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The effect of the disc support system on biaxial tensile strength of a glass ionomer cement
dental materials Dental Materials 18 (2002) 376±379 www.elsevier.com/locate/dental
The effect of the disc support system on biaxial tensile strength of a glass ionomer cement Jill A. Williams a,*, Richard W. Billington b, Gavin J. Pearson b a
b
Department of Biomaterials, Eastman Dental Institute, London, UK Department of Biomaterials in Relation to Dentistry, Queen Mary and West®eld College, London, UK Received 13 September 2000; received in revised form 7 February 2001; accepted 20 February 2001
Abstract Objective: This was to examine how varying the type of support, from a complete ring to a series of point supports, affected the biaxial tensile strength of one glass ionomer cement. Method: Three support diameters from 11.5 to 28.6 mm were achieved using 3 mm ball bearings as point supports equidistantly spaced around the diameter. From 3±30 point supports were used depending on diameter. At the maximum number of point supports for each diameter the support points were 3 mm apart. After 24 h storage in water at 378C the biaxial tensile strength of 1 mm thick glass ionomer restorative cement discs was measured using a loading rate of 1 mm min 21. The load at break was converted to biaxial tensile strength using the Timoschenko and Woinowsky-Kreiger equation using a Poisson's ratio value of 0.30. The mean strength of six specimens tested per support regime was calculated. Results: Comparison with the mean result obtained from using a continuous knife-edge support showed there to be no signi®cant difference (unpaired t-test) between the different support systems except in two cases, both being when a four-point support was used. Neither the support diameter nor the number of point supports was crucial. Signi®cance: Results from studies where different systems have been used to support brittle cement discs may be compared. q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. Keywords: Biaxial tensile strength; Support type; Glass ionomer cement
1. Introduction The biaxial tensile strength, also known as the shell strength, is said to have a number of advantages over other tensile strength tests such as diametral and uniaxial (three and four-point bend) tensile tests. It is also considered to have advantages over compressive strength measurement. Among the advantages cited are the absence of intersecting planes of shear, the application of pure tensile stress on the lower face of the specimen and the lack of additional specimen surface treatment. The elimination of specimen edge effects are also advantageous. The shell strength test was developed for brittle ceramic materials but is also ideally suited for brittle dental materials such as conventional acid-base cured glass ionomer cements, zinc phosphate and polycarboxylate cements. It uses a ¯at disc of material and has the additional advantage that small * Corresponding author. Tel.: 144-20-7915-1133; fax: 144-20-79151133. E-mail address: [email protected] (J.A. Williams).
quantities of material are used for each test specimen. This avoids the layering problems encountered when large specimens are prepared. This is a particular problem for encapsulated materials. One study [1] compared the biaxial test with uniaxial and diametral tensile tests for three types of dental cement and concluded that the biaxial strength was preferred to these other types of tensile strength tests. The test is carried out by an indentor impinging centrally at a pre-determined rate upon a disc of test material which rests on an underlying support. The load required to break the specimen is measured. Even with such a simple test, a number of variables need to be considered, particularly the loading arrangements. Some studies have used a ¯at ended indentor with others preferring a ball indentor to produce what is essentially a point loading. Ban and Anusavice [1] commented on the variety of supports used in a number of studies. Although their study used three metal spheres positioned equidistant from one another, other studies [2,3] used a continuous ring support. These two methods represent the extremes of support modalities. It would be advantageous, if
0109-5641/02/$22.00 + 0.00 q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. PII: S0109-564 1(01)00053-7
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
377
Table 1 Biaxial tensile strength results (MPa) and ranking order Support: type and number
11.5 mm diameter Mean (sd) (range)
Rank
3-ball 4-ball 6-ball 9-ball 12-ball 18-ball 20-ball 30-ball Knife-edge
48.3 (2.6) (45.0±51.5) 56.6 (7.8) (45.4±58.8) 52.1 (4.8) (44.1±58.2) 52.5 (3.8) (46.2±57.0)
15 mm diameter Mean (sd) (range)
Rank
19.1 mm diameter Mean (sd) (range)
Rank
28.6 mm diameter Mean (sd) (range)
11 3 6
12 1 4
47.7 (3.7) (42.8±49.4) 59.7 (7.2) (45.5±62.1) 53.9 (5.7) (45.5±62.1)
5
9
48.8 (9.3) (36.3±60.5)
16 7 15 8
43.1 (4.1) (38.0±47.6) 50.6 (1.0) (48.7±51.4) 44.4 (2.4) (41.6±47.8) 49.3 (3.6) (46.2±55.7)
2
57.3 (3.6) (52.8±61.6)
10
48.7 (3.7) (45.2±53.5)
14
45.5 (5.3) (38.2±54.1)
47.1 (6.6) (38.9±53.9)
studies are to be compared, to know if the type of support affects the ultimate strength obtained. The aim of the present study was to investigate how the number of point supports and the diameter of the `ring' of support given by these points affected the biaxial strength when compared to a continuous annular ring support.
2. Material and method A conventional acid-base cure glass ionomer restorative cement, HiFi, (batch number 089419-5) [Shofu Inc, Kyoto, Japan] was used. It was mixed, using weighed amounts, at a powder/liquid ratio of 4.5/1.0 according to the manufacturer's instructions. In order to determine the nature of the material a preliminary compressive strength measurement was carried out according to EN29917:1994 [4]. Analysis of the stress/strain plots showed the material to fail in a brittle manner and it was therefore considered suitable for testing under tensile mode. 1 mm thick discs were made in metal ring molds, measuring either 14, 22.5 or 30 mm diameter. Each mould was ®lled with cement within 1 min of mixing, compressed between acetate sheet and metal plates and left clamped at 378C and .80% relative humidity. Each disc of cement was then removed from the mold after 60 min had elapsed from the start of mixing and placed in water at 378C for a further 23 h before breaking. No additional surface preparation was undertaken. A total of 96 discs were prepared allowing six to be broken at each of 16 support regimes. A Universal Load Testing Machine (Houns®eld H25K) was used with the load applied at a rate of 1 mm min 21. In each case the indentor was a 3 mm steel ball-bearing. This was held onto the upper platen of the test machine by means of a magnet allowing the indentor position to be adjusted to impinge centrally upon each disc. The point supports were 3 mm steel ball bearings. Regardless of the number of point supports used, the spheres were always positioned equidistant around a drawn diameter of either 11.5, 19.1 or 28.6 mm. For all three diameters, when the maximum number of ball bearings were positioned around
13
the circumference there was continuous contact between them and thus only 3 mm of unsupported cement between each point. The number of point supports (n) used for each diameter is given in Table 1. A continuous, annular, knifeedge support, of diameter 15 mm, was also used. The load at break was converted to biaxial tensile strength (SS) using the formula for maximum tensile stress given by Timoshenko and Woinowsky-Kreiger [5] where: SS MPa
load N 1 1 v{0:485 ln a=t 1 0:52} 1 0:48 t2
1
where v is Poisson's ratio, a is the radius of the support diameter and t the thickness of the specimen (mm). For conventional glass ionomer cements the value of v has been determined as 0.30 [6]. Inclusion of this value in Eq. (1) reduced the equation to: SS
load N {0:63 ln a=t 1 1:156} t2
2
3. Results The mean biaxial tensile strengths, together with standard deviation and range at each support regime are given in Table 1. Non-parametric statistics were used to test for signi®cance and these are shown in Table 2. Of the 16 mean biaxial strengths 11 were higher and four lower than the 47.1 MPa obtained from the knife-edge. The next most supportive regimes (theoretically) were those cases where the ball Table 2 Signi®cant differences (unpaired t-test) between each point support system and a continuous knife-edge Number of supports
11.5 mm diameter
19.1 mm diameter
28.6 mm diameter
3 4 6 9 12 18 20 30
NS 0.05 NS
NS 0.01 NS
NS
NS
NS NS NS NS
0.01
NS NS NS
378
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
bearings touched, thus giving only 3 mm unsupported disc between each point. These mean results were 52.5, 57.3 and 45.5 MPa for diameters of 11.5, 22.5 and 30 mm. These ranked 5th, 2nd and 14th in magnitude. Of the varying support regimes only the 4-ball/11.5 and 19.1 mm and the 20-ball/ 19.1 mm had mean strengths signi®cantly or highly signi®cantly higher than the continuous support. When compared to the groups above and below, namely the 3 and 6-ball supports, the 4-ball system was signi®cantly or highly signi®cantly stronger than the 3-ball support of the same diameter but only for the largest diameter was it signi®cantly higher than the corresponding 6-ball support. Pooling of all the data obtained at each diameter and statistical analysis using the unpaired t-test showed no signi®cant difference in the strengths obtained at each diameter. 4. Discussion Although the equation used by Ban and Anusavice [1] appears different to that used in the present study both can be reduced to the same formula. The differences largely arise because of the use of a ¯at-ended piston in one study and a ball-ended piston in the other. Ban and Anusavice used the formula: failure stress
load : 3=4p2 1 1 vln a=r0 1 1 2 v 2a2 t2 2 r02 =2b2 1 1 1 v
(3)
where a is the radius of support, b is the radius of the specimen disc, and stated that the equivalent radius: r0 1:6r 2 1 t2 1=2 2 0:675t
4
r being the radius at the point of contact, of the ¯at-ended piston used to break the specimens of thickness t. For a point loading, such as a ball-ended piston, r ! t giving r0 t±0.675t 0.325t. Therefore ln(a/r0) ln(a/t)±ln 0.325 ln (a/t) 1 1.124. Eq. (3) then becomes:
load 0:477 1 1 vln a=t 1 0:537 1 1 v 1 0:238 1 2 v t2 2a2 2 r02 =2b2 1 0:238 1 1 v
The term (2a 2 ±r02)/2b 2 becomes, by substitution for r0, (2a 2 ±0.106t 2)/2b 2 and if t ! a and a < b is approximately 1, Eq. (3) reduces to failure stress:
load 0:477 1 1 vln a=t 1 0:537 1 1 v t2 10:238 1 2 v 1 0:238 1 1 v
load 0:477 1 1 vln a=t 1 1:015 1 0:537v t2
load 1 1 vf0:477 ln a=t 1 0:536g t2
essentially equal to the equation used in the present study. This glass ionomer cement had strengths higher than the zinc phosphate cement used by Ban and Anusavice [1] but the coef®cients of variation which ranged from 2.0 to 19.0%, were very similar in both studies. A glass polyphosphonate (ionomer) cement has been reported [7] as having a biaxial tensile strength of 34.5 MPa with a coef®cient of variation of 16.8%, a similar variability to that found in the present study. The knife-edge support theoretically should give the greatest degree of support to the discs. However continuous support did not give either the highest or lowest result. A possible explanation is that although a continuous support may be thought theoretically ideal, in practical terms continuous contact between disc and support is unlikely unless both are perfectly ¯at. Since no ®nishing treatment is given to the specimens in the present study it may well be that they are supported only at a variable number of points depending on surface geometry. Stresses may then be applied randomly and over short stretches of surface causing highly stressed areas. For a disc which is not perfectly ¯at it might be thought that the best support would consist of three points, equidistantly spaced around the circumference. However, the biaxial strength for all three diameters tested was not signi®cantly different from that obtained using the continuous support and were low in the ranking order. Rather surprisingly a 4-point support seemed generally to give the highest strengths for reasons which are not clear. There did not appear to be any relationship between strength and either the number of point supports or the disc diameter, although the largest disc size tended to produce weaker specimens. Calculations of the overall means for each diameter gave values of 52.4, 53.5 and 46.9 MPa for the 11.5, 19.1 and 28.6 mm diameters respectively. One explanation of the decrease is the increased distance between the points of indentor and support. This would, if the number of ¯aws per unit volume remained constant, increase the number of imperfections, possibly over a critical level for the largest diameter. The weights of the three sizes are of the order of 0.4, 1.0 and 1.8 g respectively, all larger than those used clinically but not so large as to provide noticeable differences in the ease of mix. In the light of these results the use of the smallest diameter would be the preferred experimental option since ¯aws, either of porosity or unreacted components, are inherent in any mixing process, whether manual or mechanical. With three diameters used the changes made in the number of point supports resulted in changes in the length of unsupported disc edge. The minimum distance was 3 mm (when the ball bearings touched) up to maxima of 9.3 mm
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
for the smallest diameter, 15.4 mm for the intermediate size and 23.1 mm for the largest disc. However, this had no systematic effect upon the biaxial strength. Using the same non-parametric statistics only two support systems differed signi®cantly from the knife edge. The 20-ball/ 19.1 mm diameter system (3 mm unsupported edge) was highly signi®cantly higher and the 4-ball/11.5 mm diameter system (7.5 mm unsupported edge) was signi®cantly higher. Discs with larger unsupported edges, such as the 3 and 4ball/28.6 mm disc did not differ signi®cantly from the knife edge support. 5. Conclusions It was concluded on the basis of this study that the type of support does not appear to cause any systematic effect. It would thus appear possible to compare results from different studies regardless of the supporting mechanism.
379
References [1] Ban S, Anusavice KJ. In¯uence of test method on failure stress of brittle dental materials. J Dent Res 1990;69(12):1791±9. [2] Sced IR, McLean JW, Hotz P. The strengthening of aluminous porcelain with bonded platinum foils. J Dent Res 1977;56(9):1067±9. [3] Piddock V, Marquis PM, Wilson HJ. The mechanical strength and microstructure of all-ceramic crowns. J Dent Res 1987;15:153±8. [4] Dental water-based cements. EN 29917:1994 Type 4.1.5 Application 4.2.3 p. 8±10, European Committee for Standardization, Central Secretariat:rue de Stassart 36, Brussels. [5] Timoschenko S, Woinowsky-Kreiger S. Symmetrical bending of circular plates. Theory of plates and shells, 2nd ed. New York: McGraw-Hill, 1959. p. 106±7. [6] Akinmade AO, Nicholson JW. Poisson's ratio of glass-polyalkenoate (`glass-ionomer') cements determined by an ultrasonic pulse method. Journal of Materials Science; Materials in Medicine 1995;6:483±5. [7] Akinmade AO. The development of a glass polyphosphonate (ionomer) cement. J Dent Res 1997;76:1036 (Abstr. No. 141).
The effect of the disc support system on biaxial tensile strength of a glass ionomer cement Jill A. Williams a,*, Richard W. Billington b, Gavin J. Pearson b a
b
Department of Biomaterials, Eastman Dental Institute, London, UK Department of Biomaterials in Relation to Dentistry, Queen Mary and West®eld College, London, UK Received 13 September 2000; received in revised form 7 February 2001; accepted 20 February 2001
Abstract Objective: This was to examine how varying the type of support, from a complete ring to a series of point supports, affected the biaxial tensile strength of one glass ionomer cement. Method: Three support diameters from 11.5 to 28.6 mm were achieved using 3 mm ball bearings as point supports equidistantly spaced around the diameter. From 3±30 point supports were used depending on diameter. At the maximum number of point supports for each diameter the support points were 3 mm apart. After 24 h storage in water at 378C the biaxial tensile strength of 1 mm thick glass ionomer restorative cement discs was measured using a loading rate of 1 mm min 21. The load at break was converted to biaxial tensile strength using the Timoschenko and Woinowsky-Kreiger equation using a Poisson's ratio value of 0.30. The mean strength of six specimens tested per support regime was calculated. Results: Comparison with the mean result obtained from using a continuous knife-edge support showed there to be no signi®cant difference (unpaired t-test) between the different support systems except in two cases, both being when a four-point support was used. Neither the support diameter nor the number of point supports was crucial. Signi®cance: Results from studies where different systems have been used to support brittle cement discs may be compared. q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. Keywords: Biaxial tensile strength; Support type; Glass ionomer cement
1. Introduction The biaxial tensile strength, also known as the shell strength, is said to have a number of advantages over other tensile strength tests such as diametral and uniaxial (three and four-point bend) tensile tests. It is also considered to have advantages over compressive strength measurement. Among the advantages cited are the absence of intersecting planes of shear, the application of pure tensile stress on the lower face of the specimen and the lack of additional specimen surface treatment. The elimination of specimen edge effects are also advantageous. The shell strength test was developed for brittle ceramic materials but is also ideally suited for brittle dental materials such as conventional acid-base cured glass ionomer cements, zinc phosphate and polycarboxylate cements. It uses a ¯at disc of material and has the additional advantage that small * Corresponding author. Tel.: 144-20-7915-1133; fax: 144-20-79151133. E-mail address: [email protected] (J.A. Williams).
quantities of material are used for each test specimen. This avoids the layering problems encountered when large specimens are prepared. This is a particular problem for encapsulated materials. One study [1] compared the biaxial test with uniaxial and diametral tensile tests for three types of dental cement and concluded that the biaxial strength was preferred to these other types of tensile strength tests. The test is carried out by an indentor impinging centrally at a pre-determined rate upon a disc of test material which rests on an underlying support. The load required to break the specimen is measured. Even with such a simple test, a number of variables need to be considered, particularly the loading arrangements. Some studies have used a ¯at ended indentor with others preferring a ball indentor to produce what is essentially a point loading. Ban and Anusavice [1] commented on the variety of supports used in a number of studies. Although their study used three metal spheres positioned equidistant from one another, other studies [2,3] used a continuous ring support. These two methods represent the extremes of support modalities. It would be advantageous, if
0109-5641/02/$22.00 + 0.00 q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. PII: S0109-564 1(01)00053-7
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
377
Table 1 Biaxial tensile strength results (MPa) and ranking order Support: type and number
11.5 mm diameter Mean (sd) (range)
Rank
3-ball 4-ball 6-ball 9-ball 12-ball 18-ball 20-ball 30-ball Knife-edge
48.3 (2.6) (45.0±51.5) 56.6 (7.8) (45.4±58.8) 52.1 (4.8) (44.1±58.2) 52.5 (3.8) (46.2±57.0)
15 mm diameter Mean (sd) (range)
Rank
19.1 mm diameter Mean (sd) (range)
Rank
28.6 mm diameter Mean (sd) (range)
11 3 6
12 1 4
47.7 (3.7) (42.8±49.4) 59.7 (7.2) (45.5±62.1) 53.9 (5.7) (45.5±62.1)
5
9
48.8 (9.3) (36.3±60.5)
16 7 15 8
43.1 (4.1) (38.0±47.6) 50.6 (1.0) (48.7±51.4) 44.4 (2.4) (41.6±47.8) 49.3 (3.6) (46.2±55.7)
2
57.3 (3.6) (52.8±61.6)
10
48.7 (3.7) (45.2±53.5)
14
45.5 (5.3) (38.2±54.1)
47.1 (6.6) (38.9±53.9)
studies are to be compared, to know if the type of support affects the ultimate strength obtained. The aim of the present study was to investigate how the number of point supports and the diameter of the `ring' of support given by these points affected the biaxial strength when compared to a continuous annular ring support.
2. Material and method A conventional acid-base cure glass ionomer restorative cement, HiFi, (batch number 089419-5) [Shofu Inc, Kyoto, Japan] was used. It was mixed, using weighed amounts, at a powder/liquid ratio of 4.5/1.0 according to the manufacturer's instructions. In order to determine the nature of the material a preliminary compressive strength measurement was carried out according to EN29917:1994 [4]. Analysis of the stress/strain plots showed the material to fail in a brittle manner and it was therefore considered suitable for testing under tensile mode. 1 mm thick discs were made in metal ring molds, measuring either 14, 22.5 or 30 mm diameter. Each mould was ®lled with cement within 1 min of mixing, compressed between acetate sheet and metal plates and left clamped at 378C and .80% relative humidity. Each disc of cement was then removed from the mold after 60 min had elapsed from the start of mixing and placed in water at 378C for a further 23 h before breaking. No additional surface preparation was undertaken. A total of 96 discs were prepared allowing six to be broken at each of 16 support regimes. A Universal Load Testing Machine (Houns®eld H25K) was used with the load applied at a rate of 1 mm min 21. In each case the indentor was a 3 mm steel ball-bearing. This was held onto the upper platen of the test machine by means of a magnet allowing the indentor position to be adjusted to impinge centrally upon each disc. The point supports were 3 mm steel ball bearings. Regardless of the number of point supports used, the spheres were always positioned equidistant around a drawn diameter of either 11.5, 19.1 or 28.6 mm. For all three diameters, when the maximum number of ball bearings were positioned around
13
the circumference there was continuous contact between them and thus only 3 mm of unsupported cement between each point. The number of point supports (n) used for each diameter is given in Table 1. A continuous, annular, knifeedge support, of diameter 15 mm, was also used. The load at break was converted to biaxial tensile strength (SS) using the formula for maximum tensile stress given by Timoshenko and Woinowsky-Kreiger [5] where: SS MPa
load N 1 1 v{0:485 ln a=t 1 0:52} 1 0:48 t2
1
where v is Poisson's ratio, a is the radius of the support diameter and t the thickness of the specimen (mm). For conventional glass ionomer cements the value of v has been determined as 0.30 [6]. Inclusion of this value in Eq. (1) reduced the equation to: SS
load N {0:63 ln a=t 1 1:156} t2
2
3. Results The mean biaxial tensile strengths, together with standard deviation and range at each support regime are given in Table 1. Non-parametric statistics were used to test for signi®cance and these are shown in Table 2. Of the 16 mean biaxial strengths 11 were higher and four lower than the 47.1 MPa obtained from the knife-edge. The next most supportive regimes (theoretically) were those cases where the ball Table 2 Signi®cant differences (unpaired t-test) between each point support system and a continuous knife-edge Number of supports
11.5 mm diameter
19.1 mm diameter
28.6 mm diameter
3 4 6 9 12 18 20 30
NS 0.05 NS
NS 0.01 NS
NS
NS
NS NS NS NS
0.01
NS NS NS
378
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
bearings touched, thus giving only 3 mm unsupported disc between each point. These mean results were 52.5, 57.3 and 45.5 MPa for diameters of 11.5, 22.5 and 30 mm. These ranked 5th, 2nd and 14th in magnitude. Of the varying support regimes only the 4-ball/11.5 and 19.1 mm and the 20-ball/ 19.1 mm had mean strengths signi®cantly or highly signi®cantly higher than the continuous support. When compared to the groups above and below, namely the 3 and 6-ball supports, the 4-ball system was signi®cantly or highly signi®cantly stronger than the 3-ball support of the same diameter but only for the largest diameter was it signi®cantly higher than the corresponding 6-ball support. Pooling of all the data obtained at each diameter and statistical analysis using the unpaired t-test showed no signi®cant difference in the strengths obtained at each diameter. 4. Discussion Although the equation used by Ban and Anusavice [1] appears different to that used in the present study both can be reduced to the same formula. The differences largely arise because of the use of a ¯at-ended piston in one study and a ball-ended piston in the other. Ban and Anusavice used the formula: failure stress
load : 3=4p2 1 1 vln a=r0 1 1 2 v 2a2 t2 2 r02 =2b2 1 1 1 v
(3)
where a is the radius of support, b is the radius of the specimen disc, and stated that the equivalent radius: r0 1:6r 2 1 t2 1=2 2 0:675t
4
r being the radius at the point of contact, of the ¯at-ended piston used to break the specimens of thickness t. For a point loading, such as a ball-ended piston, r ! t giving r0 t±0.675t 0.325t. Therefore ln(a/r0) ln(a/t)±ln 0.325 ln (a/t) 1 1.124. Eq. (3) then becomes:
load 0:477 1 1 vln a=t 1 0:537 1 1 v 1 0:238 1 2 v t2 2a2 2 r02 =2b2 1 0:238 1 1 v
The term (2a 2 ±r02)/2b 2 becomes, by substitution for r0, (2a 2 ±0.106t 2)/2b 2 and if t ! a and a < b is approximately 1, Eq. (3) reduces to failure stress:
load 0:477 1 1 vln a=t 1 0:537 1 1 v t2 10:238 1 2 v 1 0:238 1 1 v
load 0:477 1 1 vln a=t 1 1:015 1 0:537v t2
load 1 1 vf0:477 ln a=t 1 0:536g t2
essentially equal to the equation used in the present study. This glass ionomer cement had strengths higher than the zinc phosphate cement used by Ban and Anusavice [1] but the coef®cients of variation which ranged from 2.0 to 19.0%, were very similar in both studies. A glass polyphosphonate (ionomer) cement has been reported [7] as having a biaxial tensile strength of 34.5 MPa with a coef®cient of variation of 16.8%, a similar variability to that found in the present study. The knife-edge support theoretically should give the greatest degree of support to the discs. However continuous support did not give either the highest or lowest result. A possible explanation is that although a continuous support may be thought theoretically ideal, in practical terms continuous contact between disc and support is unlikely unless both are perfectly ¯at. Since no ®nishing treatment is given to the specimens in the present study it may well be that they are supported only at a variable number of points depending on surface geometry. Stresses may then be applied randomly and over short stretches of surface causing highly stressed areas. For a disc which is not perfectly ¯at it might be thought that the best support would consist of three points, equidistantly spaced around the circumference. However, the biaxial strength for all three diameters tested was not signi®cantly different from that obtained using the continuous support and were low in the ranking order. Rather surprisingly a 4-point support seemed generally to give the highest strengths for reasons which are not clear. There did not appear to be any relationship between strength and either the number of point supports or the disc diameter, although the largest disc size tended to produce weaker specimens. Calculations of the overall means for each diameter gave values of 52.4, 53.5 and 46.9 MPa for the 11.5, 19.1 and 28.6 mm diameters respectively. One explanation of the decrease is the increased distance between the points of indentor and support. This would, if the number of ¯aws per unit volume remained constant, increase the number of imperfections, possibly over a critical level for the largest diameter. The weights of the three sizes are of the order of 0.4, 1.0 and 1.8 g respectively, all larger than those used clinically but not so large as to provide noticeable differences in the ease of mix. In the light of these results the use of the smallest diameter would be the preferred experimental option since ¯aws, either of porosity or unreacted components, are inherent in any mixing process, whether manual or mechanical. With three diameters used the changes made in the number of point supports resulted in changes in the length of unsupported disc edge. The minimum distance was 3 mm (when the ball bearings touched) up to maxima of 9.3 mm
J.A. Williams et al. / Dental Materials 18 (2002) 376±379
for the smallest diameter, 15.4 mm for the intermediate size and 23.1 mm for the largest disc. However, this had no systematic effect upon the biaxial strength. Using the same non-parametric statistics only two support systems differed signi®cantly from the knife edge. The 20-ball/ 19.1 mm diameter system (3 mm unsupported edge) was highly signi®cantly higher and the 4-ball/11.5 mm diameter system (7.5 mm unsupported edge) was signi®cantly higher. Discs with larger unsupported edges, such as the 3 and 4ball/28.6 mm disc did not differ signi®cantly from the knife edge support. 5. Conclusions It was concluded on the basis of this study that the type of support does not appear to cause any systematic effect. It would thus appear possible to compare results from different studies regardless of the supporting mechanism.
379
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