Issue 51

Y. Dubyk et alii, Frattura ed Integrità Strutturale, 51 (2020) 459-466; DOI: 10.3221/IGF-ESIS.51.34 463   2 2 2 1 cos cos w mn n m D x M C n n R R           (19) Stresses were obtained using the following formulas of the shell theory, and were divided into membrane and bending part, which is very common for nuclear, oil and gas industries:   2 6 mx bx x x x N M h h      (20)   2 6 m b N M h h           (21) In the following section, this semi-analytical procedure will be tested in detail, and some properties will be discussed R ESULTS AND D ISCUSSION o analyze the dent behavior, the stress concentration factor will be introduced, which is the ratio of a local stress caused by the dent to the nominal stress level in a perfect pipe: mx bx force nom SCF      (22) m b pressure nom SCF        (23) Here nom  is a nominal stress level in a shell without a dent. In this study, two main loadings for oil and gas pipelines – internal pressure (P) and axial force (F) were considered: 2 x nom force N F h Rh     (24) nom pressure N PR h h     (25) First of all, the convergence criteria will be considered to the analysis, i.e. how many modes should be included in Fourier expansion. On Fig. 1, the convergence solution can be seen with respect to the number of modes involved (number of terms in Fourier expansion) and it is possible to conclude that 50th-60th modes were quite enough for dent assessment. Also, for internal pressure loading, it's possible to note that the proposed solution converges faster. On Fig. 2 and Fig. 3, a comparison with numerical results obtained by the commercial FEA ANSYS can be seen. As an applied load axial force (see Fig. 2) and pressure (Fig. 3) were used, the nominal stress level was equal to 1 MPa, note that the stress categorization according to Eqns. (20) and (21) was used. However, an equivalent load method underestimates the peak stress concentrated value, it predicts quite well the stress profile and from Fig. 1b it can be seen that 20-25 modes will be enough for profile prediction. The influence of the nominal stress level was analyzed in Fig. 4. It can be seen the continuous reduction of the SCF with the increasing of the stress level, this effect is introduced in the model with the initial stress matrix (6), without it horizontal lines would be obtained. The initial stress influence can be explained by the fact that high level forces, especially pressure, tries to ‘fix’ the dent and bring the shell to a perfect condition. In addition, from Fig. 4, the effect of non-proportional dent dimensions can be observed and conclude that a dent with a longer dimension perpendicular to a nominal stress is more dangerous. Thus, in dent assessment not only dent depth should be considered, but also length and width have to be taken into account. From Figs. 2-4, it's possible to conclude that internal pressure leads to bigger stress concentration factors with the same nominal stress level. T