Issue 51

Frattura ed Integrità Strutturale, 51 (2020); International Journal of the Italian Group of Fracture

Table of Contents

A. Vedernikova, A. Iziumova, A. Vshivkov, O. Plekhov Three approaches to evaluate the heat dissipated during fatigue crack propagation experiments ... 1-8 A. Chiozzi, N. Grillanda, G. Milani, A. Tralli NURBS-based kinematic limit analysis of FRP-reinforced masonry walls with out-of-plane loading ………………………………………………………………………….... 9-23 D. Vasconcelos, M. Vieira, D. Dias, L. Reis Structural evaluation of the DeepCWind offshore wind platform …….……………………. 24-44 N. Benachour, M. Benachour, M. Benguediab Experimental investigation of fatigue crack initiation from notches in 2024 T351 Al-alloy ….... 45-51 P. Naidoo, G. Drosopoulos Evaluation of the dynamic response of structures using auxetic-type base isolation ……………. 52-70 R. Basirat, K. Goshtasbi, M. Ahmadi Scaling geological fracture network from a micro to a macro scale …………………………... 71-80 P. Ferro, F. Bonollo, S.A. Cruz Alloy substitution in a critical raw materials perspective …………………………………. 81-91 C. Ferrero, P. B. Lourenço, C. Calderini Nonlinear modeling of unreinforced masonry structures under seismic actions: validation using a building hit by the 2016 Central Italy earthquake …………………………………........ A. Chikh Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations ……………….................................................................................................. S. K. Kourkoulis, E. D. Pasiou, A. Abdi, D. N. Perrea, J. Vlamis A biomechanical study of the role of sitagliptin on the bone characteristics of diabetic rats ……… F. Jafari, J. Akbari Reliability-Based Design of Reinforced Concrete Beams for Simultaneous Bending, Shear, and Torsion Loadings ……………………………… …………………..…………………… A.S. Yankin, V.E. Wildemann, N.S. Belonogov, O.A. Staroverov Influence of static mean stresses on the fatigue behavior of 2024 aluminum alloy under multiaxial loading ………………………………………………………………....…………

92-114

115-126

127-135

136-150

151-163

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Fracture and Structural Integrity, 51 (2020); ISSN 1971-9883

M. M. Konieczny, H. Achtelik, G. Gasiak Finite Element Analysis (FEA) and experimental stress analysis in circular perforated plates loaded with concentrated force ………………………………………………………... B. Zaoui, M. Baghdadi, B. Serier, M. Belhouari Finite element analysis of the thermomechanical behavior of metal matrix composites (MMC) ... D. Falliano, D. De Domenico, A. Sciarrone, G. Ricciardi, L. Restuccia, G. Ferro, J.-M. Tulliani, E. Gugliandolo Influence of biochar additions on the fracture behavior of foamed concrete ..................................... S. Merdaci, A.H. Mostefa Influence of porosity on the analysis of sandwich plates FGM using of high order shear- deformation theory …..............................................................................………………… P. Farazmand, P. Hayati, H. Shaker, S. Rezaei Relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warm-mix asphalt mixtures containing modifiers …….………….. G. S. Serovaev, N. A. Kosheleva The study of internal structure of woven glass and carbon fiber reinforced composite materials with embedded fiber-optic sensors …................................................................................................. A. A. Lakhdari, S.A. Bubnov, A. Seddak, I. I. Ovchinnikov, I. G. Ovchinnikov Finite Element Modeling of the behavior of a hollow cylinder in a hydrogen-containing environment ………………………………………………………………………. M. S. Bennouna, S. Kaddur, B. Aour, N. Damba Numerical investigation of the effect of constrained groove pressing process on the mechanical properties of polyamide PA66 ……………………………………………………….. A. Namdar The multilayered soil-structure seismic interaction and structure vibration mechanism ...……..... R. Massabò, I. Monetto Local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables ………………………………………………...…… G. Ramaglia, G. P. Lignola, And. Prota Comparison of Two Parameters Models for clay brick masonry confined by FRP ........................ F. Clementi, G. Milani, A. Ferrante, M. Valente, S. Lenci Crumbling of Amatrice clock tower during 2016 Central Italy seismic sequence: Advanced numerical insights …………………………………………………...……………... E. Mousavian, C. Casapulla The role of different sliding resistances in limit analysis of hemispherical masonry domes ……... G. Cocchetti, E. Rizzi Analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction ………………………………………………………………...

164-173

174-188

189-198

199-214

215-224

225-235

236-253

254-266

267-274

275-287

288-312

313-335

336-355

356-375

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Frattura ed Integrità Strutturale, 51 (2020); International Journal of the Italian Group of Fracture

A.Gesualdo, B. Calderoni, A. Iannuzzo, A. Fortunato, M. Monaco Minimum energy strategies for the in-plane behaviour of masonry ………………………….. K. Li, J. Wang, D. Qi The development and application of an original 3D laser scanning: a precise and nondestructive structural measurements system……………….…………………………………...…. M. Guadagnuolo, M. Aurilio, G. Faella Retrofit assessment of masonry buildings through simplified structural analysis ……….……. F. Fabbrocino, M. F. Funari, F. Greco, P. Lonetti, R. Luciano Numerical modeling based on moving mesh method to simulate fast crack propagation ………... M.-G. Masciotta, D. Pellegrini, M. Girardi, C. Padovani, A. Barontini, P. B. Lourenço, D. Brigante, G. Fabbrocino Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses ........................................................................... C. Bellini, V. Di Cocco, L. Sorrentino Interlaminar shear strength study on CFRP/Al hybrid laminates with different properties .....… M. Cauwels, L. Claeys, T. Depover, K. Verbeken The hydrogen embrittlement sensitivity of duplex stainless steel with different phase fractions evaluated by in-situ mechanical testing …...…………………………………….……… Y. Dubyk, I. Seliverstova Stress-strain assessment of plain dents in gas pipelines …………………………………... K. Bahram, M. Chaib, A. Slimane, B. Bouchouicha Simulation of the retardation effect after applying a simple overload on alloys of aluminum 2024T351 using the Willemborg model …………………………………………....…. D. O. Fernandino, N. Tenaglia, R. E. Boeri, V. Di Cocco, C. Bellini, F. Iacoviello Microstructural damage evaluation of ferritic-ausferritic spheroidal graphite cast iron ………… C. Anselmi, F. Galizia, E. Saetta 3D limit analysis of masonry pavilion domes on octagonal drum subjected to vertical loads …….. M. Pepe, M. Pingaro, P. Trovalusci, E. Reccia, L. Leonetti Micromodels for the in-plane failure analysis of masonry walls: Limit Analysis, FEM and FEM/DEM approaches …………………………………………………………... R. Landolfo, R. Gagliardo, L. Cascini, F. Portioli, M. Malena, G. Tomaselli, G. de Felice Rigid block and finite element analysis of settlement-induced failure mechanisms in historic masonry walls ……………………………...……………………………………… J. M. Djouda, D. Gallittelli, M. Zouaoui, A. Makke, J. Gardan, N. Recho, J. Crépin Local scale fracture characterization of an advanced structured material manufactured by fused deposition modeling in 3D printing …...………………………………………………

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449-458

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467-476

477-485

486-503

504-516

517-533

534-540

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Fracture and Structural Integrity, 51 (2020); ISSN 1971-9883

A. Falk, L. Marsavina, O. Pop Analysis of Printed Circuit Boards strains using finite element analysis and digital image correlation ………………………………………………………………………... K. Hectors, H. De Backer, M. Loccufier, W. De Waele Numerical framework for fatigue lifetime prediction of complex welded structures …………….

541-551

552-566

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Frattura ed Integrità Strutturale, 51 (2020); International Journal of the Italian Group of Fracture

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Co-Editor in Chief Filippo Berto

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

Section Editors Marco Boniardi

(Politecnico di Milano, Italy)

Nicola Bonora Milos Djukic

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

Stavros Kourkoulis

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

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal)

Guest Editors Michela Monaco Francesco Portioli Emanuele Reccia Patrizia Trovalusci

SI: Fracture and Damage Detection in Masonry Structures

(University of Campania "Luigi Vanvitelli", Italy)

(University of Naples Federico II, Italy)

(University of Cagliari, Italy)

(Sapienza University of Rome, Italy)

SI: Structural Integrity and Safety: Experimental and Numerical Perspectives

Guest Editor

José António Fonseca de Oliveira Correia

(University of Porto, Portugal.)

SI: IGF25 – Fracture and Structural Integrity International Conference 2019 (Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Guest Editors

Filippo Berto

Vittorio Di Cocco

(Università di Cassino e del Lazio Meridionale, Italy)

Paolo Ferro

(Università di Parma, Italy) (Università della Calabria, Italy) (Politecnico di Milano, Italy) (Università di Messina, Italy) (Università di Parma, Italy)

Carmine Maletta Luciana Restuccia Giacomo Risitano Andrea Spagnoli

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

Guest Editors

Johan Hoefnagels

(Eindhoven University of Technology, Nederland)

(KU Leuven, Belgium)

Reza Talemi

Guest Editors

SI: Additive Manufacturing

Filippo Berto Jan Torgersen

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

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Fracture and Structural Integrity, 51 (2020); ISSN 1971-9883

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)

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

Raghu Prakash

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

Luis Reis Elio Sacco

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

Aleksandar Sedmak

Dov Sherman Karel Slámečka

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

Tuncay Yalcinkaya

Petro Yasniy

Editorial Board Jafar Albinmousa Nagamani Jaya Balila

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

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

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

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

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

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

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

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Frattura ed Integrità Strutturale, 51 (2020); International Journal of the Italian Group of Fracture

Mauro Corrado

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

José António Correia

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

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

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti, Romania)

(Osaka University, Japan)

Eugenio Giner Ercan Gürses

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

Ali Javili

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

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk Paolo Lonetti Carmine Maletta

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

(Wroclaw University of Science and Technology, Poland)

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

Sonia Marfia

(Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal)

Tomasz Machniewicz

(AGH University of Science and Technology)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Kyushu University, Japan)

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

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

Mahmoud Mostafavi Vasile Nastasescu

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

Stefano Natali Andrzej Neimitz

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

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

Hryhoriy Nykyforchyn

Pavlos Nomikos

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

Marco Paggi Hiralal Patil Oleg Plekhov

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

Alessandro Pirondi Maria Cristina Porcu Dimitris Karalekas Luciana Restuccia Giacomo Risitano

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

Mauro Ricotta Roberto Roberti

Elio Sacco

Hossam El-Din M. Sallam

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

Pietro Salvini Mauro Sassu

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

Andrea Spagnoli Ilias Stavrakas

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

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

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

(Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

Shun-Peng Zhu

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

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Fracture and Structural Integrity, 51 (2020); ISSN 1971-9883

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

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

Czech Rep.: Asociace Strojních 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 Turkey: Turkish Solid Mechanics Group Ukraine: Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Frattura ed Integrità Strutturale, 51 (2020); International Journal of the Italian Group of Fracture

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

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

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

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Fracture and Structural Integrity, 51 (2020); ISSN 1971-9883

NEWS from FIS

Dear friends, this is a really rich issue, with more than 40 published papers and five “special sections”. We are grateful for the efforts of the guest editors: their work allowed to further improve the scientific level of our journal, focusing different topicss with many interesting papers. I wish to remember their names with my deepest gratitude:  Michela Monaco, Francesco Portioli, Emanuele Reccia and Patrizia Trovalusci, for the section focussed on the “Fracture and Damage Detection in Masonry Structures”;  José António Fonseca de Oliveira Correia, for the section focussed on the “Structural Integrity and Safety: Experimental and Numerical Perspectives”;  Filippo Berto, Vittorio Di Cocco, Paolo Ferro, Carmine Maletta, Luciana Restuccia, Giacomo Risitano and Andrea Spagnoli, for the section focussed on “IGF25 – Fracture and Structural Integrity International Conference 2019”;  Johan Hoefnagels and Reza Talemi, for the section focussed on the “1st Benelux Network Meeting and Workshop on Damage and Fracture Mechanics”;  Filippo Berto and Jan Torgersen for the section focussed on the “Additive Manufacturing”. THANK YOU!! Finally, I wish to remember you that, considering that FIS is characterized by many innovative features, we decided to activate a new page of the website where all these features are collected: https://www.fracturae.com/index.php/fis/Innovation. Please do not hesitate to send us your suggestions to further improve our journal. Very best,

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

Focussed on IGF25 – Fracture and Structural Integrity International Conference 2019

Three approaches to evaluate the heat dissipated during fatigue crack propagation experiments

A. Vedernikova, A. Iziumova, A. Vshivkov, O. Plekhov Institute of Continuous Media Mechanics UB RAS, 614013 Perm, Russia terekhina.a@icmm.ru, https://orcid.org/0000-0003-1069-7887 fedorova@icmm.ru, https://orcid.org/0000-0002-1769-9175 vshivkov.a@icmm.ru, https://orcid.org/0000-0002-7667-455X poa@icmm.ru, https://orcid.org/0000-0002-0378-8249 A BSTRACT . This work is devoted to the comparative analysis of three techniques for measurement of energy dissipation in metals under fatigue crack propagation: use of original contact heat flux sensor, post-processing of infrared thermography data and lock-in thermography. Contact heat flux sensors allow real-time recording of heat source values. Non-contact temperature measurements by infrared thermography techniques make it possible to calculate the heat source field on the specimen surface by solving a heat conductivity equation. Lock-in thermography is a well-established technique for measuring energy dissipation under cyclic loading conditions based on the analysis of the second harmonic amplitude of the thermal signal. This paper describes the results of the experiments with V-notched flat specimens made of stainless steel AISI 304 which were subjected to cyclic loading. It was shown that the values of energy dissipation estimated by different techniques are in good qualitative agreement. Contact and non- contact measurements can be used for investigation of energy dissipation either separately or in combination. Based on the measurements, the power dependence of fatigue crack growth rate on dissipated heat near the crack tip can be obtained. K EYWORDS . IR-thermography; Lock-in thermography; Heat flux sensor; Dissipated energy; Fatigue crack propagation.

Citation: Vedernikova, A., Iziumova, A., Vshivkov, A., Plekhov, O., Three approaches to evaluate the heat dissipated during fatigue crack propagation experiments, Frattura ed Integrità Strutturale, 51 (2020) 1-8.

Received: 27.08.2019 Accepted: 08.10.2019 Published: 01.01.2020

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

I NTRODUCTION

ne of the key problems of fracture mechanics and strength analysis is to predict the fatigue life of cracked parts of engineering constructions subjected to cyclic loading. The fatigue crack growth well correlates with energy dissipation at the crack tip [1-25]. Different experimental approaches focused on the experimental study of the dissipated energy are described in the literature. O

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

One of the techniques is based on the application of original Seebeck effect-based contact heat flux sensor, which ensures the quantitative integral heat flow values in some area near the crack tip. Such methodology was originally used for studying energy dissipation in liquid flows [3] and the failure of metals [2, 4]. The second method for heat flux estimation involves analysis of temperature distribution measurements obtained for the specimen surface by means of infrared (IR) thermography. Plastic strain-induced heat sources were calculated by solving the volume-averaged heat conduction equation. The main difficulties associated with application of the second technique can be attributed to the necessity to differentiate strongly oscillating signals and to determine the parameters responsible for the interaction between the specimen and the external environment. Nevertheless, IR thermography data are widely used to gain deeper insight in the process of plastic deformation and fracture of metallic materials [5-10]. It was shown in [11, 12] that the results of contact (heat flux sensor) and non-contact (IR thermography) measurements of energy dissipation during irreversible deformation agree well. The third, lock-in thermography, method provides space-resolved measurements, extracts thermoelastic information directly from the thermal signal [13] and investigates energy dissipation using the double frequency method proposed by Sakagami [14]. Lock-in thermography is employed to detect crack initiation and propagation in structural materials using thermographic mapping [15-25]. In this study, we have shown that the energy dissipation values measured by the thermography techniques are in good qualitative agreement with the results obtained by the method in which contact heat flux sensors are used. This provides evidence that contact and non-contact measurements can be used either separately (fast assessment of the material state at different loading stages) or in combination (verification of the heat source value and estimation of its distribution over the material surface).

E XPERIMENTAL

A

series of tests were performed on V-notched flat specimens made of stainless steel AISI 304 and subjected to cyclic loading at a frequency of 10 Hz (constant stress amplitude 12 kN and stress ratio R = 0). Fig. 1 shows the geometry of the specimens and the experimental setup scheme. The chemical composition of the material examined is given in Tab. 1.

C

Cr

Fe

Mn

Ni

P

S

Si

0.08

18-20

66.34-74

2

8-10.5

0.045

0.03

1

Table 1 : Chemical composition (wt. %) of stainless steel AISI 304.

(a) (c) Figure 1 : (a) specimen geometry; (b) schematic of the measuring equipment: 1 – test specimen, 2 – grips of the testing machine, 3 – contact heat flux sensor, 4 –potential drop measuring setup to monitor the crack length, 5 – infrared camera; (c) photo of the specimen and the measuring equipment. (b)

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

Specimens were cyclic loaded in a servohydraulic testing machine Instron 8802. The potential drop technique was used to measure and characterize the crack propagation process [26]. Crack sizes in a steel specimen were predicted by applying a constant direct current or an alternating current to the specimen and by measuring an increase in electrical resistance due to the crack propogation. To analyze the energy dissipation at the crack tip during mechanical tests, we have used the Seebeck effect-based heat flux sensor. In order to improve the heat flow, a heat-conductive paste was applied to the specimen surface beneath the sensor. The evolution of the temperature field was recorded with an infrared camera FLIR SC 5000. The features of the IR camera are as follows: the spectral range of 3-5 μm, the maximum frame size is 320×256 pixels, the spatial resolution is 10 -4 meters, and the temperature sensitivity is in the range from 25 mK to 300 K. The camera was calibrated based on the standard calibration table. The application of the LIRSC5000 MW G1 F/3.0 close-up lens (with distortion less than 0.5%) made it possible to investigate the plastic zone in detail. The specimen surface intended for infrared shooting was polished in several stages and coated by a thin layer of amorphous carbon to improve the surface emissivity. Specimens were tested and monitored by means of the infrared camera in order to acquire thermographic sequences during tests at regular intervals (1000 cycles each).

D IRECT HEAT FLUX MEASUREMENT TECHNIQUE

T

he heat flux measurement technique relies on the use of Seebeck effect-based contact heat flux sensor [2]. The heat dissipated by specimens is directly proportional to the current intensity and the time it takes for the current to pass through the specimens:

(1)

 

P

I

AB

where P is the heat flux power (W), I is the direct current (A), and  AB

is the Peltier coefficient (V), which is related

with a coefficient of thermal electromotive force. Structurally, the sensor comprises two Peltier elements ("measuring" and "cooling"), thermocouples, and a radiator. To measure the heat flow through the "measuring" Peltier element during the experiment, the temperature on its free surface is kept constant. The cooling Peltier element caulked with a radiator was connected with the "measuring" Peltier element. This cooling system has feedback and is controlled based on two temperature sensors located between "measuring" and cooling Peltier elements and far from the studied specimen in the zone with constant temperature. The heat flux emitted from the specimen surface passes through the heat flux sensor. The sensor was fixed on the specimens by applying thermal paste and then pressed against the spring to provide the necessary thermal contact. The negligibility of heat dissipation which was caused by sensor – specimen friction was experimentally proved [2]. The signal from the flux sensor was measured by the amplifier and registered in the ADC of the microcontroller. Then the data were transmitted to personal computer for further processing. The sensors were calibrated using a device with a controlled heat flux.

I NDIRECT HEAT FLUX MEASUREMENT TECHNIQUE

Estimation of the heat sources field based on the heat conductivity equation o calculate the heat source field induced by plastic deformation, we use heat conduction Eqn. (2) for processing the obtained infrared thermography data:

T

  

  

2

2

2









( T x, y,z,t

( T x, y,z,t

( T x, y,z,t

( T x, y,z,t

)

)

)

)

(2)

 c









( Q x, y,z,t

k

)

2

2

2



t







x

y

z

where ( ) T x, y,z,t is the temperature field,  is the material density (kg/m3), c is the heat capacity ( J/(kg·K)), k is the heat conductivity (W/(m·K)), ( ) Q x, y,z,t is the heat source field, x, y,z are the coordinates, and t is the time. The IR camera allows one to register the temperature distribution only over the specimen surface that is the reason why Eq. 2 has to be averaged over the z-coordinate (thickness).

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

Difference  '(

) x, y,t between the averaged specimen temperature (

) T x, y,z,t and the initial specimen temperature in the

T is defined as:

thermal balance with the environment 0

h

 /2

1

(3)





  )

 ( T dz x, y,t



x, y,t

( ( T x, y,z,t

T

'(

)

)

)

0

0

h



h

/2

where h is the specimen thickness. The following boundary conditions are considered:





T x y z t

T x y z t

( , , , )

( , , , )

 





x

z

2 h

2 h



z



z

(4)

h

/2



 T x y z t k ( , , , )









( ( , , , ) T x y z t

0 T dz )



z

h

h z





h

/2

2

where  is the heat exchange coefficient in perpendicular direction to the specimen surface. One boundary condition describes the symmetry of the heat source, whereas the second boundary condition is responsible for the heat exchange of the specimen with the environment. Therefore, integrating Eq. (2), considering expressions (3) and boundary conditions (4), we obtain relation (5) to estimate the heat source field caused by irreversible deformation:

 ( , , ) x y t



T

 

  

   c 

0

(5)

 ( , , )





 

int Q x y t

( , , ) x y t

k x y t

( , , )



where  is the time constant, which is related to the heat losses [27, 28]. The parameter  was measured before each test by the additional experimental procedure of specimen cooling after pulse point heating. The identification process consisted in estimating the time derivative and the Laplacian of the temperature function if there was no internal and external heat source on the specimen during its cooling. For steel AISI 304, the value of parameter  amounted to 10 sec. The numerical finite-difference scheme of Eqn. (5) applied to the IR thermography data allows one to investigate the heat source evolution on the specimen surface. To calculate the heat sources from the noisy temperature fields, the procedure of the movement compensation and filtering of infrared data was performed. These algorithms are described in detail in [9]. Estimation of the dissipated energy based on the lock-in thermography Energy dissipation can be estimated by applying the lock-in thermography technique. Lock-in thermography is based on a correlation in frequency, amplitude and phase of the detected signal with a reference signal coming from the loading system. Temperature variations on the specimen surface are monitored with the IR camera during mechanical tests. The evaluation of the dissipated energy is based on post-processing of the recorded thermal data using the Discrete Fourier Transformation (Eq. 6) and performed for each pixel of the recorded frames.         sin 2 sin 2 2 m E L E D L D T t T T f t T f t t                 (6)

T is the mean temperature, L

f is the mechanical loading frequency,  E

and  D

are the phase shifts, E

T is the

where m

  t  is the noise of the

D T is the plasticity effect amplitude (D-mode), and

thermo-elastic amplitude (E-mode),

temperature signal. It was shown that in case of plastic deformation the second mode coupled with the double loading frequency (D-mode) correlated with the dissipative energy [14]. Eq. (6) is integrated in the algorithm of Altair LI software. For each analysed sequence of IR frames, the evaluation provides an amplitude and a phase image for different modes.

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

R ESULTS AND DISCUSSION

I

n order to compare the heat flux sensor results and the results of thermography measurements, we have studied the temperature evolution in a small rectangular area which covered all temperature fluctuations near the crack tip. The size of the area coincides with heat flux sensor dimensions. A comparison of the results obtained by contact sensor and the infrared thermography data (heat conduction Eqn. (5)) during crack propagation tests is illustrated in Fig. 2. The heat flux sensor allows measurement of the integral heat flux only. The infrared thermography technique was used to obtain the image of temperature distribution and the field of heat source distribution in the crack tip region. To compare the IR results with the data of the contact sensor, we integrated the heat source field over the space equal to the size of contact sensor. Fig. 2a presents the characteristic curve describing the heat flux variation during the fatigue tests: solid line - heat flux measured by the contact heat flux sensor, squares - heat flux measured by the infrared thermography technique. Three zones were identified on the heat flux curve during the crack propagation experiment. The short initial increasing zone corresponds to the crack initiation stage. The second zone with a constant heat flux corresponds to the steady state crack growth stage. The last zone is characterized by a sharp increase in heat dissipation and is ended with specimen failure. It can be seen that the power heat source detected by the contact sensor and determined on the basis of IR thermography data (Eqn. (5)) are in good quantitative agreement throughout the test. Figs. 2b,c present the relation between the heat flux power   Q and crack growth rate   da 304 specimen. The power law relation for predicting the fatigue crack growth is determined as follows: dN for the stainless steel AISI

da

int . b aQ dN



(6)

(a) (c) Figure 2 : (a) IR-thermography data and heat flux sensor measurements; (b) heat flux power during crack propagation experiments; (c) relation between heat flux power and crack growth rate for the stainless steel AISI 304 specimen. The obtained results led us to conclude that the techniques applied to estimate heat dissipation on the basis of contact and non-contact measurements can be used in engineering practice for fatigue crack growth predictions.Let us now consider the possibility of using lock-in thermography to predict fatigue crack growth. With the Altair LI software it is possible to calculate the resulting amplitude of temperature variations (amplitude image) and the distribution of phase shifts between the thermographic signal and the mechanical loading (phase image) for the E-mode and D-mode, respectively (Eq. 6). As shown by Bremond [13], the D-mode provides information about the dissipated energy. The values of the amplitude related to the double loading frequency were determined. Fig. 3a shows the results of the normalized lock-in thermographic and the heat flux sensor measurements of the crack propagation experiment with a constant force exerted on the stainless steel AISI 304 specimen. For normalization of lock-in thermography data, a scaling factor was used. We assume a linear relationship between each point of thermography data and the results of the contact heat flux sensor. The scaling factor is computed for one point as the ratio of the power of heat source obtained by contact sensor to the value of D-amplitude. Then the values of D-amplitude at other time moments are multiplied by a scaling factor. For steel AISI 304, the value of scaling factor amounts to 0.32. It can be seen that the dissipated energy measured by lock-in (b)

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

thermography and the heat flux sensor are in good qualitative agreement over the high heat dissipation period. The averaged D-Amplitude values are rising with loading cycles what caused by processes in front of the crack tip. The D-amplitude behaviour and, in particular, its increase are similar to that of the crack growth rate. Therefore, the value of the D-mode amplitude can be used to describe crack propagation. Figs.3b,c present the relation between D-mode variation and crack growth rate for the stainless steel AISI 304 specimen. The power law relation is determined as follows:

da

b aS dN



(7)

d

where d S is the maximum amplitude of the thermal signal that changes at the double of loading frequency.

(a) (c) Figure 3 : (a) lock-in thermography data and heat flux sensor measurements; (b) heat flux during crack propagation experiments; (c) relation between second order temperature variation and crack growth rate for the stainless steel AISI 304 specimen. Analysis of the results has revealed that lock-in thermography can be used for evaluating the crack growth rate. It is interesting that the fatigue crack growth can be described by the D-amplitude signal in very similar to the Paris Law. (b)

C ONCLUSION

I

R-thermography data, lock-in thermography data and heat flux sensor measurements were used to investigate energy dissipation under fatigue crack propagation in stainless steel AISI 304. Comparison of the obtained results demonstrates that they are in good qualitative agreement. At the scaling factor of 0.32 the heat flux sensor results coincide quantitatively with the lock-in thermography data. The thermographic and heat flux sensor measurements showed an increase in the energy dissipated ahead of the crack tip with increasing crack growth rate. The measured energy dissipation values can be used to determine a linear correlation between these two parameters.

A CKNOWLEDGMENTS

T

his work was supported by the Russian Foundation for Basic Research (grant №18-31-00293) and the Presidium of the Russian Academy of Sciences (program no. 16 “Development of Physicochemical Mechanics of Surface Phenomena as the Fundamental Basis for the Development of Modern Structures and Technologies).

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A. Vedernikova et alii, Frattura ed Integrità Strutturale, 21 (2020) 1-8; DOI: 10.3221/IGF-ESIS.51.01

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