Beam Theory

Any understanding of FRC bridges must begin with beam theory. A beam is defined as a structural member that is subjected to loads applied transverse to the long axis. The simplest type of beam is known as a cantilever (Figure 12-1). This concept, familiar to most dentists, refers to a beam supported and retained at one end, called encastré by engineers. Near the middle of any beam is a line (or a plane in three dimensions) known as the neutral axis. This axis coincides with the centroid or geometric center of the beam. The longitudinal stresses along this line are zero. The stresses in a cantilever beam are essentially tensile above this line and compressive below it. The farther from the neutral axis, the greater the stress. This explains the success of I-bar beams, as the greatest strength of the beam structure is concentrated farthest from the neutral axis, where there is the greatest stress.

FIGURE 12-1 A cantilever beam is supported and retained at one end.

The second type of beam is a simply supported beam. This type corresponds to a board laid across a puddle. A simply supported beam is essentially two cantilevers turned back to back and upside down (Figure 12-2, A). The stresses on it are compressive above the neutral axis and tensile below it (Figure 12-2, B).

FIGURE 12-2 A, A simply supported beam can be considered two cantilever beams back to back and upside down. B, Stresses in a simply supported beam are compressive above the neutral axis and tensile below.

The third type of beam is a combination of the cantilever and the simply supported beam. This beam is supported at both ends, but both ends are retained or encastré. This is the type of beam being constructed when a dental bridge is being fabricated. It has structural elements of both types of beam. Tensile stresses are below the neutral axis, but above the neutral axis there are compressive stresses in the beam’s middle and tensile stresses toward the ends. Cutting this type of beam in the center produces two cantilevers end to end. If we release the hold on the ends, we have a simply supported beam. This may partly explain the discrepancy between the failure of FRC in the literature and its success in practice. Although it is clear that any in vitro testing requires that the material be supported at both ends to simulate what occurs when we fabricate a fixed partial denture, most studies do not specify how the material is retained for testing.

The Science of Fiber-Reinforced Composites

To understand FRC bridges, it is also important to examine the mechanism of failure of composite materials. Although a detailed discussion of fracture mechanics is beyond the scope of this book, there are factors that help to explain the discrepancy between clinical successes and laboratory failures.

Materials can be described as brittle or ductile. When the elastic limit of a material is exceeded, brittle materials fracture and ductile materials bend. Dental composites bend very little and are classified as brittle, even when the composite is reinforced with fibers.

Dental composites, like all brittle materials, fail as a result of crack propagation. Geometric defects within the structure act as points of stress concentration. These irregularities can be holes, bubbles, cracks, sharp corners, and so on. These faults cause the stresses within the material to become focused at these points, causing the initiation of fracture, even though the overall stress within the material is well within its theoretical strength. This is the same principle used in cutting glass. A small scratch is etched on the glass surface, and a stress is applied to the material. The scratch acts as a source of stress concentration, and the glass fractures cleanly along the line scratched in its surface. If the scratch does not continue completely across the sample, the fracture still begins where the scratch concentrates the stress and propagates irregularly across the glass, because the end of the fracture becomes the new point of stress concentration, until failure occurs. Clinical success or failure of FRC may be as much a function of our success in minimizing the microcracks and irregularities in the structure as of the inherent strength of the materials.

The fracture resistance of any material is less a function of its strength than of its toughness. Fracture toughness is the resistance of a material to form cracks and is a measure of the damage tolerance of the structure. Glass and steel have similar tensile strengths, but no one would suggest the two are interchangeable; steel is tougher than glass. One small crack in a pane of glass results in rapid propagation of the crack, resulting in fracture of the glass. Small cracks in steel do not necessarily produce fracture. When the structure is placed under stress, thousands of microcracks are created within the material. These microcracks tend to travel through the structure and, if they are permitted to connect with one another, eventually coalesce into macroscopic cracks, then fracture lines.

The fibers within FRC enhance the load-bearing capacity of the structure by two separate and distinct mechanisms. First, the fibers act as a stress-bearing component, as would be intuitively expected. They support the forces of occlusion much like cables in a suspension bridge. They also strengthen the composite by acting as a crack-stopping and crack-deflecting component. As microcracks propagate through the resin matrix, if they encounter a fiber, they are stopped and deflected along the interface between the fiber and resin. The fiber becomes circumferentially detached from the resin matrix. When the crack intercepts another fiber, it forks and divides, multiplying the number of cracks in the structure. The creation of each new crack consumes energy and increases the work of fracture for the material. This mechanism dissipates the energy applied to the structure. The process of branching of cracks continues until energy demands become too high or the material fractures. Over time, the accumulation of cracks within the structure begins to act as a stress relief mechanism. Stresses are relieved by the friction between the material surfaces in contact at the crack. Flexure of the prosthesis also transfers stresses to the fibers, which then support the structure as a stress-bearing component.

Which of these two mechanisms is more important is open to some debate. Rudo and Karbhari argue in their article “Physical Behaviors of Fiber Reinforcement as Applied to Tooth Stabilization” that woven material is superior to unidirectional material in vivo. Whereas unidirectional material exhibits superior strength in the direction of the fibers, there is little correlation between the stresses placed on a dental restoration and the unidirectional stresses placed on the materials in laboratory testing. Rudo and Karbhari argue that the load-bearing action of the fibers is secondary to their crack-stopping function. Therefore the fibers need not be unidirectional. Woven fibers may offer greater strength, because the intersecting fibers are more effective at stopping and deflecting cracks.

Regardless of the mechanism, the incorporation of reinforcing fibers into dental composite increases the material’s strength. The tensile (and therefore the flexural) strength of the resulting structure is enhanced by the fibers. The more fibers that can be incorporated, the greater the strength achieved. The principle is well stated in the rule of mixtures, which states that the mechanical properties of a composite material are proportional to the volume and properties of the individual components in the mix. In reality, the strength of FRC dental restorations tends to be less than theory would suggest, mainly because the limitations imposed by the space and design considerations of a dental restoration reduce the amount of fiber that can be incorporated into the structure. The literature tells us that the amount of fiber incorporated into most dental structures is low, usually on the order of 15% by volume.

Commercially Available Fiber Systems

All fiber reinforcement products are variations on two major systems: plastic or glass. Plastic fibers generally have handling characteristics superior to those of glass, whereas glass is generally the stronger material.

Most plastic fiber systems are polyethylene. The fibers are usually braided or woven into a ribbon, with each manufacturer claiming to have the superior configuration. In reality, how fibers are woven makes little difference in the strength of the resulting restoration. It can, however, result in differences in how the material handles. Concerns also arise about the ability to fully impregnate certain tightly woven configurations of fibers with resin.

The surface of plastic fibers is usually treated with cold gas plasma to enhance the bond between fibers and resin. In this technique the fibers are exposed to a partially ionized oxygen gas that acts through a process of ablation and activation. The ablation results in an etching of the fiber and an increase in the presence of chemically active groups on the fiber surface. These groups chemically bond to the resin, while the etched surface facilitates a micromechanical bond. The plasma treatment also enhances the wettability of the fiber surface, which increases the resin in contact with the fiber and helps to reduce the presence of voids and bubbles at the resin-fiber interface, which act as points of stress concentration. Cold gas plasma treatment is highly susceptible to contamination, however. The fibers therefore must be handled carefully to prevent contamination before they are impregnated with resin. One manufacturer includes a pair of cotton gloves in the kit to protect the fibers during handling, but these are not practical. Carefully avoiding touching the fibers before impregnating them is adequate.

Glass fibers are of two types, E-glass or S-glass. The two materials are different chemically, but handling is essentially identical. S-glass is the stronger of the two and has a higher modulus of elasticity. Glass fibers are stronger in theory than plastic, but their stiffness makes them much more difficult to work with clinically. S-glass fibers are stiffer, so elastic memory is more problematic in handling and placement for dental applications.

Glass fibers are etched and silanated to enhance the resin-to-fiber bond. The etching process is similar to etching porcelain before bonding, although the actual process is proprietary. Etching glass fibers is, by all reports, duration and chemistry critical. Glass fibers cannot be etched and silanated chairside. If they are over-etched, their strength diminishes dramatically; if they are under-etched, the bond to resin is inadequate.

Indirect Methods

Several manufacturers have developed FRC materials for laboratory-fabricated prostheses, with mixed success. One advantage of the indirect technique is that it uses techniques and procedures reasonably familiar to most dentists. The concepts of preparing the teeth, making an impression, and fabricating a provisional restoration differ little from making a porcelain-fused-to-metal bridge. The procedure for bonding the prosthesis is the only departure from more traditional techniques.

Another advantage to the indirect technique is that it is possible to cure the composite using heat and pressure to enhance the strength and wear resistance of the cured composite. Unfortunately, this also results in the greatest shortcoming of indirect composite techniques. When a composite restoration is fabricated in a laboratory, especially when it is cured with heat and pressure, it must be bonded using almost entirely micromechanical means, because the polymerization of the composite will have progressed to the point that there will be few free radicals left for chemical bonding to the composite resin. The composite’s surface may also become corrupted by myriad contaminants during the fabrication process, including the surface of the stone cast. These contaminants must then be removed. Whatever technique is employed to clean and etch the surface before bonding will remove any air-inhibited layer, eliminating any chance for chemical bonding. Thus there is an obvious advantage to fabricating the entire prosthesis in place in the mouth.

Direct Methods

In 1981, Belvedere placed some of the first directly bonded FRC resin bridges using Kevlar fibers. The first bridge was a four-unit prosthesis replacing two maxillary central incisors using the laterals as abutments in a 22-year-old woman. At last report (1989) the bridge was still in service and had not been repaired or replaced. Nearly 400 bridges have been reported to be in service, with a 98% survival rate over an 8-year period.

In 1994 Abel described a technique for the direct fabrication of an FRC bridge to replace incisor teeth. The technique was a bold attempt but failed to deal with several important issues. Significant in any bridge design is the tissue contact surface of the pontic, and Abel’s technique fails to address this. The article is unclear, but it appears that he simply fabricated the pontic in place, in direct contact with the tissue, and allowed the gingiva of the edentulous space to develop the tissue surface form of the pontic.

Culy and Tyas described a technique for direct fabrication of FRC anterior bridges. They replaced 26 single upper anterior teeth and one premolar using hybrid composite reinforced with plasma etched polyalkane fibers (Fibrespan, Nulite Systems, Sydney, Australia). They followed their cases for only 10 months, and two bridges failed as a result of trauma. Of the 27 bridges, 25 were of cantilever design, which the authors argue is more predictable because there is no differential movement between the abutments. This runs counter to conventional wisdom regarding bridge design. The authors also found the process to be “technically demanding,” particularly with respect to the pontic saddle design, but offered the technique as a viable option for conservative tooth replacement.

In 1998 Belvedere described how to fabricate a direct FRC bridge to replace missing central or lateral incisors. His technique addresses the problem of controlling the tissue surface of the pontic with the fabrication of a “pontic button.” The portion of the pontic in contact with the tissue is fabricated in place in the mouth and trimmed, and the tissue surface is contoured and polished before being incorporated into the restoration. The abutment teeth are prepared and bonded, the fibers are placed, and the pontic button is positioned under the fibers. The coronal portion of the pontic is then custom fabricated in place in the mouth. The technique is a marked improvement over previous attempts but requires significant clinical skill to manipulate all the parts and materials successfully into position.

Although many of the problems associated with the direct fabrication of FRC resin bridges have been solved, the clinical techniques for bridge fabrication still need refinement. Belvedere’s technique addresses the problem of controlling the tissue surface of the pontic. Unfortunately the technique is so technically demanding that few clinicians are willing to attempt it on a regular basis.

Technical Considerations for Direct Bridge Fabrication

Several issues must be considered when fabricating FRC bridges directly in the mouth. Voids and bubbles act as points of stress concentration within the structure, so it is worthwhile to minimize the bubbles trapped within the mix. The greatest problem in accomplishing this is adequately wetting the fibers. Fibers require wetting with an unfilled resin; filled or flowable materials have higher viscosity and do not wet the fibers as effectively, permitting bubbles and voids to become entrapped on the fiber surface. Once the fibers have been wetted with unfilled resin, they can be further wetted with a flowable composite before they are introduced to the more highly filled composite. Although intuitively this seems to represent the greatest potential for getting filled composite in intimate contact with the reinforcing fibers, at the time of this writing this has not been supported or disproved by research.

In deciding on the placement of the fibers within the restoration, beam theory can supply guidance. In a three-unit bridge supported at both ends, the tensile stresses are concentrated below the neutral axis of the beam. In a bridge that is encastré (retained) at both ends, as in a fixed partial denture, tensile stresses are also located above the neutral axis toward the ends of the bridge. In a cantilever beam (or a cantilever bridge), tensile stresses are located above the neutral axis of the beam. Beam theory teaches that the stress on a beam increases as the square of the distance from the neutral axis to the tensile side. Fibers should be located where they will absorb the tensile stresses within the structure, so when a cantilever bridge is being constructed, the fibers must be concentrated toward the occlusal or incisal part of the restoration. In fabricating a three-unit fixed prosthesis, fibers should be concentrated below the neutral axis—that is, toward the gingival portion of the bridge. In practical terms, it is desirable to incorporate as much fiber into the structure as possible. The limitations of fabricating a dental prosthesis, especially directly in the mouth, are such that we can seldom incorporate as much fiber as desired. The risk of using too much does not exist from a structural standpoint but can be a problem in that it must be completely covered with composite resin.

Unfortunately, the forces applied to a dental prosthesis are not as simple as they are when building a floor. Among the complex forces seen in clinical applications of fiber-reinforced technology is the phenomenon of torquing of posterior bridge pontics. When occlusal loads are applied to a posterior bridge pontic, they are not necessarily applied to the center of the pontic or beam. Off-center loading results in a torsional force, or twisting of the pontic or beam. These torsional forces are best resisted by fabricating a pontic or beam with long unidirectional fibers that are spiral wrapped with unidirectional fibers. This can be accomplished in the fabrication of indirect prostheses and is included in several of the commercially available systems used for laboratory fabrication. Unfortunately, spiral wrapping of the reinforcing fibers is an engineering principle that is difficult to achieve when fabricating the restoration directly in the mouth. For direct posterior bridge fabrication in the mouth, one must keep the bucco-lingual width of the pontic to a minimum and design the anatomy to eliminate working and balancing contacts. This reduces the potential for off-center loading of the pontic and the resulting torsional stresses on the bridge.

Bridge Fabrication

Fabrication of the pontic button is the key to this technique. Until the procedure for fabricating the pontic button and polishing it out of the mouth was developed by Belvedere, direct FRC bridges were doomed to have an irregular and potentially uncleansable tissue contact surface. Unfortunately, fabrication of the pontic button and its subsequent incorporation into the structure along with the fibers also complicate the procedure. It can be quite challenging to manipulate all of the parts into place and hold them there long enough to polymerize them without contamination with saliva. The following techniques are modifications of Belvedere’s approach and designed to simplify the process by keeping the number of components that must be positioned at the same time to a minimum.

Anterior Bridge Technique

The technique for direct intra-oral fabrication of an anterior FRC bridge begins with a set of study models. The model is modified with wax or composite to create the lingual contours desired of the completed bridge (Figure 12-3, A). The author typically uses composite to mock up the lingual portion of the pontic and then flows inlay wax onto the lingual surface of the abutment teeth on the models to simulate the thickness of the retainer and the fibers on these teeth. The labial surface of the pontic is of no concern at this stage; it will be developed in the mouth when the bridge is fabricated.

FIGURE 12-3 A, The lingual contours of the bridge are mocked up in composite or wax on a study model. B, The matrix is fabricated from vinyl polysiloxane putty. If teeth are dark or opaque, transparent material can be used to permit polymerization through the matrix. C, The matrix is inserted in the mouth to ensure good fit. It will be used as a mold to form the lingual and gingival surfaces of the pontic button. Marks on the matrix are made to simplify placement of the matrix in the mouth. D, Composite is injected into the space created by the matrix, tissues, and abutment teeth to create the basic form of the pontic button. E, The pontic button is trimmed to establish an outline form and tissue surface contours. F, Once the appropriate contours are established, the tissue surface and lingual surface of the pontic button are polished to a high shine. G, A chamfer finishing line is created around the outline of the labial surface to establish a well-defined line to finish the composite to when developing the rest of the pontic. At this time the pontic is also contoured to ensure adequate room for the fibers to pass between the pontic button and the abutment teeth. H, The completed pontic button should be reasonably stable when placed back on the matrix. I, When the fibers and the pontic button are ready, the teeth are prepared by roughening the enamel and preparing conservative class III preparations on the abutments. The teeth are then etched and a dentin adhesive applied. J, Dental tape or floss is positioned and cut to length to serve as a pattern for the fibers. K, The dental tape pattern is used to measure the length of the fibers required. The fibers are cut to length and placed on a piece of tin foil, which will be used to protect the wetted fibers from ambient light while the teeth are prepared for bonding. A light-resistant container can also be used. L, The fibers are wetted with unfilled resin and then impregnated with light body composite resin. M, The tin foil is folded over to protect the impregnated fibers from ambient light and set aside. N, As the assistant ensures the teeth remain dry and uncontaminated, the dentist places the pontic button on the matrix and a small amount of low-viscosity composite on the abutment area of the matrix. O and P, Composite is then applied to the abutment areas of the matrix. The impregnated fibers are recovered from the tin foil and placed in position on the matrix. Q, All parts of the anterior direct fiber-reinforced composite bridge are shown in place on the matrix and ready for insertion in the mouth. R, After curing with the matrix in place, the lingual surface of the bridge is essentially complete. Only minor trimming and polishing are required. S and T, The lingual surface of the completed bridge demonstrates a modified ridge lap pontic design to facilitate hygiene. U and V, This 8-year follow-up of the case demonstrates that direct fiber-reinforced bridges no longer need to be considered purely provisional or temporary restorations.

A matrix is then fabricated using clear polyvinyl impression or bite registration material. This material is mixed according to the manufacturer’s instructions and applied to the lingual surface of the model to register the contours developed in the mock-up (Figure 12-3, B). Opaque matrix material can be used as shown in Figure 12-3, B, but transparent materials allow for the structure to be polymerized through the matrix after the initial trans-enamel polymerization, which ensures all the composite will fully gel before the matrix is removed.

It has been argued that the need to do a mock-up on the study model negates its advantage of being completed in one visit. This is rarely a problem, as study models are such a routine part of the diagnostic procedure before fabrication of any bridge. Because the entire bridge fabrication procedure takes the average dentist about 2 hours, it is unlikely that the procedure will be performed on a patient who has never been seen before.

At the fabrication appointment the abutment teeth a/>