PSI - Issue 13

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 13 (2018) 868–876 K. Kouzoumis et al. / Structural Integrity Procedia 00 (2018) 000–000

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collapse, and an ordinate of K r , proximity to fracture. This point is placed on a failure assessment diagram (FAD) containing a failure assessment line (FAL), which derives from the materials’ mechanical properties. The formulae used for the calculation of L r and K r can vary in terms of accuracy, especially when considering the wide variety of applications that each of them has to cover. Hence there is a need for procedures to be validated regularly. Validation is achieved by applying them in situations in which the failure conditions are known. For example, a large scale test, in which the loading history and geometric parameters as well as mechanical properties, are known, could be used. Assessment of this test with the use of BS 7910 will demonstrate the accuracy or potential inadequacies of the procedure and give an indication of where the procedure needs to be improved. Validation is therefore primarily a process whereby the assessment procedure itself is assessed to demonstrate that it is safe and accurate. With this in mind, a validation exercise, including several hundred large scale fracture tests from the literature, is currently underway at TWI to demonstrate that the BS 7910:2013 procedure is accurate, or identify potential gaps in it. One of the aspects identified for potential modification is the proximity to plastic collapse ( L r ) of a pipe (or curved shell) containing an axial flaw, either surface-breaking or through thickness. The reference stress solutions, used for the assessment of plastic collapse for these geometries in the current version of BS 7910 include a multiplication factor of 1.2 on the membrane stresses, which (as will be demonstrated later) is not adequately explained. Since pipes are most often loaded with internal pressure and / or global bending, through-wall bending is considered to have only a small e ff ect in most cases and will thus be ignored in this analysis. Focus will be on the constituents of the formulae that relate to membrane stress (i.e. hoop stress). In this work, a modified reference stress solution with omission of the factor of 1.2 is proposed. To justify the proposed modification, example assessments will be made for comparison between the BS 7910, API / ASME and R6 procedures. Hence, in the following paragraphs, the initial step will be to provide a brief background of the equations used, in each procedure, for the example assessment of axially flawed pipes / curved shells. This will be followed by the comparison between the BS 7910 solutions and those of other procedures. Finally, the modified equation will be validated with its implementation, in parallel to the original BS 7910 reference stress solution, in assessing 173 tests, conducted on pipes, from the literature.

Nomenclature

σ re f reference stress P m the hoop (membrane) stress M T multiplication factor for translation of applied stress to reference stress for through thickness flaws / the Folias factor M S multiplication factor for translation of applied stress to reference stress for surface flaws c half crack length a depth of crack W structural width of the specimen, in this case this stands for the length of the pipe B thickness of specimen or structure

r i / o internal / external radius of pipe or curved shell r m the mid thickness radius of the curved shell λ referenced in API (2016) as shell factor λ a modified shell factor ¯ σ e the applied membrane stresses needed for failure σ ∗ the failure stress based on Gri ffi ths Theory ν the Poisson ratio G the shear modulus γ ∗ the surface energy density of the material C parameter used to define the cross-sectional area of the crack