Issue 50

Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

Table of Contents

O. Plekhov, A. Vshivkov The effect of fatigue crack rate on the heat dissipation in metals under mixed-mode loading …...... 1-8 M.F. Borges, F.V. Antunes, P. Prates, R. Branco, M.C. Oliveira Effect of yield stress on fatigue crack growth ………………………………………….... 9-19 Z.-y. Han, X.-g. Huang Stress corrosion behavior of X80 pipeline steel in the natural seawater with different dissolved oxygen contents ……………………………………………………………………. 20-28 G. Khandouzi, M. Mollashahi, M. Moosakhani Numerical simulation of crack propagation behavior of a semi-cylindrical specimen under dynamic loading ……….....................................................................................................………... 29-37 M. Eremin, A. Kulkov, I. Smolin, V. Mikushina Investigation of Failure Mechanism of Al 2 O 3 Specimens Subjected to Three-Point Bending Test 38-45 I. G. F. da Silva, A. H. P. de Andrade, W. A. Monteiro Leak-Before-Break methodology applied to different piping materials: a performance evaluation 46-53 N. Boychenko, I. Ishtyryakov Characterization of the stress-strain state in a gas turbine engine compressor disc taking into account damage accumulation ………..………………………………………………. 54-67 M. Baghdadi, B. Serier, M. Salem, B. Zaoui, K. Kaddouri Modeling of a cracked and repaired Al 2024T3 aircraft plate: effect of the composite patch shape on the repair performance. …………………………………...……………………..... 68-85 A. Sarkar, A. Nagesha, R. Sandhya, M. Okazaki Crack growth based life prediction approach under LCF-HCF interaction ………………..... 86-97 R. Boutelidja, A. Guedri, M. A. Belyamna, B. Merzoug Environmental effects on the reliability of an AISI 304 structure …………………………. 98-111 B. Benamar, M. Mokhtari, K. Madani, H. Banzaama Using a cohesive zone modeling to predict the compressive and tensile behavior on the failure load of single lap bonded joint ………………………… …………………..…………………… O. Mouhat, A. Bybi, A. El Bouhmidi, M. Rougui Effects of ply orientation on nonlinear buckling of aircraft composite stiffened panel ...…………

112-125

126-140

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

A. Tijani, M. Meknassi, H., Chaffoui, M. Elghorba Corrosion’s impact on wire rope strand response - Comparison with a theoretical predictive model M. Ameri, M. Nemati, H. Shaker, F. Jafari Experimental and numerical investigation of the properties of the Hot Mix Asphalt Concrete with basalt and glass fiber …………………………………………………………... J. Papuga, M. Nesládek, J. Kuželka, J. Jurenka Differences in the response to in-phase and out-of-phase multiaxial high-cycle fatigue loading ........ A. Benzaama, M. Mokhtari, H. Benzaama, E. Abdelouahed, T. Tamine, K. Madani, A. Slamen, M. Ilies Using XFEM Techniques to Predict the Damage of aluminum 2024T3 notched under tensile load ………..........................................................................................………………… M. Godio, K. Beyer Quantifying the out-of-plane response of unreinforced masonry walls subjected to relative support motion ……...………………………………………………………………….. B. Badarloo, F. Jafari Finite Element Analysis and ANFIS investigation of seismic behavior of sandwich panels with different concrete material in two story steel building ….............................................................. A. Salmi, M. Elajrami, M. E. A. Slimani Crack growth study under thermo-mechanical loads: parametric analysis for 2024 T3 aluminum alloy ……………………………………………………………………………... P. Livieri, F. Segala Stress intensity factor for small embedded cracks in weldments …………………………….. L. Romanin, P. Ferro, A. Fabrizi, F. Berto A metallurgical and thermal analysis of Inconel 625 electron-beam welded joints …………..... C. C. Silva, R. B. Caldas, R. H. Fakury, H. Carvalho, J. V. F. Dias Web rotational stiffness of continuous steel-concrete composite castellated beams ………...…… K. Meftah, L. Sedira A nonlinear elasto-plastic analysis of Reissner-Mindlin plates by finite element method ............... H. Saidi, M. Sahla Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al 2 O 3 ) embedded in an elastic medium …………………... P. Qiu Experimental research on fracture behavior of concrete after high temperature ………...……... V. Iasnii, P. Yasniy, D. Baran, A. Rudawska The effect of temperature on low-cycle fatigue of shape memory alloy ………………………. K. Singh, C. Robertson, A.K. Bhaduri Brittle fracture model parameter estimation for irradiated BCC material through dislocation based crystal plasticity model …………………………………………………………

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149-162

163-183

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230-240

241-250

251-263

264-275

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300-309

310-318

319-330

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

F. Larbi Chaht, M. Mokhtari, H. Benzaama Using a Hashin Criteria to predict the Damage of composite notched plate under traction and torsion behavior ….……………………………………………………………...…. N. D. Alexopoulos, N. Siskou, C.-M. Charalampidou, S. K. Kourkoulis Simulation of the corrosion-induced damage on aluminum alloy 2024 specimens with equivalent surface notches ……………………………………………………………….……. G. Belokas Probabilistic geotechnical engineering analysis based on first order reliability method ………….. 354-369 I. Dakanali, A. Marinelli Tension - torsion fatigue tests on the proton exchange membrane Nafion 115 (Perfluorosulfonic acid) …................................................................................................................................... 370-382 S. Gavela, N. Nikoloutsopoulos, G. Papadakos, D. Passa, A. Sotiropoulou Experimental uncertainty budget for concrete compressive strength test based on a multifactorial analysis ………………………………………………....……………………...… 383-394 K. Kaklis, Z. Agioutantis, S. Mavrigiannakis, P. Maravelaki-Kalaitzaki A simplified damage evolution relationship and deformation characteristics of a pozzolanic lime mortar when subjected to unloading-reloading cycles in the pre-peak region …...……………… 395-406 N. Chatzidai, D. Karalekas Experimental and numerical study on the influence of critical 3D printing processing parameters 407-413 V. N. Kytopoulos, E. Sideridis, J. Venetis, C. Riga, A. Altzoumailis A SEM-X-Ray assisted experimental approach for the determination of mechanical and thermal load – induced damage in MMCs ………………………………………………....…. 414-422 A. G. Lekatou, S. Tsouli, C. Nikolaidis, S. Kleftakis, I. K. Tragazikis, T. E. Matikas Effect of fly ash on the corrosion performance and structural integrity of stainless steel concrete rebars in acid rain and saline environments ……………………………………………. 423-437 A. Marinelli, M. R. Stewart Comparative experimental study of the mechanical and fracture properties of Portland limestone and Corsehill sandstone ………………………………………………..…………… 438-450 Christos F. Markides Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length ………………………………………………………………...… 451-470 N. Martini, V. Koukou, G. Fountos, I. Valais, I. Kandarakis, C. Michail, A. Bakas, E. Lavdas, K. Ninos, G. Oikonomou, L. Gogou, G. Panayiotakis Imaging performance of a CaWO 4 /CMOS sensor……………………………………… 471-480 A. Kakaliagos, N. Ninis Damage and failure of Orban’s gun during the bombardment of Constantinople walls in 1453 481-496 I. Papantoniou , H. P. Kyriakopoulou, D. I. Pantelis, D. E. Manolakos Metal foaming by powder metallurgy process: investigation of different parameters on the foaming 331-341 342-353

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

efficiency …...…………………………………………………………….……….. V. Saltas, D. Peraki , F. Vallianatos The use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent ………………..………………………………………….. G. V. Seretis, A. K. Polyzou, D. E. Manolakos, C. G. Provatidis Multi-parameter analysis of curing cycle for GNPs/glass fabric/ epoxy laminated nanocomposites ……………………………...…………………………….………. M. Papachristoforou, V. Mitsopoulos, M. Stefanidou Use of by-products for partial replacement of 3D printed concrete constituents; rheology, strength and shrinkage performance …………...……………………………………………... D. Triantis, S. K. Kourkoulis Fracture precursor phenomena in marble specimens under uniaxial compression by means of Acoustic Emission data ………………………………………………………...…... C. Apostolopoulos, A. Drakakaki, A. Apostolopoulos, K. Koulouris Comparison of the mechanical response of B400c and B450c dual phase steel bar categories, in long terms ……………………………………………………………………….... E. D. Pasiou Restoring stone monuments: Enlightening critical details by the combined use of innovative sensing techniques ……………………………………………………....………………… I. Stavrakas, S. K. Kourkoulis, D. Triantis Damage evolution in marble under uniaxial compression monitored by Pressure Stimulated Currents and Acoustic Emissions ………………..…......................................................... N. Fountas, A. Koutsomichalis, J. D. Kechagias, N.M. Vaxevanidis Multi-response optimization of CuZn39Pb3 brass alloy turning by implementing Grey Wolf algorithm ………………………………………………………….…………….... S. M. A. Khiat, R. Zenasni, M. Hamdi Effect of environmental conditions on the resistance of damaged composite materials ………..…. M.R.M. Aliha, H. Ghazi, F. Ataei Experimental fracture resistance study for cracked bovine femur bone samples …………..….... P. Livieri, F. Segala Stress intensity factor for small embedded cracks in weldments ……………….…................... M. Belhamiani, D. E. Belhadri, W. Oudad, O. Mansouri, W. N. Bouzitouna J integral computation and limit load analysis of bonded composite repair in cracked pipes under pressure …………………………………………………………………….….… Q. Hu, Z. Shou, J. Zeng, L. He , H. Tang, B. Li, S. Chen, X. Lu Comparative study on the deterioration of granite under microwave irradiation and resistance heating treatment …………………………………..……………..………………...

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537-547

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

L. He, Y. Gu, Q. Hu, Y. Chen, J. Zeng Structural failure process of schistosity rock under microwave radiation at high temperatures … J.M. Vasco-Olmo, F.A. Díaz, F.V. Antunes, M.N. James Experimental characterisation of fatigue crack growth based on the CTOD measured from crack tip displacement fields using DIC…………………………………………………….. A. Kostina, O. Plekhov, S. Aizikovich Numerical simulation of subsurface defect identification by pulsed thermography and improvement of this technique for noisy data ……………...………………………………………...

649-657

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

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)

SI: research activities of the Greek Society of Experimental Mechanics of Materials

Guest Editors

(National Technical University of Athens, Greece)

Stavros K. Kourkoulis

Dimos Triantis

(University of West Attica, Greece)

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.)

Guest Editors

SI: Fracture Mechanics versus Environment

Mohammed Hadj Meliani

(University of Chlef, Algeria) (University of Belgrade, Serbia ) (Lorraine University, Metz, France)

Ljubica Milovic Guy Pluvinage

Guest Editor

SI: Showcasing Structural Integrity Research in India

(Indian Institute of Technology Madras, India)

Raghu Vasu Prakash

Guest Editors

SI: New Trends in Fatigue and Fracture

Manuel Freitas

(University of Lisbon, Portugal ) (University of Lisbon, Portugal) (University of Lisbon, Portugal )

Luis Reis

Fatima Vaz

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

Guest Editors

SI: Crack Tip Fields (University of Sheffield, UK)

Luca Susmel

Michael Vormwald

(Technische Universität Darmstadt, Germany)

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)

Aleksandar Sedmak

(University of Belgrade, Serbia)

Dov Sherman Karel Slámečka Petro Yasniy

(Tel-Aviv University, Tel-Aviv, Israel)

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

Editorial Board Jafar Albinmousa Nagamani Jaya Balila

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

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

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

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

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

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

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

Mauro Corrado

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

José António Correia

Dan Mihai Constantinescu

University POLITEHNICA of Bucharest()

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

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti)

(Osaka University, Japan)

(Universitat Politecnica de Valencia, Spain)

(University of Piraeus, Greece)

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

(Wroclaw University of Science and Technology, Poland)

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

Sonia Marfia

(Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal)

Tomasz Machniewicz

(AGH University of Science and Technology)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Kyushu University, Japan)

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

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

Mahmoud Mostafavi Vasile Nastasescu

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

Stefano Natali 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 Dimitris Karalekas Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

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

Elio Sacco

Hossam El-Din M. Sallam

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

Pietro Salvini Mauro Sassu

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

Andrea Spagnoli Ilias Stavrakas

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

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

(Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

Shun-Peng Zhu

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

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

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 Ukraine: Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

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

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

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

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

NEWS from FIS

Dear friends, We have many news for our authors and our readers.

First of all, due to the high number of submissions, it was necessary to deeply transform the organization of the Journal. We cancelled the board of Associate Editors. In these years, the members of this board did a great work, continuously suggesting new ideas to further improve the journal and we are deeply grateful to Alfredo Navarro, Thierry Palin Luc, Luca Susmel and John Yates for their service for FIS. Now we created some sections and, for the next submissions, all the authors will be asked to choose a section during the submission process. We activated a “Section Editor panel” that will actively help the Editor in Chief and we wish to welcome the Section Editors, Marco Boniardi, Nicola Bonora, Milos Djukic, Stavros Kourkoulis, Liviu Marsavina, Pedro Moreira: we are sure that their contribution will help the journal to achieve new and better results. In addition, we wish to welcome the new Co-Editor in Chief, Filippo Berto: his experience in editorial processing and managing will let great improvements. Among the new services, we can remember: - The activation of the “Categories”: all the published papers are now categorized with one category at least and, selecting one of the categories available under the section “Browse” in the journal website, all the readers will be able to find immediately the papers focused on the selected category; - Visual Abstracts: all the visual abstracts are both linked to the corresponding papers and are also available in the dedicated YouTube channel. Now, in the YouTube channel, each Visual Abstract will be linked to the paper with the keywords as Tags, improving in this way the visibility both of Visual Abstracts and papers. 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. Very best,

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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Fracture and Structural Integrity, 50 (2019); ISSN 1971-9883

Special issue: “Research activities of the Greek Society of Experimental Mechanics of Materials”

he present Special Issue of Frattura ed Integrità Strutturale entitled “Research activities of the Greek Society of Experimental Mechanics of Materials (GSEMM)” contains twenty (21) papers selected from the presentations delivered during the “1st International Conference of the GSEMM”, held in Athens from May 10 to May 12, 2018. This conference was the first official scientific activity of the GSEMM, which was founded in December 2016. The core founding objective of GSEMM is to strengthen the interaction between various research teams all over Greece and disseminate the outcomes of experimental protocols implemented by these teams. This was considered of crucial importance taking into account that Experimental Mechanics of Materials is among the most rapidly developing areas of Mechanics (mainly due to the extended use of novel and innovative techniques for the detection, collection and recording/storing of experimental data, and, also, due to the explosive development of computer science, which enables rapid analysis and exploitation of huge amounts of data). On the other hand, the effective implementation of experimental protocols becomes increasingly difficult from the technical point of view and expensive from the financial point of view, rendering the cooperation of research groups of interdisciplinary background a pressing demand. In Greece, there are quite a few research groups, which are actively and quite successfully involved in the field of Experimental Mechanics of Materials. In spite of this successful involvement, the interaction among these research groups is rather limited, resulting to waste of valuable resources, in both human and financial terms. As a matter of fact, similar experimental protocols are often implemented independently in various research centers, institutes or universities. To overcome this “malfunction” and accomplish all its founding objectives arising from its Statutes (production, promotion, gathering and dissemination of scientific knowledge on matters related to the field of Experimental Mechanics of Materials and training, education and know-how transfer at all levels concerning Experimental Mechanics of Materials) GSEMM intends (among others) to: Organize national and international scientific conferences and workshops, organize schools and seminars in the direction of training young scientists on subjects related to experimental research techniques, contribute in the organization of post-graduate courses in fields related to Experimental Mechanics of Materials, disseminate and promote the scientific work and achievements of its members, provide to its members information concerning research directions of high priority for the development of the country, participate in the implementation of national and international research projects, promote collaboration between Greek and international scientific societies of similar scope, and, finally, become member of European and international scientific associations of similar statutory purposes. It is very encouraging that the list of members of GSEMM encompasses already a unique group of experimentalists, development engineers, design engineers, test engineers and technicians, and research and development scientists from industry and educational institutions. GSEMM is already representing Greece in the European Structural Integrity Society (ESIS). The publication of this Special Issue closes the cycle of actions related to the “1st International Conference of the GSEMM”, which included, among others, publication of: • The “Book of Abstracts” (pages 210, ISSN: 2623-3541), which contains the two-page extended abstracts of all the seventy eight (78) presentations (oral and poster) accepted (after being reviewed) and delivered during the conference. • A special volume (Volume 10, Pages: 1-342, 2018) of the “Procedia Structural Integrity” journal, entitled “1st International Conference of the Greek Society of Experimental Mechanics of Materials, Athens, May 10-12, 2018”. This volume contained the 8-page full texts of fourty four (44) papers, presented during the conference. • The current Special Issue of Frattura ed Integrità Strutturale . The closure of this cycle designates the onset of a new cycle of activities of GSEMM, which for the Academic Year 2019 2020 are oriented in three directions:

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Frattura ed Integrità Strutturale, 50 (2019); International Journal of the Italian Group of Fracture

• Co-organization of the “1st Virtual Conference on Structural Integrity” under the auspices of ESIS, in collaboration with the sister associations “Italian Group of Fracture”, “Portuguese Structural Integrity Society” and “(Serbian) Society for Structural Integrity and Life - DIVK” (Winter 2019-2020). • Co-organization with the sister association “Italian Group of Fracture” of the “1st Greek-Italian Symposium on Structural Integrity”, in Athens (Spring 2020). • Organization of the “2nd International Conference of the GSEMM” (Autumn 2020). Special thanks must be given to the reviewers of the manuscripts submitted during all publishing activities of our Society. Moreover, we would like to thank all the members of the Interim Board of the Society who drove the society during its fist unstable steps. Especially, words of thanks go to the Secretary of the Interim Board Dr Ermioni Pasiou for the time she spent editing the manuscripts. In addition, we thank all the members of the Society and all the participants of the 1st conference of our society. Their enthusiastic support was the cornerstone on which the success was built and at the same time it is the valuable asset that guarantees the future of our Society. Finally, on behalf of the Board of Directors of GSEMM, we would like to sincerely thank the ex-President of ESIS Leslie Bank-Sills, for encouraging the enrollment of GSEMM as a full member of ESIS. Also, we would like to express our deep gratitude to the President of the “Italian Group of Fracture” and running president of ESIS, Professor Francesco Iacoviello, for his enthusiastic and continuous support to all the actions of our Society. The editors Stavros K. Kourkoulis Laboratory for Testing and Materials, Department of Mechanics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece Dimos Triantis Electronic Devices and Materials Laboratory, University of West Attica, Greece

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

Focused on New Trends in Fatigue and Fracture

The effect of fatigue crack rate on the heat dissipation in metals under mixed-mode loading

Oleg Plekhov Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm, Russia poa@icmm.ru Aleksei Vshivkov Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm, Russia vshivkov.a@icmm.ru A BSTRACT . The study of energy balance at crack tip could give comprehensive information for estimation of durability and reliability cracked construction under cyclic loading. The first step for estimation energy balance is monitoring of dissipated part of energy (heat generation). One of the most effective techniques for investigation of temperature evolution on the surface of deformed body is infrared thermography. The work is devoted to the experimental study of energy dissipation in cracked samples made of titanium Grade 2 under multiaxial cyclic loading. To explain the experimentally obtained correlation between fatigue crack rate and power of heat dissipation we developed a phenomenological model describing the evolution of plastic work at the crack tip under arbitrary loading. The theoretical and experimental data about heat dissipation exhibit a good quantitative agreement. K EYWORDS . Energy dissipation; Crack propagation; Infrared thermography; Mixed-mode loading.

Citation: Plekhov, O., Vshivkov, A., The effect of fatigue crack rate on the heat dissipation in metals under mix mode loading, Frattura ed Integrità Strutturale, 50 (2019) 1-8.

Received: 26.12.2018 Accepted: 08.07.2019 Published: 01.10.2019

Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION

he most frequently used technique for estimation of lifetime of cracked samples is based on the correlation between stress intensity factor and fatigue crack rate (Paris` law). Paris law is results treatment of many experimental data in framework of elastic solution of crack propagation problem. As a consequence, this law doesn`t explain the physical nature of the process of crack propagation in metals and initiates a lot of scientific discussions and attempts to derive alternative description of crack propagation law. Such alternative laws of crack propagation were proposed by many authors based on correlations of the fatigue crack growth rate and mechanical-structural parameters describing the failure process at crack tip. For instance, the intensity of plastic T

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

deformation, the Rise integral, the sizes of plastic deformation zone at crack tip, the dissipated energy were used as the crack propagation control parameters [1-4]. To derive a crack propagation law valid for arbitrary loading conditions we have to consider an energy concept of crack propagation. The current state of development of experimental mechanics allows one to monitor the dissipated part of energy with very high precision using infrared thermography [5-7]. The main problem of application of thermography technique is caused by the uncertainty of the solution to the inverse thermal problem [8]. Few years ago, we proposed an effective chip solution for the problem. We developed an additional system for direct monitoring of a heat flow [9]. To treat the experimental data we need a simple description of elasto-plastic deformation in process zone valid for arbitrary (multiaxial) loading conditions. Following by idea [10], we proposed a model of energy dissipation at crack tip. The key point of this approach is a hypothesis of the link between the elastic and elasto-plastic solutions at the fatigue crack tip proposed by Dixon [11]. In the framework of the model we divided the dissipated energy into two parts corresponding to reversible (cyclic) and monotonic plastic zones. Analysis of this approximation has shown zero effect of fatigue crack advance on the energy dissipation into cyclic plastic zone. This dissipation is a function of spatial size of a cyclic plastic zone and characteristic size of the yield surface. Under isotropic hardening, the change of the applied stress amplitude leads to the change of characteristic size of the yield surface and, as consequence, to the heat dissipation at constant crack rate. The dissipation in monotonic plastic zone is a function of both crack rate and characteristic size of the yield surface. This part of the model gives correlation between fatigue crack rate and power of heat dissipation [4,7]. The previous authors’ investigations were focused on crack growth problems under an opening or mode I mechanism [9] and a relationship was proposed for the growth rate of a fatigue crack based on an analysis of the energy balance at its tip. However, most structures are failed due to mixed mode loading. Many uniaxial loaded materials, structures and components often contain randomly oriented defects and cracks which develop a mixed mode state by rotation of their orientation with respect to the loading axis. For example mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces as discussed in the following [12-15]. In this work, we verify the main hypothesis used for our phenomenological description of fatigue crack propagation law and verify the approach for fatigue cracks titanium Grade 2 samples subject to the multiaxial cyclic loading. n the previous work [9] we obtained the relation to calculate the energy of plastic deformation as a consequence, energy dissipation at fatigue crack tip:     2 2 1 2 , tot p da U W A W A dN     (1) where A τ – stress amplitude. Terms in Eqn. (1) correspond to reversible (cyclic) and monotonic plastic zones. Analysis of this approximation has shown that energy dissipation in a cyclic plastic zone is independent of crack growth. This dissipation is fully determined by the spatial size of a cyclic plastic zone and the characteristic diameter of the yield surface. For isotropic hardening materials, the change of the applied stress amplitude leads to the change in the characteristic diameter of the yield surface and, as consequence, to the energy dissipation at a constant crack rate. Dissipation in the monotonic plastic zone is a function of both crack rate and characteristic diameter of the yield surface. It was shown by Short [1], that crack growth can be determined by heat generation: I E NERGY DISSIPATION AT THE CRACK TIP UNDER CYCLIC LOADING

p da W dN J   

 

(2)

Where W p - hysteresis energy rate, Φ - heat generation rate, J - fracture energy added to V per unit crack advance, Γ - fracture energy required per unit crack advance (original notation are used). We can write the equation for heat generation from (2):

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

 p da W J dN 

    

(3)

In the general case, Eqns. (1) and (3) are same. The calculation of analytical relations for W 1 , W 2 can be carried out similarly to the monotonic loading. It allows us to predict the existence of peculiarities of energy dissipation at the crack tip reported in [17] for multiaxial loading. Thus, we have an analytical equation for calculating heat generation, obtained in two different ways. The relation (1) obtained based on Dixon’s hypothesis (Eqn. (4)) [11] about relation between elastic and plastic deformation.

1 2

s        E E

ef

el

ij 

ij 

(4)

,

where – the Young’s modulus, ௦ - secant plasticity modulus. N UMERICAL SIMULATION OF STRAIN FIELD AT THE CRACK TIP

T

he check an applicability of Dixon’s hypothesis (Eqn. (1)) about relation between elastic and plastic deformation was carried out by numerical simulation of strain field at the crack tip. There was considered a two-dimensional model of biaxial loading. Half of a sample with symmetry of inner boundary was studied. In calculation the plane strain assumption was adopted. A square grid with a concentration in the region near the crack tip was used. An element size at crack tip was up to 5e-6 m. To describe plastic deformation the isotropic hardening function was used which was obtained from the approximation of experimental data. The applied load corresponds to the experimental values. A crack path was taken from the digital image correlation data. The system of equations for modeling of a strain field near the crack tip has the following form:    σ 0 , (5)   : p   σ С ε ε , (6)

1 2

T     ε u u ,   

(7)

 

F σ

p

,

(8)



ε



where σ – stress, ε – strain, u – displacement, λ – hardening parameter, F =σ m -σ ys , σ ys =σ ys0 + σ h (ε pe ), σ h (ε pe ) - hardening function. A numerical simulation of plastic deformation near the crack tip has been carried out. The estimation of the plastic strain field was carried out using the elastic solution and the Eqn. (4) for the strain components ε 11 , ε 12 , ε 22 , maximum shear strain γ, effective plastic deformation ε pe :

 1/2  



  2

2

  2

2

3 2 2 2 12 13 23     

  





.

(9)











  



  





11 22

11 33

33 22

pe



3

2

Numerical and theoretical calculations were made for four biaxial coefficients (η = 0, 0.5, 0.7, 1). The characteristic distributions of normal to the crack path strain component and second strain invariant are shown in Figs. 1, 2. To compare the theoretical and calculated results, point-by-point error was calculated for different strain levels corresponded to the applied load (Fig. 3). The loading levels correspond to the crack growth rate 1e-8 - 1e-3m/cycle.

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

(a)

(b)

Figure 1 : Plastic strain (η=0, component ε 22

): (a) numerical simulation; (b) analytic solution by Eqn. (4).

(a)

(b)

Figure 2 : Plastic strain (η=1, component ε i

): (a) numerical simulation; (b) analytic solution by Eqn. (4).

The analysis of data presented in Fig. 3 allows us to conclude that the maximum relative error of Eqn. (1) is less than 20 percent. As a result, we can expect qualitative description of energy dissipation process at fatigue crack based on the simple hypothesis (4).

E XPERIMENTAL STUDY OF STRAIN FIELD AT THE CRACK TIP

series of samples made of Grade 2 titanium alloy were tested using servo-hydraulic biaxial testing system Biss BI 00-502, located in Kazan Scientific Center of Russian Academy of Sciences. The photo of the experimental setup is presented in Fig. 4. The geometry of the samples is shown in Fig. 5. During tests the samples were subjected to cyclic loading of 10 Hz with constant stress amplitude, different biaxial coefficient η=Px/Py (1, 0.7, 0.5, 0) and stress ratio R (0.1, 0.3, 0.5). The crack length was measured by an optic method. The strain field was measured by digital image correlation method based on StrainMaster system and Lavision software. Surface of the sample near the crack tip was polished and covered with a black matte paint before the experiment. Then, the white paint was sprayed over the black paint to obtain a high contrast image. A macro lens and an elevated Led lamp were used for recording of material displacement at the crack tip. To restore the deformation field at the crack tip area, each frame was subjected to additional processing: calibration to level distortions caused by distortion of the lens, motion compensation, regulation of the illumination with digital filters. The spatial resolution of the strain field near the crack tip was 3e-6 m. Fig. 6 shows the characteristic result of measurements for the case of uniaxial loading. The deformation field is asymmetric due to the influence of the relative direction of the crack. Fig. 7 shows the shape of the plastic area boundary and characteristic sizes which have been used for the comparison of the experimental and numerical data. Tab. 1 gives a quantitative comparison of the obtained data. A

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

30

25

11 12 22

25

20

pe

20

15

15

Error, %

Error, %

11 12 22

10

10

5

pe

5

1

2

3

4

5

6

7

1

2

3

4

5

6

7

Load, kN

Load, kN

(a)

(b)

25

10 12 14 16 18 20 22 Error, %

11 12 22

11 12 22

20

pe

pe

15

Error, %

10

6 8

5

1

2

3

4

5

6

7

1

2

3

4

5

6

7

Load, kN

Load, kN

(c) (d) Figure 3 : A relative error in plastic strain prediction (a) η = 0; (b) η = 0.5; (c) η =0.7; (d) η = 1.

Figure 4 : Testing machine Biss BI-00-502, Biaxial testing System.

Figure 5 : Geometry of samples (all sizes in millimeters).

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

B

1.0

0.5

A

1.0

0.5

0.5

1.0

C

0.5

1.0

D

1.5

Figure 6 : Measured field of strain for uniaxial loading

Figure 7 : Boundary of plastic area.

Numerical, mm

Measure, mm

AB AC AD BD

1,20E-01 1,35E-02 1,19E-01 2,18E-01

9,13E-02 3,13E-02 6,98E-02 1,27E-01

Table 1: Character size of plastic zone.

10 -4

0.7

Sensor Calculate

n=1; R=0.1 ;F=7kN n=1; R=0.1 ;F=12kN n=0.5; R=0.1 ;F=10kN n=0; R=0.1 ;F=10kN n=1; R=0.5 ;F=10kN

0.6

0.5

0.4

10 -5

0.3

0.2 Heat flux, W

Crack rate, m/cycle

0.1

Figure 9 : Crack growth versus energy dissipation at fatigue crack tip under biaxial loading 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Heat dissipation, W 10 -6

0 500 1000 1500 2000 2500 3000 3500 4000 0

Time, s

Figure 8 : Heat dissipation histories obtained under constant stress amplitude (up to 2200-th second of the test) and constant stress intensity factor (remaining time) (Solid line – approximation (1), the dotted line – experimental results).

Details of heat measurement during the fatigue test can be find in [9]. The Eqn. (1) gives a good qualitative description of peculiarities of heat dissipation in both regimes with the constant stress amplitude and constant stress intensity factor, Fig. 8. Experimental works [3, 16] have shown that the rate of the stored energy has a maximum value on the initial stage of the plastic deformation. From the analysis of the energy balance, it follows that the dissipated energy during the cycle of the deformation differs from the expended energy insignificantly. We used the assumption of the proportionality of dissipated energy and plastic work. This formally corresponds a approximation of small stored energy. For constant stress amplitude the plastic work and, as a consequence, energy dissipation at the crack tip is determined by the crack growth rate as is shown [17] but for constant crack rate we can observe the regimes with the decrease of the heat dissipation caused by the decrease

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O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01

of the applied stress amplitude. The same comparison of experimental results and approximation (1) can be obtained for biaxial test (Fig. 9).

C ONCLUSION

series of experiments was carry out. For different biaxial coefficients, the strain field at the fatigue crack tip was measured. The results of the measurements have a good agreement with numerical simulation. The theoretical calculation of plastic deformation based on the elastic solution and the secant modulus of elasticity is carried out. According to the results of calculations, the error in determining the plastic deformation through the elastic solution does not exceed 30% for each component of the strain tensor, the maximum shear strain, and the intensity of plastic deformations. This allows us to conclude that it is possible to use Eqn. (4) for the theoretical calculation of the deformation field at the fatigue crack tip and the subsequent calculation of energy dissipation. An approximation for the energy dissipation at fatigue crack tip was proposed. The proposed phenomenological equation gives a good qualitative description of peculiarities of the heat dissipation. For the constant stress amplitude the plastic work and, as a consequence, energy dissipation at the crack tip is a linear function of the crack rate but for the constant crack rate mode the scenarios with a drop in the heat dissipation takes place. This approximation was confirmed by the experimental heat measurement from the crack tip under two experimental tests (constant stress amplitude and constant stress intensity factor) and different coefficients of biaxiality.

A CKNOWLEDGMENTS

T

he work was supported by the Russian Science Foundation (grant No. 19-77-30008).

R EFERENCES

[1] Matvienko, Yu.G., Morozov, E M. (2004). Calculation of the energy J-integral for bodies with notches and cracks, International Journal of Fracture, 125, pp. 249-261. [2] Rosakis, P., Rosakis, A.J., Ravichandran, G., Hodowany, J. A, (2000). Thermodynamic internal variable model for the partitional of plastic work into heat and stored energy in metals, J. Mech. Phys. Solids, 48, pp. 581-607. [3] Oliferuk, W., Maj, M., Raniecki, B. (2004). Experimental Analysis of Energy Storage Rate Components during Tensile Deformation of Polycrystals, Materials Science and Engineering, 374, pp. 77-81. [4] Izyumova, A., Plekhov, O. (2014). Calculation of the energy J-integral in plastic zone ahead of a crack tip by infrared scanning, FFEMS, 37, pp. 1330–1337. [5] Meneghetti, G., Ricotta, M. (2016). Evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack, International Journal of Fatigue, 92(2), pp. 605-615. [6] Risitano, A., Risitano, G. (2013). Cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameter, International Journal of Fatigue, 48, pp. 214-222. [7] Ranganathan, N., Chalon, F., Meo, S. (2008). Some aspects of the energy based approach to fatigue crack propagation Original research article, International Journal of Fatigue, 30, pp. 1921-1929. [8] Fedorova, A.Yu., Bannikov, M.V., Terekhina, A.I., Plekhov, O.A. Heat dissipation energy under fatigue based on infrared data processing (2014). Quantitative InfraRed Thermography Journal, 11(1), pp. 2-9 [9] Vshivkov, А., Iziumova, A., Bär, U., Plekhov, O. (2016). Experimental study of heat dissipation at the crack tip during fatigue crack propagation, Frattura ed Integrità Strutturale, 35, pp. 131-137. [10] Raju, K.N. (1972). An energy balance criterion for crack growth under fatigue loading from considerations of energy of plastic deformation, International Journal of Fracture Mechanics, 8(1), pp. 1-14. [11] Dixon, J.R. (1965). Stress and strain distributions around cracks in sheet materials having various work-hardening characteristics, Ministry of Technology, National Engineering Laboratory, Materials Group: East Kilbride, Glasgow, Scotland, pp. 224-244.

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