Application of Artificial Neural Network to Multi-Variables Regression for Estimations of J-Integral for Surface Cracked Pipes

Crack assessment for pipe components of a nuclear power plant or oil/gas pipeline is one of the essential procedures to ensure safe operation services. To assess cracked pipes, J-integral has been considered as a theoretically robust and useful elastic-plastic fracture parameter, so that the estimations of J-integral for various pipe geometries, material properties and loading conditions are highly needed. For this reason, many engineering predictive solutions for J-estimations based on finite element (FE) analyses have been developed. Generally, many engineering predictive solutions have been suggested as a tabular-form or closed-form. Among them, the closed-form solution is more preferred than a tabular-form solution for its convenience when many lots of interpolation are required to use it. However, the accuracy of the closed-form solution tends to be significantly reduced as the number of design parameters increases. Moreover, since there is no strict rule to define the form of functions as well, the accuracy of the closed-form solution is inevitably dependent on the rule of thumb. Therefore, it is highly required to suggest a new approach for J-estimation of cracked pipes with various geometries, material properties and loading conditions. In this paper, we propose an efficient approach based on a machine learning technique to estimate J-integral for surface cracked pipes with various geometric sizes and material properties under axial displacement loading condition. Firstly, parametric FE analysis studies were systematically performed to produce the coefficients representing the engineering J-estimation for the corresponding cracked pipe. Secondly, artificial neural network (ANN) models based on deep multilayer perceptron technique were trained based on FE results. The five input neurons (pipe geometries and material properties) and the two output neurons (the coefficients representing the engineering J-estimation) were considered. Lastly, the accuracy of the trained ANN model was studied by comparing to that of the closed-form solution from multi-variable regressions.

Engineering J Estimation Equations for Spent Fuel Canisters Under Combined Mechanical and Welding Residual Stresses

This paper provides engineering J estimation equations for Spent Fuel Canisters (SFCs) under combined mechanical and welding residual stress (WRS) fields. The basic form of estimation equations is reference stress-based ones as in R6. Interaction between mechanical (primary) and residual (secondary) stresses is treated using the V-factor. Based on systematic finite element (FE) analysis and J results, the V-factors for the combined mechanical and welding residual stresses are reported.

Improvement of J Estimation Schemes Based on Reference Stress for Linear Hardening Behavior

In Elastic-Plastic Fracture Mechanics, several J-estimation schemes are based on the reference stress approach. This approach has been developed initially for creep analyses and later on for elasto-plastic fracture assessments in 1984, then included in the R6 rule. Much later, other methods, based on the reference stress concept, were derived for 3D applications like the Js method introduced in the French RSE-M code in 1997 and the Enhanced Reference Stress (ERS) method in Korea around 2001. However, these developments are based on the J2 deformation plasticity theory and well established for a pure power hardening law. Js and ERS schemes propose some corrections for recorded behavior laws which cannot be fitted by a power law. Nevertheless, their application to materials governed by a bilinear hardening law has been called into question by several studies. One of these, carried out by M. T. Kirk and R. H. Dodds [1, 2] is of great interest since addressing the practical case of a surface cracked plate.

Improved J Estimation by GE/EPRI Method for the Thin-Walled Pipes With Small Constant-Depth Circumferential Surface Cracks

Application of thin-walled high strength steel has become a trend in the oil and gas transportation system over long distance. Failure assessment is an important issue in the construction and maintenance of the pipelines. This work provides an engineering estimation procedure to determine the J-integral for the thin-walled pipes with small constant-depth circumferential surface cracks subject to the tensile loading based upon the General Electric/Electric Power Research (GE/EPRI) method. The values of elastic influence functions for stress intensity factor and plastic influence functions for fully plastic J-integral are derived in tabulated forms through a series of three-dimensional (3D) finite element (FE) calculations for a wide range of crack geometries and material properties. Furthermore, the fit equations for elastic and plastic influence functions are developed, where the effects of crack geometries are explicitly revealed. The new influence functions lead to an efficient J estimation and can be well applied for structural integrity assessment of thin-walled pipes with small constant-depth circumferential surface cracks under tension.

Improvement of the LBB.ENG2 Circumferential Through-Wall Crack J-Estimation Scheme

The LBB.ENG2[1] circumferential through-wall crack (TWC) J-estimation scheme forms the basis for the Extremely Low Probability of Rupture (xLPR)[2] probabilistic pipe fracture analysis for TWC elastic-plastic fracture mechanics (EPFM) stability assessment. The LBB.ENG2 methodology uses a reduced thickness pipe wall analogy to approximate the behavior of actual cracked pipe and sets the thickness of the reduced section by making the usual cracked pipe limit load assumption. Sometime during the original LBB.ENG2 development process, it was discovered that LBB.ENG2 was not as good as desired at predicting the maximum moment carrying capacity of pipe fracture experiments with longer cracks. Accordingly, the effective thickness equation was modified to be 1.0 at crack angles less than π/4, 4/π at angles greater than π/3, and linear between these values using a so-called ψ function. When LBB.ENG2 was coded for the TWC stability module for xLPR, TWC_fail, the behavior described above was implemented. Quite unexpectedly, with the new coding, exploration of TWC_fail’s bounds uncovered two discontinuities in the complete moment-pressure-critical crack size failure surface. Subsequently, it was found that these discontinuities were caused by the discontinuity in the derivative of the ψ function. This paper documents the approach used to smooth the TWC_fail moment-pressure-critical crack size surface by making a ψ function fit that minimizes the difference between J from LBB.ENG2 and J from finite element analyses results. The results of the finite element analyses and fitting methodology are described and the basic equations for the solution are presented. Following this, the new ψ function is applied to cases to evaluate the efficacy of the approach.

Fully-Plastic Strain-Based J Estimation Scheme for Circumferential Surface Cracks in Pipes Subjected to Reeling

Modern installation techniques for marine pipelines and subsea risers are often based on the reel-lay method, which introduces significant (plastic) strains on the pipe during reeling and unreeling. The safe assessment of cracklike flaws under such conditions requires accurate estimations of the elastic–plastic crack driving forces, ideally expressed in a strain-based formulation to better account for the displacement controlled nature of the reeling method. This paper aims to facilitate such assessments by presenting a strain-based expression of the well-known Electric Power Research Institute (EPRI) estimation scheme for the J integral, which is directly based upon fully plastic descriptions of fracture behavior under significant plasticity. Parametric finite element simulations of bending of circumferentially cracked pipes have been conducted for a set of crack geometries, pipe dimensions, and material hardening properties representative of current applications. These provide the numerical assessment of the crack driving force upon which the nondimensional factors of the EPRI methodology, which scale J with applied strain, are derived. Finally, these factors are presented in convenient graphical and tabular forms, thus allowing the direct and accurate assessment of the J integral for circumferentially cracked pipes subjected to reeling. Further results show that crack driving force values estimated using the proposed methodology and the given g1 factors are in very close agreement to those obtained directly from the finite element simulations.