Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Effect of the intermediate principal stress on 3-D crack growth Hongyu Wang a, ⁎ , Arcady Dyskin a , Elena Pasternak b , Phil Dight c , Mohammad Sarmadivaleh d a Department of Civil, Environmental and Mining Engineering, School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia b Department of Mechanical Engineering, School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia c Australian Centre for Geomechanics, 35 Stirling Hwy, Crawley, WA 6009, Australia d Department of Petroleum Engineering, Curtin University, 26 Dick Perry Avenue, Kensington, WA 6151, Australia ARTICLEINFO Keywords: Wing crack Three-dimensional crack Transparent brittle samples Biaxial compression Intermediate principal stress ABSTRACT An experimental and numerical investigation of 3-D crack growth in biaxial compression is presented. We tested a series of transparent casting resin samples, each with a single initial penny-shape crack at the sample centre. We applied biaxial compression with different ratios ( / x y ) between the lateral (the intermediate principal stress) and the axial (the major principal stress) loads. The initial penny-shape cracks were inclined at 30° to the major principal stress but parallel to the intermediate principal stress. The experimental results revealed the qualitative influence of the intermediate principal stress on shape of 3-D crack growth: in uniaxial com- pression, the initial penny-shape crack produces wings wrapping around it. The wrapping hampers the ability of the wings to grow resulting in the appearance of the maximum wing length of the order of the size of the initial crack. In biaxial compression with high intermediate prin- cipal stress the wings straighten and grow to an extent sufficient to split the sample. The threshold for the intermediate principal stress separating these two regimes of wing growth is surprisingly low: 5.7% of the major principal stress. The XFEM (extended finite element method) modelling showed that this threshold corresponds to the transition in the pattern of direction of the secondary principal tensile stress near the initial crack from directions roughly perpendicular to the intermediate principal compressive stress direction to the radial directions with respect to the initial crack; the latter pattern causes wing wrapping. 1. Introduction Direct experiments on different materials (e.g. Columbia resin 39 [1,2], polymethylmethacrilate (PMMA) [3,4], gypsum [5,6], sandstone [3,7] and marble [8] and models (e.g. the finite element method (FEM) [9], the boundary element method (BEM) [10], the displacement discontinuity method (DDM) [10,11] and the discrete element method (DEM) [12,13]) show that under uniaxial loading condition, in 2-D, the secondary wing cracks that emanate from a single inclined flaw (fully penetrating crack) or a pore can grow and propagate extensively and thus capable of leading to the 2-D sample splitting [14]. Opposite to the 2-D case, direct experiments conducted by Dyskin et al. [15,16] show that in 3-D when the initial crack is located in the centre of the sample, wing cracks are restricted to the size comparable to the initial crack and cannot substantially grow to cause the macroscopic failure of the sample. Fig. 1 shows schematics of wing crack grow in 3-D. The wings assume a special shape curving or wrapping around the initial https://doi.org/10.1016/j.engfracmech.2018.10.024 Received 16 June 2018; Received in revised form 12 October 2018; Accepted 24 October 2018 ⁎ Corresponding author. E-mail address: hywangcumt@126.com (H. Wang). Engineering Fracture Mechanics 204 (2018) 404–420 Available online 25 October 2018 0013-7944/ © 2018 Elsevier Ltd. All rights reserved. T