Semi-analytical approach to estimate railroad tank car shell puncture
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Semi-analytical approach to estimate railroad tank car shell puncture

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    This paper describes the development of engineering-based equations to estimate the puncture resistance of railroad tank cars under a generalized shell or side impact scenario. Resistance to puncture is considered in terms of puncture velocity, which is defined as the impact velocity at which puncture is expected to occur. In this context, puncture velocity represents a theoretical threshold limit. A given object striking the side of a tank car at an impact speed below the threshold velocity is not expected to penetrate the commodity-carrying tank. This definition for puncture velocity is similar to that for ballistic limit velocity, which is used to measure a target’s ability to withstand projectile impact in military applications [1]. The term “semi-analytical” is used to characterize the current approach in developing equations for shell puncture in order to distinguish the present work from the semi-empirical approach used previously to develop equations corresponding to head puncture. While several tests have been conducted to study tank car head puncture, only a limited number of tests have been performed to study tank car shell puncture. The semi-analytical approach employs a combination of three tactics to deal with the paucity of test data. The first tactic applies collision dynamics to derive an idealized relationship between impact speed and maximum force for a generalized tank car shell impact scenario. Specifically, the principle of conservation of energy is applied. The second tactic applies computational methods to simulate tank car shell impacts in greater detail. Specifically, finite element analysis is used to examine the force-deformation behavior of different tank car configurations under different loading conditions. Regression analyses are performed on the results of the detailed finite element results to develop best-fit curves to account for the effects of various factors such as shell thickness, tank diameter, internal pressure and indenter size. The third tactic is empirical, in which various factors are related to puncture force using empirical formulas that have been developed in research to examine impact resistance in pipeline applications. Results from applying the semi-analytical method to estimate shell puncture velocity are presented. Similarities and differences between the current method for shell puncture and the semi-empirical method for head puncture are discussed. In addition, results from sensitivity studies are presented to show the relative effect of different factors on estimated puncture velocity. These studies indicate that indenter size and internal pressure have the most significant effect on shell puncture velocity. Conversely, these studies indicate that tank diameter and ram car weight have a relatively weak effect on shell puncture velocity.
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