Finite Element Modelling of Serrated Chip Formation During Turning AZ31 Magnesium Alloy

Machining metal alloys such as AZ31 magnesium alloy involve thermomechanical behavior between workmaterial and cutting tools. The interaction between workmaterial and cutting tools has affected the chip formation in metal cutting and cutting performance. This paper developed a finite element model (FEM) by using Abaqus software to simulate the chip formation in cutting AZ31 magnesium alloy under dry condition. The study revealed that serrated chips were formed in dry condition. Chip segmentation increased proportionally with cutting speed as generated heat concentrated in a narrow zone, promoting the formation of an adiabatic shear band.


Introduction
Magnesium alloy has strong machinability characteristics, including low cutting force, and longer tool life.However, there is a growing scholarly interest in examining various cooling techniques, such as minimum quantity lubrication (MQL) and cryogenic cooling, in order to address the fire and ignition risk associated with cutting magnesium alloy [1] [2].Because AZ31 magnesium metal has a low melting point, built-up edge and built-up layer formed at the tool rake face when the critical cutting temperature is exceeded [3] [4].High-speed dry machining of these alloys favours melting and depositing on the cutting tool surface, which degrades surface quality and shortens tool life.Cryogenic machining is one way to keep the cutting temperature low enough to prevent this occurrence from occurring.[5] [6].Since the interaction between the cutting process and the tool involves both thermal and mechanical properties, it appears to be a complex tribological phenomenon.Cutting of metals often results in the generation of serrated chips.Serrated chips not only affect the workpiece's surface integrity, but also the stability of the machining processes.Two mechanisms, rapid thermoplastic shear and adiabatic shear, have been identified to explain the formation of serrated chips [7] [8].Material shear flowing deformation, material failure, and crack generation are all highly temperature-dependent physical phenomena that are examined in the main shear zone to understand the formation process.
The current study presents a comparative examination of chip formation under dry cutting condition.Modelling and simulation of the orthogonal cutting process of AZ31 magnesium alloy are performed.Johnson-Cooks damaged and plasticity coupled material model is used to investigate orthogonal cutting processes.Fracture mechanics-based techniques are utilised in finite element-based cutting models to describe the chip formation process [1][9].Commercial FEM-based software enables damage mechanics approaches and discontinuity initiation and evolution.The thermomechanical behaviour of AZ31 magnesium alloy and uncoated cutting tool in dry cutting is investigated in this paper.An Arbitrary Lagrangian Eulerian (ALE) finite element is developed in Abaqus/Explicit software and experimental data in orthogonal cutting was used for validation.

Machining tests
Magnesium alloy AZ31 was the material under investigation in this study.The ISO CNMA120408 uncoated carbide inserts were utilised for the orthogonal cutting tests that were carried out on a CNC machine T6 Compact Quicktech.In the investigations, rods of 30 mm in diameter and 100 mm in length was utilised.Three cutting speeds was used in this study (120, 180, and 240 m/min), while the feed rate and depth of cut were held constant (0.2 and 1 mm, respectively) for all machining experiments.Cutting forces data were measured by a Kistler type 9129AA dynamometer [10] and the cutting trial was repeated three times for each cutting speed.

Numerical Modelling
To model chip formation in dry cutting of AZ31 magnesium alloy, it is vital to note the extreme condition of plastic deformation and friction at the tool chip interface.A plane-strain assumed 2D dynamic coupled temperature-displacement finite element model was implemented using the code ABAQUS/Explicit shown in Figure 1.Tool and workpiece were modelled with CPE4RT type quadrilateral four-node elements.There was no allowance for tool deformation since the tool was treated as a rigid body.The x and y axes of the workpiece were clamped to its base and a side.The cutting tool was constrained in the y direction while a velocity was given in the x direction.It is presumed that surfaces are adiabatically insulated for dry cutting.The chip formation process should account for the extremely large strain rate and the increase in temperature caused by plastic work.To analyze chip formation process, the thermo-mechanical response of AZ31 magnesium alloy from the Johnson-Cook (JC) constitutive model is used to characterize the thermo-visco-plastic behavior of the work material, where the flow stress is represented by the equation ( 1): Fitting data for the AZ31 Mg sheet under a wide range of strain rates was validated by Hasenpouth D. [13] and averaged value of Johnson-Cook constitutive model constants both for rolling and transverse direction are listed in Table 2. To simulate serrated chip formation, a damage model is implemented in FEM.In this study, the Johnson-Cook failure model which defined the equivalent plastic strain as correspondent to the onset of damage is defined in equation ( 2): Based on the cumulative damage rule stated by equation ( 3), the damage is triggered when the scalar damage parameter  is greater than 1.
where ∆̅ is the increment of equivalent plastic strain.When ductile material damage initiates (D = 1), the connection between stress and strain no longer adequately represents the behavior of the material., in fact, damage evolution will affect flow stress and a strong mesh dependency occurs from severe strain localization [14].

Result and Discussion
The proposed numerical modelling is validated and calibrated using experimental force components in order to investigate the serrated chip morphology under dry cutting.The value of friction coefficient,  is dependent upon the predicted cutting and feed force [15].It was determined that the value of  that best predicted the component of cutting forces for cutting velocities of 120, 180, and 200 m/min in dry cutting was 0.1.As depicted in Figure 2, the average cutting and feed forces derived from experimental data were used to validate the finite element model.The maximal deviation between experimental and predicted feed forces was 8% for dry cutting.However, the cutting forces for were overestimated by up to 11%.

Serrated chip formation
Fundamentally, a serrated chip is the result of strain localization at the primary shear zone, which causes adiabatic shear instability [16].This mechanism of chip serration occurred momentarily; consequently, the deformation process was regarded as an adiabatic process.When thermal softening hinders the work hardening caused by high local strain rates, strain localization begins in the area closest to the tool's tip.Previous research on hardened steel revealed similar phenomena concluded that adiabatic shearing at the tooltip had been triggered by an instability in the main shear zone and had spread to the free surface [17].Segmentation ratio (SR) was determined by calculating the ratio of the difference in peak to the valley over the peak using equation ( 4).The peak was defined as top height of the tooth and valley was the root height of the tooth as shown in Figure 3.According to Figure 3, chip serration was produced at all cutting velocities.This was primarily attributable to the negative rake angle employed during the cutting process, as negative rake angles were prone to producing serrated chips [18].According to the obtained results, the cutting speed has great influence to the onset of chip segmentation based on the work material and machining conditions [7]. Figure 4 demonstrates a positive correlation between SR and cutting speed for dry cutting.As a general rule, a greater SR indicates a greater segmentation intensity.As depicted in Figure 4, chip serration was affected by cutting speed, and similar findings were reported when cutting aluminium and titanium alloy [16] [19].As can be seen in Figure 5, temperature was plotted along the path AB.When cutting speed was increased, strain rate increased substantially in a localised area of the chip.Since the deformation process occurs at a higher strain rate, higher temperatures were increased at the primary shear zone, which facilitated the appearance of adiabatic shear banding.At low cutting speeds (120 m/min), the heat generated can dissipate within the primary shear zone and the free surface, resulting in less SR for low cutting speeds.In contrast, for high cutting speeds (240 m/min), heat was concentrated in a confined region, resulting in catastrophic strain localization and a higher SR [16].The results match the findings in [7], whereby the cutting speed has strong relation to the initiation of serrated chip.The predicted cutting forces and chip SR were close to the experimental data, thus, the proposed FEM model satisfactory to be used in investigating the mechanisms of the serrated chip formation.It can be observed that the temperature along the path A-B and the SR increase as cutting speed increases.The was mainly attributed to the amount of heat generated in the cutting zone.As the cutting speed is increased, the amount of cutting heat produced in the tool-chip contact zone rises.As a result, the degree to which the material softens in the shear zone increases.Under the burnishing effect of cutting tools, severe plastic deformation process lead to material softening effect and increase in deformation heat [20].Consequently, the temperature along the adiabatic shear band rises with the cutting speed which occurred as well in cutting titanium and aluminium [20][16].This occurrence leads to a surging in the degree of material softening in the shear zone, thus increase in the SR of chips.
Any effort to investigate the factors that contribute to the initiation of serrated chip, the consideration of the temperature within the primary shear zone should not be negligible.Presented FEM could be further investigated to examine stress component, strain rate, and etc on the influence of onset the serrated chip of AZ31 mg alloy.However, there exist some limitations in the current model whereby the normal stress and frictional stress distribution at the tool-chip contact area were hardly inaccessible to relate with the serrated chip phenomenon.

Conclusion
In this study, a FEM was developed to simulate the chip formation in cutting AZ31 magnesium alloy using the commercial software ABAQUS Explicit under dry condition.The validation of the FEM was compared to the experimental data on the cutting force components.It was observed that the chip serration occurred for all cutting conditions.Chip segmentation was proportional increase with cutting speed as heat generated concentrated at a narrow zone promoting the adiabatic shear band.

Acknowledgments
The funding for this study was provided by the Ministry of Higher Education, Malaysia under the Fundamental Research award Scheme (FRGS), FRGS/1/2020/TK0/UNIMAP/03/15.

Figure 1 .
Figure 1.Boundary conditions of FEM

Table 1 .
Table 1 depicts the mechanical properties of AZ31 magnesium alloy and tool.Properties of AZ31 magnesium alloy and tool [11][12]