Viscoelastic finite element evaluation of transient and residual stresses in dental crowns: Design parametric study

Abstract

Porcelain-veneered zirconia (PVZ) are one of the popular choice for crown restorations. Veneer layer of these dental restorations, however, is susceptible to chipping and delamination due to the development of transient and residual stresses during the cooling phase of veneer firing. The aim of this study is to elucidate the effect of material property mismatch, veneer to core thickness ratio, and cooling rate on these transient and residual stresses of PVZ restorations. Three-dimensional viscoelastic finite element modelling (VFEM) was performed. The VFEM model was developed using the UEXPAN subroutine in ABAQUS software and was validated for transient and residual stresses in a sandwich seal problem with experimental data available. A good agreement between the simulated VFEM results and experimental data was obtained. Using validated VFEM, two PVZ systems (PM9/zirconia and ZirPress/zirconia), three veneer to core thickness ratios (2:1, 1:1 and 1:2), and two cooling rates controlled slow cooling at 1.74E-5 W/mm²°C (i.e. ~30 °C/min) and fast bench cooling at 1.74E-4 W/mm²°C (i.e. ~300 °C/min) were used. The results showed that PM9/zirconia has smaller thermal contraction mismatch, resulting in lesser residual stress (33.36 MPa) as compared to ZirPress/zirconia (37.94 MPa) for controlled cooling and 2:1 veneer to core ratio. In addition, in both systems with the decrease in veneer thickness, we observed a decrease in residual stresses developed. We also observed some effect of cooling rate on residual stresses. The controlled cooling resulted in lower residual stress (24.35 MPa) for PM9/zirconia with a 1:1 veneer to core thickness ratio as compared to bench cooling (28.04 MPa). The effect of cooling rate was more evident on transient stresses. For instance, in the PM9/zirconia with 1:1 thickness ratio model, the difference in transient stresses was 9.93 MPa between controlled and bench cooling. Therefore, properties such as elastic modulus and coefficient of thermal contraction (CTC), as well as the thickness ratio and cooling rate all play an important role in transient and residual stresses developed in the studied ceramic systems.

Keywords: Coefficient of thermal contraction; Dental ceramics; Porcelain-veneered zirconia; Residual stresses; Transient stresses; Viscoelastic finite elements.

Fig 1:

Finite element model of (a) full dental crown and b) 1/4^th simulated model. Light blue represents the zirconia core and grey represents the porcelain veneer

Fig 2:

Density at different temperatures

Fig 3:

Conductivity at different temperatures

Fig 4:

Specific Heat at different temperatures

Fig 5:

Young’s Modulus at different temperatures

Fig 6:

Thermal contraction coefficient at different temperature

Fig 7:

Normalized shear relaxation function at various high temperatures (DeHoff et al., 2006).

Fig 8:

Schematic of sandwich seal

Fig 9:

Longitudinal stress (σ_yy) for a G-11/Alumina sandwich seal cooled at 3 K/min = 0.05 °C/s from 618 to 20 °C

Fig 10:

Stress for the G-11/Alumina sandwich seal when cooled at 3 K/min= 0.05 °C/s, and held 4 hours at 465 °C.

Figure 11:

Temperature and Stress Profile for 3-D Slow Cooling in a) Model 1 and b) Model 4

Figure 11:

Temperature and Stress Profile for 3-D Slow Cooling in a) Model 1 and b) Model 4

Figure 12:

Model 1 (PM9/zirconia): Temperature; a) Temperature gradient in slow cooling b) Temperature history in Slow and Fast Cooling; Nodes represented are PT1-Porcelain top node, ZB1- zirconia top node and ZB2-zirconia bottom node

Figure 13:

Residual stresses in slow cooling: a) Model 1: PM9/zirconia; b) Model 4: ZirPress/zirconia; c) Model 2: PM9/zirconia; d) Model 5: ZirPress/zirconia; e) Model 3:PM9/zirconia; f) Model 6: ZirPress/zirconia. Nodes represented are PT1-Porcelain top node, PZI- Porcelain zirconia Interface node and PB1- Porcelain Bottom Node.

Figure 13:

Residual stresses in slow cooling: a) Model 1: PM9/zirconia; b) Model 4: ZirPress/zirconia; c) Model 2: PM9/zirconia; d) Model 5: ZirPress/zirconia; e) Model 3:PM9/zirconia; f) Model 6: ZirPress/zirconia. Nodes represented are PT1-Porcelain top node, PZI- Porcelain zirconia Interface node and PB1- Porcelain Bottom Node.

Figure 14:

Transient stress in slow cooling: a) Model 1: PM9/zirconia; b) Model 4: ZirPress/zirconia; c) Model 2: PM9/zirconia; d) Model 5: ZirPress/zirconia; e) Model 3:PM9/zirconia; f) Model 6: ZirPress/zirconia

Figure 15:

Residual stress in fast cooling: a) Model 1: PM9/zirconia; b) Model 4: ZirPress/zirconia; c) Model 2: PM9/zirconia; d) Model 5: ZirPress/zirconia; e) Model 3:PM9/zirconia; f) Model 6: ZirPress/zirconia. Nodes represented are PT1-Porcelain top node, PZI- Porcelain zirconia Interface node and PB1- Porcelain Bottom Node.

Figure 16:

Transient stress in fast cooling: a) Model 1: PM9/zirconia; b) Model 4: ZirPress/zirconia; c) Model 2: PM9/zirconia; d) Model 5: ZirPress/zirconia; e) Model 3:PM9/zirconia; f) Model 6: ZirPress/zirconia

Figure 17:

Residual Stress Summary in (a) porcelain; (b) zirconia