Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29 372 An analytical beam model for the evaluation of crack tip root rotations and displacements in orthotropic specimens Ilaria Monetto, Roberta Massabò Department of Civil, Chemical and Environmental Engineering, University of Genova, Italy ilaria.monetto@unige.it, http://orcid.org/0000-0002-5682-9315 A BSTRACT . Explicit and simple expressions for root compliance coefficients, which can be used to define root rotations and root displacements at the crack tip cross section of orthotropic cracked beams, are derived under general self-equilibrated loading conditions at the crack tip. The effects of both shear deformations and transverse elasticity are taken into account in order to accurately define displacement fields and energy release rate. The derivation builds on and extends one-dimensional formulations in the literature. The employment of the novel analytical expressions requires the determination of one a priori unknown parameter which describes the effects of the transverse elasticity and is determined through matching of well established 2D results in the literature. The one-dimensional model accurately reproduces crack tip effects in symmetric isotropic and orthotropic specimens; shear deformations are included in the formulation for an accurate derivation of the root displacement coefficients; the accuracy reduces in asymmetric specimens where the matching parameter becomes load dependent. K EYWORDS . Root rotations; Root displacements; Collinear delamination; Fracture specimens; Orthotropy. Citation: Monetto, I, Massabò, R., An analytical beam model for the evaluation of crack tip root rotations and displacements in orthotropic specimens, Frattura ed Integrità Strutturale, 53 (2020) 372-393. Received: 08.05.2020 Accepted: 25.05.2020 Published: 01.07.2020 Copyright: © 2020 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 n many problems of fracture in beam-type structures the effects of the transverse elasticity of the intact portion of the specimen ahead of the crack tip are not negligible and must be taken into account when calculating displacements and fracture parameters. Such effects are usually associated with relative rotations and displacements at the crack tip section between the two arms of the cracked portion of the specimen. They are known in the literature as root rotations and displacements and have been the object of many studies. A great deal of attention has been focused on modeling the root rotations, which have been shown to enter into some important fracture mechanics calculations, such as those of the J-integral and the energy release rate [1-3]. Among the others, e.g. [1-2,4-7], reference is made here to the results presented in [3] for orthotropic cracked beams subjected to I