CompositeSiCCreepUpdate

Irradiation creep for composite SiC. This class must be used in conjunction with ComputeMultipleInelasticStress.

Description

Two models exist for irradiation creep of composite silicon carbide: SINGH and KOYANAGI. The creep rate is taken as a combination of primary (swelling-coupled) and secondary (steady) creep.

SINGH Model

The SINGH model combines the primary creep of Singh et al. (2018) and the seconeary creep of Koyanagi et al. (2016): $var element = document.getElementById("moose-equation-c41b2d3f-4992-4ca1-a82c-e643cec3e63f");katex.render("\\dot{\\epsilon}_{creep} = \\dot{\\epsilon}_{pri} + \\dot{\\epsilon}_{sec}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-4f006f14-333a-4ce4-9eda-7e93ae1c4bbd");katex.render("\\dot{\\epsilon}_{pri} = K_{pri} \\sigma \\dot{\\epsilon}_{swell}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-d439640c-498f-43b6-99cd-e8fada4632c3");katex.render("\\dot{\\epsilon}_{sec} = K_{sec} \\sigma \\phi_f", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-5dfa2796-2b76-459c-ba84-2b65a1cfbcb3");katex.render("\\dot{\\epsilon}_{pri}", element, {displayMode:false,throwOnError:false});$ is the swelling-coupled irradiation creep rate, $var element = document.getElementById("moose-equation-14b72069-3c63-4e94-a82a-c0354b67d8df");katex.render("\\dot{\\epsilon}_{sec}", element, {displayMode:false,throwOnError:false});$ is the steady secondary creep rate, $var element = document.getElementById("moose-equation-bd743633-e53d-4c97-88ba-46c1e6d424c7");katex.render("K_{pri}", element, {displayMode:false,throwOnError:false});$ is a temperature-dependent conversion factor (TPa $var element = document.getElementById("moose-equation-f2333a6c-9051-4da6-acef-463ccb98a035");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ ) (see Katoh et al. (2013)), $var element = document.getElementById("moose-equation-2bb6fb1e-f74e-4206-8d59-3f83036bc975");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the stress in TPa, $var element = document.getElementById("moose-equation-213f4525-4b7e-45a9-ba86-d5dfa07d61ac");katex.render("\\phi_f", element, {displayMode:false,throwOnError:false});$ is the fast neutron flux, $var element = document.getElementById("moose-equation-ed89f1dc-f372-4e6a-bf3a-527f18c16e6c");katex.render("K_{sec}", element, {displayMode:false,throwOnError:false});$ is the instantaneous creep coefficient (MPa dpa $var element = document.getElementById("moose-equation-e0f99ddd-8f0c-4cdd-99f6-6e1135cc563f");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ ), and $var element = document.getElementById("moose-equation-4a0e77ce-89ba-4b92-bd34-b09afa64353f");katex.render("\\dot{\\epsilon}_{swell}", element, {displayMode:false,throwOnError:false});$ is the volumetric swelling rate. The conversion factor is given by a the following: $var element = document.getElementById("moose-equation-f27c2609-884c-40de-ae43-55004b9c7614");katex.render("K_{pri} = 3.5626 \\times 10^{-4} T^2 - 0.41704 T + 156.8507", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-ecaba2ef-c6d3-43af-aeb4-6f34a989cf2c");katex.render("K_{sec} = 1 \\times 10^{-7}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-81f6f023-eb6b-4d65-b6ed-5ffd8ed06769");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K. The swelling strain given by CompositeSiCVolumetricSwellingEigenstrain is computed in an incremental fashion and therefore the volumetric swelling rate ( $var element = document.getElementById("moose-equation-8e5f4bef-2c4d-4ad5-9868-3268d6f00749");katex.render("\\dot{\\epsilon}_{swell}", element, {displayMode:false,throwOnError:false});$ ) is calculated via: $var element = document.getElementById("moose-equation-6420c2d2-018f-4fc5-8eb0-550317d5f5f7");katex.render(" \\dot{\\epsilon}_{swell} = \\frac{S-S_{old}}{dt}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-414e525d-d53b-4c74-97f4-771d2c0894d4");katex.render("S", element, {displayMode:false,throwOnError:false});$ is the volumetric strain for the current timestep, $var element = document.getElementById("moose-equation-939ce972-8764-4aa0-a74c-e5c79f9c7e24");katex.render("S_{old}", element, {displayMode:false,throwOnError:false});$ is the volumetric strain for the previous timestep and $var element = document.getElementById("moose-equation-285a93fa-bd24-411c-8fd0-bc0210cf932c");katex.render("dt", element, {displayMode:false,throwOnError:false});$ is the timestep size for the current timestep.

KOYANAGI Model

The KOYANAGI computes a different swelling-coupled irradiation creep rate. The swelling-coupled irradiation creep $var element = document.getElementById("moose-equation-57a14375-dfd9-48fa-9be4-3fcfbf750463");katex.render("\\epsilon_{sec}", element, {displayMode:false,throwOnError:false});$ (1/dpa) is caused by irradiation induced defect formation. It is expressed as: $var element = document.getElementById("moose-equation-ec79c788-47ee-4191-8dc5-830adf61faad");katex.render("\\dot{\\epsilon}_{sec}=D \\sigma \\dot{S}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cb7b1372-2e8f-4f1f-89ef-ef8a8a37f1b8");katex.render("D", element, {displayMode:false,throwOnError:false});$ is the swelling-creep coupling coefficient (1/MPa), $var element = document.getElementById("moose-equation-1c07e0e8-2d93-4e61-8934-389d51c75980");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the stress (MPa) and $var element = document.getElementById("moose-equation-d143df34-bff6-4775-9d02-b5cf5cc491e3");katex.render("\\dot{S}", element, {displayMode:false,throwOnError:false});$ is the swelling rate (1/dpa).

The swelling rate $var element = document.getElementById("moose-equation-3a3610bf-01fb-4d38-9ba5-188a247fb743");katex.render("\\dot{S}", element, {displayMode:false,throwOnError:false});$ is expressed as: $var element = document.getElementById("moose-equation-0ea2c562-ed4c-470b-9806-6bd96ae77562");katex.render("\\dot{S} = k_s \\gamma^{-1/3} \\exp{\\left(\\frac{-\\gamma}{\\gamma_{sec}}\\right)}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-17fca695-8b76-4ba1-8a50-979abd3a2b6d");katex.render("k_s", element, {displayMode:false,throwOnError:false});$ (dpa $var element = document.getElementById("moose-equation-2c3c39e9-da48-44fd-ab54-b0a07624dfda");katex.render("^{-2/3}", element, {displayMode:false,throwOnError:false});$ ) is a temperature-dependent constant, $var element = document.getElementById("moose-equation-59329801-d98e-45b2-9950-f905f26694f0");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is the dose (dpa), and $var element = document.getElementById("moose-equation-533b22ce-f884-4e1b-bfdf-cd82a879ba6f");katex.render("\\gamma_{sec}", element, {displayMode:false,throwOnError:false});$ is the characteristic fluence for swelling saturation in dpa units. Substituting the expression for swelling rate we obtain: $var element = document.getElementById("moose-equation-2779295a-2805-46fb-b829-f133d97be199");katex.render("\\dot{\\epsilon}_{sec}=D \\sigma k_s \\exp{\\left(\\frac{-\\gamma}{\\gamma_{sec}}\\right)}", element, {displayMode:true,throwOnError:false});$ The value of $var element = document.getElementById("moose-equation-2f5c396b-c3ba-40f3-bb6b-fde08ca19025");katex.render("D k_s", element, {displayMode:false,throwOnError:false});$ has been found to be $var element = document.getElementById("moose-equation-dba3e83e-e8fb-4fbb-a2b5-acec49f05f19");katex.render("2 \\times 10^{-6}", element, {displayMode:false,throwOnError:false});$ MPa $var element = document.getElementById("moose-equation-ced33c1b-759a-4dff-b287-ae17b020678b");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ dpa $var element = document.getElementById("moose-equation-5c2be165-63e4-47c0-83ea-a47af7a8db0e");katex.render("^{-2/3}", element, {displayMode:false,throwOnError:false});$ for experimental data at 380 $var element = document.getElementById("moose-equation-a3c9f1ab-aafc-44f7-a5d3-690ed50cae7b");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C and 540 $var element = document.getElementById("moose-equation-012f37f8-cbef-4a3e-abbf-ec98cca45899");katex.render("{\\circ}", element, {displayMode:false,throwOnError:false});$ C, and $var element = document.getElementById("moose-equation-04f3c4ed-78db-43ee-807f-d0f32d8aff10");katex.render("\\gamma_{sec}", element, {displayMode:false,throwOnError:false});$ has been found to be 0.15 dpa. The secondary creep rate in the KOYANAGI model is the same as used in the SINGH model.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [composite_sic_creep]
    type = CompositeSiCCreepUpdate<<<{"description": "Irradiation creep for composite SiC. This class must be used in conjunction with ComputeMultipleInelasticStress.", "href": "CompositeSiCCreepUpdate.html"}>>>
    fast_neutron_flux<<<{"description": "The fast neutron flux"}>>> = fast_neutron_flux
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
  []
[]

Input Parameters

fast_neutron_fluxThe fast neutron flux
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The fast neutron flux
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.
irradiation_creep_modelSINGHOptions for the correlation used to calculate irradiation creep.
Default:SINGH
C++ Type:MooseEnum
Options:SINGH, KOYANAGI
Controllable:No
Description:Options for the correlation used to calculate irradiation creep.
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
scale_factor1Multiplying factor for sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiplying factor for sensitivity studies
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/sic_creep/composite_sic_creep.i)
(test/tests/solid_mechanics/sic_creep/ad_composite_sic_creep.i)

References

Y. Katoh, L. L. Snead, C. M. Parish, and T. Hinoki. Observation and possible mechanism of irradiation induced creep in ceramics. Journal of Nuclear Materials, 434:141–151, 2013.

@article{katoh2013,
    author = "Katoh, Y. and Snead, L. L. and Parish, C. M. and Hinoki, T.",
    title = "Observation and possible mechanism of irradiation induced creep in ceramics",
    journal = "Journal of Nuclear Materials",
    volume = "434",
    pages = "141-151",
    year = "2013"
}

T. Koyanagi, T. Katoh, K. Ozawa, K. Shimoda, and T. Hinoki. Neutron-irradiation creep of silicon carbide materials beyond the initial transient. Journal of Nuclear Materials, 478:97–111, 2016.

@article{koyanagi2016,
    author = "Koyanagi, T. and Katoh, T. and Ozawa, K. and Shimoda, K. and Hinoki, T.",
    title = "Neutron-irradiation creep of silicon carbide materials beyond the initial transient",
    journal = "Journal of Nuclear Materials",
    volume = "478",
    year = "2016",
    pages = "97-111"
}

G. Singh, K. Terrani, and Y. Katoh. Thermo-mechanical assessment of full SiC/SiC composite cladding for LWR applications with sensitivity analysis. Journal of Nuclear Materials, 499:126–143, 2018.

@article{singh2018,
    author = "Singh, G. and Terrani, K. and Katoh, Y.",
    title = "Thermo-mechanical assessment of full {SiC/SiC} composite cladding for {LWR} applications with sensitivity analysis",
    journal = "Journal of Nuclear Materials",
    volume = "499",
    pages = "126-143",
    year = "2018",
    publisher = "Elsevier"
}

(test/tests/solid_mechanics/sic_creep/composite_sic_creep.i)

# The mesh is a 1x1 square (single element) assuming RZ axisymmetry.
# The temperature is held constant at 1073.15 K with a varying fast fluence
# from 0 to 1e25 n/m^2 over 1e6 second. A timestep of 1e4 s is taken and
# swelling is calculated by the Katoh volumetric swelling model with 100 substeps.
# An axial pressure of -3MPa is applied (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot = e_dot_pri+e_dot_sec
# e_dot_pri = K_pri * sigma * e_dot_swell
# e_dot_sec = K_sec * sigma * phi
#
# where K_pri and K_sec are conversion factors, sigma is the Von Mises stress in TPa, phi is the fast neutron flux, and
# e_dot_swell is the swelling strain rate. The conversion factors are given by
#
# K_pri = 3.5626e-4 * T^2 - 0.41704 * T + 156.8507 (TPa)^-1
# K_sec = 1e-7 (MPa*dpa)^-1
#
# where T is the temperature in K. The swelling strain rate is calculated from
# swelling increment for the timestep divided by the timestep size.
#
# Results for selected timesteps corresponding to a particular fluence value
# are provided in the table below
#                                                     BISON        Analytical
#  Fluence     Swelling        Swelling Strain     Creep Strain   Creep Strain
#   (dpa)     Strain (-)        Rate (s^-1)         Rate (s^-1)    Rate (s^-1)
#   0.25      2.86074e-3         3.59778e-8         1.44079e-11     1.44079e-11
#   0.5       4.21743e-3         2.27542e-8         9.66361e-12     9.66362e-12
#   1.0       5.80817e-3         1.18073e-8         5.73616e-12     5.73615e-12
#   2.0       7.20081e-3         4.05640e-9         2.95533e-12     2.95533e-12
#   3.0       7.70534e-3         1.53843e-9         2.05195e-12     2.05195e-12
#   4.0       7.90061e-3         6.07271e-10        1.71787e-12     1.71787e-12
#
# Command line arguments are used to test the SINGH model at low temperatures as well as the KOYANAGI model, which
# has a slightly different form than described above. See the documentation for more details.

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

[Mesh]
  coord_type = RZ
  [cylinder]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 1073.15
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
  []
  [fast_neutron_flux]
  []
  [swell]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    block = 0
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'swelling_strain'
    generate_output = vonmises_stress
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    fast_neutron_flux = fast_neutron_flux
    variable = fast_neutron_fluence
    block = 0
    execute_on = 'timestep_begin'
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 0
    factor = 50e18
    execute_on = timestep_begin
  []
  [total_swelling]
    type = MaterialRealAux
    variable = swell
    property = swelling
    block = 0
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = DirichletBC
    boundary = 'left right bottom top'
    variable = temperature
    value = 1073.15
  []
  [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 = -3e6
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 2700.0
  []
  [swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = 0
    temperature = temperature
    swelling_model = KATOH
    number_of_substeps = 100
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = swelling_strain
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 3e11
    poissons_ratio = 0.17
  []
  [elastic_stress]
    type = ComputeMultipleInelasticStress
    block = 0
    inelastic_models = composite_sic_creep
  []
  [composite_sic_creep]
    type = CompositeSiCCreepUpdate
    fast_neutron_flux = fast_neutron_flux
    block = 0
    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
  l_tol = 1e-5

  start_time = 0.0
  dt = 1e4
  end_time = 1e6
[]

[Postprocessors]
  [avg_temperature]
    type = SideAverageValue
    boundary = 'left right top bottom'
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageValue
    block = 0
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
    block = 0
  []
  [swelling_out]
    type = ElementAverageValue
    variable = swell
    execute_on = 'initial timestep_end'
    block = 0
  []
  [fast_neutron_fluence]
    type = AverageNodalVariableValue
    variable = fast_neutron_fluence
    execute_on = 'initial timestep_end'
    block = 0
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/sic_creep/composite_sic_creep.i)

# The mesh is a 1x1 square (single element) assuming RZ axisymmetry.
# The temperature is held constant at 1073.15 K with a varying fast fluence
# from 0 to 1e25 n/m^2 over 1e6 second. A timestep of 1e4 s is taken and
# swelling is calculated by the Katoh volumetric swelling model with 100 substeps.
# An axial pressure of -3MPa is applied (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot = e_dot_pri+e_dot_sec
# e_dot_pri = K_pri * sigma * e_dot_swell
# e_dot_sec = K_sec * sigma * phi
#
# where K_pri and K_sec are conversion factors, sigma is the Von Mises stress in TPa, phi is the fast neutron flux, and
# e_dot_swell is the swelling strain rate. The conversion factors are given by
#
# K_pri = 3.5626e-4 * T^2 - 0.41704 * T + 156.8507 (TPa)^-1
# K_sec = 1e-7 (MPa*dpa)^-1
#
# where T is the temperature in K. The swelling strain rate is calculated from
# swelling increment for the timestep divided by the timestep size.
#
# Results for selected timesteps corresponding to a particular fluence value
# are provided in the table below
#                                                     BISON        Analytical
#  Fluence     Swelling        Swelling Strain     Creep Strain   Creep Strain
#   (dpa)     Strain (-)        Rate (s^-1)         Rate (s^-1)    Rate (s^-1)
#   0.25      2.86074e-3         3.59778e-8         1.44079e-11     1.44079e-11
#   0.5       4.21743e-3         2.27542e-8         9.66361e-12     9.66362e-12
#   1.0       5.80817e-3         1.18073e-8         5.73616e-12     5.73615e-12
#   2.0       7.20081e-3         4.05640e-9         2.95533e-12     2.95533e-12
#   3.0       7.70534e-3         1.53843e-9         2.05195e-12     2.05195e-12
#   4.0       7.90061e-3         6.07271e-10        1.71787e-12     1.71787e-12
#
# Command line arguments are used to test the SINGH model at low temperatures as well as the KOYANAGI model, which
# has a slightly different form than described above. See the documentation for more details.

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

[Mesh]
  coord_type = RZ
  [cylinder]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 1073.15
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
  []
  [fast_neutron_flux]
  []
  [swell]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    block = 0
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'swelling_strain'
    generate_output = vonmises_stress
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    fast_neutron_flux = fast_neutron_flux
    variable = fast_neutron_fluence
    block = 0
    execute_on = 'timestep_begin'
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 0
    factor = 50e18
    execute_on = timestep_begin
  []
  [total_swelling]
    type = MaterialRealAux
    variable = swell
    property = swelling
    block = 0
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = DirichletBC
    boundary = 'left right bottom top'
    variable = temperature
    value = 1073.15
  []
  [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 = -3e6
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 2700.0
  []
  [swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = 0
    temperature = temperature
    swelling_model = KATOH
    number_of_substeps = 100
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = swelling_strain
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 3e11
    poissons_ratio = 0.17
  []
  [elastic_stress]
    type = ComputeMultipleInelasticStress
    block = 0
    inelastic_models = composite_sic_creep
  []
  [composite_sic_creep]
    type = CompositeSiCCreepUpdate
    fast_neutron_flux = fast_neutron_flux
    block = 0
    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
  l_tol = 1e-5

  start_time = 0.0
  dt = 1e4
  end_time = 1e6
[]

[Postprocessors]
  [avg_temperature]
    type = SideAverageValue
    boundary = 'left right top bottom'
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageValue
    block = 0
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
    block = 0
  []
  [swelling_out]
    type = ElementAverageValue
    variable = swell
    execute_on = 'initial timestep_end'
    block = 0
  []
  [fast_neutron_fluence]
    type = AverageNodalVariableValue
    variable = fast_neutron_fluence
    execute_on = 'initial timestep_end'
    block = 0
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/sic_creep/ad_composite_sic_creep.i)

# The mesh is a 1x1 square (single element) assuming RZ axisymmetry.
# The temperature is held constant at 1073.15 K with a varying fast fluence
# from 0 to 1e25 n/m^2 over 1e6 second. A timestep of 1e4 s is taken and
# swelling is calculated by the Katoh volumetric swelling model with 100 substeps.
# An axial pressure of -3MPa is applied (i.e., pulling outward from the surface).
#
# The creep rate is calculated from:
#
# e_dot = e_dot_pri+e_dot_sec
# e_dot_pri = K_pri * sigma * e_dot_swell
# e_dot_sec = K_sec * sigma * phi
#
# where K_pri and K_sec are conversion factors, sigma is the Von Mises stress in TPa, phi is the fast neutron flux, and
# e_dot_swell is the swelling strain rate. The conversion factors are given by
#
# K_pri = 3.5626e-4 * T^2 - 0.41704 * T + 156.8507 (TPa)^-1
# K_sec = 1e-7 (MPa*dpa)^-1
#
# where T is the temperature in K. The swelling strain rate is calculated from
# swelling increment for the timestep divided by the timestep size.
#
# Results for selected timesteps corresponding to a particular fluence value
# are provided in the table below
#                                                     BISON        Analytical
#  Fluence     Swelling        Swelling Strain     Creep Strain   Creep Strain
#   (dpa)     Strain (-)        Rate (s^-1)         Rate (s^-1)    Rate (s^-1)
#   0.25      2.86074e-3         3.59778e-8         1.44079e-11     1.44079e-11
#   0.5       4.21743e-3         2.27542e-8         9.66361e-12     9.66362e-12
#   1.0       5.80817e-3         1.18073e-8         5.73616e-12     5.73615e-12
#   2.0       7.20081e-3         4.05640e-9         2.95533e-12     2.95533e-12
#   3.0       7.70534e-3         1.53843e-9         2.05195e-12     2.05195e-12
#   4.0       7.90061e-3         6.07271e-10        1.71787e-12     1.71787e-12
#
# Command line arguments are used to test the SINGH model at low temperatures as well as the KOYANAGI model, which
# has a slightly different form than described above. See the documentation for more details.

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

[Mesh]
  coord_type = RZ
  [cylinder]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 1073.15
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
  []
  [fast_neutron_flux]
  []
  [swell]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [square]
    block = 0
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'swelling_strain'
    generate_output = vonmises_stress
    use_automatic_differentiation = true
  []
[]

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

[AuxKernels]
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    fast_neutron_flux = fast_neutron_flux
    variable = fast_neutron_fluence
    block = 0
    execute_on = 'timestep_begin'
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = 0
    factor = 50e18
    execute_on = timestep_begin
  []
  [total_swelling]
    type = ADMaterialRealAux
    variable = swell
    property = swelling
    block = 0
  []
  [creep_rate]
    type = ADMaterialRealAux
    variable = creep_rate_aux
    property = creep_rate
    block = 0
    execute_on = 'initial linear'
  []
[]

[BCs]
  [temperature_all]
    type = ADDirichletBC
    boundary = 'left right bottom top'
    variable = temperature
    value = 1073.15
  []
  [leftX]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [bottomY]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [topY]
    type = ADPressure
    variable = disp_y
    boundary = top
    factor = -3e6
  []
[]

[Materials]
  [thermal]
    type = ADHeatConductionMaterial
    thermal_conductivity = 10.0
    specific_heat = 1.0
  []
  [density]
    type = ADStrainAdjustedDensity
    block = 0
    strain_free_density = 2700.0
  []
  [swelling]
    type = ADCompositeSiCVolumetricSwellingEigenstrain
    block = 0
    temperature = temperature
    swelling_model = KATOH
    number_of_substeps = 100
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = swelling_strain
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 3e11
    poissons_ratio = 0.17
  []
  [elastic_stress]
    type = ADComputeMultipleInelasticStress
    block = 0
    inelastic_models = composite_sic_creep
  []
  [composite_sic_creep]
    type = ADCompositeSiCCreepUpdate
    fast_neutron_flux = fast_neutron_flux
    block = 0
    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
  l_tol = 1e-5

  start_time = 0.0
  dt = 1e4
  end_time = 1e6
[]

[Postprocessors]
  [avg_temperature]
    type = SideAverageValue
    boundary = 'left right top bottom'
    execute_on = 'initial timestep_end'
    variable = temperature
  []
  [creep_rate]
    type = ElementAverageValue
    block = 0
    variable = creep_rate_aux
    execute_on = 'initial timestep_end'
  []
  [von_mises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
    block = 0
  []
  [swelling_out]
    type = ElementAverageValue
    variable = swell
    execute_on = 'initial timestep_end'
    block = 0
  []
  [fast_neutron_fluence]
    type = AverageNodalVariableValue
    variable = fast_neutron_fluence
    execute_on = 'initial timestep_end'
    block = 0
  []
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References