2.1

Strength

Strength is not an inherent property of a material. Therefore the recorded value is a function of the geometry and preparation of the specimen, as well as the testing method. Because force is applied in different ways to create internal stresses within a material, what is measured and recorded as strength, or resistance to catastrophic fracture, is dependent upon the conditions of the test. It may seem very logical to test the strength of a material under the typical loading conditions it will face in the oral cavity. To some extent this is useful, but it should be remembered that most external forces on a material will resolve themselves as stresses along various planes within the structure, often leading to tensile and shear stresses even when the specimen is placed under compression. This is especially true in the oral cavity where simple axial loading is almost never encountered due to the anatomy of teeth and the 3-dimensional nature of jaw mechanics. In addition, because the strength of the material is a function not only of its composition, but also of its quality of preparation, i.e. internal porosity, inclusions, surface flaws, etc., it is typically agreed that testing the material under its most challenging mechanical situation may be most instructive and lead to a reduced chance of accepting a material that ultimately fails prematurely due to inadequate strength under complex loading conditions. For this reason, testing of materials in tensile loading is typically considered most appropriate. Because tensile loading is also the most difficult to control experimentally, flexure is often the substituted mode, as it develops tensile, compressive and shear stresses during the test. In any case, one should keep this in mind when preparing specimens for testing to ensure that the material is sound and generally devoid of significant surface and internal flaws. The ISO standard 4049 for dental composites includes a flexure, or transverse, testing modality, and this will be described first. There is evidence from a systematic review on the correlation between flexural strength and clinical fractures of posterior resin composite restorations (31 different materials) that flexural strength correlates moderately with clinical wear but not with bulk fractures . Artificial aging by storing the specimens in ethanol or some other solvent prior to breaking them may enhance the correlation with clinical results .

2.1.1

Flexure

2.1.1.1

Transverse bending (ISO 4049 ; ASTM D790 -10 ; ISO 178-2010 )

This is a common test method for the strength of dental composites , and can be accomplished several ways based on the selection of loading supports and load applicators, and the geometry of the specimen, in addition to the method of preparing the specimen . Typically, testing is accomplished in 3-point bending ( Fig. 1 ), implying that the specimen is a beam of specific dimensions, supported on two rollers of a specified distance apart (span), and loading from a point source at the top-center of the beam. The test method for dental composites is specified in ISO 4049, and for other plastics in ASTM D790 -10. Briefly, the beam should be produced with an appropriate size for the testing supports in order to satisfy the criteria for beam mechanics (i.e. approximately 10% additional material beyond the supports on each end), and should be tested on a rigid test frame of very low compliance (i.e. any deformation of the test frame/jigs during the test can be disregarded and all load is being transferred directly to the specimen). It is emphasized not to stray from these criteria, or the outcomes may not be valid. Testing is usually accomplished to failure, and it is expected that there will be minimal plastic deformation of the specimen. Significant bending of the beam may invalidate the test, and if this occurs, one option is to calculate a yield strength, basically the point at which the load-deflection curve deviates from linearity, rather than reporting a failure load. The ideal test method includes a strain gauge or extensometer to measure the true deformation of the beam, but this is rarely done out of convenience. When the specimen is relatively rigid, and the test frame is very rigid, the true measurement of deformation during the test is less critical, and one can correlate cross-head motion to beam deflection within a reasonable error to measure the elastic modulus as well as the strength.

Schematic of the three point bend test with graphs of bending moment M, and deflection w.

Flexure strength can also be tested by loading in four-point bending ( Fig. 2 ), in which the load applicator is not a single point source, but consists of two points separated by a well prescribed distance. The benefit of the 4-point method is that it concentrates the stress over a wider area of the beam, and thus ensures that failure of the beam will occur within this region, a criterion for applying the beam equations accurately . In the 3-point method, it is possible for the beam to fail from a position not directly under the applied load, which may violate the mechanics and lead to potentially erroneous results. In general, evidence suggests that strengths may be higher when tested in 3-point vs. 4-point bending . Otherwise, the two tests are conducted in the same manner and can be performed on specimens of the same dimensions.

Schematic of the four point bend test with graphs of bending moment M, and deflection w.

2.1.1.2

Biaxial flexure (ASTM F394 -78 )

This is a method where a disk-shaped specimen is placed on top of a support, either a three legged support or on a ring that supports the entire circumference of the specimen, which provides a uniform distribution of tensile stress within the specimen emanating from the bottom surface ( Fig. 3 .). This method is typically used for brittle materials, and has only infrequently been used for dental composites. In part, this is because it is not difficult to conduct transverse flexure tests with composite. However, evidence suggests that the results from the biaxial test correlates with those from 3-point flexure tests and shows less variability in the data .

Schematic of the biaxial flexure test method, with loading and support ring (left) or with a three legged support (right).

2.1.2

Compression (ASTM D695 ; ISO 604 )

Compression testing is relatively simple in that an axial force is applied at a constant strain rate to a cylindrical specimen, setting up tensile and shear stresses within the material that cause failure ( Fig. 4 a). While it is logical that restorations should experience compressive forces, as stated previously, mostly these resolve as more complex stresses within the body of the material and failure is not due to actual compression of the material. Many materials, especially brittle ones, will appear stronger in compression than in tension, because the compression test is generally less sensitive to internal flaws compared to tensile testing. One point to consider is that frictional forces at the surface of the platens where they meet the flat ends of the cylindrical specimen can create complex stresses that violate the principles of the testing method if the specimen itself is not perfectly parallel. To overcome this problem, it is common to place a piece of thin paper over the ends of the specimens to help distribute the forces more uniformly and avoid stress concentrations that cause failure by edge chipping, as opposed to internal stresses. Because of the lack of correlation between compression testing and clinical failure , and because many lower strength composites undergo significant plastic deformation during such tests, leading to inaccurately high strength values, this test is not particularly recommended for composites, though it is frequently reported .

Schematic of the compression (a), tensile (b), and diametral tensile (c) method.

2.1.3

Tension (ASTM D638 -14 ; ISO 527-2 )

2.1.3.1

Uniaxial tensile testing

As stated previously, it is likely that most dental restoratives fail by tensile stresses set up within their structure due to complex loading of their complex geometries. This would suggest that tensile testing would be the most appropriate testing modality, and there are standards developed for other materials that can be followed. The typical shape of a specimen for tensile testing resembles a dumbbell, or dog-bone, which provides a center region (the gauge length) with a smaller diameter than the ends of the specimen, thus concentrating the stress in the middle and ensuring that failure will occur there ( Fig. 4 b). The difficulty with the test is that the specimen must be formed or shaped into the complex dumbbell, and this often leaves irregularities and stress concentrators from which failure occurs, thus nullifying the results of the test. The test therefore is fairly technique sensitive in that specimen alignment is also critical to ensure that loading is truly uniaxial. For these reasons, the tensile test is not very frequently used to measure the strength of dental composites, despite its applicability . However, the need to be vigilant in terms of the testing sequence should not deter researchers from using this test method.

2.1.3.2

Diametral tensile testing (ANSI/ADA Specification #27 )

Owing to the difficulties in conducting high quality uniaxial tensile tests for brittle materials, the diametral tensile test (otherwise known as the Brazilian test) was developed and has been used frequently for dental composites . This method is based on the breaking of a disk, or cylinder, resting on its side so that the upper and lower platens of the testing machine supply a force to a line axis across the entire length of the specimen ( Fig. 4 c). Again, specimen production is critical to ensure that the entire surface of the specimen is uniformly loaded, and for this reason, most studies with this method use a disk which has a shorter length dimension so less material must be in simultaneous contact with the loading and support platens. The diametral tensile test is only considered accurate when the specimen breaks uniformly down the middle, the principle being that as the disk is squeezed along its diameter, tensile stresses are established along its central diameter, pulling the material apart in a tensile manner. The failed specimen should be two halves of the disk or cylinder, and not a distribution of fractured pieces which would suggest a potentially invalid loading condition.

2.1.4

Impact (ASTM D256 -10 ; ISO 179-1-2010 )

Impact testing is different than a test of static strength in that in the latter, the load is applied to a specimen from the point of initial contact and continuing through to failure at a constant loading rate. In impact testing, a specimen, often a beam or plate, is subjected to a sudden, single contact load from an applicator that is swung into or dropped onto the specimen from a specified height (potential energy). The specimen is therefore either broken at a very rapid rate of force delivery, or supports the weight of the load, and impact strength is calculated as the absorbed energy per specimen cross section upon fracture. It is actually a measure of the ability of the material to absorb shock, and in fact may better reflect its toughness, i.e. ability to absorb energy. A common method is the Izod test method, in which a beam is supported on only one side, like a cantilever. In another popular method, the Charpy method, the beam is supported at both ends. Both methods may be used with a specimen with a precise notch to ensure failure at a specified position, and also to determine the notch sensitivity, or brittleness of a material. The test is not commonly used for dental composites .

2.1.5

Shear (ASTM D732 -10 )

The shear test is likely most suited to materials that are not brittle, but have ductile characteristics. Shear denotes a material’s ability to resist sliding type stresses, where the material is sliding against itself in the direction of its length, rather than across itself. However, a punch test exists for plastics and composites in which a punch tool is driven through a plate or sheet of material and the force is divided by the cross-sectional area to determine a shear punch strength. This method has been used with dental composites . Shear strength is not typically measured as a bulk property of a material, but rather is typically used to assess the adhesion between two different surfaces. A modification of a simple shear test has also been used to test the bond strength of one material to another by inserting or curing the second material within a hole in the first, and then “punching” out the circular specimen in the center by loading through a piston to determine the shear bond strength .

2.2

Fracture toughness

Fracture toughness differs from strength, in that it is an inherent property of a material, and therefore its value should be independent of testing modality or specimen geometry. Fracture toughness is a measure of a material’s resistance to the propagation of a crack from a preexisting flaw of known size and infinite sharpness, i.e. a pre-crack. Because most materials contain flaws, load application typically causes failure from such a flaw, and strength properties are reduced as compared with those measured from perfect surfaces. As the flaw characteristics are difficult to determine a priori in strength tests, the fracture toughness test requires a specimen be produced with a specified flaw from which failure will be generated through crack propagation. For dental composites, this flaw can be produced by being molded into the specimen during curing, or can be cut into the specimen after it has been cured. The ideal and most correct method for fracture toughness testing is to load a slightly notched specimen in fatigue to create a true infinitely sharp “pre-crack”. But this is often very difficult to do with brittle materials, especially those of the small size desired for testing dental composites, because the cracks are difficult to control once they are created and the specimen typically fractures during production. Therefore, alternative approaches for producing the crack initiating flaw, such as molding a very sharp notch with a razor blade or sharpening an existing notch with a sharp blade and an abrasive, have become common practice.

Because fracture is one of the primary failure modes for dental composites, this property is highly relevant for characterizing them. A systematic review has revealed a weak positive correlation (correlation coefficient rho = 0.34) between fracture toughness and clinical fractures of posterior resin composite restorations (31 different materials) . Others studies have shown correlations of fracture toughness and marginal breakdown and wear of composites

There are many ways to test this property, as described below ( Fig. 5 ). The choice is often made based on convenience. However, it is important to note that accurate and reliable testing is based on having proper equipment of very low compliance such that all deformation occurs in the specimen and is not lost to the testing jig or loading frame. This requirement is based on the fact that the equations for the calculation are based on the material being loaded in a state of linear elasticity. In fact, compliance is typically measured and then accounted for within the test to provide the most accurate result for fracture toughness, which is defined as the stress intensity factor, K. Because the test may be conducted in a number of ways, the stress intensity factor may denote a failure in plane strain (I), plane stress (II), or a combined mode. When the test is compliant with all of the requirements for minimal plastic deformation, i.e. brittle failure, the stress intensity is denoted as critical, designated by a “c”. Thus, the most common test for fracture toughness is completed by loading a specimen with a precisely measured pre-crack in tension and obtaining a load to failure to produce a value for K _Ic . Materials that have very high fracture toughness are typically not brittle, and rather fail in a ductile manner. The converse is true of brittle materials, and dental composites tend to fall into this latter category, typically having relatively low fracture toughness. However, composites do undergo some plastic deformation during testing, the extent being dependent upon the material’s characteristics, i.e. filler load predominantly, and this must be considered when testing in order to ensure that the reported value is truly accurate and valid. Sometimes a value for K will be reported, without the subscripts, because the validity of the test method cannot be confirmed. In such cases, it is possible to apply alternate analysis methods that account for significant amounts of plastic deformation, such as the J-integral method.

(a) Specimen geometry for the determination of fracture toughness by the single-edge notched method. (b) Specimen geometry for the determination of fracture toughness by the compact tension method. (c) Specimen geometry for the determination of fracture toughness by the double torsion method. (d) Specimen geometry for the determination of fracture toughness by the short rod method.

2.2.1

Single-edge notch—3-point bending (SENB) (ASTM D5045 -14 ; ISO/NP 13586 )

A common method for testing fracture toughness of dental composites is to load a sharply notched beam in 3-point bending, thus imposing a tensile force upon the notch (i.e. the pre-crack), causing fracture through the thickness of the specimen ( Fig. 5 a). The beam should have dimensions appropriate to the linear elastic fracture mechanics requirements, in which the length of the loading span is about 10× greater than the thickness of the specimen. The critical assumption in this test is that the tip of the notch is infinitely sharp, as a true pre-crack would be. For many materials, such as metals, specimens are cycled in tension to produce a crack of measureable length from the tip of the notch, thus creating a pre-crack. As previously discussed, this is difficult to impossible in brittle materials. It is possible to do with composites, but the specimen needs to be very large, and this is typically cost prohibitive. Thus other attempts have been made to create true pre-cracks of infinite sharpness, such as sawing sharp notches, sharpening the tip of notches with a very sharp blade or abrasive paste, or tapping a blade into the notch to propagate the crack. The literature is full of studies using these varied techniques, and likely the differences in the extent to which the methods truly comply with the requirements of the test method account for the sometimes highly varied outcomes reported.

2.2.2

Compact tension (ASTM D504 -14 ; ISO/NP 13586 )

The compact tension method ( Fig. 5 b) is similar to the 3-point bending method in that a tensile force is applied across a notch, but the specimen is typically in the form of a plate and the load is applied from holes in the top and bottom of the plate to produce tensile opening of the notch. This method typically requires the measurement of the opening of the crack using strain gauges or extensometers to accurately determine the distance the notch is opening for a given load. When precisely controlled, this test method can be used to provide more extensive data than the simpler beam bending method. It is possible to determine characteristics such as “R-curve behavior”, where the fracture toughness actually increases as the length of the crack increases. In other words, the material becomes tougher as the crack grows, and is more resistant to catastrophic fracture. This toughening occurs due to specific energy dissipating mechanisms that become active within the material during loading and cracking. The results from this method have been shown to correlate fairly well with those from the single-edge-notched beam .

2.2.3

Double torsion (ASTM C1421 -10 for ceramics )

The double torsion method ( Fig. 5 c) is described by placing a plate specimen containing a groove on its bottom surface within which the crack will propagate during the test . The plate is placed upon a set of parallel rods (rollers) running in its length direction, and load is applied near one end of the plate via two point surfaces placed on opposite sides of a precisely made notch to produce tension and crack propagation from the end of the notch. Once a critical load is reached, the crack will propagate down the groove and is visible and measureable on the top surface. The crack will stop when the critical stress is no longer present, thus allowing one to make several measurements on the same specimen by propagating the crack down the plate via multiple loadings and measurements of crack propagation vs. load. Another interesting aspect is that even if the notch is not infinitely sharp, the first load condition produces a fresh pre-crack, and each crack then serves as the pre-crack for the next test. For dental composites, these values have been shown to correlate fairly well with those obtained from the single-edge-notched beam and the compact tension methods .

2.2.4

Chevron notch (ASTM E1304 -97 )

The chevron notch method utilizes a cylindrical specimen that contains a chevron notch at one end, and the fracture is produced by loading the cylinder such that the notch is opened in tension ( Fig. 5 d). This method requires the notch to be either formed during curing or cut into the specimen after curing. The values from this method for dental composites have typically been shown to be higher than those obtained from the previously mentioned methods, though this may be due to the use of a testing setup of higher than acceptable compliance, allowing for extraneous deformation of the test system .

2.2.5

Indentation

A common, though controversial, method for measuring fracture toughness of ceramics is the indentation method, typically with a Vicker’s pyramid indenter . The object of the method is to create an indent on a highly polished surface, from which cracks will propagate from the tips of the indentation. This will only occur if the material displays brittle characteristics, as the cracks relieve the energy absorbed by the material from the indenter, the length being related to the toughness of the material, i.e. shorter lengths or less propagation for tougher materials. However, if the material deforms plastically to absorb the stress, crack propagation will not occur. Thus, this test method is typically not amenable to dental composites, which typically have sufficient plastic deformation and do not generate cracks during the indentation.

2.3

Edge strength—chipping

Dental materials, like resin composites, amalgam and porcelain, often suffer from chipping or fracture at the margins or at unsupported edges. This is a difficult characteristic to quantitate, but some have attempted to do this using an edge strength test where an indenter is applied near to the edge of a specimen, and the force required to cause a chip of material to be fractured off is quantitated . There is no standard test method, but some have used a piece of equipment made specifically for this purpose to make indents at specific distances from the edge of a specimen and measured force to cause fracture. There is essentially a linear relationship between force and distance from the edge, so the edge strength is chosen as the maximum force to create a chip at a distance of 0.5 mm.

2.4

Fatigue

Fatigue may be the most important property for dental materials that are exposed to periods of cyclic loading while chewing food. It is likely that failures occur over time due to the accumulation of damage produced by cyclic forces that do not exceed the fracture strength. Fatigue is a complex phenomenon, and many of the critical variables affecting fatigue of dental composites have recently been reviewed . It is likely that cracks propagate from existing flaws, not catastrophically to failure due to a single loading event, though this is of course possible, but due to extension of the crack and the formation of other localized damage until the material can no longer support the loading conditions. Fatigue is more likely to be initiated from sites subject to high stress concentrations, such as sharp edges, grooves, surface and internal flaws, and other imperfections. Fatigue testing is generally fairly labor intensive and expensive in that it requires a lot of time and material to completely characterize it. For this reason, it is not as common as measuring strength or toughness of dental composites.

2.4.1

Fatigue resistance/limit (ASTM D7791 -12 ; ASTM D7774 -12 )

The most common method for measuring fatigue is to take a material, typically in a dumbbell shape in order to concentrate stress at the smaller diameter region in the center of the specimen away from the grips holding the specimen, and cyclically load it in tension at a specified frequency that represents its usage condition. The test can also be accomplished with beams in bending. The test is begun with a high stress (S), near the tensile stress of the material, and proceeds until the material fails by fracture, recording the number of cycles required. A new specimen is then tested at a slightly lower stress and again tested until failure. This is continued, recording the number of cycles to failure (N), and a curve is plotted of stress vs. log of cycles to failure (S–N curve). At some level of stress, the specimen can be cycled for an infinite period of time, perhaps 10 million cycles or more, without failure. This stress is denoted as the fatigue resistance, endurance limit, or the fatigue strength. One can then design a material to function at stress values that never rise above this value to ensure that it does not fail under fatigue conditions. For example, in the dental situation, chewing is typically performed at a frequency of 1–2 Hz (cycles per second), or 60–120 chews per minute. To determine the fatigue resistance, which may occur at more than one million cycles, would require cyclic loading of a single specimen for one to two weeks. In addition, many additional specimens would need to be loaded for various periods of time to produce the entire S–N curve, thus likely requiring one month to complete one material. Some have investigated the fatigue resistance of dental composites by testing to a maximum number of cycles, such as 100,000 . While this may be the optimal way to describe fatigue behavior, the expense has caused the development of other methods that have been used for dental composites and other materials. The staircase method is an example.

2.4.2

Fatigue strength—staircase method

In the staircase method ( Fig. 6 ), a specimen, typically a beam, is tested in 3-point or 4-point bending beginning at some stress level approaching one-half of the fracture strength of the material as determined from a typical static test as described above . The specimen is cyclically loaded at an appropriate frequency, such as 1–2 Hz, for a pre-determined number of cycles, such as 5000–10,000. The choice of cycles is somewhat arbitrary, but should be enough to ensure that the specimen is subjected to enough cyclic stress to potentially generate internal damage. If the first specimen survives the number of applied cycles, a new second specimen is made and tested for the same number of cycles at a stress level that is raised by some amount, perhaps 5% higher. If the first specimen fails, the load level is reduced by the same amount for the second specimen. Testing proceeds in this way with about 20–30 specimens, raising and lowering the stress based on surviving or failing at the tested load in an effort to “focus in” on the fatigue strength of the material. This is calculated with an appropriate statistical method. Because loading is accomplished for a specific number of cycles, each specimen is tested for a maximum of an hour or so when 1–2 Hz is used. Thus, this test method is more economical than the fatigue resistance test, is easier to perform because a simple beam specimen can be used, and provides a value for fatigue strength, which for dental composites is typically about 55–65% of the static flexure strength .

Example of the stair-step method for two resin-based composite (RBC) formulations (σ _FFL = flexural fatigue limit).

2.1

Strength

Strength is not an inherent property of a material. Therefore the recorded value is a function of the geometry and preparation of the specimen, as well as the testing method. Because force is applied in different ways to create internal stresses within a material, what is measured and recorded as strength, or resistance to catastrophic fracture, is dependent upon the conditions of the test. It may seem very logical to test the strength of a material under the typical loading conditions it will face in the oral cavity. To some extent this is useful, but it should be remembered that most external forces on a material will resolve themselves as stresses along various planes within the structure, often leading to tensile and shear stresses even when the specimen is placed under compression. This is especially true in the oral cavity where simple axial loading is almost never encountered due to the anatomy of teeth and the 3-dimensional nature of jaw mechanics. In addition, because the strength of the material is a function not only of its composition, but also of its quality of preparation, i.e. internal porosity, inclusions, surface flaws, etc., it is typically agreed that testing the material under its most challenging mechanical situation may be most instructive and lead to a reduced chance of accepting a material that ultimately fails prematurely due to inadequate strength under complex loading conditions. For this reason, testing of materials in tensile loading is typically considered most appropriate. Because tensile loading is also the most difficult to control experimentally, flexure is often the substituted mode, as it develops tensile, compressive and shear stresses during the test. In any case, one should keep this in mind when preparing specimens for testing to ensure that the material is sound and generally devoid of significant surface and internal flaws. The ISO standard 4049 for dental composites includes a flexure, or transverse, testing modality, and this will be described first. There is evidence from a systematic review on the correlation between flexural strength and clinical fractures of posterior resin composite restorations (31 different materials) that flexural strength correlates moderately with clinical wear but not with bulk fractures . Artificial aging by storing the specimens in ethanol or some other solvent prior to breaking them may enhance the correlation with clinical results .

2.1.1

Flexure

2.1.1.1

Transverse bending (ISO 4049 ; ASTM D790 -10 ; ISO 178-2010 )

This is a common test method for the strength of dental composites , and can be accomplished several ways based on the selection of loading supports and load applicators, and the geometry of the specimen, in addition to the method of preparing the specimen . Typically, testing is accomplished in 3-point bending ( Fig. 1 ), implying that the specimen is a beam of specific dimensions, supported on two rollers of a specified distance apart (span), and loading from a point source at the top-center of the beam. The test method for dental composites is specified in ISO 4049, and for other plastics in ASTM D790 -10. Briefly, the beam should be produced with an appropriate size for the testing supports in order to satisfy the criteria for beam mechanics (i.e. approximately 10% additional material beyond the supports on each end), and should be tested on a rigid test frame of very low compliance (i.e. any deformation of the test frame/jigs during the test can be disregarded and all load is being transferred directly to the specimen). It is emphasized not to stray from these criteria, or the outcomes may not be valid. Testing is usually accomplished to failure, and it is expected that there will be minimal plastic deformation of the specimen. Significant bending of the beam may invalidate the test, and if this occurs, one option is to calculate a yield strength, basically the point at which the load-deflection curve deviates from linearity, rather than reporting a failure load. The ideal test method includes a strain gauge or extensometer to measure the true deformation of the beam, but this is rarely done out of convenience. When the specimen is relatively rigid, and the test frame is very rigid, the true measurement of deformation during the test is less critical, and one can correlate cross-head motion to beam deflection within a reasonable error to measure the elastic modulus as well as the strength.

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