Crack associated pipe axial displacement and tearing modulus solutions are derived for pipes containing internal circumferential part-through wall surface flaw under axial tension loading. The tearing modulus solution is derived for both load control and displacement control loadings. The solutions are useful for practical applications involving contained yielding in the crack section. The analytical solutions can be readily applied to pipe radius-to-thickness ratio ranging from 5 to 20. A sensitivity study was performed to assess the influence of flaw size, pipe radius and wall thickness, pipe length, and axial tension load on the applied tearing modulus. Numerical results are presented for critical stress as a function of flaw size for 4130 carbon steel pipe.

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