Mechanics of the tapered interference fit in dental implants

Transcription

1 ARTICLE IN PRESS Journal of Biomehanis 36 (2003) Mehanis of the tapered interferene fit in dental implants Bozkaya, Sinan M.uft.u* Department of Mehanial Engineering, Northeastern University, 334 Snell Engineering Center, Boston, MA 02115, USA Aepted 9 April 2003 Abstrat In evaluation of the long-term suess of a dental implant, the reliability and the stability of the implant abutment interfae plays a great role. Tapered interferene fits provide a reliable onnetion method between the abutment and the implant. In this work, the mehanis of the tapered interferene fits were analyzed using a losed-form formula and the finite element (FE) method. An analytial solution, whih is used to predit the ontat pressure in a straight interferene, was modified to predit the ontat pressure in the tapered implant abutment interfae. Elasti plasti FE analysis was used to simulate the implant and abutment material behavior. The validity and the appliability of the analytial solution were investigated by omparisons with the FE model for a range of problem parameters. It was shown that the analytial solution ould be used to determine the pull-out fore and loosening-torque with 5 10% error. Detailed analysis of the stress distribution due to tapered interferene fit, in a ommerially available, abutment implant system was arried out. This analysis shows that plasti deformation in the implant limits the inrease in the pull-out fore that would have been otherwise predited by higher interferene values. r 2003 Elsevier Siene Ltd. All rights reserved. Keywords: Dental implants; Taper lok; Morse taper; Conial interferene fit; Tapered interferene fit; Connetion mehanism; Pull-out fore; Loosening torque 1. Introdution Dental implant abutment systems are used as anhors to support single or multi-unit prostheses for partially or fully edentulous patients. A dental implant system onsists of an implant that is surgially implanted in maxilla or mandible, and an abutment that mates with the implant one the implant suessfully osseointegrates to the bone. Depending on the speifi system used, an abutment an inlude a mahined onnetion mehanism within itself or an be lamped onto the implant by means of an abutment srew. The dental prosthesis is then fabriated over the abutment. In general, the suess of the treatment depends on many fators affeting the bone implant, implant abutment and abutment prosthesis interfaes (Geng et al., 2001). In this paper we analyze the mehanis of the tapered interferene fit used in some implant abutment systems. *Corresponding author. Tel.: ; fax: address: smuftu@oe.neu.edu (S. M.uft.u). Two types of onnetion methods involving (a) a srew, and (b) a tapered interferene fit (also alled Morse taper) are ommonly used for seuring the abutment to the implant. Fig. 1 shows various implant systems: designs by Astra (Astra Teh AB, M.olndal, Sweden) and Nobel Bioare (Nobel Bioare AB, G.oteborg, Sweden) use a srew; designs by Ankylos (Degussa Dental, Hanau-Wolfgang, Germany) and ITI (Institut Straumann AG, Waldenburg, Switzerland) use a srew with tapered end; and the design by Bion (Bion In., Boston, MA, USA) uses solely a tapered interferene fit. For the systems using a srew, the onnetion between the implant and the abutment depends on the srew-preload, whih is generated by applying a predetermined amount of torque during installation. Designs in whih the srew has a large tapered end essentially work like a tapered interferene fit, and the srew threads do not appear to ontribute to the onnetion (Shwarz, 2000; Binon et al., 1994; Sutter et al., 1993). The tapered interferene fit relies on the large ontat pressure and resulting fritional resistane, in the mating region of the implant abutment interfae, to provide a seure onnetion /03/$ - see front matter r 2003 Elsevier Siene Ltd. All rights reserved. doi: /s (03)

2 1650 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Nomenlature a b a 1 b 1 a 2 b 2 a 3 b 3 r at r ab r it r ib L h L s L a L E E t E b e eq e u n n b inner radii of the ylinder outer radii of the ylinder inner radii of the abutment outer radii of the abutment inner radii of the implant outer radii of the implant inner radii of the bone outer radii of the bone top radii of the abutment bottom radii of the abutment inner top radii of inner ylinder inner bottom radii of inner ylinder depth of hole length of implant under the hole length of abutment ontat length Young s modulus Tangent modulus Young s modulus of the bone equivalent von Mises strain ultimate strain Poisson s ratio Poisson s ratio of the bone r u z z Dz d y m P P i P o P ða iþ P ði bþ s Y s eq N N b F p F b T L radial loation radial displaement position of abutment position of the abutment with no interferene insertion depth interferene depth taper angle oeffiient of frition ontat pressure pressure applied to the inner surfae of the ylinder pressure applied to the outer surfae of the ylinder Contat pressure in abutment implant interfae Contat pressure in implant bone interfae yield stress equivalent von Mises stress total normal fore ating on the ontat area due to the ontat pressure total normal fore ating on the ontat area due to biting fores pull-out fore resultant axial fore due to biting loosening torque Fig. 1. Different implant abutment attahment methods. Astra and Nobel Bioare use a srew, Ankylos and ITI use a srew with an interferene fit and Bion uses only-interferene fit. In-srew type implant abutment onnetion mehanism, mehanial ompliations suh as srew loosening when olusal loads exeed the preload, or reep deformation in the srew implant interfae an lead to linial ompliations (Shwarz, 2000). When the tapered-interferene fits are used, the abutment loosening seems to be less of a problem (M.uft.u and Chapman, 1998; Morgan and Chapman, 1999; Keating, 2001; Sutter et al., 1993). The free body diagram of the abutment in Fig. 2 shows that resultant axial fore due to biting is F b ¼ðN þ N b Þðm os y sin yþ; where m is the stati frition oeffiient, N is the resultant ontat fore due to initial interferene, N b is the additional normal fore due to biting and y is the taper angle. The biting

3 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Fig. 2. Equilibrium of the fores ating on the abutment when an axial biting fore F b is applied. A normal fore due to initial insertion N; a normal fore due to biting N b ; and a tangential fore of magnitude mðn þ N b Þ at on the tapered wall. Note that N and N b are the resultants of the axisymmetri reation fores. fore ats in the diretion of the abutment insertion, hene aids to seure the onnetion. This situation is in diret ontrast to implants using srews where the biting fore lowers the pretension in the srew. The mehanism for the tapered interferene fit to beome loose, is the appliation of a loosening torque T L or a pull-out fore F p : Brunski (1999) indiated tensile axial loading ould develop in implants supporting multi-unit splinted implant restorations and antilevered prostheses. Therefore a suffiiently large amount of pull-out fore is neessary for the long-term stability of a dental implant abutment system using the tapered interferene fit. Later in this paper, formulas are developed for T L and F p : In general, interferene fits provide a onnetion method between a hub and a shaft without using a third member suh as a key, pin, bolt, or srew. The onnetion allows load transmission due to the frition fores between the mating surfaes where the shaft has a slightly larger diameter than the hub. The tapered interferene fits are used ommonly in engineering pratie suh as Morse tapers, used to engage lathe bits (Sutter et al., 1993). In the medial appliations tapered interferene fits are used in total hip prosthesis in addition to dental implants (Chu et al., 2000). Mehanis of a ylindrial interferene fit is well understood, and an be found in design text books (e.g., Shigley and Mishke, 1989). The elasti plasti behavior of the ylindrial interferene fits has also been analyzed (Gamer and M.uft.u, 1990). No known analytial solution to the tapered interferene fit problem exists to the best of our knowledge. FE method has been used to investigate the mehanis of tapered interferene fits in hip implants (e.g., Van Rietbergen et al., 1993; Vieonti et al., 2000; Chu et al., 2000). The dependent harateristis of the interferene fit, suh as the pull-out and insertion fores and the stress distribution in the members, depend on the taper angle, ontat length, inner and outer diameters of the members, depth of insertion, material properties and oeffiient of frition. In this paper the mehanis of a general tapered interferene fit is analyzed. A losed form formula is derived to predit the ontat pressure between the tapered members, based on plane stress elastiity. The analytial solution is used to determine the interrelations between the parameters. The finite element method is used to verify the validity of the formula. A detailed analysis of the interferene fit in a Bion implant is presented inluding the analytial, purely elasti and elasti plasti FE analyses. 2. Materials and methods 2.1. Geometrial onsiderations A shemati desription of a generi tapered interferene fit of two ylinders, embedded in a ylindrial bone, is shown in Fig. 3a. The middle ylinder (implant) has an outer radius b 2 and has a tapered hole in the Fig. 3. (a) The geometry of a tapered interferene fit omposed of an outer bone, inner implant and a tapered abutment. (b) The geometry of a regular interferene fit of a solid shaft with an outer diameter of b 2 and a hollow shaft of outside diameter b 1 and inside diameter a 1 : () A hollow shaft subjeted to inner pressure p i and outer pressure p o : The initial interferene between the parts in both (a) and (b) is d:

4 1652 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) enter with top and bottom radii r it and r ib ; respetively. The depth of the hole is L h and the total height of the ylinder is L h þ L s : The inner-most part is a trunated one representing the abutment, with top and bottom radii of r at and r ab ; respetively. The length of the abutment is L a : The taper angle y is the same for both piees. A ylindrial oordinate axis is loated on the top of the implant as shown in the figure. When the abutment is plaed in the implant with no interferene, the bottom of the abutment will be loated at z ¼ z ¼ðr it r ab Þ=tan y: Appliation of an external axial fore in +z-diretion will ause the abutment to engage with the implant with an interferene fit. An axial displaement by an amount Dz measured with respet to z ¼ z; will ause an interferene d ¼ Dz tan y in the radial diretion, as shown in Fig. 3a. The total length of the ontating interfae of the abutment and the implant then beomes L ¼ðr it r ab Þ=sin y þ Dz=os y: 2.2. Analytial model The geometry of the tapered interferene fit is deeptively simple; but no known analytial treatment of this problem exists to the best of our knowledge. In order to develop a relation for the ontat pressure in a tapered interferene fit, first we revisit the formula for alulating the interferene onditions of two straight ylinders, depited in Fig. 3b. The plain stress solution to a ylinder subjeted to an inner pressure P i and an outer pressure P o ; as shown in Fig. 3, is well known (Shigley and Mishke, 1989). The radial displaement uðrþ of suh a ylinder is uðrþ ¼ 1 E a2 b 2 ðp o P i Þ ðb 2 a 2 ð1 þ nþ Þr þ P ia 2 P o b 2 ðb 2 a 2 ð1 nþr aprpb: ð1þ Þ Consider two ylinders whose radii have an initial interferene d as shown in Fig. 3b. The inner ylinder has an outer radius b 1 and the outer ylinder has inner and outer radii of a 2 and b 2 ; respetively. The initial interferene is, then, d ¼ b 1 a 2 : One the ylinders are engaged, the total radial displaement of the interfae will be equal to the initial interferene, d ¼ u 1 ðb 1 Þ u 2 ða 2 Þ: This is the geometri onstraint of the interferene. When the interferene takes plae we get P o1 ¼ P i2 ¼ P (see Fig. 3). The interferene depth d is small when ompared to the radii of the ylinders, therefore it an be assumed that interferene ours at the radius r ¼ a 2 ¼ b 1 : The ontat pressure P due to interferene is alulated by ombining Eq. (1) with the geometri onstraint as follows (Shigley and Mishke, 1989) P ¼ Edðb2 2 b2 1 Þ 2b 1 b 2 : ð2þ 2 Note that Eq. (2) is valid if the material properties of the mating ylinders are the same, i.e., E 1 ¼ E 2 ¼ E and n 1 ¼ n 2 ¼ n: O Callaghan et al. (2001) analyzed the mehanis of a tapered interferene fit by approximating the smooth tapered walls by a series of straight ylinders with hanging radii and diminishing height. By applying the plain stress formula, given in Eq. (1), to eah ylinder, the ontat pressure distribution of the whole onial interfae was approximated. Fig. 3a shows that the outer radius of the abutment b 1 ðzþ and the inner radius of the implant a 2 ðzþ vary linearly along the axis z as follows: b 1 ðzþ ¼r ab þðl os y zþtan y for 0pzpz þ Dz : a 2 ðzþ ¼r it z tan y for 0pzpL h Then, using Eqs. (2) and (3), the ontat pressure due to interferene of a tapered interferene fit, as a funtion of the axial distane beomes P ðzþ ¼ Ed½b2 2 b2 1 ðzþšos y 2b 1 ðzþb 2 : ð4þ 2 The auray of this equation is heked by omparing the results with the FE analysis The effet of the bone on the ontat pressure in the implant abutment interfae In pratie, the restal region of the implant is surrounded by the ortial bone and the remaining setions by the trabeular bone. Around the restal module of an implant, linial observations indiate that some bone loss ours. Therefore, the ortial bone does not over the entire restal module. In the following, it has been assumed that the material properties of the bone that surround the implant along its entire length is uniform, isotropi and no bone loss exists around the restal module. These assumptions an be relaxed easily, whih will result in more ompliated losed form formulas. The effet of the material properties of the bone on the ontat pressure in the abutment implant interfae is shown to be small later in the paper. In this setion, expressions for the ontat pressure in the abutment implant (a i) and implant bone (i b) interfaes are developed. In the implant abutment bone system, the interfae between the implant and the abutment, at r ¼ r 2 ð¼ b 1 ðzþþ; has an initial interferene d; and the interfae between the implant and the bone, at r ¼ r 3 ð¼ b 2 Þ; has zero interferene. These onditions are expressed as d ¼ u 1 ðr 2 Þ u 2 ðr 2 Þ at r ¼ r 2 ; ð5þ 0 ¼ u 2 ðr 3 Þ u 3 ðr 3 Þ at r ¼ r 3 : ð6þ ð3þ

5 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) By using similar assumptions as given above, the formulas for ontat pressure in the abutment implant interfae P ða iþ and in the implant bone interfae P ði bþ are found from simultaneous solution of Eqs. (1), (5) and (6) as follows: Fig. 4 shows the pull-out fore F p ; for different implant radius b 2 ; ontat length L ; and taper angle y values, typial for dental implants. Figs. 4a, and d show that inreasing ontat length auses an inrease of the pull-out fore. Similarly, Figs. 4a show that P ða iþ ¼ Ed os y 2 E½b 2 3 ð1 þ n bþþb 2 2 ð1 n bþšðb 2 2 b2 1 ðzþþ þ E b½b 2 1 ðzþð1 þ nþþb2 2 ð1 nþšðb2 3 b2 2 Þ b 1 ðzþb 2 2 fe½b2 3 ð1 þ n bþþb 2 2 ð1 n bþš þ E b ð1 nþðb 2 3 b2 2 Þg ; ð7þ P ði bþ ¼ EE b db 1 ðzþðb 2 3 b2 2 Þ b 2 2 fe½b2 3 ð1 þ n bþþb 2 2 ð1 n bþš þ E b ð1 nþðb 2 3 b2 2 Þg: ð8þ Note that, in these equations, as the elasti modulus of the bone approahes zero, P ða iþ approahes the expression given in Eq. (4) and that P ði bþ approahes zero Pull-out fore and torque The resultant ontat fore N due to the interferene fit is obtained by the integration of the ontat pressure P over the ontat area along the tapered interfae N ¼ 2p Z L os y 0 b 1 ðzþp ðzþ dz: A free body diagram of the assembly would show that the pull-out fore F p is equal to F p ¼ Nðsin y m os yþ: ð10þ When we neglet the presene of the bone, a relatively simple losed form solution for the approximate pullout fore of a tapered interferene fit is obtained by using Eqs. (4), (9) and (10) as follows: F p ¼ pedl 3b 2 ½3ðb 2 2 r2 ab Þ L sin y 2 ½3r ab þ L sin yššðsin y m os yþos 2 y: ð11þ The effet of the bone on the pull-out fore ould be evaluated by replaing Eq. (4) with Eq. (7) in this derivation. Eq. (11) shows that there are seven independent parameters that affet the pull-out fore; these are E; L ; b 2 ; r ab ; d; y; m: The pull-out fore inreases linearly with d and E; and it inreases as ðl Þ 3 : This result points the importane of a large ontat surfae in the abutment implant interfae. The formula also shows that if the taper angle is hosen suh that tan y ¼ m; then the pull-out fore will be equal to zero. The pull-out fore in Eq. (11) an be onsidered as a design metri. In priniple, the pull-out fore ould be optimized for all seven parameters. In this paper we have not performed these alulations. However, in Fig. 4, we plot the effets of L ; y and b 2 on the pull-out fore for values typial for dental implant systems. ð9þ inreasing the implant radius b 2 auses the pull-out fore to inrease. Finally, Figs. 4b and d show that the pull-out fore is higher for smaller taper angles. Close inspetion of these figures show that predited pull-out fore F p values are relatively large. For example, from Fig. 4, the pull-out fore is predited to be, F p ¼ 1700 N, for b 2 ¼ 1:5 mm, y ¼ 3 ; L ¼ 2 mm. This value is onsiderably larger than the tensile load of 200 N, that an be enountered in one of the implants supporting a full-denture as predited by Brunski (1999). The external torque value, whih auses the abutment to beome loose is given by T L ¼ 2pm Z L os y 0 b 2 1 ðzþp ðzþ dz ¼ pmedl os 2 y 4b 2 fl sin y½2ðb 2 2 3r2 ab Þ 2 L sin yð4r ab þ L sin yþš þ 4r ab ðb 2 2 r2 ab Þg: ð12þ This equation shows that the loosening-torque inreases with ðl Þ 4 : The trends of dependene of T L on b 2 ; L ; and y are similar to that of the F p : It should be noted that, other fators ould affet loosening of the abutment, suh as fatigue failure of the asperities in the ontat interfae, or redution of the effetive frition oeffiient due to presene of some liquids Interferene fit analysis using the FE method The FE method was used, here, to analyze the mehanis of the tapered interferene fit. First, the preditions of the interferene fit formula given by Eq. (4) were ompared to the results of the FE analysis. In this analysis, the material was assumed to behave elastially. Seond, the mehanis of the interferene fit in a Bion implant abutment system shown in Table 1, embedded in a ylinder to represent the bone, was analyzed. In the seond analysis, the implant and the abutment were modeled with bilinear elasti plasti material properties and large deformation elastiity option.

6 1654 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Fig. 4. Variation of the pull-out fore F p with implant radius b 2 ; ontat length L and taper angle y for r ib ¼ 0:7 mm, d ¼ and m ¼ 0:5: Table 1 The Bion implant abutment system used in the FEA of the interferene fit BICON Size Part No. Length Material Implant 3.5 mm mm Ti6Al-4V ELI Abutment mm N/A Ti6Al-4V ELI Ansys ver. 5.7 (Ansys In., Houston, Pennsylvania, USA) was used in the analyses. The CAD drawings were reated in Pro/Engineer 2000i 2 (PTC, Needham, MA, USA). First, the implant and the abutment were assembled without any interferene. Then, in order to obtain different interferene values, the abutment was displaed different Dz amounts in the axial diretion, relative to the implant. This reates overlapping of the ontat boundaries. The assemblies with overlapping boundaries were, then, imported into Ansys. The abutment implant system was modeled using axisymmetri Plane 42 elements. The tapered ontat interfaes were simulated by Target 179 and Contat 172 elements. The implant was onstrained in all degrees of freedom at the bottom fae. The ontat algorithm of the FE analysis ode, then, finds the equilibrium-state, where the overlap is eliminated. 3. Results and onlusions 3.1. Comparison of tapered interferene formula to FE analysis FE analysis was used to hek the validity of Eq. (4). The length of the solid part of the implant L s was kept large, in order to minimize the effet of the fixed boundary. All materials were assumed to be linear and isotropi with E ¼ 200 GPa, u ¼ 0:3: Three different L os y=b 1 values (4, 6, 12) and three different b 2 =b 1 values (3, 4, 5) were used for eah one of the three taper angles y ¼ 3 ; 6 and 9. Fig. 5 shows the omparison of the ontat pressure distribution predited by Eq. (4) and the FE analysis, for y ¼ 9 ; L os y=b 1 ¼ 4; b 2 =b 1 ¼ 5; and d=b 1 ¼ : The inset in Fig. 5 shows the FE mesh and the ontat pressure distribution at the abutment implant interfae. Fig. 5 shows that the FE analysis predits stress onentrations at the ends of the ontat interfae. The FE analysis and losed-form results, in general agree well; the ontat pressure inreases toward the tip (z ¼ 160 mm) where the implant is thiker, thus provides more resistane to deformation. However, it is lear that the losed-form approah, whih is based on the

7 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) plane-stress theory, does not apture the stress onentrations, partiularly near the tip where z-z þ Dz: Similar observations are made for the P vs. z omparisons of the other parameter ombinations. The two approahes are ompared onveniently, when the pull-out fore F p and loosening torque T L values are evaluated for both the FE analysis and the losed form solution. Table 2 shows the F p and T L for different y; L os y=b 1 ; b 2 =b 1 and d=b 1 values. Here we see that the losed-form formula given by Eq. (11) underestimates the FE results between 5.46% and 9.26%. Considering the assumptions involved in the derivation of Eq. (4), this is a reasonable level of agreement. Eah one of the staked ylinders used in the approximation of the onial interferene is modeled in plane stress onditions. Thus normal and shear stresses in the axial (or thikness) diretion are zero. The theory given here is apable of generating only radial and irumferential normal stresses. Due to symmetry assumption no shear stress develops in the plane of the ylinders. These assumptions hold to a ertain extent in the regions that are away from the ends of the onial interferene. But the end onditions fore the stresses to beome more ompliated and the approximation fails to predit the ontat stresses near the ends The effet of the bone on the ontat pressure in the implant abutment interfae Fig. 5. Comparison of the ontat stress distribution predited by Eq. (4) and the FEM for y ¼ 9 ; L =b 1 ¼ 4; b 2 =b 1 ¼ 3; and d=b 1 ¼ : The inset shows the FE mesh used in the solution and the variation of the ontat pressure with respet to the abutment implant interfae. Eq. (7) gives the ontat pressure distribution P ða iþ in the abutment implant interfae, with the effet of the surrounding bone. This equation shows that three parameters related to the bone, its elasti modulus E b ; Poisson s ratio n b and outer radius b 3 affet the P ða iþ distribution. Figs. 6a and b show the effet of E b and b 3 ; respetively. Here it an be seen that a 16-fold inrease in E b auses nearly 10% inrease in the ontat pressure. The relation of the ontat pressure to the outer radius of the bone is non-linear, as shown in Fig. 6b, where the ontat pressure hanges about 3.3% between b 3 ¼ 1 Table 2 Comparison of the pull-out fore F p alulated by the losed form solution given by Eq. (11) and the results of the FEA, for a tapered interferene fit by using b 1 ¼ 40 mm, E ¼ 200 GPa, n ¼ 0: y FEA Eq. (4) % Error FEA Eq. (4) % Error FEA Eq. (4) % Error b 2 =b 1 (for d=b 1 ¼ ; L os y=b 1 ¼ 4) kn 620 kn kn 663 kn kn 683 kn L os y=b 1 (for d=b 1 ¼ ; b 2 =b 1 ¼ 3) kn 620 kn kn 916 kn kn 1733 kn d=b 1 (for b 2 =b 1 ¼ 3; L os y=b 1 ¼ 4) kn 155 kn kn 620 kn kn 1240 kn

8 1656 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Fig. 6. (a) The effet of bone modulus and (b) the effet of bone radius surrounding the implant on the ontat pressure in the abutment implant interfae P ða iþ ; alulated by using Eq. (4). and 6 mm, but no appreiable hange ours for thiker bone. These results show that the bone does not affet the ontat pressure distribution in the abutment implant interfae more than 10% The FE analysis for Bion implant abutment system The ontat pressure and internal stress distribution in a Bion implant abutment system were analyzed using the FE method. Different interferene values were obtained by assembling the implant and the abutment with Dz ¼ 0:05; 0.1, 0.15, 0.2 and 0.25 mm in the vertial diretion as desribed above. The bone was approximated by a mm long ylinder with mm in diameter, leaving 4.2 mm of bone around the implant, whih is suffiient to eliminate the boundary effets in mesial-distal diretion (Teixeria et al., 1998). All the materials were assumed to be isotropi. Bone was assumed to be a linear, homogenous material with E b ¼ 10 GPa, n b =0.3. These values are more representative of the material properties of the ortial bone. Full osseointegration was assumed in the analysis and it was modeled by fixing the implant to the bone. Implant and abutment material were Ti6Al4V ELI. A bilinear, isotropi hardening model was used in order to simulate the plastiity of Ti6Al4V ELI. The material properties of this material are: elasti modulus E ¼ 113:8 GPa; tangent modulus E t ¼ 0:63 GPa; yield stress s Y ¼ 960 MPa, ultimate strain e U ¼ 0:08; Poisson s ratio n ¼ 0:34: The geometri non-linearity was also taken into aount by using the large displaement option in the FE analysis. The results of the FE analysis are presented using the equivalent von Mises stress and strain. Figs. 7a e give the von-mises stress distributions for Dz ¼ 0:0520:25 mm, and Fig. 7f shows the equivalent strain for Dz ¼ 0:25: Note that the effet of the bone is onsidered in the analysis but not shown in these figures. The maximum von Mises stress for Dz ¼ 0:05 mm, whih ours near the bottom of the ontat interfae, is 692 MPa; the abutment and the implant both deform elastially. The stresses in the implant are higher than the abutment, as the latter is stiffer due to its solid geometry. Plasti deformation starts at 0.1 mm insertion depth in the implant, near the top and the bottom of the ontat area. This is onsistent with the stress onentrations mentioned in the previous setion. The rest of the implant and the abutment are elastially deformed. For Dz values greater than 0.1 mm, the plasti deformation spreads to the other regions of the implant. A small region of plasti deformation in the abutment an be seen at Dz ¼ 0:15 mm, whih spreads deeper into the abutment at higher Dz values. Even at the highest level of abutment insertion onsidered here, the outer periphery of the implant remains elasti. The equivalent stress distribution at this level is shown in Fig. 7e for Dz ¼ 0:25 mm. The equivalent strain distribution for the same Dz value is shown in Fig. 7f, whih shows that, exept for the tip of the implant, the strain level is less than The largest equivalent strain ours also at the tip of the implant and it is greater than the ultimate strain for this material The ontat pressure distribution P ða iþ at the abutment implant interfae of the Bion system, evaluated by the FE method, was ompared to the results of Eq. (7). The outside of the Bion implant has fins as shown in Fig. 1. The results presented in Fig. 8, were alulated for the inner, (b 2 ¼ 1:14) and outer radii, (b 2 ¼ 1:75) of the fins, separately. An equivalent implant radius (b 2 ¼ 1:51) was taken to be the radii of the ylinder with a height of ontat length that has the

9 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Fig. 7. The von Mises stress distribution for interferene depth values of Dz ¼ 0:0520:25 mm are given in (a) (e). The equivalent von Mises strain for Dz ¼ 0:25 mm is given in (f). The yield stress for Ti6Al4V ELI is s Y ¼ 960 MPa, and the ultimate strain is e U ¼ 0:08: Note that the effet of the surrounding bone is inluded in the analysis but not shown in this figure for larity of presentation. same ross-setional area as the implant area along the ontat length. Fig. 8 shows stress onentrations at the lower and upper intersetion of the implant and abutment. The analytial solution annot predit the pressure values in these regions. The analytial and FE results are lose in the entral 90% of the ontat length. Sine the implant radius is maximum at the bottom of the interfae, the finite element results were well approximated by the upper urve using the largest implant radii, whereas at the top of the interfae, the ontat pressure was approximated better by the lower urve, using the smallest implant radius. The pull-out fore F p and the loosening torque T L alulated using an equivalent implant radii for this implant abutment system as a funtion of insertion depth Dz; with different approahes are shown in Fig. 9. The losed-form formula, given by Eq. (7), predits the pull-out fore with 8 9% error by using the mean radius. If the material is treated as perfetly elasti, then the F p and T L values inrease linearly as a funtion of insertion depth. When the plasti deformation of the Fig. 8. The ontat pressure distribution in the abutment implant interfae for the Bion implant alulated by the FE method for Dz ¼ 0:1 mm. The results are ompared with the preditions of the losed-form solution given by Eq. (7) for different implant outer radii.

10 1658 ARTICLE IN PRESS D. Bozkaya, S. M.uft.u / Journal of Biomehanis 36 (2003) Aknowledgements The authors would like to aknowledge the support of Bion Dental Implants, Boston, MA for this work, and the tehnial help of Dr. Ali M.uft.u at Tufts University, Shool of Dental Mediine. Referenes Fig. 9. (a) The pull-out fore and (b) the loosening torque for the Bion implant. The results represent the losed form solution, elasti FEA and elasti plasti FEA. material is onsidered, the pull-out fore and the loosening torque inrease non-linearly, and tend to level off. Based on elasti and elasti plasti FE studies, Fig. 9 indiates that the pull-out fore is redued approximately 6% at d ¼ 0:15 mm and 15% at d ¼ 0:25 mm. This result indiates that inreasing insertion depth does not neessarily orrespond to unbounded inrease in pull-out fore or loosening torque values. Binon, P., Sutter, F., Beaty, K., Brunski, J., Gulbransen, H., Weiner, R., The role of srews in implant systems. International Journal of Oral and Maxillofaial Implants 9, Brunski, J.B., In vivo bone response to biomehanial loading at the bone/dental-implant interfae. Advaned Dental Researh 13, Chu, Y.-H., Alias, J.J., Duda, G.N., Frassia, F.J., Chao, E.Y.S., Stress and miromotion in the taper lok joint of a modular segmental bone replaement prosthesis. Journal of Biomehanis 33, Gamer, U., M.uft.u, S., On the elasti-plasti shrink fit with superritial interferene. ZAMM 70 (11), Geng, J., Tan, K.B.C., Liu, G., Appliation of finite element analysis in implant dentistry: a review of the literature. The Journal of Prostheti Dentistry 85, Keating, K., Conneting Abutments to Dental Implants An Engineer s Perspetive. Irish Dentist. Morgan, K.M., Chapman, R.J., Retrospetive analysis of an implant system. Compendium of Continuing Eduation in Dentistry 20 (7), M.uft.u, A., Chapman, R.J., Replaing posterior teeth with freestanding implants: four-year prosthodonti results of a prospetive study. Journal of the Amerian Dental Assoiation 129 (8), O Callaghan, Jr., J., Goddard, T., Birihi, R., Jagodnik, J., Westbrook, S., Abutment Hammering Tool for Dental Implants. Amerian Soiety of Mehanial Engineers, IMECE-2002 Proeedings, Vol. 2, November 11 16, 2001, Paper No. DE Shwarz, M.S., Mehanial ompliations of dental implants. Clinial Oral Implants Researh 11, Shigley, J.E., Mishke, C.R., Mehanial Engineering Design. MGraw-Hill, Singapore. Sutter, F., Weber, H.P., Sorensen, J., Belser, U., The new restorative onept of the ITI dental implant system: design and engineering. International Journal of Periodonties Restorative Dentistry 13, Teixeria, E.R., Sato, Y., Akawaga, Y., Shindoi, N., A omparative evaluation of mandibular finite element models with different lengths and elements for implant biomehanis. Journal of Oral Rehabilitation 25, Van Rietbergen, B., Huiskes, R., Weinans, H., Sumner, D.R., Turner, T.R., Galante, J.O., The mehanism of bone remodeling and resorption around press-fitted THA systems. Journal of Biomehanis 26 (4/5), Vieonti, M., Muini, R., Bernakiewiz, M., Massimiliano, B., Cristofolini, L., Large sliding ontat elements aurately predit levels of bone implant miromotion relevant to osseointegration. Journal of Biomehanis 33,