3.1. Mathematics model of temperature gradient spark plasma sintering
The spline interpolation feature points, as listed in Table 3, were obtained according to the given conditions listed in Table 2.
The spline interpolation feature points during the sintering process
| || |
where T represented the sintering temperature and t was the sintering time. The sintering temperature changed evenly as time went in each temperature interval. The functional relation of temperature and time was as follows:
where Ti and Ti+1 represented the sintering temperature at i and i + 1. ti and ti+1 represented the sintering time at i and i + 1. It was indicated that the relationship between sintering temperature and time was a linear interpolating function of subsection splines, and it was a line chart. The sintering temperature was raised or reduced constantly in every temperature interval and the rising of whole temperature was decelerated. It spent approximately 30 min in the whole SPS process, in which 5 min holding time was used.
3.2. X-ray diffraction phase analysis
The X-ray diffraction phase analysis of sample AOT4 is shown in Fig. 2. It was clear that there existed Al2O3, SiO2 and Ca3SiO5 phases in sample AOT4. The following chemical reaction, yielding Ca3SiO5, may occur during the sintering process:
3CaO + SiO2→Ca3SiO5 (3)
The Gibbs free energy, of reaction (3) was − 162KJ at the temperature of 1350℃, which indicated that reaction (3) was possible to take place based on thermodynamic analysis. X-ray diffraction phase analysis of sample AOT4 confirmed reaction (3).
3.3. Mechanical properties
The mechanical properties of TGSPS sintered alumina composites are listed in Table 1. Vickers hardness, fracture toughness and flexural strength of pure alumina (sample PAO) was 17.6 GPa, 4.65 MPa·m1/2 and 391.6 MPa, respectively. Addition of tremolite significantly improved the performances of TGSPS sintered composites, whose Vickers hardness, fracture toughness and flexural strength reached their maximum value of 20.1 GPa, 4.77 MPa·m1/2 and 538.2 MPa, respectively. The hardness and toughness of the composites increased with increasing tremolite content from 2 to 4wt.%, and then decreased from 4 to 8wt.%. There were two factors influencing the hardness of composites, namely a hardness effect due to the addition of tremolite and a densification effect of the composites. In the first stage (2 to 4wt.% addition), the densification effect was dominant and the hardness was enhanced, while the hardness was reduced as the hardness effect was in turn becoming dominant (4 to 8wt.% addition) for the reason that the hardness of tremolite were lower than that of alumina. Fracture toughness increased with increasing the amount of tremolite before 4 wt.%, at which point it reached the maximum value of 4.77 MPa·m1/2, and then decreased after 4 wt.%. Flexural strength reached its maximum value for sample AOT6 with 6 wt.% tremolite addition and then decreased for further tremolite addition. This trend of flexural strength correlated with the microstructures of the composites, which would be discussed in Sect. 3.5.
It was obvious that the TGSPS sintered alumina composites exhibited significant improvement in mechanical properties. Composite with an addition of 4 wt.% tremolite showed excellent mechanical properties, the hardness, fracture toughness and flexural strength of the composite were enhanced by 14.2%, 2.6% and 28.6%, respectively, with respect to sample PAO sintered under the same conditions.
3.5. Analysis of microstructures
SEM photomicrographs of fracture surface of samples PAO, AOT4 and AOT6 are shown in Fig. 4. The grain boundaries of sample PAO were unobservable and the fracture mode was mainly transgranular. There existed apparent pores (marked with arrow in Fig. 4a) on the fracture surface of sample PAO. Pores in samples AOT4 and AOT6, however, were much fewer than that in sample PAO, which showed that the addition of tremolite decreased the amount of pores in TGSPS sintered alumina composites. The eliminating of porosities contributed to a certain extent enhanced flexural strength of samples AOT4 and AOT6. The sintering temperature was 1350 ℃, which was higher than the melting point of tremolite, liquid phase might appeare in the TGSPS process. The eliminating of porosities might be mainly due to the smooth flowing of liquid phases, which was formed by tremolite. There were some smaller grains formed in the crystal boundaries for sample AOT4 (circled in Fig. 4b). These small particles formed in a typical intergranular fracture mode, extending the path of crack growth, and contributed to the improvement of fracture toughness for sample AOT4. The fracture surfaces of sample AOT6 (Fig. 4c) were relatively rough and presented brittle character. As was previously discussed in Sect. 3.2, during the TGSPS process, interface reaction took place among CaO and SiO2 to yield Ca3SiO5, existed on the crystal boundaries of alumina composites, strengthened the grain boundaries of the composites, and as a result, contributed to the improvement in flexural strength of alumina composites.
The effect of porosity on mechanical properties is as follows: [42, 43]
M p= Mp0 exp (-bVfp) (4)
Where Mp was the mechanical property, Vfp was the volume fraction of porosity, b was an empirical constant and the subscript 0 indicated zero porosity. The following Eq. (5) could be concluded from Eq. (4):
Where R represented the thermal shock parameters, bσ and bE was empirical constant for the flexural strength and Young modulus of alumina composites, respectively. Usually bE < bσ [44–46], so the higher the Vfp is, the lower the R is, and the poorer the TSR of composites will be. There were some pores existed in the fracture surface of sample PAO (Fig. 4a), fewer pores were found in the fracture surfaces of sample AOT4 and AOT6 (Fig. 4b and c), indicating that the improved TSR was obtained for sample AOT4 and AOT6 comparing with sample PAO. It was concluded that the addition of tremolite could promote the liquid phases sintering of alumina composites, decrease the porosity, strength the grain boundaries, improve the mechanical properties, and thus contribute to the improvement in TSR of alumina composites.
Figure 5 indicates the schematic of the mechanisms of interactions between the crack and particles. Comparing Fig. 5a with b, one could find that the difference in the opening displacement of crack tip between different sizes of grains when the crack propagated the interface between different sizes of grains (Fig. 5b), which would result in the fact that the crack propagated along the big grain. This meant that the crack was locally blunted, and the propagation length of the crack was extended, which contributed to the improvement of fracture toughness for sample AOT4.
The fracture surface morphologies of alumina composites at ΔT = 400 °C are presented in Fig. 6. A flat fracture surface was found for sample PAO at ΔT = 400 °C, and the sample remained the transgranular fracture type. The flatter and large size cleavages extended over the entire fracture surfaces, indicating that the cracks propagated fairly easy across sample PAO without crack deflections like Fig. 5a, and the cracks penetrated the alumina particles at ΔT = 400 °C (Fig. 6a) without appreciable resistance, giving rise to great drops in its residual strengths, which could explain the poor TSR of sample PAO. The enhancement of the residual strength of the alumina composites was attributed to the microstructure evolution of composites after thermal shock, and the microstructure of the samples after the quenching test provided an insight on the important details of thermal shock behavior. The fracture surface of sample AOT4 and AOT6 at ΔT = 400 °C (Fig. 6b and c) showed a relatively rough surface with a fracture mode of the combination of intergranular and transgranular failure. Dimple with a characteristic of ductile fracture could be obviously observed in Fig. 6b (marked with arrow), showing the pullout of alumina grains and indicating the high residual flexural strength of sample AOT4 at ΔT = 400 °C. Transgranular cleavage was found in the fracture surface of sample AOT6 (marked with arrow in Fig. 6c), indicating a relative lower residual flexural strength of sample AOT6 than that of AOT4.
The alumina composites were sintered to a high densification rate (Table 1) and there remained few pores in alumina composite, which enhanced the resistance to the crack initiation and load-bearing capacity of alumina composites. The compact structure of alumina composites led to a better flexural strength of alumina composite. Sample AOT6 has the higher initial flexural strength (538.2 MPa) than sample AOT4 (503.5 MPa), According to the theory of thermal shock fracture, sample AOT6 was more resistant to crack initiation. However, its ΔTc was lower than that of sample AOT4. Sample AOT4 has the higher initial fracture toughness (4.77 MPa·m1/2) than sample AOT6 (4.15 MPa·m1/2), which meant sample AOT4 possessed higher resistance to crack propagation. It was confirmed that the crack propagation rather than crack initiation dominated TSR in current composite ceramic system. It is well known that the flexural strength and fracture toughness are the most important factors to influence the TSR of ceramics [47–50]. The TSR of composites could be assessed by using the critical crack length, Lc, as follows :
where KIC was the fracture toughness of the composites. The improvement of LC contributed to the enhanced TSR of alumina composites. Sample AOT4 had the higher LC value (0.014) than that of sample AOT6 (0.01), which could explain the improvement in the TSR of sample AOT4.