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The bulk compressive creep and recovery behavior of human dentine and resin-based dental materials
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The bulk compressive creep and recovery behavior of human dentine and resin-based dental materials Xiaodong Wang a,1 , Jing Zhou a,1 , Dehua Kang b , Michael V. Swain c,d , Jaroslav Menˇcík e , Yutao Jian f,∗∗ , Ke Zhao a,∗ a
Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Engineering Research Center of Technology and Materials for Oral Reconstruction, Guangdong Provincial Key Laboratory of Stomatology, Guangzhou, China b Department of Radiation Oncology, State Key Laboratory of Oncology in South China, Collaborative Innovation Center for Cancer Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China c AMME, University of Sydney, NSW 2006, Australia d Don State Technical University, Rostov-on Don, Russia e Department of Mechanics, Materials and Machine Parts, Faculty of Transport Sciences, University of Pardubice, Czech Republic f Institute of Stomatological Research, Guangdong Provincial Key Laboratory of Stomatology, Sun Yat-sen University, Guangzhou, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. To evaluate and compare the viscoelastic properties of dentine and resin-based
Available online xxx
dental materials by bulk compressive test and the Burgers model.
Keywords:
were prepared into cylindrical specimens (n = 8). A bulk compressive creep test was applied
Materials and methods. Sound dentine, three resin composites as well as a resin-based cement Viscoelastic
with a constant load of 300 N (23.9 MPa) for 2 h, followed by another 2 h recovery. The max-
Creep
imum strain, creep stain, percentage of recovery and permanent set was measured using a
Dentine
linear variable displacement transducer. The viscoelastic properties were characterized via
Resin composite
the Burgers model, and the instantaneous elastic, viscous as well as elastic delayed deforma-
Burgers model
tion 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. Results. 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
∗ Corresponding author at: Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Engineering Research Center of Technology and Materials for Oral Reconstruction, Guangdong Provincial Key Laboratory of Stomatology, 54 Ling-yuan West Street, Guangzhou 510055, China. ∗∗ Co-corresponding author at: Institute of Stomatological Research, Guangdong Provincial Key Laboratory of Stomatology, Sun Yat-sen University, Zhong- shan Er Road 74, Guangzhou 510080, China. E-mail addresses: [email protected] (X. Wang), [email protected] (J. Zhou), [email protected] ˇ (D. Kang), [email protected] (M.V. Swain), [email protected] (J. Mencík), [email protected] (Y. Jian), [email protected], [email protected] (K. Zhao). https://doi.org/10.1016/j.dental.2020.01.003 0109-5641/© 2020 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.
Please cite this article in press as: Wang X, et al. The bulk compressive creep and recovery behavior of human dentine and resin-based dental materials. Dent Mater (2020), https://doi.org/10.1016/j.dental.2020.01.003
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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). Significance. 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. © 2020 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.
1.
Introduction
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 [1]. 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 [2]. 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 [3–5], 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 [6]. 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) [7], and may essentially affect the force bearing and stress distribution in a structure [8]. In dental materials, creep may lead to failure of the adhesion interface between dentine and composite under cyclic loading, and so called “creep failure” [9,10]. 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 [11,12]. 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 [13,14]. However, in clinical practice, cavities
1
Contributed equally to this work.
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 [15,16]. Compared with enamel, dentine is composed of much more organic matrix and water [17]. The complex components and the multiscale hierarchical microstructure of dentine tubules lead to the time-dependent deformation of dentine remaining controversial [18,19]. Most previous studies with respect to dentine’s creep were conducted at the nano-scale [19,20], while the atomic force microscope or nanoindentation projected area includes limited dentine tubules, peri- and inter-tubular dentine [14], and the dentine deformation show significant spatial variations due to the density and direction of dentine tubules within the crown [21,22]. 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 [23,24]. The null hypothesis was that no difference in creep and recovery deformation would be found between sound dentine and resin-based dental materials.
2.
Materials and methods
2.1.
Dentine preparation
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, Sigmaaldrich, 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
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Fig. 1 – Steps involved in preparation of dentine samples and set-up used for the bulk compressive deformation test. a) Molar tooth prior to parallel slicing; b) cut parallel section showing presence of enamel on the margins, the white ring on the surface indicates the region from which the final sample for testing was obtained; c) finally prepared dentine specimen and d) experimental set-up showing the cylindrical sample loaded between two steel metal plates with the displacement measured directly between the loading plates using an LVDT.
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. 1a–c). The specimens were kept wet with HBSS prior to testing.
[11,12]. 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).
2.2.
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) [11,12]. If the recovery was not complete within the given time of the test, a permanent set (PS) is recorded [11,12]. The following parameters were considered to compare the time-dependent creep and recovery behavior among groups:
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 (Tegramin30) 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.
2.3.
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 m was attached to the platens to measure changes in displacement throughout the test (Fig. 1d). 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 [25]) 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)
2.4.
(1) (2) (3) (4)
Deformation strain
Maximum deformation (RD + CD) Creep deformation (CD) Percentage of recovery [(RR + VR)/(RD + CD) × 100%] Permanent set (PS)
2.5.
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 [26,27]. The time course of the specimen’s length reduction h under constant compressive load can be expressed generally as [23,24]: f [h(t)] =K (F,J,t)
(1)
in which f and K are functions of the specimen and/or indenter shape, and (F, J, t) is a function of the characteristic load F and creep compliance function J(t), which expresses the time
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Table 1 – Investigated resin-based material; manufacturer’s information, material type and composition. Product
Group
Type
Manufacturer
LOT code
Composition
Inorganic filler (wt.%)
Filtek Z350 XT
XT
Conventional resin-composite
3M ESPE, USA
N963211
78.5
Filtek Supreme Ultra
SU
Flowable resin-composite
3M ESPE, USA
N970991
Paracore
PC
Core build-up composite
Coltene Whaledent, Switzerland
166285
RelyX Unicem
UN
Self-adhesive resin cement
3M ESPE, USA
4434189
bis-GMA, UDMA, TEGDMA, bis-EMA bis-GMA, TEGDMA, Procrylat resins Methacrylates, fluoride, barium glass, amorphous silica Glass powder, methacrylated phosphoric acid esters, TEGDMA
65
68
72
Fig. 2 – Schematic representation of a specimen’s typical bulk compressive deformation and recovery curve. The strain–time curve consisted of four parts: rapid deformation, creep deformation, rapid recovery and time-dependent recovery.
Table 2 – Mean values (standard deviations, SD) of maximum deformation strain, creep strain, percentage of recovery and permanent set strain of the dentin and resin-based materials investigated. Group DU XT SU PC UN
Maximum strain (%) a
0.35 (0.06) 0.48b (0.04) 0.52b (0.03) 0.54b (0.06) 0.73c (0.09)
Creep strain (%) a
0.02 0.06b 0.06b 0.06b 0.07b
Percentage of recovery (%) a
(0.01) (0.01) (0.01) (0.01) (0.03)
90.45 (2.88) 84.83b (2.68) 86.59a,b (3.91) 87.87a,b (1.85) 71.21c (5.55)
Permanent set strain (%) 0.03a (0.01) 0.07b (0.02) 0.07b (0.02) 0.07b (0.01) 0.22c (0.05)
Maximum strain: F = 25.79, p < 0.001; Creep strain: F = 27.01, p < 0.001; Percentage of recovery: F = 18.54, p < 0.001; Permanent set strain: F = 24.68, p < 0.001 (Welch’s Test). Statistical differences between groups were signed with different letters in superscript (Games–Howell tests, p = 0.05).
course of the deformation caused by unit load. The creep compliance function for the Burgers model is J(t) =C0 +cv t+C1 [1−exp(−t/)]
(2)
with constants C0 , cv , C1 and . C0 pertains to the instantaneous elastic response (sometimes this also includes a degree of plastic deformation) associated with the spring in Maxwell model; cv characterizes the velocity of viscous deformation of the dashpot in Maxwell model; C1 and are related to the Kelvin–Voigt model, where C1 is associated with the delayed deformation, and is the retardation time, characterizing the
rate of delayed deformation. [During the period t = 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/(4r). For constant load after step change from 0 to the nominal value F =FJ(t)
(3)
However, the load increase from 0 to F always takes some time tR , and this must be considered, especially for nonnegligible tR . Oyen [28,29] proposed a simple correction for the case when the load increases from 0 to F by a constant loading
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rate R. The term C1 [1 − exp(−t/)] is replaced by the term C1 [1 − exp(−t/)], where is the ramp correction factor = (/tR )[exp(tR /)−1];tR =F/R
(4)
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 tR : h(t) =FK{C0 +cv (t−tR /2)+C1 [1−exp(−t/)]}
(5)
The constants C0 , cv , C1 , and 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: C0 , cv tR /2 and . Therefore, they cannot be determined individually, but only as a whole, as constants in the modified regression function: h(t) =FK[B+cv t−Dexp(−t/)]
(6)
The series of h(t) values is fitted by Eq. (6) using the least squares method and a suitable solver, and constants B, cv , D and are found. Then, the ramp correction factor is calculated for the known duration tR of load increase and the retardation time . Finally, the constant C1 is determined as C1 = D/, and C0 is found as C0 = B + cv tR /2 − C1 . The quality of fit was illustrated by the relative differences between measured and calculated values at each test point, namely rel(%) = [hm (t)–hc (t)]/hm (t)
(7)
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).
2.6.
Statistical analysis
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).
2.7.
Morphology evaluation
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).
Table 3 – Constants for creep compliance of dentine and resin-based materials. Test parameters: bulk compressive test, F = 300 N, time under load: 7200 s. Model: Spring + Dashpot + Kelvin–Voigt body. Group
C0 (mm2 /N)
cv (mm2 s/N)
C1 (mm2 /N)
(s)
DU XT SU PC UN
2.195E-04 2.815E-04 3.055E-04 3.211E-04 4.463E-04
3.250E-10 2.179E-09 2.699E-09 2.284E-09 2.850E-09
8.028E-06 2.252E-05 1.964E-05 2.278E-05 2.908E-05
390 818 729 837 798
All constants were based on the average data of time-strain curves of 8 specimens in each group as shown in Fig. 3a and obtained by the least squares method.
3.
Results
3.1.
Deformation strain
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). Fig. 3a shows the best fitting time-strain curve up to 15,000 s of each group developed by Matlab R2016a software. The sound dentine presented a flatter creep curve from 300 s to 7500 s compared to resin-based materials. All groups demonstrated similar strain-time change tendency curves, thus a higher maximum deformation strain indicates a greater permanent set. Fitting results of creep strain-ln(time) curves from 300 s to 7500 s are shown in Fig. 3b. The strain presented well fitted linearly (R2 ≥ 0.99) with the logarithm of the time for all groups, which indicated that the creep rate decreased with time from 300 s to 7500 s.
3.2.
Burgers model
Constants in creep compliance functions (Eq. (2)) for Burgers model (Spring + Dashpot + one Kelvin–Voigt body) are calculated according to the average creep curves in Fig. 3a and listed in Table 3. The creep compliance function proved to be suitable and good fits for the characterization of viscoelastic processes of both dentine and resin-based dental materials with relative errors (rel) less than 0.2% for most points and not exceeding 1% anywhere for all groups as shown in Fig. 4. The mean values and standard deviations of the three components of the deformation strain and their percentage in total strain are calculated according to Eq. (6) and illustrated in Table 4. For all groups, instantaneous elastic deformation remained unchanged during the constant loading process, while the viscous as well as elastic delayed deformation
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Fig. 3 – Best fitting curves for each group by Matlab software. Each curve is the fitting result of 8 specimens. (a) Loading, creep and recovery strain-time curves. (b) Creep strain – ln(time) curves from 300 s to 7500 s under a constant 300 N. Dotted lines indicate the fitting curves. All groups show well fitting linear results with R2 ≥ 0.99.
Table 4 – Instantaneous elastic deformation, viscous deformation, elastic delayed deformation and their percentage in total strain under constant loading of 300 N after 7200 s for each group [mean (SD)]. Group Total deformation
DU XT SU PC UN
Viscous deformation
Instantaneous elastic deformation (constant)
Elastic delayed deformation
Strain (%)
Strain (%)
Percentage in total strain (%)
Strain (%)
Percentage in total strain (%)
Strain (%)
Percentage in total strain (%)
0.35a (0.06) 0.48b (0.04) 0.52b (0.03) 0.54b (0.06) 0.73c (0.09)
0.33a (0.04) 0.41b (0.04) 0.45b (0.03) 0.47b (0.04) 0.64c (0.05)
94.40a 85.85b 86.27b 86.60b 88.77b
0.00a 0.03b 0.03b 0.03b 0.03b
1.14a 5.41b 5.55b 5.35b 3.98b
0.02a 0.04b 0.04b 0.05b 0.05b
4.47a 8.75b 8.31b 8.05b 7.25b
(1.78) (1.56) (2.72) (1.75) (3.15)
(0.00) (0.00) (0.01) (0.01) (0.01)
(0.69) (0.99) (1.68) (0.85) (1.46)
(0.01) (0.01) (0.01) (0.01) (0.02)
(1.17) (1.04) (1.49) (1.04) (2.03)
Total strain: F = 25.79, p < 0.001 (Welch’s Test); constant strain: F = 61.10, p < 0.001 (ANOVA); constant strain percentage: F = 19.42, p < 0.001 (ANOVA); viscous strain: F = 52.30, p < 0.001 (Welch’s Test); viscous strain percentage: F = 19.60, p < 0.001 (ANOVA); delayed strain: F = 25.09, p < 0.001 (Welch’s Test); delayed strain percentage: F = 11.69, p < 0.001 (ANOVA). Statistical differences between groups were signed with different letters in superscript (Tukey−Kramer HSD and Games−Howell tests, p = 0.05).
increased over time as shown in Fig. 5. Most of the maximum strain after constant loading with 300 N for 7200 s consists of instantaneous elastic strain (including some plastic deformation) with a percentage that ranged from 85.85% to 94.40%. Sound dentine showed a significantly lower instantaneous elastic strain of 0.33% but with the highest percentage of 94.40%, and the viscous strain could be considered almost negligible as well as a significantly lower delayed elastic strain of 0.02% (p < 0.001). XT, SU and PC presented comparable strains and percentage parameters with higher values for all three components of deformation compared to those of sound dentine (p < 0.001). Group UN showed a significantly higher instantaneous elastic strain than other groups (p < 0.001). However, the viscous and delayed elastic strain is similar to those of group XT, SU and PC (p > 0.05).
3.3.
Morphology evaluation
Fig. 6 shows the SEM images for surface morphology of sound dentine before and after loading. Dentine demonstrated a typical morphology of uniformly distributed dentinal tubules,
intertubular dentine and highly mineralized peritubular dentine with a direction perpendicular to the surface (Fig. 6A–B). After loading (creep), dentine showed cracks limited to the peritubular dentine with slight to moderate deformation of dentinal tubules (Fig. 6C–D).
4.
Discussion
In the current study, the time-dependent viscoelastic behavior of dentine and resin based dental materials by bulk compressive creep test were evaluated and compared. The test’s methodology used was modified according to the ISO 8013:2012(E) [30], since the required dimensions of the material to be tested were not feasible using human’s teeth. The maximum height of coronal dentine that can be obtained is reported as only about 3 mm [31]. Accordingly, the height of cylindrical specimens of compressive test had to be shortened to 2.5 mm to make sure that the dentinal tubules in each specimen had a maximum resemblance of the dentine structure from enamel-dentinal junction (EDJ) to pulp.
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Fig. 4 – Thickness reduction under constant load from 300 s to 7500 s for each group based on the following equation h(t) = FK[B + cv t – Dexp(−t/)]. These plots also display the relative error (Eq. (7)) during the constant maximum load portion of the test.
Under a constant load of 300 N, sound coronal dentine presented a maximum strain of 0.35%, a creep strain of 0.02% and a permanent set of 0.03% after 2 h unloading process. Most published studies on coronal dentine creep behavior were based on nanoindentation test [19,20], which could not compare with the current results directly. In a previous study on creep behavior of human root dentine by bulk compressive test, a 6–10 mm root dentin samples with 3.5 mm outer diameter and 1.5 mm internal canal diameter presents a similar maximum creep strain of about 0.40% under 300 N after 1.5 h, while the viscoelastic properties such as creep and irreversible deformation were not separately studied [18]. The multiscale hierarchical microstructure of dentine leads to mechanical properties variation from pulp to EDJ [22]. As the amount of mineral content increases and the dentinal tubule lumens decreases from the pulp to the EDJ [32], coronal dentine exhibits a stiffening effect with reduced strain rate and significant lower deformation strain compared to pulpal dentine [22]. In clinical practice, a restorative dental mate-
rial is often located within dentine at different depths [15,16]. Coronal dentine provides reliable support for the restorations, and it deforms under chewing loading from EDJ to pulp as a whole. In this respect, a bulk compressive test has some advantages for dentine viscoelastic behavior research compared to nanoindentation testing. It is worth noting that a maximum strain of 0.35% and a creep strain of 0.02% in the current study should be considered as macroscopic, comprehensive and representative results based on 2.5 mm coronal dentine. Creep behavior of resin composites are well evaluated in previous studies [11,12,33]. In a series of studies by Watts et al. [11,12,33], dental resin composites presented a maximum strain that ranged from 0.45% to 1.80% and a permanent set that ranged from 0.03% to 0.68% under a constant stress of 20 MPa after 2 h, which is consistent with the results of the current study. The viscoelastic behaviors of dentine and resinbased dental materials were compared directly in the current study, which earlier studies have not addressed to the best
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Fig. 5 – Instantaneous elastic strain (constant), viscous strain as well as delayed elastic strain in each group. The sum of the three types of strain equals to the total strain at each time point.
of our knowledge. Sound dentine presented the lowest maximum strain, creep strain, as well as permanent set, followed by 3 resin composite filling materials, while the resin cement presented the highest strain and permanent set. The differences in deformation could possible lead to a stress concentration at the adhesive layer or dentin – cement interface, and thus a potential risk of microleakage. Singh et al. evaluated the creep and fatigue properties of an adhesive compositesdentine model, in their calculation of fatigue life, samples can be considered as resulting from creep failure when the strain of the adhesive layer is larger than 2.1% [10]. Although there is still absence of direct clinical evidence that creep causes failures of bonding, the significant difference in viscoelastic properties between dentine and resin based materials should not be ignored and requires further study. All techniques have advantages and disadvantages. Bulk compressive tests have their own complications especially
because the surface of tested specimen as well as the loading planes are hardly perfectly parallel and absolutely smooth [34]. The imperfect parallelism and surface roughness could create complex stresses at the surface of the cylindrical specimen during the initial loading, which is unavoidable at present [35]. As the value of maximum displacement in the current study is very small and ranged from 8.75 m (0.35% × 2.5 mm) to 18.3 m (0.73% × 2.5 mm), even slight imperfect parallelism or surface roughness of only 1 m might lead to a plastic deformation strain due to stress concentration, which is hard to separate from the final permanent set. Therefore, a direct comparison of the parameters in Table 3 only provides semiquantitative impressions or even slight misunderstandings of the viscoelastic properties. To overcome these problems, the Burgers model was introduced to evaluate and predict the viscoelastic behaviors more accurately.
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Fig. 6 – SEM micrograph ×2000 and its local magnification ×10,000 for surface morphology of sound and long-term loaded dentine. (a–b) Sound dentine before loading presents a typical morphology of uniformly distributed open dentinal tubules; (c) dentine surface after creep. Dentinal tubules are slightly to moderately deformed; (d) magnification of (c). After loading, dentine presents cracks around dentinal tubules which are limited to peritubular dentine without propagating into the intertubular dentine (arrow). (D – dentinal tubules, P – peritubular dentine, I – intertubular dentine).
A four element Burgers model is a simple and classic viscoelastic model, widely used to represent the viscoelastic behavior of polymer [36]. Although some studies reported that it could fit creep curves of the composites well [37], so far, there is limited research which investigated the viscoelastic behaviors of dental resin composites and dentine with the Burgers model. Dental resin composites are considered as typical viscoelastic materials [11,12], and present an acceptable characterization of their creep response with Burgers model in the current study with relative errors not exceeding a few tenths of a percent [24]. However, for the initial stage of creep curve (from 300 s to 1000 s) thus the stage of transformation from elastic deformation to viscous deformation, it presented
larger discrepancies between the measured and calculated curves. Compared to resin composites, sound dentine presented a superior fitting effect especially for the initial stage, which demonstrated that dentin could also be considered as a viscoelastic material although the viscous strain is limited. More complex Burgers models with more than one K–V bodies in series might obtain a more accurate fitting result in a mathematical sense [23,24], while more creep parameters could also make it difficult for calculating and to explain the source of the viscosity associated with the composition of dentine or materials, as well as the clinical significance of the parameters. For the most general case of viscoelastic solid, the total strain is the sum of three essentially separate parts: instanta-
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neous elastic strain which appears instantly after loading and is absent after the load is removed, irreversible creep strain subjected to a constant stress which leads to a permanent set, and delayed elastic strain that increases under the applied stress, and is recovered once the stress is removed for an indefinite period of time [36]. Therefore, under ideal conditions, the permanent set should be related only to irreversible creep deformation. However, comparing the permanent set measured in Table 2 with the viscous deformation calculated in Table 4, a 0.03% to 0.04% higher strain was found for groups DU, XT, SU and PC, which could be due to the plastic deformation during the loading stage. Group UN presented a significantly higher permanent set of 0.22%, while the calculated viscous strain of 0.03% is similar to other resin composites. As the only resin cement material, it is well known that UN shows significantly lower mechanical properties including compression and flexural strength compared to filling resin composites [38], which make it more sensitive to stress concentrating due to the imperfect parallelism or surface roughness than other resin composites. Therefore, when characterizing viscoelastic properties of dentin and dental materials, Burgers model is useful to evaluate more accurately and to correct possible errors caused during testing. Creep curves can be divided into three stages: (i) the primary creep stage corresponds to a decay of the strain rate following the application of the constant stress; (ii) the secondary regime describes a constant strain rate in which strain is proportional to time; (iii) tertiary creep stage in which the strain rate accelerates up to rupture [39]. When stress and temperature are low (as in the current study), the secondary creep stage is probably not reached, and strain increased linearly with the logarithm of the time with a decreasing strain rate as shown in Fig. 3b, which is called logarithmic creep [40]. Logarithmic creep could be explained due to “work hardening” effect [39]. Creep of a composite occurs by cross-linked polymer chains untangling and slipping like dislocations movement in crystalline materials relative to one another, which generated flow continuously from the beginning. With increasing time, more dislocations appear and produce increasing interference with each other, thus decreasing the creep rate [39]. Meanwhile, the nanoparticles (fillers) in resin composites are usually brittle materials with higher hardness and elastic modulus, which have the greatest volume fraction and could lead to a significant improvement of the creep stability by effectively restricting the motion of cross-linked polymer [41]. This also accords with earlier observations, which showed that increased filler loading in resin composites decreased the creep strain magnitude [11,33]. Besides chain movement of cross-linked polymers, residual monomer could also play an important role in creep. As the most fluidic component, it is reported that lowering the residual monomer content could increase the creep resistance of composites [42]. Therefore, it is expected the creep of resin composites to be associated with the movement of crosslinked polymer chains and residual fluid monomer. When it comes to dentine, which consists of hydroxyapatite (HAP), collagen and water. Similar to fillers in composites, it is unlikely the ceramic component HAP itself will creep. However, the collagen will deform and the water will displace if there is sufficient permeability of the sample. Human
dentine is a porous hydrated composite material, and the dentinal fluid in tubules plays an important role in dentine deformation [19,42]. It is reported that the hardness, elastic modulus, and yield strength decrease with increasing orientation angle of dentine [21], which indicates increasing in strain with stress in the direction perpendicular to the dentinal tubules compared to that parallel to the dentinal tubules [42]. When dentine was compressed, the fluid in tubules were compressed and squeezed out in the direction of dentinal tubules, which is probably the basis for creep. Dentine samples used in this study were acquired below the central fossa, and the tubules were almost aligned parallel to the stress as shown in Fig. 6. Highly mineralized peritubular dentine and the sealed incompressible fluid in it leads to the greatest support against deformation and difficulty for fluid movement as the secondary tubules in this direction are very small and the permeability through the intertubular space is difficult, thus results in a non-significant creep behavior.
5.
Conclusions
With the limitations of bulk compressive test, sound dentine exhibited significantly decreased irreversible creep deformation thus superior creep stability compared to resin-based dental materials. Dentine creep could be related to the fluid movement in dentine tubules, and could be ignored when loading parallel to dentine tubules. The Burgers model could be used to evaluate the viscoelastic property of dentine and resin-based dental materials.
Declarations of interest None.
Acknowledgments This work was supported by the National Natural Science Foundation of China under grant Nos. 81600907, 81470767 and 81771110.
references
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.intl.elsevierhealth.com/journals/dema
The bulk compressive creep and recovery behavior of human dentine and resin-based dental materials Xiaodong Wang a,1 , Jing Zhou a,1 , Dehua Kang b , Michael V. Swain c,d , Jaroslav Menˇcík e , Yutao Jian f,∗∗ , Ke Zhao a,∗ a
Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Engineering Research Center of Technology and Materials for Oral Reconstruction, Guangdong Provincial Key Laboratory of Stomatology, Guangzhou, China b Department of Radiation Oncology, State Key Laboratory of Oncology in South China, Collaborative Innovation Center for Cancer Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China c AMME, University of Sydney, NSW 2006, Australia d Don State Technical University, Rostov-on Don, Russia e Department of Mechanics, Materials and Machine Parts, Faculty of Transport Sciences, University of Pardubice, Czech Republic f Institute of Stomatological Research, Guangdong Provincial Key Laboratory of Stomatology, Sun Yat-sen University, Guangzhou, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. To evaluate and compare the viscoelastic properties of dentine and resin-based
Available online xxx
dental materials by bulk compressive test and the Burgers model.
Keywords:
were prepared into cylindrical specimens (n = 8). A bulk compressive creep test was applied
Materials and methods. Sound dentine, three resin composites as well as a resin-based cement Viscoelastic
with a constant load of 300 N (23.9 MPa) for 2 h, followed by another 2 h recovery. The max-
Creep
imum strain, creep stain, percentage of recovery and permanent set was measured using a
Dentine
linear variable displacement transducer. The viscoelastic properties were characterized via
Resin composite
the Burgers model, and the instantaneous elastic, viscous as well as elastic delayed deforma-
Burgers model
tion 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. Results. 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
∗ Corresponding author at: Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Engineering Research Center of Technology and Materials for Oral Reconstruction, Guangdong Provincial Key Laboratory of Stomatology, 54 Ling-yuan West Street, Guangzhou 510055, China. ∗∗ Co-corresponding author at: Institute of Stomatological Research, Guangdong Provincial Key Laboratory of Stomatology, Sun Yat-sen University, Zhong- shan Er Road 74, Guangzhou 510080, China. E-mail addresses: [email protected] (X. Wang), [email protected] (J. Zhou), [email protected] ˇ (D. Kang), [email protected] (M.V. Swain), [email protected] (J. Mencík), [email protected] (Y. Jian), [email protected], [email protected] (K. Zhao). https://doi.org/10.1016/j.dental.2020.01.003 0109-5641/© 2020 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.
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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). Significance. 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. © 2020 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.
1.
Introduction
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 [1]. 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 [2]. 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 [3–5], 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 [6]. 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) [7], and may essentially affect the force bearing and stress distribution in a structure [8]. In dental materials, creep may lead to failure of the adhesion interface between dentine and composite under cyclic loading, and so called “creep failure” [9,10]. 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 [11,12]. 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 [13,14]. However, in clinical practice, cavities
1
Contributed equally to this work.
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 [15,16]. Compared with enamel, dentine is composed of much more organic matrix and water [17]. The complex components and the multiscale hierarchical microstructure of dentine tubules lead to the time-dependent deformation of dentine remaining controversial [18,19]. Most previous studies with respect to dentine’s creep were conducted at the nano-scale [19,20], while the atomic force microscope or nanoindentation projected area includes limited dentine tubules, peri- and inter-tubular dentine [14], and the dentine deformation show significant spatial variations due to the density and direction of dentine tubules within the crown [21,22]. 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 [23,24]. The null hypothesis was that no difference in creep and recovery deformation would be found between sound dentine and resin-based dental materials.
2.
Materials and methods
2.1.
Dentine preparation
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, Sigmaaldrich, 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
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Fig. 1 – Steps involved in preparation of dentine samples and set-up used for the bulk compressive deformation test. a) Molar tooth prior to parallel slicing; b) cut parallel section showing presence of enamel on the margins, the white ring on the surface indicates the region from which the final sample for testing was obtained; c) finally prepared dentine specimen and d) experimental set-up showing the cylindrical sample loaded between two steel metal plates with the displacement measured directly between the loading plates using an LVDT.
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. 1a–c). The specimens were kept wet with HBSS prior to testing.
[11,12]. 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).
2.2.
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) [11,12]. If the recovery was not complete within the given time of the test, a permanent set (PS) is recorded [11,12]. The following parameters were considered to compare the time-dependent creep and recovery behavior among groups:
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 (Tegramin30) 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.
2.3.
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 m was attached to the platens to measure changes in displacement throughout the test (Fig. 1d). 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 [25]) 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)
2.4.
(1) (2) (3) (4)
Deformation strain
Maximum deformation (RD + CD) Creep deformation (CD) Percentage of recovery [(RR + VR)/(RD + CD) × 100%] Permanent set (PS)
2.5.
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 [26,27]. The time course of the specimen’s length reduction h under constant compressive load can be expressed generally as [23,24]: f [h(t)] =K (F,J,t)
(1)
in which f and K are functions of the specimen and/or indenter shape, and (F, J, t) is a function of the characteristic load F and creep compliance function J(t), which expresses the time
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Table 1 – Investigated resin-based material; manufacturer’s information, material type and composition. Product
Group
Type
Manufacturer
LOT code
Composition
Inorganic filler (wt.%)
Filtek Z350 XT
XT
Conventional resin-composite
3M ESPE, USA
N963211
78.5
Filtek Supreme Ultra
SU
Flowable resin-composite
3M ESPE, USA
N970991
Paracore
PC
Core build-up composite
Coltene Whaledent, Switzerland
166285
RelyX Unicem
UN
Self-adhesive resin cement
3M ESPE, USA
4434189
bis-GMA, UDMA, TEGDMA, bis-EMA bis-GMA, TEGDMA, Procrylat resins Methacrylates, fluoride, barium glass, amorphous silica Glass powder, methacrylated phosphoric acid esters, TEGDMA
65
68
72
Fig. 2 – Schematic representation of a specimen’s typical bulk compressive deformation and recovery curve. The strain–time curve consisted of four parts: rapid deformation, creep deformation, rapid recovery and time-dependent recovery.
Table 2 – Mean values (standard deviations, SD) of maximum deformation strain, creep strain, percentage of recovery and permanent set strain of the dentin and resin-based materials investigated. Group DU XT SU PC UN
Maximum strain (%) a
0.35 (0.06) 0.48b (0.04) 0.52b (0.03) 0.54b (0.06) 0.73c (0.09)
Creep strain (%) a
0.02 0.06b 0.06b 0.06b 0.07b
Percentage of recovery (%) a
(0.01) (0.01) (0.01) (0.01) (0.03)
90.45 (2.88) 84.83b (2.68) 86.59a,b (3.91) 87.87a,b (1.85) 71.21c (5.55)
Permanent set strain (%) 0.03a (0.01) 0.07b (0.02) 0.07b (0.02) 0.07b (0.01) 0.22c (0.05)
Maximum strain: F = 25.79, p < 0.001; Creep strain: F = 27.01, p < 0.001; Percentage of recovery: F = 18.54, p < 0.001; Permanent set strain: F = 24.68, p < 0.001 (Welch’s Test). Statistical differences between groups were signed with different letters in superscript (Games–Howell tests, p = 0.05).
course of the deformation caused by unit load. The creep compliance function for the Burgers model is J(t) =C0 +cv t+C1 [1−exp(−t/)]
(2)
with constants C0 , cv , C1 and . C0 pertains to the instantaneous elastic response (sometimes this also includes a degree of plastic deformation) associated with the spring in Maxwell model; cv characterizes the velocity of viscous deformation of the dashpot in Maxwell model; C1 and are related to the Kelvin–Voigt model, where C1 is associated with the delayed deformation, and is the retardation time, characterizing the
rate of delayed deformation. [During the period t = 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/(4r). For constant load after step change from 0 to the nominal value F =FJ(t)
(3)
However, the load increase from 0 to F always takes some time tR , and this must be considered, especially for nonnegligible tR . Oyen [28,29] proposed a simple correction for the case when the load increases from 0 to F by a constant loading
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rate R. The term C1 [1 − exp(−t/)] is replaced by the term C1 [1 − exp(−t/)], where is the ramp correction factor = (/tR )[exp(tR /)−1];tR =F/R
(4)
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 tR : h(t) =FK{C0 +cv (t−tR /2)+C1 [1−exp(−t/)]}
(5)
The constants C0 , cv , C1 , and 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: C0 , cv tR /2 and . Therefore, they cannot be determined individually, but only as a whole, as constants in the modified regression function: h(t) =FK[B+cv t−Dexp(−t/)]
(6)
The series of h(t) values is fitted by Eq. (6) using the least squares method and a suitable solver, and constants B, cv , D and are found. Then, the ramp correction factor is calculated for the known duration tR of load increase and the retardation time . Finally, the constant C1 is determined as C1 = D/, and C0 is found as C0 = B + cv tR /2 − C1 . The quality of fit was illustrated by the relative differences between measured and calculated values at each test point, namely rel(%) = [hm (t)–hc (t)]/hm (t)
(7)
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).
2.6.
Statistical analysis
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).
2.7.
Morphology evaluation
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).
Table 3 – Constants for creep compliance of dentine and resin-based materials. Test parameters: bulk compressive test, F = 300 N, time under load: 7200 s. Model: Spring + Dashpot + Kelvin–Voigt body. Group
C0 (mm2 /N)
cv (mm2 s/N)
C1 (mm2 /N)
(s)
DU XT SU PC UN
2.195E-04 2.815E-04 3.055E-04 3.211E-04 4.463E-04
3.250E-10 2.179E-09 2.699E-09 2.284E-09 2.850E-09
8.028E-06 2.252E-05 1.964E-05 2.278E-05 2.908E-05
390 818 729 837 798
All constants were based on the average data of time-strain curves of 8 specimens in each group as shown in Fig. 3a and obtained by the least squares method.
3.
Results
3.1.
Deformation strain
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). Fig. 3a shows the best fitting time-strain curve up to 15,000 s of each group developed by Matlab R2016a software. The sound dentine presented a flatter creep curve from 300 s to 7500 s compared to resin-based materials. All groups demonstrated similar strain-time change tendency curves, thus a higher maximum deformation strain indicates a greater permanent set. Fitting results of creep strain-ln(time) curves from 300 s to 7500 s are shown in Fig. 3b. The strain presented well fitted linearly (R2 ≥ 0.99) with the logarithm of the time for all groups, which indicated that the creep rate decreased with time from 300 s to 7500 s.
3.2.
Burgers model
Constants in creep compliance functions (Eq. (2)) for Burgers model (Spring + Dashpot + one Kelvin–Voigt body) are calculated according to the average creep curves in Fig. 3a and listed in Table 3. The creep compliance function proved to be suitable and good fits for the characterization of viscoelastic processes of both dentine and resin-based dental materials with relative errors (rel) less than 0.2% for most points and not exceeding 1% anywhere for all groups as shown in Fig. 4. The mean values and standard deviations of the three components of the deformation strain and their percentage in total strain are calculated according to Eq. (6) and illustrated in Table 4. For all groups, instantaneous elastic deformation remained unchanged during the constant loading process, while the viscous as well as elastic delayed deformation
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Fig. 3 – Best fitting curves for each group by Matlab software. Each curve is the fitting result of 8 specimens. (a) Loading, creep and recovery strain-time curves. (b) Creep strain – ln(time) curves from 300 s to 7500 s under a constant 300 N. Dotted lines indicate the fitting curves. All groups show well fitting linear results with R2 ≥ 0.99.
Table 4 – Instantaneous elastic deformation, viscous deformation, elastic delayed deformation and their percentage in total strain under constant loading of 300 N after 7200 s for each group [mean (SD)]. Group Total deformation
DU XT SU PC UN
Viscous deformation
Instantaneous elastic deformation (constant)
Elastic delayed deformation
Strain (%)
Strain (%)
Percentage in total strain (%)
Strain (%)
Percentage in total strain (%)
Strain (%)
Percentage in total strain (%)
0.35a (0.06) 0.48b (0.04) 0.52b (0.03) 0.54b (0.06) 0.73c (0.09)
0.33a (0.04) 0.41b (0.04) 0.45b (0.03) 0.47b (0.04) 0.64c (0.05)
94.40a 85.85b 86.27b 86.60b 88.77b
0.00a 0.03b 0.03b 0.03b 0.03b
1.14a 5.41b 5.55b 5.35b 3.98b
0.02a 0.04b 0.04b 0.05b 0.05b
4.47a 8.75b 8.31b 8.05b 7.25b
(1.78) (1.56) (2.72) (1.75) (3.15)
(0.00) (0.00) (0.01) (0.01) (0.01)
(0.69) (0.99) (1.68) (0.85) (1.46)
(0.01) (0.01) (0.01) (0.01) (0.02)
(1.17) (1.04) (1.49) (1.04) (2.03)
Total strain: F = 25.79, p < 0.001 (Welch’s Test); constant strain: F = 61.10, p < 0.001 (ANOVA); constant strain percentage: F = 19.42, p < 0.001 (ANOVA); viscous strain: F = 52.30, p < 0.001 (Welch’s Test); viscous strain percentage: F = 19.60, p < 0.001 (ANOVA); delayed strain: F = 25.09, p < 0.001 (Welch’s Test); delayed strain percentage: F = 11.69, p < 0.001 (ANOVA). Statistical differences between groups were signed with different letters in superscript (Tukey−Kramer HSD and Games−Howell tests, p = 0.05).
increased over time as shown in Fig. 5. Most of the maximum strain after constant loading with 300 N for 7200 s consists of instantaneous elastic strain (including some plastic deformation) with a percentage that ranged from 85.85% to 94.40%. Sound dentine showed a significantly lower instantaneous elastic strain of 0.33% but with the highest percentage of 94.40%, and the viscous strain could be considered almost negligible as well as a significantly lower delayed elastic strain of 0.02% (p < 0.001). XT, SU and PC presented comparable strains and percentage parameters with higher values for all three components of deformation compared to those of sound dentine (p < 0.001). Group UN showed a significantly higher instantaneous elastic strain than other groups (p < 0.001). However, the viscous and delayed elastic strain is similar to those of group XT, SU and PC (p > 0.05).
3.3.
Morphology evaluation
Fig. 6 shows the SEM images for surface morphology of sound dentine before and after loading. Dentine demonstrated a typical morphology of uniformly distributed dentinal tubules,
intertubular dentine and highly mineralized peritubular dentine with a direction perpendicular to the surface (Fig. 6A–B). After loading (creep), dentine showed cracks limited to the peritubular dentine with slight to moderate deformation of dentinal tubules (Fig. 6C–D).
4.
Discussion
In the current study, the time-dependent viscoelastic behavior of dentine and resin based dental materials by bulk compressive creep test were evaluated and compared. The test’s methodology used was modified according to the ISO 8013:2012(E) [30], since the required dimensions of the material to be tested were not feasible using human’s teeth. The maximum height of coronal dentine that can be obtained is reported as only about 3 mm [31]. Accordingly, the height of cylindrical specimens of compressive test had to be shortened to 2.5 mm to make sure that the dentinal tubules in each specimen had a maximum resemblance of the dentine structure from enamel-dentinal junction (EDJ) to pulp.
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Fig. 4 – Thickness reduction under constant load from 300 s to 7500 s for each group based on the following equation h(t) = FK[B + cv t – Dexp(−t/)]. These plots also display the relative error (Eq. (7)) during the constant maximum load portion of the test.
Under a constant load of 300 N, sound coronal dentine presented a maximum strain of 0.35%, a creep strain of 0.02% and a permanent set of 0.03% after 2 h unloading process. Most published studies on coronal dentine creep behavior were based on nanoindentation test [19,20], which could not compare with the current results directly. In a previous study on creep behavior of human root dentine by bulk compressive test, a 6–10 mm root dentin samples with 3.5 mm outer diameter and 1.5 mm internal canal diameter presents a similar maximum creep strain of about 0.40% under 300 N after 1.5 h, while the viscoelastic properties such as creep and irreversible deformation were not separately studied [18]. The multiscale hierarchical microstructure of dentine leads to mechanical properties variation from pulp to EDJ [22]. As the amount of mineral content increases and the dentinal tubule lumens decreases from the pulp to the EDJ [32], coronal dentine exhibits a stiffening effect with reduced strain rate and significant lower deformation strain compared to pulpal dentine [22]. In clinical practice, a restorative dental mate-
rial is often located within dentine at different depths [15,16]. Coronal dentine provides reliable support for the restorations, and it deforms under chewing loading from EDJ to pulp as a whole. In this respect, a bulk compressive test has some advantages for dentine viscoelastic behavior research compared to nanoindentation testing. It is worth noting that a maximum strain of 0.35% and a creep strain of 0.02% in the current study should be considered as macroscopic, comprehensive and representative results based on 2.5 mm coronal dentine. Creep behavior of resin composites are well evaluated in previous studies [11,12,33]. In a series of studies by Watts et al. [11,12,33], dental resin composites presented a maximum strain that ranged from 0.45% to 1.80% and a permanent set that ranged from 0.03% to 0.68% under a constant stress of 20 MPa after 2 h, which is consistent with the results of the current study. The viscoelastic behaviors of dentine and resinbased dental materials were compared directly in the current study, which earlier studies have not addressed to the best
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Fig. 5 – Instantaneous elastic strain (constant), viscous strain as well as delayed elastic strain in each group. The sum of the three types of strain equals to the total strain at each time point.
of our knowledge. Sound dentine presented the lowest maximum strain, creep strain, as well as permanent set, followed by 3 resin composite filling materials, while the resin cement presented the highest strain and permanent set. The differences in deformation could possible lead to a stress concentration at the adhesive layer or dentin – cement interface, and thus a potential risk of microleakage. Singh et al. evaluated the creep and fatigue properties of an adhesive compositesdentine model, in their calculation of fatigue life, samples can be considered as resulting from creep failure when the strain of the adhesive layer is larger than 2.1% [10]. Although there is still absence of direct clinical evidence that creep causes failures of bonding, the significant difference in viscoelastic properties between dentine and resin based materials should not be ignored and requires further study. All techniques have advantages and disadvantages. Bulk compressive tests have their own complications especially
because the surface of tested specimen as well as the loading planes are hardly perfectly parallel and absolutely smooth [34]. The imperfect parallelism and surface roughness could create complex stresses at the surface of the cylindrical specimen during the initial loading, which is unavoidable at present [35]. As the value of maximum displacement in the current study is very small and ranged from 8.75 m (0.35% × 2.5 mm) to 18.3 m (0.73% × 2.5 mm), even slight imperfect parallelism or surface roughness of only 1 m might lead to a plastic deformation strain due to stress concentration, which is hard to separate from the final permanent set. Therefore, a direct comparison of the parameters in Table 3 only provides semiquantitative impressions or even slight misunderstandings of the viscoelastic properties. To overcome these problems, the Burgers model was introduced to evaluate and predict the viscoelastic behaviors more accurately.
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Fig. 6 – SEM micrograph ×2000 and its local magnification ×10,000 for surface morphology of sound and long-term loaded dentine. (a–b) Sound dentine before loading presents a typical morphology of uniformly distributed open dentinal tubules; (c) dentine surface after creep. Dentinal tubules are slightly to moderately deformed; (d) magnification of (c). After loading, dentine presents cracks around dentinal tubules which are limited to peritubular dentine without propagating into the intertubular dentine (arrow). (D – dentinal tubules, P – peritubular dentine, I – intertubular dentine).
A four element Burgers model is a simple and classic viscoelastic model, widely used to represent the viscoelastic behavior of polymer [36]. Although some studies reported that it could fit creep curves of the composites well [37], so far, there is limited research which investigated the viscoelastic behaviors of dental resin composites and dentine with the Burgers model. Dental resin composites are considered as typical viscoelastic materials [11,12], and present an acceptable characterization of their creep response with Burgers model in the current study with relative errors not exceeding a few tenths of a percent [24]. However, for the initial stage of creep curve (from 300 s to 1000 s) thus the stage of transformation from elastic deformation to viscous deformation, it presented
larger discrepancies between the measured and calculated curves. Compared to resin composites, sound dentine presented a superior fitting effect especially for the initial stage, which demonstrated that dentin could also be considered as a viscoelastic material although the viscous strain is limited. More complex Burgers models with more than one K–V bodies in series might obtain a more accurate fitting result in a mathematical sense [23,24], while more creep parameters could also make it difficult for calculating and to explain the source of the viscosity associated with the composition of dentine or materials, as well as the clinical significance of the parameters. For the most general case of viscoelastic solid, the total strain is the sum of three essentially separate parts: instanta-
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neous elastic strain which appears instantly after loading and is absent after the load is removed, irreversible creep strain subjected to a constant stress which leads to a permanent set, and delayed elastic strain that increases under the applied stress, and is recovered once the stress is removed for an indefinite period of time [36]. Therefore, under ideal conditions, the permanent set should be related only to irreversible creep deformation. However, comparing the permanent set measured in Table 2 with the viscous deformation calculated in Table 4, a 0.03% to 0.04% higher strain was found for groups DU, XT, SU and PC, which could be due to the plastic deformation during the loading stage. Group UN presented a significantly higher permanent set of 0.22%, while the calculated viscous strain of 0.03% is similar to other resin composites. As the only resin cement material, it is well known that UN shows significantly lower mechanical properties including compression and flexural strength compared to filling resin composites [38], which make it more sensitive to stress concentrating due to the imperfect parallelism or surface roughness than other resin composites. Therefore, when characterizing viscoelastic properties of dentin and dental materials, Burgers model is useful to evaluate more accurately and to correct possible errors caused during testing. Creep curves can be divided into three stages: (i) the primary creep stage corresponds to a decay of the strain rate following the application of the constant stress; (ii) the secondary regime describes a constant strain rate in which strain is proportional to time; (iii) tertiary creep stage in which the strain rate accelerates up to rupture [39]. When stress and temperature are low (as in the current study), the secondary creep stage is probably not reached, and strain increased linearly with the logarithm of the time with a decreasing strain rate as shown in Fig. 3b, which is called logarithmic creep [40]. Logarithmic creep could be explained due to “work hardening” effect [39]. Creep of a composite occurs by cross-linked polymer chains untangling and slipping like dislocations movement in crystalline materials relative to one another, which generated flow continuously from the beginning. With increasing time, more dislocations appear and produce increasing interference with each other, thus decreasing the creep rate [39]. Meanwhile, the nanoparticles (fillers) in resin composites are usually brittle materials with higher hardness and elastic modulus, which have the greatest volume fraction and could lead to a significant improvement of the creep stability by effectively restricting the motion of cross-linked polymer [41]. This also accords with earlier observations, which showed that increased filler loading in resin composites decreased the creep strain magnitude [11,33]. Besides chain movement of cross-linked polymers, residual monomer could also play an important role in creep. As the most fluidic component, it is reported that lowering the residual monomer content could increase the creep resistance of composites [42]. Therefore, it is expected the creep of resin composites to be associated with the movement of crosslinked polymer chains and residual fluid monomer. When it comes to dentine, which consists of hydroxyapatite (HAP), collagen and water. Similar to fillers in composites, it is unlikely the ceramic component HAP itself will creep. However, the collagen will deform and the water will displace if there is sufficient permeability of the sample. Human
dentine is a porous hydrated composite material, and the dentinal fluid in tubules plays an important role in dentine deformation [19,42]. It is reported that the hardness, elastic modulus, and yield strength decrease with increasing orientation angle of dentine [21], which indicates increasing in strain with stress in the direction perpendicular to the dentinal tubules compared to that parallel to the dentinal tubules [42]. When dentine was compressed, the fluid in tubules were compressed and squeezed out in the direction of dentinal tubules, which is probably the basis for creep. Dentine samples used in this study were acquired below the central fossa, and the tubules were almost aligned parallel to the stress as shown in Fig. 6. Highly mineralized peritubular dentine and the sealed incompressible fluid in it leads to the greatest support against deformation and difficulty for fluid movement as the secondary tubules in this direction are very small and the permeability through the intertubular space is difficult, thus results in a non-significant creep behavior.
5.
Conclusions
With the limitations of bulk compressive test, sound dentine exhibited significantly decreased irreversible creep deformation thus superior creep stability compared to resin-based dental materials. Dentine creep could be related to the fluid movement in dentine tubules, and could be ignored when loading parallel to dentine tubules. The Burgers model could be used to evaluate the viscoelastic property of dentine and resin-based dental materials.
Declarations of interest None.
Acknowledgments This work was supported by the National Natural Science Foundation of China under grant Nos. 81600907, 81470767 and 81771110.
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Please cite this article in press as: Wang X, et al. The bulk compressive creep and recovery behavior of human dentine and resin-based dental materials. Dent Mater (2020), https://doi.org/10.1016/j.dental.2020.01.003