2.1

Indentation Fracture (IF)

The IF method became very popular in the dental materials field due to its non-destructive nature and simplicity. This method involves making a Vickers hardness indentation on the polished surface of a ceramic material with sufficient load to generate radial cracks emanating from the indentation corners. By measuring the size of these cracks, defined as the distance between the center of the indentation and the end of the radial crack, it is possible to obtain an approximate measure of fracture toughness using one of several empirical and semi-empirical equations. These equations were based on previously collected fracture toughness data for different types of ceramic materials and correlate the crack size, elastic modulus and Vickers hardness of the material in order to give a fracture toughness value. Thus, for a given material, the greater the extent of the produced cracks, the lower the calculated toughness . It has been shown that when comparing K _Ic results obtained by the IF method with those obtained by other methods that use some sort of precrack, there is only about 30% agreement of results .

Making a Vickers indentation onto a brittle material results in the following sequence of events: 1) the indenter produces a plastic deformation; 2) after reaching the critical load, one or more defects in the plastic deformation zone become unstable and initiate the formation of radial cracks at the subsurface; 3) with the increase in the load, the crack propagates downwards; 4) when the load is removed, the crack closes underneath the surface and opens on the surface, where there is a residual stress field; 5) prior to removal of the Vickers indenter, radial cracks emanate from the plastic deformation zone; 6) continuous growth of radial cracks may lead to chipping of the material .

One reason for the popularity of the IF test may be that it is a relatively non-destructive method . Also, the methodology is considered simple, fast and needs very little amount of material for testing . Some researchers also take into consideration the fact that the cracks generated in this type of test are similar in size compared to those naturally occurring in ceramic prostheses .

K _Ic values measured by the IF test are considered less accurate than those obtained by means of macroscopic tests. According to Anstis et al. , one of the problems related to the IF method is the high coefficient of variation, which can reach values between 30% and 40%. However, smaller coefficients (between 10% and 25%) have been reported for dental ceramics . The spread in the fracture toughness data obtained by the IF test is related in part to the difficulties in making the appropriate measurement of the crack length. To facilitate the measurements, it is possible to sputter a layer of 20 nm of gold on the polished surface of the specimen before making the indentation .

Another problem that leads to variability in the IF data is the subcritical crack growth (“slow crack growth”, SCG) that may occur due to environmental humidity . Thus, it is recommended that crack measurements should be done immediately after indentation. SCG can be delayed when the indentation is made in oil instead of air . However, subcritical crack growth was observed even in oil for dental porcelains, which suggests a high susceptibility of moisture-assisted crack propagation for glassy dental ceramics . Residual stresses resulting from polishing can also accelerate crack growth, so annealing of specimens is recommended prior to the testing . However, it is important that high temperatures are avoided during annealing so as not to cause microstructural changes of the crystalline phase(s) in the material being tested .

Some indentations lead to chipping at the material surface and also sometimes to the growth of crack branches . In both cases, it is recommended that the measurement should be discarded and another indentation should be placed . Scherrer et al. reported that in their study, it was necessary to make 30 indentations in order to obtain 10 satisfactory ones. According to these authors, to obtain a satisfactory indentation in glassy dental ceramics, the load should vary between 1 and 2 kg, i.e. , loads lower than 1 kg are not sufficient to produce cracks that are at least twice as large as the diameter of the indentation and loads higher than 2 kg produce many branches and chips after the indentation is placed. Porosity at the material surface may also hinder crack size measurement.

Another difficulty related to the IF technique is the fact that there are many equations available for the calculation of K _Ic . The choice of equation depends on the type of crack produced and the relationship between the crack length (b) and half the diagonal of the Vickers indentation (a) (b/a ratio). When using these equations, one must consider that they were obtained empirically based on the behavior of crystalline ceramics; however, many dental ceramics exhibit a different microstructure with large amounts of a glassy phase.

2.2

Single Edge “V” notch beam (SEVNB)

The SEVNB method has been widely used for fracture toughness determination of ceramic materials due to its relative simplicity in comparison to the other tests that will be discussed later in this paper. The methodology involves the production of bar-shaped specimens that receive a narrow notch into one of the largest surfaces, perpendicular to the specimen long axis .

The notch is usually produced with the help of a diamond disc in a cutting machine. However, the tips of the notches made with diamond discs generally have width in the range of 100 μm. This dimension is considered too large and tends to overestimate the fracture toughness values. In addition, it has been shown that the notch root radius should be up to the same size of the major microstructural feature in order to validate the test, and therefore this test is not recommended for materials that do not allow for crack tip sharpening, such as yttria-stabilized zirconia pollycristal (Y-TZP). After a proper notch is achieved, the specimen is fast fractured in flexure with the notch placed on the tensile side. Fracture toughness is calculated based on fracture load and size/shape of the notch, which is measured on the fracture surface of the specimen.

One technique was introduced to sharpen the notch tip in ceramic specimens . This study suggested that a razor blade embedded in diamond paste should be placed within the notch, moving it back and forth to sharpen the crack. Scherrer et al. were able to use this technique to produce notches with tip radii ranging from 10 to 20 μm. The radius of the notch tip varies according to the microstructure of each material . Also, one must be aware that one of the limitations of the SEVNB is the chance of crack formation ahead of the notch during machining. The critical crack size measured in the test should take into account the size of these small defects, otherwise the K _Ic value is underestimated . Further studies evaluated the influence of the notch root radius on the fracture toughness of ceramic materials and found that the wider the notch tip, the higher was the measured fracture toughness.

A recent publication showed that the SEVNB test procedure can be modified toward the assessment of fracture toughness under clinically relevant shear loading. Placing an eccentric notch on a testing specimen, one could calculate K _IIc ( i.e. , fracture toughness in mode II/sliding), instead of the pure tensile information in mode I .

2.3

Single Edge Precracked Beam (SEPB)

The SEPB test is widely accepted among researchers for K _Ic determination of ceramic materials because it uses the traditional configuration of uniaxial flexural strength tests and provides results with good accuracy. The method is a variation of the SEVNB method and uses a particular procedure for creating a precrack in the specimen .

The test consists of introducing one or more centralized Vickers indentations onto the surface of a bar-shaped specimen. The indented specimen is taken to a specific precracking device in which a compressive load is applied until a “pop-in” sound is acoustically registered. Immediately after the sound is heard, the load is removed from the specimen. The specimen containing the precrack is fractured in a flexural strength test (3 or 4-point) with the indented surface facing the tensile side of the test setup. Fracture toughness is calculated using equations that take into account the dimensions of the specimen and the size of the precrack, which is measured at the fracture surface under a microscope. A detailed description of the method can be found in a standard .

One of the main features of the SEPB method is the way the precrack is introduced by means of a device in which the indented specimen is compressed and deflected after having the indented region positioned on its central groove. The tensile stresses generated in the indented region lead to the formation of precracks that stop growing when their lengths reach about half the thickness of the specimen. .

The load required to grow a precrack depends on the specimen geometry and the properties of the material used to build the device. The precrack growth rate can be adjusted by choosing grooves with different widths in the device . The loading rate to form a precrack is usually in the range of 100 N/s. When the ceramic material presents R-curve behavior, the K _Ic values measured by the SEPB test can be artificially high if the compression load is not removed immediately after detection of the “pop-in” phenomenon . One advantage of this test is that the precrack tip is significantly sharp, which is an important prerequisite for valid fracture toughness testing .

To facilitate measurement of the precrack after fracturing the specimen, it is possible to apply a dye to the precracked surface of the specimen , however it is necessary to make sure the dye is completely dried afterwards to avoid subcritical crack growth before and/or during loading . According to ASTM C 1421 (2016), the difference between the maximum and minimum sizes of the precrack in relation to the average value should be smaller than or equal to 10%. Also, the average size of the precrack should be between 0.35 and 0.6 times the specimen thickness. The minimum limit (0.35) was determined so that it is possible to ensure that residual stresses associated with indentation do not affect the crack front during the test . In cases where the precrack is too short or when it develops unevenly along the specimen, it is possible to correct it and make it longer by means of cyclic loading . It is important to note that it is difficult to assess the occurrence of slow crack growth on the fracture surface of SEPB specimens; therefore, it is possible to underestimate the size of the precrack, leading to an incorrect calculation of fracture toughness .

In the SEPB method, the precracked specimen may be fractured using either three- or four-point bending configuration, however, centralizing the precrack is much less critical in the latter configuration. According to previous studies, the loading rate does not affect the obtained K _Ic value . In addition, a previous work did not detect significant differences between fracture toughness values obtained with specimens of different lengths (46 and 23 mm), and same cross-sectional area (3 × 4 mm ² ).

According to the ASTM fracture toughness standard the stress–strain curves or load–displacement curves must be observed at the end of each test in order to determine if slow crack growth occurred. If humidity is causing subcritical crack growth, it is recommended that the test is performed in an inert atmosphere.

One of the main difficulties reported for the SEPB test is the generation of the precrack . The following difficulties were reported for this procedure: 1) controlling the depth of the precrack, 2) unwanted changes in the precrack path that often grows in different planes and 3) the frequent production of long precracks that results in the measurement of K _Ic values that are too high for materials that have R-curve behavior .

An international round robin involving 20 laboratories (“Versailles Advanced Materials and Standards—VAMAS”) evaluated the fracture toughness of different ceramic materials using the SEPB method. Although some of the participants reported very low success rates with respect to precracking the specimen, the study showed excellent repeatability (within laboratories) with a 4.5% coefficient of variation, and great reproducibility (between laboratories) with an 8.8% coefficient of variation .

2.4

Surface Crack in Flexure (SCF)

The SCF method is also known as the “controlled surface flaw” test . This method combines the use of a surface defect generated by a Knoop indentation with a conventional bending strength test carried out after removal of the residual stress area of the indentation . The amount of material to be removed is calculated based on the size of the indentation. The dimensions of the defect in the fracture surface are measured by means of a fractographic analysis . For K _Ic calculation, it is necessary to obtain the depth and width of the flaw, which may be semi-elliptical or semi-circular . Considering these crack shapes, the geometric factor Y is determined for the deepest point of the periphery of the precrack (Y _d ) and the most outward point (Y _s ) . These factors are calculated from equations proposed by Newman and Raju in 1981 and the highest Y value (Y _d or Y _s ) is used for K _Ic calculation using Eq. (1) introduced earlier.

Defects induced by indentations have been used since the 1970s to determine the fracture toughness of ceramic materials . In the decades that followed, these techniques were refined and became an alternative to methods such as the double torsion technique, which uses large specimens and long cracks produced with a diamond disk. Initially, Vickers indenters were more usual for the SCF test , but with time Knoop indentations became the preferred method because of the simpler crack patterns created by them .

Petrovic et al. observed that the residual stresses accompanying the indentation have a pronounced effect on the fracture toughness value obtained for the tested material. This residual stress adds up to the stress applied to the specimen, resulting in a lower fracture strength and consequently lower fracture toughness values. It was observed that the elimination of residual stresses by removing material or by annealing resulted in toughness values similar to those obtained with the double-torsion method. Removing the indentation is the preferred method for elimination of residual stresses, since annealing may cause crack closure and microstructural changes to the material .

One of the main advantages of the SCF test is that K _Ic is obtained using precracks with a very small size, which are measured at a microstructural level. In addition, the calculations are based on solid fracture mechanics solutions . The accuracy of measurements made with the test depends on how difficult it is to identify the defect limits on the fracture surface, which in turn depends on the microstructure of the material evaluated. The SCF method is more easily applied to materials that are not very porous and do not have a coarse microstructure . Defects in this context are also a microstructural inhomogeneity, and therefore the SCF method is especially useful for highly homogeneous materials. Another advantage of the test is that it provides fracture toughness values that are based on precracks with size and shape similar to natural defects present in dental prostheses.

The greatest difficulty related to the SCF test is to perform the fractographic analysis, in particular to determine accurately the location and size of the fracture origin . In fact, one study reported that the SCF test showed relatively high variability in the results due to the difficulty of measuring the precrack. In this study, for some cases, a variety of possible precrack sizes were used for K _Ic calculation in the same specimen. The authors also observed that the difficulty varied according to the analyzed material: a glass-ceramic with coarse particles presented the most difficulties in performing the fractographic analysis, as approximately half of the defects could not be measured, even with a persistent effort and a wide variety of fractographic techniques. Defects placed on the fracture surface of another glass-ceramic with finer microstructure were more easily measured, and the standard deviation obtained for this material was five times lower than that obtained for the material with coarse microstructure. It is important to note that small precrack measurement errors have little influence on the calculated toughness values due to the fact that this property is related to the square root of the precrack size. In fact, SCF data are more sensitive to the fracture load than to the size of the precrack .

In the SCF method, precracks are more easily detected when they: 1) are placed on a slightly different plane in relation to the fracture plane, usually an angulation of 0.5°, 2) display an arrest line 3) are stained or 4) show radial hackle lines that change direction when passing through the crack limit. Additional details on how to find and characterize the precrack can be found in the appendix of the ASTM standard C-1421 .

The fractographic analysis of a feldspathic porcelains is not simple because the fracture surfaces are rough and uneven, making it difficult to identify the fracture origins . For correct measurement of the precrack, it is necessary to use: 1) optical microscopy with low angle of light incidence, 2) observation of pairs of fractured specimens under scanning electron microscope, 3) photographs taken under scanning electron microscope with different magnifications, angles, contrast and also in the backscattering mode. There are rare occasions in which the fracture surface has a slightly different reflectivity in relation to the surrounding area because of differences in the fracture planes. One study reported that it is possible to detect darker or clearer halos around the precracks during fractographic analysis. The authors suggest that there are a number of possible explanations for the appearance of these halos around defects induced by Knoop indentations:

• a)

  Slow crack growth (SCG) due to the environment. SCG may occur before the removal of the residual stresses associated with the indentation or during the 15–30 s required to run the flexural strength test.

• b)

  Reorientation of the crack. If the precrack is not initially aligned according to applied stress field, realignment may occur during the fracture event. In the SCF method, the specimen is tilted 0.5° before being indented to increase the chances of retrospective precrack identification.

• c)

  SCG due to residual stresses resulting from indentation. Although the SCF method stipulates that the residual stress should be removed before the bending test, these stresses still affect the precrack for some time before removal, leading to some extent of stable growth.

The appearance of halos around the precrack results in a critical size that is higher than the initial crack size. For K _Ic calculation, the real critical size, as opposed to the initial one, should always be used.

Recently, a study adapted the SCF method to use plate-shaped and disk-shaped specimens tested in a biaxial flexure configuration (ball-on-three-balls) to measure the fracture toughness of silicon nitride specimens . Nevertheless, for precise measurements it is important to position the crack within ±120 μm of the maximum stress, to know the exact Poisson’s ratio and to test cracks that have the maximum stress intensity factor at their deepest point.

2.5

Chevron Notch Beam (CNB)

This test gained popularity because it requires a relatively small amount of material for specimen production . The test can be performed with different specimen configurations, namely “short bar” or “short rod” for tensile tests and bend bars for flexural configuration . The technique requires the insertion of a groove with a “V” shape named chevron notch, which is considered difficult to be obtained with cutting discs . The angle of the notch may vary between 30 and 50°. During the test, a crack will develop from the tip of the “chevron” notch and progress steadily as the load is increased up to the point when catastrophic fracture occurs . In summary, the crack front increases in width from zero to the full thickness of the specimen as the crack length increases in the notch plane .

This methodology started to be used with the objective of overcoming the difficulty of inserting precracks into ceramic specimens by means of fatigue. The method has the advantage of only requiring the fracture load value for K _Ic calculation, as there is no need to measure the size of the precrack . The technique is also considered very effective in situations in which the specimens need to be submitted to high temperatures or reactive environments. In such situations, the phenomenon of crack healing is not a concern since it does not affect the chevron notch .

In a previous study the authors compared the CNB test with the SEVNB test for borosilicate glass and found that both specimen geometries were equally suitable for the determination of fracture toughness in terms of average values and data variability. These authors claimed that the CNB technique was well suited for reproducible and accurate determination of fracture toughness in glasses.

Others have reported problems with respect to unstable crack growth in chevron notches applied to bend bars of soda-borosilicate glass , although most works have been successful in measuring fracture toughness for ceramics and composite materials using the CNB method . Slow loading rates and induction of crack formation in compression as a pre-cracking step have been shown to overcome the problem of having a percentage of the tests that do not yield a valid result .

A recent work determined the fracture toughness of four different yttria-stabilized zirconia ceramics, using the CNB method in four point bending. The objective of these authors was to assess the influence of slow crack growth on this type of test. The SEVNB test was also used for comparison purposes. It was concluded that the CNB method yielded well-reproducible results. However, slow crack growth significantly affected the measured fracture toughness values, especially when slow loading rates were used. To minimize the effect of slow crack growth, the application of high loading rates was recommended, as it reduces data scatter.