ZrSnCreepUpdate

Computes creep for Zr-0.3%Sn, which is used as a liner in BWRs. This class must be used in conjunction with ComputeMultipleInelasticStress.

Description

The ZrSnCreepUpdate model computes the inelastic strain induced by creep for Zr-0.3%Sn. This material is used for liners in boiling water reactors (BWRs). The creep rate is a given by Jha et al. (2019):

$var element = document.getElementById("moose-equation-80ddc47c-28e5-4c8b-ab08-f8aa42249def");katex.render(" \\dot{\\epsilon} = A \\left(\\sinh\\left(\\alpha \\sigma\\right)\\right)^n \\exp\\left(-\\frac{Q}{RT}\\right)", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-a145f018-39b4-434c-9664-9c421273e231");katex.render("A", element, {displayMode:false,throwOnError:false});$ (s $var element = document.getElementById("moose-equation-933ce1dd-9b61-46f0-bf1f-1dd6c3c950e1");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-8c11ef1e-2e8f-48b3-a5fb-090b7c1ef2e6");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ (MPa $var element = document.getElementById("moose-equation-6c5dce17-bc11-421a-b3c2-2e9702d04346");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-7332e87e-82ac-4ac2-bfb6-45d7234a8d3d");katex.render("n", element, {displayMode:false,throwOnError:false});$ (dimensionless), and $var element = document.getElementById("moose-equation-447a7b59-f825-4a76-9dca-526c5a1fef90");katex.render("Q", element, {displayMode:false,throwOnError:false});$ (kJ/mol) are material parameters, $var element = document.getElementById("moose-equation-4cf2b316-07b7-42c2-a6a1-9157476eb41c");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the ideal gas constant (kJ/mol-K), and $var element = document.getElementById("moose-equation-96928d89-41d3-4b37-b861-264de09cac25");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K). The material constants are are all fourth order polynomials of the inelastic strain, $var element = document.getElementById("moose-equation-36b5ce89-c7a0-4e1a-8f14-6c68feb2361f");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false});$ , as follows

$var element = document.getElementById("moose-equation-8c16dd40-09bd-4686-bd36-80139c5df515");katex.render(" \\ln A = A_0 + A_1\\epsilon + A_2\\epsilon^2 + A_3\\epsilon^3 + A_4\\epsilon^4", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-f3062f56-29ba-400b-8d70-df11ad142b01");katex.render(" \\alpha = B_0 + B_1\\epsilon + B_2\\epsilon^2 + B_3\\epsilon^3 + B_4\\epsilon^4", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-4c8b2686-d229-40d6-aa5f-71e05e6d6ce2");katex.render(" n = C_0 + C_1\\epsilon + C_2\\epsilon^2 + C_3\\epsilon^3 + C_4\\epsilon^4", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-2800c3a6-6fe7-45a3-ba37-3ee99ae2ae05");katex.render(" Q = D_0 + D_1\\epsilon + D_2\\epsilon^2 + D_3\\epsilon^3 + D_4\\epsilon^4", element, {displayMode:true,throwOnError:false});$ where the coefficients are provided in Table 1.

Table 1: Coefficients used in the polynomial fits for the material constants used in the Zr-0.3%Sn creep correlation.

Coefficient	Value	Coefficient	Value	Coefficient	Value	Coefficient	Value
A $var element = document.getElementById("moose-equation-8eee7971-250e-4300-a43c-80821efa707f");katex.render("_0", element, {displayMode:false,throwOnError:false});$	53.365	B $var element = document.getElementById("moose-equation-39a095cf-fe4a-472d-8675-474b178baad8");katex.render("_0", element, {displayMode:false,throwOnError:false});$	0.0347	C $var element = document.getElementById("moose-equation-014ea5e0-92bc-4775-ba0f-1bb918b8a1b0");katex.render("_0", element, {displayMode:false,throwOnError:false});$	3.6422	D $var element = document.getElementById("moose-equation-cc5142ac-0f00-4856-974f-e98058dea5ac");katex.render("_0", element, {displayMode:false,throwOnError:false});$	506.22
A $var element = document.getElementById("moose-equation-010d214d-0d65-4ff3-befa-622105cac241");katex.render("_1", element, {displayMode:false,throwOnError:false});$	-39.774	B $var element = document.getElementById("moose-equation-2434b460-5df7-455b-9bd3-468d1b32ff29");katex.render("_1", element, {displayMode:false,throwOnError:false});$	-0.2091	C $var element = document.getElementById("moose-equation-d955540a-7f08-4d26-98c8-0cd96fa9decb");katex.render("_1", element, {displayMode:false,throwOnError:false});$	40.123	D $var element = document.getElementById("moose-equation-754d8540-6446-45fd-9ca9-91d9916b0dd0");katex.render("_1", element, {displayMode:false,throwOnError:false});$	-730.03
A $var element = document.getElementById("moose-equation-666e7140-d978-4e44-ba40-b31291556d8b");katex.render("_2", element, {displayMode:false,throwOnError:false});$	-40.405	B $var element = document.getElementById("moose-equation-746aa6b9-4e4e-4c25-bdca-61f137a7a694");katex.render("_2", element, {displayMode:false,throwOnError:false});$	0.817	C $var element = document.getElementById("moose-equation-9bd6253b-a123-4510-8659-2e41894609d9");katex.render("_2", element, {displayMode:false,throwOnError:false});$	-201.32	D $var element = document.getElementById("moose-equation-d660135d-8b72-49ff-942d-0fa24c462496");katex.render("_2", element, {displayMode:false,throwOnError:false});$	1345.3
A $var element = document.getElementById("moose-equation-251c4dcb-0f29-477b-9ed9-4cb7efb0bc4e");katex.render("_3", element, {displayMode:false,throwOnError:false});$	287.21	B $var element = document.getElementById("moose-equation-5ad6d61b-e8c5-408f-961b-28f6dfcfd1c5");katex.render("_3", element, {displayMode:false,throwOnError:false});$	-1.3775	C $var element = document.getElementById("moose-equation-5a44450c-3f5d-40ea-8f8a-35f38085c8d6");katex.render("_3", element, {displayMode:false,throwOnError:false});$	373.51	D $var element = document.getElementById("moose-equation-c1955502-a4b3-4f31-9ff1-f680acb77ad2");katex.render("_3", element, {displayMode:false,throwOnError:false});$	-466.67
A $var element = document.getElementById("moose-equation-3d0a5561-37dd-4a14-862c-d7da9757b3bd");katex.render("_4", element, {displayMode:false,throwOnError:false});$	-264.92	B $var element = document.getElementById("moose-equation-718a2714-936c-44f6-9e0c-567ee0bb8a07");katex.render("_4", element, {displayMode:false,throwOnError:false});$	0.85420	C $var element = document.getElementById("moose-equation-b633e667-b3b1-424f-8a54-e9fa925750fc");katex.render("_4", element, {displayMode:false,throwOnError:false});$	-242.19	D $var element = document.getElementById("moose-equation-ebb17d34-a297-4b6c-ad9d-fb11aa38cde2");katex.render("_4", element, {displayMode:false,throwOnError:false});$	-433.33

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [zrsn_creep]
    type = ZrSnCreepUpdate<<<{"description": "Computes creep for Zr-0.3%Sn, which is used as a liner in BWRs. This class must be used in conjunction with ComputeMultipleInelasticStress.", "href": "ZrSnCreepUpdate.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

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
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.
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

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/zrsn_creep/zrsn_creep_low_temperature.i)
(test/tests/solid_mechanics/zrsn_creep/zrsn_creep_high_temperature.i)

References

S.K. Jha, S. Dixit, and D. Srivastava. Study of thermomechanical behavior of zirconium-0.3 tin alloy. Journal of Matterials Engineering and Performance, 28:5127–5137, 2019. doi:10.1007/s11665-019-04204-x.

@article{jha2019,
    author = "Jha, S.K. and Dixit, S. and Srivastava, D.",
    title = "Study of Thermomechanical Behavior of Zirconium-0.3 Tin Alloy",
    journal = "Journal of Matterials Engineering and Performance",
    volume = "28",
    pages = "5127-5137",
    doi = "10.1007/s11665-019-04204-x",
    year = "2019"
}

(test/tests/solid_mechanics/zrsn_creep/zrsn_creep_low_temperature.i)

# The mesh is a 1x1 square (single element) assuming RZ axisymmetry.
# The temperature is ramped from 300 K to 800 K over 5e4 seconds.
# A timestep of 1e3 s is taken. An axial pressure of -50MPa is applied
# (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot_cr = A * sinh(alpha * sigma)^n * exp (-Q/RT)
#
# where A, alpha, n, and Q are material parameters that are represented by
# fourth order polynomials that are functions of the creep strain. The applied
# stress, sigma, is in MPa, and T is the temperature in K.
#
# Results for selected timesteps corresponding to a particular temperature values
# are provided in the table below:
#
#                      BISON         Analytical
#  Temperature       Creep Strain    Creep Strain
#   (K)               Rate (s^-1)     Rate (s^-1)
#   400              4.6619e-42       4.6619e-42
#   500              7.7566e-29       7.7566e-29
#   600              5.0553e-20       5.0553e-20
#   700              9.9888e-14       9.9888e-14
#   800              5.2674e-09       5.2674e-09


[GlobalParams]
  displacements = 'disp_x disp_y'
  order = SECOND
  family = LAGRANGE
[]

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

[Mesh]
  coord_type = RZ
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    elem_type = QUAD8
    xmax = 500e-6
    ymax = 10e-3
  []
[]

[Functions]
  [temperature_ramp]
    type = PiecewiseLinear
    x = '0 5e4'
    y = '300 800'
  []
[]

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

[AuxVariables]
  [temperature]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    add_variables = false
    strain = FINITE
    generate_output = vonmises_stress
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature_ramp
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  []
[]

[BCs]
  [leftX]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [bottomY]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [topY]
    type = Pressure
    variable = disp_y
    boundary = top
    factor = -50e6
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    strain_free_density = 6530.0 # For pure Zr
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 9.5e10 # For pure Zr
    poissons_ratio = 0.34 # For pure Zr
  []
  [elastic_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = zrsn_creep
  []
  [zrsn_creep]
    type = ZrSnCreepUpdate
    temperature = temperature
  []
[]

[Executioner]
   type = Transient

   solve_type = PJFNK

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

   line_search = 'none'

   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10


   start_time = 0.0
   dtmax = 1e3
   dtmin = 1e3
   dt = 1e3
   end_time = 5e4
   snesmf_reuse_base = false
[]

[Postprocessors]
  [avg_temperature]
    type = ElementAverageValue
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageMaterialProperty
    mat_prop = creep_rate
    execute_on = 'initial timestep_end'
  []
  [effective_creep_strain]
    type = ElementAverageMaterialProperty
    mat_prop = effective_creep_strain
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/zrsn_creep/zrsn_creep_low_temperature.i)

# The mesh is a 1x1 square (single element) assuming RZ axisymmetry.
# The temperature is ramped from 300 K to 800 K over 5e4 seconds.
# A timestep of 1e3 s is taken. An axial pressure of -50MPa is applied
# (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot_cr = A * sinh(alpha * sigma)^n * exp (-Q/RT)
#
# where A, alpha, n, and Q are material parameters that are represented by
# fourth order polynomials that are functions of the creep strain. The applied
# stress, sigma, is in MPa, and T is the temperature in K.
#
# Results for selected timesteps corresponding to a particular temperature values
# are provided in the table below:
#
#                      BISON         Analytical
#  Temperature       Creep Strain    Creep Strain
#   (K)               Rate (s^-1)     Rate (s^-1)
#   400              4.6619e-42       4.6619e-42
#   500              7.7566e-29       7.7566e-29
#   600              5.0553e-20       5.0553e-20
#   700              9.9888e-14       9.9888e-14
#   800              5.2674e-09       5.2674e-09


[GlobalParams]
  displacements = 'disp_x disp_y'
  order = SECOND
  family = LAGRANGE
[]

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

[Mesh]
  coord_type = RZ
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    elem_type = QUAD8
    xmax = 500e-6
    ymax = 10e-3
  []
[]

[Functions]
  [temperature_ramp]
    type = PiecewiseLinear
    x = '0 5e4'
    y = '300 800'
  []
[]

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

[AuxVariables]
  [temperature]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    add_variables = false
    strain = FINITE
    generate_output = vonmises_stress
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature_ramp
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  []
[]

[BCs]
  [leftX]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [bottomY]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [topY]
    type = Pressure
    variable = disp_y
    boundary = top
    factor = -50e6
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    strain_free_density = 6530.0 # For pure Zr
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 9.5e10 # For pure Zr
    poissons_ratio = 0.34 # For pure Zr
  []
  [elastic_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = zrsn_creep
  []
  [zrsn_creep]
    type = ZrSnCreepUpdate
    temperature = temperature
  []
[]

[Executioner]
   type = Transient

   solve_type = PJFNK

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

   line_search = 'none'

   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10


   start_time = 0.0
   dtmax = 1e3
   dtmin = 1e3
   dt = 1e3
   end_time = 5e4
   snesmf_reuse_base = false
[]

[Postprocessors]
  [avg_temperature]
    type = ElementAverageValue
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageMaterialProperty
    mat_prop = creep_rate
    execute_on = 'initial timestep_end'
  []
  [effective_creep_strain]
    type = ElementAverageMaterialProperty
    mat_prop = effective_creep_strain
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/zrsn_creep/zrsn_creep_high_temperature.i)

# The mesh is a 500e-6 x 10e-3 rectangle (single element) assuming RZ axisymmetry.
# The temperature is ramped from 800 K to 1150 K over 50 seconds.
# A timestep of 0.1 s is taken. An axial pressure of -2MPa is applied
# (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot_cr = A * sinh(alpha * sigma)^n * exp (-Q/RT)
#
# where A, alpha, n, and Q are material parameters that are represented by
# fourth order polynomials that are functions of the creep strain. The applied
# stress, sigma, is in MPa, and T is the temperature in K.
#
# Results for selected timesteps corresponding to a particular temperature values
# are provided in the table below:
#
#                      BISON         Analytical
#  Temperature       Creep Strain    Creep Strain
#   (K)               Rate (s^-1)     Rate (s^-1)
#   850.4            7.3035E-13       7.3035E-13
#   900.1            3.8055E-11       3.8055E-11
#   950.5            1.3744E-09       1.3744E-09
#   1000.2           3.3148E-08       3.3148E-08
#   1050.6           6.1468E-07       6.1468E-07
#   1100.3           8.4073E-06       8.4073E-06
#   1150             8.9756E-05       8.9756E-05


[GlobalParams]
  displacements = 'disp_x disp_y'
  order = SECOND
  family = LAGRANGE
[]

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

[Mesh]
  coord_type = RZ
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    elem_type = QUAD8
    xmax = 500e-6
    ymax = 10e-3
  []
[]

[Functions]
  [temperature_ramp]
    type = PiecewiseLinear
    x = '0 50'
    y = '800 1150'
  []
[]

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

[AuxVariables]
  [temperature]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    add_variables = false
    strain = FINITE
    generate_output = vonmises_stress
    extra_vector_tags = 'ref'
    use_finite_deform_jacobian = true
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    variable = temperature
    function = temperature_ramp
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  []
[]

[BCs]
  [leftX]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [bottomY]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [topY]
    type = Pressure
    variable = disp_y
    boundary = top
    factor = -2e6
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    strain_free_density = 6530.0 # For pure Zr
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 9.5e10 # For pure Zr
    poissons_ratio = 0.34 # For pure Zr
  []
  [elastic_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = zrsn_creep
  []
  [zrsn_creep]
    type = ZrSnCreepUpdate
    temperature = temperature
  []
[]

[Executioner]
   type = Transient

   solve_type = PJFNK

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

   line_search = 'none'

   nl_rel_tol = 1e-7
   nl_abs_tol = 1e-10


   start_time = 0.0
   dtmax = 0.1
   dtmin = 0.1
   dt = 0.1
   end_time = 50
   snesmf_reuse_base = false
[]

[Postprocessors]
  [avg_temperature]
    type = ElementAverageValue
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageMaterialProperty
    mat_prop = creep_rate
    execute_on = 'initial timestep_end'
  []
  [effective_creep_strain]
    type = ElementAverageMaterialProperty
    mat_prop = effective_creep_strain
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References