eigenstrain_names = eigenstrain_MA956
  []
[]

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = 3
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = '1 2'
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor_APMT]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress_APMT]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 1
    temperature = temp
    fecral_material_type = APMT
    eigenstrain_name = eigenstrain_APMT
    stress_free_temperature = 300
  []

  [elasticity_tensor_MA956]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
  []

  [stress_MA956]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []

  [eigenstrain_MA956]
    type = FeCrAlThermalExpansionEigenstrain
    block = 2
    temperature = temp
    fecral_material_type = MA956
    eigenstrain_name = eigenstrain_MA956
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp_1]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 101
  []

  [disp_2]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 102
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)

# This tests the thermal expansion coefficient function for both
# APMT and MA956 FeCrAl alloys.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s. Block one is treated as APMT and block two as
# MA956. The thermal strain is calculated by using the method of:
#
# M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in
# finite element calculations. Nuclear Engineering and Design, 243:356-359, Feb. 2012.
#
# for MA956 because the thermal expansions are given as mean values.
#
# The analytical and BISON calculations of displacement is shown below for the
# two materials. The calculation is done using finite strain formulation.
#
#                       APMT                               MA956
#            ------------------------------------------------------------------
#  Temp      BISON Disp.    Analytical Disp.     BISON Disp.   Analytical Disp.
#  (K)          (m)              (m)                (m)              (m)
#  300           0                0                 0                 0
#  420       1.333321e-3      1.333321e-3       1.374670e-3      1.374670e-3
#  540       2.709371e-3      2.709371e-3       2.839372e-3      2.839372e-3
#  660       4.132522e-3      4.132522e-3       4.424986e-3      4.424986e-3
#  780       5.607399e-3      5.607399e-3       6.133877e-3      6.133877e-3
#  900       7.138883e-3      7.138883e-3       7.907337e-3      7.907337e-3
#  1020      8.732114e-3      8.732114e-3       9.880418e-3      9.880418e-3
#  1140      1.039249e-2      1.039249e-2       1.204799e-2      1.204799e-2
#  1260      1.212570e-2      1.212570e-2       1.436627e-2      1.436627e-2
#  1380      1.393768e-2      1.393768e-2       1.690892e-2      1.690892e-2
#  1500      1.583466e-2      1.583466e-2       1.880200e-2      1.880200e-2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 'blocks.e'
  []
[]

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [APMT]
    block = 1
    strain = finite
    eigenstrain_names = eigenstrain_APMT
  []
  [MA956]
    block = 2
    strain = finite
    eigenstrain_names = eigenstrain_MA956
  []
[]

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = 3
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = '1 2'
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor_APMT]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress_APMT]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 1
    temperature = temp
    fecral_material_type = APMT
    eigenstrain_name = eigenstrain_APMT
    stress_free_temperature = 300
  []

  [elasticity_tensor_MA956]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
  []

  [stress_MA956]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []

  [eigenstrain_MA956]
    type = FeCrAlThermalExpansionEigenstrain
    block = 2
    temperature = temp
    fecral_material_type = MA956
    eigenstrain_name = eigenstrain_MA956
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp_1]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 101
  []

  [disp_2]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 102
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/PM2000_Fecralloy.i)

# This tests the thermal expansion coefficient function for both
# PM2000 and Fecralloy FeCrAl alloys using linear interpolation internal
# to the material model of the mean thermal expansion coefficient.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s. Block one is treated as PM2000 and block two as
# Fecralloy. The thermal strain is calculated by using the method of:
#
# M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in
# finite element calculations. Nuclear Engineering and Design, 243:356-359, Feb. 2012.
#
# The analytical and BISON calculations of displacement is shown below for the
# two materials.
#
#                      PM2000                             Fecralloy
#            ------------------------------------------------------------------
#  Temp      BISON Disp.    Analytical Disp.     BISON Disp.   Analytical Disp.
#  (K)          (m)              (m)                (m)              (m)
#  300           0                0                 0                 0
#  420       1.457023e-3      1.457023e-3       1.320775e-3      1.320775e-3
#  540       2.946627e-3      2.946627e-3       2.659975e-3      2.659975e-3
#  660       4.471406e-3      4.471406e-3       4.169178e-3      4.169178e-3
#  780       6.046689e-3      6.046689e-3       5.803214e-3      5.803214e-3
#  900       7.942676e-3      7.942676e-3       7.697647e-3      7.697647e-3
#  1020      9.993473e-3      9.993473e-3       9.770111e-3      9.770111e-3
#  1140      1.220001e-3      1.220001e-3       1.202169e-2      1.202169e-2
#  1260      1.456329e-2      1.456329e-2       1.445356e-2      1.445356e-2
#  1380      1.647041e-2      1.647041e-2       1.635862e-2      1.635862e-2
#  1500      1.831380e-2      1.831380e-2       1.818958e-2      1.818958e-2

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

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 'blocks.e'
  []
[]

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [PM2000]
    block = 1
    strain = finite
    eigenstrain_names = eigenstrain_PM2000
  []
  [Fecralloy]
    block = 2
    strain = finite
    eigenstrain_names = eigenstrain_Fecralloy
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = 3
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = '1 2'
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor_PM2000]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 1.6e11
    poissons_ratio = 0.3
  []

  [stress_PM2000]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [eigenstrain_PM2000]
    type = FeCrAlThermalExpansionEigenstrain
    block = 1
    temperature = temp
    fecral_material_type = PM2000
    eigenstrain_name = eigenstrain_PM2000
    stress_free_temperature = 300
  []

  [elasticity_tensor_Fecralloy]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.8e11
    poissons_ratio = 0.3
  []

  [stress_Fecralloy]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []

  [eigenstrain_Fecralloy]
    type = FeCrAlThermalExpansionEigenstrain
    block = 2
    temperature = temp
    fecral_material_type = Fecralloy
    eigenstrain_name = eigenstrain_Fecralloy
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp_1]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 101
  []

  [disp_2]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 102
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  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_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)

# This tests the thermal expansion coefficient function for both
# APMT and MA956 FeCrAl alloys.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s. Block one is treated as APMT and block two as
# MA956. The thermal strain is calculated by using the method of:
#
# M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in
# finite element calculations. Nuclear Engineering and Design, 243:356-359, Feb. 2012.
#
# for MA956 because the thermal expansions are given as mean values.
#
# The analytical and BISON calculations of displacement is shown below for the
# two materials. The calculation is done using finite strain formulation.
#
#                       APMT                               MA956
#            ------------------------------------------------------------------
#  Temp      BISON Disp.    Analytical Disp.     BISON Disp.   Analytical Disp.
#  (K)          (m)              (m)                (m)              (m)
#  300           0                0                 0                 0
#  420       1.333321e-3      1.333321e-3       1.374670e-3      1.374670e-3
#  540       2.709371e-3      2.709371e-3       2.839372e-3      2.839372e-3
#  660       4.132522e-3      4.132522e-3       4.424986e-3      4.424986e-3
#  780       5.607399e-3      5.607399e-3       6.133877e-3      6.133877e-3
#  900       7.138883e-3      7.138883e-3       7.907337e-3      7.907337e-3
#  1020      8.732114e-3      8.732114e-3       9.880418e-3      9.880418e-3
#  1140      1.039249e-2      1.039249e-2       1.204799e-2      1.204799e-2
#  1260      1.212570e-2      1.212570e-2       1.436627e-2      1.436627e-2
#  1380      1.393768e-2      1.393768e-2       1.690892e-2      1.690892e-2
#  1500      1.583466e-2      1.583466e-2       1.880200e-2      1.880200e-2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 'blocks.e'
  []
[]

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [APMT]
    block = 1
    strain = finite
    eigenstrain_names = eigenstrain_APMT
  []
  [MA956]
    block = 2
    strain = finite
    eigenstrain_names = eigenstrain_MA956
  []
[]

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = 3
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = 1
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = '1 2'
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor_APMT]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress_APMT]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 1
    temperature = temp
    fecral_material_type = APMT
    eigenstrain_name = eigenstrain_APMT
    stress_free_temperature = 300
  []

  [elasticity_tensor_MA956]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.72e11
    poissons_ratio = 0.3
  []

  [stress_MA956]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []

  [eigenstrain_MA956]
    type = FeCrAlThermalExpansionEigenstrain
    block = 2
    temperature = temp
    fecral_material_type = MA956
    eigenstrain_name = eigenstrain_MA956
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp_1]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 101
  []

  [disp_2]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 102
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C35M.i)

# This tests the thermal expansion coefficient function for C35M.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s.
#
# The analytical and BISON calculations of displacement is shown below.
# The calculation is done using finite strain formulation.
#
#  Temp      BISON Disp.    Analytical Disp.
#  (K)          (m)              (m)
#  300           0                0
#  420       1.351420e-3      1.351420e-3
#  540       2.756038e-3      2.756038e-3
#  660       4.212559e-3      4.212559e-3
#  780       5.720825e-3      5.720825e-3
#  900       7.281823e-3      7.281823e-3
#  1020      8.897695e-3      8.897695e-3
#  1140      1.057175e-2      1.057175e-2
#  1260      1.230846e-2      1.230846e-2
#  1380      1.411351e-2      1.411351e-2
#  1500      1.599376e-2      1.599376e-2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

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

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

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

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = 0
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 0
    temperature = temp
    fecral_material_type = C35M
    eigenstrain_name = thermal_strain
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp]
    type = NodalExtremeValue
    variable = disp_x
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C36M.i)

# This tests the thermal expansion coefficient function for C36M.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s.
#
# The analytical and BISON calculations of displacement is shown below.
# The calculation is done using finite strain formulation.
#
#  Temp      BISON Disp.    Analytical Disp.
#  (K)          (m)              (m)
#  300           0                0
#  420       1.383886e-3      1.383886e-3
#  540       2.812008e-3      2.812008e-3
#  660       4.287033e-3      4.287033e-3
#  780       5.812033e-3      5.812033e-3
#  900       7.390491e-3      7.390491e-3
#  1020      9.026306e-3      9.026306e-3
#  1140      1.072380e-2      1.072380e-2
#  1260      1.248771e-2      1.248771e-2
#  1380      1.432321e-2      1.432321e-2
#  1500      1.623593e-2      1.623593e-2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

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

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

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

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = 0
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 0
    temperature = temp
    fecral_material_type = C36M
    eigenstrain_name = thermal_strain
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp]
    type = NodalExtremeValue
    variable = disp_x
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C06M.i)

# This tests the thermal expansion coefficient function for C06M.
#
# In this test two 1x1x1 meter cubes are subjected to a linear temperature rise
# from 300 K to 1500 K over 1 s.
#
# The analytical and BISON calculations of displacement is shown below.
# The calculation is done using finite strain formulation.
#
#  Temp      BISON Disp.    Analytical Disp.
#  (K)          (m)              (m)
#  300           0                0
#  420       1.332430e-3      1.332430e-3
#  540       2.705701e-3      2.705701e-3
#  660       4.123996e-3      4.123996e-3
#  780       5.591722e-3      5.591722e-3
#  900       7.113503e-3      7.113503e-3
#  1020      8.694185e-3      8.694185e-3
#  1140      1.033883e-2      1.033883e-2
#  1260      1.205274e-2      1.205274e-2
#  1380      1.384140e-2      1.384140e-2
#  1500      1.571055e-2      1.571055e-2


[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

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

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

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
[]

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

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

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [bottom]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []

  [back]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[AuxKernels]
  [temp]
    type = FunctionAux
    variable = temp
    block = 0
    function = temp_func
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 2.2e11
    poissons_ratio = 0.3
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []

  [eigenstrain_APMT]
    type = FeCrAlThermalExpansionEigenstrain
    block = 0
    temperature = temp
    fecral_material_type = C06M
    eigenstrain_name = thermal_strain
    stress_free_temperature = 300
  []
[]

[Functions]
  [temp_func]
    type = PiecewiseLinear
    xy_data = '0 300
               1 1500'
  []
[]

[Postprocessors]
  [disp]
    type = NodalExtremeValue
    variable = disp_x
    block = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  l_max_its = 100
  l_tol = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

Description
Range of Applicability and Uncertainty
Example Input Syntax
Input Parameters
Input Files
References