%5b6%5d+jacs09-45-2-zhang-transient+modelling+of+thermal+processing+for+ceramic+prostheses

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Journal of the Australian Ceramic Society Volume 45[2], 2009, 40-48

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Transient Modelling of Thermal Processing forCeramic ProsthesesZhongpu Zhang 1, Qing Li 1, Wei Li 1 and Michael Swain 2

1) School of Aerospace, Mechanical and Mechatronic Engineering2) Faculty of DentistryUniversity of Sydney, NSW 2006, Australia

Available Online at: www.austceram.com/ACS-Journal-2009vol2.asp

AbstractThis study aims to present a numerical and experimental transient characterisation for mono- or bi-layeredceramic samples and dental restorations under a controlled cooling process from high temperature (typically900C) to room temperature (25C). The processes may undergo different cooling rates: namely rapid cooling,normal cooling and slow cooling. The cooling rate is not a constant during convection. Cooling ratedependencies of the temperature distribution about the glass transition temperature during cooling will be takeninto account. The heat transfer coefficients used in this numerical simulation are derived from experimental data.The FEA results are correlated to experimental results and a good agreement is achieved. The transient material

processing models showed a significant potential for development of optimal prosthetic devices.

Keywords: ceramics, transient thermal, cooling rate, finite element, temperature distribution

INTRODUCTION All-ceramic dental restorations are being usedextensively because of their superior aesthetics,chemical durability, and biocompatibility. Thetypical core veneered all-ceramic restorations hasthe frameworks made of stronger, less aestheticceramic materials such as zirconia, alumina orglass-ceramic. To satisfy increasing aestheticdemand, core frameworks are veneered with tooth-coloured porcelains, and its strength is of primaryimportance. However, there have been a substantialnumber of reports showing the failure of somezirconia- or alumina-based devices [1, 2]. In fewstudies evaluated the clinical performance of In-Ceram Alumina crowns have reported survival ratesof greater than 90 percent. The main causes offailure reported in all these studies werecatastrophic fractures, secondary caries andchipping of the veneer ceramic [3, 4]. In a long-term clinical study, success rate of alumina-basedceramic systems was 90% after 5 years and survivalrate 65% after 11 years, and success rate ofzirconia-based ceramic systems were 100% after 2or 3 years clinical study [5]. It is noted that thefracture mode of alumina crowns (total fractures)differs from that zirconia crowns (veneer fractures)

because of zirconia core is stronger than thealumina core. In a five-year follow-up study of 3-and 4- unit posterior fixed partial dentures, thesuccess rate of the zirconia frameworks was 97.8%

but the survival rate was 73.9% because ofsecondary caries and chipping of the veneeringceramic [6]. One study evaluated the clinical

performance of two to five-unit implant-supported

all-ceramic restorations, where Denzir (DZ) andIn-Ceram Zirconia (InZ) exhibited anunacceptable amount of veneering porcelainfractures in short-term study [7]. In an average 31months follow-up study, minor chipping fracturesof veneering porcelain were detected in five fixed

partial dental prostheses of sixteen restorations intotal [8].

Several studies have measured the transient andresidual stresses in porcelain component of a

porcelain-fused-to-metal restoration subjected tovariable cooling rates. DeHoff and Anusavicedeveloped an analytical model to calculate thetransient and residual stress in felspathic porcelain

plates subjected to certain cooling rates [9]. Tocalculate temperature distributions, three differentlevels of convective heat transfer coefficients wereset in 57 W/mC for slow cooling, 114 W/mCfor normal cooling and 170 W/mC for forcedcooling. However, the coefficients at normal orforced cooling were arbitrarily selected and werenot associated with specific cooling conditions.DeHoff et al. [10] also applied the visco-elastictheory to determine transient and residual stressesin metal-opaque porcelain-body porcelain (MOB)disks that were affected by different cooling rates.The constant convective heat transfer coefficients atall exposed surfaces were 560 W/mC fortempering and 57 W/mC for fast cooling. Asaokaand Tesk calculated the tempering stresses thatwere developed in constant cooling rates [11].However, cooling rate is not a constant valueduring cooling.


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Zhongpu Zhang, Qing Li, Wei Li and Michael Swain

Asaoka et al. pointed out that the calculatedresidual stresses at the surface and the centre oftheir 1.5, 2, and 10 mm-thick porcelain disks fromhigh temperature to 30C [12]. The cooling rates inthe temperature range of 650 to 450C were tocalculated to be 6.9 to 4.7C/s and 28 to 19C/s for

the 10mm and 1.5 mm-thick porcelain specimens,respectively, subjected to cooling in air from1000C. For a 10mm in diameter, 1.5 mm-thick

porcelain disk subjected to slow cooling in ambientair, cooling rate was experimentally determined as28 to 10C/s from 650 to 300C. For a 2 mm-thick

porcelain disk, cooling rate was 21.7 to 9.5C/scooled from 650 to 300C. Such findings indicatethat the cooling rate is lower in thicker porcelaindisks. The 2mm porcelain specimens cooled byforced air, the cooling rate was calculated to be52.4C/s at 600C. In their study, the convectiveheat transfer coefficient was 210 W/mC.

For layered all-ceramic systems, some studies havecharacterised the transient and residual stressaffected by different cooling conditions. Gardonreported that transient stress was measured byquenching a 6.1mm thick glass plate from an initialtemperature of 616C with heat convectioncoefficient of h = 222 W/mC [13]. Hojjatiedeveloped a two-dimensional analytical model todetermine the effects of tempering process ontransient stresses in ceramics [14]. The majorvariables responsible for controlling thetemperature gradient, and residual stress within the

ceramics were reported to be specimen thickness,heat transfer coefficient, and initial coolingtemperature. The values of heat transfer coefficientsmeasured for free convective cooling and temperingin air were 70 and 560 W/mC, respectively.These values were estimated from the experimentalresults by using embedded thermocouples tomeasure the temperature vs. time profiles for 2 mm-thick porcelain disks cooling from 982C. DeHoffet al. adopted the viscoelastic options of theANSYS finite element analysis program tocalculate residual stresses in an all-ceramic fixed

partial denture (FPD) for four different ceramic-

ceramic combinations [15]. A free convectivecooling (heat transfer coefficient h = 35 W/mC)from high temperature to room temperature wasapplied. Another test calculated temperatures andstresses for cylindrical and spherical bi-layeredceramic systems by using axisymmetric thermaland viscoelastic elements [16]. This studysimulated free convective cooling of the modelsfrom an initial temperature of 700C to roomtemperature. A constant convective heat transfercoefficient of 17 W/mC was applied to theexposed surfaces to provide an initial cooling rate atthe surface of approximately 640C/min.

The objective of this study was to adopt the finiteelement method to simulate the transient cooling

process in terms of temperature change that is

developed in the mono- or bi-layered ceramicsamples under a controlled cooling process fromhigh temperature 900C to room temperature. The

processes subject different cooling conditions:namely rapid cooling, normal cooling and slowcooling. In this study, the convection and

conduction affected by different cooling procedureswere measured from experimental data. It will alsoexamine the dependencies of the glass transitiontemperature and thickness of either mono- or bi-layered ceramic-ceramic restorations on the coolingrates.

MATERIALS AND METHODS

Specimen PreparationCommercial monolayer dental porcelain (VitadurAlpha porcelain) was used for gathering the

experimental data. The samples are made ofcylindrical shape of porcelain with 10mm indiameter and 2 or 4mm in thickness. Since thecritical temperature for developing residual stressesis glass transition ranging from 700 to 400C, the

porcelain was heated at 700C and held there for 5minutes. For bilayer samples, the plate shape ofcore-veneered ceramics consisting of 1215.5mmcross-section area, a 0.6 mm-thick layer of zirconiacore ceramic, and a 3.46 mm-thick layer of zirconia

porcelain are made according to the manufacturersrecommended procedure.

To determine the transient temperature versus time profiles during different cooling process formonolayer dental porcelain, a thermo-couple was

placed on the surface of porcelain disk. For the bilayer core-veneered ceramics, one thermo-couplewas used to measure temperature on the surface ofveneering porcelain; another thermo-couple was

placed at the interface between porcelain layer andcore ceramic layer. A computer program wasdeveloped to record the temperature values as afunction of time. The time and temperature datawere recorded, and thereafter the thermal historyfor each cooling procedure was plotted.

The experimental protocol of different cooling ratesare set up: (1) it was cooled sufficiently slowly inthe furnace in the slow cooling; (2) it was removedfrom the furnace and cooled in ambient air at roomtemperature as normal cooling; (3) the monolayer

porcelain disk tempered by blasting compressed airdirectly on it as it was removed from the furnace.

Transient Thermal AnalysisA transient thermal analysis determines thevariations in temperature and other thermalquantities under certain conditions over a specific

period. The rate of convection heat transfer isexpressed by Newtons law of cooling as:


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1 where h is the convective heat transfer coefficientin W/mC, given by a average value from hightemperature to room temperature, A s is the surfacearea through which convection heat transfer takes

place, T s is the surface temperature in C, and T a isthe temperature of ambient air around the samples.

Thermal diffusivity, D, represents the ratio ofthermal conductivity to volumetric heat capacity,expressed in Eqn 2. It is not at steady state intransient heat transfer problems, but gives anindication of the rate of rise of temperature at one

point due to a heat source at another point.

2

where k is thermal conductivity, is the density,and Cp is the specific heat of the sample material.

Newtons law of cooling states that the rate ofchange of the temperature of an object is

proportional to the difference between its owntemperature and ambient temperature, expressed inEqn 3:

3 Asaoka et al [12] stated that the gradient k is given

by Eqn 4, when a lumped thermal capacity modelof transient heat transfer is assumed as a Biotnumber less than 0.1:

4 The Biot number is defined as:

5 Lc is characteristic length, which is commonlydefined as the volume of the body divided by thesurface area of the body which is exposed toambient air in the study.

Cooling rates can be adjusted by changing theconvective heat transfer coefficient in thermalanalysis. Since convective heat transfer coefficientsare not material properties of the sample, it is anexperimentally determined parameter whose value

depends on all the variables influencing convection process such as the surface geometry, the nature ofair motion, the thermo-physical properties of theambient air, and the bulk air velocity. If thecoefficient of convective heat transfer isindependent of the volume and surface area of thesolid, Eqn 4 can be repressed as follows:

: 1 1 6

where r is the radius of cylinder, and t is thickness.

: 2 2 2 7 where a, b, and t are length, width and thickness of

plate, respectively.

Finite Element MethodANSYS program is employed in this study. Theconvection cooling of the mono- or bi-layeredmodels from an initial temperature 900C to roomtemperature is first modelled in two-dimensional(2D) thermal element PLANE55. The dimensionsof 2D monolayer were 10mm in length, and 2 or 4mm in thickness.

The convective cooling of three-dimensional (3D)mono- or bi-layered models was also created by theeight-node thermal element (SOLID70) in ANSYS.The material of the cores and the veneering

porcelain layers were assumed to be homogeneous,isotropic and linearly elastic. In this study, VitadurAlpha and Vita VM9 were used as a veneeringmaterial. The core ceramics were Vita In-CeramAlumina and a conventional yttria-stabilizedtetragonal zirconia polycrystals (Y-TZP). The dataof the thermo-mechanical properties of eachmaterial are determined from the literature [17] andmanufacturer, as summarised in Table 1.

Table 1: Thermo-physical properties of materials used for finite element analysisMaterials Youngs

Modulus(GPa)

PoissonsRatio

Thermalexpansioncoefficient(m/mK)

ThermalConductivity(W/m-K)

Specific Heat(J/K .kg)

Density(kg/m 3)

Y-TZP base 200 0.32 10.5 2.5 465 6000

In-Ceram Alumina 260 0.27 7.6 14 500 4000

Vita VM9 Porcelain 70 0.26 9 1 800 2500

Vita Alpha Porcelain 64 0.19 7.1 1.1 840 2400


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RESULTSFig. 1 shows the temperature vs cooling time for the2mm thick monolayer porcelain specimen for threedifferent cooling procedures over the from glasstransition temperature ranging 700 to 400C. Both2D and 3D finite element results are presented. The

values of heat transfer coefficient from numericalsimulation are adopted from Table 2. In the 2Dtransient simulation, the convective heat transfercoefficient is 95 W/mC for fast cooling, 25W/mC for normal cooling, and 4.2 W/mC forslow cooling. The coefficients from 3D analysis are

91 W/mC for fast cooling, 26 W/mC fornormal cooling, and 4 W/mC for slow cooling. Itis observed that the numerical models match theexperimental results fairly well in the normal andfast cooling process. Since the convective heat

transfer coefficient is an average value assigned inANSYS, plots of slow cooling is not as accurate asthe normal and fast cooling in terms of thedeviations between the numerical and experimentalresults.

Fig. 1: Experimental and numerical profiles of surface temperature of 2mm thick monolayer porcelain disc vstime for three cooling procedures:(a)2D finite element results(left), (b)3D finite element results(right)

Table 2: Convective heat transfer coefficients generated by numerical analysis (W/mC)

2D Finite Element Analysis 3D Finite Element Analysis Final Results for further

simulation

FastCool

NormalCool

SlowCool

FastCool

NormalCool

SlowCool

FastCool

NormalCool

SlowCoo

2mm thickmonolayer 95 25 4.2 91 26 4

98 25 6.34mm thickmonolayer 105 24 9 100 25 8

4.06mm thick bilayer*

55 V28 C

44 V25 C

16 V4 C

55 V22 C

45 V21 C

14 V6 C

55 V25 C

44.5 V23 C

15 V5 C

*V means at veneering ceramic surface, C means at core ceramic surface.

The temperature distribution of 4mm thickmonolayer porcelain specimen during threedifferent cooling procedures is shown in Fig. 2. In

both 2D and 3D finite element results, theconvective heat transfer coefficient are almostmatched, such as 105 vs 100 W/mC for fastcooling, 24 vs 25 W/mC for normal cooling, 9 vs8 W/mC for slow cooling. However, theconvective heat transfer coefficients are differentfor 2 and 4 mm-thick porcelain discs, due toinaccuracy measurement in experiments. Therefore,to calculate the means of coefficients, the finalconvection heat transfer coefficients based onexperimental measurement are 98 W/mC for fastcooling, 25 W/mC for normal cooling and 6.3W/mC for slow cooling. Since the Biot number is

less than 0.1, Eqn 6 can be considered to apply. TheBi< 0.1 for both 2mm and 4mm porcelain disc, sovalue of K is 0.034/s & 0.022/s for fast cooling,0.0087/s & 0.0056/s for normal cooling, 0.0022/s &0.0014/s for slow cooling. The values of coolingrate in the temperature range from 700 to 400Ccalculated by Eqn 3 are 23.8-13.6 C/s and 15.4-8.8C/s (fast), 6.09-3.48C/s and 3.92-2.24C/s(normal), 1.54-0.88C/s and 0.98-0.56C/s (slow)for the 2 and 4mm-thick porcelain discs,respectively. However, cooling rates fromconvection cooling numerical simulation of 2 and4mm porcelain specimen are 26.8-9.15C/s and35.3-16.7C/s for fast cooling, 8.7-4.61C/s and5.92-2.30C/s for normal cooling, 1.42- 0.75C/sand 1.74-0.76C/s for slow cooling.

Type ofmodel

Type of finite

elementanalysis


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Fig. 2: Experimental and numerical profiles of surface temperature of 4mm thick monolayer porcelain disc vstime for three cooling procedures: (a)2D finite element results (left); (b)3D finite element results (right)

Fig. 3 shows temperature variation as a function oftime at the surface of porcelain layer and theinterface of 4.06 mm-thick bilayer specimens. The

convective heat transfer coefficients are the same asthose in 2D and 3D numerical simulations. With therapid cooling, the heat transfer coefficients used forfurther simulation are 55 W/mC at porcelainsurface, 25 W/mC at surface of core layer. Thecoefficients are 44.5 W/mC at porcelain surface,23 W/mC at core surface for normal cooling, and

15 W/mC at porcelain surface, 5 W/mC atcore layer ceramic for slow cooling. The coolingrates in temperature range of 700 to 400C for 4.06

mm-thick bilayer plate are 2.52-0.80C/s at porcelain surface, 1.66-0.82C/s at interface forslow cooling, 8.88-2.60C/s at surface, 6.01-2.77C/s at interface for normal cooling, and 12.6-3.28C/s at surface, 6.65-3.55C/s at interface forslow cooling.

(a)2D fast cooled 4.06mm thick bilayer specimen (b)2D normal cooled 4.06mm thick bilayer specimen

(c)2D slow cooled 4.06mm thick bilayer specimen (d)3D fast cooled 4.06mm thick bilayer specimen


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(e)3D normal cooled 4.06mm thick bilayer specimen (f)3D slow cooled 4.06mm thick bilayer specimen

Fig. 3: Experimental and numerical results of surface & interface temperatures of total 4.06mm thick bilayered plate vs time for three cooling procedures:(a)2D 4.06mm thick Fast cooling; (b)2D 4.06mm normal cooling;(c)2D 4.06mm Slow cooling; (d)3D 4.06mm Fast cooling; (e)3D 4.06mm Normal cooling; (f)3D 4.06mm Slowcooling.

The surface temperature changes of 4mm VitaVM9 porcelain discs that underwent three differentcooling procedures are plotted in Fig. 4. With therapid cooling, the specimen reaches 25C from900C in 320 seconds. The porcelain disc reachesroom temperature in 4300s for slow cooling, and1510s for normal cooling. The highest cooling ratesin this temperature for 4mm thick Vita VM9

porcelain disc are 1.49C/s for slow cooling,5.36C/s for normal cooling, and 37.7C/s for fastcooling.

Fig. 4: Profiles of surface temperature of 3D 4mmVita VM9 porcelain for three cooling procedures

Fig. 5 shows the profiles of surface temperature for3D 4mm monolayer disc of Vitadur Alpha, Y-TZPBase, Vita VM9 and In-Ceram Alumina. If material

properties are independent on temperature, thevalues of thermal diffusivity in Eqn 2 are 910 -7 m/s for Y-TZP base, 710 -6 m/s for In-CeramAlumina, 510 -7 m/s for Vita VM9 porcelain, and5.4510 -7 m/s for Vitadur Alpha porcelain. Thetemperature plots of two porcelains and Aluminaare overlapped. This phenomenon shows thattemperature decrease mainly depends on the

product of the specific heat and density, but lessdependent on the thermal conductivity in this case.

Fig.5: Profiles of surface temperature of 3D 4mmmonolayer disc (Vita Alpha, Y-TZP Base, Vita VM9,

In-Ceram Alumina).

Fig. 6 illustrates temperature profiles at selectedtimeframes through the 2mm bilayer plate (0.6mmY-TZP and 1.4mm porcelain) with rapid coolingand slow cooling. As shown in Fig. 6(a), the

maximum temperature occurs at in the range of -0.2to 0.1mm which is located at the zirconia core layeraround the interface. It can be also clearly seen thatthe minimum temperature occurs on the surface of

porcelain layer. The largest difference is 25C at25s, 7.5C gives the lowest difference at 100sthrough the bilayer plate. Temperature changes as afunction of time for slow cooling are illustrated inFig. 6(b). In this situation, the maximumtemperature is at the same location of the bilayerspecimen as well as minimum temperature. Theonly difference is the value of temperature, becausetemperature will decrease quickly for fast cooling.


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(a) Temperature at 25s, 50s, 75s, 100s by fast cooling (b) Temperature distribution at 50s, 100s by slow cooling

Fig. 6: Temperature profiles in the 2mm bilayer plate (0.6mm Y-TZP and 1.4mm porcelain) at selectedtimeframes undergoing different cooling procedures: (a) rapid cooling; (b) slow cooling.

As illustrated in Fig. 7, with the rapid cooling, thetemperature distribution through the 4mm bilayer

plate at 25s, 50s, 75s, and 100s. It is clearly seenthat the maximum temperature occurs in the rangeof 0.2 to 0.4mm located within the porcelain layernear the interface. The minimum temperature is atthe surface of porcelain layer similar to that

mentioned above in Fig. 6. It is seen that for athinner specimen the temperature will decreasemore quickly if other conditions are the same, suchas material properties, cooling procedure, heattransfer coefficient. The largest difference betweentemperatures at a specific time step is 56C.

(a) Temperature distribution at 25s, 50s (b) Temperature distribution at 75s, 100s

Fig. 7: Temperature profiles in the 4mm bilayer plate at selected timeframes with rapid cooling: (a) selectedtime at 25s, 50s; (b) selected time at 75s, 100s

DISCUSSIONIn this study, the convection heat transfercoefficients generated from numerical simulationfor different cooling procedures are average values

based on experimental results. The coefficientsfinally used to distinguish different cooling

procedures are lower than those from the literature.These values are not unique and constant, becausethey are strongly dependent on various other

conditions. For free normal convection cooling, theheat transfer coefficient is a temperature-dependentcoefficient, which can be a function of thetemperature difference [18]. For this reason, the

experimental and numerical profiles of surfacetemperature of both mono- and bi-layer specimensvs time are not perfectly matched. The mismatchingmay be caused by temperature-dependentconvective heat transfer coefficient, temperature-dependent specific heat in the glass transitiontemperature range or delay of thermocouple readingof temperature. As illustrated in Fig. 3, theconvective heat transfer coefficient applied on thesurfaces of core layer and porcelain layer isdifferent. The reason for this phenomenon is thecooling process.


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In the thermo-coupled measurement experiment,the ambient air temperature at the core layer side ishigher than that at the surface of the porcelain layer.

The glass transition temperature of each material isnot unique value. Transformation temperature from

manufacturers specification was 603C for VitadurAlpha veneering porcelain and 600C for Vita VM9.However, as shown in Fig. 4, T g shifted to a highertemperature for the rapid cooling. In contract, withthe slow cooling process, T g shifted to a lowertemperature.

As shown in Fig. 5, the temperature variationmainly depends on the specific heat and materialdensity, not related on thermal conductivity.Thermal conductivity is an important factor inthermal conduction heat transfer. If thermalconductivity is larger with a thinner specimen, more

heat will be transferred by thermal conduction.Therefore, it is not crucial in the convective heattransfer problems.

The maximum temperature occurs close to thelocation of core layer near the interface in Fig. 6.As illustrated in Fig. 7, the maximum temperatureis at the area of porcelain layer. Since the flexurestrength of zirconia core layer is higher than that ofthe porcelain layer, so that with the rapid cooling, athicker specimen may generate higher thermalstresses and may fracture more easily.

In further study, the effects from thermal residualstresses induced by the temperature change,viscoelastic properties of porcelain from sinteringtemperature to glass transition temperature,mismatched thermo-mechanical material properties,such as temperature-dependent coefficient ofthermal expansion, modulus of elastic, will beconsidered.

CONCLUSIONSThe heat transfer coefficients for convectivecooling procedures are not unique and constant.The experimental and numerical results concludethat glass transition temperature of dental ceramicsis not unique. Higher values of T g are beingobserved for rapid cooling, and lower values of T g for slow cooling. In convective heat transfersimulations, thermal conductivity is not animportant material property, but it is a significantfactor in conduction heat transfer. With the rapidcooling, a thicker bi-layered specimen may fracturemore easily, its fracture parameter as a mixedmodel crack.

ACKNOWLEDGMENTSThe support from Australian Research Council(ARC) is grateful.

REFERENCE 1. I. Denry, J.R. Kelly, State of the art of zirconia

for dental applications, J. Dent. Mater., Vol.[24 ], 3, (2008), 299-307

2. S.D. Heintze, A. Cavalleri, A.G. Zellweger, A.Bchler, G. Zappini, Fracture frequency of all-

ceramic crowns during dynamic loading in achewing simulator using different loading andluting protocols, J. Dent. Mater., Vol. [ 24 ], 10,(2008): 1352-1361.

3. A. Bindl and W.H. Mrmann, An up to 5-yearsclinical evaluation of posterior In-CeramCAD/CAM core crowns, Int. J. Prosthodont.,Vol. [ 15 ], 5, (2002), 451-456.

4. E.A. McLaren and S.N. White, Survival of In-Ceram crowns in a private practice: A

prospective clinical trial, J. Prosthet. Dent., Vol.[83 ], 2, (2000), 216-222.

5. P.V. Von Steyern, All-ceramic fixed partialdentures: Studies on aluminium oxide- andzirconium dioxide-based ceramic systems,Swed. Dent. J. Suppl., Vol. [ 173 ], (2005), 1-69.

6. I. Sailer, A. Feher, F. Filser, LJ. Gauckler, H.Luthy, CHF. Hammerle, Five-year clinicalresults of zirconia frameworks for posteriorfixed partial dentures, Int. J. Prosthodont., Vol.[20 ], 4, (2007), 383-388.

7. C. Larsson, P.V. von Steyern, B. Sunzel, K. Nilner, All-ceramic two- and five-unit implant-supported reconstructions. A randomized,

prospective clinical trial, Swed. Dent. J., Vol.[30 ], 2, (2006), 45-53.

8. A. J. Raigrodski, G.J. Chiche, N. Potiket, J.L.Hochstedler, S.E. Mohamed, S. Billiot, D.E.Mercante, The efficacy of posterior three-unitzirconium-oxide-based ceramic fixed partialdental prostheses: a prospective clinical pilotstudy, J. Prosthet. Dent., Vol. [ 96 ], 4, (2006),237-44.

9. P.H. DeHoff, K.J. Anusavice, Temperingstresses in feldspathic porcelain, J. Den. Res.,Vol. [ 68 ], 2, (1989), 134-138.

10. P.H. DeHoff, K.J. Anusavice, S.B. Vontivillu,Analysis of temperin stresses in metal-ceramic disks, J. Dent. Res., Vol. [ 75 ], 2,(1996), 743-751.

11. K. Asaoka, J.A. Tesk, Transient and residualstress in dental porcelains as affected bycooling rates, J. Dent. Mater., Vol. [ 8], 1,(1989), 9-25.

12. K. Asaoka, N. Kuwayama, J.A. Tesk,Influence of tempering method on residualstress in dental porcelain, J. Den. Res., Vol.[71 ], 9, (1992), 1623-1627.

13. R. Gardon, Thermal tempering of glass,Elasticity and Strength in Glasses, in: GlassScience and Technology , Volume 5, AcademicPress, New York, (1980), 144-216.

14. B. Hojjatie, Thermal tempering of layeredceramic structures, Ph.D. Thesis, Universityof Florida, USA, (1990).


9/9

48


15. P.H. DeHoff, K.J. Anusavice, N.Gtzen,Viscoelastic finite element analysisof an all-ceramic fixed partial denture, J.Biomech., Vol. [ 39 ], 1, (2006), 40-48.

16. P.H. DeHoff, A.A. Barrett, R.B. Lee, K.JAnusavice,Thermal compatibility of dental

ceramic systems using cylindrical and

spherical geometries, J. Dent. Mater., Vol.[24 ], 6, (2008), 744-752.

17. O' Brien WJ, Dental materials and theirselection, Carol Stream QuintessensePublishing Co. Inc, (2002), Chapter 2.

18. A. Bejan, A.D. Kraus,Heat transfer

handbook, (2003), chapter 3, 229-231.

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