Residual stresses in dental composites

Sammanfattning: In several European countries, dental composites are replacing mercury-containing amalgams as the most common restorative materials. The problems with dental composites are they can induce pain for the patient, fracture of the tooth, gap between the tooth and the filling what will induce secondary caries. The main reason is residual stresses. The factors affecting residual stresses are known; it is Young's modulus, volume changes, relaxation, geometry, but their importance is unknown. A model approach has been chosen in order to determine what are the main factors. An experimental set-up, shown in the second paper, to measure residual stresses has been made based on the bimetallic experiment. The dental composite is cured on an aluminum substrate and two strain gages register the bending of the substrate. From this experiment, the residual stresses in the composite could be determined. The modeling, treated in the second paper of this thesis, can be divided in sub-models. The first one is the cure kinetics in order to obtain the degree of cure. From this sub-model, the volume change and the Young's modulus can be determined. From the two last sub-models and the geometry, the stresses can be calculated. The chemical shrinkage was considered as linearly dependent on the degree of conversion. A simple pseudo-autocatalytic model was used for the cure kinetics. In order to do the calculation the change of modulus as a function of degree of cure has to be model. The viscoelastic properties of pure resin samples light-cure at different degree of conversion were determined using dynamic mechanical analysis and time-temperature superposition. The viscoelastic Young's modulus has been represented by a discrete exponential series and it has been observed that time-cure superposition works, what means that the weight factors do not depend on the degree of cure. Only the relaxed modulus, the unrelaxed modulus, and the principal relaxation time (time at which the relaxation spectrum has its maximum) depend on the degree of cure. A linear relation was found between the logarithm of these parameters and the degree of cure. An elastic Young's modulus model was done by taking the same expression as for viscoelasticity, but replacing the time by 1s what corresponds to the change of the 1Hz modulus as a function of degree of cure. The calculations were done for 2D-constraint geometry like for the bimetallic experiment. Finite difference was used for the calculations. The changes of physical properties as a function of degree of cure were done on pure resin, but we need the changes for different filler content. This is the reason why the first paper deals with micro-mechanical models to predict the effect of filler on the Young's modulus and the chemical shrinkage. The Young's modulus is well described by the upper bound of Hashin's sphere model. Whereas the chemical shrinkage is well described by a modified Rosen and Hashin's model that was developed for the thermal coefficient expansion. Since this two models work well they were used for the calculation of the composite chemical shrinkage and the calculation of relaxed and unrelaxed Young's modulus considering that the weight factors and relaxation time were the same as for the resin. Two isothermal models have been done: one elastic and one viscoelastic. The viscoelastic model gives stresses that are 15% lower than elastic case. The viscoelastic model gives good results at the beginning compare to the experimental data, but after it overestimates a lot the stresses. There are two main reasons. First the modeling of shrinkage is inadequate, it is believed that the shrinkage decreases near vitrification so the linear relation do not hold and induce an overestimation of stresses. The second factor is the fact that there is an exotherm from room temperature to 55ºC in the case of pure resin, so the isothermal conditions are not fulfilled. This study shows us the validity of time-cure superposition. It also demonstrates that the modeling of shrinkage should be done more carefully and that the non-isothermal conditions should certainly be taken into account. The results of this thesis are presented in following papers:
P. Lingois and L. Berglund, "Modeling Young's modulus and volume shrinkage of dental composites"
P. Lingois, L. Berglund, A. Mafezzoli, and A. Greco, "Chemically induced residual stresses in dental composites"