Incoloy800HThermalExpansionEigenstrain

Computes an eigenstrain due to thermal expansion for Incoloy800H using a temperature-dependent instantaneous coefficient of thermal expansion.

Description

This computes the instantaneous coefficient of thermal expansion, $var element = document.getElementById("moose-equation-e72ba4b8-4e23-40d2-92ee-4fb9b997e73a");katex.render("\\alpha_i", element, {displayMode:false,throwOnError:false});$ , for Incoloy800H as a function of temperature. The function is applicable in the temperature range of $var element = document.getElementById("moose-equation-96f35583-c5b6-4a3a-ba46-41c9ad686e11");katex.render("293 \\leq T \\leq 1073", element, {displayMode:false,throwOnError:false});$ K (SMBV, ). To avoid extrapolation, temperatures, $var element = document.getElementById("moose-equation-55ff6af0-2a86-4947-921b-f0114581fd2b");katex.render("T", element, {displayMode:false,throwOnError:false});$ , outside this range are held at either the upper or lower temperature bound. The instantaneous linear coefficient of thermal expansion, K $var element = document.getElementById("moose-equation-1ec8cc96-ddfa-4910-826f-0c2159fd905b");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ , is

$var element = document.getElementById("moose-equation-984e7142-6b4c-4044-afcb-0052d1b4fa17");katex.render(" \\alpha(T) = 11.15 \\times 10^{-6} + 1.424 \\times 10^{-7} T - 2.750 \\times 10^{-10} T^2 + 2.334 \\times 10^{-13} T^3 - 7.197 \\times 10^{-17} T^4", element, {displayMode:true,throwOnError:false});$

An incremental approach using the average coefficient of thermal expansion over the time step computes the thermal strain as

$var element = document.getElementById("moose-equation-9d3f7a26-8acb-4bf1-9b2a-bc540aefd923");katex.render(" \\epsilon^{current}_{thermal} = \\epsilon^{old}_{thermal} + (T_{current}-T_{old}) \\frac{\\alpha_i(T_{current}) + \\alpha_i(T_{old})}{2},", element, {displayMode:true,throwOnError:false});$

where the subscripts denote if the current time step's value or previous time step's value is used. For the first time step, the thermal strain is assumed to be zero and the stress free temperature is used in place of the old temperature.

An automatic differentiation (AD) version is also available by adding the prefix AD to the name for the "type" parameter.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [Incoloy800H_cte]
    type = Incoloy800HThermalExpansionEigenstrain<<<{"description": "Computes an eigenstrain due to thermal expansion for Incoloy800H using a temperature-dependent instantaneous coefficient of thermal expansion.", "href": "Incoloy800HThermalExpansionEigenstrain.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."}>>> = thermal_eigenstrain
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 300.0
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

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.
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

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/incoloy800H_thermal_expansion/exact.i)
(test/tests/solid_mechanics/incoloy800H_thermal_expansion/ad_coupled.i)

References

SMBV. Data sheet for Inconel 800/H/800HT. [Online; accessed 28-Aug-2021]. URL: https://salomons-metalen.com/products/inconel-800h-ht.

@MISC{salomonsmetalen,
    author = "SMBV",
    title = "Data sheet for {I}nconel 800/{H}/800{HT}",
    note = "[Online; accessed 28-Aug-2021]",
    url = "https://salomons-metalen.com/products/inconel-800h-ht",
    institution = "Salomons Metalen B.V.",
    year = ""
}

(test/tests/solid_mechanics/incoloy800H_thermal_expansion/exact.i)

# Compares Incoloy800HThermalExapnsionEigenstrain to exact calculations of thermal expansion coefficient.
# The thermal strain should equal the amount of displacement in a single direction.
# A hand calculation shows this should be:
#   alpha_i         displacement
#   1.254E-05     0
#   1.329E-05     0.000322890
#   1.393E-05     0.000663163
#   1.650E-05     0.005481230
#   1.760E-05     0.010880414
#   1.797E-05     0.016511664
#   1.797E-05     0.022200911

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

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 3
    x_length = 1
    y_length = 1
    z_length = 1
  []
[]

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

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 20.0 80.0 100.0'
    y = '300.0 350.0 1050 1250.0'
  []
  [exact_therm_exp]
    type = ParsedFunction
    symbol_names = temp
    symbol_values = avg_T
    expression = 'T := if(temp < 293, 293, if(temp > 1073, 1073, temp)); (-7.197e-11 * T^4 + 2.334e-7 * T^3 - 2.750e-4 * T^2 + 1.424e-1 * T - 11.15) * 1e-6'
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    decomposition_method = EigenSolution
    add_variables = true
    eigenstrain_names = thermal_eigenstrain
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = DirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
  [back]
    type = DirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 196.5e9
    poissons_ratio = 0.339
  []
  [Incoloy800H_cte]
    type = Incoloy800HThermalExpansionEigenstrain
    eigenstrain_name = thermal_eigenstrain
    stress_free_temperature = 300.0
    temperature = temperature
    outputs = all
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_x_right]
    type = SideAverageValue
    boundary = right
    variable = disp_x
    execute_on = 'initial timestep_end'
  []
  [exact_instant_alpha]
    type = FunctionValuePostprocessor
    function = exact_therm_exp
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 10
  nl_abs_tol = 1e-19
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/incoloy800H_thermal_expansion/exact.i)

# Compares Incoloy800HThermalExapnsionEigenstrain to exact calculations of thermal expansion coefficient.
# The thermal strain should equal the amount of displacement in a single direction.
# A hand calculation shows this should be:
#   alpha_i         displacement
#   1.254E-05     0
#   1.329E-05     0.000322890
#   1.393E-05     0.000663163
#   1.650E-05     0.005481230
#   1.760E-05     0.010880414
#   1.797E-05     0.016511664
#   1.797E-05     0.022200911

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

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 3
    x_length = 1
    y_length = 1
    z_length = 1
  []
[]

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

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 20.0 80.0 100.0'
    y = '300.0 350.0 1050 1250.0'
  []
  [exact_therm_exp]
    type = ParsedFunction
    symbol_names = temp
    symbol_values = avg_T
    expression = 'T := if(temp < 293, 293, if(temp > 1073, 1073, temp)); (-7.197e-11 * T^4 + 2.334e-7 * T^3 - 2.750e-4 * T^2 + 1.424e-1 * T - 11.15) * 1e-6'
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    decomposition_method = EigenSolution
    add_variables = true
    eigenstrain_names = thermal_eigenstrain
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = DirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
  [back]
    type = DirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 196.5e9
    poissons_ratio = 0.339
  []
  [Incoloy800H_cte]
    type = Incoloy800HThermalExpansionEigenstrain
    eigenstrain_name = thermal_eigenstrain
    stress_free_temperature = 300.0
    temperature = temperature
    outputs = all
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_x_right]
    type = SideAverageValue
    boundary = right
    variable = disp_x
    execute_on = 'initial timestep_end'
  []
  [exact_instant_alpha]
    type = FunctionValuePostprocessor
    function = exact_therm_exp
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 10
  nl_abs_tol = 1e-19
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/incoloy800H_thermal_expansion/ad_coupled.i)

# Couples ADIncoloy800HThermalExapnsionEigenstrain to temperature using Automatic Differentiation
[GlobalParams]
  displacements = 'disp_x'
[]

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 500.0
  []
[]

[Kernels]
  [diffusion]
    type = ADHeatConduction
    variable = temperature
  []
  [dtime]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    decomposition_method = EigenSolution
    add_variables = true
    eigenstrain_names = thermal_eigenstrain
    use_automatic_differentiation = true
  []
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [temp_left]
    type = ADDirichletBC
    variable = temperature
    value = 1000
    boundary = left
  []
  [right_temp]
    type = ADDirichletBC
    variable = temperature
    value = 1000
    boundary = right
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 196.5e9
    poissons_ratio = 0.339
  []
  [Incoloy800H_cte]
    type = ADIncoloy800HThermalExpansionEigenstrain
    eigenstrain_name = thermal_eigenstrain
    stress_free_temperature = 500.0
    temperature = temperature
    outputs = all
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
  [therm]
    type = ADGenericConstantMaterial
    prop_names = 'density thermal_conductivity specific_heat'
    prop_values = '7940 11.5 460'
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [disp_x_right]
    type = SideAverageValue
    boundary = right
    variable = disp_x
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  num_steps = 10
  dt = 600
  nl_abs_tol = 1e-19
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References