A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses



To evaluate the biaxial and short-beam uniaxial strength tests applied to resin composites based upon their Weibull parameters, fractographic features and stress distribution.


Disk- (15 mm × 1 mm) and beam-shaped specimens (10 mm × 2 mm × 1 mm) of three commercial composites (Concept/Vigodent, CA; Heliomolar/Ivoclar-Vivadent, HE; Z250/3M ESPE, FZ) were prepared. After 48 h dry storage at 37 °C, disks and beams were submitted to piston-on-three-balls (BI) and three-point bending (UNI) tests, respectively. Data were analyzed by Weibull statistics. Fractured surfaces were observed under stereomicroscope and scanning electron microscope. Maximum principal stress ( σ 1 ) distribution was determined by finite element analysis (FEA). Maximum σ 1-BI and σ 1-UNI were compared to FZ strengths calculated by applying the average failure loads to the analytical equations ( σ a-BI and σ a-UNI ).


For BI, characteristic strengths were: 169.9a (FZ), 122.4b (CA) and 104.8c (HE), and for UNI were: 160.3a (FZ), 98.2b (CA) and 91.6b (HE). Weibull moduli ( m ) were similar within the same test. CA and HE presented statistically higher m for BI. Surface pores (BI) and edge flaws (UNI) were the most frequent fracture origins. σ 1-BI was 14% lower than σ a-BI . σ 1-UNI was 43% higher than σ a-UNI .


Compared to the short-beam uniaxial test, the biaxial test detected more differences among composites and displayed less data scattering for two of the tested materials. Also, biaxial strength was closer to the material’s strength estimated by FEA.


Long-term clinical studies showed composite fracture as one of the primary reasons for restoration failure . Therefore, ideally, in vitro characterization of composite materials must include a testing method capable of accessing the composite strength. The International Organization for Standards (ISO) indicates the use of uniaxial three-point bending test with beam-shaped specimens measuring 25 mm × 2 mm × 2 mm (length × width × height) . Notwithstanding, specimen of smaller dimensions and other fracture strength tests, such as diametral tensile strength, compressive and biaxial flexural strength tests are also found in the literature .

Beam-shaped specimens often have edge flaws, which act as stress concentration sites and lead to undesirable edge failures, instead of having a fracture that originates from a material’s intrinsic flaw . Another drawback of the ISO specimen is that because of its length, multiple overlapping irradiations are necessary, which may lead to heterogeneous polymerization . In order to eliminate this problem, some researchers used smaller beam-shaped specimens, for example, 15 mm × 2 mm × 2 mm, 10 mm × 2 mm × 1 mm or 5 mm × 1 mm × 1 mm, with span distances varying from 3 to 6 mm .

However, the calculation of flexural strength using the standard analytical solution assumes that a ratio between the span distance ( l ) and the height ( h ) equals 10 . When l / h < 10, considerable shear stresses will develop in the specimen, which goes against one of the assumptions of the analytical solution, that is, specimen fracture occurs when maximum principal stress (maximum tensile stress, σ 1 ) reaches a critical value . Any modification in specimen’s dimensions is acceptable only if the stress state of the specimen does not compromise the premise that the calculated flexural strength ( σ a ) should express σ 1 . As the flexural strength equation considers the specimen as a linear elastic solid free of processing flaws, such premise can be verified by comparing σ a to σ 1 obtained by finite elements analysis (FEA).

Despite the specimen’s dimensions, the flexural bending test design may also influence the reliability of the measured data. In the uniaxial three-point bending test, particular concerns involve wedging stresses at the contact points and counter moments produced by friction at the loading-point-specimen interface . As an alternative to the uniaxial test, the biaxial flexural test has been used to determine the fracture strength of resin composites . The piston-on-three-ball disk test method described on ISO 6872, was originally developed in the 1960s to evaluate the strength of ceramic substrate materials . The original stress analysis and formulas were presented in and the results of a full interlaboratory comparison exercise with 14 participating laboratories (round robin) were presented . This method was adopted as ASTM standard F 394 in 1978 with 32 mm diameter specimens . The method was considered to be adequate for ceramic quality control purposes . In 1980, two papers appeared which summarized finite element analyses as well as strain gage experimental analysis that identified serious shortcomings in the original stress solutions . Errors of 10–40% were identified for the specific configurations that were investigated . They showed that stresses were not uniform under the piston and that, once a specimen deflected, loading was not uniform over the piston area but concentrated at the piston rim. The National Physical Laboratory in the United Kingdom organized a 10 laboratory comparison study in 1987 . Participants generally experienced no problems measuring the strength of a commercial alumina, but a bimodal strength distribution complicated the analysis of the results. The specimens and fixture sizes in ISO 6872 are smaller than in the earlier publications out of necessity for the needs of the dental materials community, but the fixture design and stress equations are identical. The maximum tensile stress occurs at the center of the surface opposite to load application and, consequently, edge flaws do not influence the results . When applied to composites, specimen dimensions allow photoactivation without overlapping curing . The comparison between composite uniaxial flexural strength following the ISO 4049 standards and biaxial tests showed higher values for the later . However, contradictory results were reported regarding the reliability of both tests.

Fractographic analysis is another important tool to understand the fracture mechanisms, allowing to identify whether the fracture was a result of design deficiency, material deficiency (fabrication process) or high stress-induced condition . The fracture strength of a material is influenced by variations in flaw population of the specimens. Weibull analysis offers an interesting statistical approach that takes that aspect into consideration, by correlating the probability of failure ( P f ) and failure stress ( σ ):

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Pf=1−exp−Vσ−σuσ0m’>Pf=1exp(V(σσuσ0)m)Pf=1−exp−Vσ−σuσ0m
P f = 1 − exp − V σ − σ u σ 0 m

where σ 0 (characteristic strength) and m (Weibull modulus) are material constants. V is the volume of the specimen under effective stress and σ u is the stress value corresponding to probability of failure close to zero . σ 0 is defined as the strength value, in MPa, in which the cumulative probability of specimen failure is 63.2%. The parameter m indicates the scattering of the data. The higher m value, the lower dispersion of the data .

The aim of this study was to compare the biaxial and the short-beam uniaxial flexural tests applied to three commercial composites using Weibull, fractographic and finite element analyses. The tested hypotheses were: (1) both tests provide the same material ranking, in terms of characteristic strength; (2) Weibull modulus of the composites is similar in both tests; (3) the ISO 4049 formula is not applicable for short-beam specimens. The third hypothesis was verified by comparing flexural strength values obtained experimentally with σ 1 obtained by FEA. Finally, fractured surfaces of the specimens were analyzed under stereomicroscope and scanning electron microscope (SEM).

Materials and methods

Specimen preparation

Three commercial resin composites (shade A3) tested are described in Table 1 . Thirty disk-shaped (15 mm in diameter; 1 mm in height) and 30 beam-shaped specimens (10 mm in length; 2 mm in width; 1 mm in height) of each composite were built for biaxial and uniaxial tests, respectively, by inserting the uncured composite in steel split moulds. In both cases, a Mylar strip was placed on the composite surface during photoactivation.

Table 1
Resin composites tested. a
Commercial brand Group Manufacturer Monomers Particle type Particle size (μm) Particle volume (%) Batch
Filtek™ Z250 FZ 3M ESPE, St. Paul, MN, USA Bis-GMA, UDMA, Bis-EMA Zirconia; silica 0.19–3.3 60 7JH
Concept Advanced (enamel) CA Vigodent, Rio de Janeiro, RJ, Brazil Bis-GMA, UDMA Barium and aluminum silicate 0.001–2 77.5 115/07
Heliomolar HE Ivoclar-Vivadent, Schaan, Liechtenstein Bis-GMA, UDMA Silicon dioxide; trifluoride of ytterbium; copolymers 0.04–0.2 46 F58116

a Manufacturers’ information.

The specimens were photoactivated using a quartz-tungsten-halogen light unit (VIP Junior, Bisco, Schaumburg, IL, USA) at 600 mW/cm 2 irradiance, checked by a radiometer (model 100, Demetron/Kerr, Danbury, CT, USA), during 2 min on each surface. The long exposure was necessary to compensate for the distance between the light tip and the composite surface (21 mm) defined in order to make sure that the entire specimen was included in the irradiated area. This distance was standardized with the use of a dark truncated-cone-shaped spacer (21 mm of height), with the small diameter (12.6 mm) attached to the light-cure tip and the large diameter (15.0 mm) covering the surface of the specimen. A total radiant exposure of 8 J/cm 2 was applied to the specimen. After photoactivation, the specimens were stored in dry at 37 °C for 48 h prior to the mechanical tests. Specimen’s dimensions were recorded with a digital caliper (model IP66, Mitutoyo Corp., Japan).

Biaxial flexural test

A piston-on-three-balls device was used for the biaxial flexural test, according to ISO 6872 standard ( Fig. 1 ). Three 2.5 mm diameter steel spheres were positioned 120° apart on a 10 mm diameter circumference. The specimen was positioned concentrically on the spheres and the load was applied at the center of the specimen using a flat piston with a 1.2 mm diameter. The device was positioned in a universal testing machine (model 5565, Instron Corp., Canton, MA, USA) and specimens were tested at a cross-head speed of 0.5 mm/min. Maximum tensile stress value ( σ BI ), in MPa, was calculated with the following formulas:

σ BI = − 0.2387 P X − Y h 2
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Nov 30, 2017 | Posted by in Dental Materials | Comments Off on A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses
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