- 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
Unit:(no unit assumed)
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
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) where is the instantaneous thermal expansion coefficient , , , and are fitting constants, and is the temperature in K. The fitting coefficients are tabulated in Table 1.
Table 1: Coefficients for instantaneous thermal expansion function
Alloy | ( 10) | ( 10) | ( 10) | |
---|---|---|---|---|
|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 (C) | CTE (m/m-K) 10 |
---|---|
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 (C) | CTE (m/m-K) 10 |
---|---|
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 (C) | CTE (m/m-K) 10 |
---|---|
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]
[eigenstrain_APMT]
type = FeCrAlThermalExpansionEigenstrain
block = 1
temperature = temp
fecral_material_type = APMT
eigenstrain_name = eigenstrain_APMT
stress_free_temperature = 300
[]
[]
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)The eigenstrain name must also be passed to the strain calculator, as shown below:
[Physics]
[SolidMechanics]
[QuasiStatic]
[APMT]
block = 1
strain = finite
eigenstrain_names = eigenstrain_APMT
[]
[MA956]
block = 2
strain = finite
eigenstrain_names = eigenstrain_MA956
[]
[]
[]
[]
(test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)Input 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
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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.
- 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.
- temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature
- 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
Unit:(no unit assumed)
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.
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
Outputs Parameters
Input Files
- (test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/APMT_MA956.i)
- (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/C36M.i)
- (test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C06M.i)
- (test/tests/solid_mechanics/fecral_eigenstrains/fecral_thermal_expansion/C35M.i)
References
- Special Metals Corporation.
Special Metals Incoloy alloy MA956.
www.specialmetals.com/documents/Incoloy+alloy+MA956.pdf, 2004.[BibTeX]
- 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.[BibTeX]
- MatWeb.
Resistalloy International Fecralloy Electrical Resistance Steel.
http://www.matweb.com/search/datasheet.aspx?MatGUID=c2427c6297594858bedac2a4e5981d2f, 2014.[BibTeX]
- MatWeb.
Schwarzkopf Plansee PM 2000.
http://www.matweb.com/search/datasheet.aspx?matguid=21e9ec9a0de24b47bcf69ab11c375567, 2014.[BibTeX]
- M. Niffenegger and K. Reichlin.
The proper use of thermal expansion coefficients in finite element calculations.
Nuclear Engineering and Design, 243:356–359, 2012.[BibTeX]