Available online at ScienceDirect. Procedia Engineering 160 (2016 )

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1 Aville online t ScienceDirect Procedi Engineering 160 (2016 ) XVIII Interntionl Colloquium on Mechnicl Ftigue of Metls (ICMFM XVIII) Clcultion of stress intensity fctors K I, K II nd K III of crcked components sumitted to flexurl nd torsionl lods J. Isidoro, Rui F. Mrtins * Fculty of Sciences nd Technology, Universidde NOVA de Liso, DEMI, Monte de Cpric, Portugl UNIDEMI, Deprtment of Mechnicl nd Industril Engineering (DEMI), Fculty of Sciences nd Technology, Universidde NOVA de Liso, Monte de Cpric, Portugl Astrct Components sujected to flexurl nd torsionl lodings, such s power trnsmission shfts, re elements tht sometimes fil due to ftigue crck propgtion. Other exmple of mechnicl element tht occsionlly fil nd tht cn e simultneously sumitted to ending nd torsion re endodontic files, which re eing widespred used in mechnized endodontic tretments. With the intent of nlyzing the influence of ending nd torsion on the Stress Intensity Fctors (SIF), KI,II,III, t different crck geometries (/r), two CAD 3D models were creted, nmely one cylindricl shft nd one endodontic file. The evlution of KI, KII nd KIII for the two components under study ws crried out t severl points long the crck front using the Finite Element Method (FEM) together with Liner Elstic Frcture Mechnics (LEFM) concepts. The Finite Element Anlyses (FEA) crried out shown tht flexurl lods hve prepondernt impct on KI vlues, lthough torsion my hve influence on it depending on the order of mgnitude of the torsionl loding vlues pplied on the component. However, when pure torsion loding ws considered, KII nd KIII vlues ecome dominnt t crck tip. Finlly, numericl results otined reveled tht geometric complexity nd reduced dimensions of components cn ply n importnt role when nlyzing SIF, eing this prticulrly relevnt on the cse of endodontic file The Authors. Pulished y Elsevier y Elsevier Ltd. This Ltd. is n open ccess rticle under the CC BY-NC-ND license ( Peer-review under responsiility of the University of Oviedo. Peer-review under responsiility of the University of Oviedo Keywords: Stress Intensity Fctors; Flexurl nd torsionl lodings; Power shft trnsmission; Endodontic files; Finite Element Method. * Corresponding uthor. Tel.: ; fx: E-mil ddress:rfspm@fct.unl.pt The Authors. Pulished y Elsevier Ltd. This is n open ccess rticle under the CC BY-NC-ND license ( Peer-review under responsiility of the University of Oviedo doi: /j.proeng

2 132 J. Isidoro nd Rui F. Mrtins / Procedi Engineering 160 ( 2016 ) Introduction The onset nd propgtion of ftigue crcks re frequent in mny engineering components or structures, s cn e perceived y the lrge numer of mechnicl filures tht occur every yer due to ftigue crck propgtion. In fct, high demnding lodings re frequently comined with very hrsh environmentl conditions, nd re cuse of ftigue filures. Some exmples could e found elsewhere [1-3]. In the reserch herey presented, two crcked geometries were nlyzed, nmely cylinder nd Hyflex CM endodontic file ref..06/20. In the cse of endodontic files, those could e simultneously sujected to ending nd torsion during clinicl tretment of tooth, when rottion nd torque re simultneously pplied to the endodontic file y micro motor. Additionlly, cylindricl power shfts could lso e sumitted to flexurl nd torsionl lods, nd, similrly to the endodontic files referred erlier, should not present in-service ctstrophic filures. With the intent of nlyzing the influence of ending nd/or torsion on the Stress Intensity Fctors (SIF) K I, K II, K III present t the crck tip of cylinder (Fig.1) or t the crck tip of n endodontic file (Fig.1), Finite Element Anlysis (FEA) were crried out using ANSYS softwre. The evlution of SIF ws crried out for different crck geometries (/r), where reltes to the mximum crck depth nd r represents the rdius of curvture of the endodontic file or of the shft s circulr cross section. For tht purpose, two CAD 3D models were creted nd SEM imges were used to model the endodontic file. Additionlly, Liner Elstic Frcture Mechnics concepts (LEFM) ply n importnt role during the design stge of engineering components or structures, s well s during its service lifetime, nd re frequently used to ssess the cceptility of flws in structures nd to predict crck growth, in order to define inspection periods nd to void premture ctstrophic filure of components [4]. LEFM concepts were pplied throughout this work. 2. Numericl results 2.1. Vlidtion In order to vlidte numericl results, cylinder contining semi-ellipticl crck (/2c) ws firstly sujected to pure ending with nominl stress equl to 200 MP t cross section of interest. Hence, cylinder with dimeter of 80 mm nd length of 120 mm ws meshed with tetrhedrl finite elements (Fig.1), nd semi-ellipticl superficil crcks (/2c=0.1, 0.25 nd 0.5) were introduced t its mid-spn. A fixed surfce ws defined t one end of the cylinder nd ending force ws pplied t the opposite end. Then, K I numericl vlues were clculted for eight different (/r) rtios, rnging etween 0.1 nd 0.9, nd those were compred with K I vlues determined ccording the equtions given in BS 7910, Annex J [4] (Fig.1c). c DETAIL A A Fig. 1. () View of cylinder with superficil semi-ellipticl crck; () Detiled view of the endodontic file Hyflex CM ref..06/20 with semiellipticl crck; (c). K I vlues clculted t free surfce nd deepest point of crck front, either using BS 7910 (BS) or numericl vlues from FEA (/2c=0.5). Young s Modulus nd Poisson s Coefficient equl to 200 GP nd 0.3, respectively.

3 J. Isidoro nd Rui F. Mrtins / Procedi Engineering 160 ( 2016 ) Anlysis of crcked cylinder under pure ending, pure torsion, or under torsion nd ending As previously seen in section 2.1, the cylindricl geometry ws firstly sujected to pure ending, Bs=200 MP, nd totl of eight different (/r) rtios nd three different (/2c) rtios were considered in the nlyses, where () represents crck depth nd (2c) corresponds to the crck length mesured t the crck surfce. In cse of pure ending, K II nd K III vlues were lmost zero nd could e considered non relevnt (Fig. 2) when compred with K I vlues clculted (Fig.1c, Fig.2). The results otined for K I when considering cylinder with crck sujected to ending (Bs=200MP) nd torsion (Ts=100, 200, 420 MP) did not disclose significnt differences to the results otined under pure ending t ll points under study (Fig. 1c). Additionlly, when torsion (Ts=100, 200, 420 MP) ws superimposed to ending (Bs=200MP), or when it ws the single lod pplied (Ts=200 MP), two extr points were considered in the nlysis of SIF vlues t crck front, nmely points B nd C, corresponding to the intersection etween the crck nd the outer surfce of the cylinder/endodontic file (Fig. 2). Concerning K II nd K III vlues, figures 2 to 2d show the effect of superimposing torsionl to ending lods. It cn e seen tht solute vlues of K II present t externl cylindricl surfce, either t point B or C, increse with rising vlues of torsionl stress pplied, nd could chieve SIF vlues in the sme order of mgnitude of K I (Fig. 2). In ddition, K II vlues t points B nd C were more or less symmetric. When considering K III vlues (Fig. 2d), it cn e concluded tht they were lwys lower thn zero for ll (/r) rtios considered, nd did not increse s much s it ws verified for K I nd K II vlues, remining etween 0 nd -16 MP.m 0.5 for (/2c) rtio equl to 0.5. c d Fig. 2. () K I, K II nd K III vlues for cylinder with superficil semi-ellipticl crcks (/2c=0.5) under pure ending (Bs=200 MP); () K II vlues t point B for cylinder with superficil semi-ellipticl crcks (/2c=0.5) under ending nd torsion (Bs, Ts); (c). K II vlues t point C for cylinder with superficil semi-ellipticl crcks (/2c=0.5) under ending nd torsion (Bs, Ts); (d) K III vlues t point B for cylinder with superficil semi-ellipticl crcks (/2c=0.5) under ending nd torsion (Bs, Ts).

4 134 J. Isidoro nd Rui F. Mrtins / Procedi Engineering 160 ( 2016 ) Similrly, K I, K II nd K III vlues were clculted for the cylindricl geometry under study when sujected to pure torsion (Ts=200 MP) (Fig. 3). c Fig. 3. () K I vlues for cylinder with superficil semi-ellipticl crcks (/2c=0.25; 0.5) under pure torsion (Ts=200 MP) nd under torsion (Ts=200 MP) comined with smll ending stresses (Bs=20 MP); () K II vlues t point B for cylinder with superficil semi-ellipticl crcks (/2c=0.25; 0.5) under pure torsion (Ts=200 MP); (c) K III vlues t point B for cylinder with superficil semi-ellipticl crcks (/2c=0.25; 0.5) under pure torsion (Ts=200 MP). As cn e seen in Fig. 3, when pure torsionl loding ws pplied, K I results showed ner zero vlues for ll crck geometries considered. However, K II vlues t points B nd C (Fig. 3) were continuously incresing nd it cn e seen tht, unless for the cse where (/r) equls 0.1, were similr for the two crck shpes considered (/2c=0.25 nd 0.5). Finlly, K III vlues t surfce points showed decresing tendency for incresing (/r) rtios, eing this ehviour more perceptile for the semi-ellipticl crck shpe (/2c=0.25) thn for semi-circulr crcks Anlysis of crcked endodontic file under ending nd/or torsion Endodontic files re responsile for removing the pulp nd the infected tissues contined in root cnls of the teeth, nd, ecuse they could e quite curved, endodontic instruments must e flexile nd ductile. Hence, in the lte 80 s new genertion of instruments, which were mde from nickel-titnium lloy (Ni-Ti), egn to e used [5]. These lloys re chrcterised y superelstic ehviour nd shpe memory effect, which depend on the thermomechnicl tretments pplied to the lloy nd on its chemicl composition [6]. Additionlly, superelsticity nd shpe memory effect (CM) re relted with phse trnsition etween ustenitic nd mrtensitic phses t some specific tempertures. This lloy is le to undergo deformtions up to 8% (350 MP) in the non-liner elstic regime without permnent deformtion pssing from n initil ustenite phse (liner elstic with Young s Modulus of 67 GP) to mrtensite phse (lso liner elstic nd with Young s Modulus of 30GP) t out 200

5 J. Isidoro nd Rui F. Mrtins / Procedi Engineering 160 ( 2016 ) MP (Tle 1) [7-9]; the tensile strength of this type of lloys is out 1300 MP corresponding to strin rupture equl to 12% [7-9]. The endodontic file modelled in the reserch herein presented (Fig.1) ws considered to e simultneously sujected to torsion nd ending, which in the lter cse ws chieved y imposing displcements to the endodontic file s tip, in order to simulte root cnl with rdius of curvture tht will induce high tensile stress-stte in the instruments during clinicl tretment [10]. In ddition, two torque vlues, T, were pplied during numericl simultions, nmely 2.5 N.cm nd 4 N.cm; the first is recommended to e used y the endodontic file s mnufcturer, while the second vlue is mximum reference vlue tht generlly could e pplied y the micro motor tht ctivtes the endodontic file. Crck propgtion (/2c=0.25; 0.1 (/r) 0.35 nd /2c=0.5; 0.1 (/r) 0.4) (Fig. 4) ws ssumed to occur 5 mm wy from the tip of the endodontic file, where, ccording to previous reserch nd the loding conditions referred, it showed tendency to frcture [10]. The superelstic ehviour ws defined in the numericl model hving into ccount the mechnicl properties given in Tle 1. Tle 1. Mechnicl properties of the superelstic Ni-Ti lloy simulted in ANSYS t room temperture (RT) [7-9]. Properties Young s Modulus, Austenite phse Young s Modulus, Mrtensite phse Strting vlue for the conversion of ustenite into single-vrint mrtensite during loding (A- S), Finl vlue for reverse trnsformtion (A- S), Strting vlue for the conversion of single-vrint mrtensite into ustenite during unloding (S- A), Strin correspondent to 0.07 Finl vlue for trnsformtion of single-vrint mrtensite into ustenite (S- A), Poisson s coefficient GP 27 GP 300 MP 400 MP 250 MP 25 MP Fig. 4. K I vlues for n endodontic file sujected to ending nd/or torsion (T=2.5 N.cm nd 4 N.cm) t points B () nd C (). (/2c)=0.5 nd 0.1 (/r) Discussion of results When cylinder contining crck is sujected to pure ending nd the crck is t erly stge of propgtion, nmely for (/r) equl to 0.1, K I vlues show slight differences etween them (Fig. 1c) either considering its clcultion t the deepest point of the crck or t the intersection etween the crck nd the externl cylindricl surfce. However, once the crck propgtes, differences etween K I vlues re noticed for the points referred (Fig. 1c); those differences were not so relevnt for (/2c) rtio equl to 0.1 or In ddition, the results otined t the deepest point re higher on the semi-ellipticl crck geometries when compred with the verified t free surfce

6 136 J. Isidoro nd Rui F. Mrtins / Procedi Engineering 160 ( 2016 ) points; the opposite occurs for the semi-circulr geometry (Fig.1c), which indictes tht crck geometry is n importnt fctor on the SIF t the crck front. The superposition of torsion nd ending to the cylinder with superficil crck resulted in relevnt K II vlues t points B nd C (Fig. 2, c), which will ssume lmost symmetricl vlues, depending on the torsion moment sense pplied, contriuting to the crck growth or retrdtion t the cylinder s surfce, respectively. In ddition, K I vlues showed to e highly dependent from ending stresses pplied nd K III vlues incresed with the incresing torsionl lod vlues pplied. However, K III ssumed negtive vlues oth t the deepest point of the crck nd t points B nd C (Fig. 2d), nd lower solute vlues when compred with K I nd K II vlues clculted. For the endodontic file under study, nd for the oundry nd loding conditions defined, K I vlues induced t semi-circulr superficil crck shown to e quite relevnt during clinicl tretment. Moreover, torsionl lods contriuted to lower K I vlues during crck growth - for incresing (/r) rtios, prticulrly t point B; t point C, the introduction of torsion resulted in higher K I vlues for (/r) Conclusion Stress Intensity Fctors, nmely K I, K II nd K III were determined through FEA t the deepest point nd t surfce points of semi-circulr or semi-ellipticl crcks inserted on cylinder nd on n endodontic file sujected either to ending, torsion or comintion of oth. Crck growth ws simulted y incresing (/r) rtios in the FEA crried out. Regrding the influence of torsionl lod, it ws possile to conclude tht it did not introduce significnt chnges on K I vlues for the cylinder nlysis, eing ending the relevnt lod for this to occur. However, prticulrly when nlysing the endodontic file, it ws possile to oserve tht torsion diminished K I vlues present t surfce points B nd C for specific (/r) rnges, incresing in some other rnges. In ddition, torsion plyed n importnt role on incresing K II nd K III solute vlues induced t crck tip, either t the deepest point or t surfce s points. Acknowledgements The uthors would like to thnk the Portuguese Foundtion for Science nd Technology through project ref. UID/EMS/00667/2013. References [1] Tigo M. A. Bugio, Rui F. Mrtins, L. Lel ds Neves, Filure Anlysis of Fuel Tnks of Lightweight Ship, Engineering Filure Anlysis 35 (2013) [2] Rui F. Mrtins, Hugo Rodrigues, L. Lel ds Neves, P. Pires d Silv, Filure nlysis of ilge keels nd its design improvement, Engineering Filure Anlysis 27 (2013), [3] Rui F. Mrtins, C. Mour Brnco, A.M. Gonçlves-Coelho, E.C. Gomes, A filure nlysis of exhust systems for nvl gs turines - Prt II: Design chnges, Engineering Filure Anlysis 16 (2009), [4] BS 7910: 2013, Guide on Methods for Assessing the Acceptility of Flws in Structures, Annex J, British Stndrds Institution, London. [5] H Wli, W.A. Brntley, H Gerstein, An initil investigtion of the ending nd torsionl properties of Nitinol root cnl files, Journl of Endodontics 14 (1988), [6] F.C.N. Borges, Iron Bsed Shpe Memory Alloys: Mechnicl nd Structurl Properties, in: F.M.B. Fernndes (Ed.), Shpe memory lloys processing, chrcteriztion nd pplictions, InTech, Croti, 2013, pp [7] S. Govindjee, G.J. Hll, A computtionl model for shpe memory lloys, Interntionl Journl of Solids nd Structures 37 (2000) [8] F. Auricchio, R.L. Tylor, J. Luliner, Shpe-Memory Alloys: mcromodelling nd numericl simultions of the superelstic ehviour, Computer Methods Appl. MEch. Engrg, 146 (1997) [9] J. Ryhänen, Biocomptiility evolution of nickel titnium shpe memory lloy, Oulu, 1999, pp [10] A. Fernndes, Ftigue ehviour of Ni-Ti files used for endodontic pplictions (MSc Thesis, in portuguese), Fculty of Sciences nd Technology, The New University of Lison, Portugl, 2013.