Issue 33

Frattura ed Integrità Strutturale, 33 (2015); International Journal of the Italian Group of Fracture

Table of Contents

D. Nowell, S.J. O’Connor, K.I. Dragnevski Measurement and analysis of fatigue crack deformation on the macro- and micro-scale ……………. 1 A. Shanyavskiy Spherical particles formation under biaxial cyclic loading due to mesotunneling effect …………… 8 F. Berto, A. Campagnolo, L. P. Pook Three-dimensional effects on cracked components under anti-plane loading ………………………. 17 L. Malíková, V. Veselý, S. Seitl Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria …………………………………………………………………………………. 25 G. Meneghetti, A. Campagnolo, F. Berto Some relationships between the peak stresses and the local strain energy density for cracks subjected to mixed-mode (I+II) loading ……………………………………………………………….. 33 Y. Hos, M. Vormwald, J.L.F. Freire Measurement and simulation of strain fields around crack tips under mixed-mode fatigue loading ….. 42 D. Shiozawa, I. Serrano-Munoz, S. Dancette, C. Verdu, J. Lachambre, J.-Y. Buffiere 3D Analyses of crack propagation in torsion ………………………………………………... 56 D. A. Hills, R. Flicek Fretting in complete contacts - the use of Williams’ solution …………………………………… 61 M.-L. Zhu, Y.-W. Lu, C. Lupton, J. Tong Near tip strain evolution of a growing fatigue crack …………………………………………... 67 G.P. Nikishkov, Yu.G. Matvienko Specimen thickness effect on elastic-plastic constraint parameter A …………………………….... 73 A. Spagnoli, A. Carpinteri, S. Vantadori Interpreting experimental fracture toughness results of quasi-brittle natural materials through multi parameter approaches …………………………………………………………………….. 80 R.C.O. Góes, J.T.P. Castro, M.A. Meggiolaro 3D thickness effects around notch and crack tip stress/strain fields …………………………….. 89 J.T.P. Castro, M.A. Meggiolaro, J.A.O. González Can  K eff be assumed as the driving force for fatigue crack growth? …………………………….. 97 C. Bagni, H. Askes, L. Susmel Gradient-enriched linear-elastic tip stresses to perform the high-cycle fatigue assessment of notched plain concrete ………………………………………………………………………………… 105

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Fracture and Structural Integrity, 33 (2015); ISSN 1971-9883

F. Iacoviello, V. Di Cocco, M. Cavallini Fatigue crack tip damaging micromechanisms in a ferritic-pearlitic ductile cast iron ………………. 111 V. Veselý, J. Sobek, D. Tesa ř , P. Frantík, T. Pail, S. Seitl Multi-parameter approximation of stress field in a cracked specimen using purpose-built Java applications …………………………………………………………………………….. 120 C. Simpson, P.J. Withers, T. Lowe, S. Roy, A. Wanner Damage evolution in freeze cast metal/ceramic composites exhibiting lamellar microstructures …….... 134 M. Mokhtari, P. Lopez-Crespo, B. Moreno Some experimental observations of crack-tip mechanics with displacement data …………………... 143 P. J. Withers, P. Lopez-Crespo, M. Mostafavi, A. Steuwer, J. F. Kelleher, T. Buslaps 2D mapping of plane stress crack-tip fields following an overload ………………………………. 151 C. Montebello, S. Pommier, K. Demmou, J. Leroux, J. Mériaux Multi-scale approach for the analysis of the stress fields at a contact edge in fretting fatigue conditions with a crack analogue approach …………………………………………………………… 159 G. Laboviciute, C. J. Christopher, M. N. James, E. A. Patterson Growth of inclined fatigue cracks using the biaxial CJP model ……………………………….... 167 S. Beretta, S. Rabbolini, A. Di Bello Multi-scale crack closure measurements with digital image correlation on Haynes 230 ……………. 174 Enrico Maggiolini, Roberto Tovo, Paolo Livieri Effective stress assessment at rectangular rounded lateral notches ……………………………….. 183 J.M. Vasco-Olmo, F.A. Díaz Experimental evaluation of plasticity-induced crack shielding from crack tip displacements fields …… 191 F.V. Antunes, R. Branco, L. Correia, AL Ramalho A numerical study of non-linear crack tip parameters ……………………………………….... 199 X. Zhou, A. Hohenwarter, T. Leitner, H.P. Gänser, R. Pippan Load history effects on fatigue crack propagation: Its effect on the R-curve for threshold …………… 209 P. Lorenzino, J.-Y. Buffiere, S. Okazaki, H. Matsunaga, Y. Murakami, H. Matsunaga Synchrotron 3D characterization of arrested fatigue cracks initiated from small tilted notches in steel ... 215 J. Toribio, B. González, J.C. Matos Crack tip fields and mixed mode fracture behaviour of progressively drawn pearlitic steel …………... 221 A. Bolchoun, H. Kaufmann, C. M. Sonsino Numerical measures of the degree of non-proportionality of multiaxial fatigue loadings ……………. 238 M. Vormwald Multi-challenge aspects in fatigue due to the combined occurrence of multiaxiality, variable amplitude loading, and size effects ………………………………………………………………….... 253 A. Winkler, G. Kloosterman A critical review of fracture mechanics as a tool for multiaxial fatigue life prediction of plastics ……... 262

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Frattura ed Integrità Strutturale, 33 (2015); International Journal of the Italian Group of Fracture

T. Itoh, M. Sakane, T. Morishita Evaluation and visualization of multiaxial stress and strain states under non-proportional loading … 289 M. Kurek, T. Łagoda, S. Vantadori Estimation of fatigue life of selected construction materials under cyclic loading …………………… 302 V. Anes, L. Reis, M. de Freitas Random accumulated damage evaluation under multiaxial fatigue loading conditions ……………... 309 M. Sakane, T. Itoh Microstructural study of multiaxial low cycle fatigue ………………………………………….. 319 V. Shlyannikov, R. Yarullin, I. Ishtyryakov Surface crack growth in cylindrical hollow specimen subject to tension and torsion ………………… 335 Y. Wang, L. Susmel Critical plane approach to multiaxial variable amplitude fatigue loading ………………………... 345 M.A. Meggiolaro, J.T.P. Castro, H. Wu On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue ……………………………………………………………………….. 357 M.A. Meggiolaro, J.T.P. Castro, H. Wu Shortcuts in multiple dimensions: the multiaxial racetrack filter ……………………………….. 368 A. Carpinteri, A. Spagnoli, C. Ronchei, S. Vantadori Time and frequency domain models for multiaxial fatigue life estimation under random loading ……. 376 D. G. Hattingh, M. N. James, L. Susmel, R. Tovo Multiaxial fatigue of aluminium friction stir welded joints: preliminary results …………………... 382 M. Cova, P. Livieri, R. Tovo Fast assessment of the critical principal stress direction for multiple separated multiaxial loadings …... 390 F. Fremy, S. Pommier, E. Galenne, S. Courtin Crack tip fields in elastic-plastic and mixed mode I+II+III conditions, finite elements simulations and modeling …………………………………………………………………………… 397 F. Morel, R. Guerchais, N. Saintier Competition between microstructure and defect in multiaxial high cycle fatigue …………………… 404 JM. Ayllon, C Navarro, J. Vázquez, J. Domínguez Comparison of two multiaxial fatigue life prediction models to dental implants …………………... 415 J. A. Araújo, F. C. Castro, S. Pommier, J. Bellecave, J. Mériaux Equivalent configurations for notch and fretting fatigue ……………………………………….. 427 J. Toribio, M. Lorenzo, D. Vergara Role of multiaxial stress state in the hydrogen-assisted rolling-contact fatigue in bearings for wind turbines ……………………………………………………………………………….... 434 F. C. Castro, J. A. Araújo, M. S. T. Pires, L. Susmel Estimation of fretting fatigue life using a multiaxial stress-based critical distance methodology ............. 444 R. Sepe, A. Pozzi Static and modal numerical analyses for the roof structure of a railway freight refrigerated car .............. 451

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Fracture and Structural Integrity, 33 (2015); ISSN 1971-9883

J. Fan, D. Dong, L. Chen, X. Chen, X. Guo Weight Function Method for computations of crack face displacements and stress intensity factors of center cracks ……………………………………………………………………………. 463 C. Gao, Y. Lu, Y.T. Zhu A new micromechanical model of CNT-metal nanocomposites with random clustered distribution of CNTs …………………………………………………………………………………. 471

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Frattura ed Integrità Strutturale, 33 (2015); International Journal of the Italian Group of Fracture

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) (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 Editor (Characterization of crack tip fields) Y. Hong

(Institute of Mechanics, CAS, China)

F. Iacoviello M. N. James

(Università di Cassino e del Lazio Meridionale, Italy)

( University of Plymouth, UK) ( University of Sheffield, UK)

L. Susmel

Guest Editor ( Challenges in Multiaxial Fatigue ) F. Berto (Università di Padova, Italy) A. Fatemi ( University of Toledo, USA) D. F. Socie ( University of Illinois, USA) L. Susmel ( University of Sheffield, UK)

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 Elisabeth Bowman Roberto Citarella Claudio Dalle Donne Manuel de Freitas Vittorio Di Cocco Giuseppe Ferro Eugenio Giner Tommaso Ghidini Daniele Dini Editorial Board Stefano Beretta Nicola Bonora

(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)

(University of Sheffield) (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)

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

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Fracture and Structural Integrity, 33 (2015); ISSN 1971-9883

Paolo Leonetti Carmine Maletta Liviu Marsavina

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

Lucas Filipe Martins da Silva

Hisao Matsunaga Mahmoud Mostafavi

(Kyushu University, Japan) (University of Sheffield, UK) (Politecnico di Torino, Italy)

Marco Paggi Oleg Plekhov

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

Alessandro Pirondi

(Università di Parma, Italy)

Luis Reis

(Instituto Superior Técnico, Portugal)

Giacomo Risitano Roberto Roberti

(Università di Messina, Italy) (Università di Brescia, Italy) (Università di Bologna, Italy) (Università di Parma, Italy)

Marco Savoia

Andrea Spagnoli Charles V. White

(Kettering University, Michigan,USA)

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Frattura ed Integrità Strutturale, 33 (2015); International Journal of the Italian Group of Fracture

Journal description and aims Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (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

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

VII

Fracture and Structural Integrity, 33 (2015); ISSN 1971-9883

Foreword

Third IJFatigue & FFEMS Joint Workshop: Characterisation of Crack Tip Fields ingle parameter characterisation of the crack/notch tip field using fracture mechanics parameters like K, J or CTOD has been extremely powerful in advancing predictive technologies for critical or sub-critical crack growth. It has also become clear over the last 40 years that single parameter approaches have limitations particularly in dealing with crack growth phenomena arising from crack tip shielding, often resulting from the plastic enclave surrounding a crack. Influences of this enclave on the crack tip stress field ahead of the crack are maximised during cyclic loading. In the case of a parameter like stress intensity factor, K, which characterises the crack tip field via an elastic approximation, it is not surprising that any set of plasticity-induced circumstances which perturb the size of the plastic enclave and its associated strain field lead to predictive difficulties. Over the last 30 years, notable areas of activity related to such difficulties include short cracks, plasticity-induced closure, variable amplitude and multiaxial loading and notch effects. Thus an increasing number of authors and research groups, particularly in Europe, are working on the topic of characterisation of crack tips using more than one fracture mechanics parameter. Attention has been directed, for example, towards incorporating the T-stress into life prediction methods. The T-stress is the second term in a Williams type expansion of the crack tip stresses and it affects the extent and shape of crack tip plasticity. It would therefore be expected to be influential in plasticity-related crack growth phenomena and a number of publications have demonstrated this to be true. The situation is further complicated where a crack experiences multiaxial loading and Mode II and III fracture mechanics parameters are also necessary. Alongside this, new analytical models have been proposed and advanced experimental techniques allow greatly improved measurement of 2D and 3D fields associated with the crack tip zone. Very successful workshops on this topic have been held in Forni di Sopra, Udine, Italy in March 2011 and Málaga, Andalusia, Spain in April 2013. Guest Editors S First International Workshop on Challenges in Multiaxial Fatigue n situations of practical interest, mechanical components are subjected to complex systems of cyclic forces resulting in local multiaxial stress/strain states. Due to the scientific/industrial relevance of such an engineering problem, since the pioneering work done by Gough, a tremendous effort has been made by the international scientific community both to understand the cracking behaviour of materials damaged by bi/tridimensional cyclic stress/strain states and to devise safe engineering procedures suitable for designing mechanical components against multiaxial fatigue. Due to such extensive and systematic investigations, nowadays, when assessing real components, engineers can take full advantage of many well-established methods as well as of many experimental findings. In this complex scenario, the present workshop aimed to gather together those researchers systematically working on multiaxial fatigue to revisit and perhaps revise those ideas and concepts which have been proposed and validated so far. This was done by collegially discussing state-of-the-art solutions, trying to answer the most critical open questions about this complex problem. Guest Editors I Prof. L. Susmel, University of Sheffield, UK Prof. F. Iacoviello, University of Cassino, Italy Prof. M. N. James, University of Plymouth, UK Prof. Y. Hong, Institute of Mechanics, CAS, China

Prof. A. Fatemi - University of Toledo, USA Prof. D. F. Socie - University of Illinois, USA Prof. L. Susmel - University of Sheffield, UK Prof. F. Berto - University of Padova, Italy

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Frattura ed Integrità Strutturale, 33 (2015); International Journal of the Italian Group of Fracture

News from Fracture and Structural Integrity

D

ear friends, We are proud and happy to announce to the fracture and structural integrity community that, since this issue on, the IGF Journal Fracture and Structural Integrity ( Frattura ed Integrità Strutturale, F&SI ) will offer two new service: - Video embedded: F&SI Authors will be allowed to publish papers containing videos. As a consequence, it will be possible for the authors to describe both figures and videos. Videos will be available for all the OS and all the devices (desktop, laptop and mobile). - Audioslides: F&SI Authors will be allowed to offer to the readers their Audioslides containing a description of their paper. The Audioslides will be embedded in the paper and will be available for all the OS and all the devices (desktop, laptop and mobile). For file size smaller than 20 Mb, Authors can directly send their files to gruppofrattura@gmail.com. Larger files can be sent using services like www.wetransfer.com, www.dropsend.com or www.sendspace.com, or sharing a Dropbox folder with iacoviello@unicas.it. In order to assist the Audioslides production, a short Tutorial is available here: http://www.gruppofrattura.it/video/Tutorial.mp4. Very best Considering the videos, there are no Mb limits and all the main codec are allowed. Considering the Audioslides, there are neither slides number nor MB limits.

Francesco Iacoviello F&IS Chief Editor

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

Focussed on characterization of crack tip fields

Measurement and analysis of fatigue crack deformation on the macro- and micro-scale

D. Nowell, S.J. O’Connor, K.I. Dragnevski University of Oxford, UK david.nowell@eng.ox.ac.uk, samuel.oconnor@eng.ox.ac.uk, kalin.dragnevski@eng.ox.ac.uk

A BSTRACT . The paper describes an experiment which performs in-situ loading of a small compact tension specimen in a scanning electron microscope. Images are collected throughout a number of successive loadincg cycles. These are then analysed using digital image correlation (DIC) in order to produce crack flank displacements as a function of load. This data is then compared with a simple elastic approach, and it is concluded that elastic-plastic analysis is required in order to accurately capture the displacements close to the crack tip. A simple approach due to Pommier and Hamam is therefore employed. This gives a better representation of the data, but predicts a variation of crack tip displacement,  , which is difficult to explain from a physical perspective. The need for a more sophisticated analysis of the data is therefore highlighted. K EYWORDS . Crack Tip Displacements; Digital Image Correlation; Elastic-Plastic Fracture Mechanics. Recent work at Oxford has been presented at the Forni di Sopra [2,3] and Malaga [4] IJ Fatigue/FFEMS workshops and has concentrated on the use of digital image correlation to measure and analyse the displacements fields around a crack. Our work has made use of a long-range optical microscope to examine deformations in a region within 0.5 mm of the crack tip. Analysis of these deformations has allowed stress intensity factors to be calculated and crack closure assessed. In the current paper we will seek to extend this approach by reporting measurements taken during in-situ loading of a fatigue crack in a scanning electron microscope. This permits more detailed examination of the displacement field in the neighbourhood of the crack tip. T I NTRODUCTION he understanding of fatigue crack propagation is an essential pre-requisite to safe operation of many engineering structures and systems. Most damage tolerant life prediction approaches are based on the application of experimental crack propagation data to the real system. For example, the Paris Law [1] is frequently used to apply experimental da/dN vs delta K data to service loads and to the system geometry. However, most experimental data is obtained for constant amplitude loading whereas engineering systems frequently experience non-uniform loading. The presence of history effects in fatigue crack propagation is well known and this means that life prediction under service loading conditions remains a challenging problem in many cases. A detailed understanding of the crack tip response to a range of load histories is the key to improvements in this area.

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

M ACROSCOPIC M EASUREMENTS

O

ur earlier work on the measurement of crack tip displacement fields has employed a long range microscope, focused on an area approximately 600 x 400  m close to the crack tip [2]. A number of images were captured at intervals during the loading cycle, and digital image correlation carried out using a public domain Matlab script produced by Erbl et al [5]. The data obtained were processed in a number of ways, but a particularly convenient means of presenting the results is to determine the experimental stress intensity factor by comparing the measured crack tip opening displacements with those predicted by an elastic model. The crack flank displacements for an elastic crack are given by 4 2 I i K r u E    (1) where K I is the elastic stress intensity factor, E is Young’s Modulus, and r is the distance from the crack tip. Hence, a plot of u i against  r should yield a straight line and the stress intensity factor can be extracted from the gradient. Fig. 1(a) shows results from a typical experiment conducted under constant amplitude loading. The dotted line represents the theoretical variation of elastic stress intensity factor with load for the size and type of specimen used (a standard Compact Tension specimen). It will be seen that the experimental results broadly follow the theoretical ones, and that the slope of the load vs K line is very similar. However the experimental results exhibit an offset, and the experimental K values are lower than predicted. This may be interpreted as being due to plasticity induced crack closure, which causes superposition of an additional negative residual K term ( K r ). It can be seen from the results that the crack does not open until about 0.5kN of applied load (approximately 25% of the maximum load).

.5)

.5)

Figure 1 : Variation of measured stress intensity factor with load for specimen CTF6 [4] (a) After constant amplitude loading and (b) Immediately after an overload. Fig. 1(b) shows results from the same specimen immediately after a 50% overload cycle. Although the slope of the experimental line remains parallel to the theoretical one, these results exhibit some unusual features. In particular, negative K values are measured, which at first sight appears physically unreasonable. However, if there is a large plastic opening displacement at the crack tip, a crack shape of this form is possible, and closer inspection of the experimental results suggests that this is the measured deformation. The results presented here were obtained by analysing the relative displacement of 5 pairs of points from the recorded images, and the first pair is approximately 100  m from the crack tip. In order to investigate the crack tip deformation in more detail, a novel experiment was therefore proposed, which involved in-situ loading of a small specimen in the scanning electron microscope.

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

M ICROSCOPIC MEASUREMENTS

E

xperiments were conducted in the Laboratory for In-situ Microscopy and Analysis (LIMA), which is part of the Solid Mechanics and Materials Engineering Group in the Department of Engineering Science at the University of Oxford. The imaging device used was a Carl Zeiss Evo LS15 VP-Scanning Electron Microscope. The chamber of the SEM was large enough so that in-situ testing could be performed with a Deben testing stage similar to that shown in Fig. 2. A 5 kN load cell was attached to the testing stage and an extension rate of 1:25 mm/min was used for this testing. Computer software was used to set the drive parameters and to collect live data on the force applied and extension from the testing stage during loading. The specimen design was a modified compact tension specimen and the material used was aluminium alloy with a yield stress of approximately 320 MPa.

Figure 2 : Deben In-Situ Microtest tensile & compression stage with a 2 kN load cell.

The specimen was pre cracked before being loaded on the Deben stage with the same tensile testing rig used for macroscopic specimen loading. The specimen was loaded at a frequency of 5 Hz, signicantly faster than could be achieved with the Deben testing stage. 17,000 cycles were applied to the specimen to grow the crack approximately 7mm at the same loads to be used for later testing on the Deben stage. Once pre cracked and placed on the Deben testing stage, the crack was grown slightly further to approximately 7:2mm before in-situ SEM images were captured. The maximum applied load was 1:25 kN and the minimum load was 0:125 kN, giving an R ratio of 0.1. A single overload cycle of 1:875 kN was applied as part of the experiment, but only constant amplitude results will be reported here. Imaging was carried out using a secondary electron detector at an operating voltage of 15kV and working distance of 9mm and images were captured at a resolution of 3072 x 2304 pixels over an image area of approximately 215  m x 161  m. Images were taken every 0:125 kN to give 19 images for a complete cycle between 0:125 kN and 1:25 kN. The images were taken with the crack in approximately the same location within the image. To do this, the load was held at the desired value while the microscope stage and the electron bean were aligned with the crack before the next image was captured. Once images were collected, a series of sets of points were selected on either side of the crack and relative displacement was obtained using the DIC algorithm [5] for pairs of points within each set. Each set of points contained 2000 points (with 200 points in the horizontal x direction and 10 in the y direction), see Fig. 4. The procedure adopted therefore produced relative displacement in the y direction at 200 different x direction distances from the crack tip over the series of images. The points were distributed from close to the crack tip up to a distance of approximately 150  m along the crack flanks. Displacement data could have been obtained with fewer points, however a large number of points were selected to reduce the chance that badly tracked points may influence the results. Due to the high resolution of the images, displacements around the crack were quite large at high loads when measured in pixels. Therefore, in order to better track the points, the area surrounding each point that is used for image correlation was increased from a 30 x 30 pixel square used in earlier work up to a 200 x 200 pixel area. In addition to the images taken to analyse displacements around the crack tip, images of the full crack were captured in order to measure crack length for calculation of K. The loading was paused at the highest load of a loading cycle (1:25 kN), magnification reduced and a series of images taken along the full crack. These images were then fitted together using normalised 2-D cross-correlation with the Matlab Image Processing Toolbox to give an image of the full crack length to measure from. An example is shown in Fig. 5.

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

Figure 3 : Dimensions (in mm) of specimens used for in-situ SEM testing. Specimens were cut from a sheet of aluminium alloy 6082 T6.

Figure 4 : Typical image collected from the experiment at a load of 1:25 kN. Sets of points are selected on either side of the crack to measure displacements.

Figure 5 : Series of images aligned to give an image of the full crack length at a load of 1:25 kN

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

R ESULTS

A

s shown in Eq. (1), if an elastic model is assumed, a plot of log u y vs. log r should be expected to give a straight line with a gradient of 0:5. This can then be used to obtain an experimental measurement of K. Fig. 6 shows a typical set of results obtained with a crack length (Measured from the notch tip) of approximately 7:2 mm. It will be apparent that the data falls into two distinct sets. Points more than about 25  m from the crack tip seem to give a good straight line fit, although the slope differs from 0.5 for all but the highest load. Points closer to the crack tip give a much shallower slope. It is instructive to compare this distance with the Irwin [6] estimate of plastic zone size. 2 1 2 p y K r            (2) where  y is the yield stress of the material. This gives a figure of r p  330  m, for the maximum load, although the cyclic plastic zone size will only be about a quarter of this value. Hence, whilst an initial elastic analysis sheds some useful light on the problem, an elastic/plastic analysis is likely to be more appropriate at this level of plasticity. In common with our earlier work we will choose to employ a model proposed by Pommier and Hamam [7]. This partitions the total displacement field into elastic and plastic components. In terms of displacements along the crack flanks, the model leads to 8 2 I y K r u E     (3) i.e., that a constant plastic displacement component  is added to the elastic solution given in Eq. (1). In practice, of course the plastic deformation at the tip is unlikely to give rise to a constant deformation along the crack flanks, but close to the tip, Eq. (3) is a reasonable approximation. Plotting u y against  r should give a straight line with a gradient related to K and an intercept of  . The data in Fig. 6 is re-plotted in this way in Fig. 7.

Figure 6 : Variation of relative displacement (u y

) with distance from the crack tip (r) at five different values of load (P/P max

) during the

loading phase of a loading cycle.

From Fig. 7 it can be seen that the data gives a good straight line fit for  r > 5  m 0.5 , i.e. r > 5  m. The data can be used to plot the loading history in K vs  space. Pommier and Hamam [7] have suggested that the relationship should look like that shown schematically in Fig. 8. In particular, they suggest that in cyclic loading, such as the loop indicated by (C) in the figure, there is little change in  in the first part of each cycle. This observation can be used to explain the existence of a threshold  K in fatigue. It is postulated that, until the application of a certain level of  K , there is very little cyclic plasticity (characterised by  ) and the crack does not grow. The experimental data is plotted in Fig. 9a, where it can be seen that the experimental loops are similar in general form to those predicted in [7]. However, there is significant variation in  throughout the cycle. In particular,  seems to continue to increase for a while after load reversal at maximum load (and similarly decrease for a while at the minimum load reversal). This feature is difficult to explain physically, and may simply

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

vs  r data. This is illustrated in Fig. 10, where it can be seen that fitting a

be an artefact of the straight line fitting to the u y straight line for the data corresponding to P/P max

= 0.5 leads to a negative value for  . This may be thought to be physically inadmissible, although it should be remembered that the datum image for the DIC is that at minimum load, rather than corresponding to the undeformed material. Hence, only variations in  are measured, not the absolute value.

0.5

Figure 7 : Variations of relative displacement (u y

) with distance from the crack tip (r) at eight different values of load (P/P max

) during the

loading phase of a single cycle.

Figure 8 : Pommier and Hamam’s suggested behaviour in K vs  space [7]. Cyclic behaviour is indicated by the loop (C).

Figure 9 : Variation of K and  for loading cycles. Loading phase [black] and unloading [red] are shown for the first cycle. In Fig. 9b a second cycle of loading [blue] and unloading [magenta] is included.

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D. Nowell et alii, Frattura ed Integrità Strutturale, 33 (2015) 1-7; DOI: 10.3221/IGF-ESIS.33.01

0.5

Figure 10 : Variations of relative displacement ( u y ) during the initial loading phase of a single cycle. A line of best fit produced with a least squares method is included for each load in the matching colour. Finally, in Fig. 9b, data from two consecutive loading cycles are presented. It will be seen that the cycles are very similar, illustrating the reproducibility of the technique. However, a small increase in  can be seen between the first and the second cycle, corresponding to the accumulation of damage at the crack tip and, possibly, crack tip extension. ) with distance from the crack tip ( r ) at four different values of load ( P/P max

C ONCLUSIONS

T

he paper has presented a technique for in-situ loading of a small compact tension specimen in a scanning electron microscope. It has proved possible to take high quality images of the area close to the crack tip during complete loading cycles. Constant amplitude data are reported here, but images from a single overload cycle have also been captured. Digital image correlation has been used to analyse the data using both an elastic and an elastic-plastic approach. Unsurprisingly, the elastic approach does not model the measured displacements well, particularly close to the crack tip. An elastic-plastic approach provides a better fit, but there are still deficiencies in capturing deformations close to the tip. This may be partly because the existence of the process zone at the tip affects the displacements measured at the grid locations, and these may no longer represent purely crack flank displacement. A more sophisticated elastic-plastic model is almost certainly in order to model the data more accurately, but the experiment had demonstrated the capability to measure displacements close to the crack tip which will be useful in calibrating other models. [1] Paris, P., Erdogan, F., A critical analysis of crack propagation laws, Jnl Basic Engineering, 85 (1963) 528-534. [2] Nowell, D., Kartal, M.E., de Matos, P.F.P., Measurement and modelling of near-tip displacement fields for fatigue cracks in 6082 T6 aluminium, Proc. First I.J. Fatigue & FFEMS Joint Workshop, Forni di Sopra, Italy, March 7-9, 2011, Gruppo Italiano Frattura, (2011). [3] Nowell, D., Kartal, M.E., de Matos, P.F.P., Digital image correlation measurement of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, Fatigue Fract. Engng Mater. Struct., 36 (2013) 3-13. [4] Nowell, D., Kartal, M.E., and de Matos, P.F.P., Characterisation of crack tip fields under non-uniform fatigue loading, Proc. Second I.J. Fatigue & FFEMS Joint Workshop, Malaga, Spain, April 15-17, 2013, Gruppo Italiano Frattura, (2013). [5] Eberl, C. Thompson, R., Gianola, R., Digital image correlation and tracking with Matlab, Matlab Central file exchange (2006) http://www.mathworks.co.uk/matlabcentral/fileexchange/12413-digital-image-correlation-and-tracking. [6] Irwin, G.R., Plastic zone near a crack and fracture toughness, Mechanical and Metallurgical Behavior, Proc. Seventh Sagamore Ordnance Materials Research Conference, IV(1960) 63-78. [7] Pommier, S., Hamam, R., Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic-plastic displacement fields, Fatigue Fract. Engng Mater. Struct., 30 (2006) 582-598. R EFERENCES

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A. Shanyavskiy, Frattura ed Integrità Strutturale, 33 (2015) 8-16; DOI: 10.3221/IGF-ESIS.33.02

Focussed on characterization of crack tip fields

Spherical particles formation under biaxial cyclic loading due to mesotunneling effect

A. Shanyavskiy State Centre for Civil Aviation Flights Safety, Airport Sheremetievo-1, PO Box 54, Moscow region, Chimkinskiy State, 141426, Russia shanantal@mailfrom.ru A BSTRACT . Fatigue fracture surfaces of Al-based alloys with fatigue striations pattern and such wear debris pattern as spherical particles were investigated fractographically, on the bases of the OG’e spectroscopic analysis. The sequence of events during fatigue crack edges opening was discovered when the elliptical or spherical shapes of wear debris build up on the fracture surface in crosspieces between mesotunnels under mode III of mode I fatigue crack opening because of volume rotation. The cause of black colour of places with fretting patterns on the fracture surfaces of Al-based alloys is discussed. K EYWORDS . Mesoscopic fatigue fracture; Fractography; Spherical particles; OG’e spectroscopy; Rotation plastic deformation. metal with a growing crack represents an open dynamic system, which is far from equilibrium [1]; the system is exercising a series of sequential transitions from one to another stability state and the continued energy exchange with the environment. An open system evolves by passing through the critical states, referred to as the bifurcation points, to, alternatively, a stability or instability condition [2]. As longer as the system experiences fluctuations, it cannot avoid instability immediately before a bifurcation point. The newly activated processes of damage accumulation develop or, alternatively, die out, depending on whether the system is able to the self-organized absorption of energy in the ways that shift the construction element toward a greater stability, i.e. longer life-time. The evolution of an open system is commonly discussed in the terms of microscopic, mesoscopic, or macroscopic scale levels [3]. The first is relevant to the effects on the atomic spacing; the second, to the behaviour of atomic ensembles, and the third, to the creation of bulky space structures. As cyclic loading of a construction element is continuing, mechanisms of damage accumulation replace one another sequentially for the three scale levels, each starting and keeping on for a certain time [4]. The microscopic (Stage I) and mesoscopic (Stage II) scale levels of crack growth are in common with one another as concerns the subjects of forming shear lips at the free surface of the work-piece [5], mesoscopic tunnelling (or holes) of crack, or combining shear and cleavage in the metal when subjected to uniaxial tension, Fig.1. Isolated regions of the failed metal, formed all along the crack front, are stretched in the crack-growth direction and separated by unbroken crosspieces. Mesotunnels (or holes, see Fig.1) are formed by shear during Stage I, and the crosspieces can fail, during Stage I, by the type-III shear or by growing a crack from one to other tunnel just like growing the tunnels themselves. However, rotational instability of deformation and fracture of the inter tunnel crosspieces may A I NTRODUCTION

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A. Shanyavskiy, Frattura ed Integrità Strutturale, 33 (2015) 8-16; DOI: 10.3221/IGF-ESIS.33.02

become the case at Stage II (Fig. 2, (b), (c), and (d)). Changing from the shear- to rotation-type instability in crosspiece is associated with further complication of the way in that energy is being absorbed in the material before fracture.

Figure 1 : Schema of metals fatigue cracking with simultaneously holes (mesotunnels) formation and crosspieces between them failure because of shearing or fatigue striation creation [6].

a)

b)

c) d) Figure 2 : Combined mode-I, II and III opening of a fatigue crack under uniaxial stretch condition with (a) mesotunnels- 1, (b) , (c) material rotations in crosspieces (2) between mesotunnels, and (d) cascade of oriented in chain cylindrical, ellipsoidal and spherical particles.

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A. Shanyavskiy, Frattura ed Integrità Strutturale, 33 (2015) 8-16; DOI: 10.3221/IGF-ESIS.33.02

It was fractographically confirmed [7] that, at the microscopic scale level, the crack-growth behaviour is quite sensitive to the microstructure of the materials, and dislocation slip is dominated. Ivanova V.S. and Shanyavskiy A.A [4] have shown that the crack growth, at Stage I, in mesotunnels is associated with the development of slip: multiple-slip traces, slip steps or extrusion sites can be seen at the background of the pseudo-striations pattern. The fatigue crack propagation is quite fast in the mesotunnels at the Stage I. Consequently, the system experiences a self-organized transition to more complicated ways of energy absorption by the material, subjected to deformation, in which new free surface is being formed for meso-tunnels; this transition to the mesoscopic scale level (Stage II) occurs once the critical conditions at the crack tip were created [8]. The energy-absorption process becomes more complicated since the rotation effects are dominating in the deformation and fracture of the material at the meso-tunnel tip. Fractographic analyses of fatigue surfaces attest to Stage II (tensile Mode I) striation formation [4, 7], following Stage I crack growth. The dramatic decrease in crack growth acceleration between the two Stages is strongly exhibited by the kinetic (da/dN v  K) diagram for long cracks at the point of change in slope (or deviation) is witnessed under a regular cyclic loading condition. Therefore, a self-organized transformation from one form of energy absorption to another is occurring near to the crack tip. The shear mode of material separation (the mode II process) is the dominant mechanism of metal fracture below this deviation point whereas the opening mode (mode I process) is dominant above this point. This paper presents an analysis of the mechanisms involved in the formation of spherical particles at the mesoscopic scale level based on a rotation effect and the shear sliding process for aluminium based alloys. Both mechanisms were investigated fractographically, and, also, on the bases of the OG’e spectroscopy analyses. Let be consider a process of spherical particles formation in crosspieces between meso-tunnels. pherical particles wear formation under various cyclic loads conditions is well-known phenomenon [9-11]. They were discovered in compositions of wear debris are formed during rolling contact fatigue [9]. Further these particles were looking on the fretting surface [10, 11]. Fatigue cracks development in components or specimens is accompanied by processes of wear debris patterns formation on the fatigue surface because of crack edges interaction [4, 12-14]. The main idea for the interaction based on the process [13], which due to the mode II shearing of the mode I cracks growth under external tension loading for the near threshold fatigue cracks development. Rewelding occurs at the contact points across the crack as  I K falls [14]. Wear debris become detached from both fatigue surfaces during the rewelding and tearing processes. The leading role of the mode II K in contact points across cracks front have to be attracted to discuss the first stage of the fatigue crack growth because of the shearing mechanism which directed to the roughed surface formation. Suresh S. and Ritchie R.O [13] performed the roughness-model to calculate effective stress intensity factor for fatigue cracks growth under Modes  ( ) I II K K . The Mode II crack growth in specimens from Fe- and Al-based alloys was modelled under compressive cyclic loads, and spherical particles on the fatigue surface were shown [15]. There were places with wear debris of the black colour on the fatigue fracture surfaces for Al-based alloy. Two sizes for different particles shapes were discovered: (10...40)  m , and smallest than 10  m . The smallest particles were dominant. Small particles were often associated with small sockets and wear tracks, where the particles have been removed using replicating tape. The higher contrast suggested that they might contain a significant proportion of oxide. Their higher contrast in micrographs and their apparently greater hardness than the matrix tend to suggest that they contained a large amount of oxide. But it had not yet been possible to determine their exact composition. Various models [9-11] were discussed in the paper [15] and it was shown that they cannot explain a mechanism of the small particles formation. The well-known model [10] of wear particles formation by adhesive wear processes which trapped them in cavities in the sliding surface and became soothed by burnishing processes, can explain big particles formation only. According to the model, spherical particles to be anticipated in slow uniaxial sliding, in fretting and within cracks of a material being fatigued. Below results of the spherical particles fractographic analysis for fatigued specimens from Al-based alloys is discussed, and OG’e analysis uses to explain a mechanism of their creation during fatigue cracks growth. S S PHERICAL PARTICLES DUE TO M ODE III OF M ODE I FATIGUE CRACK GROWTH

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A. Shanyavskiy, Frattura ed Integrità Strutturale, 33 (2015) 8-16; DOI: 10.3221/IGF-ESIS.33.02

Fractographic analysis Spherical particles fractographic analysis was performed on the fatigue surface of specimens from Al-alloys tested earlier under various cyclic loads conditions [4]: bending of cylindrical bars with rotation; uniaxial tension of prismatic specimens with tension decreasing so that a crack retardation for the semi-elliptically shaped cracks took place, then spherical particles formation process is occurred after the retardation; biaxial tension-compressive of cruciform specimens with semi-elliptically shaped cracks; biaxial overloads of cruciform specimens for through-thickness cracks. Materials compositions used for the investigation have shown in Table 1.

Mg

Si

Cu

Mn

Fe

Zn

Ti

Cr 0.2

Al

AVT D1T D16T AK6T

0.82 0.73

0.67 0.62

0.38 0.46

0.24 0.77 0.65 0.42

0.48 0.36 0.42 0.57

0.19 0.21 0.15 0.24

0.1

remained remained remained remained

0.06 0.07 0.08

- - -

1.4

0.3

4.2

0.47

1.13

2.25

Table 1 : The composition (in %) of investigated Al-alloys.

The bending with rotation of cylindrical specimens of 12mm in diameter from the AVT-alloy was realized in the tension stress range of 100...150 MPa at frequency 10 Hz. Specimens from D1T-alloy of 40x20 mm in their section were tested under uniaxial tension at the stress of 160 MPa at the stress ratio R=0.1 and the frequency of 5 Hz. First, the semi-elliptically shaped crack was performed up to its sizes in the depth direction near to 10 mm and on the specimen surface near to 2c=20 mm. Then, the maximum stress level was only decreased down to the stress of 80 MPa and under this cyclic loads stress the crack length was increased up to the depth near to 20 mm. Biaxial tension-compressive of the 10 mm thick cruciform specimens from AK6 Al-alloy (see Tab. 1) with semi-elliptical shaped cracks was performed under regular cyclic loads at frequency of 5 Hz and the principal stresses ratio       2 1 / 0.9 in the range of 100 MPa    1 160 MPa [16]. The biaxial stresses state was uniform within the central zone of the specimen of 20 mm in diameter. Irregular cyclic loads with biaxial overloads were performed on the specimens from D16T Al-alloy (analogue of 2024T3) [17]. The spherical particles were formed on the fracture surfaces after the overloads factor 0 Q of 1.8 and 1.5 when the shear lip width 2t reached near to the have of the specimen thickness. The fatigue surfaces were cut from specimens and their analysis was developed fractographically in the scanning electron microscope EVO40 of Karl Zeiss instruments with resolution 3 nm, CD50, and Hitachi. Wear debris were seen on the fatigue surface between facets with fatigue striations pattern. Places with wear debris were oriented in the parallel direction to the crack growth. Three shapes of particles such as cylinder, ellipsoid, and sphere can be seen on the places with wear debris, Fig. 3. The length of cylinders reached 70 mm and they have diameter in the range of 1...5  m . Some particles are placed into oriented sockets. The cylindrical sockets are situated equidistantly one after another one. Their axes orientation being in the parallel to the crack growth direction is dominant. The cylindrical particles fragmentation have made as a result of their rotations between free surfaces. The spiral crack, as shown in Fig. 3, performs because of the twisting process of the particles fragmentation due to the mode III opening. The rotation created a specific border between fragments such-like as a conic-cavity on the one piece and a just out conic on the other one, Fig. 3. That confirmed the rolling mechanism of their formation from the fragments of the cylindrical particles. In some cases the particles associated with wear tracks, where they were removed by replicating tape. They apparently had greater hardness the matrix. The tracks orientation coincides with the crack surfaces moving due to mode III opening. The material heaped up from the tracks on the facets with fatigue striations pattern. Therefore this material heaped up from tracks sometimes later than the fatigue relief was formed. After uniaxial overloads there is wear debris evident on the fracture surface following the stretched or dimpled zones at R=0.1. The density of debris decreases as the R-ratio increases. The original shapes of the wear debris were ellipsoidal and spherical particles formed on the fracture surface after overloads more than factor 1.5, Fig.4 (a). As the double shear lip width increased near to the specimen’s half-thickness (as the crack developed) the particles appeared the moment an overload was applied. They lay on facets, which are parallel the crack growth direction. Because

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