Dentine exhibited superior creep stability compared to resin-based dental materials.
Dentine is considered as a viscoelastic material with limited viscous deformation.
Burgers model is suitable to evaluate the viscoelasticity of dentine and resins.
To evaluate and compare the viscoelastic properties of dentine and resin-based dental materials by bulk compressive test and the Burgers model.
Materials and methods
Sound dentine, three resin composites as well as a resin-based cement were prepared into cylindrical specimens (n = 8). A bulk compressive creep test was applied with a constant load of 300 N (23.9 MPa) for 2 h, followed by another 2 h recovery. The maximum strain, creep stain, percentage of recovery and permanent set was measured using a linear variable displacement transducer. The viscoelastic properties were characterized via the Burgers model, and the instantaneous elastic, viscous as well as elastic delayed deformation were separated from the total strain. Data were analysed via ANOVA (or Welch’s Test) and Tukey (or Games–Howell Test) with a significance level of 0.05.
Sound dentine presented the lowest maximum strain, creep strain, permanent set and the highest percentage of recovery, followed by 3 resin composites with comparable parameters, while the cement showed a significantly higher maximum strain, permanent set and lower percentage of recovery ( p < 0.001). The Burgers model presented acceptable fits for characterization viscoelastic processes of both dentine and resin-based dental materials. Viscous and elastic delayed strain of dentine was significantly lower than those for tested materials ( p < 0.001) with the highest instantaneous elastic strain percentage. Similar viscous and delayed strain was found among the 4 resin-based materials ( p > 0.05).
Sound dentine exhibited superior creep stability compared to resin-based dental materials. The viscous deformation in sound dentine could be ignored when loading parallel to dentine tubules.
Teeth have a remarkable and hierarchically organized structure. Considering their composition and formation, teeth display enviable mechanical properties in terms of their damage resistance under the complicated loading associated with occlusion and mastication of foodstuffs [ ]. Substitute biomaterials for teeth, including a wide range of restorative, and cement materials, have been developed to match the mechanical properties of natural teeth to lower the failure rate and enable a longer service life. This is because the closer the mechanical properties of restorative materials to those of the natural tooth tissue results in significantly less stress concentration at the interface between teeth and restorations which accordingly leads to lower failure rate [ ]. A comprehensive and full-scale understanding of the mechanical properties of natural teeth and restorative materials is thus of importance for improving the durability of dental materials and developing innovative biomimetic materials.
In previous investigations [ ], hardness and elastic modulus of tooth tissue have been well studied as an indication of the instant mechanical properties, whereas many questions in the field of time-dependent properties, such as viscoelastic properties, remain and are still unclear [ ]. Creep, which is one of the major viscoelastic properties of a material, is defined as the tendency to continuously deform, either permanently or possibly recover (upon unloading) due to constant loading (static creep strain) or cyclic loading (dynamic creep strain) [ ], and may essentially affect the force bearing and stress distribution in a structure [ ]. In dental materials, creep may lead to failure of the adhesion interface between dentine and composite under cyclic loading, and so called “creep failure” [ , ]. The difference and latency of creep deformation between the two materials potentially forms a stress concentration or even a gap at the adhesive interface, which eventually results in adhesion failure. Creep behavior of resin composites have been evaluated in previous studies, resulting in maximum bulk compressive creep strains that ranged from 0.47% to 1.80% depending on the resin composition and filler percentage [ , ]. The question as to whether the creep and recovery properties are consistent with those of teeth has not been compared to the best of our knowledge.
Researches have previously found that enamel has creep deformation [ , ]. However, in clinical practice, cavities and tooth preparation often involves the entire enamel, and the interface between hard tissue and dental material is often located within dentine rather than in enamel [ , ]. Compared with enamel, dentine is composed of much more organic matrix and water [ ]. The complex components and the multiscale hierarchical microstructure of dentine tubules lead to the time-dependent deformation of dentine remaining controversial [ , ]. Most previous studies with respect to dentine’s creep were conducted at the nano-scale [ , ], while the atomic force microscope or nano-indentation projected area includes limited dentine tubules, peri- and inter-tubular dentine [ ], and the dentine deformation show significant spatial variations due to the density and direction of dentine tubules within the crown [ , ]. To generate a more holistic view of the time-dependent deformation behavior of coronal dentine and to understand the contribution of fluid-filled tubules in deformation, requires the use of a macroscopic methodology.
Therefore, the aim of this study was to evaluate the viscoelastic properties including creep and recovery behavior of sound dentine by bulk compressive test, and to compare with those of typical resin-based restorative and cement materials. Moreover, the Burgers model was used to quantitatively describe the viscoelastic behavior and to understand the deformation mechanisms of dentine and resin-based materials [ , ]. The null hypothesis was that no difference in creep and recovery deformation would be found between sound dentine and resin-based dental materials.
Materials and methods
Fourteen fresh non-caries molars free from fracture and irregularities in shape were obtained from patients with signed written consent and following all the protocols approved by the Ethics Committee of the Dental Subsidiary, Guanghua School of Stomatology, Sun Yat-sen University. Specimens were stored in Hank’s balanced salt solution (HBSS, Sigma-aldrich, USA) at 4 °C, and fabricated within 24 h. The coronal dentine of the molars was trimmed cylindrically. Sagittal dentine discs (2.8 mm–3.0 mm height) were cut from coronal region of the teeth using a water-cooled diamond-cutting saw (Accutom-50, Struers, Denmark). Then the discs were fixed on an automatic grinding machine (Tegramin-30, Struers, Denmark) with special wax, and finished/polished with wet carborundum papers from #500 to #1000 grits. The finished discs were 2.50 ± 0.01 mm in height with upper and lower surfaces plano-parallel. Additionally, the surface (close to enamel-dentinal junction) was etched with 37% phosphoric acid for 10 s to ensure the removal of enamel. The discs were further trimmed down into cylinders with diameter of 4 mm with the aid of a stainless steel mold ( Fig. 1 a–c). The specimens were kept wet with HBSS prior to testing.
Resin specimens preparation
Four resin-based dental materials were investigated as listed in Table 1 (n = 8). Specimens were prepared using stainless steel molds (4.0 mm diameter, 2.7 mm height). Materials were filled (or injected) into the mold and light cured according to the manufacturer’s instructions (Elipar Freelight, 3M ESPE, USA). After irradiation, specimens were polished (Tegramin-30) using carborundum papers to #1000 grits as described above, and reached the final size of 2.50 ± 0.01 mm in height with upper and lower surfaces plano-parallel. Specimens were then stored in HBSS at 25 °C for 1 week before testing.
|Product||Group||Type||Manufacturer||LOT code||Composition||Inorganic filler (wt.%)|
|Filtek Z350 XT||XT||Conventional resin-composite||3M ESPE, USA||N963211||bis-GMA, UDMA, TEGDMA, bis-EMA||78.5|
|Filtek Supreme Ultra||SU||Flowable resin-composite||3M ESPE, USA||N970991||bis-GMA, TEGDMA, Procrylat resins||65|
|Paracore||PC||Core build-up composite||Coltene Whaledent, Switzerland||166285||Methacrylates, fluoride, barium glass, amorphous silica||68|
|RelyX Unicem||UN||Self-adhesive resin cement||3M ESPE, USA||4434189||Glass powder, methacrylated phosphoric acid esters, TEGDMA||72|
Bulk compressive creep and recovery test
A universal material testing machine (E3000, Instron, UK) was used to conduct the bulk compressive creep test. Two platens were constructed from high tensile steel alloy with highly polished surfaces. A linear variable displacement transducer (LVDT) (SPN-S2, SANSEER, China) with precision of 0.1 μm was attached to the platens to measure changes in displacement throughout the test ( Fig. 1 d). A platen-to-platen loading test was conducted before each test to ensure the stability of the loading cells and the creep due to machine compliance was negligible.
Specimens were immersed in HBSS during testing at 25 °C. A pre-load of 2 N was applied, and then increased to 300 N (24 MPa, corresponding to the maximum stress of normal occlusion [ ]) at a loading rate of 1 N/s. The constant load of 300 N was held for 2 h. After that, it was decreased to 2 N at an unloading rate of 1 N/s, followed by a 2 h recovery after load removal (the 2 N load was applied during the recovery 2 h) [ , ]. The resulting time, load and displacements signal from LVDT was recorded via WaveMatrix software at a frequency of 1 Hz. Strain at each time point was calculated and the best fitting curve was developed using Matlab R2016a (MathWorks, Natick, US).
A schematic representation of a typical creep and recovery curve (strain-time curve) is illustrated in Fig. 2 , which consisted of four parts: rapid deformation (RD), creep deformation (CD), rapid recovery (RR), and a further time-dependent viscoelastic recovery (VR) [ , ]. If the recovery was not complete within the given time of the test, a permanent set (PS) is recorded [ , ]. The following parameters were considered to compare the time-dependent creep and recovery behavior among groups:
Maximum deformation (RD + CD)
Creep deformation (CD)
Percentage of recovery [(RR + VR)/(RD + CD) × 100%]
Permanent set (PS)
Burgers model analysis
The load response of polymeric materials can be approximated by various viscoelastic models. A simple model of wide applicability is Burgers model, which is based on a combination of a Maxwell model in series with a Kelvin–Voigt model described in detail in previous studies [ , ]. The time course of the specimen’s length reduction h under constant compressive load can be expressed generally as [ , ]:
in which f and K are functions of the specimen and/or indenter shape, and ψ ( F , J , t ) is a function of the characteristic load F and creep compliance function J ( t ), which expresses the time course of the deformation caused by unit load. The creep compliance function for the Burgers model is
with constants C 0 , c v , C 1 and τ . C 0 pertains to the instantaneous elastic response (sometimes this also includes a degree of plastic deformation) associated with the spring in Maxwell model; c v characterizes the velocity of viscous deformation of the dashpot in Maxwell model; C 1 and τ are related to the Kelvin–Voigt model, where C 1 is associated with the delayed deformation, and τ is the retardation time, characterizing the rate of delayed deformation. [During the period t = τ the deformation increases to (1 − e −1 ) ≈63% of its final value.] For a cylindrical specimen of radius r , compressed between two rigid plates, f = h ( t ), and K = 1/(4 r ). For constant load after step change from 0 to the nominal value F
However, the load increase from 0 to F always takes some time t R , and this must be considered, especially for non-negligible t R . Oyen [ , ] proposed a simple correction for the case when the load increases from 0 to F by a constant loading rate R . The term C 1 [1 − exp(− t / τ )] is replaced by the term C 1 [1 − ρ exp(− t / τ )], where ρ is the ramp correction factor
Combining Eqs. (1)–(4) and rearrangement gives the following expression for the time course of thickness reduction h ( t ) under constant load F after ramp loading lasting t R :
The constants C 0 , c v , C 1 , τ and ρ can be obtained by minimizing the sum of the squared differences between the measured and calculated h ( t ) values for various times t under constant load. However, the procedure must be modified. Eq. (5) contains several terms that do not depend on time: C 0 , c v t R /2 and ρ . Therefore, they cannot be determined individually, but only as a whole, as constants in the modified regression function:
The series of h ( t ) values is fitted by Eq. (6) using the least squares method and a suitable solver, and constants B , c v , D and τ are found. Then, the ramp correction factor ρ is calculated for the known duration t R of load increase and the retardation time τ . Finally, the constant C 1 is determined as C 1 = D / ρ , and C 0 is found as C 0 = B + c v t R /2 − C 1 . The quality of fit was illustrated by the relative differences between measured and calculated values at each test point, namely
After that, instantaneous elastic deformation, viscous deformation and elastic delayed deformation under a constant load of 300 N as well as their percentage in total strain were calculated by Eq. (6) .
Normally distributed deformation and recovery parameters in Section 2.4 as well as for the three types of deformation and their percentage in total strain related to Burgers model in Section 2.5 were analyzed and compared using One-way ANOVA and Tukey–Kramer HSD when variances were homogeneous, and with Welch’s Test and Games–Howell Tests when variances were heterogeneous (Levene’s test, p ≤ 0.05). Differences were considered statistically significant at the level of 0.05 (SPSS v24, IBM, Armonk, US).
Six additional dentine specimens were sputter coated to observe the direction and distribution of dentine tubules, and compare the surface morphology before and after loading and recovery using a scanning electron microscopy (SEM) (Phenom ProX, Phenom-World, Netherlands).
The mean values and standard deviations of maximum deformation strain, creep strain, percentage of recovery and permanent set strain are summarized in Table 2 , with statistically significant differences between groups. Sound dentine presented the lowest maximum deformation strain, creep strain, permanent set and the highest percentage of recovery compared to all resin-based materials ( p < 0.001). Comparable parameters were exhibited among the 3 resin-based dentine restorative materials XT, SU and PC ( p > 0.05). As the only resin-based cement material, group UN showed a significantly higher maximum deformation strain, permanent set and lower percentage of recovery compared to other filling resin composites ( p < 0.001).