4.1. Influence of Microstructure Type
In nanocomposite ceramic tool materials, nanoparticle size is under nanoscale and matrix grain size is under microscale or sub-microscale. Therefore, nanoparticles distribute in matrix grains as well as along GBs. According to the distribution of nanoparticles in matrix phases, nanocomposite ceramic tool materials can be divided into three microstructure types, which are intragranular, intergranular and intragranular/intergranular structures. In order to explore the influences of nanoparticle distribution on mechanical properties, models of the intergranular, intragranular and intragranular/intergranular microstructures for Al
2O
3/SiC
n have been established, as shown in
Figure 5. The average size of Al
2O
3 matrix grains is
, while the average size of nano SiC is
= 70 nm and the volume content of nano SiC is
= 10%.
The cracking paths of microstructure models are shown in
Figure 6. It can be observed that transgranular cracking is predominant in the intergranular structure (
Figure 6a), and the crack is deflected continuously into Al
2O
3 grains by SiC nanoparticles located along matrix GBs. For the intragranular structure (
Figure 6b), only intergranular cracking happens. The transgranular fracture in the intragranular/intergranular structure is less remarkable than that in the intergranular structure (
Figure 6c). As for Al
2O
3/SiC
n nanocomposite ceramic tool materials, SiC nanoparticles and Al
2O
3 matrix grains usually bond tightly together and no glass phases exist. Many researchers have observed this phenomenon by means of high resolution TEM.
Figure 7 displays the interface between the Al
2O
3 matrix and the SiC nanoparticle in Al
2O
3/SiC
n [
20]. In addition, S. Jiao [
21] concluded that the fracture surface energy of interfaces between Al
2O
3 and SiC in Al
2O
3/SiC
n is higher than that of Al
2O
3 grains at home temperature, according to experimental results and empirical formulae. The high-strength interfaces between nanoparticles and matrix grains have a pinning effect on the intergranular crack. At matrix GBs without nano SiC particles, the intergranular cracking is predominant. When the intergranular crack encounters nano SiC located along GBs, it is liable to be deflected into Al
2O
3 matrix grains, and transgranular cracking occurs. As the crack travels along GBs without nanoparticle distribution, the intergranular cracking continues until it is deflected into matrix grains again by another nanoparticle located at GBs.
Figure 8 shows the SEM morphologies of Al
2O
3-based nanocomposite ceramic tool materials, in which typical cleavage steps caused by transgranular fractures are clearly observed, and nanoparticles located at GBs are indicated by red arrows [
22]. In the case of the intragranular structure (
Figure 6b), the intergranular cracking will not be hindered by nanoparticles located in matrix grains. Therefore, the transgranular fracture hardly arises.
Based on the energy equilibrium theory of cracking systems [
23], as a crack propagates for the length of
c, the critical fracture energy release rate
GC can be expressed as:
where
is the fracture energy dissipated during facture, which can be obtained through simulation.
The critical fracture energy release rate
GC is usually regarded as a quantitative description of the fracture resistance of materials. The relationship between fracture toughness
and the critical fracture energy release rate
is given by:
Figure 11 shows the calculation results of
GC during the fracture process. The
GC of the intergranular structure is higher than that of the intragranular/intergranular structure, and the intragranular structure exhibits the lowest level of
GC. Since the fracture surface energy of matrix grains is above that of matrix GBs (shown in
Table 1), the transgranular fracture will consume more energy than the intergranular fracture during the cracking process. Therefore, if taking no consideration of residual stress and merely analyzing the effect of interface bonding strength, nanoparticles located along GBs dominate in the fracture mode transformation from intergranular to transgranular cracking, and in the improvement of fracture toughness for nanocomposite ceramic tool materials.
4.2. Influence of Nanoparticle Size
Figure 9 shows two intergranular microstructure models with different nanoparticle sizes (
in
Figure 9a and
in
Figure 9b). The two models have the same matrix morphologies, with the average matrix grain size
and the volume content of nanoparticles
= 10%.
The cracking paths of the two microstructure models after FEM calculation are shown in
Figure 10. For the single phase ceramic tool materials, the main fracture mode is basically intergranular cracking due to weak grain boundaries, while transgranular cracking is more liable to occur in metals with strong grain boundaries [
24,
25,
26]. Compared with the intergranular cracking in single phase ceramic tool materials, the fracture mode of nanocomposite ceramic tool materials has changed to the mixed mode of intergranular and transgranular cracking. And the transgranular cracking is more obvious in the microstructure with smaller nanoparticles (
). Nanoparticles located along GBs represent strong obstacles to crack propagation due to their higher mechanical properties. The intergranular crack tends to be deflected into matrix phases when meeting nanoparticles at GBs.
The results of
GC for the intragranular, intergranular and intragranular/intergranular microstructures with two different sizes of nanoparticles (150 nm and 70 nm) are summarized in
Figure 11. It can be found that microstructure models with smaller nanoparticles generally exhibit higher levels of
GC, and the characteristics of
GC resulting from different nanoparticle sizes are most remarkable in the intergranular microstructure. As for nanocomposite with the same content of nanoparticles, the toughening effect of microstructures with smaller nanoparticles is improved. That is because microstructures with smaller nanoparticles have nanoparticles that are more widely dispersed along GBs, which results in more significant effects on crack pinning and deflection into matrix grains. Crack deflection will absorb extra fracture energy, and the transgranular cracking consumes more energy compared with the intergranular cracking during the fracture process.
In addition, based on the grain growth theory, nanoparticles located along matrix GBs have a pinning influence on the migration of matrix GBs. The relationship between average matrix grain size and nanoparticle size is given as follows [
27]:
where
is the average matrix grain size,
is the nanoparticle size and
is the volume content of nanoparticles.
Smaller nanoparticles have a stronger pinning effect on matrix GB migration during the sintering procedure, which will lead to a refinement of matrix grains in microstructures. Cheng [
28] observed this phenomenon by fabricating nanocomposite ceramic tool materials with different sizes of nanoparticles at the same volume content. It is known that grain refinement contributes to improving the fracture strength of materials, since the length of inherent cracks in ceramic materials is commonly the same as the maximum grain size, and materials containing shorter inherent cracks exhibit higher fracture strength based on the Griffith fracture theory [
3,
29]. From the above, conclusions can be drawn that smaller nanoparticles are useful for the enhancement of the fracture strength and toughness of nanocomposite ceramic tool materials.
4.3. Influence of Nanoparticle Volume Content
Figure 12 shows microstructure models for nanocomposite with
Vnano = 3%, 5%, 10%, 15%, 20% and 30%, respectively. The microstructures have the same matrix morphology, with
and
.
The cracking paths for the microstructures are shown in
Figure 13. When the volume content of nanoparticles (
Vnano) is lower (3%~10%), the intergranular cracking dominates. The microstructure with 15 vol% nanoparticles exhibits obvious transgranular cracking. As
Vnano arrives at 20%, nanoparticle agglomeration does not arise and the transgranular cracking appears at some sites of the crack path, although
Vnano is at a higher level and the distances among nanoparticles are relatively small. Some nanoparticles agglomerate together when
Vnano reaches 30%. The main crack propagates from some region with weaker properties at the bottom of the microstructure model, rather than from the initial crack. The transgranular cracking still exists at some sites of the crack path, but is at a relatively lower level.
The results of
GC are plotted in
Figure 14. As depicted in
Figure 14,
GC firstly shows an increase, and then a decrease trend as the nanoparticle content increases.
GC reaches the peak at
Vnano = 15%, which indicates that the fracture resistance is at its highest. Many researchers carried out theoretical and experimental investigations on the effect of the volume content of nano SiC on the fracture toughness. Niihara et al. [
30] found that the fracture toughness of Al
2O
3/SiC
n reached the maximum with 5 vol% SiC through experiments, as depicted in
Figure 15. Levin et al. [
31] investigated the relationship between the fracture toughness of Al
2O
3/SiC
n and the SiC volume content, and obtained similar results to Niihara. Conclusions can be drawn from the modeling results in this paper that the microstructure with 15 vol% SiC has the maximum fracture toughness, which is obviously higher than the results published by other researchers. The primary reason for this difference is that the residual stress caused by the thermal expansion mismatch between nano SiC and matrix Al
2O
3 is not taken into account in our model. As the nanoparticle content is at a relatively higher level, there are more nanoparticles in the matrix grains, and the area of residual tensile stress (the thermal expansion coefficient of the Al
2O
3 matrix is higher than that of the SiC nanoparticle) increases as well. Cracking happens easily under the residual tensile stress. That is why the predicted nano SiC content with the maximum fracture toughness is higher in this work compared with other researchers’ results.
The dispersion of nanoparticles in this work is well controlled by programming. For instance, nanoparticles’ dispersion remains excellent in the microstructure as nano SiC content is 20 vol% (
Figure 13e), while the agglomeration usually occurs as the nano SiC content arrives at 10% and higher in sintering experiments. Compared with the sintering experiments, more excellent nanoparticle dispersion in our work may be another reason why the predicted nanoparticle volume content with optimum toughening effect is relatively higher. Under the condition of excellent nanoparticle dispersion, fracture toughness increases as the nanoparticle content rises. All of the above analysis leads up to the conclusion that excellent dispersion procedures contribute to improving the fracture toughness of materials.
4.4. Influence of Interface Fracture Energy
In nanocomposite ceramic tool materials, there exist not only GBs among matrix grains, but also interfaces between nanoparticles and matrix grains. Interface bonding strength, matrix GB strength and matrix grain strength will affect the macroscopic strength and fracture toughness of materials through their effects on cracking paths. Interface bonding strength between matrix grains and nanoparticles can vary from different processing methods and conditions, and many investigations have shown that it has a significant effect on the fracture mode. Due to the small grain size and complicated microstructure morphologies, it is very difficult to measure the interface bonding strength by means of experiments. In this section, the influence of the interface bonding strength between nanoparticles and matrix grains on cracking paths and fracture toughness will be discussed.
In actual ceramic tool materials, the strength of nanoparticles is usually higher than that of matrix grains in order to obtain a good toughening effect. Therefore, only the influence of the fracture energy proportions among the interface, matrix grain and matrix GB on the fracture mode is taken into account in this work. Three levels of the proportions of the fracture energy of the interface
, the matrix grain
and the matrix GB
(
,
and
) are considered. These values indicate strong, intermediate and weak interfaces, respectively.
Figure 16 represents three different microstructure models, which are the intergranular, intragranular/intergranular and intragranular structures. The average size of the matrix grain and the average nanoparticle size are
and 150 nm, respectively. The volume content of nanoparticles is equal to 10%.
Figure 17 shows the cracking paths of all microstructures with different fracture energy proportions. It can be seen from
Figure 17(a1) that transgranular cracking occurs in the intergranular microstructures with strong interfaces (
). Since the interface fracture energy is higher than that of the matrix grain, the intergranular crack is liable to extend into the matrix when encountering nanoparticles located at GBs. Comparing
Figure 17(a1) with
Figure 18 (
), it can be concluded that the higher the interface bonding strength, the stronger the pinning and deflecting effect of nanoparticles at GBs on the intergranular crack, and the more remarkable the transgranular fracture phenomenon. In
Figure 17(b1), where the interfaces are stronger than GBs but weaker than matrix grains (
), the intergranular crack tends to surround nanoparticles as it encounters those located at GBs, and continue travelling along GBs when meeting matrix GBs. Similar fracture patterns appear in the intergranular microstructures with weaker interfaces (as shown in
Figure 17(c1) with
).
As for the intragranular/intergranular microstructures, transgranular cracking still exists in the model with strong interfaces (
Figure 17(a2)). Due to relatively fewer nanoparticles located at GBs in the intragranular/intergranular microstructure, the transgranular fracture phenomenon is less pronounced compared with that in the intergranular microstructure with the same material parameters. In microstructures with intermediate
and
(
Figure 17(b2,c2)), where the interfaces are weaker than matrix grains, cracks are liable to propagate around nanoparticles lying at GBs if they encounter them. And the intergranular fracture continues once the crack meets the matrix GB.
In the case of the intragranular microstructures, the intergranular cracking is predominant for the three fracture energy proportions (
Figure 17(a3–c3)), which indicates that nanoparticles distributed in matrix grains have little pinning and deflecting effect on the intergranular crack.
Figure 19 shows the results of
GC for microstructures with different interface strengths. It can be found that for the same microstructure type, materials with strong interfaces (
) exhibit the highest level of
GC, as well as the highest fracture toughness. This is in good agreement with the simulation results, that the most remarkable transgranular fracture can be observed in microstructures with
. In models with weak interfaces (
), although a few transgranular cracks arise,
GC is the lowest due to the low interface fracture energy. From the above, strong interfaces (
) seem to have a positive effect on the fracture toughness of materials, while weak interfaces (
) may be disadvantageous for material toughening. The results of
GC are in accordance with the results of cracking paths presented in
Figure 17. The results of
GC in the intergranular models are relatively higher than other microstructures with the same interface bonding strength. Compared with other microstructure types,
GC in intragranular microstructures is at the lowest level no matter how strong the interface bonding effect is, since nanoparticles in this matrix have negligible impact on the transition of the intergranular cracking to the mixed mode of intergranular and transgranular cracking. Actually, nanocomposite ceramic materials prepared using the sintering method primarily possess the intragranular/intergranular microstructure. Thus, in actual nanocomposite ceramic tool materials, strong interfaces have a significant effect on the fracture mode transition to the mixed mode of intergranular and transgranular cracking, which is advantageous for the enhancement of fracture toughness of materials.
Yu [
32] modeled the cracking extension in Al
2O
3/TiB
2 composite ceramic tool materials and investigated the relation between Al
2O
3/TiB
2 interface bonding strength and cracking behavior. He found that high interface bonding strength (higher than that of matrix grains) would result in the transition of the fracture mode from purely intergranular cracking to a mix of intergranular and transgranular cracking, as well as the enhancement of the fracture toughness of materials. Zhai [
4] studied the influences of interface bonding strength on the cracking behavior of Al
2O
3/TiB
2 composite ceramic materials and reached the conclusion that strong interfaces contribute to enhancing the critical energy release rate of microstructures. These results agreed well with our conclusion.
It should be noted that the conclusion drawn from the numerical results—that weak interfaces are disadvantageous for enhancing the fracture toughness of materials—is based on the premise of the simulation model, in which the interfaces between second phases and matrix phases are all weakly bonded and an intergranular main crack is easily formed under an applied load. However, things may be different in materials with weak-interface-bonding particles independently distributed through the strong interface network. On one hand, weak interfaces are liable to fracture to form microcrack zones under an applied load, which can facilitate microcrack toughening. On the other hand, strong interfaces are able to prevent the coalescence of the main crack and microcracks, and the material strength will not be reduced [
33,
34]. This is the toughening mechanism for the weak-interface-toughening materials, which is not dealt with in this paper.