LPG rail tank cars under head-on collisions

Abstract

This paper presents a general methodology for calculating the critical velocity of a train part striking the head of a LPG rail tank car. The energy dissipation during the collision is mainly due to collapse of the underframe, plastic deformation of the tank head and friction. The collapse behaviour of a two and four axle underframe is studied by means of a two dimensional beam model with the plastic deformations confined to local zones, or plastic hinges. The impact vulnerability of tank car heads is studied by tests on geometrically scaled models of tank heads, finite difference calculations and an analytical approach. The experiments and finite difference calculations show that an unsymmetric deformation pattern develops in the centre part of the shell when the indentation exceeds the thickness by approximately one order of magnitude. The experimental results and the finite difference calculations indicate however that the force-indentation relation for the centrally loaded heads can be calculated sufficiently accurately using an axisymmetric model for indentations exceeding the thickness by two orders of magnitude. The analytical approach is based on an axisymmetric model and the assumption that the plastic deformations are confined to a relatively narrow axisymmetrical section moving outwards with increasing penetration. This assumption is only valid for indentations larger than approximately three times the shell thickness. However, before puncturing of the tank head, indentations of more than 30 times the shell thickness will occur. A simple closed-form solution is derived for centrally loaded pressurized spherical shells. The experiments indicate that this solution is also applicable for eccentrically loaded pressurized spherical shells. Finally two accident scenarios that can lead to puncturing of a tank car head are discussed. The initial collapse load of the first car, the effective mass of the colliding train part, the friction with the ground and the pressure in the LPG tank prove to be important parameters.