Fracture assessments with elastic follow-up for combined primary and secondary loadings

Abstract

This paper presents comparisons of finite element (FE) results with the J estimation equations proposed in Part 1 for treating fracture under combined primary and secondary loadings. The FE analyses are performed for a pipe with a circumferential internal surface crack subjected to axial tension combined with thermal loading. The crack depth and length, the relative magnitude of axial tension and thermal loadings, loading sequence and material properties are systematically varied. Based on the FE results, the applicability of the proposed equations in Part 1 is discussed and new estimation equations obtained by modifying the existing equations are proposed and validated.

Fracture assessments with elastic follow-up for combined primary and secondary loadings part 1: Predictive models

“…This provides a practical method for estimating the elastic follow-up factor from an elastic-plastic analysis for a large secondary loading, as noted in [15], and would provide a conservative approach for smaller magnitudes of secondary loading. This is examined in part 2 [8].…”

“…Furthermore, a number of these methods require an estimate of the elastic follow-up factor, Z. Part 2 of this paper [8] examines the accuracy of the above estimates when € Z s is used as an estimate of Z, that is if J can be estimated without a separate estimate of elastic follow-up under combined primary and secondary.…”

“…A number of estimates of J for combined loading, written in terms of the equivalent parameter V used in R6, have been presented in this paper. Part 2 of the paper [8] examines the accuracy of these estimates for combined loading by comparison with detailed finite element solutions for geometries, crack sizes and material properties leading to a range of values of elastic follow-up in order to develop practical proposals for treating elastic follow-up in fracture assessments under combined loading.…”

“…The applicability of this estimate for combined primary and secondary loading is discussed in Section 4 where a number of potential estimation methods are presented. Part 2 of this paper [8] examines these estimation methods by comparison with numerical estimates of Z from analyses of cracked components in order to provide guidance on simplified estimation schemes.…”