A comparative study of probabilistic and Non-probabilistic models for the stress intensity factors of embedded cracks. (January 2022)

• Record Type: Journal Article
• Authors: Qiu, Zhiping; Ju, Chengyi
• Is Part Of: Engineering fracture mechanics. Volume 259(2022)
• Publication Date: 2022-01
• Subjects: Embedded crack -- Stress intensity factor -- Non-probability model -- The first-order Taylor expansion -- Chebyshev's inequality; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2021.108105
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: A non-probabilistic solution model is proposed to evaluate the effect of uncertainty. The non-probability model is efficiently solved based on interval mathematics and Taylor expansion. The comparison of probabilistic and non-probabilistic models is presented based on Chebyshev's inequality. Abstract: The embedded crack is affected by many factors which are often difficult to measure accurately for the crack located in the component. In this paper, a non-probabilistic solution model for the stress intensity factor based on the interval analysis method is proposed to evaluate the effect of crack size uncertainty. Using the interval analysis method and the convex model theory for the first-order Taylor expansion expression, the non-probability model was constructed. The comparison between the non-probabilistic models and probabilistic models (including normal and uniform distribution) is conducted by Chebyshev's inequality. The non-probability model obtains a more conservative interval than the probabilistic model. The results of numerical examples verify the correctness of the theory.