The bending stress distribution in bilayered and graded zirconia-based dental ceramics

Abstract

The purpose of this study was to evaluate the biaxial flexural stresses in classic bilayered and in graded zirconia-feldspathic porcelain composites. A finite element method and an analytical model were used to simulate the piston-on-ring test and to predict the biaxial stress distributions across the thickness of the bilayer and graded zirconia-feldspathic porcelain discs. An axisymmetric model and a flexure formula of Hsueh et al. were used in the FEM and analytical analysis, respectively. Four porcelain thicknesses were tested in the bilayered discs. In graded discs, continuous and stepwise transitions from the bottom zirconia layer to the top porcelain layer were studied. The resulting stresses across the thickness, measured along the central axis of the disc, for the bilayered and graded discs were compared. In bilayered discs, the maximum tensile stress decreased while the stress mismatch (at the interface) increased with the porcelain layer thickness. The optimized balance between both variables is achieved for a porcelain thickness ratio in the range of 0.30-0.35. In graded discs, the highest tensile stresses were registered for porcelain rich interlayers (p=0.25) whereas the zirconia rich ones (p=8) yield the lowest tensile stresses. In addition, the maximum stresses in a graded structure can be tailored by altering compositional gradients. A decrease in maximum stresses with increasing values of p (a scaling exponent in the power law function) was observed. Our findings showed a good agreement between the analytical and simulated models, particularly in the tensile region of the disc. Graded zirconia-feldspathic porcelain composites exhibited a more favourable stress distribution relative to conventional bilayered systems. This fact can significantly impact the clinical performance of zirconia-feldspathic porcelain prostheses, namely reducing the fracture incidence of zirconia and the chipping and delamination of porcelain.

Keywords: Biaxial strength; functionally graded ceramic; multilayer; zirconia.

Fig. 1

Schematic of the classic bilayered (a) and graded (b,c) zirconia-feldspathic porcelain systems.

Fig. 2

Variation in the volume fraction of porcelain throughout the graded region for different values of the scaling exponent p in Eq.(1).

Fig. 3

Procedures to calculate the layers thickness of the graded region for p=4.

Fig. 4

Diagram of piston-on-ring biaxial test. P is the applied force by the piston and t is the thickness of each layer.

Fig. 5

Stress distribution in a biaxial test along the z-axis at the disc centre for a bilayered sample. Results for FEM simulation (a) and the analytical model (b).

Fig. 6

Variation of the simulated maximum tensile stresses and stress mismatch against the thickness ratio t_p/t_T (t_p: porcelain thickness; t_T: total thickness). Note the different stress ranges shown in the y-axis for maximum tensile stress and stress mismatch at the interface.

Fig. 7

Stress distribution throughout the disc thickness for a biaxial test in a FGM. Results for the simulated models: continuous transition (a) and stepwise transition (b); and analytical model (c).

Fig. 8

Maximum tensile stress as function of the scaling exponent p in Eq. (1). Maximum difference between simulated and analytical results was registered for p=8 and was ~5%.