Modeling of residual stresses in dental composites

Abstract: In several European countries, dental composites are replacing mercury- containing amalgams as the most common restorative materials. The problems with dental composites are that they can induce pain for the patient, fracture in the tooth, and gaps between the tooth and the filling which will induce secondary caries. One reason for these problems is residual stress. The factors affecting residual stress are known; it is Young's modulus, volume change, stress relaxation, light absorption, and geometrical constraint, but their relative importance is unclear. A combined modeling and characterization approach has been chosen to determine and quantify the main factors. The material studied was a model composite of known methacrylate resin composition, where the filler fraction was varied. An experimental set-up to measure residual stress was developed based on the bimaterial experiment. The dental composite is cured on an aluminum substrate and two strain gauges register strains in the substrate. From this experiment, the residual stresses in the composite during curing are determined. The numerical master model is divided in submodels. The first one is the cure kinetics model, in order to obtain the degree of conversion of the matrix as a function of time. From this sub-model, the volume change and the Young's modulus of the matrix are obtained from separate submodels. Micromechanical models are then used to determine composite shrinkage and Young's modulus. From composite properties, substrate properties, and geometry, the stresses in the composite can be predicted from a stress model. To simplify the problem isothermal conditions were supposed. Modeling of the vitrification event is critical as well as the influence of geometrical constraint on vitrification, through free volume. For this reason, special efforts have been put to accurately describe the influence of vitrification on the different submodels. For this reason, a modified pseudo-autocatalytic model was used for the cure kinetics model. A chemical shrinkage model based on viscoelasticity was developed in order to take into account the non-linear shrinkage with degree of conversion during vitrification. A viscoelastic model for the Young's modulus is also needed, which was obtained using the time-cure superposition principle. The good agreement between experimental data and the model predictions support our model and indicates that the essential physics of the residual stress development process has been captured. The model shows the necessity of a non-linear shrinkage model and the influence of free volume induced by geometrical constraints on all the others properties during vitrification. The parametric study shows the complex interactions between cure kinetics, volume change, modulus development, free volume effects, and rate of volume change. Obviously, shrinkage, modulus, and geometrical constraint are important parameters. But the width of the relaxation spectrum has also strong effects. Light power density has also some effects on the stress level, but much less than expected. This is due to the complex interactions between the different submodels and the fact that some factors, like light absorption or non-isothermal conditions, are not taken into account. The influence of the cavity design and the filling procedure were not studied. I. P. Lingois and L. Berglund, "Modeling Elastic Properties and Volume Change in Dental Composites" submitted to J. Mat. Sci. II. P. Lingois, L. Berglund, A. Greco, and A. Mafezzoli, "Chemically Induced Residual Stresses in Dental Composites" submitted to J. Mat. Sci. III. P. Lingois and L. Berglund, "Modelling of Chemically Induced Residual Stresses in Dental Composites Including Free Volume Effects" IV. P. Lingois and L. Berglund, "Factors Affecting Residual Stresses in Dental Composites: A Parametric Study"