Silicon nitride: the engineering material of the future

Abstract

The purpose of this review is to present the recent developments in silicon nitride (Si₃N₄) ceramics and to examine the achievements regarding our understanding of the relationship between processing conditions, chemical composition, microstructure and mechanical properties of Si₃N₄. Si₃N₄ is one of the most important structural ceramics because it possesses a combination of advanced properties such as good wear and corrosive resistance, high flexural strength, good fracture resistance, good creep resistance and relatively high hardness. These properties are obtained through the processing method involving liquid phase sintering in which a tailored microstructure, with high aspect ratio grains and chemistry of intergranular phase, triggers the toughening and strengthening mechanisms leading to the development of high fracture toughness and fracture strength. However, despite high fracture toughness and strength, Si₃N₄ ceramic materials still break catastrophically, and the fracture behaviour of this ceramic is considered to be the major obstacle for its wider use as a structural material. In addition to the macrostructure–mechanical properties relationship, this paper also reviews new designs involving laminates possessing no plane of weakness and some theoretical developments involving crack opening displacement. Proposals of how to improve the fracture resistance were also discussed.

Introduction

In 1994 Poper [1] published a paper on the application of Si₃N₄ ceramics, which was based on computer-searching in the American chemical abstracts system from the years 1967–1992, carried out by the Gmelin Institute (Staffordshire, UK). All suggested applications result from the basic properties of Si₃N₄. These properties were very good refractoriness due to its high thermal shock resistance (low thermal expansion coefficient), chemical inertness to many molten metals, high temperature stability, high wear resistance and abrasiveness due to its hardness, and for ceramic material, relatively high fracture toughness and strength. Summary of the Si₃N₄ material properties are given in Table 1. One of the earliest uses of Si₃N₄ was in the Si₃N₄-bonded refractory brick for blast furnaces in the 1950s. It probably, in terms of the volume used, represents the largest application of Si₃N₄ in industry. In the general field of metallurgy, processes such as continuous casting which requires casting nozzles materials of high durability. Si₃N₄ appears to be very suitable for this application. Berroth et al. [2] reported on application of Si₃N₄-base ceramics in light metal and non-ferrous foundry industry. The applications include components like thermocouple sheaths, heather sheaths, riser tubes, valve seats and plungers, degassing agitators and a number of other specific parts which are in use or recommended and tested to be in use.

Table 1 Materials properties of hot-pressed, pressureless sintered and reaction sintered Si₃N₄

Metal cutting is another field of application for Si₃N₄ in which high wear resistance is required. The high thermal shock resistance of Si₃N₄-based cutting tools permits fast machining of cast-iron, steel and Ni-alloys. Tool tips of silicon nitride have been coated with diamond by microwave plasma CVD (chemical vapour deposition) for cutting Al–Si alloys [1].

The combination of properties such as temperature and corrosion resistance, thermal conductivity together with a low-specific weight and specific electrical properties make Si₃N₄ suitable for use in a construction of motors as a material for thermal conductors, valves, turbo-charger rotors, gas turbines, catalyst carriers and spark plugs [3]. Since Si₃N₄ is an electrical insulator, its uses for electrical purposes are largely to protect an electrical conductor in the form of an embedded wire or conducting film. Lately, Si₃N₄ has been suggested as a protective coating for high-T _c superconductors. Si₃N₄ has also been considered as a material for nuclear fusion reactors in high temperature gas-cooled reactors and for very high temperature reactors. The main application of Si₃N₄ in semiconductor technology is as the container for molten Si and semiconducting compounds. Thin coatings of Si₃N₄ on quartz vessels reduce the oxygen diffusion into Si. It has also been used in the protection of Si sheets and ribbons for solar cells [1].

In optical fibre technology, Si₃N₄ has been used to protect fibres from moisture and other damaging contaminants by coating them with films of Si₃N₄ by CVD.

Mazzocchi and Bellosi [4], Mazzocchi et al. [5] and Neumann et al. [6] have investigated and reported on the possibility of Si₃N₄ to be used as a biomaterial for orthopaedic implants. At present, Si₃N₄ indeed has become a biomaterial which found its application in spinal implants.

Despite an excellent combination of properties (Table 1), which make Si₃N₄ one of the most important ceramic materials for structural applications, its wider use is limited by Si₃N₄ fracture behaviour which occurs catastrophically. In the last two decades, scientists and researchers have been trying to increase the resistance of crack propagation in Si₃N₄ and to improve its fracture behaviour. The approach was to design a processing condition, in terms of chemical composition and sintering technique capable of providing the conditions for toughening and strengthening mechanisms to take place. In addition to microstructural development, a new structural design, providing conditions for crack deflection and crack bridging, has been an objective of many researchers.

In 1976 a thorough review was conducted by Jack [7] on sialons and related nitrogen ceramics where the emphasis was placed on the effect of processing conditions and chemical composition on fracture strength of these materials. In addition, he suggested an alternative approach using the principles of ceramics “alloying” in the production of “sialons” (phases that had been discovered independently in Japan and England). Jack regarded Si₃N₄ as the first of very wide field of nitrogen ceramics in which there seems to be excellent possibilities on designing materials starting from an atomic scale. At the time, these new oxynitrides included structure types based upon α and β-Si₃N₄, silicon-oxynitride, aluminium nitride, silicon carbide, eucryptite, spinel, melilite and apatite. They were being explored for their thermal, mechanical, chemical and electrical properties.

In 1981 Weiss [8] published a review on silicon nitride ceramics in which he discussed thermodynamics and phase equilibria of these materials. The review includes nitridation of metallic silicon, crystal structure, processing, microstructure and mechanical properties of Si₃N₄, as well as oxidation of Si₃N₄ materials. Weiss also described the relationship between the sintering conditions and the properties of Si₃N₄. The effect of the level of sintering aids on density and chemical composition of secondary phase was also examined in that review. In addition, the relation between grain size, flow size and fracture strength has been reviewed.

In 2007 Hampshire [9] published a review of structure, processing and properties of silicon nitride ceramics. Besides crystalline structure and phase transformations, Hampshire discussed microstructure–property relationships. He stressed that the amount of additives initially introduced determines the quantity and chemistry of the grain boundary glassy phase which in turn affects such properties as fracture toughness, ambient and high temperature strength, creep resistance and oxidation resistance. As well, Hampshire indicated that, in addition to controlling the nature of the intergranular phase, the morphology of the β-Si₃N₄ is important in determining the strength and fracture toughness of Si₃N₄ ceramics. In the Hampshire’s review it has also been shown that, for the same level of porosity, larger volume/number of elongated grains with higher aspect ratio have higher resistance to crack propagation. On the other hand, the number of elongated grains and their aspect ratio are controlled by the level and ration of (Y₂O₃) yttria to (Al₂O₃) alumina sintering aids. In his review, Hampshire examined the significance of volume fraction of the elongated grains on fracture toughness and its effect on toughening mechanisms such as crack bridging, grain rotation and grain pull out. Also, he pointed out that high fracture resistance and high fracture strength can be developed in self-reinforced Si₃N₄ by controlling the size and volume fraction of β-Si₃N₄ grains with high aspect ratio well-dispersed in fine-grained matrix.

Crystal structures of Si₃N₄

Silicon nitride exists in two major crystalline forms: α- and β-phase. α-Si₃N₄ is the low temperature modification and β-Si₃N₄ is the high temperature modification. Both phases have a hexagonal crystal structure. The lattice parameters of α-Si₃N₄ are a = 7.7541(4) Å, and c = 5.6217(4) Å, with an atomic layer sequence of ABCD (Fig. 1); the corresponding parameters for β-Si₃N₄ are a = 7.6044(2) Å, c = 2.9075(1) Å, and an atomic layer sequence of ABAB (Fig. 1) [10–12]. Both structures are built up from a SiN₄ tetrahedron and can be transformed into each other by a 180° rotation around an axis normal to the C direction (Fig. 2). At normal pressures, Si₃N₄ does not melt but dissociates at around 1877 °C according to the reaction [3]:

$$ {\text{Si}}_{3} {\text{N}}_{4} \,\left( {\text{solid}} \right) \to 3{\text{Si}}\,\left( {\text{liquid}} \right) + 2{\text{N}}_{2} \,\left( {\text{gas}} \right) $$

(1)

Fig. 1

Crystal structures of a α-Si₃N₄ and b β-Si₃N₄

Fig. 2

Crystal structure of a SiN₄ tetrahedron and b unit cell of SiN₄. Bigger ions are silicon; smaller ions are nitrogen

Sintering of Si₃N₄ ceramics

Si₃N₄ ceramics are usually sintered to high density using pressure sintering techniques such as hot-pressing (HP) and hot-isostatic-pressing (HIP), and pressureless sintering technique where densification of the powders occurs without the application of external pressure. The pressureless sintering method is preferred since complex-shaped components can easily be densified and the cost of the products is significantly lower.

In order for sintering to take place, two conditions must be met: (1) the diffusion rate of the atoms must be high, and (2) the energy of newly formed grain boundaries must be sufficiently low to cause a decrease in system free energy [13].

The activation energy required for self-diffusion of covalent bonded solids, such as Si₃N₄, is extremely high and self-diffusion coefficients are, therefore, low. Since appreciable shrinkage of the powder compacts can occur only when matter is transported to the surfaces of pores by volume and grain boundary diffusion, it is predicted that there will be little material transport in these covalently bonded solids [14]. This, combined with very high grain boundary energy of pure Si₃N₄, makes its densification very difficult even at a very high temperature and for a long time. Therefore, sintering aids are always needed to bring down the grain boundary energy of Si₃N₄ and to increase diffusivity. Every powder particle of Si₃N₄ contains a surface layer of SiO₂ which during sintering reacts with sintering aids, oxide additives, and some of the nitride itself. At sintering temperatures, this reaction forms a liquid phase which promotes densification first by rearrangement and at the same time by solution of α-Si₃N₄ into the liquid phase and then by precipitation of β-Si₃N₄. The term liquid-phase sintering is used to describe the sintering process when a portion of material being sintered is in the liquid phase. In liquid-phase sintering, the liquid provides the vehicle for rapid mass transport and thus rapid densification. The driving force for densification is the capillary pressure of the liquid phase between the fine solid particles [15]. Furthermore, the kinetics of densification in solution-precipitation stage of sintering is much higher then in the solid state sintering. In liquid phase sintering the diffusion occurs in the liquid where the diffusivities are order of magnitude higher then those in the solid state sintering [15]. In this stage of sintering shrinkage follows the equation [16, 17]:

$$ \frac{\Updelta L}{{L_{0} }} = \frac{1}{3}\frac{\Updelta V}{{V_{0} }} = \left[ {\frac{{12 \cdot \delta \cdot D \cdot C \cdot \gamma_{\text{LV}} \cdot \Upomega }}{k \cdot T}} \right]^{1/3} r^{ - 4/3} \cdot t^{1/3} $$

(2)

where r is the radius of the particle, D is diffusion coefficient of the solid in the liquid, T is the absolute temperature, k is the gas constant, δ is the width/thickness of the liquid film between the grains, C is the solubility of the solid in the liquid, Ω is the atomic volume, t is the sintering time and γ_LV is the liquid–vapour interfacial energy.

With the purpose of determining the diffusion coefficient of Si₃N₄ during the liquid phase sintering, in 2002, Krstic and Krstic [18] experimented with isothermal sintering of Si₃N₄ containing ~10 wt% oxide additives (Y₂O₃ + Al₂O₃). The sintering was carried out at 1780 °C for 20, 45, 60, 90 and 120 min. The result of isothermal sintering was plotted in terms of log-shrinkage and -sintering time (Fig. 3) in order to determine the slope of the curve.

Fig. 3

Log-shrinkage versus log-sintering time

From the graph in Fig. 3 it was determined that the slope of the straight line is ~1/3 confirming the validity of Eq. 2. Based on the experimentally determined slope of the curve and knowing other values in Eq. 2, it was possible to estimate the diffusion coefficient responsible for mass transport. Introducing values for δ = 4 × 10⁻¹⁰ m, Ω = 4.36 × 10⁻²⁸ m³, C = 0.8–0.95, γ = 8.5 J/m², and r = 2.4 × 10⁻⁷ m, the diffusion coefficient of Si₃N₄ at 1780 °C was estimated to be in the range from 10⁻¹³ to 6.39 × 10⁻¹² cm²/s.

In 1980, Thummler [19] reported values for the self-diffusion coefficient at 1300–1400 °C between 3 × 10⁻¹⁸ and 5 × 10⁻¹⁹ cm²/s, which is 5–6 orders of magnitude lower than the measured values reported in Fig. 3 (i.e., at 1780 °C). Considering that the diffusion coefficient is 3–5 orders of magnitude lower than that of a substance in a liquid, the value of 10⁻¹³ to 6.39 × 10⁻¹² cm²/s determined in these experiments is considered reasonable.

Not only the presence of liquid phase during sintering has a significant affect on Si₃N₄ diffusion rate and in turn on its sinterability, but also on the phase transformation in Si₃N₄.

α → β phase transformation in Si₃N₄

The presence of a liquid phase during sintering of Si₃N₄ is also important for the α → β phase transformation which is believed to occur after dissolution of the fine α particles in the liquid phase formed between sintering aids and subsequent precipitation of the β nuclei [20]. For the formation of β phase from α phase, layer C must be changed to layer A and layer D must be changed to layer B (Fig. 1) [21]. This reconstruction of the crystal structure requires short-range diffusion rather than simple translation, and diffusion occurs as a result of the concentration gradient of α-Si₃N₄ rich powders. The diffusion of silicon and nitrogen takes place through the liquid phase followed by precipitation of β phase in the form of small nuclei on the existing β-Si₃N₄ grains (Fig. 4).

Fig. 4

α → β microstructure change and phase transformation during liquid phase sintering of Si₃N₄ [22]

Another outcome of this analysis indicated in Fig. 4 is that, regardless of the initial phase composition of the powder, if there is a sufficient amount of liquid phase during sintering, the α–β phase transformation will be complete, resulting in final structure consisting of only elongated β-Si₃N₄ phase. As a consequence, it is expected that with prolonged heating time at sintering temperatures, β-Si₃N₄ grains which are in equilibrium with the reactive liquid, will grow anisotropically. The growth of elongated β-grains in the presence of a liquid can be controlled either by the diffusion of the atoms through the liquid or by reaction at the grain/liquid interface. For those two mechanisms of grain growth, (diffusion control and interface-reaction control), a kinetic equation was developed [23, 24] and is known as the LSW theory:

$$ D^{n} - D_{0}^{n} = K_{\text{D}} \cdot t $$

(3)

where D is the average grain size, D ₀ is the initial grain size, n is the growth exponent, K is the rate constant and t is the time. The rate constant K and growth exponent n are different for the length and width directions of the β-Si₃N₄ grains. The aspect ratio, length/width, was defined as [25]:

$$ {\text{AR}} = \frac{L}{W} = \left( {\frac{{K_{\text{L}}^{1/3} }}{{K_{\text{W}}^{1/5} }}} \right) \cdot t^{(1/3 - 1/5)} = \left( {\frac{{K_{\text{L}}^{1/3} }}{{K_{\text{W}}^{1/5} }}} \right) \cdot t^{2/15} = \left( {\frac{{K_{\text{OL}}^{1/3} }}{{K_{\text{OW}}^{1/5} }}} \right) \cdot t^{2/15} \exp \left[ {\frac{{\left( {\frac{{Q_{\text{L}} }}{3} - \frac{{Q_{\text{W}} }}{5}} \right)}}{kT}} \right] $$

(4)

where L is the average length of the β-Si₃N₄ grains, W is the average width of the β-Si₃N₄ grains, K _L and K _W are the rate constants in the length and width direction of the β-Si₃N₄ grains, Q _L and Q _W are the activation energies (Q _L = 686 J/mol and Q _W = 772 J/mol for length and width, respectively), k is the gas constant, t is the time and T is the absolute temperature. Lai and Tien [26] showed that the growth exponent n equals 3 in the length direction and 5 in the width direction. Due to the prismatic configuration of β-Si₃N₄ grains, the growth of length in the C direction [0001] is controlled mainly by the solute diffusion through multigrain junctions, while the growth of width in the [2100] direction is controlled by the diffusion along grain boundaries. According to this, the growth rate in the width direction is lower than the growth rate in the length direction, resulting in the formation of elongated β-Si₃N₄ grains. Figure 5 shows a bi-modal microstructure of Si₃N₄ sintered pressureless sintered and hot isostatically pressed (HIP) with Y₂O₃ and Al₂O₃ consisting of elongated β-Si₃N₄ grains and a matrix with slightly elongated and equiaxed grains. As expected the thickness and the aspect ratio were found to develop in a pressureless sintered samples and significantly smaller grains in HIP-ed samples. It is not surprising that HIP-ed material exhibits higher strength and hardness with minimal or no increase in fracture toughness. Elongated grains with large aspect ratio are the key to high fracture toughness of β-Si₃N₄.

Fig. 5

Bi-modal microstructure of Si₃N₄ sintered with Y₂O₃ and Al₂O₃ additions a pressureless sintered at 1780 °C, plasma etched Si₃N₄, b HIP-ed Si₃N₄ at 1760 °C, and chemically etched [27]

Over the last decade large effort was centered on atomic-level structural modelling in order to understand the mechanism of growth of elongated grains which are the key to toughening and strengthening of silicon nitride ceramics. A series of papers conducted by Painter and co-workers [28, 29] have shown that the formation of elongated grains is sensitive to cations used as the sintering additives. For example, using aberration corrected Z-contrast scanning transmission electron microscopy Shibata et al. [30] have shown that La (lanthanum) atoms preferentially segregate to the crystalline interfaces rather than within the amorphous film located at the grain boundaries. The significance of the atomic level study of the dopants distribution at the grain boundaries has been confirmed from the study of the adsorption of La atoms at the prism plane of β-Si₃N₄ employing self-consistent partial-wave method [31]. Similarly, using the example of Lu (lutetium) doped Si₃N₄ ceramics, it has been shown that the transition from crystalline to amorphous region at the interface is not atomically abrupt but is composed of sub-nanometer-scale ordered regions [32].

Si₃N₄ sintering aids

The mechanical properties of Si₃N₄ ceramics strongly depend on the sintering conditions. The type of aids used to sinter Si₃N₄ determines density and the chemical composition of the grain boundary phase. Other factors, such as the amount of the liquid phase and the heat treatment, influence the grain size and grain morphology as well. The chemistry of the liquid phase, along with the characteristics of the initial powder and processing conditions, are the key factors which determine the microstructure and properties of Si₃N₄ ceramics.

Magnesium oxide (MgO) was the first sintering additive ever used to densify Si₃N₄ ceramics [33]. Beside MgO, other sintering aids were also used including (Y₂O₃) [34, 35], alumina (Al₂O₃) [36, 37], beryllia (BeO) [38], zirconia (ZrO₂) [39], ceria (CeO₂) [40], hafnia (HfO₂) [41], ytterbium oxide (Yb₂O₃) and silica (SiO₂) [42], alumina and calcium oxide (CaO) [43], yttria and neodymium oxide (Nd₂O₃) [44], Y₂O₃ and SiO [2, 45] lanthanum oxide (La₂O₃) and niobium carbide (NbC) [46], etc. Amongst all oxide sintering aids the best-known system is the yttria–alumina (Y₂O₃–Al₂O₃).

Besides oxides, a number of metals, such as calcium (Ca), iron (Fe), manganese (Mg) and their mixtures were used as sintering aids [47].

Si₃N₄ microstructure–chemical composition–fracture toughness relationship

Microstructure evolution during sintering and its effect on mechanical properties of the Si₃N₄ ceramics, especially fracture toughness, has been the subject of many investigations in the last two decades. Some researchers believe that the width of the grains plays the most important role in determining the mechanical properties of Si₃N₄ ceramics [48]. Others believe that the aspect ratio of the elongated grains is the prevailing microstructural feature which determines mechanical properties of these ceramics [49]. In 1991, Lai and Tien [26] showed that the fracture strength and fracture toughness of Si₃N₄ ceramics with 10 wt% oxide additives (Y₂O₃ + Al₂O₃), sintered under 10 atm pressure of nitrogen, depend on the aspect ratio of the β-Si₃N₄ grains (Fig. 6). Even though the tendency of the Si₃N₄ to grow elongated grains has been observed for a long time [50], the control of the process towards the maximization of the fracture toughness is relatively recent. Lange [51] in 1979 reported an improvement of fracture strength and fracture toughness to the level of K _IC = 6 MPa m^1/2 when the β-Si₃N₄ grains with high aspect ratio were formed during sintering. In 1986 Woetting et al. [52] produced Si₃N₄ with 15% Y₂O₃ and 3.4% Al₂O₃ having a K _IC of 7.8 MPa m^1/2 (measured by micro-indentation technique). Tani et al. [53] obtained elongated Si₃N₄ grains in the Si₃N₄–Y₂O₃–Al₂O₃ system having a toughness of 6 MPa m^1/2 (measured by chevron notch technique). Compositions containing less liquid phase (5% Y₂O₃ and 1.13% Al₂O₃) and densified by a hot isostatic pressing (HIP) technique achieved a fracture toughness of 8.2 MPa m^1/2 [54]. Similar compositions (5% Y₂O₃ and 2% Al₂O₃) were also investigated by Mitomo et al. [55]. Their materials were heated under a nitrogen gas pressure of 980 kPa at 1950 °C for 1 h, producing a grain aspect ratio of 4.2. The fracture toughness of these materials, fabricated from α and β powders, ranged from 5.8 to 6.3 MPa m^1/2. Using a single-edge-pre-cracked beam method Neil et al. [56] reported a value for K _IC of 5.5 MPa m^1/2 for a hot pressed composition containing 6% Y₂O₃ and 1.5% Al₂O₃.

Fig. 6

Microstructural dependence of fracture strength and toughness of Si₃N₄ ceramics [26]

The effect of the aspect ratio of β-Si₃N₄ grains on mechanical properties of Si₃N₄, ceramics, sintered with different amounts of oxide additives (Y₂O₃ + Al₂O₃) and different oxide compositions (Y₂O₃/Al₂O₃), has been systematically investigated and reported by Krstic and Krstic [57, 58] who showed that the aspect ratio of elongated grains is the most important factor in controlling mechanical properties in these ceramics.

Strengthening and toughening of Si₃N₄

Owing to the brittle nature of Si₃N₄, over the years, there has been a continuous interest in exploring a variety of approaches for enhancing its fracture toughness and reliability. In general, fracture of brittle materials involves very little dissipation of the applied strain energy by processes other than breaking of the atomic bonds. In extremely brittle systems, the fracture surface energy often approaches the bonding energy. By employing an energy rate criterion Griffith [59, 60] showed that the critical stress for crack extension (the fracture strength) is:

$$ \sigma_{\text{f}} = \sqrt {\frac{{2E\gamma_{\text{eff}} }}{\pi c}} $$

(5)

where c is the half length of the elliptical crack, γ _eff is the fracture surface energy or fracture toughness and E is the Young’s modulus. Equation 5 shows that the strength of a real material depends on the size of the crack present in the structure.

Over the years, a variety of approaches have been used to enhance the fracture toughness of ceramics. The basic idea behind all toughening mechanisms is to develop a microstructure capable of reducing the crack tip stress field and increasing the applied stress required for crack extension.

The two most important mechanisms of toughening in the so-called self-reinforced Si₃N₄ ceramics are crack bridging (Fig. 7) and crack deflection (Fig. 8). Whether or not the above two mechanisms of toughening will be operational depends on the interface between the elongated β-Si₃N₄ grains and the surrounding intergranular phase. To promote crack bridging and deflection, the interface must break down and allow elongated β-Si₃N₄ grains to pull out as the crack front approaches them. The relationship between the fracture toughness and the interfacial strength is given by the equation [49]:

$$ K_{\text{IC}} = K_{\text{m}} \cdot (1 - V) + \left\{ {\frac{4E\tau Vu}{{(1 - \nu^{2} )}} \cdot K_{\text{m}} } \right\} \cdot \frac{l}{d} $$

(6)

where K _IC is the total fracture toughness, K _m is the fracture toughness of the matrix (with equiaxed grains), V is the volume fraction of the elongated grains, u is the pullout length, τ is the strength of the interface, E is the Young’s modulus, ν is the Poisson’s ratio and l/d is the grain aspect ratio.

Fig. 7

Crack bridging, in which unbroken ligaments are left behind the crack tip. The upper figure shows frictional bridges, while the lower figure shows ductile bridges

Fig. 8

Schematics of crack deflection a the crack path tilts to avoid obstacles and b the crack front twists to by-pass obstacles [61]

Recently, using Eq. 6, Krstic [49] has shown that theoretically it is possible to achieve fracture toughness as high as 46.3 MPa m^1/2, provided that all elongated grains are perpendicular to the crack plane and thus all contribute to the toughening.

Crack deflection is defined as a twist and tilt of the crack front between microstructural elements (Fig. 8), which reduce the stress intensity at the crack tip.

The fracture toughness increment by pull-out can be expressed by Eq. 7 [62]:

$$ K_{\text{IC}}^{\text{p}} = K_{\text{m}}^{\text{p}} \sqrt {\frac{1}{{(1 - V_{\text{p}} )A}}\left[ {1 + 2\left( {\frac{{2V_{\text{p}} (l/d)\tau }}{\sigma }} \right)^{3} } \right]} $$

(7)

where K ^p_IC is the overall fracture toughness due to pull-out, K _m is the fracture toughness of the matrix without pull-out, A is a constant, τ is the strength of the interface and σ is the fracture strength. l and d have the same meaning as in Eq. 6. Close inspection of Eqs. 6 and 7 show that a high-volume fraction of reinforcement phases with high-aspect ratio is required for toughening.

For rod-shaped reinforcing particles, the fracture toughness, due to the local deflection of a planar crack by these reinforcing particles, can be expressed by Eq. 8 [61] of the form:

$$ K_{\text{IC}}^{\text{d}} = K_{\text{m}} \cdot \sqrt {1 + V_{\text{p}} ((0.6 + 0.007(l/d) - 0.0001(l/d)^{2} )} $$

(8)

where K ^d_IC is the fracture toughness due to crack deflection, K _m is the fracture toughness of the matrix without crack deflection, V _p is the volume fraction of rods, l is the length of the rods, d is the diameter of the rods and l/d is the aspect ratio.

Figure 9 shows crack deflection, crack pull-out and crack bridging operating simultaneously in Si₃N₄ sintered with Y₂O₃ and Al₂O₃ additives. As already mentioned, these mechanisms operate most effectively in systems with β-Si₃N₄ elongated grains of high aspect ratio as is the case for the composition with ~10 wt% additives (7 wt% Y₂O₃ and 3 wt% Al₂O₃). In microstructures with equiaxed grains, the contribution of this mechanism is expected to be minimal.

Fig. 9

Crack profiles from indentation cracks in Si₃N₄ sintered at 1780 °C with oxide additives of ~10 wt% a crack deflection, b crack deflection and pull-out (black arrows show direction of crack propagation) [58]

Although the static fracture toughness measurements method, based on linear-elastic fracture mechanics method, has been well-suited for fracture toughness determination in equiaxed grain structures its application to ceramics with highly developed process zone such as fully or partially stabilized zirconia or silicon nitride with large pull-out and crack bridging zone has been highly controversial. Even the most carefully made R-curve measurements could not accurately assess the initial toughness point. This is best illustrated with the example of silicon nitride doped with rare-earth elements such as La, Gd (gadolinium) and Lu [63]. In this context, rigorous and approximate methods were proposed for determining the onset of fracture in materials with steeply raising R-curves. These methods are based on the crack opening displacement concept on Vickers indented cracks [64].

Unified approach to fracture of ceramics

Since the development of energy rate theory expressed in the form of a Griffith [59] equation, there has been continuous interest to broaden the concept of energy rate theory to include the effects of microstructural features such as porosity, grain size and residual stresses. Although the Griffith equation has been successfully used to predict the strength of a homogenous pore- and residual stress-free material, when it comes to a non-fully dense polycrystalline and anisotropic materials, the theory does not explain the effect of any of the key microstructural features. Over the last several decades, a number of papers have been published on the effect of porosity [65–69], grain size [70, 71] and residual stresses [72–74] on the strength of ceramics. All of these studies were centered on the role of each microstructural feature in strengthening of ceramics independent from the effect of others. By adopting a stress intensity factor approach and based on crack opening displacement concept, in 1998 a unified approach to the fracture of brittle materials was proposed which incorporates the effects of porosity, grain size and anisotropic residual stresses in the form of a continuous model [75, 76].

It is now well-accepted that fracture of ceramics and brittle materials originates either from a single pore of the largest size or from the cluster of pores linked together to create a largest size pore [77]. In the past, many empirical and semi-empirical models were used to correlate porosity to strength of a porous ceramic but failed to explain why an increase in porosity leads to an increase in strain. By adopting the concept of crack opening displacement it was possible to account for the increase displacement/strain of the material under the same applied stress in which not only pore volume fraction but also the pore size and inherent flaw size play role in controlling fracture strength of a porous ceramics (Fig. 10). In this concept the total crack size responsible for fracture, C, consists of pore size, D, and flaw size, s.

Fig. 10

Relation between pore size, D, and an annular flaw size, s

Based on this concept, it has been shown that the relationship between the number of pores per unit volume N ^p (related to the pore volume fraction V and pore radius R through the equation N ^p = 3V/4πR ³) is given by the equation [77]:

$$ E = E_{0} \left\{ {1 + 16[(1 - \nu^{2} )N^{\text{p}} R^{3} \Upphi ]/3} \right\}^{ - 1} $$

(9)

where Φ = (1 + s/R)³ + 9/2(7 − 5ν)(1 + s/R)² + (4 − 5ν)/2(1 − 5ν), ν is the Poisson’s ratio and E ₀ is the Young’s modulus of a pore-free ceramics.

In terms of pore volume fraction the Young’s modulus is expressed as:

$$ E = E_{0} \left[ {1 + 4V\left( {1 - \nu^{2} } \right)\left( {1 + s/R} \right)^{3} /\pi } \right]^{ - 1} $$

(10)

Note that in Eq. 9 Φ is assumed to be equal to 1. The change of Young’s modulus as a function of pore volume fraction and pore radius is illustrated in Fig. 11.

Fig. 11

Predicted variation of Young’s modulus with pore volume fraction, pore radius and inherent flaw size

The key result of this theoretical approach is the finding that, for a given pore volume fraction, the level of Young’s modulus decrease with porosity depends critically on the pore radius and the annular/inherent flaw size present in the material. With this theoretical model it was possible to predict the variation of Young’s modulus with pore volume fraction in many materials including metallic materials like nanocrystalline palladium. More specifically, it was possible to explain why nanocrystalline palladium with a lower pore volume fraction can have lower Young’s modulus (if it contains larger cracks/inherent flaw size) and nanocrystalline palladium with higher pore volume fraction can have higher Young’s modulus (see Fig. 12) (if it contains smaller size inherent flaws) [67]. Here, it should be noted that nanocrystalline palladium possesses limited plasticity and fractures in a brittle fashion just like most polycrystalline ceramics.

Fig. 12

Predicted and measured Young’s modulus of nanocrystalline palladium as a function of pore volume fraction, pore size and inherent flaw size (measured values for the Young’s modulus are taken from Ref. [77])

The validity of the crack opening displacement concept was confirmed by using Embedded-Atom Model on a single-crystal Ni cluster of 4000 atoms arranged in a cubic form [78].

Somewhat different behaviour was observed in porous silicon nitride ceramics with porosity level varying for 0.4% to over 6 vol% [79] as presented in Fig. 13. Figure 13 shows that as the pore volume fraction increases so does the pore size and the flow size and thus proper characterization of a porous silicon nitride must include the variation of pore size and the inherent flaw size. For example, at low level of porosity (0.5%) the flaw size is much smaller that the pore size (s/R = ~0.1) and at higher level of porosity (6%) the flaw size is larger than the pore size (s/R = ~2.5).

Fig. 13

Effect of porosity on elastic modulus of Si₃N₄ sintered with Y₂O₃ and Al₂O₃ additions. Predicted values for Young’s modulus were obtained based on E ₀ = 320GPa, ν = 0.18, γ_eff = 40 J/m², s/R = 1, and s/R = 2.5 [27, 77]

Following the same pore-size inherent flaw-size concept, and assuming that the reduction in strain energy stored in the porous ceramics is due to a decrease in Young’s modulus in the presence of pores, the theory was extended to explain the fracture strength-porosity relationship [76]:

$$ \sigma_{\text{f}} = \left[ {\pi \gamma E_{0} /D\left( {1 - \nu^{2} } \right)} \right]^{1/2} \left[ {1 + 16(1 + s/R)N^{\text{p}} \left( {1 - \nu^{2} } \right)R^{3} /3} \right]^{ - 1/2} $$

(11)

Replacing the number of pores per unit volume with pore volume fraction (V) and pore diameter (R) Eq. 11 takes the form:

$$ \sigma_{\text{f}} = \left[ {\pi \gamma E_{0} /D\left( {1 + s/R} \right)} \right]^{1/2} \left[ {1 + 4V\left( {1 + s/R} \right)/\pi } \right]^{ - 1/2} $$

(12)

The predicted variation of strength (based on Eq. 12) with pore volume fraction, pore size and the inherent flaw size is shown in Fig. 14, along with experimentally measured strength for porous silicon nitride [79]. Identical to Young’s modulus-dependence on porosity, there are three equally important factors which control the strength of a porous ceramics, i.e. pore volume fraction, pore size and the inherent flaw size.

Fig. 14

Effect of porosity on fracture strength of Si₃N₄ sintered with Y₂O₃ and Al₂O₃. Predicted values for fracture strength were obtained based on E ₀ = 320 GPa, ν = 0.18, R = 30 μm, γ _eff = 40 J/m², s/R = 1 and s/R = 1.3 [76, 80]

Inspection of Fig. 14 shows that along with an increase in pore volume fraction there is an attendant increase in inherent flaw size. For example, at low porosity volume fractions (<1%), the flaw size is approximately equal to the pore size (s/R = 1) and as the porosity volume fraction increases to >2 vol% the flaw size increased to by 30% compared to the pore radius (s/R = 1.3).

Application of the theory to fracture of polycrystalline ceramics

The crack opening displacement concept was further extended to incorporate fracture of polycrystalline ceramics possessing thermo-elastic anisotropy and fracture of brittle matrixes with second phase particles having different thermal and elastic properties from that of the matrix [70, 71]. For the purpose of this analysis, ceramic materials are classified into two structural categories; isotropic and anisotropic, depending on whether or not they have a cubic or non-cubic structure. This division is based on the theoretical analysis and experimental findings [70, 71] which show that there is quite different fracture response between anisotropic and isotropic polycrystalline ceramics. For example, it was observed that the anisotropic ceramics show strong grain size dependence whereas isotropic ceramics show weak or no dependence of fracture stress with grain size, at least for grain sizes ranging from a few microns to several hundred microns [72].

The concept of crack opening displacement can best be understood by considering a cavity situated in a polycrystalline ceramic of the same size and shape as the grain, as illustrated in Fig. 15. For the case of a randomly oriented grain structure it is expected that, statistically, there will be at least one cluster of grains in which the central grain with axis of minimum thermal expansion is perpendicular to the axis of maximum thermal expansion of the surrounding grains. On cooling from high temperature this grain orientation will place the central grain under compressive stress and the surrounding grains under tensile stress. This will favour opening of the annular crack around the grain and be responsible for fracture of the ceramic. The compressive stress developed within the central grain is given by the expression [81]

$$ P = 2E\left( {\alpha_{\max } - \, \alpha_{\min } } \right)\left( {T_{\max } -T_{\min } } \right)/3\left( {1 - \nu } \right) $$

(13)

where α_max is the linear thermal expansion in the direction of highest expansion/contraction, α_min is the linear thermal expansion in the direction of lowest thermal expansion/contraction, T _max is the temperature from which the ceramic is cooled and T _min is the temperature to which the ceramic is cooled. Based on this grain configuration, the expression for the strength of an anisotropic ceramic is developed [72, 76]:

$$ \sigma_{\text{f}} = \left[ {\pi E_{0} \gamma_{\text{eff}} /G\left( {1 - s/r} \right)\left( {1 - \nu } \right)^{2} } \right]^{1/2} - AP\Upphi_{\text{t}} $$

(14)

where G is the grain diameter, r is the grain radius, s is the inherent flaw size, A is a constant that takes into consideration of the level of residual stress relaxation and

$$ \Upphi = \left\{ {1 - \left[ {1/\left( {1 + s/r} \right)^{2} } \right]^{1/2} + \left[ {1/2\left( {1 + s/r} \right)^{5/2} } \right]\left[ {1 - 1/\left( {1 + s/r} \right)^{2} } \right]^{1/2} } \right\} $$

(15)

Fig. 15

Schematic of a hexagonal grain being inserted into the cavity of the same size and shape at high temperature. Assuming that the surrounding grains are oriented such that their direction of maximum thermal expansion is perpendicular to the central grain, on cooling from high temperature, the central grain will be under compression and surrounding grains will be under tension

The significance of Eq. 15 is that it embodies the effects of grain size, inherent/annular flaw size and anisotropic residual tress on strength of a polycrystalline anisotropic ceramic into a single equation. The key result of the above theory is that the inherent flaw size and the grain size are not necessary equal in size and that the reduction in grain size does not necessary lead to the reduction in flaw size responsible for fracture. This is illustrated in Fig. 16 which shows the change of fracture strength as a function of grain size in polycrystalline alumina [82].

Fig. 16

Predicted (from Eq. 6) and measured flexural strength of polycrystalline alumina. Measured values for strength are taken from Ref. [82]

Inspection of Fig. 16 shows that the strength of alumina can vary widely for the same grain size depending on the inherent or (often called) processing flaw size. For example, samples with grain sizes of <1 μm have lower strength than the samples with grain sizes of 4 μm simply because samples with grain size of <1 μm contained larger flaw sizes. This has an important practical implication in that the high strength alumina can be fabricated not only by keeping the grain size low but by keeping both the grain size and the flaw size small. Again, this finding confirms the assertion introduced earlier that the grain size and the flaw size are the two independent microstructural features.

Application of the theory to thermal shock fracture-porous material

Homogeneous and isotropic material

Since Hasselman [83] thermal shock theory, which describes the role of thermal expansion coefficient and flaw size in the fracture of brittle materials, there has been continued interest in expanding the theory to include the effect of porosity and anisotropic stresses on fracture. One obvious approach to incorporating the effect of porosity into the equation for thermal shock is by adopting the same concept of crack-pore configuration as in Fig. 10 which assumes that the crack size responsible for fracture consists of pore radius and inherent flaw size C = R + s. In this approach, fracture of a porous, isotropic single phase material occurs when a crack (C = R + s) reaches a critical size or the residual quenching stress P = αEΔT/(1 − 2ν) reaches a critical value [75]. Based on this, an equation for a critical temperature difference ΔT _c was developed:

$$ \Updelta T_{\text{c}} = \left[ {\pi \gamma_{\text{eff}} \left( {1 - 2\nu } \right)^{2} /2(R + s)\alpha^{2} E_{0} \left( {1 - \, \nu^{2} } \right)} \right]^{1/2} \left[ {1 + 16\left( {1 - \nu^{2} } \right)N^{\text{p}} (R + s)^{3} /3} \right] $$

(16)

where α is the linear thermal expansion, γ_eff is the effective fracture surface energy, N ^p is the number of pore per unit volume (equivalent to pore volume fraction, N ^p = 3V/4πR ³), R is the pore radius and E ₀ is the Young’s modulus of a pore-free material. Equation 16 and Fig. 17 show that the thermal shock resistance of a material is controlled not only by the flaw size (inherent flaw size in Eq. 16) but also by the pore volume fraction and pore size.

Fig. 17

Predicted change of critical temperature drop with pore volume fraction and s/R for a homogeneous single phase ceramic

For a small pore size (R → 0) Eq. 16 recovers Hasselman’s equation for thermal shock fracture of a homogeneous brittle ceramic [83].

Anisotropic polycrystalline ceramics

It has been shown that the theoretical approach used to describe the strength dependence of grain size can easily be extended to include the thermal shock fracture involving the effect of grain size and residual anisotropic stress [70, 76]. As before, fracture is assumed to originate from cracks associated with a single grain or group of grains oriented relative to neighbouring grains such that they are subjected to compressive stress acting to open the crack and surrounding grains to a tensile stress acting to close the crack. Assuming that there are N ^g grains per unit volume favourably oriented for crack extension, the equation for a critical temperature difference (ΔT _c) was developed:

$$ \Updelta T_{\text{c}} = \left[ {\pi \gamma_{\text{eff}} /2(r + s)E_{0} \left( {1 - \nu^{2} } \right)} \right]^{1/2} \left[ {1 + \, 16\left( {1 - \nu^{2} } \right)N^{\text{g}} (r + s)^{3} /3} \right]^{1/2} \left[ {\alpha_{\text{av}} \left( {1 - 2\nu } \right) \, + \, \Updelta \alpha /(3\left( {1 - \nu } \right)\Upphi } \right]^{ - 1} $$

(17)

where r is the grain radius, α_av is an average linear thermal expansion of a polycrystalline anisotropic ceramic, Δα is the difference between the direction of maximum thermal expansion and the direction of minimum thermal expansion of a single grain and Φ is a constant. Although Eq. 17 was developed for an anisotropic solid, it can be applied to cubic/isotropic ceramics by taking Δα → 0 in which case Eq. 17 takes the form:

$$ \Updelta T_{\text{c}} = \left[ {\pi \gamma_{\text{eff}} (1 - 2\nu )^{2} /2s\alpha^{2}_{\text{av}} E_{0} (1 - \nu^{2} )} \right]^{1/2} \left[ {1 + 16(1 - \nu^{2} )N^{\text{g}} (r + s^{3} /3} \right]^{1/2} $$

(18)

where s is the crack size and N ^g is the number of cracks per unit volume. Again, expression (18) recovers the equation for thermal shock fracture for isotropic pore-free ceramics developed by Hasselman [83]. The role of grain size on thermal shock of a ceramic is presented in Fig. 18 which shows that, for a given flaw size, a decrease in grain size from r = 200 μm to r = 75 μm leads to an increase in thermal shock resistance a factor of 2–3.

Fig. 18

Predicted change of thermal shock (ΔT _c) with inherent flaw size for a material with four different grain sizes

Macrostructure–fracture toughness relationship

Despite improvements in fracture toughness, the reliability of Si₃N₄ ceramics is considerably lower compared to metals and this is considered to be a major obstacle for their wider use as structural material. One way of preventing catastrophic/brittle failure of a Si₃N₄ component is to design a structure with dense and strong Si₃N₄ layers separated by weak and/or porous layers of the same or different materials [84]. The weak interface serves to deflect the propagating crack and lower its stress intensity.

Laminated structures

Traditionally, the crack deflection is achieved by incorporating fibres into ceramic matrices [85, 86]. However, fabrication of the fibre-reinforced ceramics is considered to be relatively expensive and often unsuccessful in achieving required mechanical properties [87]. A far more economical way of enhancing fracture toughness of ceramics is by incorporating the weak or often porous interlayers which serve to deflect the crack as it meets the interlayer. Atkins [88] was the first who proposed this method of toughening followed by Clegg et al. [84], Zhang and Krstic [89] and Tu et al. [90]. One of the prerequisites for achieving a high apparent fracture toughness of the laminate is that the interface material must not retard the sintering process and be chemically and physically compatible with the lamina, so that they can be co-fired at an elevated temperature without any undesired reactions and delamination. This delamination, caused by internal stresses due to uneven sintering shrinkage and differences in thermal expansion coefficients, can be easily prevented by incorporating porosity in the ceramic matrix forming a porous and thus weak interlayer. Therefore, a pre-determined level of interlayer porosity required to ensure crack deflection for the situation where residual stresses were not present, has been investigated and reported by Blanks et al. [91] and Davis et al. [92]. The process of adding Si₃N₄ fibres to Si₃N₄ powder to produce porous interlayers has been reported by Ohji et al. [93]. However, one of the problems associated with a porous interlayer laminate is the difficulty of controlling the level of porosity and shape of the pores in the path of the growing interfacial crack.

In the last two decades, efforts have been directed towards the development of a plate-form laminated ceramic composite with a weak interface such as a SiC layer with a graphite interface [84, 89], which exhibits fracture toughness as high as 14 MPa m^1/2. Following this study, a number of different plate-form laminate systems were designed and fabricated including: ZrO₂/ZrO₂ [94], Al₂O₃/LaPO₄ [95], Si₃N₄/BN [96], Si₃N₄/Si₃N₄ and Si₃N₄/TiN [97], β-SiAlON/Si₃N₄ [98], Al₂O₃/SiC [87], Al₂O₃/ZrO₂ [99] and Al₂O₃/Al₂TiO₅ [100].

Because of their high fracture resistance and reliability, laminates have received considerable attention in the past decades. While the monolithic Si₃N₄ exhibits linear elastic behaviour until fracture (Fig. 19a), the laminated material shows a slow increase of load after the first load drop followed by further increase in load prior to fracture (Fig. 19b). This behaviour is almost identical to the fibre reinforced composites with work of fracture and apparent fracture toughness approaching those of metals. Recently, Wang et al. [101] managed to fabricate planar laminates with an apparent fracture toughness of 15.1 MPa m^1/2 by controlling the composition and structure in Si₃N₄/BN laminates. An even higher fracture toughness of 28.1 MPa m^1/2 was reported by Kovar et al. [102] who incorporated secondary reinforcement such as SiC whiskers to the BN interface. The same authors have shown that it is also possible to achieve combination of high fracture strength (>600 MPa) and work (~8000 J/m²) by hot-pressing Si₃N₄/BN laminates [102]. In 2005 a new type of laminated structure was designed and fabricated by Yu et al. [103]. The novelty in this design is the conversion of planar form laminates into a concentric ring structure which eliminates the direction of easy crack propagation and offers a high damage-tolerance with work of fracture of 406 kJ/m³ and fracture toughness of over 21 MPa m^1/2.

Fig. 19

Load–displacement curves for a monolithic Si₃N₄ and b laminated Si₃N₄/SiC [103]

Up until 2005, nearly all of the research in the development of Si₃N₄ laminated structures has been focused on plate-form laminates produced by tape casting and hot-pressing. Although the improvements in fracture resistance in these planar laminates were sufficient to ensure their safe use in many structural applications, delamination and easy crack propagation along the weak interface between the two layers has been the major impediment for wider use of these structures (Fig. 20) [104].

Fig. 20

a Peeling and b delamination in the plate-form laminates

To overcome this unwanted delamination/peeling problem associated with the plate-form laminates, a concentric circular and rectangular designs have been developed and fabricated (Figs. 21, 22) in such a way that the potential delamination direction is completely eliminated [105, 106]. In addition to the absence of the direction of easy crack propagation, this new Si₃N₄/BN composite structure exhibits fracture resistance characteristics far beyond those of monolithic ceramics or planar laminates. Fracture toughness of these structures was reported to be as high as 22 MPa m^1/2 [105], fracture strength of 515 MPa [105], and work of fracture of 320 kJ/m³ [105].

Fig. 21

New design concept-structure changes from the plate-form laminate to a concentric ring (self-sealed) structure [105]

Fig. 22

SEM micrographs of cross-section of concentric Si₃N₄/BN laminated structures with a 6 and b 13 Si₃N₄ layers [105]

The work of fracture and apparent fracture toughness measured in these laminates are equivalent to those of unidirectional fibre reinforced composites and approach those of some metals. From a practical viewpoint, concentric ring structures do not require the employment of expensive fabrication methods such as Hot Pressing (HP) and Hot isostatic pressing (HIP) and can effectively be produced by employing traditional ceramic processing methods such as slip- and tape-castings. There are a number of variables which have to be controlled in fabricating the concentric ring structures, the most important being casting time, composition and structure of the interface and viscosity of the slurry [105]. So far, systematic studies of concentric ring structures revealed that, in addition to the composition and structure of the interface, the thickness and the number of Si₃N₄ layers control both the fracture toughness and strength of the laminate. This is shown in Fig. 23 which displays the change of apparent fracture toughness and flexural strength as a function of the number of the Si₃N₄ layers. The peak in fracture toughness and flexural strength is obtained for seven layers.

Fig. 23

Variation of apparent fracture toughness and fracture strength of concentric Si₃N₄/BN laminated structure with the number of Si₃N₄ layers [104]

Similarly, a peak in apparent fracture toughness and strength was found to appear at some critical layer thickness which, in the case of silicon nitride laminates, is between 200 and 250 μm (Fig. 24).

Fig. 24

Effect of Si₃N₄ layers thickness on fracture toughness and strength of concentric Si₃N₄/BN laminated structure [104]

A systematic study of the crack propagation and detailed examination of the interface revealed that the main toughening mechanisms in these laminates are the crack deflection at the weak interface and crack deflection and bridging within the Si₃N₄ layer by elongated β-Si₃N₄ phase. It was observed that some of these elongated particles also grew through the weak interface bridging the two silicon nitride layers. To the authors’ knowledge this is the first example of the weak interface encouraging growth of elongated grains from one Si₃N₄ layer to another (Fig. 25). This appears to provide the additional strengthening and toughening to the system and makes the interface significantly stronger then otherwise it would be. This interfacial reinforcement by the elongated silicon nitride grains, bridging the two BN-based interface layers, allows creation of residual stresses which put the entire inner layers and the core of the concentric ring structure under significant compressive stress. The existence of residual stress was also recognized by Orlovskaya et al. [97], in planar Si₃N₄-based laminates, and Krstic and Krstic [106] in the concentric ring Si₃N₄ laminates who found that the level of residual stress depends on the nature/composition of the interface and Si₃N₄ layer thickness. The importance of these stresses in toughening of the concentric ring structures can best be realized by comparing the indentations made in the monolithic silicon nitride (Fig. 26a) and in the core of the concentric ring structure applying the same indentation load of 30 kg. While cracks larger than 300 μm were observed in unstressed monolithic Si₃N₄, no cracks were detected in laminated Si₃N₄ (Fig. 26b) [106]. Also, the indentation diagonal is approximately 100% larger in monolithic silicon nitride compared to its laminated counterpart. This demonstrates clearly that the residual stress puts the inner volume of the concentric ring structure under compression inhibiting crack propagation and providing the additional degree of toughening. The level of residual stress was found to also depend on the composition of the “weak” interfacial layer. For example, laminates with interfacial layers with BN and Si₃N₄ exhibit a lower degree of toughening compared to layers produced with BN and Al₂O₃. The toughening mechanism operating in concentric Si₃N₄/BN laminated composites is shown in Fig. 25. The direction of the crack propagation (pointed by the black arrow), and the bridging grain pull out at the surface of the crack, within the Si₃N₄ layers (the white arrow), and the crack deflection which was arrested at the weak interface is clearly shown in Fig. 25.

Fig. 25

SEM image of chemically etched Si₃N₄/BN laminated structure showing crack propagation and its deflection and arrest at the week interface, and elongated β-Si₃N₄ bridging grain pull out at the surface of the crack [104]

Fig. 26

Comparison of crack lengths developed under the same load of 30 kg in a unstressed monolithic Si₃N₄ (K _IC = 7.98 MPa m^1/2) and b stressed Si₃N₄/BN-based laminated structures (K _IC = 18.87 MPa m^1/2) [106]

Summary

Over the last decades, significant progress has been made in the development of a new generation of silicon nitride ceramics with mechanical properties far exceeding those of classical counterparts. Specifically, there are three general areas where the effort was focused.

First is the area of microstructure development where it was possible to grow β-Si₃N₄ grains with an almost perfect circular cross-section and an aspect ratio that encouraged crack pull-out and crack bridging, both of which are identified as the most powerful mechanisms of toughening and strengthening. This, combined with compositional refinement of the interface, has led to a major enhancement of the fracture toughness of monolithic silicon nitride ceramics to a level not found in the past.

The second major development lies in the design and fabrication of a concentric ring structure consisting of dense homogeneous silicon nitride layers and a weak, partially porous interface that encourages crack deflection and toughening. The advantage of this type of structure is that it eliminates the direction of easy crack propagation which was the major problem with classical planar laminates. An enormous increase in fracture toughness was achieved with measured apparent fracture toughness of over 21 MPa m^1/2. This high toughness, which approaches that of aluminium alloys, has not been found in other ceramics and opens the avenue for the use of silicon nitride ceramics in applications previously reserved only for metals.

The third area of advancement is in the theoretical understanding of fracture of ceramics and its implications for the future development of a strong and reliable ceramic. The theory developed describes a unified approach to fracture, one that embodies the effect of key microstructural features on strength. While in the past the effects of crack size, grain size and residual stresses were treated in isolation, the new approach unifies these effects into a single equation. For example, it has been shown that the full characterization of a porous ceramics involves not only the knowledge of pore volume fraction but also the pore size and the crack size. The theory shows that the presence of larger number of smaller size pores is much more beneficial for an achieved higher strength than the smaller size of larger pores. Similarly it has been shown that the strength of polycrystalline anisotropic ceramic, such as silicon nitride, is controlled not only by the grain size but also by the inherent flaw size and residual anisotropic stress. An important practical implication of this theoretical finding is that the fabrication of high strength polycrystalline anisotropic ceramics may be achieved not only by reducing grain size but also by decreasing the inherent flaw size (also called the processing flaws). A decrease in grain size to a submicron and nanosize will not lead to an increase in strength unless the flaw size is also kept small.