# FeCrAl Elasticity Tensor

Calculates Young's modulus and Poisson's ratio as a function of temperature for FeCrAl alloys.

## Description

This model computes the isotropic elasticity tensor for FeCrAl alloys by calculating the Young's modulus and poisson's ratio as a function of temperature. The Young's modulus of various commercial FeCrAl alloys (MA956, PM2000, Kanthal APMT, and Fecralloy) as a function of temperature have been obtained from the datasheets of the manufacturers and are tabulated below. In Bison, the Young's modulus is linearly interpolated between the known values.

Table 1: The Young's modulus as a function of temperature for MA956 (Corporation, 2004)

Temperature (K)Young's Modulus (GPa)
310.45172
362.30170
424.44167
506.42161
592.27153
657.76146
754.04139
828.41131
900.57121
984.39114
1066.55107
1146.4499.4
1208.1989.1
1269.0277.0
1347.6572.7

Table 2: The Young's modulus as a function of temperature for PM2000 (MatWeb, 2014)

Temperature (K)Young's Modulus (GPa)
473.15160
673.15145
873.15125
973.15115
1073.15110
1223.1595

Table 3: The Young's modulus as a function of temperature for Kanthal APMT (Sandvik, 2012)

Temperature (K)Young's Modulus (GPa)
293.15220
373.15210
473.15205
673.15190
873.15170
1073.15150
1273.15130

For Fecralloy (MatWeb, 2014) the Young's modulus is only given at room temperature (293.15 K) as 180 GPa.

Table 4: The Poisson's ratio of the commercial FeCrAl alloys

AlloyPoisson's Ratio
MA9560.3
PM20000.33
Kanthal APMT0.3
Fecralloy0.3

For the laboratory optimized FeCrAl alloy under development at the Oak Ridge National Laboratory known as C35M, the temperature dependent Young's modulus and Poisson's ratio are given by Thompson et al. (2015): (1) (2) where is the Young's modulus (GPa), is Poisson's ratio, and is the temperature (C). These equations are valid for temperatures ranging from 25-850C.

## Example Input Syntax

[./elasticity_tensor]
type = FeCrAlElasticityTensor
temperature = temp
fecral_material_type = MA956
block = 1
[../]
(test/tests/tensor_mechanics/fecral_elasticity_tensor/youngsFeCrAl_MA956_test_tm.i)

## Input Parameters

• temperatureThe coupled temperature (K)

C++ Type:std::vector

Description:The coupled temperature (K)

### Required Parameters

• 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.

• elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.

C++ Type:FunctionName

Description:Optional function to use as a scalar prefactor on the elasticity tensor.

• 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

Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

• poissons_ratio_functionPoisson's ratio as a function of temperature.

C++ Type:FunctionName

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

• fecral_material_typeAPMTThe FeCrAl alloy being used for the cladding material. Choices are: APMT MA956 PM2000 FECRALLOY C35M

Default:APMT

C++ Type:MooseEnum

Description:The FeCrAl alloy being used for the cladding material. Choices are: APMT MA956 PM2000 FECRALLOY C35M

• 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

• 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

• youngs_modulus_functionYoung's modulus as a function of temperature.

C++ Type:FunctionName

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

### 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

• 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

### Outputs Parameters

• poissons_ratio_scale_factor1Scale factor to be applied to the Poisson's ratio. Used for calibration and sensitivity studies

Default:1

C++ Type:double

Description:Scale factor to be applied to the Poisson's ratio. Used for calibration and sensitivity studies

• youngs_modulus_scale_factor1Scale factor to be applied to the Young's modulus. Used for calibration and sensitivity studies

Default:1

C++ Type:double

Description:Scale factor to be applied to the Young's modulus. Used for calibration and sensitivity studies