Reliability Analysis of Fatigue at Multiple Locations

There are multiple load paths and numerous structural welds in tank car structures. As such, experience shows that fatigue cracks may often occur at multiple locations in a tank car. In developing and illustrating the reliability analysis methodology for railroad tank cars with fatigue damage at multiple locations, example cases for a tank car with fatigue damage at four different locations are considered. The four fatigue locations represent the most critical fatigue location determined from the damage tolerance analysis we performed previously. The previous page on Reliability Analysis for Fatigue Crack Growth shows one such a location. It is located outside the tank along the weld toe between the front sill pad and the tank head, and induced by the downward vertical coupler force (VCF) load. Tank car failure occurs if leakage happens at one or more of the fatigue locations. Therefore, the tank car failure event is a union of the failure event at each individual location.

The lower-left figure shows the result obtained for a tank car with fatigue damage at four different locations as described above. The failure probability, Pf, for each individual location (or, component) is labeled as (1), (2), (3) and (4), respectively. The tank car (or, system) failure probability is the upper curve denoted as (f4_ac), which is significantly higher than the highest failure probability of the four individual locations. The sensitivity information of the system failure probability with respect to each component (location) is given in the lower-right figure. It can be seen that the components (1) and (2) are much more important to the system than components (3) and (4). Being able to assess the effect of damage at different individual locations on the reliability of a tank car as a whole provides necessary information needed for prioritizing the inspection, maintenance and repair.