Molecular dynamics simulation method for solution strengthening and grain boundary strengthening of molybdenum-regulated nickel-based superalloy

Abstract

The invention discloses a molecular dynamics simulation method for solution strengthening and grain boundary strengthening of molybdenum-regulated nickel-based superalloy, and belongs to the technical field of computational material science and molecular dynamics simulation. The method comprises the following steps: constructing a solid solution strengthening model and a grain boundary strengthening model; a multi-element MEAM alloy potential is adopted; performing energy minimization processing; performing balancing; performing stretching simulation; and carrying out data calculation on the solid solution strengthening model and the grain boundary strengthening model, drawing a performance diagram, and analyzing the solid solution strengthening and grain boundary strengthening effects of the molybdenum-regulated nickel-based superalloy. According to the method, the influence of different Mo contents on solution strengthening and grain boundary strengthening of the NiCoMo alloy in dislocation evolution, stress distribution, phase change behavior and the like is obtained through molecular dynamics simulation, so that the key effect of the Mo element in improving the mechanical property of the material is disclosed from the atomic scale, and theoretical support is provided for design and optimization of the NiCoMo alloy.

Description

Technical Field

[0001] The present invention relates to the technical fields of computational materials science and molecular dynamics simulation, and particularly relates to a molecular dynamics simulation method for molybdenum-regulated solid solution strengthening and grain boundary strengthening of nickel-based superalloys. Background Art

[0002] The information disclosed in the background art of the present invention is only intended to increase the understanding of the overall background of the present invention, and is not necessarily regarded as an admission or an indication in any form that this information constitutes the prior art already known to those of ordinary skill in the art.

[0003] In recent years, the demand for high-performance alloys with excellent mechanical properties has been increasing, especially in engineering applications that require high strength, stability, and resistance to plastic deformation. Solid solution strengthening and grain boundary strengthening are two key mechanisms for improving the properties of metallic materials. By optimizing the content and distribution of alloying elements, the mechanical behavior of materials can be effectively improved at the atomic scale and the microstructural level.

[0004] Molybdenum (Mo), as an important alloying element, has a significant strengthening effect in nickel-based and cobalt-based alloys. Although current research has explored the strengthening effect of Mo elements in different alloy systems, the influence of Mo content on dislocation evolution, stress distribution, and strain-induced phase transformation behavior has not been deeply revealed. When using traditional experimental methods to study the influence of Mo content on nickel-cobalt alloys, due to its complex strengthening mechanism, it is difficult to study the influence mechanism of a single factor; at the same time, the use cost of TEM equipment for atomic observation and characterization is expensive. With the development of computer science and the development of more accurate interatomic potential functions, molecular dynamics simulation can model materials at the atomic scale and provide direct observations of phenomena occurring on the nanosecond time scale. Therefore, it can study the influence of Mo content on nickel-cobalt alloys from the atomic scale. The rationality of molecular dynamics simulation depends to a large extent on the modeling strategy. However, there is currently no modeling study on the influence of Mo content on the solid solution strengthening and grain boundary strengthening of nickel-cobalt alloys. Summary of the Invention

[0005] In view of this, the present invention provides a molecular dynamics simulation method for molybdenum-regulated solid solution strengthening and grain boundary strengthening of nickel-based superalloys. Using the method provided by the present invention, the influence of solid solution strengthening on the mechanical behavior of materials under different Mo contents can be studied, which can effectively reduce experimental costs and consumption and shorten time costs.

[0006] The present invention provides a molecular dynamics simulation method for molybdenum-regulated solid solution strengthening and grain boundary strengthening of nickel-based superalloys, including the following steps:

[0007] (1) The Voronoi algorithm in the ATOMSK software was first used to construct an FCC-structured NiCo polycrystalline model with random grain orientations, and Mo atoms were randomly replaced with Ni and Co atoms to make the atomic percentage of Mo range from 0 to 20% to obtain a solid-solution strengthening model; in the grain boundaries of the solid-solution strengthening model, Ni and Co atoms were randomly replaced with Mo atoms to make the atomic percentage of Mo in the grain boundaries range from 22 to 32% to obtain a grain-boundary strengthening model;

[0008] (2) The multi-component MEAM alloy potential was used as the potential function;

[0009] (3) The constructed solid-solution strengthening model and grain-boundary strengthening model were respectively subjected to energy minimization;

[0010] (4) Under the NPT ensemble, the solid-solution strengthening model and grain-boundary strengthening model were brought to thermodynamic equilibrium;

[0011] (5) Tensile simulations were respectively carried out on the solid-solution strengthening model and grain-boundary strengthening model, and the tensile simulations were carried out along the y direction;

[0012] (6) The crystal structures, dislocation densities, dislocation lengths, phase contents, flow stresses, shear stresses, and root-mean-square displacements of grain-boundary atoms of the solid-solution strengthening model and grain-boundary strengthening model were calculated;

[0013] (7) Mechanical property analyses were respectively carried out on the solid-solution strengthening model and grain-boundary strengthening model. Stress-strain curves, dislocation density diagrams, shear strain distribution diagrams, and evolution diagrams of atomic mean-square displacements with strain were plotted based on the calculation data in step (5). By analyzing the above property diagrams, the effects of solid-solution strengthening and grain-boundary strengthening of molybdenum-regulated nickel-based superalloys were obtained.

[0014] Compared with the prior art, the present invention has achieved the following beneficial effects:

[0015] (1) The present invention established solid-solution strengthening and grain-boundary strengthening models of molybdenum content on nickel-cobalt superalloys, and obtained the effects of different Mo contents on solid-solution strengthening and grain-boundary strengthening of NiCoMo alloys in terms of dislocation evolution, stress distribution, and phase transformation behavior through molecular dynamics simulations, thereby revealing the key role of Mo elements in improving the mechanical properties of materials at the atomic scale and providing theoretical support for the design and optimization of NiCoMo alloys;

[0016] (2) Through the above molecular dynamics simulation method, the present invention has determined the optimal distribution range of Mo content in solid solution strengthening and grain boundary strengthening. The results show that in solid solution strengthening, when the Mo content is 12%, lattice distortion effectively inhibits dislocation slip, significantly improving the matrix strength. In grain boundary strengthening, when the Mo content in the grain boundary is 30%, the pinning effect of the grain boundary is significantly enhanced, the local stress distribution is uniform, and the shear strain region is the least, showing the best strengthening effect. The synergistic effect of solid solution strengthening and grain boundary strengthening realizes the dual improvement of material strength and stability, providing theoretical support for the design and optimization of NiCoMo alloys. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The attached drawings forming a part of this specification are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. Obviously, for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 is a schematic diagram comparing the solid solution strengthening model and the grain boundary strengthening model of NiCoMo in Embodiment 1 of the present invention;

[0019] Figure 2 is a schematic diagram of strain-induced phase transformation and dislocation evolution in the NiCoMo solid solution strengthening model in Embodiment 2 of the present invention;

[0020] Figure 3 is the influence of Mo content on the solid solution strengthening and grain boundary strengthening properties of NiCoMo alloys in Embodiment 2 of the present invention. Among them, a is the stress-strain curve of different solid solution strengthening models, b is the stress-strain curve of the grain boundary strengthening model, c is the relationship between the average flow stress and the Mo content, and d is the relationship diagram between the atomic mean square displacement (ΔMSD) and the strain;

[0021] Figure 4 is a schematic diagram of phase transformation and dislocation evolution of the 6% Mo solid solution strengthening model (a1-a4) and the GB-22 grain boundary strengthening model in Embodiment 2 of the present invention (b1-b4);

[0022] Figure 5 is the stress concentration distribution and dislocation analysis of the NiCoMo6 solid solution strengthening model and the Mo18-GB22 grain boundary strengthening model in Embodiment 2 of the present invention at a strain ε = 0.12; among them, a is a schematic diagram of the stress concentration distribution of the NiCoMo6 solid solution model, b is a schematic diagram of the stress concentration distribution of the Mo18-GB22 grain boundary strengthening model, c is a schematic diagram of the dislocation distribution of the NiCoMo6 solid solution model, and d is a schematic diagram of the dislocation distribution of the Mo18-GB22 grain boundary strengthening model;

[0023] Figure 6It is a dislocation evolution comparison diagram between the NiCoMo6 solid solution strengthening model (a) and the Mo18-GB22 grain boundary strengthening model (b) in Embodiment 2 of the present invention;

[0024] Figure 7 It is the influence of Mo content on the dislocation density and phase transformation behavior of NiCoMo alloy in Embodiment 2 of the present invention; among them, a is the relationship diagram between the dislocation density and strain of the solid solution strengthening model, b is the relationship diagram between the dislocation density and strain of the grain boundary strengthening model, c is the relationship diagram between the percentage of FCC atoms, Mo content, and strain, and d is the relationship diagram between the percentage of HCP phase and strain;

[0025] Figure 8 It is the influence of different grain boundary Mo contents on shear strain, structural stability, and phase transformation behavior in Embodiment 2 of the present invention; among them, a - c are the shear strain distributions of the grain boundary strengthening models with different Mo contents under the strain condition of ε = 0.12; d is the evolution diagram of the mean square displacement of atoms (ΔMSD) with strain; e is the radial distribution function diagram; f is the relationship diagram between the percentage of FCC atoms, Mo content, and strain; g is the relationship diagram between the percentage of HCP phase and strain. Detailed implementation mode

[0026] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0027] The present invention provides a molecular dynamics simulation method for regulating solid solution strengthening and grain boundary strengthening of molybdenum-containing nickel-based superalloys, including the following steps:

[0028] (1) First, a FCC-structured NiCo polycrystalline model with random grain orientations was constructed using the Voronoi algorithm in the ATOMSK software, and Ni and Co atoms were randomly replaced with Mo atoms to make the atomic percentage of Mo 0 - 20% to obtain a solid solution strengthening model; in the grain boundaries of the solid solution strengthening model, Ni and Co atoms were randomly replaced with Mo atoms to make the atomic percentage of Mo in the grain boundaries 22 - 32% to obtain a grain boundary strengthening model;

[0029] (2) The potential function uses the multi-element MEAM alloy potential; it can accurately describe the mechanical behavior of metals;

[0030] (3) The constructed solid solution strengthening model and grain boundary strengthening model were respectively subjected to energy minimization treatment;

[0031] (4) Under the NPT ensemble, the solid solution strengthening model and the grain boundary strengthening model were brought to thermodynamic equilibrium;

[0032] (5)Tensile simulations are respectively carried out on the solid solution strengthening model and the grain boundary strengthening model, and the tensile simulation is carried out along the y direction;

[0033] (6)Calculate the crystal structure, dislocation density, dislocation length, phase content, flow stress, shear stress and root mean square displacement of grain boundary atoms of the solid solution strengthening model and the grain boundary strengthening model;

[0034] (7)Conduct mechanical property analyses on the solid solution strengthening model and the grain boundary strengthening model respectively, draw stress-strain curves, dislocation density diagrams, shear strain distribution diagrams and evolution diagrams of atomic mean square displacement with strain according to the calculation data in step (5), and obtain the solid solution strengthening and grain boundary strengthening effects of molybdenum-regulated nickel-based superalloys by analyzing the above property diagrams.

[0035] In one or more embodiments of the present invention, the atomic percentage of Mo in the solid solution strengthening model is more preferably 0-18%, and further, it is set to 0, 6%, 12% and 18%. In the grain boundary strengthening model, the atomic percentage of Mo in the grain boundary is preferably 22-30%, and further, it is set to 22%, 26% and 30%.

[0036] In step (1) of the present invention, the ATOMSK software is used for random replacement to achieve the effect of random doping of Mo in the crystal and grain boundary, so as to study the influence of the solid solution and grain boundary strengthening models on the mechanical properties. The Voronoi algorithm simulates the grain structure by dividing the space into distance-based regions, ensuring the randomness of the grain distribution.

[0037] In the present invention, the atomic ratio of Ni and Co in the solid solution strengthening model of step (1) is 1:1.

[0038] In the present invention, the atomic percentage of Mo in the solid solution strengthening model used in the construction of the grain boundary strengthening model is 6-18%. In one or more embodiments of the present invention, the atomic percentage of Mo in the solid solution strengthening model used in the construction of the grain boundary strengthening model is 18%.

[0039] In the present invention, steps (2)-(6) are carried out in the LAMMPS software, and the LAMMPS software is suitable for large-scale molecular dynamics simulations.

[0040] In the present invention, in step (3), the conjugate gradient algorithm is used for energy minimization to remove any unreasonable structures and ensure that the model is in the lowest energy state at the beginning of the simulation.

[0041] In the present invention, in step (4), the method for bringing the solid solution strengthening model and the grain boundary strengthening model to thermodynamic equilibrium is as follows: The solid solution strengthening model and the grain boundary strengthening model are equilibrated at 298 - 308 K and 0 - 0.1 GPa for 90 - 110 ps to ensure that the system reaches thermodynamic equilibrium, preparing for subsequent tensile simulations. Further, the equilibration process is achieved using a Nose - Hoover thermostat.

[0042] In the present invention, in step (5), the strain rate of the tensile simulation is 1×10 8 s -1 ~1×10 9 s -1 , and the maximum tensile strain is 30% - 50%; selecting this strain rate is to simulate quasi - static tensile conditions in order to observe the plastic deformation behavior of the material. The time step of the tensile simulation is 1 fs to ensure the accuracy and stability of the simulation.

[0043] In the present invention, in step (7), the mechanical property analysis is carried out using OVITO software. Further, the dislocation extraction algorithm and common neighbor analysis in OVITO software are used for the mechanical property analysis. The dislocation extraction algorithm (DXA) is used to analyze the evolution of dislocations, which helps to understand the influence of dislocation slip and multiplication mechanisms on the material strength. The common neighbor analysis (CNA) is used to identify and analyze surface defects such as stacking faults and twins, and these defects play an important role in the plastic deformation of the material.

[0044] Through the above - mentioned molecular dynamics simulation of the present invention, it can be known that: In solid solution strengthening, the Mo element effectively inhibits dislocation slip and improves the material strength by causing lattice distortion. When the Mo content is 12% (NiCoMo12), the solid solution strengthening effect is the best. In grain boundary strengthening, the Mo element enhances the pinning effect of grain boundaries, restricts dislocation movement, and optimizes the stress distribution. A Mo content of 30% (GB - 30) makes the grain boundary strengthening effect reach the optimum. Shockley dislocations are the dominant dislocation type in plastic deformation, and dislocation pile - up and interaction in the grain boundary strengthening model are more significant, further improving the material strength. At the same time, the increase in Mo content promotes the strain - induced FCC→HCP phase transformation, but an appropriate Mo content (GB - 30) can effectively inhibit the phase transformation and maintain a high FCC structure stability. The synergistic effect of solid solution strengthening and grain boundary strengthening significantly improves the mechanical properties and stability of the material. Mo doping can not only increase the matrix strength but also enhance the stress - bearing capacity of grain boundaries, providing an important basis for the design and optimization of NiCoMo alloys.

[0045] The technical solution of the present invention will be further elaborated below in conjunction with specific embodiments. The present invention has no special restrictions on the sources of the reagents used in the following embodiments, and commercially available products well-known to those skilled in the art can be used.

[0046] Example 1

[0047] 1. Model construction: First, a polycrystalline model of FCC-structured NiCo with random grain orientations was constructed using the Voronoi algorithm in the ATOMSK software, and Mo atoms were randomly substituted for Ni and Co atoms to make the atomic percentage of Mo in the crystal 0%, 6%, 12%, and 18%, obtaining solid-solution strengthening models, denoted as NiCo or Mo0, NiCoMo6 or Mo6, NiCoMo12 or Mo12, and NiCoMo18 or Mo18, respectively. In the grain boundaries of the solid-solution strengthening model with an atomic percentage of Mo in the crystal of 18%, Mo atoms were randomly substituted for Ni and Co atoms to make the atomic percentage of Mo in the grain boundaries 22%, 26%, and 30%, obtaining grain-boundary strengthening models, denoted as Mo18-GB22 or Mo18-22, Mo18-GB26 or Mo18-26, and Mo18-GB30 or Mo18-30, respectively.

[0048] Figure 1 Shows a schematic diagram comparing the NiCoMo solid-solution strengthening model and the grain-boundary strengthening model. Figure 1 (a) in shows the crystal structure of the NiCoMo solid-solution strengthening model, and the colors identify different grain regions, indicating that the model has a polycrystalline structure. The grain size and distribution are uniform, and there are obvious grain boundaries between the grains. This type of solid-solution strengthening mainly depends on the solid-solution strengthening effect of solute atoms with different compositions on the matrix. Figure 1 (b) in highlights the difference between the grain-boundary region (orange part) and the grain interior (blue part). The grain-boundary distribution is network-like, indicating that the connectivity between different grains and the grain-boundary characteristics play a key role in the mechanical properties of the material. The NiCoMo model relies on solid-solution strengthening, that is, solute atoms (such as Mo) enter the crystal matrix, causing local lattice distortion, thereby hindering dislocation movement and enhancing strength. The NiCoMo18-GB model further strengthens the grain boundaries by introducing different contents of Mo atoms on the basis of solid-solution strengthening, thereby achieving grain-boundary strengthening. Figure 1 The larger grains in (a) in may affect dislocation slip and strength. Figure 1 The highlighted grain-boundary region (containing Mo atoms) in (b) in may enhance the blocking ability of the grain boundaries, thereby improving the strength and plasticity coordination of the material.

[0049] 2. Simulation method:

[0050] The simulation was carried out using the LAMMPS software, and the multi-component MEAM alloy potential was adopted to describe the interactions between atoms. Before the simulation started, the conjugate gradient algorithm was used to minimize the energy of the solid solution strengthening model and the grain boundary strengthening model in step 1, so as to remove any unreasonable structures and ensure that the model was in the lowest energy state at the beginning of the simulation. Then, under the NPT ensemble, the Nose-Hoover thermostat was used to equilibrate the model at 300 K and 0 GPa for 100 ps to ensure that the system reached thermodynamic equilibrium and prepare for the subsequent tensile simulation.

[0051] The tensile simulation was carried out along the y direction, and the strain rate was 1×10 9 s -1 ⁻¹, the maximum tensile strain was 30%, and the time step of the simulation was 1 fs to ensure the accuracy and stability of the simulation.

[0052] 3. Calculation and result analysis:

[0053] The calculation was carried out using the LAMMPS software, and then the results were analyzed using the OVITO software, including the dislocation extraction algorithm and the common neighbor analysis. The crystal structure, dislocation density, dislocation length, phase content, flow stress, shear stress, and root mean square displacement of the grain boundary atoms of the solid solution strengthening model and the grain boundary strengthening model were calculated. Stress-strain curves, dislocation density maps, shear strain distribution maps, and evolution maps of the atomic mean square displacement with strain were plotted based on the calculated data. By analyzing the above performance maps, the effects of solid solution strengthening and grain boundary strengthening of molybdenum-regulated nickel-based superalloys were obtained.

[0054] Example 2

[0055] This example provides the model simulation and calculation result analysis of Example 1.

[0056] Figure 2 It shows the schematic diagram of strain-induced phase transformation and dislocation evolution in the NiCoMo solid solution strengthening model. In Figure 2 a1, b1), c1 and d1, the crystal structure is almost completely green (FCC phase), indicating that the NiCoMo solid solution of all compositions shows a stable face-centered cubic structure in the initial state, without dislocations or phase transformations, and the crystal is complete. As the strain increases, the red region (HCP phase) gradually appears and becomes more significant with the increase of the Mo content (especially Figure 2 d2, d3, d4 in). It shows that the strain induces the FCC→HCP phase transformation, which is a typical structural evolution phenomenon caused by solid solution strengthening. The high Mo content (Mo12, Mo18) promotes the formation of the HCP phase, indicating that the Mo element enhances the phase transformation tendency of the crystal structure under stress. In Figure 2In figures such as a2, b2, c2, d2, etc., the black circles mark the obvious dislocation slip bands, indicating that the externally applied load induces the generation and movement of dislocations. The dislocations slip within the crystal, resulting in local strain concentration, which further induces the HCP phase transformation. As the Mo content increases, the dislocation distribution becomes denser and the slip bands become more obvious, reflecting that the Mo element strengthens the dislocation hindrance effect in the solid solution. At low Mo content (Mo6, row b), the dislocation movement initially appears, and the distribution of the HCP phase is less and scattered. The contribution of Mo element to solid solution strengthening is limited at low content; at medium Mo content (M12, row c), the HCP phase increases significantly and the dislocation slip bands become denser. This shows that the Mo element begins to play an obvious solid solution strengthening role, which helps the accumulation of dislocations and the generation of phase transformation; at high Mo content (M18, row d), the distribution of the HCP phase is the widest and the dislocation slip bands are the most obvious, indicating that the Mo element maximizes the solid solution strengthening effect at high concentration. The high Mo content makes the phase transformation of the crystal structure and the dislocation movement more intense, further improving the strength and strain hardening ability of the material.

[0057] Figure 3 It shows the effect of Mo content on the solid solution strengthening and grain boundary strengthening properties of NiCoMo alloys. Figure 3 In a, the stress-strain curves of different solid solution strengthening models are shown. It can be seen from the figure that when the Mo content gradually increases from 0 to 6%, 12%, and 18%, both the yield strength and the average flow stress of the material first increase and then decrease, and NiCoMo12 shows the best mechanical properties, showing an obvious strengthening effect. The reason for this phenomenon may be that as the Mo content increases, the Mo element gradually precipitates from the crystal grains to form a second phase, resulting in the first increase and then decrease of the mechanical properties of the material. Figure 3 The inset in a shows the evolution of stress in the small strain region (0 - 0.07). The trends of each group of data are the same, but the models with high Mo content have a faster stress increase in the initial loading stage. The increase in Mo content significantly improves the solid solution strengthening effect, especially the NiCoMo model with 12% Mo content, which shows higher yield strength and flow stress.

[0058] Figure 3 In b, the stress-strain curves of the grain boundary strengthening models are shown. It can be seen from the figure that after introducing different grain boundary Mo contents (GB22, GB26, GB30) based on the NiCoMo18 model, the mechanical properties of the grain boundary strengthening models are further improved. The grain boundary strengthening models with higher Mo content (GB26, GB30) show higher yield strength and better flow stress retention ability. Figure 3The illustration in b shows the stress evolution trend of different grain boundary strengthening models in the small strain stage. It can be seen that the grain boundary strengthening effect is obvious. The increase in the Mo content in the grain boundary region can effectively strengthen the material, and the effect is the best when the grain boundary Mo content is 30%, further verifying the importance of the grain boundary strengthening mechanism.

[0059] Figure 3 c shows the relationship between the average flow stress and the Mo content. The horizontal axis represents the Mo content, and the vertical axis represents the average flow stress. The trend of first increasing and then decreasing is presented in the figure, indicating that the increase in Mo content does not linearly improve the mechanical properties. When the Mo content is 12%, the average flow stress reaches the maximum value. Figure 3 The illustration in c shows the average flow stress of the grain boundary strengthening models (Mo18-GB22, Mo18-GB26, Mo18-GB30). The effect is the best when the grain boundary Mo content is 30%. There is a critical value for the optimal Mo content (solution strengthening is 12%). Excessive Mo content may cause Mo elements to gradually precipitate from the crystal grains to form the second phase or other adverse factors, reducing the overall mechanical properties.

[0060] Figure 3 d is a graph showing the relationship between the mean square displacement of atoms (ΔMSD) and strain. It can be seen from the figure that ΔMSD shows an upward trend with the increase in strain. For models with different Mo contents at low strain (0.05 - 0.15), ΔMSD almost overlaps, but at high strain (>0.2), the ΔMSD of NiCo is slightly lower than that of other models. It can be explained that the increase in Mo content promotes atomic migration and displacement. Especially at high strain, the solution strengthening effect is more significant, which helps to improve the strength and toughness of the material.

[0061] Figure 4 shows the schematic diagrams of phase transformation and dislocation evolution of the 6% Mo solution strengthening model (NiCoMo6) and the GB-22 grain boundary strengthening model (Mo18-GB22). In the 6% Mo solution model, the HCP phase is mainly distributed along the slip bands inside the grains, and dislocations are easier to slip, showing the solution strengthening mechanism. In the GB-22 grain boundary strengthening model, the HCP phase is preferentially generated near the grain boundaries, and the grain boundaries have a stronger hindering effect on dislocation slip, showing the contribution of the grain boundary strengthening mechanism. At the same strain, the HCP phase is generated earlier and more densely in the grain boundary strengthening model (GB-22), indicating that the Mo element at the grain boundaries effectively improves the deformation resistance of the material. It can be explained that the 6% Mo solution model mainly improves the material properties through solution strengthening, and dislocation slip leads to the distribution of the HCP phase along the inside of the grains. The GB-22 grain boundary strengthening model inhibits dislocation slip by introducing grain boundary strengthening, making the HCP phase preferentially form near the grain boundaries, further improving the deformation resistance of the material. The synergistic effect of grain boundary strengthening and solution strengthening can significantly improve the comprehensive mechanical properties of the material.

[0062] Figure 5 Shows the stress concentration distribution and dislocation analysis of the NiCoMo6 solid solution strengthening model and the Mo18-GB22 grain boundary strengthening model at a strain ε = 0.12. Figure 5 In [a], it is the NiCoMo6 solid solution model. The stress distribution shows obvious stress concentration in the grain boundary region (red high-stress region), indicating that the stress is mainly concentrated at the grain boundaries. The stress distribution inside the grains is relatively uniform, but the dislocation activity mainly spreads around the grain boundaries, showing that the grain boundaries are the main obstacles to dislocation movement. Figure 5 In [b], it is the Mo18-GB22 grain boundary strengthening model. The stress concentration region is more obvious and wider in distribution. Especially, an obvious stress concentration band (red region) is formed at the grain boundaries. This shows that after introducing Mo element to strengthen the grain boundaries, the grain boundaries have a stronger stress-bearing capacity, suppressing the stress transfer inside the grains and strengthening the hindering effect of the grain boundaries. Figure 5 In [c], it is the NiCoMo6 solid solution model. The dislocation distribution is relatively dispersed, mainly consisting of screw dislocations and a small amount of edge dislocations. The dislocations spread inside the grains and at the grain boundaries. The hindering effect of the grain boundaries on the dislocations is limited, showing the characteristics of the solid solution strengthening mechanism. The region marked by the red circle shows the dislocation aggregation points, indicating that local plastic deformation has occurred. Figure 5 In [d], it is the Mo18-GB22 grain boundary strengthening model. The dislocation distribution is more intensive, and the number of edge dislocations (green) increases significantly, indicating that the hindering effect of the grain boundaries on dislocation movement is enhanced. The dislocations mainly aggregate in the grain boundary region (marked by the red circle). The Mo content in the grain boundaries strengthens the "pinning" effect on the dislocations, hindering the further slip of the dislocations. This shows that the grain boundary strengthening model more effectively inhibits dislocation movement and significantly improves the anti-deformation ability of the material. All in all, solid solution strengthening (NiCoMo6) mainly improves the strength through the lattice distortion caused by Mo element, but has limited hindrance to dislocations. On the basis of solid solution strengthening, grain boundary strengthening (Mo18-GB22) significantly improves the hindering force of dislocation movement by enhancing the "pinning" effect of Mo element on dislocations at the grain boundaries.

[0063] Figure 6Shows the dislocation length evolution laws of various types of dislocations (Perfect, Shockley, Stair-rod, Hirth, Frank) in the NiCoMo6 solid solution strengthening model and the Mo18-GB22 grain boundary strengthening model under different strain conditions. The dislocations in the solid solution strengthening model (NiCoMo6) mainly achieve through Shockley dislocation slip. The dislocation movement is relatively free, showing good plastic deformation ability. There is less dislocation interaction, and the lengths of the step dislocations and Hirth dislocations are shorter. The grain boundaries in the grain boundary strengthening model (Mo18-GB22) have a significant hindering effect on dislocation slip, resulting in a relatively slower growth rate of Shockley dislocations. At the same time, grain boundary strengthening triggers more dislocation interactions, manifested as an increase in the lengths of the step dislocations and Hirth dislocations. Dislocations pile up at the grain boundaries, forming a stronger dislocation pinning effect, which helps to improve the strength of the material. All in all, Shockley dislocations dominate the plastic deformation of the two models, but the grain boundary strengthening model effectively hinders the free slip of dislocations. Grain boundary strengthening triggers more dislocation interactions and pile-ups, showing a stronger dislocation pinning effect, and the strengthening effect is better than that of the solid solution strengthening model. The distribution characteristics of dislocation types indicate that solid solution strengthening mainly improves plasticity through dislocation slip, while grain boundary strengthening significantly improves the strength of the material through dislocation pile-up and interaction.

[0064] Figure 7 Shows the dislocation density evolution, crystal structure transformation (FCC→HCP) under strain conditions, and the influence of Mo content on the structural stability in the solid solution strengthening model and the grain boundary strengthening model with different Mo contents. Figure 7 Figure a in [reference] is the diagram of the relationship between the dislocation density and strain of the solid solution strengthening model. It can be seen that as the strain increases, the dislocation density gradually increases. Models with different Mo contents show different dislocation density distributions. The NiCo dislocation density is the highest and increases rapidly, indicating that when the Mo content is low, dislocations are more likely to be generated and slip. The dislocation density gradually decreases from NiCoMo6→NiCoMo12→NiCoMo18. The increase in Mo content inhibits the generation of dislocations. It can be explained that the solid solution strengthening of Mo element inhibits the generation and slip of dislocations, resulting in a decrease in dislocation density. NiCoMo18 shows the lowest dislocation density, indicating that the higher the Mo content, the stronger the solid solution strengthening effect and the better the crystal stability. Figure 7The b in it is the graph of the relationship between the dislocation density and strain of the grain boundary strengthening model. It can be seen that the dislocation density gradually increases with the increase of strain, but the difference in dislocation density among models with different Mo contents in the grain boundary is small. Mo18-GB22 → Mo18-GB26 → Mo18-GB30: The change trend of dislocation density is relatively close, and Mo18-GB30 is slightly lower than other models. It can be shown that in the grain boundary strengthening model, the difference in Mo content has little effect on the dislocation density. The existence of grain boundaries effectively hinders the free slip of dislocations, increases the dislocation density, and demonstrates the effectiveness of the grain boundary strengthening mechanism. Figure 7 The c in it is the graph of the relationship between the percentage of FCC atoms, Mo content, and strain. The percentage of FCC atoms gradually decreases with the increase of strain, showing strain-induced phase transformation (FCC → HCP). When the Mo content increases (from 6% to 18%), the stability of the FCC phase decreases more significantly, especially at high strains, and the content of the FCC phase decreases faster. Low Mo content (NiCo, NiCoMo6): The FCC content is higher and the structure is relatively stable. High Mo content (NiCoMo12, NiCoMo18): The FCC phase decreases significantly, indicating that high Mo content promotes phase transformation. It can be shown that the higher the Mo content, the easier it is to induce the FCC → HCP phase transformation, resulting in a decrease in the stability of the FCC phase. The solid solution of Mo atoms induces lattice distortion, promotes dislocation movement and structural phase transformation. Figure 7 The d in it is the graph of the relationship between the percentage of HCP phase and strain. It can be seen that the percentage of HCP phase gradually increases with the increase of strain, showing the significant characteristics of strain-induced phase transformation. When the Mo content is relatively high (NiCoMo12), the content of the HCP phase is the highest, indicating that the Mo element accelerates the FCC → HCP phase transformation. NiCo (without Mo): The content of the HCP phase is the lowest and the structure is relatively stable. High Mo content improves the mechanical properties of the material by promoting phase transformation and enhancing solid solution strengthening.

[0065] Figure 8 It shows the comparative analysis graphs of stress distribution, atomic displacement, crystal structure stability, and phase transformation behavior under different grain boundary Mo contents (GB-22, GB-26, GB-30). It can be seen that Figure 8 The (a)-(c) in it are the shear strain distributions of models with different grain boundary Mo contents under the strain condition of ε = 0.12. The red area represents high shear strain, and the blue area represents low shear strain. Figure 8 The (c) in it shows a more extensive and uniform stress distribution, with fewer red high-strain areas, indicating that when the grain boundary Mo content is 30%, the grain boundary has the best stress dispersion effect. Figure 8 In the (a) and (b) in it, there are more local high-strain areas, indicating that the strengthening effect of the grain boundary is relatively weak or there is stress concentration. GB-30 has the optimal shear stress dispersion ability, which helps to improve the load-bearing capacity and stability of the grain boundary. Figure 8In (d), it is the evolution diagram of the mean square displacement of atoms (ΔMSD) with strain. It can be seen that ΔMSD (atomic displacement) gradually increases with the increase of strain, reflecting the degree of plastic deformation of the crystal. The ΔMSD among the three models (GB-22, GB-26, GB-30) is almost coincident, indicating that the Mo content at the grain boundary has little effect on the overall atomic displacement. It can be shown that the change in the Mo content at the grain boundary has little effect on the atomic displacement distribution, but has an important effect on the local stress distribution (refer to figures a-c). Figure 8 In (e), it is the radial distribution function diagram. The g(r) curve shows the radial distribution characteristics between atoms in different models. The peaks of Mo18-GB22, GB26, and GB30 are relatively higher and sharper, indicating that the crystal structure of the grain boundary strengthening model is more ordered. The g(r) curves of NiCoMo6 and NiCoMo12 show broader peaks, indicating that the atomic structure in the solid solution strengthening model is relatively disordered. It can be seen that the increase in the Mo content at the grain boundary helps to maintain the ordered arrangement between atoms and improve the stability of the crystal structure. Figure 8 In (f), it is the diagram of the percentage of FCC atoms versus the Mo content and strain. It can be seen that the percentage of FCC atoms gradually decreases with the increase of strain, indicating that a strain-induced FCC→HCP phase transformation has occurred. The percentage of FCC atoms in GB-30 under various strain conditions is significantly higher than that in GB-22 and GB-26, indicating that when the Mo content at the grain boundary is 30%, the FCC structure has higher stability and relatively fewer phase transformation behaviors. Figure 8 In (g), it is the diagram of the percentage of the HCP phase versus strain. It can be seen that the percentage of the HCP phase gradually increases with the increase of strain, indicating that the FCC→HCP phase transformation is one of the main mechanisms of plastic deformation. The generation rate of the HCP phase in GB-30 is the lowest, indicating that when the Mo content at the grain boundary is 30%, the occurrence of the phase transformation is inhibited and relatively high structural stability is maintained.

[0066] Based on the above analysis, it can be known that:

[0067] 1. In solid solution strengthening, the Mo element effectively inhibits dislocation slip and improves the material strength by causing lattice distortion. When the Mo content is 12% (NiCoMo12), the solid solution strengthening effect is the best. In grain boundary strengthening, the Mo element enhances the pinning effect of the grain boundary, restricts dislocation movement, and optimizes the stress distribution. When the Mo content is 30% (GB-30), the grain boundary strengthening effect reaches the optimum.

[0068] 2. The comparative analysis of dislocation evolution and phase transformation behavior reveals that Shockley dislocations are the dominant type of dislocations in plastic deformation. The dislocation pile-up and interaction in the grain boundary strengthening model are more significant, further improving the material strength. At the same time, the increase in the Mo content promotes the strain-induced FCC→HCP phase transformation, but an appropriate Mo content (GB-30) can effectively inhibit the phase transformation and maintain relatively high FCC structure stability.

[0069] 3. The synergistic effect of solid solution strengthening and grain boundary strengthening significantly improves the mechanical properties and stability of the material. Mo doping can not only increase the matrix strength but also enhance the stress-bearing capacity of grain boundaries, providing an important basis for the design and optimization of NiCoMo alloys.

[0070] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A molecular dynamics simulation method for solid solution strengthening and grain boundary strengthening of molybdenum-regulated nickel-based superalloys, characterized in that, It includes the following steps: (1) First, a polycrystalline model of FCC-structured NiCo with random grain orientations was constructed using the Voronoi algorithm in the ATOMSK software, and Mo atoms were randomly substituted for Ni and Co atoms to make the atomic percentage of Mo 0-20% to obtain a solid-solution strengthening model; in the grain boundaries of the solid-solution strengthening model, Mo atoms were randomly substituted for Ni and Co atoms to make the atomic percentage of Mo in the grain boundaries 22-32% to obtain a grain-boundary strengthening model; (2) The potential function uses a multi-component MEAM alloy potential; (3) The constructed solid-solution strengthening model and grain-boundary strengthening model were respectively subjected to energy minimization; (4) Under the NPT ensemble, the solid-solution strengthening model and grain-boundary strengthening model were brought to thermodynamic equilibrium; (5) Tensile simulations were respectively carried out on the solid-solution strengthening model and grain-boundary strengthening model, and the tensile simulations were carried out along the y direction; (6) The crystal structures, dislocation densities, dislocation lengths, phase contents, flow stresses, shear stresses, and root-mean-square displacements of grain-boundary atoms of the solid-solution strengthening model and grain-boundary strengthening model were calculated; (7) Mechanical property analyses were respectively carried out on the solid-solution strengthening model and grain-boundary strengthening model, stress-strain curves, dislocation density maps, shear strain distribution maps, and evolution maps of atomic mean-square displacement with strain were plotted according to the calculation data in step (5), and by analyzing the above property maps, the effects of solid-solution strengthening and grain-boundary strengthening of molybdenum-regulated nickel-based superalloys were obtained.

2. The molecular dynamics simulation method according to claim 1, wherein In the solid-solution strengthening model of step (1), the atomic ratio of Ni and Co is 1:

1.

3. The molecular dynamics simulation method according to claim 1, characterized in that In the solid-solution strengthening model used for constructing the grain-boundary strengthening model, the atomic percentage of Mo is 6-18%.

4. The molecular dynamics simulation method according to claim 1, characterized in that, Steps (2)-(6) are carried out in the LAMMPS software.

5. The molecular dynamics simulation method according to claim 1, wherein In step (3), the conjugate gradient algorithm is used for energy minimization.

6. The molecular dynamics simulation method according to claim 1, wherein In step (4), the method for bringing the solid-solution strengthening model and grain-boundary strengthening model to thermodynamic equilibrium is: equilibrating the solid-solution strengthening model and grain-boundary strengthening model at 298-308 K and 0-0.1 GPa for 90-110 ps.

7. The molecular dynamics simulation method according to claim 1, wherein The strain rate of the stretching simulation is 1×10 8 s -1 ~1×10 9 s -1 , and the maximum tensile strain is 30% - 50%.

8. The molecular dynamics simulation method according to claim 1, characterized in that, In step (5), the time step of the tensile simulation is 1 fs.

9. The molecular dynamics simulation method according to claim 1, wherein In step (7), the mechanical property analysis is carried out using the OVITO software.

10. The molecular dynamics simulation method according to claim 9, wherein, The mechanical property analysis uses the dislocation extraction algorithm and common neighbor analysis in the OVITO software.

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