Molecular dynamics study on the effects of nanorolling processes on the properties of nickel-based superalloy GH4169

Rolling is a process that can improve the performance and roughness of machined parts and has a special economic value; therefore, the optimization of rolling process parameters is crucial to workpiece performance. In this paper, three rolling methods are used in molecular dynamics (MD) rolling simulations to study their effects on the surface of nickel-based superalloy GH4169 at the nanoscale. The surface and subsurface of the workpiece after rolling with the three different rolling methods are studied separately; in particular, a comparative analysis of the dislocation generation and movement on the subsurface, crystal defect evolution, and surface roughness was performed. The results show that the increase in subsurface dislocation density by average rolling has a significant influence on the work hardening effect, and the average roughness of the rolled groove surface is the lowest. This is an important reference for the optimization of the parameters of actual rolling processes.


Introduction
Rolling is an important process in which a rolling tool applies a certain pressure to the surface of a workpiece and uses the plastic deformation of metal at room temperature to shape the material [1]. Research shows that gradient nanostructures (GNS) are formed by the rolling process, and GNS can improve the wear resistance, corrosion resistance and fatigue resistance of the rolled surface of the workpiece [2][3][4][5], therefore, the rolling process is widely used in ultraprecision machining technology [6,7].
The nickel-based superalloy GH4169 is widely used in the aviation, nuclear and petroleum industries for its good fatigue resistance, radiation resistance, corrosion resistance, and excellent yield strength below 650°C [8][9][10]. Because GH4169 is used in these important fields, its performance requirements after processing have greatly improved. Currently, to increase the surface strength and improve the surface roughness of nickel-based alloys, the surface is usually treated with a rolling process to meet performance requirements [11].
Current research on this rolling process focuses on the effects of rolling parameters on rolling surface strengthening and surface roughness [12][13][14][15][16]. M H et al conducted rolling experiments on Steel-37, and the results showed that the number of rolls had a significant effect on the surface microhardness and roughness [17]. Banh et al investigated the surface roughness and hardness of the workpiece through rolling experiments, and the results showed that the surface roughness decreased and the hardness increased when the number of rolls was increased from 1 to 3 [18]. Unfortunately, there is less literature on the effect of rolling 3 times on GH4169 and the depth of each roll; however, understanding the effect of rolling 3 times on GH4169 not only helps us to improve the rolling quality but also provides an important reference for optimizing the rolling process parameters. Therefore, it is very important to study the effect of rolling 3 times on GH4169.
To study and predict the processing deformation behaviour of materials at the nanoscale, atomic simulation has proven to be a very powerful computational method [19,20]. Therefore, this paper uses a molecular dynamics approach to study the effect of multiple rolls on GH4169 from the nanoscale. The surface properties of the rolled workpiece and the evolution of subsurface plastic deformation dislocations and crystal defects were where E tot is the total energy, F is the element type embedding energy of atoms i and j, ∅ is the short-range pair potential, R is the distance between atoms i and j, and ρ h,i is the sum of the atomic density.
The Morse function is used between the roller C atom and the workpiece. Specific parameters are shown in table 3 [33]. The equation of the Morse function is calculated as follows [34]: where E is the Morse potential energy, D is the energy coefficient, a is the atomic strength of the interaction, r is the atomic distance, and r c is the cut-off. To make the rolling model structurally stable, the model is optimized for energy minimization before rolling, and the workpiece is fully relaxed at 300 K for 100 ps before rolling to allow the atoms to reach equilibrium. Calculations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [35], and the whole simulation process is performed under a microcanonical ensemble (NVE) [36], and visualized with the Open Visualization Tool (Ovito) [37].

Dislocation analysis
The microscopic mechanism of GH4169 plastic deformation is the generation and movement of dislocations in the deformation region [38], and an increase in the number of interacting dislocations captured in the minimum energy configuration with each other leads to work hardening effects [39]. Therefore, the plastic deformation and work-hardening microscopic mechanism of the GH4169 rolling process can be studied by analysing dislocations and dislocation density. We use the dislocation analysis (DXA) method [40,41]. The visualization software Ovito is used to count the dislocation lines of the workpiece after rolling. The dislocation density of workpieces with different rolling methods is calculated with the dislocation density formula, and the dislocation density equation is expressed as follows [42]: where ρ is the volume per unit of different types of dislocation line lengths in the workpiece in m m −3 , L is the total length of different types of dislocation lines, and V is the workpiece volume.
The density of Shockley dislocations in the final rolling stage for different rolling methods is shown in figure 2(a). The overall Shockley dislocation density increases as the rolling distance increases; however, the increasing trend of pattern A and pattern B is more significant, while pattern C first tends to decrease and then starts to increase slowly and flatly. This is because the rolling depth of the pattern C rolling method is controlled to decrease, and the rolling depth at the 3rd roll is minimal (0.5 nm); therefore, at the beginning of rolling, the contact between the roller and the rolling groove is not complete, and the rolling contact surface is mainly based on elastic deformation, so the dislocation density tends to decrease. However, as the rolling distance increases and the roller is in full contact with the rolling groove, the elastic deformation of the workpiece transitions to plastic deformation, but the deformation is small, so the dislocation density increases slowly. Figure 2(b) shows the total dislocation line length of the workpiece with different rolling methods. It is obvious that the variation in the total dislocation line length is consistent with the trend of the Shockley dislocation density. This indicates that throughout the rolling process, the workpiece undergoes plastic deformation, dislocations are generated and change, and Shockley-type dislocations dominate, which is consistent with the literature macroscopic experimental results [43]. Figure 2(c) compares the changes in the subsurface temperature of the workpiece with increasing rolling distance for different rolling methods. It can be seen that as the rolling distance increases, the temperature first rises sharply, reaches a maximum temperature and then begins to decrease slowly. We also observe that the highest subsurface temperature is obtained by controlling the incremental depth of rolling, the temperature decreases with the average depth of rolling, and the lowest subsurface temperature is obtained with the decreasing depth of rolling. This is because the different ways of controlling the rolling volume lead to different depths of each roll, suggesting that the amount of material deformation in contact with the front of the roller is different. When rolling incrementally, the last stage of rolling is the largest, and the larger the deformation, the higher the kinetic energy of the atoms in the deformation area and the higher the temperature. When controlling the rolling volume to decrease, the last stage of rolling is the smallest, the material deformation is the smallest, the kinetic energy of the atoms in the deformation area is smaller, and the temperature is the lowest. In addition, we can see that the maximum subsurface temperature and the maximum dislocation density of the workpiece are not rolled in the same way, which means that the variation in the subsurface temperature of the workpiece is not closely and positively correlated with the dislocation density and the total length of dislocation lines. This indicates that the temperature fluctuations do not contribute significantly to the damage of the workpiece structure, which is generally consistent with the literature simulation results [39]. Figure 3 shows a cross-sectional diagram of the distribution of subsurface dislocation types for the different rolling methods to better display the different types of dislocations, where perfect dislocations and atoms are removed. We observe that the dislocations are mainly concentrated in the area directly below and to the left of the workpiece in contact with the roller. As the roller travels in the rolling direction, the material in the area directly below the roller is in a state of flux as plastic deformation occurs, and the dislocation line moves from generation to expansion and finally annihilation [44]. As shown in the red circle in figure 3, the dislocation build-up at the front end of the contact between the workpiece and the roller is more significant when using the pattern A rolling method, and the dislocation build-up at the front end of the workpiece and the roller is slowed down when using the pattern B rolling method, while the dislocation build-up is mainly in the contact area directly below the roller when using the pattern C rolling method. This is due to the reduction in the rolling depth, which leads to more plastic deformation of the atoms by the downwards extrusion of the roller, and dislocations are generated along with the plastic deformation, which gathers more towards the bottom of the roller. The dislocations on the subsurface of pattern B are more uniformly distributed, while the dislocations on the subsurface of pattern A are intertwined and aggregated, and the dislocation lines of pattern C are dispersed in the subsurface region, as shown in figure 3, because the dislocations formed during the plastic deformation of the material release energy through slip [45]. The large plastic deformation leads to some hindrance of energy release during the movement of dislocations, and eventually, the dislocations become significantly intertwined with each other.
Dislocation density, as one of the important microscopic property parameters for describing the strength of crystals, is often used to analyse the strength change during crystal deformation [46]. As can be seen in figure 2 and figure 3, pattern B has the highest subsurface dislocation density and the strongest work hardening effect. We found that the effect of the rolling method alone on the dislocation density of the workpiece is considered, and the subsurface strengthening effect of the average rolling method is better than that of the incremental and decremental rolling methods.

Crystal defect analysis
The number of atomic evolutions of crystal defects is an important measure of the degree of plastic deformation occurring in a material, and common neighbour analysis (CNA) [47,48] allows the excellent identification and statistics of defective atomic evolution. Houfu Dai et al [22] investigated subsurface defective atoms after silicon polishing by CAN, and the results showed that the structured tool largely influences the dislocations on the penetrated surface. ZhaoPeng Hao et al [26] investigated the defect atoms of nickel-based single crystal cutting by CAN and showed that the change in cutting distance leads to changes in the area and extent of the distribution of subsurface defect atoms. Therefore, we compare the evolution of the atomic number of defects in crystals with different rolling methods by CNA, as shown in figure 4. It is obvious that during the plastic deformation of GH4169, the crystal defects mainly have an amorphous and close-packed hexagonal (HCP) structure, as well as a small amount of body-centred cubic (BCC) structure. This is in agreement with the results of Ping Zhang et al [27] on the evolution of GH4169 subsurface crystal defects by MD cutting simulations. The amorphous structure of pattern B increases significantly with increasing rolling distance, while the increasing trend of pattern A and pattern C is not obvious. The increase in the number of HCP atoms is very flat for all three rolling methods, and the number of atoms in the BCC structure increases and fluctuates significantly with increasing rolling distance. The highest number of defect atoms evolved in the three rolling methods is in pattern B, while the number of defect atoms in pattern A and pattern C is significantly lower than that in pattern B, and there is no significant difference in the number of defect atoms between pattern A and pattern C, which indicates that among the three rolling methods, the area where plastic deformation occurs on the subsurface of pattern B is larger, while those of pattern A and pattern C are smaller and close. Figure 5 shows the distribution of defect atoms on the subsurface for the different rolling methods. The BCC structure is removed to better show the distribution of defect atoms on the subsurface. After rolling, the subsurface amorphous structure of the workpiece exists mainly in the form of atomic clusters, the HCP structure exists mainly in the form of stacking fault tetrahedra (SFT), and the BCC structure exists mainly in the form of point dislocations. We found that the crystal defect structure of the subsurface of pattern B is more uniformly distributed, while those of pattern A and pattern C are irregularly distributed, and the crystal defect structure has a deeper impact on the subsurface depth.
The centrosymmetry parameter (CSP) is a useful measure of the local lattice disorder around an atom and can be used to characterize whether the atom is part of a perfect lattice, a local defect, or located at a subsurface or surface [49]. The CSP value is given by [50]: where r i and / + r i N 2 are two neighbour vectors from the central atom to a pair of opposite neighbour atoms. In this paper, the workpiece has an FCC structure, so the value of N is 12. The calculated CSP values for different structures and their corresponding colour labels are shown in table 4 [42] and figure 6. Figure 6 compares the distribution of crystal defects on the subsurface of the workpiece for the different rolling methods. To visualize the distribution of crystal defects, the perfect crystal structure is deleted. As the roller rolls forwards, various crystal defects, such as point dislocations, SFTs, atomic clusters, stair-rod dislocations, etc., are formed on the subsurface of the workpiece during the process of dislocation generation, movement, and annihilation, as shown in figure 6. We find by comparison that the subsurface crystal defects in pattern B are dense but uniformly distributed, and the depth of subsurface influence is 7 nm, while in pattern A and pattern C, although the number of crystal defects is small, their distribution is widespread, and the depth of impact on the subsurface of the workpiece is deeper at 7.8 nm and 7.6 nm, respectively.
In nickel-based alloys, the generation and evolution of point, line, and plane dislocations and crystal defects control plastic deformation [51], and the nucleation and diffusion of dislocations are one of the main causes of the generation of subsurface crystal defects on the workpiece. Single-layer HCP represents twins, and doublelayer HCP represents SFT during the evolution of crystal defects. There is a large amount of dislocation aggregation near the twin boundary, which indicates that the twin boundary has a certain obstructing effect on the dislocation motion. Z. Sun et al [38], through an experimental study of GH4169, found that the increase in dislocation density and the interactions between dislocations and defects during plastic deformation lead to dislocation entanglement, and then the mobility of dislocations is restricted, and eventually a work hardening effect occurs. M. Sudmanns et al [52], through theoretical calculations and simulation studies, found that physical, dislocation interaction processes and hindrance interactions contribute to strain hardening. A Prakash et al [53] investigated the mechanism of dislocation and precipitation phase interactions by the atom probe simulation technique and verified the strengthening mechanism of dislocation and precipitation phase interactions at the microscopic level. We found by a comparative analysis that with pattern B rolling, the dislocation density of the subsurface increases with more intensive crystal defect interactions, and rolling has a more pronounced effect on subsurface strengthening. Figure 7 compares the surface morphology of the different rolling methods in the Z-direction. It can be seen that as the roller advances in the rolling direction, the workpiece atoms are squeezed and pile up at both ends of the rolling groove and the front of the roller, forming rolling chips. Our comparison shows that with the pattern B rolling method, the atoms accumulate more uniformly at both ends of the rolling groove, while with the pattern A and pattern C rolling methods, the atoms at both ends of the rolling groove are more severely biased and accumulate. This is because the atoms are squeezed by the roller to move towards the ends of the rolling groove, and when the strain energy stored in the squeezed deformed lattice exceeds a certain critical value, the atoms rearrange themselves into the lower-energy lattice in turn to undergo plastic deformation [25]. The dislocations formed during plastic deformation release energy through slip [45]. When a controlled average depth of each roll is used, the randomness of atoms piling up towards the ends of each roll has an equal probability of having less effect on the next roll. In the case of the step rolling method, the previous roll and the next roll have different probabilities of atom accumulation at both ends due to the different rolling depths, and the previous roll has a guiding or hindering effect on the direction of atom accumulation in the next roll, resulting in uneven atom accumulation at both ends. In nanorolling, the surface roughness is an important parameter for measuring the quality of the process. The atomic surface roughness can be expressed as r, where R a is the radius of the surface atoms [54,55]. To visually reflect the rolling surface roughness, this paper actually expresses it by counting the average position of atoms in the Z-direction, and the surface roughness R a statistical formula is as follows [46]: where n is the total atom number, Z i is the vertical coordinate of the surface particles andZ is the average vertical coordinate. Figure 8 compares the average surface roughness of rolled grooves for the different rolling methods. It can be seen that the average surface roughness is the smallest with the pattern B rolling method, while it is larger with pattern A and the largest with pattern C. This is because the atoms are squeezed downwards by the roller in an even rolling way, and the transition from elastic to plastic deformation is more uniform. When using the step rolling method, the atoms increase in volatility during extrusion, leading to an increase in roughness when the decreasing rolling method is used. The last rolling depth is the smallest, fewer atoms are extruded and deformed, and the atomic volatility is further increased, resulting in the largest average roughness of the rolled groove surface.

Conclusion
This study investigates the effects of using multiple rolling on the properties of nickel-based superalloy GH4169 at the nanoscale and provides a theoretical reference for optimizing nickel-based rolling parameters. To this end, we proposed three rolling methods and analysed the effect of each of the three rolling methods on the dislocation and crystal defect evolution on the subsurface of the workpiece. The effect of the three rolling methods on the workpiece subsurface work-hardening effect is discussed. Finally, we compared the workpiece surface morphology in terms of rolling chip stacking and rolled groove surface roughness. Several conclusions can be drawn from the analysis as follows: (1)Using the average rolling method, the dislocation density increases more significantly, and the subsurface strengthening effect on the workpiece is more obvious.
(2)With the step rolling method, the number of crystal defects evolved is less, but at the same time, the evolution and movement hindrance of dislocations are reduced, which does not contribute much to the processing strengthening effect.
(3)The use of average rolling has a positive effect on the average surface roughness of the rolled grooves, and the atomic build-up at both ends of the rolled grooves is more uniform.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

Funding
This work is supported by the Guizhou Province Science and Technology Planning Project (Grant No. [2022] 196).