## Abstract

## Objectives

To measure the flexural strengths and moduli of endodontic post materials and to assess the effect on the calculated flexural properties of varying the diameter/length ( *D */ *L *) ratio of three-point bend test samples.

## Methods

Three-point bend testing of samples of 2 mm diameter metal and fiber-reinforced composite (FRC) rods was carried out and the mechanical properties calculated at support widths of 16 mm, 32 mm and 64 mm. Weibull analysis was performed on the strength data.

## Results

The flexural strengths of all the FRC post materials exceeded the yield strengths of the gold and stainless steel samples; the flexural strengths of two FRC materials were comparable with the yield strength of titanium. Stainless steel recorded the highest flexural modulus while the titanium and the two carbon fiber materials exhibited similar values just exceeding that of gold. The remaining glass fiber materials were of lower modulus within the range of 41–57 GPa. Weibull modulus values for the FRC materials ranged from 16.77 to 30.09. Decreasing the *L */ *D *ratio produced a marked decrease in flexural modulus for all materials.

## Significance

The flexural strengths of FRC endodontic post materials as new generally exceed the yield strengths of metals from which endodontic posts are made. The high Weibull modulus values suggest good clinical reliability of FRC posts. The flexural modulus values of the tested posts were from 2–6 times (FRC) to 4–10 times (metal) that of dentin. Valid measurement of flexural properties of endodontic post materials requires that test samples have appropriate *L */ *D *ratios.

## 1

## Introduction

The restoration of extensively damaged teeth presents a challenge for clinicians. Where there is little coronal tissue it is difficult to attach restorations to what remains. This will be of particular relevance to the smaller teeth in the jaws, those in the anterior region. In such situations it has historically been common practice to treat the tooth endodontically to allow a post to be placed into the root canal to achieve retention for a restoration placed over the coronal end of the post. This is most appropriate for anterior teeth which generally have single, long roots with little curvature. Post-restored teeth however, have a reputation as poor restorations with a high failure rate . The main mode of failure is loss of retention, i.e. either a separation of the post from the luting cement or of the luting cement from the walls of the post space. This is followed, but less frequently, by root fracture . While it may be possible simply to recement a loose post crown which can then continue to function adequately, the consequence of root fracture is far more serious as the tooth usually must be extracted. Traditionally, endodontic posts have been fabricated from cast or prefabricated metals and the influence of different design features of the post on root fracture has been extensively reported . A number of different metal alloys are in clinical use, each with different elastic moduli and yield strengths but the impact on performance of these differences in mechanical properties has not attracted as much interest as the effects of the design of metal posts. With the introduction of alternative post materials, in particular fiber-reinforced composites (FRC), these factors have assumed greater importance to researchers. Opinion is divided as to whether a post should have an elastic modulus close to that of dentin or whether it should be more rigid . One of the principle advantages claimed for FRC posts is that their elastic moduli are close to that of dentin and that this will allow a more favorable distribution of stress in the root thereby leading to a lower incidence of root fracture than occurs with metal posts . The mechanical properties of fiber-reinforced composites are determined not only by the properties of the different constituents but by the bond between filler and matrix and also by the shape, orientation and relative proportions of the reinforcing filler phase . Endodontic posts from different manufacturers contain different matrix resins, different proportions, diameters and types of fiber and may vary in their interfacial bonding. Therefore, before comparing the relative performance of metal and FRC posts, it is first necessary to determine the mechanical properties of different post materials and ascertain to what extent they approach the properties of dentin. Three-point loading in a universal testing machine is commonly used to determine the flexural modulus and flexural strengths of samples of materials. The applied load is plotted against the resulting deflection of the sample until failure and, using an appropriate formula, the flexural modulus and, in the case of brittle materials, the flexural strength can be calculated . Bending samples will induce shear stresses within the material affecting the validity of the calculated flexural properties . The shear force is proportional to the diameter/length ratio of the sample . To minimize this problem, standards organizations set appropriate dimensions for three-point bend testing of rods made of roving reinforced resin. ISO 3597-2:1993, Method 1008B:1996 stipulates that the distance between the supports should be at least 16 times the diameter of the rod. Despite this, three-point bend tests have been conducted on short endodontic posts which present a length/diameter ( *L */ *D *) ratio far below this 16:1 ratio and the results then expressed as the flexural modulus and flexural strength for that post material . Examining the effect that varying the aspect ratio of samples has on the derived property values will allow a better interpretation of the results of such studies on samples with small *L */ *D *ratios.

The aims of this study were therefore to measure the flexural strengths and flexural moduli of a range of currently available endodontic post materials and to assess the effect on these calculated flexural properties of varying the diameter/length ratio of three-point bend test samples.

## 2

## Materials and methods

Lengths of 100 mm wrought stainless steel and titanium, glass fiber and carbon fiber composites were obtained from several manufacturers. To provide a comparison with a cast precious metal alloy, rods of a type IV gold alloy, Engelhard EC 620 (Engelhard-Clal (UK) Ltd., Chessington, England) were fabricated. The samples were cast by the lost wax process using rigid rods of non-residual plastic as the burn-out patterns. The composition, dimensions and manufacturers of all the tested materials are listed in Table 1 .

Material | Manufacturer | Diameter (mm) | Composition (manufacturer’s information except where indicated) |
---|---|---|---|

Carbon fiber composites (mean fiber diameter, filler volume fraction) | |||

Composipost | RTD, France | 1.9 | Carbon fibers 8 μm 64%; epoxy resin |

Carbonite | Harald Nordin, Switzerland | 2.1 | Carbon 6 μm 65%; epoxy resin |

Glass fiber composites (mean fiber diameter, filler volume fraction) | |||

Aesthetiplus | RTD, France | 1.9 | E-glass fibers 8 μm 62%; epoxy resin |

Lightpost | 2.5 | Quartz glass 8 μm 60%; epoxy resin | |

Glassix | Harald Nordin, Switzerland | 2.1 | E-glass 8 μm 60%; epoxy resin |

Snowpost | Carbotech Ganges, France | 2.0 | E-glass with 18% zirconia 8 μm 60%; epoxy resin |

Snowlight | E-glass with 18% zirconia 8 μm 65%; polyester/methacrylate resin. | ||

Postec | Ivoclar Schaan, Leichtenstein | 2.5 | E-glass 8 μm 55%;filler ytterbium trifluoride and dispersed silicon dioxide; urethane dimethacrylate/TEGMA |

Easypost | Dentsply, Ballaigues, Switzerland | 1.9 | E-glass with 18% zirconia 8 μm 60%; epoxy resin |

Metals (alloy composition) | |||

Stainless steel | Coltene/Whaledent, USA | 1.7 | Fe 72.21%, Cr 18.18%, Ni 8.62% |

Titanium | 1.7 | Ti 90%, Al 6%, Va 4% | |

Cast gold | Custom made BDH Dental Laboratory | 2.1 | Au 60%, Ag 22%, Cu 12.5%, Pd 4%, Zn, In < 2% |

## 2.1

## Flexural testing of post materials

To carry out flexural testing, each material was cut into 48 mm lengths using a diamond disk (H 355C190, Horico, Berlin, Germany) running at slow speed in a dental handpiece. These were subjected to three-point bending in an Instron universal testing machine (Instron UK, High Wycombe, England), model 5544 according to ISO 3597-2. The distance between the supports was set at 32 mm. The diameter of each rod was measured at six points close to the center of the rod using a digital micrometer accurate to 0.01 mm (Mitutoyo, Japan), and a mean diameter calculated. A stainless steel loading nose with a 3 mm cylindrical cross-section was used and loads were applied at 1 mm/min. Data was exported to a computer spreadsheet programme, Excel 2003 (Microsoft Corp. USA) for analysis. Thirty samples of each material were tested and the mean flexural moduli and flexural strengths calculated using the appropriate equations .

Flexural modulus of a cylindrical rod using three-point bending .

Flexural strength of a cylindrical rod using three-point bending .

where *E *was the flexural modulus (MPa), *σ *was the flexural strength (MPa), *F *was the applied load (N), *F *_{m }was the maximum load at break, *L *was the length of span between supports (mm), *D *was the mean diameter of the sample (mm), and *F */ *Y *was the slope of the initial linear segment of the load–deflection curve. For metal samples, the 0.2% offset yield strength was calculated. Data was entered into a statistical computer package SPSS V12 (SPSS Inc., Chicago, USA) for analysis. The Shapiro–Wilk and Levene’s tests confirmed that the data had a normal distribution and homogeneity of variance and so a one-way ANOVA and post hoc Scheffé tests were used to identify any significant differences among the tested materials for both parameters ( *p *< 0.05).

Brittle materials such as fiber-reinforced composites fail as a consequence of crack growth from flaws within the material. Obtaining a mean flexural strength value does not give an indication as to the variability in strength, as this is dependent on the distribution of flaws. A more complete description of the variability in strength can be derived by determining the Weibull distribution . The Weibull modulus ( *m *) (or shape parameter) is a constant which describes the slope of the distribution and indicates the variation in the distribution of strength values which in turn may reflect clinical reliability. The characteristic strength (scale parameter) is the stress responsible for 63.2% of the sample failures. The flexural strength data was placed in rank order and an Anderson–Darling test used to confirm that the data was described by a Weibull distribution using the computer programme Easy-Fit 5.2 (MathWave Technologies, USA). This showed that the *A *^{2 }statistic was less than the critical value for each material’s strength data at the 95% significance level. A regression method was then carried out to derive the characteristic strength and Weibull modulus for each FRC material. Statistical differences in modulus values were determined by comparing the upper and lower bounds of the 95% confidence intervals for each material. Where no overlap occurred, the differences were considered to be significant. Plots of survival probability were also created to assess the distribution of flexure strengths.

## 2.2

## Effect of variation of sample aspect ratio

To examine the effects of altering the *L */ *D *ratio on the calculated flexural properties, ten rods of each of the post materials were also tested in three-point bend with inter-support distances of 64 mm and 16 mm. This provided samples with aspect ratios which were twice and half the length of the 32 mm samples. Because long samples of the cast gold could not be fabricated, this material was excluded from this part of the study. As a further examination of the effects on flexural modulus values of varying the length of the samples, three-point bending was carried out on five samples of a metal—steel, a carbon fiber composite (Composipost) and a glass fiber composite (Aesthetiplus) at gradually decreasing support widths from 80 mm to 12 mm. Statistical analysis with separate one-way ANOVA and post hoc Scheffé tests was carried out for all nine products with support widths ( *n *= 3) as the independent variable.

## 2

## Materials and methods

Lengths of 100 mm wrought stainless steel and titanium, glass fiber and carbon fiber composites were obtained from several manufacturers. To provide a comparison with a cast precious metal alloy, rods of a type IV gold alloy, Engelhard EC 620 (Engelhard-Clal (UK) Ltd., Chessington, England) were fabricated. The samples were cast by the lost wax process using rigid rods of non-residual plastic as the burn-out patterns. The composition, dimensions and manufacturers of all the tested materials are listed in Table 1 .