Multiaxial Strength and Stress Forming Behavior of Four Light-Curable Dental Composites

The resulting internal stress situation in curing dental composites is still oversimplified due to analytical inaccessibility of local information of state and loading. Similar applies to the strength behavior of cured dental composites. Using recent progress of a finite-element-based curing model, we developed and attempted to benchmark dental composites based on their mechanical behavior and tendency to form internal stress. Additionally, in order to understand the influence of restoration techniques on the mechanical loading, curing simulations were necessary. Three-point flexural strength, compressive strength and diametral tensile strength and the necessary curing parameters were studied for four state-of-the-art dental composites (Tetric EvoCeram, Venus Diamond, EsthetX, Filtek Supreme XT). The investigated composites fracture can be analyzed by the Drucker Prager failure criteria for each composite. The lowest resulting curing stresses were found for Tetric EvoCeram because of its low volumetric shrinkage and a high ratio of initiation phase to dark phase conversion. Venus Diamond showed the best overall mechanical properties because it can withstand tensile as well as compressive stress. In order to draw conclusions on comparisons between several composites, flexural strength tests, volume shrinkage measurements, cavity classifications and general preparation recommendations may still be a suitable way for the simplification of the immense complexity in curing and restoration. Nevertheless, finite-element-based simulations are necessary to include fundamental effects such as stress relaxation by flow and multiaxial strength of the composite.


Introduction
For nowadays tooth restorations, a great variety of materials can readily be used.Amongst them, light curable composites are suitable for many different applications and are not limited to cavity filling.Dental composites fulfill high aesthetic demands and their properties have been improved significantly over the last few decades.Their assessment however should include their resistance to mechanical loading and _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766their mechanical burden on the necessary adhesive material by induced shrinkage stress.Loading stresses arise also in the adhesive material due to heterogeneous compliance.To achieve a suitable restoration the mechanical properties of the replaced tooth material should be considered.Human teeth have a compliant dentin core.Barak et al (2009) mentioned that this core supports an abrasion resistant tough outer enamel layer connected with a soft zone that hinders the delamination from the enamel.A mechanically suitable restorative material withstands stress and strain deformation without overloading its adhesive bonding and the surrounding natural tooth structure.There are typically two possibilities to meet the challenges of durable replacement and adequate load transfer to the root, as long as practitioners are still limited to using artificial homogeneous restoration material.One choice would be to use a material with superior strength and adapt the tooth basis to a shape that limits adhesive bonding to compressive situations.But the minimal invasive procedures require mimicked tooth material for high C-factors, otherwise the mechanical mismatch of compliance will induce excessive loading of the weakest component -the bonding.Braga et al (2013) mentioned a higher C-factor will lead to higher stress.The setting of the material is another important aspect that influences the quality of the bonding.Despite intensive research, light cured composites still undergo polymerization shrinkage that induces internal stresses in a cavity as was mentioned by Watts et al. (2003), Lu et al. (2004) and Stansbury et al. (2005).The shrinkage is of a hydrostatic nature, but since the ratio of free surface to bonded surface is small the deviatoric material can only compensate shrinkage with the similar ratio.Therefore stresses built up, that result from hindered shrinkage and viscoelastic shear flow.The goal of material development is to sustain a material with high strength that does not overload the critical bond to the tooth.To prevent failure after restoration suitable model experiments have to be conducted.In fact this is a challenging task, since material strength and polymerization strength are usually optimized separately.Following this need we developed a testing approach for dental composites which includes a coupled experimental and numerical method.Resulting with a successful model we are able to numerical estimate loading and shrinking stress of arbitrary cavity geometries, preparation techniques and mastication assumptions.The resulting stress distribution is very inhomogeneous, dependent on the cavity geometry and on its position.The character of the stress transfer to the adhesive bond changes continuously from normal dominant to shear dominant fractions.The level of adhesive strength, set by a preparation in optimal laboratory conditions, indicates that highest local shrinkage stress requirements could be met.In a research study Sano et al. (1994) pointed out that local stress can easily exceed mean strength due to small defects in the bonding zone or if the full adhesive strength was simply not achieved due to a contaminated bonding area as was mentioned by Sunico et al. (2002).The mechanical strength necessary to withstand internal stress and chewing load of composites is typically measured by three-point bending tests, a suitable method with easily achievable specimen geometry.Under bending load, the strength of a brittle material is determined by fracture at a certain tensile stress.Since chewing also induces excessive compressive stresses, other mechanical testing methods should be taken into account for restorations in load bearing areas.Relying on uniaxial composite strength tests does not take the complexity of the inner heterogeneous stress and strain behavior into account.The composite viscoelastic and shrinkage behavior results from heterogeneous material deformation tangential and normal to the filler surface causing loading of the adhesive bond of the filler and polymer.In conclusion the multiaxial strength of the composite should be incorporated for a comprehensive study by a variety of testing geometries.De Groot et al. (1987) and others already introduced the phenomenological Drucker Prager multiaxial failure criteria that was originally used for concrete but can _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766similarly be applied on precursor ceramics after hot and dry pressing.In contrast to a principal stress criteria, as should be used for brittle homogeneous material in absence of shear strain, the Drucker Prager criteria is based on a critical von Mises to hydrostatic stress ratio.Maybe the simplest way to describe the effect inshort, the von Mises stress should be used for tests on a pure viscoelastic polymer material itself and the superposition with the hydrostatic stress includes the effect of adhesively incorporated particles as was investigated by Lohbauer et al. (2006).The aim of this paper is to present experimental und numerical methods to compare a simplified but comprehensive mechanical short term behavior of four dental composites.This behavior includes multiaxial mechanical resistance to load and strain as well as mechanical loading of the adhesive bond during setting.The loading of the adhesive bond has to be numerically calculated and the necessity of a simulation with or without material flow was investigated.Since there is no standardized way for curing a composite in a cavity, first simulations on the impact of layering technique or slanting of edges were tested.

Materials
The materials used in this study are commercially available, light -activated resin composites (see table 1).For photoinitiation, a Translux Energy (Heraeus Kulzer GmbH & Co. KG, Hanau, Germany) halogen light source was employed.

Setup of Strength Measurements
For each test 10 specimens were incrementally cured and then treated with 300-grit sand paper on the basis of EN ISO 4049.The experimental procedure was as follows: Three-point flexural strength was measured according to EN ISO 4049 at loading speed of 0.75 mm/min.The flexural modulus was estimated by linear regression at strains from 0.01 to 0.02.The compressive strength was determined with cylinder shaped specimen Ø = 4mm, l = 8mm at a (facial) loading rate of 29 N/min and the diametral tensile strength was _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766measured with cylinder shaped specimen Ø = 6mm, d = 3mm at a loading speed of 5300 N/min until fracture.The loading speed at chewing is debatable but much higher than for the standardized flexural experiment.

Experimental Procedure for Parameter Estimation of the Curing Model
The experimental setup was designed to fit in a servo-hydraulic testing machine.For each composite 5 disc shaped specimens (height 2.5 mm, diameter 5 mm) were prepared and loaded longitudinally to the cylinder axis in compression.A strainoptimized load-step-recovery series was chosen with increasing step length to produce low but sufficient strain steps of ~0.5% in order to obtain a linear material behavior as well as a good signal-to-noise ratio.For these conditions, the loads had to be increased in magnitude and in duration.By this strategy the additive strain behavior of the composite can be divided during a load step: shrinkage, elastic, viscous and viscoelastic behavior (i.e. a behavior which can be described by a Kelvin-Voigt model) due to their phenomenology.A detailed description was given by Koplin et al. (2009).

Curing Model
The kinetic behavior of curing dental composites has been described by Koplin et al. (2008) using a macroscopic polymerization model, based on the mixed termination model that was mentioned in the review of Andrzejewska (2001) (1).During polymerization the evolution of the »participating monomer« concentration [M(t)] passing the concentration level [M] τ at the end of photo-initiation and the evolution of »radical-activated centers« is determined by the initiation, propagation and termination steps of the reaction.As a simplification a »participating monomer« concentration level of zero is reached, when the material is vitrified and the left monomer immobilized or trapped.The coefficients kp (propagation) and kt b (bimolecular termination) are diffusioncontrolled.These coefficients change during the polymerization process partially due to the change in dominance occurring between different diffusion processes.The coefficient kt m is a more structure dependent coefficient (monomolecular termination) and was fixed to a probable value.The resultant volume shrinkage ∆v was assumed to be linearly connected to the concentration of already converted participating monomer reaching the final value ∆v (2).

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This kinetic model includes descriptions of the initiation phase as well as the dark phase but does not include the autoacceleration.
The three-dimensional behavior of the composite is simulated using the four-parameter viscoelastic model with a volumetric shrinkage component (figure 1).Gel

Cavity Simulations
The finite-element based simulations were conducted on ABAQUS software by Simulia using an implicit solver and user defined material behavior.Knowing that an inclusion of full complexity of a tooth restoration would encrypt fundamental results of stress and strain distributions by trying to parameterise tooth behavior and true geometric situations, it was simplified.Instead of that the strategy was chosen to simplify wherever possible and detail whenever necessary.Following this strategy, two different cylindrical shapes (fig.2; A: r=5mm, h= 10mm; B: r=4mm, h= 4mm) with an averaged tooth-like material behavior for enamel (E=75 GPa and ν=0.3), dentin (E=16 GPa and ν=0.3), and a softer transition zone (E=6 GPa and ν=0.3) were chosen.Cavity B was chosen to result in comparable curing conditions as were chosen by the authors before, but at the same time providing a more relevant simplification for detailed simulations by using cavity A. Since the material behavior of the tooth and composite was modeled with linear stress dependence, the entire size is scalable leaving stress and strains unaltered.The results can therefore be used on small cavities in small teeth as well as bigger cavities in bigger teeth, as long as aspect ratios are similar.But in fact the tooth behavior is highly orthotropic, individually and spatially distributed, as well as size-dependent as was mentioned _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766 by Ang et al. (2010).The simplifications were done on literature data for validated finite-element models by Barak et al. (2009).The outer geometry was set containing a cavity with nearly cylindrical geometry (A: r=2.1mm, h=1.5mm or B: r=1.3mm, h=1.75mm) which then was filled by curing the composite (figure 2).

Parameter of a Curing Model
The moduli relating strain and stress for an isotropic material can be expressed by the moduli obtained through 1D loading tests and the Poisson constants for all four of the constitutive elements of the viscoelastic model (see table 3).They increase to a maximum value for the experiment after 300s.E0, η0 determine the elastic behavior, η2, ν2 determine the viscous behavior and The input of a single parameter on the internal stress development will be discussed later with the cavity simulations.
A comparison of the overall viscoelastic moduli, by assuming additive strain components, gives a qualitative similar ranking of the observed three-point flexural moduli (see figure 4).The observed elastic moduli clearly differ, since the observation frequency for the final loading step is 1/40 s -1 and by this roughly 10 times slower than the inverse rate for the bending method.16) 209 ( 23) 204 ( 90) 173 ( 40 A maximum of the stress is formed after ~2 minutes, except for EsthetX.The rate of the increasing stress is highest for Filtek Supreme XT.

Parameter Study
A variational study for the parameter of Venus Diamond was done by calculating the increase in one parameter by 10% and recording the change for the highest stress in % at the same position as above (see table 3).

Simulation of Different Cavity Aspects
An easy and straightforward incremental layering approach was chosen (fig. 2 A) to simulate the resulting curing stress.The formerly identified localized region of highest stress at the top of the adhesive zone (fig.5) was chosen to investigate this specific incremental layering effect.200 seconds delay from the initiation of one increment to the other was chosen, and after a maximum value was reached the plot of the development of stress was truncated to simplify the resulting diagram (fig.7).

Discussion
The approaches that can be found for the kinetic model of the curing differ from each other.Often the effect of auto-acceleration is included but the dark phase is not.An interesting review article has been given by Watts (2005).The first combining approach for a numerical kinetic model that includes initiation phase, autoacceleration, temperature as well as spatial components seems to have been given by Matias et al. (2009) for photo-fabrication processes.A methodological approach that allows the necessary parameter estimation for this challenging model is still missing.
Based on these findings the authors chose an approach estimating the development of mechanical parameter in correlation with the underlying monomeric conversion by its volumetric change rather than parameters determined at specific states.The practicability of this approach was recently affirmed by the explorative research on multiple correlations on material parameters by Li et al. (2009).The constitutive viscoelastic material model for curing dental composites can be simplified   Meerbeek (2011).By slanting the edge, the adhesive area is increased as well as material flow is allowed towards the center.In doing that the normal stress is drastically reduced but the high shear stress is accumulated at the newly generated edge.The positive effect of this type of slanting can only be judged by knowing the shear and normal strength of adhesives at the enamel and dentine.The slanting technique at the bottom of the cavity seems to have mostly negative effects with respect to solely shrinkage stress, since high localized normal stress is induced.The original sharp edge at this point does not lead to a high localized stress peak.This is due to the fact that the average normal to the fillet adhesive surface is not orthogonal to the stress vector.Following common knowledge that an increased ratio of free to bonded surface area increases material flow and therefore, decreases the shrinkage stress, incremental techniques are often applied for deeper cavities.The incremental layering technique seems to be a powerful method to prevent an overload of the adhesive bond at the geometrically disadvantageous positions.The technique leads to lower stress and disrupts the cylindrical symmetry resulting in a higher loaded side in the part of the last layer.In this special case the localized stress could be reduced to 50 % by layering, and certain aspects should be further on considered.Quite often cavity simulations are done neglecting the material flow of dental composites.It can clearly be seen, that a corrected effective volume shrinkage can mimic the adhesive stress to a certain degree quite well, but they lead to false conclusions for sharp geometrical features e.g. at the edge at the bottom of the cavity.

Conclusion
The multiaxial mechanical load on restored teeth should be thoroughly investigated and used in rating procedures for mechanical performance of composite restaurations.As a simple choice the Drucker Prager criteria is a feasible tool for including the critical multiaxial stress of these composites for failure assessment.
The magnitude of the shrinkage stress cannot be predicted by a single model parameter and flowability should be included in the simulation of the adhesive bond.The slanting technique can be useful for the prevention of highly localized normal stresses at the top of the bonding by allowing an increased shear relaxation at this position and increasing the bonding area to enamel.Slanting at the inner edge has no positive influence on internal stress.In a nutshell the FE-simulations prove to be a necessary choice to understand the complex interferences for the mechanical behavior and development of restorations under loading or during curing.
Figure 1.The Constitutive Four Parameter Viscoelastic Model is Symbolically Illustrated as a 1D Additive Strain Model Including a Volumetric Shrinkage Component This model predicts the evolution of various material parameters (i.e. increase of stiffness and viscosity) during the polymerization reaction, based on the progress of the polymerization reaction.As a result, an integral description of the mechanical behavior during the curing process is obtained.As a simplification

Figure 4 .Figure 5 .Figure 6 .
Figure 4. Elastic Modulus for the Composites Investigated in this Study.Three Point Flexural Modulus ( ) and Overall Final Viscoelastic Modulus of the Curing Model ( )Cavity SimulationIn order to simulate the build-up of internal stresses during the curing of a dental filling, two different cylinder shapes (fig.2) with an averaged tooth-like material were chosen.Each contains a cavity with nearly

Figure 7 .
Figure 7. Development of Stress Component at the Top of the Adhesive Bond for Venus Diamond Using a Three Layer Technique.(One Increment Restoration: Normal Stress  , Shear Stress  ; Three Increment Restoration: Normal Stress at First Layer   and at Third Layer  , Shear Stress at First Layer   and at Third Layer  ) Whether a slanting technique leads to decreased stresses, was investigated by the finite element simulations for slanted and normal cavities (fig. 2 A, part a).The 45° slanted edge results in a dramatic decrease of the high localized stress (fig.8) but leads to other effects.The chosen ordinate either corresponds to the depth starting from the surface of the cavity or the radial position at the bottom of the cavity.The typical stress vector on the adhesive zone basically points to a position slightly below the geometrical center of the cavity.By allowing an increase of material flow and a
Journal of Research and Practice in Dentistry _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766

Table 2 : Strength Values of the Composites Used in this Study
Journal of Research and Practice in Dentistry _______________ Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766Figure 3.

Table 3 : Parameter of the Curing Model for All Resins Used in this Study
Christof Koplin, Guilherme Valença da Silva Rodriguez and Raimund Jaeger (2014), Journal of Research and Practice in Dentistry, DOI: 10.5171/2014.396766