e strength -integrated
of cantilevered prostheses
Robert B. Stewart, DDS, MS,a Ronald P. Desjardins, DMD, MSD,b William R. Laney, DMD, MS,b and Edmund Y. S. Chao, PhD” Ohio State University, College of Dentistry, Columbus, Ohio, and Mayo Clinic, Rochester, Minn. The design of the metal alloy framework in cantilevered sections of fixed tissueintegrated prostheses, is critical. Several cross-sectional designs have been advocated, including the popular L-shaped beam, which permits the economical use of space for tooth placement. The fatigue strengths of 15 L-shaped cantilevered framework sections of the same metal alloy were tested. The castings were divided into three groups of five according to vertical wall heights of 4,5, and 6 mm. Fatigue durability of each sample was determined by counting the number of cycles of vertical forces required to induce catastrophic failure. Statistical analysis revealed significant differences between all three groups in the cycles counted at failure (p < 0.0019). Fatigue strengths improved significantly with increasing vertical wall height of the L-shaped cantilevered frameworks. In addition, beam tlexure was shown to be indirectly proportional to fatigue strength. Theoretical beam deflection was calculated and shown to correlate with the actual beam deflection during the testing. Theoretical calculations in static bending specific for a cross-sectional design may aid in the predictability of fatigue strength. (J PROSTHET DENT 1992;68:83-92.)
eeent investigations have demonstrated that occlusal forces are concentrated at the cantilevered terminal abutment sections of fixed tissue-integrated prostheses (TIP).lm4 Lundgren et al1 found that nearly 55% of the total forces were registered in the posterior cantilevered sections with average values of 12 to 18 pounds. In a subsequent study, Falk et al4 demonstrated that the preferred posterior segment for chewing assumed nearly 40 % of the total load, while the contralateral cantilevered segment assumed 30 % . Lundgren et a1.2 by altering or eliminating posterior contacts, recorded mean chewing forces approximating 25 pounds and maximum chewing forces approaching 36 pounds on the cantilevered structure. Because of the magnitude of these forces, information regarding design requirements of the cantilevered framework for long-term clinical service would be beneficial in considering the available intermaxillary and buccolingual space of the patient (Fig. 1). In the early evolution of pros-
Based on a thesis submitted to the graduate faculty in partial fulfillment of the requirements for the MS degree, Mayo Graduate School of Medicine. “Associate Professor, Department of Restorative and Prosthetic Dentistry, Ohio State University, College of Dentistry; formerly prosthodontic resident, Mayo Clinic, Mayo Graduate School of Medicine. bConsultant in Prosthodontics, Department of Dentistry; Professor, Mayo Medical School. cProfessor, Department of Riomechanical Engineering, Mayo Medical School. 10/l/36544 TNE
thesis fabrication, clinicians reported prosthesis fracture primarily at the distal abutment and cantilever junction of 4.9 % , 17 % , and 46 % .5-7 Fatigue is the primary factor in clinical durability.4 8
Fatigue Fatigue of metal alloys consists of (1) the deformation and development of slip lines and bands of the material until the structure can withstand the applied stress by strain hardening, (2) the continuation of strain hardening until crack initiation (the predominant condition of structures under function), and (3) propagation of the crack until failure.g-ll The fatigue limit of a structure is affected by surface roughness, mechanical and physical properties of the material, and design of the structure. The mechanical properties of the material and a design that minimizes deflection may be the most critical.l’-r2
No directly related mechanical property is available to accurately predict the fatigue limit of a structure.12 However, a relationship between the fatigue limit and the ultimate tensile strength of metal alloys (the fatigue limit approximates 50% of this value for many metal alloys) has been postulated.1°,12 This relationship may be valid in considering the apparent improvement in fatigue resistance of the material after strain hardening as a result of repeated stress. I2 The modulus of elasticity of a material is also related to the fatigue limit of a structure and reflects the interatomic or intermolecular forces of the material, 83
Fig. 2. Wax patterns
Fig. 1. Considerations sis (A) and underlying term clinical service.
in design of cantilevered framework (B) critical
and, unlike other physical properties, is unrelated to heat or mechanical treatment.* Cox and Zarb7,r3 noted that fractures in the cantilevered segment decreased when the superstructure was cast with a metal alloy with increased ultimate tensile strength and modulus of elasticity. Further material considerations include limiting grain size to improve physical properties, minimizing porosities throughout the casting, controlling residual stresses in the casting process, and selecting a material that is resistant to corrosion.lO
The longitudinal and cross-sectional designs of a cantilevered structure are directly related to resistance to deflection. Smydl* and Rinaldi et al.15 described the physics of bending as directly proportional to the length of the beam cubed. Ideally no cantilevered sections need to be implemented. However, the necessity to cantilever is dependent on the surgical placement of the implants and the requirements of tooth placement, based on anatomic and biomechanical needs.2-4, rels Skalaklg postulated that the maximum load to a fixture nearest a cantilevered segment is as great as 1.5 to 2 times the maximum load of the prosthesis. Rangert et al. l6 described the bending moment cre84
Fig. 3. Wax patterns
prior to investing.
ated by a cantilever as equal to the applied force multiplied by the length of the lever arm. The length of the cantilever is significant in flexure; therefore its use should be well justified clinically. The factor least discussed in deflection is the cross-sectional shape of the cantilevered beam. Deflection of a cantilevered structure is affected by cross-sectional designzO The maximum deflection (D) of any cantilevered beam is (P)(1)3/3(E)(l), where (P) equals force, (1) equals length, (E) is modulus of elasticity, and (I) is the moment of inertia.20 If (P), (1), and (E) are held constant, the significance of (I) increases. If (I) is increased by altering cross-sectional design, flexure decreases. Assuming pure bending and no torsional forces for a given structure, (I) = (t)(h)3/12 + (a)(t)(h/2 - Y)z.ao It can be seen that the height of the beam (h) is the most influential on (I) since it is cubed. Investigators achieved good rigidity and improved durability by increasing the bulk at the junction of the cantilever and distal abutment.* However, the benefits of limit-
*References 1, 2, 4, 6, 7, 13, 21-23. JULY
4. Castings of 5 mm group ready for machining.
ring the dimensions of the prosthesis include reduced interference with oral structures and adequate access for hygiene. 24-26 Vertical extension of the framework is determined by the occlusal-most extension of the replacement teeth. The buccolingual width of the frame is influenced by tooth placement and width and spatial relation to the tongue and cheek. The framework should allow at least 2 mm of clearance from the tissue for hygiene.26,27 Investigators have recommended an l-beam cross-sectional configuration to minimize the strain concentrations at the terminal fixtures of a fixed tissue-integrated prosthesis3a 13128 However, an L-shaped cross-sectional design enables the replacement teeth to be arranged within the confines of the L-a more efficient use of space. This factor may have increased importance in framework design and material selection in considering jaw relationship, intermaxillary space, and implant-host factors. Recommendations that the vertical arm height should be no less than 6 mm to increase durability remain untested.21 By holding all other dimensions constant, varying the vertical height of the L-shaped cantilevered frameworks, and THE
Fig. 6. Schematic diagram of one end casting.
of custom jig for rigid fixation
Fig. 7. Rigid fixation and positioning of sample in jig. Center of aperture of each sample placed at edge of jig to ensure consistent placement. Jig is fixed to testing machine so that push rod is placed over round depression cast in each sample.
applying cyclical forces, fatigue strengths with vertical arm height.
can be correlated
Fatigue strengths of the cantilevered sections of 15 fixed tissue-integrated prostheses metal frameworks were tested. The 15 castings were divided into three groups of five according to vertical wall heights of 4, 5, or 6 mm. The relative fatigue strengths of each group were determined by counting the number of vertically oriented force cycles required to fracture the cantilevered section. The null hypothesis was that the dimension of vertical wall height would not affect fatigue strength.
A two-piece mold was made by reproducing a metal prototype with polyvinyl siloxane impression material (Pres85
Fig. 8. Load versus displacement to determine proportional limit of 4 mm prototypes was estimated by first deviation from linearity of each sample. Values averaged to derive mean proportional limit before all fatigue tests.
group Proportional limit (lb)
A B c D E
100 io5 105 120 113
of 4, 5, and 6 mm castings Group
Sample 1 2 3 4 5 6 I 8 9 10 11
124,123 71,900 380,900 86,097 135,155 30,118 22,270 24,388 24,700 22,352 Not
12 13 14 15 16
failure) 3,400 11,250 8,228 8,596 6,125
ident, Coltene Ag, Altsattien, Switzerland). The impression unit was encased in an improved stone (Velmix, Kerr Manufacturing Co., Romulus, Mich.) to form a flask that could be separated along the interface of the impression layers (Fig. 2). Each pattern was then formed by injecting molten blue inlay wax (Kerr Manufacturing Co.,) into the flask and allowing the wax to bench cool. The flask was separated and the wax pattern removed. Twenty wax patterns of identical dimensions and sprue design within 0.1 mm were made. The patterns were waxed to a sprue-former (Fig. 3) and invested in phosphate-bound investment (Ceramigold, Whip Mix Corp., Louisville, KY.). Each set of patterns was invested with the seam of the investment ring along the long axis of the two casting patterns to standardize the orientation of each ring in the casting machine. The patterns were cast in a palladium-based alloy (Option, J. M. Ney Co., Bloomfield, Conn.) at 2300’ F with an induction casting machine (Thermotrol 2500, Jelenko Dental Health Products, Armonk, N.Y.). The rings were heat soaked at 1350” F for 3 hours and positioned so that the seam was facing the direction of centrifugal force. New metal alloy ingots were placed in the muffle, preheated at 2100’ F, and cast immediately upon melting (at approximately 2300“ F). No greater than 50% of the casting weight was previously used, and previously cast metal was only reused once. All casting surfaces were inspected for irregularities and finished so that they were of equal dimension within 0.1 mm (Fig. 4). The horizontal arm lengths were 8 mm, and the thickensses of the vertical and horizontal walls were 2 mm. The overall length of the castings was 54 mm. This dimension allowed approximately 32 mm of the framework to be fixed in a custom jig, 2 mm to index the
d Deflection Vertical forces create shear stress on “L” beam through shear center (circle) y = h2 + bt / 2(a+b)
nuetral axis for pure bending about X axis
I=th3/12 +[ht (h/2 - y)2]*
* will equal zero with all “L” designs
Therefore, I = th3 I 12 &mole Grouus (hJ 6mm
16= 36.0 mm4
Fig. 9. Values for moment of inertia (Table 1) may be usedas meansof comparison(relative values) for deflection with static loads. This is possiblesinceI is only value tested.
Fatigue failure of 2 mm (flat) castings
1287 1780 1860
17 18 19 Mean,
Fig. 10. Catastrophic failure of 5 mm sampleand simultaneous termination of test.
push rod, and 20 mm to be exposed as a cantilever. The vertical arm length of each casting wasmilled to either 4, 5, or 6 mm t 0.01 mm (Fig. 5). Testing
A custom jig was made from stainless steel in the Department of Engineering for rigid fixation of one end of the casting (Fig. 6). The castingwassecuredin a jig so that the center of the aperture wasaligned with the edgeof the jig. The jig was oriented on the platform of the testing machine (Universal testing machine, model 1321, Instron Corp., Canton, Mass.) so that the push rod was centered over the depressionof the sample (Fig. 7). This position consistently provided a 20 mm cantilever for each test.
One of the requirements of a fatigue test is that the cyclical stressesbe within the proportional limit of the sample.8,gThis limit wasdetermined by making an extra 4 mm group of castingsand subjectingthem to an increasingdisplacement of 0.02 inch/set until catastrophic failure occurred. The 4 mm design was tested instead of the 5 or 6 mm designsto ensure that the maximum load of the fatigue test was within the proportional limits of all samples. Load versus displacementinformation wasrecorded for all five samples(Fig. 8). The averageproportional limit of the group was109.6lb. (Table I). As a result, a maximum force of 100poundswasselectedto provide a low cycle fatigue test within the observed proportional limit of the samples. Fatigue
The three groups of sampleswere subjected to a computer-aided, load-controlled fatigue test. The load-controlled test wasdesignedto compensatefor warpageof the samplewhile maintaining the preassigned(1 to 100 lbs) force. A frequency of 4 cycles/set was selected.The number of cycles at failure was recorded (F.L.A.P.S. software program, Technical Software Consultants Limited, Can-
. 8 8E
4 Wall height
Fig. 11. Cycles versus wall height of 2, 4, 5, and 6 mm castings. Vertical wall height and resistance to fatigue are directly related. Addition of 2 mm samples consistent with general trends shown in previous data.
Fig. 12. Cycles versus vertical wall height of 4,5, and 6 mm castings. Vertical and resistance to fatigue are directly related.
5 2 I
Fig. 13. Displacement
versus cycles for 4,5, and 6 mm castings. Observed upturn of each plotted line indicates maximum deflection before catastrophic failure of samples (end of line). AIso demonstrates large intragroup variability, and intergroup differences in ability to resist, fatigue. Individual samples in each group failed regardless of displacement val-
ton, Mass.) as well as values of force versus displacement. This information verified the uniformity of the load to each sample and provided a graphic demonstration of the deflection of the castings. Relative differences in deflection were compared with actual theoretical calculations of deflection based on the moment of inertia (I) of each design group.
The number of cycles to failure was recorded and the group mean and standard deviations for all groups were tabulat,ed. The Kruskal-Wallis test, a nonparametric oneway analysis of variance, was used to evaluate the statistical significance of the differences in plots. The direction of the differences recorded was analyzed with Iinear regression methods.
RESULTS Before the fatigue strength of the castings was tested, theoretical deflection calculations were made (Fig. 9). This was done by solving for the moment of inertia (I) while other factors in the deflection equation were held constant, All castings tested (both in static-load and load-controlled fatigue tests) failed catastrophically (Fig. 10). This phenomenon enabled each test (recordingapparatusF.L.A.P.S. software program) to be precisely terminated when the displacement limit was reached (fracture of the casting). The number of cycles obtained at fracture for all samples, and the mean and standard deviation for each group are
shown in Table II. All three groups (4, 5, and 6 mm castings) showed significant differences in mean cycles. Increasing this dimension provided increased resistance to fatigue (Kruskal-Wallis test, p = 0.0019, chi-square 12.50, 2 df). The direction of the differences (by linear regression) was highly significant (p < 0.0001,16 df, residual standard deviation 0.54). The differences between the three sample groups were plotted (Fig. 11). Intergroup variability, however, was quite large, with the 6 mm group having the largest standard deviation from the mean. Sample No. 11, a 4 mm casting, was not included for statistical analysis because of technical error in programming the apparatus. The pronounced effect of the vertical wall height in fatigue durability of the three groups prompted the testing of a group of samples without a vertical wall. The fourth group of castings (h = 2 mm) was made and subjected to the same fatigue testing parameters as the 4, 5, and 6 mm designs (Table III). The statistical analysis of all four groups included linear regression to compare the amount of cycles counted at failure versus vertical wall height (Fig. 12) and again were found to be highly significant (p < 0.0001, 16 df, residual standard deviation = 0.046). Further analysis demonstrated that (1) displacement of the beam during the course of the fatigue tests was directly proportional to number of cycles (Fig. 13), (2) displacement of the beam was indirectly proportional to vertical wall height (Fig. 14), and (3) testing results of individual samples within each group revealed large variability. The fractures occurred roughly at the diameter of the
R = 0.993
Fig. 14. Displacement versus vertical wall height‘ during fatigue testing of 2,4, 5, and 6 mm samples. Parallels theoretical calculations of deflection with static load (Table II). Data points represent maximum deflection at catastrophic failure of each sample. Increased wall height decreased displacement.
Fig. 15. Fracture interface fied most of those observed.
of samples No. 2 and 3 typi-
aperture, did not follow the straight line of the jig when inspected from above, and were quite variable among samples. Observation of the fracture interface with low (x2) magnification (Leeds Microscope, Leeds Precision Instrument Inc., Minneapolis, Minn) revealed qualitative differences between samples in porosity and uniformity throughout the cross section. However, no appreciable burnished surfaces representing shear points were noticed. The topography of the interface was complex, with tortuous indentations and matching projections throughout. The fracture interface of samples No. 2 and 3 typified most of those observed (Fig. 15).
The data obtained from the 2, 4, 5, and 6 mm L-shaped designs demonstrated the importance of the vertical wall for durability of the cantilevered segment of the fixed TIP. There was, however, no absolute point at which fatigue strength was increased disproportionately when wall height was altered. Specific recommendations as to a critical minimum height could not be made. The highly significant differences in fatigue strengths of the 2, 4, 5, and 6 mm designs are sharply contrasted by the relatively large inconsistencies observed within each sample group. These intragroup inconsistencies could be the result of at least three possibilities: (1) inconsistencies inherent in the casting process, (2) variations in sample dimensions, and (3) variations in testing apparatus. Inconsistencies in the testing apparatus were probably least significant, because each sample was subjected to computer-controlled cyclical forces and the uniformity of testing was recorded and verified. Some problems in fatigue testing may have occurred with the new 2 mm samples, in that the maximum force of 100 lb may have created permanent deformation by being above the proportional limit. Intragroup variations caused by lack of dimensional uniformity may be a larger possible source of error. However if this were true, a larger variability in cycles to failure should have been observed with the samples with 2 and 4 mm walls because vertical wall height variability (kO.01 mm) would be most significant.
The inherent problems in casting metal alloys is undoubtedly the primary factor in fatigue strength. Problems in casting include inclusions from dissolved gasses, such as Hz and 02 with palladium alloys, and a lack of uniformity in crystallization and grain growth from the molten state.s 2g The alloy may also have been embrittled because a carbon crucible was used for casting (not recommended by the manufacturer). The use of a porcelain crucible and complementary casting machine was not available. In addition, the effect of a carbon-containing phosphate-bound investment may have compounded this problem. It is not clear how this may have effected the complex actions of initiation and propagation of a fracture line along slip planes and/or grain boundaries of the alloy. Observation of the fracture interface with higher magnification could not be addressed and will be included in subsequent investigations. It may seem intuitive that the beam with increased wall height would allow less flexure. Rinaldi et a1.15 and Smyd14 described this relationship as a deflection of the beam being indirectly proportional to the height of the beam cubed. The trend toward this relationship was seen in this study when a cyclical load was applied (Fig. 14). It is important to recognize that computations of deflection from a static load are not equal to deflection during a cyclical load. However, as the beams were increasingly displaced by stress, the material was increasingly deformed, which presumably initiated fracture. In this sense, flexure characteristics and fatigue strength appeared inseparable. The testing parameters used in this investigation were chosen to create a low-cycle test. The assumption that a low-cycle test would yield results similar to those of a high-cycle test may be misleading, because residual stress could create a different response with lesser maximum loads. However, this factor was assumed ‘co have an insignificant effect in the differences among groups. The maximum force used in laboratory fatigue testing is probably unrealistic in a clinical setting. Patients probably do not generate quadrant or even total forces of 100 pounds repeatedly. The forces experienced by the framework in clinical application might be dampened by (1) acrylic resin teeth or other similar mechanism, (2) factors associated with the opposing occlusion that would cause decreased impact forces, (3) a significantly smaller masticatory force production, and most important, (4) a decreased length of the cantilevered arm of the prosthesis. A significant assumption in this study was that the deflection of the L-beam was pure bending. Vertical masticatory forces are oriented to the horizontal arm of the L-shaped design by means of the tooth position in relation to the frame. This creates a rotational force about the shear center (Fig. 9). An asymmetric structure creates a very destructive asymmetrical bending.g,10 A design that has symmetry in every plane would minimize shear forces and perhaps optimize fatigue strength.
Davis30 postulated that an increased stress production on the anterior-most implants accounts for the increased bone loss in these regions. This localized magnification of stress is the result of the leverage created by the rigid framework around the terminal abutments. Arch curvature and cantilevered portions of the prosthesis impart bending and shear stresses to the implants. The ideal crosssectional design that optimizes the distribution of stress to all attached implants has yet to be elucidated. It remains to be seen whether the benefits of fatigue strength could be improved or maintained if (1) the walls were confined only to the regions immediately mesial and distal to the terminal fixture abutment, (2) the portion of the framework was bulked only near the terminal abutment, and (3) solid, elliptical or other cross-sectional designs were substituted for the L-shaped design.
CONCLUSIONS 1. Resistance to fatigue failure significantly increased when the vertical wall height of an L-shaped cross-sectional design was maximized. The clinical durability of a metal framework for fixed tissue-integrated prostheses of this design may be improved by extending the vertical wall as far occlusally as allowable. 2. The displacement, or flexure, of the structure from cyclical stress was significantly higher when extension of the vertical wall was limited. 3. Fatigue strength of a cast, metal structure is dependent on the variables associated with the casting process. 4. General tendencies of fatigue strength of cast metal structures can be determined from theoretical calculations of deflection under static loads. Cross-sectional design has high significance in the fatigue strengths of cantilevered structures.
SUMMARY Framework design of implant-supported prostheses has had limited documentation and may result in either excessively bulky restorations or fractures at the distal fixture. Specific cross-section design modifications in cantilevered regions would improve these shortcomings. Cast framework samples of four vertical wall dimensions of the L-shaped cross-sectional design were subjected to a loadcontrolled fatigue test. The number of cycles recorded at failure and the associated flexure during testing revealed that the presence of a vertical wall decreased deflection of the beam and increased fatigue strength. Variability of samples within each group was attributed to inherent errors in the casting process.
We acknowledge the assistance of Lawrence J. Berglund, Department of Orthopedics, Biomechanics Laboratory Technician, Mayo Clinic, Rochester, Minn.; and Richard D. Lee, Dental Laboratory Technician, Department of Dentistry, formerly at the Mayo Clinic, Rochester, Minn.
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DR.ROBERT B.STEWART COLLEGEOF DENTISTRY THE OHIO STATE UMVERSITY 305 W.lSTH AVE. COLUMBUS,OH 43210-1241