International Journal of Advances in Engineering & Technology, May 2012. ©IJAET ISSN: 2231-1963 108 Vol. 3, Issue 2, pp. 108-116 BIFURCATION BUCKLING OF PRESSURIZED CONICAL VESSELS Mohammad Zehsaz, Farid Vakili Tahami and Yasser Ashraf Gandomi Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran ABSTRACT Metallic thin shell structures are used in different branches of industry, and the components of these structures such as dished ends show different modes of failure depending upon the geometrical and loading conditions. These are mainly gross plastic deformation under static load, loss of stability (buckling), fatigue crack initiation at highly stressed locations under cyclic loading (especially in the low cycle regime), progressive plastic deformation (ratcheting) and creep at high temperatures. In this paper, failure modes of a conical pressure vessel subjected to internal pressure has been investigated. Also, to study the effect of vessel geometry, a set of conical cylindrical vessels with the cap-cone apex half angles of 20 to 85 degrees, internal radius of 500 to 1000 mm and thickness of 1 to 10 mm has been selected. The failure modes of these vessels which include gross plastic deformation and bifurcation buckling have been taken into account. In this work, a new plastic criterion has been established which is based on the plastic work dissipation in the vessel by increasing the internal pressure. This plastic criterion can be used for structures subjected to single or a combination of loading condition. The calculated plastic limit loads, which have been obtained using the plastic criterion, are determined purely by the inelastic response of the vessel, and they are not altered by initial elastic behavior. In addition, a design graph for designing pressure vessels with conical heads subjected to internal pressure has been presented via comprehensive parametric study. The results show that when the ratio of the internal pressure to the limit pressure (Load Factor) approaches 0.5, the material yielding initiates and with further increase in the Load Factor, the plastic regions develop. Also, by increasing the ratio of cylinder radius to wall thickness (R/t), plastic buckling failure becomes more dominant. KEYWORDS: Plastic work criterion, Bifurcation buckling, Gross plastic deformation, Plastic load I. INTRODUCTION Cone-cylinder intersections are found in many shell structures. Examples include steel silos and tanks with a conical roof, conical water tanks with a cylindrical shell support, large tubular members, transition cones between two cylinders or pipes with different diameters and pressure vessels with a conical end closures. Internal pressurization is often an important loading condition for these intersections. For the intersection of a large end of a cone and a cylinder (Fig. 1), internal pressure causes large circumferential compressive stresses in the intersection by either axi-symmetric collapse involving excessive inward gross plastic deformations or non-symmetric bifurcation buckling featuring periodical waves around the circumference. In the majority of the practical cases, gross plastic deformation under static loading is the fundamental failure mode that has been widely discussed in international standards such as PD5500 unfired fusion welded pressure vessels [1], ASME boiler and pressure vessel code, section III and IV [2] and EN13445-3: unfired pressure vessels [3]. Teng [4] has conducted a comprehensive study on the gross plastic deformation of the pressure vessels with conical caps under internal pressure and Mackenzie et al. [5,6,7] have proposed a plastic work criterion for evaluating gross plastic deformations in metallic shell structures with tori- spherical caps. In addition, a buckling failure of a cone-cylinder intersection was reported and analyzed in detail by Teng and Zhao [8]. Also, Blachut and K. Magnucki [9] have studied the stress concentrations at the junction of cylinder-ellipsoidal end closures in detail.