PSI - Issue 42

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ScienceDirect

Procedia Structural Integrity 42 (2022) 498–505 Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000

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23 European Conference on Fracture – ECF23 Numerical investigation on the e ff ect of fillers on the fracture behavior of adhesives 23 European Conference on Fracture – ECF23 Numerical investigation on the e ff ect of fillers on the fracture behavior of adhesives

Pauline Herr a,1 , Felix Bo¨deker a,1, ∗ , Stephan Marzi a a Technische Hochschule Mittelhessen, Wiesenstraße 14, Gießen 35390, Germany Pauline Herr a,1 , Felix Bo¨deker a,1, ∗ , Stephan Marzi a a Technische Hochschule Mittelhessen, Wiesenstraße 14, Gießen 35390, Germany

© 2022 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 23 European Conference on Fracture – ECF23 Abstract Adhesives are usually heterogeneous materials and contain fillers, e.g., glass beads, and voids, which are crucial for its fracture properties. Multiscale approaches using computational homogenization can link model descriptions of the microstructure and the mechanical properties of the constituents to the macroscopic properties, which allows for a virtual optimization of materials. The fracture behavior of full adhesive layers is often modeled by cohesive zone models. Recently, a Fast Fourier Transform (FFT) based homogenization scheme for cohesive zone modelling has been introduced, which is expected to be computationally more e ffi cient than FE-based computational homogenization for many materials. Nevertheless, FFT-based homogenization still requires too many computational resources for a large scale industrial application of coupled multiscale simulations, which is why we propose a machine learning based surrogate cohesive law for mode I fracture which is trained o ffl ine. Our model can take into account the e ff ect of di ff erent filler volume fractions and is implemented in the commercial FE software Abaqus. We furthermore demonstrate its capabilities with FE simulations of a Double Cantilever Beam (DCB) test exemplary. © 2020 The Authors. Published by Elsevier B.V. his is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) er-review under responsibility of 23 European Conference on Fracture – ECF23 . Keywords: Computational Homogenization; Micromechanics of Fracture; Machine Learning Abstract Adhesives are usually heterogeneous materials and contain fillers, e.g., glass beads, and voids, which are crucial for its fracture properties. Multiscale approaches using computational homogenization can link model descriptions of the microstructure and the mechanical properties of the constituents to the macroscopic properties, which allows for a virtual optimization of materials. The fracture behavior of full adhesive layers is often modeled by cohesive zone models. Recently, a Fast Fourier Transform (FFT) based homogenization scheme for cohesive zone modelling has been introduced, which is expected to be computationally more e ffi cient than FE-based computational homogenization for many materials. Nevertheless, FFT-based homogenization still requires too many computational resources for a large scale industrial application of coupled multiscale simulations, which is why we propose a machine learning based surrogate cohesive law for mode I fracture which is trained o ffl ine. Our model can take into account the e ff ect of di ff erent filler volume fractions and is implemented in the commercial FE software Abaqus. We furthermore demonstrate its capabilities with FE simulations of a Double Cantilever Beam (DCB) test exemplary. © 2020 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 23 European Conference on Fracture – ECF23 . Keywords: Computational Homogenization; Micromechanics of Fracture; Machine Learning

1. Introduction 1. Introduction

Adhesive bonds have several advantages compared to other joining methods, which is why they play an important role in many industries such as automotive and aerospace sectors. The high mechanical requirements lead to a constant search for ways to improve the mechanical properties of bonded joints. The addition of fillers has proven to be a simple and cost-e ff ective solution to modify the mechanical properties of an adhesive. Several examples can be found in the literature dealing with the e ff ect of fillers on the mechanical properties of adhesive joints, e.g., Kinloch et al. (2003). Cohesive zone models are often used for adhesive layers in structural FE simulations at the component scale. They are a simplification of the material behavior, as only deformation and stress components in through thickness Adhesive bonds have several advantages compared to other joining methods, which is why they play an important role in many industries such as automotive and aerospace sectors. The high mechanical requirements lead to a constant search for ways to improve the mechanical properties of bonded joints. The addition of fillers has proven to be a simple and cost-e ff ective solution to modify the mechanical properties of an adhesive. Several examples can be found in the literature dealing with the e ff ect of fillers on the mechanical properties of adhesive joints, e.g., Kinloch et al. (2003). Cohesive zone models are often used for adhesive layers in structural FE simulations at the component scale. They are a simplification of the material behavior, as only deformation and stress components in through thickness

∗ Corresponding author. Tel.: + 49-641-309-2230 ; fax: + 49-641-309-2905. 1 The authors declare shared first authorship and contributed equally to this work. E-mail address: felix.boedeker@me.thm.de ∗ Corresponding author. Tel.: + 49-641-309-2230 ; fax: + 49-641-309-2905. 1 The authors declare shared first authorship and contributed equally to this work. E-mail address: felix.boedeker@me.thm.de

2452-3216 © 2022 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 23 European Conference on Fracture – ECF23 10.1016/j.prostr.2022.12.063 2210-7843 © 2020 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 u der responsibility of 23 European Conference on Fracture – ECF23 . 2210-7843 © 2020 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 23 European Conference on Fracture – ECF23 .