Numerical verification of two-component dental implant in the … · 2016-05-06 · Numerical...

Acta of Bioengineering and Biomechanics Original paperVol. 18, No. 1, 2016 DOI: 10.5277/ABB-00323-2015-02

Numerical verification of two-component dental implantin the context of fatigue life for various load cases

KRZYSZTOF SZAJEK*, MARCIN WIERSZYCKI

Poznań University of Technology, Institute of Structural Engineering, Poznań, Poland.

Purpose: Dental implant designing is a complex process which considers many limitations both biological and mechanical in nature.In earlier studies, a complete procedure for improvement of two-component dental implant was proposed. However, the optimizationtasks carried out required assumption on representative load case, which raised doubts on optimality for the other load cases. This paperdeals with verification of the optimal design in context of fatigue life and its main goal is to answer the question if the assumed loadscenario (solely horizontal occlusal load) leads to the design which is also “safe” for oblique occlussal loads regardless the angle from animplant axis. Methods: The verification is carried out with series of finite element analyses for wide spectrum of physiologically justifiedloads. The design of experiment methodology with full factorial technique is utilized. All computations are done in Abaqus suite. Re-sults: The maximal Mises stress and normalized effective stress amplitude for various load cases are discussed and compared with theassumed “safe” limit (equivalent of fatigue life for 5e6 cycles). Conclusions: The obtained results proof that coronial-appical load com-ponent should be taken into consideration in the two component dental implant when fatigue life is optimized. However, its influence inthe analyzed case is small and does not change the fact that the fatigue life improvement is observed for all components within wholerange of analyzed loads.

Key words: dental implant, optimization, fatigue life, genetic algorithm

1. Introduction

Nowadays, dental implants are common way oftreatment in the case of edentulous patients. However,in spite of high rate of success there are still a fewproblems observed. Among other things, one of themost important, from patient’s safety point of view, isimplant fracture due to both the static overloading aswell as fatigue damage. While capability for staticload can be relatively easily estimated the fatigue lifeprediction is still the subject of many investigations.

A systematic review of twenty-six follow-upstudies estimated a cumulative incidence of implantfractures after 5 years at a level of 0.14% [12]. How-ever, the fracture ratio for the follow-up studies for upto 15 years [1] rises drastically and can reach even16% in the maxilla. This proves both fatigue fracture

nature of recorded failure and weakness of follow-upstudies limited to 5 years in the context of sufficientdental implant fatigue life confirmation.

Fatigue fracture is a complex process stronglydepending on mechanical and biomechanical factorssuch as marginal bone loss and screw stability [10],[19]. Many approaches considering dental implantlife estimation are present in the literature basedon laboratory tests [5]–[7], [11], [20], 21] and nu-merical approach, mostly finite element method [8],[9], [24]. A review of them allows us to concludethat as regards implant fatigue life the most crucialfactors are implant–abutment connection geometry,a screw preload, dental implant fixation and crownloading.

In order to meet the need of dental implant designtool, a complete procedure for improvement of two-component dental implant was proposed [22]. The

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* Corresponding author: Krzysztof Szajek, Institute of Structural Engineering, Poznań University of Technology, ul. Piotrowo 5,60-965 Poznań, Poland. Phone number: +48 61 6652103, e-mail: [email protected]

Received: May 15th, 2015Accepted for publication: May 26th, 2015

K. SZAJEK, M. WIERSZYCKI104

procedure is based on genetic algorithm hybridizedwith Hooke–Jeeves technique. The objective functionis estimated through finite element analysis with sim-plified model, yet, capable to estimate all necessarydental implant features. The optimization problemformulation in the context of fatigue life is proposedas finding a configuration of geometry parameters forwhich the optimal screw preload maximizes the num-ber of cycles to fatigue. Static failure risk and ade-quate levels of screw loosening/tightening momentswere constrained. An optimal solution with meaning-ful fatigue life improvement and meeting the assumedconstraints was proposed. The elementary verificationconsidering influence of FE model simplification hasbeen done [22] and revealed small quantitative differ-ences; yet, the correctness of qualitative measure hasbeen proved.

A few questions arise in the context of formulatedoptimization problem and optimal design obtained.The most important considers assumed load scenarioand boundary conditions. Load scenario, in order toeliminate individual variability, should represent a sim-ple but the worst possible case. In the literature, theoblique direction is frequently proposed [11], [13]which is biologically justified and causes superimpo-sition of bending and compression in the joint compo-nent [15]. However, the problem is what should be theload angle from an implant axis. The bucco-lingual(horizontal) component has clear effect on fatigue life.It causes extreme tension in the screw [2], which usu-ally leads to the minimal fatigue life. It was also con-firmed by Genna [8], [9] for low-cycle fatigue failure.Therefore, this load component was assumed solely inthe optimization problem [22]. However, an influenceof coronial-appical (vertical) component cannot beeasily predicted. On the one hand, it can lead to theplastic deformation on the fixture-abutment interfaceand circumferential region of the fixture [23]. On theother hand, it reduces tensile stresses generated due tobending [2] and preload, which decreases both themean stress and its amplitude. Thus, in the context ofscrew fatigue life, coronial-appical load componentseems to make it higher. This leads to the conclusionthat as long as screw is the weakest element, the as-sumption of only coronial-appical load componentrepresent the worst case. Regardless of right selectionof the most adverse case, unfortunately, there is stillno guarantee that the final optimal solution is still“optimal” for other component combinations. An-other problem to be verified is the influence of loadmagnitude on optimal solution. A dental implant isa nonlinear system and the region most jeopardizedto a fatigue fracture can change place depending on

the load magnitude. Even though, it is possible tomeet elastic regime constraints in the optimization,possible relative movement on contacting surfacesbetween all implant components can change failuremode. Additionally, one should also note that the op-timization problem formulation did not include re-striction of sensitivity of the fatigue life to load mag-nitude. It was assumed that the choice of the worstload component leads to the “safe” design also forslightly different load magnitudes, especially lowerones. All these doubts give rise to the question ofwhether the optimal design obtained for load withfixed angle and magnitude is also optimal or at least“safe” for other loads. The answer is especially im-portant when the implant is expected to be used ina wide spectrum of applications and various toothreplacement. Therefore, in this study, the optimalimplant fatigue life for various load component com-binations and their magnitudes is verified. The resultsare also compared with the initial design to see theimprovement achieved.

The numerical verification utilizes design of ex-periment scheme with a full factorial pattern. Onlytwo parameters are introduced, vertical and horizontalcomponent magnitude. The analyses were done usingAbaqus suite. The fatigue life estimation utilizes stressbased approach with linear Goodman theory.

2. Materials and methods

2.1. Optimization definitionand result

A detailed description of the problem and opti-mization strategy can be found in [22]. Becausesome elements are common to computational modelused in this study and for the sake of verificationclarity, below the most important information isrecalled.

An example of two-component implantologicalsystem is considered (Fig. 1a). The geometry is sim-plified to axisymmetric one, however, the asymmetricdeformations are considered. The components aremade with titanium or its alloys modeled as non-linearelastic-plastic materials. Between all componentscontact conditions are defined – “hard” Hertz contactin normal direction and isotropic Coulomb frictionmodel in tangential direction. A two step procedure isassumed, simulation of tightening (425 N) and bend-ing (load of 30 N perpendicular to axisymmetric axis,

Numerical verification of two-component dental implant in the context of fatigue life for various load cases 105

tip of the abutment). The implant root is fixed assum-ing moderate three millimeter bone loss.

The fatigue life estimation in the optimization aswell as in the following verification uses stress basedapproach with Goodman linear theory where the ef-fective stress amplitude at zero mean stress is calcu-lated as follows

01

σσσ

σm

afar

K

−= . (1)

In the above, the effective amplitude of stresses,

aσ , is calculated on the basis of Mises stress, effec-tive mean value of stresses, mσ , is given as a firstinvariant of stress tensor, while Kf is the fatigue-reduction factor (for fixture 1.25 – strongly roughedsurface). Assuming constant values of stress ampli-tude and stress mean value, the number of maximalcycles to fatigue failure can be given by

f

arar

barN

σσσσ′

=′′= ,)(21 1

(2)

where fσ ′ is fatigue strength coefficient. Equation (2)

shows that an increase of arσ ′ prolongs the fatiguelife. Therefore the following problem formulation wasproposed

)(max xarXxσ ′

∈.

Subject to:

0.1)( ≤xS ,

150)( ≥xL Nmm, (3)

300)( ≤xT Nmm,

where x denotes seven geometrical parameters (Fig. 1)

and screw preload, yield

Mises)(σσ

=xS represents static risk

factor, while L(x) and T(x) denote loosening andtightening moments calculated using Bozkaya’s for-mula [3].

A penalty method was used as a constraint-handlingtechnique. Let us assume that hi,viol is a measure of thei-th constraint violation which equals if constraint isnot violated, otherwise |hi – hi,limit|, where hi and hi,limit

denote values of constraint function and assumed limit,respectively. The problem expressed in equation (3)can then be transformed into

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−′ ∑

=

)]([)(max viol,1

xhΦkx i

n

iiarσ (4)

where Φ is the penalty function while ki denotes pen-alty coefficient. The following exterior and dynamicpenalty function was assumed

βξρ )]([)()]([ viol,viol, xhtxhΦ ii ⋅= (5)

Fig. 1. Dental implant geometry: (a) the initial model with assumed geometric design parameters(parameter E is defined as a fraction of * distance), (b) the best solution, (c) optimal configuration of design parameters


where ξ = 2.0, β = 2.0 and ρ = 1.0, while t denotesiteration number. The penalty coefficient is defined asfollows

2extreme,imit,

min,max,

)](1.0[||

ili

arari hh

k−

′−′=

σσ(6)

where hi,extreme is the estimation of extreme (maximal ifconstraints create upper bound, otherwise minimal)value of the i-th constraint, max,arσ ′ and min,arσ ′ de-note estimation of maximal and minimal possiblevalue of the objective function (the estimation forhi,extreme, max,arσ ′ and min,arσ ′ is based on the largenumber of analysis carried out during the preliminarystudy and reliability test for various design parameterconfigurations, while hi,limit is the assumed limit for thegiven constraint.

The genetic algorithm hybridized with the Hooke–Jeeves procedure was used to solve the problem. Inthe first stage a population of sixty random solu-tions was generated. Each individual representedone design parameter configuration encoded inchromosomes using Gray coding. Next, the popula-tion was iteratively subjected to genetic operatorssuch as crossover and mutation. Forming the nextpopulation the individual with higher value of ob-jective function was preferred (rank-based selec-tion). After ten iterations the best solution obtainedwas the start point for Hooke–Jeeves procedurewhich quickly found the design minimizing theobjective function.

The best solution is presented in Fig. 1b. The ob-jective function is reduced by 95% to 0.0197, which isen equivalent of 4.5e17 cycles to fatigue fracture. Allconstrained values fulfil assumed limits and equal0.49, 217 Ncm and 285 Ncm for static risk factor,loosening and tightening moment, respectively.

The optimization problem definition due to simpli-fications ignored the influence of new geometry onchange of stresses/strains in bone–implant interface[18]. Therefore, the additional analyses were carriedout with full spatial geometry implant loaded with30 N of horizontal load and fixed in bone-like mate-rial (D1, linear, elestic with Young’s modulus equal13 GPa and 9.5 for cortical and cancellous bone, re-spectively) with and without 3 mm marginal boneloss. The results showed the stresses/strains concen-tration in marginal regions for all the cases, which isin agreement with other studies [25]. The optimaldesign leads to stress/strain reduction of 25% modelwithout marginal bone loss, which proves the riskreduction of bone overloading. No stress/strains

change was observed when marginal bone loss wasincluded.

2.2. Finite element analyses

Fully spatial FE model with the same definition ofmaterial and contact conditions as in the axisymmetricone (used in optimization) has been used for verifica-tion. The geometry follows the geometric parametersconfiguration for the initial and optimized design.However, helix thread for both fixture and screw,hexagonal slot (fixture–abutment connection) andhexagonal mortise are considered. Additionally, theimplant root is fixed in bone-like material (linearelastic, E = 9.5 GPa, D1 according to Lekholm andZarb index). The FE model consists of 155 K 8-nodelinear brick elements and 200 K nodes (556 K DOF).The analysis was divided into two steps – screwprestress and the abutment loading with occlussalloads (vertical and horizontal loads are applied simulta-neously). Fatigue life is calculated according to therules given in 2.

A series of 40 numerical simulations were pre-pared for various magnitudes of occlusal load compo-nents and for both the initial and the optimized design.The horizontal load varied from 0 to 90 N with step of30 N, while the vertical one from 0 N to 400 N withstep of 100 N. The screw preload of 425 N and 520 Nis applied for the initial and the optimized design,respectively. Due to the small number of variables,full factorial technique of design of experimentwas chosen. The computations were carried outusing Abaqus/Standard v.6.11 and Fujitsu-SiemensPRIMERGY RX300 S6 (Intel Xeon X5680 6C/12T3.33 GHz, RAM 8 GB, OS GNU Linux). The com-putations were automated with home-made Pythonscript using Abaqus Scripting Interface.

3. Results

The maximal Mises stress and normalized effec-tive stress amplitude (see 2) are presented in Fig. 2and Fig. 3 for the initial design and the optimized one,respectively. In order to make the interpretation eas-ier, Fig. 2 presents contour plots of cycles to fatiguefailure (see 2) depending on occlusal load magni-tude/angle. The isolines were calculated using equa-tion (2) transformed to the form of arσ ′ = (2N)b. Thelimit of 5e6 cycles is indicated with thick isoline.


Dotted areas indicate a region of design where thenumber of cycles to failure is higher than 5e6. Thecontour plots are also supplemented with the dottedlines indicating a relation between transversal andvertical components for various angles of loads. Ad-ditionally, detail results for fatigue life estimation and

various levels of vertical components are listed inTable 1.

The stress field was examined only in exteriornodes excluding contact surfaces and threads as wellas internal surface of a fixture (artificial stress con-centration in the vicinity of contact surfaces).

Table 1. Detail results for particular components in various load scenarios for the optimized design

Abutment Screw FixtureLoadH/V σm σa σar N σm σa σar N σm σa σar N30/0 –33.6 24.1 23.1 1.3e19 731.7 6.8 56.0 1.7e15 –40.6 60.3 70.7 6.2e12

30/400 165.3 40.9 51.5 2.9e15 706.5 28.5 188.9 4.8e9 –3133 131.7 109.1 6.5e10

Fig. 2. Initial design. Mises stresses (left column) and normalized effective stress amplitudeat zero mean stress (right column) for various combinations of occlusal loads and particular components:

(a–b) screw, (c–d) fixture, (e–f) abutment

a) b)

c) d)

e) f)


4. Discussion

Let us start from recalling the main question setfor this study in the introduction, that is “if the opti-mal design obtained for load with fixed angle anda magnitude is also optimal or at least “safe” forother loads”. Proving the optimality for such a com-plex system requires solving a series of optimizationproblems for combinations of occlusal loads insteadof single analyses and, therefore, it cannot be donebased on the obtained results. However, from thepractical point of view, it would be enough to prove

the optimized implant is “safe” for physiologicallyjustified occlusal loads, which the presented study islimited to.

A further discussion requires formulation of thedefinition of “safe” solution which appears at the be-ginning of this section. The optimization done consid-ers screw loosening/tightening limitations themselvesand due to the fact that they do not depend on occlusalloads it can be assumed they are fulfilled. Static fail-ure directly depends on Mises stresses which are alsoincluded in the formula for fatigue life estimation andtherefore there is no need to control it separately. Fi-nally, within the limitations of this study it is enough

Fig. 3. Optimized design. Mises stresses (left column) and normalized effective stress amplitudeat zero mean stress (right column) for various combinations of occlusal loads and particular components:

(a–b) screw, (c–d) fixture, (e–f) abutment

a) b)

c) d)

e) f)


to rely solely on fatigue life. Following the proposi-tion in the standard ISO 14801:2007 the limit of 5e6cycles to failure was assumed as a limit for “safe”design. It correspond with normalized stress ampli-tude equal arσ ′ = (2N)b = (5⋅1e6)–0.095 = 0.231. How-ever, it should be pointed out that the utilized stressbased fatigue life estimation is a rather rough measureand, as a consequence, the assumed level of cyclesshould be considered as a qualitative measure which

can be used for comparison but very carefully as ab-solute measure.

Another important thing to determine is a set ofpossible, physiologically justified, load scenarios.According to in vivo force measurement in implantssupporting different types of superstructure done byMericske-Stern et al. [14] the maximal functionalforces during chewing food (bread and apple) equal50 N and 150 N for horizontal and vertical compo-

Fig. 4. Contour plot of the number of cycles to fatigue, N, for particular components and various combinationsof occlusal loads: (a) screw (initial), (b) screw (optimized), (c) fixture (initial), (d) fixture (optimized),

(e) abutment (initial), (f) abutment (optimized)

a) b)

c) d)

e) f)


nents. Similar values of vertical masticatory forces arereported by Morneburg et al. [16], [17]. The maximalvalues were mostly registered during the first cycle ofchewing and it can be assumed that the frequent value,although hard to estimate, is much lower. As there isno information whether these maximal values canoccur simultaneously, in this study the most adversecase is assumed. Therefore, the possible area of func-tional loads would be represented with a rectangularregion. However, taking into account that although loadangles from implant axis higher than 30 degrees canoccur, but are not frequent, the upper left corner of thetriangle is cut off as indicated in Fig. 4. The assumptioncan also be justified with the guideline of the standardISO 14801:2007 where the angle of 30 degrees is alsoproposed for test set-up. The determined region iscalled “functional load range” further on.

Each component: screw, fixture and abutment isdiscussed independently. Because of the assumptionmade in the optimization that the “worst” load case isrepresented by solely horizontal load of 30 N, an in-fluence of vertical component introduction is analyzedfirst. Then, viewed from wider perspective, the wholerange of assumed magnitudes of particular compo-nents is presented based on contour plots in Fig. 4.The discussion covers both the “safety” of the opti-mized design as well as its improvement in compari-son with the initial one.

Fig. 5. Mises stresses in a screw of optimized dental implantfor horizontal load of 30 N. Red area indicates stress concentration

Let us start the discussion with a screw which isthe weakest element in the context of fatigue fracture inthe initial design. The maximal stresses for the screware localized at the transition point from a shank andscrew head. This is also the place where fatigue cracksare the most likely to occur (Fig. 5). The fatigue and

static mechanism of failure is an effect of screwbending which was rightly modeled in the optimiza-tion with solely horizontal load. Let us discuss aneffect of vertical load. The abutment undergoing com-pressive load is pushed into the fixture and causesscrew preload reduction. The range of reduction ifclosely connected with vertical stiffness of an implant[4]. Because the optimal solution is characterized byhorizontal interface between abutment and fixture,which increases vertical stiffness significantly, in thecase of 30 N horizontal load, the introduction of verti-cal load of 200 N (even more than defined functionalload range) reduces Mises stresses by only 25 MPa(less than 5%) from 534 MPa down to 509 MPa. Thereduction follows the common intuition that moreprestressed implant is more resistant to bending. Un-fortunately, there is no such obvious relation in thecase of fatigue fracture. In stress based approach (seeequation (1)) a number of fatigue cycles is a function ofan average value of the first invariant of stress tensor(effective mean value, σm) and effective stresses (am-plitude of Mises stress during a cycle, σa). Table 1presents both values for load combinations (horizon-tal/vertical) 30 N/0 N and 30 N/400 N. It can be seenthat vertical load reduces effective mean value but in-creases effective stresses at the same time. As a conse-quence, the effective amplitude at zero mean stressincreases (the number of cycles to fatigue decreases)when vertical load is introduced and, additionally, thescrew becomes the weakest component (the lowestnumber of cycles to fatigue). Thus, the decrease offatigue life is caused by decreasing Mises stresses incompressed implant. This effect is clearly observedfor the case without horizontal load (Fig. 3b). Themaximal Mises stresses are reduced from 533 MPa to483 MPa when vertical load of 400 N is applied, how-ever, the normalized effective amplitude increasesfrom 0.036 to 0.106 (equivalently N = 9.1e9). Theeffect of fatigue life decreasing due to the highervalue of vertical load is also observed for horizontalload of 60 N. Yet, vertical load raising up to 100 Nfirstly provides stabilization which prevents screwbending effect. As long as the reduction does notcause the stresses to be lower than the value obtainedfor pure tightening, the fatigue life increases. Forvertical load higher than 100 N, the Mises stressdecreases below this limit and effective stress ampli-tude increases due to the previously described reason.A similar effect can be noticed for 90 N of horizontalload but in this case 300 N of vertical load is neces-sary to provide abutment stabilization.

Based on the obtained results and utilizing the fa-tigue life estimation approach, it can be concluded


that the assumption that solely transversal load canrepresent the worst load case for a screw is not cor-rect. The observed fatigue life reduction due to verti-cal load introduction is an effect of screw preloadreduction during a load cycle. In the shakedownanalysis done by Genna an effect of screw tighteningis incorporated in indirect way on the basis of addi-tional analyses [9]. Therefore, the preload reductionmentioned could not be covered. However, two im-portant results should be highlighted. Firstly, the fa-tigue life decrease due to vertical load is caused bystresses reduction, which is generally small. Secondly,even if 400 N and 30 N of vertical and horizontalloads, respectively, are assumed, the number of cyclesto fatigue failure exceeds 9.1e9 which is still aboveassumed “safe” limit. Taking into account the above,the observed fatigue life change does not negate thehigh fatigue life of the obtained design.

The screw component fatigue life improvementachieved due to optimization for solely 30 N of trans-verse load was proved in the previous study [22].However, the contour plots presented in Fig. 4 allowus to make the assessment from a wider perspectivefor other load component combinations. Analyzingthe results for the initial design firstly, the “safe”value of transverse load can be estimated at the levelof 18 N. The contour plot presents the effect of abut-ment stabilization when the vertical load component isapplied and the allowed value of transverse load ex-ceeds 30 N if it acts together with a vertical load of100 N at least (equivalently, load of 105 N which acts18 degrees off implant axis). The “safe” limit becamealmost horizontal for higher value of vertical load.This is a result of increasing amplitude caused bysmall stiffness of implant in axial direction [2] and, inturn, screw preload reduction in response to compres-sive load. The limit increases again for vertical loadhigher than 300 N. It is important to note that the im-

plant is entirely in “safe” zone for the load which iscoincident with an implant axis or acts maximally5 degrees off it. For higher value of load angle themaximal allowed magnitude decreases to 196.2 N,130.7 and 52,4 N for 10, 15 and 30 degrees, respec-tively. Although it can be assumed that a number ofcycles for load with particular variation from implantaxis decrease when the angle increases there is stillsmall “unsafe” region which is inside the functionalload range. In the case of predominant loads withangles higher than 15 degrees the screw is jeopardizedto fatigue fracture.

From the comparison of “safety” zones it can beeasily seen that the crucial weakness of the initialdesign, low screw fatigue life, was extremely im-proved. The screw is able to withstand 5e6 cycles for60 N of solely horizontal load. The implant failurewithin presented “unsafe” zone is clearly the result ofscrew bending, yet, the previously described stabili-zation due compressive loading makes the allowedtransverse load higher reaching the assumed upperlevel of 90 N for 250 N of compressive load. It thecase of an optimized implant the “safe” load angledeviation from implant axis reaches 20 degrees whilefor 30 degrees still a high magnitude of 135 N is al-lowed.

The fatigue life for the screw is improved as muchas the fixture became a component which is the mostendangered to fatigue crack. Therefore, let us nowconcentrate on the influence of vertical load on itsfatigue life. In the implant loaded with only horizontalload of 30 N there are two points with the highesteffective stress amplitude exceeding 60 MPa (an ef-fect of unloading or compression due to bending).They are located on the opposite sides of the fixture–abutment interface (Fig. 6). In accordance with theGoodman linear theory used in this study, the pointwith higher value of mean stresses is characterized by

Fig. 6. Mises stresses in a fixture for horizontal load of 30 N in the initial (a) and optimized (b) design.Red areas indicate stress concentration


a lower number of fatigue cycles to failure (unloadedside). When vertical load is applied maximal Misesstresses on the compressed side increase significantlyfrom 318 MPa (30 N/0 N) to 449 MPa (30 N/400 N)(Table 1). As a consequence, effective stress ampli-tude which is a combination of compression andbending effects reaches almost 100 MPa and movesthe point of expected fatigue crack initiation to anopposite side of the interface. However, the compres-sive mean stress at this point is increased from31 MPa to 313 MPa, which limits the increase of ef-fective amplitude at zero mean stress. Thus, it changesonly by 56%, while effective stress amplitude changesby 120%. Analyzing the vertical load influence with-out horizontal load, similarly to the screw, there isalmost a linear relation between effective stress andvertical load magnitude. The influence of verticalload diminishes along with horizontal load increase(Fig. 3d). For the value of 60 N and 90 N the changeof fatigue life is negligible. Summarizing the resultsfor the fixture, the effect of vertical load introductionis analogous to that in the screw. Fatigue life is de-creased if vertical load is present. For the highestvalue of vertical load of 400 N the number of cyclesto fatigue fracture still exceeds 1.5e9.

Considering solely horizontal load in the initial de-sign, the fixture seemed to be less endangered to fa-tigue fracture than the screw. However, analyzing thecomponent for a wider spectrum of loads, the “safe”zone is smaller and meaningful region of functionalload range overlaps “unsafe” zone. There are twomechanisms responsible for that. Firstly, the trans-verse load causes abutment rotation which opposeswedging in a hexagonal mortise. As a result, thestresses increase in an interior corner indicated by anarrow in Fig. 6. Secondly, the vertical load pushes theabutment into the fixture and due to conical contactsurface it leads to the same effect. Therefore, althoughthe vertical load stabilizes the abutment, the summa-rized effect of both components acting simultaneouslyis a reduction of fatigue life. The maximal magnitudeof vertical load acting solely can reach almost 400 Nwithout risk of fatigue fracture while the variation ofload direction for implant axis reduces the allowedvalue to 170.4 N, 110.5 N and only 44,65 N for 5, 10and 30 degrees, respectively.

Among the three components, the biggest im-provement can be seen in the case of the fixture. Al-most complete elimination of hexagonal slot alongwith horizontal contact surface between the fixtureand the abutment causes that the fatigue fracture is nota problem anymore. The “safe” zone for this compo-nent covers the whole range of analyzed loads. What

is more, the number of cycles to failure is higher tan1e10 for all points within functional load range.

In the case of the last component, the abutment,fatigue life and Mises stresses in the optimized designincrease when vertical load is applied for horizontalload up to 60 N. Higher value of the vertical load sta-bilizes the abutment. In the initial design an abutmentis wedged into a hexagonal slot, which is the mainreason for stress concentrations. Almost completeelimination of the slot in optimized design results inmeaningful reduction of both maximal Mises stressesand fatigue fracture risk. The Mises stresses are belowthe limit of 282 MPa while the lowest number of cy-cles to fatigue failure is always higher than 6.1e13(the worst case is 90 N/0 N of horizontal/vertical load)and 1e15 considering only functional load range.Thus, the influence of vertical load as well as a highervalue of horizontal load can be neglected from thepractical point of view.

5. Conclusions

The obtained results prove that coronial-appicalload component should be taken into consideration inthe analyzed two component dental implant whenfatigue life is considered. In some range of analyzedloads compressive load reduces screw preload in thescrew increasing stress amplitude during a load cycle.Furthermore, in a dental fixture the vertical loadpushes in the abutment into the fixture and, due toconical contact surface between these components,makes stress concentration in hexagonal slot higher.Both phenomena, in turn, decrease fatigue life. Frompractical point of view, however, the reduction is notsignificant in the analyzed optimal design. It can be“safely” used within the assumed range of functionalload and, with small exception for screw component,within the whole analyzed physiologically justifiedload range. Yet, it has to be noted that the optimaldesign is a concept only – the technological issues ofproduction and requirements of medical procedureswere not taken into consideration. Therefore, the re-sults can slightly vary when necessary modificationsare implemented.

A wider perspective for different combinationsof load component magnitudes also allows us tomake some interesting observations. Firstly, althoughin the initial design undergoing pure bucco-lingualload a screw is the weakest element, the “safe” area forthe implant fixture is significantly smaller. The cycliccompression of the wedged abutment exceeds an in-


fluence of screw preload fluctuation to fatigue lifedecrease. Thus, hexagonal slot although beneficial toloosening resistance can cause fatigue life decrease.Secondly, as long as occlusal load direction agreeswith implant axis, there is no risk of fatigue fracture.Thirdly, an abutment “safe“ zone overlaps entirely thefunctional load range for both the initial and opti-mized design and, therefore, no fatigue fracture risk isobserved for this component within functional loadrange. Finally, the optimization improves fatigue lifefor all components within the whole analyzed range ofloads moving the “safe” limit away from functionalload range.

Acknowledgements

This article was financially supported within the project “En-gineer of the Future. Improving the didactic potential of the PoznańUniversity of Technology” – POKL.04.03.00-00-259/12, imple-mented within the Human Capital Operational Programme, co-financed by the European Union within the European Social Fund.

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