Reliability Analysis of Tank Car Fatigue Crack Growth  
To effectively deal with the fatigue cracking problems in the aging U.S. railroad tank car fleet, damage tolerance analysis (DTA) has been performed to determine inspection intervals. It is widely realized that the DTA process, due to complexities involved, is subject to uncertainty arising from incomplete knowledge and/or intrinsic variability of parameters such as material properties, defect location and geometry, load spectrum, service history or usage projection, and inspection and manufacturing variability. Built on the probability and statistics concepts, reliability methods based on limitstate formulation provide a useful tool to quantitatively assess uncertainties involved in the DTA process, which, in turn, assists in a better risk management. In this project, a methodology for assessing structural reliability of railroad tank cars undergoing fatigue crack growth is developed. A threedegreeof freedom (3dof) surface crack is employed to account for an asymmetric stress field existing at a fatigue critical location in tank car structures as shown in the lowerleft figure. A threedimensional weight function method was used to determine the stress intensity factor for the 3dof surface crack. A fatigue life prediction program using the Walker equation to account for stress ratio effects is developed for the 3dof surface crack model. A component reliability problem is formulated as a limit state function and solved using a firstorder reliability method along with importance sampling method. The methodology is demonstrated using illustrative railroad tank car examples. The results, such as those in the lowerright figure, show that (a) failure probability, Pf, increases as tank car mileage increases; (b) welding residual stresses in the tank structure can significantly increase Pf; (c) uncertainty in the stress amplitude also has a significant effect on Pf; and (d) the correlation between initial crack depth and initial crack aspect ratio is an important parameter. 
