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Teeth restored using fiber-reinforced posts: In vitro fracture tests and finite element analysis
Acta Biomaterialia 6 (2010) 3747–3754
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Teeth restored using fiber-reinforced posts: In vitro fracture tests and finite element analysis M. Schmitter a, P. Rammelsberg a, J. Lenz b, S. Scheuber c, K. Schweizerhof b, S. Rues a,b,* a
Department of Prosthodontics, University of Heidelberg, Germany Research Group on Biomechanics, Institute for Mechanics, University of Karlsruhe, Germany c Department of Fixed Prosthodontics, University of Bern, Switzerland b
a r t i c l e
i n f o
Article history: Received 6 October 2009 Received in revised form 1 March 2010 Accepted 8 March 2010 Available online 19 March 2010 Keywords: Dentistry Endodontic posts Preparation design In vitro tests Finite element analysis
a b s t r a c t In dentistry the restoration of decayed teeth is challenging and makes great demands on both the dentist and the materials. Hence, fiber-reinforced posts have been introduced. The effects of different variables on the ultimate load on teeth restored using fiber-reinforced posts is controversial, maybe because the results are mostly based on non-standardized in vitro tests and, therefore, give inhomogeneous results. This study combines the advantages of in vitro tests and finite element analysis (FEA) to clarify the effects of ferrule height, post length and cementation technique used for restoration. Sixty-four single rooted premolars were decoronated (ferrule height 1 or 2 mm), endodontically treated and restored using fiber posts (length 2 or 7 mm), composite fillings and metal crowns (resin bonded or cemented). After thermocycling and chewing simulation the samples were loaded until fracture, recording first damage events. Using UNIANOVA to analyze recorded fracture loads, ferrule height and cementation technique were found to be significant, i.e. increased ferrule height and resin bonding of the crown resulted in higher fracture loads. Post length had no significant effect. All conventionally cemented crowns with a 1-mm ferrule height failed during artificial ageing, in contrast to resin-bonded crowns (75% survival rate). FEA confirmed these results and provided information about stress and force distribution within the restoration. Based on the findings of in vitro tests and computations we concluded that crowns, especially those with a small ferrule height, should be resin bonded. Finally, centrally positioned fiber-reinforced posts did not contribute to load transfer as long as the bond between the tooth and composite core was intact. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Since the introduction of fiber-reinforced posts [1,2] the assessment of their different mechanical properties [3] has revealed that survival [4], failure characteristics [5] and fatigue resistance [6] are acceptable and, consequently, that clinical use is possible. Most studies have found that sufficient ferrule height is essential [7,8]. The results obtained for other variables were inconsistent – some studies found post length to be crucial [9] while others could not confirm this [10]. Consequently, it might be useful to assess the effect of different variables using reliable methods. Although clinical trials would be the best way to assess the effects of different variables [7], this type of study is time consuming, expensive and ethically questionable. Other types of study are helpful, including in vitro studies [11] and finite element analyses (FEA) [12,13]. Both methods have advantages and disadvantages. In vitro tests can
* Corresponding author at: Department of Prosthodontics, University of Heidelberg, Germany. E-mail address: [email protected] (S. Rues).
simulate almost realistic conditions, but are time consuming and only a limited number of specimens can be tested. The transfer of results from in vitro tests to clinical situations is also challenging. FEA enables simulation of any situation, but the accuracy of the results depends on construction of an appropriate model. A meticulous construction process is therefore necessary. The objective of this study was to combine the advantages of both methods to assess the effects of fiber post length, cementation technique, using either a resin or a glass ionomer cement, and ferrule height on the fracture load of artificial crowns anchored with fiber posts. 2. Material and methods 2.1. In vitro tests Sixty-four intact single rooted human premolars were collected directly after extraction and stored in 0.1% thymol solution for 6 weeks (at most). The teeth were randomly assigned to eight groups, endodontically treated and the roots were filed to ISO Stan-
1742-7061/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actbio.2010.03.012
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dard 35 (taper 2%) (FlexMaster Kit, VDW, Munich, Germany). After rinsing (3.0% H2O2) the roots were obturated with gutta percha (Roeko, Langenau, Germany) and resin sealant (AH plus, Dentsply/De Trey, Constance, Germany). The teeth were decoronated 1 mm coronal to the most incisal point of the cement–enamel junction. The root canals were enlarged to ISO Standard 90 (0.9 mm diameter, length 25 mm) using a reamer (Brasseler, Lemgo, Germany) [14], roughened (diamond abrasive, Brasseler) and preconditioned using 37% phosphoric acid and a single dose of Excite DSC Soft Touch (Ivoclar-Vivadent, Schaan, Liechtenstein). The posts (ER-Dentin-post-yellow, 60% glass fiber, caliber 090, apical diameter 0.9 mm, Brasseler) were tribochemically coated with Rocatec-pre (110 lm at 2 bar; 3MEspe, Seefeld, Germany) then Rocatec-plus (3MEspe). Silanization was performed with Monobond-S (Ivoclar-Vivadent). The post was inserted 2 mm into the root canal of half the teeth, 7 mm for the other half. All posts were cemented with Variolink II (Ivoclar-Vivadent). The teeth were treated with 34.5% phosphoric acid (Vocoid, Voco, Cuxhaven, Germany), Solobond-Plus primer and SolobondPlus adhesive (Ivoclar-Vivadent). Subsequently, the cores were built up using Rebilda-SC-Blue (Voco). All teeth were prepared at an angle of 2° using a high speed turbine (Bien-Air-Dental SA, Bienne, Switzerland) mounted in a parallel milling machine (Fraesgeraet-F1, Degussa, Frankfurt, Germany) and using special burs (Sirius-Prothetik-Systems, Hafner, Pforzheim, Germany), which create a chamfer finish line. Because the angle was 2°, no part of the preparation was parallel to the long axis of the tooth. For half the teeth the ferrule height (H) was 1 mm, for the other half 2 mm. The mean height of the preparations (ferrule height + filling) was 5.6 mm. Silicone impressions (Adisil, Siladent, Munich, Germany) were taken. Casts were made from stone gypsum (GC-Fujirock, GC Europe, Leuven, Belgium) and standardized artificial crowns were fabricated (Remanium-Star, Dentaurum, Ispringen, Germany). The axial thickness of the parallel milled crowns was 0.5 mm and the occlusal thickness was 1 mm. All crowns had a standardized occlusal region (Fig. 1a–c). In one of the groups the crowns were cemented with a chemical resin cement (Panavia F 2.0, Kuraray, Japan). The crowns were sand-blasted (50 lm aluminum oxide, 2.5 bar) and an alloy primer (Kuraray) was applied. The ferrule area was etched with 35% phosphoric acid (Kuraray) and primed (New Bond, Kuraray). In the other group the crowns were cemented using a glass ionomer cement (Ketac-cem, 3MEspe). Finally, the roots of all restored teeth were embedded in a cubic resin block (edge length 27 mm) (Palapress, Heraeus Kulzer, Hanau, Germany). The distance between the block surface and finish line was 2 mm (Fig. 1b). All teeth were exposed to 10,000 thermal cycles between 6.5 and 60 °C (Willytec, Graefelfing, Germany) and 600,000 cycles in a chewing simulator (m = 5 kg, v = 30 mm/s ? maximum force 70–80 N, static force 49 N) (Willytec). The angle between the tooth axis and the loading direction was 45° (Fig. 1a). All specimens surviving the chewing simulation were loaded until fracture in a universal testing machine with a cross-head speed of 0.5 mm min1 (Universal-Pruefmaschine 1445, Zwick, Ulm, Germany). Loads were applied at an angle of 45° (Fig. 1a, b and e). Statistical analysis was performed using SPSS (SPSS Inc., Chicago, IL). The v2 test was used to assess differences between survival during chewing simulation. UNIANOVA was used to assess the effect of the variables on first damage and on failure load of the specimens during fracture testing. 2.2. Finite element analysis The FE models had the same dimensions as the tested samples for the resin block, fiber post, composite filling and crown. Mean
values for all gathered teeth were used for the dimensions of the supposed elliptical cross-section and the root length of the virtual tooth. The cement layer between the crown and tooth was modeled with a constant thickness of 0.1 mm (Fig. 1b). In addition to the in vitro conditions ferrule height (H = 1 or 2 mm), post length (L = 2 or 7 mm) and cementation technique (Ketac-cem or Panavia) different damage levels, i.e. idealized debonding states at the dentin/crown and dentin/composite core interfaces were investigated: A1, intact restoration with Panavia; A2, intact restoration with Ketac-cem; B, debonding at the dentin/crown interface (modeled between the cement and crown); C, additional debonding at the dentin/composite core interface (Fig. 1d). For crowns cemented using Ketac-cem there was no adhesive bonding at the dentin/crown interface, i.e. the opening of a gap between dentin and crown, as can be seen in the deformed state for case A2 in Fig. 1d, could not be restricted by tensile stresses. However, a relative sliding movement of the crown parallel to the dentin surface was blocked by the cement layer. Such a relative sliding movement occurred at the crown/dentin interface for ferrule heights H > 1 mm. This explains the different intact states when using adhesives (Panavia) or glass ionomer cements (Ketac-cem). Bonding was perfect at the complete crown/dentin interface when the crowns were luted (case A1). ‘Bonding’ (restriction of the relative sliding movement) took place in areas with a constant taper angle (1 mm above the finish line, case A2) for classic cementation. Because for H = 1 mm there was no bonding at the crown/dentin interface from the beginning, states A2 and B are identical, leading to 22 combinations of variables and, therefore, to 22 different FE models. The volumes were meshed completely with eight node hexahedral elements. For reasons of symmetry only half of the specimen geometry was used (Fig. 1c). Despite damage level A1, frictionless area-to-area contact (four node target and contact elements) was implemented at debonded interfaces associated with the actual damage level, thus tensile stresses were not transferred there. The final meshes, consisting of approximately 95,000 elements and 100,000 nodes, were obtained by mesh refinement in convergence studies. Before computation with ANSYS 11.0 (ANSYS Inc., Canonsburg, PA), loads, boundary conditions and material properties were defined. In addition to complete restriction of all nodes at the sides and bottom of the resin block, the nodes in the symmetry plane (x,z-plane) had to be restricted in the y-direction. Loads Fx = Fz = 100 N were applied to the FE models in the occlusal p reffiffiffi gion (Fig. 1c and e), which corresponded to a total load of 2 2 100 N = 283 N in the complete model. All materials except the fiber post were assumed to be homogeneous, isotropic and linear elastic. Young’s moduli and Poisson’s ratios are given in Table 1A. No reliable data for the five independent material properties could be found in the literature for the transverse isotropic fiber posts used in this study, nor could they be provided by the manufacturer. A representative cube (edge length 0.2 mm, 60% fiber) of glass fiber-reinforced epoxy resin was therefore generated on the basis of a micrograph of a post cross-section. Twenty node hexahedral elements were used and the final FE model consisted of approximately 54,000 elements and 230,000 nodes. The homogenized material properties derived from uniaxial tension and shear tests are given in Table 1B. The order of the indices of the Poisson’s ratios (mij is the negative ratio of strain in direction i and strain in direction j caused by normal stress in direction j) is of great importance, because mji = Ej/Eimij. The main objective of the FE computation was to identify the distribution of the external forces among the different internal substructures. These internal forces can only be seen when virtually separating crown and filling from the root (Fig. 1e). They were calculated by integration of the stresses acting on the virtually cutfree surface. In detail, the internal forces transferred at the ferrule,
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Fig. 1. (a) Experimental set-up of the in vitro tests with 0.4 mm tin foil between the mechanical device and sample. (b) Geometry and dimensions of the samples each consisting of (top down) a standardized CoCr alloy crown, cement layer, composite core, fiber post, tooth (dentin), gutta percha and resin block. (c) FE model (typical) with mesh refinement in the regions of interest. (d) Damage levels simulating different debonding states, i.e. intact states for both cementation techniques (cases A1 and A2), debonding at the crown/dentin interface (case B) and additional debonding at the dentin/composite core interface (case C). (e) Transfer of external loads (Fx, Fz) to internal substructures (fer, ferrule; cem, cement; com, composite core; post, fiber post; l, loaded side; r, remote side). At the section through the restoration presented all internal forces have to equilibrate the external forces. Table 1A Properties of the homogeneous, isotropic materials [26–28]. Material a
Remanium Rebilda SCa Ketac-cem Panavia Palapressa Gutta percha Dentin Glassa Epoxy resina a
E (GPa)
m ()
200.0 6.0 22.0 18.6 3.0 0.1 18.0 60.0 3.0
0.30 0.35 0.35 0.28 0.35 0.40 0.30 0.25 0.35
Information provided by the respective manufacturer.
Table 1B Properties of the fiber-reinforced post materials (fibers oriented in the z-direction). Ex = Ey Ez
mxy mxz = myz Gxy Gxz = Gyz
13.5 GPa 39.0 GPa 0.350 0.285 5.0 GPa 6.5 GPa
Ei, Young’s modulus in direction i, (mij is the negative ratio of strain in direction i and strain in direction j caused by normal stress in direction j); Gij, shear modulus in the i, j-plane.
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cement layer, composite core and fiber post were evaluated on the loaded (index l) and remote (index r) sides (Fig. 1e). Together, all internal forces have to equal the external force. The internal forces, the maximum tensile stresses – which are most critical for brittle materials – and stresses normal and parallel to the material interfaces – which may not exceed bond strength values – were also of interest and were therefore analyzed. 3. Results 3.1. Chewing simulation There was a difference between specimens with different ferrule heights. In the Ketac-cem and Panavia groups 100% and 25% of the specimens, respectively, failed in restorations with a ferrule height of 1 mm. In contrast, in the 2 mm ferrule group 37.5% of the specimens cemented with Ketac-cem and 12.5% cemented using Panavia failed. This different failure during chewing simulation was statistically significant (v2 test, P = 0.002). In this context the effect of cementation technique was also significant (P < 0.001). In contrast, there was no significant difference between failure during chewing simulation of restorations with long and short posts (v2 test, P = 0.599). 3.2. Fracture tests Three measurements were documented: (1) the load F1d at which damage first occurred, i.e. when a decrease in the stiffness
of the specimen was observed; (2) the ratio of stiffness after and before first damage; (3) the ultimate load Fu the specimen could withstand (Fig. 2). After first damage, which occurred at mean values of F1d between 158 and 220 N for crowns surviving chewing simulation, the remaining stiffness was between 50% and 78% of the initial stiffness, resulting in larger deflections of the restoration under the same load conditions (Table 2A). This decrease in stiffness was more pronounced for restorations cemented using Ketac-cem than for those cemented using Panavia (approximately 10% difference). The mean ultimate loads, which were higher for restorations cemented using Panavia (P = 0.011 for H = 2 mm), ranged between 231 and 378 N. Results from UNIANOVA including all specimens showed that the effect of both ferrule height and cementation technique were significant (P < 0.05), whereas post length had no significant influence. The mode of fracture (Table 2B) was highly dependent on ferrule height. For restorations with ferrule height H = 1 mm the crown, filling and fiber post were usually decemented. For ferrule height H = 2 mm tooth fractures starting at the ferrule on the remote side were most common.
3.3. FE simulations FE models with damage level A1 (no debonding) were linear elastic. For FE models with other damage levels an almost linear relationship between the magnitudes of the internal forces (stresses integrated over the regions of interest) and external forces was observed. Therefore, the relative internal forces, i.e. the ratio of internal
Fig. 2. Typical force–displacement diagram obtained from the in vitro tests at a cross-head speed of 0.5 mm min1. The diagram also contains the definitions for first damage F1d and ultimate load Fu and those for stiffnesses k1 and k2 before and after first damage.
Table 2A Results from in vitro experiments with different ferrule heights (H) and post lengths (L). Ferrule height 1 mm n Ketac-cem L = 2 mm L = 7 mm
0 0
Panavia L = 2 mm L = 7 mm
6 6
2 mm F1d (N)
170 ± 42 158 ± 41
Fu (N)
231 ± 72 262 ± 71
k2/k1 (%)
50 ± 30 55 ± 17
n
F1d (N)
Fu (N)
k2/k1 (%)
6 4
180 ± 32 186 ± 25
240 ± 54 296 ± 40
63 ± 10 63 ± 12
6 8
217 ± 39 220 ± 89
340 ± 96 378 ± 103
78 ± 6 73 ± 10
n, number of samples surviving the chewing simulation; F1d, load at first damage; Fu, ultimate load; k2/k1, ratio of stiffnesses after and before first damage.
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M. Schmitter et al. / Acta Biomaterialia 6 (2010) 3747–3754 Table 2B Failure modes observed in in vitro tests (chewing simulation and fracture tests). Observed failure mode
Crown, core, and post decemented Tooth fracture starting above or at the finish line Root fracture (below finish line) Crown decemented
Ferrule height 1 mm
Ferrule height 2 mm
Post length 7 mm
Post length 2 mm
Post length 7 mm
Post length 2 mm
Ketac
Panavia
Ketac
Panavia
Ketac
Panavia
Ketac
Panavia
7a
6 2
8
4 4
2 5 1
4 4
6 2
5 3
1
The number of fractures associated with each of the four failure modes is given for each group of specimens (n = 8) differing in ferrule height (H), post length (L) and cementation technique. a In one sample the post was damaged.
forces to external force, had the same value for any magnitude of external force. For stresses in the contact areas, however, a linear relationship was not observed, because contact area size depended on the magnitude of the force. Consequently, only stresses at a sufficient distance from the contact regions can be interpolated when other than the actual magnitude of the external force is of interest. The distribution of relative forces for ferrule height H = 2 mm is displayed in Fig. 3. Fig. 3a illustrates the effect of post length and Fig. 3b the effect of cementation technique for the different (virtual) damage levels. Positive values refer to positive directions of the coordinate system (Fig. 1e). It is apparent that the results for both post lengths are almost identical (Fig. 3a), i.e. post length has a minor effect on force distribution. For the intact restorations (state A1 or A2) the forces were almost exclusively transferred at the dentin/crown interface, because of the high stiffness of the crown compared with that of the composite core or fiber post. In
the z-direction especially, high internal forces occurred: Ffer,l 200% of the external z-force, transferred mainly by compression on the loaded side, and Ffer,r 100% of the external z-force, transferred mainly by tension on the remote side. The results for ferrule height H = 1 mm are not displayed because the force distributions were similar to those presented in Fig. 3, but with one difference – because the complete dentin/crown interface was debonded from the beginning for the small ferrule height (state A2 was identical to B) when Ketac-cem was used for cementation, the force distribution showed the same characteristics as state B for ferrule height H = 2 mm. Even in this damaged state, the post contributed only very small forces. The post did not contribute to load transfer until damage level C was reached, i.e. until the bond between the composite core and dentin failed. Because the stresses at critical interfaces were of most interest, individual x0 ,y0 ,z0 -coordinate systems were defined as follows for
Fig. 3. Distribution of relative internal forces, i.e. the internal forces are given as percentages of the external forces, for all damage levels and (a) H = 2 mm, cementation using Panavia, and both post lengths, and (b) H = 2 mm, L = 2 mm and both cementation techniques. These figures demonstrate how effective each structure is for load transfer.
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each finite element located at an interface: z0 -axis perpendicular to the dentin surface, x0 -axis oriented in a circumferential direction, y0 -axis following the slope line (Fig. 4a). These coordinate systems enabled quantitative evaluation (Table 3) of normal stresses (rz0 ) and shear stresses (rz0 x0 and rz0 y0 ) transferred at the complete dentin/crown and dentin/composite core interface areas (Fig. 5) and normal stresses inside the dentin surface (ry0 ,) (Fig. 4b–d). Maximum tensile stresses (rI) were determined for the fiber post. Results for H = 2 mm and L = 2 mm are summarized in Table 3.
4. Discussion
4.1. In vitro tests
Fig. 5. Distribution of normal stresses rz0 at the dentin/composite core and dentin/ crown interface (positive values, tension; negative values, compression) for ferrule height H = 2 mm, post length L = 2 mm comparing the initial states after cementation using Panavia and Ketac-cem. Because no tensile stresses, which occur at the remote side (right side of the image), can be transferred to the ferrule with the glass ionomer cement (Ketac-cem) the differences between the two cementation techniques become obvious.
The in vitro tests showed that both ferrule height and cementation technique of the final restoration had a significant effect on the ultimate load that the crown–core–post complex could withstand. It was also shown that failures were usually reversible, but that in some cases irreversible (root) fracture occurred. This result is in accord with other studies [15].
Numerous studies have assessed different aspects of the use of posts [16,17] and many have revealed that ferrule height is very important to fracture resistance [11,18]. This result was confirmed by this study. Since for a constant crown height a reduced ferrule height will result in a higher lever arm for the horizontal force component combined with reduced mechanical retention, these
Although FEA has been used in several studies reported in the literature, this study is the first to combine in vitro tests and FEA when assessing the effect of different variables.
Fig. 4. (a) Definition of individual x0 ,y0 ,z0 -coordinate systems for each finite element adjacent to the interface areas with the z0 -axis perpendicular to the interface surface and the x0 -axis oriented in the circumferential direction. The two coordinate systems displayed are representative of all defined coordinate systems with these coordinate systems normal (rz0 ) and shear stresses (rz0 x0 , rz0 y0 ) transferred at the interfaces and normal stresses within the dentin surface (rx0 , ry0 ) could be evaluated. (b–d) Normal stresses within the dentin surface in the y0 -direction (positive values, tension; negative values, compression) for ferrule height H = 2 mm, post length L = 2 mm, cementation technique Panavia are depicted for (b) damage level A1, (c) damage level B and (d) damage level C.
Table 3 Maximum normal (rz0 ,min, greatest compressive stress; rz0 ,max, greatest tensile stress) and shear stresses (rz0 y0 ) acting at the dentin/crown and dentin/composite core interfaces and tensile stresses inside the dentin surface (ry0 , highest tensile stress in the slope direction) and fiber post (rI, maximum tensile stress). Dentin/crown interface
A1, Panavia A2, Ketac-cem B, Panavia C, Panavia
Dentin
Post
rz´,min (MPa)
r´z,max (MPa)
rz´y´,max (MPa)
r´z,min (MPa)
Dentin/composite core interface
r´z,max (MPa)
r´zy´,max (MPa)
ry´,max (MPa)
rI (MPa)
76 98 165 218
54 40 22 16
32 33 0 0
12 15 110 119
9 16 90 486
7 13 22 261
16 27 96 66
19 34 56 751
All presented stress values refer to a bite force of 283 N and a restoration with ferrule height H = 2 mm and post length L = 2 mm.
M. Schmitter et al. / Acta Biomaterialia 6 (2010) 3747–3754
findings are conclusive. Many studies have also revealed that fiber post length is less important [8,10], which is confirmed, as we found no significant influence of fiber post length for both failures during chewing simulation and fracture load. However, other studies have not confirmed these results [19]. An explanation for the minor influence of post length is that in the intact state the post cannot contribute much resistance in a bending dominated load case due to its central position. Thus, the mean recorded first damage loads for restored teeth differing only in post length were nearly equal. The slightly higher, but not significantly so, ultimate loads for long posts may be due to the higher pull-out resistance. Finally, some studies have shown that cementation technique in the final restoration also affects fracture load [14]. This, again, is in good agreement with our results: resin-bonded restorations performed better with regard to ultimate load, which may be explained by the higher bond strengths and the ability to transfer tensile stresses at the crown/dentin interface, in contrast to classical cementation. Consequently, first damage starts later and higher forces are needed for complete debonding of the whole interface area. Again, however, other studies have not confirmed these results [20], emphasizing the need to use standardized in vitro study designs [21] and/or other methods (e.g. FEA) for a direct comparison of results. When looking at the failure modes, however, it becomes clear that enhancement of ultimate load is an ambiguous result for a clinician. Higher ultimate loads may reduce failures in vivo, but the risk of irreversible failure may be increased.
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the dentin/composite core interface. This value exceeds reported bond strengths, i.e. failure should occur at a lower load. Such an effect is even more pronounced for the upper part of the dentin/post interface, i.e. a short post will probably be pulled out when the bond between crown and dentin fails. This mode of failure was the most prominent in these in vitro tests (Table 2B) in the ferrule H = 1 mm group and is responsible for the finding in other studies that failures in teeth restored using fiber-reinforced posts are usually reversible [17,25]. Some root fractures were observed (Table 2B) after first damage exclusively in the ferrule H = 2 mm group. This is comprehensible, because the results of the FEA (Fig. 4b–d) show that high tensile stresses occur within the prepared tooth surface on the remote side. Because these stresses reach a maximum value (Table 3 and Fig. 4c) after debonding of the crown/dentin interface, i.e. damage level B, tooth fractures are most likely to occur in this state. Whether a tooth fractures or the dentin/composite core interface fails depends on both the stresses in operation and their strengths. Restorations with a low ferrule height (H = 1 mm) and cementation using Ketac-cem (? damage level B from the beginning) failed during chewing simulation. In this case stresses at the dentin/composite core interface were much higher (Table 3 shows this for H = 2 mm as an example), in contrast to maximum stresses occurring in the interface areas for all other restorations (? start with intact states A1 and A2). This might explain why the ageing process was more critical for this group. For a clinician this demonstrates that the final restoration should be anchored by adhesive cementation when the ferrule height is small.
4.2. FEA The results of this study reveal that agreement between the in vitro tests and FE computations is convincing when first failure is analyzed. For H = 2 mm and L = 2 mm in the in vitro tests the mean value of F1d for resin-bonded restorations was 217 N. Therefore, mean bond strength at the dentin/crown interface was approximately 217 N/289 N 54 MPa = 41 MPa, in good agreement with values given in the literature [22]. Standardization of in vitro tests is challenging and FEA seems to be the method of choice, as seen in other disciplines (e.g. engineering). In this context it is worthy of note that FEA calls into question the use of a post to optimize the rigidity of intact restorations. This result is not surprising, because the post is positioned along the tooth axis and cannot contribute much resistance to ‘bending’ of the filling under eccentric and/or horizontal bite forces. Technically, therefore, insertion of multiple posts might be useful [23], which is clinically practically impossible (especially in single rooted teeth). Although FEA calls into question the use of single posts, clinically their use might have benefits, e.g. the filling material can be more easily fixed [24]. In addition to this benefit of FEA, the method enables assessment of the effects of many variables, which explains the efforts expended to establish FEA in dentistry. FEA is, however, always dependent on model assumptions and simplifications, e.g. material properties, constitutive equations, geometry and boundary conditions, so post-processing and interpretation of the results is challenging. Nevertheless, if all assumptions and material properties resemble the real situation, FEA is a powerful tool. In this study the results from FEA and in vitro tests were compared, with excellent agreement. Further calculations could therefore be performed to assess those aspects, e.g. internal load transfer, which are difficult to investigate using in vitro models. 4.3. Failure modes The stresses reported refer to a resultant force of 289 N. This load is arbitrary, because stresses at other loads may be interpolated. In Table 3, a maximum tensile stress of 90 MPa is given for
5. Conclusions Within the limitations of this study the following conclusions can be drawn. Finite element analysis precisely predicted the load at first damage. Centrally positioned fiber-reinforced posts do not contribute to load transfer as long as the bonding between the tooth and composite core is intact. Failure loads were higher for resin-bonded crowns than for conventionally cemented crowns. Crowns with small ferrule heights should be resin bonded.
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[11] Schwartz RS, Robbins JW. Post placement and restoration of endodontically treated teeth: a literature review. J Endod 2004;30:289–301. [12] Boschian Pest L, Guidotti S, Pietrabissa R, Gagliani M. Stress distribution in a post-restored tooth using the three-dimensional finite element method. J Oral Rehabil 2006;33:690–7. [13] Pegoretti A, Fambri L, Zappini G, Bianchetti M. Finite element analysis of a glass fiber reinforced composite endodontic post. Biomaterials 2002;23:2667–82. [14] Schmitter M, Huy C, Ohlmann B, Gabbert O, Gilde H, Rammelsberg P. Fracture resistance of upper and lower incisors restored with glass fiber reinforced posts. J Endod 2006;32:328–30. [15] Hayashi M, Takahashi Y, Imazato S, Ebisu S. Fracture resistance of pulpless teeth restored with post–cores and crowns. Dent Mater 2006;22:477–85. [16] Rosentritt M, Furer C, Behr M, Lang R, Handel G. Comparison of in vitro fracture strength of metallic and tooth-coloured posts and cores. J Oral Rehabil 2000;27:595–601. [17] Cormier CJ, Burns DR, Moon P. In vitro comparison of the fracture resistance and failure mode of fiber, ceramic, and conventional post systems at various stages of restoration. J Prosthodont 2001;10:26–36. [18] Peroz I, Blankenstein F, Lange KP, Naumann M. Restoring endodontically treated teeth with posts and cores – a review. Quintessence Int 2005;36:737–46. [19] Buttel L, Krastl G, Lorch H, Naumann M, Zitzmann NU, Weiger R. Influence of post fit and post length on fracture resistance. Int Endod J 2009;42:47–53.
[20] al-Hazaimeh N, Gutteridge DL. An in vitro study into the effect of the ferrule preparation on the fracture resistance of crowned teeth incorporating prefabricated post and composite core restorations. Int Endod J 2001;34:40–6. [21] Naumann M, Metzdorf G, Fokkinga W, et al. Influence of test parameters on in vitro fracture resistance of post-endodontic restorations: a structured review. J Oral Rehabil 2009;36:299–312. [22] Salameh Z, Sorrentino R, Ounsi HF, Sadig W, Atiyeh F, Ferrari M. The effect of different full-coverage crown systems on fracture resistance and failure pattern of endodontically treated maxillary incisors restored with and without glass fiber posts. J Endod 2008;34:842–6. [23] Maceri F, Martignoni M, Vairo G. Mechanical behavior of endodontic restorations with multiple prefabricated posts: a finite-element approach. J Biomech 2007;40:2386–98. [24] Ounsi HF, Salameh Z, Carvalho CA, Cantoro A, Grandini S, Ferrari M. Bond strength of composite core build-up materials to fiber-reinforced posts: a microtensile comparison between conventional and wet-ethanol bonding systems. J Adhes Dent 2009;11:375–80. [25] Bitter K, Kielbassa AM. Post-endodontic restorations with adhesively luted fiber-reinforced composite post systems: a review. Am J Dent 2007;20:353–60. [26] Lanza A, Aversa R, Rengo S, Apicella D, Apicella A. 3D FEA of cemented steel, glass and carbon posts in a maxillary incisor. Dent Mater 2005;21:709–15. [27] Mori K, Inage H, Kawamoto R, et al. Ultrasonic monitoring of the setting of glass ionomer luting cements. Eur J Oral Sci 2008;116:72–6. [28] Camps J, Pertot W. Young’s modulus of warm and cold gutta-percha. Endod Dent Traumatol 1996;12:50–3.
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Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Teeth restored using fiber-reinforced posts: In vitro fracture tests and finite element analysis M. Schmitter a, P. Rammelsberg a, J. Lenz b, S. Scheuber c, K. Schweizerhof b, S. Rues a,b,* a
Department of Prosthodontics, University of Heidelberg, Germany Research Group on Biomechanics, Institute for Mechanics, University of Karlsruhe, Germany c Department of Fixed Prosthodontics, University of Bern, Switzerland b
a r t i c l e
i n f o
Article history: Received 6 October 2009 Received in revised form 1 March 2010 Accepted 8 March 2010 Available online 19 March 2010 Keywords: Dentistry Endodontic posts Preparation design In vitro tests Finite element analysis
a b s t r a c t In dentistry the restoration of decayed teeth is challenging and makes great demands on both the dentist and the materials. Hence, fiber-reinforced posts have been introduced. The effects of different variables on the ultimate load on teeth restored using fiber-reinforced posts is controversial, maybe because the results are mostly based on non-standardized in vitro tests and, therefore, give inhomogeneous results. This study combines the advantages of in vitro tests and finite element analysis (FEA) to clarify the effects of ferrule height, post length and cementation technique used for restoration. Sixty-four single rooted premolars were decoronated (ferrule height 1 or 2 mm), endodontically treated and restored using fiber posts (length 2 or 7 mm), composite fillings and metal crowns (resin bonded or cemented). After thermocycling and chewing simulation the samples were loaded until fracture, recording first damage events. Using UNIANOVA to analyze recorded fracture loads, ferrule height and cementation technique were found to be significant, i.e. increased ferrule height and resin bonding of the crown resulted in higher fracture loads. Post length had no significant effect. All conventionally cemented crowns with a 1-mm ferrule height failed during artificial ageing, in contrast to resin-bonded crowns (75% survival rate). FEA confirmed these results and provided information about stress and force distribution within the restoration. Based on the findings of in vitro tests and computations we concluded that crowns, especially those with a small ferrule height, should be resin bonded. Finally, centrally positioned fiber-reinforced posts did not contribute to load transfer as long as the bond between the tooth and composite core was intact. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Since the introduction of fiber-reinforced posts [1,2] the assessment of their different mechanical properties [3] has revealed that survival [4], failure characteristics [5] and fatigue resistance [6] are acceptable and, consequently, that clinical use is possible. Most studies have found that sufficient ferrule height is essential [7,8]. The results obtained for other variables were inconsistent – some studies found post length to be crucial [9] while others could not confirm this [10]. Consequently, it might be useful to assess the effect of different variables using reliable methods. Although clinical trials would be the best way to assess the effects of different variables [7], this type of study is time consuming, expensive and ethically questionable. Other types of study are helpful, including in vitro studies [11] and finite element analyses (FEA) [12,13]. Both methods have advantages and disadvantages. In vitro tests can
* Corresponding author at: Department of Prosthodontics, University of Heidelberg, Germany. E-mail address: [email protected] (S. Rues).
simulate almost realistic conditions, but are time consuming and only a limited number of specimens can be tested. The transfer of results from in vitro tests to clinical situations is also challenging. FEA enables simulation of any situation, but the accuracy of the results depends on construction of an appropriate model. A meticulous construction process is therefore necessary. The objective of this study was to combine the advantages of both methods to assess the effects of fiber post length, cementation technique, using either a resin or a glass ionomer cement, and ferrule height on the fracture load of artificial crowns anchored with fiber posts. 2. Material and methods 2.1. In vitro tests Sixty-four intact single rooted human premolars were collected directly after extraction and stored in 0.1% thymol solution for 6 weeks (at most). The teeth were randomly assigned to eight groups, endodontically treated and the roots were filed to ISO Stan-
1742-7061/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actbio.2010.03.012
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dard 35 (taper 2%) (FlexMaster Kit, VDW, Munich, Germany). After rinsing (3.0% H2O2) the roots were obturated with gutta percha (Roeko, Langenau, Germany) and resin sealant (AH plus, Dentsply/De Trey, Constance, Germany). The teeth were decoronated 1 mm coronal to the most incisal point of the cement–enamel junction. The root canals were enlarged to ISO Standard 90 (0.9 mm diameter, length 25 mm) using a reamer (Brasseler, Lemgo, Germany) [14], roughened (diamond abrasive, Brasseler) and preconditioned using 37% phosphoric acid and a single dose of Excite DSC Soft Touch (Ivoclar-Vivadent, Schaan, Liechtenstein). The posts (ER-Dentin-post-yellow, 60% glass fiber, caliber 090, apical diameter 0.9 mm, Brasseler) were tribochemically coated with Rocatec-pre (110 lm at 2 bar; 3MEspe, Seefeld, Germany) then Rocatec-plus (3MEspe). Silanization was performed with Monobond-S (Ivoclar-Vivadent). The post was inserted 2 mm into the root canal of half the teeth, 7 mm for the other half. All posts were cemented with Variolink II (Ivoclar-Vivadent). The teeth were treated with 34.5% phosphoric acid (Vocoid, Voco, Cuxhaven, Germany), Solobond-Plus primer and SolobondPlus adhesive (Ivoclar-Vivadent). Subsequently, the cores were built up using Rebilda-SC-Blue (Voco). All teeth were prepared at an angle of 2° using a high speed turbine (Bien-Air-Dental SA, Bienne, Switzerland) mounted in a parallel milling machine (Fraesgeraet-F1, Degussa, Frankfurt, Germany) and using special burs (Sirius-Prothetik-Systems, Hafner, Pforzheim, Germany), which create a chamfer finish line. Because the angle was 2°, no part of the preparation was parallel to the long axis of the tooth. For half the teeth the ferrule height (H) was 1 mm, for the other half 2 mm. The mean height of the preparations (ferrule height + filling) was 5.6 mm. Silicone impressions (Adisil, Siladent, Munich, Germany) were taken. Casts were made from stone gypsum (GC-Fujirock, GC Europe, Leuven, Belgium) and standardized artificial crowns were fabricated (Remanium-Star, Dentaurum, Ispringen, Germany). The axial thickness of the parallel milled crowns was 0.5 mm and the occlusal thickness was 1 mm. All crowns had a standardized occlusal region (Fig. 1a–c). In one of the groups the crowns were cemented with a chemical resin cement (Panavia F 2.0, Kuraray, Japan). The crowns were sand-blasted (50 lm aluminum oxide, 2.5 bar) and an alloy primer (Kuraray) was applied. The ferrule area was etched with 35% phosphoric acid (Kuraray) and primed (New Bond, Kuraray). In the other group the crowns were cemented using a glass ionomer cement (Ketac-cem, 3MEspe). Finally, the roots of all restored teeth were embedded in a cubic resin block (edge length 27 mm) (Palapress, Heraeus Kulzer, Hanau, Germany). The distance between the block surface and finish line was 2 mm (Fig. 1b). All teeth were exposed to 10,000 thermal cycles between 6.5 and 60 °C (Willytec, Graefelfing, Germany) and 600,000 cycles in a chewing simulator (m = 5 kg, v = 30 mm/s ? maximum force 70–80 N, static force 49 N) (Willytec). The angle between the tooth axis and the loading direction was 45° (Fig. 1a). All specimens surviving the chewing simulation were loaded until fracture in a universal testing machine with a cross-head speed of 0.5 mm min1 (Universal-Pruefmaschine 1445, Zwick, Ulm, Germany). Loads were applied at an angle of 45° (Fig. 1a, b and e). Statistical analysis was performed using SPSS (SPSS Inc., Chicago, IL). The v2 test was used to assess differences between survival during chewing simulation. UNIANOVA was used to assess the effect of the variables on first damage and on failure load of the specimens during fracture testing. 2.2. Finite element analysis The FE models had the same dimensions as the tested samples for the resin block, fiber post, composite filling and crown. Mean
values for all gathered teeth were used for the dimensions of the supposed elliptical cross-section and the root length of the virtual tooth. The cement layer between the crown and tooth was modeled with a constant thickness of 0.1 mm (Fig. 1b). In addition to the in vitro conditions ferrule height (H = 1 or 2 mm), post length (L = 2 or 7 mm) and cementation technique (Ketac-cem or Panavia) different damage levels, i.e. idealized debonding states at the dentin/crown and dentin/composite core interfaces were investigated: A1, intact restoration with Panavia; A2, intact restoration with Ketac-cem; B, debonding at the dentin/crown interface (modeled between the cement and crown); C, additional debonding at the dentin/composite core interface (Fig. 1d). For crowns cemented using Ketac-cem there was no adhesive bonding at the dentin/crown interface, i.e. the opening of a gap between dentin and crown, as can be seen in the deformed state for case A2 in Fig. 1d, could not be restricted by tensile stresses. However, a relative sliding movement of the crown parallel to the dentin surface was blocked by the cement layer. Such a relative sliding movement occurred at the crown/dentin interface for ferrule heights H > 1 mm. This explains the different intact states when using adhesives (Panavia) or glass ionomer cements (Ketac-cem). Bonding was perfect at the complete crown/dentin interface when the crowns were luted (case A1). ‘Bonding’ (restriction of the relative sliding movement) took place in areas with a constant taper angle (1 mm above the finish line, case A2) for classic cementation. Because for H = 1 mm there was no bonding at the crown/dentin interface from the beginning, states A2 and B are identical, leading to 22 combinations of variables and, therefore, to 22 different FE models. The volumes were meshed completely with eight node hexahedral elements. For reasons of symmetry only half of the specimen geometry was used (Fig. 1c). Despite damage level A1, frictionless area-to-area contact (four node target and contact elements) was implemented at debonded interfaces associated with the actual damage level, thus tensile stresses were not transferred there. The final meshes, consisting of approximately 95,000 elements and 100,000 nodes, were obtained by mesh refinement in convergence studies. Before computation with ANSYS 11.0 (ANSYS Inc., Canonsburg, PA), loads, boundary conditions and material properties were defined. In addition to complete restriction of all nodes at the sides and bottom of the resin block, the nodes in the symmetry plane (x,z-plane) had to be restricted in the y-direction. Loads Fx = Fz = 100 N were applied to the FE models in the occlusal p reffiffiffi gion (Fig. 1c and e), which corresponded to a total load of 2 2 100 N = 283 N in the complete model. All materials except the fiber post were assumed to be homogeneous, isotropic and linear elastic. Young’s moduli and Poisson’s ratios are given in Table 1A. No reliable data for the five independent material properties could be found in the literature for the transverse isotropic fiber posts used in this study, nor could they be provided by the manufacturer. A representative cube (edge length 0.2 mm, 60% fiber) of glass fiber-reinforced epoxy resin was therefore generated on the basis of a micrograph of a post cross-section. Twenty node hexahedral elements were used and the final FE model consisted of approximately 54,000 elements and 230,000 nodes. The homogenized material properties derived from uniaxial tension and shear tests are given in Table 1B. The order of the indices of the Poisson’s ratios (mij is the negative ratio of strain in direction i and strain in direction j caused by normal stress in direction j) is of great importance, because mji = Ej/Eimij. The main objective of the FE computation was to identify the distribution of the external forces among the different internal substructures. These internal forces can only be seen when virtually separating crown and filling from the root (Fig. 1e). They were calculated by integration of the stresses acting on the virtually cutfree surface. In detail, the internal forces transferred at the ferrule,
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Fig. 1. (a) Experimental set-up of the in vitro tests with 0.4 mm tin foil between the mechanical device and sample. (b) Geometry and dimensions of the samples each consisting of (top down) a standardized CoCr alloy crown, cement layer, composite core, fiber post, tooth (dentin), gutta percha and resin block. (c) FE model (typical) with mesh refinement in the regions of interest. (d) Damage levels simulating different debonding states, i.e. intact states for both cementation techniques (cases A1 and A2), debonding at the crown/dentin interface (case B) and additional debonding at the dentin/composite core interface (case C). (e) Transfer of external loads (Fx, Fz) to internal substructures (fer, ferrule; cem, cement; com, composite core; post, fiber post; l, loaded side; r, remote side). At the section through the restoration presented all internal forces have to equilibrate the external forces. Table 1A Properties of the homogeneous, isotropic materials [26–28]. Material a
Remanium Rebilda SCa Ketac-cem Panavia Palapressa Gutta percha Dentin Glassa Epoxy resina a
E (GPa)
m ()
200.0 6.0 22.0 18.6 3.0 0.1 18.0 60.0 3.0
0.30 0.35 0.35 0.28 0.35 0.40 0.30 0.25 0.35
Information provided by the respective manufacturer.
Table 1B Properties of the fiber-reinforced post materials (fibers oriented in the z-direction). Ex = Ey Ez
mxy mxz = myz Gxy Gxz = Gyz
13.5 GPa 39.0 GPa 0.350 0.285 5.0 GPa 6.5 GPa
Ei, Young’s modulus in direction i, (mij is the negative ratio of strain in direction i and strain in direction j caused by normal stress in direction j); Gij, shear modulus in the i, j-plane.
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cement layer, composite core and fiber post were evaluated on the loaded (index l) and remote (index r) sides (Fig. 1e). Together, all internal forces have to equal the external force. The internal forces, the maximum tensile stresses – which are most critical for brittle materials – and stresses normal and parallel to the material interfaces – which may not exceed bond strength values – were also of interest and were therefore analyzed. 3. Results 3.1. Chewing simulation There was a difference between specimens with different ferrule heights. In the Ketac-cem and Panavia groups 100% and 25% of the specimens, respectively, failed in restorations with a ferrule height of 1 mm. In contrast, in the 2 mm ferrule group 37.5% of the specimens cemented with Ketac-cem and 12.5% cemented using Panavia failed. This different failure during chewing simulation was statistically significant (v2 test, P = 0.002). In this context the effect of cementation technique was also significant (P < 0.001). In contrast, there was no significant difference between failure during chewing simulation of restorations with long and short posts (v2 test, P = 0.599). 3.2. Fracture tests Three measurements were documented: (1) the load F1d at which damage first occurred, i.e. when a decrease in the stiffness
of the specimen was observed; (2) the ratio of stiffness after and before first damage; (3) the ultimate load Fu the specimen could withstand (Fig. 2). After first damage, which occurred at mean values of F1d between 158 and 220 N for crowns surviving chewing simulation, the remaining stiffness was between 50% and 78% of the initial stiffness, resulting in larger deflections of the restoration under the same load conditions (Table 2A). This decrease in stiffness was more pronounced for restorations cemented using Ketac-cem than for those cemented using Panavia (approximately 10% difference). The mean ultimate loads, which were higher for restorations cemented using Panavia (P = 0.011 for H = 2 mm), ranged between 231 and 378 N. Results from UNIANOVA including all specimens showed that the effect of both ferrule height and cementation technique were significant (P < 0.05), whereas post length had no significant influence. The mode of fracture (Table 2B) was highly dependent on ferrule height. For restorations with ferrule height H = 1 mm the crown, filling and fiber post were usually decemented. For ferrule height H = 2 mm tooth fractures starting at the ferrule on the remote side were most common.
3.3. FE simulations FE models with damage level A1 (no debonding) were linear elastic. For FE models with other damage levels an almost linear relationship between the magnitudes of the internal forces (stresses integrated over the regions of interest) and external forces was observed. Therefore, the relative internal forces, i.e. the ratio of internal
Fig. 2. Typical force–displacement diagram obtained from the in vitro tests at a cross-head speed of 0.5 mm min1. The diagram also contains the definitions for first damage F1d and ultimate load Fu and those for stiffnesses k1 and k2 before and after first damage.
Table 2A Results from in vitro experiments with different ferrule heights (H) and post lengths (L). Ferrule height 1 mm n Ketac-cem L = 2 mm L = 7 mm
0 0
Panavia L = 2 mm L = 7 mm
6 6
2 mm F1d (N)
170 ± 42 158 ± 41
Fu (N)
231 ± 72 262 ± 71
k2/k1 (%)
50 ± 30 55 ± 17
n
F1d (N)
Fu (N)
k2/k1 (%)
6 4
180 ± 32 186 ± 25
240 ± 54 296 ± 40
63 ± 10 63 ± 12
6 8
217 ± 39 220 ± 89
340 ± 96 378 ± 103
78 ± 6 73 ± 10
n, number of samples surviving the chewing simulation; F1d, load at first damage; Fu, ultimate load; k2/k1, ratio of stiffnesses after and before first damage.
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M. Schmitter et al. / Acta Biomaterialia 6 (2010) 3747–3754 Table 2B Failure modes observed in in vitro tests (chewing simulation and fracture tests). Observed failure mode
Crown, core, and post decemented Tooth fracture starting above or at the finish line Root fracture (below finish line) Crown decemented
Ferrule height 1 mm
Ferrule height 2 mm
Post length 7 mm
Post length 2 mm
Post length 7 mm
Post length 2 mm
Ketac
Panavia
Ketac
Panavia
Ketac
Panavia
Ketac
Panavia
7a
6 2
8
4 4
2 5 1
4 4
6 2
5 3
1
The number of fractures associated with each of the four failure modes is given for each group of specimens (n = 8) differing in ferrule height (H), post length (L) and cementation technique. a In one sample the post was damaged.
forces to external force, had the same value for any magnitude of external force. For stresses in the contact areas, however, a linear relationship was not observed, because contact area size depended on the magnitude of the force. Consequently, only stresses at a sufficient distance from the contact regions can be interpolated when other than the actual magnitude of the external force is of interest. The distribution of relative forces for ferrule height H = 2 mm is displayed in Fig. 3. Fig. 3a illustrates the effect of post length and Fig. 3b the effect of cementation technique for the different (virtual) damage levels. Positive values refer to positive directions of the coordinate system (Fig. 1e). It is apparent that the results for both post lengths are almost identical (Fig. 3a), i.e. post length has a minor effect on force distribution. For the intact restorations (state A1 or A2) the forces were almost exclusively transferred at the dentin/crown interface, because of the high stiffness of the crown compared with that of the composite core or fiber post. In
the z-direction especially, high internal forces occurred: Ffer,l 200% of the external z-force, transferred mainly by compression on the loaded side, and Ffer,r 100% of the external z-force, transferred mainly by tension on the remote side. The results for ferrule height H = 1 mm are not displayed because the force distributions were similar to those presented in Fig. 3, but with one difference – because the complete dentin/crown interface was debonded from the beginning for the small ferrule height (state A2 was identical to B) when Ketac-cem was used for cementation, the force distribution showed the same characteristics as state B for ferrule height H = 2 mm. Even in this damaged state, the post contributed only very small forces. The post did not contribute to load transfer until damage level C was reached, i.e. until the bond between the composite core and dentin failed. Because the stresses at critical interfaces were of most interest, individual x0 ,y0 ,z0 -coordinate systems were defined as follows for
Fig. 3. Distribution of relative internal forces, i.e. the internal forces are given as percentages of the external forces, for all damage levels and (a) H = 2 mm, cementation using Panavia, and both post lengths, and (b) H = 2 mm, L = 2 mm and both cementation techniques. These figures demonstrate how effective each structure is for load transfer.
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each finite element located at an interface: z0 -axis perpendicular to the dentin surface, x0 -axis oriented in a circumferential direction, y0 -axis following the slope line (Fig. 4a). These coordinate systems enabled quantitative evaluation (Table 3) of normal stresses (rz0 ) and shear stresses (rz0 x0 and rz0 y0 ) transferred at the complete dentin/crown and dentin/composite core interface areas (Fig. 5) and normal stresses inside the dentin surface (ry0 ,) (Fig. 4b–d). Maximum tensile stresses (rI) were determined for the fiber post. Results for H = 2 mm and L = 2 mm are summarized in Table 3.
4. Discussion
4.1. In vitro tests
Fig. 5. Distribution of normal stresses rz0 at the dentin/composite core and dentin/ crown interface (positive values, tension; negative values, compression) for ferrule height H = 2 mm, post length L = 2 mm comparing the initial states after cementation using Panavia and Ketac-cem. Because no tensile stresses, which occur at the remote side (right side of the image), can be transferred to the ferrule with the glass ionomer cement (Ketac-cem) the differences between the two cementation techniques become obvious.
The in vitro tests showed that both ferrule height and cementation technique of the final restoration had a significant effect on the ultimate load that the crown–core–post complex could withstand. It was also shown that failures were usually reversible, but that in some cases irreversible (root) fracture occurred. This result is in accord with other studies [15].
Numerous studies have assessed different aspects of the use of posts [16,17] and many have revealed that ferrule height is very important to fracture resistance [11,18]. This result was confirmed by this study. Since for a constant crown height a reduced ferrule height will result in a higher lever arm for the horizontal force component combined with reduced mechanical retention, these
Although FEA has been used in several studies reported in the literature, this study is the first to combine in vitro tests and FEA when assessing the effect of different variables.
Fig. 4. (a) Definition of individual x0 ,y0 ,z0 -coordinate systems for each finite element adjacent to the interface areas with the z0 -axis perpendicular to the interface surface and the x0 -axis oriented in the circumferential direction. The two coordinate systems displayed are representative of all defined coordinate systems with these coordinate systems normal (rz0 ) and shear stresses (rz0 x0 , rz0 y0 ) transferred at the interfaces and normal stresses within the dentin surface (rx0 , ry0 ) could be evaluated. (b–d) Normal stresses within the dentin surface in the y0 -direction (positive values, tension; negative values, compression) for ferrule height H = 2 mm, post length L = 2 mm, cementation technique Panavia are depicted for (b) damage level A1, (c) damage level B and (d) damage level C.
Table 3 Maximum normal (rz0 ,min, greatest compressive stress; rz0 ,max, greatest tensile stress) and shear stresses (rz0 y0 ) acting at the dentin/crown and dentin/composite core interfaces and tensile stresses inside the dentin surface (ry0 , highest tensile stress in the slope direction) and fiber post (rI, maximum tensile stress). Dentin/crown interface
A1, Panavia A2, Ketac-cem B, Panavia C, Panavia
Dentin
Post
rz´,min (MPa)
r´z,max (MPa)
rz´y´,max (MPa)
r´z,min (MPa)
Dentin/composite core interface
r´z,max (MPa)
r´zy´,max (MPa)
ry´,max (MPa)
rI (MPa)
76 98 165 218
54 40 22 16
32 33 0 0
12 15 110 119
9 16 90 486
7 13 22 261
16 27 96 66
19 34 56 751
All presented stress values refer to a bite force of 283 N and a restoration with ferrule height H = 2 mm and post length L = 2 mm.
M. Schmitter et al. / Acta Biomaterialia 6 (2010) 3747–3754
findings are conclusive. Many studies have also revealed that fiber post length is less important [8,10], which is confirmed, as we found no significant influence of fiber post length for both failures during chewing simulation and fracture load. However, other studies have not confirmed these results [19]. An explanation for the minor influence of post length is that in the intact state the post cannot contribute much resistance in a bending dominated load case due to its central position. Thus, the mean recorded first damage loads for restored teeth differing only in post length were nearly equal. The slightly higher, but not significantly so, ultimate loads for long posts may be due to the higher pull-out resistance. Finally, some studies have shown that cementation technique in the final restoration also affects fracture load [14]. This, again, is in good agreement with our results: resin-bonded restorations performed better with regard to ultimate load, which may be explained by the higher bond strengths and the ability to transfer tensile stresses at the crown/dentin interface, in contrast to classical cementation. Consequently, first damage starts later and higher forces are needed for complete debonding of the whole interface area. Again, however, other studies have not confirmed these results [20], emphasizing the need to use standardized in vitro study designs [21] and/or other methods (e.g. FEA) for a direct comparison of results. When looking at the failure modes, however, it becomes clear that enhancement of ultimate load is an ambiguous result for a clinician. Higher ultimate loads may reduce failures in vivo, but the risk of irreversible failure may be increased.
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the dentin/composite core interface. This value exceeds reported bond strengths, i.e. failure should occur at a lower load. Such an effect is even more pronounced for the upper part of the dentin/post interface, i.e. a short post will probably be pulled out when the bond between crown and dentin fails. This mode of failure was the most prominent in these in vitro tests (Table 2B) in the ferrule H = 1 mm group and is responsible for the finding in other studies that failures in teeth restored using fiber-reinforced posts are usually reversible [17,25]. Some root fractures were observed (Table 2B) after first damage exclusively in the ferrule H = 2 mm group. This is comprehensible, because the results of the FEA (Fig. 4b–d) show that high tensile stresses occur within the prepared tooth surface on the remote side. Because these stresses reach a maximum value (Table 3 and Fig. 4c) after debonding of the crown/dentin interface, i.e. damage level B, tooth fractures are most likely to occur in this state. Whether a tooth fractures or the dentin/composite core interface fails depends on both the stresses in operation and their strengths. Restorations with a low ferrule height (H = 1 mm) and cementation using Ketac-cem (? damage level B from the beginning) failed during chewing simulation. In this case stresses at the dentin/composite core interface were much higher (Table 3 shows this for H = 2 mm as an example), in contrast to maximum stresses occurring in the interface areas for all other restorations (? start with intact states A1 and A2). This might explain why the ageing process was more critical for this group. For a clinician this demonstrates that the final restoration should be anchored by adhesive cementation when the ferrule height is small.
4.2. FEA The results of this study reveal that agreement between the in vitro tests and FE computations is convincing when first failure is analyzed. For H = 2 mm and L = 2 mm in the in vitro tests the mean value of F1d for resin-bonded restorations was 217 N. Therefore, mean bond strength at the dentin/crown interface was approximately 217 N/289 N 54 MPa = 41 MPa, in good agreement with values given in the literature [22]. Standardization of in vitro tests is challenging and FEA seems to be the method of choice, as seen in other disciplines (e.g. engineering). In this context it is worthy of note that FEA calls into question the use of a post to optimize the rigidity of intact restorations. This result is not surprising, because the post is positioned along the tooth axis and cannot contribute much resistance to ‘bending’ of the filling under eccentric and/or horizontal bite forces. Technically, therefore, insertion of multiple posts might be useful [23], which is clinically practically impossible (especially in single rooted teeth). Although FEA calls into question the use of single posts, clinically their use might have benefits, e.g. the filling material can be more easily fixed [24]. In addition to this benefit of FEA, the method enables assessment of the effects of many variables, which explains the efforts expended to establish FEA in dentistry. FEA is, however, always dependent on model assumptions and simplifications, e.g. material properties, constitutive equations, geometry and boundary conditions, so post-processing and interpretation of the results is challenging. Nevertheless, if all assumptions and material properties resemble the real situation, FEA is a powerful tool. In this study the results from FEA and in vitro tests were compared, with excellent agreement. Further calculations could therefore be performed to assess those aspects, e.g. internal load transfer, which are difficult to investigate using in vitro models. 4.3. Failure modes The stresses reported refer to a resultant force of 289 N. This load is arbitrary, because stresses at other loads may be interpolated. In Table 3, a maximum tensile stress of 90 MPa is given for
5. Conclusions Within the limitations of this study the following conclusions can be drawn. Finite element analysis precisely predicted the load at first damage. Centrally positioned fiber-reinforced posts do not contribute to load transfer as long as the bonding between the tooth and composite core is intact. Failure loads were higher for resin-bonded crowns than for conventionally cemented crowns. Crowns with small ferrule heights should be resin bonded.
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