PSI - Issue 51

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ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 51 (2023) 44–50

© 2023 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 ICSID 2022 Organizers Abstract A lengthwise fracture analysis of an inhomogeneous beam with three parallel cracks is developed. The cracks are located symmetrically with respect to the mid-span. The loading consists of two axial forces applied at the ends of the beam. A vertical notch is cut-out in the mid-span so as the upper three crack arms are free of stresses. Only half of the beam is analyzed due to the symmetry. The cracks are located arbitrary along the beam height. Therefore, the heights of the cross-sections of crack arms are different. The beam exhibits continuous material inhomogeneity in the height direction. The material has non-linear elastic behaviour. Three solutions to the strain energy release rate are derived. For this purpose, the complementary strain energy in the beam is differentiated with respect to the areas of the three cracks. The J -integral approach is applied in order to verify the solutions to the strain energy release rate. The influence of the locations of the three cracks along the beam height on the lengthwise fracture behaviour is studied in detail. The influence of the material inhomogeneity on the lengthwise fracture behaviour of the beam is also analyzed. © 2023 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 ICSID 2022 Organizers Keywords: Beam structure; inhomogeneous material; non-linear elastic behavior; lengthwise cracks; axial forces 1. Introduction Continuously (smoothly) inhomogeneous structural materials are increasingly applied in a wide range of load bearing applications in different areas of the present-day engineering. A distinguishing feature of the inhomogeneous materials is that their properties are functions of coordinates. The strong interest towards these materials is due in a high degree to the widespread application of functionally graded materials for the recent decades (Chikh (2019), Kou 6th International Conference on Structural Integrity and Durability (ICSID 2022) Fracture of inhomogeneous beam with three parallel lengthwise cracks Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria Abstract A lengthwise fracture analysis of an inhomogeneous beam with three parallel cracks is developed. The cracks are located symmetrically with respect to the mid-span. The loading consists of two axial forces applied at the ends of the beam. A vertical notch is cut-out in the mid-span so as the upper three crack arms are free of stresses. Only half of the beam is analyzed due to the symmetry. The cracks are located arbitrary along the beam height. Therefore, the heights of the cross-sections of crack arms are different. The beam exhibits continuous material inhomogeneity in the height direction. The material has non-linear elastic behaviour. Three solutions to the strain energy release rate are derived. For this purpose, the complementary strain energy in the beam is differentiated with respect to the areas of the three cracks. The J -integral approach is applied in order to verify the solutions to the strain energy release rate. The influence of the locations of the three cracks along the beam height on the lengthwise fracture behaviour is studied in detail. The influence of the material inhomogeneity on the lengthwise fracture behaviour of the beam is also analyzed. © 2023 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 ICSID 2022 Organizers Keywords: Beam structure; inhomogeneous material; non-linear elastic behavior; lengthwise cracks; axial forces 1. Introduction Continuously (smoothly) inhomogeneous structural materials are increasingly applied in a wide range of load bearing applications in different areas of the present-day engineering. A distinguishing feature of the inhomogeneous materials is that their properties are functions of coordinates. The strong interest towards these materials is due in a high degree to the widespread application of functionally graded materials for the recent decades (Chikh (2019), Kou 6th International Conference on Structural Integrity and Durability (ICSID 2022) Fracture of inhomogeneous beam with three parallel lengthwise cracks Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria

* Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863 E-mail address: v_rizov_fhe@uacg.bg * 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 © 2023 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 ICSID 2022 Organizers 2452-3216 © 2023 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 ICSID 2022 Organizers

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