Closure to “Discussion of ‘Mechanics of Confined Thin-Walled Cylinders Subjected to External Pressure,’” (Vasilikis, D., and Karamanos, S., 2014, Appl. Mech. Rev., 66(1), p. 010801)

Abstract

The authors would like to thank Prof. Gresnigt for reading their paper and for preparing an extensive commentary, which addresses interesting issues stemming from his long-time experience in pipeline mechanics and behavior. It is the authors’ opinion that his commentary identifies several demanding problems on this subject and can be used as guidance for future research work. Our closure is aimed at complementing the commentary in further discussing those issues.In the course of our study, we examined several parameters that affect buckling behavior of confined thin-walled cylindrical shells. Nevertheless, a few additional parameters are stated by Prof. Gresnigt, namely residual stresses, Bauschinger effect, and heat treatment that may influence the mechanical properties. Residual stresses and the Bauschinger effect are mainly related to the manufacturing process. For large-diameter, thin-walled cylinders (D/t > 100), the most popular manufacturing method is spiral welding of a steel coil. Unfortunately, there exists little information on the residual stresses of such pipes. In the course of a European research program, the authors are currently working on the finite element simulation of spiral-welding pipe-manufacturing process to determine residual stresses, including the effects of decoiling. Furthermore, residual stress measurements are also performed for comparison purposes. By completion of this research, information on the distribution of residual stresses will be available and appropriate stress distribution can be considered as the initial stress state for external pressure analysis under confined conditions.Heat treatment is another factor for external pressure capacity. There exist several publications for the beneficial effects of heat treatment on external pressure buckling of thick-walled offshore steel pipes. On the other hand, there is no information for such effects on the response of thin-walled confined pipes, mainly due to pipe coating. Therefore, more research is necessary on this subject.Prof. Gresnigt also refers extensively to “mechanically lined pipe”, a novel pipe product, very promising for hydrocarbon pipeline applications. When this double-wall pipe is bent, the thick-walled outer cylinder deforms rather smoothly, whereas the thin-walled liner is susceptible to wrinkling under lateral confinement conditions, provided by the outer cylinder, as pointed out by several recent publications, experimental and computational. For lined pipes used in offshore applications, their structural behavior and buckling under external pressure is of particular interest, not given attention in the literature. This problem is somewhat different than the one described in the present paper; external pressure is not applied at the interface between the outer cylinder and the liner, but it is applied at the outer surface of the double-wall lined pipe. This means that both the outer and the liner pipe shrink and eventually buckle, most likely in the form of an oval shape. However, it would be interesting to analyze externally pressurized lined pipes with the numerical tools of the present paper and, in particular, to examine the detachment and the deformation shape of the thin-walled liner.The effects of gravity loading on the structural behavior of buried thin-walled cylinders under external pressure conditions have been examined in Sec. 4.2 of the present paper, referring mainly to buried steel water pipelines, with values of D/t ratio greater than 100. Initial ovalization of the buried pipe due to gravity will reduce its external pressure capacity. Using the finite element models of the present study, it would be helpful to extend the present work in determining a rational allowable value of initial ovalization due to gravity, so that external pressure capacity is not significantly reduced. This would be of significant interest to the water steel pipeline community.In several engineering applications mentioned by Prof. Gresnigt, confined cylinders subjected to external pressure can be made of other materials, and prediction of their buckling and postbuckling behavior under external pressure would require accurate modeling of material behavior. Nevertheless, it is the authors’ opinion that, conducting an elastic analysis similar to the one described in Sec. 3 of our paper and considering a simple criterion for material failure at the critical location, one may obtain reasonable estimates of the ultimate pressure capacity.Finally, we would also point out the lack of adequate experimental evidence on this subject of our paper. It is our understanding that conducting full-scale tests on large-diameter cylinders would be quite difficult and expensive. Nevertheless, a series of tests on appropriately scaled cylinders may be more feasible and helpful towards better understanding of buckling and postbuckling of thin-walled cylinders embedded in a deformable medium.