PSI - Issue 28

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000–000 vailable online at w .sciencedirect.co i i t Structural Integrity Procedia 0 (2019) 0 –0

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Procedia Structural Integrity 28 (2020) 1212–1225

© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Abstract The present paper deals with longitudinal fracture analysis of a continuously inhomogeneous beam with stress relaxation. The beam is loaded in torsion. The stress relaxation behavior is treated by using two linear viscoelastic models under constant applied shear strain. The cross-section of the beam is a circle of linearly varying radius along the beam length. The longitudinal crack is a circular cylindrical surface. The beam is continuously inhomogeneous in both radial and length directions. The shear modulii and the coefficients of viscosity are distributed exponentially along the radius and along the length of the beam. The longitudinal fracture behavior is analyzed in terms of the strain energy release rate. A solution to the strain energy release rate is obtained by differentiating the strain energy. The solution is verified by considering the balance of the energy. The influence of the varying radius of the cross-section on the longitudinal fracture is studied. The effects of the varying shear modulii and coefficients of viscosity in radial and length directions of the beam on the longitudinal fracture behavior are evaluated. The change of the strain energy release rate with the time is analyzed. © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Keywords: Inhomogeneous beam; Longitudinal crack; Viscoelastic behavior; Torsion 1. Introduction The inhomogeneous structural materials of continuously varying material properties along one or more directions in the solid are widely used in various areas of practical engineering. The advancement in the methods for analysis of inhomogeneous load-bearing structural members requires consideration of a wide range of material parameters. l i i t r i it tr r l ti i t r i epartment of Technical Mechanics, University of Architecture, Civil Engine ring and Geodesy, 1 Chr. S irnensky blvd., 1046 – Sofia, Bulgaria bstract The present paper deals ith longitudinal fracture analysis of a continuously inho ogeneous bea ith stres relaxation. The bea is loaded in torsion. The stres relaxation behavior is treated by using two linear viscoelastic models under constant ap lied shear strain. The cros -section of the bea is a circle of linearly varying radius along the bea length. The longitudinal crack is a circular cylindrical surface. The bea is continuously inho ogeneous in both radial and length directions. The shear moduli and the coef icients of viscosity are distributed exponential y along the radius and along the length of the bea . The longitudinal fracture behavior is analyzed in ter s of the strain energy release rate. A solution to the strain energy release rate is obtained by dif erentiating the strain energy. The solution is verified by considering the balance of the energy. The influence of the varying radius of the cros -section on the longitudinal fracture is studied. The ef ects of the varying shear oduli and coef icients of viscosity in radial and length directions of the bea on the longitudinal fracture behavior are evaluated. The change of the strain energy release rate with the time is analyzed. © 2020 The Authors. Published by ELSEVIE B.V. This is an open acces article under the CC BY-NC-ND license (ht ps:/ creativeco ons.org/licenses/by-nc-nd/4.0) Pe r-revie under responsibility of the European Structural Integrity Society (ESIS) Ex o Keywords: Inho ogeneous bea ; Longitudinal crack; Viscoelastic behavior; Torsion 1. Introduction The inho ogeneous structural materials of continuously varying material properties along one or more directions in the solid are widely used in various areas of practical engine ring. The advance ent in the methods for analysis of inho ogeneous load-bearing structural e bers requires consideration of a ide range of aterial para eters. 1st Virtual European Conference on Fracture Longitudinal fracture analysis of continuously inhomogeneous beam in torsion with stress relaxation Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria st irt al r ea fere ce ract re it i l fr t r l i f ti

* Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863. E-mail address: v_rizov_fhe@uacg.bg * Cor esponding author. Tel.: + (359-2) 963 52 45 / 6 4; fax: + (359-2) 86 56 863. E-mail ad res : v_rizov_fhe uacg.bg

2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 2452-3216 © 2020 The Authors. Published by ELSE IER B.V. This is an open ac es article under the C B -NC-N license (ht ps:/ creativeco ons.org/licenses/by-nc-nd/4.0) Pe r-revie under responsibility of the European Structural Integrity Society (ESIS) ExCo

2452-3216 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.11.103