ABSTRACT
Abstract Statistical features of brittle fracture such as tortuousity of crack path, scale effect and scatter of toughness parameters are well documented. The apparent randomness of the process is closely associated with the distribution of defects on various scales within a solid. The phenomenological description of microdefects is represented by a random field of specific fracture energy y following the framework of Statistical Fracture Mechanics (SFM). A brief review of SFM is presented. SFM is a first theory that proposed a way to relate the fracture toughness and roughness of crack path using continuum mechanics formalism. At the same time, the engineering application of the model was limited due to its mathematical complexity. We employ the Monte Carlo method to overcome the analytical difficulties of SFM. Fracture toughness dependency on the tortuousity of crack trajectories, loading conditions and material microstructure are illustrated by computer simulation of tests for common specimen geometries. The ambiguity of the concept of conventional toughness is addressed. Keywords: brittle fracture, toughness, tortuousity, scale effect, defects, Monte Carlo
1 Introduction Fractal properties of fracture surfaces have been widely discussed in literature [ 1, 2J. Appearance of fracture surfaces may range from relatively smooth (see Fig. 1) to very rough and irregular (Fig. 2) where even the term 'surface' should be used with
Fig. 2. SEN micrograph of the fracture surface in CC-composite (Four-Point-Bending specimen) [3]. quotation marks. It is also recognized [4] that there exists a correlation between the roughness of crack profiles and an apparent fracture toughness. The first theory that proposed a way to relate the fracture toughness and roughness of crack path within the continuum mechanics framework was formulated in [5] and later evolved into Statistical Fracture Mechanics (SFM) [6, 7]. SFM bridges conventional Fracture Mechanics with the Weakest Link theory. It addresses the problem of brittle fracture, when a crack propagation is controlled by a pre-existing field of defects and does not cause noticeable changes to this field. In this case the random location and orientation of the individual microdefects result in an irregular, stochastic crack trajectory, scatter of the main fracture parameters and scale effect. SFM explicitly incorporates the fractographic information, e.g. fractal characterization of fracture surfaces, in the probabilistic description of brittle fracture.
