Atomistic simulations of the surface severe plastic deformation-induced grain refinement in polycrystalline magnesium: The effect of processing parameters

Xiaoye Zhou, Hui Fu, Ji-Hua Zhu, Xu-Sheng Yang

a Guangdong Province Key Laboratory of Durability for Marine Civil Engineering, School of Civil Engineering, Shenzhen University, Shenzhen, Guangdong 518060, China

b State Key Laboratory of Ultra-precision Machining Technology, Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

c Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China

Abstract

Keywords: Mg alloy; Grain refinement; Surface severe plastic deformation; MD simulations.

1.Introduction

Magnesium (Mg) and its alloys have many applications in the automobile, aerospace [1], electronic and medical device industries [2]owing to their low density and high specific strength.However, Mg often suffers from low strength and ductility.Efforts have been made to enhance the strength[3–5]and ductility [6]of Mg and its alloys, and tremendous improvements have been achieved.Grain refinement is a commonly adopted strategy to improve the strength of metals[7].The higher density of grain boundaries (GBs) in the refined materials can impede dislocation movement and thereby increase the yield strength and hardness.Nowadays, metals with grain sizes of nanometer scale can be fabricated.However, although extremely strong, the nanograined metals usually suffer from low ductility.To improve strength without the severe degradation of ductility, the concept of gradient nanostructured (GNS) metals [8-9]was proposed, and several manufacturing methodologies were developed.The GNS metals typically have a hard, nanograined surface and a soft coarse-grained inner core that can retain the ductility of theoriginal material.Apart from evading the strength-ductility trade-off dilemma, GNS metals have also shown improved surface hardness, wear and fatigue resistance.

Various surface severe plastic deformation (SSPD) approaches, such as surface mechanical attrition treatment(SMAT) [10-11], surface mechanical rolling grinding treatment (SMRGT) [12], and laser shock processing (LSP) [13-14]etc., have been developed to produce the GNS surface in Mg alloys.In these processes, the surface layer of a material is subjected to high-strain-rate deformation, producing nanostructures on the surface and a high density of crystalline defects in the subsurface layers due to the gradient plastic strain field.The grain refinement mechanisms involved in these techniques have been extensively discussed in hexagonal close-packed (HCP) Mg alloys.To name a few, Shi et al.[10]studied the grain refinement process of GNS Mg-Gd alloy produced by SMAT technique.The results showed that twinning dominates the initial stage of the plastic deformation when the dislocation slips are obstructed.And till all the coarse grains are divided into substructures by twin–twin interactions and twin-dislocation arrays intersections, dislocation slips and stacking faults begin to play an important role in impelling subgrains to nanograins by lattice rotating through dislocation arrays slipping.Chen et al.[12]prepared a GNS surface layer on AZ31B Mg alloy by SMRGT method.The mechanism of grain refinement was supposed to be the compressive strain-induced deformation twining, dislocation slip systems movement, the refinement effect of subgrain boundaries, and preferred orientation of local grains and boundaries from the slightly deformed region to the topmost surface.Ren et al.[14]studied the grain refinement mechanisms of GNS AZ91 Mg alloy prepared by LSP method.The authors pointed out that the grain refinement process was attributed to dislocation glide and mechanical twining.The above studies indicate that the grain refinement process of the SSPD-induced GNS layer in Mg alloys are still needed to be clarified due to the complexed deformation modes caused by inherent low crystallographic symmetry.

In the current research, we employed Single Point Diamond turning (SPDT) technique to improve the surface mechanical properties of an Mg-Li alloy workpiece.SPDT is a high-speed mechanical machining technique using a cutting tool with a diamond tip and is widely adopted for processing workpiece with high precision.SPDT can generate severe plastic deformation at metal surfaces, thus can also be regarded as a kind of SSPD process, as schematically shown in Fig.1(a-b).SPDT has the advantage of ultra-high precision and surface quality, great controllability, relatively lower cost and wide availability compared with other SSPD techniques.In addition, it has been widely reported that Li can decrease the stress for cross-slip in Mg at room temperature which can subsequently improve the plasticity of Mg alloy.The good room-temperature ductility of Mg-Li alloys enables them to have many potential applications.It is found that the surface layers of the workpiece were refined to the nanometer scale without surface cracking, and a substantial improvement in the surface hardness was achieved after the SPDT treatment.Molecular dynamics (MD) simulations were then performed to reveal the deformation mechanism.Owing to its ability of revealing real-time atom movements and microstructure evolutions during the deformation process with atomic-level detail[15–17], MD simulation has become a commonly used tool for studying SSPD processes [18–19]and the deformation mechanisms of Mg alloys [20–22].By performing MD simulations to investigate the plastic deformation during SPDT machining, we uncovered the defect generation and microstructure evolution processes that occurred during cutting.The influence of different cutting parameters was studied by performing a series of cutting simulations with different combinations of rake angle, cutting depth and cutting speed.It is suggested that when the workpiece was processed with an increased cutting depth, rake angle and cutting speed, the depth of the regions near the surface of the workpiece that were affected increased, and an improved grain refinement was achieved.It was also found that an increased cutting speed activated non-basal plane slip systems, thereby improving the ductility of the workpiece.The findings of the current research work confirmed that the SPDT technique effectively refined grains in the surface layers of Mg workpieces and improved the surface hardness.The parameter analysis conducted through MD simulations may provide a guidance for choosing proper cutting parameters for the SPDT of the Mg workpiece to achieve improved surface mechanical properties.

2.Experimental and simulation methodologies

2.1.The SPDT process

The single-phase Mg alloy containing 4wt.% Li was received as a 20mm diameter extruded bar and was annealed at 200°C for 1h.A cylindrical workpiece 10mm in diameter and 15mm in length was cut from the annealed sample for SPDT.The SPDT surface machining was conducted by a Moore Nanotech 450UPL SPDT machine.A schematic drawing of the SPDT is shown in Fig.1a and Fig.1b.The cutting depth was 30μm.The surfaces of the samples were barely turned at a spindle speed (V1) of 500rpm.The tool rake angle(α) was 45°.The feed rate (V2) was 5mm/min.The cutting was repeated 20 times to accumulate a large strain at the sample surface.The SPDT was conducted at room temperature,and the cooling medium was oil.

2.2.Microstructure characterization and nanoindentation testing

The microstructure of the cross section of the sample after SPDT was observed by optical microscopy (OM) on a Leica DMLM microscope.To reveal the grain refinement during the SPDT process, transmission electron microscopy (TEM)samples of layers at different depths were prepared.The highresolution TEM(HRTEM)observations were performed using a field emission JEM-2100F operated at a voltage of 200kV.Nanoindentation tests were conducted to demonstrate the im-provement in the surface hardness achieved from the SPDT process.The tests were conducted at room temperature using a Hysitron TI-900 Triboindentor with a Berkovich diamond indenter.Before the indentation test, efforts were made to minimize the effects of thermal drift by allowing several hours for thermal equilibrium to be reached.The specimens obtained from the Mg sample that underwent SPDT were mechanically polished to a mirror finish.The samples were loaded to a maximum load of 5 mN with a loading rate of 0.25 mN/s and were then followed by the unloading process after a duration time of 5s.

Fig.1.(a) Schematic illustration of the SPDT treatment.(b) Schematic of plane-strain cutting by SPDT.(c) Schematic drawing of the polycrystalline Mg workpiece for the MD simulations.

2.3.MD simulations

MD simulations were conducted using Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS) software[23].The visualization of the atomic configurations was performed by the Open Visualization Tool (OVITO) [24]software.The polycrystalline Mg workpiece model was built using the 2-D Voronoi tessellation method.Each polyhedron was filled with hexagonal closed-packed (HCP) Mg atoms aligned along a random orientation.Atoms near the GBs that overlapped (distance<0.1nm) were deleted.The asbuilt model had 12 grains with an average in-plane grain size of 30nm, while the out-of-plane dimension was 10nm.The size of the workpiece was 120nm×90nm×10nm.Periodic boundary conditions were imposed along all directions.The Mg-Mg interatomic interaction was described by an embedded atom method (EAM) potential developed by Sun et al.[25].The Morse potential was adopted to describe the Mg-C interaction, which is defined by:

whereDis the cohesive energy,ais the elastic modulus,γijis the atomic distance, andγ0is the equilibrium atomic distance.The parameters in Eq.(1) for the Mg-C interaction were determined by fitting first-principles calculation results,and the obtained values were 1.72eV forD, 1.35-1foraand 2.18forγ0.The C–C interatomic interaction was described by the Tersoff potential developed by Thompson[26].

After the construction of the polycrystalline Mg workpiece model,an annealing process was applied to obtain the equilibrium GB structures of the workpiece.The workpiece was first heated to 600K and kept for 1ns.It was then cooled to 300K in 0.1ns.The annealing temperature and time were selected to avoid grain growth.The diamond tool was modeled as a rigid body diamond quadrangular with the same out-of-plane dimension as the workpiece.The tool was first placed on top of the workpiece.The grain arrangement of the workpiece,the starting position of the tool and the cutting parameters are demonstrated in Fig.1(c).The atoms of the workpiece were colored using the common neighbor analysis module in OVITO, with the dark blue color representing HCP atoms and the black color representing atoms that had lost crystal symmetry.

To study the influence of the cutting parameters on the grain refinement process during SPDT, combinations of different rake angles, cutting depths and cutting speeds, as listed in Table 1, were adopted to conduct the cutting simulations.For each parameter, we selected three values to represent low,medium, and high levels of that parameter.When studying the effect of one parameter, the other two parameters were kept constant.In total, 7 combinations of parameters were simulated.

Table 1Cutting parameter combinations.

Table 2The number of each type of deformation twin in workpiece after SPDT.

Fig.2.(a) OM image of the cross section of the sample surface after SPDT treatment.(b) The variation of grain size and hardness along the depth of the sample after SPDT treatment.(c) Nanograins at the topmost layer of the sample after SPDT treatment.(d) Stacking faults found in the sample after SPDT treatment.(e) HRTEM image of a 1/6<20¯23> partial dislocation (I1 SF).(f) HRTEM image of a 1/3<100> partial dislocation (I2 SF).(g) A {101}contraction twin (CTW) found at a depth of 30μm of the sample after SPDT treatment.(h) A {102} tension twin (TTW) found at a depth of 50μm of the sample after SPDT treatment.

3.Results

3.1.Experimental results

Fig.2(a-h) display the microstructure observations of the Mg alloy sample surface after the SPDT treatment.The grain size distribution along the depth of the sample is displayed in Fig.2a-b, suggesting the grain refinement is significant.The HRTEM observation in Fig.2c suggests that the grain sizes at the topmost layer were approximately 60nm.The hardness and grain size variation along the depth of the sample is shown in Fig.2b.As the grain size decreased from 20μm to 60nm, the hardness of the surface layer has increased to 1.17GPa, which is approximately 1.6 times the hardness of the untreated sample.Fig.2(d-f) illustrate the stacking faults (SFs) found in the SPDT treated workpiece.Fig.2e and Fig.2f are the HRTEM images of two types of intrinsic SFs frequently found in Mg.The I1SF with a stacking sequence of …AB|ABC|BCBC….is shown in Fig.2e, and the I2SF with a stacking sequences of …AB|ABCA|CAC…is shown in Fig.2f.It has been suggested that I1results from the removal of a basal plane followed by a shearing of a 1/3<100>partial dislocation.This process results in the formation of a 1/6<20¯23>partial dislocation.The reaction of two I1can form a perfectthus can contribute greatly to the ductility of Mg.I2simply results from the shearing of a 1/3<100>partial dislocation.Fig.2(g) and (h) {101} contraction twin (CTW) and {102} tension twin (TTW) foundin the sample after SPDT treatment.These three types of defects are important plastic deformation modes for Mg ang Mg alloys[27].The atomic details of the evolution of the SFs,CTW and TTW during SPDT are elaborated upon in the MD simulation results.

Fig.3.Main deformation mechanisms during the SPDT.(a) {102} TTW and I2 SF, (b) {101} CTW and I1, and (c) {11¯21} TTW.The dark blue atoms correspond to HCP atoms, while the green atoms represent face-centered cubic (FCC) atoms and the black atoms represent atoms that have no symmetry.

3.2.MD simulation results

3.2.1.Main deformation mechanisms during the SPDT process

Although the HRTEM characterization confirmed the grain refinement generated by the SPDT process, the detailed microstructure evolution during the cutting process was not revealed.MD simulations, on the other hand, can give realtime microstructure evolution with atomic-level details.Fig.3 demonstrates several important deformation mechanisms during the SPDT of the workpiece and their evolution over time.Fig.3a displays the growing process of one{102}TTW.The{102} TTW nucleated from the GB, and the twin embryo had a triangular shape with boundaries consisting of two basal plane/prismatic plane (B-P) interfaces and one {102} twin boundary (TB).The B-P interfaces then propagated along their normal directions, and the twin subsequently increased in size.As the twin nucleated, several I2SFs emerged from the GB and propagated within the matrix.When the twin increased in size, additional I2SFs were emitted from the GB, and then propagated into the matrix.Finally, the I2SFs reached the boundaries of the twin, creating steps at the boundary.The boundaries of this {102} TTW became serrated and were made up of B-P planes,{102}TBs and steps.Fig.3b displays the evolution of a {101} CTW.Unlike the{102} TTW, the {101} CTW had an almost straight TB.The TB propagated rightwards with the help of I1SFs.In contrast with the I2SFs, which can terminate inside a grain, the I1SFs observed here all started and end at GBs, as illustrated in Fig.3a, c displays the growing process of a {11¯21} TTW,which was not observed by HRTEM.The{11¯21}TTWs were observed several times in the MD simulations, although this type of deformation twin is not frequently observed by experimental studies.A {11¯21} TTW was observed by Stanford in a WE54 Mg-based alloy [28].However, removal of the alloying elements inhibited the twin mode, indicating that the formation of {11¯21} TTWs is an uncommon deformation mode in Mg alloys and might be limited to pure Mg, which is the currently simulated system.Besides, in our MD simulation,the grains were extremely small compared with grains in the samples used in the experimental studies.Certain deformation modes that are unfrequently observed in experiments may appear in the MD simulations owing to the small grain size, as shown in Fig.3c.The {11¯21} TTW also nucleated from the GBs and had straight TBs.The twin started as a thin and short embryo and increased in width and length as the deformation continued.The three types of deformation twins and two types of SFs shown in Fig.3 were commonly observed in the MD simulation results, with {102} TTW being the most frequent and {11¯21} TTW being the least frequent.This suggests that twinning and SFs were the main deformation mechanisms during the SPDT of the polycrystalline Mg workpiece.

Fig.4.(a) Atomic configuration of the workpiece after the SPDT with cutting parameters of d10-v500-α30.Enlarged plots of (b) a {102} TTW, (c) a low-angle grain boundary (LAGB) of 10°, (d) a {11¯21} TTW, and (e) I1 SF.

3.2.2.The influence of the rake angle on the microstructure evolution

To reveal the influence of the tool rake angle on the microstructure during SPDT, 30°, 45° and 60° were chosen as the rake angles to perform MD simulation of the cutting process,with the cutting depth and cutting speed set as 10nm and 500m/s, respectively.The microstructures of the workpieces after the removal of the first layers are shown in Fig.4-6.The rake angle obviously had a strong impact on the microstructure of the workpiece after deformation.As shown in Fig.4, when the rake angle was 30°, only the surface layer with a thickness of approximately 15nm had a significant microstructure change.Low-angle grain boundaries(LAGBs) that were made of several 1/3<1¯210>full dislocations (Fig.4c), {11¯21} TTW and I1SF s were found near the surface.A {102} TTW was found in the middle part of the workpiece where the stress and strain levels were much lower than those at the surface layer, indicating that {102}TTWs need a relatively lower shear stress to be activated.

In Fig.5, where the rake angle is 45°, we found additional {102} TTWs and SFs.As shown in Fig.5c and d,large numbers of I1and I2SFs were found inside the {102}TTWs, indicating an increased degree of deformation.From Fig.5e, we can see that the surface layer after cutting was refined.There were also many point defects at the surface layer, which may have resulted from the dynamic recrystallization (DRX) process [29].The DRX process is also an important grain refinement mechanism of the Mg workpiece and has been discussed in the literature [27].Here, we found that DRX was the most significant in the surface layer where the deformation was the most severe and the temperature was the highest.

Fig.6 shows the atomic configuration of the workpiece after the SPDT with the rake angle of 60° The affected region in Fig.6 was the thickest among the 3 cases with different rake angles.LAGBs were found inside a grain located at the bottom of the workpiece, as shown in Fig.6d.Refined grains were not only observed at the surface layer (Fig.6b) but also observed inside a grain that lies in the middle part of the workpiece (Fig.6e).In the {102} TTW shown in Fig.6c,highly dense SFs were found in the twin and the matrix,meaning that the region was severely deformed.Upon comparing the microstructures in Fig.4–6, we can conclude that as the rake angle increased, the stress and deformation induced by the cutting spread deeper into the workpiece, causing additional grains to undergo microstructure change and generating an increased grain refinement.

Fig.7 demonstrates the microstructure evolution in the 4 grains in the middle-top region of the workpiece under the cutting conditions in Fig.4–6.Since the atoms that had the HCP crystal structure were removed, the dislocations, TBs,SFs, and GBs can be clearly seen.The basal slip, TBs and non-basal slip are denoted with a diamond, a triangle, and an arrow, respectively.The images in the left-most column show the microstructure of the 4 grains when the tool was right above the grains and the deformation in the grains was the most severe.Large amounts of SFs, twins, and GBs were generated as the tool cut though the surface of the 4 grains.As the tool moved leftwards, stress was released; hence, the deformation decreased in severity.Comparing the microstructure evolution of the workpiece cut with different rake angles,we can see that increasing the rake angle created additional deformation at deep regions in the workpiece and generated an increased grain refinement.In the grains of workpieces cut with rake angles of 45° and 60°, several dislocations that correspond to non-basal slip can be found, indicating that high rake angles not only resulted in additional plastic deformation but also activated non-basal slip systems that require a much higher resolved shear stress than basal slip systems.

3.2.3.The influence of the cutting speed on the microstructure evolution

Fig.8–10 demonstrate the influence of the cutting speed on the microstructure during SPDT.We can see that increas-ing the cutting speed increased the microstructure changes in the workpiece.As shown in Fig.8a, when the cutting speed was 250m/s, the microstructure changes were limited to the surface layer, with only one {11¯21} TTW in the middle part of the workpiece.Some SFs and one LAGB were found near the surface.Some grains at the surface layer were refined after the SPDT process, but the thickness of the refined region was much lower than that in Fig.9.A void was found in the workpiece after the SPDT process with a cutting speed of 250m/s, as shown in Fig.8e.

Fig.5.(a) Atomic configuration of the workpiece after the SPDT with cutting parameters of d10-v500-α45.Enlarged plots of (b-d) {102} TTWs found in different grains and (e) refined grains at the surface layer.

Fig.6.(a) Atomic configuration of the workpiece after the SPDT with cutting parameters of d10-v500-α60.Enlarged plots of a (b) refined grains at the surface layer, (c) {102} TTW, (d) LAGB of 10° found far away from the surface, and (e) new GBs formed within a grain in the middle region of the workpiece.

Compared with that in Fig.8, Fig.9 shows more deformation mechanisms.The workpiece after SPDT in Fig.9 not only had {11¯21} TTWs and SFs at the surface layers but also had a {11¯21} TTW in a grain lying at the bottom of the workpiece (Fig.9b).Basal and non-basal slips (Fig.9d, e)dislocations were also found.The deformation modes in the workpiece increased as the cutting speed increased, indicating that an increased cutting speed, which generates an increasing strain rate, can activate additional slip systems and twinning modes.

The microstructure evolution shown in Fig.10 also suggests that increasing the cutting speed increased the microstructure change and the grain refinement.The amount of basal slip dislocations and TBs found in the workpiece cut with the highest speed was significantly higher than that found in the workpiece cut with the lowest speed.Although there was a large degree of plastic deformation in the workpiece processed with a high speed, the workpiece had no fracture at the GBs.It is well-known that Mg and its alloys usually suffer from low ductility due to the lack of active slip systems.Here, we showed that increasing the cutting speed might be a useful way to improve the ductility and avoid fracture during the machining of Mg and its alloys.

3.2.4.The influence of cutting depth on the microstructure evolution

The influence of the cutting depth on the microstructure during SPDT was revealed by comparing the microstructure changes in Fig.11, Fig.5, and Fig.12, in which the cutting speed and rake angle were fixed while the cutting depths were 5nm, 10nm and 15nm, respectively.When the cutting depth was 5nm, only the topmost layer with a thickness of approximately 10nm had a microstructure change after the SPDT.Several deformation twins (Fig.11c-e) and a LAGBwere found near the surface.The region that underwent a microstructure change increased in thickness as the cutting depth increased.In Fig.12, even grains at the bottom of the workpiece had deformation twins (Fig.12d) and SFs.The grains near the surface were refined into very small grains(Fig.12b), and a large amount of deformation twins and SFs(Fig.12c, e) were found.

Fig.7.Microstructure evolution in the 4 grains in the middle-top region of the workpiece under the cutting conditions of d10-v500-α30, d10-v500-α45, and d10-v500-α60.The atoms that have the HCP crystal structure are removed to show dislocations, TBs, SFs, and GBs.

Fig.8.Atomic configuration of the workpiece after the SPDT process with cutting parameters of d10-v250-α45.Enlarged plots of (b) a {11¯21} TTW, (c) I1 SFs, (d) a LAGB of 15°, and (e) a void formed in a GB.

Fig.13 provides a direct demonstration of the influence of the cutting depth on the microstructure evolution in the workpiece.The amount of basal slip and twinning increased significantly with increasing cutting depth.The original grain shapes were greatly changed, and the grain refinement was also the strongest under thed15-v500-α45 cutting condition.Fig.11–13 shows that increasing the cutting depth induced additional microstructure changes in the workpiece and achieved increased grain refinement.

3.2.5.Atomic displacement magnitude and stress distributions in the workpieces

To understand the surface deformation in the workpiece during SPDT, the atomic displacement magnitude and atomic stress were calculated and are illustrated in Fig.14 and Fig.15.The atomic displacement magnitude plotted in Fig.14 wascalculated and visualized by OVITO, which calculated the displacement vectors of a particle by subtracting its reference position from its current position.To ensure that the atomic displacement magnitudes of the workpieces processed with different cutting parameters in Fig.14 were comparable, all the reference configurations were chosen by the same criterion: the tools moved by the same length of 2nm from the reference configuration to the current configuration.

Fig.9.Atomic configuration of the workpiece after the SPDT process with cutting parameters of d10-v750-α45.Enlarged plots of (b) a {11¯21} TTW, (c)refined grains at the surface layer, (d) basal slip, and (e) non-basal slip.

Fig.10.Microstructure evolution in the 4 grains in the middle-top region of the workpiece under the cutting conditions of d10-v250-α45, d10-v500-α45, and d10-v750-α45.

In Fig.15, the stress distributions along the y direction after the first layer were removed and plotted.The stress at a certain y coordinate is the integrated atomic stress of the atoms with the same y coordinate.The atomic stress was calculated according to:

where (i, j) takes the values ofx, yandz; βtakes the values of 1 to N neighbors of atomα;Rαiis the position of atomαalong directioni;Fαβ jis the force along directionjon atomαgiven by atomβ; Vis the total volume;mαis the mass of atomα;andvαiis the velocity of atomα[30].

The atomic displacement and stress distributions shown in Fig.14 and Fig.15, respectively, indicate that the surfaces of the workpieces were severely deformed after the removal ofthe first layer,and the cutting parameters had a great influence on the deformation distributions.In Fig.15, where the stress distributions are plotted,there are small stress peaks at the position approximately 30nm from the workpiece bottom.The stress peaks originated from the GBs located approximately 30nm from the bottom (see Fig.1c).Since GBs usually have an increased stress due to the lack of crystal symmetry, there were stress concentrations at the GBs.

Fig.11.(a) Atomic configuration of the workpiece after the SPDT with cutting parameters of d5-v500-α45.Enlarged plots of (b) a LAGB of 15°, (c) a{101} CTW, (d) a {11¯21} TTW, and (e) a {102} TTW.

Fig.12.(a) Atomic configuration of the workpiece after the SPDT with cutting parameters of d15-v500-α45.Enlarged plots of (b) refined grains near the surface, (c-d) {102} TTWs found in grains located at different depths of the workpiece, and (e) a {101} CTW.

Fig.14(a-c) and Fig.15(a) demonstrate the influence of the rake angle on the surface deformation.As the rake angle increased, the stress increased, and the pressure exerted by the diamond tool moved downward.Subsequently, the stress dispersed deeply into the workpiece, and thick regions were influenced.When the rake angle was 30°, the force exerted by the tool was mainly toward the front; therefore, the deformation in the workpiece was not as severe as the cases with higher rake angles.Fig.14(d-f)and Fig.15(b)reveal the influence of cutting speed on the surface deformation.The atomic displacement distribution of the workpiece processed with a slower cutting speed (Fig.14a) seemed to be more uniform,while with a faster cutting speed (Fig.14d), the deformation was more localized.From the stress distributions, we can see that the cutting speed not only had a strong influence on the stress near the surface but also influenced the stress in the lower region in the workpiece.Slower cutting allowed additional time for the deformation to disperse into deeper regions.Since the stress was dispersed more into the workpiece, the decrease in stress from the topmost layer to the inner layers was not as severe as for the cases with high cutting speeds.In contrast,a high cutting speed restricted the strain and stress to the surface layer.Fig.14(h-j) and Fig.15(c) reveal the influence of the cutting depth on the surface deformation.As the cutting depth increased, the stress near the surface increased,and the surface deformation increased in severity.

The results shown in Fig.14 and Fig.15 are in accordance with the results shown in Fig.4 to Fig.13.We can now summarize the influences of the rake angle,cutting speed and cutting depth: to achieve better grain refinement after the removal of the first layer though SPDT, a high rake angle that can generate an increased downward pressure is recommended; a high cutting speed that can activate additional slip systems and avoid GB fracture is recommended; and a highcutting depth that can increase the stress near the surface is recommended.

Fig.13.Microstructure evolution in the 4 grains in the middle-top region of the workpiece under the cutting conditions of d5-v500-α45, d10-v500-α45, and d15-v500-α45.

3.2.6.Frequency of the three types of deformation twins

As shown in Fig.3, three types of deformation twins were observed during the simulated cutting process of the Mg workpiece.From the microstructures of the workpiece after SPDT (Fig.4–13), we can see that the {102} TTW, {101}CTW, and {11¯21} TTW had different frequencies of occurrence.Table 2 lists the number of the three types of twins in the workpiece after SPDT.The {102} TTW was the most frequently observed deformation twin type, with the {101}CTW being the second and the {11¯21} TTW being the third.The abundance of {102} TTWs is in accordance with many experimental observations that found {102} TTWs to be an important deformation mechanism [31–33].The other two types of deformation twins, although not as prevalent as the{102} TTWs, are also important deformation mechanisms that greatly contributed to the grain refinement of the workpiece.

The cutting parameters also had a great influence on the occurrences of the three types of twins.The influence of each parameter is in accordance with the previous analysis,which suggests that an increased rake angle,cutting depth and cutting speed increased the plastic deformation in the workpieces.

4.Discussion

According to the experimental results,the specimen treated by the SPDT process has an average grain size of approximately 60nm, while the original grain size of the untreated specimen is approximately 20μm.The surface hardness is enhanced by approximately 60% after the SPDT, showing that refined grains at the surface can improve the surface hardness.The HRTEM observation and the MD simulation results further indicate that the generations of various crystal defects,including SFs, twinning, basal and non-basal plane slips play important roles in the plastic deformation of the workpiece.

In Mg alloys, basalslip is widely accepted as the primary deformation mode at ambient temperature to accommodate the strain parallel to the a-axis during plastic deformation.However, this slip mode alone cannot provide five independent slip systems to satisfy von Mises criterion to undergo homogeneous deformation.Non-basal slip systems and deformation twins thus acts as the supplementary deformation modes to accommodate the strain along the c-axis.The preference for active non-basal slip systems and twin modes canbe reflected by their critical resolved shear stress(CRSS).The CRSS of non-basal slip and twinning are significantly higher thanslip in the coarse-grained Mg alloys.In addition,the CRSS increases and the corresponding anisotropy ratio for different slip systems decreases with reduced grain size.For example, the CRSS anisotropy ratio for non-basal slip and basal slip decreases from ～100 to ～2 when the grain size reduces from microns to nanoscale [34].Therefore, the deformation mechanism of GNS layer depends on whether the stress generated during the processing can activate the corresponding slip systems and twin modes.In general, the stress generated by cutting process is attributed to the variation of strain and strain rate caused by change of the cutting parameters.

Fig.14.Atomic displacement magnitude distributions in the workpieces after the removal of the first layer with different cutting parameters: (a-c) workpieces processed with different rake angles, (d-f) workpieces processed with different cutting speeds, and (g-i) workpieces processed with different cutting depths.

The MD simulation results using different combinations of cutting parameters show that the cutting parameters have a great influence on the plastic deformation in the workpiece.Among the three parameters, the cutting speed seems to have the largest impact on the deformation and stress distribution in the workpiece.As illustrated in Fig.11e, a void formed due to the high stress concentration at the GBs.As Mg has a limited number of slip systems compared with FCC and BCC metals, its toughness is relatively low, and GB fractures are likely to occur when the selection of machining conditions is inappropriate.The MD simulations using a fast cutting speed show that non-basal slip can be activated,and GB fracture can be avoided.The fast cutting speed leads to high strain rate.The importance of a high strain rate on the grain refinement of Mg alloys has also been suggested by Sun et al.[31]and Zhu et al.[35]It is suggested that a high strain rate could not only facilitate the nucleation of twins but also activate deformation modes that require a high resolved shear stress.Subsequently, a high strain rate can facilitate plastic deformation and the absorption of additional strain energy, thereby preventing fracture.Therefore, the use of a high cutting speed is recommended to avoid GB fracture and improve the grain refinement.However, the selection of the cutting speed in real cases should be based on the capacity of the SPDT machine.

The second most important parameter is the rake angle.A high rake angle can exert downward pressure, while a low rake angle mainly ‘pushes’ material forward.From Fig.14ac, we can see the effect of the rake angle on chip or prow formation.When the rake angle is the highest, as shown in Fig.14c, the material piles up beneath the front of the tool,forming a prow rather than a chip, and an increased compressive force can be generated [36].Therefore, to increase the grain refinement, the selection of a high rake angle is recommended.The deep cutting depth also can impose large strain in the surface by surface prow deformation and multiple passes enable accumulation of much larger strains at the surface.

Fig.15.Stress distributions along the y direction of the workpieces during the SPDT using (a) different cutting depths, (b) different rake angles and (c)different cutting speeds.

It should be noted that the original grain sizes of the polycrystalline Mg in our simulations are only 30nm.Therefore,the grain refinement mechanism revealed from the simulation results can be regarded as the very last stage of the grain refinement of a coarse-grained material rather than the whole process.The complete grain refinement process of Mg alloy from coarse grains to nanosized grains has been proposed by Zhu and Ringer [27].It is suggested that the mechanisms are not independent of each other but rather contribute to grain refinement in a progressive way.It is also reported that different plastic deformation mechanism could be dominant in grains with different grain sizes [4].Due to the limitations of MD simulations, it is difficult for the simulations to cover the whole process of grain refinement from coarse grains.However, some important mechanisms, with atomic-level details,can be revealed from our simulations, which can provide a theoretical basis for the design of machining methods for Mg alloys.

Another limitation of the current MD simulation work is that due to the timescale limitation,the cutting speeds adopted in the simulations are about 103times faster than the actual experimental values.Therefore, while we can use the simulation results to understand the influence of cutting speed in the microstructure evolution during cutting, the simulated cutting speed cannot be used in experiments.It is also worth noticing that the interatomic potential used in the MD simulations is for pure Mg rather than Mg-Li alloy.Note that the addition of Li in Mg, which forms the solid-solutionα-Mg phase,would not change the crystal structure of pure Mg.It has been reported that the addition of Li reduces the stress for the activation of non-basal slip systems in Mg alloys, therefore an interatomic potential that can account for the influence of Li should better reveal the deformation mechanism of the Mg-Li alloy during SPDT.However, it has been widely reported that the EAM potential for pure Mg developed by Sun et al.can precisely reveal the basal and non-basal dislocation evolutions and the formation of deformation twins [37–39], which are the main deformation mechanisms during SPDT.Since the influence of cutting parameters on the plastic deformation of the Mg workpiece during SPDT is the main objective of the current research,the influence of Li alloying is not considered in the MD simulation investigations.

5.Conclusions

In this paper, atomistic MD simulations were mainly conducted to investigate the effect of processing parameters on the microstructural evolution and corresponding plastic deformation during a novel SPDT technique to refine the surface grains and improve the surface hardness of Mg alloys.After 20 passes of cutting, the grains near the surface were refined to approximately 60nm, and the hardness was enhanced by approximately 60%.Microstructure observations and MD simulation results both suggested that SFs and twinning were the main plastic deformation modes.Twin nucleation and growth were revealed with atomic-level details.Parameter analysis of the cutting speed, cutting depth and rake angle was performed to clarify the influence of each parameter on the microstructure, atomic displacement, and stress distribution underneath the surface.The cutting parameters had a great influence on the surface deformation.The selection ofthe parameters is crucial for achieving good grain refinement without surface cracking.To improve the grain refinement after the removal of the first layer though SPDT, a high rake angle, cutting speed and cutting depth are recommended.

Acknowledgement

The research described in this paper was supported by the National Key Research and Development Program of China(2018YFE0124900), the National Natural Science Foundation of China (51861165204/51778370/51701171/51971187),the Natural Science Foundation of Guangdong(2017B030311004), the Shenzhen Science and Technology Project (GJHZ20180928155819738) and the Partner State Key Laboratories in Hong Kong from the Innovation and Technology Commission (ITC) (Project Code: 1-BBXA).