This paper provides two types of engineering J estimation equations for cylinders with finite internal axial surface cracks under internal pressure. The first type is the so-called GE/EPRI type J estimation equation based on Ramberg-Osgood (R-O) materials. Based on detailed 3-D FE results using deformation plasticity, plastic influence functions for fully plastic J components are tabulated for practical ranges of the mean radius-to-thickness ratio, the crack depth-to-length ratio, the crack depth-to-thickness ratio, the strain hardening index for the R-O material, and the location along the semi-elliptical crack front. Based on tabulated plastic influence functions, the GE/EPRI-type J estimation equation along the crack front is proposed and validated for R-O materials. For more general application, for instance, to general stress-strain laws, the developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such a re-formulation provides a simpler equation for J, which is then further extended to combined internal pressure and bending. The proposed reference stress based J estimation equation is compared with elastic-plastic 3-D FE results using actual stress-strain data for a Type 304 stainless steel. Good agreement between the FE results and the proposed reference stress based J estimation provides confidence in the use of the proposed method for elastic- plastic fracture mechanics of pressurised piping.
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