Influence of Chip Breaker Geometric Shape on the Cutting Performance of Cermet Tools

Abstract

Ti(C,N)-based cermet turning inserts with two distinct chip breaker groove structures were employed to investigate the influence of chip breaker geometry on cutting performance. Chip removal performance and wear resistance of the inserts were evaluated according to chip morphology. The results reveal that, compared with inserts with the V-type groove, those with the SF-type groove exhibit superior chip removal capability and enhanced flank wear resistance. Based on two key parameters of the equivalent groove width and initial chip curl radius, an oblique cutting model was proposed for turning inserts with three-dimensionally complex grooves. The model incorporates the coupled effects of chip breaker geometry, workpiece material properties, inserts material properties and cutting process parameters. By controlling chip morphology, the proposed model effectively realizes the improvement and rational optimization of cutting performance, providing a theoretical basis for the design and optimization of complex groove turning inserts.

1. Introduction

Ti(C,N)-based cermets have attracted considerable attention owing to their high hot hardness and chemical stability, as well as their relatively low friction coefficient against metals [1,2,3,4,5]. The application range of cermet cutting tools bridges the gap between ceramic tools and cemented carbides, exhibiting notable advantages in high-speed machining and environmentally benign (green) cutting conditions. Particularly, cermet cutting tools can enable the “turning instead of grinding” process, rendering them a highly promising category of tool materials [6,7]. Tool geometry plays a crucial role in realizing cutting performance; accordingly, improving tool durability and machining performance through the coordinated design of tool structure and cutting-process parameters has become a central research topic in modern machining.

In 1962, Nakayama [8] proposed the concept of a tool “chip breaker groove.” In 1988, Jawahir et al. [9] introduced the mechanism of the restricted contact effect (RCE), namely, when the chip breaker groove shortens the actual tool-chip contact length to below the natural (unrestricted) tool-chip contact length, the chip leaves the rake face with a larger backflow angle and intensified lateral squeezing, thereby enabling a stable, periodic chip-breaking behavior characterized by bending compression fracture. Extensive studies have confirmed the advantages of grooved tools in efficient chip evacuation; moreover, tailoring the groove profile and its geometric parameters can reduce cutting forces and improve tool life and machining reliability [10,11]. Three-dimensional complex grooves (e.g., curved profiles) are more likely to satisfy chip breaking criteria and to reduce wear depth in low-feed turning [12]. Lotfi et al. [13] reported that, for AISI 1045 steel with high ductility and a tendency to generate continuous long chips, the groove depth and cutting edge land width are the primary factors governing the reduction of actual tool-chip contact length and the main cutting force. A comprehensive consideration of the coupling between chip breaker geometry and cutting parameters is therefore an important route to synergistically optimize tool design and process conditions, thereby enhancing machining efficiency and surface quality. Pacella et al. [14] fabricated a low-feed, curved-surface chip breaker on the rake face of WC tools using a nanosecond laser, achieving pronounced reductions in cutting force and chip length during carbon steel turning, and lowering the feed threshold for chip breaking to 0.1 mm/r. Furthermore, introducing micro-grooves into the chip breaker groove, alongside the induced “secondary cutting” effect, can facilitate localized chip deformation and stress concentration, enabling chip form control and controllable chip breaking. This approach also further reduces cutting forces and adhesive wear, making it particularly valuable for machining workpiece materials with high strength, low thermal conductivity, and strong adhesion tendencies [15,16,17]. Moreover, different chip breaker grooves induce variations in cutting forces by modifying chip curl and deformation degrees, directly influencing energy consumption during the cutting process. Additionally, recent review papers have highlighted the critical roles of tool geometry and interface conditions in energy consumption [18,19,20].

In recent years, numerical simulation has become one of the key approaches for investigating machining mechanisms. Among the available techniques, the finite element method (FEM) has been widely applied to orthogonal cutting simulations, with substantial progress reported in the development of constitutive models, thermo-mechanical coupled analyses, and sustainability-oriented machining assessments [21,22,23,24]. The incorporation of experimental validation—such as cutting force and cutting temperature measurements, chip morphology characterization, and tool-chip contact length determination—provides multidimensional criteria for evaluating model fidelity, thereby enabling orthogonal cutting simulations to guide the optimization of practical machining parameters [25,26,27]. However, when the cutting edge inclination angle is non-zero (λ_s ≠ 0), the chip flow departs from the orthogonal plane and generates a chip flow angle ψ. As λ_s increases, ψ increases accordingly, which can lead to large errors if a two-dimensional orthogonal assumption is used for numerical fitting [28,29,30].

Accordingly, related studies have mainly focused on modeling the geometric relationships in oblique cutting, elucidating material-removal mechanisms, and addressing multi-physics coupling. Representative model frameworks include the Merchant model, upper-bound energy models, analytical models based on inverse identification of material flow/rheology, three-dimensional equivalent parameter models, and three-dimensional equivalent parameter FEM models [31]. Oblique cutting models are important for reducing cutting loads, improving the thermal distribution within the cutting zone, enhancing process stability, and optimizing surface integrity. In particular, the Merchant and upper-bound models determine the shear angle and chip flow angle based on energy criteria [32], and recent developments have further incorporated tool geometry factors such as tool-nose radius and inclination angle to improve predictive accuracy [33]. Analytical models based on inverse identification of material rheology start from constitutive behavior and can yield improved predictions of cutting forces and chip flow direction [34]. The three-dimensional equivalent parameter approach introduces two key parameters, equivalent backflow angle and equivalent groove width, yet these parameters typically rely on empirical calibration [35]. Although three-dimensional equivalent parameter FEM can explicitly resolve detailed features of the 3D cutting process, it often suffers from a complex workflow, difficult model construction, and high sensitivity to constitutive and friction parameters [36]. In practical cutting operations, coupling effects exist among tool material and tool geometry, chip breaker groove geometry, workpiece material, and process parameters, resulting in strong time-varying behavior and uncertainty in the cutting process. Most existing oblique cutting models mainly employ the inclination angle to characterize chip flow direction and curling degree, and thus fail to accurately describe the chip removal performance governed by three-dimensional complex chip breaker geometries, such as chip-breaking thresholds and curl-radius control. Therefore, considerable room still exists for improving the evaluation of chip control reliability and machining adaptability for tools with complex groove designs.

In this study, Ti(C,N)-based cermet turning inserts were adopted to clarify the coupled effects of chip breaker groove geometry and cutting parameters on chip morphology and cutting performance. A structure-property relationship was established between the plasticity of the workpiece material and the chip bending fracture strain, and an oblique cutting model was developed for turning inserts with three-dimensionally complex grooves. This model integrates four core influencing factors, i.e., chip breaker geometry, properties of the workpiece material, the insert material, and cutting process parameters. By optimizing chip types, the model realizes the improvement and optimization of cutting performance, which can provide key basic data for the big data-driven tool process database and offer reliable technical support for precision machining in high-end equipment manufacturing industries, such as aerospace and automotive manufacturing.

2. Materials and Methods

2.1. Tool Materials and Performance Testing

The cutting tools utilized in this study were home-fabricated Ti(C,N)-based cermet turning inserts coded as CNMG160608, specifically CNMG160608-SF and CNMG160608-V. The room-temperature mechanical properties of the cermet are listed as follows: transverse rupture strength (TRS) of 1954 MPa, Vickers hardness of 1525 HV, and fracture toughness of 8.95 MPa·m^1/2.

TRS was determined via three-point bending tests in accordance with BS EN ISO 3327-2009. Hardness was characterized using the same specimens after TRS testing. Before measurement, the cross sections of the specimens were ground and polished. High-temperature Vickers hardness testing was conducted using an HTV-PHS30 high-temperature hardness tester (Archimedes Industrial Technology Co., Ltd., London, UK) at temperatures ranging from 20 to 800 °C. Room-temperature Vickers hardness (HV10) was measured using an HVS-30Z Vickers hardness tester (Laizhou Huayin Testing Instrument Co., Ltd., Laizhou, China). The fracture toughness (K_IC) of cermet is always determined by measuring the crack lengths departing from the Vickers indentation corners using the expression derived by Shetty et al. [37]:

$$K_{\mathrm{IC}}=\beta \sqrt{{\displaystyle \frac{\mathrm{HV}\cdot P}{4\overline{l}}}},$$

(1)

where HV is the Vickers hardness (kg/mm²), P is the indentation load (in kg), $\overline{l}$ is the average length of cracks departing from the indentation corners and β = 0.0889 is an empirical (calibration) constant [37].

A pin-on-disk friction and wear test was performed on an MMW-1 vertical universal friction and wear tester (Jinan Shijin Group Co., Ltd., Jinan, China) to characterize the frictional behavior between the cermet and workpiece materials. Specimens were machined from mechanical test bars, ground with a diamond grinding wheel, and prepared into flat-ended pin samples with dimensions of Ø4.8 mm × 12.7 mm. The counterpart disk was fabricated from AISI 1045 steel with a hardness of 210 HB and a diameter of Ø54.0 mm. A single-pin configuration with a large wear-track radius of 23.1 mm was adopted under dry sliding conditions.

Table 1. Process parameters for friction and wear experiments.

Parameter	Unit	Value
Test Specimen	Dimensions	Ø4.8 × 12.7 mm
Counterpart Disk	Material	AISI 1045
	Diameter	Ø54.0 mm
	Hardness	210 HB
Pin Configuration	Shape	Single Pin
Wear Track Radius	mm	23.1
Wear Track Diameter	mm	46.2
Environment	Type	Dry Sliding
Load	N	40, 80
Contact Pressure	MPa	2.21, 4.42
Sliding Speed	m/s	0.2, 0.7, 2.0, 5.0
Test Duration	min	90
Sliding Distance	km	1.08, 3.78, 10.8, 27.0

lists the detailed process parameters. As presented in Table 1, normal loads of 40 N and 80 N were applied to the pins, yielding contact pressures of 2.21 MPa and 4.42 MPa, respectively. The sliding speed was set to 0.2, 0.7, 2.0, and 5.0 m/s for a total test duration of 90 min, with the corresponding sliding distances being 1.08, 3.78, 10.8, and 27.0 km, respectively. The friction coefficient was automatically recorded by the built-in data acquisition system of the testing apparatus.

2.2. Tool Geometry and Chip Breaker Groove Dimensions

Two representative commercial chip breaker groove designs, namely the SF-type and V-type, were selected for comparison. These two grooves are intended to satisfy the typical chip-control requirements in semi-finishing and semi-roughing turning, respectively, and represent mainstream designs for industrial turning inserts. The three-dimensional surface topographies of both inserts were measured using a NANOVEA ST400 non-contact optical profilometer (NANOVEA Inc., Irvine, CA, USA). The ST400 provides a maximum vertical resolution down to 0.1 μm; its lateral accuracy depends on the sensor configuration and typically ranges from approximately 0.8 to 11.0 μm; the height repeatability can reach the nanometer level. Prior to dimension extraction, the measured 3D topography of both groove types was trued using an identical preprocessing workflow: a least squares reference plane was fitted to the rake face region for alignment and levelling; this fitted plane was then subtracted to eliminate rigid body tilt; isolated spikes and outliers were removed via thresholding and denoising; and any non-measured points were filled by interpolation. The corresponding photographs of the inserts, reconstructed 3D surface topographies, and schematic cross-sections of the chip breaker grooves are depicted in Figure 1. For the CNMG160608-SF insert, the chip breaker exhibits a straight arc groove configuration. A boss-type chip breaker land is located at 1.40 mm from the tool tip along the bisector of the nose angle; the boss has a spherical radius of 0.82 mm, and the corresponding intersection circle radius on the rake face is 0.60 mm, resulting in a locally three-dimensional complex groove feature near the tool nose. At the narrowest location on the intersection circle relative to the main cutting edge, the A-A cross section was taken along the normal direction to the main cutting edge. The minimum normal groove width at the main cutting edge is W_n = 1.22 mm, the groove rake angle is γ₀ = 18°, the groove depth is 0.13 mm, the boss height is 0.13 mm, and the edge-land width is 0.20 mm; the groove width increases to 1.40 mm in the mid-region of the main cutting edge. For the CNMG160608-V insert, the chip breaker is a double linear groove, and the B-B cross section was taken along the normal direction to the main cutting edge. The normal groove width at the main cutting edge is W_n = 2.85 mm, the height difference between the insert body and the cutting edge, namely the step height, is h = 0.24 mm, the groove rake angle is γ₀ = 16°, the edge-land width is 0.20 mm, and the groove depth is 0.45 mm.

2.3. Cutting Test Design

Turning tests were conducted on a CDA6140A lathe (Dalian Machine Tool Group, Dalian, China), using variable speed external dry turning. The workpiece was a normalized AISI 1045 steel bar with dimensions of Ø65 mm × 300 mm and a hardness of 210 HB. Its relative machinability index is set to 1.0 under identical cutting conditions and tool wear criteria and used as the reference for evaluating other materials.

Turning was performed using an MCLNR2525M16 toolholder (Seco Tools AB, Fagersta, Sweden). The toolholder geometry was as follows: the principal cutting edge angle K_r was 95°, the auxiliary cutting edge angle K_r′ was 5°, the toolholder rake angle γ₀′ was −5°, and the toolholder clearance angle α′ was 5°. The two cermet inserts were mounted in the toolholder and installed on the tool post. The effective working rake angle of the tool was calculated as γ_oe = γ₀ + γ₀′, and the corresponding combined working angles are listed in

Table 2. Effective working angles of the cermet inserts in the cutting experiments.

Insert Designation	Kr	Kr′	γoe	αoe	λs
CNMG160608-SF	95°	5°	13°	5°	−4°
CNMG160608-V	95°	5°	11°	5°	−4°

. In Table 2, α_oe denotes the effective working clearance angle of the insert, and λ_s denotes the effective cutting edge inclination angle generated by mounting the insert on the toolholder.

The cutting parameters employed for chip morphology analysis, namely cutting velocity v_c, feed rate f, and back engagement of the cutting edge a_p, were selected based on typical parameter ranges in industry for semi-roughing, semi-finishing, and finishing operations of ductile engineering materials. The cutting parameters were set as v_c = 116–229 m/min, a_p = 1.0–2.0 mm, and f = 0.10–0.28 mm/r. The effects of v_c, f, and a_p on chip morphology were assessed via a one-factor-at-a-time experimental design. No strong interactions that would contradict the proposed C-type chip window were observed within the tested parameter range. The chips collected during machining were subsequently prepared as metallographic specimens. After grinding and polishing, the specimens were etched using a 4% nital solution. Chip microstructures were then examined by optical microscopy, and the chip thickness h_ch and the initial chip curl radius ρ₀ were measured. For each cutting condition, the reported values represent the average of ten measurements.

Tool life tests of the two inserts were carried out by dry turning. The cutting conditions were v_c = 145–237 m/min, a_p = 1.5–2.0 mm, and f = 0.23–0.28 mm/r. The tool-wear criterion followed an industrial wear limit: the tool was considered worn out when the maximum flank wear, VB_max, reached 0.6 mm, or alternatively, the maximum flank wear on the flank face after a cutting length of 5000 m was used to evaluate wear resistance and tool life. The flank wear width at the tool nose was measured using a toolmakers microscope (model NJF-120A, Ningbo Yongxin Optics, Ningbo, China) under 40× magnification. The flank face of the cutting tool was sputter-coated with gold prior to observation. The flank wear morphology was characterized using a scanning electron microscope (SEM, Quanta 250 FEG, FEI Company, Hillsboro, OR, USA) operated in secondary electron mode at an accelerating voltage of 20 kV and a magnification of 100×. The average values of five tests were adopted.

3. Results and Discussion

3.1. Chip Morphology and Cutting Performance

Chip morphologies formed by the two inserts during turning of normalized AISI 1045 steel are presented in Figure 2 and Figure 3, respectively. The results indicate that the CNMG160608-SF insert primarily generated three types of chips: long coiled chips, helical chips, and C-shaped chips, with the long coiled chips frequently entangled. By contrast, the CNMG160608-V insert mainly produced ribbon chips and tangled chips.

For the SF-type insert, long coiled chips were dominant at f = 0.10 mm/r, while helical chips were formed at a_p = 1.0–1.3 mm. When a_p was increased to 1.3–2.0 mm with f = 0.15–0.28 mm/r, regular C-shaped chips were obtained, and the chip morphology was largely insensitive to the cutting speed. For the V-type insert, tangled chips were generated at f = 0.10–0.15 mm/r, whereas ribbon-type continuous chips were formed under the other cutting conditions. These results demonstrate that the final chip morphology and fracture behavior are collectively governed by the chip breaker groove geometry and the cutting parameters, with the groove geometry playing a dominant role. The SF-type chip breaker imposes a strong constraint on chip flow; when the cutting parameters exceed the corresponding threshold values, the chip undergoes intense curling and bending, resulting in periodic fracture. In contrast, the V-type chip breaker exerts a weaker constraint, and the chip does not meet the fracture criterion within the experimental range of cutting parameters.

At v_c = 143 m/min, a_p = 1.5 mm, and f = 0.10 mm/r, the long coiled chips produced by the SF-type insert exhibited a light-brown surface. According to Yeo’s suggestion [38], this corresponds to a chip temperature in the range of 630–660 °C (Figure 4 shows). As f increased to 0.15–0.28 mm/r, the C-shaped chips gradually changed in color from brown to blue-brown, indicating that, with increasing cutting parameters, the chip temperature rose from 630 to 670 °C to 670 to 700 °C. For the V-type insert, under the same cutting conditions of v_c = 143 m/min, a_p = 1.5 mm, and f = 0.10 mm/r, the long coiled chips were brown in color. When f increased to 0.15–0.28 mm/r, the chip color changed from blue-brown to dark blue, suggesting that the chip temperature increased from 670 to 700 °C to about 690 to 770 °C. Although these temperatures are indirectly estimated from the color-temperature correlation in Ref. [38] with certain uncertainty, they are believed to being reliable for relative comparison under identical cutting conditions. These results suggest that, under identical cutting conditions, the chip surface temperature generated by the SF-type insert is lower than that produced by the V-type insert, implying a lower interfacial temperature at the tool-chip contact zone for the SF-type insert.

Tool life test results obtained from machining normalized AISI 1045 steel using the two inserts are summarized in

Table 3. Cutting performance test results for the two insert types.

Insert Designation	Cutting Parameters			Cutting Length (m)	VBmax (mm)	Failure
	vc (m/min)	f (mm/r)	ap (mm)
CNMG160608-SF	145	0.28	2.0	5000	0.38	No
	237	0.23	1.5	5000	0.43	No
CNMG160608-V	145	0.28	2.0	4100	Collapse	Yes
	237	0.23	1.5	5000	0.51	No

, and representative SEM images of flank face wear are shown in Figure 4. Under the specified cutting conditions, the SF-type insert produced C-shaped chips, whereas the V-type insert yielded ribbon chips. Under all tested conditions, the SF-type insert exhibited no failure, and its flank wear values were consistently lower than those of the V-type insert. In contrast, the V-type insert experienced edge chipping failure, as ribbon chips intermittently struck and damaged the cutting edge. As shown in Figure 5, the worn flank faces of both inserts display distinct ploughing grooves, a typical characteristic of abrasive wear. The V-type insert presents significantly deeper grooves, indicative of severe abrasive damage. These results demonstrate that the SF-type groove offers superior flank wear resistance, which reduces the tool-workpiece contact area and lowers interfacial friction, leading to lower cutting forces and consequently reduced specific cutting energy. That is, the SF groove type exhibits superior energy saving potential.

3.2. Chip Removal Characteristics in Orthogonal Cutting

Once the tool nose engages the workpiece, the chip undergoes shear plastic deformation before entering the chip breaker groove, where it experiences curling deformation. When the curled chip subsequently impinges on the tool flank face, its flow is impeded by the flank face, leading to chip fracture, as illustrated in Figure 6a. The measured values of the chip deformation coefficient ξ, the initial chip curl radius ρ₀, and the reverse curl radius ρ_L are listed in Table 3. The chip deformation coefficient ξ is obtained from the ratio of the chip thickness h_ch to the undeformed chip thickness h_D, namely:

$$\xi ={\displaystyle \frac{h_{\mathrm{ch}}}{h_{\mathrm{D}}}},$$

(2)

where h_D is the undeformed chip thickness in the workpiece, h_D = fsinK_r.

Based on the chip fracture strain criterion proposed by Nakayama and the extensions reported in subsequent chip control studies, ε_wp can be expressed as [39]:

$${\epsilon }_{\mathrm{wp}}={\displaystyle \frac{h_{\mathrm{ch}}}{2}}\left({\displaystyle \frac{2}{{\rho }_0}}-{\displaystyle \frac{1}{{\rho }_{\mathrm{L}}}}\right)\ge {\epsilon }_0,$$

(3)

where ε_wp is the chip bending fracture strain, ε₀ is the fracture strain limit of the workpiece material, ρ₀ is the initial chip curl radius, and ρ_L is the reverse chip curl radius.

According to an empirical relation reported in the literature [40], the relationship between the chip breaker groove geometry and the initial chip curl radius ρ₀ can be expressed as:

$${\rho }_0={\displaystyle \frac{{\left(W_{\mathrm{n}}-l_{\mathrm{f}}\right)}^2}{2t}}+{\displaystyle \frac{t}{2}}$$

(4)

In the above equation, l_f denotes the tool-chip contact length [41]:

$$l_{\mathrm{f}}={\displaystyle \frac{f\sin \frac{\pi }{2}}{\sin \phi \sin \left(\frac{\pi }{2}+\phi -{\gamma }_{\mathrm{oe}}\right)}},$$

(5)

where W_n is the chip breaker groove width, φ is the shear angle, and t is the chip breaker step height. Based on principles of materials science and mechanics of materials, the shear angle for steels can be estimated using Merchant’s relation [42]:

$$\phi ={\displaystyle \frac{\pi }{4}}-\left(\beta -{\gamma }_{\mathrm{oe}}\right),$$

(6)

where β = arctanμ, and μ is the average coefficient of friction on the rake face. In this work, the friction coefficient μ was determined via pin-on-disk friction and wear tests.

With increasing temperature, both the hardness and fracture toughness of the cermet tool material show a decreasing trend (Figure 7). Nevertheless, at 800 °C the tool material still maintains a hardness above 930 HV and a fracture toughness above 4.8 MPa·m^1/2. Figure 8 shows the coefficient of friction between the cermet and a normalized AISI 1045 steel disk under normal loads of 40 N and 80 N. The results indicate that the coefficient of friction decreases markedly with increasing relative sliding speed and decreases slightly as the normal load increases. It is inferred that the friction coefficient at the tool-chip interface tends to decrease with increasing cutting speed. Throughout the entire test, dry sliding conditions induced pronounced frictional heating and a consequent temperature rise in both the pin specimen and the steel disk. When the sliding speed exceeded 2.0 m/s (corresponding to 120 m/min), the coefficient of friction remained at a low level of 0.35–0.40, and the influences of load and temperature variations on the friction coefficient became negligible. However, the friction and wear conditions encountered during cutting differ significantly from those in pin-on-disk tests. According to our previous work [43,44], the dominant wear and failure mechanisms of the investigated cermet during machining of normalized AISI 1045 steels are hard phase debonding and abrasive wear, which are similar to the wear characteristics observed at pin-on-disk friction tests. Although apparent sliding friction involves much lower contact pressure, weaker frictional heating and temperature gradient, as well as pure sliding without severe chip plastic deformation, the friction coefficient at the tool-chip interface is slightly lower than that measured under sliding conditions. Accordingly, in the calculation of Equation (6), the friction coefficient is set within the range of 0.35–0.40 and is moderately reduced with increasing cutting parameters to capture the variation trend of interfacial friction under actual cutting conditions.

The measured and calculated values of the chip deformation coefficient ξ, the initial chip curl radius ρ₀, and the chip bending fracture strain ε_wp are summarized in

Table 4. Measured and calculated values of the chip deformation coefficient, initial chip curl radius, and bending fracture strain for chips produced by the two insert types.

Insert Designation	Cutting Parameters			ξ	Measured Data			Calculated Data		Chip Type
	vc (m/min)	f (mm/r)	ap (mm)		ρ0 (mm)	ρL (mm)	εwp	ρ0 (mm)	εwp
CNMG160608-SF	116	0.18	1.5	2.17	1.5 ± 0.2	2.3 ± 0.5	0.171	3.7	0.064	C
	143			1.85	1.7 ± 0.3	2.8 ± 0.4	0.135	3.8	0.063	C
	178			1.85	1.8 ± 0.3	4.1 ± 0.8	0.136	3.9	0.062	C
	229			1.85	1.8 ± 0.3	3.5 ± 0.6	0.136	3.9	0.062	C
	143	0.10	1.5	2.90	2.2 ± 0.9	4.5 ± 0.8	0.071	4.6	0.036	Curled
		0.15		2.32	1.7 ± 0.4	5.5 ± 0.9	0.135	4.1	0.052	C
		0.28		1.35	1.3 ± 0.2	1.6 ± 0.3	0.266	2.9	0.114	C
		0.18	1.0	1.92	2.6 ± 0.5	3.1 ± 0.5	0.087	3.8	0.063	Spiral
			1.3	1.65	1.9 ± 0.3	5.1 ± 0.8	0.128	3.8	0.063	Spiral
			2.0	1.80	1.8 ± 0.2	4.9 ± 0.9	0.145	3.8	0.063	C
CNMG160608-V	116	0.18	1.5	1.90	9.7 ± 0.8	—	0.036	11.6	0.025	Strip
	143			1.90	9.6 ± 1.7	—	0.036	11.7	0.024	Strip
	178			1.65	11.9 ± 1.5	—	0.025	11.8	0.023	Strip
	229			1.60	10.9 ± 0.7	—	0.026	12.0	0.024	Strip
	143	0.10	1.5	2.45	11.2 ± 1.3	—	0.021	13.6	0.015	Curled
		0.15		1.60	10.8 ± 1.5	—	0.023	13.1	0.019	Curled
		0.28		1.46	10.5 ± 1.0	—	0.039	11.2	0.038	Strip
		0.18	1.0	1.90	9.7 ± 1.1	—	0.034	11.8	0.023	Strip
			1.3	1.95	11.2 ± 1.2	—	0.031	11.7	0.024	Strip
			2.0	1.95	9.9 ± 1.6	—	0.033	11.6	0.025	Strip

. As shown in Table 4, ξ decreases with increasing cutting parameters, indicating a reduced degree of chip thickening and deformation during chip formation. When ε_wp ≤ 0.071, long coiled chips and ribbon chips are formed; for 0.071 < ε_wp ≤ 0.128, helical chips are produced; and at ε_wp > 0.128, C-shaped chips are obtained. Considering that high temperature increases the fracture strain of the steel via thermal softening, while high strain rate reduces it by restricting plastic deformation, the coupled thermomechanical effects in actual cutting will hardly alter the fracture strain [45]. Thus, a fixed quasi-static fracture strain of 0.15 was adopted for normalized AISI 1045 steel to provide a unified baseline for comparison. The results indicate that C-shaped chips tend to form when ε_wp approaches the plastic strain limit of the workpiece material. The SF-type groove produces a much smaller ρ₀ than the V-type groove, thereby imposing larger plastic bending deformation and stronger strain hardening on the chip, which makes chip breakage easier. Compared with the experimental data, the theoretical predictions overestimate ρ₀ for the CNMG160608-SF insert by 35% to 192% and underestimate ε_wp by 57% to 103%. For the CNMG160608-V insert, the corresponding deviations between the theoretical predictions and experimental data are approximately 30% for ρ₀ and 25% for ε_wp. It indicates that the SF-type chip breaker groove exhibits pronounced three-dimensional local features near the tool nose, which significantly alter chip flow and the curvature distribution across the chip width; thereby changing the values of W_n, φ and l_f, which in turn leads to a large deviation in calculations. Moreover, these parameters in Equations (3)–(6) neglect the coupling influence of the inclination angle λ_s, which further increase the deviation. Therefore, to improve the priori prediction of chip breaking performance for complex groove geometries similar to the SF-type design, the above classical empirical equations need to be further modified.

3.3. Oblique Cutting Model

For cutting tools with three-dimensional complex chip breaker grooves, quantitative description of chip morphology using classical equations often yields large errors. In the preceding calculations, the influence of the cutting-edge inclination angle λ_s was not considered. For the two investigated inserts, under the condition that λ_s ≠ 0, the cutting process corresponds to oblique cutting rather than orthogonal cutting. Therefore, an orthogonal-cutting-based analysis alone is inadequate to predict the chip morphology of the CNMG160608-SF insert featuring a three-dimensional complex groove.

In orthogonal cutting, the major cutting edge remains perpendicular to the cutting velocity direction, and the angle between the major cutting edge and the normal to the cutting velocity direction equals the effective working rake angle γ_oe. In oblique cutting, the chip flow direction deviates from the orthogonal plane and is discharged along the chip flow plane, which encompasses both the cutting velocity vector and the chip flow direction. Accordingly, an equivalent cutting edge and an equivalent rake angle γ_ne must be employed in the analysis of oblique cutting [46]. The oblique cutting model adopts the reference system of planes P_re, P_se, and P_fe, as shown in Figure 9. P_re is the reference plane perpendicular to the cutting velocity, P_se is the cutting-edge plane that intersects the cutting edge and is parallel to the cutting velocity direction, and P_fe is the working plane perpendicular to the cutting edge and parallel to the workpiece axis. The angle between the projections of P_se and P_fe on P_re is the principal cutting-edge angle K_r. The angle between the projection of the rake face and P_re on P_se corresponds to the cutting-edge inclination angle λ_s.

A Cartesian coordinate system at the tool nose is established with the center of the chip-breaking boss as the origin O, the negative feed direction as the x-axis, and the radial direction pointing toward the workpiece axis as the y-axis; a schematic of the chip breaker geometry for the SF-type insert is presented in Figure 10. When the tool advances by one feed increment, the line segment connecting points I and Q, which are the engaged endpoints of the major and minor cutting edges, forms the cutting-edge chord IQ. This chord is taken as the equivalent cutting edge in oblique cutting. The chip flows out in a direction normal to the cutting-edge chord, that is, the chip flow direction is perpendicular to the equivalent cutting edge. The angle between the chip flow direction and the direction normal to the major cutting edge is defined as the chip flow angle ψ [47]:

$$\psi =\arctan ({\displaystyle \frac{r_{\mathsf{\epsilon }}}{a_{\mathrm{p}}}}\tan {\displaystyle \frac{K_{\mathrm{r}}}{2}}+{\displaystyle \frac{f}{2a_{\mathrm{p}}}}+\cot K_{\mathrm{r}})+K_{\mathrm{r}}-{90}^{°},$$

(7)

where r_ε is the tool nose radius, and K_r is the principal cutting-edge angle.

The slope of the projection of the equivalent cutting-edge chord IQ is k_IQ = tan (K_r − ψ), and the corresponding line equation is written as:

$$y=x\tan (K_{\mathrm{r}}-\psi )+b_1,$$

(8)

where b₁ is a constant.

Define point I as the intersection of the projection of the equivalent cutting-edge chord IQ with the major cutting edge, where I have coordinates I(x₁, y₁). During cutting, the depth of cut a_p determines a tangency point P on the tool nose arc, whose Cartesian coordinates are (x₀, y₀). The slope of the major cutting-edge line MS is k_MS = tan K_r. The tool nose angle is 80°, and the length of segment MN can be calculated from the tool geometric dimensions. According to the geometric relationships of the right triangle MOS in Figure 10, the coordinates of point M are defined as M(x₂, y₂). Therefore, the equation of the major cutting-edge line MS is:

$$y=\left(x-x_2\right)\tan K_{\mathrm{r}}+y_2$$

(9)

Using Equation (9) and the geometric relationships shown in Figure 10, the coordinates of point I can be obtained as $I\left({\displaystyle \frac{y_0-a_{\mathrm{p}}-y_2}{\tan K_{\mathrm{r}}}}+x_2,y_0-a_{\mathrm{p}}\right)$. Substituting the coordinates of point I into Equation (8) yields the constant $b_1=\left(y_0-a_{\mathrm{p}}\right)-\left({\displaystyle \frac{y_0-a_{\mathrm{p}}-y_2}{\tan K_{\mathrm{r}}}}+x_2\right)\tan \left(K_{\mathrm{r}}-\psi \right)$. Accordingly, Equation (8) can be rewritten as

$$y=x\tan \left(K_{\mathrm{r}}-\psi \right)+y_0-a_{\mathrm{p}}-\left({\displaystyle \frac{y_0-a_{\mathrm{p}}-y_2}{\tan K_{\mathrm{r}}}}+x_2\right)\tan \left(K_{\mathrm{r}}-\psi \right)$$

(10)

The distance from the center O of the intersecting circle on the rake face of the chip-breaking boss to its tangent line VT is equal to the circle’s radius r_M. The equation of the tangent line VT is given by:

$$y=x\tan \left(K_{\mathrm{r}}-{\psi }_{\mathrm{r}}\right)+r_{\mathrm{M}}\sqrt{{\tan }^2\left(K_{\mathrm{r}}-\psi \right)+1}$$

(11)

Accordingly, the equivalent groove width W_ne can be obtained as:

$$W_{\mathrm{ne}}=\left|r_{\mathrm{M}}-{\displaystyle \frac{\left[y_0-a_{\mathrm{p}}-k_{\mathrm{IQ}}\left(\frac{y_0-a_{\mathrm{p}}-y_2}{\tan K_{\mathrm{r}}}+x_2\right)\right]}{\sqrt{k_{\mathrm{IQ}}^2+1}}}\right|$$

(12)

Figure 11 illustrates a cross-sectional schematic of the chip curling configuration as the chip travels through the SF-type chip breaker groove. As shown in Figure 11, the equivalent groove width of the chip breaker is W_ne. Propelled by the rake face, the chip enters the chip breaker groove along a direction normal to the equivalent cutting edge and undergoes curling upon encountering the chip-breaking boss, constrained by the spherical surface of the boss. The included angle between the chip inflow plane and the rake face is defined as the equivalent rake angle γ_ne.

Within the P_re–P_se–P_fe orthogonal reference system, the plane GFH is defined as the plane that contains the chip exit direction GF and is parallel to the tool reference plane P_re. GJ denotes the major cutting edge, and the plane GFH intersects the major cutting edge at point G. The projection of GJ onto the plane GFH is GH. The plane GHJ is the major cutting plane P_se. In the triangular plane GFH, line HF is perpendicular to line GH. Plane HJKF, which contains line HF, represents the orthogonal plane P_fe and is perpendicular to both P_re and P_se; lines HJ and FK are both perpendicular to the reference plane P_re. Within the cutting plane, the angle between the horizontal line GH and the major cutting edge corresponds to the cutting-edge inclination angle λ_s. According to the definition of the chip flow angle, FG is the chip flow direction on the rake face, and the angle between FG and FH is the chip flow angle ψ. A horizontal segment IJ is constructed in quadrilateral FHJK, and the angle between IJ and JK is the effective working rake angle γ_oe. Triangle FGK is a vertical section along the chip flow direction, and the angle between FG and GK is the equivalent rake angle γ_ne. Therefore, the equivalent rake angle γ_ne can be defined as [48]:

$${\gamma }_{\mathrm{ne}}=\arctan \left(\tan {\gamma }_{\mathrm{oe}}\cos \psi +\sin \psi \tan {\lambda }_{\mathrm{s}}\right)$$

(13)

Based on the geometric relationships of the right triangles AEF and BDE in Figure 11a, the length d of segment BE can be obtained as:

$$d={\displaystyle \frac{W_{\mathrm{ne}}}{\cos {\gamma }_{\mathrm{ne}}}}-l_{\mathrm{f}}$$

(14)

From the geometric relationship of triangle ODC, ∠ODC = π/2 − γ_ne, and the lengths of sides OD, DC, and OC are ρ₀ + dtanγ_ne, d/cosγ_ne + r_M, and ρ₀ + r_M, respectively. It can be obtained from the trigonometric relationship that:

$$O{C}^2=O{D}^2+D{C}^2-2OD\cdot DC\sin {\gamma }_{\mathrm{ne}}$$

(15)

Substituting the angle and side length relationships into Equation (15) and rearranging the equation yields the initial chip curl radius ρ₀ as follows:

$${\rho }_0={\displaystyle \frac{d^2{\sin }^2{\gamma }_{\mathrm{ne}}+d^2+2d{r}_{\mathrm{M}}\cos {\gamma }_{\mathrm{ne}}-2d(d+r_{\mathrm{M}}\cos {\gamma }_{\mathrm{ne}}){\sin }^2{\gamma }_{\mathrm{ne}}}{2\cos {\gamma }_{\mathrm{ne}}[r_{\mathrm{M}}\cos {\gamma }_{\mathrm{ne}}-d\sin {\gamma }_{\mathrm{ne}}+(d+r_{\mathrm{M}}\cos {\gamma }_{\mathrm{ne}})\sin {\gamma }_{\mathrm{ne}}]}}$$

(16)

3.4. Chip Curling Behavior in the Oblique Cutting Model

Using the coordinate system defined in Figure 10, the coordinates of key points P(x₀, y₀) and M(x₂, y₂) were measured via the 3D optical profilometer as (−0.6, 1.4) and (−2.3, −2.3), respectively. The nominal spherical radius of the chip-breaking boss is r_M = 0.26 mm. Based on Equation (12), the variation in the equivalent groove width W_ne with feed rate f and depth of cut a_p was calculated, and the resulting surface of W_ne as a function of f and a_p is shown in Figure 12a for v_c = 143 m/min, a_p = 1.0–2.0 mm, and f = 0.10–0.28 mm/r. Using Equation (16), the initial chip curl radius ρ₀ was calculated and is plotted in Figure 12b. As shown in Figure 12a, within the selected cutting parameter range, the equivalent groove width of the SF-type chip breaker is 0.86–1.16 mm, and W_ne decreases as the cutting parameters increase. Figure 12b shows that the initial chip curl radius ρ₀ produced by the SF-type groove is 1.23–3.66 mm and decreases with increasing cutting parameters, being primarily governed by the feed rate f.

Table 5. Fitted results for the equivalent groove width, initial chip curl radius, and chip bending fracture strain of the CNMG160608-SF insert under the oblique-cutting model.

Cutting Parameters			Equivalent Groove Width Wne (mm)	Chip Initial Curling Radius, ρ0 (mm)		Chip Fracture Strain, εwp
vc (m/min)	f (mm/r)	ap (mm)		Calculated Values	Deviations from Test Values
143	0.10	1.5	1.13	2.5	13.6%	0.063
143	0.15	1.5	1.02	1.9	11.7%	0.131
143	0.18	1.5	1.01	1.8	5.3%	0.144
143	0.28	1.5	0.98	1.5	15.4%	0.211
143	0.18	1.0	1.13	3.1	13.1%	0.064
143	0.18	1.3	1.05	2.2	15.8%	0.107
143	0.18	2.0	0.89	1.9	5.6%	0.135

reports the fitted results of the equivalent groove width W_ne, the initial chip curl radius ρ₀, and the chip bending-fracture strain ε_wp for the CNMG160608-SF insert under the oblique-cutting framework. Combining Figure 12a and Table 4, when f < 0.15 mm/r and a_p ≤ 1.3 mm, the SF chip breaker corresponds to W_ne = 1.03–1.13 mm, which is consistent with the experimental observation of spiral chips and long coiled chips under these conditions. When f ≥ 0.15 mm/r and a_p > 1.3 mm, W_ne decreases to 0.89–1.02 mm; within this groove-width range, chips are more prone to fracture, consistent with the experimentally observed C-shaped chips. Hence, the equivalent groove width range associated with C-shaped chips for the SF groove can be taken as W_ne = 0.89–1.02 mm. Furthermore, from Table 4, ε_wp is 0.063–0.107 for spiral chips and long coiled chips, whereas it increases to 0.131–0.211 for C-shaped chips, whose lower bound approaches the plastic limit of the work material, 0.15. Moreover, the mean absolute percentage deviation (MAPD) and maximum absolute percentage deviation (Max APD) for ρ₀ predicted by the proposed oblique-cutting model are 11.5% and 15.8%, respectively, considerably lower than the 107.7% and 141.2% in Table 4. For ε_wp, the MAPD and Max APD from the proposed model are 13.0% and 26.4%, respectively, markedly lower than the 50.9% and 61.5% in Table 4. The reduced deviations demonstrate that the proposed model yields higher accuracy in predicting chip features under three-dimensional complex chip breaker conditions. The corresponding errors, ranging from 5% to 20%, agree well with values reported in the literature for oblique cutting or complex groove prediction models [49,50]. Furthermore, the cutting parameters optimized based on chip morphology are consistent with existing experimental studies on CNMG120408 indexable inserts; under similar cutting conditions, inserts from different manufacturers exhibited comparable chip formation and tool wear behaviour, validating the effectiveness of the proposed method [51,52].

4. Conclusions

Ti(C,N)-based cermet turning inserts with two distinct chip breaker grooves, designated as CNMG160608-SF and CNMG160608-V, were employed to investigate the influence of chip breaker geometry on cutting performance. Based on the chip bending fracture strain criterion, a fitted computational model derived from oblique cutting theory was established. The main conclusions are drawn as follows:

(1)

Chip breaker groove geometry determines the resulting chip type. Under the employed cutting parameters, the SF-type groove delivers superior chip removal performance compared with the V-type groove. Groove geometry also affects tool life, with the SF-type insert showing higher flank wear resistance than the V-type counterpart.

(2)

Taking the equivalent groove width and initial chip curl radius as two key parameters, a fitted computational model derived from oblique cutting theory was developed to account for the coupled effects of chip breaker geometry, workpiece material properties, inserts material properties and cutting process parameters.

(3)

Grounded in the formation mechanism of C-shaped chips, the proposed model allows for more precise prediction of chip control performance for tools featuring three-dimensional complex chip breaker grooves. It shows promise for the intelligent design of chip breaker grooves and adaptive optimization of cutting parameters under complex service conditions, thus promoting the practical implementation of data-driven tool manufacturing technology.