Now, such coalescences may not be as straightforward as intuitively imagined. Note that crack growth occurs through coalescence of micro-cracks with the main crack. There are also other possible mechanisms for crack trapping. On the other hand, Laures and Kachanov (1991) showed that the stress intensity factor ‡ varies along the crack front, which may cause the front to advance along portions with low stress intensity factor, until it is trapped by a local micro-crack array that causes a sufficiently high increase of this factor. They found that only the micro-cracks closest to the edge of the main crack had a significant influence on its stress intensity factor, and they argued that this speaks against a continuum model. They were not able to detect any statistically convincing toughening effect. Laures and Kachanov (1991) considered the influence of three-dimensional configurations of randomly oriented penny-shaped micro-cracks on stress shielding. Even negative effects (λ < 1) may occur: an obvious example is a micro-crack that is coplanar with the main crack. However, this micro-crack configuration is rather peculiar, and other configurations yielded substantially lower toughening ratios. Thus, the toughening ratio could be as high as λ = K I S S / K I ( i n n e r ) S S = 2 †.

The introduction of four micro-cracks, two on each side of the main crack, almost parallel to each other and inclined with respect to the plane of the main crack, was found to lower the stress intensity factor at the main crack to one half. Shum and Hutchinson (1990) considered certain special two-dimensional micro-crack configurations. Some of these investigations show that micro-cracks quite clearly may have a shielding effect. Several authors have treated micro-crack clusters as discrete arrays rather than as a continuum, e.g., Rubinstein (1986), Hori and Nemat-Nasser (1987), Hutchinson (1987), Kachanov (1986, 1987), Kachanov and Laures (1989), Shum and Hutchinson (1990), and Laures and Kachanov (1991). Bertram Broberg, in Cracks and Fracture, 1999 Discrete approach to micro-crack clusters

Current mirc crack