Study on Indentation Experiments and Mechanical Behavior of RB-SiC

In this work, we studied on the mechanical behavior of RB-SiC by the indentation experiments. The Vickers hardness tester and the laser scanning confocal microscope are used to process and observe the RB-SiC sample pieces. The indentations result shows that the hardness at the Si phase is lower than the SiC phase, thus it is easier to remove the Si than SiC. The morphology of indentations are complicated, there were no accumulation phenomenon at indentation edge. When the loading was 0.1kgf, 0.2kgf and 0.3kgf, only the radical cracking can be observed and the cracking was not obvious at Si and SiC mixed phase. Avalanche crushed phenomenon occurred when the load increased to 0.4kgf. According to the Evans’ fracture toughness formula, the fracture toughness of SiC phase is about 2.5MPam1/2, and the fracture toughness of Si-SiC mixed phase is bigger than 3.0 MPam1/2. The critical cutting depth (dc) of RB-SiC was calculated by empirical formula presented by T. G. Bifano, and the value is 22.54nm.


Introduction
RB-SiC have excellent mechanical and chemical properties, such as high hardness, high thermal conductivity, wide band gap etc.Thus, RB-SiC has been considered as one of the most promising materials for lens molds and space telescope mirror [1][2][3].
Because of the high hardness of the RB-SiC, it is very difficult to remove the material of RB-SiC.Many methods for processing RB-SiC were presented, such as chemical mechanical polishing [4], electro-chemical mechanical polishing [5] and plasma-assisted polishing [6].But these methods still may leave damage and scratch on the surface.Thus, it is important to understand the mechanical behavior of RB-SiC to realize the ductile material removal.In the previous study, some research of ductile removing of glass materials [7][8] and properties of RB-SiC [9] were studied.
In this work, we studied the properties of RB-SiC on Vickers hardness, fracture toughness and critical depth by Vickers indentation experiment.This will help us know more about RB-SiC so that we can adjust the processing parameters in the future study.

Vickers indentation experiment
The size of sample pieces in the experiments isΦ10x8mm.The sample pieces were preprocessed on the Tegra System Modular sample preparation system (shown in Fig. 1).Before processing, the samples were mounted in the epoxy resin as shown in Fig. 2. Fig. 3 shows the white light interferometer images of the RB-SiC surface morphology.As indicated by Fig. 3, RB-SiC consists of two phases, and the distribution of the two phases is not uniform.The 'Island' is the SiC phase, and the dark part is the Si phase.
Table .1 is the experiment parameters of the indentation experiments.The Tukon 2500 full automatic Vickers hardness tester (Wilson hardness Ltd.) was used to press on three points on the sample pieces under different loads.The OLS3000 laser scanning confocal microscope (OLYMPUS Ltd.) was used to analyze the indentations.2 sin 68 1.854 where HV is the Vickers hardness(kgf/mm 2 ), F is the load, (kgf), S is the area of the indentation(mm 2 ), and d is the average length of diagonal of the indentation.Table .2shows the Vickers hardness of RB-SiC under different loads.According to Table 2, there is no size effect between the Vickers hardness and the load.Because there are two phases exist in RB-Si and the distribution and size of two phases are not uniform, the indenter contact different phases at each time.For the indentation load of 0.2kgf, the contact area and the Vickers hardness are shown in Fig. 4 and Table .3respectively.In Fig. 4(a) and (b), the indenter was pressed on the SiC phase, thus the Vickers hardness is similar as indicated in Table .3.In Fig. 4(c), the indenter was pressed on the mixed phase where the particle size of SiC is small.Thus, the Vickers hardness is lower than SiC phase.We can infer that the Vickers hardness of Si is much lower than SiC.In Fig. 4(d), the indentation was almost pressed on SiC phase, thus the Vickers hardness is similar to pure SiC phase.
According to the analysis above, when grinding or polishing RB-SiC, the Si phase can be removed easier than the SiC phase.As a result the 'step' structure appeared.It is quite hard to obtain high surface quality of RB-SiC.Fig. 6 shows the morphology of the indentation under different loads.The morphology is complicated, black area is the SiC phase, the white area is the the Si phase, and the distribution of two phases are not uniform.Under the low load (0.05kgf), only plastic deformation occurred.With the increasing of loads (0.1kgf, 0.2kgf and 0.3kgf), there were obvious radical cracks at the diagonal of indentation of the SiC phase, but the cracks at the Si and SiC mixed phase were shorter.No material accumulation appeared at the edges of the indentation on the mixed phase.When load increased to 0.4kgf, radical cracks could be clearly seen at the diagonal of indentation.In addition, a 'shell' like mass breakage occurred which is shown in Fig. 6e.Because of the heavy load, the lateral cracks spread from subsurface to surface which results in the fall off of SiC.But for RB-SiC, since its Vickers indentation cracks are complicated, it is hard to define the system it belongs to.Since the RB-SiC is a typical polycrystalline ceramic materials.Therefore, the fracture toughness formula of RB-SiC (KIC) can be calculated by the equation of the fracture toughness presented by Evans [10], which gives: where 1.59 0.34 2.02 11.23 24.97 15.32 and In Eq(2), E is the elastic modulus of the material, H is the hardness, c is the half length of the crack, and a is the half length of the diagonal of the indentation.According to Eq.( 2), ( 3) and ( 4), the fracture toughness is calculated and the results are shown in Table .4.
The fracture toughness of SiC phase is about 2.5MPam 1/2, the fracture toughness of mixed phase is larger than 3.0MPam 1/2 .

Critical depth dc
It is necessary to calculate the critical depth so that the hard brittle material can be removed (grinding) ductile under this depth and left no cracks and damage [8][9].T. G. Bifano [8], presented the critical depth model of the glass material by the indentation method based on the Griffith crack extension criterion, which gives: where a is a constant of system, E is the elastic modulus of the material, H v is the hardness of the material, and K IC is the fracture toughness of the material.The scanning After calculation, the critical depth of RB-SiC is shown in Table .5.

Conclusions
(1) The morphology of RB-SiC is complicated.No material accumulation appeared at the edge of the mixed phase indentation.When the load is 0.1kgf, 0.2kgf and 0.3kgf, the radical cracks appeared at SiC phase.When the load is 0.4kgf, the massive avalanche crushed phenomenon appeared.
(2) The modulus presented by Evans was used to calculate the fracture toughness under different load.The fracture toughness of SiC phase is about 2.5MPam 1/2 , the fracture toughness of mixed phase is larger than 3.0MPam 1/2 .
(3) The critical depth of ductile-brittle translation of RB-SiC is 22.54nm on average.

Figure. 6
Figure.6The morphology of indentation of RB-Si

Table 2 .
Hardness of RB-SiC under different load Load(kgf)

Table . 3
The Vickers hardness of different contact area under 0.2kgf

Table . 4
The fracture toughness of RB-SiC under different load 2 0.15