Issue 30

Frattura ed Integrità Strutturale, 30 (2014); International Journal of the Italian Group of Fracture

Table of Contents

D. Taylor Fracture mechanics: inspirations from nature ……………………………………...……...….. 1 E. T. Bowman Friction, fragmentation and flow - mechanics of rock bursts, falls and avalanches ………...……...... 7 A. Martín-Meizoso, J. Aldazabal, J.L. Pedrejón, S. Moreno Resilience and ductility of oxy-fuel HAZ cut ………………………………………………... 14 R. Louks, H. Askes, L. Susmel Static assessment of ductile/brittle notched materials: an engineering approach based on the Theory of Critical Distances ……………………………………………………………………….. 23 G. Bolzon, G. Gabetta, B. Molinas An investigation on corrosion protection layers in pipelines for hydrocarbon transportation ………… 31 J. Toribio, M. Lorenzo, D. Vergara, V. Kharin Numerical analysis of hydrogen-assisted rolling-contact fatigue of wind turbine bearings …………… 40 F. Felli, A. Brotzu, D. Pilone, C. Vendittozzi, M. Caponero Use of FBG sensors for monitoring cracks of the equestrian statue of Bartolomeo Colleoni in Venice .. 48 L. Náhlík, P. Hutař, K. Štegnerová Critical applied stresses for a crack initiation from a sharp V-notch ………………………….. 55 V. Di Cocco, F. Iacoviello, A. Rossi, M. Cavallini Damaging micromechanisms characterization in a ferritic-pearlitic ductile cast iron ……………….. 62 F. Burgio, L. Pilloni, M. Scafè, P. Fabbri, A. Brentari, A. Brillante, T. Salzillo Cf/C composites: correlation between CVI process parameters and Pyrolytic Carbon microstructure ... 68 G. A. Ferro, S. Ahmad, R. A. Khushnood, J. M. Tulliani, L. Restuccia Improvements in self-consolidating cementitious composites by using micro carbonized aggregates ……. 75 S. Baragetti, F. Villa SCC and corrosion fatigue characterization of a Ti-6Al-4V alloy in a corrosive environment – experiments and numerical models …………………………………………………………. 84 B. Tyson, P. Ding, X. Wang Elastic compliance of single-edge-notched tension SE(T) (or SENT) specimens ………………….. 95 T. Voiconi, R. Negru, E. Linul, L. Marsavina, H. Filipescu The notch effect on fracture of polyurethane materials ……………………….……………….... 101

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Frattura ed Integrità Strutturale, 30 (2014); ISSN 1971-9883

J. Vázquez, C. Navarro, J. Domínguez Effect of the model’s geometry in fretting fatigue life prediction …………………………………. 109 R. Batista, R. Claudio, L. Reis, J. Aguilar Madeira, M. de Freitas Design optimization of cruciform specimens for multixial fatigue loading ………………………... 118 G. Pitarresi, A. Toscano, M. Scafidi, M. Di Filippo, S. Alessi, G. Spadaro Photoelastic stress analysis assisted evaluation of fracture toughness in hydrothermally aged epoxies …. 127 A. Namdar, X. Feng Evaluation of safe bearing capacity of soil foundation by using numerical analysis method ………… 138 A. Spagnoli, M. Migliazza, M. Zucali, A.M. Ferrero Thermal degradation in Carrara marbles as the cause of deformation of cladding slabs ……………. 145 C. Madrigal, V. Chaves, A. Navarro Numerical implementation of a multiaxial cyclic plasticity model for the Local Strain Method in low cycle fatigue ……………………………………………………………………………... 153 A. Chmel, I. Shcherbakov Damage initiation in brittle and ductile materials as revealed by a fractoluminescence study ………... 162 C. Maletta, L. Bruno, E. Sgambitterra Stress induced martensite at the crack tip in NiTi alloys during fatigue loading ………………….. 167 S. Seitl Wedge splitting test method: quantification of influence of marble tool bar by two-parameter fracture mechanics ………………………………………………………………………………. 174 J. Toribio, J.C. Matos, B. González, J. Escuadra Evolution of crack paths and compliance in round bars under cyclic tension and bending …………... 182 G. Meneghetti, M. Ricotta, B. Atzori The specific heat loss combined with the thermoelastic effect for an experimental analysis of the mean stress influence on axial fatigue of stainless steel plain specimens ……………………………….. 191 A. Risitano, G. Fargione, E. Guglielmino Determination of the linearity end for surface temperature curve in traction static tests …………….. 201 C. Barile, C. Casavola, G. Pappalettera, C. Pappalettere Considerations on the choice of experimental parameters in residual stress measurements by hole- drilling and ESPI ………………………………………………………………………. 211 T. Yin, A. Tyas, O. Plekhov, L. Susmel On the use of the Theory of Critical Distances to estimate the dynamic strength of notched 6063-T5 aluminium alloy ………………………………………………………………………… 220 N. Petrone, M. Saraceni Field Load Acquisition and variable amplitude fatigue testing on maxi-scooter motorcycles …...…… 226 C. Putignano, L. Afferrante,G. Carbone, G. Demelio Double peeling of elastic pre-tensioned tapes …………………………………………………. 237 P. Lopez-Crespo, B. Moreno, A. Garcia-Gonzalez, J. Zapatero, A. Lopez-Moreno Study of short cracks under biaxial fatigue ………………………………………………….. 244 D. Gentile, I. Persechino, N. Bonora, G. Iannitti, A. Carlucci Use of Circumferentially Cracked Bar sample for CTOD fracture toughness determination in the upper shelf regime ………………………………………………………………………... 252

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Frattura ed Integrità Strutturale, 30 (2014); International Journal of the Italian Group of Fracture

V. Veselý, P. Konečný, P. Lehner, D. Pieszka Electrical resistivity and ultrasonic measurements during sequential fracture test of cementitious composite ……………………………………………………………………………….. 263 V. Chaves, C. Madrigal, A. Navarro Biaxial fatigue tests and crack paths for AISI 304L stainless steel ……………………………. 273 V. Anes, L. Reis, B. Li, M. de Freitas Evaluation of the AZ31 cyclic elastic-plastic behavior under multiaxial loading conditions ………... 282 M. Neil James Fracture-Safe and Fatigue-Reliable Structures ………………………………………………. 293 P. Corigliano, V. Crupi, E. Guglielmino, W. Fricke FE analysis of cruciform welded joints considering different mechanical properties for base material, heat affected zone and weld metal ………………………………………………………….. 304 Y. Matvienko The effect of thickness on out-of-plane constraint in terms of the T-stress ………………………… 311 D. Tumino, T. Ingrassia, V. Nigrelli, G. Pitarresi, V. Urso Miano Mechanical behavior of a sandwich with corrugated GRP core: numerical modeling and experimental validation ………………………………………………………………………………. 317 A. Fernández-Canteli S. Blasón, J.A.F.O. Correia, A.M.P. de Jesus A probabilistic interpretation of the Miner number for fatigue life prediction …………………….. 327 A. A. Shanyavskiy, A. L. Toushentsov In-service fatigue cracking of propeller shafts in spline-pinned joints connecting with engine shafts of AN-24, AN-26, and IL-18 aircraft ……………………………………………………... 340 A. Carofalo, V. Dattoma, R. Nobile, F.W. Panella, G. Alfeo, A. Scialpi, G.P. Zanon Modification of creep and low cycle fatigue behaviour induced by welding ………………………… 349 M. da Fonte, L. Reis, M. de Freitas The effect of steady torsion on fatigue crack growth under rotating bending loading on aluminium alloy 7075-T6 ………………………………………………………………………………. 360 P. Lorenzino, G. Beretta, A. Navarro Application of digital image correlation (DIC) in resonance machines for measuring fatigue crack growth …………………………………………………………………………………. 369 O. Sucharda, J. Brozovsky Numerical modelling of reinforced concrete beams witch fracture-plastic material ………………….. 375 A. Fernández-Canteli, L. Castañón, T. Holusová, B. Nieto, M. Lozano, S. Seitl Determining fracture energy parameters of concrete from the modified compact tension test ………….. 383 D. Nappini, G. Zonfrillo Evaluation of the material’s damage in gas turbine rotors by instrumented spherical indentation …… 394 N. Mortaş, P. N. B. Reis, J. A.M. Ferreira Impact response of balsa core sandwiches ……………………………………………………. 403 G. Zucca, M. Amura, L. Allegrucci, M. Bernabei Failure of cargo aileron’s actuator ………………………………………………………….. 409 D. S. Paolino, A. Tridello, H. S. Geng, G. Chiandussi, M. Rossetto Duplex S-N fatigue curves: statistical distribution of the transition fatigue life ………………….... 417

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Frattura ed Integrità Strutturale, 30 (2014); ISSN 1971-9883

J. Toribio, B. González, J.C. Matos, F.J. Ayaso Role of the microstructure on the mechanical properties of fully pearlitic eutectoid steels …………….. 424 P. N.B. Reis, A. M. Pereira, J.A.M. Ferreira, José D.M. Costa Interlaminar fracture in woven carbon/epoxy laminates ………………………………………. 431 L. Guerra Rosa, J. Cruz Fernandes, B. Li Integrated assessment model for the fracture strength of glass components in CSP systems …………. 438 F. Curà, A. Mura, C. Rosso Investigation about crack propagation paths in thin rim gears …………………………………. 446 V. Di Cocco, F. Iacoviello, A. Rossi, S. Natali Fatigue crack behavior on a Zn-Cu-Al SMA ……………………………………………… 454 V. Di Cocco, F. Iacoviello, A. Rossi, M. Cavallini Stress triaxiality influence on damaging micromechanisms in a pearlitic ductile cast iron …………... 462 G. Belingardi, F. Curà, V. Cuffaro Dynamic additional loads influencing the fatigue life of gears in electric vehicles transmissions ……… 469 A. de Iorio, M. Grasso, F. Penta, G. P. Pucillo, P. Pinto, S. Rossi, M. Testa, G. Farneti Transverse strength of railway tracks: part 1. Planning and experimental setup ………………….. 478 W. Changfeng, Z. Long, C. Xingchong Effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge …………………………………………………………………………...... 486 G. Jingran, L. Jian, Q. Jian, G. Menglin Degradation assessment of waterlogged wood at Haimenkou site ……………………...………... 495 C.J.Su, X.H.Dong, S.M.Guo, Q.L.Li, T.T.Li Research on parameters optimization of bilateral ring gear blank-holder in thick-plate fine blanking ... 502 L. Zhang, M. Ren, S. Ma, Z. Wang Energy dissipation mechanism and damage model of marble failure under two stress paths ………… 515 L. Bing, Q. Yaoguang, D. Jiyun Time-history simulation of civil architecture earthquake disaster relief- based on the three-dimensional dynamic finite element method ……………………………………………………………... 526 W. Tao, D. Tao, Z. Xiaohong, S. Yiming A research on detecting and recognizing bridge cracks in complex underwater conditions …..……...... 537 C.Yunyu An analysis research of the stiffness characteristics of hospital building materials ………………...... 545 M. Rossi, M. Sasso, G. Chiappini, E. Mancini, D. Amodio Identification of the plastic zone using digital image correlation ………………………………… 552 E. Maggiolini, P. Livieri, R. Tovo On the notch sensitivity of cast iron under multi-axial fatigue loading …………………………... 558 V. Crupi, G. Epasto, E. Guglielmino, G. Risitano Investigation of very high cycle fatigue by thermographyc method ………………………………... 569 A. De Iorio, M. Grasso, F. Penta, G. P. Pucillo, V. Rosiello Transverse strength of railway tracks: part 2. Test system for ballast resistance in line measurement ... 578 A. De Iorio, M. Grasso, F. Penta, G. P. Pucillo, V. Rosiello, S. Lisi, S. Rossi. M. Testa Transverse strength of railway tracks: part 3. Multiple scenarios test field ........................................... 593

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Frattura ed Integrità Strutturale, 30 (2014); International Journal of the Italian Group of Fracture

Editor-in-Chief Francesco Iacoviello Associate Editors Alfredo Navarro

(Università di Cassino e del Lazio Meridionale, Italy)

(Escuela Superior de Ingenieros, Universidad de Sevilla, Spain) (Ecole Nationale Supérieure d'Arts et Métiers, Paris, France)

Thierry Palin-Luc

Luca Susmel John Yates

(University of Sheffield, UK) (University of Manchester, UK)

Guest Editors Paulo De Castro Manuel de Freitas

(Universidade do Porto, Portugal)

(EDAM MIT, Portugal)

Antonio Martín-Meizoso

(Universidad de Navarra, Spain) (Universidad de Salamanca, Spain)

Jesús Toribio

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (University of Plymouth, UK)

Alberto Carpinteri Andrea Carpinteri Donato Firrao M. Neil James Gary Marquis Ashok Saxena Darrell F. Socie Shouwen Yu Ramesh Talreja David Taylor Robert O. Ritchie Cetin Morris Sonsino Editorial Board Stefano Beretta Nicola Bonora Roberto Citarella Claudio Dalle Donne Manuel de Freitas Vittorio Di Cocco Giuseppe Ferro Tommaso Ghidini Paolo Leonetti Carmine Maletta Liviu Marsavina Daniele Dini

(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)

(Politecnico di Milano, Italy)

(Università di Cassino e del Lazio Meridionale, Italy)

(Università di Salerno, Italy) (EADS, Munich, Germany) (EDAM MIT, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(Imperial College, UK)

(Politecnico di Torino, Italy)

(European Space Agency - ESA-ESRIN) (Università della Calabria, Italy) (Università della Calabria, Italy) (University of Timisoara, Romania) (University of Porto, Portugal)

Lucas Filipe Martins da Silva

Hisao Matsunaga

(Kyushu University, Japan) (University of Sheffield, UK) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Università di Messina, Italy) (Università di Brescia, Italy) (Università di Bologna, Italy) (Università di Parma, Italy)

Mahmoud Mostafavi

Marco Paggi Oleg Plekhov

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

Alessandro Pirondi Giacomo Risitano Roberto Roberti Marco Savoia Andrea Spagnoli Charles V. White

(Kettering University, Michigan,USA)

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Frattura ed Integrità Strutturale, 30 (2014); 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 iacoviello@unicas.it. The paper may be written in English or Italian (with an English 1000 words abstract). 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 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

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Frattura ed Integrità Strutturale, 30 (2014); International Journal of the Italian Group of Fracture

Multilateral Italy-Portugal-Spain

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ear Friend, this issue is one of the most rich we ever published!! Dozens of high quality papers mainly, but not uniquely, connected to the Multilateral workshop organized in cooperation with our portuguese and spanish friends. Grupo Español de Fractura, Gruppo Italiano Frattura and Sociedade Portuguesa de Materiais (SPM)/Fracture Division organized The First Multi-Lateral Workshop on Fracture and Structural Integrity related Issues in Catania, in the same venue that will be used in 2016 for the 21 st European Conference on Fracture (ECF21)… a test is always better! The organizers of The First Multi-Lateral Workshop on Fracture and Structural Integrity related Issues were: - Paulo De Castro (Universidade do Porto, Portugal); - Manuel de Freitas (EDAM MIT, Portugal); - Francesco Iacoviello (Università di Cassino e del Lazio Meridionale, Italy); - Antonio Martín-Meizoso (Universidad de Navarra, Spain); - Luca Susmel (University of Sheffield, UK); - Jesús Toribio (Universidad de Salamanca, Spain) More than 70 presentations are an undoubted success … and the success of this event was also due to the efforts of all the members of the IGF ExCo… without their help, the organization of this event, and also of all the IGF events, would be simply impossible. Beppe and Donato (the Vice Presidents), Angelo (the Treasurer) and Andrea, Carmine, Giacomo, Vittorio … THANK YOU!! Finally, a few words about the cover. After some years, we decided to change the cover of the IGF journal, simplifying the content and modifying the main picture. As you can see, this picture is a “scheme” of the Eiffel Tower with some evident modifications, in order to underline the main topics of our journal. Hoping that the new cover will be appreciated, we wish to propose to all of you to send us your ideas for new covers. The best ones will be used for the next issues, obviously with warm acknowledgements to the authors!!

Francesco Iacoviello F&IS Chief Editor

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

Focussed on: Fracture and Structural Integrity related Issues

Fracture Mechanics: Inspirations from Nature

David Taylor Trinity College Dublin, Ireland dtaylor@tcd.ie

A BSTRACT . In Nature there are many examples of materials performing structural functions. Nature requires materials which are stiff and strong to provide support against various forces, including self-weight, the dynamic forces involved in movement, and external loads such as wind or the actions of a predator. These materials and structures have evolved over millions of years; the science of Biomimetics seeks to understand Nature and, as a result, to find inspiration for the creation of better engineering solutions. There has been relatively little fundamental research work in this area from a fracture mechanics point of view. Natural materials are quite brittle and, as a result, they have evolved several interesting strategies for preventing failure by crack propagation. Fatigue is also a major problem for many animals and plants. In this paper, several examples will be given of recent work in the Bioengineering Research Centre at Trinity College Dublin, investigating fracture and fatigue in such diverse materials as bamboo, the legs and wings of insects, and living cells. K EYWORDS . Fracture; Toughness; Fatigue; Insect Cuticle; Bamboo; Osteoctyes. n this paper (and accompanying lecture) I will be considering two material properties of vital importance in engineering: fracture toughness and fatigue strength. I will show the results of measurements of these two properties in various materials and discuss the significance of these results for the mechanical structures in which these materials are used. However, the materials and structures that I will consider are not from the world of engineering components; instead, they come from nature. If we look around us we see many natural, biological structures which are load-bearing and which are required to provide mechanical support and to ensure rigidity and long-term durability. These structures have not been designed in the way that engineering parts are designed, rather they have evolved over millions of years. In some ways these materials and structures are very different from their engineering equivalents, but nevertheless it can be interesting and perhaps useful to study them from an engineering perspective. Such studies shed light on aspects of the world in which we live, and may also lead to the development of improved engineering materials and components via a Biomimetics approach in which nature is seen as an inspiration and starting point for creative design activities. Very little such work has been done to date from a fracture mechanics point of view. We have hardly any data on fracture toughness (K c ) and fatigue properties for natural materials, and little understanding about how these materials resist crack propagation and other failure mechanisms. In my research group we have been addressing this problem, starting some years ago with work on the fracture of bone, and moving in recent years to some of the other structural biological materials. In what follows I will describe three projects, spanning a large range of sizes from plants (which grow to heights I I NTRODUCTION

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

of several metres), to insects (of the order of millimetres) and finally to living cells in our bodies where the relevant scale falls below one micron.

I NSECT WINGS

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ig. 1 shows a crack-propagation test carried out on the wing of an insect – in this case a locust. We cut samples approximately 10mm x 10mm, introduced a notch of length approximately 1mm into one side, and applied axial tension. Further details can be found in a recent publication [1]. The wing consists of a sheet of material which is very thin (approximately 3  m) and which has veins of thicker material running through it at a spacing of approximately 1mm. We found that these veins improved K c by about 50% and that the spacing of veins was optimal: if they had been more closely spaced this would not have improved the stress to failure because the tensile strength of the material would be exceeded. Propagating cracks were seen to arrest at veins; on further loading the crack first blunted and then propagated via void formation on the far side of the vein, as shown in the figure.

Figure 1 : The image on the left shows a fracture toughness test on material from the wing of a locust, with a propagating crack arrested at a vein. The image on the right shows the entire wing; the different colours indicate the local spacings of the veins. This experiment illustrates, in a very simple way, a concept which is applicable to all materials: the idea of a “critical distance”. I have investigated in some detail the Theory of Critical Distances as applied to engineering materials (see for example [2]). The concept that any given material possesses a critical distance L which controls fracture and fatigue behaviour can be difficult to understand when applied to materials with complex microstructures: the insect wing presents a simple, two dimensional example of the essential idea: that materials contain microstructural features which inhibit crack propagation. When considering the effect of a crack or notch it is useful to compare the physical dimensions of the feature, and of the disturbance which it creates in the surrounding stress field, with the critical distance. he stems of plants must be sufficiently rigid to allow upward growth and support of the leaves, and sufficiently strong and tough to resist mechanical forces, especially periodic wind loading. Bamboo is an important engineering material in its own right, extensively used in Asia and of great future interest because its fast growth makes it a renewable resource. However there have been relatively few publications on the mechanical properties of the bamboo stem, which is known as a “culm”. Culms grow to heights of over ten metres, in the form of hollow tubes of almost constant thickness (see Fig. 2), with periodic nodes which carry thin branches to which the leaves are attached. In a recent project (the results of which are currently in review for publication) we assessed the mechanical effect of these nodes, showing that (despite previous assumptions to the contrary) they do not improve the stiffness or strength of the bamboo culm, and that (unlike the veins of the insect wing) they are too far apart to significantly improve toughness. T B AMBOO

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

Figure 2 : (Photograph): the bamboo culm consists of a hollow tube with periodic nodes. (a) We measured K c by propagating cracks along the tube axis by means of a pair of point loads. (b) We constructed a finite element model including the layered structure. (c) A typical load/displacement trace from a toughness test. Measuring the fracture toughness of this material is quite challenging. It is highly anisotropic, and in fact it always fails by splitting (i.e. propagation of cracks in the longitudinal direction) whatever type of load is applied to it. Furthermore the tubular shape of the culm and the graded structure (consisting of layers of material varying in stiffness from outside to inside) make it impossible to use standard fracture toughness specimens. A number of previous studies have been published, reporting K c values which vary greatly, from as little as 0.18MPam 1/2 [3] to as much as 200MPam 1/2 [4]. In fact, the assessment of these various studies is a good lesson for the student of fracture mechanics, demonstrating how incorrect results can be obtained if one does not fully understand the underlying principles. We measured K c by propagating cracks from notches, using a pair of point loads at one end of a tube sample (see Fig. 2a). Fracture toughness was estimated in two different ways: (i) using the maximum force at failure, along with a finite element model (Fig. 2b) to relate this force to the local stress intensity factor; (ii) using the fracture energy (the area under the force/displacement curve) divided by the area of new crack propagation to obtain the strain energy release rate. The two methods gave slightly different results (by about 30%) and consistently recorded a 55% increase when the crack tip was located at a node, suggesting a mechanical role for the nodes in limiting failure by splitting. However, subsequent calculations showed that the separation of the nodes was much too great: any crack which initiates would be able to propagate through the node on reaching it. Our conclusion is that these nodes fulfill a biological function (as branch points) but do not confer any mechanical benefit on the plant. yclic loading is very common in nature, and many biological materials fail by fatigue, but as yet we know very little about their fatigue characteristics. One exception is bone, which has been studied quite extensively [5]: fatigue cracks initiate in bone as a result of normal daily activities but usually do not propagate to failure thanks to bone’s self-healing ability. Excessive loading (e.g. in professional athletes) or poor-quality bone (e.g. due to osteoporosis) gives rise to fatigue failures which are referred to by doctors as “stress fractures”. Recently we have been carrying out tests to measure, for the first time, fatigue behaviour in three other natural materials: insect cuticle; bamboo and cells. C F ATIGUE OF NATURAL MATERIALS

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

Fig. 3 shows fatigue data on the legs and wings of insects, from a recent publication [6]. These body parts are made from essentially the same material – known as “cuticle” – but the cuticle found in the legs contains more fibres of chitin and is significantly anisotropic. This is reflected in the smaller fatigue range for leg material, with an endurance limit at one million cycles around 70% of the failure stress, in contrast to the wing material which shows fatigue at less than 50% of its tensile strength. Legs (which are essentially hollow, thin-walled tubes) were tested in cyclic cantilever bending and displayed two different failure modes: traditional cracking on the tensile side and progressive buckling on the compression side, suggesting that the evolution of these body parts has generated an optimal structure, equally resistant to failure in compression and tension.

Figure 3 : Stress-life fatigue data for insect legs and wings. Fig. 4 shows data (as yet unpublished) for bamboo. Surprisingly, we could find no fatigue data for this material in the published literature, despite its widespread use. These data were generated by cutting tube samples from the culm and loading them in compression across the diameter, thus generating fatigue failure by longitudinal splitting. A large fatigue range exists, which should be taken into account when this material is employed for structural purposes.

Figure 4 : Stress-life data for bamboo culm samples

My final example of fatigue in natural materials concerns living cells. Our bodies, and those of animals and plants, contain different types of cells, which perform specific functions. Many cells experience cyclic loading, so the question arises as to whether they ever fail by fatigue. This is a difficult question to answer by experimental means: cells are small (typically 10- 100  m in diameter) and very soft and flexible, consisting of an outer membrane of lipid molecules supported by a

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

cytoskeleton consisting of relatively stiff protein molecules which line the membrane and also pass across the cell body, conferring some overall rigidity and allowing the cell to move and change shape. Though there have been a number of studies to measure the elastic stiffness and viscoelastic properties of cells, there are only a very few reports of monotonic tests to failure, and no data on fatigue failure for any type of cell. We devised a test which makes use of the fact that a certain type of cell – known as an osteocyte – lives inside our bones. These cells are connected to each other via long, thin extensions of the cell body known as cellular processes (see Fig. 5).

Figure 5 : Osteocytes are linked together in a network via numerous cellular processes: these images show examples of cells with and without the surrounding bone matrix [7]. We noticed that, where a bone contains cracks, these cellular processes can be seen passing across the open crack. Therefore, by applying cyclic loading to the bone, causing these cracks to open and close, we could conduct fatigue tests on individual cellular processes. Our initial results were published showing the number of cycles to failure as a function of cyclic crack opening [8]; in more recent work (shortly to be published in the Journal of the Mechanical Behavior of Biomedical Materials ) we used finite element modelling to estimate the cyclic strain and therefore generate the first ever strain-life curve for material taken from a living cell (see Fig. 6).

Figure 6 : Strain-life data for osteocyte cellular processes.

This work has some significant limitations: in order to observe failure of these cellular processes (which are only 200nm in diameter) we had to conduct the tests inside a scanning electron microscope using an in situ loading stage. Limits on resolution meant that we were only able to measure relatively large strains and therefore small numbers of cycles to failure, up to 10. Interestingly the results are quite similar to fatigue of metallic materials in the very low cycle regime.

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D. Taylor, Frattura ed Integrità Strutturale, 30 (2014) 1-6; DOI: 10.3221/IGF-ESIS.30.01

These findings are of importance because we believe that the fatigue failure of these cellular processes, at the point where they span an open crack in the bone matrix, could be a crucial step in the complex system by which fatigue cracks in bone are repaired, ensuring the continued integrity of the skeleton.

C ONCLUDING REMARKS

T

here are perhaps two different reasons for engaging in the type of research described above. The first is simple curiosity. It has been fascinating to discover how Nature solves the same problems of structural integrity as those faced by engineering designers and materials scientists. The second reason is that in this way, inspiration may be provided to create new, biomimetic materials and structures. Nature’s materials are, in many ways, not as good as modern engineering materials. They tend to have lower fracture toughness values and to suffer from fatigue at least as much. But Nature has evolved some clever strategies to overcome these limitations – strategies such as self-repair and the use of functionally graded materials – so that keeping an eye on Nature may help us to create new, better solutions for engineering applications.

A CKNOWLEDGEMENTS

W

e are grateful to Science Foundation Ireland and to the Irish Research Council for financial support.

R EFERENCES

[1] Dirks, J.-H., Taylor, D., Veins improve fracture toughness of insect wings, PLoS ONE, 7(8) (2012) e43411. [2] Taylor, D., The Theory of Critical Distances: A New Perspective in Fracture Mechanics, Elsevier, Oxford, UK (2007). [3] Mitch, D., Harries, K. A., Sharma, B., Characterisation of splitting behavour of bamboo culms, Journal of Materials in Civil Engineering, 22 (2010) 1195-1199. [4] Amada, S., Untao, S., Fracture properties of bamboo, Composites Part B: Engineering, 32 (2001) 451-459. [5] Taylor, D., Hazenberg, J. G., Lee, T. C., Living with Cracks: Damage and Repair in Human Bone, Nature Materials, 2 (2007) 263-268. [6] Dirks, J. H., Parle, E., Taylor, D., Fatigue of insect cuticle, Journal of Experimental Biology, 216(10) (2013) 1924- 1927. [7] Klein-Nulend, J., Bacabac, R. G., Mullender, M. G., Mechanobiology of bone tissue, Pathologie Biologie, 53(10) (2005) 576-580. [8] Dooley, C., Cafferky, D., Lee, T. C., Taylor, D., Fatigue failure of osteocyte cellular processes: implications for the repair of bone, European Cells and Materials, 27(2014) 39-49.

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E. T. Bowman, Frattura ed Integrità Strutturale, 30 (2014) 7-13; DOI: 10.3221/IGF-ESIS.30.02

Focussed on: Fracture and Structural Integrity related Issues

Dynamic rock fragmentation: thresholds for long runout rock avalanches

E.T. Bowman University of Sheffield e.bowman@sheffield.ac.uk

A BSTRACT . The dynamic fragmentation of rock within rock avalanches is examined using the fragmentation concepts introduced by Grady and co-workers. The analyses use typical material values for weak chalk and limestone in order to determine theoretical strain rate thresholds for dynamic fragmentation and resulting fragment sizes. These are found to compare favourably with data obtained from field observations of long runout rock avalanches and chalk cliff collapses in spite of the simplicity of the approach used. The results provide insight as to the energy requirements to develop long runout behaviour and hence may help to explain the observed similarities between large rock avalanches and much smaller scale chalk cliff collapses as seen in Europe. K EYWORDS . Flow; Dynamic fragmentation; Rock avalanche; Strain rate. Large terrestrial rock avalanches generally comprise volumes of order 0.01 - 500 million m 3 , covering areas from 1 - 500 km 2 , and initial potential energies between 10 14 – 10 18 J [1]. They also have a fall height to length ratio (the tangent of which is known as the “farboschung angle”) that is a reducing function of volume [2]. A method to characterize the size dependence of rock avalanche mobility is the “spreading efficiency” defined as the ratio of runout length to the cube root of volume (L/V 1/3 ), which has been show to vary from 6-10 [3]. In comparison, simple small scale experiments in which dry sand or rock blocks have been released to flow down a slope, generally produce spreading efficiencies of 1.5-3 [3]. The value is much lower than found for field scale rock avalanches, implying a much lower mobility for small experimental flows. Equally significantly, this value has not been found to increase with volume which suggests that potential energy is not so important for the emplacement of these small flows. One promising hypothesis for the extraordinary mobility of large rock avalanches involves the process of dynamic fragmentation of rock and how this may lead to a reduced frictional resistance within the mass [4, 5]. L I NTRODUCTION arge rock avalanches present a serious mountain hazard, however, there is a still considerable debate over the mechanisms of their collapse and transport. Due to the size and temporal unpredictability of rock avalanches there is currently no possibility to militate against their effects other than by infrastructure planning. As a result, the extremely long travel distances and high velocities that may be attained is of great concern to hazard modellers and engineers. Understanding the mechanical processes that govern rock avalanche behaviour may lead to better predictive modelling. This paper discusses dynamic rock fragmentation which is thought to play a major role in the high transport mobility of rock avalanches.

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E.T. Bowman, Frattura ed Integrità Strutturale, 30 (2014) 7-13; DOI: 10.3221/IGF-ESIS.30.02

F IELD OBSERVATIONS

F

ield observations may help us to understand what additional processes are at work during rock avalanche propagation and arrest, beyond sliding, rolling, shearing and frictional dissipation, as observed for small scale experiments. Common observations of large rock avalanches are that: they attain high velocities (e.g. 75 m/s average was determined for the Huarscaran rock avalanche in Peru, 1970, with some boulders flung out at up to 280 m/s [6]); the deposits are very thin (e.g. averaging 5 m thick at Elm, Switzerland [7] in 1881; Fig. 1, left); there is a lack of sorting and mixing of debris, with geological layers being preserved intact; and, there is an extremely high degree of fragmentation of the rock within the deposit typically below a surface shell or “carapace” of intact blocks [5]. Recently, the spreading efficiency of rock avalanches has been found to correlate positively with the degree of fragmentation of the deposit [4] – i.e. the change in grain size distribution from the commencement to arrest – indicating that high mobility is linked to dynamic rock fracture.

Figure 1 : Left: Mt Haast rock avalanche (also known as Mt Dixon rock avalanche) that occurred on 21 st January 2013 in the southern Alps of New Zealand (details in Hancox & Thomson, 2013 [8]). Right: Chalk cliffs of south Kent. Collapse deposits are generally rapidly eroded by wave action but leave characteristic rock shelf extensions. Photos: Author. The large size of high mobility rock avalanches is, in itself, interesting to note. Below 0.01 million m 3 , and potential energy of 10 14 J, rock falls, characterised by bouncing, rolling and breaking blocks, are common but long runout behaviour is almost unknown. The exception to this appears to be the long runout collapses of chalk cliffs that occur in parts of Europe (Fig. 1, right). Such collapses can behave very much like large rock avalanches, displaying low to high spreading efficiency (L/V 1/3 from 0.5 – 7) [9] at much smaller volumes (10 3 m 3 - 10 6 m 3 ) and with much lower initial potential energy (up to 10 10 J). As discussed by Bowman and Take (2014) [10], the reasons for the similarities with rock avalanches are likely to be due to the low strength of the chalk in comparison with more typical rocks, with weak chalk producing the greatest spreading efficiency. These observations point to two processes: a high degree of particle fragmentation via communition, and a predominance of collisional stress transfer between closely spaced (or even touching) fractured particles. This paper examines how the dynamic fragmentation of rock during avalanche propagation may lead to enhanced mobility. The paper focuses on comparisons between events involving two different rock types – i.e. limestone, which is a common source rock in long

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E. T. Bowman, Frattura ed Integrità Strutturale, 30 (2014) 7-13; DOI: 10.3221/IGF-ESIS.30.02

runout avalanches, and weak chalk, which is found to produce long runout behaviour in chalk cliff collapses. In doing so we attempt to shed light on the role of dynamic fragmentation on generating high mobility via high speed fragment dispersal.

D YNAMIC FRAGMENTATION

A

s discussed by Zhang (2002) [11], the empirically noted close relationship between tensile strength  and fracture toughness K IC for rock appears to be related to the general failure mode of rock. During compressive loading, rock fails by tensile splitting, with little shearing of the surfaces – such that the ultimate compressive strength  c is found to be approximately 8-15 times  [12]. Indeed failure, whether in shear, compression or tension, tends to occur by the growth of tensile microcracks, supporting the use of fracture mechanics to examine failure. This view is further supported by examining the failure surfaces of fracture toughness and tensile strength test specimens, which are similar – with the samples of static tests showing the extension of a single flaw or the coalescence of a few microcracks, and those of dynamic tests revealing branching macrocracks and additional damage beyond the main surface [11]. It is generally accepted that rocks exhibit strain rate dependent strength, with a very weak to weak dependence at low strain rates and a much stronger dependence once a threshold strain rate is exceeded [13-15] – a behavioural regime we refer to here as “dynamic”. For rocks with larger grains, larger flaws, or a greater degree of heterogeneity, the threshold strain rate tends to be lower [16]. Over this threshold, dynamic fragmentation produces a more damaged material, and more, smaller, fragments with increasing strain rate. The fragments produced possess increased kinetic energy with strain rate, creating inefficiencies in industrial processing [17] and, it is hypothesized here, resulting in greater mobility of rock avalanches.

A NALYSIS

T

ab. 1 lists properties typical of the two rock types that are used in the following analyses. In this analysis, we follow the mechanism of dynamic fragmentation proposed by Grady [18] to compare theoretical fragment sizes produced under rock avalanche conditions with observations made in the field. In Grady and Kipp’s analyses [16, 19] they show that the initiation of dynamic fragmentation is dependent on the inherent flaw size as with static breakage. They treat the problem in two ways – first by examining material failure through an inherent flaw concept, and second through the use of fracture mechanics.

Property

Weak chalk

Limestone

0.3

8

Tensile strength  (MN/m 2 )

(MN/m 3/2 )

0.045 1610 2300

1.1

Quasistatic fracture toughness K IC

2700 5000

Density  (kg/m 3 )

Speed of sound c (m/s)

Table 1 : Properties used in analysis

In quasistatic breakage of a brittle material, the largest or most critical flaw is considered to be responsible for fracture [20]. Using the Griffith / Irwin failure criterion, the theoretical failure stress may be determined by assuming tensile loading of an isolated flaw that is (for example) penny-shaped. Conversely, if the fracture toughness K IC and tensile strength  of the material are known, a theoretical maximum flaw size r 0 amongst a distribution of flaw sizes r may be determined [20]: 2 0 2 4 IC K r    (1) From Eq. 1 and Tab. 1, for chalk, r 0 is found to be 16.6mm and for limestone, r 0 is found to be 14.8mm. These values are rather similar, despite the large differences in strength of the materials, possibly reflecting their similar geological origins.

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E.T. Bowman, Frattura ed Integrità Strutturale, 30 (2014) 7-13; DOI: 10.3221/IGF-ESIS.30.02

At higher loading rates, it is not possible for the critical (largest) flaw to grow fast enough to relieve the applied stress in the time provided. As a result, other, smaller, flaws must come into play, leading to multiple fractures and a material that is more pervasively damaged or fragmented [16]. Under constant strain rate loading and an assumed Weibull distribution of flaws, and by assuming that all activated cracks / flaws propagate at constant velocity, Grady and Kipp (1987) determined a relationship for the peak failure stress dependent on several properties of the material (elastic modulus, Weibull parameters, and crack propagation velocity), and of strain rate as a function of the Weibull modulus. Their second treatment addresses the crack growth process explicitly for a single isolated crack under dynamic loading. Here, linear elastic fracture mechanics is applied to a (for example) penny-shaped crack. An expression for the stress to initiate fracture on an isolated crack / flaw under dynamically applied stress is obtained that is a function of several material constants (pseudostatic K IC, elastic modulus, and speed of sound in the material), and of the cube root of the applied strain rate. To reconcile the two approaches, the Weibull parameter m, must be equal to 6, which is a good fit to many rock types, albeit not all [16, 21]. The theoretical dynamic strength for a penny-shaped crack undergoing constant strain rate loading [19] is therefore: 1 3 2 3 9 16 IC d cK dt            (2) Where  is the density and c is the speed of sound in the material. Fig. 2 shows this relationship for the weak chalk and limestone, respectively, compared with the static strength (assumed to be negligibly rate dependent here) of both. It may be expected that the static strength will be valid below the crossover points, upon which the behaviour will converge to the rate dependent reponse with increasing strength with strain rate.

Figure 2 : Predicted theoretical dynamic strength against strain rate compared with static strength for typical weak chalk and limestone.

Further analyses are needed to indicate at what strain rate the dynamic regime commences and to give information as to the size of the fragments produced in the dynamic regime. Once again invoking fracture mechanics principles, Grady and Kipp (1979) [19] determine a minimum strain rate (d  /dt) min at which pseudostatic fracture gives way to dynamic fragmentation, as follows:   min 3 min 2 0 IC K d dt cr       (3) Fig. 3 shows this relationship plotted using typical data for weak chalk and limestone, respectively. The intersections of the predicted maximum flaw sizes r 0 obtained from the static analyses (Eq. 1) are also plotted, giving a minimum strain rate at which dynamic fragmentation is predicted to occur for the two materials. Although r 0 is very similar for the two rocks types, the resultant (d  /dt) min is quite different; 5.5s -1 for chalk and 45s -1 – i.e. an order of magnitude increase from chalk to limestone.

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E. T. Bowman, Frattura ed Integrità Strutturale, 30 (2014) 7-13; DOI: 10.3221/IGF-ESIS.30.02

Figure 3 : Theoretical relationship between maximum flaw size r 0

and resultant minimum strain rate for dynamic fragmentation,

compared with actual flaw size predicted from the pseudostatic condition for a typical weak chalk and limestone.

Finally, in order to determine fragment sizes produced during a dynamic event, following Grady (1982) [18], Grady and Kipp (1987) [16] adopt an energy approach to the dynamic loading regime in which a balance between local kinetic energy and fracture energy is made. That is, once this regime is reached, the fragment size no longer depends on the initial size of the flaws but rather upon the kinematic conditions imposed. The numbers of fragments are found to depend on the strain rate applied, with smaller and greater number of fragments being produced at higher strain rates. The resulting relationship for fragment size d is: 2 3 20 IC K d dc dt            (4) Eq. 4 and its derivatives have been found to reasonably approximate the characteristic size of fragments from different experimental arrangements on different brittle and quasi-brittle materials [22, 23]. Fig. 4 plots the relationship predicted by Eq. 4 for weak chalk and limestone, respectively.

Figure 4 : Theoretical relationship between the nominal fragment size produced and the strain rate during a constant rate of strain dynamic event, compared with mean field values typical for long runout rock avalanches in limestone and cliff collapses in weak chalk.

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