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A B S T R A C T This paper provides net-section limit pressures and a reference stress based J estimation method for pipes with constant depth, internal axial surface cracks under internal pressure. Based on systematic small strain finite element (FE) limit analyses using elastic perfectly plastic materials, net-section limit pressures are firstly determined, and based on FE results, a closed-form limit pressure solution is proposed. Furthermore, based on the proposed limit pressure solution, a method to estimate elastic-plastic J is proposed based on the reference stress approach. When the reference stress is defined by the proposed (global) limit pressure, estimated J values based on the reference stress approach are overall slightly lower than FE results, implying that the method is non-conservative. By re-defining the reference using optimised reference loads, resulting J estimates agree well with FE results.Keywords axial part-through surface crack; finite element analysis; J estimation; limit pressure; reference stress approach. N O M E N C L A T U R Ea = crack depth c = half crack length E = Young's modulus E = = E/(1−ν 2 ) for plane strain; = E for plane stress F = shape function for linear elastic stress intensity factor J, J e = J-integral and its elastically calculated value K = linear elastic stress intensity factor n = strain hardening index (1 ≤ n < ∞) for the Ramberg-Osgood model, Eq.(2) P = internal pressure P L = limit pressure of a cracked pipe P o = limit pressure of an un-cracked pipe P OR = optimized reference pressure for reference stress based J estimates P ref = reference pressure to define the reference stress r m = mean pipe radius t = thickness of a pipe α = coefficient of the Ramberg-Osgood model, Eq. (2) ρ = normalized half crack length, = c /. √ r m t ν = Poisson's ratio ε = strain ε ref = reference strain σ = stress Correspondence: Y. J. Kim.

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