Issue 53

Frattura ed Integrità Strutturale, 53 (2020); International Journal of the Italian Group of Fracture

Table of Contents

L. Hadid, F, Bouafia, B. Serier, Sa. Sikandar Hayat https://youtu.be/i54VM8ZkC-A Finite element analysis of the interface defect in ceramic-metal assemblies: Alumina-Silver …….. 1-12 M. C. Oliveira, D. V. C. Teles, D. L. N. F. Amorim https://youtu.be/j1eI78UNrr4 Shear behaviour of reinforced concrete beams under impact loads by the Lumped Damage framework ………………………………………………………………………... 13-25 P. R. Jaiswal, R. I. Kumar, W. De Waele https://youtu.be/WxnctVLKLDo Unified methodology for characterisation of global fatigue damage evolution in adhesively bonded joints ……..……………………………………………………………………... 26-37 V. Rizov, H. Altenbach https://youtu.be/wsEtDVFgdss Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length …………………………………................................. 38-50 K. Sadek, B. Aour, M. S. Bennouna, A. Talha, B. Bachir Bouiadjra, M. Fari Bouanani https://youtu.be/kNxwiJNfgLI Effect of corrosion on the quality of repair of the aluminum alloy A5083 H11 by bonded composites ………………………………………………………………………... 51-65 K. Afaf, B. Serier, K. Kaddouri, M. Belhouari https://youtu.be/UNgkYXqpFhg Experimental Analysis of the Physical Degradation of Polymers – The Case of Polymethyl Methacrylate ……………………………………………….……………………... 66-80 Z.-q. Wang, X.-g. Huang, D.-h. Zhang https://youtu.be/7TOBKfvR4S0 Low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach …………………………………………………………………………. 81-91 J. Akbari, O. Salami, M. Isari https://youtu.be/KbS1egQsYWI Numerical Investigation of the Seismic Behavior of Unanchored Steel Tanks with an emphasis on the Uplift Phenomenon ……………….………………………...……………........ 92-105

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Fracture and Structural Integrity, 53 (2020); ISSN 1971-9883

R. Reda, Z. Omar, H. Sallam, S. S. E. Ahmad https://youtu.be/VkOTlHiOTts Effect of different parameters controlling the flexural behavior of RC beams strengthened with NSM using nonlinear finite element analysis …………………………………………... 106-123 A.M. Amaro, A. Loureiro, P.N.B. Reis https://youtu.be/UAyTqXI1UQE Comparison of mechanical performance between friction-stir spot welded and adhesive bonded joints …………………..………………………………………………………… 124-133 E. Nurullaev, N. Y. Lyubimova, T. A. Gertsen https://youtu.be/VIJptiD2FwQ Physical Parameters of Polymer Composite Materials Created on the Basis of Low and High Molecular Weight Rubbers …………………………………………………………. 134-140 Q. Zheng, N. Wang, P. Zhu, J. Liu, W. Ma https://youtu.be/fcyIPaKxw1w Fatigue Life Simulation and Analysis of Aluminum Alloy Sheet Self-piercing Riveting ……… 141-151 A. Grygu ć , S.K. Shaha, S.B Behravesh, H. Jahed, M. Wells, B. Williams https://youtu.be/iWDPjjEmXcw Improvement of Fatigue Properties of AZ31B Extruded Magnesium Alloy through Forging … 152-165 G. Giuliano, G. Parodo, L. Sorrentino https://youtu.be/604qGvmoUZs Uniformity of thickness of metal sheets by patchwork blanks: potential of adhesive bonding …… 166-176 M. Ameri, R. Mohammadi, M. Mousavinezhad, A. Ameri, H. Shaker, A. Fasihpour https://youtu.be/PpLMXiWn6sg Evaluating Properties of Asphalt Mixtures Containing polymers of Styrene Butadiene Rubber (SBR) and recycled Polyethylene Terephthalate (rPET) against Failures Caused by Rutting, Moisture and Fatigue ………….……………………………........................................ 177-186 M. Abdelmadjid, Z. M. El Sallah, S. Abderahmane, A. k. Djafar, Z. Rachid https://youtu.be/2M6yriwuZMo Comparative study of the repair of cracked plates with two different composite patches ………… 187-201 S. M. Damadi, A. Edrisi, M. Fakhri, S. Rezaei, M. W. Khordehbinan https://youtu.be/YHA_jj5P4eI Fatigue Analysis of Bitumen Modified with Composite of Nano-SiO 2 and Styrene Butadiene Styrene Polymer ………………………....………………………………...……….. 202-209 R.R. Yarullin, V.N. Shlyannikov, I.S. Ishtyriakov, M.M. Yakovlev https://youtu.be/fYD0E-96Q6c Stress intensity factors for mixed-mode crack growth in imitation models under biaxial loading . 210-222

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Frattura ed Integrità Strutturale, 53 (2020); International Journal of the Italian Group of Fracture

A. Zakharov, V. Shlyannikov, A. Tartygasheva https://youtu.be/2Bsa-ml8TiQ Plastic stress intensity factor behavior at small and large scale yielding ……………………… 223-235 D. Wang, Y. Dong, D. Zhang, W. Wang, X. Lu https://youtu.be/jDPIw4gAGhg Monitoring and analysis of reinforced concrete plate-column structures under room temperature and fire based on acoustic emission …………………………………………………… 236-251 P. Ferro, L. Romanin, F. Berto https://youtu.be/29JF6c3f5rM Understanding powder bed fusion additive manufacturing phenomena via numerical simulation . 252-284 A. Namdar https://youtu.be/TgeBLuZPLhg Forecasting the bearing capacity of the mixed soil using artificial neural network ……………... 285-294 R. Harbaoui, O. Daghfas, A. Znaidi, V. Tuninetti https://youtu.be/bWqOf7KlBWs Mechanical behavior of materials with a compact hexagonal structure obtained by an advanced identification strategy of HCP material, AZ31B-H24 …………………………………. 295-305 A. Chatzigeorgiou, E. E. Theotokoglou, G. I. Tsamasphyros https://youtu.be/DtSjK-4Wr7E Code development for the computational analysis of crack propagation in structures …………... 306-324 Y. Lu, Y. Xing, X. Li, S. Xu https://youtu.be/2l4sJlj15GY A new approach of CMT seam welding deformation forecasting based on GA-BPNN………. 325-336 C. Navarro, J. Vázquez, J. Domínguez, A. Periñán, M. H. García, F. Lasagni, S. Bernarding, S. Slawik, F. Mücklich, F. Boby, L. Hackel https://youtu.be/JCzCRJbmVMg Effect of surface treatment on the fatigue strength of additive manufactured Ti6Al4V alloy …… 337-344 S. Kirin, L. Jeremi ć , A. Sedmak, I. Marti ć , S. Sedmak, I. Vu č eti ć , T. Golubovi ć https://youtu.be/2o838DsBI2w Risk based analysis of RHPP penstock structural integrity ………………………………. 345-352 H. M. Fawzy, S. A. A. Mustafa, A. E. AbdEl-Badie https://youtu.be/5pq5LVFQxGc Thermal Effect on Bond Strength of Rubberized Concrete Filled Steel Tubular Sections ……… 353-371 I. Monetto, R. Massabò https://youtu.be/8yfzVBNXz3U An analytical beam model for the evaluation of crack tip root rotations and displacements in orthotropic specimens ……………………………………………………………….. 372-393

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Fracture and Structural Integrity, 53 (2020); ISSN 1971-9883

A. Kostina, M. Zhelnin, O. Plekhov, I. Panteleev, L. Levin, M. Semin https://youtu.be/LmyKQbPy_Ik Applicability of Vyalov’s equations to ice wall strength estimation ………………………… 394-405 E. M. Strungar, V. E. Wildemann https://youtu.be/4z8EHiZagaI Inelastic deformation and destruction of fiber-laminated polymer composites in stress concentration zones …………………………………………………..………………………… 406-416 Y. Saadallah https://youtu.be/9k9lQqXPjKs Modeling of mechanical behavior of cork in compression ………………………………….. 417-425 A. Desai, C. M. Sharanaprabhu, S. K. Kudari https://youtu.be/mMcNPzernfY Glass/epoxy fiber orientation effects on translaminar fracture toughness under Mixed mode(I/II) load using FPB specimen …………………………………………………………… 426-433 Y. Shou, J. Zhang, F. Berto https://youtu.be/X0c-hyzm5Eg Experimental and analytical investigation on the coupled elastoplastic damage model of coal-rock 434-445 Z. Li, Y. Shou, D. Guo, F. Berto https://youtu.be/QcLdO-EFMZ4 A coupled elastoplastic damage model for brittle rocks …………………………………… 446-456 P. Fathi, A. N. Oskouei, K. Vahedi, A. M. Petrudi https://youtu.be/smJaa48YK3U Numerical and experimental analysis of stacking sequences effects in composite mechanical joints under impact loadings ……………………………………………………………… 457-473

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Frattura ed Integrità Strutturale, 53 (2020); International Journal of the Italian Group of Fracture

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Co-Editor in Chief Filippo Berto

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Section Editors Marco Boniardi

(Politecnico di Milano, Italy)

Nicola Bonora Milos Djukic

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

Stavros Kourkoulis

(National Technical University of Athens, Greece) (University Politehnica Timisoara, Romania)

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal)

Guest Editor

SI: Structural Integrity and Safety: Experimental and Numerical Perspectives

José António Fonseca de Oliveira Correia

(University of Porto, Portugal.)

Guest Editors

SI: 1st Benelux Network Meeting and Workshop on Damage and Fracture Mechanics

Johan Hoefnagels

(Eindhoven University of Technology, Nederland)

Reza Talemi

(KU Leuven, Belgium)

Guest Editors

SI: Additive Manufacturing

Filippo Berto Jan Torgersen

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway) (Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Tel Aviv University, Israel) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Giuseppe Ferro

Donato Firrao

Emmanuel Gdoutos

(Democritus University of Thrace, Greece) (Chinese Academy of Sciences, China)

Youshi Hong M. Neil James Gary Marquis

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(Ecole Nationale Supérieure d'Arts et Métiers | ENSAM · Institute of Mechanics and Mechanical Engineering (I2M) – Bordeaux, France)

Thierry Palin-Luc Robert O. Ritchie Ashok Saxena Darrell F. Socie Shouwen Yu

(University of California, USA)

(Galgotias University, Greater Noida, UP, India; University of Arkansas, USA)

(University of Illinois at Urbana-Champaign, USA)

(Tsinghua University, China)

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Fracture and Structural Integrity, 53 (2020); ISSN 1971-9883

Cetin Morris Sonsino

(Fraunhofer LBF, Germany) (Texas A&M University, USA) (University of Dublin, Ireland)

Ramesh Talreja David Taylor John Yates Shouwen Yu

(The Engineering Integrity Society; Sheffield Fracture Mechanics, UK)

(Tsinghua University, China)

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

Dorota Koca ń da Stavros Kourkoulis Carlo Mapelli Liviu Marsavina

(Military University of Technology, Poland) (National Technical University of Athens, Greece)

(Politecnico di Milano, Italy)

(University of Timisoara, Romania) (Tecnun Universidad de Navarra, Spain)

Antonio Martin-Meizoso

Raghu Prakash

(Indian Institute of Technology/Madras in Chennai, India)

Luis Reis Elio Sacco

(Instituto Superior Técnico, Portugal) (Università di Napoli "Federico II", Italy) (University of Belgrade, Serbia) (Tel-Aviv University, Tel-Aviv, Israel)

Aleksandar Sedmak

Dov Sherman Karel Sláme č ka

(Brno University of Technology, Brno, Czech Republic) (Middle East Technical University (METU), Turkey) (Ternopil National Ivan Puluj Technical University, Ukraine)

Tuncay Yalcinkaya

Petro Yasniy

Editorial Board Jafar Albinmousa Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia)

(Indian Institute of Technology Bombay, India) (Indian Institute of Technology Kanpur, India)

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway) (GM Institute of Technology, Dept. Of Mechanical Engg., India)

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

(University of Oviedo, Spain) (Università di Parma, Italy)

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

Mauro Corrado

(Politecnico di Torino, Italy) (University of Porto, Portugal)

José António Correia

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

Manuel de Freitas Abílio de Jesus Vittorio Di Cocco Andrei Dumitrescu Riccardo Fincato Milos Djukic

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti, Romania)

(Osaka University, Japan)

Eugenio Giner Ercan Gürses

(Universitat Politecnica de Valencia, Spain) (Middle East Technical University, Turkey)

Ali Javili

(Bilkent University, Turkey) (University of Piraeus, Greece)

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk Paolo Lonetti Carmine Maletta

(G.V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, Ukraine)

(Wroclaw University of Science and Technology, Poland)

(Università della Calabria, Italy) (Università della Calabria, Italy)

Sonia Marfia

(Università di Cassino e del Lazio Meridionale, Italy)

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Frattura ed Integrità Strutturale, 53 (2020); International Journal of the Italian Group of Fracture

Lucas Filipe Martins da Silva

(University of Porto, Portugal)

Tomasz Machniewicz

(AGH University of Science and Technology)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Kyushu University, Japan)

(Innovation centre of Faculty of Mechanical Engineering in Belgrade, Serbia)

(University of Porto, Portugal) (University of Bristol, UK)

Mahmoud Mostafavi Vasile Nastasescu

(Military Technical Academy, Bucharest; Technical Science Academy of Romania)

Stefano Natali Andrzej Neimitz

(Università di Roma “La Sapienza”, Italy) (Kielce University of Technology, Poland)

(Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukraine)

Hryhoriy Nykyforchyn

Pavlos Nomikos

(National Technical University of Athens) (IMT Institute for Advanced Studies Lucca, Italy)

Marco Paggi Hiralal Patil Oleg Plekhov

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India) (Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi Maria Cristina Porcu Dimitris Karalekas Luciana Restuccia Giacomo Risitano

(Università di Parma, Italy) (Università di Cagliari, Italy) (University of Piraeus, Greece) (Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Padova, Italy) (Università di Brescia, Italy) (Università di Napoli "Federico II")

Mauro Ricotta Roberto Roberti

Elio Sacco

Hossam El-Din M. Sallam

(Jazan University, Kingdom of Saudi Arabia) (Università di Roma "Tor Vergata", Italy)

Pietro Salvini Mauro Sassu

(University of Cagliari, Italy) (Università di Parma, Italy)

Andrea Spagnoli Ilias Stavrakas

(University of West Attica, Greece) (Lublin University of Technology)

Marta S ł owik Cihan Teko ğ lu Dimos Triantis Sabrina Vantadori Natalya D. Vaysfel'd Charles V. White

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

(Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

Shun-Peng Zhu

(University of Electronic Science and Technology of China, China)

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Fracture and Structural Integrity, 53 (2020); ISSN 1971-9883

Frattura ed Integrità Strutturale is an Open Access journal affiliated with ESIS

Sister Associations help the journal managing Australia: Australian Fracture Group – AFG

Czech Rep.: Asociace Strojních Inženýr ů (Association of Mechanical Engineers) Greece: Greek Society of Experimental Mechanics of Materials - GSEMM India: Indian Structural Integrity Society - InSIS Israel: Israel Structural Integrity Group - ISIG Italy: Associazione Italiana di Metallurgia - AIM Italy: Associazione Italiana di Meccanica Teorica ed Applicata - AIMETA Italy: Società Scientifica Italiana di Progettazione Meccanica e Costruzione di Macchine - AIAS Poland: Group of Fatigue and Fracture Mechanics of Materials and Structures Portugal: Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia: Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Spain: Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF Turkey: Turkish Solid Mechanics Group Ukraine: Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Frattura ed Integrità Strutturale, 53 (2020); International Journal of the Italian Group of Fracture

Journal description and aims Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (January, April, July, October). Frattura ed Integrità Strutturale encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians. Contributions Frattura ed Integrità Strutturale is a medium for rapid dissemination of original analytical, numerical and experimental contributions on fracture mechanics and structural integrity. Research works which provide improved understanding of the fracture behaviour of conventional and innovative engineering material systems are welcome. Technical notes, letters and review papers may also be accepted depending on their quality. Special issues containing full-length papers presented during selected conferences or symposia are also solicited by the Editorial Board. Manuscript submission Manuscripts have to be written using a standard word file without any specific format and submitted via e-mail to gruppofrattura@gmail.com. Papers should be written in English. A confirmation of reception will be sent within 48 hours. The review and the on-line publication process will be concluded within three months from the date of submission. Peer review process Frattura ed Integrità Strutturale adopts a single blind reviewing procedure. The Editor in Chief receives the manuscript and, considering the paper’s main topics, the paper is remitted to a panel of referees involved in those research areas. They can be either external or members of the Editorial Board. Each paper is reviewed by two referees. After evaluation, the referees produce reports about the paper, by which the paper can be: a) accepted without modifications; the Editor in Chief forwards to the corresponding author the result of the reviewing process and the paper is directly submitted to the publishing procedure; b) accepted with minor modifications or corrections (a second review process of the modified paper is not mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. c) accepted with major modifications or corrections (a second review process of the modified paper is mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. d) rejected. The final decision concerning the papers publication belongs to the Editor in Chief and to the Associate Editors. The reviewing process is usually completed within three months. The paper is published in the first issue that is available after the end of the reviewing process.

Publisher Gruppo Italiano Frattura (IGF) http://www.gruppofrattura.it ISSN 1971-8993 Reg. Trib. di Cassino n. 729/07, 30/07/2007

Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0)

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Fracture and Structural Integrity, 53 (2020); ISSN 1971-9883

NEWS from FIS

Dear friends, due to the Covid-19, many scientific associations recently discovered the web. Considering that, for example: YouTube was born in 2005 YouTube became in 2007 an independent subsidiary of Google Inc. I am proud to remember that: IGF videorecords all its events since 2007 and all the videos are available in the IGF YouTube channel. IGF streamed on the FB page its first event in 2017 (IGF24 in Urbino). IGF organized its first virtual conference in 2019 (VCSI1). IGF is online since 2007. IGF website: https://www.gruppofrattura.eu/ IGF FB page (since January 2009): https://www.facebook.com/GruppoItalianoFrattura IGF YouTube channel: https://www.youtube.com/c/IGFTube Frattura ed Integrità Strutturale (since 2007): https://www.fracturae.com/index.php/fis/index Frattura ed Integrità Strutturale Visual Abstracts YouTube Channel: https://www.youtube.com/c/VisualAbstractsFIS Please, do not hesitate to send us your suggestions to further improve our journal. Very best,

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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L. Hadid et alii, Frattura ed Integrità Strutturale, 53 (2020) 1-12; DOI: 10.3221/IGF-ESIS.53.01

Finite element analysis of the interface defect in ceramic-metal assemblies: Alumina-Silver

Lamia Hadid LMPM, Mechanical Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria l.hadid@outlook.fr , http://orcid.org/0000-0002-9628-193X Farida Bouafia LMPM, Mechanical Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria Mechancal Engineering Department, University centre of Ain Temouhent 46000, Algeria fbouafia2011@yahoo.fr , http://orcid.org/0000-0002-1695-1500 Boualem Serier LMPM, Mechanical Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria boualems@yahoo.fr, http://orcid.org/0000-0002-1460-9322 Sardar Sikandar Hayat* Department of Physics, International Islamic University, Islamabad 44000, Pakistan sikandariub@yahoo.com, https://orcid.org/0000-0001-6018-7354

A BSTRACT . In the present work, the finite element analysis was employed to study the distribution of mechanical stress generated in metal-ceramic bimaterial. A micromechanical model is proposed to explain a phenomenon of defect observed in the metal-ceramic interface. The distribution of this stress in the ceramic around this defect was the subject of a numerical analysis using the finite element method. The analysis has been extended to the effect of defect-defect interaction, defect size and form. K EYWORDS . Finite element method; Mechanical stress; Defects; Interface; Metal; Ceramic.

Citation: Hadid, L., Bouafia, F., Serier, B., Sikandar Hayat, S., Finite element analysis of the interface defect in ceramic-metal assemblies: Alumina-Silver, Frattura ed Integrità Strutturale, 53 (2020) 1-12.

Received: 06.09.2019 Accepted: 27.04.2020 Published: 01.07.2020

Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION etal-ceramic bi-materials offer superior properties over conventional alloys and have been widely studied because of their many potential applications. Ceramics such as zirconia, silicon carbides, silicon nitrides and alumina find a great number of applications in the field of mechanics and thermo-mechanics. The alumina remains practically the technical most current ceramics. In addition to the mechanical applications, it also gains first place M

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L. Hadid et alii, Frattura ed Integrità Strutturale, 53 (2020) 1-12; DOI: 10.3221/IGF-ESIS.53.01

in the electronics industry and electro-technical due to its interesting electrical properties such as great resistivity, significant dielectric constant and weak dielectric loss factor. Very often to benefit the maximum of these advantages, it is necessary to bind ceramics and more particularly alumina with metals and their alloys. Under the simultaneous action of the temperature and the elaboration constraint of the bimaterial, the metal deforms plastically and becomes encrusted in the roughness defects of the ceramic. This incrustation leads to a good mechanical attachment between these two protagonists and ensures very good adhesion between metal and ceramic. The joining of ceramics with metals is inherently difficult because of their distinctly different properties. During recent past years, considerable studies have been devoted to the technology development of ceramic/metal joining. It has been led to significant successes [1]. Dissimilar materials need to be joined together in many technical areas. One example of the ceramic to metal joint combines the wear resistance, high temperature strength and thermal or electrical resistance of the ceramic with the ductility of the metal. Due to the difference of the elastic properties and the thermal expansion coefficients of the ceramic and metal, high stresses occur at the intersection of edges which leads the interface of the joint under mechanical or thermal loading [2-3]. The joining of ceramics with metals is a critically important technology for the effective use of advanced materials [4]. Metal-ceramic interfaces have wide applications, and the interface fractures play an important role in determining mechanical behaviours of related structures [5]. The study of the interface separation behaviours of interfaces with the atomic vacancy and dislocations indicates that the interface strength decreases for the interfaces with defects, and the defects decrease the catastrophic tendency [5]. Joining dissimilar materials implies property mismatches and structure discontinuities [6]. Interfaces must typically sustain mechanical and thermo-elastic stresses without failure. Consequently, they exert an important influence on the performance of the material [7-8]. Due to differences in thermal and mechanical properties, the stresses and strains can develop near a ceramic-metal interface stress concentration. This can result in the plastic deformation of metal during both fabrication and under subsequent thermal or mechanical loading (cracking within the ceramic). Tremendous efforts have been made to understand these phenomena [7–12]. Nevertheless, the effects of material properties and specimen geometry on stress and strain distributions, and fracture mechanisms are reasonably well understood. The realization of Silver-Alumina junction is made in solid state. The mechanical resistance of this assembly depends primarily on the conditions of its elaboration, particularity on the atmosphere of elaboration. The fracture resistance is generally determined according to the nature of the elaboration the atmosphere of this kind of junctions [12–14]. Silver is a noble metal and reacting with the alumina does not give an intermediate compound. The assembly of this metal in alumina form no-reactive junction. The objective of this study is to numerically analyse silver-alumina junction by the finite element method. The effect of the interface defect between the metal and ceramic on the stress level has been studied in this work. he finite element model is already explained in our previous work [15-17]; however, salient features of the model which is used in this work are discussed here. A three-dimensional finite element analysis is developed for this investigation. A 2–D schematic view of the metal / ceramic bi-materials with an interface defect is shown in Fig. 1(a). One half of the model is selected as the analysis model (because of the symmetry) in order to reduce the calculation time (see Fig. 1(b)). The geometrical characteristics of the structure are the length L (L= 350 µm), the width w and the thickness ( e 1 and e 2 ) such as L / e 1 = 7, e 2 / e 1 = 6, L / w = 2. The plate is subjected to a uniformly distributed tensile load with P = 70 MPa. The diameter of the interface defect is 50 µm which characterize an average size of interface defect site. These defects are simulated with half-spherical cavities located at alumina interface with well-defined size ((see Fig. 1(e)). Numerical modelling has been taken using the ABAQUS [18] finite element program. The precision of numerical computation is strongly related to the quality of the mesh in the structure. Additionally, due to the stress concentrations expected at the metal/ceramic interface, the mesh is refined at this zone and a 4-node linear tetrahedron (C3D4) finite element is used for the model (see Fig. 1(c)). The finite element model with 75801 elements is shown in Fig. 1(c). It has a fine grid at the metal/ceramic interface. The refinement of the mesh also shows its influence on the accuracy of numerical results, and number of elements higher than 75801 leads to similar and much more precise values (Fig. 2). The surface between the metal and the ceramic is defined as the surface to surface contact (perfect surface). Here, the ceramic has been selected as a slave and the metal as a master surface. T F INITE ELEMENT MODEL

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L. Hadid et alii, Frattura ed Integrità Strutturale, 53 (2020) 1-12; DOI: 10.3221/IGF-ESIS.53.01

Silver bonded to alumina is selected in this study. Pure silver is defined as an elastic - plastic material (Fig. 3) with a value of the modulus of elasticity E = 81.90 GPa and Poisson's ratio ν = 0.31. The behaviour of alumina is considered as an isotropic elastic material. Alumina is assumed to be elastic with modulus of elasticity value E= 390 GPa and Poisson’s ratio ν = 0.25.

Y

e 1

Metal

Defect

e 2

Ceramic

X

(b)

(c)

L

(a)

P

d

Path1

Interface defect

U Z =0

P

(e)

(d)

Figure 1: (a) A 2–D schematic view of metal/ceramic with the site of interface defect, (b) Geometry of model, (c) Finite element mesh, (d) Boundary condition and loading condition and (e) site of interface defect-defect interaction.

Figure 2: Effect of mesh size convergence on ceramic/defect interface for P = 70 MPa.

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Figure 3 : The true stress-strain curve of pure silver [19].

R ESULTS AND DISCUSSION

T

he simultaneous action of the pressure and temperature (thermo-compression) during the elaboration of connecting ceramics-metal involves a plastic flow of the metal. The plastic flow speed of deformation is overall high as these two physical parameters are significant. This plastic flow leads to a friction interface between ceramics and metal. Thus involve a significant wrenching of the surface grains of alumina contact. In this context, here the results are discussed to numerically analyse the stress distribution near the interface defect using tri- dimensional the finite element method.

Figure 4: Von-Mises equivalent and normal stress distribution for P = 70 MPa.

Stresses distribution The distribution of normal and Von Mises equivalent stresses for the silver and alumina near the interface defect during the preparation of their junction is represented in Fig. 4. The normal stress induced along the x-direction is highly concentrated on the metal at the interface near the edge of the connection, while the volume of silver is in the opposite direction of this site (see Fig. 4(b)). The stress generated along the z-direction is on the same level and its distribution is comparable to that induced following the first axis (x-axis) of the assembly (see Fig. 4(d)). The normal stress along the y-

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axis, which is the axis of application of mechanical loading, is at a much higher level than the other two normal stresses, which are highly concentrated for the alumina and silver in the neighborhood near the defect (see Fig. 4(c)). The Von Mises equivalent stress is highly concentrated near the site. Its distribution reflects the normal stresses (see Fig. 4(a)). The illustrations of results in Fig. 4 clearly show that the defect is at a special place of stress concentration by notch effect. Effect of loading Fig. 5 shows the variation of normal stresses for the ceramic and metal near the defect as a function the normalized distance (X-values correspond to each point’s distance along the path as a fraction of the total length of the path (see Fig.1d)) and according to the applied mechanical load. These stresses are heavily concentrated around the interfacial defects. Interfacial defects effects are increased with increasing applied stress. This type of loading compresses the cavity along x- and z-direction. The compression ratio becomes higher when the intensity of loading increases. These stresses vanish for the defect. Stresses along the y-direction of mechanical stress set the cavity in tension. The intensity of these stresses holds more importance than those for the other two axes of the structure. The variation of Von Mises stresses around the defect as a function of the applied stress is shown in Fig. 5(a). The analysis of this Figure clearly shows that the presence of this defect on the surface of the ceramic-related metal plays a leading role of stress concentration, whose intensity increases with the increase in mechanical loading of the junction.

100

20 40 60 80 100

(a)

(c)

80

60

40

S YY (MPa)

S equi (MPa)

P = 50 MPa P = 70 MPa P = 100 MPa

P = 50 MPa P = 70 MPa P = 100 MPa

20

0.0 0.2 0.4 0.6 0.8 1.0 0

0,0 0,2 0,4 0,6 0,8 1,0 0

Normalize distance Normalized distance

Normalize distance Normalized distance

20 40

20 40

(b)

(d)

-100 -80 -60 -40 -20 0

-80 -60 -40 -20 0

P = 50 MPa P = 70 MPa P = 100 MPa

S XX (MPa)

P = 50 MPa P = 70 MPa P = 100 MPa

S ZZ (MPa)

Interface Ceramic/Defect

Interface

Metal/Defect

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Normalize distance Normalized distance

Normalize distance Normalized distance

Figure 5: Variation of equivalent and normal stresses according to mechanical loading.

Effect of defect size The size of interfacial defect does not merely determine the distribution and the level of the stresses of this defect, nevertheless, also measures the surface of effective adhesion. Its analysis carries great importance for the performance and the mechanical resistance of the junction. Fig. 6 illustrates the variation of induced normal stresses nearby to the defect applying a mechanical stress as a function of its diameter. This Figure shows that large defects induce more significant

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stresses. These results show that the stress concentration increases proportionally with the increase of the defect size to reach the maximum value for the biggest size. Such a behaviour can present a risk of decoherence of the junction. The site of the interface defect (seat of stress concentration) is a privileged place of initiation and propagation of cracks. .

S equi S XX S YY

100 150

-150 -100 -50 0 50

Defect size

Mechanical Stress (MPa)

60 80 100 120 140 160 180 200

Defect Size (  m)

Figure 6: Variation of mechanical stresses according to a defect size in Metal/defect interface for P = 70 MPa

The variation of stress concentration factor as a function of the interface defect size is represented in Fig. 7. This Figure well illustrates that this factor varies almost linearly with the variation in size. This clearly shows that the presence of large defects on the surface of the ceramic can lead to the initiation and the propagation of cracks and consequently to the damage of alumina-silver assembly by cohesive or adhesive rupture depending the mechanical strength of the interface. Thus, they are able to lead to a cohesive or adhesive rupture, according with the resistance.

2.5 3.0 3.5 4.0 4.5 5.0 Stress Concentration Factor (K t )

Size

60 80 100 120 140 160 180 200

Defect Size (  m)

Figure 7: Variation of stress concentration factor according to a defect size for P = 70 MPa.

Stresses distribution around the defect The level of stresses around the site of interface defect exploits a dominating role in the start-up and the performance of the ceramics-metal junction. Its analysis carries great importance for the mechanical resistance and the durability of this junction. Figs. 8(b), 8(c) and 8(d) represent the distribution of induced normal stresses according to three axes of the structure along the perimeter (path 2) of the interfacial defect (see Fig. 8(a)). The analysis of this Figure shows that according to the x-direction, at the ends, i.e. in the vicinity of the interface with metal, (when θ < 20°) the defect is subject to the normal stresses of tension, and far from this zone to compressive stresses. Along the direction of applied load, which is y-

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direction, the normal stresses of tension are higher at the defect/metal interface (when θ = 0° and θ = 180°) and very low in the zone far from the plane of the alumina-silver junction (when θ = 90°) (see Fig. 8(c)). A contrary behaviour is observed along the z -direction; indeed, the compression stresses are intensively concentrated in ceramics,(when θ = 90°), while their level decreases considerably in the mid of this interface (when θ = 0° and θ = 180°) (see Fig. 8(d)). The tangential stresses are most significant specific to the xoy planes of the assembly. The highest stresses are localized at θ = 45° and 135° (see Fig. 8(e)).

10 20

(a)

Metal

(b)

160

P = 50 MPa P = 70 MPa P = 100 MPa

180 o

0 o

-50 -40 -30 -20 -10 0

Ceramic

120

Path2

80

S XX (MPa)

S equi (MPa)

40

P = 50 MPa P = 70 MPa P = 100 MPa

0 30 60 90 120 150 180 0

0 30 60 90 120 150 180

Peripheral Angle 

Peripheral Angle 

120 150 180

0 30 60 90 120 150 180 -50 -40 -30 -20 -10 0 10 (d) S ZZ (MPa) Peripheral Angle  P = 50 MPa P = 70 MPa P = 100 MPa

(c)

P = 50 MPa P = 70 MPa P = 100 MPa

30 60 90

S YY (MPa)

0 30 60 90 120 150 180 0

Peripheral Angle 

10 15

(e)

0 5

-15 -10 -5

S XY (MPa)

P = 50 MPa P = 70 MPa P = 100 MPa

0 30 60 90 120 150 180

Peripheral Angle 

Figure 8: Variation of equivalent, normal and shear stresses according to peripheral angle and mechanical loading.

Effect of defect geometry The effect of the defect form, which is defined by the x/y ratio, is analysed, and the effect of the defect volume on the distribution of equivalent and normal stresses near to the interface with metal is characterized. This analysis is made for an invariable size x along path 1 (see Fig. 1). The obtained results are represented in Figs. 9 and 10.

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10 20 30

60 (a)

(b)

Metal

50

Interface Metal/Defect

40

-30 -20 -10 0

S XX (MPa)

30

x/y =2 x/y =4 x/y =6

S equi (MPa)

x/y =2 x/y =4 x/y =6

20

0,0 0,2 0,4 0,6 0,8 1,0 10

0.0 0.2 0.4 0.6 0.8 1.0

Normalize Distance Normalized distance

Normalized i

Normalize distance

10 20 30

10 20 30 40 50 60 70 80 (c)

(d)

-30 -20 -10 0

S ZZ (MPa)

x/y =2 x/y =4 x/y =6

S YY (MPa)

x/y =2 x/y =4 x/y =6

0.0 0.2 0.4 0.6 0.8 1.0 0

0,0 0,2 0,4 0,6 0,8 1,0

Normalize Distance Normalized distance

Normalize distance

alized distance

Figure 9: Variation of equivalent and normal stresses depending on defect geometry in Metal.

The influence of the parameter y on the level of the normal stresses is generated in the silver along x- and z- direction of the junction. Along these directions and far from the interface, the metal is in tension, whereas in its close vicinity it is in compression. The intensity of these stresses increases with the volume of interface defect (see Figs. 9(a) and 9(c)). Along the y-axis, which is the direction of mechanical load application, the normal stresses decrease approaching the interface with ceramics. An increase in the x/y ratio involves a light amplification of these stresses. Their amplitude is annulled in the plane of the junction (see Fig. 9(b)). The Von Mises equivalent stress in the metal gradually decreases towards the interface with alumina, then grows slightly near to this defect. This stress is overall more significant as the x/y ratio increases (see Fig. 9(d)). The distribution and level of the Von Mises and normal stresses induced in alumina as a function of the x/y ratio are represented in Fig. 10. The induced normal stresses along x- and z -direction seems not to dependent on the shape of the interface defect. Indeed, the intensity of these stresses practically does not vary with the variation in the x/y ratio (see Figs. 10(b) and 10(d)). An increase in the x/y ratio involves an increase in the Von Mises and y-direction normal stresses generated in the vicinity of interface defect (see Figs. 10(a) and 10(c)). The effect of the defect shape on the distribution of equivalent stress and its intensity is analysed in terms of stress concentration factor (see Fig. 11). This figure shows that the decrease in the parameter involves a high stress concentration factor. The interface defect having such a form is the seat of stress concentration. Effect of defect-defect interaction The previously obtained results show that the alumina defect is a privileged place of stress concentration whose level and distribution does not merely depend on its size, but also on its form. However, several grains are snatched by interfacial friction between these two components during the realization of metal-ceramics junction. These sites are represented by interfacial defects of spherical symmetry. This is why, an analysis of the effect of defect-defect interaction at the interfacial

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level and the distribution of stresses is carried out. The so obtained results are illustrated in Fig. 12. This last one shows the variation of Von Mises and normal stresses according to the distance separating the sites from two defects.

0,0 0,2 0,4 0,6 0,8 1,0 40 50 60 70 80 90 (a) Ceramic x/y =2 x/y =4 x/y =6

-70 -60 -50 -40 -30 -20 -10 0 10 -70 -60 -50 -40 -30 -20 -10 0 10

(b)

S equi (MPa)

x/y =2 x/y =4 x/y =6

S XX (MPa)

Interface

Ceramic/Defect

0.0 0.2 0.4 0.6 0.8 1.0

Normalize Distance

Normalize Distance Normalized distance

r alized distance

10 20 30 40 50 60 70

(c)

(d)

x/y =2 x/y =4 x/y =6

x/y =2 x/y =4 x/y =6

S ZZ (MPa)

S YY (MPa)

-10 0

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Normalize Distance Normalized distance

Normalized distance

Normalize Distance

Figure 10: Variation of equivalent and normal stresses according to defect geometry in ceramic.

1.5 2.5 Stress Concentration Factor (K t ) Ratio x/y 2.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0

Figure 11: Variation of stress concentration factor according to defect geometry.

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d

-0.10 -0.05 0.00 0.05 0.10 20 30 40 50 60 70 (b) S XX (MPa) Distance (mm) d1=25  m d2=40  m d3=100  m d4=160  m

d1=25  m d2=40  m d3=100  m d4=160  m

100 120 140

(a)

S equi (MPa)

-0,10 -0,05 0,00 0,05 0,10 60 80

Distance (mm)

60

d1=25  m d2=40  m d3=100  m d4=160  m

d1=25  m d2=40  m d3=100  m d4=160  m

100 120 140 160

(d)

(c)

50

40

S ZZ (MPa)

30

S YY (MPa)

-0.10 -0.05 0.00 0.05 0.10 60 80

-0.10 -0.05 0.00 0.05 0.10 20

Distance (mm)

Distance (mm)

10 20 30

(e)

d

-0.10 -0.05 0.00 0.05 0.10 -40 -30 -20 -10 0 d1=25  m d2=40  m d3=100  m d4=160  m

S XY (MPa)

(x, y, z)= (0, 0, 0)

Distanc (mm)

Figure 12: Variation of internal equivalent and normal stresses according to the defect-defect interaction for P = 70 MPa.

The stress intensity induced along the x- and z -direction of the assembly grows with the reduction in the defect- defect interdistance. Indeed, bringing together these two defects leads to the intensification of these stresses. These last tend towards their maximum level when the sites of the interface defect are very close to the other one (see Figs. 12(b) and 12(c)). A tendency of an interfacial defect towards the other involves an amplification of the normal stresses which are generated along the y-direction which is requested by the external mechanical loads. Two defects are close neighbors which generate much more intense normal stresses, whose level is approximately twice more significant than that of the load applied (see Fig. 12(c)). The tangential stresses are most significantly related to the plane (x, o, y) of the structure. The level of these stresses grows with the reduction in the defect-defect inter-distance. Maximum sites of the interface defect are close to each other and the shear stresses induced in this plane are strong (see Fig. 12(e)). Fig. 12(a) shows the effect of

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this inter-distance on the amplitude of Von Mises stress. This figure shows that bringing together these sites leads to the strong intensification of equivalent stress. The results obtained in this analysis clearly show that the distance separating the sites from the defect with the metal determines the level and distribution of the stresses induced with their interface. Indeed, the more these sites are close to each others, the more their stress field is reacting between them. Thus, the amplification of these constraints is involved with the effect of the interaction. This effect is dominated when the vicinity sites are very close to each other. The distance of one of these sites compared to the others minimizes the effect of the interaction. This finally is annulled when the sites of the interface defect are very far from each other, then their stress fields are isolated from each other. n the present work, 3-dimensional finite element method was used to investigate the effects of the defect in metal– ceramic bimaterial. The results obtained in this study allow us to draw the following conclusions: - The sites of interface defect during the elaboration by interfacial friction with the silver are the privileged places of stress concentration by notch effect. The level and the distribution of the normal, tangential and the Von Mises equivalent stresses are not dependent merely on the intensity of the mechanical loading, nevertheless, also on the size of the sites of interface defect (characteristic of the site volume). These stresses are overall higher as the volume of this site grows. The stress concentration factor grows with the increase in the volume. Thus, the coarse interface defects do concentrate more stresses relative to the small ones. - The form which is defined by the x/y ratio of this defect plays a role to determine the level of the Von Mises and normal stresses. A small ratio involves an increase in the induced normal stresses of the silver, relating to the x- and z -direction of the assembly, while a reduction of the normal stress relating to the y-axis. The Von Mises stress is overall weak as the x/y ratio is small. In alumina, the normal stresses generated along x- and z -axes of the structure seem not dependent on the form of the site of interface defect. In this component, the stress induced according to the direction is not very sensitive to the form of this site. The Von Mises stress grows with the increase in x/y ratio. The stress concentration factor decreases with the increase of this ratio. - The intensity and the distribution of the normal, tangential and equivalent stress depend on the defect-defect inter- distance. Bringing together these sites one towards the other, lead to an intensification of these constraints. These stresses are overall higher as the defects are very close to each other. [1] Boutabout, B., Chama, M., Bouiadjra, B.A.B., Serier, B., Lousdad, A. (2009). Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile, Comput. Mater. Sci., 46(4), pp. 906–911. DOI: 10.1016/j.commatsci.2009.04.039. [2] Yang, Y.Y., Munz, D. (1997). Stress singularities in a dissimilar materials joint with edge tractions under mechanical and thermal loadings, Int. J. Solids Struct., 34(10), pp. 1199–1216. DOI: 10.1016/S0020-7683(96)00097-2. [3] Nikbakt, S., Kamarian, S., Shakeri, M. (2018). A review on optimization of composite structures Part I: Laminated composites, Compos. Struct., 195, pp. 158–185. DOI: 10.1016/j.compstruct.2018.03.063. [4] Williamson, R.L., Rabin, B.H., Byerly, G.E. (1995). FEM study of the effects of interlayers and creep in reducing residual stresses and strains in ceramic-metal joints, Compos. Eng, 5(7), pp. 851–863. DOI: 10.1016/0961-9526(95)00035-L. [5] You, X.M., Liang, L.H., Wei, Y.G. (2018). The atomistic simulation study of Ag/MgO interface tension fracture, Comput. Mater. Sci., 142, pp. 277–284. DOI: 10.1016/j.commatsci.2017.10.029. [6] Nascimento, R.M. do., Martinelli, A.E., Buschinelli, A.J.A. (2003). Review Article: recent advances in metal-ceramic brazing, Cerâmica, 49(312), pp. 178–198. DOI: 10.1590/S0366-69132003000400002. [7] Li, V. (2004). Fracture mechanics of concrete structures: proceedings of the Fifth International Conference on Fracture Mechanics of Concrete and Concrete Structures, Vail Colorado, {USA}, April 12 - 16. [8] Drake, J.T., Williamson, R.L., Rabin, B.H. (1993). Finite element analysis of thermal residual stresses at graded ceramic/metal interfaces, part II: optimization for residual stress reduction, J. Appl. Phys., 74(2), pp. 1321-1326. DOI:10.1063/1.354911. R EFERENCES I C ONCLUSIONS

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