ADADStainlessSteelThermalExpansionEigenstrain

Calculates eigenstrain due to isotropic thermal expansion in AISI 304 Stainless Steel in base SI units

Description

This material computes the coefficient of thermal expansion, in 1/K, for AISI 304 stainless steel based on the material properties given for a spark plasma sintering die in (Cincotti et al., 2007). The coefficient of thermal expansion value is computed solely as a function of temperature, T: $(1)var element = document.getElementById("moose-equation-4deec06a-15f0-4d98-8128-4216bd543b55");katex.render(" \\alpha = \\begin{cases} 1.72 \\times 10^{-5} & \\text{ if } 273.3 < T < 373 K \\\\ 1.78 \\times 10^{-5} & \\text{ if } 373 \\leq T < 588 K \\\\ 1.84 \\times 10^{-5} & \\text{ if } 588 \\leq T < 810.5 K \\end{cases}", element, {displayMode:true,throwOnError:false});$ where the calibration range is 273.3 to 810.5K.

The relationship for this thermal material property was set as a piecewise function with constant values based on the experimental data points (Cincotti et al., 2007), as shown in Figure 1.

Figure 1: Piecewise constant values for the coefficient of thermal expansion for AISI 304 stainless steel.

The local temperature is checked against the calibration range limits only once at the start of each timestep, using the value of the temperature from the previous converged timestep. The value of the coefficient of thermal expansion is calculated with the current value of the temperature.

Example Input File Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [stainless_steel_thermal_expansion]
    type = ADStainlessSteelThermalExpansionEigenstrain<<<{"description": "Calculates eigenstrain due to isotropic thermal expansion in AISI 304 Stainless Steel in base SI units", "href": "StainlessSteelThermalExpansionEigenstrain.html"}>>>
    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."}>>> = stainless_steel_thermal_expansion
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 300
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
  []
[]

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
coeffient_thermal_expansion_scale_factor1The scaling factor for the coefficient of thermal expansion
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor for the coefficient of thermal expansion
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.
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
use_old_temperatureFalseFlag to optionally use the temperature value from the previous timestep.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to optionally use the temperature value from the previous timestep.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/materials/stainless_steel/mechanical/ad_stainless_steel_thermal_expansion.i)

References

A. Cincotti, A. M. Locci, R. Orrù, and G. Cao. Modeling of SPS apparatus: temperature, current and strain distribution with no powders. AIChE Journal, 53(3):703–719, 2007. doi:10.1002/aic.11102.

@article{cincotti2007sps,
    author = "Cincotti, A. and Locci, A. M. and Orrù, R. and Cao, G.",
    title = "Modeling of {SPS} apparatus: Temperature, current and strain distribution with no powders",
    journal = "AIChE Journal",
    volume = "53",
    number = "3",
    pages = "703-719",
    doi = "10.1002/aic.11102",
    year = "2007"
}

(test/tests/materials/stainless_steel/mechanical/ad_stainless_steel_thermal_expansion.i)

# This model includes only mechanics on a patch mesh and is intended
# verify the implementation of the piecewise function for the coefficient of
# thermal expansion from Cincotti et al (2007) AIChE Journal, Vol 53 No 3,
# page 711 Figure 8d. The piecewise function is given as a function within
# the input file (thexp_exact), and the value of that function is compared
# at each timestep against the computed strain_{xx} calculated value

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
  coord_type = RZ
[]

[AuxVariables]
  [temperature]
    initial_condition = 300.0
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temperature
    function = temp_ramp
  []
[]

[Functions]
  [temp_ramp]
    type = ParsedFunction
    expression = '300 + 100.0/60.*t' #stand-in for a 100C/min heating rate
  []
  [thermal_expansion]
    type = ParsedFunction
    symbol_names = T
    symbol_values = temperature
    expression = 'if(T>588, (1.84e-5), if(T>373, (1.78e-5), (1.72e-5)))'
  []
  [thexp_exact]
    type = ParsedFunction
    symbol_names = 'ref_temperature thermal_expansion temperature'
    symbol_values = '300.0 thermal_expansion temperature'
    expression = 'thermal_expansion * (temperature - ref_temperature)'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = SMALL
        decomposition_method = EigenSolution
        add_variables = true
        use_automatic_differentiation = true
        eigenstrain_names = stainless_steel_thermal_expansion
        generate_output = 'strain_xx'
      []
    []
  []
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = ADDirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [stainless_steel_thermal_expansion]
    type = ADStainlessSteelThermalExpansionEigenstrain
    eigenstrain_name = stainless_steel_thermal_expansion
    stress_free_temperature = 300
    temperature = temperature
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = true

  petsc_options_iname = '-pc_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm          ilu         1'
  nl_max_its = 20
  l_max_its = 50
  dt = 20
  dtmin = 1.0e-8
  end_time = 250
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [thexp_exact]
    type = FunctionValuePostprocessor
    function = thexp_exact
  []
  [thexp_diff]
    type = DifferencePostprocessor
    value1 = strain_xx
    value2 = thexp_exact
    outputs = none
  []
  [thexp_max_diff]
    type = TimeExtremeValue
    postprocessor = thexp_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
  perf_graph = true
  file_base = stainless_steel_thermal_expansion_out
[]

(test/tests/materials/stainless_steel/mechanical/ad_stainless_steel_thermal_expansion.i)

# This model includes only mechanics on a patch mesh and is intended
# verify the implementation of the piecewise function for the coefficient of
# thermal expansion from Cincotti et al (2007) AIChE Journal, Vol 53 No 3,
# page 711 Figure 8d. The piecewise function is given as a function within
# the input file (thexp_exact), and the value of that function is compared
# at each timestep against the computed strain_{xx} calculated value

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
  coord_type = RZ
[]

[AuxVariables]
  [temperature]
    initial_condition = 300.0
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temperature
    function = temp_ramp
  []
[]

[Functions]
  [temp_ramp]
    type = ParsedFunction
    expression = '300 + 100.0/60.*t' #stand-in for a 100C/min heating rate
  []
  [thermal_expansion]
    type = ParsedFunction
    symbol_names = T
    symbol_values = temperature
    expression = 'if(T>588, (1.84e-5), if(T>373, (1.78e-5), (1.72e-5)))'
  []
  [thexp_exact]
    type = ParsedFunction
    symbol_names = 'ref_temperature thermal_expansion temperature'
    symbol_values = '300.0 thermal_expansion temperature'
    expression = 'thermal_expansion * (temperature - ref_temperature)'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = SMALL
        decomposition_method = EigenSolution
        add_variables = true
        use_automatic_differentiation = true
        eigenstrain_names = stainless_steel_thermal_expansion
        generate_output = 'strain_xx'
      []
    []
  []
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = ADDirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [stainless_steel_thermal_expansion]
    type = ADStainlessSteelThermalExpansionEigenstrain
    eigenstrain_name = stainless_steel_thermal_expansion
    stress_free_temperature = 300
    temperature = temperature
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = true

  petsc_options_iname = '-pc_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm          ilu         1'
  nl_max_its = 20
  l_max_its = 50
  dt = 20
  dtmin = 1.0e-8
  end_time = 250
[]

[Postprocessors]
  [temperature]
    type = ElementAverageValue
    variable = temperature
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [thexp_exact]
    type = FunctionValuePostprocessor
    function = thexp_exact
  []
  [thexp_diff]
    type = DifferencePostprocessor
    value1 = strain_xx
    value2 = thexp_exact
    outputs = none
  []
  [thexp_max_diff]
    type = TimeExtremeValue
    postprocessor = thexp_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
  perf_graph = true
  file_base = stainless_steel_thermal_expansion_out
[]

Description
Example Input File Syntax
Input Parameters
Input Files
References