Experimental investigation on material removal and brittle–ductile transition of SiC ceramics milling regarding milling force characteristic and tool wear

： This research of SiC ceramics milling with diamond tool is paid attention to the milling mechanism and the cracks formation to found the brittle–ductile transition. The ductile material removal process of ceramics milling was discussed based on milling geometric models. Based on the material characteristics and fracture mechanics theory of SiC ceramics, the chip formation process and the brittle–ductile transition of ceramics milling were analyzed. The milling experiments of SiC ceramics were carried out, and the effect of cutting parameters on material removal mode was investigated. Based on milling forces, surface topography and chip morphology, the removal mechanism of ceramics milling was analyzed. Diamond tool wear on the material removal and milling forces during milling was investigated. Different methods were compared to identify the critical milling parameters of brittle–ductile transition, which can be used to recommend the milling parameters for crack control and high quality cutting.


Introduction 1
SiC ceramics is widely used in aerospace, automotive, electronics, optics and other fields for its advantages of high hardness and good wear resistance. The processing of SiC ceramics can be accomplished by diamond grinding which is the main machining method. Zhou [1] found the critical chip formation thickness and critical ductile-brittle transition thickness based on the mechanic deformation behavior of SiC.
Zhang [2] investigated the influence of the dressing method of monolayer brazed diamond wheel on the material removal mechanism. In addition to the traditional grinding methods, SiC ceramics can also be removed by a variety of processing methods.
Laser-assisted grinding is a promising method for cost-effective machining of hard and brittle materials, such as (RB)-SiC ceramics [3] and Al2O3 ceramics [4]. The assisting electrode machining is another practical and effective methods to machine SiC ceramics. Researchers like Rao [5] presented a research on surface characteristics for RB-SiC ceramics by electrical discharge diamond grinding. Liu [6] carried out a study on SiC ceramics with electrical resistivity of 500 Ωcm by electrical discharge milling to solve the problems of costly and inefficient by using common diamond grinding. Guo [7] studied the influence of the process parameters including polarity of electrode, peak current, pulse-on time and pulse-off time on material removal rate, side gap, and surface roughness. Naotake Mohri [8] provide a method with a copper electrode in sinking * Corresponding author. Tel.: +86 024 25191396, Fax.: +86 024 25191670 E-mail address: qiuj1981@163.com (J. Qiu).
EDM or with brass wire electrode in WEDM using kerosene as working fluid to machine ceramics, which make the machining very easy. Sánchez [9] described the development of sinking and wire electro-discharge machining technology for ceramics as silicon infiltrated silicon carbide, which could obtain an excellent surface finish and high removal rates for the industrial application. Ultrasonic vibration machining is also a good processing method to solve the ceramics machining problems of high hardness, low efficiency, high cost and easy to break [10].
Zhao [11] revealed the mechanisms governing machined surface formation of hard brittle monocrystalline 3C-SiC in ultrasonic elliptical vibration-assisted diamond cutting by molecular dynamics simulations, which demonstrate the effectiveness of applying ultrasonic vibration of cutting tool in decreasing machining force and suppressing crack events. But, with the development of diamond cutting tools, the machining of SiC ceramics can also be carried out by diamond milling. It needs to overcome the difficulties of rapid tool wear and high processing cost, the poor surface quality control, and the low processing efficiency. Among them, the most important problem is that the hard and brittle property of ceramics is easy to produce cracks in the cutting process, which results in the decrease of cutting quality.
The hardness and brittleness of ceramics are relative concepts on the macro scale. When the cutting parameters are optimized, the cutting process can be improved to satisfy ductile material removal. The purpose of this research is to analyze the cutting mechanism of SiC ceramics using diamond tool on a machining center, to establish corresponding cutting models, to master the critical parameter interval of brittle-ductile transition, and to 月 optimize cutting parameters, so as to achieve high efficiency and high quality. The cutting mechanism of brittle-ductile transition has received much attention over the past two decades, especially on the experimental and investigation research. Goel [12] performed an experimental study on diamond turning of single crystal 6H-SiC on an ultra-precision diamond turning machine to elucidate the microscopic origin of ductile-regime machining.
They obtained fine surface finish better than any previously reported value on SiC while significant wear marks on the cutting tool was observed. Liang [13] performed an elliptical ultrasonic assisted scratching experiments and found material removal ratio in elliptical ultrasonic assisted grinding (EUAG) of mono crystal sapphire is increased in ductile-brittle transition region. It is prone to achieve ductile region with greater vibration amplitude in EUAG. Wang [14] presented an investigations of critical cutting speed on ductile-to-brittle transition mechanism by modelling and micrographs observation on chips, chip roots and finished surfaces. Simon [15] described an application of a "semi-elastic" machining method called shape adaptive grinding using an elastic tool combined with rigid pellets and super abrasives to finish aspheric mirror and reduce form error with no residual damage. And the mechanics driving brittle-ductile transition on finishing optical ceramic materials was more understood.
In addition to the research carried out by experimental methods, molecular dynamics studies have been conducted to investigate the atomicscale details of the cutting zone during the brittle-ductile cutting mode transition due to the difficulties in directly observing by experimental techniques [16]. The result verified by a plunge cutting experiment shows that tensile stress exists around the cutting zone and increases with undeformed chip thickness and finally induces brittle fractures.

Experimental set-up
The cutting test was carried out on a NC machining center VMC850e manufactured by Shenyang Machine Tool Group.
The machine tool and test equipment are shown in Fig. 1

Test workpiece and cutting tool
In the cutting test, the workpiece is SiC ceramic with size of 120 mm × 80 mm × 80 mm. The material properties of SiC ceramics and parameters of diamond tool are shown in Table 1. Table 1 Material properties and tool parameters [17] Material

Forces characteristics of SiC ceramics milling
By analyzing the combination of cutting forces in X and Y directions with cutting parameters of n=4000 r/min, fz=0.01 mm/z, ap=0.1 mm, it can be found that the X-Y plot of cutting forces is variable. The range of forces trajectory at the early cutting stage is large and discrete. In the later stage of cutting, the range of the trajectory in Y axis is larger. 月 the cutting force is close to the peak value of each tool tooth cycle, the force will be superimposed by the generation of brittle fracture. But, with the increasing of feed rate beyond the region of brittle-ductile transition, the proportion of brittle removal increases, and the cutting forces reduce.
(2) It is concluded that the increasing of spindle speed will soften the ceramics to improve the cutting load. One evidence is that the sinusoid-like forces signals are changed more stable and smoother from 2000 r/min to 4000 r/min, as shown in Fig. 4abc.  f e 月 ductile removal range, the number of frequency components at feed rate of 0.015 mm/z is more than that of 0.005 mm/z. The peak values of worn tool with feed rate of 0.015 mm/z are greater than that of 0.005 mm/z. And when the feed rate exceeds 0.015 mm/z to 0.02 mm/z, the frequency of worn tool, the number of the high frequency components of worn tool reduce, and the peak values decrease obviously. The peak frequency at 0.02 mm/z is obviously smaller than that of the other two parameters, and the difference between the first 3 orders is larger. These indicate that the material removal mode has changed.  Evidence shows that the region B in Fig. 9ab has a lot of tiny cracks on the machined surface. When the cutting depth decreases and relative larger spindle speed and feed rate with the parameters of n=3000 r/min，fz=0.015 mm/z，ap=0.1 mm, the machined surface shows no obvious micro cracking, such as region C in Fig. 9f. And both sides of the groove shoulders are integrity and no material spalling, as shown in Fig. 9d. The chips are powder chips with the same morphology as Fig. 9e shows.
The chips produced at the two sides of the groove shoulders are block chips formed by brittle fracture as shown in Fig. 9c.
Evidence of the forming of block chips is that the crack propagation in the cutting process is very easy to cause massive spalling due to the low bonding strength of SiC ceramics, especially at the shoulder of cutting groove, as region A shown in

Surface topography and roughness
Surfaces in three cutting tests with the same material removal rate of 192 cm 3 /min and different cutting parameters in Table 2 are compared in order to determine the effect of cutting parameters on the brittle-ductile transition [18]. Some researchers also used 3D profilometer [19] or SEM [20] to study the brittleductile transition of brittle materials cutting.
The cutting mechanism of SiC ceramics is different from plastic shear in metal cutting, but also different from the usual The surface roughness Sa and Sq increase linearly with the spindle speed increasing from 1000 r/min to 3000 r/min. When the spindle speed increases to 4000 r/min, the surface roughness increases, as shown in Fig. 10(a). The surface skewness coefficient increases and the kurtosis coefficient decreases monotonically with the spindle speed increasing from 1000 r/min to 3000 r/min while the skewness coefficient and kurtosis coefficient of surface greatly reduces when the spindle speed increases to 4000 r/min, as shown in Fig. 11 (a).
In the cutting test of varied cutting depth, Sq, Sa, Ssk increase with cutting depths changing from 0.05 mm to 0.15 mm (, while Sku decreases, as shown in Fig. 10 (b) and Fig. 11 Evidence shows that the material removal mode changes from ductile removal to brittle removal in this interval of spindle speed from 3000 r/min to 4000 r/min, cutting depth from 0.15 mm to 0.2 mm and feed rate from 0.015 mm/z to 0.02 mm/z.

Chip formation analysis based on stress-strain
The chip formation of metal cutting is simplified as shown in where, f(σ) is fracture probability; m is Webb coefficient, the greater the value, the smaller the probability of fracture; σ0 is characteristic stress; σ and σ' are the internal stress and its maximum value.
where, λ0 and μ0 are geometric constants related to materials properties; P is critical load, kW; l is crack length, μm; Kc is fracture toughness, which is a characterization to resistance material fracture; H is material's hardness.
The critical chip thickness of ceramics cutting can be extended from the critical indentation size in the indentation fracture mechanics [21] as shown in Eq.(4).
where, E is elastic modulus, GPa, K is the coefficient relate to critical chip thickness.
When the cutting thickness beyond the critical value of brittle-ductile transition, cutting of brittle materials produces significant volume expansion before broken and chip formation.
The strain produced by ceramic cutting under steady load tends to be inelastic and non-recoverable as Fig. 12c1 shows. It is difficult to describe the chip shape in the deformation of ceramic cutting.
The chip geometric of ceramics is different from the undeformed chip with no broken calculated in Eq. (1). The undeformed chip will crack under the deformation force as shown in Fig. 12c2.
These cracks tend to expand, causing chips to break suddenly in a very small form and further to fracture. Therefore, the cutting of ceramics will cause chips to break, and the broken chip will form powder like crystalline particles. Explain from the view of, the metal material is deformed by the loading force F (Fig. 12a4) in the elastic deformation stage as shown in stress-strain curve of Fig. 12a1. When the force F is unloaded, the material rebounds almost without deformation (Fig.   12a5). In the stage of plastic deformation in Fig. 12b1, the material deforms under the action of force F (Fig. 12b6). When the force F is unloaded, the material is partly rebound, but the overall deformation is larger than before loading (Fig. 12b7). The geometric of metal will change before fracture, and some phenomena can be used to predict fracture. But the ceramics will hardly deform before break, the fracture will happen in a flash and randomness difficult to predict. From the stress-strain curve of ceramics material, it is approximately consistent with Hooke's law when the stress produced by the loading force F is small, as shown in Fig. 12c1, and the material will not yield as there is no yield stage in the curve. When the loading force is beyond the critical force, material broken in the stage almost with no plastic deformation but break (Fig. 12c4). And the elongation is almost negligible.

Critical stability interval of brittle-ductile transition
Lawn and Marshall [21] proposed an empirical relationship model between the critical load and the crack length on the machined surface. The ductile material removal model of SiC ceramics milling with straight diamond tool can be seen as shown in Fig. 13. When the chip thickness h reaches a critical thickness of hc, the material begins to be removed from ductile to brittle. If the chip thickness is less than the critical thickness, material removal mode can be considered as ductile removal. Conversely, it tends to brittle removal and initial cracks will generate. When the cracks generate, it will extend to the ceramics surface and result in processing defective. The conditions to achieve the ductile cutting of SiC ceramics [17,24] The relationship between cutting parameters such as feed rate and radial depth of cut and ductile -brittle transition is concluded in Fig. 14. (1) When the feed rate and depth of cut are much smaller than the critical value, the interaction between abrasive grain and workpiece is shown as ploughing.
(2) When the feed rate and depth of cut are smaller than the critical value but not much smaller, the material are removed as ductile removal.
(3) When the feed rate is larger than the critical depth of cut and critical feed rate, the cutting cracks will generate. The mechanism of crack formation during ceramics cutting is the same as that of indentation fracture mechanics.
(4) When the feed rate and cutting depth satisfy that one of the parameters is smaller than the critical value and the other is higher than the critical value, brittle and ductile removal exist simultaneously. In addition, when any parameter is greater than the critical value, the material removal includes brittle removal thickness and plastic removal thickness. The fracture of ceramics materials is a combination of material properties and external loads, and undeformed chip morphology.

Determination of brittle-ductile transformation region
The ceramics cutting generally have different degrees of micro cracks appear [26,27]. The fracture strength of brittle materials does not depend on the number of microcracks, but depends on the length and depth of microcracks. When the crack size exceeds a certain value, it will expand rapidly. Table 3 shows the tendency of material removal mode transition with cutting parameters increasing according to the experimental data. With the increasing of spindle speed, cutting depth and feed rate, the effect of material strain hardening increases and strain softening decreases. As a result, the material removal mode changes from ductile to brittle.  Table 4 gives a comparison of the determination of the brittle-ductile transition region of SiC ceramics obtained by surface detection and processing signals. The critical interval of feed rate is 0.015 mm/z -0.02 mm/z. The critical interval of cutting depth is 0.15 mm -0.2 mm, and the cutting depth will lead to material breakage when the tool wear to a certain extent, such as less than 0.05 mm. Spindle speed in the interval of 3000-4000 r/min shows a slight change, but combined with other means of analysis, it cannot clearly determine the critical interval of spindle speed.

Conclusion
(1) An experimental study using diamond tool for SiC ceramics milling was carried out. It is found that the brittle-ductile transition of SiC ceramics cutting is existed. Better surface integrity of milling ceramics can be controlled in the ductile cutting, while surface defects such as cracks, spalling of materials, or pores can be found on the brittle removal surfaces.
(2) The proportion of the two kinds of material removal mode will determine material removal difficulty and surface quality. (3) It is found that the cutting force in Z axial direction is the main cutting force. The cutting force of brittle materials is related to the proportion of brittle-ductile removal. The wearing tool is easy to cause brittle removal, where the signal of cutting force in frequency domain has more frequency related to spindle rotation.
The cutting process is usually accompanied by the fracture of ceramics materials, chip spalling, and tool impacting. With the increasing of cutting volume, the tool edges are worn into arc shape. The wear area increases sharply when material removal volume exceeds 3000 mm 3 .