Experimental and numerical crashworthiness investigation of empty and foam-ﬁlled end-capped conical tubes Ali Ghamarian a , Hamid Reza Zarei b,n , Mohammad Taha Abadi c a Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran b Aeronautical University, Tehran, Iran c Aerospace Research Institute, Ministry of Science, Research and Technology, P.O. Box 14665-834, Tehran, Iran article info Article history: Received 17 September 2010 Received in revised form 26 February 2011 Accepted 17 March 2011 Available online 8 July 2011 Keywords: End-capped conical tubes Axial crushing Energy absorption abstract Foam-ﬁlled thin-wall structures exhibit signiﬁcant advantages in light weight and high energy absorption. They have been widely applied in automotive, aerospace, transportation and defense industries. Quasi-static tests were done to investigate the crash behavior of the empty and poly- urethane foam-ﬁlled end-capped conical tubes. Non-linear dynamic ﬁnite element analyses were carried out to simulate the quasi-static tests. The predicted numerical crushing force and fold pattern were found to be in good agreement with the experimental results. The energy absorption capacities of the ﬁlled tubes were compared with the empty end-capped conical tubes. The results showed that the energy absorption capability of foam-ﬁlled tube is somewhat higher than that of the combined effect of the empty tube and the foam alone. Finally, the crash performance of the empty and foam ﬁlled conical and cylindrical tubes were compared. Results from this study can assist aerospace industry to design sounding rocket carrier payload based on foam-ﬁlled conical tubes. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction There has been considerable activity on dynamic crush of thin walled aluminum tubes during the past decade. A signiﬁcant part of this effort has been concerned with the use of these structures in energy absorbing systems. Increased interest on safety has led to a comprehensive research of the crash response of aluminum tubes with different cross sections geometries and in several points of view namely, analytical, numerical and experimental. Wierzbicki and Abramowicz [1] presented a simple formula to predict the axial crash response of thin walled columns. Their method is based on the balance of external and internal work. This model was validated experimentally by Abramowizc and Jones [2]. Alexander [3], Pugsley [4], Abramowicz [5] and Abramowicz and Jones [6], Singace and Elsobky [7] and Wierzbicki and Bhat [8] also used the same method to predict the crash behavior of circular tubes. Some researchers used crashworthiness optimization technique to ﬁnd optimum aluminum tubes which have maximum energy absorption capacity [9,10]. According to previous investigations, thin-walled conical tubes under crushing load achieve different crushing modes based on their length and cross section dimensions. They collapse either in axisymmetric mode (concertina or ring mode) or non-axisymmetric mode (diamond mode) or mixed mode [11]. Energy absorption normally takes place by progressive buckling of tubes walls. A distinctive feature of such a deformation mechanism is that the rate of energy dissipation is concentrated over relatively narrow zones. Prasad and Gupta [12] performed some crush experiments on conical frusta samples with large semi-apex angles at various strain rates. Numerical and experimental studies were carried out by Gupta et al. [13] to study the inﬂuence of rolling and stationary plastic hinges in the post-buckling pattern of quasi-statically loaded conical tubes. They ﬁnally compared their experimental and numerical results. Gupta and Venkatesh [14] reported experi- mental studies on the performance of conical frusta subjected to quasi-static and dynamic axial crush loadings. Cellular solids are increasingly used in many engineering applications like energy absorption, thermal insulation and light- weight structures due to their unique property of high porosity. These materials show a distinct plateau of almost constant stress under compressive uniaxial load with the nominal strain value up to 80% [15], which indicates high energy absorption capacity. For lightweight energy absorber designs, low density metal ﬁllers, such as aluminum honeycomb or foam, are preferred to tube with thicker tube walls in terms of achieving the same energy absorp- tion. Metal ﬁllers are able to increase the energy absorption of a thin-walled column. This increase is the result of the large compressive deformation of the ﬁller. The investigations indicated Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.03.005 n Corresponding author. E-mail address: H.R.Zarei@yahoo.com (H.R. Zarei). Thin-Walled Structures 49 (2011) 1312–1319