PSI - Issue 42

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Procedia Structural Integrity 42 (2022) 1692–1699 Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000

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23 European Conference on Fracture – ECF23 Phase field modelling of fatigue crack growth at constant and variable amplitude loading 23 European Conference on Fracture – ECF23 Phase field modelling of fatigue crack growth at constant and variable amplitude loading

Sarim Waseem a , ˙Izzet Erkin U¨ nsal a , Tuncay Yalc¸inkaya a, ∗ a Department of Aerospace Engineering, Middle East Technical University, 06800, Ankara, Turkey Sarim Waseem a , ˙Izzet Erkin U¨ nsal a , Tuncay Yalc¸inkaya a, ∗ a Department of Aerospace Engineering, Middle East Technical University, 06800, Ankara, Turkey

© 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 The phase field method is a di ff use boundary solution to complex multi-phase problems with temporally evolving boundaries. In this work, through a methodology based on the variational approach to fracture, the phase field method is used to predict fatigue crack growth numerically. Rather than user elements, an analogy between heat transfer and the phase field equation is exploited to allow the use of pre-existing coupled temperature-displacement elements. The influence of material fatigue parameters on the crack propagation path is studied in benchmark cases. Crack propagation paths confirmed by experimental data are achieved. An alteration to existing fatigue damage formulations is proposed, to capture the crack closure phenomenon. This addition is found capable of simulating crack retardation e ff ects due to an overload, allowing the establishment of a phase field fatigue model capable of realistically modeling variable amplitude loading in the tensile region. © 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 / ) eer-review under respons bility of 23 European Conference on Fracture – ECF23 . Keywords: Phase field; Fatigue; Fracture; Crack Closure; Overload E ff ects Abstract The phase field method is a di ff use boundary solution to complex multi-phase problems with temporally evolving boundaries. In this work, through a methodology based on the variational approach to fracture, the phase field method is used to predict fatigue crack growth numerically. Rather than user elements, an analogy between heat transfer and the phase field equation is exploited to allow the use of pre-existing coupled temperature-displacement elements. The influence of material fatigue parameters on the crack propagation path is studied in benchmark cases. Crack propagation paths confirmed by experimental data are achieved. An alteration to existing fatigue damage formulations is proposed, to capture the crack closure phenomenon. This addition is found capable of simulating crack retardation e ff ects due to an overload, allowing the establishment of a phase field fatigue model capable of realistically modeling variable amplitude loading in the tensile region. © 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: Phase field; Fatigue; Fracture; Crack Closure; Overload E ff ects Fatigue failure is one of the most prevalent forms of mechanical failure in engineering applications and remains one of the primary considerations in structural design where a fluctuating load well below the plastic limit could eventually lead to complete mechanical breakdown and potentially fatal consequences. The bulk of fatigue considerations remain empirical, with Paris and Erdogan (1963) producing one of the most prolific fatigue laws governing the fatigue life of a material under a given loading. This formulation related the crack growth rate to the di ff erence in stress intensity factors at the maximum and minimum loads ∆ K = K max − K min . Numerical simulations of fatigue have also been done through a variety of methods such as the extended FEM (see e.g. Dirik and Yalc¸inkaya (2016), Dirik and Yalc¸inkaya (2018)) and the phase field method is an alternative method rapidly gaining popularity for such applications. Phase field models provide di ff use boundary solutions to otherwise complex numerical problems with evolving boundary conditions through the introduction of a phase field variable φ . Originally developed to model transitions in Fatigue failure is one of the most prevalent forms of mechanical failure in engineering applications and remains one of the primary considerations in structural design where a fluctuating load well below the plastic limit could eventually lead to complete mechanical breakdown and potentially fatal consequences. The bulk of fatigue considerations remain empirical, with Paris and Erdogan (1963) producing one of the most prolific fatigue laws governing the fatigue life of a material under a given loading. This formulation related the crack growth rate to the di ff erence in stress intensity factors at the maximum and minimum loads ∆ K = K max − K min . Numerical simulations of fatigue have also been done through a variety of methods such as the extended FEM (see e.g. Dirik and Yalc¸inkaya (2016), Dirik and Yalc¸inkaya (2018)) and the phase field method is an alternative method rapidly gaining popularity for such applications. Phase field models provide di ff use boundary solutions to otherwise complex numerical problems with evolving boundary conditions through the introduction of a phase field variable φ . Originally developed to model transitions in 1. Introduction 1. Introduction

∗ Corresponding author Tel.: + 90-312-210-4258 ; fax: + 90-312-210-4250. E-mail address: yalcinka@metu.edu.tr ∗ Corresponding author Tel.: + 90-312-210-4258 ; fax: + 90-312-210-4250. E-mail address: yalcinka@metu.edu.tr

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.2022.12.213 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 onference 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 .