Issue 48

T. Profant et alii, Frattura ed Integrità Strutturale, 48 (2019) 503-512; DOI: 10.3221/IGF-ESIS.48.48 503 Focussed on “Crack Paths” Microcrack interaction with circular inclusion and interfacial zone Tomas Profant, Miroslav Hrstka Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic profant@fme.vutbr.cz, mira.hrstka@gmail.com Jan Klusák CEITEC IPM, Institute of Physics of Materials; Zižkova 22, 616 62, Brno, Czech Republic klusak@ipm.cz A BSTRACT . A geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. The crack is arbitrarily oriented and modelled using the distribution dislocation technique. This model represents the inner solution of the studied problem. The corresponding fundamental solution is based on the application of Muskhelishvili complex potentials in the form of the Laurent series. The coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the enclosing matrix. The fundamental solution is also used in the solution of the boundary integral method approximating the stress and strain relations of the so-called outer solution. The asymptotic analysis at the point of the crack initiation combines the inner and the outer solution and results in the evaluation of the stress intensity factors of the crack tip, which lies in the matrix. The topological derivative is subsequently used to approximate the energy release rate field associated with the perturbing crack in the matrix. The extreme values of the energy release rate allow one to assess the crack path direction of the initiated microcrack. K EYWORDS . Crack path assessment; Complex potentials; Interfacial zone; Circular inclusion; Fundamental solution; Topological derivative. Citation: Profant, T., Hrstka, M., Klusák, J., Microcrack interaction with circular inclusion and interfacial zone, Frattura ed Integrità Strutturale, 48 (2019) 503-512. Received: 29.11.2018 Accepted: 22.01.2019 Published: 04.01.2019 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 icrocracking is a phenomenon appearing in the vicinity of some stress rising features, where relatively short cracks rise and grow. An inclusion whose material properties differ from the ones of the surrounding matrix can be taken into account as a potential generator of such stresses [1], [2], [3]. The stress distribution generated by the presence of the inclusion can be influenced by its interfacial zone between the inclusion and the matrix. In spite of M