STRENGTH OF NANO CRYSTALLINE SIC Preamble

4.2. STRENGTH OF NANO CRYSTALLINE SIC Preamble

The mechanical properties like flexural strength and the fracture toughness have been studied on

a sintered silicon carbide, which is prepared by the pressureless sintering route from the nano crystalline silicon carbide particles of an Acheson type α-SiC that is processed by high energy attrition grinding route. The average flexural strength is found to be 390 MPa and the average fracture toughness is found to be 4.3 MPa . m 1/2 . This gives some insights as well as interest in such type of study.

4.2.1. The Basic Concepts

It is seen in the chapter 2 that the sintering behaviour of nano particles of SiC is very interesting indeed [9-11]. The non-oxide ceramics are attractive candidates for structural materials because of their

153 high temperature strength, which makes them highly suitable for the applicastions in ceramic engines

MECHANICAL PROPERTIES

and gas turbines [12]. The silicon carbide seems to be particularly well suited because of its high tem- perature strength and intrinsic resistance to oxidation. However, silicon carbide ceramic has a strong

covalent bonding character and a small amount of sintering aids such as AlN or B 4 C are usually neces- sary to make dense materials [9, 10]. Usually, the dense silicon carbide materials have lower strength compared to silicon nitride materials. The latter experience a degradation of strength at 1200°C - 1300°C, while silicon carbide materials do not show any decrease of strength up to 1500°C. Moreover, the reliability of silicon carbide ceramic in high performance applications is still in doubt. The silicon car- bide, like other ceramics, shows a ‘wide scattered distribution’ in flexural strength. This 'distribution' of strength is a matter of concern and hence an important topic to be studied.

The strength distribution of silicon carbide varies while obeying Weibull statistics [13], as it is typical for many other ceramic materials. Most of earlier work is based on a 4-point bending test. De- pending on the manufacturer and the type of silicon carbide, the average room temperature strength varies between 350 and 550 MPa. For such cases, the Weibull modulus which is a measure of the 'dispersion' in strength varies between 6 and 15 depending on the strength of the ceramic materials [11].

Contrary to the observed behaviour in metals, the room temperature strength of the sintered α- silicon carbide increases, as the exaggerated grain growth is intentionally introduced by a suitable heat- treatment [14]. However, the comparisons between the grain sizes should be made between two differ- ent materials having a uniform distribution of ‘small grain sizes’ versus a uniform distribution of ‘large grain sizes’. In this study, with the isolated rise to a ‘mixed grain-size’ matrix, it should be pointed out that the mechanical strength of the sintered silicon carbide remains unaltered at temperatures up to 1500°C, which has a definite advantage in the high temperature applications such as gas turbines and ceramic engines (see the section 2.1). A further increase of strength has been observed in this material, when heated in the argon atmosphere [15, 16].

Schwetz and Lipp [17, 18] also studied the effect of the dopants on the flexural strength. They observed that the materials doped with aluminium had a higher strength than that doped with boron, and with the improvement in the processing parameters, it would be as strong as the 'hot-pressed' SiC mate- rials. They also found that the production of the materials with ultrafine grains occurred in a very narrow range of sintering temperature (2050-2075°C). The exaggerated grain growth at temperatures above 2075°C was the cause of the reduction in strength of boron doped materials. The materials sintered with aluminium nitride, which acted as a grain growth inhibitor, showed a higher strength [17, 18].

Moreover, as said earlier, the reliability of silicon carbide materials in high performance applica- tions is still in doubt. The silicon carbide, like other ceramics, shows a wide distribution in strength. One common way of characterizing the variability of strength of brittle materials is by using the Weibull modulus [13]. A high Weibull modulus material (i.e. m > 20) will give a narrow distribution of fracture strength, whereas a low Weibull modulus material (i.e. m < 5) has a wide distribution in fracture strength, and hence a low reliability [19-22]. However, a number of workers indicated that the structural reliabil- ity of ceramics is primarily dependent on the ‘flaw size distribution’ during the processing [23-28]. The studies on the strength and Weibull data of silicon carbide materials, which are prepared from the nano- crystalline particles, are somewhat limited in the literature [11].

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The ability of a material to ‘resist’ cracking and once cracks start appearing, its ability to ‘resist’ further crack propagation leading to catastrophic failure, can be characterized by the ‘manner of crack initiation and propagation’, which is a function of fracture toughness The fracture tougness remains more or less constant with temperature, for the ‘hot-pressed’ and sintered silicon carbide, varying be- tween 3 and 5 MPa.m 1/2 . However their experimental data were limited to relatively ‘large grain’ size region [29]. Kodama and Miyoshi [30] studied the fracture behaviour of the ‘fine-grained’ silicon car- bide materials, which were prepared by ‘hot-pressing’ with AlN additives. They observed a dependence of the fracture toughness on grain size. The maximum fracture toughness of 5.1 MPa.m 1/2 was observed for a grain size of 700 nm, and for grain sizes that are ‘finer’ or ‘coarser’ than 700 nm, the fracture toughness decreased. This was larger than that of the ordinary silicon carbide materials with the grains having micrometer grain-sizes. They also found that the maximum fracture toughness was observed mainly in the inter-granular mode. Dutta [31] observed that the mechanical failure of silicon carbide materials occurred minly due to the defects introduced during the fabrication of the materials These defects are normally ‘surface flaws’, ‘inclusions’, ‘voids’, having a a very large diameter of 100 mm.

The above literature survey then gives us the ‘basic concepts’ by adequately covering almost all aspects of fracture mechanical behaviour of silicon carbides that are doped with various additives, par- ticularly boron carbide and aluminium nitride, which are relevant for the present study. However, a glimpse of the Weibull statistics need to be given here, since it is the most fundamental aspect for the understanding of the ‘dispersion’ behaviour of fracture strength in materials. It should be clearly pointed out that the theoretical discussion on silicon carbides, which are given here and in the previous section on fracture strength and theoretical strength, are equally relevant for many other materials including nano-materials.

4.2.2. Wiebull Theory

It is pertinent to write about this theory due to its tremendous importance in interpreting the fracture mechanical data of materials. The determination of the ‘reliability’ of the material components is based on Weibull’s ‘weakest link theory’, which is very simple and is based on an assumption that “a part is like a chain of many links”. If any link (i.e. small element of the part) fails, then the whole chain or the part has failed. Similarly, if any small volume in a material part is sufficiently stressed to cause a crack, the part will generally fail. Thus, the key is to determine if any of the elements in a part is likely to fail. Since the strength properties of the materials are variable due to the ‘random distribution’ of flaws, there is a variation of strengths of different elements of a part. Thus, the strength of various elements can be considered to have a ‘statistical distribution’ with the values below and above some characteristic strength.

If an element is subjected to some stress, there is a certain probability that the local strength of the material will be exceeded. As the number of elements in a chain is increased, the probability that “a weak link will occur and cause a failure” also increases. Similarly, the probability of a material compo- nent is a function of volume of the material, which are subjected to various stress levels. By combining the ‘probability of failure’ of all the elements, the probability of failure of the total part can be deter- mined. That's a simple concept !

One common way of characterizing the variability of strength of brittle materials is by using the theory of Weibull [13], who established that the function, which would describe the 'cumulative prob- ability of failure’ of all the elements of a part of N elements, can be expressed as :

MECHANICAL PROPERTIES

where, P is the ‘fracture probability’ at stress σ, σ 0 is a normalising parameter, which is defined as the characteristic stress at which a volume of the material (V 0 ) would fail in an uniaxial tension, σ u the threshold stress i.e the minimum stress for which the fracture can occur, and m the Weibull modulus. For

a fixed volume and shape of the samples, the equation (4.9) can be written as :

(4.10) For a conservative estimate, the threshold stress is taken to be zero. Thus the equation (4.10) can

P = 1 – exp{– [( σ–σ u )/ σ 0 ] m }

be written as :

P = 1 – exp{– ( σ/σ 0 ) m }

A high Weibull modulus material (m > 20) will give a narrow distribution of the fracture stresses, whereas a low Weibull modulus material (m < 5) has a wide distribution of the fracture strength, and hence a low reliability, as pointed out earlier [11].

Here, the studies on the strength properties of nano-crystalline α-silicon carbide ceramics with the addition of boron carbide and aluminium nitride are described. The strength of the materials is characterised in terms of the baseline strength, the strength distribution and the microstructure.

4.2.3. Stress Intensity Factor

First of all, a little background on the theoretical aspect of fracture toughness should be given before the measurement technique is discussed. It is well established that the brittle fracture in ceramic materials, viz. silicon carbide, occurs through the propagation of ‘pre-existing’ flaws. The most com- mon ‘fracture-inducing’ flaws are micro-cracks. The stress intensity at the crack tip, which is denoted by

K 1 , is related to the ‘applied stress’ by the equation as : K 1 = σY a

(4.12) where, Y is a dimensionless parameter, which depends on the geometry of loading and the crack con-

figuration, and ‘a’ is the half of the crack length. Here, K 1 is called the ‘stress intensity factor’. Actually, it is the driving force at the crack tip. At the time of the fracture, it is reasonably assumed that the normal stress reaches the ‘critical value’, which is just sufficient for the ‘rupture’ of the atomic bonds. Conse-

quently, the ‘stress intensity factor’ (K 1 ) will also attain its ‘critical value’.

It should be pointed out here that, like many other physical phenomena, there is also a “criticality” in the ‘stress intensity factor’, which surely depends on the ‘velocity of crack propagation’. If we make

a plot of crack velocity vs. K 1 , then we would normally notice ‘three zones’. In the first zone, the crack velocity increases moderately, then it increase slowly or remains almost constant (i.e. sub-critical growth), and finally at a critical value of K 1 , the crack velocity moves upwards very fast → leading to fracture or failure of a brittle material [21].

Thus, the “critical stress intensity factor” (K 1C ) or the ‘fracture toughness’ is a measure of the stress required to initiate a rapid crack propagation. Alternatively, it can be said that K 1C is a measure of the ‘resistance’ of a brittle material to crack propagation. K 1C can be easily considered as a ‘material

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parameter’ provided certain conditions are fulfilled. The fracture toughness has been expressed in terms of the ‘surface energy’ and the Young’s modulus, which are measurable material parameters, by Irwin [5] as :

(4.13) This equation forms the basis of evaluation of the fracture mechanical parameters of interest.

K 1C = (2 γ E) 1/2

The above equation for ‘critical stress intensity factor’ was derived by assuming an infinite size of the samples. For the sample of finite size, this equation becomes :

(4.14) where, w = width of the sample, a = crack length, σ = stress. The function f(a/w) has to be known before

K 1 = σ π a f(a/w)

K 1 can be determined. Obviously, f(a/w) approaches → 1 for small values of (a/w). For the samples with larger (a/w) values, as mentioned earlier, the general equation is wriiten as :

K 1 =Y σ (4.15) where, Y is a polynomial in (a/w). The factor π a is incorporated in Y. The general equation was

derived by assuming a crack inside the material.