Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article Limit load analysis of thin-walled as-fabricated pipe bends with low ovality under in-plane moment loading and internal pressure Sherif S. Sorour a , Mostafa Shazly a,* , Mohammad M. Megahed b a Mechanical Engineering Department, the British University in Egypt, El-Sherouk City, Cairo, Egypt b Mechanical Design and Production Engineering Department, Cairo University, Giza, Egypt ARTICLE INFO Keywords: Thin-walled Pipe bend Limit load analysis Ovality Residual stresses ABSTRACT The fabrication of pipe bends using rotary pipe bending (RPB) process results in geometrical imperfections as described by cross-sectional ovality and wall thickness variations which affect the pipe bends performance during service. Previous studies whether ignores these imperfections (Ideal pipe bend (IB)) or assume these imperfections in their analysis (Assumed shape bend (AS)). The objective of the present work is to investigate, using non-linear finite element analysis, the effect of the residual stresses and the presence of the inherited geometrical imperfections (low ovality) obtained from RPB process of 90° pipe bends on their load carrying capacities as compared with the IB and AS models. RPB process with basic tooling configuration is first simulated to obtain the as-fabricated 90° pipe bend. The results of this step were verified against published experimental results and analytical solutions, and compensated for springback. The pipe bend was then subjected to different combinations of loads (in-plane moment and internal pressure) to construct a comparative limit load diagram. Within the scope of our study, results have shown that the presence of the residual stresses remarkably reduces the pipe bend load-carrying capacity. IB model results in non-conservative results as geometrical imperfections lower the load carrying capacity of the pipe bend, while the AS model has been found to be invalid for cases where a mandrel is used in RPB process. 1. Introduction Pipe bends are curved pipe segments that are frequently used in process industries for changing flow direction and accommodating thermal expansions. Unlike straight pipes, pipe bends have unique de- formation characteristics due to their increased flexibility and stress intensification as compared with a straight pipe of the same size and material [1]. Pipe bends fabricated by pipe bending process inherent inevitably geometrical imperfections as shown in Fig. 1. This deviation is con- ventionally characterized by % ovality and % wall thinning/thickening as per the definitions below: = D %Ovality 100%x(D —D )/ max min (1) = t t t % Wall thinning 100% x ( — )/ min (2) = t t t % Wall thickening 100% x ( — )/ max (3) According to ASME B31.1-2016/B31.3-2002 [2,3], the admissible initial ovality for pipe bends are 8% for internally pressurized pipe bends while for the admissible wall thickness variations is 21% if the ratio of pipe bend radius R to pipe nominal diameter D is 3 or less. Being based on elasticity assumptions and ignoring geometrical imperfections, the analytical solutions are only applicable when the pipe bend is subjected to low loading conditions which are close to the pipe's operational loads. However, under severe loading conditions, these analytical solutions fail to predict the plasticity behavior of the pipe bend, especially when material and geometrical nonlinearities are considered [1,4–6]. The plastic behavior of pipe bends can be described by conducting limit load analysis (LLA). This approach relies on de- termining the limiting loads before pipe failure is attained and conse- quently a limiting diagram is constructed to provide the in-service al- lowable loads and visualize safety margin for operational pipes. A limit load usually refers to limit moment (collapse and instability moments) and limit pressure. However, due to the complexity associated with analytical solutions, this term refers only to collapse moment (CM). The analytical limit loads are usually obtained for a perfect pipe bend assuming elastic-perfectly plastic material model with few studies considering the effect of the straight pipe segment attached to the pipe bend. Both small and large-displacement theories are adopted in the development of the analytical limit load formulae. In small https://doi.org/10.1016/j.tws.2019.106336 Received 24 February 2019; Received in revised form 22 July 2019; Accepted 1 August 2019 * Corresponding author. E-mail address: mostafa.shazly@bue.edu.eg (M. Shazly). Thin-Walled Structures 144 (2019) 106336 0263-8231/ © 2019 Elsevier Ltd. All rights reserved. T