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A B S T R A C T This paper describes enhanced J-integral estimation schemes for pipes with circumferential semi-elliptical cracks subjected to tensile loading, global bending and internal pressure. These schemes are given in two different forms to cover the wide ranges of geometries and material parameters; the modified GE/EPRI method and the modified reference stress method. In the former method, new plastic influence functions for fully plastic J-integral estimation are developed based on extensive three-dimensional finite element calculations. In the latter method, new optimized reference loads are suggested and utilized to predict the J values. To verify the feasibility of these two schemes, Jintegral values obtained from further detailed FE analyses are compared to those from the proposed schemes. Because the estimated J-integrals agree fairly well with the detailed FE analysis results, the new solutions can be applied for accurate structural integrity assessment of different size pipes with a circumferential surface crack.Keywords GE/EPRI method; J-integral estimation scheme; plastic collapse; reference stress method; R m /t ratio; semi-elliptical surface crack. N O M E N C L A T U R Ea = crack depth c = half crack length C 1 = coefficient of characteristic length in SC.TNP1 method E = Young's modulus E = E/ (1 -v 2 ) for plane strain; = E for plane stress F = shape function for linear elastic stress intensity factor h 1 (n) = plastic influence function for J p in the GE/EPRI method h 1 (n = 1) = value of h 1 for the elastic case (n = 1) H 1 = normalized h 1 (n) by using h 1 (n = 1) J = J-integral J e = elastic component of J-integral J p = plastic component of J-integral K I = mode I stress intensity factor L = characteristic length L w = characteristic length in SC.TNP1 method M = global bending moment M L = global limit bending moment M oR = optimized reference moment for the definition of the reference stress n = strain hardening exponent of Ramberg-Osgood fit

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Effective modulus of elasticity Finite-element analysis Ligament efficiency Natural frequency Perforated plate RayleigheRitz method Square plate a b s t r a c t In this study, the natural frequencies of the perforated square plate with a square penetration pattern are obtained as a function of ligament efficiency using the commercial finite-element analysis code ANSYS. In addition, they are used to extract the effective modulus of elasticity under an assumption of a constant Poisson's ratio. The effective modulus of elasticity of the fully perforated square plate is applied to the modal analysis of a partially perforated square plate using a homogeneous finite-element analysis model.The natural frequencies and the corresponding mode shapes of the homogeneous model are compared with the results of the detailed finite-element analysis model of the partially perforated square plate to check the validity of the effective modulus of elasticity. In addition, the theoretical method to calculate the natural frequencies of a partially perforated square plate with fixed edges is suggested according to the RayleigheRitz method.

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