This report describes the methods, results, and conclusions of the analysis of 11 scenarios defined to exercise various options available in the xLPR (Extremely Low Probability of Rupture) Version 2 .0 code. The scope of the scenario analysis is three - fold: (i) exercise the various options and components comprising xLPR v2.0 and defining each scenario; (ii) develop and exercise methods for analyzing and interpreting xLPR v2.0 outputs ; and (iii) exercise the various sampling options available in xLPR v2.0. The simulation workflow template developed during the course of this effort helps to form a basis for the application of the xLPR code to problems with similar inputs and probabilistic requirements and address in a systematic manner the three points covered by the scope.
This paper examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a transient dynamics finite element model of a ductile steel can being slowly crushed. An elastic-plastic constitutive model is employed in the large-deformation simulations. Over 70 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) are tracked in the simulations. Each response quantity’s behavior varies according to the particular stress-strain curves used for the materials in the model. The present work assigns the same material to all the can parts: lids, walls, and weld. We desire to estimate response variability due to variability of the input material curves. When only a few stress-strain curve samples are available from material testing, response variance will usually be significantly underestimated. This is undesirable for many engineering purposes. A simple classical statistical method, Tolerance Intervals, is tested for effectively compensating for sparse stress-strain curve data. The method is found to perform well on the highly nonlinear input-to-output response mappings and non-standard response distributions in the can-crush problem. The results and discussion in this paper, and further studies referenced, support a proposition that the method will apply similarly well for other sparsely sampled random functions.
In pressurized water reactors, the prevention, detection, and repair of cracks within dissimilar metal welds is essential to ensure proper plant functionality and safety. Weld residual stresses, which are difficult to model and cannot be directly measured, contribute to the formation and growth of cracks due to primary water stress corrosion cracking. Additionally, the uncertainty in weld residual stress measurements and modeling predictions is not well understood, further complicating the prediction of crack evolution. The purpose of this document is to develop methodology to quantify the uncertainty associated with weld residual stress that can be applied to modeling predictions and experimental measurements. Ultimately, the results can be used to assess the current state of uncertainty and to build confidence in both modeling and experimental procedures. The methodology consists of statistically modeling the variation in the weld residual stress profiles using functional data analysis techniques. Uncertainty is quantified using statistical bounds (e.g. confidence and tolerance bounds) constructed with a semi-parametric bootstrap procedure. Such bounds describe the range in which quantities of interest, such as means, are expected to lie as evidenced by the data. The methodology is extended to provide direct comparisons between experimental measurements and modeling predictions by constructing statistical confidence bounds for the average difference between the two quantities. The statistical bounds on the average difference can be used to assess the level of agreement between measurements and predictions. The methodology is applied to experimental measurements of residual stress obtained using two strain relief measurement methods and predictions from seven finite element models developed by different organizations during a round robin study.