Influence of specimen dimensions and their derivatives ( C-factor and volume) on polymerization stress determined in a high compliance testing system



To verify the null hypothesis that in a high compliance testing system stress magnitude was not influenced by specimen dimensions and, therefore, by its cavity configuration factor ( C -factor) and volume.


Twelve experimental groups were defined according to the specimen height (0.5, 1, 2 or 4 mm) and diameter (4, 6 or 8 mm). A selfcure composite (Bisfil 2B, Bisco) was inserted between the flat surfaces of two acrylic rods attached to the opposite ends of a universal testing machine. An extensometer with a gauge length of 10 mm was attached to both rods to monitor specimen height. Force development was monitored for 30 min and nominal stress was calculated dividing the maximum force value by the crossection of the rod. A second set of data was obtained dividing nominal stress by the corresponding longitudinal compliance (LC) of the system for that particular specimen size. Data was analyzed using two-way ANOVA/Tukey test (nominal stress), Kruskal/Wallis (normalized stress), both at alpha = 5%, and regression analysis having either C -factor or volume as independent variable.


Regression analysis involving nominal stress did not reveal strong relationships with the independent variables ( C -factor: 0.437, volume: 0.662). A strong relationship was found between normalized stress and specimen volume ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Radj2=0.886′>R2adj=0.886Radj2=0.886
R a d j 2 = 0.886
). Normalized stress showed no relationship with specimens’ C -factor. Pairwise comparisons between groups with similar volumes revealed that normalized stress increased at higher C -factors.


By eliminating the influence of longitudinal compliance, a strong relationship between polymerization stress and specimen volume was revealed in a high compliance testing system.


Composite polymerization stress has been associated to potential clinical problems, namely, interfacial debonding, microleakage, enamel cracks and tooth deformation . Though determined by composite shrinkage, viscous flow and elastic modulus polymerization stress per se is not a material property, meaning that its magnitude is highly dependent on external factors such as the dimensions of the specimen, bonded to unbonded ratio, and the compliance of the testing apparatus . By analogy, the same external factors are expected to somehow affect stress development in the clinical situation.

The compliance of the testing system refers to the elongation of its components, both in the longitudinal and transversal direction, when subjected to forces during the test. In broad terms, low compliances are associated to high stress values . The compliance of a testing system is dictated by the overall stiffness of the testing apparatus and by the elastic modulus of the bonding substrate. In universal testing machines (UTM), low compliance levels are usually determined by the use of glass or metal as bonding substrate, associated to a closed loop feedback mechanism to maintain the specimen initial height . Devices based on cantilever beams allow for the adjustment of the compliance simply by changing the distance between the specimen and the beam holder or the material of the beam . More recently, data obtained in UTM systems using acrylic rods as bonding substrate became available . The use of acrylic as bonding substrate in substitution of glass increases the longitudinal compliance of UTM system by 15 times, reducing the calculated nominal stress by approximately 60% .

When polymerization stress is measured in low compliance testing systems, values increase linearly with the ratio between the bonded and the unbonded area of the specimen, termed “cavity configuration factor” ( C -factor), and no relationship is observed between stress and the volume of shrinking composite . However, in less rigid systems, a dominant effect of the volume of the shrinking composite corresponded to an opposite relationship between stress and C -factor . Indeed, a systematic evaluation of the effect of specimen height and diameter on polymerization stress verified that the relationship between stress and C -factor is not straightforward and that composite volume also plays an important role .

Notwithstanding, over the years the C -factor has become a “rule of thumb” to attribute a poor prognostic to composite restorations with high C -factors and also to justify the indication of incremental placement techniques . In fact, some authors observed lower bond strengths, increased microleakage and gap formation associated to higher C -factors . However, other in vitro studies found a direct correlation between microleakage and restoration volume and no relationship between microleakage and C -factor, except in cases where cavities with similar volumes were compared . The choice of adhesive system and photoactivation protocol also seem to modulate the influence of C -factor on microleakage .

Recently, studies have shown that stress data from high compliance UTM systems are better predictors of the performance of commercial composites in microleakage, gap formation and bond strength tests, in comparison to data from low compliance systems (Boaro, unpublished data). That suggests that the behavior of the dental substrate subjected to the mechanical stress originated from composite polymerization is more akin to those of less rigid testing systems. Therefore, the lack of correlation between C -factor and interfacial quality tests observed in the above-mentioned studies could be explained by the fact that the C -factor is only valid in low compliance situations (seldom found in the clinic) or in cases where restorations with similar volumes are compared.

The aim of the present study was to verify the influence of specimen dimensions (diameter and height) on polymerization stress determined in a high compliance UTM system using acrylic as bonding substrate for the composite. The null hypothesis was that stress magnitude was not influenced by specimen dimensions.


Poly(methyl methacrylate) rods, 40 mm in length and 4, 6 or 8 mm in diameter, had one of their flat surfaces sandblasted using 250 μm alumina and then coated with methyl methacrylate monomer (JET Acrílico Auto Polimerizante, Artigos Odontológicos Clássico, São Paulo, Brazil). The application of acrylic monomer improved the wetting of the rod surface by an unfilled resin (Scotchbond Multipurpose Plus, bottle #3, 3M ESPE, St. Paul, MN, USA), which was cured for 30 s under 400 mW/cm 2 . Two rods with the same diameter were attached to the opposite fixtures of a universal testing machine (Instron 5565, Canton, MA, USA). Then, a chemically activated composite (Bisfil 2B, Bisco Inc., Schaumburg, IL, USA) was mixed for 20 s, inserted between the treated surfaces of the rods and contoured following the perimeter of the rods. A self-cured material was used in this study to eliminate the influence of composite curing kinetics and degree of conversion (and, consequently, its shrinkage, viscous flow and elastic modulus) on stress values. Specimen height was defined by adjusting the distance between them to 0.5 mm, 1 mm, 2 mm or 4 mm. By doing so, twelve experimental groups were constituted, with C -factors ranging between 0.5 and 8 and volumes between 6.3 and 201 mm 3 ( Table 1 ). The formulas used to calculate C -factor and volume are shown below.

C = d 2 × h
volume = π × d 2 2 × h

where d is the diameter and h is the height of the PMMA rod (both in mm).

Table 1
Experimental groups tested in this study, defined by specimen height and diameter, with respective C -factors, volumes and longitudinal compliance (LC), averages and standard deviation for nominal stress and stress normalized for LC (in the same column, values followed by the same superscript are not statistically different, p > 0.05).
Diameter (mm) Height (mm) C -factor Volume (mm 3 ) LC (×10 −5 mm/N) Nominal stress (MPa) Normalized stress (×10 5 MPa N/mm)
4 0.5 4 6 24.7 1.4 (0.1) E 0.06 (0.01) H
1 2 13 23.4 1.8 (0.3) DE 0.08 (0.01) G
2 1 25 20.8 2.3 (0.2) CD 0.11 (0.01) F
4 0.5 50 15.6 3.8 (0.3) A 0.24 (0.02) E
6 0.5 6 14 11.0 1.3 (0.2) E 0.11 (0.02) F
1 3 28 10.4 2.5 (0.2) CD 0.24 (0.01) D
2 1.5 57 9.3 2.3 (0.1) CD 0.25 (0.01) D
4 0.8 113 7.0 3.4 (0.4) AB 0.48 (0.06) B
8 0.5 8 25 6.2 2.3 (0.2) CD 0.37 (0.03) C
1 4 50 5.8 2.7 (0.5) BC 0.47 (0.08) BC
2 2 101 5.2 2.7 (0.4) BC 0.52 (0.07) B
4 1 201 3.9 3.8 (0.7) A 0.97 (0.19) A

A transducer (model 2630-101, Instron) was clamped to both rods to monitor the distance between them and command the actuator to restore the initial height, counteracting the composite shrinkage force (resolution: 0.1 μm). The systems longitudinal compliance (LC, in mm/N) was calculated according to the formula below :

LC = 2 × L 0 A × E adhesive + L 0 A × E rod
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Nov 25, 2017 | Posted by in Dental Materials | Comments Off on Influence of specimen dimensions and their derivatives ( C-factor and volume) on polymerization stress determined in a high compliance testing system
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