PSI - Issue 68

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Procedia Structural Integrity 68 (2025) 1259–1265 Structural Integrity Procedia 00 (2024) 000–000 Structural Integrity Procedia 00 (2024) 000–000

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European Conference on Fracture 2024 Closed-form analysis of crack initiation in layered systems under thermal loading D. Linn ∗ ,W. Becker Technical University of Darmstadt, Institute of Applied Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany Abstract In this work a closed-form analytical model of a two-layer system is analyzed. Therefor a higher-order displacement approach, which takes the singularity order into account is used to approximate the displacements and the strain and stress field within these two linear elastic layers. For three configurations – a patch on a substrate under thermal loading, a Double Cantilever Beam and a Single Lap Joint under mechanical loading – the interlaminar stresses at the interface between both layers are discussed. The configuration of a patch on a substrate under thermal loading is analyzed in more detail. Here, within the framework of Finite Fracture Mechanics also the initiation of a debonding crack is also investigated. All results are compared to a Finite Element Model for validation. © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of ECF24 organizers. Keywords: Finite Fracture Mechanics; Crack initiation; Analytical model; Interlaminar stresses European Conference on Fracture 2024 Closed-form analysis of crack initiation in layered systems under thermal loading D. Linn ∗ ,W. Becker Technical University of Darmstadt, Institute of Applied Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany Abstract In this work a closed-form analytical model of a two-layer system is analyzed. Therefor a higher-order displacement approach, which takes the singularity order into account is used to approximate the displacements and the strain and stress field within these two linear elastic layers. For three configurations – a patch on a substrate under thermal loading, a Double Cantilever Beam and a Single Lap Joint under mechanical loading – the interlaminar stresses at the interface between both layers are discussed. The configuration of a patch on a substrate under thermal loading is analyzed in more detail. Here, within the framework of Finite Fracture Mechanics also the initiation of a debonding crack is also investigated. All results are compared to a Finite Element Model for validation. © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of ECF24 organizers. Keywords: Finite Fracture Mechanics; Crack initiation; Analytical model; Interlaminar stresses © 2025 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 ECF24 organizers There are many applications in mechanical, aerospace and civil engineering in which di ff erent materials are lo cally connected to each other. One example are patches of finite length that are applied to structures for repair or reinforcement, such as concrete structures that are locally reinforced with carbon fiber reinforced plastic (CFRP) patches. Frhaan et al. provide an overview of these reinforcements in Frhaan et al. (2021). Due to the geometry and the dissimilar material properties of the patch and substrate, stress concentrations occur at the interface, which are at their maximum at the edges of the patch. These stress concentrations can lead to the formation of interlaminar cracks, which eventually cause the patch to peel o ff . Another example where the formation of interlaminar cracks is a typical failure case are adhesive joints, like in a Double Cantilever Beam or a Single Lap Joint. In order to predict the formation of interlaminar cracks in such structural situations, within the framework of Finite Fracture Mechanics a coupled criterion is used, which was postulated by Leguillon (Leguillon (2002)) and has been used successfully in There are many applications in mechanical, aerospace and civil engineering in which di ff erent materials are lo cally connected to each other. One example are patches of finite length that are applied to structures for repair or reinforcement, such as concrete structures that are locally reinforced with carbon fiber reinforced plastic (CFRP) patches. Frhaan et al. provide an overview of these reinforcements in Frhaan et al. (2021). Due to the geometry and the dissimilar material properties of the patch and substrate, stress concentrations occur at the interface, which are at their maximum at the edges of the patch. These stress concentrations can lead to the formation of interlaminar cracks, which eventually cause the patch to peel o ff . Another example where the formation of interlaminar cracks is a typical failure case are adhesive joints, like in a Double Cantilever Beam or a Single Lap Joint. In order to predict the formation of interlaminar cracks in such structural situations, within the framework of Finite Fracture Mechanics a coupled criterion is used, which was postulated by Leguillon (Leguillon (2002)) and has been used successfully in 1. Introduction 1. Introduction

∗ Corresponding author. E-mail address: linn@ad.tu-darmstadt.de (D. Linn) ∗ Corresponding author. E-mail address: linn@ad.tu-darmstadt.de (D. Linn)

2452-3216 © 2025 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 ECF24 organizers 10.1016/j.prostr.2025.06.196 2210-7843 © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of ECF24 organizers. 2210-7843 © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of ECF24 organizers.