PSI - Issue 23

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Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000

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Procedia Structural Integrity 23 (2019) 419–424

9th International Conference on Materials Structure and Micromechanics of Fracture Notch Tip Singularities of Elastic Piezoelectric Bi-materials 9th International Conference on Materials Structure and Micromechanics of Fracture Notch Tip Singularities of Elastic Piezoelectric Bi-materials

Miroslav Hrstka a , Michal Kotoul a , Tomáš Profant a, * "Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic" Miroslav Hrstka a , Michal Kotoul a , Tomáš Profant a, * "Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic"

Abstract Abstract

© 2019 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 the scientific committee of the ICMSMF organizers © 201 9 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 the scientific committee of the IC MSMF organizers. The paper investigates an asymptotic in-plane problem of clamp d piezoelectric bi-material notch using the expanded Lehknitskii Eshelby-Stroh formalism. It is established the eig nvalue pr blem f r the r gular and auxilia y solution of the problem from the boundary cond tions prevailing at the notch tip where the one of the notch face is clamped. The re ula as well as auxiliary soluti n enter to the Ψ -integral g neralized for piez electric bi-materials, which is used to evaluate the generalized stress intensity factors of the particular piezoelectric bi-material notch configuration. © 201 9 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. The paper investigates an asymptotic in-plane problem of clamped piezoelectric bi-material notch using the expanded Lehknitskii Eshelby-Stroh formalism. It is established the eigenvalue problem for the regular and auxiliary solution of the problem from the boundary conditions prevailing at the notch tip where the one of the notch face is clamped. The regular as well as auxiliary solutions enter to the Ψ -integral generalized for piezoelectric bi-materials, which is used to evaluate the generalized stress intensity factors of the particular piezoelectric bi-material notch configuration. Keywords: piezoelectric bi-material; bi-material notch; Lekhnitchkii-Eshelby-Stroh formalism; generalised stress intensity factor; Keywords: piezoelectric bi-material; bi-material notch; Lekhnitchkii-Eshelby-Stroh formalism; generalised stress intensity factor; An algorithm of traction free and electrically open notch faces for modelling a piezoelectric bi-material notch with one clamped face is proposed. Some studies, in which a single or interface permeable crack was considered, were reported in Qun and Yiheng (2007), Sladek et al. (2012), Soh et al. (2001) and Wang and Sun (2004). It was shown that equations for piezoelectric anisotropic problems have the same structure as those for corresponding anisotropic pure elastic materials. For this reason the expanded form of the Lekhnitskii-Eshelby-Stroh formalism is used in the analysis of the singularities in piezoelectric materials. The Lehnitskii-Eshelby-Stroh formalism is also connected with An algorithm of traction free and lectrically open notch faces for modelling a piezo lectric bi-material notch ith one clamped face is proposed. Some studies, in which a single or interface permeable crack was considered, were reported in Qun and Yiheng (2007), Sladek et al. (2012), Soh et al. (2001) and Wang and Sun (2004). It was sh wn that equations for piezoelectric anisotropic problems have the same structure as those for corresponding anisotropic pure elastic materials. For this r ason the expanded form of the Lekhnitskii-Eshelby-Stroh form lism is used in the analysis of the singularities in piezoelectric materials. The Lehnitskii-Eshelby-Stroh formalism is also connected with 1. Introduction 1. Introduction

* Corresponding author. Tel.: +420 5 4114 2877. E-mail address: profant@fme.vutbr.cz * Correspon ing author. Tel.: +420 5 4114 2877. E-mail address: profant@fme.vutbr.cz

2452-3216 © 2019 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 the scientific committee of the IC MSMF organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

2452-3216 © 2019 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 the scientific committee of the ICMSMF organizers 10.1016/j.prostr.2020.01.123