Effect of grain refinement on cutting force of difficult-to-cut metals in ultra-precision machining

Renjie JI, Qian ZHENG, Yonghong LIU, Hui JIN, Fan ZHANG, Shenggui LIU,Baokun WANG, Shuaichen LU, Baoping CAI, Xiaopeng LI

College of Mechanical and Electronic Engineering, China University of Petroleum (East China), Qingdao 266580, China

KEYWORDS Grain size;Cutting force;Difficult-to-cut metals;Grain refinement;Ultra-precision machining;Cou-pled ultrasonic and electric pulse treatment

Abstract The nickel-based superalloy Inconel 718 is treated with Coupled Ultrasonic and Electric Pulse Treatment (CUEPT), and the surface grain is refined from the average size of 9550.0 nm to 287.9,216.3,150.5,126.3,25.8 nm by different effective treatment currents,respectively.The ultraprecision turning experiments are carried out on the processed workpiece after CUEPT.The experimental results show that the average cutting force increases with the decrease of surface grain size.Moreover, a mathematical model that can describe the relationship between grain size and cutting force is established, and the calculated results match the experimental results well. The calculated results also indicate that the variation of cutting force caused by the same variation of grain size decreases as the degree of grain refinement increases. Finally, the influence mechanism of grain refinement on cutting force is analyzed. The improvement of stability of grain boundaries and the increase of number of grain boundaries cause the increase of cutting force after grain refinement.

1. Introduction

Recently, difficult-to-cut metals such as titanium alloy and superalloy are widely used in aviation, automobile, nuclear power and other fields due to their excellent physical and mechanical properties.To improve the machinability of difficult-to-cut metals, some methods such as Ultrasonic Vibration Assisted (UVA) cutting,cryogenic cuttingand Laser Assisted Machining(LAM)have gradually attracted the interest from researchers, and lots of researches have been conducted.

UVA cutting applies high-frequency ultrasonic vibration to the tool or workpiece.The tool periodically cuts and leaves the workpiece during UVA cutting, which can reduce the cutting force and friction and improve the machinability of difficultto-cut metals.Zhang and Wangconducted conventional cutting and UVA cutting experiments for Ti6Al4V.The results showed that UVA cutting effectively reduced the cutting force,stress, temperature and tool wear, which can improve the machinability of Ti6Al4V. Cryogenic cutting mainly applies uses nitrogen disturbed flow system to reduce the temperature of the cutting part, which can improve the machinability of difficult-to-cut metals and enhance the machining precision and surface quality of parts.Bordin et al.conducted cryogenic cutting experiments on Ti6Al4V. They investigated the effects of cutting speed and feed rate on the surface integrity,chip morphology and tool wear. The results showed that the cryogenic cutting effectively improved the surface quality and chip fragility and enhanced the machinability of Ti6Al4V.Researchers carried out a series of cryogenic cutting experiments on titanium alloy TC4.They found that cryogenic cutting can effectively reduce the cutting temperature, cutting force,surface roughness,tool wear and the microscopic defects of material. Pusavec et al.and Kenda et al.conducted the liquid nitrogen ultra-low temperature machining experiments of Inconel 718,and they found that ultra-low temperature processing technology can increase the residual compressive stress and hardness of the workpiece surface,thus improving the fatigue life and abrasive resistance of the workpiece,extending the tool life and reducing the roughness of the machined surface.The high-energy laser beam during LAM enables the workpiece to reach the optimal softening cutting temperature before it is removed, which can facilitate the plastic deformation of material during cutting and reduce the cutting force, surface roughness and tool wear. As a result, LAM can enhance the machinability of the material and it has been widely used in the machining of difficult-to-cut metals.Bejjani et al.investigated the laser-assisted turning of Titanium Matrix Composites (TiMMCs). They found that LAM increased the tool life by 80%, which indicated that the machining efficiency of TiMMCs was improved and the machinability was enhanced.Wu et al.and Hedberg et al.conducted laser assisted milling for superalloy GH4698 and titanium alloy Ti6Al4V.They found that laser assisted milling can effectively reduce the cutting force, surface residual stress and roughness. Zhao et al.proposed a laser-induced oxidation assisted micromilling compound process. Nanosecond laser was applied to induce the oxidation of cemented carbide WC-20% Co, and loose oxide which could be easily removed was produced,thus reducing tool wear during micro-milling of cemented carbide and improving surface quality.

The above methods improve the machinability of difficultto-cut metals by changing the experimental conditions such as cutting temperature, ultrasonic frequency, laser power, etc.However, the effect of grain size on machinability is not considered. In the process of metal cutting, especially in ultraprecision turning, the grain size is usually equivalent to the thickness of the uncut chip and the single grain is removed in the direction of cutting depth. The microstructure of the material will mainly affect the machining performance because grain boundary effect and dislocation distribution can influence the removal of grains.Therefore,it is of great importance to investigate the effect of grain size on machinability.

Researchers investigated the effect of grain refinement on the machinability of nickel-based superalloy K4169.The grain sizes of 3170,2870,2670,1650,81,73 μm were obtained by different processes of casting fine grain. They found that grain refinement can reduce milling force by more than 50%and effectively reduce surface roughness, which indicated that grain refinement can effectively improve the machinability of K4169. Wu et al.investigated the influence of the grain size of oxygen-free copper on the cutting force in micro-cutting.The grain sizes of 20 μm and 60 μm were obtained by two different recrystallization annealing treatments. The results showed that both cutting force and specific cutting energy increased with the decrease of grain size. Wanginvestigated the influence of grain size of pure copper on cutting characteristics and surface integrity. By rolling and heat treatment, the T2 pure copper workpieces with grain sizes of 360 μm,145 μm and 45 μm were obtained at different annealing temperatures.The results showed that both strengthening of grain boundary and main cutting force increased with the decrease of surface average grain size. Therefore, the grain size had a significant effect on the machinability of the material.Komatsu et al.investigated the effect of grain size on the cutting process of stainless steel in micro-milling. Ultrafine grain stainless steel with an average grain size of 1.52 μm was obtained by repeated plastic deformation and inverse phase transition. Besides, the cutting force and surface quality of ultrafine grain steel were compared with those of ordinary grain steel.It was found that the cutting force had no obvious change and the shear force became smaller after grain refinement.The results also showed that reducing grain size can control formation of burr and improve surface quality.

The above researches mainly discussed the effect of grains with micron size on the machinability of metallic materials by experiments. However, nano-metallic materials have excellent properties due to their fine microstructure and they are increasingly widely used in electronics, aviation and other fields.The crystal structure of nano-metallic materials is obviously different from that of metallic materials with micron-sized grains due to their extremely small grain size,large amount of boundary structure and high volume fraction of grain boundaries.Besides,nano-metallic materials also have some special effects such as small-size effect, surface effect,interface effect, etc. The differences in the microstructure and those special effects have a noticeable impact on the processing of nano-metallic materials,which makes the machining process of nano-metallic materials greatly different from that of metal materials with micron grain size.

Therefore, it is significant to investigate the machinability of difficult-to-cut metals when the grain size is refined to nanoscale. In this paper, the surface grain size of the nickelbased superalloy Inconel 718 is refined to nanoscale by Coupled Ultrasonic and Electric Pulse Treatment (CUEPT).Most importantly, the effect of grain refinement on cutting force in ultra-precision machining is investigated by mathematical modeling and theoretical analysis, and the relevant results are obtained.

2. Materials and experimental procedures

The chemical composition of Inconel 718 used in the experiments was examined with an electron probe microanalyzer(EPMAJEOL JXA-8230, Japan), and the results are shown in Table 1. The diameter of the sample was 20 mm. As shown in Fig. 1, the average grain size (D) of matrix material of Inconel 718 was 9550 nm.

The samples were processed on the self-developed equipment of CUEPT. The schematic diagram of CUEPT is shown in Fig. 2. As shown in Fig. 2, the workpiece rotated along its axial direction with the velocity V. Meanwhile, the treatment tool acted on the cylindrical surface of the workpiece and slidalong the cylindrical axis with the velocity V. It can be observed from Fig.2 that, during CUEPT, the workpiece surface was acted by both the force and the heat from tool impacting. The thermal impacting can raise the temperature at the touch point to the expected value rapidly, which can make the material plasticity at the touch point increase, the plastic zone is generated rapidly, and then the ultrasonicfrequency mechanical impacting can cause the severe plastic deformation at the plastic zone, so the grain can be refined at the plastic region. The ultrasonic frequency and amplitude of CUEPT were 26 kHz and 10 μm, respectively. The pulse current was provided by the self-developed pulsed power supply. The electrical parameters used during CUEPT are shown in Table 2. In addition, the cooling water was used during treatment and CUEPT experiments were repeated 10 times for every sample.

Table 1 Chemical composition of Inconel 718.

Fig. 1 Average grain size of matrix material.

Fig. 2 Schematic diagram of CUEPT equipment.

The ultra-precision turning experiments were carried out with a machine tool (Nanotech 350FG). The spindle speed was 150 r/min,the cutting depth was 4 μm,and the feed speed was 4 mm/min.The blade edge radius of Cubic Boron Nitride(CBN) turning tool was 0.610 mm, the rake angle was 0° and the front clearance angle was 15°. The cutting force was measured by a dynamometer (Kistler9252A). The microstructure of the treated workpiece was observed by a Transmission Electron Microscope(TEM,TECNAI G2 F20 S-Twin).The grain statistics of all TEM graphs were performed by Gatan Digital Micrograph software. Besides, the Electron Backscatter Diffraction (EBSD) analysis was conducted by a thermal field emission scanning electron microscope (JEOL JSM-7001F,JEOL Ltd.), fitted with an EBSD analysis apparatus (TSL Incorporated, USA).

Fig. 3 illustrates the surface average grain size at different effective currents. Fig. 4(a) shows the cutting force obtained at different effective currents during ultra-precision turning,and the average cutting force shown in Fig. 4(b) is obtained from Fig. 4(a). As shown in Fig. 3, the average surface grain size is 287.9,216.3,150.5,126.3,25.8 nm with the effective currents of 0,100,150,200,260 A,respectively.The surface average grain size decreases with the increase of effective current.It can be seen from Fig. 4 that the average cutting force during ultra-precision machining is 7.8, 8.4, 8.9, 10.4, 10.8 N with the effective currents of 0, 100, 150, 200, 260 A, respectively.The cutting force increases with the increase of effective current. By comparing Fig. 3 with Fig. 4, it can be seen that the average cutting force increases as the degree of grain refinement increases.

According to the cutting force and the average grain size shown in Figs.3 and 4,the results of cutting force and average grain size were similar at the effective current of 100 A and 150 A.Similarly,the results of cutting force and average grain size were similar at the effective current of 200 A and 260 A.For the sake of effective conciseness, the results of cutting force and average grain size at the effective current of 0, 150,260 A were chosen for subsequent analysis.

3. Modeling and analysis of relationship between grain size and cutting force

Combined with the range of grain size in the Hall-Petch relationship,the range of grain size is from 20 nm to a few microns. The cutting force model is shown in Fig. 5.

In Fig. 5, the resultant force F can be expressed as

Table 2 Electrical parameters used during CUEPT.

Fig. 3 TEM observations of material surface with different effective currents.

where bis the cutting depth;h is the cutting thickness;τis the shear stress;φ is the shear angle;ψ is the angle between the cutting force F and the shear force F.

According to the geometric relationship in Fig.5,the angle ψ can be expressed as

where βis the average friction angle; αis the rake angle of tool.

Fig. 4 Cutting force and average cutting force at different effective currents.

Fig. 5 Cutting force model and force diagram of grains.

It is supposed that the shear stress τand the applied stress τ have the relationship

MATLAB software is used to calculate the established D-F model.The values of parameters used in the calculation are shown in Table 3 and the results of calculation are shown in Fig. 6.

The experimental values of average cutting force at different effective currents were substituted into the D-F model to obtain the calculated value of the surface average grain size.The calculated values in comparison with the experimental values are presented in Table 4. It can be seen that the relative error is about 10%, which indicates that the calculated values match the experimental values well. As a result, the D-F model derived is feasible and reasonable in the range of average grain size from 20 nm to several microns.

Moreover, it can be seen from Fig. 6 that the cutting force increases with the decrease of surface average grain size, and the degree of grain refinement gradually increases with the increase of effective current. In addition, it can also be seen that as the degree of grain refinement increases, the slope of the curves increases and the variation of cutting force caused by the same variation of grain size decreases.Therefore, a larger current should be selected as far as possible within the reasonable current range in the actual work,which can reduce the fluctuation of cutting force, improve the stability of machining and enhance the machinability.

4. Influence mechanism of grain refinement on cutting force

The influence mechanism of grain refinement on cutting force has been discussed from the stability and the number of grain boundaries.The stability of grain boundaries after grain refinement has been analyzed by the proportion of low-angle grain boundaries and low-Σ Coincident Site Lattice (CSL) grainboundaries. Σ is the multiplicity index, which is defined as the ratio between the crystal lattice site density of the two grains meeting at the grain boundary and the density of sites that coincide when superimposing both crystal lattices. Low-energy grain boundaries are highly resistant to grain boundary sliding,intergranular cavitation, fracture and local corrosion,so the stability of low-energy grain boundaries is higher.The proportion of low-angle grain boundaries and low-Σ CSL grain boundaries has an important influence on the stability of grain boundaries because they are both low-energy.

Table 3 Values and description of parameters.

Fig.6 Relationship between average grain size and cutting force at different effective currents.

Table 4 Comparison between calculated and experimental values of average grain size.

As is well-known, the grain boundaries are low-angle boundary while misorientation angle θ < 15° and the grain boundaries are high-angle boundary while θ > 15°.Some investigations have indicated that the low-angle grain boundaries have lower energy than high-angle grain boundaries.Fig. 7 shows the distribution of misorientation angle and its mean value at different surface average grain sizes.

It can be obtained from Fig. 7(a) that the proportion of low-angle grain boundaries is the lowest 12.8% at the surface average grain size of 287.9 nm. It can also be obtained from Fig. 7(b) and (c) that the proportion of grain low-angle grain boundaries increases obviously at the surface average grain sizes of 150.5 nm and 25.8 nm, both of which are 33.9%. As a result, the energy of grain boundaries is the highest and the grain boundaries are the most unstable at surface average grain size of 287.9 nm. Although the proportion of low-angle grain boundaries at the surface average grain sizes of 150.5 nm and 25.8 nm are the same,the average misorientation angle at the surface average grain size of 25.8 nm is smaller,which indicates that the energy of grain boundaries is the lowest and the grain boundaries are the most stable at the surface average grain size of 25.8 nm.

Fig. 8 shows the distribution of low-Σ CSL grain boundaries (Σ ≤29) at different surface average grain sizes, and different colors represent different types of low-Σ CSL grain boundaries. Moreover, the lower the Σ-value is, the lower the energy of CSL grain boundaries is and the higher the stability of grain boundaries is.It can be obtained from Fig. 8 that the total proportion of low-Σ CSL grain boundaries is 64.8%,67.4%and 71.7%and the proportion of ΣCSL grain boundaries is 62.1%,64.7%and 69.3%at the different surface average grain sizes of 287.9, 150.5, 25.8 nm, which indicates that the energy of grain boundaries is the highest and lowest at the surface average grain size of 287.9 nm and 25.8 nm,respectively. It can be concluded that the proportion of low-Σ CSL grain boundaries and ΣCSL grain boundaries increases with the decrease of surface grain size, which indicates that the grain boundaries become more stable after grain refinement. In summary, the energy of grain boundaries decreases successively at the surface average grain sizes of 287.9, 150.5, 25.8 nm, and the grain boundaries become gradually stable with the decrease of surface average grain size.

Fig. 7 Misorientation angle and its mean value at different surface average grain sizes.

The number of grain boundaries with different surface average grain sizes can be obtained from the EBSD results.Fig. 9 shows the distribution and number of grain boundaries at different misorientation angles and surface average grain sizes. It can be obtained from Fig. 9 that the number of grain boundaries is 261534, 264662 and 366759 at the different surface average grain sizes of 287.9, 150.5, 25.8 nm, respectively.The results show that the total number of grain boundaries within the same area increases with the decrease of surface average grain size.

Fig. 8 Distribution and proportion of low-Σ CSL grain boundaries (Σ ≤29) at different surface average grain sizes.

Fig. 9 Distribution and number of grain boundaries at different surface average grain sizes.

Fig. 10 Schematic diagram of damaged grain boundaries of grains with different sizes during cutting.

From Figs. 7–9, the energy of grain boundaries decreases gradually with the decrease of surface average grain size. As the energy of the grain boundaries decreases,the grain boundaries become stable.The more stable the grain boundary is,the less likely it is to be broken during cutting,so the required cutting force increases. Moreover, as shown in Fig. 10, the number of grain boundaries in the same area increases because of grain refinement, which causes that the number of broken grain boundaries increases. Thus, the required cutting force increases. In conclusion, the improvement of stability of grain boundaries and the increase of number of grain boundaries make the cutting force increase after grain refinement.

5. Conclusions

The surface grain size of the nickel-based superalloy Inconel 718 was refined to nanoscale by CUEPT.The influence of grain refinement on the cutting force was investigated and the influence mechanism of grain refinement on the cutting force was analyzed. The main conclusions are drawn as follows:

(1) Based on the experimental findings, the D-F model is proposed to describe the relationship between grain size and cutting force, which matches the experimental results well.

(2) Both experimental and computational results show that the cutting force increases as the average grain size decreases within grain size range from 20 nm to a few microns. Besides, as the degree of grain refinement increases, the variation of cutting force caused by the same variation of grain size decreases.

(3) As a result of grain refinement, the grain boundary becomes stable as the energy of grain boundaries decreases and the total number of grain boundaries in the same area increases.With the improvement of stability of grain boundaries and the increase of number of grain boundaries, the cutting force increases after grain refinement.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This research is supported by National Natural Science Foundation of China (No. 51875579), the Fundamental Research Fund for the Central Universities, China (No.19CX02023A), the Major Research Project of Shandong Province,China(No.2019GGX104068),the Science and Technology Support Plan for Youth Innovation of Universities in Shandong Province, China (No. 2019KJB016), and Source Innovation Project of Qingdao West Coast New Area, China(No. 2020-82).