Issue 41

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 41 (2017) 175-182; DOI: 10.3221/IGF-ESIS.41.24 175 Focused on Crack Tip Fields Fracture toughness of rough and frictional cracks emanating from a re-entrant corner Andrea Carpinteri, Andrea Spagnoli, Michele Terzano, Sabrina Vantadori Department of Engineering and Architecture, University of Parma, Viale Usberti 181/A, 43124 Parma, Italy spagnoli@unipr.it A BSTRACT . In mixed-mode conditions, the competing contribution of the different stress intensity factors predicts fracture initiation load as well as crack propagation direction. Commonly, mixed-mode fracture resistance is based on the assumption of smooth and frictionless cracks. However, the effect of friction and roughness cannot be neglected when mixed mode loading occurs, as in the case of a crack emanating from a re-entrant corner. In this paper, the effect of friction and roughness is evaluated through a simple saw-tooth model in a three-quarter-infinite plane (corresponding to a 90 degree re-entrant corner). The crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. The solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. The effect of friction and roughness angle is discussed for a simple case. K EYWORDS . Fracture toughness; Friction; Roughness; Distributed dislocation method; Re-entrant corner. Citation: Carpinteri, A., Spagnoli, A., Terzano, M., Vantadori, S., Fracture toughness of rough and frictional cracks emanating from a re-entrant corner, Frattura ed Integrità Strutturale, 41 (2017) 175-182. Received: 28.02.2017 Accepted: 15.04.2017 Published: 01.07.2017 Copyright: © 2017 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 significant part of fracture mechanics deals with the determination of stress intensity factors and fracture toughness, used to predict the load as well as the angle of crack propagation. A large number of analyses has been carried out, and stress intensity factors at the crack tips are available in literature, for instance in the compendium by Murakami [1]. A case of interest in practical applications is that of a short crack emanating from a re-entrant corner in a body under general loading conditions, where often multiple-parameter characterization of the crack/notch tip stress/strain field is required. If the crack is short compared to the other sizes of the body, the effect of other free boundaries can be neglected and the loading experienced by the crack in this geometry is well described by the Williams asymptotic solution [2]. In particular, the problem of a smooth and frictionless crack lying on the projection line of a A