ADZryAnisoCreepLOCAUpdate

Computes the secondary thermal creep under loss-of-coolant accident conditions using the Erbacher (default), Kaddour, or Donaldson models; the Limback-Andersson primary thermal creep; and the Hoppe irradiation creep for Zircaloy cladding. This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

This class uses a generalized return mapping that allows for simulating anisotropic plastic and creep behavior. In short, ADZryAnisoCreepLimbackHoppeUpdate allows to employ the isotropic ADZryCreepLimbackHoppeUpdate class physics with anisotropic creep defined by Hill coefficients, i.e. $var element = document.getElementById("moose-equation-c8e006bb-039c-4db3-8f1f-925246a3a335");katex.render("F", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-29b39d50-a047-4eb6-a6eb-d3500d2cb192");katex.render("G", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-06e22833-5817-467a-a8c6-61fab4d6355d");katex.render("H", element, {displayMode:false,throwOnError:false});$ , for axial deformation; and $var element = document.getElementById("moose-equation-6ed24f8a-a41e-4a38-abff-40a9819f101a");katex.render("L", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-3356f515-d3c9-43d7-8c72-343a94fa9be6");katex.render("M", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-57db8ef9-5713-4574-b80f-f00e2df55f17");katex.render("N", element, {displayMode:false,throwOnError:false});$ , for shear deformation. These parameters are intended to capture the overall engineering-scale behavior of cladding metals due to their grain texture.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [hill]
    type = ADHillConstants<<<{"description": "Build and rotate the Hill Tensor. It can be used with other Hill plasticity and creep materials.", "href": "../HillConstants.html"}>>>
    hill_constants<<<{"description": "Hill material constants in order: F, G, H, L, M, N"}>>> = "0.5 0.5 0.5 1.0 1.0 1.0"
  []
[]

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [zry_thermal_creep]
    type = ADZryAnisoCreepLOCAUpdate<<<{"description": "Computes the secondary thermal creep under loss-of-coolant accident conditions using the Erbacher (default), Kaddour, or Donaldson models; the Limback-Andersson primary thermal creep; and the Hoppe irradiation creep for Zircaloy cladding. This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "ZryCreepLOCAUpdate.html"}>>>
    high_temperature_creep_model<<<{"description": "The model to use in calculating high temperature creep. Choices are: Erbacher Kaddour Donaldson"}>>> = erbacher
    temperature<<<{"description": "Coupled temperature (K)"}>>> = temp
    model_primary_creep<<<{"description": "Set true to activate primary creep"}>>> = false
    model_irradiation_creep<<<{"description": "Set true to activate irradiation induced creep"}>>> = false
    fract_beta_phase_name<<<{"description": "The name of the beta phase fraction material property"}>>> = 'ad_fract_beta_phase'
  []
[]

ADZryAnisoCreepLimbackHoppeUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below (used through ADZryAnisoCreepLOCAUpdate):

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [stress]
    type = ADComputeMultipleInelasticStress<<<{"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": "../ADComputeMultipleInelasticStress.html"}>>>
    inelastic_models<<<{"description": "The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second."}>>> = 'zry_thermal_creep'
  []
[]

Input Parameters

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
inelastic_strain_rate_namecreep_strain_rateName of the material property that stores the inelastic strain rate
Default:creep_strain_rate
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the inelastic strain rate

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
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
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.
fast_neutron_fluenceThe fast neutron fluence
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The fast neutron fluence
fast_neutron_fluxThe fast neutron flux
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The fast neutron flux
initial_fast_fluence0The initial fast neutron fluence
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The initial fast neutron fluence
max_creep_increment0.001Maximum creep strain increment allowed by accuracy time step criterion
Default:0.001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum creep strain increment allowed by accuracy time step criterion
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
max_integration_error0.0005The maximum inelastic strain increment integration error allowed
Default:0.0005
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The maximum inelastic strain increment integration error allowed
model_irradiation_creepTrueSet true to activate irradiation induced creep
Default:True
C++ Type:bool
Controllable:No
Description:Set true to activate irradiation induced creep
model_primary_creepTrueSet true to activate primary creep
Default:True
C++ Type:bool
Controllable:No
Description:Set true to activate primary creep
model_thermal_creepTrueSet true to activate steady state thermal creep
Default:True
C++ Type:bool
Controllable:No
Description:Set true to activate steady state thermal creep
outputThe reporting postprocessor to use for the max_iterations value.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor to use for the max_iterations value.
primary_creep_modelLIMBACKThe model to be used for primary thermal creep.
Default:LIMBACK
C++ Type:MooseEnum
Options:MATSUO, LIMBACK
Controllable:No
Description:The model to be used for primary thermal creep.
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
start_time0Start time (if not zero)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Start time (if not zero)
temperatureCoupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature (K)
use_transformationTrueWhether to employ updated Hill's tensor due to rigid body or large deformation kinematic rotations. If an initial rigid body rotation is provided by the user in increments of 90 degrees (e.g. 90, 180, 270), this option can be set to false, in which case the Hill's coefficients are extracted from the transformed Hill's tensor.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to employ updated Hill's tensor due to rigid body or large deformation kinematic rotations. If an initial rigid body rotation is provided by the user in increments of 90 degrees (e.g. 90, 180, 270), this option can be set to false, in which case the Hill's coefficients are extracted from the transformed Hill's tensor.
zircaloy_material_typeSTRESS_RELIEF_ANNEALEDType of zircaloy material properties to use in calculating creep. Note: ESCORE_IRRADIATIONGROWTHZR4 is not valid.
Default:STRESS_RELIEF_ANNEALED
C++ Type:MooseEnum
Options:STRESS_RELIEF_ANNEALED, RECRYSTALLIZATION_ANNEALED, PARTIAL_RECRYSTALLIZATION_ANNEALED, ZIRLO, M5, ESCORE_IRRADIATIONGROWTHZR4
Controllable:No
Description:Type of zircaloy material properties to use in calculating creep. Note: ESCORE_IRRADIATIONGROWTHZR4 is not valid.

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

creeprate_scale_factor1scaling factor for total creep rate. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:scaling factor for total creep rate. Used for calibration and sensitivity studies

Advanced: Scaling Factors 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

References

No citations exist within this document.

(test/tests/solid_mechanics/zry_creep/erbacher/ad_operating_to_loca_hill_creep_5.i)

#   This test case is prepared to test the transition from the standard, or normal operation creep to loca creep in ZryCreepUpdate..
#   There are a series of 5 tests, with different effective stress, temperature, and fraction of beta phase.
#
#   - Geometry:
#     1x1x1 cube, single element
#
#   - Temperature = 1250 K
#
#   - Boundary conditions:
#     Symetric boundary conditions for uniform expansion or contraction (in xy-plane disp_z = 0, xz-plane disp_y = 0, yz-plane disp_x = 0)
#
#   - Stresses
#     5 MPa applied to the top of the block.  This is the effective stress.
#
#
#  -  Loca creep rate from the Norton power equation:
#
#     Cs. Gyori, Z. Hozer, K. Lassmann, A. Schubert, J. van de Laar, M. Cvan, B. Hatala,
#     Conserted Actions (FISA-2003), Proceedings - EUR 21026, Luxembourg, 10-13 November 2003, p. 584
#     and
#
#     V. J. Betten, Creep Mechanics, Springer, 2002. p. 327.
#
#     Loca Thermal Creep rate = A * exp(-Q/R*T + B(x)) * (sigma_effective)^n
#
#     where A, Q, and n depend on the fraction of beta phase, phi, which is supplied by the material model ZrPhase.C
#
#     ln(A_ab) = (1-phi)*ln(A_a) + phi*ln(A_b)
#     Q_ab = (1-phi)*Q_a + phi*Q_b
#     n_ab = (1-phi)*n_a + phi*n_b
#
#     Phase     Temp(K)         A(MPa^-n s^-1)  Q(J/mol)        n
#     a(alpha)  900-1085        1.94e4          320,000         5.89
#     b(beta)   1248-1873       7.9             142,000         3.78
#
#     In this test, temperature = 1150K and stays constant.  The creep coefficients A, Q, and n values correspond to the beta phase =
#     0.  B(x) = 0 for now (a third degree polynomial of the oxygen weight concentration of the cladding).
#
#     Because the temperature in this test remains above the lower bound for the loca creep regime,
#     the standard Matsuo thermal creep model is not used in this test.
#
#  -  Closed form solution results:
#     For Temperature = 1250K,  and temperature_loca_creep_begin = 900K, where the fraction of beta
#     phase is 0.9842320, the creep rate, from the loca model is,
#
#        where A_alpha = 19370, Q_alpha = 329070.0, n_alpha = 5.89,
#          and A_beta = 7.9, Q_beta = 1.41919e+05, and n_beta = 3.78
#          such that the weighted paramaters, using the expressions given as a function of phi above, are
#          A_ab = 8.9345, Q_ab = 144870, n_ab = 3.813
#
#     creep_rate_loca = 0.003651 1/s (at temperature = 1250 K, beta fraction 0.9842320)
#
#     The Bison-calculated creep strain rate = 0.003651 1/s.
#
#
#--------------------------------------------------------------------------------
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = cube.e
  []
[]

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

[Variables]
  [temp]
    initial_condition = 1250
  []
[]

[AuxVariables]
  [ratep_zrphase] # rate parameter
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_bp_equilibrium] # equilibrium beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_beta_phase] # actual beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_function]
    type = PiecewiseLinear
    x = '0 99 100'
    y = '0 0  0.01'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0   10'
    y = '1250 1250'
  []
  [time_function]
    type = PiecewiseLinear
    x = '0  98 99   100'
    y = '10 10 0.01 0.01'
  []
[]

[Physics/SolidMechanics/QuasiStatic/clad]
  strain = FINITE
  add_variables = true
  generate_output = 'stress_xx stress_yy stress_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz creep_strain_xx creep_strain_yy creep_strain_zz vonmises_stress'
  use_automatic_differentiation = true
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [rateparam]
    type = MaterialRealAux
    variable = ratep_zrphase
    property = ratep_zrphase
  []
  [fractbp_eq]
    type = MaterialRealAux
    variable = fract_bp_equilibrium
    property = fract_bp_equilibrium
  []
  [fract_bphase]
    type = MaterialRealAux
    variable = fract_beta_phase
    property = fract_beta_phase
  []
  [creep_rate_aux]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = ADMaterialRealAux
    variable = effective_creep_strain
    property = effective_creep_strain
  []
[]

[BCs]
  [Pressure]
    [outer_surface]
      boundary = 5
      factor = 5e8
      function = pressure_function
      use_automatic_differentiation = true
    []
  []
  [u_x_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  []
  [u_y_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []
  [u_z_fix]
    type = DirichletBC
    variable = disp_z
    boundary = 3
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = 4
    function = temperature_function
  []
[]

[Materials]
  # Model for Zircaloy phase transition
  [phase]
    type = ZrPhase
    temperature = temp
    numerical_method = 2
  []
  [converter]
    type = MaterialADConverter
    reg_props_in = 'fract_beta_phase'
    ad_props_out = 'ad_fract_beta_phase'
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1.0e11
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'zry_thermal_creep'
  []
  [hill]
    type = ADHillConstants
    hill_constants = "0.5 0.5 0.5 1.0 1.0 1.0"
  []
  [zry_thermal_creep]
    type = ADZryAnisoCreepLOCAUpdate
    high_temperature_creep_model = erbacher
    temperature = temp
    model_primary_creep = false
    model_irradiation_creep = false
    fract_beta_phase_name = 'ad_fract_beta_phase'
  []
  [clad_density]
    type = ADStrainAdjustedDensity
    strain_free_density = 6500
  []
  [thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'
  automatic_scaling = true

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  l_tol = 1e-5
  start_time = 0.0
  end_time = 100
  dtmin = 0.1
  timestep_tolerance = 2e-13
  [TimeStepper]
    type = FunctionDT
    function = time_function
  []
[]

[Outputs]
  file_base = operating_to_loca_hill_creep_5_exodus
  csv = true
  [exodus]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/zry_creep/erbacher/ad_operating_to_loca_hill_creep_5.i)

#   This test case is prepared to test the transition from the standard, or normal operation creep to loca creep in ZryCreepUpdate..
#   There are a series of 5 tests, with different effective stress, temperature, and fraction of beta phase.
#
#   - Geometry:
#     1x1x1 cube, single element
#
#   - Temperature = 1250 K
#
#   - Boundary conditions:
#     Symetric boundary conditions for uniform expansion or contraction (in xy-plane disp_z = 0, xz-plane disp_y = 0, yz-plane disp_x = 0)
#
#   - Stresses
#     5 MPa applied to the top of the block.  This is the effective stress.
#
#
#  -  Loca creep rate from the Norton power equation:
#
#     Cs. Gyori, Z. Hozer, K. Lassmann, A. Schubert, J. van de Laar, M. Cvan, B. Hatala,
#     Conserted Actions (FISA-2003), Proceedings - EUR 21026, Luxembourg, 10-13 November 2003, p. 584
#     and
#
#     V. J. Betten, Creep Mechanics, Springer, 2002. p. 327.
#
#     Loca Thermal Creep rate = A * exp(-Q/R*T + B(x)) * (sigma_effective)^n
#
#     where A, Q, and n depend on the fraction of beta phase, phi, which is supplied by the material model ZrPhase.C
#
#     ln(A_ab) = (1-phi)*ln(A_a) + phi*ln(A_b)
#     Q_ab = (1-phi)*Q_a + phi*Q_b
#     n_ab = (1-phi)*n_a + phi*n_b
#
#     Phase     Temp(K)         A(MPa^-n s^-1)  Q(J/mol)        n
#     a(alpha)  900-1085        1.94e4          320,000         5.89
#     b(beta)   1248-1873       7.9             142,000         3.78
#
#     In this test, temperature = 1150K and stays constant.  The creep coefficients A, Q, and n values correspond to the beta phase =
#     0.  B(x) = 0 for now (a third degree polynomial of the oxygen weight concentration of the cladding).
#
#     Because the temperature in this test remains above the lower bound for the loca creep regime,
#     the standard Matsuo thermal creep model is not used in this test.
#
#  -  Closed form solution results:
#     For Temperature = 1250K,  and temperature_loca_creep_begin = 900K, where the fraction of beta
#     phase is 0.9842320, the creep rate, from the loca model is,
#
#        where A_alpha = 19370, Q_alpha = 329070.0, n_alpha = 5.89,
#          and A_beta = 7.9, Q_beta = 1.41919e+05, and n_beta = 3.78
#          such that the weighted paramaters, using the expressions given as a function of phi above, are
#          A_ab = 8.9345, Q_ab = 144870, n_ab = 3.813
#
#     creep_rate_loca = 0.003651 1/s (at temperature = 1250 K, beta fraction 0.9842320)
#
#     The Bison-calculated creep strain rate = 0.003651 1/s.
#
#
#--------------------------------------------------------------------------------
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = cube.e
  []
[]

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

[Variables]
  [temp]
    initial_condition = 1250
  []
[]

[AuxVariables]
  [ratep_zrphase] # rate parameter
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_bp_equilibrium] # equilibrium beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_beta_phase] # actual beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_function]
    type = PiecewiseLinear
    x = '0 99 100'
    y = '0 0  0.01'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0   10'
    y = '1250 1250'
  []
  [time_function]
    type = PiecewiseLinear
    x = '0  98 99   100'
    y = '10 10 0.01 0.01'
  []
[]

[Physics/SolidMechanics/QuasiStatic/clad]
  strain = FINITE
  add_variables = true
  generate_output = 'stress_xx stress_yy stress_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz creep_strain_xx creep_strain_yy creep_strain_zz vonmises_stress'
  use_automatic_differentiation = true
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [rateparam]
    type = MaterialRealAux
    variable = ratep_zrphase
    property = ratep_zrphase
  []
  [fractbp_eq]
    type = MaterialRealAux
    variable = fract_bp_equilibrium
    property = fract_bp_equilibrium
  []
  [fract_bphase]
    type = MaterialRealAux
    variable = fract_beta_phase
    property = fract_beta_phase
  []
  [creep_rate_aux]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = ADMaterialRealAux
    variable = effective_creep_strain
    property = effective_creep_strain
  []
[]

[BCs]
  [Pressure]
    [outer_surface]
      boundary = 5
      factor = 5e8
      function = pressure_function
      use_automatic_differentiation = true
    []
  []
  [u_x_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  []
  [u_y_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []
  [u_z_fix]
    type = DirichletBC
    variable = disp_z
    boundary = 3
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = 4
    function = temperature_function
  []
[]

[Materials]
  # Model for Zircaloy phase transition
  [phase]
    type = ZrPhase
    temperature = temp
    numerical_method = 2
  []
  [converter]
    type = MaterialADConverter
    reg_props_in = 'fract_beta_phase'
    ad_props_out = 'ad_fract_beta_phase'
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1.0e11
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'zry_thermal_creep'
  []
  [hill]
    type = ADHillConstants
    hill_constants = "0.5 0.5 0.5 1.0 1.0 1.0"
  []
  [zry_thermal_creep]
    type = ADZryAnisoCreepLOCAUpdate
    high_temperature_creep_model = erbacher
    temperature = temp
    model_primary_creep = false
    model_irradiation_creep = false
    fract_beta_phase_name = 'ad_fract_beta_phase'
  []
  [clad_density]
    type = ADStrainAdjustedDensity
    strain_free_density = 6500
  []
  [thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'
  automatic_scaling = true

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  l_tol = 1e-5
  start_time = 0.0
  end_time = 100
  dtmin = 0.1
  timestep_tolerance = 2e-13
  [TimeStepper]
    type = FunctionDT
    function = time_function
  []
[]

[Outputs]
  file_base = operating_to_loca_hill_creep_5_exodus
  csv = true
  [exodus]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/zry_creep/erbacher/ad_operating_to_loca_hill_creep_5.i)

#   This test case is prepared to test the transition from the standard, or normal operation creep to loca creep in ZryCreepUpdate..
#   There are a series of 5 tests, with different effective stress, temperature, and fraction of beta phase.
#
#   - Geometry:
#     1x1x1 cube, single element
#
#   - Temperature = 1250 K
#
#   - Boundary conditions:
#     Symetric boundary conditions for uniform expansion or contraction (in xy-plane disp_z = 0, xz-plane disp_y = 0, yz-plane disp_x = 0)
#
#   - Stresses
#     5 MPa applied to the top of the block.  This is the effective stress.
#
#
#  -  Loca creep rate from the Norton power equation:
#
#     Cs. Gyori, Z. Hozer, K. Lassmann, A. Schubert, J. van de Laar, M. Cvan, B. Hatala,
#     Conserted Actions (FISA-2003), Proceedings - EUR 21026, Luxembourg, 10-13 November 2003, p. 584
#     and
#
#     V. J. Betten, Creep Mechanics, Springer, 2002. p. 327.
#
#     Loca Thermal Creep rate = A * exp(-Q/R*T + B(x)) * (sigma_effective)^n
#
#     where A, Q, and n depend on the fraction of beta phase, phi, which is supplied by the material model ZrPhase.C
#
#     ln(A_ab) = (1-phi)*ln(A_a) + phi*ln(A_b)
#     Q_ab = (1-phi)*Q_a + phi*Q_b
#     n_ab = (1-phi)*n_a + phi*n_b
#
#     Phase     Temp(K)         A(MPa^-n s^-1)  Q(J/mol)        n
#     a(alpha)  900-1085        1.94e4          320,000         5.89
#     b(beta)   1248-1873       7.9             142,000         3.78
#
#     In this test, temperature = 1150K and stays constant.  The creep coefficients A, Q, and n values correspond to the beta phase =
#     0.  B(x) = 0 for now (a third degree polynomial of the oxygen weight concentration of the cladding).
#
#     Because the temperature in this test remains above the lower bound for the loca creep regime,
#     the standard Matsuo thermal creep model is not used in this test.
#
#  -  Closed form solution results:
#     For Temperature = 1250K,  and temperature_loca_creep_begin = 900K, where the fraction of beta
#     phase is 0.9842320, the creep rate, from the loca model is,
#
#        where A_alpha = 19370, Q_alpha = 329070.0, n_alpha = 5.89,
#          and A_beta = 7.9, Q_beta = 1.41919e+05, and n_beta = 3.78
#          such that the weighted paramaters, using the expressions given as a function of phi above, are
#          A_ab = 8.9345, Q_ab = 144870, n_ab = 3.813
#
#     creep_rate_loca = 0.003651 1/s (at temperature = 1250 K, beta fraction 0.9842320)
#
#     The Bison-calculated creep strain rate = 0.003651 1/s.
#
#
#--------------------------------------------------------------------------------
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = cube.e
  []
[]

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

[Variables]
  [temp]
    initial_condition = 1250
  []
[]

[AuxVariables]
  [ratep_zrphase] # rate parameter
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_bp_equilibrium] # equilibrium beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [fract_beta_phase] # actual beta/alpha phase fraction
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [pressure_function]
    type = PiecewiseLinear
    x = '0 99 100'
    y = '0 0  0.01'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0   10'
    y = '1250 1250'
  []
  [time_function]
    type = PiecewiseLinear
    x = '0  98 99   100'
    y = '10 10 0.01 0.01'
  []
[]

[Physics/SolidMechanics/QuasiStatic/clad]
  strain = FINITE
  add_variables = true
  generate_output = 'stress_xx stress_yy stress_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz creep_strain_xx creep_strain_yy creep_strain_zz vonmises_stress'
  use_automatic_differentiation = true
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [rateparam]
    type = MaterialRealAux
    variable = ratep_zrphase
    property = ratep_zrphase
  []
  [fractbp_eq]
    type = MaterialRealAux
    variable = fract_bp_equilibrium
    property = fract_bp_equilibrium
  []
  [fract_bphase]
    type = MaterialRealAux
    variable = fract_beta_phase
    property = fract_beta_phase
  []
  [creep_rate_aux]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = ADMaterialRealAux
    variable = effective_creep_strain
    property = effective_creep_strain
  []
[]

[BCs]
  [Pressure]
    [outer_surface]
      boundary = 5
      factor = 5e8
      function = pressure_function
      use_automatic_differentiation = true
    []
  []
  [u_x_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  []
  [u_y_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 2
    value = 0.0
  []
  [u_z_fix]
    type = DirichletBC
    variable = disp_z
    boundary = 3
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temp
    boundary = 4
    function = temperature_function
  []
[]

[Materials]
  # Model for Zircaloy phase transition
  [phase]
    type = ZrPhase
    temperature = temp
    numerical_method = 2
  []
  [converter]
    type = MaterialADConverter
    reg_props_in = 'fract_beta_phase'
    ad_props_out = 'ad_fract_beta_phase'
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1.0e11
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'zry_thermal_creep'
  []
  [hill]
    type = ADHillConstants
    hill_constants = "0.5 0.5 0.5 1.0 1.0 1.0"
  []
  [zry_thermal_creep]
    type = ADZryAnisoCreepLOCAUpdate
    high_temperature_creep_model = erbacher
    temperature = temp
    model_primary_creep = false
    model_irradiation_creep = false
    fract_beta_phase_name = 'ad_fract_beta_phase'
  []
  [clad_density]
    type = ADStrainAdjustedDensity
    strain_free_density = 6500
  []
  [thermal]
    type = ADHeatConductionMaterial
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'
  automatic_scaling = true

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  l_tol = 1e-5
  start_time = 0.0
  end_time = 100
  dtmin = 0.1
  timestep_tolerance = 2e-13
  [TimeStepper]
    type = FunctionDT
    function = time_function
  []
[]

[Outputs]
  file_base = operating_to_loca_hill_creep_5_exodus
  csv = true
  [exodus]
    type = Exodus
  []
[]

Description
Example Input Syntax
Input Parameters
References