TRISOStressCorrelationFunction

Description

The stress for a multi-dimensional particle having parameter that varies from its mean value by an amount is approximated as: where is the stress of the SiC layer for a multi-dimensional particle having all parameters set at the mean values, is the stress of the SiC layer for an intact 1D spherical particle having all parameters set at the mean values, is the stress of the SiC layer for a 1D spherical particle having statistically varying parameters, and is a fitted function that describes the variation of maximum stress in the SiC layer of a cracked/aspherical particle:

Currently, we consider a statistical variation of the IPyC, SiC and OPyC layer thicknesses because they strongly affect particle failure. When they are varied from mean values, the stress is then approximated as:

To obtain the function, we typically sample seven points where , and is the standard deviation. At the midpoint, has a value of 1 because . At other data points, we perform both multi-dimension and one-dimension analysis to determine the value of the function. A polynomial curve fit is finally performed on the data points to generate the quadratic function.

The coefficients of "1", "", and "" are assigned to polynomial_coefficients_IPyC, polynomial_coefficients_SiC and polynomial_coefficients_OPyC. The ratio of is assigned to correlation_factor.

Example Input Syntax

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction<<<{"description": "Computes the stress correlation function.", "href": "TRISOStressCorrelationFunction.html"}>>>
    triso_geometry<<<{"description": "Name of the UserObject that computes TRISO geometry."}>>> = particle_geometry
    polynomial_coefficients_IPyC<<<{"description": "Fitted polynomial function's coefficents for IPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 6922 -2.359e8'
    polynomial_coefficients_SiC<<<{"description": "Fitted polynomial function's coefficents for SiC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.257e4 1.82e8'
    polynomial_coefficients_OPyC<<<{"description": "Fitted polynomial function's coefficents for OPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.257e4 1.82e8'
    correlation_factor<<<{"description": "The correlation factor."}>>> = -1.1932
  []
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction<<<{"description": "Computes the stress correlation function.", "href": "TRISOStressCorrelationFunction.html"}>>>
    triso_geometry<<<{"description": "Name of the UserObject that computes TRISO geometry."}>>> = particle_geometry
    polynomial_coefficients_IPyC<<<{"description": "Fitted polynomial function's coefficents for IPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.716e4 2.123e8'
    polynomial_coefficients_SiC<<<{"description": "Fitted polynomial function's coefficents for SiC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 2.688e4 -1.414e7'
    polynomial_coefficients_OPyC<<<{"description": "Fitted polynomial function's coefficents for OPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.716e4 2.123e8'
    correlation_factor<<<{"description": "The correlation factor."}>>> = 0.2923
  []
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction<<<{"description": "Computes the stress correlation function.", "href": "TRISOStressCorrelationFunction.html"}>>>
    triso_geometry<<<{"description": "Name of the UserObject that computes TRISO geometry."}>>> = particle_geometry
    polynomial_coefficients_IPyC<<<{"description": "Fitted polynomial function's coefficents for IPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.664e4 1.929e8'
    polynomial_coefficients_SiC<<<{"description": "Fitted polynomial function's coefficents for SiC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 2.625e4 -1.112e7'
    polynomial_coefficients_OPyC<<<{"description": "Fitted polynomial function's coefficents for OPyC thickness that correspond to constant, linear and quadratic terms."}>>> = '1 -1.664e4 1.929e8'
    correlation_factor<<<{"description": "The correlation factor."}>>> = 0.5241
  []
[]

Input Parameters

Input Files

• (examples/TRISO/failure_probability_monte_carlo/triso_1d_function.i)
• (test/tests/triso_failure/higher_order_correlation.i)
• (test/tests/triso_failure/triso_1d_ipyc_weibull_probability.i)
• (test/tests/triso_failure/ad_triso_1d_ipyc_weibull_probability.i)
• (test/tests/triso_failure/triso_failure_diffusivity.i)
• (examples/TRISO/failure_probability_direct_integration/triso_1d.i)
• (examples/TRISO/failure_probability_monte_carlo/triso_1d_constant.i)