Issue 47

A. Spagnoli et alii, Frattura ed Integrità Strutturale, 47 (2019) 401-407; DOI: 10.3221/IGF-ESIS.47.30 401 Focussed on “Crack Paths” Size effect on the fracture resistance of rough and frictional cracks Andrea Spagnoli, Andrea Carpinteri, Michele Terzano Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy spagnoli@unipr.it A BSTRACT . Elastic fracture mechanics commonly defines the fracture resistance of brittle materials within an idealized picture of planar and traction-free cracks. An efficient approach to describe the interface conditions in real cracks, such as those occurring in concrete, ceramics or stones, is to include the effect of both roughness and friction by means of a constitutive relationship between opposite points on the interface. In the present paper, we use a numerical technique, based on the solution of singular integral equations, to derive the near-tip stress field with various interface conditions. Then, the technique is applied to investigate the size effect of the interface roughness, where such an effect is related to the ratio between the characteristic length of the roughness and the nominal length of the crack. It is found that the resulting near-tip stresses can be profoundly influenced by the crack path, particularly for short cracks. K EYWORDS . Interface models; Friction; Roughness; Distributed dislocation technique; Size effect. Citation: Spagnoli, A., Carpinteri, A., Terzano, M., N., Size effect on the fracture resistance of rough and frictional cracks, Frattura ed Integrità Strutturale, 47 (2019) 401-407. Received: 26.10.2018 Accepted: 08.11.2018 Published: 01.01.2018 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION n linear elastic fracture mechanics (LEFM), the stress field in proximity of the tip of a crack is described by a single parameter, the stress intensity factor (SIF), which is consequently used to give a measure of the fracture resistance of a certain material. Such an approach is based on the assumption of small-scale yielding, and considers a crack with flat and smooth interfaces, neglecting any interaction between its surfaces. This rather idealised picture might be satisfactory for mode I crack growth, because the surface interaction is somehow limited; however, when the fracture surfaces are displaced relative to one another in shear, the interaction cannot be neglected. Observations on the failure of quasi-brittle and brittle materials, such as concrete, ceramics, rocks or glass, revealed that crack growth does not proceed planarly, but on the contrary tortuous topologies of the crack paths are noticed. A combination of different factors is used to explain the observed behaviour, including the effect of far field multi-axial stresses, residual stresses, microstructural inhomogeneities, and material properties dispersion [1–5]. In many polycrystalline and aggregate materials, the crack surfaces are not macroscopically flat, instead they consist of several asperities, with peculiar size, which interact in a complex combination of sliding, sticking, climbing and deforming [6]. As a consequence, the fracture strength can be strongly altered, particularly in the presence of mixed-mode loading as a result I