Creep functions of dental ceramics measured in a beam-bending viscometer

Dental Materials (2004) 20, 297–304

http://www.intl.elsevierhealth.com/journals/dema

Creep functions of dental ceramics measured in a beam-bending viscometer Paul H. DeHoffa,*, Kenneth J. Anusaviceb a

Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA b Department of Dental Biomaterials, University of Florida, Gainesville, FL, USA Received 19 December 2001; received in revised form 31 March 2003; accepted 28 April 2003

KEYWORDS Creep functions; Dental ceramics; Shear viscosity; Creep rate; Beam deflection; Enthalpy; Arrhenius equation; Activation energy; Glass transition

Summary Objective. To characterize the high temperature viscoelastic properties of several dental ceramics by the determination of creep functions based on mid-span deflections measured in a beam-bending viscometer (BBV). Methods. Six groups of beam specimens (58 £ 5.5 £ 2.5 mm) were made from the following materials: (1) IPS Empress2w body—a glass veneer ceramic (E2V); (2) an experimental glass veneer (EXV); (3) Vita VMK 68 feldspathic body porcelain—a low-expansion body porcelain (VB); (4) Will-Ceram feldspathic body porcelain—a highexpansion body porcelain (WCB); (5) Vita feldspathic opaque porcelain-a mediumexpansion opaque porcelain (VO); and (6) Will-Ceram feldspathic opaque porcelain—a high-expansion opaque porcelain (WCO). Midpoint deflections for each specimen were measured in a BBV under isothermal conditions at furnace temperatures ranging from 450 to 675 8C. Non-linear regression and linear regression analyses were used to determine creep functions and shear viscosities, respectively, for each material at each temperature. Results. The shear viscosities of each group of dental ceramics exhibited bilinear Arrhenius behavior with the slope ratios ðxÞ ranging from 0.19 for WCB to 0.71 for EXV. At the higher temperature ranges, activation energies ranged from 363 kJ/mol for VO to 386 kJ/mol for E2V. Significance. The viscoelastic properties of dental ceramics at high temperatures are important factors in understanding how residual stresses develop in all-ceramic and metal –ceramic dental restorations. Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Introduction For the past 40 years the concept of thermal compatibility became an important system analysis property because it is a primary controlling factor *Corresponding author. Tel.: þ1-704-687-4324; fax: þ1-704687-6069. E-mail address: [email protected]

in the magnitude of stresses that can develop in metal – ceramic prostheses. Because the metal – ceramic dental structure is fabricated by fusing two or more materials together at high temperature, transient and residual stresses develop within the component parts as the system cools to room temperature. If the transient stresses are high enough, instantaneous cracking within the ceramic can occur during cooling or the presence of high

0109-5641/$ - see front matter Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S0109-5641(03)00107-6

298

P.H. DeHoff, K.J. Anusavice

residual stresses can cause delayed failure of the restoration while in storage or in service. Metal – ceramic or ceramic – ceramic systems are considered to be thermally compatible if the transient and residual stress states are low enough to ensure that instantaneous or delayed failures do not occur. Traditionally, it was assumed that compatibility was assured if the coefficients of thermal expansion of the component parts were closely matched from some set point to room temperature. At the same time it was known that perfect matching was not possible. Thus, a number of researchers sought to establish limits of thermal coefficient mismatch values that would ensure reliable clinical performance. Based on elastic equations for a compound sphere, Nielsen and Tuccillo1 defined a safe mismatch difference of 0.225 ppm/8C while Walton and O’Brien2 tested metal –porcelain disks and spheres to establish an allowable contraction difference of 28 and 10%, respectively. However, these authors recognized that porcelain – metal thickness ratios and specimen geometry affect the limits. More recently, Steiner et al.3 fired nine commercially available body porcelains on central incisor copings of a high expansion core ceramic to yield an absolute difference limit between core and veneer of 1 ppm/8C. A number of investigators have recognized that the residual stress state in metal – ceramic and ceramic – ceramic dental restorations depends on many factors, including contraction mismatch, cooling rate, firing temperature, geometry, and fabrication techniques. To account for the effect of cooling rate or temperature distribution on stress development, it is necessary to obtain the time-dependent material properties of dental ceramics at high temperature. Previous experimental studies related to time-dependent properties of dental ceramics include the measurement of shear viscosities of several dental porcelains by Bertolotti and Shelby,4 Twiggs et al.,5 and Asaoka et al., 6 and uniaxial stress relaxation functions of several

experimental dental porcelains by DeHoff et al..7 In the present study, the beam-bending viscometer (BBV) was used to measure creep functions of two glass ceramics and four feldspathic porcelains. The objective of this study was to characterize the high temperature viscoelastic properties of several dental ceramics by the determination of creep functions based on mid-span deflections measured in a BBV.

Materials and methods Beam-bending measurements The ceramic materials and firing procedures used in this study are presented in Table 1. Six groups of beam specimens were fabricated following the manufacturers’ instructions (Ivoclar AG, Schaan, Liechtenstein; Vident, Brea, CA and Ivoclar/Williams. Amherst, NY). The specimen groups were as follows: (1) a glass – ceramic veneer (E2V); (2) an experimental glass – ceramic veneer (EXV); (3) a low-expansion feldspathic body porcelain (VB); (4) a high-expansion feldspathic body porcelain (WCB); (5) a medium-expansion opaque porcelain (VO); and (6) a high-expansion opaque porcelain (WCO). All specimens were fabricated using a metal mold and the green-body E2V bars were fired according to manufacturer’s instructions (Table 1). All specimens were finished with a 15 mm diamond wheel (Mark V Laboratory, East Granby, CT, USA) to the final dimensions (58 £ 5.5 £ 2.5 mm). They were ultrasonically and steam cleaned using distilled water and examined for flaws using light microscopy (microscope model SCW30L, Fisher Scientific, Thailand). For each bar, 3 g of powder was mixed with 20% (by mass) distilled water and vibrated into a metal mold. The mixture was vibrated until it flowed together. Excess water was blotted away and the bar was pressed out of the mold and placed on a firing tray covered with powdered silica.

Table 1 Dental ceramics and firing procedures used in this study. Dental Ceramics

Starting T (8C)

Heating rate (8C/min)

Firing T (8C)

Holding t (min)

Vacuum T on–off (8C)

E2V-IPS Empress2w body EXV-Evisionw body WCO-Will-Ceram opaque WCB-Will-Ceram body VO-VMK68 opaque VB-VMK68 body

403 403 538 538 650 650

35 35 42 42 28 28

800 760 982 954 990 990

2 2 0.5 0.5 0 0

450– 799 450– 759 538– 982 538– 954 650– 990 650– 990

T ¼ Temperature; t ¼ time.

Creep functions of dental ceramics measured in a beam-bending viscometer

Each specimen was subjected to a constant three-point flexure loading at its midpoint while positioned on a vertical quartz tube in a beambending viscometer (Theta Industries, Port Washington, NY). The BBV consists of a vertically oriented furnace, which contains a vertical quartz tube 52 mm in outer diameter and 47 mm in inner diameter with a slot cut across the top end. A vertical pull-rod with loading platform was used to apply loads across the midpoint of the beam. The viscometer was interfaced to a microcomputer by an analog-to-digital converter. Temperature, time, and mid-span deflection data were recorded at predetermined intervals by a data acquisition program. Mid-span deflection was recorded via a linear variable differential transducer (LVDT) and an analog-to-digital converter. The furnace temperature was controlled by means of a type K thermocouple inserted at the midpoint of the furnace while the specimen temperature was recorded through a type K thermocouple located adjacent to the specimen. In general, for a set temperature at the controller thermocouple, the temperature recorded at the specimen surface was slightly higher than the controller temperature and would vary (^ 1.0 8C) for each run at a given furnace temperature. At the start of each test, the temperature of the furnace was raised to a predetermined value at a heating rate of 10 8C/min, held at this temperature for at least 5 min to stabilize the temperature, and then the load, 9.8 or 0.53 N, (depending on temperature), was suddenly lowered onto the beam by use of a lab jack. Midpoint deflection and specimen temperatures were recorded at variable time intervals for a period of up to 10 min depending on the temperature. At the end of each isothermal test, the load was removed from the specimen and the temperature was then raised to the next level in 25 8C steps at a heating rate of 5 8C/min. At each temperature the loading process described earlier was repeated. All output data were recorded on a PC utilizing a Lotus 123 spreadsheet through an IEEE-488 interface.

Creep functions In the present study, the mathematical form of the creep function for dental ceramics is based on the requirement in the ANSYS finite element program (ANSYS, Inc., Canonsburg, PA) that up to a 10-term generalized Maxwell model be used to represent the shear relaxation behavior. In the present study a four-term shear relaxation model was selected, which leads to the eight-parameter discrete viscoelastic model showed in Fig. 1. It can be shown that

299

Figure 1 Eight-parameter discrete viscoelastic model.

this model leads to a creep function, JðtÞ that can be represented by:
 1 1 1 1 t 1 E t þ þ þ þ 2 exp 2 1 JðtÞ ¼ E0 E1 E2 E3 h0 E1 h1

 1 E t 1 E t 2 exp 2 2 2 exp 2 3 ð1Þ E2 E3 h2 h3 where E0 is the initial elastic modulus ðt ¼ 0Þ usually determined by sonic measurements. Although, it is expected that E0 is temperature dependent, the equipment necessary to measure this effect at the high temperatures pertinent to our study was not available in our laboratories. While there are a number of studies presenting elastic modulus data at high temperatures for several oxides,8,9 we are aware of only one study presenting elastic modulus data at elevated temperatures for dental ceramics. Kase et al.10 reported elastic properties covering a temperature range from room temperature to 500 8C for two commercial body porcelains, one of which (VB) was also used in the present study. The elastic modulus for VB demonstrated essentially linear behavior as a function of temperature from 25 to 500 8C. Based on this study, we assumed a similar behavior for all of the dental ceramics used in the present study to account for changes to E0 as a function of temperature. The room temperature moduli for E2V and EXV were determined from ultrasonic time-of-flight data measured in a highfrequency ultrasonic pulser/receiver (Nuson Inc., Boalsburg, PA) while those for VB, VO, WCB and WCO were obtained from the literature.10,11 Calculated values of E0 at the testing temperatures for each ceramic are presented in Table 2. Based on elastic conditions, the midpoint deflection for a rectangular beam oriented in the three-point bending configuration in the BBV is given by: y¼

PL3 48EI

ð2Þ

where P is the total load ðNÞ; L is the distance between supports (mm), and E is the elastic modulus (N/mm2). I is the centroidal moment of inertia of the beam cross section, I ¼ 1/12 bh3, where b is the beam width (mm), and h is the beam

300

Table 2 Experimentally determined moduli and viscosities for six ceramics at high temperature range for the eight-parameter creep function (Eq. (1)). Tempp (8C)

E0 (N/mm2)

E1 (N/mm2)

E2 (N/mm2)

E3 (N/mm2)

h0 (N·s/mm2)

h1 (N·s/mm2)

h2 (N·s/mm2)

h3 (N·s/mm2)

Correlation coefficient

E2V

525 550 575 600

5.97 £ 104 5.94 £ 104 5.91 £ 104 5.89 £ 104

4.87 £ 104 3.07 £ 104 1.10 £ 104 7.96 £ 103

1.24 £ 105 5.98 £ 104 2.32 £ 104 6.72 £ 103

5.38 £ 104 1.18 £ 104 1.05 £ 103 1.10 £ 102

3.45 £ 106 5.49 £ 105 9.81 £ 104 1.85 £ 104

4.88 £ 106 1.48 £ 106 4.27 £ 105 1.57 £ 105

8.91 £ 105 6.04 £ 105 1.85 £ 105 8.43 £ 104

7.28 £ 106 3.19 £ 106 4.75 £ 105 2.31 £ 105

0.9938 0.9985 0.9976 0.9965

EXV

475 500 525 550 575

6.38 £ 104 6.35 £ 104 6.33 £ 104 6.32 £ 104 6.29 £ 104

7.07 £ 104 4.16 £ 104 1.20 £ 104 4.10 £ 103 2.91 £ 103

5.00 £ 104 2.60 £ 104 6.23 £ 103 1.20 £ 103 8.73 £ 102

4.80 £ 104 2.51 £ 104 1.85 £ 103 2.80 £ 102 1.00 £ 102

6.35 £ 106 6.60 £ 105 1.10 £ 105 2.00 £ 104 4.43 £ 103

2.20 £ 106 9.52 £ 105 1.08 £ 105 5.87 £ 104 8.71 £ 103

1.40 £ 107 1.05 £ 106 1.80 £ 105 4.45 £ 104 8.39 £ 103

9.80 £ 106 1.19 £ 106 3.01 £ 105 6.99 £ 104 3.00 £ 104

0.9934 0.9958 0.9964 0.9969 0.9742

VB

550 575 600 625 650

6.35 £ 104 6.32 £ 104 6.29 £ 104 6.27 £ 104 6.24 £ 104

5.55 £ 104 3.75 £ 104 2.41 £ 104 1.99 £ 104 9.88 £ 103

4.12 £ 105 1.51 £ 105 5.11 £ 104 1.75 £ 104 9.22 £ 103

1.47 £ 105 4.31 £ 104 9.61 £ 103 1.51 £ 103 1.10 £ 103

1.78 £ 107 3.35 £ 106 6.22 £ 105 1.39 £ 105 3.78 £ 104

1.61 £ 107 5.58 £ 106 8.21 £ 105 1.10 £ 105 8.80 £ 104

3.80 £ 106 1.24 £ 106 4.88 £ 105 2.80 £ 105 8.86 £ 104

9.09 £ 106 3.66 £ 106 1.47 £ 106 2.96 £ 105 1.02 £ 105

0.9764 0.9939 0.9979 0.9983 0.9979

VO

550 575 600 625 650

6.74 £ 104 6.71 £ 104 6.69 £ 104 6.66 £ 104 6.63 £ 104

2.83 £ 105 7.41 £ 104 1.96 £ 104 9.90 £ 103 5.19 £ 103

8.31 £ 104 2.72 £ 104 2.98 £ 103 8.44 £ 102 6.00 £ 102

1.84 £ 105 4.14 £ 104 7.03 £ 103 4.23 £ 103 3.00 £ 102

1.95 £ 107 3.25 £ 106 1.10 £ 106 2.68 £ 105 7.10 £ 104

2.00 £ 106 8.95 £ 105 2.86 £ 105 8.66 £ 104 2.92 £ 104

1.66 £ 107 4.33 £ 106 1.00 £ 106 2.40 £ 105 4.05 £ 104

1.21 £ 107 3.18 £ 106 9.40 £ 105 1.63 £ 105 9.92 £ 104

0.9530 0.9869 0.9969 0.9877 0.9995

WCB

550 575 600 625 650

5.74 £ 104 5.71 £ 104 5.69 £ 104 5.66 £ 104 5.63 £ 104

5.52 £ 105 3.10 £ 105 7.09 £ 104 1.33 £ 104 3.39 £ 103

5.63 £ 105 2.70 £ 105 3.30 £ 104 5.00 £ 103 3.92 £ 102

2.01 £ 105 6.90 £ 104 1.05 £ 104 1.81 £ 103 2.31 £ 102

2.65 £ 107 1.10 £ 107 2.28 £ 106 4.45 £ 105 1.35 £ 105

7.72 £ 106 3.50 £ 106 5.20 £ 105 2.98 £ 105 9.73 £ 104

7.52 £ 106 6.03 £ 106 1.30 £ 106 4.50 £ 105 1.48 £ 105

1.32 £ 107 7.50 £ 106 3.19 £ 106 9.20 £ 105 2.41 £ 105

0.9893 0.9944 0.9900 0.9800 0.9987

WCO

575 600 625 650 675

5.71 £ 104 5.69 £ 104 5.66 £ 104 5.63 £ 104 5.61 £ 104

9.07 £ 105 1.92 £ 105 9.58 £ 104 8.39 £ 103 3.91 £ 103

5.59 £ 105 9.73 £ 104 2.04 £ 104 6.39 £ 103 1.15 £ 103

1.50 £ 105 2.69 £ 104 8.81 £ 103 8.61 £ 102 5.00 £ 102

1.88 £ 107 5.56 £ 106 1.16 £ 106 4.27 £ 105 1.01 £ 105

5.10 £ 106 1.10 £ 106 5.68 £ 105 9.93 £ 104 3.92 £ 104

8.79 £ 106 3.12 £ 106 9.90 £ 105 3.33 £ 105 2.86 £ 105

7.36 £ 106 3.26 £ 106 1.15 £ 106 3.86 £ 105 9.09 £ 104

0.9872 0.9757 0.9917 0.9786 0.9762

*Temperature recorded by the furnace thermocouple.

P.H. DeHoff, K.J. Anusavice

Ceramic

Creep functions of dental ceramics measured in a beam-bending viscometer

301

thickness (mm). The deflection caused by the weight of the beam is neglected because it is small compared with that caused by the load. In a creep test of a linear viscoelastic beam, the midpoint deflection as a function of time can be obtained from Eq. (2) by replacing 1=E by the creep function as follows: PL3 yðtÞ ¼ 4bh3



1 1 1 1 t þ þ þ þ 2 E0 E1 E2 E3 h0

 E t 1 E t exp 2 2 2  exp 2 1 2 E2 h1 h2
 E t  exp 2 3 h3

1 E1 1 E3 ð3Þ

Note that if we take the time rate of change of the deflection and consider long-time creep behavior ðt ! 1Þ; we obtain the creep rate C : _ ¼ C ¼ yðtÞ

d yðtÞ PL3 ¼ ð1=h0 Þ dt 4bh3

ð4Þ

In BBV testing, it is common practice to define the shear viscosity as hs ¼ h0 =3; from which:

hs ¼

PL3 12bh3 C

ð5Þ

From the deflection versus time curves at each temperature, the creep function was determined by a non-linear regression fit to Eq. (3) using the software package, CurveExpert 1.3 (David Hyams, Starkville, MS). Shear viscosities at each temperature were determined using Eq. (5).

Figure 2 Non-linear curve fit of the creep behavior for three E2V specimens at a furnace temperature of 550 8C.

temperature on a Ln (variable) versus 1=T plot with correlation coefficients ranging from 0.9600 to 0.9996. Shown in Fig. 3 is a plot of the Log of the creep function versus time at four temperatures for one of the dental ceramics (E2V). For each series of creep tests, the shear viscosity was calculated from Eq. (5) by first using linear regression to obtain the creep rate from the longtime deflection versus time data at each temperature. A typical plot showing a linear fit from 200 to 600 s is shown in Fig. 4 for an E2V specimen at a furnace temperature of 550 8C. Viscosity values for all groups at all temperatures are available but, because of the volume of data, only the values for E2V are presented in Table 3. Bertolotti and Shelby4 characterized the shear viscosity of dental porcelains at high temperatures

Results Deflection and time data were collected for four specimens within each material group at each of the isothermal temperature levels. Generally, consistent data were obtained for three out of the four specimens and the regression analyses were based on these selected cases. Although data are available for each BBV run, only a typical plot of mid-span deflection versus time for three E2V specimens at a furnace temperature of 550 8C is presented in Fig. 2. Also shown in Fig. 2 is the regression fit of the data to Eq. (3) with a correlation coefficient of 0.9985. The regression coefficients for all groups at each applicable furnace temperature are presented in Table 2. The elastic moduli ðE1 ; E2 ; E3 Þ and viscosities ðh0 ; h1 ; h2 ; h3 Þ of the model exhibit a linear decrease with

Figure 3 Logarithm of calculated creep function versus time for the E2V ceramic at four temperatures.

302

P.H. DeHoff, K.J. Anusavice

using an Arrhenius equation in the form:
 DH hs ¼ hi exp RT

Figure 4 Creep behavior of an E2V specimen at a furnace temperature of 550 8C.

Table 3 Shear viscosities for ceramic E2V for all specimens tested. Specimen

Furnace T* (8C)

Specimen T # (8C)

Shear viscosity (N·sec/mm2)

R2

1 2 3 4

450

463.6(0.54) 461.5(0.07) 459.0(0.11) 455.7(0.47)

1.51 £ 107 2.79 £ 107 2.82 £ 107 1.35 £ 107

0.9934 0.9967 0.9857 0.9849

1 2 3 4

475

490.4(0.42) 487.9(0.18) 485.0(0.18) 483.5(0.09)

2.28 £ 107 1.1 £ 107 1.15 £ 107 1.43 £ 107

0.9870 0.9939 0.9983 0.9943

1 2 3 4

500

515.4(0.18) 515.0(0.09) 512.1(0.06) 509.3(0.10)

4.84 £ 106 5.33 £ 106 5.70 £ 106 5.74 £ 106

0.9987 0.9994 0.9993 0.9986

1 2 3 4

525

541.3(0.48) 541.5(0.10) 537.9(0.08) 534.9(0.16)

1.09 £ 106 1.09 £ 106 1.15 £ 106 1.20 £ 106

0.9993 0.9996 0.9999 0.9995

1 2 3 4

550

564.9(0.92) 567.8(0.05) 563.8(0.07) 560.1(0.15)

1.55 £ 105 1.72 £ 105 1.76 £ 105 1.83 £ 105

0.9999 0.9999 0.9998 0.9999

1 2 3 4

575

593.0(0.23) 593.9(0.06) 589.7(0.08) 585.0(0.05)

2.38 £ 104 2.83 £ 104 2.98 £ 104 3.16 £ 104

0.9998 0.9998 0.9998 0.9999

1 2 3 4

600

612.1(0.19) 619.8(0.07) 615.0(0.17) 610.4(0.08)

7.21 £ 103 5.63 £ 103 5.68 £ 103 5.66 £ 103

0.9998 0.9999 0.9998 0.9999

*Furnace T is the furnace set temperature indicated on the processor meter; #Specimen T is the mean (SD) temperature during the creep run recorded by a thermocouple located near the specimen.

ð6Þ

where hi (N·s/mm2) and the activation energy, DH (kJ/mole), are experimentally determined constants, R is the universal gas constant (kJ/ mole·K) and T is the absolute temperature (K). In general, the Arrhenius behavior for dental ceramics is applicable only over a limited temperature range and in the present study it was possible to identify two linear segments on plots of ln ðhs Þ versus 1=T: Scherer12 reported that the slope of the curve above the glass transition temperature is DH=R while below the glass transition temperature the slope decreases to XDH=R where 0 # X # 1: Shown in Fig. 5 is the plot for the E2V group for which the intersection of the two straight lines occurs at a temperature of approximately 514 8C. Although the transition from liquid to glassy behavior occurs over a range of temperatures, we have selected the intersection as the glass transition temperature ðTg Þ for the dental ceramics. In addition to other material properties, the viscoelastic element in ANSYS requires the activation energy that is based on the slope of the high temperature linear segment and the ratio ðXÞ of the slope of the low temperature segment to the high temperature segment. Listed in Table 4 are values for hi and DH for the high temperature range and experimentally determined values of X and Tg for all groups. Glass transition temperatures ranged from 472 8C for EXV to 578 8C for WCO, activation energies ranged from 363 kJ/mole for VO to 386 kJ/mole for E2V and X values varied from 0.19 for WCB to 0.71 for EXV.

Figure 5 Natural logarithm of shear viscosity versus inverse absolute temperature for all E2V specimens.

Creep functions of dental ceramics measured in a beam-bending viscometer

303

Table 4 Regression coefficients at the high temperature range, glass transition temperatures, and X values for all dental ceramics. Ceramic

Temp range* (8C)

ln ðhI Þ (N·sec/mm2)

DH (kJ/mole)

Tg (8C)

X

R2

E2V EXV VB VO WCB WCO

500–600 475–575 550–650 550–650 550–650 575–675

227.386 211.363 222.950 220.798 220.003 220.182

386 369 379 363 366 371

514 472 558 549 565 578

0.30 0.71 0.27 0.20 0.19 0.28

0.9908 0.9864 0.9893 0.9767 0.9532 0.9934

*Temp range refers to the furnace set temperature.

Discussion The continuing introduction of new dental alloys and dental ceramics for use in the fabrication of metal – ceramic and all-ceramic restorations makes it critically important that manufacturers understand how stresses develop when these restorations are cooled from the firing temperatures. Manufacturers continue to rely on an allowable maximum mismatch between average expansion coefficients of the component materials as a first step to predict clinical success. Naturally, the manufacturers conduct extensive laboratory tests on typical bridges and crowns prior to introduction of new materials to the marketplace, but that does not always ensure clinical success. In some cases, residual tensile stress levels induced by a thermal contraction mismatch can be acceptable in laboratory situations but they become detrimental in long-term applications under occlusal loading in the oral environment. It seems obvious that residual tensile stresses should be minimized to the extent possible and this condition can only be accomplished with a better understanding of how these stresses develop during fabrication of dental restorations. We believe that the viscoelastic element in ANSYS and other commercial finite element codes provides the opportunity to more completely identify process variables that lead to transient and residual stress development in dental restorations. However, the utilization of this element requires input property information that has not generally been available for dental ceramics. The present study provides measurements of viscoelastic properties for two glass –ceramics and four feldspathic porcelains that will lead to the required input properties for these materials. A number of previous investigators1,13,14,15 have predicted residual stress levels in metal –ceramic systems based on elastic behavior and the following equation: ð T1 sðtÞ ¼ Ks DaðTÞdT ð7Þ T0

where Ks is a geometry and material factor, DaðTÞ is the temperature dependent difference in contraction coefficients, T0 is the temperature of interest, and T1 is the stress-free temperature (usually taken as Tg Þ: For a given geometry and similar contraction behavior, higher residual stresses are predicted for a higher Tg : Thus in the case of E2V and EXV, which have similar contraction behavior, we would expect higher residual stresses in a ceramic – ceramic restoration for E2V, which has a Tg of 514 8C compared with 472 8C for EXV. Preliminary calculations based on viscoelastic behavior for a simple geometry indicate that the elastic predictions may lead to erroneous results. As indicated previously, the ANSYS finite element program requires shear stress relaxation functions whereas we have reported creep functions in the present study. It is possible to use standard linear viscoelastic theory to transform creep behavior to the required relaxation behavior and that will be covered in a subsequent study.

Acknowledgements This study was partially supported by NIH-NIDCR grant DE06672 and the Mechanical Engineering Department at UNC Charlotte. The authors thank Mr Robert B. Lee and Ms Allyson Barrett of the University of Florida for their assistance with specimen preparation. We also thank Ivoclar AG, Liechtenstein, for providing the Empress ceramic materials used in this study.

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