A comparative study between crack analysis and a mechanical test for assessing the polymerization stress of restorative composites

Abstract

Objectives

To verify the hypothesis that crack analysis and a mechanical test would rank a series of composites in a similar order with respect to polymerization stress. Also, both tests would show similar relationships between stress and composite elastic modulus and/or shrinkage.

Methods

Soda-lime glass discs (2-mm thick) with a central perforation (3.5-mm diameter) received four Vickers indentations 500 μm from the cavity margin. The indent cracks were measured (500×) prior and 10 min after the cavity was restored with one of six materials (Kalore/KL, Gradia/GR, Ice/IC, Wave/WV, Majesty Flow/MF, and Majesty Posterior/MP). Stresses at the indent site were calculated based on glass fracture toughness and increase in crack length. Stress at the bonded interface was calculated using the equation for an internally pressurized cylinder. The mechanical test used a universal testing machine and glass rods (5-mm diameter) as substrate. An extensometer monitored specimen height (2 mm). Nominal stress was calculated dividing the maximum shrinkage force by the specimen cross-sectional area. Composite elastic modulus was determined by nanoindentation and post-gel shrinkage was measured using strain gages. Data were subjected to one-way ANOVA/Tukey or Kruskal–Wallis/Mann–Whitney tests (alpha: 5%).

Results

Both tests grouped the composites in three statistical subsets, with small differences in overlapping between the intermediate subset (MF, WV) and the highest (MP, IC) or the lowest stress materials (KL, GR). Higher stresses were developed by composites with high modulus and/or high shrinkage.

Significance

Crack analysis demonstrated to be as effective as the mechanical test to rank composites regarding polymerization stress.

Introduction

Recent clinical data have shown an improvement in the longevity of resin-based composite restorations placed in posterior teeth, with annual failure rates of approximately 2% . However, a survey with private practitioners revealed that posterior composite restorations usually require replacement after six years of service versus 14 years for amalgam restorations . A randomized clinical trial observed that for large restorations ( i.e ., those involving three or more surfaces) 90% of the amalgam restorations were clinically acceptable after seven years, while only 60% of composite restorations received similar rating . The size of the composite restoration was also found to negatively affect its longevity in a 10-year retrospective study . Clinical studies agree that the most prevalent causes of failure are bulk fracture and secondary caries . Post-operative sensitivity is also a common occurrence associated with composite restorations, being reported in 26% of mesio-occlusal-distal (MOD), 15% of MO/OD and 5% of shallow to mid-depth occlusal restorations placed under well-controlled conditions . Though there is no clinical data to support a cause–effect relationship, it is not unreasonable to associate secondary caries and post-operative sensitivity, as well as marginal staining, to the debonding of the tooth/restoration interface.

Interfacial debonding may occur as the result of improper adhesive application and also, in the long term, due to hydrolysis of the adhesive layer and/or degradation of the collagen of the hybrid layer . Cyclic thermal changes and occlusal loading also are well known causes of interfacial debonding over time . Finally, an important source of interfacial stress is the composite polymerization shrinkage. When composite is cured in a cavity preparation, it cannot freely shrink due to bonding to the cavity walls. Shrinkage associated with elastic modulus development result in stress build up, which may cause tooth flexure and enamel cracks or, if stress magnitude surpasses the bond strength between the tooth and adhesive layer, to the formation of interfacial gaps .

Most of the information available in the literature on the material-related factors associated with polymerization stress development comes from mechanical tests, referred to by some authors as “tensilometer”. In systems using glass or steel as bonding substrate, polymerization stress of commercial composites was shown to increase with composite elastic modulus . However, when low-viscosity (flowable) composites are tested, their high shrinkage is responsible for increased stress values, in spite of their relatively low stiffness . Indeed, such findings are supported by a recent finite element analysis (FEA) study demonstrating that in low-compliance testing systems, the highest stress levels are developed by composites with the highest shrinkage and elastic modulus. As for most commercial composites both properties are inversely related, the main determinant depends on the actual shrinkage and modulus values displayed by a particular material . Despite the fact that in vitro studies have shown a direct relationship between microleakage at the tooth/restoration interface and polymerization stress values obtained by mechanical testing such tests can be criticized for bearing no resemblance in terms of specimen geometry and boundary conditions with those found in the clinical situation. Another limitation is that the complex tri-axial stresses developed in the composite are reduced to a nominal (average) stress value calculated assuming a uniaxial stress state .

Recently, a method was proposed where residual stresses in the bonding substrate due to composite shrinkage are calculated based upon the increase in length of indentation cracks introduced at the margin of a restored cavity . Cavities have been prepared in glass-ceramic rods or soda-lime glass discs, both materials having elastic modulus and fracture toughness similar to the human enamel. The crack analysis method is based on the fact that, in brittle materials, residual tensile stresses may induce crack propagation and, therefore, they can be estimated using indentation fracture mechanics . Furthermore, by knowing the stress at the crack site and the distance between the indentation and cavity margin, it is possible to calculate the radial tensile stresses at the bonded interface. Thus far, crack analysis has been used to calculate residual stresses produced at the bonding substrate through different photoactivation methods and at different distances from the restoration margin . Considering the large amount of information available on composite polymerization stress obtained with mechanical testing devices, it is important to verify the extent to which the results from both methods are comparable.

Therefore, the aim of the present study was to verify the working hypothesis that both the crack analysis and a mechanical test performed in a universal testing machine would rank a series of commercial restorative composites in a similar order with respect to polymerization contraction stress, and that both tests would show similar relationships between stress and composite elastic modulus and/or shrinkage.

Material and methods

Material selection and density measurements

The composites chosen for the study are described in Table 1 . All the tested materials were A2 shade. Two of them (MF and WV) were low-viscosity composites, while one of the composites (MP) was chosen for its extremely high filler content. Among the regular viscosity composite materials, two contained prepolymerized particles (KL and GR) and the actual inorganic filler fraction were unknown. Because this information is key to explain the composite elastic modulus, a density versus filler content curve was obtained for the materials with known inorganic content by volume (IC, WV, MF and MP). An unfilled resin (SDI Ltd., Bayswater, Australia) was used to provide the density of the organic matrix, while the density of the filler alone was set at 2.8 g/cm 3 (technical information, Schott AG, Germany). It was assumed that the densities of the organic and inorganic phases were similar for all the tested composites. The inorganic contents of KL and GR were estimated by applying their density values to the linear regression equation.

Table 1
Materials tested in this study, with respective filler contents (both informed by the manufacturers – except for KL, obtained from Takahashi et al. – and inorganic content obtained from density measurements), filler sizes and batch numbers.
Composite (Manufacturer) Coding Filler content informed by manufacturer (vol%) Inorganic content determined by density measurements (vol%) Average filler size Batch number
GC Kalore (GC Corp., Tokyo, Japan) KL 69 a 55 Prepolimerized filler: 17 μm (0.1–0.4 μm glass); glass: 0.7 μm; nanofiller: 16 nm 1007231
Gradia Direct X (GC Corp.) GR 65 a 47 Prepolimerized filler: 16 μm (16-nm silica) and 12 μm (1-μm glass); glass: 0.85 μm; nanofiller: 16 nm 1003161
Ice (SDI Ltd., Bayswater, Australia) IC 61 52 Glass: 1.5 μm; nanofiller: 40 nm 100655T
Wave MV (SDI Ltd.) WV 43 41 1.5 μm 100806
Majesty Flow (Kuraray Medical Inc., Okayama, Japan) MF 62 66 3 μm 00310B
Majesty Posterior (Kuraray Medical Inc.) MP 82 84 Glass: 1.5 μm; nanofiller: 20 nm 00105A

a Includes inorganic and prepolimerized fillers.

Discs 7 mm in diameter and 2 mm in thickness were prepared using a polyacetal mold. The mold was placed over a mylar strip and filled with composite (or the unfilled resin). Another mylar strip was placed on top of the uncured material, followed by a microscope glass slide. Photoactivation was carried out using a LED (light-emitting diode) unit (Radii-Cal, SDI) with the tip of the curing unit placed in contact with the glass slide. The material was irradiated for 25 s at 1200 mW/cm 2 (according to manufacturer’s information and periodically checked with the unit’s built-in radiometer). Specimens ( n = 3) were removed from the mold and kept dry at 37 °C for 3 days before testing.

The specimens were weighed in an analytical scale with resolution of 0.1 mg and had their height and diameter determined with the use of a digital caliper (Dick Smith Electronics, Australia, resolution: 0.01 mm). Density was calculated according to the following equation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='ρ=mπr2h’>ρ=mπr2hρ=mπr2h
ρ = m π r 2 h

where ρ is the density (in g/cm 3 ), m is the specimen mass (in g), r is the radius and h is the height (both in cm).

Elastic modulus determination by nanoindentation

Discs 7 mm in diameter and 2 mm in height were prepared as described above for the density measurements. Specimens ( n = 3) were kept dry at 37 °C for 1 h before testing. The nanoindenter (UMIS 2000 – Ultra Micro Indentation System, CSIRO – Commonwealth Scientific and Industrial Research Organization, Australia) used a Berkovich triangular based diamond pyramid indenter to load the surface under force control. Load–displacement data were recorded by the control software with 10 nm resolution. The loading–unloading curve followed a square-root progression, with 20 increments in each segment of the cycle. The initial contact load was 0.1 mN and, based on preliminary tests, the maximum load was set at 50 mN. Maximum load was held for 60 s prior to unloading.

A combined (or reduced) modulus ( E *) was obtained according to the “multiple-point unload method” that uses the slope of the tangent to the initial unloading to calculate the contact stiffness ( dP / dh ). E * can be calculated from the recovery rate recorded during unloading from the maximum load as follows:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml="E1−υ’2=dPdhePmax12η(h)khplmax”>E1υ2=(dPdhe)Pmax12η(h)khplmaxE1−υ’2=dPdhePmax12η(h)khplmax
E 1 − υ ‘ 2 = d P d h e P max 1 2 η ( h ) k h p l max

where υ ′ is the Poisson’s ratio of the indenter ( υ ′ = 0.07) , <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='dP/dhePmax’>(dP/dhe)PmaxdP/dhePmax
d P / d h e P max
is the rate of the elastic recovery from the maximum load ( P max ), η ( h ) is an area function to correct for the rounding of the indenter tip, k is a constant related to the angle formed by the faces of the diamond indenter and the axis at the apex of the pyramid, and h pl max is the maximum penetration of the plastic component.

Knowing the indenter’s elastic modulus ( E ′ = 1000 GPa) and Poisson’s ratio, as well as the composite’s Poisson’s ratio ( υ = 0.3), composite elastic modulus ( E ) was calculated using the equation :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml="1E=1−υ2E+1−υ2E'”>1E=1υ2E+1υ2E1E=1−υ2E+1−υ2E’
1 E = 1 − υ 2 E + 1 − υ 2 E ‘

which can be re-arranged as:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml="E=1−υ2(1/E)−(1−υ’2)/E'”>E=1υ2(1/E)(1υ2)/EE=1−υ2(1/E)−(1−υ’2)/E’
E = 1 − υ 2 ( 1 / E ) − ( 1 − υ ‘ 2 ) / E ‘

Additionally, a predictive model for the elastic modulus of the composites based on their inorganic filler fraction was also investigated. Experimental data was compared with the Voigt model (Eq. (1) ), the Reuss model (Eq. (2) ), and the Halpin-Tsai model (Eq. (3) ) described below:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='Ec=VfEf+VmEm’>Ec=VfEf+VmEmEc=VfEf+VmEm
E c = V f E f + V m E m
<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='1Ec=VfEf+VmEm’>1Ec=VfEf+VmEm1Ec=VfEf+VmEm
1 E c = V f E f + V m E m
<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='Ec=Em1+ξηVf1−ηVf’>Ec=Em(1+ξηVf1ηVf)Ec=Em1+ξηVf1−ηVf
E c = E m 1 + ξ η V f 1 − η V f

where E c is the composite elastic modulus (in GPa), E f (70 GPa, technical information, Schott AG) and E m (3.3 GPa, determined by nanoindentation as described above) are the modulus of the filler and the matrix, respectively, V f and V m are the volume fractions of the filler and the matrix. ξ is a filler parameter dependent upon its geometry, packing and loading conditions. A value of 1.2 was used for this parameter . The η parameter is calculated as:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='η=(Ef/Em)−1(Ef/Em)+ξ’>η=(Ef/Em)1(Ef/Em)+ξη=(Ef/Em)−1(Ef/Em)+ξ
η = ( E f / E m ) − 1 ( E f / E m ) + ξ
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Nov 28, 2017 | Posted by in Dental Materials | Comments Off on A comparative study between crack analysis and a mechanical test for assessing the polymerization stress of restorative composites
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