Issue 23

Anno VII Numero 23 Gennaio 2013

Rivista Internazionale Ufficiale del Gruppo Italiano Frattura

Editor-in-chief:

Francesco Iacoviello

ISSN 1971-8993

Guest Editors: Eugenio Dragoni Franco Furgiuele Aurelio Soma’

Associate Editors:

Luca Susmel John Yates

Editorial Advisory Board:

Harm Askes Alberto Carpinteri Andrea Carpinteri

Donato Firrao M. Neil James Gary Marquis

Robert O. Ritchie Darrell F. Socie Cetin Morris Sonsino Ramesh Talreja David Taylor

Frattura ed integrità strutturale The International Journal of the Italian Group of Fracture

www.gruppofrattura.it

Frattura ed Integrità Strutturale, 23 (2013); Rivista Ufficiale del Gruppo Italiano Frattura

R. Casati, M. Vedani, S.A.M. Tofail, C. Dikinson, A. Tuissi On the preparation and characterization of thin NiTi shape memory alloy wires for MEMS ................. 7 C. Maletta, F. Furgiuele, E. Sgambitterra Fracture mechanics of pseudoelastic NiTi alloys: review of the research activities carried out at University of Calabria ……………………………………………………………………………….... 13 G. Scirè Mammano, E. Dragoni Functional fatigue of NiTi Shape Memory wires for a range of end loadings and constraints …………... 25 M. Bocciolone, M. Carnevale, A. Collina, N. Lecis, A. Lo Conte, B. Previtali, C.A. Biffi, P. Bassani, A. Tuissi Application of martensitic SMA alloys as passive dampers of GFRP laminated composites …………... 34 R. Vertechy, G. Berselli, M. Bergamasco, V. Parenti Castelli, G. Vassura Compliant actuation based on dielectric elastomers for a force-feedback device: modeling and experimental evaluation …………………………………………………………………..……………… 47 A. Spaggiari Properties and applications of magnetorheological fluids …….……………...…….......…………...... 57 F. Bucchi, P. Forte, F. Frendo, R. Squarcini A magnetorheological clutch for efficient automotive auxiliary device actuation …….……………......... 62 A. Spaggiari, E. Dragoni Effect of pressure on the physical properties of magnetorheological fluids …….……………...………... 75 D. Castagnetti Design and characterization of a fractal-inspired multi-frequency piezoelectric energy converter …………. 87 A. Somà, G. De Pasquale Electro-mechanical coupled design of self-powered sensing systems and performances comparison through experiments ……………………………………………………...….……................…...…... 94 M.F. Pantano, L. Pagnotta, S. Nigro A numerical study of squeeze-film damping in MEMS-based structures including rarefaction effects …… 103 G. De Pasquale, A. Somà Experimental methods for the characterization of fatigue in microstructures …..………….....……....... 114 F. Felli, A. Brotzu, C. Vendittozzi, A. Paolozzi, F. Passeggio Wear surface damage of a Stainless Steel EN 3358 aeronautical component subjected to sliding ………. 127

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Frattura ed Integrità Strutturale, 23 (2013); ISSN 1971-9883

Editor-in-Chief Francesco Iacoviello

( Università di Cassino e del Lazio Meridionale, Italy)

Associate Editors Luca Susmel

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

John Yates

Guest Editors Eugenio Dragoni Franco Furgiuele

( Università di Modena e Reggio)

( Università della Calabria) ( Politecnico di Torino)

Aurelio Somà

Advisory Editorial Board Harm Askes

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

Alberto Carpinteri Andrea Carpinteri

Donato Firrao M. Neil James Gary Marquis

( University of Plymouth, United Kingdom) ( Helsinki University of Technology, Finland)

Robert O. Ritchie Darrell F. Socie Cetin Morris Sonsino

( University of California, USA)

( University of Illinois at Urbana-Champaign)

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

Ramesh Talreja David Taylor

Journal Review Board Stefano Beretta

( Politecnico di Milano, Italy)

Nicola Bonora Lajos Borbás Francesca Cosmi

( Università di Cassino e del Lazio Meridionale, Italy) ( Budapest University Technology and Economics, Hungary)

( Università di Trieste, Italy) ( EADS, Munich, Germany)

Claudio Dalle Donne Vittorio Di Cocco Josef Eberhardsteiner Giuseppe Ferro Tommaso Ghidini Mario Guagliano Carmine Maletta Liviu Marsavina

( Università di Cassino e del Lazio Meridionale, Italy)

( IMWS, Wien, Austria)

( Politecnico di Torino, Italy)

( European Space Agency - ESA-ESRIN)

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

( University of Timisoara, Romania) Lucas Filipe Martins da Silva (University of Porto, Portugal) Marco Paggi ( Politecnico di Torino, Italy) Alessandro Pirondi ( Università di Parma, Italy) Ivatury S. Raju ( NASA Langley Research Center, USA) Giacomo Risitano ( Univ. Telematica Guglielmo Marconi ) Roberto Roberti ( Università di Brescia, Italy) Marco Savoia ( Università di Bologna, Italy) Andrea Spagnoli ( Università di Parma, Italy)

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Frattura ed Integrità Strutturale, 23 (2013); Rivista Ufficiale del Gruppo Italiano Frattura

Descrizione e scopi Frattura ed Integrità Strutturale è la rivista ufficiale del Gruppo Italiano Frattura . E’ una rivista open-access pubblicata on-line con periodicità trimestrale (luglio, ottobre, gennaio, aprile). Frattura ed Integrità Strutturale riguarda l’ampio settore dell’integrità strutturale, basato sulla meccanica della fatica e della frattura, per la valutazione dell’affidabilità e dell’efficacia di componenti strutturali. Scopo della rivista è la promozione di lavori e ricerche sui fenomeni di frattura, nonché lo sviluppo di nuovi materiali e di nuovi standard per la valutazione dell’integrità strutturale. La rivista ha un carattere interdisciplinare e accetta contributi da ingegneri, metallurgisti, scienziati dei materiali, fisici, chimici e matematici. Contributi Frattura ed Integrità Strutturale si prefigge la rapida disseminazione di contributi originali di natura analitica, numerica e/o sperimentale riguardanti la meccanica della frattura e l’integrità strutturale. Si accettano lavori di ricerca che contribuiscano a migliorare la conoscenza del comportamento a frattura di materiali convenzionali ed innovativi. Note tecniche, lettere brevi e recensioni possono essere anche accettati in base alla loro qualità. L’ Editorial Advisory Board sollecita anche la pubblicazione di numeri speciali contenenti articoli estesi presentati in occasione di conferenze e simposia tematici. Istruzioni per l’invio dei manoscritti I manoscritti devono essere scritti in formato word senza necessità di utilizzare un particolare stile e devono essere inviati all'indirizzo iacoviello@unicas.it. Il lavoro proposto può essere in lingua Italiana (con riassunto in inglese di almeno 1000 parole e didascalie bilingue) o Inglese. La conferma della ricezione avverrà entro 48 ore. Il processo di referaggio e pubblicazione on-line si concluderà entro tre mesi dal primo invio. 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.

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, 23 (2013); ISSN 1971-9883

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entilissimo lettore, nell’ultima Newsletter IGF sono stati riportate le attività organizzate dall’IGF nel 2012. Molto brevemente: - Ha organizzato il Workshop Problematiche di Frattura ed Integrità Strutturale di Materiali e Componenti Ingegneristici , Forni di Sopra, marzo 2012. Nel sito IGF sono disponibili gli atti e le videoregistrazioni (queste ultime sono disponibili anche nel canale IGF in iTunesU) - Ha organizzato la Scuola Estiva Multiaxial fatigue assessment of engineering materials and components , relatore il Prof. Darrell F. Socie della University of Illinois ad Urbana-Champaign, luglio 2012, Udine. Le videoregistrazioni sono disponibili nel sito IGF e nel canale IGF in iTunesU. - Ha ottenuto l'assegnazione dell'organizzazione dell'evento ESIS del 2016, ovvero l' ECF21 , che si terrà quindi a Catania nel giugno 2016 - Ha organizzato una sessione IGF nel convegno internazionale CompImage 2012 , Roma settembre 2012. Le videoregistrazioni sono disponibili nel sito IGF e nel canale IGF in iTunesU. - Ha contribuito all'organizzazione del Crack Paths 2012 , Gaeta settembre 2012. Gli atti sono disponibili nel sito IGF. - Ha organizzato il Wokshop Virtual testing of heterogeneous materials , Torino ottobre 2012. Purtroppo, per motivi tecnici, le videoregistrazioni non sono disponibili. Inoltre: - Ha rinnovato completamente il sito IGF, rendendolo pienamente fruibile anche da device mobili. - Ha pubblicato uno scaffale in Google Books contenente tutti i volumi pubblicati dall'IGF nei suoi trent'anni di vita: in questo servizio è possibile effettuare ricerche anche all'interno del testo (sia dei volumi in pdf “nativo” che digitalizzati mediante scansione). Nel 2012 sono state visualizzate oltre 180000 pagine!! - Ha ottenuto la pubblicazione di un canale dedicato in iTunesU-Beyond Campus , incrementando la visibilità delle videoregistrazioni effettuate dal 2007 in poi. - Ha ottenuto l'indicizzazione Scopus della rivista IGF Frattura ed Integrità Strutturale ; inoltre la rivista è stata inserita in numerose banche dati quali, ad esempio, EBSCO e ProQuest. Il successo di queste iniziative è merito di un gruppo di persone entusiasta: i membri del Consiglio di Presidenza ( Giuseppe Ferro, Angelo Finelli, Donato Firrao, Carmine Maletta, Marco Paggi, Giacomo Risitano, Andrea Spagnoli, Luca Susmel), i componenti dei due Board che supportano le attività della rivista e tutti gli amici IGF che ci seguono con interesse sempre crescente. Grazie a tutti !!! Infine qualche parola sul presente numero della rivista IGF. Avrete forse notato nella copertina la presenza per questo numero di tre Guest Editor: in questo numero pubblichiamo infatti le versioni estese di alcuni lavori presentati al simposio The Italian research on smart materials and MEMS, che si è tenuto a Scilla (RC) lo scorso 31 maggio-1 giugno con il supporto dell’Associazione Italiana di Analisi delle Sollecitazioni (AIAS) e della sezione italiana dell’ASME. Ringraziamo gli autori per il loro contributo, ed i tre Guest Editor per l’accurato lavoro svolto: Eugenio Dragoni, Franco Furgiuele, Aurelio Somà. Con i migliori auguri di un felice e prospero 2013, tanti cari saluti, Francesco Iacoviello Presidente IGF Direttore Frattura ed Integrità Strutturale

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Frattura ed Integrità Strutturale, 23 (2013); Rivista Ufficiale del Gruppo Italiano Frattura

The Italian research on smart materials and MEMS

R

ecent developments in the field of material science and semiconductor technologies are fostering the engineering use of smart materials and micro-electromechanical-systems (MEMS) for the production of intelligent products. The term smart material applies when a material can react in a useful, reliable, reproducible and usually reversible manner to some stimulus picked up from its environment. A really smart material will use its reaction to the external stimulus to initiate or actuate an active response, e.g. with an active control system. There are materials that are designed to change their colour at a particular temperature. They find uses in bath plugs that show when the bath water is too hot, or in children’s feeding spoons and coffee or tea mugs that testify chromatically the temperature of their content. Other examples include water mixers incorporating self-energized shape memory springs to ensure a constant flow temperature despite fluctuating supply temperatures and pressures due to water being used elsewhere in the home. Besides these examples, the class of smart materials and applications is very large and rapidly growing, especially thanks to the steady development of new formulations and manufacturing techniques. Micro electromechanical systems (MEMS) merge mechanical and electrical components and have feature sizes ranging from micrometers to millimetres. They are typically fabricated using methods borrowed from the industry of integrated circuits and they have the potential of providing significant cost advantages when fabricated in large batches. Their small size also makes it possible to integrate them into a wide range of systems. Feature sizes may be scaled down to the order of the wavelength of light, thus making them attractive for many optical applications. Microsensors (e.g., accelerometers for automobile crash detection and pressure sensors for biomedical applications) and microactuators (e.g., for moving arrays of micromirrors in projection systems) are examples of commercial applications of MEMS. A relatively new and very promising field of application involves the integration of smart materials within MEMS to produce adaptive systems on a microscale. Thermally-activated, single-piece microgrippers or smart microvalves based on magnetorheological fluids are just two instances of the many possibilities disclosed by this fruitful hybrid technology. Although the chemistry and the physics behind the development of most smart materials and MEMS are well established, there is a definite need for engineering tools to help the designer incorporate those materials into marketable industrial products. This Special Issue collects papers aimed at providing fundamental background and useful design methods to the readers approaching this stimulating area of research. The papers were presented at the seminar held in Scilla from May 31 to June 2, 2012, by the Smart Materials and MEMS working group of the Italian Association of Stress Analysis (AIAS). We wish to thank the Italian section of the ASME for their support and Ingg. L. Bruno, C. Maletta and E. Sgambiterra for their fruitful collaboration.

Eugenio Dragoni, Università di Modena e Reggio Emilia Franco Furgiuele, Università della Calabria Aurelio Somà, Politecnico di Torino

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

Scilla 2012 - The Italian research on smart materials and MEMS

On the preparation and characterization of thin NiTi shape memory alloy wires for MEMS

Riccardo Casati, Maurizio Vedani Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 34, Milano, Italy Syed A. M. Tofail, Calum Dikinson Materials and Surface Science Institute, University of Limerick, Limerick, Ireland Ausonio Tuissi National Research Council (CNR-IENI), Corso Promessi Sposi 29, Lecco, Italy

A BSTRACT . Shape memory alloy (SMA) wires are employed as actuators in small devices for consumer electronics, valves and automotive applications. Because of the continued miniaturization of all the industrial products, nowadays the tendency is to produce MEMS (micro electromechanical systems). Among the most promising functional MEMS materials, the thin SMA wires that are offering a rapid actuating response with high power/weigh ratio of the material, are attracting a world wide interest. This paper is aimed at showing the production process and the characterizations of thin NiTi shape memory wires. The activity was focused on drawing procedure and on functional and TEM characterizations of the final products. In particular, it was evaluated the performance of the SMA wires for actuators in terms of functional fatigue and thermo-mechanical properties by means of an experimental apparatus design ad hoc for these specific tests. K EYWORDS . Shape memory alloys; SMA; MEMS; Thin wire; Actuators; TEM. MAs are basically functional materials which exhibit peculiar thermo-mechanical properties such as the Shape Memory Effect and the Superelasticity. These properties are consequence of a reversible thermo-elastic martensitic transformation occurring at the solid state [1]. Because the martensite phase shows a strong amplitude-dependent internal friction, SMA have also an high damping capacity [2, 3]. When SMA is used as actuator, it can be classified as “ Smart Material” because it combines both sensor and actuator functions. SMA alloys are applied with success in several commercial fields: biomedical (stents, orthodontic arc wire, orthopaedics devices, surgical tools); sensor/actuator (valves, active actuators, on/off devices); coupling (pipe fastener, electric fastener); sport; manufactures; antennas, gadgets etc. [4,5]. In the modern world, great emphasis has been placed in miniaturization and huge research efforts are oriented to develop MEMS (Micro Electro-Mechanical Systems) to perform a multitude of tasks [6]. Among MEMS materials the SMA, in form of films or thin wires, are attracting a particular interest for the development of new highly functionalized devices on micro/meso scale [7-10]. SMA elements are characterized by a significant amount of actuation with an extremely small total volume over conventional actuator mechanisms. Another advantage that shape memory alloys have is the versatility since they can be actuated thermally or electrically [7-10]. In this work, Ti rich NiTi alloy, with high transformation temperatures, is produced by vacuum induction melting and thin wire are manufactured by hot and cold working. The main processing aspects of thin NiTi wire manufacturing are reported with specific reference to the effect S I NTRODUCTION

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

of cold drawing steps on the wire characteristics. The process can be scale down to diam. 10 micron wire for the developing of SMA device within meso/micro scale. For both the drawn and the trained wires, longitudinal cracks, localized around inclusions, were highlighted by TEM analyses. Again, functional properties of the produced wires are studied by both DSC scans and electrically actuated thermal cycling under constant applied stress up to 300.000 cycles.

E XPERIMENTAL METHODS t was chosen a Ni rich Ni 49

I

Ti 51 ( at.%) composition, which is very commonly employed for the production of shape memory materials for actuators with transformation temperature above room temperature. Electrolytic grade nickel and pure titanium (Grade 1) were melted by VIM (Vacuum Induction Melting) furnace in carbon crucible under argon atmosphere [11]. The ingot was hot forged and hot rolled at 950°C and finally cold drawn with intermediate annealing. The first steps of the drawing process (down to the diameter of 0.5 mm) were performed by means of a conventional drawing machine reaching values of area reduction of about 10-20% before each thermal annealing (700 °C). The final steps of drawing were indeed carried out employing a special experimental drawing system (MGS mod. TRF 6/25 M) modified to prevent breakings of wires (Fig. 1a). This machine was equipped by a controlled drawing speed system, an electrical clutch coiler and a laser sensor-controlled spooling system for correct distribution of the wire on the spool (Fig. 1b), diamond dies, load cell, die cooling system, camera for checking correct wire pay-on (Fig. 1b). In Tab. 1, the die used and the heat treatments parameters carried out during the cold drawing process are resumed. The evolution of functional properties, in particular of the residual strain, during thermo-mechanical cycling by means of an experimental apparatus designed ad hoc for these specific tests is here reported. Specimens (100 mm in length) were vertically gripped in the testing equipment and axially loaded (250 MPa). They were heated by electrical pulses (see Fig.2 for details of pulse parameters) and cooled by natural air convection. The wire displacement was measured by LVDT and relative strain was continuously monitored and evaluated as  L/Lo (Lo wire length for each cycle before heating). The same experimental apparatus detailed reported elsewhere [13] was used in order to carried out the first 500 thermal cycles under 250 MPa as well as fatigue tests under 200 MPa. For the latter the total recovered strain was set at 3.8% and the stress at 200 MPa.

( a) ( b) Figure 1 : a) Experimental drawing system b) laser sensor-controlled spooling system for correct distribution of the wire on the spool and camera for checking correct wire pay-on . Before and after thermo-mechanical cycling calorimetric test were carried out by DSC Seiko 220C. The temperature range investigated was 223K/403K (-50°C/130°C). Thermo-mechanical loop was performed by DMA TA Q800 equipped with tension clamps for uniaxial tests. The temperature range investigated was 273K/423K (0°C/150°C), the heating and cooling rate was 5K/min and the applied stress was 200 MPa. Microstructural analysis was executed by JEOL JEM-210 operating at 80 - 200 kV. Thin slice for TEM investigation were extracted from the center of the wire by Focus Ion Beam FEI 200 (Fig.3a). In Fig.3b a picture of a thin slice FIB cutting is depicted.

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

Area reduction

 Die (  m)

200 - Heat treatment: 300s 550°C + Water Quenching 175 23,4% 150 26,5% Heat treatment: 300s 550°C + Water Quenching 130 24,9% 110 28,4% Heat treatment: 300s 550°C + Water Quenching 100 17,4% 90 19,0% 80 21,0% Heat treatment: 1200s 400°C + Water Quenching Table 1 : Drawing steps and corresponding area reduction.

Figure 2 : Step waveform electrical pulse: t ON

= 0,4 s, t OFF

= 2,5 s, I MAX

= 0.13 A

Figure 3 : a) Scheme of TEM sample preparation. b) NiTi thin slice used for TEM analysis.

R ESULTS

he whole working process was carried out without any formation of macroscopic cracks on the surfaces of the bars and the wires. The microstructure of the final product (80 μm wire) after heat treatment (400°C, 1200s) was investigated by TEM. This analysis revealed a very fine polycrystalline microstructure (grain size was about 20nm) and the presence of inclusions (Fig.4). T

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

20 um

Figure 4 : TEM images of the wire after the last heat treatment (1200 s, 400°C).

Figure 5 : Thermal cycling under constant stress (250MPa). This process is performed to stabilize the SM properties of the material. A high content of Ti 4 Ni 2 O x confirmed by selected area electron diffraction (SAED) were observable. The drawing procedures caused the breaking of these ceramic compounds into fine inclusions that lined up in the drawing direction inducing significant amount of cracks into the matrix (Fig.4). The inset diffraction pattern indexed space group Fd-3m and lattice parameter 1.19 nm viewed down the [01-1] zone axis (in this respect, see the previous work by Tuissi and co workers [12]). Before their application, SMAs must be thermo-mechanical cycled to stabilize their functional properties [13]. In order to reproduce a standard process of stabilization of the material, 500 thermal cycles under an applied stress of 250 MPa were carried on the wires (Fig.5). During the first few hundreds cycles, the material accumulates irreversible plastic deformation. From the curve in Fig.5 the lengthen of the wire is noticeable (about 2%). This phenomenon involves the increase of transition temperatures. Fig.6a shows the results of calorimetric analyses performed on two samples of the wire taken before and after the thermo-mechanical cycling. Both the samples exhibit a single-stage inverse transformation ( between B19’ and B2) and a two-stage direct transformation (from B2 to R-phase and then to B19’). The main gap between the two curves consists in the transformation peaks broadening and in a increasing of transition temperature due to the cycling. Similar results were obtained by thermal loop under constant stress (200 MPa) by DMA. As depicted in Fig.6b, the T-ε curves show a double inflexion on the cooling branch due to a two-stage direct transformation. The load leads to an increase in all transition temperatures, this is in according with the Clausius-Clapeyron relationship [1]. The increase in transformation temperature due to thermo-mechanical cycling is detectable even under an applied constant load. The cycling promoted an increase of R  M transition temperature which, summed to the effect of the applied load, implies the disappearance of R-phase during the cooling and then a narrow thermal hysteresis.

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

In Fig. 7 the strain-cycles curves are reported: the wire was subjected to 300,000 cycles under constant stress (200 MPa) and the strain recovered was set at 3.8%. This fatigue test shows that even if the metal matrix exhibits a significant amount of cracks, the wire could withstand a very high number of thermo-mechanical cycles, indeed no wire failure occurred.

( a) ( b) Figure 6 : a) DSC curves and b) Thermal loop under constant load before and after 500 cycles

Figure 7 : Fatigue test: thermal cycling under constant stress (200 MPa).

C ONCLUSIONS

T

he results obtained through this research can be summarized as follow:  80 μm Ni49Ti51 (at.%) wire was produced without any formation of macroscopic cracks on the surfaces of the final product. Then, the procedure revealed to be suitable for the production of very thin shape memory wire employable in MEMS, actuators and other applications.  TEM analysis revealed a mean grain size of few tens nanometers and the presence of rather big inclusions (less than 1 μm). SAED pattern revealed these particles to be Ti 4 Ni 2 O x inclusions. These ceramic compounds did not impaired significantly the fatigue behavior of the SMA wire, since it could reach 300000 cycles without failing.  The wire shows characteristic transformation temperature higher than room one. Thermo-mechanical cycling leads to a reduction of thermal hysteresis. These are good points for the using of the material as shape memory actuator.

A CKNOWLEDGEMENTS

T

he authors would like to thanks Marco Pini; Nicola Bennato; Enrico Bassani (CNR IENI Lecco) for melting and technical assistance Serguei Belochapkines (University of Limerick) for TEM assistance.

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R. Casati et alii, Frattura ed Integrità Strutturale, 23 (2013) 7-12; DOI: 10.3221/IGF-ESIS.23.01

R EFERENCES

[1] K. Otsuka, C.M. Wayman, Shape Memory Materials. Cambridge University Press, (1998). [2] J.Van Humbeek, Journal of Alloys and Compounds, 355(1–2) 30 (2003) 58. [3] B. Coluzzi, A. Biscarini, G. Mazzolai, F.M. Mazzolai, A. Tuissi, E. Villa, Key Engineering Materials, 319 (2006) 1. [4] T. Duerig, A. Pelton, D. Stöckel, Materials Science and Engineering A, 273-275 (1999) 149. [5] J. Van Humbeck, Materials science and Engineering A, 273-275 (1999) 134. [6] T. Hsu, In: IEEE/ASME International conference on Advanced Manufacturing Technologies and Education in the 21 st Century, Chia-Yi, Taiwan, Republic of China, (2002). [7] K. Ikuta, Micro/miniature shape memory alloy actuator. IEE-ICRA (1990). [8] L. Sun, W.M. Huang, Z. Ding, Y. Zhao, C.C. Wang, H. Purnawali, C. Tang, Materials and Design 33 (1) (2012) 577. [9] A. Nespoli, S. Besseghini, S. Pittaccio, E. Villa, S. Viscuso, Sen Actuators, A158 (2010) 149. [10] Y. Fu, H. Du, W. Huang, S. Zhang , M. Hu, Sensors and Actuators A, 112(2-3) (2004) 395. [11] A. Tuissi, P. Bassani, A. Mangioni, L. Toia, In: Proceedings SMST 2004, ASM International, Materials Park, OH, (2006) 501. [12] R. Casati, A. Tuissi, S. Belochapkine, C. Dickinson, S.A.M. Tofail, Functional materials letters, 5(1) (2012) 1250009. [13] R. Casati, A. Tuissi, Journal of Materials Engineering and Performance, 21(12) (2012) 2633.

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C. Maletta et alii, Frattura ed Integrità Strutturale, 23 (2013) 13-24; DOI: 10.3221/IGF-ESIS.23.02

Scilla 2012 - The Italian research on smart materials and MEMS

Fracture mechanics of pseudoelastic NiTi alloys: review of the research activities carried out at University of Calabria

C. Maletta, F. Furgiuele, E. Sgambitterra Dept. of Mechanical Engineering, University of Calabria, 87036 Rende (CS), Italy. carmine.maletta@unical.it

A BSTRACT . This paper reports a brief review of the research activities on fracture mechanics of nickel-titanium based shape memory alloys carried out at University of Calabria. In fact, this class of metallic alloys show a unusual fracture response due to the reversible stress-induced and thermally phase transition mechanisms occurring in the crack tip region as a consequence of the highly localized stresses. The paper illustrates the main results concerning numerical, analytical and experimental research activities carried out by using commercial NiTi based pseudoelastic alloys. Furthermore, the effect of several thermo-mechanical loading conditions on the fracture properties of NiTi alloys are illustrated. K EYWORDS . Shape Memory alloys; Stress-Induced Martensitic transformation; Fracture mechanics. ickel-Titanium alloys (NiTi) are the most useful shape memory alloys, because they combine high recovery capabilities with good mechanical performances and biocompatibility. These alloys are also known as Nitinol, which stands for Nickel Titanium Naval Ordnance Laboratory (White Oak, Maryland), where in 1961 their shape memory capabilities were discovered. After their discovery NiTi alloys have attracted the interest of the scientific and engineering community due to their unique properties, namely pseudoelastic effect (PE) and shape memory effect ( SME). These functional properties are due to a reversible solid state phase transformation between a parent phase (B2 - austenite) and a product phase (B19’ - martensite), the so called thermoelastic martensitic transformation (TMT), which can be activated either by temperature (thermally-induced martensitic transformation, TIM) or by applied stress (stress induced martensitic transformation, SIM) [1]. As a result of these microstructural changes, NiTi alloys are able to recover high values of mechanical deformations (up to 12%), by either heating the material above the characteristic transition temperatures (SME) or by removing the mechanical load (PE). However, due to their unique microstructural evolutions elastic and elastic plastic theories cannot be applied to study the mechanical response of NiTi alloys and, consequently, ad hoc models should be developed which take into account the thermally-induced and/or stress induced transformations. In particular, it is widely accepted by the scientific community that crack formation and propagation are significantly affected by the phase transitions mechanisms and, consequently, NiTi alloys exhibit unusual fatigue and fracture responses with respect to common metals. This topic is of great technological and scientific interest as demonstrated by several recent experimental studies, which have been aimed to evaluate the evolution of cracks under both static [2-8] and cyclic loading conditions [9-12]. Furthermore, several numerical studies have been carried out, by using standard finite element codes and plasticity concepts [13-15] as well as by special constitutive models for SMAs [16-17]. Finally, some analytical models have been proposed recently [18-27], which are mainly based on modified linear elastic fracture mechanics concepts. In the present paper a review of the research activities on fracture mechanics of NiTi alloys, carried out at the Department of Mechanical Engineering at University of Calabria (Italy), is illustrated. The stress-induced martensitic transformation occurring in the crack-tip region, as a consequence of the high values of local stresses, and the resulting stress distribution N I NTRODUCTION

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have been analyzed by numerical simulations [15], analytical modeling [23-26] and experimental measurements [7-8]. In particular, Finite Element (FE) simulations have been carried out, by using commercial software codes and standard non linear plasticity analyses, i.e. by modeling the monotonic stress-strain of SMAs as a plastic-like behavior. Preliminary FE studies have been carried out in [15], where Single Edge Crack specimens (SEC) have been analyzed by two-dimensional plane stress FE analyses. In this study the crack tip transformation mechanisms have been analyzed together with their effects on the stress distribution. In addition, a first attempt to model these phase transition mechanisms by modified Linear Elastic Fracture Mechanics (LEFM) concepts is illustrated. Subsequently, an analytical model has been proposed in [23] based on the Irwin’s correction of LEFM [28] which allows to simulate both the stress-induced crack-tip transformation region and the resulting stress distribution under plane stress conditions. In addition, numerical simulations have been carried out by considering a central crack in a plate subjected to mode I loading conditions; systematic comparison between numerical and analytical results have been carried out and good agreements have been observed. Finally, the effects of thermo-mechanical parameters and loading conditions have been analyzed. The model has been subsequently updated in [24] to analyze both plane stress and plane strain conditions, by considering a tri-axial constraint factor for phase transition mechanisms. Furthermore, the model prediction have been compared with experimental literature data [5] concerning synchrotron X-ray microdiffraction experiments of miniature CT specimens. The reference analytical model has been also used to define possible fracture control parameters for SMAs in [25] based on the definition of Stress Intensity Factor in LEFM. Finally, the reference model has been recently modified in [26] to overcome one of the basic limitation, i.e. the assumption of constant stress transformation. In particular, the stress-strain response is modeled as a tri-linear material with a generic slope of the transformation plateau. Experimental tests have been carried out in [7] for a comparative study between base and laser welded materials, by using SEC specimens obtained from a commercial pseudoelastic NiTi sheet (Type S, Memry, USA). However only the notch strength was calculated for the comparative analysis, and no further considerations have been made about the complex fracture mechanisms in SMAs. More recently the effects of temperature, within the stress-induced transformation regime, in SEC specimens have been analyzed [8], by experimental measurements and analytical studies. The tests were carried out at different values of the testing temperature the critical values of the stress intensity factor were computed, based on LEFM theory on the reference analytical model [25].

Figure 1 : Schematic depiction of the crack-tip stress distribution and transformation region in pseudoelastic NiTi SMAs.

F RACTURE MECHANICS OF SMA S : BASIC FEATURES

he high values of local stresses in the crack tip region of pseudoelastic NiTi alloys cause a stress-induced martensitic transformation and, consequently, marked differences are observed with respect to common linear elastic or elastic plastic materials as schematically shown in Fig. 1. In fact, due to this microstructural evolution T

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three different regions are observed in the crack tip region: the austenitic untransformed region (A), the phase transformation region (A → M) and the fully transformed martensitic region (M). The size of the fully transformed martensitic region ( 1 M   ) and of the transformation region ( 0 1 M    ), along the plane of the crack, are identified by the radii M r and A r , namely martensitic and austenitic radii, respectively. In addition, due to the large transformation strain occurring at the very crack tip, a marked non-linearity and a complex stress distribution are observed, as schematically shown in Fig. 1, with respect to common metallic alloys. The figure also illustrates a schematic depiction of the stress-strain response of a pseudoelastic alloy together with the main mechanical parameters: the direct transformation stresses, σ AM S and σ AM f , the transformation strain, L  , and the effective Young’s moduli of austenite, A E , and martensite, M E . The transformation strain and the Young’s moduli are considered as material constants while the transformation stresses can be expressed as a function of the temperature, T , according to the Clausius–Clapeyron relation:   0 0 σ σ AM AM S S M b T T    (1)   0 0 σ σ AM AM f f M b T T    (2) where 0 σ AM S and 0 σ AM f are the transformation stresses at the reference temperature 0 T and M b is a material constant. he crack tip stress distribution and transformation region in pseudoelastic SMAs have been studied by Finite Element (FE) simulations carried out by using commercial software codes and standard non-linear plasticity analyses. In fact, monotonic loads to fracture are generally applied to specimens for toughness measurements and, consequently, the stress-strain hysteretic behavior, observed during loading-unloading cycles, is not taken into account. Due to this reason the monotonic nonlinear behavior of SMAs is treated as a plastic-like response. Preliminary FE studies have been carried out in [15], where Single Edge Crack specimens (SEC) have been analyzed by two-dimensional plane stress FE analyses, carried out with the commercial finite element code MSC Marc ® . The geometry of the SEC specimen is illustrated in Fig. 2a, while the corresponding FE model is illustrated in Fig. 2b together with an highlight of the crack tip. Particularly fine mesh has been adopted to model the crack tip region in order to describe the high stress gradient as well as for an accurate prediction of the non-linear stress distribution due to the stress induced transformation mechanisms (A → M). T N UMERICAL MODELING

a) b) Figure 2 : SEC specimen: a) geometry and b) FE model with an highlight of the crack tip [15]

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Several simulations have been carried out for different thermo-mechanical loading conditions as well as by varying the main thermo-mechanical parameters of the alloy, in terms of transformation strain ( L  ) and transformation stresses ( σ AM S and σ AM f ). As an example Fig. 2a illustrates the transformation region near the crack tip, i.e. the contours of the martensite fraction M  , while and the effects of the testing temperature T on the transformation radii, M r and A r , are illustrated in Fig. 3.b. These results have been obtained under a remote tensile stress 20.5 MPa    for a SMA with Young’s moduli 39 A E GPa  and 20 M E GPa  . The figure shows that both M r and A r decrease with increasing the temperature T ; resulting in an overall reduction of the transformation zone. These preliminary results have been confirmed by subsequent numerical simulations carried out in [23] and in [8] where systematic comparison with the estimates of a novel analytical approach have been carried out, as illustrated in the following section.

a) b) Figure 3 : FE results of the crack tip transformation behavior in a pseudoelastic SMA: a) contours of the martensite fraction ( M  ) and b) transformation radii ( M r and A r ) as a function of the testing temperature [15].

A NALYTICAL M ODELING

novel analytical approach has been developed recently [23], which is based on a modified Irwin’s correction [28] of Linear Elastic Fracture Mechanics (LEFM). In particular, the model allows to describe the crack tip stress distribution and transformation region in pseudoelastic NiTi alloys under plane stress conditions. The model has been subsequently improved in [24] to describe both plane stress and plane strain conditions while in [25] two fracture control parameters have been proposed, based on modified Stress Intensity Factors (SIF). Finally, a new version of the model has been developed in [26] to overcome a limitation of the reference model, i.e. the assumption of constant stress transformation. For the sake of completeness and readability the basic expression of the stress components and of the transformation radii, M r and A r , are given in the following but complete and detailed descriptions of the model are reported in the reference papers [23-24]. Eq. 3 gives the expression of the principal stress components along the plane of the crack ( 0   ), in the austenitic region:       1 2 2 Δ Ie A A K r r r r       (3) The stress equation A  is obtained by a modified Irwin’s correction [28] of the LEFM, i.e. by using effective crack length and SIF, namely e a and Ie K : Δ e a a r   (4) A

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  

K

a



(5)

Ie

e

where the distance Δr is given by: * Δ A r r r  

(6)

with



  

K

1

*

r

 

(7)

I

AM

f  

2



tc

where AM  is the direct A → M transformation stress and it is assumed to be constant ( AM AM AM s f      ); tc f can be regarded as a transformation constraint factor, i.e. it is defined based on the plastic constraint factor in LEFM [29], and varies in the range between 1 and   1 1 2    , with the lower and upper bounds corresponding to the plane stress and plane strain conditions, respectively. The stress distribution in the martensitic region can be obtained by modified relations for bilinear materials and it is given by the following equation:         1 1 2 1 1 1 2 1 2 2 1 2 AM Ie M M L A tc K r r E f r                          (8) where  represents the Young’s modulus ratio ( / M A E E   ) while   1     and 1 / 2   for plane stress and    1 1 2       and 3 / 2   under plane strain conditions. The martensitic radius M r , can be calculated by using the condition   1 AM M M tc r f    :

2

1 2 2   

  

K

2



r

 

(9)

Ie

M

AM

f

E

2







tc

L A

A r can be calculated by imposing the equilibrium condition at the crack tip, as described in [23], and,

The austenitic radius

thus, the following relation can be obtained:

2

K

    

1

1

1

  

*   

2 r r

Ie

(10)









A

AM

AM

f

E

/

  



1    

f

2

1



tc

L A

tc

Several analysis have been carried out in [23] by considering a central crack with length 2 a in an infinite plate subjected to mode I loading conditions. In particular, the effects of the main thermo-mechanical parameters of the alloy, in terms of the transformation strain ( L  ) and stress ( AM  ), on the crack tip stress distribution and transformation region have been analyzed, as illustrated in Fig. 4. In addition, comparisons with FE results are also illustrated in the figure and good agreements are observed. In particular, Fig. 4.a illustrates the crack tip stress distribution for a SMA with Young’s moduli 50 A E GPa  and 25 M E GPa  , while Fig. 4.b illustrates the values of / A r a and / M r a as a function of the transformation strain ( L  ) for two values of the transformation stress ( AM  ). A marked decrease of / A r a is clearly observed together with a decrease of / M r a when increasing the transformation stress AM  , as a direct consequence of the increased values of local stresses near the crack tip in the austenitic region. Furthermore, a slight increase of / A r a together with a reduction of / M r a is observed when increasing the transformation strain and these effects become more evident when reducing the transformation stress. The estimates of the analytical model on crack tip stress-induced transformation have been also compared with experimental literature data in [24]; these latter have been obtained by synchrotron X-ray microdiffraction experiments of a miniature CT specimen, under opening mode conditions with a constant load P =2860 N and a crack length-to-width ratio / 0.55 a W  [5]. In particular, in Fig. 5 the contours of the austenitic radius, A r , under both plane stress and plane strain conditions, are compared with the microdiffraction patterns. The experimentally observed transformation region is between plane stress and plane strain contours and this is the expected result as X-ray observations represents volume-

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averaged data along the specimen thickness ( i.e. between plane stress at the specimen surfaces and plane strain in the center). Furthermore, the martensitic radius M r is not illustrated as it is about one order of magnitude less than austenitic radius A r and it is not illustrated in the microdiffraction patterns, which show only the region with 30-40% volume fraction of martensite (B19’).

a) b) Figure 4 : Comparisons between analytical and FE results: a) crack tip von Mises stress and b) transformation radii as a function the transformation strain ( L  ) and for two values of the transformation stress ( tr AM    ) [23].

Figure 5 : Comparison of the crack-tip transformation region between numerical predictions and experimental observations by synchrotron X-ray microdiffraction observations [24]. The analytical model have been also used to define possible fracture control parameters in SMAs based on the stress equations in both austenitic and martensitic region and on the definition of Stress Intensity Factor in LEFM. In particular, two different SIFs have been defined in [25]: an austenitic SIF, namely IA K , and a martensitic or crack tip SIF, namely

IM K . In particular, the austenitic SIF,

IA K , can be directly obtained from the modified Irwin’s approach described in the

previous section, and it can be regarded as the effective SIF Ie K :

K

r K   

0 ˆ lim 2 ˆ r 



(11)

IA

A

Ie

with ˆ

Δ r r r   ; the martensitic SIF,

IM K , is given by:

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 2 1







K

r  

K

lim 2





(12)

  1      



 2 1

IM

M

IA

1

r

0



IM K can be expressed ad a function of

IA K ,  and of the Young’s modulus ratio  . However, it is

Eq. 12 shows that

r , is required to calculate both

K

worth noting that the knowledge of the extent of transformation region, in terms of A IM K and an iterative approach is required to calculate these parameters as described in [25]. Fig. 6a shows the values of IA K and IM K , normalized with respect to the applied SIF I K a      and

IA

, as a function of the

L  , and for different values of the transformation stress, AM 

0.3   ,

, for an alloy with

transformation strain,

40 A E GPa  and

0.5   . Note that the same curves are used to represent IA K and IM K , as / IM IA K K

is a constant

depending on the elastic properties of the alloy, as shown in eq. 12. The figure illustrates that both IA K and IM K increase with increasing the transformation strain, and this effect is more evident when decreasing the transformation stress, as a direct consequence of the increase of the transformed region near the crack tip [23]. Furthermore, IA K is always greater than I K  , with / 1 IA I K K   when AM   and 0 L   , i.e. in the case of linear elastic materials. In addition, the martensitic SIF, IM K , is always smaller than I K  , which indicates a reduction of the stresses at the very crack tip if compared with linear elastic materials. Fig. 6b, illustrates the effects of the testing temperature on both IA K and IM K for a commercial superelastic NiTi alloy. The figure shows that a decrease of both SIFs is observed when increasing the temperature, as a direct consequence of the increase of the transformation stress. In particular, a reduction of about 20% is observed in the temperature range between 273 K and 343 K, which correspond to a range of transformation stress between about 90 MPa and 800 MPa. However, IA K and IM K decrease rapidly from 273 K to 290 K, while a small variation, i.e. of about 2%, is observed when the temperature is above 290 K. This effect is a direct consequence of the increase of the transformation stress with increasing the temperature, which causes a marked reduction of the transformation region, as discussed in [23], and, consequently, IA K approaches to the applied SIF I K  , i.e. the alloy behaves like a linear elastic material. Furthermore, it is worth noting that the temperature range is limited by a lower bound, min T , which corresponds to a transformation stress equal to zero, and by an upper bound min d T M  , which represents a characteristic maximum temperature for stress induced transformation.

a)

b)

K  , as a function of: a) the

IA K and IM

K , normalized with respect to the applied SIF, I

Figure 6 : Martensitic and austenitic SIFs,

t AM r   

 ) and for different values of the transformation stress (

transformation strain  ( L

), b) the testing temperature ( T ) [25].

The reference model has been recently modified in [26] to overcome one of the basic limitation, i.e. the assumption of constant stress transformation. In fact, it has been demonstrated that the slope of the stress-strain transformation plateau increases under specific loading conditions, such when increasing the loading rate or under cyclic loads [30]. To this aim,

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