Investigation of energy release rate under mode II loading in a rectangular orthotropic plate with a band crack using 3D
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ICCESEN 2017
Investigation of energy release rate under mode II loading in a rectangular orthotropic plate with a band crack using 3D finite element analysis Arzu Turan Dincel 1 Received: 1 January 2019 / Accepted: 12 April 2019 / Published online: 9 May 2019 # Saudi Society for Geosciences 2019
Abstract A rectangular plate containing a band crack and made of orthotropic elastic material is considered and the energy release rate (ERR) component in mode II at this crack front is investigated. It is assumed that the crack’s edge planes are parallel to the upper and lower face planes of the plate and the edge planes of the crack are loaded with uniformly distributed sliding forces. The corresponding boundary value problem is formulated within the scope of the three-dimensional linear theory of elasticity and the solution to this problem is found by employing 3D finite element method (3D FEM) modeling. Numerical results on the ERR for mode II and on the influence of the mechanical-orthotropic properties of the plate material are presented and discussed. In particular, it is established that the influence of the shear modulus in a plane which is simultaneously perpendicular to the crack’s front and crack’s plane on the ERR is more significant than that caused by the change of another modulus of the orthotropic material. Keywords Energy release rate (ERR) . Band crack . 3D FEM (three-dimensional finite element method) . Mode II
Introduction Fracture processes are essential for a variety of engineering problems because discontinuities or cracks are common in structures (Mansoor and Shahid 2015; Mao et al. 2018; Zhou et al. 2016). To be able to characterize fracture processes, the fracture parameters such as stress intensity factors (SIF) or energy release rates (ERR) at the tips or fronts of the crack are of importance. In connection with this, up to now, various numerical methods have been developed such as the methods by Davis et al. (2014), Gosz et al. (1998), Moghaddam and Alfano (2015), Hein and Kuna (2017), Judt and Ricoeur (2016), Barani and Rahimi (2007), and others listed therein for study of 3D crack problems (or 2D crack problems) which are based mainly on the use of 3D FEM modeling of the corresponding boundary value problems. However, in
This article is part of the Topical Collection on Geo-Resources-EarthEnvironmental Sciences * Arzu Turan Dincel [email protected] 1
Mathematical Engineering Department, Yildiz Technical University, Istanbul, Turkey
these investigations, concrete numerical results are obtained for the cases where the material that contained the crack is isotropic. Due to extensive use of composite materials in many modern branches of industry, it has become necessary to investigate their corresponding crack problems. Such investigations were made in Tay et al. (1999), Prombut et al. (2006), Yang and Cox (2005), Zubillaga et al. (2014), and in many others listed therein. Note that the approaches used in these investigations can be classified based on the piecewise non-homogeneous body m
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