Mech FeCrAl

Computes the elastic moduli, coefficient of thermal expansion, and thermal creep of FeCrAl alloys

warning:Deprecated Solid Mechanics Material

The functionality of this solid mechanics material is being replaced in the TensorMechanics system:

Description

The MechFeCrAl model computes the elastic moduli, coefficient of thermal expansion, and thermal creep of a variety of FeCrAl alloys being considered for accident tolerant cladding.

Mechanical Properties

The mechanical properties of the FeCrAl alloys include Young's Modulus, Poisson's ratio, coefficient of thermal expansion, thermal creep and irradiation creep. Similarly to the thermal material properties introduced in the previous section, the Young's Modulus and coefficient of thermal expansion are provided in tabular format. The material property of interest is linearly interpolated between the data points available for the respective material. Note that the coefficient of thermal expansion is provided as an incremental coefficient and is converted into an instantaneous coefficient prior to interpolation inside the code. The tabulated data for MA956 (Corporation, 2004), PM2000 (MatWeb, 2014), Kanthal APMT (Sandvik, 2012), and Fecralloy (MatWeb, 2014) are reproduced in Table 1, Table 2, Table 3, and Table 4 respectively. The Poisson's ratio of MA956, PM2000, Kanthal APMT, and Fecralloy are 0.3, 0.33, 0.3 and 0.3 respectively.

A fifth FeCrAl alloy has been added called C35M that has been developed at ORNL (Thompson et al., 2015). The temperature dependent equations for Young's Modulus and Poisson's Ratio of C35M are given by: (1) and (2) respectively, where T is the temperature in K, and E is the Young's Modulus in GPa.

Table 1: Temperature dependent Young's Modulus and CTE of MA956 alloy

Temperature (K)Young's Modulus (GPa)Temp. Range (C)CTE (m/m-K)
310.4517220-
362.3017020 - 10011.3
424.4416720 - 20011.6
506.4216120 - 30011.9
592.2715320 - 40012.3
657.7614620 - 50012.7
754.0413920 - 60013.0
828.4113120 - 70013.4
900.5712120 - 80013.9
984.3911420 - 90014.4
1066.5510720 - 100014.9
1146.4499.420 - 110015.5
1208.1989.1
1269.0277.0
1347.6572.7

Table 2: Temperature dependent Young's Modulus and CTE of PM2000 alloy

Temperature (K)Young's Modulus (GPa)Temp. Range (C)CTE (m/m-K)
473.151602012.4
673.1514520 - 10013.1
873.1512520 - 25013.6
973.1511520 - 50014.7
1073.1511020 - 100015.4
1223.1595

Table 3: Temperature dependent Young's Modulus and CTE of Kanthal APMT alloy

Temperature (K)Young's Modulus (GPa)Temp. Range (C)CTE (m/m-K)
293.1522020 - 25010.7
373.1521020 - 50012.0
473.1520520 - 75012.2
673.1519020 - 100012.5
873.1517020 - 120015.1
1073.15150
1273.15130

Table 4: Temperature dependent Young's Modulus and CTE of Fecralloy

Temperature (K)Young's Modulus (GPa)Temp. Range (C)CTE (m/m-K)
293.1518020 - 25011.0
20 - 50012.0
20 - 100015.0

Thermal Creep

Thermal creep data exists for Incoloy MA956, Kanthal APMT, Fecralloy and C35M. However, the data provided for Kanthal APMT is not in a correlated form that allows for implementation into Bison. Therefore the thermal creep strain for both Kanthal APMT and PM2000 is set to zero in this material model until further data is available. The details of the thermal creep correlations for MA956, Fecralloy and C35M is provided in the following sections.

MA956

The thermal creep rate of MA956 is calculated by a Norton creep law as proposed by Seiler et al. (2011): (3) where Q is the activation energy, n is the creep exponent and an additional factor. The creep behavior of MA956 is characterized by three regimes with independent sets of creep parameters. The transition from one regime to another takes place at the critical stress and . These critical stresses are calculated during the simulation by equating two equations with the different creep parameters in the two regimes. For example the first critical stress is defined as (4) where and are parameters in the range , and and are parameters in the range , respectively. Table 5 lists the creep parameters of MA956 for the various stress regimes.

Table 5: Creep parameters of MA956

()n (-)Q (kJ/mol) ()
78.9784.98274530.0
3.466 41.04530.1
8.68 5.2911486-0.0122

Fecralloy

The model for thermal creep of Fecralloy is in the form of a Norton creep law as proposed by Saunders et al. (1997). The coefficient in the Norton law is in the form of an Arrhenius equation. (5) where is the effective stress in Pa and T is the temperature in K.

C35M

The model for thermal creep of C35M is in the form of a Norton creep law. As proposed Terrani et al. (2016), below 873 K the following correlation for thermal creep is adopted (6) while above 873 K, the correlation proposed by Saunders et al. (1997) is employed (7) where is the creep rate (s), the effective stress (Pa) and T (K) is the temperature.

The model incorporated into Bison for irradiation creep of FeCrAl alloys is taken from Terrani et al. (2016). The coefficient for irradiation creep recommended is per MPa per dpa. Utilizing the following conversion factor: n/m = 0.9 dpa, a correlation for irradiation creep can be derived. (8) where is the effective stress in MPa and is the fast neutron flux in n/m-s.

Example Input Syntax


[./APMT]
type = MechFeCrAl
block = 1
temp = temp
material = APMT
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
youngs_modulus = 2.2e11
poissons_ratio = 0.3
model_thermal_expansion = true
model_elastic_modulus = false
model_thermal_creep = false
stress_free_temperature = 300
formulation = Nonlinear3D
[../]
(test/tests/fecral/mech/thexpFeCrAl_APMT_MA956_test.i)

Input Parameters

• constitutive_modelConstitutiveModel to use (optional)

C++ Type:std::string

Description:ConstitutiveModel to use (optional)

• cracking_stress0The stress threshold beyond which cracking occurs. Must be positive.

Default:0

C++ Type:double

Description:The stress threshold beyond which cracking occurs. Must be positive.

• scale_factor_alpha1Scale factor to be applied to the temperature coefficient

Default:1

C++ Type:double

Description:Scale factor to be applied to the temperature coefficient

• scale_factor_A1Scale factor to be applied to the creep prefactor

Default:1

C++ Type:double

Description:Scale factor to be applied to the creep prefactor

• model_thermal_expansionTrueSet true to turn on thermal expansion model

Default:True

C++ Type:bool

Description:Set true to turn on thermal expansion model

• scale_factor_nu1Scale factor to be applied to the poisson's ratio

Default:1

C++ Type:double

Description:Scale factor to be applied to the poisson's ratio

• cracking_releaseabruptThe cracking release type. Choices are abrupt (default) and exponential.

Default:abrupt

C++ Type:std::string

Description:The cracking release type. Choices are abrupt (default) and exponential.

• activation_energy29709Activation energy for thermal creep of C35M

Default:29709

C++ Type:double

Description:Activation energy for thermal creep of C35M

• acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

Default:10

C++ Type:double

Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

• stress_exponent5.5Exponent applied to the stress for thermal creep of C35M

Default:5.5

C++ Type:double

Description:Exponent applied to the stress for thermal creep of C35M

• formulationElement formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

C++ Type:MooseEnum

Description:Element formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

• fast_neutron_fluxThe fast neutron flux

C++ Type:std::vector

Description:The fast neutron flux

• cracking_beta1The coefficient used in the exponetional model.

Default:1

C++ Type:double

Description:The coefficient used in the exponetional model.

• strain_zzThe zz strain

C++ Type:std::vector

Description:The zz strain

• compute_InteractionIntegralFalseWhether to compute the Interaction Integral.

Default:False

C++ Type:bool

Description:Whether to compute the Interaction Integral.

• thermal_expansion_reference_temperatureReference temperature for mean thermal expansion function.

C++ Type:double

Description:Reference temperature for mean thermal expansion function.

• stress_free_temperatureThe stress-free temperature. If not specified, the initial temperature is used.

C++ Type:double

Description:The stress-free temperature. If not specified, the initial temperature is used.

• youngs_modulusYoung's modulus of the material.

C++ Type:double

Description:Young's modulus of the material.

• initial_stressThe initial stress tensor (xx, yy, zz, xy, yz, zx)

C++ Type:std::vector

Description:The initial stress tensor (xx, yy, zz, xy, yz, zx)

• poissons_ratioPoisson's ratio for the material.

C++ Type:double

Description:Poisson's ratio for the material.

• compute_methodThe method used in the stress calculation.

C++ Type:MooseEnum

Description:The method used in the stress calculation.

• increment_calculationRashidApproxThe algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

Default:RashidApprox

C++ Type:std::string

Description:The algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

• disp_xThe x displacement

C++ Type:std::vector

Description:The x displacement

• model_elastic_modulusFalseSet true to calculate elastic moduli internally

Default:False

C++ Type:bool

Description:Set true to calculate elastic moduli internally

Default:1

C++ Type:double

Description:Scale factor to be applied to the irradiation creep

• volumetric_locking_correctionTrueSet to false to turn off volumetric locking correction

Default:True

C++ Type:bool

Description:Set to false to turn off volumetric locking correction

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• creep_coefficient2.89e-36Pre-exponential coefficient in the thermal creep correlation of C35M

Default:2.89e-36

C++ Type:double

Description:Pre-exponential coefficient in the thermal creep correlation of C35M

• max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step

Default:0.0001

C++ Type:double

Description:The maximum inelastic strain increment allowed in a time step

• scale_factor_n1Scale factor to be applied to the creep stress exponent

Default:1

C++ Type:double

Description:Scale factor to be applied to the creep stress exponent

• active_crack_planesPlanes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

C++ Type:std::vector

Description:Planes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

• scalar_strain_zzThe zz strain (scalar variable)

C++ Type:std::vector

Description:The zz strain (scalar variable)

• disp_zThe z displacement

C++ Type:std::vector

Description:The z displacement

• disp_yThe y displacement

C++ Type:std::vector

Description:The y displacement

• cracking_residual_stress0The fraction of the cracking stress allowed to be maintained following a crack.

Default:0

C++ Type:double

Description:The fraction of the cracking stress allowed to be maintained following a crack.

• shear_modulusThe shear modulus of the material.

C++ Type:double

Description:The shear modulus of the material.

• materialAPMTThe FeCrAl alloy of interest, choices are APMT, MA956, PM2000, FECRALLOY. Default is Kanthal APMT

Default:APMT

C++ Type:MooseEnum

Description:The FeCrAl alloy of interest, choices are APMT, MA956, PM2000, FECRALLOY. Default is Kanthal APMT

• thermal_expansion_function_typeType of thermal expansion function. Choices are: instantaneous mean

C++ Type:MooseEnum

Description:Type of thermal expansion function. Choices are: instantaneous mean

• disp_rThe r displacement

C++ Type:std::vector

Description:The r displacement

• appended_property_nameName appended to material properties to make them unique

C++ Type:std::string

Description:Name appended to material properties to make them unique

• bulk_modulusThe bulk modulus for the material.

C++ Type:double

Description:The bulk modulus for the material.

• poissons_ratio_functionPoisson's ratio as a function of temperature.

C++ Type:FunctionName

Description:Poisson's ratio as a function of temperature.

• dep_matl_propsNames of material properties this material depends on.

C++ Type:std::vector

Description:Names of material properties this material depends on.

• compute_material_timestep_limitFalseWhether to compute the matl_timestep_limit material property

Default:False

C++ Type:bool

Description:Whether to compute the matl_timestep_limit material property

• large_strainFalseWhether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

Default:False

C++ Type:bool

Description:Whether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

• store_stress_olderFalseParameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

Default:False

C++ Type:bool

Description:Parameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

• relative_tolerance1e-08Relative convergence tolerance for Newton iteration

Default:1e-08

C++ Type:double

Description:Relative convergence tolerance for Newton iteration

• scale_factor_Q1Scale factor to be applied to the creep activation energy

Default:1

C++ Type:double

Description:Scale factor to be applied to the creep activation energy

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• tempCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

• max_its30Maximum number of Newton iterations

Default:30

C++ Type:unsigned int

Description:Maximum number of Newton iterations

• cracking_neg_fractionThe fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

C++ Type:double

Description:The fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

• thermal_expansion_functionThermal expansion coefficient as a function of temperature.

C++ Type:FunctionName

Description:Thermal expansion coefficient as a function of temperature.

• compute_JIntegralFalseWhether to compute the J Integral.

Default:False

C++ Type:bool

Description:Whether to compute the J Integral.

Default:True

C++ Type:bool

Description:Set true to model irradiation creep

• max_cracks3The maximum number of cracks allowed at a material point.

Default:3

C++ Type:unsigned int

Description:The maximum number of cracks allowed at a material point.

• scale_factor_youngs1Scale factor to be applied to the youngs modulus

Default:1

C++ Type:double

Description:Scale factor to be applied to the youngs modulus

• thermal_expansionThe thermal expansion coefficient.

C++ Type:double

Description:The thermal expansion coefficient.

• scale_factor_cte1Scale factor to be applied to the thermal expansion coefficient

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal expansion coefficient

• cracking_stress_functionThe cracking stress as a function of time and location

C++ Type:FunctionName

Description:The cracking stress as a function of time and location

• absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

Default:1e-11

C++ Type:double

Description:Absolute convergence tolerance for Newton iteration

• youngs_modulus_functionYoung's modulus as a function of temperature.

C++ Type:FunctionName

Description:Young's modulus as a function of temperature.

• model_thermal_creepTrueSet true to model thermal creep

Default:True

C++ Type:bool

Description:Set true to model thermal creep

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

• lambdaLame's first parameter for the material.

C++ Type:double

Description:Lame's first parameter for the material.

Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• internal_solve_output_onon_errorWhen to output internal Newton solve information

Default:on_error

C++ Type:MooseEnum

Description:When to output internal Newton solve information

• internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.

Default:False

C++ Type:bool

Description:Set true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output.

Debug Parameters

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

References

1. Special Metals Corporation. Special Metals Incoloy alloy MA956. www.specialmetals.com/documents/Incoloy, 2004.[BibTeX]
2. MatWeb. Resistalloy International Fecralloy Electrical Resistance Steel. http://www.matweb.com/search/datasheet.aspx?MatGUID=c2427c6297594858bedac2a4e5981d2f, 2014.[BibTeX]
3. MatWeb. Schwarzkopf Plansee PM 2000. http://www.matweb.com/search/datasheet.aspx?matguid=21e9ec9a0de24b47bcf69ab11c375567, 2014.[BibTeX]
4. Sandvik. Kanthal APMT Material Database. http://kanthal.com/en/products/material-datasheets/tube/kanthal-apmt/, 2012.[BibTeX]
5. S. R. J. Saunders, H. E. Evans, M. Li, D. D. Gohil, and S. Osgerby. Oxidation growth stresses in an alumina-forming ferritic steel measured by creep deflection. Oxidation of Metals, 48:189â€“200, 1997.[BibTeX]
6. P. Seiler, M. BÃ¤ker, and J. RÃ¶sler. Variation of creep properties and interfacial roughness in thermal barrier coating systems. Advanced Ceramic Coatings and Materials for Extreme Environments, 32:129â€“136, 2011.[BibTeX]
7. K. A. Terrani, T. M. Karlsen, and Y. Yamamoto. Input correlations for irradiation creep of FeCrAl and SiC based on in-pile Halden test results. Technical Report ORNL/TM-2016/191, ORNL, May 2016.[BibTeX]
8. Z. T. Thompson, K. A. Terrani, and Y. Yamamoto. Elastic Modulus Measurement of ORNL ATF FeCrAl Alloys. Technical Report ORNL/TM-2015/632, Oak Ridge National Laboratory, October 2015.[BibTeX]