Issue 20

R. Brighenti et alii, Frattura ed Integrità Strutturale, 20 (2012) 6-16; DOI: 10.3221/IGF-ESIS.20.01 15 Fig. 10 shows the crack path determined for an initially straight crack developing at a vertical distance equal to one-third between two horizontal lines of inclusions (see Fig. 4b, with 0 / 0.0037 a y     ). As in the previous case, the crack path evaluated by the Erdogan-Sih criterion is rather similar to that determined by the R-criterion. (a) (b) Figure 10 : (a) Path of an initially straight crack developing at one-third distance between two lines of inclusions in an infinite plane under remote uniform tensile stress 0 y  . (b) Detail of the crack path at the microscale where the distribution of inclusions is shown. By comparing Fig. 9 and Fig. 10, it can be observed that the kinking angle of the crack tends to increase with increasing the value of the 0 / a y    ratio. C ONCLUSIONS n the present paper, a simple analytical model to describe the trajectory of a plane crack propagating within an inhomogeneous material is proposed. With reference to metals, the inhomogeneities are treated by considering a two-phase material with an equivalent mean inclusion characterized by a regular spatial distribution. Even under remote uniaxial loading, the equivalent inclusions generate a multiaxial fluctuating stress field which is assumed to be responsible for mixed-mode crack propagation. By adopting different mixed-mode crack growth criteria, the crack path can be connected with the main features of the material microstructure, here accounted in terms of an appropriate microstress field. It is shown that both the maximum principal stress criterion and the R- criterion (based on the minimum extension of the core plastic zone) predict a zig-zag crack pattern, characterised by a length scale related to both the volume fraction of inclusions and their mean size. Moreover, it is shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks. A CKNOWLEDGEMENTS he authors gratefully acknowledge the research support for this work provided by the Italian Ministry for University and Technological and Scientific Research (MIUR). R EFERENCES [1] S. Suresh Metallurgical Trans, 14A (1985) 2375. [2] F. Erdogan, G. C. Sih, J Basic Engng, 85 (1963) 519. I T