Influence of size strength relation in modeling the behaviour of quasi-brittle materials

Abstract

Modeling the behaviour of quasibrittle materials (concrete, rock, fiber composites, ceramics, etc.) is a challenging task for engineers. A comprehensive approach and methodology are required for the fracture mechanics problems of quasibrittle materials. In quasi brittle materials, the fracture process zone ahead of the crack tip is not negligible compared to the characteristic cross-sectional dimension of the specimen. Influence of strain softening zones due to cracking must be considered. This paper illustrates the importance of size effect and its salient features in the field of fracture mechanics. According to Bazant Size effect law¹, the asymptotic deviation of nominal strength with respect to structural size varies from strength criteria for small size specimen to linear elastic fracture mechanics (LEFM) for large size specimen. The salient characteristics of Weibull’s statistical weak link theory and nonlocal damage theory for modeling are explained. Influence of size effect on modulus of rupture, brittleness number and rate of loading are illustrated. Salient features of crack band model, microplane model and their applications have also been summarized. Recent trends in developing virtual internal pair bond model for quasibrittle materials are also included. These concepts are essential for carrying out analytical investigations and development of design guidelines. Relatively large fracture process zone present in concrete enhances the need for extensive research in experimental methods, appropriate physical process and numerical techniques to simulate the fracture behaviour of quasibrittle materials. A summary of various models for quasibrittle materials using fracture mechanics is also presented.