Issue 59

Frattura ed Integrità Strutturale, 59 (2022); International Journal of the Italian Group of Fracture

Table of Contents R. Fincato, S. Tsutsumi https://youtu.be/oy5Pl_PjVRs Ductile fracture modeling of metallic materials: a short review ……………………………... 1-17 S. Meriem, N. Djamel, B. Djilali, S. Khatir, M. Abdel Wahab https://youtu.be/ChoC2q7ncQM Crack prediction in beam-like structure using ANN based on frequency analysis …………… 18-34 A. Behtani, S. Tiachacht, T. Khatir, S. Khatir, M. Abdel Wahab, B. Benaissa, M. Slimani https://youtu.be/23QmYy-OzD8 Residual Force Method for damage identification in a laminated composite plate with different boundary conditions ………………………………………………………………….. 35-48 Z. Xia, X. Duan https://youtu.be/WIOvobS5BJo Analysis of the bond-slip performance of steel bars and steel fiber recycled concrete based on the constitutive relationship model .………………………………………………………… 49-61 Finite element modeling of flexural behavior of reinforced concrete beams externally strengthened with CFRP sheets … ………………………………………………………………... 62-77 N. Ekabote, K. G. Kodancha, P. P. Revankar https://youtu.be/_4ebbmQNLYs Elastic-plastic fracture analysis of anisotropy effect on AA2050-T84 alloy at different temperatures: a numerical study ……………………………………………………….. 78-88 P. Munafò, F. Marchione, G. Chiappini, M. Marchini https://youtu.be/dPawPvwAwrE Effect of nylon fabric reinforcement on the mechanical performance of adhesive joints made between glass and GFRP …………………...………………………………………………... 89-104 J. L. González-Velázquez, E. Entezari, J. A. Szpunar https://youtu.be/uN6Auk1uHIQ On the Assessment of non-metallic inclusions by part 13 of API 579 -1/ASME FFS-1 2016 105-114 Yu. G. Matvienko , S. I. Eleonsky, V.S. Pisarev, M.D. Zajtsev https://youtu.be/Y_sTJJY0aZI Damage accumulation near the cold-expanded hole due to high-cycle fatigue by crack compliance method ……………………………………………………………………………... 115-128 M. Madqour, H. Hassan, K. Fawzy https://youtu.be/fsvMDDevrec

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Fracture and Structural Integrity, 59 (2022); ISSN 1971-9883

H. Rezzag, L. Kahloul, H. Chadli, A. Mebrek, A. Saoudi https://youtu.be/ftfvS3IF6V4 Tribological performance and corrosion behavior of CoCrMo alloy ………..………………… 129-140 T. Sang-To, H.-L. Minh, T.-T. Danh, S. Khatir, M. A. Wahab, T. Cuong-Le https://youtu.be/xd_S9i1sCdM Combination of Intermittent Search Strategy and an Improve Particle Swarm Optimization algorithm (IPSO) for model updating .......................................................................................... 141-152 N. Kouider, Y. Hadidane, M. Benzerara https://youtu.be/d5fSQYrdDQM Numerical investigation of the cold-formed I-beams bending strength with different web shapes …. 153-171 T.-H. Nguyen, A.-T. Vu https://youtu.be/KejsDoE45bI Weight optimization of steel lattice transmission towers based on Differential Evolution and machine learning classification technique ……………………………………………….... 172-187 T.-K. Nguyen, T.-T. Vo, N.-H. Nguyen https://youtu.be/8cHjpaVhltE Discrete-element modeling of strain localization in a dense and highly coordinated periodic granular assembly …………………………………………………………………… 188-197 H.A. Mobaraki, R.-A. Jafari-Talookolaei, P.S. Valvo, R. Haghani https://youtu.be/npteD1PABPg Forced vibration analysis of laminated composite plates under the action of a moving vehicle …… 198-211 A. Houari, A.S. Bouchikhi, M. Mokhtari , K. Madani https://youtu.be/KnTyoTSeWQk Numerical analysis of the elastic-plastic behavior of a tubular structure in FGM under pressure and defect presence ….................................................................................................................. 212-231 T. Cuong-Le, H.-L. Minh, T. Sang-To https://youtu.be/2uQYvnhmwhA A nonlinear concrete damaged plasticity model for simulation reinforced concrete structures using ABAQUS ………………………………………………………………………… 232-242 N. Amoura, H. Hocine, A. Benzerdjeb https://youtu.be/mHpWgtvesgU 3D crack identification using the Nelder-Mead Simplex algorithm combined with a random generation of crack positions …………………………………………………………... 243-255 A-T. Vu, N-D. Han, D-H.Nguyen, T-K Nguyen, https://youtu.be/zKS09c5PVpI The influences of the number of concrete dowels to shear resistance based on push out tests …….... 254-264

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Frattura ed Integrità Strutturale, 59 (2022); International Journal of the Italian Group of Fracture

A. Cao, A.A. Sipos https://youtu.be/rHrnffLVzRY Cracking patterns of brittle hemispherical domes: an experimental study …………………….. 265-310 S. Smirnov, D. Konovalov, I. Veretennikova, A. Pestov, V. Osipova https://youtu.be/YaiHjd44ILQ Effect of the stress state on the adhesive strength of an epoxy-bonded assembly ………………... 311-325 J. W. S. Brito, L. F. F. Miguel https://youtu.be/Re9zARD1d3s Optimization of a reinforced concrete structure subjected to dynamic wind action …………….... 326-343 O. Rahim, D. Achoura, M. Benzerara, C. Bascoulès-Perlot https://youtu.be/-XU_IDapYkA Experimental contribution to the study of the physic-mechanical behavior and durability of high- performance concretes based on ternary binder (cement, silica fume and granulated blast furnace slag) ……………………………………………………………………………….. 344-358 C. Mallor, S. Calvo, J.L. Núñez, R. Rodríguez-Barrachina, A. Landaberea https://youtu.be/0Dubv-ac1T8 A probabilistic fatigue crack growth life approach to the definition of inspection intervals for railway axles ………………………………………………………………………... 359-373 S. Anouar, B. Zeineddine https://youtu.be/DrIrchPhi90 Reinforced soft soil by CSV with/without polypropylene fiber: experimental and numerical analysis …………………………………………………………………………….. 374-395 H. Nykyforchyn, O. Zvirko, M. Hredil, H. Krechkovska, O. Tsyrulnyk, O. Student, L. Unigovskyi https://youtu.be/tn0n4TjWoPk Methodology of hydrogen embrittlement study of long-term operated natural gas distribution pipeline steels caused by hydrogen transport .....……………….…………………………... 396-404 S. K. Kourkoulis, C. F. Markides, E. D. Pasiou, A. Loukidis, D. Triantis https://youtu.be/p8BWx0005AU The critical influence of some “tiny” geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length …………………………………………..……. 405-422 M. Shariyat https://youtu.be/eLJJMe2qB8o Novel 2D strain-rate-dependent lamina-based and RVE/phase-based progressive fatigue damage criteria for randomly loaded multi-layer fiber-reinforced composites .………………...…..…… 423-443 M. Gaci, K. Fedaoui, L. Baroura, A. Talhi https://youtu.be/9eEHuZHQglg Numerical study of TRIP transformation in 35NCD16 steel-effects of plate orientation and some criteria ……………………………………………………………………………... 444-460

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Fracture and Structural Integrity, 59 (2022); ISSN 1971-9883

D. Bui-Ngoc, H. Nguyen-Tran, L. Nguyen-Ngoc, H. Tran-Ngoc, T. Bui-Tien, H. Tran-Viet https://youtu.be/dEjrGlr_lsw Damage detection in structural health monitoring using hybrid convolution neural network and recurrent neural network ……………………………………………….…………..…. 461-470 E. S. M. M. Soliman https://youtu.be/L7pXkKd_r7I Mode I stress intensity factor with various crack types …………………………………….. 471-485 M.A.R. Elmahdy, A.A. ELShami, E.-S. M. Yousry, S. S. E. Ahmad https://youtu.be/EIQw0dtEskI Self-healing mortar using different types, content, and concentrations of bacteria to repair cracks ... 486-513 L. Malíková, P. Miarka, S. Seitl, P. Doubek https://youtu.be/PMu50kluR_s Influence of the interphase between laser-cladded metal layer and steel substrate on the fatigue propagation of a short edge crack ……………………………………………………..... 514-524 G. Risitano https://youtu.be/-nJqyxwPO54 Fatigue strength evaluation of PPGF35 by energy approach during mechanical tests ………....... 537-548 F. M. F. Agag, S. S. E. Ahmad, H. E. M. Sallam https://youtu.be/jUOtipI2Nx8 Experimental assessment of different strengthening techniques for opening in reinforced concrete beams .……….......................................................................................................................... 549-565 T. Djedid, M. Mani, A. Guettala, A. Hima https://youtu.be/J6gURLx4gm0 Analysis of workability, mechanical strength and durability by the FT-IR method of concrete based on silica-limestone sand preserved in aggressive environments …………………….......... 566-579 T. Djedid, M. Mani, A. Ouakouak, A. Guetttala https://youtu.be/f_P15iNZMVk Effect of varying silica-limestone sand fines on the physical-mechanical performance of concrete ….. 580-591 D. Rigon, F. Berto, G. Meneghetti https://youtu.be/ISaoCOHFE_Y Crack paths in multiaxial fatigue of C45 steel specimens and correlation of lifetime with the thermal energy dissipation ........................................................................................................... 525-536

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Frattura ed Integrità Strutturale, 59 (2022); 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 Sara Bagherifard

(Politecnico di Milano, Italy) (Politecnico di Milano, Italy) (University of Porto, Portugal) (University of Belgrade, Serbia)

Marco Boniardi

José A.F.O. Correia

Milos Djukic

Stavros Kourkoulis

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

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal) (Chinese Academy of Sciences, China)

Guian Qian

Aleksandar Sedmak Sabrina Vantadori

(University of Belgrade, Serbia) (Università di Parma, Italy)

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 Cetin Morris Sonsino

(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)

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)

(RMIT University, Aerospace and Aviation department, Australia)

Raj Das

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)

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Fracture and Structural Integrity, 59 (2022); ISSN 1971-9883

Antonio Martin-Meizoso Mohammed Hadj Meliani

(Tecnun Universidad de Navarra, Spain)

(LPTPM , Hassiba Benbouali University of Chlef. Algeria) (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 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 Mohammad Azadi Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia) ( Faculty of Mechanical Engineering, Semnan University, Iran)

(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)

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

(Universitat Politecnica de Valencia, Spain) (Université-MCM- Souk Ahras, Algeria) (Middle East Technical University, Turkey) (Hassiba Benbouali University of Chlef, Algeria)

Abdelmoumene Guedri

Ercan Gürses

Abdelkader Hocine

Ali Javili

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

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk

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

(Wroclaw University of Science and Technology, Poland)

Paolo Lonetti

(Università della Calabria, Italy)

Tomasz Machniewicz

(AGH University of Science and Technology)

Carmine Maletta

(Università della Calabria, Italy)

Fatima Majid Sonia Marfia

(University Chouaib Doukkali, El jadida, Morocco) (Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

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

Hisao Matsunaga Milos Milosevic Pedro Moreira

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

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)

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Frattura ed Integrità Strutturale, 59 (2022); International Journal of the Italian Group of Fracture

(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 Zoran Radakovi ć D. Mallikarjuna Reddy

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

(University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India)

Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Padova, Italy) (Università di Brescia, Italy)

Elio Sacco

(Università di Napoli "Federico II")

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 Marta S ł owik Cihan Teko ğ lu Dimos Triantis

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

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

Paolo Sebastiano Valvo Natalya D. Vaysfel'd

(Università di Pisa, Italy)

(Odessa National Mechnikov University, Ukraine)

Charles V. White Shun-Peng Zhu

(Kettering University, Michigan,USA)

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

Special Issue

Steels and Composites for Engineering Structures

Roberto Capozucca

(Polytechnic University of Marche, Italy)

(Ghent University, Belgium)

Samir Khatir

Cuong Le Thanh

(Ho Chi Minh City Open University, Vietnam) (Lublin University of Technology, Poland)

Marta S ł owik

IGF26 - 26th International Conference on Fracture and Structural Integrity

Special Issue Sara Bagherifard Chiara Bertolin Luciana Restuccia Sabrina Vantadori

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway)

(Politecnico di Torino, Italy) (Uiversità di Parma, Italy)

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Fracture and Structural Integrity, 59 (2022); ISSN 1971-9883

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

Sister Associations help the journal managing Algeria: Algerian Association on Fracture Mechanics and Energy -AGFME 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 Group of Fatigue and Fracture Mechanics of Materials and Structures

Poland:

Portugal: Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia:

Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF

Spain: Turkey: Ukraine:

Turkish Solid Mechanics Group

Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Frattura ed Integrità Strutturale, 59 (2022); 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, 59 (2022); ISSN 1971-9883

FIS news

D

ear friends, being this the first issue of the new year, we wish to show you a report of our activities in the last years. In the following table, you find some details about the submission received, the accepted ones etc.

2021

2020

2019

2018

Submissions received Submissions accepted Submission declined

365 116 233 164

210 103 133

311 224 117

273 119

94 38 56

Submissions Declined (Desk Reject) Submissions Declined (After Review)

71 62

72 45

69 78 64 11 1

Submissions Published

109

235

105

Days to First Editorial Decision

1

2

3

Days to Accept Days to Reject Acceptance Rate Rejection Rate Desk Reject Rate

81 42

87 53

89 38

33% 67% 48% 19%

42% 58% 34% 24%

60% 40% 23% 17%

64% 36% 14%

After Review Reject Rate 23% Our effort to improve the journal is quite evident. In the last four years, the submissions increased (now we are near to 400 per year!), the days to first editorial decision decreased from 3 to 1 day, the days to accept decreased from 89 to 64, the days to reject decreased from 38 to 11 and the rejection rate increased from 36% to 67%. All these numbers confirm the effort of our community to improve our journal. These great results are only due to the continuous efforts of our Section Editors, of the Editorial Board Members, of all the Reviewers and, last but not least, of all the Authors! Now, in order to further improve the visibility of our journal, and of all the papers, it is necessary the contribution of all of you. The editorial world is really competitive and, in order to improve the “value” of the papers, it is important that some “numbers” are high. For example, considering CiteScore, FIS value continuously improved from 0.2 in 2013 to 2.0 in 2020. Now, the perspective value in 2021 is 2.3, but we can further improve this value… if you find in “Frattura ed Integrità Strutturale” a paper of your interest, do not hesitate to add it in your References! Q2 is near and it is a possible goal for 2022! … and after that … why not a Q1? I wish you and your families a happy 2022 … better than the last two years! Ciao!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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R. Fincato et alii, Frattura ed Integrità Strutturale, 59 (2022) 1-17; DOI: 10.3221/IGF-ESIS.59.01

Ductile fracture modeling of metallic materials: a short review

Riccardo Fincato, Seiichiro Tsutsumi University of Osaka, JWRI, Japan

fincato@jwri.osaka-u.ac.jp, http://orcid.org/ 0000-0003-4058-0460 tsutsumi@jwri.osaka-u.ac.jp, http://orcid.org/ 0000-0002-9279-0657

A BSTRACT . Since the end of the last century a lot of research on ductile damage and fracture process has been carried out. The interest and the attention on the topic are due to several aspects. The margin to reduce the costs of production or maintenance can be still improved by a better knowledge of the ductile failure, leading to the necessity to overcome traditional approaches. New materials or technologies introduced in the industrial market require new strategies and approaches to model the metal behavior. In particular, the increase of the computational power together with the use of finite elements (FE), extended finite elements (X-FE), discrete elements (DE) methods need the formulation of constitutive models capable of describing accurately the physical phenomenon of the damaging process. Therefore, the recent development of novel constitutive models and damage criteria. This work offers an overview on the current state of the art in non- linear deformation and damaging process reviewing the main constitutive models and their numerical applications. K EYWORDS . Ductile damage; Finite element method; Experimental characterization; Numerical modeling.

Citation: Fincato, R., Tsutsumi, S., Ductile fracture modelling of metallic materials: a short review, Frattura ed Integrità Strutturale, 59 (2022) 1-17.

Received: 04.10.2021 Accepted: 09.10.2021 Published: 01.01.2022

Copyright: © 2022 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

he generation of large inelastic deformations accompanied by the progressive degradation of mechanical properties, and finally by the material failure, is a relevant topic in many competitive industrial sectors (automotive, construction, naval, etc.). An underestimation of the material capability of bearing loads, or an incorrect design of components can lead to a catastrophic outcome with severe consequences in terms of lives or economic impact. The understanding of the damaging process has a key role under several aspects. Firstly, the prediction of the failure mechanism can lead to a better design of components and structure, with a consistent reduction in the costs production and, more importantly, in maintenance costs. It can help the development and use of new materials and technologies, especially in applications linked to emerging industrial sectors such as biomedical, robotics, and aerospace. Lastly, recent experimental investigations on non-linear deformations and rapture under various loading/boundary conditions provide useful information for the development of constitutive models or empirical formulas for the description of the damage processes. T

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R. Fincato et alii, Frattura ed Integrità Strutturale, 59 (2022) 1-17; DOI: 10.3221/IGF-ESIS.59.01

In particular, the increase of the computational power incentivized the theoretical research on mechanical models on ductile damage thanks to their implementation in in-house or commercial software based on the finite element (FE) or discrete elements (DE) methods. The great interest around numerical simulations derives from the possibility of conducting parametric studies on components, varying geometrical features, or loading conditions without additional experimental costs. Numerical codes can be applied for the simulation of the service life of large structures such as bridges, skyscrapers, ships, for which full-scale experimental approaches would be unfeasible or too costly. Moreover, experimental campaigns on cyclic loading or low cycle fatigue (LCF) problems can require a considerable time, especially if the investigations are applied to several specimens. FE or DE simulations can speed up the computation process and can be applied on several problems [1–4]. The continuous development of robust damage and fracture models represented, and still represents, an essential point to obtain a more realistic description of the material behavior. On the other hand, since the pioneering works on ductile damage in the second half of the last century, several researchers developed alternative theories for the description of the phenomenon. The present work aims to offer an overview on the current state of the art, pointing out the different aspects that characterize the main constitutive models. The reader should keep in mind that a detailed description of all the existing models is unrealistic since the literature on the topic is quite vast. For the same reason the authors did not report the constitutive equations of the models discussed, the reader is referred to the referenced literature for a in depth description of single theories. The paper is organized as follows. Initially, a brief introduction deals with the definition of the nature of the damage. The experimental characterization of the damaging process is discussed, describing some of the current measuring techniques. Subsequently, an overview of the available models for the damage description, and a discussion of the main aspects of each theory, is offered together with references of recent applications. Finally, some computational aspects are presented.  Ductile fracture. This type of fracture is accompanied by a large amount of irreversible deformations that alter the geometry or shape of the components (i.e. necking, shear bands, etc.). The process is generally triggered by the presence of internal material defects (voids, inclusions) around which a stress localization induces crystallographic slips and the progressive decohesion at the interface between the inclusion and the matrix. Alternatively, the inclusion can break under the effect of the surrounding stress fields. Ductile fracture is characterized by internal micro-cracks formation, driven by high stress triaxialities (see Fig. 1a). The progressive application of the load increases the number and volume of voids and decohesion around defects until their coalescence into a macroscopic crack that quickly propagates until the material failure. In case of low stress triaxiality three failure mechanisms can be observed. In the first, the void nucleation tends to take place in a shear band (see Fig. 1b). The subsequent elongation of the voids induced by shear strain leads to their coalescence and finally to the macroscopic rapture. The second one is named ‘void sheeting’ where the void nucleation takes place in multiple shear plane that coalesce under shear straining (see Fig. 1c). Finally, the so- called Orowan alternating slip mechanism (OAS). The void nucleation and subsequent coalescence takes place into two intersecting shear bands forming a prismatic cavity at the core of the material (see Fig. 1d). An exhaustive explanation of the different mechanisms is offered in [7]. Ductile rapture is typical of loading conditions that induce a non-negligible amount of plastic deformations, including cyclic mobility and low cycle fatigue (LCF) problems [8–10].  Low Ductility fracture (often referred as brittle fracture). The type of fracture that belongs to this category is characterized by the formation of cavities between grain boundaries. The cause for these micro-cracks formation can be due to accumulation of dislocation, low melting-point impurity phases or concentration of impurity elements (e.g. V-group elements in steels, Bi and Pb in coppers). In particular the presence of impurities is known to promote embrittlement [11,12]. The number and size of cavities increase under the effect of the load on the structure or component and the effect of the temperature. The coalescence of the cavities leads to break some grain boundaries, causing a brittle fracture which can propagates or influence the macro-crack formation and material failure (see Fig. B D AMAGE DEFINITIONS efore dealing with the experimental characterization and the numerical modeling of the damage phenomenon it is necessary to point out some different mechanisms that lead to the formation of macro cracks. In fact, even if the outcome of the process is the material failure, the causes for initiation and the evolution of the phenomena are quite different depending on the loading and boundary conditions. Here, a brief description of the fracture processes is given, the reader is referred to [5,6] for an in-depth discussion. In summary, fracture can be distinguished in three mechanisms:

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2). Detailed information and few examples on numerical modeling of the low ductility fracture can be found in [13– 15].  Progressive fracture mechanisms (fatigue or creep). In case of fatigue mechanism, it has to be excluded the scenario where the metallic material fails under cyclic loading conditions after the generation of large plastic deformation (for instance in very low/ low cycle fatigue). In fact, in this case, the fracture mechanism belongs to the aforementioned ductile fracture. Fatigue fracture is characterized by three stages. Firstly, the crack nucleation takes place in persistent slip bands, close or at the free surface, with an inclination of 45° compared to the loading direction, along the crystallographic slip planes [16]. During the second stage the crack propagates along a plane, more or less, perpendicular to the pulling direction up to a point that the cross section cannot withstand the applied cyclic loading (see Fig. 3). Finally, the third stage consists in the ultimate crack propagation the rate of which is roughly half of the speed of sound in the material [17]. Recent works on fatigue fracture with some numerical applications can be found in [18–22]. Creep fracture is particularly relevant in components that operate at high temperatures (e.g., turbine, petrochemical or nuclear plants, etc.). In this case, creep progressively developed from nucleated intergranular void depending on the loading and heating conditions in the form of irreversible deformations. The evolution of plastic deformation is associated with the enlargement of the voids and their coalescence following three stages: primary, secondary and tertiary creep. After an initial increase of the creep rate during the primary stage a constant creep rate is reached and is kept throughout the second stage. During the tertiary creep a consistent increase of the creep rate is registered until failure. Few works on the topic of creep fracture are reported in [23–28]. The present paper focuses the attention in reviewing the first fracture process. In the following sections we will refer to a damage variable associated with the ductile fracture mechanism. In particular, it is important to point out that the characteristics that define the damage are substantially different from the ones proper of the deformation process. Damage itself consists in the rapture of bonds (atomic bonds between the matrix and defects, atomic bonds between atoms of the defects or the matrix), while elastic deformations are reversible variations of the atomic distances and plastic deformations account for the accumulation or movements of dislocations. Therefore, a new variable must be introduced to describe the damaging process, in addition to the standard variables (i.e., stress, elastic strain, plastic strain, etc.). This aspect will be discussed from a theoretical in the following section ‘theoretical damage characterization’. In the next section a more practical approach is introduced, giving some information about the experimental characterization of the damaging process.

Figure 1: Typical ductile fracture mechanism (simplified and redrawn version of Fig. 2 in [7]).

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Figure 2: Typical low ductility fracture.

Figure 3: Typical fatigue fracture.

E XPERIMENTAL DAMAGE CHARACTERIZATION

T

he measurement of the ductile damage in the ongoing of an experiment is a challenging aspect since the damage variable can hardly be measured directly such as other variables (i.e., total force, displacements, strain, geometrical variations, etc.). As mentioned before the damage variable gives an indication about the void formation and growth during the loading and, therefore, it is intrinsically associated with the development of internal cracks. Currently, there are several techniques that allow a more or less accurate measurement of the damage evolution. A very simple, however time-consuming technique, consists in cutting part of the sample to have a direct observation of the state of void formation. As it can be imagined, the damage evolution can be estimated by a series of tests, performed under the same conditions, where the cut and void observation is done at predefined stages of the loading sequence. A valid alternative is represented by hardness evaluation by means of indentation. This method consists in recording, throughout the experiment, the magnitude of the applied load and the indentation depth. By the technique proposed by Oliver and Pharr [29], the indentation measure can be correlated to the decrease of the elastic modulus and therefore to the measure of the damage evolution. This expedient can return very accurate values of the local damage and it can be used to evaluate the degradation in strain localization areas (i.e. necking, shear bands, etc.) [30,31]. The electrical resistance of the material can also be used to evaluate the resisting area and therefore to measure the level of damage in the material. The changes in electrical resistance measured during the material loading are mainly due to the generation of plastic deformations and damage. As shown in [30], it is possible to obtain a formula that relates the change in resistance with the evolution of the damage. The damage evaluation seems to be quite good and able to predict a realistic evolution. This last method was proposed by Lemaitre and Dufally [32] and used for the first time by Kumar et al. [33].

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Micrographic SEM pictures were mentioned by Lemaitre and Dufally [32] as a method to obtain the damage by the comparison of the area fraction that corresponds to voids to the total area observed. SEM picture can be used a posteriori to investigate the nature of the rapture (brittle, ductile, fatigue) [34] giving high resolution images of the damaged area. A recent work by Hutiu et al. [35] proposed the use of optical coherence tomography (OTC) to perform fracture analyses as a valid alternative to SEM pictures. Even though the images obtained with the OTC method are characterized by a much lower resolution of the SEM, the OTC low costs and portability of the equipment make this approach particularly suitable for in situ investigations. Recently transmission electron microscopy (TEM) has been used to investigate the deformation and fracture mechanisms of materials [36–38]. Thanks to the high-resolution and real-time imaging of this technique it was possible to observe several micro-scale and atomic-scale phenomena leading to the material failure (e.g., dislocation-dominated, twinning-dominated, mechanical annealing, phase transformation). Zhang et al. [39] proposed a methodology that adopts a microelectromechanical systems-based thermomechanical testing apparatus that enabled to observe the atomic-scale ductile mechanism in single crystal tungsten at high temperatures. This type of material is characterized by a brittle type of fracture at room temperature, but the failure mechanism shifts to ductile fracture with the increase of the temperature. The development of a custom-designed transmission electron microscope showed direct evidence of strain induced phase transformation at the crack tip that prevents the brittle fracture improving the ductility. X-ray micro-tomography can be also used to obtain the volume of the void [40]. One of the advantages of the use of the micro-tomography is the possibility to monitor the whole process from the micro-cracks formation, their growth, coalescence and final macro crack formation. In particular, several authors recurred to this technique for the estimation of the material parameters in numerical simulations. On the other side, micro-tomography requires specialized technicians for its application and it is characterized by high costs compared to other strategies [41–43]. Another technique, often referred in the literature as ultrasonic testing (UT) technique, consists in observing the response of the material to ultrasonic pulses, in order to evaluate the density of voids and internal defects. The difference of the ultrasonic pulse velocity of the sample before and during the experiment can be correlated to the damage evolution [44]. An interesting work by Chiantoni et al. [45] provides an interesting comparison between the micro-tomography and the UT methods for the assessment of the damage evolution in P91 steel at high temperature. It is concluded that both techniques are in good agreement in catching the damage evolution. However, micro-tomography can offer detailed pictures of the actual distribution of voids in the damage localized area, while UT gives an overall evolution of the damage variable in the sample. The lack of resolution of the UT is somehow compensated by the low costs and easy use of the ultrasonic equipment. The most common technique for the evaluation of the damage is the stiffness or elastic modulus reduction measurement as largely developed and adopted by Lemaitre and Dufally [32] and Bonora et al. [46]. Its application is quite simple, and it consists of a series of measurements of the effective elastic modulus during partial unloading of the sample. The decrease of the modulus can be associated with the progressive loss in the load-carrying capacity of the material caused by the void formation. This technique is quite easy to actuate, and it does not require the use of sophisticated equipment (i.e., SEM pictures, X-ray micro-tomography, ultrasonic pulse). Damage preliminaries and characterization of the stress state o describe the process that leads to the progressive degradation of the mechanical properties, it is important to understand the factors that influence the nucleation, growth, and coalescence of micro-voids in metallic materials. Firstly, it is worth mentioning that the growth of the cavities, defects, decohesion inside the material tends to be oriented by the macroscopic load that created them. This means that the variable that should be selected for the description of the process should have a tensorial nature (first, second or even fourth order tensors) or, at least, it should be able to take into account the shape and the orientations of the voids. However, for metallic materials, and in most of industrial applications, the adoption of an isotropic scalar variable can give satisfactory results. For sake of completeness, the reader is referred to [47,48] for examples of tensorial damage variables. Usually, the process discussed in the ‘ductile fracture’ bullet point of the previous section can be described by the addition of one, or more, internal variables in elastoplastic constitutive theories. This new variable, or variables, are responsible for describing the formation and progression of cracks until the complete failure of the material. Although the material degradation description depends on the selected constitutive model, a common aspect among several approaches is to T T HEORETICAL DAMAGE CHARACTERIZATION

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consider a variable (or variables) limited between two extremes (a scalar variable is assumed in Eq. (1) and generically indicated with D ):

  0 1 D non damaged material D material failure 

(1)

A D = 0 condition implies an undamaged material, without voids. A D = 1 condition characterizes the material failure. Often, in finite element analyses, a threshold value c D < 1 is used (e.g., [49–51]) to indicate the formation of a crack, or the material failure, in order to avoid numerical problems such as damage localization or convergence issues. These aspects are discussed later.

Figure 4: Typical dependency of the equivalent strain to fracture on the stress triaxiality.

An important aspect in the numerical modeling of the damaging process consisted, and still consists, in formulating a constitutive law for the description of the evolution of the D variable, from the non-damaged state until the final failure. In particular, the challenge is represented by formulating the simplest law that includes the main factors governing the void nucleation, growth and coalescence. The extensive experimental campaign conducted in the second half of the last century [52–58] pointed out the dependency of the damage process on a dimensionless stress parameters: the stress triaxiality  (e.g.,[59–63]). In fact, for metallic materials was found that the ductile fracture mechanism and final deformation to fracture (i.e., equivalent strain to fracture  f ) are strongly related to the magnitude of the stress triaxiality (Fig. 4). While the effect of the stress triaxiality has been initially incorporated in most of the constitutive models for the description of metal failure, the role of the Lode angle [59]  became evident later, when experiments under different loading conditions showed that the equivalent strain to fracture changes for different values of the Lode angle under the same stress triaxiality. The effect of the Lode angle is often taken into account by introducing the Lode angle parameter  (e.g., [59–66]), a dimensionless scalar variable that assumes values between -1 and +1 (-1 in case of compression, 0 in case of shear or plane stress condition and +1 for tension), see Fig. 5. Most of the recent constitutive models account for damage evolution laws that consider the effects of both stress triaxiality and Lode angle parameters. Ductile damage models The ductile damage evolution and fracture prediction represent the central points for the scientific and engineering community in the framework of material failure. Several works have been carried out developing various theories for the description of the damage. In the literature they can be divided into three main categories:

 Group I : Empirical failure criteria.  Group II : Phenomenological models.

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 Group III : Micromechanics-based models. It should be mentioned that the classification of the theories is not unique. In this work, the classification proposed by De Souza Neto et al. [67], Besson [68] and others [6,69] is followed. Sometimes, group II is referred as continuum damage mechanics (CDM) models (e.g. [70,71]). In this work it is considered that both group II and group III belong to the CDM framework since they both offer a continuous description of the damage.

Figure 5: Typical dependency of the equivalent strain to fracture on the Lode angle parameter.

Group I . To this first category belong the models that consider the damaging process as independent form the plastic behavior of the material. Often in the literature this approach is referred as ‘uncoupled´ meaning that the damage internal variable has no influence on the other plastic internal variables nor the elastic properties of the material and vice versa. Therefore, the variable D is merely indicator of the state of the material without an actual contribution on the degradation of the mechanical properties. Due to their simplicity, the empirical failure criteria spread widely, especially for industrial applications [72]. The Cockcroft-Latham criterion [73] and its subsequent modification into the Cockcroft-Latham-Oh [74] represent a widely used criteria for the prediction of the rapture. In the last decade, several papers and technical reports adopted this approach due to its simplicity and the extremely low number of parameters required. On the other side, due to their simple form, they do not consider the effect of the Lode angle and returns qualitative results in case of significant variation of the stress state. Wilkins et al. [54] tried to consider the effect of the stress triaxiality together with the Lode angle, where the Lode angle was considered by a scalar factor A that describes the stress asymmetry of the principal stress deviators. A good description of the rapture under different stress states can be obtained if the material does not show a pronounced Lode angle sensitivity. Johnson and Cook [53] developed a material constitutive model that is still widely used. In particular, even if the Lode angle effect is still neglected, this approach includes the effect of the strain rate and temperature beside the stress triaxiality. Its calibration requires the definition of a total of 8 material parameters, which can be reduced to 3 in case of quasi-static and isothermal conditions. The J-C criteria is particularly suitable to predict failure at impact or high rate loading conditions [75]. Recently, Bai and Wierzbicki [60] proposed a modified Mohr-Coulomb criterion (MMC) for the prediction of ductile fracture. The MMC can take into consideration the effect of the stress triaxiality and Lode angle and it requires a total of 8 material parameters in its general form, or 4 material parameters in case a von Mises yield function is assumed. This last criterion seems to predict quite accurately the ductile failure and it has found a large application in the recent literature. A comparative study on failure criteria is offered in [76]. An interesting work by Bao and Wierzbicki [77] pointed out that all the aforementioned criteria are not able to describe the material failure under a wide range of stress triaxiality. Modifications of the criteria are needed in case of low or negative values of the stress triaxiality. Moreover, it should be also pointed out that the construction of the failure envelope (i.e., locus of the final strain to fracture as a function of the stress triaxiality and/or Lode angle parameter) is valid only for proportional loading paths. Exceptions are represented by the use of empirical criteria coupled with plastic internal variables [64,78–80]. A recent interesting work from Ganjiani and Homayounfard [81] presented a ductile failure criterion based on an analytical definition of the plastic strain onset of the fracture capable to account for proportional and non-proportional loading conditions. The coupled elastoplastic and damage model in [81] can consider plastic anisotropy by means of the Hill48 yield criterion [82] and resulted in a good prediction

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