Issue 47

A. Spagnoli et alii, Frattura ed Integrità Strutturale, 47 (2019) 401-407; DOI: 10.3221/IGF-ESIS.47.30 402 of far field stresses, or geometrical and material discontinuities. Specifically, Ballarini and Plesha [7] noticed that a pure mode I crack growth occurs in very few cases, since the mode mixity is often a result of the crack tortuosity. The same Authors presented an interface model, previously proposed by Plesha [8], to deal with the effect of roughness and friction along the crack surfaces in a simplified way, and included such a model in a numerical algorithm based on the solution of singular integral equations. The same effect, appropriately defined ‘sliding mode crack closure’, was observed by Tong et al. [9] in the analysis of cracks under shear fatigue loading. On the other hand, the interaction of the crack surfaces through the asperities generates a mode I component, even if the remote loading is purely mode II. This phenomenon is generally known as dilatancy , that is, an opening displacement caused by the coupling between normal and tangential directions along the nominal crack line. In the present paper, we adopt an interface model to account for the effects of friction and roughness, which follows from the work of Plesha [8], and whose complete formulation has been firstly presented by the authors in [10]. Frictional effects are described with the classical Coulomb’s law, while the roughness is exemplified by a uniform distribution of rigid saw-tooth asperities. The solution technique follows an analytical method derived from the application of the complex function theory, generally known as the Distributed Dislocation Technique (DDT), which has been applied successfully in the solution of crack problems with different geometric configurations [11] . We have previously showed its potential in characterising the near-tip stress fields of cracks under mixed mode loading, specifically the effect of the interface interaction with respect to the onset of crack propagation under monotonic loading [12]. The aim of this study is to further explore the effects of interface interaction, by exploring the possible influence on the fracture resistance of a size effect , introduced by a characteristic length of the material roughness. It is well known that the strength of materials, both the fracture resistance and the fatigue limit, is generally affected by the size of the specimen or its microstructural properties. Studies have tried to explain this phenomenon by adopting a fractal description of the microstructure of brittle and disordered materials, and noticed that the fatigue crack growth rate depends not only on a fractal dimension but also, in an explicit fashion, on the crack length [13–16]. For sinusoidally-patterned surfaces, the size effect on the critical load has been related to the ratio between the amplitude and the wave length [17]. In this work, the size effect is related to the ratio between the crack roughness period and the length of the crack. Specifically, we explore the influence of both the height and the length of the saw-tooth asperities on the mode II stress intensity factor, under a mixed-mode loading condition. The paper is structured in two main sections. We start with a Formulation section where we review the interface model and give some details on the numerical algorithm that we have used to compute the stress intensity factor; following, we present the Results, obtained by an application of the method to a simple edge-cracked geometry, and discuss the implications of the interface asperities and the size effect. Figure 1 : a) The saw-tooth asperity model, showing the local and global reference systems adopted in the formulation, Eqns. (1)-(4). b) Schematic model of the geometry with an edge crack of length c .