Issue 48

Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

Table of Contents

R. Brighenti, A. Carpinteri, F. Artoni Crack paths in soft thin sheets .………………………………………………………..…….. 1 J. Lewandowski, D. Rozumek, Z. Marciniak, G. Lesiuk , R. Brighenti Fatigue crack growth in welded S355 specimens subjected to combined loading ……………………... 10 S. Bressan, F. Ogawa, T. Itoh, F. Berto Low cycle fatigue behavior of additively manufactured Ti-6Al-4Vunder non-proportional and proportional loading………................................................................................................................ 18 Y. Yamazaki Isothermal and thermomechanical fatigue interaction in fatigue crack propagation behavior of a low-carbon nitrogen-controlled 316 stainless steel ………………………………………………………... 26 L. Malíková, S. M. J. Razavi, F. Berto Crack propagation in a brittle DCB specimen assessed by means of the Williams’ power expansion …… 34 A. Kurek, T. Łagoda Fracture of elastic-brittle and elastic-plastic material in cantilever cyclic bending …………………….. 42 O. Plekhov, A. Vshivkov, A. Iziumova, A. Zakharov, V. Shlyannikov The experimental study of energy dissipation during fatigue crack propagation under biaxial loading …... 50 M. Schuscha, M. Leitner, M. Stoschka, S. Pusterhofer, G. Meneghetti Numerical crack growth study on porosity afflicted cast steel specimens ………………………..…… 58 D. Alexiane, G. M. D. Almaraz, N. J. Trujillo Alonso Granite stone subjected to ultrasonic fatigue tests under three point bending loading ………………….. 70 V. Shlyannikov, A. Tumanov The effect of creep damage model formulation on crack path prediction ……………………………... 77 A. Zakharov, V. Shlyannikov, A. Tumanov The crack path in fuselage panel under mixed mode biaxial loading ....................................................... 87 P. Bernardi, R. Cerioni, D. Ferretti, F. Leurini, E. Michelini Experimental characterization of fiber-reinforced cementitious mortar under tension ………………… 97 S. Gerbe, U. Krupp, W. Michels Influence of secondary dendrite arm spacing (SDAS) on the fatigue properties of different conventional automotive aluminum cast alloys ……………………………………………………………. 105

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

L. Romanin, A. Vinogradov, F. Berto, P. Ferro A novel algorithm for crack path identification based on infrared images ………………………...… 116 K. Okuda, K. Ogawa, Y. Ichikawa, T. Shiozaki, N. Yamaguchi Influence of microstructure on fatigue property of ultra high-strength steels ………………………….. 125 S. Henkel, C. H. Wolf, H. Biermann, A. Burgold, M. Kuna Cruciform specimens used for determination of the influence of T-stress on fatigue crack growth with overloads on aluminum alloy Al 6061 T651……………………………………….................... 135 D. Yang, X. Wang Damage evolution law on the surface field of argillaceous dolomite based on Brazilian test and 3D digital image correlation ……...…………………………………………………………………... 144 A. Metehri, M. Kouider, A. Lousdad Effect of crack position and size of particle on SIF in SiC particles reinforced Al composite …...………. 152 J.-g. Liu, X.-j. Zhou, W. Zhao, Y.-s. Shen, Q.-h. Xiao A new method for testing the interfacial shear properties between rock and early-aged shotcrete ………… 161 A. S. Bouchikhi, A. Lousdad, K. Yassine, N. E. Bouida, S. Gouasmi, A. Megueni Finite Element Analysis of Interactions between two cracks in FGM notched Plate under Mechanical Loading ……………………………………………………………...………….………. 174 M. Laredj, A. Miloudi, A. Lousdad, B. Benguediab Prediction and optimizing residual stress profile induced by cold expansion in aluminum alloys using experimental design …......................................................................................................................... 193 Y. Khalfi, A. S. Bouchikhi, Y. Bellebna Mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory ………………………………………………………………... 208 V. P. Berardi, M. Perrella, G. Cricrì Cohesive fracture in composite systems: experimental setup and first results ………………………… 222 O. A. Mocian, D. M. Constantinescu, Ş. Sorohan, M. Sandu Low velocity failure and integrity assessment of foam core sandwich panels ……...…………………... 230 T. Febra, J.A.M. Ferreira, J. D. Costa, J. da Silva, C. Capela Response of fabric insert injection overmolding pp based composites subjected to single and muti-impact ... 242 S. E. Oliveira, J.A.M. Ferreira, J. da Silva, C. Capela, Effect of machining parameters on the mechanical properties of high dosage short –carbon- fiber reinforced composites …………………………………………...………………………………….... 249 R. Baptista, J. Marques, V. Infante Algorithm for automatic fatigue crack growth simulation on welded high strength steels ………………. 257 R. Maciel, V. Infante, D. Braga, P.M.G.P. Moreira, L. da Silva, T. Bento Development of hybrid friction stir welding and adhesive bonding single lap joints in aluminium alloys ... 269

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Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

F.A.L. Viana, R.D.S.G. Campilho, R.J.B. Rocha, D.F.O. Silva, R.V.C. Araújo, J.P.S.M.B. Ribeiro Fracture modelling of adhesively-bonded joints by an inverse method ………………………………. 286 V. M.G. Gomes, M. Rodrigues, J.A.F.O. Correia, M.A.V. Figueiredo, A.M.P. de Jesus, A.A. Fernandes Monotonic and fracture behaviours of bolted connections with distinct bolt preloads and surface treatments 304 L. Reis, J. Caxias, H. Soares, P. R. Costa, V. Anes, M. Freitas Damage evaluation under complex fatigue loading conditions ……………………………………. 318 J.P.S.M.B. Ribeiro, R.D.S.G. Campilho, R.J.B. Rocha, A.J.S. Leal, F.A.L. Viana Validation of fracture envelopes of structural adhesives for mixed-mode strength prediction of bonded joints 332 M. Estrada, D. L. Linero, C. Takeuchi Numerical model of cracking pattern in laminated bamboo specimens under tensile and shear loads ……. 348 M. Tirenifi, B. O. Chikh, B. Bouchouicha, A. Bensari Numerical comparison of cruciform weld and butt weld simulation and a study of fracture mechanics on two types of welds …………………………………………………………………………. 357 P. H. Nayak, H. K. Srinivas , M. Nagaral, V. Auradi Characterization and tensile fractography of nano ZrO 2 reinforced Copper-Zinc alloy composites ……… 370 H. S. Patil, D. C. Patel, C. S. Patil Characterizations of TIG welded joints of unalloyed commercially pure Titanium Gr-2 for weld process parameters …..………………………………………………………………………….... 377 B. Chen, P. Zhi, Y. Li Fatigue strength analysis of bogie frame in consideration of parameter uncertainty …………………… 385 J. F. Barbosa, J.A.F.O. Correia, P. A. Montenegro, R. C. S. Freire Júnior, G. Lesiuk, A. M.P. De Jesus, R.A.B. Calçada A comparison between S-N Logistic and Kohout-Věchet formulations applied to the fatigue data of old metallic bridges materials …………………………………………………………………... 400 C.A.C.P. Coelho, F.V.P. Navalho, P.N.B. Reis Impact response of laminate cylindrical shells ………………………………………………….. 411 S. Bhowmik, S. Dubey, S. Ray Investigation on fracture process of concrete ……………………………………………………. 419 K. Kimakh, A. Chouaf, A. Saoud, E. H. Mallil, S. Aghzer Experimental investigation of surface roughness effect on fatigue performance of AISI 1045 carbon steel and fatigue limit prediction …………………………………………………………………. 429 C. Santus Initial orientation of the fretting fatigue cracks in shrink-fit connection specimens …………………… 442 O. Plekhov, A. Vshivkov, A. Iziumova. B. Venkatraman A model of energy dissipation at fatigue crack tip in metals ……………………………………… 451

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

E. Maiorana Contribution of longitudinal stiffener rigidity and position to bridge girder integrity ………………….. 459 A. Takahashi, A. Suzuki, M. Kikuchi Fatigue crack growth simulation of two non-coplanar embedded cracks using s-version finite element method ………………………………………………...……………………………….... 473 X.-g. Huang, Z.-q. Wang Durability method on corrosion fatigue performance of AH 32 steel ………………………………. 481 M. Bezzerrouki, K. Madani, A. Sahli, S. Touzain, S. Mallarino Innovative geometric design improves the resistance of simple metal / metal lap joint ……..………….... 491 T. Profant, M. Hrstka, J. Klusák Microcrack interaction with circular inclusion and interfacial zone ………………………………... 503 J. Prawin, A. Rama Mohan Rao Damage localization of closing cracks using a signal decomposition technique ………………………. 513 R. Nikhil, S.A. Krishnan, G. Sasikala, A. Moitra Limit load based evaluation of plastic η factor for C(T) specimen with a mismatched weld ……………. 523 C. E. Cruz Gonzalez, R. Perez Mora, S. D. Santillan Gutierrez, J. J. Taha-Tijerina, B. Vargas Arista, A. Barba Pingarron Fatigue strength evaluation and fracture behavior of joined dual phase steel/AA6061-T6 aluminum alloy ……………………………………………………………………............................. 530 S. Kikuchi, Y. Nakatsuka, Y Nakai, M. Natakani, M. O. Kawabata, K. Ameyama Evaluation of fatigue properties under four-point bending and fatigue crack propagation in austenitic stainless steel with a bimodal harmonic structure ………………..…………………………….... 545 J. Christopher, C. Praveen, B.K. Choudhary Comparative evaluation of two physically based models for the description of stress-relaxation behaviour of 9% chromium containing steel ………………………..………………………………….... 554 J. Bär, R. Urbanek Determination of dissipated Energy in Fatigue Crack Propagation Experiments with Lock-In Thermography …….…………………………………………………………………….... 563 H. S. Bedi, B. K. Billing, P. K. Agnihotri Interfacial shear strength of carbon nanotubes based hybrid composites: effect of loading rate …………... 571 S.C.S.P. Kumar Krovvidi, S. Goyal, A. K. Bhaduri Low cycle fatigue and creep-fatigue response of the 316Ti stainless steel ………….………………… 577 A. Ghosh In-plane anisotropy in deformation micro-mechanism of commercially pure titanium during monotonic tension and cyclic loading………………………………………………………………….... 585

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Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

M. K. Hussain, K.S.R.K. Murthy Evaluation of mixed mode (I/II) notch stress intensity factors of sharp V-notches using point substitution displacement technique ...………………………………………………………………….... 599 A. C. de Oliveira Miranda, R. Marques, M. A. Meggiolaro, J. T. Pinho de Castro Stress Intensity Factor Equations for the Evolution of Surface and Corner Cracks to Through Cracks . 611 P. Dhaka, R. V. Prakash Effect of contact geometry on the contact stresses ina flat with rounded edge contact ………………….... 630 V. Giannella, M. Perrella Multi-axial fatigue numerical crack propagations in cruciform specimens ...……………………….... 639 Y. Sun, L. Yan, B. Chen, W. Song, F. Berto Localized wrinkling of metal films on elastic and liquid substrates ……...……………………….... 648 F.V. Antunes, R. Branco, P. Prates, J.D.M. Costa Fatigue crack growth in notched specimens: a numerical analysis …………………………………. 666 F.V. Antunes, R. Branco, J.A.M. Ferreira, L.P. Borrego Stress intensity factor solutions for CTS mixed mode specimen ………………………………….. 676 R. S. Y. R. C. Silva, E. U. L. Palechor, L. M. Bezerra, M. V. G. de Morais, W. V. da Silva Damage detection in a reinforced concrete bridge applying wavelet transform in experimental and numerical data ………………………………………………………………………….... 693 M. L. Puppio, M. Ferrini Parametric analysis on external dissipative link system for seismic protection of low rise R.C. buildings . 706 C. Bellini, F. Carlino Intermetallic phase kinetic formation and thermal crack development in galvanized DCI …………….. 740 C. M. S. Vicente, J. Fernandes, L. Reis, A. M. de Deus, M.F. Vaz, M. Leite Effect of protective coatings on the water absorption and mechanical properties of 3D printed PLA……. 748 Y. Shao, P. Lu, B. Wang, Q. Xiang Fatigue reliability assessment of small sample excavator working devices based on Bootstrap method …... 757 A. Fesenko, N. Vaysfel’d An uncoupled thermoelasticity problem for a semi-infinite layer with regard to its proper weight ………... 768

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Associate Editors Alfredo Navarro

(Escuela Superior de Ingenieros, Universidad de Sevilla, Spain)

Thierry Palin-Luc

(Arts et Metiers ParisTech, France) (University of Sheffield, UK) (University of Manchester, UK)

Luca Susmel John Yates

Guest Editors Sabrina Vantadori Andrea Carpinteri Andrea Spagnoli Guest Editors Paulo N. B. Reis Abilio M. P. Silva

Crack Paths

(Università di Parma, Italy) (Università di Parma, Italy) (Università di Parma, Italy)

Portuguese contributions for Structural Integrity

(Universidade da Beira Interior, Portugal)

(University of Porto, Portugal)

Guest Editor

Showcasing Structural Integrity Research in India (Indian Institute of Technology Madras, India)

Raghu Vasu Prakash

Guest Editors

Design of Civil Environmental Engineering

Mauro Sassu

(Università di Cagliari, Italy) (Università di Cagliari, Italy) (Università di Cagliari, Italy)

Fausto Mistretta Flavio Stochino Franco Bontempi

(Università di Roma “La Sapienza”, Italy) (Università di Roma “La Sapienza”, Italy)

Konstantinos Gkoumas

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)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Emmanuel Gdoutos Youshi Hong M. Neil James Gary Marquis Ashok Saxena Darrell F. Socie Shouwen Yu Ramesh Talreja David Taylor Robert O. Ritchie Cetin Morris Sonsino Donato Firrao

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

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(University of California, USA)

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

(University of Illinois at Urbana-Champaign, USA)

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

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Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

Dorota Kocańda 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

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

Raghu Prakash

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 Slámečka Petro Yasniy

(Brno University of Technology, Brno, Czech Republic) (Ternopil National Ivan Puluj Technical University, Ukraine)

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

Luca Collini

Mauro Corrado

José António Correia

Dan Mihai Constantinescu

University POLITEHNICA of Bucharest()

Manuel de Freitas Abílio de Jesus Vittorio Di Cocco Andrei Dumitrescu Giuseppe Ferro Riccardo Fincato Eugenio Giner Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk Paolo Lonetti Carmine Maletta 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)

(Politecnico di Torino, Italy) (Osaka University, Japan)

(Universitat Politecnica de Valencia, Spain)

(University of Piraeus, Greece)

(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)

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

(Università di Roma “La Sapienza”, Italy)

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

Andrzej Neimitz

(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 Dimitris Karalekas Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

(Università di Parma, 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")

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) (University of West Attica, Greece)

Marta Słowik Dimos Triantis Sabrina Vantadori Natalya D. Vaysfel'd Charles V. White

(Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

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

Shun-Peng Zhu

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Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

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

Czech Rep.: Asociace Strojních Inženýrů (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 Ukraine: Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

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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Frattura ed Integrità Strutturale, 48 (2019); International Journal of the Italian Group of Fracture

News from Frattura ed Integrità Strutturale

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ear friends, this is a very rich issue for Frattura ed Integrità Strutturale . 70 papers organized both in “regular submissions” and “special issues” (maybe, better, “Focused on” sections) confirm the success of our Journal. This time I wish to warmly thank all the Guest Editors of the “Focused on” section for their hard work: they all followed the reviewing process, allowing to publish a really high quality issue. For the Crack Paths section, we have the contribution of Sabrina Vantadori, Andrea Carpinteri and Andrea Spagnoli (all of them from the Università di Parma, Italy). For the Portuguese contributions for Structural Integrity the issue had the contribution of Paulo N. B. Reis (from the Universidade da Beira Interior, Portugal) and of Abilio M. P. Silva (from the University of Porto, Portugal). Last but not least, the Showcasing Structural Integrity Research in India section was organized by Raghu Vasu Prakash (from the Indian Institute of Technology Madras, India) and the Design of Civil Environmental Engineering organized by Mauro Sassu, Fausto Mistretta, Flavio Stochino (from Università di Cagliari)

and Franco Bontempi, Konstantinos Gkoumas (from Università di Roma “La Sapienza” ) THANK YOU ALL FOR YOUR ENTHUSIASM AND CONTINUOUS SUPPORT! I wish to remember you some services we recently activated:

Visual Abstract : this is the forth issue with all the papers connected with their Visual Abstracts. Short videos (less than 2 minutes long) with the core of the paper allow the reader to have a quick view of the papers content. We wish to thank all the authors for their efforts. These Visual Abstract are really appreciated and we hope they will increase the papers visibility. Please, remember that we publish the Visual Abstract also in a YouTube channel: https://www.youtube.com/channel/UC3Ob2GNW8i0phNiiKjEVv0A Please, join the channel… if the subscribers number will increase, we will be able to obtain a customized url!! Material and Design and Processing Communications (MDPC) , it is the new publication media published by Wiley. All the Frattura ed Integrità Strutturale authors are suggested to submit short versions of their papers to MDPC following the

procedure described in the Frattura ed Integrità Strutturale website: https://www.fracturae.com/index.php/fis/announcement/view/18

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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Fracture and Structural Integrity, 48 (2019); ISSN 1971-9883

FIS Special Issue on Crack Paths

Editorial

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he direction or path of the initial crack and its subsequent growth path in most engineering structures and components must be taken into account both in design and in the analysis of failures under static and fatigue loading. Knowledge of potential crack paths is needed for both the solution of a crack growth problem and the selection of appropriate non-destructive testing procedures. Interest on this challenging issue has steadily increased during the last few decades. This FIS special issue contains 31 selected papers which show a significant progress in the understanding of crack path behaviour and in the application of this knowledge to practical engineering problems. The papers cover a wide range of materials, such as metals (stainless steel and aluminum alloys), cementitious composites (concrete and mortar), natural stones as well as soft matter. Theoretical and numerical methods are used to investigate the materials behaviour in a wide range of scales, up to the nanoscale of a single crystal. Different experimental techniques, including for instance Digital Image Correlation, infrared thermography, ultrasonic fatigue testing, are adopted in the investigations. Understanding of the fracture behaviour of composites, layered materials and foams has also increased during last years. Authors of the selected papers come from 12 countries around the world (in alphabetical order: Austria, Brasil, Colombia, Czech Republic, Germany, India, Italy, Japan, Mexico, Norway, Poland, Russia). Some of the papers are the result of international collaborations, with authors from more than one country. The papers have been subjected to the normal FIS review process. We thank the many anonymous reviewers who assisted us in the reviewing process.

Andrea Carpinteri, Andrea Spagnoli, Sabrina Vantadori Department of Engineering and Architecture University of Parma Parco Area delle Scienze 181/A, 43124 Parma, Italy

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

Focussed on “Crack Paths”

Crack paths in soft thin sheets

Roberto Brighenti, Andrea Carpinteri, Federico Artoni Department of Engineering and Architecture, University of Parma, Viale Usberti 181/A, 43124 Parma, Italy brigh@unipr.it ,https://orcid.org/0000-0002-9273-0822

andrea.carpinteri@unipr.it, https://orcid.org/0000-0002-8489-6005 federico.artoni@studenti.unipr.it, https://orcid.org/0000-0001-9032-2959

A BSTRACT . Highly deformable materials (elastomers, gels, biological tissues, etc.) are ubiquitous in nature as well as in technology. The understanding of their flaw sensitivity is crucial to ensure a desired safety level. Fracture failure in soft materials usually occurs after the development of an uncommon crack path because of the non-classical near-tip stress field and the viscous effects. In a neo-Hookean material, the true opening stress singularity along the crack path (evaluated normal to the crack line) is of the order 2 r  , while it is of the order 1/2 s  ahead of the crack tip, promoting the appearance of a crack tip splitting leading to a tortuous crack. In the present paper, experimental tests concerning the fracture behavior of highly deformable thin sheets under tension are discussed, and the observed crack paths are interpreted according to the crack tip stress field arising for large deformations. The study reveals that higher strain rates facilitate the development of a simple Mode I crack path, while lower strain rates induce a mixed Mode in the first crack propagation stage, leading to the formation of new crack tips. The above described behavior seems to not be affected by the initial crack size. K EYWORDS . Rubber; Highly deformable materials; Crack path; Strain rate; Crack tip splitting.

Citation: Brighenti, R., Carpinteri, A., Artoni, F., Crack paths in soft thin sheets, Frattura ed Integrità Strutturale, 48 (2019) 1 -9.

Received: 15.10.2018 Accepted: 06.01.2019 Published: 01.04.2019

Copyright: © 2019 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

oft materials such as rubbers, elastomers, gels, foams, granular and many biological materials are usually prone to easily deform, leading to a highly nonlinear response under mechanical actions [1, 2]. On the other hand, the capability to modulate their toughness or viscosity has promoted a wide attention in advanced applications (from materials science to bioengineering) where such materials can be conveniently exploited to get smart and functional materials such as artificial muscles, active and self-morphing materials [3, 4]. Furthermore, highly deformable materials often exhibit a rate-dependent response [5, 6], and in some cases (such as for natural rubbers) when sufficiently stretched at room temperature, show a strain-induced crystallization inducing a change S

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

from an amorphous into a semicrystalline-like microstructural configuration due to the appearance of a highly oriented microstructure developing along the tensile direction [7]. The microstructure of polymer materials is fully amorphous and, at the molecular level, is formed by a three-dimensional network of polymer chains linked at several discrete points (cross-links). The mechanics of these materials depends on the relative interaction and motion of the entangled linear macromolecules; the physical-chemistry basis of such a class of materials has been firstly established by Paul J. Flory, P.G. de Gennes and L.R.G. Treloar [8-10], through their fundamental theoretical and experimental research work. Another key aspect of soft materials is their ability to withstand defects (such as cracks and notches) in presence of mechanical actions, without showing brittle failure [11, 12]; in the near tip region of a crack, the local large deformation induces a microstructure rearrangement (chains alignment) and promotes a change in the macroscopic shape of the defect. These mechanisms enhance a material strengthening-like mechanism, leading to a noticeable defect tolerance capability. In the present study, we consider the fracture behavior of highly deformable thin cracked sheets under tension. Experimental tests performed at various strain rates on pre-cracked soft rubber specimens are presented, and the experimentally observed crack paths are interpreted according to the crack tip stress field arising in the case of large deformations. The experimental outcomes show that, for cracks tested in Mode I, higher strain rates facilitate the development of a simple Mode I crack path, while lower strain rates can induce a mixed Mode in the first stage of the crack propagation. Moreover, during the loading process the appearance of new crack tips due to the Mode mixity has been observed as a consequence of the non- classical stress field existing around the crack tip. Tests have confirmed that the above described mechanical response in terms of crack path is not influenced by the initial crack size. typical way to measure the flaw tolerance of materials is through the determination of the fracture energy; experiments conducted on soft polymers indicated a strong rate and temperature dependency for such a fracture property because of the energy dissipation produced by viscoelasticity [13]. Some different approaches to explain the failure in rubber-like materials have been proposed; among them the so-called cavitation criterion assumes the presence of intrinsic small defects that lead to failure under a sufficiently large hydrostatic stress state provoking void expansion and coalescence [14]. On the other hand, within the classical fracture mechanics approach, the near crack tip stress field governs the local failure of the material in terms of chains failure and growth of small existing microdefects and voids. Because of the high deformation capability of this class of materials, the classical Linear Elastic Fracture Mechanics (LEFM) approach - valid for infinitesimal strains - is not applicable anymore, and the large displacement effects must be accounted for instead. Further, the isochoric (incompressible) deformation process, typically shown by polymers, must be also considered in the determination of the singular stress field induced by a crack [15, 16]. In Fig. 1 the geometry of the considered cracked plate is shown; the global reference coordinate system , X Y and the crack tip reference coordinates 1 2 , x x are depicted in Fig. 1a, while the current (deformed) crack tip coordinates are indicated with 1 2 , y y (Fig. 1b). Note that the crack tip moves from the initial position o to the current one ' o . Formulation of the problem in large deformation In the reference coordinate system 1 2 , x x , the equilibrium equations in absence of body forces and the traction-free boundary conditions are / 0 ij j P x    , , 1, 2  i j  , 22 12 ( 0, π) ( 0, π) 0 P r P r           (1) where the nominal stress tensor P (Piola stress) has been used, while the true stress referred to the current deformed configuration (Cauchy stress σ ) is related to the nominal Piola stress through the relationship 1 T J   σ PF , / ij ij i j F u x       F being the deformation gradient tensor of the displacement i u and det J  F being the volume variation which, for an incompressible material, must be equal to 1. A C RACK TIP STRESS FIELD IN HIGHLY DEFORMABLE MATERIALS

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

Figure 1 : Cracked plate: main geometrical sizes and reference systems in the (a) undeformed and (b) deformed configuration.

Constitutive models Constitutive models for polymers are usually defined in terms of the strain energy function ˆ  ; several models suitable for rubber-like materials have been proposed in the literature. Among them, the well-known neo-Hookean, Gent and Ogden models can be mentioned [17]. In particular, the following energy expression   r  for the deformation of a single chain is assumed by the neo-Hookean model, and the strain energy density follows the Gent model, respectively:

 

 

B k T

E

J

3

  1 J   ˆ

  r

2

1  







r

J

,       

ln 1

(2)

m

2

J

6

Nb

2

m

where B k is the Boltzmann constant and T the absolute temperature. Further, N is the number of Kuhn’s segments in a single polymer chain and b is their length, whereas E is the small strain Young modulus, 1 1 3 J I   is a stretch invariant, and m J is the limit value of 1 J . The energy per unit volume of the material  can be obtained from the following relationship:     Ω Ω ˆ d      r r (3)

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

where  3 Ω    r indicates the chain configuration space and    r is the chains’ end-to-end distance distribution function, i.e. it provides the number of chains per unit volume whose end-to-end distance is comprised between r and d  r r . Once the energy function is known, the nominal stress tensor can be obtained from the strain energy as 

ˆ

    F F

    r 

  r d p t J  Ω

Ω 



T

P

F

 



(4)

where p is the hydrostatic pressure, introduced as a Lagrange multiplier to enforce the incompressibility condition herein assumed for the polymer as usually observed for this class of materials, being det 1 J   F . The above expression(3), in the case of the standard Gaussian distribution   r  of r (typically adopted in rubber elasticity), leads to   1 3 / 2 I     , where 2 2 2 1 1 2 3 I       , is the first invariant of the right Cauchy-Green deformation tensor T  C F F ,  is the small strain shear modulus and 1 2 3 , ,    are the three stretches along the Cartesian directions. An energy expression valid for large strains of a single chain  is the one proposed by Kuhn, namely   ln sinh B r Nk T r bN              , where 1 1 r bN N                     , 1   is the inverse Langevin function, while b , N and  are the Kuhn’s segment length, the number of segments per chain and the chain stretch, respectively. Crack tip stress field It is well-known that, in a 2D problem, the Mode I crack tip stress field within the LEFM hypothesis is expressed by: hypothesis, the nominal ( ij  ) tensor components are identical. Within the LEFM, the stresses are linear function of strain, and can be superimposed. Further, all the stress components have the same inverse square root singularity for the three deformation modes (Mode I, Mode II and Mode III). Within the large displacement field context, Knowles and Sternberg [18] performed the crack-tip asymptotic analysis through a series expansion of the deformed coordinates, consisting of separable functions of the polar coordinates ( , r  ) in the undeformed material, in a way similar to the William’s expansion approach in LEFM [19]. The crack tip stress field under large deformation results to be quite different from the one valid in the LEFM hypothesis and depends upon the constitutive model in turn; such a problem has been solved applying the asymptotic analysis method [20] by writing the crack tip deformed coordinates, 1 2 , y y , with respect to the undeformed material coordinate system, 1 2 , x x , through a series of separable functions of the polar coordinates , r  (Fig. 1). It can be shown that, under large deformation the true (Cauchy) stress components for a neo-Hookean incompressible material are given by P ) and true stress ( ij    I . . . 2π ij ij    ij K P f h o t r  , , 1,2 i j  (5) where   ij f  is an angular function, I K is the Mode I Stress-Intensity Factor (SIF) and, thanks to the small deformation







  , r 

  , r 



2 1 

2

1/2



21    











C

ACr

A r

(6)

,   

sin ,   

11

12

22

2

2

4

where , A C are unknown positive amplitudes depending on loading and geometry of the configuration being examined, and the pressure field required to enforce the incompressibility condition (usually assumed for polymeric materials since they can undergo only isochoric deformations) turns out to be 1 1/2 2 cos 2 p CA r      . The stress field is thus governed by these two parameters instead of the only one (the SIF, I K ) needed in the LEFM. From Eq. (6) it is evident that, differently from the LEFM case, the singularity of the opening stress component 22  is different from the singularity of the shear stress component 12  as r approaches the crack tip.

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

The knowledge of the kinematic relationship between deformed and reference configuration,

[20], allows to express the true stress components in terms of the polar coordinates ( ,   )

y cr 

y a r  

sin / 2 

cos , 

1

2

in the deformed (current) configuration (Fig. 1b, Fig. 2). Along the deformed upper parabolic crack profile, the true stress components are:





π 2

π

  

  

  

 

1    , 

4 2 

2

2 A C









,  

,  









  

 



C

A

,  

,  

0

(7)

11

12

21

22

4

2 8 

where only the singular terms have been reported and the relationship has been considered due to the fact that the deformed crack profile at the crack tip becomes parallel to the vertical axis (the tangent to the parabolic profile is vertical) [20]. / 2   

(a)

(b)

Figure 2 : (a) Undeformed cracked plate and deformed configuration with the related reference systems. (b) Crack tip detail of the stress field. In large deformation, the singularity of the true stress 22  is sharper along the 2 y axis than along the 1 y axis.

Expected crack path in large deformation From Eqs (6),(7) it can be remarked that the stress component 22

 along the deformed parabolic crack profile (

π / 2   )

has a singularity -2 (i.e. 0   ). This different singularity can trigger the appearance of a secondary crack, departing from the blunted deformed one (crack tip splitting), leading to a tortuous crack path or to a rough crack profile. In other words, the singularity of the true stress 22  is sharper along the 2 y axis than along the 1 y one (see Fig. 2); thus the material tends easily to break apart close to the crack tip along 2 y , leading to the appearance of secondary cracks, responsible for curved crack paths. 2   ), while the same stress component has a singularity -1 (i.e. 1 r  ) ahead of the crack tip (

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

Finally, the rate-dependence of failure in elastomers is a well-known phenomenon and has been explained through the internal energy dissipation mechanism by assuming that the chains bond lifetime depends on the applied stress level  [21]. A slower strain rate allows the material to easily flow in time, while a faster rate entails a more elastic behavior. The experimental outcomes have shown that the crack branching easily occurs for slower strain rates.

E XPERIMENTAL TESTS

T

he mechanical response under tension of a pre-cracked elastomeric sheet, made of a common silicone polymer, has been experimentally investigated. The evolution of the deformation and of the crack path have been controlled and monitored through the “contact-free” Digital Image Correlation (DIC) measurement technique. The specimens, having width equal to W = 112 mm, are characterized by an initial elastic modulus of about 1.12 MPa E  and Poisson’s ratio 0.42   , whereas samples’ geometric characteristics are shown in Tab.1. The ratio 2 / L W is assumed to be sufficiently high to ensure a uniaxial stress state in the central part of the sample, by limiting the boundary effects. The dimensionless small deformation stress intensity factors   * I I ,0 / π  y K K a   are also reported in Tab. 1. The tests have been conducted by applying a controlled displacement to the edge of the plate placed at Y L   , while the other has been kept fixed; three different strain rates have been adopted, namely: 3 1 1 9.615 10 s       , 3 1 2 5.769 10 s       and 4 1 3 1.603 10 s       (   / 2 d L     , d  being the applied displacement rate), in order to investigate the effect of the deformation velocity on the mechanical response of the cracked plates.

2 / a W (---)

Spec. No.

2 a (mm)

t (mm)

* I K (---)

C2a C2b C2c C3a C3b C3c C4a C4b C4c

20 20 20 30 30 30 40 40 40

2.75 2.85 2.75 3.00 3.00 2.60 2.75 1.80 2.00

0.179 0.179 0.179 0.268 0.268 0.268 0.357 0.357 0.357

1.019 1.019 1.019 1.045 1.045 1.045 1.084 1.084 1.084

Table 1 : Geometric characteristics of the tested specimens and related dimensionless SIF, * I b, c) refers to plates with different crack lengths tested at strain rates: α = a, strain rate 1

K . The symbol Cnα (n = 2, 3, 4, 5; α = a,

  ; α = b, strain rate 2

  ; α = c, strain rate 3   .

The true stress vs stretch behavior of the examined material under tension is reported in Fig. 3a; the true stress has been obtained from the nominal stress by exploiting the incompressibility assumption. Both the neo-Hookean model and the Gent model are also reported to underline which is the best fitting theoretical model. In Fig. 3b, the variation of the Poisson’s ratio measured experimentally vs the stretch value and the corresponding curve for a perfectly incompressible material are displayed; in particular, the theoretical Poisson’s ratio vs stretch for an isochoric deformation is expressed as     1 2 1 / 1         [22]. From the above-mentioned mechanical tests, it can be concluded that the material behaves very close to the predictions deduced according to the Gent model, and is nearly incompressible. From the tested material, the mechanical parameters have been found to be 1.5MPa E  and 2.35 m J  .

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

Figure 3 : (a) True stress vs stretch for the examined material. (b) Variation of the Poisson’s ratio with the deformation. Experimental and theoretical values are reported. In Fig. 4 the crack tip splitting phenomenon is shown at the incipient failure for the specimens C2b, C3b and C4b, while the whole crack paths after failure are depicted in Fig. 4 for the three strain rates adopted, 1   , 2   , 3   .

(a)

(b)

(c)

Figure 4 : Crack tip splitting at the incipient failure for specimens (a) C2b, (b) C3b and (c) C4b.

a =10 mm

(a) 1  

(b) 2  

(c) 3  

a =15 mm

(f) 3  

(e) 2  

(d) 1  

a =20 mm

(g) 1   (i) 3   Figure 5 : Crack paths for specimens (a) C2a, (b) C2b, (c) C2c, (d) C3a, (e) C3b, (f) C3c, (g) C4a, (h) C4b and (i) C4c (only half of each specimen corresponding to 0 Y  , see Fig. 1, is shown). The initial crack (blue straight line) grows as is indicated by the red line. (h) 2  

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R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01

Fig. 5 shows the crack paths obtained for the different cracked samples by changing the initial crack length 2 20,30,40mm a  and the applied strain rate (only half of the specimen is shown). It can be appreciated that the resulting crack paths, observed after the final failure of the specimen, are only slightly influenced by the initial crack size, while the strain rate plays a crucial role. It’s worth noting that, because of the testing imperfections, the final failure pattern in the specimens usually appeared to be symmetric with respect to the Y axis, while in some cases the crack propagated only in one side of the sheet. In these latter cases, only the cracks half of the specimens have been shown (Fig. 5). The observed results allow us to obtain a physical interpretation to the way how the crack behaves: under a fast deformation, the material behaves in an elastic way, so that the theoretical stress singularities shown in Eq. (6) are fulfilled. On the other hand, a low strain rate allows the material to damage locally in preferential directions, according to the severity of the stress component singularity, leading to a more marked crack kinking. In this case, the crack initially tends to propagate practically in almost pure Mode II, i.e. in a direction normal to the crack line. From the crack tip stress field viewpoint (see Eqs (6), (7) ), when the material deforms elastically – such as in the small deformation regime – the stress component 22  along the deformed parabolic crack profile ( π / 2   ) is more singular ( 2   ) than along the crack symmetry axis ( 0   , 1 r  ). This fact justifies the crack tip split taking place at the crack tip at the very early stage of the deformation process. The numerical analysis reported in Krishnan et al. [23] shows that a concentration of shear deformation exists near the crack tips, especially when the material display a less pronounced strain hardening behavior, such as happens in the case of low strain rates. This justifies the more evident persistence of the Mode II deformation in cases where the material is subjected to low strain rates (Fig. 5c, f, i) with respect to the cases characterized by high strain rates (Fig. 5a, d, g). n the present paper, the crack behavior of soft cracked plates has been examined. The crack tip stress field under large displacements as well as the rate-dependent behavior have been considered. The remarkable result from the literature that the singularity of the true stress in large deformation is quite different from the one according to the LEFM theory has been adopted. Moreover, the different order of singularity of the stress components in large deformation gives rise to crack tip splitting and, consequently, curved crack paths develop even under remote pure Mode I loading. This behavior is enhanced at slow strain rates (see the curved crack paths in Fig. 3c, f, i), while faster strain rates have a lower effect in terms of promoting such a weird crack growth (see Fig. 3a, d, g). In fact, because of the existence of the strain rate effect that typically arises in this class of materials, the purely linear behavior is recovered only when the strain rate is sufficiently small, while a more severe crack tilting is observed (with a consequent curved crack path) thanks to the more pronounced damage arising locally in preferential directions according to the severity of the stress component singularity. In the latter case, the crack tends to propagate seemingly in pure Mode II, i.e. in a direction almost normal to the crack line. Moreover, the observed crack paths deviate from the pure Mode I propagation irrespective of the initial crack length. The experimental results have shown that the crack tip singular stress field arising in highly deformable materials can lead to complex curved crack paths which cannot be predicted by using the standard LEFM approach. [1] Treloar, L.R.G. (1975). Physics of Rubber Elasticity, Oxford University Press . [2] Doi, M. (2013). Soft Matter Physics. Oxford: Oxford Univ. Press. [3] Chen, D., Yoon, J., Chandra, D., Crosby, A.J., Hayward, R.C. (2014). Stimuli-responsive buckling mechanics of polymer films. J. Polym. Sci., part B: Pol. Phys, 52, pp. 1441–1461. DOI: 10.1002/polb.23590. [4] Roland, C.M. (2006). Mechanical behavior of rubber at high strain rates. Rubber Chem. Tech., 79(3), pp. 429–459. DOI: 10.5254/1.3547945. [5] Bergström, J.S., Boyce, M.C. (2016). Constitutive modelling of the large strain time-dependent behaviour of elastomers. J. Mech. Phys. Sol., 46, pp. 931–954. DOI: 10.1016/S0022-5096(97)00075-6. [6] Brighenti, R., Vernerey, F.J., Artoni, F. (2017). Rate-dependent failure mechanism of elastomers. J. Mech. Sci., 130, pp. 448–457. DOI: 10.1016/j.ijmecsci.2017.05.033. [7] Candau, N., Laghmach, R., Chazeau, L., Chenal, J-M., Gauthier, C., Biben, T., Munch, E. (2014). Strain-induced crystallization of natural rubber and cross-link densities heterogeneities. Macromolecules, 47(16), pp. 5815–5824. DOI:10.1021/ma5006843. I C ONCLUSIONS R EFERENCES

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