Al6061CreepUpdate

Computes the thermal creep behavior of Al6061 cladding for plate fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

Thermal creep of Al6061 is calculated by the Al6061CreepUpdate model. This model must be run in conjunction with ComputeMultipleInelasticStress. Two models are available: a model for 6061-T6 (Summers et al., 2015) and a power law model.

Summers

The Summers thermal creep correlation uses a hyperbolic sine law. The creep strain rate, $var element = document.getElementById("moose-equation-07266fa4-b06c-4b01-8b26-04c2dae8e378");katex.render("\\dot{\\epsilon}", element, {displayMode:false,throwOnError:false});$ (1/s) is expressed as $var element = document.getElementById("moose-equation-713a8862-6637-46dc-9dfd-a0c7d65b3540");katex.render(" \\dot{\\epsilon} = A \\left[ \\sinh\\left(B\\sigma\\right) \\right]^n\\exp\\left(\\frac{-Q}{RT}\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f75a22bb-97bb-407d-b9ba-962830213226");katex.render("A = 2.91\\times10^{11}", element, {displayMode:false,throwOnError:false});$ (1/s), $var element = document.getElementById("moose-equation-760af565-496e-440f-af7e-ca00de22ff6f");katex.render("B = 0.0404", element, {displayMode:false,throwOnError:false});$ (1/MPa), $var element = document.getElementById("moose-equation-ac68a4c2-b360-480e-97b3-751f68c14b8c");katex.render("n = 1.74", element, {displayMode:false,throwOnError:false});$ (unitless), $var element = document.getElementById("moose-equation-8ec2ae04-41a2-42b8-9057-4fb714da619c");katex.render("Q = 204\\times10^{3}", element, {displayMode:false,throwOnError:false});$ (J/mol), $var element = document.getElementById("moose-equation-b378b0ae-41a1-45ba-9d34-a560bf6eca34");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the ideal gas constant (J/mol-K) and $var element = document.getElementById("moose-equation-04763764-44d6-4f39-845e-0c4670124b56");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K).

Power Law

In the power law model, the prefactor and exponent are functions of temperature. The creep strain rate, $var element = document.getElementById("moose-equation-3dfa7ac0-8a62-49ba-a17b-98565004a7f3");katex.render("\\dot{\\epsilon}", element, {displayMode:false,throwOnError:false});$ (1/s) is expressed as $var element = document.getElementById("moose-equation-d32f153f-00b9-45e7-83df-e747c5a9f29a");katex.render(" \\dot{\\epsilon} = A(T) \\sigma^{n(T)}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-9fc1c0f8-9368-40f8-b02f-fd19df227584");katex.render("A(T)", element, {displayMode:false,throwOnError:false});$ is the prefactor (1/MPa $var element = document.getElementById("moose-equation-e2112f8b-9e76-4306-bec7-eaea49feac45");katex.render("^n", element, {displayMode:false,throwOnError:false});$ s), $var element = document.getElementById("moose-equation-8f0b3453-218f-409f-ba0a-b01c9c0f8bd9");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the effective stress (MPa), $var element = document.getElementById("moose-equation-50bc3bb3-f077-43ad-b48c-8dc1379c5c36");katex.render("n", element, {displayMode:false,throwOnError:false});$ is the exponent (unitless), and $var element = document.getElementById("moose-equation-4b0e3e8d-1e7f-4858-9faf-bce4a3d0cecd");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K). The code converts stress from Pa to MPa internally for this model.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [creep]
    type = Al6061CreepUpdate<<<{"description": "Computes the thermal creep behavior of Al6061 cladding for plate fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "Al6061CreepUpdate.html"}>>>
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temperature
  []
[]

Al6061CreepUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [stress]
    type = ComputeMultipleInelasticStress<<<{"description": "Compute state (stress and internal parameters such as plastic strains and internal parameters) using an iterative process.  Combinations of creep models and plastic models may be used.", "href": "../ComputeMultipleInelasticStress.html"}>>>
    tangent_operator<<<{"description": "Type of tangent operator to return.  'elastic': return the elasticity tensor.  'nonlinear': return the full, general consistent tangent operator."}>>> = nonlinear
    inelastic_models<<<{"description": "The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second."}>>> = 'creep'
  []
[]

Input Parameters

temperatureThe coupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled temperature (K)

Required Parameters

absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute convergence tolerance for Newton iteration
acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Controllable:No
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
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
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
creep_modelSummersThe active creep model.
Default:Summers
C++ Type:MooseEnum
Options:power_law, Summers
Controllable:No
Description:The active creep model.
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.
max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The maximum inelastic strain increment allowed in a time step
maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.
Default:25
C++ Type:unsigned int
Controllable:No
Description:The maximum number of substeps allowed before cutting the time step.
power_law_exponent_functionThe function to use for the temperature-driven exponent in the power_law model.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function to use for the temperature-driven exponent in the power_law model.
power_law_prefactor_functionThe function to use for the temperature-driven prefactor in the power_law model.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function to use for the temperature-driven prefactor in the power_law model.
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping

Optional Parameters

activation_energy_scale_factor1Scale factor to be applied to the thermal creep activation energy. 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 creep activation energy. Used for calibration and sensitivity studies.
pre_exponential_scale_factor1Scale factor to be applied to the thermal creep exponential prefactor. 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 creep exponential prefactor. Used for calibration and sensitivity studies.
stress_exponent_scale_factor1Scale factor to be applied to the thermal creep stress exponent. 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 creep stress exponent. Used for calibration and sensitivity studies.

Advanced: Scaling Factors Parameters

apply_strainTrueFlag to apply strain. Used for testing.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to apply strain. Used for testing.
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.
effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain
Default:effective_creep_strain
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the effective inelastic strain
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
substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
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

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
Controllable:No
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.
internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Options:never, on_error, always
Controllable:No
Description:When to output internal Newton solve information

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<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/Al6061_creep/creep_power_law_ad.i)
(test/tests/solid_mechanics/Al6061_creep/creep_ad.i)
(test/tests/solid_mechanics/Al6061_creep/missing_exponent_function.i)
(test/tests/solid_mechanics/Al6061_creep/creep.i)
(test/tests/solid_mechanics/Al6061_creep/creep_power_law.i)

References

P. T. Summers, Y. Chen, C. M. Rippe, B. Allen, A. P. Mouritz, S. W. Case, and B. Y. Lattimer. Overview of aluminum alloy mechanical properties during and after fires. Fire Science Reviews, 2015. doi:10.1186/s40038-015-0007-5.

@article{Summers2015,
    author = "Summers, P. T. and Chen, Y. and Rippe, C. M. and Allen, B. and Mouritz, A. P. and Case, S. W. and Lattimer, B. Y.",
    title = "Overview of aluminum alloy mechanical properties during and after fires",
    journal = "Fire Science Reviews",
    volume = "4",
    year = "2015",
    doi = "10.1186/s40038-015-0007-5",
    publisher = "Springer"
}

(test/tests/solid_mechanics/Al6061_creep/creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the implementation of the thermal creep model that has been
#  added to Bison for Al6061.  The model was taken from:
#
#  Summers, P.T., Chen, Y., Rippe, C.M. et al. Overview of aluminum alloy
#  mechanical properties during and after fires. Fire Sci Rev 4, 3 (2015).
#  https://doi.org/10.1186/s40038-015-0007-5
#
# The correlation is given by:
#
#  e_dot = A * sinh(B*sigma)^n * exp(-Q/RT)                (s^-1)
#
#  where A ia 2.91e11 (s^-1), B is 0.0404 (MPa^-1), n is 1.74 (-), Q is
#  204e3 (J/mol), and R is the ideal gas constant taken as 8.314 J/mol-K.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a constant stress of 100 MPa under varying temperatures.
#  Results are taken from different times in the
#  simulation: 2e5, 4e5, 6e5, 8e5 and 1e6 seconds. The creep rate predicted by
#  Bison is compared to the analytical solution for these conditions.
#
#    Time (s)     Temperature     Analytical Creep       Bison Creep
#                     (C)            Rate (s^-1)          Rate (s^-1)
#
#      2e5           473.15          1.9000e-12           1.9000e-12
#      4e5           523.15          2.6988e-10           2.6988e-10
#      6e5           573.15          1.6145e-08           1.6145e-08
#      8e5           623.15          5.0093e-07           5.0093e-07
#      1e6           673.15          9.3303e-06           9.3303e-06
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y disp_z'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [temperature]
    initial_condition = 423.15
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '423.15 673.15'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        incremental = true
        generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress stress_yy'
        extra_vector_tags = 'ref'
      []
    []
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -10e6
    []
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 69e9
    poissons_ratio = 0.33
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'creep'
  []
  [creep]
    type = Al6061CreepUpdate
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 1e6

  dt = 1e4
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
  [stress_yy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = creep_out
    time_step_interval =  20
  []
[]

(test/tests/solid_mechanics/Al6061_creep/creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the implementation of the thermal creep model that has been
#  added to Bison for Al6061.  The model was taken from:
#
#  Summers, P.T., Chen, Y., Rippe, C.M. et al. Overview of aluminum alloy
#  mechanical properties during and after fires. Fire Sci Rev 4, 3 (2015).
#  https://doi.org/10.1186/s40038-015-0007-5
#
# The correlation is given by:
#
#  e_dot = A * sinh(B*sigma)^n * exp(-Q/RT)                (s^-1)
#
#  where A ia 2.91e11 (s^-1), B is 0.0404 (MPa^-1), n is 1.74 (-), Q is
#  204e3 (J/mol), and R is the ideal gas constant taken as 8.314 J/mol-K.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a constant stress of 100 MPa under varying temperatures.
#  Results are taken from different times in the
#  simulation: 2e5, 4e5, 6e5, 8e5 and 1e6 seconds. The creep rate predicted by
#  Bison is compared to the analytical solution for these conditions.
#
#    Time (s)     Temperature     Analytical Creep       Bison Creep
#                     (C)            Rate (s^-1)          Rate (s^-1)
#
#      2e5           473.15          1.9000e-12           1.9000e-12
#      4e5           523.15          2.6988e-10           2.6988e-10
#      6e5           573.15          1.6145e-08           1.6145e-08
#      8e5           623.15          5.0093e-07           5.0093e-07
#      1e6           673.15          9.3303e-06           9.3303e-06
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y disp_z'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [temperature]
    initial_condition = 423.15
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '423.15 673.15'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        incremental = true
        generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress stress_yy'
        extra_vector_tags = 'ref'
      []
    []
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -10e6
    []
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 69e9
    poissons_ratio = 0.33
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'creep'
  []
  [creep]
    type = Al6061CreepUpdate
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 1e6

  dt = 1e4
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
  [stress_yy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = creep_out
    time_step_interval =  20
  []
[]

(test/tests/solid_mechanics/Al6061_creep/creep_power_law_ad.i)

#--------------------------------------------------------------------------------
#  This test exercised a thermal creep law of the form
#  e_dot = A(T)*sigma^(n(T))
#
#  The loading reverses sign after the first solve.  The prefactor A and
#  the exponent n change but their effect is identical in each of the
#  two loads steps.  The result is that the net creep strain at the end
#  of the test is zero.
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y disp_z'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [temperature]
    initial_condition = 423.15
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '423.15 423.15 673.15'
  []
  [prefactor]
    type = PiecewiseLinear
    x = '423.15 673.15'
    y = '1e2 2e2'
    scale_factor = 1e-6
  []
  [exponent]
    type = PiecewiseLinear
    x = '423.15 673.15'
    y = '2 1'
  []
  [pressure]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 2e6 -2e6'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    incremental = true
    generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress stress_yy'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      function = pressure
      use_displaced_mesh = false
      use_automatic_differentiation = true
    []
  []
  [fix_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [fix_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.33
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
  [creep]
    type = ADAl6061CreepUpdate
    temperature = temperature
    creep_model = power_law
    power_law_prefactor_function = prefactor
    power_law_exponent_function = exponent
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 2

  dt = 1
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
  [stress_yy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/solid_mechanics/Al6061_creep/creep_ad.i)

#--------------------------------------------------------------------------------
#  This test verifies the implementation of the thermal creep model that has been
#  added to Bison for Al6061.  The model was taken from:
#
#  Summers, P.T., Chen, Y., Rippe, C.M. et al. Overview of aluminum alloy
#  mechanical properties during and after fires. Fire Sci Rev 4, 3 (2015).
#  https://doi.org/10.1186/s40038-015-0007-5
#
# The correlation is given by:
#
#  e_dot = A * sinh(B*sigma)^n * exp(-Q/RT)                (s^-1)
#
#  where A ia 2.91e11 (s^-1), B is 0.0404 (MPa^-1), n is 1.74 (-), Q is
#  204e3 (J/mol), and R is the ideal gas constant taken as 8.314 J/mol-K.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a constant stress of 100 MPa under varying temperatures.
#  Results are taken from different times in the
#  simulation: 2e5, 4e5, 6e5, 8e5 and 1e6 seconds. The creep rate predicted by
#  Bison is compared to the analytical solution for these conditions.
#
#    Time (s)     Temperature     Analytical Creep       Bison Creep
#                     (C)            Rate (s^-1)          Rate (s^-1)
#
#      2e5           473.15          1.9000e-12           1.9000e-12
#      4e5           523.15          2.6988e-10           2.6988e-10
#      6e5           573.15          1.6145e-08           1.6145e-08
#      8e5           623.15          5.0093e-07           5.0093e-07
#      1e6           673.15          9.3303e-06           9.3303e-06
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y disp_z'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [temperature]
    initial_condition = 423.15
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '423.15 673.15'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    incremental = true
    generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress stress_yy'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -10e6
      use_automatic_differentiation = true
    []
  []
  [fix_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [fix_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 69e9
    poissons_ratio = 0.33
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
  [creep]
    type = ADAl6061CreepUpdate
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 1e6

  dt = 1e4
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
  [stress_yy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = creep_ad_out
    time_step_interval =  20
  []
[]

(test/tests/solid_mechanics/Al6061_creep/missing_exponent_function.i)

[Materials]
  [creep]
    type = Al6061CreepUpdate
    temperature = temperature
    creep_model = power_law
    power_law_prefactor_function = prefactor
  []
[]

(test/tests/solid_mechanics/Al6061_creep/creep.i)

#--------------------------------------------------------------------------------
#  This test verifies the implementation of the thermal creep model that has been
#  added to Bison for Al6061.  The model was taken from:
#
#  Summers, P.T., Chen, Y., Rippe, C.M. et al. Overview of aluminum alloy
#  mechanical properties during and after fires. Fire Sci Rev 4, 3 (2015).
#  https://doi.org/10.1186/s40038-015-0007-5
#
# The correlation is given by:
#
#  e_dot = A * sinh(B*sigma)^n * exp(-Q/RT)                (s^-1)
#
#  where A ia 2.91e11 (s^-1), B is 0.0404 (MPa^-1), n is 1.74 (-), Q is
#  204e3 (J/mol), and R is the ideal gas constant taken as 8.314 J/mol-K.
#
#  In this test a uniaxial specimen is pulled in the axial direction by
#  a constant stress of 100 MPa under varying temperatures.
#  Results are taken from different times in the
#  simulation: 2e5, 4e5, 6e5, 8e5 and 1e6 seconds. The creep rate predicted by
#  Bison is compared to the analytical solution for these conditions.
#
#    Time (s)     Temperature     Analytical Creep       Bison Creep
#                     (C)            Rate (s^-1)          Rate (s^-1)
#
#      2e5           473.15          1.9000e-12           1.9000e-12
#      4e5           523.15          2.6988e-10           2.6988e-10
#      6e5           573.15          1.6145e-08           1.6145e-08
#      8e5           623.15          5.0093e-07           5.0093e-07
#      1e6           673.15          9.3303e-06           9.3303e-06
#--------------------------------------------------------------------------------

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y disp_z'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxVariables]
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [temperature]
    initial_condition = 423.15
  []
[]

[Functions]
  [temperature]
    type = PiecewiseLinear
    x = '0 1e6'
    y = '423.15 673.15'
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        incremental = true
        generate_output = 'elastic_strain_yy creep_strain_yy vonmises_stress stress_yy'
        extra_vector_tags = 'ref'
      []
    []
  []
[]

[AuxKernels]
  [creep_rate_aux]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -10e6
    []
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 69e9
    poissons_ratio = 0.33
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'creep'
  []
  [creep]
    type = Al6061CreepUpdate
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its  = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 1e6

  dt = 1e4
[]

[Postprocessors]
  [creep_rate]
    type = ElementAverageValue
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [vonmises_stress]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
  [stress_yy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'initial timestep_end'
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = creep_out
    time_step_interval =  20
  []
[]

(test/tests/solid_mechanics/Al6061_creep/creep_power_law.i)

[Materials]
  [creep]
    type = Al6061CreepUpdate
    temperature = temperature
    creep_model = power_law
    power_law_prefactor_function = prefactor
    power_law_exponent_function = exponent
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References