StressCorrosionCrackingExponential

Description

This Reporter for stress corrosion crack growth computes the growth increment for each active crack front node in the CrackMeshCut3DUserObject. The growth increment for each node is computed by first finding the crack front node where $var element = document.getElementById("moose-equation-27166a56-9290-4ddd-bb60-ccf9d778ae48");katex.render("K_I", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ provided by the DomainIntegralAction is largest and computing the amount of time, $var element = document.getElementById("moose-equation-dd8010ad-5d2c-4c1a-bb21-0eb246df13b1");katex.render("t_{cmax}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , it will take for that node to extend by the amount given by "max_growth_increment". $var element = document.getElementById("moose-equation-67aabc71-c8eb-49d5-8549-d491cb2a8bc1");katex.render("t_{cmax}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is stored in the scalar reporter "time_to_max_growth_increment_name". The growth increment for the other nodes in the crack front are then computed by multiplying their growth rates by $var element = document.getElementById("moose-equation-5cd64988-14d4-40f9-9b5a-35de82408a0c");katex.render("t_{cmax}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . The growth rate comptuted by StressCorrosionCrackingExponential is based on the equation for stress corrosion cracking given by Li et al. (2015) for stainless steel 316L exposed to water at 288C given by

$(1)var element = document.getElementById("moose-equation-244edd73-a8e7-4e05-940d-86a27db23bca");katex.render("v_c = \\begin{cases} 2 \\times 10^{-9}, & K_I < 6.7 \\ \\text{MPa} \\sqrt{\\text{m}} \\\\ 3.33 \\times 10^{-11} K_I^{2.161}, & 6.7 \\ \\text{MPa} \\sqrt{\\text{m}} \\leq K_I < 59 \\ \\text{MPa} \\sqrt{\\text{m}} \\\\ 2.01 \\times 10^{-7}, & K_I \\geq 59 \\ \\text{MPa} \\sqrt{\\text{m}} \\end{cases} ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

which is input into StressCorrosionCrackingExponential using the following input file syntax:

text [Reporters] [scc_crack_growth] type = StressCorrosionCrackingExponential growth_increment_name = "growth_increment" time_to_max_growth_increment_name = "max_growth_timestep" crackMeshCut3DUserObject_name = cut_mesh max_growth_increment = 0.0004 k_low = 6.7e6 k_high = 59e6 growth_rate_mid_multiplier = 3.601e-24 #3.33e-11*(1e-6)**2.161 growth_rate_mid_exp_factor = 2.161 [] [] `` The growth rate below "k_low" and above "k_high" is constant and computed from the equation for the mid growth rate.

Example Syntax

This example from the test suite demonstrates the time to grow the crack by "max_growth_increment" is the same as that produced using a constant timestep size. This implements the following equation for the stress growth increment

$(2)var element = document.getElementById("moose-equation-29379ea5-7259-4a8b-8201-07cf062606d7");katex.render("\\Delta a = \\begin{cases} 0.1\\Delta t, & K_I < 10 \\\\ (0.01*K_I-0.05)\\Delta t, & 10 \\leq K_I < 20 \\\\ 0.15\\Delta t, & K_I \\geq 20 \\ \\text{MPa} \\sqrt{\\text{m}} \\end{cases} ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

[Reporters<<<{"href": "../../syntax/Reporters/index.html"}>>>]
  [scc_crack_growth]
    type = StressCorrosionCrackingExponential<<<{"description": "This reporter computes the crack growth increment at all active crack front points in the CrackMeshCut3DUserObject for stress corrosion cracking fit to an exponential function. Crack growth rates computed by this reporter are stored in the same order as in the fracture integral VectorPostprocessors.", "href": "StressCorrosionCrackingExponential.html"}>>>
    growth_increment_name<<<{"description": "ReporterValueName for storing computed growth increments for the crack front points."}>>> = "crack_growth"
    time_to_max_growth_increment_name<<<{"description": "ReporterValueName for storing computed timestep to reach max_growth_increment."}>>> = "max_growth_timestep"
    crackMeshCut3DUserObject_name<<<{"description": "The CrackMeshCut3DUserObject user object name"}>>> = cut_mesh
    max_growth_increment<<<{"description": "the max growth size at the crack front in each increment of a fatigue simulation"}>>> = 0.1
    k_low<<<{"description": "Value of K_I below which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_low."}>>> = 10
    k_high<<<{"description": "Value of K_I above which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_high."}>>> = 20
    growth_rate_mid_multiplier<<<{"description": "Growth rate multiplier when K_I is between k_low and k_high"}>>> = 0.00075
    growth_rate_mid_exp_factor<<<{"description": "Growth rate exponential factor"}>>> = 1
  []
[]

Input Parameters

crackMeshCut3DUserObject_nameThe CrackMeshCut3DUserObject user object name
C++ Type:UserObjectName
Controllable:No
Description:The CrackMeshCut3DUserObject user object name
growth_rate_mid_exp_factorGrowth rate exponential factor
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Growth rate exponential factor
growth_rate_mid_multiplierGrowth rate multiplier when K_I is between k_low and k_high
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Growth rate multiplier when K_I is between k_low and k_high
k_highValue of K_I above which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_high.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value of K_I above which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_high.
k_lowValue of K_I below which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_low.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value of K_I below which the crack growth rate is constant and equal to the mid growth rate function evaluated with a K_I=k_low.
max_growth_incrementthe max growth size at the crack front in each increment of a fatigue simulation
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:the max growth size at the crack front in each increment of a fatigue simulation

Required Parameters

growth_increment_namegrowth_incrementReporterValueName for storing computed growth increments for the crack front points.
Default:growth_increment
C++ Type:ReporterValueName
Controllable:No
Description:ReporterValueName for storing computed growth increments for the crack front points.
ki_vectorpostprocessorII_KI_1The name of the vectorpostprocessor that contains KI
Default:II_KI_1
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the vectorpostprocessor that contains KI
time_to_max_growth_increment_namemax_growth_timestepReporterValueName for storing computed timestep to reach max_growth_increment.
Default:max_growth_timestep
C++ Type:ReporterValueName
Controllable:No
Description:ReporterValueName for storing computed timestep to reach max_growth_increment.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onXFEM_MARK TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:XFEM_MARK TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
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
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

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

(modules/xfem/test/tests/solid_mechanics_basic/edge_crack_3d_scc_crit.i)

References

Yongkui Li, Shanping Lu, Dianzhong Li, and Yoshiyuki Kaji. Remaining life prediction of the core shroud due to stress corrosion cracking failure in bwrs using numerical simulations. Journal of Nuclear Science and Technology, 52(1):96–103, 2015.

@article{li_scc_2015,
    author = "Li, Yongkui and Lu, Shanping and Li, Dianzhong and Kaji, Yoshiyuki",
    title = "Remaining life prediction of the core shroud due to stress corrosion cracking failure in BWRs using numerical simulations",
    journal = "Journal of Nuclear Science and Technology",
    volume = "52",
    number = "1",
    pages = "96--103",
    year = "2015",
    publisher = "Taylor \\& Francis"
}

(modules/xfem/test/tests/solid_mechanics_basic/edge_crack_3d_scc_crit.i)

# This takes 1 step of max_growth_increment and back computes a time of 11s which
# is the amount of time edge_crack_3d_scc.i takes to grow a crack of similar length.

[Reporters]
  [scc_crack_growth]
    type = StressCorrosionCrackingExponential
    growth_increment_name = "crack_growth"
    time_to_max_growth_increment_name = "max_growth_timestep"
    crackMeshCut3DUserObject_name = cut_mesh
    max_growth_increment = 0.1
    k_low = 10
    k_high = 20
    growth_rate_mid_multiplier = 0.00075
    growth_rate_mid_exp_factor = 1
  []
[]
[UserObjects]
  [cut_mesh]
    type = CrackMeshCut3DUserObject
    mesh_generator_name = mesh_cutter
    growth_dir_method = MAX_HOOP_STRESS
    size_control = 1
    n_step_growth = 1
    growth_increment_method = REPORTER
    growth_reporter = "scc_crack_growth/crack_growth"
    crack_front_nodes = '7 6 5 4'
  []
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y disp_z'
  crack_front_points_provider = cut_mesh
  number_points_from_provider = 4
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
[]

#function for BC on top surface
[Functions]
  [top_trac_y]
    type = ConstantFunction
    value = 10
  []
  [top_trac_x]
    type = ConstantFunction
    value = 0
  []
[]

[Outputs]
  file_base = edge_crack_3d_scc_crit_out
  execute_on = 'FINAL'
  [json_out]
    type = JSON
    execute_system_information_on = none
  []
[]

(modules/xfem/test/tests/solid_mechanics_basic/edge_crack_3d_scc_crit.i)

# This takes 1 step of max_growth_increment and back computes a time of 11s which
# is the amount of time edge_crack_3d_scc.i takes to grow a crack of similar length.

[Reporters]
  [scc_crack_growth]
    type = StressCorrosionCrackingExponential
    growth_increment_name = "crack_growth"
    time_to_max_growth_increment_name = "max_growth_timestep"
    crackMeshCut3DUserObject_name = cut_mesh
    max_growth_increment = 0.1
    k_low = 10
    k_high = 20
    growth_rate_mid_multiplier = 0.00075
    growth_rate_mid_exp_factor = 1
  []
[]
[UserObjects]
  [cut_mesh]
    type = CrackMeshCut3DUserObject
    mesh_generator_name = mesh_cutter
    growth_dir_method = MAX_HOOP_STRESS
    size_control = 1
    n_step_growth = 1
    growth_increment_method = REPORTER
    growth_reporter = "scc_crack_growth/crack_growth"
    crack_front_nodes = '7 6 5 4'
  []
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y disp_z'
  crack_front_points_provider = cut_mesh
  number_points_from_provider = 4
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
[]

#function for BC on top surface
[Functions]
  [top_trac_y]
    type = ConstantFunction
    value = 10
  []
  [top_trac_x]
    type = ConstantFunction
    value = 0
  []
[]

[Outputs]
  file_base = edge_crack_3d_scc_crit_out
  execute_on = 'FINAL'
  [json_out]
    type = JSON
    execute_system_information_on = none
  []
[]

Description
Example Syntax
Input Parameters
Input Files
References