FCG computer code, NASGRO [2], developed by Forman et al., [3] for NASA, and remaining life assessments of mechanically damaged gas transmission pipelines [4]. In addition to these, the developed methodology is finding direct applications in other industrial areas involving LCF of structures, such as the assessment of the effects of pipe reeling and straightening during the installation of offshore pipelines, and start-up and shutdown of industrial gas turbine engines. Under small-scale yielding (SSY) conditions the DJ methodology reduces to LEFM approaches based on DK, the cyclic change in the stress intensity factor, K. The extension of the elastic-plastic fracture mechanics parameter, J, to EPFCG based on DJ was pioneered by Dowling [5,6]. The methodology presented herein employs a closure-corrected modification to DJ designated as DJeff, developed from the work of Newman [7]. The present paper briefly reviews recent efforts by SwRI in developing and validating DJeff estimation schemes for LCF applications involving cyclic loading of cracks at notches and cracks subjected to constant cyclic strains. HYBRID EPRI-RS J ESTIMATION SCHEME The proposed J scheme combines the EPRI approach [8] with the RS approach [9] and is herein referred to as the hybrid EPRI-RS method. J is resolved into elastic and plastic components, Je and Jp, respectively, n o o p ref o o ref ref p ref e e e p P P E = , P P = , E V J (a) E K (a ) J J J ÷÷ ø ö çç è æ ú ú û ù ê ê ë é + = + = s s e a s s e m ' 2 (1) Here E´ = E, Young’s modulus, for plane stress and E/(1-ne 2) for plane strain, where ne is Poisson’s ratio. P is the applied load, Po is the plastic limit load and V is a dimensionless engineering parameter and m = 1 for plane stress, ( ) ( ) n n 2 e 2 p / 1 1 - - for plane strain, where np is the plastic Poisson’s ratio. The strain P ref e is the plastic component of the reference strain corresponding to the reference stress, sref, on the stress-strain curve. The effective crack depth, y ea a rf = + , depends on a plastic zone size ry and a load-dependent parameter f that are defined below for a Ramberg-Osgood material where ÷÷ ø ö çç è æ s s a s s e e 0 n 0 0 + = and a, so and n are material constants and eo=so/E. K n+1 n-1 1 , r = P P 1 + 1 = 2 o y o ÷÷ ø ö çç è æ úû ù êë é ÷÷ ø ö çç è æ s bp f 2 (2) In this equation, b equals 2 for plane stress and 6 for plane strain. The limit load Po can be obtained from the EPRI handbooks of J solutions [10] or the review of solutions performed by Miller [11]. An optimization procedure proposed in [12] used 189 finite element analysis (FEA) solutions for Jp covering an extensive assortment of structures, crack shapes and sizes, and applied load types to determine values for Po and V that gave the best fit between Eqn. 1 and the FEA results. This scheme enables Eqn. 1 to be generalized to arbitrary stress-strain behaviors. The mean value of V was 1.169, which is close to the value of 1 generally assumed in
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