Commercially available silicon carbide (SiC) powder was firstly mixed with carbon and boron carbide as sintering additives by general ball-milling. The mixtures were then dried, sieved, and put through a dry press and a cold-isostatical press of 200 MPa. Finally, the as-prepared green bodies were sintered at 2200℃ for 1 h in the atmosphere-pressure argon flow to obtain SSiC samples.

The prepared SSiC bars were cut, grinded to a standard size of 3 mm×4 mm×36 mm for strength test, and then mirror-polished for loading indenters. Indentations were made in the center of the mirror-polished surface by a hardness tester (Wilson Tukon 2100B). The Vickers indentation load P varied from 0.1 N to 150 N and Knoop indentation load P ranged from 0.5 N to 10 N. For the two indenters, the contact time was fixed at 11 s. Typical values of the indentations were measured immediately after loading process. The Vickers hardness was obtained as well as the fracture toughness after loading Vickers indenter. And the bending strength σ of SSiC samples was tested. At least 8 sample bars were employed for credible crack length and bending strength values.

Before the bending strength evaluation, the microstructures of SSiC samples were considered. Figure 1 shows the SEM images of the fractured surface and polish- etched surface of SSiC sample. The as-prepared SSiC ceramic samples, with the relative density above 98%, homogeneously consist of equiaxed grains of 3~5 μm dimension, and the rigid matrix is almost free of pore, as shown in Fig. 1(a). And the fractured surface in Fig. 1(b) shows typical intergranular fracture mode. These micro-structural features largely affect the average bending strength. From the microstructures of the fractured surface and polish-etched surface, the sample nature is representative and good bending strength is expected.

Fig. 1

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	Fig. 1 Microstructure of SSiC ceramics (a) and polish-etched surface fracture surface (b)

The Vickers indenter was loaded in the middle of SSiC surface with loads varying from 0.1 N to 150 N. The characteristic indentation size was measured immediately after unloading. The crack size and corresponding bending strength σ by 3-point bending method was collected in Fig. 2(a). When the indentation load P increases from 0.1 N to 150 N, the Vickers crack length c increases from 2 μm to 264 μm. Meanwhile, the bending strength σ drops dramati-cally from 482 MPa to 190 MPa within 0.1~ 20 N loads, and then slowly decreases to 119 MPa at 150 N. The average bending strength after 0.1 N and 0.2 N indentations are 482 MPa, and 472 MPa, respectively, close to that of indentation-free samples (~485 MPa). It is inferred that artificial defects by 0.1 N and 0.2 N indentations affect little to the fracture. Figure 2(b) demonstrates the relationship between crack size and the corresponding strength of materials. It is found that the bending strength σ linearly fits with c^-1/2 at indentation loads above 0.5 N^{[ 5]}, identified with the Griffith microcrack theory of σ∝ c^{-1/2 [ 9]}; but at 0.2 N and lower loads, σ deviates the theory that it changes little with the indentation load as shown in Fig. 2(b). It is reasonable to assume that the crack size at 0.5 N (~10 μm) is about the critical size of defective flaws based on the inflection point of 0.5 N as shown in Fig. 2(b). It also proves that defects as small as indentations at 0.1 N or 0.2 N barely harms the material bending strength; the reason is that the dimension of these small indentations is of the same order as SiC grain size and the small cracks barely extend from the indentation at such small external loads^{[ 19]}. The higher bending strength error at indentation loads lower than 1 N can be attributed to irregular crack extending - cracks emerging from small indentations are not regular as those extending orthogonally. It is reasonable to conclude that the inclined angle of crack influences the material strength in a way that the large enough or appropriately inclined cracks result to a lower strength value; and those not large enough or inappropriately inclined cracks do not affect the bending strength and a higher strength value is obtained. The bending strength error of 1 N and smaller indentations are therefore huge.

The dimension of intrinsic defect of SSiC ceramic is determined about 3 μm (Vickers crack after 0.2 N), since 0.2 N is about the up limit that the bending strength σ maintains the same as that of the indentation-free samples; in other words, artificial defects smaller than 3 μm has limited influence on the fracture and bending strength of SSiC. The critical size of defective flaws is about 10 μm, which is the Vickers crack dimension after being loaded with 0.5 N, as shown in the inflection point of bending strength curve (Fig. 2(b)).

Fig. 2

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	Fig. 2 Vickers crack length c and bending strength σ of SSiC ceramics at different indentation loads (a) and their relation (b)[ 5]

The inclined angle of cracks influences the stress distribution and then the fracture process, because the material fracture depends on an existing flaw and the stress necessary to fracture it. The inclined angle of cracks was investigated using Knoop indenter. Knoop indenter well restricts the inclined crack direction, so it is suitable for studying the influences of crack inclined angle on the bending strength. The inclined angle θ represents the angle between the longitudinal axes of Knoop indenter and the sample bar, as shown in Fig. 3(a), i.e. 90° indicates that the Knoop indentation is perpendicular to the longitudinal axis of sample bar and 0° indicates that the two are parallel. And Fig. 3(b) shows the schematic of 4-point bending test to measure the material strength.

Fig. 3

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	Fig. 3 Schematic diagrams of inclined angle θ (a) and fracture process of 4-point bending test (b)

The Knoop indenter was loaded on the middle of SSiC sample surfaces with different loads; and also, different inclined angles were made at the same indentation load. As shown in Fig. 4(a), Knoop crack length increases with the indentation load, following a similar trend as the Vickers crack length. The bending strength σ of SSiC samples after indentations at 0°, 30°, 45° and 90° are collected in Fig. 4(b). The bending strength σ steadily decreases with the increasing indentation load P when θ is 90°, and also generally decreases at other angles of 45°, 30° and 0°. At higher indentation loads of 1 N and 2 N, σ is randomly affected by the inclined crack angle θ. At 5 N and 10 N indentation loads, the influences of inclined angle become clear - σ declines with the angle θincrement. Nevertheless, σ is always the lowest when θ is 90° at each indentation load. These effects can be analyzed from the point of fracture process.

Fig. 4

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	Fig. 4 Knoop crack length c (a) and material strength σ of SSiC ceramic (b) at different indentation loads

Figure 3(b) shows the illustration of the fracture process. When external force is loaded along z axis, the destructive stress originating from the external force distributes along y axis. If the crack inclined angle θ is 90°, it will propagate directly without deflection, the flexure strength is therefore the lowest, and the sample finally fractures along the crack, i.e. along y axis. However, if the crack inclined angle is 0°, 30° or 45°, the crack will be hindered from propagating along its original direction by the external force. Two conditions can be expected: the sample bar fractures from the Knoop crack, or the sample bar breaks from some intrinsic defect rather than the artificial Knoop indentation. For the former condition, the Knoop crack deflects from its original direction towards y axis as shown in Fig. 5(a), or it extends from the short axis toward y axis and fractures directly as shown in Fig. 5(b). Both the consequences are that the inclined crack deflects toward the distribution direction of external stress, i.e. y axis, with a higher flexure strength. In the latter condition, some intrinsic defects propagate large enough firstly to fracture the sample, that the sample fractures from the intrinsic defect rather than the artificial crack. Consequently, the flexure strength widely arranges, because the intrinsic defects are randomly located and their propagation consume more concentrated stress.

Fig. 5

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	Fig. 5 Deflection of the Knoop crack (a) and propagation of the Knoop crack along y axis (b)

For the samples fractured from the artificial Knoop crack, their strength is gradually decrease as inclined angle increases when the load is large enough as 5 N or 10 N in Fig. 4(a). According to the fracture mechanics of Griffith and Irwin^{[ 9]}, there is a critical condition if the sample breaks from a sharp precrack: σ_c = (3 T₀)/(4 φc_e^1/2).

σ_c is the unstably critical flexure strength for SSiC sample with Knoop pre-crack, T₀ is toughness, φ is a parameter relating to material and indentation geometry etc., and c_e is the effective crack length in y axis. Considering the inclined angle θ of Knoop crack, the inclined crack can be decomposed into a component perpendicular and another parallel to the external force. The critical condition can be deduced as follow: σ_c = (3 T₀)/[4 φc^1/2(sin θ)^1/2] (1)

By data collected in Fig. 4(b), the flexure strength, is evidently related to inclined angle. Knoop cracks much longer than intrinsic defects such as after 5 N and 10 N loads make it easier to deflect along the external stress, and the samples break from the Knoop crack. The relationship of flexure strength σ and inclined angle θ was analyzed when the indentation load is 5 N and 10 N, as shown in Fig. 6. It is obviously that the relationship between σ and θ corresponds with the formula (1), i.e. σ∝(sin θ)^-1/2, which explains the decreasing strength as inclined angle increases.

Fig. 6

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Fig. 6 The relationship between flexure strength σ and inclined angles θ of SSiC ceramicWhile the artificial Knoop crack is not large enough after 1 N or 2 N indentation load, Knoop crack deflection and intrinsic defect propagation happen randomly since the intrinsic defects randomly scatter; and the randomness makes the flexure strength irregularly influenced by the inclined angle as shown in Fig. 4(b).