Engineering Fracture Mechanics 275 (2022) 108811 Available online 28 September 2022 0013-7944/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Numerical analysis of crack path stability in brittle porous materials S. Chen * , J.J. Espadas-Escalante , P. Isaksson Division of Applied Mechanics, Uppsala University, Uppsala, Sweden A R T I C L E INFO Keywords: Porous material Mixed-mode fracture Crack path stability Phase-field theory ABSTRACT Porous materials are widely used in engineering applications because of their high stiffness, strength, and low density. Those advantages are mainly due to their open microstructures, which also makes it challenging to obtain a thorough understanding of their fracture mechanisms and to predict trustworthy crack paths. In this study, we analyse numerically fracture trajectories in brittle porous solids with varying porosity (or relative density) subject to different mixed-mode loading conditions using a phase-field theory for brittle fracture. The results reveal that the crack paths in porous solids with high porosity (low relative density) are very different from those in porous solids with low porosity (high relative density). The latter resemble stable crack paths in homogeneous solids, whereas the former seems somewhat arbitrary, more stochastic. In high porosity materials, the crack paths are governed by the local microstructure rather than by the global remote loading. A key observation is that there is a transition of the fracture behaviour in porous materials at relative densities of around 50%. At relative densities above 50%, the ma- terial behaves nearly as a classical continuum, and the crack paths are reasonably well captured by traditional fracture mechanics theories. The stochastic nature of the porous microstructure is also examined. 1. Introduction Engineering porous (cellular) materials, manufactured or natural ones, such as paper, foam, tissue, fabric, honeycombs or bone, have often excellent mechanical and physical properties, besides having a relative low weight. They are frequently subject to complex mechanical loading conditions, e.g. when used as cores in sandwich structures [1], bone-repairing materials [2], packaging solutions [3], or filters [4]. To design light-weight materials able to resist catastrophic fracture, a deeper understanding of the fracture mechanisms in cellular materials is needed. With such knowledge, it would be possible to architect the microstructure, e.g. by opti- mizing pore size distributions in microstructural regions subject to different loading conditions. Fracture in homogeneous brittle materials can, in some cases, be reasonably well described by traditional linear elastic fracture mechanics (LEFM) [5]. According to LEFM, a stationary straight crack subject to a pure opening load in its orthogonal direction will grow along its crack plane, while under a mixed opening/shear load, the crack will grow along a path that maximizes the local opening of the crack while reducing shear movements of the crack lips in the tip region, cf. [6,7]. For linear elastic crack growth in homo- geneous materials, an assumption of an opening kink in a direction giving a pure opening mode is frequently used, which is equivalent to assuming crack growth in a direction that minimizes shear crack growth, cf. [8–10]. In strong contrast to homogeneous materials, * Corresponding author. E-mail address: [email protected] (S. Chen). Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech https://doi.org/10.1016/j.engfracmech.2022.108811 Received 5 July 2022; Received in revised form 1 September 2022; Accepted 13 September 2022
Numerical analysis of crack path stability in brittle porous materials
May 29, 2023
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