Issue 41

Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

Table of Contents

M. A. Meggiolaro, J. T. Pinho de Castro, H. Wu A two-step multiaxial racetrack filter algorithm for non-proportional load histories …............................ 1 G. Meneghetti, A. Campagnolo, F. Berto, K. Tanaka Crack initiation life in notched Ti-6Al-4V titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach ……………………………………. 8 M. Sakane, T. Itoh Cracking directions in multiaxial low cycle fatigue at high and room temperatures …………….…… 16 M. Kurek, T. Łagoda Determination of the critical plane orientation depending on the fatigue curves for bending and torsion ..... 24 V. Shlyannikov, R. Yarullin, I. Ishtyryakov Effect of different environmental conditions on surface crack growth in aluminum alloys …….....……… 31 A. Carpinteri, A. Spagnoli, S. Vantadori Effect of spectral cross-correlation on multiaxial fatigue damage: simulations using the critical plane approach ………......…………………………………………………………………...… 40 T. Morishita, F. Ogawa, T. Itoh Evaluation and visualization of multiaxial fatigue behavior under random non-proportional loading condition ............................................................................................................................................ 45 A. S. Cruces, P. Lopez-Crespo, B. Moreno, A. Lopez-Moreno, S. Suman Evaluation of new multiaxial damage parameters on low carbon steel …................................................. 54 J. Toribio, J.C. Matos, B. González Influence of crack micro-roughness on the plasticity-induced fatigue propagation in high strength steel ….... 62 A. Carpinteri, G. Fortese, C. Ronchei, D. Scorza, S. Vantadori, F. Berto Joined application of a multiaxial critical plane criterion and a strain energy density criterion in low-cycle fatigue .……....................................................................................................................................... 66 T. Morishita, Y. Takada, T. Itoh Multiaxial fatigue property of type 316 stainless steel using hollow cylinder specimen under combined pull loading and inner pressure ………………………………………………………………….. 71

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Fracture and Structural Integrity, 41 (2017); ISSN 1971-9883

F. Berto, A. Campagnolo, T. Welo, S. Vantadori, A. Carpinteri Multiaxial fatigue strength of titanium alloys …………………………………………...……... 79 M.V.C Sá, J.L.A Ferreira, C.R.M da Silva, J.A. Araújo Notched multiaxial fatigue of Al7050-T7451: on the need for an equivalent process zone size ……….. 90 M. A. Meggiolaro, J. T. Pinho de Castro, S. E. Ferreira, H. Wu On the applicability of Miner’s rule for multiaxial fatigue life calculations under non-proportional load histories …………………………………………………………………………………. 98 J.V. Sahadi, D. Nowell, R.J.H. Paynter Prediction of fatigue crack initiation under biaxial loading …………………………………..…... 106 M. Vormwald, E. Shams Sharp three-dimensional notches under combined nominal normal and shear fatigue loading …………... 114 K. Slámečka, J. Pokluda Simple criterion for predicting fatigue life under combined bending and torsion loading ……………… 123 S. E. Ferreira, J. T. Pinho de Castro, M. A. Meggiolaro A model to quantify fatigue crack growth by cyclic damage accumulation calculated by strip-yield procedures ……………………………………………………………………………....... 129 J. Toribio, B. González, J.C. Matos Crack tip field in circumferentially-cracked round bar (CCRB) in tension affected by loss of axial symmetry …………………………….……................................................................................ 139 D.-Q. Wang, M.-L. Zhu, F.-Z. Xuan, J. Tong Crack tip strain evolution and crack closure during overload of a growing fatigue crack ……………...... 143 F.V. Antunes, R. Simões, R. Branco, P. Prates Effect of numerical parameters on plastic CTOD ………………………………...………..…... 149 J.M. Vasco-Olmo, F.A. Díaz, F.V. Antunes, M.N. James Experimental evaluation of CTOD in constant amplitude fatigue crack growth from crack tip displacement fields ……………………………....………………………………………… 157 J.M. Vasco-Olmo, F.A. Díaz, M.N. James, C.J. Christopher, E.A. Patterson Experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields ……………......................................................................................................... 166 A. Carpinteri, A. Spagnoli, M. Terzano, S. Vantadori Fracture toughness of rough and frictional cracks emanating from a re-entrant corner ……………… 175 J. Klon, J. Sobek, L. Malíková, S. Seitl Impact of specific fracture energy investigated in front of the crack tip of three-point bending specimen ........ 183 P. Lorenzino, J.-Y. Buffiere, C. Verdu Influence of forging conditions on the fatigue mechanisms of low alloy steels: a 3D study………...……... 191 D. Nowell, K.I. Dragnevski, S.J. O’Connor Measurement and analysis of fatigue crack deformation at the micro-scale ...................................……... 197

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Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

P. Lopez-Crespo, J. Vazquez-Peralta, C. Simpson, T. Buslaps, P. J. Withers Mid-thickness studies of the stress intensity factor in the bulk of bainitic steel ……………………….. 203 H. Šimonová, M. Vyhlídal, B. Kucharczyková, P. Bayer, Z. Keršner, L. Malíková, J. Klusák Modelling of interfacial transition zone effect on resistance to crack propagation in fine-grained cement based composites ……………........................................................................................................... 211 Y. Nadot, D. Halm, F. Dal Cero Coelho Gradient approach for the evaluation of the fatigue limit of welded structures under complex loading ......... 220 J. A. O. González, J. T. P. de Castro, G. L. G. Gonzáles, M. A. Meggiolaro, J. L. F. Freire On DIC measurements of  K eff to verify if it is the FCG driving force ………….................................. 227 V. M. Machado, J. T. P. de Castro, M. A. Meggiolaro On short cracks that depart from elastoplastic notch tips …………………………….……............ 236 T. Vojtek, S. Žák, J. Pokluda On the connection between mode II and mode III effective thresholds in metals ………………………. 245 A. A. Ahmed, L. Susmel On the use of length scale parameters to assess the static strength of notched 3D-printed PLA………… 252 F. Berto, M.R. Ayatollahi, S. Vantatori, A. Carpinteri Review of the Influence of non-singular higher order terms on the stress field of thin welded lap joints and small inclined cracks in plates ………………………………………………..……….……... 260 S. Beretta, L. Patriarca, S. Rabbolini Stress Intensity Factor calculation from displacement fields …………………………………….... 269 L. Patriarca, P.G. Luccarelli, S. Foletti Study of strain localizations in a polycrystalline medium in presence of a quasi-static crack …………..... 277 V. Shlyannikov, A. Tumanov The effect of creep damage formulation on crack tip fields, creep stress intensity factor and crack growth assessments …………………………….……............................................................................. 285 A.S. Chernyatin, Yu.G. Matvienko, I.A. Razumovsky The effect of residual stress on the nonsingular T-stresses ………………………………….……... 293 G. Meneghetti, M. Ricotta The heat energy dissipated in a control volume to correlate the crack propagation rate in stainless steel specimens …………………………….………………………………………………....... 299 A. Cernescu The influence of crack tip shielding on fatigue crack propagation …………...……………….……... 307 M. Vormwald, Y. Hos, J. L.F. Freire, G.L.G. Gonzáles, J.G. Díaz Variable mode-mixity during fatigue cycles – crack tip parameters determined from displacement fields measured by digital image correlation ……….…………………….……………………....…... 314

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S. Seitl, L. Malíková, J. Sobek, P. Frantík, P. Lopez-Crespo Williams expansion-based approximation of the stress field in an Al 2024 body with a crack from optical measurements …………………………….……............................................................... 323 G. G. de Cunto, A. H. Paes de Andrade, W. A. Monteiro Application of Leak-Before-Break concept in 316LN austenitic steel pipes welded using 316L ……… 332 Y. Yang, J. Zheng, S. Lv Research on differences and correlation between tensile, compression and flexural moduli of cement stabilized macadam ………………………………………………………………...……... 339 R. M. De Salvo An original method of direct calculation for the identification of the last hinge and the definition of the deformative state at collapse …………………………….…………………………………... 350 L. Zhang, S. Li, Q. Yan, L. Zhu Study on the effect of new type liquid accelerator on the performance of shotcrete ……………………... 356 E. Nurullaev, A. S. Ermilov, N. Yu. Lyubimova Dependence of mechanical characteristics from composition and structure and optimization of mechanical fracture energy of polymer composite material based on high-molecular rubbers ……………………… 369 Z. Li, Z. Zhao Residual welding stress of I-section members beyond the limits of width-thickness ratio ……………….. 378 X. Wu, L. Dai Carbon nano-tubes in improving the mechanical property of cement-based composite materials ………… 388 C. F. Markides, S. K. Kourkoulis Parametric study of the deformation of transversely isotropic discs under diametral compression ……… 396 S. Zhao, L. Chen, Y. Fu An experimental study on mechanical properties of fiber-reinforced concrete of energy piles …………….. 412 S. Doddamani, M. Kaleemulla Fracture toughness investigations of Al6061-Graphite particulate composite using compact specimens ..... 484 V. Rizov Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non linearity …………………………….……………………………………………….…... 491 A. Mardalizad, R. Scazzosi, A. Manes, M. Giglio Four-point bending test on a middle strength rock: numerical and experimental investigations ………… 504 M. F. Funari, F. Greco, P. Lonetti Dynamic debonding in layered structures: a coupledALE-cohesive approach……………………....... 524 S. K. Kourkoulis, I. Dakanali, E. D. Pasiou, I. Stavrakas, D. Triantis Acoustic Emissions versus Pressure Stimulated Currents during bending of restored marble epistyles: Preliminary results …………………………….…….................................................................. 536

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Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

E. Tolmacheva (Lyapunova), M. Davydova, V. Chudinov, S. Uvarov, D. Zaytsev, P. Panfilov, O. Naimark Regularities of fracture pattern formation in alumina ceramics subjected to dynamic indentation ……….. 552

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Fracture and Structural Integrity, 41 (2017); ISSN 1971-9883

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Associate Editors Alfredo Navarro

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

Thierry Palin-Luc

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

Luca Susmel John Yates

Guest Editors ( “ Multiaxial Fatigue” and “ C rack Tip Fields” ) Franck Morel (Arts et Metiers ParisTech, France ) Thierry Palin-Luc (Arts et Metiers ParisTech, France) Neil James (University of Plymouth, UK) Youshi Hong (Chinese Academy of Sciences, China) Luca Susmel (University of Sheffield, UK) Nicolas Saintier (Arts et Metiers ParisTech, France) Sylvie Pommier

(ENS Paris-Saclay, University Paris Saclay, France)

Advisory Editorial Board Harm Askes

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

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

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

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(University of California, USA)

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

(University of Illinois at Urbana-Champaign, USA)

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

Editorial Board Stefano Beretta

(Politecnico di Milano, Italy)

Filippo Berto Nicola Bonora

(Norwegian University of Science and Technology, Norway) (Università di Cassino e del Lazio Meridionale, Italy)

Elisabeth Bowman

(University of Sheffield) (Università di Parma, Italy) (Politecnico di Torino, Italy) (EADS, Munich, Germany) (EDAM MIT, Portugal)

Luca Collini

Mauro Corrado

Claudio Dalle Donne Manuel de Freitas Vittorio Di Cocco

(Università di Cassino e del Lazio Meridionale, Italy)

Daniele Dini

(Imperial College, UK)

Giuseppe Ferro Tommaso Ghidini

(Politecnico di Torino, Italy)

(European Space Agency - ESA-ESRIN) (Universitat Politecnica de Valencia, Spain)

Eugenio Giner

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Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

Stavros Kourkoulis Paolo Lonetti Carmine Maletta Liviu Marsavina Hisao Matsunaga Mahmoud Mostafavi Lucas Filipe Martins da Silva

(National Technical University of Athens, Greece)

(Università della Calabria, Italy) (Università della Calabria, Italy) (University of Timisoara, Romania) (University of Porto, Portugal)

(Kyushu University, Japan) (University of Sheffield, UK)

Marco Paggi Oleg Plekhov

(IMT Institute for Advanced Studies Lucca, Italy)

(Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi

(Università di Parma, Italy)

Luis Reis

(Instituto Superior Técnico, Portugal)

Luciana Restuccia Giacomo Risitano Roberto Roberti Aleksandar Sedmak Andrea Spagnoli Sabrina Vantadori Natalya D. Vaysfel'd Charles V. White Marco Savoia

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Brescia, Italy) (Università di Bologna, Italy) (University of Belgrade, Serbia) (Università di Parma, Italy) (Università di Parma, Italy)

(Odessa National Mechnikov University, Ukraine)

(Kettering University, Michigan,USA)

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Fracture and Structural Integrity, 41 (2017); 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 (July, October, January, April). 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, 41 (2017); International Journal of the Italian Group of Fracture

International Congress on Fracture (ICF) Announces Winners of 2017 ICF Medals Shouwen Yu, President David Taplin, Treasurer-Chief Executive Officer, President Emeritus Alberto Carpinteri, ICF Awards Committee Chair

Each quadrennium, the International Congress on Fracture, ICF, the world’s premier professional society of researchers pursuing the understanding and causes of fracture to prevent fracture and damage progression in engineering materials and structures, recognizes select members for their outstanding contributions to this important field of research. The field of Fracture and Structural Integrity is relevant to Aerospace, Power Generation, Chemical Process, Biomedical, Structural Materials, Electronics, and Recreation industries and in Geophysics and engages researchers in several academic disciplines. Four gold medals, and one silver medal named after pioneers in the field of fracture are presented at its quadrennial conference. The selection of winners was made by a committee consisting of past medal recipients. The Takeo Yokobori Gold Medal , named after the founder of ICF, an outstanding researcher in the field, and the organizer of its first quadrennial conference in 1965 in Sendai, Japan, is presented to individuals who have excelled in research in the field of fracture and have also provided life-time service to ICF. Previous recipients of the medal are Professors David Taplin (2009), Yiu Wing Mai, Palle Rama Rao, and Teruo Kishi (2013). Alan H. Cottrell Gold Medal is named after a pioneer in the field whose many scientific contributions in the field of micromechanisms of fracture are well known for decades and have provided deep understanding of fracture in structural materials. This award is presented to senior researchers in the field of fracture who have similarly made pioneering contributions to the understanding of the phenomenon of fracture. Previous recipients of this medal are Professors Robert O. Ritchie (2009), John F. Knott and Subra Suresh (2013). George R. Irwin Gold Medal is named after the individual who is widely known as the “Father of Modern Fracture Mechanics” and whose work provided the scientific basis for this interdisciplinary field. This award is presented to a senior

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Fracture and Structural Integrity, 41 (2017); ISSN 1971-9883

researcher whose pioneering contributions have had lasting impact on engineering applications of fracture theories. Previous recipients of this medal are Professors Paul C. Paris (2009), James R. Rice, and John A. Hutchinson (2013). Paul C. Paris Gold Medal honours the many pioneering contributions of Prof. Paul C. Paris to the field of Fracture Mechanics. His contributions in field of sub-critical crack growth include the discovery of the “Paris-Law” for fatigue crack growth. This award is presented to senior researchers whose pioneering contributions have had a lasting impact on structural integrity assessment methods. Previous winners of this medal include Professors Alberto Carpinteri and Y. Murakami (both in 2013). Constance F. Tipper Silver Medal honours the memory and contributions of Constance Tipper who was a true pioneer in the field of fracture and the author of the popular book “The Brittle Fracture Theory”. The silver medal is awarded to a mid-career scientists/engineers who have made significant contributions in any aspect of research in the field of fracture. Previous recipients are Professors Julia King (Baroness Brown of Cambridge), Diane Lados, and Namrata Gundiah (all 2013). In 2017, ICF named six scientists to receive its highest honour, the gold medals, and two mid-career scientists to receive silver medals. These medals will be awarded in a ceremony to be held at the Fourteenth International Conference on Fracture, ICF14, in Rhodes, Greece between June 18-23, 2017 (see www.icf14.org ) for details of the conference.

Professors A. Toshimitsu Yokobori (Japan) and Emmanuel Gdoutos (Greece) are the co-recipients of the 2017 ICF Takeo Yokobori Gold Medal

A. Toshimitsu Yokobori Emmanuel E. Gdoutos Professor Yokobori, Jr. is Professor Emeritus of Tohoku University and Visiting Professor at Teikyo University in Japan. He has made seminal contributions in multiscale fracture analyses across nano, meso, to macro scales and is widely recognized for his contributions. His dislocation dynamics theory of fatigue crack growth and threshold stress intensity factor is cited in many books and review articles and is popularly known as Yokobori’s theory. He has also contributed extensively to characterizing fracture and crack growth at elevated temperatures and has led several national programs in these areas. The Q* concept that he co-authored with his father, Prof. Takeo Yokobori, is based on a thermally activated theory of creep crack growth has enabled the prediction of creep crack growth rate and fracture life. Prof. Yokobori has served as the Secretary General of ICF continuously since 2001 and as a member of the ICF Council from Japan since 1989. He was named Honorary Fellow of ICF in 2013. Professor Emmanuel E. Gdoutos serves as Full Member of the Academy of Athens, the most prestigious academic institute in Greece. He has made seminal contributions in the field of Experimental Mechanics, Fracture Mechanics, Nanotechnology and their applications to composite materials and sandwich structures for civil engineering structures. He has authored/co-authored more than 300 technical papers and 40 reference and text books, among them the book “Fracture Mechanics – An Introduction” used for fracture mechanics courses worldwide. He has served as President/Chair of several technical societies including the European Structural Integrity Society and conferences. He is member of European, American and foreign national academies and received awards from international societies. He was awarded a Doctorate Honoris Causa from the Russian Academy of Sciences and from the University of Nis, Serbia. He is the Sr. Vice President and Fellow of ICF and is the Executive Chair of ICF14 in Rhodes, Greece in June 2017.

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Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

Professor Michael F. Ashby (Cambridge University, UK) will receive the 2017 ICF Alan Cottrell Gold Medal Professor Ashby is Emeritus Professor in the Engineering Department at Cambridge University in the U.K and the co founder and Chairman of Granta Design, Cambridge, UK, a company specializing in Materials Informatics. He has made seminal contributions in the systematic materials selection and to the understanding of deformation in metals and its relationship to fracture mechanisms. His books on material selection are widely used throughout the world. He is the past ICF Honour Lecturer and an Honorary Fellow of ICF. He is a Fellow of the Royal Society, the Royal Academy of Engineering. He was made an CBE in 1997.

Michael F. Ashby

Professor Robert V. Goldstein (A.Yu. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Russia) will receive the 2017 ICF George R. Irwin Gold Medal Professor Goldstein is well known for his seminal contributions to understanding resonance phenomena accompanying interface crack propagation, for developing conditions of crack deviation in isotropic and orthotropic bodies, and for modeling the processes of formation of ordered crack systems under multiaxial loading. His contributions to qualitative methods of fracture mechanics led to estimates of the stress intensity factors for cracks of complex shapes and also sufficiency conditions for fracture in structural components. He developed a semi-empirical approach to fracture analysis of elastoplastic materials and suggested the similarity criteria for modeling fracture conditions of large-scale structures using results from testing their small-scale models. He has conducted innovative work in mechanics of ice and ice cover fracture under compression. Professor Goldstein has served ICF as Vice-President, Director, Member of Executive Committee and the Nominations Committee. He is Honorary Fellow of ICF (1993) and Emeritus Vice-President (2010).

Robert V. Goldstein

Professors Richard W. Hertzberg (Lehigh University, USA) and Ashok Saxena (University of Arkansas, USA) are co-recipients of the 2017 ICF Paul C. Paris Gold Medal. Professor Richard Hertzberg is New Jersey Zinc Professor Emeritus and former Chair of Lehigh University’s Materials Science and Engineering Department. His investigations emphasized the fatigue crack propagation (FCP) response in metals, composites, and polymeric solids. These investigations examined microstructural and atomistic variables in metal

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alloys; estimation of short crack behavior, utilizing Kmax-constant test procedures; interpretation of macroscopic and microscopic fatigue fracture surface markings; and studies of overload interaction effects on FCP behavior. His and Dr. John Manson’s pioneering studies associated with the FCP response of engineering plastics explored the role of molecular weight, second phase particles, test frequency, and identified unique fractographic features in polymeric solids. In addition, Prof. Hertzberg has had a distinguished university teaching career along with organizing and teaching numerous fracture mechanics short courses in Asia, Europe and U.S. His six textbooks on fracture mechanics and fatigue of engineering plastics are highly regarded. He is recipient of the TMS Educator Award, Fellow of ASMI, and numerous research and teaching awards.

Richard Hertzberg Ashok Saxena Professor Saxena is a Distinguished Professor and Dean Emeritus in the Department of Mechanical Engineering at the University of Arkansas. His contributions to time-dependent fracture mechanics (TDFM) enabled its use in materials selection and in establishing criteria for reliability assessment and fracture resistance of high temperature components. His specific contributions include proposing, and validating the Ct parameter for predicting creep crack growth under small scale-creep and transient conditions and its extension for use under simultaneous creep and fatigue loading. These developments have led to several international material test standards. He has held leadership positions in ICF as Vice President and the Awards Committee Chair. He is an honorary fellow of ICF and has received awards including the George Irwin Medal and the Fracture Mechanics Medal from ASTM and the Wohler Fatigue Medal from ESIS; he is an elected member of the European Academy of Sciences. Professors Sylvie Pommier (University Paris Saclay, France) and Francesco Iacoviello (University of Cassino, Italy) are the co-recipients of the Constance Tipper Silver Medal

Sylvie Pommier Francesco Iacoviello Professor Sylvie Pommier serves as a Full Professor in the Department of Mechanical Engineering at Ecole Normale Supérieure Paris-Saclay (Université Paris-Saclay). She is recognized for her contributions to the advancement of nonlinear fracture mechanics for fatigue crack growth under complex loading conditions in metals and structures. She developed an incremental model for crack growth based on principal components analysis and the thermodynamics of irreversible processes. This method allows modeling of crack growth that is accompanied by non-linear material behavior with a formalism based on non-local state variables especially tailored for characterizing the non-linear behavior of the material

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Frattura ed Integrità Strutturale, 41 (2017); International Journal of the Italian Group of Fracture

around moving singularities, such as crack fronts, with the minimum possible independent degrees of freedom. The approach was applied to complex loading conditions (variable amplitude fatigue, non-proportional mixed mode loading, non-isothermal loading conditions, fatigue & oxidation) and various materials. Professor Iacoviello serves as Professor in the Department of Civil and Mechanical Engineering at the University of Cassino, Italy. He is recognized for his contribution to mechanical metallurgy, specifically for his work on fracture and crack growth behavior of alloys such as duplex steels and ductile cast irons and the influence of environment on their performance. His work has led to a better understanding of the effect of chemical composition and microstructure on environmentally assisted fatigue crack propagation and the underlying micro-mechanisms, in air and in hydrogen charged conditions. His work on ductile cast irons has included characterization of the micro-mechanisms of damage development using a low cost and patented micro testing machine that he designed and developed allowing him to perform in situ SEM observations during the mechanical testing. He has been a long-term contributor to ICF including holding important leadership positions as ICF Director.

Pictures of Y. Murakami (left) and Alberto Carpinteri (right) receiving the Paul C. Paris Gold Medal from Late Prof. Paris at ICF13 in Beijing, June 2013. April 15, 2017 For more information, contact,

Professor Alberto Carpinteri, Chair of Structural Mechanics Dept. of Structural, Geotechnical and Building Engineering Politecnico di Torino, Corso Duca degli Abruzzi, 24 10129 Torino (Italy) Tel. +39.011.564 4850, alberto.carpinteri@polito.it

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

Focused on Multiaxial Fatigue

A two-step multiaxial racetrack filter algorithm for non-proportional load histories

Marco Antonio Meggiolaro, Jaime Tupiassú Pinho de Castro Pontifical Catholic University of Rio de Janeiro, PUC-Rio, R. Marquês de São Vicente 225, Rio de Janeiro, 22451-900, Brazil meggi@puc-rio.br, jtcastro@puc-rio.br Hao Wu School of Aerospace Engineering and Applied Mechanics Tongji University, Siping Road 1239, 200092, Shanghai, P.R.China wuhao@tongji.edu.cn

A BSTRACT . The recently proposed multiaxial racetrack filter (MRF) is able to deal with general non-proportional multiaxial load histories. While only requiring a single user-defined scalar filter amplitude, the MRF is able to synchronously eliminate non-damaging events from any noisy multiaxial load history without changing the overall shape of its original path, a necessary condition to avoid introducing errors in fatigue damage assessments. The MRF procedures are optimized here by the introduction of a pre-processing “partitioning” step on the load history data, which selects candidates for the reversal points in a robust partitioning process, highly increasing the filter efficiency and decreasing its computational time. The improved MRF is evaluated through the fatigue analyses of over-sampled tension-torsion data measured in 316L stainless steel tubular specimens under non-proportional load paths. K EYWORDS . Multiaxial racetrack filter (MRF); Partitioning operation; Multiaxial variable amplitude loading; Amplitude filter.

Citation: Meggiolaro, M.A., Castro, J.T.P., Wu, H., A two-step multiaxial racetrack filter algorithm for non-proportional load histories, Frattura ed Integrità Strutturale, 41 (2017) 1 7.

Received: 28.02.2017 Accepted: 15.04.2017 Published: 01.07.2017

Copyright: © 2017 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

atigue load histories measured under actual field conditions usually are noisy, over-sampled, and contain too many non-damaging low-amplitude events that can largely increase the subsequent fatigue damage calculation burden. This problem has long been recognized and properly dealt with in traditional uniaxial analyses, but it is still much more important for multiaxial fatigue damage calculations, which can even become impractical if not properly filtered to remove from the data non-damaging events before performing such complex calculations, in particular under non proportional (NP) loading conditions, so common in practical applications. F

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

Consequently, a most important practical issue in multiaxial fatigue analyses is how to reduce a large amount of redundant multiaxial data to a manageable size to decrease their intrinsically high computational cost, while maintaining all the essential features of the load history that contribute to plasticity memory effects. Needless to say, this is an unavoidable step to not underestimate fatigue damage, an inadmissible feature in practical applications. Uniaxial amplitude filters can be directly implemented in the cycle counting algorithm, usually based on the rainflow method [1-4]. But the original rainflow procedure can only be started after the entire load history is known, increasing even more the computational cost as well as computer memory requirements, which can be quite significant for very long histories. Computational cost can be dramatically reduced with ‘‘real-time” rainflow algorithms, such as the pioneer Martin–Topper–Sinclair’s 1971 method [5], which essentially reproduces in real time the uniaxial rainflow algorithm as the load events are provided or measured. The original racetrack filter, proposed by Fuchs et al. in 1973 [6], can sequentially filter small amplitudes, but it is limited to uniaxial histories. Simplistic amplitude filters based on the uniaxial racetrack are not recommended in multiaxial analyses, because the path between two load reversals is needed to evaluate the path-equivalent stress or strain amplitude associated with each rainflow count, e.g. using a convex-enclosure method [7, 8]. Moreover, the reversal points obtained from a multiaxial rainflow algorithm might not occur at the reversal of one of the stress or strain components [9]. In this work, a multiaxial version of the racetrack filter proposed by the authors in [10-13] is reviewed and optimized. While only requiring a single user-defined scalar filter amplitude, it is able to synchronously filter complex loading histories while preserving all key features of the loading path. The filtering process is optimized through the introduction of a pre-processing “partitioning” operation on the load history data, highly increasing its efficiency. Over-sampled experimental data from tension-torsion experiments in 316L stainless steel tubular specimens under NP load paths are used to verify the efficiency and robustness of the proposed method. n the multiaxial racetrack filter (MRF) algorithm originally proposed in [10], the load history path must first be represented in an appropriate stress or strain space. Several spaces were proposed in [11], some of them separating the stresses or strains in their deviatoric and hydrostatic components, to allow for a filtering metric based on Mises equivalent values or even damage parameters. Fig. 1 shows an example of a tension-torsion loading following an elliptical stress path, represented in a normal vs. effective shear stress space  x   xy  3 through a series of 238 over-sampled points (for each periodic cycle), represented as “  ” marks. However, spaces with higher dimensions would be necessary for general 6D multiaxial load histories. Several of these points could be filtered out without compromising the subsequent multiaxial fatigue life calculations. This amplitude-filtering process is a most desirable step in practical applications, to eliminate unavoidable measurement noise and redundant over-sampled data, as well as small amplitudes that do not cause fatigue damage [12]. But it is important to avoid filtering out important counting points from multiaxial rainflow algorithms, or significant history paths that can affect the calculation of a path-equivalent stress or strain, since all stress or strain components contribute altogether for the reversals that can be eliminated. The MRF requires a user-defined scalar filter amplitude r, which is graphically represented in Fig. 1 as the radius of the small dashed circle centered at point 1. In this example, r  80MPa was chosen as the amplitude, which in the  x   xy  3 space has a clear physical meaning: r is the Mises distance between two stress states, due to the adopted  3 scaling factor used in the shear component. The MRF algorithm, thoroughly described in [10-13], was able to reduce the 238 over sampled measurements to only 8, guaranteeing that no filtered-out data lies beyond r  80MPa of the resulting polygonal path 1-2-3-4-5-6-7-8-1. This filtering process results in a dramatic decrease of the computational time needed for further multiaxial fatigue life calculations, especially considering that the original 238 points were from a single elliptical path. More refined outputs can be achieved simply by reducing the user-defined value of the (combined) amplitude filter r. For instance, in the above example, r  5MPa would better describe the elliptical shape of the original stress path, but it would need 31 points instead of 8 to represent it; still, 31 is much better than the original 238 points per cycle. The filter amplitude r can also be varied as a function of the instantaneous normal stresses, to better consider mean and peak-stress effects, as discussed in [12]. Moreover, the MRF also works with non-periodic load histories, using the same algorithm. I T HE M ULTIAXIAL R ACETRACK F ILTER (MRF)

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

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Figure 1 : Application of the MRF on a tension-torsion  x   xy

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It is important to note that the MRF does not filter out load reversals, which can be interpreted as sudden changes in path direction of more than 90 degrees. This is a major advantage over simplistic algorithms such as the “Peaks Procedure” [14], which filters out all points (events) whose components are not peaks or valleys. This non-conservative procedure potentially eliminates important load points that could have the highest Mises stresses or strains of the load history, even though each individual load component was not maximized. Moreover, the “Peaks Procedure” stores each and every event that constitutes a peak or valley from any single component, which for (unavoidably noisy) real measurements could result in no events at all being filtered out, even if the noise had very low amplitudes. Despite its efficiency and robustness, the MRF can still be optimized to better describe the original path using the same number of sampling points. For instance, in Fig. 1 it can be seen that the segment 4-5 faithfully describes the original sampled points, however the segments 6-7 and 7-8 do not reproduce well the originally curved path. One way to improve this issue is to use a smaller filter amplitude, lower than the adopted r = 80MPa, however at a cost of filtering out fewer points, requiring more than 8 to represent the load path in this case. A more efficient way is proposed next, where a pre processing “partitioning” operation is performed on the original sampled points, resulting in a better description of the path with fewer data points. efore applying the MRF algorithm, it is here proposed to perform an improved pre-processing “partitioning” operation on the multiaxial load history data, described as follows. The first step involves choosing the first sample point of the multiaxial load history, tagged with the number 1. For periodic histories, point 1 can be any point from the cyclic load path, see Fig. 2(a). Then, find the sampled point most distant to 1, labeling it as 2, creating two partitions of the original sample points, defined by the paths {1  2} and {2  1}. In the considered tension-torsion example in the  x   xy  3 space, point 2 results in the one with the highest relative Mises stress range with respect to point 1. If more than one point has the same maximum distance from 1, then choose any one of them to become point 2, ignoring the others. Note however that, for non-periodic load histories, points 1 and 2 should be simply defined as the first and last ones from the entire history, respectively. B MRF O PTIMIZATION THROUGH P ARTITIONING

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

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Figure 2 : Improved partitioning operation on tension-torsion data, showing: (a) joining the previously defined points 1 and 2 of the load history with a straight line; (b) finding the load points 3 and 4 most distant from this line, creating two partitions; (c) finding the points most distant to each segment to subdivide it into additional segments; and (d) continuing the process until reaching the chosen filter amplitude value. The next step of the pre-processing involves joining points 1 and 2 with a straight line, and then finding the load points 3 and 4 most distant from it. Note that point 3 lies in the 1  2 path whereas point 4 lies in the 2  1, as shown in Fig. 2(b). Since this maximum distance is higher than the chosen filter amplitude r, create further partitions {1  3}, {3  2}, {2  4} and {4  1} of the original path, see Fig. 2(b). Next, look for the load point in the {1  3} partition that is most distant from the straight line joining 1 and 3; if this maximum distance is higher than r, then create additional two partitions {1  5} and {5  3} from {1  3}, see Fig. 2(c). Analogously, look for the load point in the {3  2} partition that is most distant from the straight line joining 3 and 2; if this maximum distance is higher than r, then create two partitions {3  6} and {6  2} from {3  2}. The process continues for the remaining partitions, as long as the associated maximum distance is still higher than r. The pre-processing process continues for all created partitions, ending only when all such maximum distances are not higher than the chosen filter amplitude r. Consequently, each of the resulting partitions is such that all points it contains are within a distance r of the straight line joining its extremes. Note that the remaining sample points that were not labeled are not yet eliminated, because they could contain load reversions that are not detected in this pre-processing step, as discussed later.

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

In the studied tension-torsion example, this partitioning results in the 8 points from Fig. 2(c) for r  80MPa. Note how the resulting polygonal path better represents the original history than the one from Fig. 1, where no pre-processing had been performed, using the same number of points. Fig. 2(d) shows the partitioning results if the filter amplitude is refined adopting r  5MPa, resulting in 16 points per cycle, but with a better description of the load path. After (and only after) the pre-processing partitioning ends, the MRF is individually applied to each partition, with a filter surface translation direction [10-12] defined from the extremes of each partition. For instance, for r  80MPa, the partitioning output shown in Fig. 2(c) would require the application of the MRF on the points in the {1  5} path, starting from 1 and with a filter surface translation direction defined by the segment 1  5; then apply the MRF again in the {5  3} path, starting from 5 and in the 5  3 direction; and so on, until processing the segment {8  1}. In this particular example, all non-labelled sample points ended up filtered out by the MRF, but this might not be the case in more complex paths, as exemplified below. As a result, the output of the MRF will consist of all load points (from all partitions) that did not suffer static or dynamic filtering. This combination of partitioning followed by the MRF is very efficient, resulting in quasi-optimal filtered histories for a given r, without the need to arbitrarily define or optimize the hyper-sphere translation directions [10-12] in higher-dimensional cases. Fig. 3 shows a more complex NP tension-torsion stress path that needs both partitioning and MRF steps to properly filter its 488 sample points (per cycle) without losing significant load reversions. Point 1 is arbitrarily chosen as the initial one in the tension-torsion cycle, and a filter amplitude of r = 80MPa is considered (graphically represented as the radius of the dashed circle around point 1). The pre-processing step then finds point 2 as the most distant from 1. Points 3 and 4 are then the ones most distant from the 1  2 straight line, both with distances greater than r = 80MPa. Since all points in the {1  3} path are within r = 80MPa of the straight segment 1  3, no further points are selected in this portion. The same applies for the {3  2}, {2  4} and {4  1} portions of the load path, ending the pre-processing step with only 4 identified points, marked with squares in Fig. 3. The MRF is then individually applied to each of these portions, using the same filter amplitude r = 80MPa, to be able to identify the important load reversal points 5, 6, 7, 8, 9 and 10, marked with triangles in Fig. 3. Note that a few load reversal points are purposely not identified, such as the ones in the {4  1} path, because their associated oscillation amplitudes are smaller than the chosen r = 80MPa, a desirable feature that the simplistic “Peaks Procedure” [14] would not be able to reproduce.

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M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01

E XPERIMENTAL V ERIFICATION

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o verify the efficiency of the optimized MRF, tension-torsion experiments are performed on annealed tubular 316L stainless steel specimens in an MTS 809.25 multiaxial testing machine, shown in Fig. 4(a). A relatively thin wall of 2 mm is used for the tubular specimens, to avoid having to deal with stress gradient effects across its thickness. Engineering stresses and strains are calculated from load/torque cell measurements and from an MTS 632.68 axial/torsional extensometer, and then converted to true stresses and strains [13]. The cyclic properties of this 316L steel are obtained from uniaxial tests, resulting in fitted Ramberg-Osgood uniaxial cyclic hardening coefficient 874MPa and exponent 0.123, with Young’s modulus 193GPa, Poisson ratio 0.3, and shear modulus 74GPa .

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The tests consist of strain-controlled  x

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challenging cyclic path sequence OABHAOCBDCOEDFEOGHFGO, see Fig. 4(b). Fig. 5 shows the resulting experimentally measured stabilized σ×τ  3 stress path (samples with  markers ) , as well as the optimized MRF output including the proposed pre-processing step (square markers) for a filter amplitude r = 15MPa. The measured σ×τ  3 stress paths are reduced from 1227 data points per cycle to only 52, showing a very good agreement in both ranges and shape. Notice that, despite being highly filtered, the optimized MRF outputs can almost exactly describe the original multiaxial load history, capturing not only all reversal points but also the load path shape, which is a most important feature for path-equivalent range calculations used in fatigue damage assessments.

C ONCLUSIONS

I n this work, an optimized version of the multiaxial racetrack filter (MRF) was proposed, applicable to general non proportional multiaxial histories. The MRF preserves load order, allowing the synchronous filtering of stress and strain histories, without filtering out important multiaxial load reversal points. The optimized version is based on a pre processing step that selects candidates for the reversal points, in a robust partitioning process. The filter efficiency was validated from tension-torsion experiments following complex non-proportional histories, without losing information on significant reversals, ranges or load path shapes.

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