PSI - Issue 33

ScienceDirect

Structural Integrity Procedia 00 (2019) 000 – 000

www.elsevier.com/locate/procedia

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 33 (2021) 428–442

IGF26 - 26th International Conference on Fracture and Structural Integrity Lengthwise fracture of functionally graded beams: a study of stress relaxation effects

Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria

© 2021 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 scientific committee of the IGF ExCo Abstract The present paper is focussed on analyzing the strain energy release rate for a lengthwise crack in a cantilever beam that exhibits stress relaxation. The beam is continuously inhomogeneous in the thickness direction. A linear viscoelastic model is used for treating the stress relaxation. The balance of the energy is analyzed in order to derive a time-dependent solution to the strain energy release rate. The equilibrium of the lower crack arm and the un-cracked beam portion is considered to determine the curvatures and the coordinates of the neutral axes which are involved in the solution. The compliance method is applied in or der to verify the solution to the strain energy release rate. A time-dependent solution to the strain energy release rate is derived also for the case of material exhibiting different viscoelastic behaviour in tension and compression. The solutions derived are used to investigate the evolution of the strain energy release rate with the time. The influence of the crack location along the thickness of the beam and the material inhomogeneity on the time-dependent strain energy release rate under stress relaxation is also investigated. © 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 rod; Longitudinal fracture; Material non-linearity; Torsion

* Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863. E-mail address: 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 © 2021 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 scientific committee of the IGF ExCo 10.1016/j.prostr.2021.10.050