Influence of thermal gradients on stress state of veneered restorations



To assess transient and residual stresses within the porcelain of veneered restorations (zirconia and metal) as a result of cooling rate and porcelain thickness.


Porcelain-on-zirconia (PZ) and porcelain-fused-to-metal (PFM) crowns were fabricated with 1 or 2 mm of porcelain. Thermocouples were attached both internally and externally to the crowns to record transient temperatures. For fast cooling, the furnace was opened after the holding time and switched off. Slow cooling was accomplished by opening the furnace at 50 °C below the glass transition temperature ( T g ) of the material. An axially symmetric FEA model simulated thermal stresses. Time-dependent temperature equations from thermocouple readings were set as boundary conditions. Framework materials and the porcelain below T g were considered to behave elastically. Visco-elastic behavior was assumed for porcelain above the T g modeling properties as dependent on cooling rate.


Differences in residual stress were found for fast and slow cooled PZ and PFM crowns. Significant transient stress waves were observed within the porcelain when fast cooling through T g . They are believed to be related to non-uniform volumetric changes originated from thermal gradients. Results were confirmed by modeling and physical testing of crowns containing a defect.


Residual stresses do not distinguish PZ from PFM. High magnitude transient stresses observed within the porcelain during fast cooling may explain clinical fractures involving internal defects. Stress waves may also originate internal micro-cracking which could grow under function. Therefore, slow cooling, especially for all-ceramic crowns with thick porcelain, is important to prevent thermal gradients and high-magnitude transient stresses.


Porcelain–zirconia systems are used in dentistry due to zirconia’s high strength and the esthetics of porcelain veneers. The zirconia framework has some translucency and allows light transmission through the restoration conferring more natural appearance than metal copings .

Clinical studies on zirconia-based restorations reported survival rates of 81–100% in 3 years and 74% in 5 years . An especial concern has been raised regarding the potential susceptibility of porcelain on zirconia to premature chipping and fracture . The percentage of porcelain fractures (chipping, cracking, delaminations and large fractures) are high when compared to the same modes of porcelain fractures observed for metal–ceramic restorations .

Regarding this particular porcelain issue (early fracture) with zirconia restorations, some main practical questions arise, such as: can veneered-zirconia restorations be handled as it has been successfully done for metal–ceramic systems? Which differences in material’s properties or processing techniques contribute to stresses development and distribution through the porcelain? How can this problem be fixed?

Possible causes of porcelain early fracture were raised in previous studies, such as: lower elastic modulus and fracture toughness of the porcelain material ; inhomogeneous or thick layers of porcelain ; thermal incompatibility ; poor bond strength (wetting) of porcelain on zirconia ; inadequate design of framework or insufficient support of porcelain ; inadequate porcelain processing (firing) ; inadequate cooling rate .

Internal and subsurface origin are frequently related to the porcelain fracture as described by Swain and illustrated in Fig. 1 , which shows a clinical porcelain–zirconia crown fractured by porcelain chipping. The electronic microscopy analysis showed that the fracture origin was within the porcelain bulk and not related to its external surface. In addition, cracks were observed at the subsurface area (approximately 0.5 mm below the surface) following the direction of (parallel to) the occlusal surface. The internal origin of the fracture and the subsurface cracks suggest an association of the fracture related to a thermal response.

Fig. 1
Scanning electron microscopy images of a porcelain–zirconia crown fractured by porcelain chipping. Wake hackles from defects (White arrows in A–F) showed fracture origin inside the porcelain bulk (G). The picture shows a subsurface area with cracks parallel to the occlusal surface (B). Crown was provided by Dr. Patchanee Rungruanganunt, from the undergraduate dental clinic of the University of Connecticut Health Center.

As demonstrated in previous studies , thermal gradients are frequently related to fast cooling of porcelain–zirconia and metal–porcelain crowns. Thus, the potential association of temperature gradients to the development of residual and transient stresses within the porcelain should be investigated.

The temperature-dependence of the thermo-mechanical properties (especially close to the glass transition temperature) of dental porcelains may play an important role in the stress state of porcelain on veneered-zirconia restorations. Asaoka and Tesk highlighted important factors that have been studied by a number of investigations and should be considered for determination of the transient and residual stresses and their importance to the final state of the porcelain: (1) geometric shape ; (2) elastic modulus dependency on temperature ; (3) coefficient of thermal expansion dependency on temperature ; (4) temperature distribution during cooling process ; (5) temperature-dependent viscosity ; and (6) cooling rate-dependency of the glass transition temperature ( T g ) . These factors were incorporated to the analyses performed in the present study.

Dental porcelains are silicate glasses containing modifying cations, such as aluminum, potassium and sodium, to adapt its properties (basically viscosity and the glass transition temperature) to a specific function . Above the glass transition temperature ( T g generally between 400 and 600 °C for dental porcelains), porcelains behave as a viscous liquid and any force applied to the structure results in creep or plastic deformation; and therefore no residual stress is accumulated . Below the T g , the porcelain behaves closely to an ideal elastic solid and any stress applied to the porcelain results in a proportional instantaneous (more exactly, at the speed of sound) strain . It does not creep under continuous load and, when the stress is removed the deformation is instantaneously recovered. The porcelain change from viscous-liquid to solid during cooling is followed by a change in volume and, consequently, in its density. Changes in length/volume usually depend on temperature and heating/cooling rate.

Cooling viscous-liquid porcelain to temperatures below the glass transition not only reduces the quantity of energy available for structural rearrangements, increasing viscosity and decreasing density, but also has an effect on thermal-dynamic properties, such as heat capacity ( C p ) and thermal conductivity ( k ). In this work the terms heat capacity and specific heat are used interchangeably.

Glass transition temperature ( T g ) is also strongly influenced by cooling rate: the faster the cooling, the higher the transition temperature . Higher cooling rates usually result in development of thermal gradients within the ceramic body. Non-uniform thermal contraction (volume and density changes) and solidification (viscosity change) are likely generated by the temperature gradients, and result in the development of stresses.

Understanding the cooling-rate dependence of T g and the solidification process are important for the investigation of potential development of transient and residual stresses in the porcelain. Whether these so-called “transient” stresses influence the porcelain cracking or early fracture is a subject to be explored in the present work.

Therefore, the present study investigates possible reasons for fracture of porcelain–zirconia restorations originated from cracks and defects localized inside or at the subsurface of the porcelain. The study analyzed the development of transient and residual stresses in porcelain–zirconia and porcelain-fused-to-metal (PFM) restorations as a result of slow and fast cooling. Finite element analysis was used to simulate cooling from temperatures above the glass transition temperature to room temperature.

The study tested the following hypotheses: (1) residual stresses generated after fast cooling are greater than for slow cooling; (2) magnitude and distribution of residual stresses in the porcelain on zirconia and on metal are similar; (3) thermal gradients originated during fast cooling contribute to the development of transient stresses; (4) transient stresses allows nucleation and propagation of cracks from defects in porcelain.

Materials and methods

Thermal analyses

Porcelain-on-zirconia (PZ) and porcelain-fused-to-metal (PFM) crowns were fabricated with 1 or 2 mm of compatible porcelain: Lava Ceram (LCeram-batch # 192164, 3M-ESPE, St. Paul, Minnesota, USA) for zirconia and Vita Omega 900 (V900—dentin #9336 and opaque #9306, Vita Zahnfabrik, Bad Säckingen, Germany) for metal. Metal (gold metal alloy) and zirconia frameworks (Lava Frame Zirconia, Lot #391266, 3M-ESPE, St. Paul, Minnesota, USA) had a homogeneous thickness of 1.0 mm at the occlusal surface and 0.7 at the axial walls.

A flexible mold was used to obtain the desired external shape of porcelain. A mixture of porcelain and distilled water was poured into the space available between the mold and the zirconia substructure, previously positioned inside the mold. The excess of water was removed to promote porcelain powder compaction.

Thermocouples were attached to the cementation (T1–intaglio) and the external (T2) surfaces of the crowns to acquire temperature readings by time (model XC-24-K-24-SWPW-M; Omega Engineering Inc., Stamford CT, USA). The porcelain was sintered (Programat P500/G2, Ivoclar-Vivadent AG, Schaan/Liechtenstein) according to the protocol recommended by the manufacturer ( Table 1 ).

Table 1
Firing schedule for porcelains as recommended a by the manufacturer, the slow and the fast cooling protocols used in this study.
Lava Ceram (3M-ESPE) Vita Omega 900 (VITA)
Dentin a Opaque a Dentin a
Pre-drying temperature (°C) 450 600 600
Pre-drying time (min) 6 2 2
Heating rate (°C/min) 45 75 50
Final temperature (°C) 810 900 900
Holding time (min) 1 2 2
Vacuum on (°C) 450 600 600
Vacuum off (°C) 810 900 900
Time under vacuum (min) 1 2 2
Long-term cooling (°C) a From 500 to 25 From 530 to 25
Cooling temperature rate (°C) a 10 10

a Valid just for the slow cooling protocol.

Temperature readings were performed simultaneously during cooling ( Table 1 ) using a thermometer (HH 390/309A, OMEGA Engineering Inc, Stamford, CT, USA). For “fast” cooling, the chamber was opened and the furnace was switched off 1 min (holding time) after the temperature inside reached the final temperature (800 °C). For “slow” cooling procedure, the chamber was kept closed until the furnace reached 50 °C below the glass transition temperature ( T g ) and opened all the way down. The built-in thermocouple of the furnace provided the reference temperature for these experiments. Using the Testlink SE309 v.3.5 software (OMEGA Engineering Inc, Stamford, CT, USA), thermal data were transferred to Microsoft Excel for analyses. The methodology used in this part of the study was previously published .

Finite element analyzes (FEA)

A simultaneous time-dependent thermo-mechanical analysis was conducted combining heat transfer mode by conduction and structural mechanics analysis of developed stresses. COMSOL Multiphysics (Version 3.5, COMSOL Inc, Burlington, MA, USA) was the FEA software used for the simulation.

An axial-symmetric crown-like geometry was created with 2 different layers: the framework (metal or zirconia), considered to behave elastically at the temperature range of evaluation (25–810 °C); and the veneering porcelain, considered to have an elastic behavior from room temperature to the glass transition ( T g ), and viscoelastic (as a viscous silicate glass melt) at temperatures above the T g .

Structural mechanics set-up

All boundaries were considered free, except for the axial-symmetry axis.

The values of elastic properties for the isotropic materials (metal and zirconia) are presented in Table 2 . Porcelain shear modulus, heat capacity, density and coefficient of thermal expansion were defined as a function of temperature. T g was calculated for each cooling rate measured by the thermocouples.

Table 2
Values for materials’ properties used in the time-dependent thermo-mechanical simulation.
Description Value Unit
Gold alloy a (Isotropic)
Young’s Modulus 93e + 3 MPa
Poisson’s ratio 0.39
Thermal expansion coefficient 14e−6 1/K
Density 14e−6 g/cm 3
Heat capacity 130 J/kg K
Zirconia a (Isotropic)
Young’s Modulus 200e + 3 MPa
Poisson’s ratio 0.32
Thermal expansion coefficient 10e−6 1/K
Density 6e−6 g/cm 3
Heat capacity 450 J/kg K
Porcelain (Viscoelastic)
Bulk Modulus 45300 b MPa
Shear Modulus (initial) 22900 b MPa
Shear Modulus n_Shear c MPa
Thermal expansion coefficient n_CTE c 1/K
Density n_Density c g/cm 3
Heat capacity n_Cp c J/kg K

a Values from Swain .

b Values from DeHoff et al. .

c Properties defined as a function of temperature.

Defining density as a function of temperature

Density ( ρ ) curves versus temperature were obtained for different compositions of glass melts using a calculation program developed by Fluegel et al. . Oxide concentrations were changed from the baseline glass (soda-lime-silicate) to a composition that represents dental porcelain, within the concentration range suggested by the authors. Small amount of other oxides that did not significantly influence the results and they were not included in the calculation. Silica (SiO 2 ) amount was considered to be the difference to 100%.

Eq. (1) , representing the curve of porcelain density changing with temperature ( T ) above the T g , was used to feed the FEA model:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='ρ=−0.00022347896×T+2.5590223′>ρ=0.00022347896×T+2.5590223ρ=−0.00022347896×T+2.5590223
ρ = − 0.00022347896 × T + 2.5590223

Density was considered constant (2.4 × 10 −6 g/cm 3 ), from T g to room temperature.

Defining shear modulus as a function of temperature

The shear modulus values presented by De Hoff et al. for of IPS Empress 2 veneering ceramic were used to obtain its temperature-dependency curve. Eq. (2) that defines the shear modulus ( G ) as a function of temperature ( T ) was obtained using curve-fitting software with r 2 = 0.99 (Table-Curve 2D. v.5.1, SYSTAT Software Inc., San Jose, CA, USA):

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='G=24395.88−1.8364903×10−6×T3′>G=24395.881.8364903×106×T3G=24395.88−1.8364903×10−6×T3
G = 24395.88 − 1.8364903 × 10 − 6 × T 3

An initial shear modulus was set as 22900 MPa and final (from T g to room temperature) was 25800 MPa.

Defining coefficient of thermal expansion as a function of temperature

Below T g , the CTE was defined as 9.5 × 10 −6 and 13.55 × 10 −6 K −1 for porcelain compatible with zirconia and metal, respectively. Richet calculated the changes in length of silicate melts during heating. In the present study, anorthite glass behavior was taken as model to calculate CTE because it has composition (43.54 SiO 2 , 36.37 Al 2 O 3 , 18.86 CaO in %wt) and CTE (7–9 × 10 −6 K −1 below T g ) comparable to dental porcelains. An expression (Eq. (3) ) for the CTE of melted porcelain was obtained by curve-fitting Δ V / V o versus T ( r 2 = 0.996):

<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='y=−0.16955453+0.0042892251×ln(T)2′>y=0.16955453+0.0042892251×ln(T)2y=−0.16955453+0.0042892251×ln(T)2
y = − 0.16955453 + 0.0042892251 × ln ( T ) 2

where T is the temperature in °C. The coefficient of thermal expansion for the porcelain melt ( α m ) was calculated by the derivative of Eq. (3) as follows:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='αm=ddT−0.16955453+0.0042892251ln(T)2=0.008574502ln(T)T’>αm=ddT(0.16955453+0.0042892251ln(T)2)=0.008574502ln(T)Tαm=ddT−0.16955453+0.0042892251ln(T)2=0.008574502ln(T)T
α m = d d T − 0.16955453 + 0.0042892251 ln ( T ) 2 = 0.008574502 ln ( T ) T
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Nov 25, 2017 | Posted by in Dental Materials | Comments Off on Influence of thermal gradients on stress state of veneered restorations

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