Issue 21

Anno VI Numero 21 Luglio 2012

Rivista Internazionale Ufficiale del Gruppo Italiano Frattura Fondata nel 2007

Editor-in-chief:

Francesco Iacoviello

ISSN 1971-8993

Associate Editors:

Luca Susmel John Yates

Editorial Advisory Board:

Alberto Carpinteri Andrea Carpinteri Donato Firrao M. Neil James Gary Marquis Robert O. Ritchie 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, 21 (2012); Rivista Ufficiale del Gruppo Italiano Frattura

C. Maletta, F. Furgiuele, E. Sgambitterra, M. Callisti, B. G. Mellor, R. J.K. Wood Indentation response of a NiTi shape memory alloy: modeling and experiments ..................................... 5 D. Croccolo, M. De Agostinis, N. Vincenzi Interference fit effect on holed single plates loaded with tension-tension stresses …....................................… 13 A. De Iorio, M. Grasso, F. Penta, G.P. Pucillo A three-parameter model for fatigue crack growth data analysis …………………...……………..… 21 R. Valentini, C. Colombo, M. De Sanctis, G. Lovicu Hydrogen Re-Embrittlement of Aerospace grade High Strength Steels …….………….....…………... 30 D. Benasciutti, M. Gallina, M. Gh. Munteanu, F. Flumian A numerical approach for the analysis of deformable journal bearings …….………….......…………... 37 A.Yu. Fedorova, M.V. Bannikov, O.A. Plekhov, E.V. Plekhova Infrared thermography study of the fatigue crack propagation …….…………...…….......…………... 46

Segreteria rivista presso: Francesco Iacoviello Università di Cassino – Di.M.S.A.T. Via G. Di Biasio 43, 03043 Cassino (FR) Italia http://www.gruppofrattura.it iacoviello@unicas.it

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Frattura ed Integrità Strutturale, 21 (2012); ISSN 1971-9883

Editor-in-Chief Francesco Iacoviello

(Università di Cassino, Italy)

Associate Editors Luca Susmel

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

John Yates

Advisory Editorial Board Alberto Carpinteri

(Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy)

Andrea Carpinteri

Donato Firrao M. Neil James Gary Marquis

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

Robert O. Ritchie Cetin Morris Sonsino

(University of California, USA) (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) (Università di Cassino, Italy) (Università di Trieste, Italy) (EADS, Munich, Germany) (IMWS, Wien, Austria) (Politecnico di Torino, Italy) (Politecnico di Milano, Italy) (Università della Calabria, Italy) (University of Porto, Portugal) (Politecnico di Torino, Italy) (Università di Parma, Italy)

Nicola Bonora Lajos Borbás Francesca Cosmi

(Budapest University Technology and Economics, Hungary)

Claudio Dalle Donne Josef Eberhardsteiner Giuseppe Ferro Tommaso Ghidini Mario Guagliano Carmine Maletta

(European Space Agency - ESA-ESRIN)

Lucas Filipe Martins da Silva

Marco Paggi

Alessandro Pirondi

Ivatury S. Raju

(NASA Langley Research Center, USA) (Univ. Telematica Guglielmo Marconi )

Giacomo Risitano Roberto Roberti Marco Savoia Andrea Spagnoli

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

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, 21 (2012); 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.

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Frattura ed Integrità Strutturale, 21 (2012); ISSN 1971-9883

S

olo cinque anni fa, nel 2007, il Consiglio di Presidenza guidato dall’amico Beppe Ferro decise di pubblicare una rivista legata alle tematiche proprie dell’IGF con alcune “specifiche progettuali” ben precise: - struttura organizzativa agile; - processo di revisione rapido e puntuale; - modalità di divulgazione moderna e … poco onerosa!! Il risultato è stato Frattura ed Integrità Strutturale , una rivista on line ed open access che in soli cinque anni (e venti numeri pubblicati) è riuscita ad essere inserita in numerosissime biblioteche on line e repository, ottenendo solo poche settimane fa l’inclusione in Scopus con la seguente motivazione: “The journal has been accepted because of its sustained and regular record of publishing articles having high academic and editorial standards.” Ovviamente ho subito comunicato la notizia ai Soci ed ai simpatizzanti IGF con estremo piacere, con una di quelle Newsletter che spero troviate utili, ringraziando di cuore tutti coloro che sin dall’inizio hanno creduto in questa iniziativa: colleghi, amici, membri dei vari Board che hanno sostenuto la rivista, e, anzitutto, gli autori, linfa vitale per qualunque rivista, che non hanno mai fatto mancare il loro appoggio e sostegno, consentendo alla rivista una uscita regolare e costante. Ora bisogna certamente guardare avanti: ottenuta l’indicizzazione Scopus ci sono altri obiettivi da raggiungere, che permetteranno di incrementare ulteriormente sia la visibilità che l’utilità della rivista. Desidero quindi sottolineare ancora una volta che la rivista IGF è uno strumento a disposizione dell’intera comunità scientifica legata alla frattura ed all’integrità strutturale, e che chiunque appartenga a questa comunità (non importa se Socio IGF!!) può dare il suo contributo alla rivista, inviando un proprio lavoro, proponendo Special Issue dedicate a qualche specifico argomento oppure a qualche evento, o magari, ancora, rendendosi disponibile per le operazioni di revisione. Tanti cari saluti, Francesco Iacoviello Presidente IGF Direttore Frattura ed Integrità Strutturale

Ultima notizia : poco prima di chiudere il numero mi è giunta una splendida notizia che ho il piacere di condividere con tutti voi: l’amico Andrea Carpinteri, componente dell’ Advisory Editorial Board della rivista IGF, è stato nominato “…ESIS Fellow for outstanding contributions to the field of Structural Integrity… ”. Desidero esprimere, a nome mio e del Consiglio di Residenza IGF, le più sentite congratulazioni per un meritatissimo riconoscimento … COMPLIMENTI ANDREA!!!!!

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Indentation response of a NiTi shape memory alloy: modeling and experiments

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

M. Callisti, B. G. Mellor, R. J.K. Wood Engineering Sciences, University of Southampton, UK. mc3a09@soton.ac.uk

A BSTRACT . The indentation response of a pseudoelastic nickel-titanium based shape memory alloy (SMA) has been analyzed. Indentation tests have been carried out at room temperature using a spherical diamond tip and indentation loads in the range 50-500 mN in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. The measured load-displacement data have been analyzed to obtain information on the pseudoelastic response of the alloy. To aid this analysis numerical simulations were performed, by using a commercial finite element (FE) software code and a special constitutive model for SMAs, so as to understand better the microstructural evolution occurring during the indentation process. Finally, the FE model has been used to analyze the effects of temperature on the indentation response of the alloy. This analysis revealed a marked variation of both the maximum and residual penetration depths with increasing test temperature. S OMMARIO . Nel presente lavoro è stata analizzata la risposta all’indentazione di una lega a memoria di forma (SMA – Shape Memory Alloy) a base di nickel e titanio. In particolare, sono state eseguite prove di indentazione mediante l’utilizzo di un indentatore sferico e per livelli di carico compresi tra 50 e 500 mN, al fine di favorire la formazione di zone di trasformazione ampie e, pertanto, evitare effetti locali dovuti a variazioni microstrutturali. Le curve carico-spostamento sono state analizzate al fine di ottenere informazioni utili per la comprensione del comportamento pseudoelastico della lega. A tale scopo, sono state condotte analisi numeriche, utilizzando un software commerciale agli elementi finiti, per meglio comprendere i cambiamenti microstrutturali, che avvengono durante il processo di indentazione. Infine, il modello numerico è stato utilizzato per analizzare l’effetto della temperatura sulla risposta all’indentazione delle SMAs. I risultati hanno mostrato una marcata variazione della profondità di penetrazione e della profondità residua al variare della temperatura. K EYWORDS . Shape Memory alloys; Indentation tests; Finite element simulations.

I NTRODUCTION

ickel-titanium (NiTi) based shape memory alloys (SMAs) have, over recent decades, attracted the interest of the scientific and engineering community due to their unique functional properties, namely the pseudoelastic effect (PE) and the shape memory effect (SME) [1], coupled with their good mechanical properties and biocompatibility. The unique functional response of NiTi alloys is due to a reversible solid state phase transformation between a parent phase (austenite) and a product phase (martensite), the so called thermoelastic martensitic N

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transformation (TMT); the latter is a diffusionless phase transition 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 show high recovery capabilities (up to a maximum deformation of 12%), by either raising the temperature of the material above the characteristic transition temperatures (SME) or by removing the mechanical load (PE). However, despite the increasing interest and the efforts of many researchers to understand these unusual mechanisms, the use of NiTi alloys is currently limited to high-value applications (e.g. medical devices, MEMS, etc.), due to high raw material and manufacturing costs, the latter resulting from the need to control precisely the processing parameters since the functional and mechanical properties of NiTi alloys are significantly affected by the thermo-mechanical loading history experienced during manufacturing. The design of NiTi based components also needs accurate knowledge of the mechanical and functional response of the material, as well as how this evolves during subsequent thermo-mechanical processes. In addition, as most NiTi components are characterized by complex shape and small size scale (e.g. endovascular stents, micro-surgery devices, MEMS etc.) their properties cannot be directly obtained from the bulk raw material. Thus the use of non-destructive techniques to analyze the mechanical and functional properties of small volumes of material is essential. Among the techniques available, nanoindentation is widely used to measure mechanical properties [2], such as hardness, elastic modulus, scratch resistance, creep, etc., of small volumes of materials with negligible damage to the surface. However, despite the aforementioned advantages, various difficulties arise in analyzing the mechanical properties of SMAs from the indentation response, due to micro-structural changes, such as phase transition and martensite variant re-orientation. In fact, the latter is expected to play a significant role in the indentation response of SMAs, as this takes place in the indentation region due to the presence of highly localized stresses. As a consequence, well known contact mechanics theories for conventional metals cannot be directly applied to SMAs and work has been carried out, in recent years, to understand better the effects of microstructural transitions on the indentation response of both thin films [3-8] and bulk specimens [9-15]. These studies revealed marked effects of material composition, as well as the thermo-mechanical treatments carried out during material processing, on the indentation response of SMAs. In particular, both the mechanical and thermal recovery mechanisms of nanoindents have been analyzed in order to study the pseudoelastic and shape memory capabilities of the alloys, respectively. Furthermore, the effects of the test temperature on the indentation response of a pseudoelastic alloy have been analyzed [11] by numerical simulations. In addition, a method to estimate the phase transformation stresses of a pseudoelastic alloy has been proposed in [13], based on comparing the indentation response of the SMA with that of a conventional elastic material. Finally, cyclic instrumented indentation was carried out in [14] so as to capture the stress-induced phase transition mechanisms from the experimentally measured load-displacement curves. However, notwithstanding the encouraging results obtained recently, considerable research needs to be carried out to elucidate the relationship between the indentation response of SMAs and their mechanical and functional properties. In this study a commercial pseudoelastic NiTi alloy (Type S, Memory Metalle, Germany) has been analyzed by indentation tests and finite element analysis. In particular, indents have been made at room temperature using a spherical diamond indenter and indentation loads in the range 50-500 mN, in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. Experimentally measured force-displacement curves have been analyzed to obtain information on the pseudoelastic response of the alloy. Furthermore, Finite Element (FE) simulations were developed, by using a special constitutive model for SMAs implemented in a commercial FE software code, to study the microstructural mechanisms occurring during indentation. The FE models have been used to analyze the stress induced transformation zone in the indentation region and systematic analyses have been carried out to understand better the relationship between the nanoindentation response and the typical thermo-mechanical parameters of SMAs. Finally, the FE model has been used to analyze the effects of temperature and transformation stresses, calculated from the Clausius-Clapeyron relationship, on the indentation response of the alloy.

M ATERIAL AND METHODS

Material commercial pseudoelastic NiTi sheet (Type S, Memory metalle, Germany), with a nominal chemical composition of 50.8 at.% Ni-49.2 at.% Ti and thickness t = 1.5 mm, has been used in this investigation. It was supplied in the flat annealed condition. The raw material was first analyzed by Differential Scanning Calorimetry (DSC) and standard tensile tests in order to determine the main thermo-mechanical parameters of the alloy. Fig. 1.a illustrates the A

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DSC thermogram of the raw material which was obtained at a heating/cooling rate of 1.6 Ks-1 in the temperature range - 100°C to 100°C. This analysis revealed the presence of a two-stage phase transformation (B2 R B19’) during cooling, with the presence of R-phase (Rhombohedral phase), while a single-stage phase transformation (B2 B19’) was observed during heating, as is usual in Ni-rich NiTi alloys. The figure also gives the values of the transformation temperatures (M s , M f , A s , A f , R s and R f ), which have been estimated by the tangent line method; the alloy shows an austenite finish temperature A f = 13,7°C, which indicates a fully austenitic structure at room temperature, i.e. the alloy exhibits a pseudoelastic response. Fig. 1.b presents a stress-strain curve of the alloy obtained from an isothermal ( T = 298 K) displacement controlled loading-unloading cycle up to a maximum deformation of 6.2% which corresponds to the maximum deformation of the stress-strain transformation plateau. The figure also shows the values of the main mechanical parameters of the alloy, Young’s moduli ( E A and E M ), transformation stresses   , , , s f s f AM AM MA MA     and transformation strain   L  , together with the Clausius-Clapeyron constants   / , / A MA M AM C d dT C d dT     , which have been obtained from isothermal tests carried out at different temperatures.

(a)

(b) Figure 1 : Thermo-mechanical properties of the alloy investigated: a) DSC thermograph with transformation temperatures and b) Loading-unloading isothermal stress-strain cycle (298 K). Indentation tests The indentation response of the alloy investigated has been determined by using a NanoTest 600 (Micro Materials Ltd, United Kingdom) nanoindenter. Rectangular shaped samples (20 mm x 10 mm), were cut from the as-received sheet and prepared, prior to indentation tests, by grinding with progressively finer silicon carbide papers (#800-#4000), and polishing with 1  m diamond compound; finally, the specimens were cleaned with acetone and dried in air. After the mechanical polishing procedure the specimens were analyzed by a 3-D optical profilometer (Infinite Focus, Alicona, Austria) to ensure that the surface finish was within acceptable limits for micro indentation measurements. Indentation tests were carried out at room temperature, using a spherical indenter (R=25  m), as a sharp tip indenter (such as Berkovich, Vickers, etc.), causes high strain gradients immediately beneath the indenter which promote plastic deformation, which inhibits the subsequent reverse transformation from martensite to the parent phase. In fact, previous research [11] has demonstrated that there is no evidence of superelastic recovery upon unloading when a Berkovich indenter is used, while a large recovery is observed when using a spherical tip indenter. Preliminary indentation tests were performed to identify optimum test parameters, such as maximum load range, loading/unloading rate and dwell time, in order to reduce measurement errors and avoid creep effects on the P-  curve. Several indents were made at increasing values of maximum load (50, 150, 300 and 450 mN), with a loading/unloading rate of 2.5 mNs -1 and a holding time of 60 seconds at the maximum load; furthermore, a set of 20 indentations were carried out for each value of the maximum load, so as to capture the average response of the material, i.e. to analyze different grains of the polycrystalline structure.

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F INITE ELEMENT MODELING

F

inite Element Analyses (FEA) have been carried out, by using a commercial FE software code and a special SMA constitutive model [16, 17] in order to study the microstructural evolution during indentation tests as well as to estimate the evolution of the indentation response of the alloy as a function of the test temperature. In particular, two-dimensional axisymmetric FE analyses were carried out by exploiting the axisymmetry of the indenter, while the sample was assumed to be a cylinder with radius equal to 10 times the diameter of the indenter, in order to avoid boundary effects [18]. The model, illustrated in Fig. 2, consists of approximately 50400 2D four-noded quadrilateral elements. The figure also illustrates that a very fine mesh has been used to model the contact region in order to capture the high stress gradient and the complex non-linear effects due to plastic deformation and stress-induced transformation mechanisms, in addition to those due to the contact. This model results from a preliminary convergence study, which was developed by analyzing a standard elastic-plastic material; in particular, systematic comparisons between numerical results and elastic-plastic contact theory have been carried out in order to obtain an optimal balance between accuracy and computational efficiency.

Figure 2 : Axisymmetric FE model used to analyze the indentation process.

Subsequently, the constitutive model for SMAs, which is directly implemented in the numerical code, was calibrated using the thermo-mechanical parameters illustrated in the previous section, while linear elastic behavior has been adopted for the diamond indenter (elastic constant: E=1141 GPa,  =0.07). The numerical results were compared with the experimentally measured load-displacement curves and, subsequently, the influence of test temperature on the indentation response of the SMA has been numerically analyzed, as described in the following section.

R ESULTS AND DISCUSSIONS

Preliminary FE analysis reliminary FE studies have been carried out to investigate the phase transition mechanisms in the indentation region as well as to understand better the main differences with respect to conventional elastic-plastic metals. Fig. 3.a illustrates the transformation boundaries in the contact region, for a maximum load of 300 mN, which have been obtained from the FE simulations by comparing the von Mises equivalent stress with the characteristic transformation stresses of the SMA. Starting from the outer region, a fully untransformed austenitic zone is observed (A), i.e. where the von Mises stress is below the start transformation stress s AM    . The area B represents the transformation zone, i.e. von Mises stress between s AM  and f AM  and consequently the volume fraction of martensite is between 0 and 1. Finally, C and D represent the fully transformed martensitic regions, i.e. where the von Mises stress is higher than the transformation stress, f AM  ; however, in C only elastic deformation of the martensitic structure is observed while in D the local stress exceeds the yield stress of martensite and permanent deformation is observed leading to stabilization of the martensite. This stabilized martensite does not revert to austenite on unloading. It is worth noting that the contours in P

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Fig. 3.a represent an average estimate of the different regions near the indenter, i.e. they are obtained from the macroscopic stress field and do not take into account the real microstructure of the alloy. In fact, local stress-induced transformation mechanisms, due to different orientations of the martensite variants, and dislocation movement, could occur around the contact region as a consequence of the stress field. Fig. 3.b presents a comparison of the indented profile of a SMA and an equivalent elastic-plastic material having the same Young’s modulus as the austenite phase and a yield stress equal to the start transformation stress Y s AM    . In particular, the profiles at the maximum load of 300 mN and upon unloading, normalized with respect to the maximum depth , are compared. The figure clearly illustrates a smaller residual depth in the SMA after unloading, i.e. it exhibits higher recovery deformation as a consequence of the reversible stress-induced martensitic transformation in the indentation region. In fact, the recovery mechanisms in SMAs can be attributed to both elastic and pseudoelastic properties.

B : Transformation region C : Transformed martensite D : Stabilized martensite f AM   

s 

f

 

 

AM

AM

A : Untransformed austenite

s AM

  

a) b) Figure 3 : Preliminary FE results: a) stress-induced transformation contours near the contact region; b) comparison of the indentation profile between an elastic-plastic material and a SMA. Indentation tests Fig. 4 shows the load-displacement (P-  ) curves obtained from indentation tests carried out at increasing values of maximum load: 50 mN (a), 150 mN (b), 300 mN (c) and 450 mN (d). It is worth noting that good repeatability of the P-δ curves was observed, especially at higher values of indentation load; this results from an optimal choice of the test parameters. In fact, the load-displacement curves become smoother and differences between repeat tests decrease with increasing indentation load, due to both a reduction in experimental errors and the greater amount of material undergoing phase transformation. The reversible stress-induced phase transition mechanisms are also demonstrated by the pop-out events [18] which occur in the unloading stage. In addition, as observed from the preliminary FE simulations, the residual depth upon unloading is a useful measure of the functional behavior of the SMA in terms of its pseudoelastic recovery capability. Fig. 5.a shows the values of the maximum depth ( h max ), residual depth ( h r ) and residual depth ratio ( h r / h max ) as a function of the indentation load. The figure illustrates that both the residual depth and the residual depth ratio increase with increasing indentation load, which indicate an overall reduction of the pseudoelastic response of the SMA due to an increased volume fraction of dislocations and stabilized martensite (region D in Fig. 3.a) immediately beneath the indented surface. Similar considerations can be made from an energetic point of view, as illustrated in Fig. 5.b. Specifically, this figure presents the recovery energy ( E e ), i.e. the energy associated with the unloading path, the dissipated energy ( E d ), i.e. the area between loading and unloading curve, the total energy ( E t = E e +E d ), the recovery energy ratio ( E e / E t ) and the dissipated energy ratio ( E d / E t ) as a function of the indentation load. The figure clearly shows an increase of both dissipated and recovery energy with increasing indentation load, which indicate an overall increase of both permanent and recovery deformation, as is also illustrated in Fig. 5.a. Fig. 5.b shows that the difference between the recovery energy and dissipated energy increases gradually with indentation load above 150 mN. This indicates that, although the residual depth increases with increasing load (Fig. 5.a) the recovery energy also increases counteracting the energy dissipated in the formation and movement of dislocations. Fig. 5.b also demonstrates almost constant values of the Dissipated energy ratio and the

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Recovery energy ratio for indentation loads above 150 mN. This suggests that the greater amount of material stressed reversibly at higher indentation loads, and thus the greater recovery energy available, balances the increased amount of dissipated energy involved in the indentation process at higher indentation loads. Although plastic deformation beneath the indenter reduces the amount of shape recovery this plastically deformed material decreases the stress gradient in the material surrounding the plastically deformed volume favoring the reverse phase transformation.

Figure 4 : Single quasi-static indentation tests for different values of maximum load: (a) 50 mN, (b) 150 mN, (c) 300 mN and (d) 450 mN.

a) b) Figure 5 . Recovery and residual capability of the SMA after unloading: a) depth recovery and b) energy recovery.

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Effects of test temperature The effects of test temperature on the indentation response of the SMA have been analyzed by FE simulations by using the Clausius-Clapeyron relationship to calculate the relevant transformation stresses. To that end the FE model was first validated by comparison with experimental measurements carried out at room temperature, as it was not possible to perform indentation tests under temperature-controlled conditions. Fig. 6 compares the load-displacement curves obtained from FE simulation and experiment for indentation at room temperature to a maximum load of 300 mN. The figure clearly illustrates good agreement between the numerical results and experiments in terms of both maximum depth and residual depth, as well as in terms of the recovery and dissipated energy.

Figure 6 : Comparison of the Load-Displacement curves obtained from FE simulations and experimentally measured (T=293 K, P=300 mN). Fig. 7 shows the load-displacement curves obtained for different test temperatures (T=293 K, T=303 K, T=313 K) for an indentation load of 300 mN. As expected, a marked effect of temperature on the indentation response of the SMA is observed, in terms of both maximum depth and residual depth, which is a direct consequence of the changes in transformation stresses of the alloy. The evolution of these parameters as a function of temperature and the direct transformation stress   s AM  for an indentation load of 300 mN is illustrated in Fig. 7.b.

a) b) Figure 7 . Effects of test temperature on the indentation response of the SMA: a) Load-Displacement curves of the SMA at different temperatures; b) Maximum depth and residual depth vs temperature and direct transformation stress. The figure shows a reduction of both maximum depth and residual depth with increasing test temperature; however the residual depth decreases more rapidly, which indicates an overall improvement of the pseudoelastic response of the SMA

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and an associated reduction in the amount of stabilized martensite present resulting from the increase of transformation stresses with temperature.

C ONCLUSIONS

T

he indentation response of a pseudoelastic NiTi shape memory alloy (SMA) has been analyzed in this study, by experimental measurements and numerical simulations. Single quasi-static indentation tests have been carried out and load-displacement data have been analyzed to obtain valuable information on the pseudoelastic response of the alloy. In addition, numerical simulations have been carried out to understand better the microstructural evolution occurring during the indentation process, as well as to analyze the effects of test temperature on the indentation response of the SMA. The main results of this study are summarized as follows:  Stress induced transformation mechanisms occur in the indentation region, as demonstrated by the preliminary FE simulations, which significantly affect the indentation response of SMAs with respect to conventional elastic plastic materials;  A spherical indenter should be used in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. This allows the overall macroscopic response of the alloy to be measured;  The volume fraction of stabilized martensite immediately beneath the indented surface increases with increasing indentation load in single quasi-static tests, which results in an overall reduction of the shape recovery during unloading;  The functional behavior of NiTi superelastic alloys is clearly governed by an energy balance between martensite formation and the plastic deformation involved in the indentation process.  Systematic finite element (FE) studies revealed a significant effect of the test temperature and the corresponding transformation stress on the indentation response of the alloy in terms of both maximum and residual depth. [1] K. Otsuka, X. Ren, Progr. Mater. Sci., 50 (2005) 511. [2] W.C. Oliver, G.M. Pharr, J. Material Res., 7 (1992) 1564. [3] G. Satoh, A. Birnbaum, Y.L. Yao, In: Proc. Of Int. Congress on Applications of Lasers and Electro-Optics, Temecula CA (2008). [4] P.D. Tall, S. Ndiaye, A.C. Beye, Z. Zong, W.O. Soboyejo, H.J. Lee, A.G. Ramirez, K. Rajan, Mater. Manuf. Processes, 22 (2007) 175. [5] A.K. Nanda Kumar, C.K. Sasidharan Nair, M.D. Kannan, S. Jayakumar, Mater. Chem. Phys., 97 (2006) 308. [6] G.A. Shaw, W. C. Crone, Mater Res Soc Symp Proc., 791 (2003) 215. [7] W.C. Crone, G.A. Shaw, D.S. Stone, A.D. Johnson, A.B. Ellis, In: Society for Experimental Mechanics, SEM Annual Conference Proceedings, Carlotte, NC (2003). [8] G.A. Shaw, D.S. Stone, A.D. Johnson, A.B. Ellis, W.C. Crone, Appl. Phys. Lett., 83 (2003) 257. [9] C. Liu, Y.P. Zhao, T. Yu, Mater. Design, 26 (2005) 465. [10] C. Liu, Y. Zhao, Q. Sun, T. Yu, Z. Cao, J. Mater. Sci., 40 (2005) 1501. [11] A.J. M. Wood, T.W. Clyne, Acta Materialia, 54 (2006) 4607. R EFERENCES

[12] A.J.M. Wood, J.H You, T.W. Clyne, Proc. SPIE , 5648(39) (2205) 216. [13] W. Yan, Q. Sun, X.Q. Feng, L. Qina, Int. J. Solids Struct., 44 (2007) 1.

[14] M. Arciniegas, Y. Gaillard, J. Pena, J.M. Manero, F.J. Gil, Intermetallics, 17 (2009) 784. [15] R. Liu, D.Y. Li, Y.S. Xie, R. Llewellyn, H.M. Hawthorne, Scripta Materialia, 41(7) (1999) 691. [16] M. Saeedvafa, A Constitutive Model for Shape Memory Alloys, Internal MSC Report (2002).

[17] M. Saeedvafa, R.J Asaro, LA-UR-95-482, Los Alamos Report, (1995). [18] A.C. Fisher-Cripps, Nanoindentation, Second Edition, Springer (2002).

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D. Croccolo et alii, Frattura ed Integrità Strutturale, 21 (2012) 13-20; DOI: 10.3221/IGF-ESIS.21.02

Interference fit effect on holed single plates loaded with tension-tension stresses

D. Croccolo DIEM, University of Bologna, Bologna (Italy) dario.croccolo@unibo.it M. De Agostinis DIEM, University of Bologna, Bologna (Italy) m.deagostinis@unibo.it N. Vincenzi DIEM, University of Bologna, Bologna (Italy) nicolo.vincenzi@unibo.it

A BSTRACT . This paper deals with the influence of interference fit coupling on the fatigue strength of holed plates. The effect was investigated both experimentally and numerically. Axial fatigue tests have been carried out on holed specimens made of high performance steel (1075MPa of Ultimate strength and 990MPa of Yield strength) with or without a pin, made of the same material, press fitted into their central hole. Three different conditions have been investigated: free hole specimens, specimens with 0.6% of nominal specific interference and specimens with 2% of nominal specific interference. The experimental stress-life (S–N) curves pointed out an increased fatigue life of the interference fit specimens compared with the free hole ones. The numerical investigation was performed in order to analyse the stress fields by applying an elastic plastic 2D simulation with a commercial Finite Element software. The stress history and distribution along the contact interference of the fitted samples indicates a significant reduction of the local stress range due to the externally applied loading (remote stress) since a residual and compressive stress field is generated by the pin insertion. S OMMARIO . In questo lavoro è stata analizzata l'influenza di un accoppiamento per interferenza sulla resistenza a fatica di piastre forate. L'effetto è stato studiato sia sperimentalmente sia numericamente. Le prove di fatica sono state condotte su provini forati in acciaio ad alte prestazioni (1075MPa di sollecitazione massima e 990MPa di snervamento) con o senza un perno dello stesso materiale, inserito per interferenza nel foro centrale. Tre diverse condizioni dei provini sono state studiate: provini con foro libero, provini con 0,6% d’interferenza specifica nominale generata dal perno e provini con 2% di interferenza specifica nominale generata dal perno. La curva di vita a fatica (S-N) ottenuta ha evidenziato un’influenza positiva dell’interferenza sulla resistenza a fatica dei provini. L'indagine numerica è stata realizzata al fine di calcolare lo stato di deformazione e sollecitazione in campo elasto-plastico su una geometria semplificata 2D del provino in esame; allo scopo è stato impiegato un software commerciale agli elementi finiti. La storia di carico e la distribuzione delle sollecitazioni intorno al foro generato sia dall’interferenza sia dal carico esterno applicato, mostra una significativa riduzione dell'ampiezza della sollecitazione locale nel caso di interferenza dovuta alla presenza di tensioni residue di compressione. K EYWORDS . Fatigue; Interference-fit; Holed single plate.

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D. Croccolo et alii, Frattura ed Integrità Strutturale, 21 (2012) 13-20; DOI: 10.3221/IGF-ESIS.21.02

I NTRODUCTION

F

ailure of mechanical components is mainly caused by the fatigue stresses especially in the presence of geometric discontinuities such as the holes machined in order to join two different parts through, for instance, bolts or pins [1]. In the case of bolted connections the holes have, normally, a clearance coupling with the shank of bolts because the connection leverages the friction forces generated between the mating parts [2]. On the other hand the pins connections (shaft-hub connections) can be realised with different amount of interference [3-5]. The holes cause a geometrical discontinuity, which leads to stress concentration during the loading; furthermore, the drilling operation creates rough surfaces or damages so that the fatigue life of the component may be drastically reduced. Such situation forces a compensation of the fatigue life reduction that can be obtained with different techniques such as the cold expansion [6, 7] or the interference fit connections. The present paper aims at investigating the effect of the interference fit level on the fatigue life of holed plates, which can be used in riveted connections schematically sketched in Fig. 1. Since some catastrophic failures may occur in this type of joints, it was decided to investigate the relation between the amount of interference and the fatigue life. There are a lot of studies concerning the effect of interference fit on the fatigue life [8 12]; however, these papers are mainly devoted to the study of aluminium alloys (2xxx and 7xxx series) or the direct effect of interference fit is shadowed by either cold expansion or bolt clamping effect. On the opposite the material investigated in this paper is high strength steel so that no previous tests or results can be found concerning this application.

Figure 1 : Example of rivet connection.

E XPERIMENTAL METHODS AND TOOLS

T

he specimens are reported in the draft of Fig. 2. They were machined in order to obtain the actual dimension (160mm high, 18mm width and 4mm of thickness with a hole diameter D=5mm). The material properties are the following: Ultimate stress 1075MPa, Yield point 990MPa, Young’s modulus 209GPa, slope of the plastic curve 578MPa, Poisson’s ratio 0.3, density 7.850kg/m 3 . In order to analyse the interference effect on the fatigue strength, some pins made of the same material have been machined. Two different pin diameters were investigated: d=5.03mm and d=5.1mm in order to obtain a specific interference of 0.6% (low level) and 2% (high level), respectively, the specific interference being calculated as I%=(d-D)/D . A set of 7 specimens has been tested for each of the three different conditions: i) open hole ( OH ), ii) low interference level ( I06 ) and iii) high interference level ( I2 ). An additional specimen has been used for the I2 level in order to find the run out point. Therefore a total of 22 specimens have been machined and tested. The testing machine was an hydraulic press with a load cell of 100kN (frequency up to 25Hz) manufactured by Giuliani s.r.l.. The pins have been press fitted into the plates by the same standing press while standard clamps provided by the press manufacturer have been used to lock the specimens; the pin insertion, the specimen lock system and an example of fracture surface are shown in Fig. 3a, 3b and 3c respectively. The white circle of Fig 3c indicates the starting point of the crack. The maximum remote stresses ( RS=F/A ) were set in the range of 725MPa and 200MPa: such nominal stresses have been calculated as the ratio between the external force applied by the standing press and the specimen gross section A=18*4=72mm 2 . The OH specimens have been tested with steps of 75MPa from 650MPa to 200MPa whereas the IXX specimens have been tested with steps of 37.5MPa (from 650MPa to 425MPa for I06 specimens and from 725MPa to 500MPa plus a single point at 425MPa for I2 specimens). The stress ratio for all the specimens was taken equal to R=0.1.

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D. Croccolo et alii, Frattura ed Integrità Strutturale, 21 (2012) 13-20; DOI: 10.3221/IGF-ESIS.21.02

Figure 2 : Specimen draft: K t

=3.31.

a)

b) c) Figure 3 : Pin insertion, specimen lock system and fracture surface .

T ESTS ’ RESULTS

T

he test plan and results are reported in Tab. 1, 2 and 3 for OH , I06 and I2 respectively, whereas the corresponding S-N curves are reported in Fig. 4.

Open Hole

Point # 1

Point # 2

Point # 3

Point # 4

Point # 5

Point # 6

Point # 7

External load (kN) Remote maximum stress (MPa)

46.8 650

41.4 575

36

30.6 425

25.2 350

19.8 275

14.4 200

500

2,000,000 (run out)

Cycles

5,897

14,306

21,907

62,105

150,633

252,338

Table 1 : Stress results for the OH specimens.

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D. Croccolo et alii, Frattura ed Integrità Strutturale, 21 (2012) 13-20; DOI: 10.3221/IGF-ESIS.21.02

I06

Point # 1

Point # 2

Point # 3

Point # 4

Point # 5

Point # 6

Point # 7

External load (kN) Remote maximum stress (MPa)

46.8 650

44.1

41.4 575

38.7

36

33.3

30.6 425

612.5

537.5

500

462.5

Cycles

11,710

98,239

136,289

232,356

684,844

692,557

1,347,271

Table 2 : Stress results for the I06 specimens.

I2

Point # 1 Point # 2 Point # 3 Point # 4 Point # 5 Point # 6 Point # 7 Point # 8

External load (kN) Remote maximum stress (MPa)

52.2 725

49.5

46.8 650

44.1

41.4 575

38.7

36

30.6 425

687.5

612.5

537.5

500

Cycles

35,260

70,017

112,800 136,490 193,510 300,535 430,877 2,000,000 (run out)

Table 3 : Stress results for the I2 specimens.

Figure 4 : S-N Diagram.

D ISCUSSION

y focusing attention on the S-N diagram reported in Fig. 4, it is possible to confirm that the interference fit level has a strong and positive influence on the fatigue strength of the OH specimen, as widely demonstrated in [5, 7]. However, a remarkable difference can be noticed between the two levels, I06 and I2 : the higher is the interference level, the higher is the fatigue strength at the highest levels of remote stress. Conversely, by reducing the remote stress, the fatigue strength and the Endurance Limit is quite the same for different interference levels. This experimental evidence can be explained by advocating the actual amplitude of the local stress field in the vicinity of the hole. The observed cracking behaviour indicates a crack initiation close to the cross section of the holed surface (see Fig. 3), so that, it is clear that the actual amplitude of axial stress, normal to the cross section of the specimen, is the driving force of the crack propagation. The amplitude depends on both the remote stress and the local residual (compressive) stresses due to overcoming of the Yielding point. For this reason the local amplitude, depending on both the remote stress and the interference level, has been calculated and analysed. A number of Finite Element Analyses ( FEA ) have been carried out in order to confirm what stated above by directly following the method proposed by [6, 7, 13]. In Fig. 5 an example of the FEA model (mesh and contour plot of results) is reported. The analyses are conducted on a 2D elastic-plastic plane stress model (6 nodes triangular elements), in which three different steps have been simulated: i) the interference (if present), ii) the application of the maximum remote stress and iii) the unloading with R=0.1. The actual stress amplitude along the cross section of the specimens, which can be related to fatigue life, has been calculated as the difference between the axial stresses of the phases ii) and iii) and reported in Fig. 6a, 6b and 6c for the OH , I06 and I2 specimens respectively: the B

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D. Croccolo et alii, Frattura ed Integrità Strutturale, 21 (2012) 13-20; DOI: 10.3221/IGF-ESIS.21.02

diagrams refer to a remote stress of RS=357.5 ± 292.5 (black curves) and to a remote stress of RS=233.75 ± 191.25 (gray curves) which correspond to a high and low fatigue remote stress respectively. The diagrams of Fig. 6 point out a significant discrepancy among the three actual stress ranges, especially when they are calculated close to the hole; the OH specimen exhibits a stress range of about 1,800MPa, the I06 exhibits a stress range of about 1,050MPa and I2 exhibits a stress range of about 800MPa when RS=357.5 ± 292.5MPa (black curves of Fig. 6). If the remote stress decreases the discrepancies among actual ranges change: the OH range remains greater than I06 and I2 ones, but the I06 and I2 ranges tend to become equal. Indeed when RS=233.75 ± 191.25MPa (gray curves of Fig. 6) the OH specimen exhibits a stress range of about 1,200MPa whereas the I06 and the I2 specimens exhibit the same stress range of about 400MPa. This is the reason why the fatigue strength of I06 and I2 specimens tends to be the same when the remote stress decreases. This occurrence is well indicated in Fig. 7 where the stress ranges are plotted as a function of the specific interference for different remote stresses: in the diagram of Fig. 6b the stress range at I06 and at I2 is, again, the same so that the fatigue strength should be similar; this event is also confirmed by the S-N diagram of Fig. 4 in which at 425MPa of maximum remote stress the number of cycles reached by I06 and by I2 specimens is quite the same. The diagrams of Fig. 7 are also useful to indicate the minimum interference level sufficient to improve the fatigue strength for a stated remote stress; for instance, in the case of 357.5 ± 292.5MPa of remote stress an interference level of 0.6% is high enough for increasing the fatigue strength, whereas for 357.5 ± 292.5MPa of remote stress an interference level of about 1% is suggested.

Figure 5 : FEA Model.

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