Analysis of Uncertainties in Stress Intensity Factors with Interval Numbers

In this study, the effects of uncertainties on stress intensity factors (SIFs) within the framework of Linear Elastic Fracture Mechanics (LEFM) are investigated using the interval analysis. The main aim of this study is to develop a practical and reliable interval-based approach for evaluating stress intensity factors under bounded uncertainties and to examine the relative influence of load uncertainty, crack length uncertainty, and the choice of geometric factor on uncertainty propagation. For this purpose, load and crack-length related geometric uncertainties, are modeled using interval numbers, and their effects on stress intensity factors are systematically examined. The originality of this study lies in the simultaneous consideration of load and crack length uncertainties, in analyzing their individual and combined effects on stress intensity factors, and in comparing established geometric correction factor formulations in terms of the resulting uncertainty bandwidths. Accordingly, stress intensity factors for center-cracked plates subjected to tensile loading are computed using interval arithmetic. Interval arithmetic is applied to compute stress intensity factors for center-cracked plates under tensile loading, and uncertainty propagation is carried out using interval analysis implemented in the MATLAB-based toolbox (IntLab) within the framework of linear elastic fracture mechanics. Numerical results demonstrate that stress intensity factors are more sensitive to load uncertainty than to crack length uncertainty, and that the choice of geometric correction factor noticeably affects uncertainty propagation. Overall, the study presents a deterministic framework for assessing fracture mechanics problems that provides reliable bounds without relying on probabilistic assumptions.