PSI - Issue 13

Rodrygo Figueiredo Moço et al. / Procedia Structural Integrity 13 (2018) 1915–1923 1919 Rodrygo F. Moço, Fábio G. Cavalcante and Gustavo H. B. Donato / Structural Integrity Procedia 00 (2018) 000–000 5

were adopted. The first input was the strain distribution obtained from the numerical models of UOE and calendaring processes. Then, it was assumed the pre-existence of a circumferential through-wall semi-elliptical crack with relative depth to thickness ( a/t ) varying from zero to one and that the value of the maximum stress intensity factor ( K max ) could be modelled according to API 579 (2007) standard as presented in Eq. 4. For the purpose of this analyses K min was considered zero. Finally, the parameters C and m of the Paris law, which are function of the prestrain as presented in by Eqs. (2-3), were added to the routine and it was possible to obtain the Fatigue Crack Growth rate results that are presented in the next section. � � � � �� � � � � � �� � � �� � � � (4) where: � � � �,� � � �,� � � �,� � � � �,� � � � �,� � � � �,� � � � �,� � , � 2 , � � ��� � ����� � � ���� , � ��� where φ is angular position, a is the crack length and A i,0 are influence coefficients interpolated from table C.14 of API 579 (2007) standard. It is important to mention that the objective of the developed FE simulation was just to obtain representative strain distributions in order to illustrate how the proposed model for FCG as a function of plastic prestrain can be used to predict crack growth rate in real components including prestraining from manufacturing processes. Thus, the simulations were not supposed to reproduce the manufacturing processes in all its aspects. 3. Results 3.1. Strain fields in UOE pipe The strain fields obtained from the FE simulation for the UOE process can be seen in Fig. 4. It can be noted that the equivalent plastic strain varies significantly during the process and along the structure, since the imposed hardening depends on the position and the deformation level. The crimp process (Fig. 4a) induces a bending stress that causes a symmetrically distributed strain field, then the U forming (Fig. 4b) induces a somewhat more severe strain field that is still approximately symmetrically distributed; after that the O forming (Fig. 4c), which is the most severe and responsible for some instability in this simulation, takes place and, finally, the expansion (Fig. 4d), which is responsible to guarantee that the geometry of the pipe meet the standards, also changes the strain field. It is important to mention again that the simulation was conducted only to analyze the trends that should be expected during real applications, without the interest in describing the manufacturing processes in full details. For the same exploratory reason, ASTM A36 steel was considered for the investigation; the authors suggest further studies including pipeline steels like API-5L X60, X80 and X100. Essentially similar results can be found in Fig. 5 for the calendaring process; thus, they won’t be discussed in details and UOE process is focused for further discussion. The evolution of plastic strain as a function of angular position and radius, which was extracted from the results obtained after expansion stage (Fig 4d) using a Matlab routine, can be seen in Fig. 6a. The almost symmetrical through thickness distribution is expected since the major part of the process, as commented above, involved in the UOE forming impose a bending stress to the plate, which means that a neutral zone was expected. Once the strain distribution was obtained, it was admitted that an elliptical crack nucleated at the inner radius and started to propagate through the thickness in a crack growth rate obtained by the model proposed in this work, that takes into account the influence of strain in the C e m coefficients of the Paris law, according to Eqs. (2-3) respectively. The stress intensity factor range was obtained be calculating the Kmax with the API 579 (2007) standard formulations, Eq. 4, for semi elliptical radial cracks and considering Kmin as zero. Figure 6b shows the crack growth rate as a function of the angular position for the pipe’s through thickness from inner to outer radius. It can be seen that the strain values affect the crack growth rate. It is important to notice that to calculate the fatigue crack growth rate to each radial position it was assumed that the crack length was from the inner radius to the position of calculation, which means, for example, that for the inner radius the crack length was zero and for the outer radius it was the value of the thickness. Therefore it was expected that maintaining the angular position the fatigue crack growth rate would increase as the analysis moves from the