Stagnation points and theoretical modeling of dead metal zone in extrusion machining with chamfered tool

Abstract

To investigate the mechanism of extrusion machining with chamfered tool (CT-EM) and establish the prediction models, experiments and numerical simulations were performed. By varying the chamfer angles (γ₂) and widths (w_c), the mechanical properties and microstructure of prepared strips were thoroughly studied. The results revealed that γ₂ affected the gravity center of dead metal zone (DMZ) and the relative position of stagnation points, while w_c mainly affected the DMZ area. Lower γ₂ and higher w_c increased effective strain and cutting temperature in DMZ, improving strip hardness and tensile strength. Furthermore, the predictive models of cutting force and deformed layer thickness matched experimental results. This study enriches the theory and modeling of CT-EM, further expanding the application of chamfered tools.

Keywords

chamfered tool prediction model dead metal zone stagnation point extrusion machining

Introduction

As an efficient approach of enhancing the mechanical properties of metals by altering grain size, grain refinement enables the convenient fabrication of materials with superior structures.^1–3 Ultrafine-grained (UFG) materials tend to exhibit improved strength,^4,5 wear resistance,^6,7 and higher hardness,^8,9 showing great application prospects.

Extrusion machining (EM) enables one-step fabrication of UFG strips by the extrusion channel formed by the constraint and sharp tools.^10–12 Issahaq et al.¹³ prepared pure aluminum strips with lower surface roughness and higher strength by EM process. Through cutting experiments and numerical simulation, Deng et al.^14,15 clarified that reducing the tool rake angle and chip compression ratio increased the effective strain. Based on Taguchi method, signal-to-noise ratio, and variance analysis, Pi et al.¹⁶ investigated the effects of process parameters on response variables. Shu et al.¹⁷ systematically revealed the evolution of microstructure and mechanical properties in the cryogenic EM process.

Sharp tools are commonly used in current EM studies^18,19 and theoretical models of EM are mainly based on sharp tools.^20–22 Hu et al.²³ improved the slip-line field model and further derived the analytical thermal model. Liu et al.²⁴ established an analytical model of mechanical properties and successfully validated it with pure copper. A strain estimation model was proposed by Cai et al.²⁵ according to the deformation field measured by high-speed imaging and digital image correlation.

To reduce tool wear and improve cutting performance, cutting with chamfered tools have attracted extensive exploration by researchers. Wu et al.²⁶ found that a dead metal zone (DMZ) was developed below the chamfer and served as an effective cutting edge. By comparing the cutting with different geometric tools, Asad et al.²⁷ demonstrated that chamfered tools produced chips with higher curl, while honed tools caused crack propagation and longer end-burrs. Gao et al.²⁸ found that the size of formed chips tended to decrease with increasing cutting-edge chamfer lengths through cutting experiments. Barelli et al.²⁹ revealed that higher cutting speed increased the shear angle, resulting in greater chip curvature. However, there are gaps in the theoretical modeling of extrusion machining with chamfered tools (CT-EM), and mechanical properties and microstructures of strips prepared by CT-EM process remain unclear.

In this paper, T2 pure copper was selected to establish the CT-EM theoretical models and explore the positional variation of stagnation point in DMZ ahead of the chamfered tool. Through experiments and simulation, mechanical properties and microstructures of strips machined using CT-EM under different chamfer angles (γ₂) and chamfer widths (w_c) were investigated. To explore the CT-EM process in depth, cutting temperature, effective strain, and contact length were further studied by finite element analysis. Additionally, the cutting force model and deformed layer thickness model of CT-EM matched the actual results, offering a reference for the engineering application of chamfered tools.

Stagnation point formation and theoretical modeling of CT-EM

Formation of the stagnation point in DMZ ahead of the chamfered tool

As presented in Figure 1(a), the chamfered tool creates a smaller shear angle φ compared to the sharp tool, and there is a DMZ formation ahead of the chamfered tool in CT-EM. Because the DMZ ahead of the chamfered tool is theoretically regarded as a fixed metal block, it can replace the tool tip to some extent. Additionally, the DMZ boundary AG is co-linear with the tool rake face, resulting in equal rake angles for both the chamfered tool and the sharpened tool. Figure 1(b) shows the machining schematic of CT-EM, where the UFG strip is formed in the extrusion channel between the constraint and chamfering tool. The surface metal of thickness t₀ is removed and a strip of thickness t_ch is formed along the flow direction (FD in Figure 1b). Accordingly, there must exist a stagnation point (red point S) near the chamfer, leading to material flow in two directions. As can be seen in Fig. 1(c), the prepared strip can theoretically be any length as long as the tubular workpiece is long enough.

Figure 1.

Schematic diagram of CT-EM process: (a) comparison of cutting with sharp and chamfered tools, (b) side view of CT-EM process, (c) front view of CT-EM process.

Assumptions for theoretical model establishment

The assumptions of the theoretical models are the basis for analysis and research, and influence the accuracy and reliability of the models profoundly. Too many factors may result in higher complexity and more unknowns in the model, while too few factors may reduce the accuracy and applicability. Therefore, the CT-EM models proposed in this paper need to make the following assumptions about the material deformation and contact conditions: (1) The metal workpiece is isotropic; (2) Material deformation coincides with the plane strain condition; (3) No material side flow occurs during CT-EM process; (4) The variables in the model are all in the steady state; (5) The workpiece never contacts the rear face of the chamfered tool; (6) Constraint never contact with the extruded strip.

Predictive model of cutting force predictive model

According to the slip-line models proposed by previous researchers,^30,31 the improved cutting force model for CT-EM is shown in Figure 2. During CT-EM, some material accumulates and forms the DMZ (region AGH) due to the obstruction of chamfer GH. The slip-line field can be divided into the following parts: (1) The region BCJ represents the flow direction deflection of material before it enters the shear plane AB. This is due to the constraint effect in EM, where the material flow is deflected by an angle of β²⁵ to obtain a new velocity V’, which is then deflected to V'’ by region BCJ; (2) The region ABCJIF represents the first deformation zone and φ is the shear angle. After passing through the shear plane AB, the material flow direction is deflected by θ in the region ABE and flows towards the extruded strip; (3) The triangular region AGH is the DMZ, α is the included angle between line AH and the horizontal direction, and ζ₂ is the friction angle between material and DMZ boundary. The formation of region AHF is extruded by DMZ, through which the material flows to the machined surface; (4) The plane ED is a stress-free surface and thus at an angle of 45° to the shear planes EK and DK. The triangle AKD is a friction region between the extruded strip and rake face, while ξ₁ is the friction angle of GD.

Figure 2.

Cutting force model for CT-EM: (a) new slip-line model, (b) velocity vector diagram, (c) diagram of the cutting force and thrust force.

Based on the geometric relationship in Figure 2(a), the chamfer GH length l_GH is calculated as:

\begin{matrix} l_{G H} = \frac{w_{c}}{\cos | γ_{2} |} \end{matrix}

(1)

By the triangle sine theorem, the length of the DMZ boundary AH is given by the following equation:

\begin{matrix} l_{A H} = \frac{l_{G H} \sin (γ_{1} + | γ_{2} |)}{\sin (\frac{π}{2} - γ_{1} + α)} \end{matrix}

(2)

where γ₁ means the tool rake angle, and the shear angle φ can be obtained as follows:

\begin{matrix} φ = \tan^{- 1} [\frac{t_{0} - l_{A H} \sin α}{\tan γ_{1} (\frac{t_{c h}}{\tan γ_{1}} - t_{0} + l_{A H} \sin α + t_{c h} \sin γ_{1})}] \end{matrix}

(3)

Additionally, θ and δ in the slip-line field are calculated as follows, respectively:

\begin{matrix} θ = ξ_{1} + γ_{1} - φ \end{matrix}

(4)

\begin{matrix} δ = φ + ξ_{2} - α \end{matrix}

(5)

where the friction angles ξ₁ and ξ₂ are given by the following expressions³²:

\begin{matrix} ξ_{1} = 0.5 \cos^{- 1} \frac{τ_{1}}{k} \end{matrix}

(6)

\begin{matrix} ξ_{2} = 0.5 \cos^{- 1} \frac{τ_{2}}{k} \end{matrix}

(7)

where τ₁ and τ₂ represent the frictional shear stresses on GD and AH, respectively, and k is the shear flow stress, which is a constant and related to the material properties. The value of τ/k represents the friction coefficient on the contact surface and takes values between 0 and 1.

Based on the triangle sine theorem, the contact length l_AG of the chamfered tool (containing DMZ) with the extruded strip is obtained:

\begin{matrix} l_{A G} = \frac{l_{G H} \sin α}{\sin (\frac{π}{2} - γ_{1} + α)} = \frac{w_{c} \sin α}{\cos γ_{2} \cdot \sin (\frac{π}{2} - γ_{1} + α)} \end{matrix}

(8)

\begin{matrix} l_{G D} = l_{A D} - l_{A G} = \\ t_{c h} [\cot (\frac{π}{2} - ξ_{1}) + \cot (\frac{π}{4} + ξ_{1})] - \frac{w_{c} \sin α}{\cos γ_{2} \cdot \sin (\frac{π}{2} - γ_{1} + α)} \end{matrix}

(9)

Consequently, positive pressure N₁ and friction F₁ on AD and positive pressure N₂ and friction F₂ on AH (see Figure 2(c)) are:

\begin{matrix} N_{1} = (1 + 2 θ + \sin 2 ξ_{1}) k w l_{A G} + (1 + \sin 2 ξ_{1}) k w l_{G D} \end{matrix}

(10)

\begin{matrix} F_{1} = k w l_{A G} \cdot \cos 2 ξ_{1} + k w l_{G D} \cdot \cos 2 ξ_{1} \end{matrix}

(11)

\begin{matrix} N_{2} = (1 + 2 θ + 2 δ + \sin 2 ξ_{2}) k w l_{A H} \end{matrix}

(12)

\begin{matrix} F_{2} = k w l_{A H} \cdot \cos 2 ξ_{2} \end{matrix}

(13)

where w is the extruded strip width, the main cutting force F_c and thrust force F_t for CT-EM are:

\begin{matrix} F_{c} = N_{1} \cos γ_{1} - F_{1} \sin γ_{1} + N_{2} \sin α + F_{2} \cos α \end{matrix}

(14)

\begin{matrix} F_{t} = N_{1} \sin γ_{1} + F_{1} \cos γ_{1} + N_{2} \cos α - F_{2} \sin α \end{matrix}

(15)

Predictive model of deformed layer thickness on machined surface

During the CT-EM process, in addition to the shear strain flowing towards the strip, the material under the tool is also strained. Accordingly, a deformed layer exists under the machined surface, whose thickness relates to chamfered tool edge parameters. Concerning the work done by Yang et al.,³³ the modeling schematics of the machined surface in CT-EM are shown in Figure 3.

Figure 3.

Modelling of the machined surface: (a) stress distribution under the concentrated force, (b) composition of the deformed layer, and strain distribution.

The stress distribution under concentrated force is illustrated in Figure 3(a), where the mechanical stresses on the machined surface are³⁴:

\begin{matrix} {\begin{matrix} σ_{r}^{m e c h} = \frac{2 (F_{t} \cos θ - F_{c} \sin θ)}{π ρ (θ) ω} \\ σ_{θ}^{m e c h} = τ_{r θ}^{m e c h} = 0 \end{matrix} \end{matrix}

(16)

\begin{matrix} {\begin{matrix} τ_{z θ}^{m e c h} = τ_{r z}^{m e c h} = 0 \\ σ_{z}^{m e c h} = v_{0} (σ_{r}^{m e c h} + σ_{θ}^{m e c h}) \end{matrix} \end{matrix}

(17)

where

σ_{r}^{m e c h}

σ_{θ}^{m e c h}

σ_{z}^{m e c h}

are principal stresses,

τ_{r θ}^{m e c h}

τ_{z θ}^{m e c h}

τ_{r z}^{m e c h}

are shear stresses, w is the extruded strip width, and θ is the polar angle from polar coordinate system. Furthermore, the thermal stress under the machined surface can be expressed by the classical thermoelastic equation³⁵:

\begin{matrix} σ_{z}^{t h e r m} = σ_{r}^{t h e r m} = σ_{θ}^{t h e r m} = α_{c} E Δ T \end{matrix}

(18)

where α_c is the material linear expansion coefficient, E represents elastic modulus, and ΔT is a temperature variation in polar coordinates. The stress calculation expressions are³⁶:

\begin{matrix} {\begin{matrix} σ_{r} = σ_{r}^{m e c h} + σ_{r}^{t h e r m} \\ σ_{θ} = σ_{θ}^{m e c h} + σ_{θ}^{t h e r m} \\ σ_{z} = σ_{z}^{m e c h} + σ_{z}^{t h e r m} \end{matrix} \end{matrix}

(19)

When the material surface is subjected to force, elastic and plastic deformation occurs in sequence. According to the fourth yield strength theory, the relationship between total stress and yield strength is governed by the von Mises yield criterion³⁷:

\begin{matrix} \sqrt{\frac{1}{2} [{(σ_{r} - σ_{θ})}^{2} + {(σ_{θ} - σ_{z})}^{2} + {(σ_{z} - σ_{r})}^{2}]} = σ_{s} \end{matrix}

(20)

where

σ_{s}

represents material yield strength. The deformation depth can be derived as³⁸:

\begin{matrix} ρ_{m a x} = {ρ (θ) |}_{θ = 0} = \frac{2 F_{t} \sqrt{v_{0}^{2} - v_{0} + 1}}{π w σ_{s}} \end{matrix}

(21)

where v₀ means Poisson's ratio. As illustrated in Figure 3(b), the deformation layer of the machined surface consists of an elastic deformation layer and a plastic deformation layer. In the CT-EM process, the deformation layer represents a layer that undergoes severe plastic deformation near the machined surface. The elastic deformation is obtained from the elastic deformation layer following Hooke's law³⁴:

\begin{matrix} U_{ρ m a x} = {U ρ (θ) |}_{θ = 0} = \frac{2 F_{t} l n (ρ_{m a x}) + F_{t} (1 + v_{0})}{π E} \end{matrix}

(22)

and the thickness of the plastic deformation layer:

\begin{matrix} B_{h} = ρ_{m a x} - U_{ρ m a x} = \frac{2 F_{t} \sqrt{v_{0}^{2} - v_{0} + 1}}{π w σ_{s}} - \frac{2 F_{t}}{π E} \\ l n \frac{2 F_{t} \sqrt{v_{0}^{2} - v_{0} + 1}}{π w σ_{s}} - \frac{F_{t} (1 + v_{0})}{π E} \end{matrix}

(23)

Simulation and experimental method

Simulation modeling

Finite element analysis of CT-EM process was performed by Deform software, providing a reference for actual experimental results. To increase the computational rate, a simplified 2D finite element model was created, as shown in Figure 4, where only the workpiece, constraint, and chamfered tool were retained. The workpiece material utilized in this study was pure copper that has undergone annealing treatment (600°C), aligning perfectly with the material used in the study. The workpiece was plastic pure copper with a constitutive model of³⁹: $\bar{σ} = 330 {\bar{ε}}^{0.235}$ . The constitutive model effectively characterized the stress-strain correlation of pure copper post-annealing and softening treatment, which was suitable for the finite element simulation employed in this study.

Figure 4.

Simplified simulation model and refinement region.

Additionally, the workpiece was divided into a substrate and a deformation layer, where the substrate had fewer meshes (about 2000) due to smaller deformation, while the deformation layer was divided into 10000 meshes. To increase the simulation precision, the meshes of deformation layer were further refined. The relevant parameters in cutting simulation were displayed in Table 1. Furthermore, the results after stable forming were used for analysis.

Table 1.

Relevant parameters in the simulation.

Parameters	Experiments
Parameters	1	2
Temperature T (°C)	20
Cutting speed V (mm/s)	92.0
Cutting thickness t₀ (mm)	0.3
Rake angle γ₁ (°)	25
Chip thickness t_ch (mm)	0.6
Single step length (mm)	0.05
Chamfer angle γ₂ (°)	−5, −15, −25, −35	−25
Chamfer width w_c (mm)	0.35	0.05, 0.20, 0.35, 0.50

3.2 Experimental method and setup

The experimental workpiece was a T2 pure copper round tube with an outside diameter of 70 mm, a length of 150 mm, and a wall thickness (equal to the extruded strip width) of 10 mm. The chemical composition of the workpiece was presented in Table 2. To improve the forming performance and eliminate the internal stress, the workpiece was completely annealed before experiments. The workpiece was heated to 600°C with a heating rate of 20 °C/min, holding time of 1 h, and then removed from the furnace after cooling to room temperature to obtain a uniformly organized copper tube. The microstructure of annealed pure copper was shown in Figure 5, and the original average grain size was about 60 μm.

Figure 5.

The initial microstructure of annealed pure copper.

Table 2.

The detailed components of T2 pure copper (wt.%).

Cu	Zn	P	Sb	Sn	Bi	Ni	S	O	As	Fe	Pb
99.95	0.005	0.002	0.002	0.002	0.002	0.002	0.0013	0.001	0.001	0.001	0.001

This study focused on influences of different chamfer angles (γ₂) and chamfer widths (w_c) upon the strips fabricated by CT-EM, including the microstructures, hardness, and tensile properties. Additionally, γ₂ of −5°, −25° and w_c of 0.05 mm, and 0.35 mm were selected as the experimental variables, and other parameters were kept consistent with the simulations (see Table 1). Based on the principle of CT-EM, a combined tool was designed consisting of a chamfered tool, a constraint, shims, nuts, and bolts. The values of t₀ and t_ch were controlled by shims of different thicknesses, and chamfered tool geometry parameters could be adjusted by different chamfered tools. As illustrated in Figure 6(a), the workpiece was extruded as a long strip by the combined effects of the constraint and chamfered tool. To further demonstrate the structure of the chamfered tool, Figure 6(b) showed the tip profile of the chamfered tool with γ₂ = –25° and w_c = 0.35 mm.

Figure 6.

(a) Experimental setup of CT-EM process, (b) tip profile of the chamfered tool, and (c) inlay process and tensile sample dimensions.

A stably formed section of each prepared strip was selected for wire cutting and then inlaid into the resin for better observation. Surfaces of prepared samples were ground with sandpaper from 600# to 4000# and eventually polished using diamond polish. The Vickers hardness tester (MVS-1000D) was applied to measure the microhardness of ND-FD surface using a load of 200 g and a dwell time of 15 s. A universal testing machine (AG-IC 300 KN) was used to conduct tensile tests on pure copper strips prepared by CT-EM and annealed original samples. To avoid dynamic effect interference, a strain rate of 1.0 mm/min was selected to ensure uniform material deformation. Additionally, dog-bone-shaped tensile samples (see Figure 6(c) for detailed dimensions) were cut along the material flow direction prior to the tests.

Before observation by metallographic microscope (DMI 5000 M), the corrosion solution (5 g FeCl₃, 16 ml HCl, and 60 ml C₂H₅OH) was employed to corrode the observation surface for 2 s. The samples were then immediately washed with anhydrous ethanol and dried, and finally observed the extruded strip, the deformation zone and DMZ, and machined surfaces for microstructure, respectively. Additionally, the microstructure of ND-FD surface was deeply characterized by the electron backscatter diffraction system (EBSD).

Results and discussion

Numerical simulation results

Through the mesh deformation in simulation, the CT-EM process could be divided into different stages. The workpiece was divided into 200 uniformly sized meshes, as shown in Figure 7(a), which could reveal the grain variation characteristics. Figure 7(b) showed the material diversion stage, in which some material flowed into the extrusion channel to form the extruded strip, while the other part flowed toward the rear face. Due to the different directions of material flow, there existed a stagnation point S on the chamfer, which was the greatest significance of the chamfered tool in CT-EM. As demonstrated in Figure 7(c), the DMZ was formed at the chamfer, affecting the material deformation of the extruded strip bottom and machined surface. Figure 7(d) showed the stable stage of strip formation, in which the mesh deformation of the strip bottom was severe and dense, indicating that the strain near the tool was larger than in the strip middle and top. Meanwhile, the meshes near the tool rear face were elongated, revealing that the chamfered tool had a plowing and extrusion effect on the material at a certain depth below the machined surface.

Figure 7.

Different stages of strip formation in CT-EM.

As shown in Figure 8, the tool-strip contact length could be divided into strip contact length with tool rake face and with chamfer edge (line GH). Figure 8(a) displayed the contact length at different γ₂ and the total contact lengths were 0.91 mm,0.84 mm,0.82 mm, and 0.66 mm when γ₂=–5°, −15°, −25°, and −35°, respectively. Additionally, the tool rake face contact length reduced from 0.61 mm to 0.29 mm and the GH length increased from 0.30 mm to 0.37 mm. As γ₂ decreased, the chamfer GH length increased, the contact length between the strip and tool rake face decreased. Meanwhile, the total contact length decreased, indicating that the contact length of tool rake face was the main factor affecting the total contact length. As depicted in Figure 8(b), the contact length at different w_c and the total contact lengths were 0.45 mm,0.57 mm,0.82 mm, and 1.17 mm when w_c = 0.05 mm, 0.2 mm, 0.35 mm, and 0.5 mm, respectively. With increasing w_c, both tool rake face contact length and GH length increased, revealing that proper chamfer width could reduce the contact area and decrease tool wear.

Figure 8.

The tool-strip contact length in CT-EM under (a) different γ₂ and (b) different w_c.

Figure 9(a) to (d) illustrated the temperature distribution at different γ₂. As γ₂ decreased, the material plastic deformation increased, and the cutting heat increased, leading to rising cutting temperatures. When γ₂ = –5°, −15°, −25°, and −35°, the average temperatures of the strip were 49.3°C, 53.8°C, 54.6°C, and 57.8°C, respectively. Frictional heat generation was significant in DMZ due to the most intense material deformation, leading to the highest temperatures distributed around the DMZ. The temperature distribution at different w_c was shown in Figure 9(e)-(h), and the cutting temperature dramatically increased as w_c increased. The average temperatures of the strip were 43.2°C, 47.5°C, 54.6°C和 63.9°C when w_c = 0.05 mm, 0.2 mm, 0.35 mm, and 0.5 mm, respectively. Changing w_c showed a greater increase in cutting temperature compared to γ₂, indicating that w_c has a more significant effect on cutting heat.

Figure 9.

Cutting temperature distribution at different chamfered tool parameters.

The effective strain reflected the degree of material plastic deformation in CT-EM, which elongated or even shattered the grains, thus high strain led to grain refinement. As depicted in Figure 10(a) to (d), the largest effective strain occurred ahead of the chamfer GH, the values were 5.28, 6.9, 7.84, 8.1 when γ₂=–5°, −15°, −25°, and −35°, respectively. The large strain in DMZ was attributed to heavy material accumulation and severe extrusion and friction in this region. With decreasing γ₂, the stagnation point (S₁) tended to move towards point G, resulting in less material flowing to the extruded strip and more material flowing to the machined surface. Consequently, the zone II thickness decreased, and the zone III thickness increased, while the effective strains were smaller in zones I and IV because they were far from the DMZ.

Figure 10.

Simulation results of effective strain at different γ₂: (a)-(d) distribution diagrams, (e) variation curves along trajectory P₁P₂, and (f) trajectory P₃P₄.

Figure 10(e) displayed strain variation along track P₁P₂, which rose slowly before the distance of 0.5 mm, and then rose sharply. As γ₂ decreased from −5° to −25°, the maximum effective strain tended to increase, while it dropped when γ₂ was −35°. This was because when γ₂ = –35°, the stagnation point S₁ was close to point G, resulting in little influence of DMZ on the material before flowing into zone II, and thus the maximum effective strain decreased instead of increasing. Along track P₃P₄ in the machined surface, the effective strain tended to decrease with depth, as shown in Figure 10(f). With decreasing γ₂, the effective strain on the machined surface (point P₃) increased, while the effective strain at point P₄ all converged to 0.

Figure 11(a) to (d) exhibited the effective strain distribution at different w_c, the maximum effective strains were 5.31, 7.35, 7.84, and 8.06 when w_c =0.05 mm, 0.2 mm, 0.35 mm, and 0.5 mm, respectively. Due to the special structure of the chamfered tool, DMZ formed, and in which the effective strain was the largest. As w_c increased, the DMZ area increased, representing a wider effect range of DMZ and more drastic material deformation. Similarly, point S₁ divided the material flow into two directions, flowing to zone II and zone III, respectively. As shown in Figure 11(e), along the track P₁P₂, the effective strain variation increased slowly before the distance of 0.5 mm and then grew sharply. The maximum effective strain of the strip was at point P₂, and its value increased with increasing w_c. Along track P₃P₄ in the machined surface, the effective strain tended to decrease with depth, as shown in Figure 11(f). As w_c increased, the effective strain at point P₃ increased, while it tended to 0 at point P₄.

Figure 11.

Simulation results of effective strain at different w_c: (a)-(d) distribution diagrams, (e) variation curves along trajectory P₁P₂, and (f) trajectory P₃P₄.

Microstructures and mechanical properties

Figure 12 showed the metallographic diagrams of strips fabricated by CT-EM under different chamfered tool parameters, where each strip was divided into strip top (constraint side), strip middle, and strip bottom (tool side). There are several defects at the strip top, and the strip bottom could be subdivided into a low strain region (I) and a high strain region (II) based on effective strain level. Because of the intense extrusion and cutting by the chamfered tool and the significant influence of DMZ, the grains in Zone II were further fragmented and refined, while those in Zone I were simply elongated.

Figure 12.

Metallographic diagrams of the fabricated strips under different parameters.

As exhibited in Figure 12, there were varying degrees of defects at the chip top, such as cracks and burrs. When w_c = 0.35 mm, as depicted in Figure 12(a) and (b), the maximum crack depth at strip top increased from 64.10 μm to 144.22 μm, and the zone II thickness at strip bottom reduced from 62.63 μm to 42.03 μm when γ₂ decreased from −5° to −25°. It matched the effective strain simulations in Figure 10(a) and (c), where the reduced γ₂ decreased high strain region (II) thickness, but increased shear strain (according to white flow line deflection). As γ₂ decreased, the constraint effect on the strip shape regularization weakened and was accompanied by tearing, leading to the formation of deeper cracks. When γ₂ = –25°, as presented in Figure 12(b) and (c), the maximum crack depth at strip top increased from 28.37 μm to 144.22 μm, and the zone II thickness at strip bottom increased from 35.33 μm to 42.03 μm when w_c grew from 0.05 mm to 0.35 mm. The effect of chamfer tool was more pronounced with increasing w_c, resulting in multiple and deep top cracks, while the enlarged DMZ area increased effective strain and zone II thickness. Additionally, as γ₂ decreased and w_c increased, the length of burrs on the chip surface tended to increase.

To deeply explore the microstructure of the strip prepared by CT-EM, the observation regions in Figure 12(b) were selected for EBSD. Figure 13 showed EBSD results of the CT-EM sample, where the inverse pole figures (IPFs) and grain size distribution of Zone I and II reflected different strain levels. Due to the intense friction and extrusion in DMZ, the material close to the extrusion channel was violently deformed and then flowed into Zone II, resulting in larger strain and finer grains. As depicted in Figure 13(a) and (b), the grain orientation in Zone I was largely focused on <101 > and <001 > directions, while that in Zone II focused mainly in the <111 > direction. Figure 13(c) and (d) showed that the average grain size of Zone I was 2.601 μm, which was 44.2% higher than that of Zone II (1.452 μm). Compared with the initial annealed pure copper (approximately 60 μm), the grains in Zones I and II were effectively refined. Additionally, the proportions of high-angle grain boundaries (HAGBs, 2°-15°) in the two regions were 86.3% and 96.9%, respectively, as shown in Figure 13(e) and (f).

Figure 13.

EBSD results of the strip at w_c = 0.35 mm and γ₂ = - 25°: (a)-(b) IPFs, (c)-(d) grain size distribution, (e)-(f) misorientation angle distribution.

During the CT-EM process, the initial coarse grains were continuously elongated and deformed under the imposed strain. As the strain increased, the dislocation sub-boundaries formed at low strain gradually transformed into finer grains with high-angle boundaries, which was known as continuous dynamic recrystallization (CDRX). The fine grains with HAGBs observed in Zones 1 and 2 were transformed from subgrains through dislocation accumulation. Therefore, CDRX was identified as the primary grain refinement mechanism, driven by high shear strain imposed by the DMZ. Since the materials all underwent severe deformation, this coincided with the grain refinement mechanism involved in most SPD processes reported previously.^40–42

Figure 14 demonstrated the distribution of Vickers hardness with length from the constraint side for different parameters. The hardness of the initial sample was 68.1 HV, and CT-EM effectively improved the hardness. The average hardnesses of fabricated strips were 132.71 HV when γ₂ = −5° and w_c = 0.35 mm, 141.05 HV when γ₂ = –25° and w_c = 0.35 mm, and 130.68 HV when γ₂ = –25° and w_c = 0.05 mm. With decreasing γ₂ and increasing w_c, the average hardness of the strip improved and the hardness near tool side was higher than that near the constraint side. This is due to the material near tool side being strongly affected by DMZ, with stronger friction and extrusion effects, leading to larger strain and finer grains. Accordingly, the hardness distribution agreed with the results of effective strain and microstructures.

Figure 14.

The hardness distribution with length from the constraint side for different parameters.

To further investigate the tensile properties of prepared strips for different parameters, Figure 15(a) illustrated the stress-strain curves and Figure 15(b) exhibited the corresponding tensile properties. Compared to the tensile properties of prepared strips, the ultimate tensile strength (σ_UTS) of original samples was the minimum (204.4 MPa) and the elongation at fracture (ε_EF) was the maximum (66.9%). As γ₂ decreased from −5° to −25°, σ_UTS increased from 389.6 MPa to 433.2 MPa and ε_EF dropped from 11.3% to 9.1%. As w_c grew from 0.05 mm to 0.35 mm, σ_UTS increased from 370.8 MPa to 433.2 MPa and ε_EF reduced from 13.9% to 9.1%. With decreasing γ₂ and increasing w_c, the grain refinement and dislocation density grew, and microhardness enhanced, resulting in improved σ_UTS and reduced ε_EF.

Figure 15.

Tensile results for different parameters: (a) stress-strain curves, (b) detailed properties, and (c) strain-hardening rate-engineering strain curves.

As shown in Figure 15(c), the strain hardening rates (n) of the strips prepared by CT-EM were greater compared to original samples when the engineering strain was 0.15, and they all decreased rapidly thereafter. Since the higher n value was favorable for suppressing local deformation and delaying necking, it indicated the best plasticity of the original sample, whereas n values of strips prepared by CT-EM under different parameters all dropped to 0 before the engineering strain of 0.06. To obtain strips with better performances, smaller γ_2, and larger w_c are preferred in the design of chamfer tool parameters, sacrificing only a little plasticity with higher strength.

The decrease in grain refinement led to lower ultimate tensile strength, while ductility and strength were inversely related. That was, the increase in strength was necessarily at the expense of ductility. Tensile properties of copper sheet processed by some other techniques were shown in Table 3. These samples showed limited ductility, this was because ultrafine-grained structures exhibited high strength characteristics. The strips prepared by CT-EM sample showed higher ductility than ultrafine-grained counterpart. In addition to fine grain in the strips prepared by CT-EM process, the presence of coarse grains allowed the sample to retain a certain degree of ductility. Thus, the strips prepared by CT-EM exhibited higher ductility than others.

Table 3.

The tensile properties of the sheets processed by CT-EM and other SPD process.

SPD process		σ_UTS (MPa)	ε_EF (%)	Reference
CT-EM	(t_ch = 0.6 mm, γ₂ = −5°, w_c = 0.35 mm)	389.6	11.3	This study
	(t_ch = 0.6 mm, γ₂ = −25°, w_c = 0.35 mm)	433.2	9.1	This study
	(t_ch = 0.6 mm, γ₂ = −25°, w_c = 0.05 mm)	370.8	13.9	This study
CR	(t = 1.5 mm)	358.6	1.0	⁴³
RTR	(t = 1.5 mm)	347.0	2.1	⁴³
RTR	(t = 1 mm)	421.8	7.5	⁴⁴
ECAP	(1 pass)	319.9	12.4	⁴⁵
ECAP	(4 passes)	373	9.4	⁴⁵
ECAP	(8 passes)	400	8.2	⁴⁵
ECAP	(12 passes)	408	11.6	⁴⁵
ARB	(t = 1.1 mm, 1 pass)	363	5.5	⁴⁵
ARB	(t = 1.1 mm, 5 passes)	445	5.7	⁴⁵
ARB	(t = 1.1 mm, 9 passes)	480	5.2	⁴⁵
ARB	(t = 1 mm, 8 passes)	430	5.0	⁴⁶

Investigation of stagnation points in DMZ

There existed some correlation between the stagnation point, DMZ, and the material velocity, as shown in Figure 16, so DMZ could be investigated by the flow velocity distribution ahead of the chamfer. Since the DMZ shape in the simulation was approximate to a triangle, the region AGH was used to represent the DMZ in Figure 16(a) to (d). To better analyze the diversion effect of the chamfer tool, the inflow point (S₁) and stagnation point (S₂) were marked on the AGH boundary. The white line between S₁ and S₂ divided the DMZ into two parts, in which the material flowed to the formed strip and machined surface, respectively. As γ₂ decreased from −5°to −35°, the DMZ area grew from 0.027 mm² to 0.049 mm², and point S₁ tended to approach point G, leading to larger amount of material entering the machined surface. Figure 16(e) and (f) exhibited changes of DMZ shape and point S₁ location under different γ₂. Lengths of d_S1 and d_A reduced with decreasing γ₂, indicating a gradual shift of the gravity center to side G. Additionally, as γ₂ reduced from −5° to −35°, the relative position d_S1/d_H of stagnation point on chamfer GH decreased from 0.95 to 0.15, showing that more material flowed to the machined surface.

Figure 16.

Flow velocity distribution in simulation and point S₁ location under different γ₂.

As depicted in Figure 17(a) to (d), the DMZ areas were 0.001 mm², 0.011 mm², 0.037 mm², and 0.108 mm² when w_c = 0.05 mm, 0.2 mm, 0.35 mm, and 0.5 mm, respectively. Therefore, the increased w_c significantly enlarged the DMZ area, leading to a larger effective strain in the prepared strip. Figure 17(e) and (f) showed the DMZ changes and point S₁ location under different w_c. As w_c grew, the lengths of d_S1, d_H, d_A, and d_S1/d_H all increased, suggesting little variation in the shape and gravity center of DMZ. Furthermore, compared to γ₂, w_c had less influence on point S₁ affecting the material flow ratio.

Figure 17.

Flow velocity distribution in simulation and point S₁ location under different w_c.

To verify the regularity of the DMZ and stagnation points for different parameters in the simulation, Figure 18 showed microstructures of the deformation zone and the DMZ in CT-EM. Based on the white auxiliary quadrangles in Figure 18(a), (c), and (e), the material was deformed before reaching the first deformation zone and subsequently experienced elongation and refinement. With decreasing γ₂ and increasing w_c, the shear angle φ in CT-EM decreased, resulting in more drastic material deformation and larger shear strain. Notably, the absence of obvious crack defects on the workpiece surface proved the constraint's effect on workpiece morphology, whereas the crack defects in Figure 12 were generated after extruded strip formation.

Figure 18.

Microstructures of the deformation zone in CT-EM and the DMZ ahead of tool under different parameters.

As presented in Figure 18(b), (d), and (f), the real shape of DMZ was arched and the grains in it were severely refined. Based on the microstructure within DMZ, the approximate locations of points S₁ and S₂ were marked and the line between them demarcated the two material flow directions. By comparative analysis, the reduced γ₂ mainly affected the stagnation point location and thus reduced the material proportion flowing to the strip, while the increased w_c raised effective strain by enlarging the DMZ area. Additionally, the thickness of zone II decreased with reducing γ₂ and w_c, which was consistent with the simulation results. Similarly, the machined surface could be divided into a high strain zone (III) and a low strain zone (IV), where zone III underwent a large plastic deformation under DMZ influence and was also called the deformed layer. The thickness of Zone III was also attributed to the stagnation point location in DMZ and had the opposite trend to Zone II.

The quantitative analysis of the “DMZ - stagnation point - material flow” through finite element simulation (see Figures 16 and 17), alongside qualitative observations of microstructure (including the area of DMZs and the location of point S) via CT-EM experiments (see Figure 18), established a comprehensive verification closed loop. The DMZ defined by simulations exhibited high consistency with the microscopic characteristics from experimental results, mainly reflected in the variation patterns of the DMZ area and stagnation points.

Furthermore, the effects of key parameters (γ₂ and w_c) on DMZ behaviors, stagnation points, and material flow demonstrated alignment between the quantitative trends derived from the simulation and qualitative characteristics identified in experiments. The experimental findings further validated critical conclusions drawn from simulations–specifically that “the constraint ensured surface quality of the workpiece” and “the impact of w_c on material flow ratio was less significant than that of γ₂.” This provided robust experimental support at a micro level for affirming the reliability of simulation results.

Validation of prediction models

Table 4 showed the relevant parameters required for cutting force modeling, where the angle α between the DMZ boundary AH and the horizontal direction, and the friction coefficient τ₁/k on the contact length l_GD between strip and tool rake face were obtained from the simulation results. Additionally, the friction coefficient τ₂/k of AH was 0.8³⁰ and the flow shear stress k could be calculated from the yield strength σ_s⁴⁷: $k = \frac{σ_{s}}{\sqrt{3}}$ . The yield strength σ_s of annealed pure copper was obtained as 76 MPa by tensile test, and the shear angle φ in CT-EM was obtained by simulation results.

Table 4.

The deformed layer thickness h within the machined surface in CT-EM.

Parameters	γ₂ (°)	w_c (mm)	α (°)	τ₁/k	τ₂/k	φ (°)
γ₂	−5	0.3	23.16	0.47	0.8	23.65
	−15	0.3	18.36	0.43		23.22
	−25	0.3	15.75	0.35		22.55
	−35	0.3	9.28	0.32		24.29
w_c	−25	0.05	3.91	0.35	0.8	28.51
	−25	0.20	11.44	0.35		27.17
	−25	0.35	15.75	0.35		22.55
	−25	0.50	8.53	0.35		23.01

To verify the cutting force model, Figure 19 presented relevant results under different parameters. With decreasing γ₂ and increasing w_c, the main cutting force F_t thrust F_c, and F_t/F_c in CT-EM tended to increase, which coincided with the variations in DMZ and stagnation point location analyzed above. The expanded DMZ area resulted in higher cutting forces, and the shifting of stagnation points to the strip led to more material flow into the machined surface, increasing F_t/F_c. Through comparative analysis, varying w_c had a greater effect on cutting force, while the model accuracy was higher under different γ₂. Furthermore, the cutting force model under different parameters was consistent with the actual results, offering a guideline for the practical application of CT-EM.

Figure 19.

Predicted and simulated results of cutting force under (a) different γ₂ and (b) different w_c.

Figure 20 displayed microstructures and finite element results of the machined surface in CT-EM under different parameters, where zone III thickness was equal to the deformed layer thickness (B_h), while zone IV was a low strain zone with no significant grain refinement. As shown in Figure 20(a) to (c), the deformed layer thickness was 71.04 μm when γ₂ = –5° and w_c = 0.35 mm, 154.95 μm when γ₂ = –25° and w_c = 0.35 mm, and 44.21 μm when γ₂ = –25° and w_c = 0.05 mm. As γ₂ decreased and w_c increased, the stagnation point moved to the strip, resulting in more material flowing to the machined surface and an increase in deformed layer thickness. As illustrated in Figure 20(d) to (f), the simulation results of effective strain could reflect the deformation of the machined surface. Notably, the trend in deformation layer thickness was consistent with the microstructure observed in the experiments.

Figure 20.

Deformed layer thickness of machined surface in CT-EM under different parameters: (a) microstructure and (b) simulation results.

Combining Equation (23) and cutting force results, the deformed layer thickness B_h was obtained as shown in Table 5, where the elasticity model E and Poisson's ratio v₀ were from the research of Johnson et al.⁴⁸ With decreasing γ₂ and increasing w_c, both experimental and calculated B_h tended to increase, and the relative deviations were all less than 5%, indicating that the predictive model was highly accurate. The analysis above revealed that finite element stimulation, experimental results, and predictive models shared the similar trends, demonstrating a high degree of consistency.

Table 5.

The deformed layer thickness B_h within the machined surface in CT-EM.

γ₂ (°)	w_c (mm)	σ_s (MPa)	E (GPa)	v₀	Experimental B_h (μm)	Calculated B_h (μm)	Relative deviation (%)
−5	0.35	76	124	0.34	71.04	67.62	4.8
−25	0.35				154.95	147.28	4.9
−25	0.05				44.21	43.29	2.1

Conclusions

This paper proposed a new process of CT-EM and successfully prepared UFG strips with DMZ using chamfered tools. The strip forming mechanism, effective strain distribution, microstructure, and mechanical properties for varying chamfered tool parameters γ₂ and w_c were analyzed in detail. Additionally, the stagnation point ahead of the chamfered tool was deeply explored, and the models of cutting force and deformed layer thickness were developed and validated. The main conclusions were summarized below:

The CT-EM process was divided into three stages: material divergence, DMZ formation, and strip stable formation. The reduced γ₂ and increased w_c tended to enlarge the DMZ area, and γ₂ mainly contributed to DMZ shape and stagnation point location, while w_c primarily affected the DMZ area. Notably, the movement of the stagnation point toward the strip would increase the material ratio flowing to the machined surface.

According to the effective strain distribution, the extruded strips could be categorized into high and low strain zones (II and I), and the machined surfaces were categorized into zones III and IV. As γ₂ decreased from −5° to −25°, the strip effective strain tended to increase, while it dropped when γ₂ was −35°, indicating that the stagnation point moved close to point G and little material in DMZ flowed to Zone II. With increasing w_c, the effective strain on both the strip and the machined surface increased.

Compared to the annealed pure copper (68.1 HV, 204.4 MPa), CT-EM effectively improved the hardness and strength of prepared strips. With decreasing γ₂ and increasing w_c, the grain refinement and dislocation density grew, and microhardness enhanced, resulting in improved σ_UTS and reduced ε_EF. Smaller γ₂ and larger w_c were preferred in chamfer tool design to obtain higher strength while sacrificing only a little plasticity.

Based on the chamfered tool shape and slip line field theory, the predictive models of cutting force and deformed layer thickness for CT-EM were established. By comparing the actual and predicted values under different parameters, both predictive models proved to be highly accurate. Furthermore, the tool-strip contact length reduced with decreasing γ₂ and w_c, while the decreased γ₂ and increased w_c significantly increased the cutting temperature.

Footnotes

Ethical standards

This research did not involve any human participants or animals.

Author contribution(s)

Xueqin Pang: Conceptualization; Formal analysis; Formal analysis; Project administration; Validation; Writing – original draft.

Xiaodong Yu: Formal analysis; Investigation; Writing – review & editing.

Peixuan Zhong: Data curation; Resources; Software; Validation.

Zizhao Li: Methodology; Software.

Wenjun Deng: Formal analysis; Project administration; Supervision.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China [grant number 52075187, 52505487]; the Yunnan Fundamental Research Projects [grant numbers 202301BE070001-021, 202401CF070145]; and the Analysis and Testing Foundation of Kunming University of Science and Technology [grant numbers 2023T20230023].

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability

The authors do not have permission to share data.

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