Yim H. Tang

Damage tolerance analysis of detail fractures in rail

Abstract This paper describes a fracture mechanics approach for analyzing the growth of internal transverse defects in rails known as detail fractures. Analyses are used specifically to determine: (1) the defect size at which a rail failure can be expected when a train is traveling over it and (2) the time for a detail fracture to grow from a given size to the size at which rail failure can be expected. The results from these analyses are shown to depend strongly on ambient temperature. Moreover, the results can be applied to develop damage-tolerant strategies for rail inspection.

Analyses of Full-Scale Tank Car Shell Impact Tests

This paper describes analyses of a railroad tank car impacted at its side by a ram car with a rigid punch. This generalized collision, referred to as a shell impact, is examined using nonlinear finite element analysis (FEA) and threedimensional (3-D) collision dynamics modeling. Moreover, the analysis results are compared to full-scale test data to validate the models. Commercial software packages are used to carry out the nonlinear FEA (ABAQUS and LS-DYNA) and the 3-D collision dynamics analysis (ADAMS). Model results from the two finite element codes are compared to verify the analysis methodology. Results from static, nonlinear FEA are compared to closed-form solutions based on rigid-plastic collapse for additional verification of the analysis. Results from dynamic, nonlinear FEA are compared to data obtained from full-scale tests to validate the analysis. The collision dynamics model is calibrated using test data. While the nonlinear FEA requires high computational times, the collision dynamics model calculates gross behavior of the colliding cars in times that are several orders of magnitude less than the FEA models.

Analysis of Impact Energy to Fracture Unnotched Charpy Specimens Made From Railroad Tank Car Steel

This paper describes a nonlinear finite element analysis (FEA) framework that examines the impact energy to fracture unnotched Charpy specimens by an oversized, nonstandard pendulum impactor called the Bulk Fracture Charpy Machine (BFCM). The specimens are made from railroad tank car steel, have different thicknesses and interact with impact tups with different sharpness. The FEA employs a Ramberg-Osgood equation for plastic deformations. Progressive damage and failure modeling is applied to predict initiation and evolution of fracture and ultimate material failure. Two types of fracture initiation criterion, i.e., the constant equivalent strain criterion and the stress triaxiality dependent equivalent strain criterion, are compared in material modeling. The impact energy needed to fracture a BFCM specimen is calculated from the FEA. Comparisons with the test data show that the FEA results obtained using the stress triaxiality dependent fracture criterion are in excellent agreement with the BFCM test data.

FINITE ELEMENT ANALYSES OF RAILROAD TANK CAR HEAD IMPACTS

This paper describes engineering analyses of a railroad tank car impacted at its head by a rigid punch. This type of collision, referred to as a head impact, is examined using dynamic, nonlinear finite element analysis (FEA). Commercial software packages ABAQUS and LS-DYNA are used to carry out the nonlinear FEA. The sloshing response of fluid and coupled dynamic behavior between the fluid inside the tank car and the tank structure are characterized in the model using both Lagrangian and Eulerian mesh formulations. The analyses are applied to examine the structural behavior of railroad tank cars under a generalized head impact scenario. Structural behavior is calculated in terms of forces, deformations, and puncture resistance. Results from the two finite element codes are compared to verify this methodology for head impacts. In addition, FEA results are compared to those from a semi-empirical method.

Comparison of two crack growth rate models with laboratory spectrum and field tests on rail steel

Abstract Lives predicted by two crack growth rate models are compared with the lives measured in field and laboratory spectrum tests on rail steel. The two models are shown to be equivalent, except that one model reflects average rates and the other, the fastest, measured rates from constant amplitude tests. Comparison with the field test suggests that the stress intensity factor model used to represent a detail fracture growing in a rail head requires some minor modifications. The laboratory tests, performed with load spectra in real sequence order, are shown to be reasonable simulations of the field test. Both the field and laboratory spectrum test crack growth lives are shorter than the lives predicted from the average rate model. This result is attributed to acceleration (load interaction) in the tests.

MODELING THE EFFECT OF FLUID-STRUCTURE INTERACTION ON THE IMPACT DYNAMICS OF PRESSURIZED TANK CARS

This paper presents a computational framework that analyzes the effect of fluid-structure interaction (FSI) on the impact dynamics of pressurized commodity tank cars using the nonlinear dynamic finite element code ABAQUS/Explicit. There exist three distinct phases for a tank car loaded with a liquefied substance: pressurized gas, pressurized liquid and the solid structure. When a tank car comes under dynamic impact with an external object, contact is often concentrated in a small zone with sizes comparable to that of the impacting object. While the majority of the tank car structure undergoes elasticplastic deformations, materials in the impact zone can experience large plastic deformations and be stretched to a state of failure, resulting in the loss of structural integrity. Moreover, the structural deformation changes the volume that the fluids (gas and liquid) occupy and consequently the fluid pressure, which in turn affects the structural response including the potential initiation and evolution of fracture in the tank car structure. For an event in which the impact severity is low and the tank car maintains its structural integrity, shell elements following elastic-plastic constitutive relations can be employed for the entire tank car domain. For events in which the impact severity is higher and the tank car is expected to be punctured, an equivalent plastic strain based fracture initiation criterion expressed as a function of stress triaxiality is adopted for the material in the tank car’s impact zone. The fracture initiation is implemented for ductile, shear and mixed fracture modes and followed by further material deterioration governed by a strain softening law. Multi-layered solid elements are employed in the impact zone to capture this progressive fracture behavior. The liquid phase is modeled with a linear Us–Up Hugoniot form of the Mie-Gruneisen equation of state, and the gas phase is modeled with the ideal gas equation of state. Small to moderate amounts of fluid sloshing are assumed for an impacted tank car in this study. As such, the FSI problem can be solved with the Lagrangian formulation of ABAQUS, and appropriate contact algorithms are employed to model the multi-phase interactions. The force, displacement and impact energy results from the finite element analysis show good correlations with the available shell (side) impact test data. The puncture energy of a tank car in a shell impact scenario is further analyzed. It is demonstrated that the FSI effect needs to be adequately addressed in an analysis to avoid overestimating the puncture resistance of a tank car in an impact event.

Semi-Analytical Approach to Estimate Railroad Tank Car Shell Puncture

This paper describes the development of engineeringbased 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.

Deformation Behavior of Welded Steel Sandwich Panels under Quasi-Static Loading

For the past two decades, the Federal Railroad Administration (FRA) Office of Research and Development has sponsored research conducted by the Volpe National Transportation Systems Center (Volpe Center) in safety matters related to the transportation of hazardous materials by railroad tank cars. Recent research conducted by the Volpe Center has included the application of semi-empirical and computational (i.e., finite element analysis) methods to estimate the puncture resistance of conventional railroad tank cars under generalized head and shell impact scenarios. Subsequent work identified sandwich structures as a potential technology to improve the puncture resistance of the commodity-carrying tank under impact loading conditions. This paper summarizes basic research (i.e., testing and analysis) conducted to examine the deformation behavior of flat-welded steel sandwich panels under two types of quasi-static loading: (1) uniaxial compression; and (2) bending through an indenter. The objectives of these tests were to: (1) confirm the analytical and computational (i.e., finite element) modeling of sandwich structures, (2) examine the fabrication issues associated with such structures (e.g., material selection and welding processes), and (3) observe the deformation behavior and local collapse mechanisms under the two different types of loading. In addition, the uniaxial compression tests were performed to rank or screen different core geometries. Five core geometries were examined in the compression tests: pipe or tubular cores with outer diameters equal to 2, 3, and 5 inches; a 2-inch square diamond core; and a double-corrugated core called an X-core with a 5-inch core height. The compression tests showed excellent repeatability of structural (i.e., force-crush) response for panels with similar cores and welding. The 3-inch pipe core and the diamond core were selected as candidate cores for the next test series because they possess attributes of moderate strength and moderate relative density. In addition, force-crush curves calculated from finite element analysis were in reasonable agreement with the measured curves for all cores. Bend tests using a 12-inch by 12-inch indenter with 1-inch radius rounded edges were also conducted. The panels were simply-supported over 4-inch diameter rollers spanning 24 inches between the centers of the rollers. The bend tests included three variables: (1) core type (diamond core and 3-inch pipe core); (2) core orientation relative to the supports (cores running either parallel or perpendicular to the rollers used to support the panels); and (3) face sheet type (solid plates on both sides, strips used as face sheets on both sides, and a combination of solid plates and strips. Finite element analysis of the bend tests produced nearly identical shapes to the measured force-displacement curves.Copyright