Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 © 2017 Journal of Mechanical Engineering. All rights reserved. D0I:10.5545/sv-jme.2017.4443 Original Scientific Paper Received for review: 2017-03-10 Received revised form: 2017-06-19 Accepted for publication: 2017-09-07 Modelling of the Relationship of Adiabatic Shear and Cutting Conditions for Higher Cutting Speed Ranges Guohe Li* - Yujun Cai - Houjun Qi - Meng Liu Tianjin University of Technology & Education, Tianjin Key Laboratory of High-speed Cutting & Precision Machining, China The serrated chip is a typical characteristic of high-speed cutting due to the occurrence of adiabatic shear. Based on an adiabatic shear sensitivity index proposed via linear perturbation analysis, which considers the pressure-shear condition in machining, the relationship of adiabatic shear and cutting conditions is established. The corresponding relation between the cutting conditions and the deformation conditions is established based on the model of a parallel boundary shear zone. The influence of cutting parameter on adiabatic shear is analysed, and the results show that the adiabatic shear in high speed machining tends to occur under the condition of higher cutting speed, greater depth of cut and smaller rake angle. An orthogonal cutting experiment was performed to validate the proposed model. Furthermore, the influence mechanism of cutting conditions on adiabatic shear is discussed in detail, and one application of the model is introduced. Keywords: high speed machining, adiabatic shear, linear perturbation analysis, cutting parameter Highlights • The relationship of adiabatic shear and cutting conditions was established. • The influence of cutting parameter on adiabatic shear is analysed. • An orthogonal cutting experiment was carried out to validate the proposed model. 0 INTRODUCTION High-speed machining (HSM) has a series of advantages, such as smaller cutting force, higher precision, better surface quality, higher productivity, lower cost, and it can be used for difficult-to-process materials. Therefore, it is extensively applied in the fields of aerospace, automotive and moulding, etc., and is widely used [1]. The main difference between high speed cutting and conventional cutting is that the serrated chip is often produced in high speed cutting [2] and [3], and the continuous chip is produced in conventional cutting. Fig. 1 shows diagrams of a continuous chip and serrated chip. Although some scholars ascribed the occurrence of serrated chips to a periodic crack initiated in the free surface of the work-piece ahead of the tool [4] and [5]. Other researchers, including Recht [6], Komandui [7], Davies [8], Molinari [9] and Ma [10], attributed the formation of serrated chips to a repeated thermo-plastic instability occurring in the primary shear zone, particularly for ductile materials [2] and [11]. On one side, the occurrence of adiabatic shear in high speed cutting will increase the tool wear and influence the quality of the finished surface. On the other side, it is beneficial to the rupture of chip and favourable automation machining. Therefore, in order to control the cutting process effectively, more attention should be paid to the adiabatic shear localization in HSM. Fig. 1. Sketch map of chip: a) continuous chip, and b) serrated chip Extensive research has been conducted on adiabatic shear in the machining of various materials. Sun et al. [12] examined the chip formation during the dry turning of Ti6Al4V in association with dynamic cutting force measurements under different cutting speeds, feed rates, and depths of cut. Huang et al. [13] carried out the perturbation analysis of thermo-viscoplastic instability in chip formation to establish the relation for the segment spacing which was obtained by multiplying the chip flow velocity by the characteristic time of instability. Duan and Zhang [14] presented an in-depth investigation into the formation mechanisms and microstructures of adiabatic shear bands (ASBs) in hardened AISI 1045 steel induced by HSM. A systematic analysis, both experimental and theoretical, showed that a low cutting speed leaded to deformed ASBs, and a high cutting speed resulted in transformed ASBs. Molinari et al. [15] investigated the role of cutting conditions on adiabatic shear banding and chip serration by combining *Corr. Author's Address: : Tianjin University of Technology & Education, Tianjin Key Laboratory of High-speed Cutting & Precision Machining, China, lgh790723@126.com 673 Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 finite element calculations and analytical modelling. Miguelez et al. [16] focused on the numerical analysis of adiabatic shear banding in orthogonal cutting of Ti6Al4V alloy. The influence of cutting velocity and feed in chip segmentation was studied. Moreover, the role of friction at the tool-chip interface and the effect of rheological parameters of the constitutive equation were analysed. Gu et al. [17] investigated the damage evolution mechanism of adiabatic shear localized fracture (ASLF) in chip formation under an optical microscope and scanning electron microscope (SEM) through an HSM experiment of hardened AISI 1045 steel at a relatively high cutting speed. They further investigated the induced mechanism of adiabatic shear fracture and the corresponding damage process in high-speed machining through quick-stop tests and chip morphology examinations [18]. On the basis of saturation limit model, the critical fracture energy was predicted by cutting conditions and compared with the experimental results. Ye et al. [3] set up an experimental device, based on the light-gas gun technology, to realize high speed cutting over a wide range of cutting speed from 30 m/s to 200 m/s. Highspeed cutting experiments were performed on AISI 1045 steel. The investigation of chip morphology, micro-structure, micro-hardness and the finished surface integrity were carried out. Furthermore, they performed the cutting experiments on Ti6Al4V alloy over a wide range of cutting speed [19]. The transition of chip morphology from continuous to serrated was observed with increasing the cutting speeds. A new theoretical model was developed to predict the segment spacing, in which the momentum diffusion due to unloading within the shear band had been considered. They also proposed an explicit expression of the critical cutting speed for the onset of serrated chip flow, which is given in terms of material properties, uncut chip thickness and tool rake angle, based on dimensional analysis and numerical simulations. It could give reasonable predictions of the critical cutting speeds at which chips change from continuous to serrated chip for various metallic materials over wide ranges of uncut chip thickness and tool rake angle [20]. Recently, Ye et al. [21] systematically analysed the experimental results of high-speed cutting on various typical metallic materials over wide ranges of cutting speeds. By considering the coupling effects of inertial, tool-chip compression and material convection, the critical condition for the onset of serrated chip flow was determined based on a stability analysis of the deformation inside the primary shear zone. It is found that the emergence of the serrated chip flow is dominated by a dimensionless number that characterized the competition among the effects of inertia, thermal softening, strain hardening, elastic unloading, viscous diffusion and thermal diffusion. Wang et al. [22] studied the formation condition of continuous and saw-tooth chips and various characteristics of the saw-tooth chip, such as cutting speed, feed rate, axial depth of cut, and others. The results showed that the chip of materials with different hardness could be controlled to the continuous chip through the optimization of a combination of cutting speed, feed per tooth, and depth of cut. Wu and Sandy [23] investigated the cutting mechanism of a new emerging high temperature and high strength titanium alloy named TC21 using the finite element method (FEM), a modified high temperature split Hopkinson pressure bar (SHPB) test system was employed to obtain the stress-strain curves of TC21 alloy under different temperatures and strain rates. Jomaa et al. [24] developed a 2D FEM based on a Lagrangian approach for simulating and analysing the serrated chip formation during HSM of the AA7075-T651 alloy. Wang and Liu [25] presented an investigation of chip morphology from the viewpoint of a chip-free surface and cross-section. The research showed that the microstructure of chip-free surface evolves from lamellae to folds and then to dimples. According to the experimental results, a new model of serrated chip formation based on mixed mode of ductile fracture and adiabatic shear was proposed. They further investigated the influence mechanism of stress triaxiality on the serrated chip formation during HSM [26]. The fracture loci of ASBs in serrated chips under different cutting speeds have been obtained and validated by experimental results. The research has proven that the stress triaxiality plays a vital role in serrated chip formation during HSM. They also found that the chip serrated frequencies for the two work-piece materials during HSM are found to be nearly equal to their corresponding AE-dominant frequencies [27]. These pioneering works give important indications to study the influence of cutting parameters on adiabatic shear in HSM. In the next section, the pressure-shear stress state of the primary shear zone to build the continuum mechanics basic equations of machining is considered. An adiabatic shear sensitivity index is proposed by linear perturbation analysis. In Section 2, the model of deformation conditions in shear plane AB based on the model of parallel boundary shear zone is presented so as to build the corresponding relations between the deformation conditions and the cutting parameters of orthogonal cutting (i.e. cutting speed, depth of cut, and rake angle). In Section 3, AISI 1045 steel is taken as an 674 Li, G. - Cai, Y. - Qi, H. - Liu, M. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 example to analyse the influence of cutting parameter on adiabatic shear according to the adiabatic shear sensitivity index. An orthogonal cutting experiment was carried out and the changes of chip with cutting parameters were shown to validate the analysis results in Section 4. The influence mechanism of cutting parameters on adiabatic shear is discussed in detail in Section 5. The concluding remarks of the paper are Section 6. Fig. 3. Stress state of the primary shear zone 1 ADIABATIC SHEAR SENSITIVITY INDEX It is usually thought that the deformation in HSM is a plane strain because the width of cut aw is far greater than the depth of cut ac. Stable cutting is assumed and the built-up edge is neglected. The narrow zone in Fig. 2, named as CAEFBD, is the primary shear zone with length of 2l and width of 5. Where the CD plane and EF plane are the upper and lower boundaries of the primary deformation zone respectively. The AB plane in the middle of the primary deformation zone, is the shear plane. The deformation in each plane that is parallel to AB is homogeneous. The inclination between the shear plane AB and cutting speed V is the shear angle y1 is the rake angle of cutting tool. rCD , rAB and rEF, are the shear stress of CD, AB, and EF plane, respectively. aAB is the compression stress of shear plane AB. Fr is the cutting force. Fs and Fm are the component forces along and perpendicular to the shear direction, respectively. Fr' is the reaction force of Fr . Ff, and Fn are the friction force and pressure force on rake face. Therefore, there is a pressure-shear stress state in the primary deformation zone, as shown in Fig. 3. According to the stress state of the primary deformation zone, the basic foundations of continuum mechanics in HSM for the coordinate system in Fig. 3 are as follows, P P dt dVy_ dt T dy < dy (1) dT , d T dVy dvz pc-= k-- + ßfo pc2Q0 > 1. (6) Eq. (6) shows that the influence factors of adiabatic shear in HSM are material characteristics and deformation conditions. The value of parameter B reflects the degree of adiabatic shear evolution and can be taken as the adiabatic shear sensitivity index. The deformation condition of HSM is determined by cutting parameters. If the corresponding relations between the cutting parameters and the deformation conditions can be established, the relationship between cutting parameters and adiabatic shear can be given. 2 MODEL OF DEFORMATION CONDITION IN THE PRIMARY SHEAR ZONE We can use the method of lattice line or streamline to get the distribution of strain rate in machining. The analysis results of these two methods showed that the distribution of the strain rate in the primary shear zone nears to a quadratic curve [29] and [30], as shown in Fig. 4. If the coordinate of Fig. 5 is adopted, the strain rate distribution in the primary shear zone can be expressed as follows: Hz) = 2aV sin^ [(s/2 - z )2 + (s/2)2 ] (7) a = - 16 sin tgy1 + ctgfy) f v v= 2.6 m/s r»=20° / a, = 0.26 mm / 1.4 m/s\° /-t/ 0.5 nvs\ \ 0.1 m/s0"^^^. " " i "—* , -10 -8 -6 -4 -2 2 4 6 8 AB Distance to the AB plane x0.023 [mm] Fig. 4. Strain rate distribution From Fig. 4, we can see that the strain rate of AB plane is maximum. According to the adiabatic shear theory, the adiabatic shear should occur in AB plane first. Therefore, in this paper, the deformation conditions of AB plane are taken as that leads to the adiabatic shear in HSM. On the AB shear plane, z = s/2, so the strain rate of AB plane can be calculated as follows: Yab = 2aV sin< s s 2 2 2V sin + ß - ft ). (15) (16) Thus, the compression stress can be expressed as follows: Fns Fr sin(^ + ß - y )sin $ A ~ A ~ a= =f tg (p+ß-7l). (17) According to Merchant's formula of shear angle, there is, $ + ß-yl =n /4. (18) Therefore, the expression of compression stress becoming, ^AB =TAB, (19) where Tab = f(YabYabTab) and can be calculated by a constitutive relationship. Modelling of the Relationship of Adiabatic Shear and Cutting Conditions for Higher Cutting Speed Ranges 677 Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 3 INFLUENCE OF CUTTING PARAMETERS ON ADIABATIC SHEAR IN HSM Now, the influence of cutting parameters on adiabatic shear in HSM can be analysed based on the model proposed. Where AISI 1045 steel is taken as an example and its constitutive relationship is expressed by the Johnson-Cook model, considering that the t =a /V3 and y=43s , its expression is as follows, 1 + C ln fr [1 - (T ' )m ], (20) where A, B, C, n and m are parameters of constitutive relationship and their value are shown in Table 1 [35], Yr is the reference strain rate. T * = (T - Tr) / (Tm - Tr) is the homogenization temperature, Tr is room temperature and Tm is melting point. The density of AISI 1045 steel is 7860 kg/m3, and its melting point is 1460 °C. The heat capacity and thermal conductivity are functions of temperature and can be calculated by, c [jkg-1K-1 ] = 420 + 0.5047 [°C], (21) k [ Wm-1K-1 ] = 45.48 - 0.02037 [°C]. (22) Table 1. Parameters of J-C constitutive relation for AISI 1045 steel Constitutive parameters A [MPa] B [Mpa] C. n m value 553.1 600.8 0.0134 0.234 1 The influences of cutting parameters, including cutting speed, depth of cut, and rake angle, are analysed. Each time one parameter is changed to study its effect while others are fixed and the results are shown in Fig. 7. Fig. 7a gives the influence of cutting speed on adiabatic shear. It can be seen that the adiabatic shear will occur when the cutting speed is larger. The influence of depth of cut is similar with that of cutting speed, as shown in Fig. 7b. Fig. 7c indicates that the adiabatic shear will appear easier when the rake angle is smaller. At the same time, the influence of cutting speed is the biggest, the influence of depth of cut is the second, and that of rake angle is the least. The influence mechanism of these phenomena will be discussed in Section 5. 4 EXPERIMENT VALIDATION An orthogonal cutting experiment was carried out for the validation of the prediction results. The work-piece is a cylindrical tube of AISI 1045 steel with an inside diameter of 151.75 mm and thickness of 2.5 mm. Fig. 8 shows the experiment device. A cemented carbides YT15 cutting tool (TCMT110204 insert and STFCR1616H11 holder) was adopted. The experiment was done on a CA6140 lathe by dry cutting. The tool was replaced after each experiment for keeping the tool sharp. The range of cutting speed of V = 48.7 m/ min to 480.7 m/min, three depths of cut of ac = 0.11 mm, ac = 0.15 mm and ac = 0.2 mm; three rake angles of y1 = 10°, Yj = 0°, and y1=-10° were selected as the cutting conditions. (a) 1. 6 1. 4 s- « II 1-2 C ■S 'I 1 11 0.8 < § * 0.6 0. 4 v j = 0 ° ac = 0.15 mm 100 200 Cutting speed V [m/min] 300 (b) 1. a 1- I1' .2 -o < s O.i 0. 0. Y\ =0 ° V = 240.3 m/min 0. 1 0. 2 Cutting depth a, [mm] V = 240.3 m/min ac = 0.11 mm 0. 3 0. 9 -10 10 -5 0 5 Rake angle y \ [°] Fig. 7. Influence of cutting conditions on adiabatic shear in HSM: a) influence of cutting speed, b) influence of depth of cut, and c) influence of rake angle The collected chip was fixed vertically in the admixture of epoxy resins and solidified agent (ratio 678 Li, G. - Cai, Y. - Qi, H. - Liu, M. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 is 1:1) and then the samples (as shown in Fig. 9) were ground to the midsection of the chip. A Neuphot-II type optical microscope was used to observe the chip after grinding, polishing, and eroding. Fig. 8. Experiment device Fig. 9. Observation sample The influences of cutting conditions on chip morphology are shown in Figs. 10 to 12. It is clear that larger cutting speed, greater depth of cut and smaller Fig. 10. Influence of cutting speed (y1 = 0°, ac = 0.15 mm: a) V = 96.1 m/min, b) V = 151.4 m/min, and c) V = 240.3 m/min) Fig. 11. Influence of depth of cut (y1 = 0°, V = 240.3 m/min: a) ac = 0.07 mm, b) ac = 0.11 mm) Fig. 12. Influence of rake angle (V = 240.3 m/min, ac = 0.11 mm: a) y1 = 10°, b) y1 = -10°) Modelling of the Relationship of Adiabatic Shear and Cutting Conditions for Higher Cutting Speed Ranges 679 Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 rake angle will promote the occurrence of adiabatic shear and lead to the forming of serrated chips. These are consistent with the analysis results and show the effectiveness of the proposed model. 5 DISCUSSION The adiabatic shear localization under simple shear is usually explained by the theory of thermoplastic instability (Fig. 13), namely that the competition between strain hardening and thermal softening controls the occurrence of adiabatic shear. When strain hardening exceeds thermal softening, the plastic deformation is steady. Otherwise, the plastic deformation is unstable and the further plastic deformation occurs at smaller stresses until fracture. Fig. 13. Thermoplastic instability curve The influence of cutting parameters on adiabatic shear can be explained by the proposed model. According to Eq. (6), the influence of strain and strain rate on adiabatic shear easily can be explained easily. The results are shown in Fig. 14. According to Eqs. (8) and (13), the strain rate increases with the increase of cutting speed and the strain decreases with the increase of rake angle. Therefore, the adiabatic shear in machining occurs under the condition of larger cutting speed and smaller rake angle. These influence also can be explained by the above thermoplastic instability theory. The influence of depth of cut is difficult to explain with the existing theory. Because as the depth of cut increases, the strain decreases according to the cutting theory, and the strain rate also decreases according to Eqs. (8) and (11). According to the theory of thermoplastic instability, the adiabatic shear should occur under smaller depths of cut. This is in conflict with the experiment result. From Fig. 13, it can be seen that in the zone of unstable plastic deformation, the stress increases with the decrease of strain. According to proposed model (Eq. (6)), this will lead to the increase of adiabatic shear sensitivity index B, which means the adiabatic shear will occur under larger depths of cut. (a) 1.08 1.06 "O 1.04 o 1.02 3 1 g 0.98 j5 0.96 £ 0.94 0. 92 0.9 0.7 0.8 0.9 1 1.1 1.2 1.3 shear strain 7 cc <£ 1.01 3 1 1 0.99 Ji 0.98 0. 97 ' 0.96 -'-1-' 0.00E-00 5.00E-05 1.00E+06 1.50E+06 shear strain rate Fig. 14. Influences of deformation conditions on adiabatic shear: a) influence of strain, and b) influence of strain rate The existing research on adiabatic shear in machining mostly focuses on the influence of cutting speed. Using the proposed model in this paper, not only can the system analysis of the influence of cutting parameters (including cutting speed, depth of cut and rake angle) on adiabatic shear be conducted but a reasonable explanation for these influences can also be given. Furthermore, researches show that the evolution of adiabatic shear leads to the change of serrated chip, from partial to complete separation. This change will lead to the reduction of tool life, degradation of the machined surface integrity and the reduction of part accuracy. As mentioned in Section 1, the value of adiabatic shear sensitivity index B reflects the degree of adiabatic shear evolution. The relationship between cutting conditions and adiabatic shear sensitivity index B is also established. If the relationship between the evolution of adiabatic shear and the tool life, or machined surface integrity, etc., can be revealed in the future, the optimization of cutting parameters can be realized by combining the proposed model. Therefore, the proposed model can not only deepen the understanding of adiabatic shear in HSM, but also in favour of the optimization of cutting parameters. 680 Li, G. - Cai, Y. - Qi, H. - Liu, M. Strojniški vestnik - Journal of Mechanical Engineering 63(2017)11, 673-682 6 CONCLUSIONS • Based on an adiabatic shear sensitivity index proposed by linear perturbation analysis which considers the pressure-shear condition in machining, the relationship of adiabatic shear and cutting conditions are built. The corresponding relation between the cutting conditions and the deformation conditions is established based on the model of parallel boundary shear zone. The proposed model is validated by experiments. • The adiabatic shear in HSM tends to occur under the condition of higher cutting speed, greater cutting depth and smaller rake angle. Furthermore, the influence of cutting speed is the biggest, the influence of cutting depth is the second, and that of rake angle is the least. • The proposed model not only can reveal the mechanism of adiabatic shear in high-speed cutting, but can also be used in the optimization of cutting parameters. 7 ACKNOWLEDGEMENT This work is supported by the Innovation Team Training Plan of Tianjin Universities and colleges (Grant No. TD12-5043), Tianjin Science and Technology Innovation System and Platform Construction Plan (14TXGCCX00011), Tianjin Universities "Training Plan of Subject-Leading Personnel" (RC14-02), the project of excellent young teachers (RC14-17) and that of young scholar broad (201307760011). This work is also supported by National-Local Joint Engineering Laboratory of Intelligent Manufacturing Oriented Automobile Die & Mould. 8 REFERENCES: [1] Ai, X. (2003). Technology of High Speed Machining. National Defense Industry Press, Beijing, p. 1-5. [2] Barry, J., Byrne, G. 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