Subcritical crack growth and in vitro lifetime prediction of resin composites with different filler distributions



Verify the influence of different filler distributions on the subcritical crack growth (SCG) susceptibility, Weibull parameters ( m and σ 0 ) and longevity estimated by the strength–probability–time (SPT) diagram of experimental resin composites.


Four composites were prepared, each one containing 59 vol% of glass powder with different filler sizes ( d 50 = 0.5; 0.9; 1.2 and 1.9 μm) and distributions. Granulometric analyses of glass powders were done by a laser diffraction particle size analyzer (Sald-7001, Shimadzu, USA). SCG parameters ( n and σ f0 ) were determined by dynamic fatigue (10 −2 to 10 2 MPa/s) using a biaxial flexural device (12 × 1.2 mm; n = 10). Twenty extra specimens of each composite were tested at 10 0 MPa/s to determine m and σ 0 . Specimens were stored in water at 37 °C for 24 h. Fracture surfaces were analyzed under SEM.


In general, the composites with broader filler distribution (C0.5 and C1.9) presented better results in terms of SCG susceptibility and longevity. C0.5 and C1.9 presented higher n values (respectively, 31.2 ± 6.2 a and 34.7 ± 7.4 a ). C1.2 (166.42 ± 0.01 a ) showed the highest and C0.5 (158.40 ± 0.02 d ) the lowest σ f0 value (in MPa). Weibull parameters did not vary significantly ( m : 6.6 to 10.6 and σ 0 :170.6 to 176.4 MPa). Predicted reductions in failure stress ( P f = 5%) for a lifetime of 10 years were approximately 45% for C0.5 and C1.9 and 65% for C0.9 and C1.2. Crack propagation occurred through the polymeric matrix around the fillers and all the fracture surfaces showed brittle fracture features.


Composites with broader granulometric distribution showed higher resistance to SCG and, consequently, higher longevity in vitro.


Bulk fracture is one of the main causes of resin composite restoration failure in the clinic . Resin composites are frequently evaluated in relation to their mechanical strength, which can be related to static loads that cause fracture of the restoration. However, such tests do not provide much information about failure mechanisms that occur during clinical use, which are related to the complex fatigue scenario found in the oral cavity, i.e., low cyclic loads and high humidity. In addition to strength tests, the association of other methods, such as fatigue tests, methods for determining subcritical crack growth (SCG) parameters, fractographic and Weibull analyses are necessary to understand the causes of failure .

Based on results of different mechanical tests and qualitative analyses, it seems that in the oral environment, repeated mechanical loads even at physiological levels can contribute to decrease the longevity of composite restorations due to the subcritical growth of flaws present in the material which eventually result in catastrophic failure . The growth of a crack in a material depends on the material’s behavior (plastic or elastic), temperature, strain rate and the stress state at the crack tip. The principles of the Linear-Elastic Fracture Mechanics (LEFM) are used to understand fracture events that occur without being preceded by extensive plastic deformation. The type of deformation observed during fracture is directly related to the material’s properties and geometric factors, such as specimen thickness .

Plastic deformation occurs in brittle and ductile fractures. However, in brittle materials the crack needs minimal plastic deformation to propagate, while in ductile fracture this deformation is necessarily greater. Although the polymeric matrix of resin composites presents viscoelastic properties, fractographic analyses revealed features of brittle failure such as SCG . This finding makes possible the application of the LEFM principles to study the failure mechanisms of resin composites.

The strength of many brittle materials is environment- and time-dependent, i.e., it decreases due to SCG in the presence of a reactive medium, such as water, and increases with the stress rate. This time-dependent strength is exponentially related to the material’s susceptibility to SCG . The susceptibility of a material to SCG, expressed by the stress corrosion coefficient ( n ), and the material’s resistance in the initial stages of mechanical loading ( σ f0 ) can be determined by direct and indirect in vitro methods .

Direct methods are very complex, use large specimens and simulate large flaws, which do not correspond to the small flaws usually found in dental restorations . For those reasons, indirect methods, as the dynamic fatigue test, are often used to obtain the SCG parameters based on mathematical relationships among fracture resistance values obtained at different stress rates . High values of n (>100) indicate a significant resistance against SCG and low values (5–30) indicate a high susceptibility to this phenomenon . In the scientific literature, it is possible to find n values ranging from 7 to 34 for resin composites, 15–28 for feldspathic porcelains and glass-ceramics and 60–95 for high-density alumina .

Weibull analysis associates the failure probability ( P f ) of a material with the corresponding stress values ( σ f ), resulting in an approach that takes into account the population of defects in a specimen . The association between Weibull statistics and the results of a time-dependent analysis, as the dynamic fatigue, allows the estimation of a material’s failure probability over its lifetime of for a given stress level . This information is displayed in a strength–probability–time (SPT) diagram . Such diagram is commonly used for dental ceramics to predict the maximum stress at which the material should survive for both a given time span and percentage probability of failure . For resin composites, however, this analytical tool has not been explored in depth. SPT diagrams of commercial resin composites were previously constructed based on the compressive strengths obtained at crosshead speeds of 1, 5 and 10 mm min −1 and showed that for a lifetime of 10 2 s, with a failure probability of 38%, the working stress should not exceed 150 MPa, whereas for a lifetime of 10 3 s, with the same probability of failure, the applied stress should not exceed 100 MPa .

The mechanical behavior of resin composites is determined by the degree of conversion of the polymeric matrix, the inorganic fraction characteristics and the bonding between the fillers and the matrix . In general, the fracture strength of composites increases with higher inorganic content . Studies with experimental composites showed an inverse relationship between fracture strength and mean particle size. However, they did not explore the possible mechanisms responsible for that . Besides, long term analyses as the SPT diagram using a clinically relevant failure probability of 5% are important to gather information about the lifetime of these materials . The present study sought to verify the influence of different filler sizes and distributions of experimental resin composites in the SCG ( n and σ f0 ) and Weibull ( m and σ 0 ) parameters and the longevity estimated by the SPT diagram. Such information could contribute to the understanding of the underlying mechanisms leading to bulk fractures found in clinical practice, as well as to the development of resin composite improved formulations. The null hypothesis was that there is no relationship between the filler size and/or distribution and the evaluated properties and parameters.

Materials and methods

Composite characterization

Four experimental resin composites were prepared ( Table 1 ). All composites presented 22 wt% (41 vol%) of organic matrix and 78 wt% (59 vol%) of inorganic content. The inorganic fraction was constituted by 67 wt% (49 vol%) of glass particles and 11 wt% (10 vol%) of pyrogenic silica (Aerosil OX-50, Degussa Corporation, New Jersey, USA). All fillers were equally silanized using a solution containing hydrolyzed gamma-methacrylyloxypropyltrimethoxysilane (gamma-MPS, Dynasylan Memo, Degussa Corporation) by FGM Produtos Odontológicos (Joinville, SC, Brazil). Thermogravimetric analyses (TGA) showed that the content of gamma-MPS was 5.6% (w/w) for all the fillers. The organic matrix was the same for all composites, containing 59 wt% of BisGMA (bisphenol A glycidyl dimethacrylate, Degussa Corporation), 39 wt% of TEGDMA (triethyleneglycol dimethacrylate, Degussa Corporation), 0.5 wt% of camphorquinone (Sigma Aldrich, St. Louis, USA), 1.0 wt% of the co-initiator ethyl N,N-dimetil-4-aminobenzoate (EDMAB, Sigma Aldrich,) and 0.1 wt% of the inhibitor butyl-hydroxytoluene (BHT, Sigma Aldrich).

Table 1
Glass filler compositions used in the formulation of the experimental resin composites.
Experimental group a Density (g/cm 3 ) b Composition Manufacturer Batch
C0.5 2.80 SiO 2 (55 wt%)
BaO (25 wt%)
B 2 O 3 (10 wt%)
Al 2 O 3 (10 wt%)
Schott Electronic Packaging, Southbridge, MA, USA. GM27884
C0.9 2.80 SiO 2 (55 wt%)
BaO (25 wt%)
B 2 O 3 (10 wt%)
Al 2 O 3 (10 wt%)
Schott Electronic Packaging, Southbridge, MA, USA. GM27884
C1.2 3.03 SiO 2 (50–60 wt%)
BaO (25–35 wt%)
Others components not informed.
Ferro Corporate Headquarters, Cleveland, OH, USA. EGO 2810 SRRG
C1.9 2.89 SiO 2 (50–60 wt%)
BaO (25–35 wt%)
Others components not informed.
Specialty Glass Products, Willow Grove, PA, USA. SP345

a Group coding defined based on glass filler d 50 .

b The density values and compositions were informed by the respective manufacturers.

Each composite was labeled based on the d 50 value of its inorganic phase, which indicates that 50% of the fillers are smaller than this value. One sample of each particle type was mixed with distilled water and dispersed by sonication. After that, the granulometric distribution of the glass powders was determined by a laser diffraction particle size analyzer (Sald-7001, Shimadzu Scientific Instruments, Columbia, USA). This reading was repeated three times always after increasing sonication periods to guarantee minimal particle agglomeration and to confirm the former analyses. Besides the granulometric distribution curves, the analysis determined the d 25 , d 50 , d 90 values, the minimum and maximum size of each glass powders.

The specific surface areas of the silanized glass fillers were obtained by a surface area analyzer (model NOVAe 1200, Quantachrome Instruments, Boynton Beach, USA) under nitrogen atmosphere. The operation of this equipment is based on the theory of Brunauer, Emmett and Teller (B.E.T.), which estimates the specific surface area of the filler by the product of the number of gas molecules needed to cover the particle surface and the cross-sectional area of these molecules.

The degree of conversion (DC, n = 5) of the experimental composites was obtained by Fourier transform near-infrared spectroscopy (FTIR, Vertex 70, Bruker Optik GmbH, Germany). The uncured composite was placed in a silicone rubber mold (0.8 mm thick and r = 3.5 mm), sandwiched between two glass slides and the initial spectrum was obtained (4 scans, 6 cm −1 resolution). Subsequently, the specimen was photoactivated through the glass for 15 s on each surface using a LED unit delivering 1200 mW/cm 2 (Radii-cal, SDI, Bayswater, Australia). After 24 h dry storage at 37 °C, the spectrum for the polymerized specimen was obtained. The areas under the first overtone absorption band of the vinyl bond at 6165 cm −1 of the initial and the 24 h spectra were calculated by the software Opus v.6 (Bruker Optics). Then, the DC of each specimen was calculated using the followed equation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='DC=100×1−apolymerizedanon-polymerized’>DC=100×(1apolymerizedanon-polymerized)DC=100×1−apolymerizedanon-polymerized
DC = 100 × 1 − a polymerized a non-polymerized

DC data was submitted to one-way ANOVA and Tukey tests at a global significance level of 5% ( α = 0.05).

Dynamic fatigue test

Seventy disk-shaped specimens (12 mm in diameter; 1.2 mm in thickness) of each experimental composite were built by inserting the uncured composite in a stainless steel split mold. The top surface was covered with a Mylar strip during photoactivation. Both top and bottom surfaces of the disk were photoactivated for 40 s, 10 s in each quadrant (Radii-cal, SDI), at 1200 mW/cm 2 . After photoactivation, the edges were finished using 600 grit sandpaper and the specimens were stored in distilled water at 37 °C for 24 h. Specimens’ dimensions were recorded with a digital caliper (model IP66, Mitutoyo Corp., Japan).

According to the findings of a previous study, in order to detect more differences among the composites, display less data scattering and obtain strength values closer to the strength estimated by finite element analysis, a piston-on-three-balls device was used for the dynamic fatigue test . Three 2.5 mm diameter steel spheres were positioned 120° apart on a 10 mm diameter circumference ( Fig. 1 ). The specimen was positioned concentrically on the spheres and the load was applied at the center of the specimen using a flat piston with 1.2 mm in diameter. The device was placed inside a glass container with distilled water at 37 °C positioned under the actuator of a universal testing machine (model 5565, Instron Corp., Canton, MA, USA).

Fig. 1
Diagram of the “piston-on-three-ball” biaxial flexural test, where P is the applied load. (A) Side view; (B) upper view.

The tests were conducted at five different stress rates: 10 −2 , 10 −1 , 10 0 , 10 1 and 10 2 MPa/s. Ten specimens were tested at each stress rate, except for 10° MPa/s, in which thirty specimens were tested in order to obtain enough sample size to be analyzed using Weibull statistics. In order to reduce testing time for the lowest stress rate (10 −2 MPa/s), a pre-load equivalent of 40% of the estimated fracture load was used. The fracture load was estimated based on a regression analysis using the fracture loads of the other stress rates .

The biaxial flexural strength ( σ f ), in MPa, was calculated with the following equations :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='σf=−0.2387P(X−Y)b2′>σf=0.2387P(XY)b2σf=−0.2387P(X−Y)b2
σ f = − 0.2387 P ( X − Y ) b 2
<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='X=(1+υ)lnr2r32+1−υ2r2r32′>X=(1+υ)ln(r2r3)2+(1υ2)(r2r3)2X=(1+υ)lnr2r32+1−υ2r2r32
X = ( 1 + υ ) ln r 2 r 3 2 + 1 − υ 2 r 2 r 3 2
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Nov 28, 2017 | Posted by in Dental Materials | Comments Off on Subcritical crack growth and in vitro lifetime prediction of resin composites with different filler distributions
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