Processing surface hardness prediction method based on impact imprinting nanoindentation experiment

Abstract

The invention provides a machining surface hardness measuring method based on an impact imprinting nanoindentation experiment. The method comprises the steps that material basic parameters and crystal parameters of a to-be-machined alloy workpiece are obtained in advance, and an analysis area is selected on the to-be-machined alloy workpiece to serve as a dislocation evolution area; according to the material basic parameters and the crystal parameters, a discrete dislocation kinetic model is established, and the model is used for simulating a dislocation evolution behavior of an area below a pressure head; and dislocation density calculation is conducted on the analysis area, and the surface hardness of the to-be-machined alloy workpiece is obtained. According to the method, the dislocation behavior is simulated based on the discrete dislocation kinetic model, the dislocation density is obtained, and therefore the hardness of the machined surface is visually, rapidly and accurately calculated, and the method has high application value.

Description

Technical Field

[0001] The present invention relates to the technical field of nanoindentation, and in particular to a method for measuring the hardness of a machined surface based on an impact imprint nanoindentation experiment. Background Art

[0002] Many micron and nanometer-scale indentation experiments have shown that the hardness of the machined surface decreases significantly with increasing indentation depth, a phenomenon known as the indentation size effect. However, for polycrystalline materials, due to the effect of grain boundaries, the indentation hardness changes with the change of grain size. For grains with larger grain sizes, the hardness always decreases with increasing indentation depth. However, for grains with smaller grain sizes, the hardness exhibits the opposite behavior, that is, it increases with increasing indentation depth.

[0003] In the early 1950s, Hall and Petch proposed the now well-known Hall-Petch relationship, which gives the yield strength σ at room temperature as y Relationship with average grain size D:

[0004]

[0005] The Taylor dislocation model also gives a relationship between shear flow stress and dislocation density:

[0006]

[0007] Dislocation density has a significant impact on nanoindentation experiments, but the quantitative research and scaling relationship between hardness and dislocation source density has not yet been determined.

[0008] Therefore, it is necessary to provide a method to predict the hardness of the processed surface by impact imprint nanoimprinting experiment based on grain size and dislocation density. Summary of the Invention

[0009] The purpose of the present invention is to provide a method for predicting the surface hardness of impact stamping. By discrete dislocation dynamics, the internal dislocation evolution behavior of the material alloy during the stamping process is simulated, thereby deducing the surface hardness change of the material alloy. The surface hardness of the machined surface can be obtained quickly and accurately, saving process costs and time, and has high application value.

[0010] In order to achieve the above object, the technical solution of the present invention is:

[0011] A method for measuring the hardness of a machined surface based on an impact imprint nanoindentation experiment, the specific steps are as follows:

[0012] Obtaining in advance the basic material parameters and crystal parameters of the alloy workpiece to be processed, and selecting an analysis area on the alloy workpiece to be processed as a dislocation evolution area;

[0013] According to the material basic parameters and the crystal parameters, a discrete dislocation dynamics model is established, and the model is used to simulate the dislocation evolution behavior of the area under the indenter;

[0014] The dislocation density of the analysis area is calculated to obtain the surface hardness of the alloy workpiece to be processed.

[0015] The step of selecting an analysis area on the alloy workpiece to be processed as a dislocation evolution area comprises:

[0016] According to the initial position of the imprint, an analysis area of a certain size is selected on the alloy workpiece to be processed, and the analysis area is a rectangular area directly below the initial position of the diamond indenter with a certain length c and width d as the midpoint of the upper edge of the indenter.

[0017] The alloy workpiece to be processed comprises any one of nickel-based alloy and titanium alloy;

[0018] The material basic parameters include any one or a combination of multiple of the elastic modulus, Poisson's ratio and shear modulus;

[0019] The crystal parameters include any one or a combination of multiple of the Burgers vector, dislocation source quantity, dislocation line length, dislocation obstacle, dislocation multiplication time and slip plane spacing.

[0020] According to the material parameters and the crystal parameters, a discrete dislocation dynamics model of the analysis area is established, and the specific steps comprise:

[0021] According to the slip plane spacing and the slip direction and the slip plane normal direction in the alloy workpiece to be processed, a crystal slip system with a slip direction of 0°, 60° and -60° is established;

[0022] According to the size of the analysis area, a suitable grain size is selected to divide the grain boundaries, and the area is divided into several units;

[0023] According to the slip system, the intersection of different direction slip systems is determined to obtain the position of the forest dislocation;

[0024] The dislocation sources and dislocation obstacles are evenly distributed in the three slip systems and different grains to obtain the initial dislocation source and dislocation obstacle positions, wherein the dislocation obstacles are distributed at both ends of the dislocation source along the slip system, and the number is 1.5 times that of the dislocation source;

[0025] According to the impact imprinting speed and the depth of the processing area, the total prediction calculation time is obtained, and according to the crystal slip system, the position of each dislocation source and the position of each dislocation obstacle, a discrete dislocation dynamics model is established based on the discrete dislocation dynamics.

[0026] The step of iteratively analyzing the dislocations in the region based on the discrete dislocation dynamics model comprises:

[0027] Initializing dislocation sources, dislocation barriers, and dislocation multiplication intensity, etc.

[0028] According to the position of the current time dislocation on the slip system, the shear force and the long-range interaction stress (dislocation interaction force) of the dislocation are determined, and are expressed as:

[0029]

[0030] In the formula,

[0031]

[0032] Wherein, represents the normal stress of j dislocation on i dislocation in the x direction, represents the normal stress of dislocation j on dislocation i in the y direction, represents the shear stress, G represents the shear modulus, v represents the Poisson's ratio, b represents the Burgers vector, and x and y represent the distance of dislocation i and dislocation j in the x direction and the y direction;

[0033] In addition to the long-range interaction force, the dislocation also receives external stress, which can be calculated by Hooke's law, and is expressed as:

[0034] σ ext = Lε *

[0035] Wherein, L is the elastic stiffness matrix, which is only related to the elastic modulus and Poisson's ratio for isotropic materials, and ε * is the elastic strain;

[0036] The driving force (P-K force) of dislocation i is the resultant force of the external stress and the dislocation interaction force, and is expressed as:

[0037]

[0038] Wherein, n i represents the normal direction of the slip plane of dislocation i, s i represents the slip direction of the slip system, and a represents the number of dislocations;

[0039] The average value of the driving force (P-K force) of all dislocations can be expressed as:

[0040]

[0041] According to the shear modulus, Poisson's ratio, Burgers vector and dislocation line length, Poynting force and dislocation proliferation intensity of the analysis region are calculated, and the Poynting force in the region is represented as:

[0042]

[0043] In the formula,

[0044]

[0045] Wherein, ω represents dislocation width, and d represents the slip surface spacing

[0046] The dislocation proliferation intensity is represented as:

[0047]

[0048] Wherein, L0 is the dislocation line length, and L0 is the dislocation proliferation intensity, and the dislocation proliferation intensity is prevented from proliferating simultaneously to make the dislocation proliferation intensity satisfy the normal distribution;

[0049] According to the driving force and resistance of each dislocation source, the corresponding dislocation source combined stress is obtained, and the movement speed of the dislocation along the slip system is obtained according to the combined stress, and is represented as:

[0050]

[0051] Wherein, B g is a linear resistance coefficient, and for slip action, B g = 1000b;

[0052] According to the comparison of the size of the combined stress and the proliferation intensity, if the combined stress is greater than the proliferation intensity, the dislocation overcomes the proliferation and continues to move along the slip system, otherwise the dislocation pile-up occurs, and the position of the dislocation is the final position of the dislocation;

[0053] According to the dislocation movement speed, the corresponding dislocation current position is obtained, and whether dislocation annihilation occurs is judged according to the distance between each dislocation, if the distance between positive and negative dislocations on the same slip system is less than 6b, dislocation annihilation occurs;

[0054] The current time dislocation movement position is represented as:

[0055] X t+Δt = X t + VΔt

[0056] Wherein, X t is the position of the dislocation at the last time, X t+Δt is the current position of the dislocation, and Δt is the movement time;

[0057] The dislocation movement position is determined based on the dislocation movement position, and the dislocation quantity in each unit and grain is obtained.

[0058] The steps of calculating the dislocation density of the analysis area and obtaining the surface hardness of the alloy workpiece to be processed are:

[0059] According to the number of dislocations, the geometric necessary dislocation density in the region is obtained, which is expressed as:

[0060]

[0061] Where n represents the number of geometrically necessary dislocations in the unit cell, A represents the area of ​​the unit cell, and c and d represent the length and width of the unit cell.

[0062] In addition to geometrically necessary dislocations, there are also statistical storage dislocations, and the modified density calculation formula can be expressed as:

[0063]

[0064] Where, E is Young's modulus, A is the initial yield stress, B is the strain hardening modulus, C is the strain rate sensitive parameter, n is the hardening exponent, ε is the plastic strain, is the reference strain rate, α is a dimensionless coefficient, generally taken as 0.5;

[0065] According to the dislocation density and grain size, the hardness of the machined surface is obtained and expressed as:

[0066]

[0067] Where D is the grain size, α and β are dimensionless constants, and ρ GND is the geometrically necessary dislocation density, ρ SSD is the statistical storage dislocation density. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of the method for predicting the hardness of a processed surface based on an impact imprint nanoindentation experiment in the present invention.

[0069] Figure 2 This is the analysis area selected as the dislocation evolution area on the alloy workpiece to be processed in the embodiment of the present invention.

[0070] Figure 3 This is a schematic diagram of dividing grain boundaries by selecting appropriate grain sizes according to the size of the analysis area in an example of the present invention.

[0071] Figure 4 This is a schematic diagram of the distribution of initial dislocation sources and dislocation obstacles in the slip system.

[0072] Figure 5is a schematic diagram of dislocation distribution at a certain time in the impact imprinting process.

[0073] Figure 6 is a schematic diagram of dislocation distribution after the imprinting is completed.

[0074] Figure 7 is a schematic diagram of the iterative process of the present application. DETAILED DESCRIPTION

[0075] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the following drawings. Obviously, the following described embodiments are a part of the present application, and all other embodiments obtained by those of ordinary skill in the art without creative labor on the basis of the embodiments in the present application also belong to the scope of protection of the present application.

[0076] The present application will be further described below in conjunction with specific embodiments.

[0077] In one embodiment, as shown in Figure 1 a hardness measurement method for a machined surface based on impact imprinting nanoindentation experiments is proposed, including the following steps:

[0078] S10: The material basic parameters and crystal parameters of the alloy workpiece 110 to be machined are obtained in advance, and an analysis region 120 is selected as a dislocation evolution region on the alloy workpiece 110 to be machined; wherein the alloy workpiece 110 to be machined includes any one of nickel-based alloy and titanium alloy, the material basic parameters include one or more of elastic modulus, Poisson's ratio and shear modulus, and the crystal parameters include one or more of Burgers vector, dislocation source number, dislocation line length, dislocation obstacle, dislocation multiplication time and slip plane spacing.

[0079] Table 1 shows some known material basic parameters

[0080]

[0081] The crystal parameters are: dislocation line length L0=100e-3um, Burgers vector b=0.25e-3um, initial dislocation source number is 1500, slip plane spacing d=5000*b, and dislocation obstacle strength is 500MPa.

[0082] According to the initial position of the imprint, an analysis region 120 of a certain size is selected on the alloy workpiece 110 to be processed, which is a rectangular region directly below the initial position of the diamond indenter 100 with a certain length and width as the midpoint of the upper edge of the indenter, and the specific size is related to the size of the workpiece. The bottom of the alloy workpiece 110 to be processed should be completely constrained 130. For specific implementation methods, refer to Figure 2 .

[0083] S20: According to the material basic parameters and crystal parameters, a discrete dislocation dynamics model is established, which is used to simulate the dislocation evolution behavior of the analysis region 120 under the diamond indenter 100, including dislocation multiplication, dislocation pile-up, dislocation motion, and dislocation annihilation. The specific steps are as follows:

[0084] According to the slip plane spacing and slip direction in the alloy workpiece 110 to be processed, a crystal slip system is established, and the crystal slip direction is the close-packed direction of the crystal. For face-centered cubic, the slip plane is {111}, which is the most compact face of the three lattices, and there are 4 groups, each with 3 slip directions, which are 0° direction, 60° direction and -60° direction, i.e. <110>;

[0085] The analysis region 120 is divided into grain boundaries according to the appropriate grain size, and the dislocations are divided into intragranular dislocations 160 and grain boundary dislocations 170. For details, refer to Figure 3 and Figure 5 , and the region is divided into several units, and the unit size depends on the overall model size. The grain size is microns, and the total geometric dislocation density is the sum of the dislocation densities in each unit;

[0086] According to the slip system, the intersection of different direction slip systems is determined to obtain the forest dislocation position. The forest dislocation has an obstacle effect on the motion of dislocations. Specifically, the strength of the node on the slip system is the shear stress required for the dislocation to pass through the forest dislocation, which is related to the local average spacing between the forest dislocations on the remaining slip system. The average free path L i of the moving dislocation before stopping by interacting with the forest dislocations on other slip systems is represented as:

[0087]

[0088] where K is a constant depending on the loading direction, and for double slip orientation, the value of K is 10, is the forest dislocation density in a certain slip system;

[0089] The dislocation sources 150 and dislocation obstacles 140 are evenly distributed in three slip systems and different grains to obtain the initial dislocation source 150 and dislocation obstacle position 140. For details, refer to Figure 4Wherein, the dislocation source position 150 does not change after the distribution is completed, only new dislocations are generated by dislocation multiplication, the barrier 140 is distributed along the slip system at both ends of the dislocation source 140, and has a certain strength, when the driving force is greater than the strength, the dislocation can continue to move;

[0090] According to the slip system, the dislocation source position 150, the dislocation barrier position 140 and the slip surface spacing, a discrete dislocation dynamics model is established, and the specific process is referred to Figure 7 .

[0091] S30: According to the dislocation evolution behavior, the dislocation distribution at different times is obtained, the dislocation density of the analysis area is calculated, and the surface hardness of the alloy workpiece 110 to be processed is obtained, and the specific steps are as follows:

[0092] Firstly, the dislocation source 150, the dislocation barrier 140 and the multiplication strength and other dislocation related factors are initialized, and the dislocation source 150, the dislocation barrier 140 and the like are updated every iteration;

[0093] In the actual calculation process, the dislocation distribution at any time can be output according to the determination of the number of iterations and the iteration time;

[0094] For the dislocations in the analysis area 120 under the diamond indenter 100, not only the inter-dislocation force exists, but also the external stress acts, according to the position of the dislocation at the current time, the inter-dislocation force received by a single dislocation can be obtained, which is represented as:

[0095]

[0096] In the formula,

[0097]

[0098] Wherein, The positive stress of the j dislocation on the i dislocation in the x direction is represented as: The positive stress of the j dislocation on the i dislocation in the y direction is represented as: The shear stress is represented as, G represents the shear modulus, v represents the Poisson's ratio, b represents the Burgers vector, and x and y represent the distance between the dislocation i and the dislocation j in the x direction and the y direction;

[0099] The dislocation not only receives the long-range interaction force, but also receives the external stress, that is, the elastic force, which can be calculated by using Hooke's law, and is represented as:

[0100] σ ext =Lε *

[0101] Wherein, L is the elastic stiffness matrix, for isotropic material, only related to the elastic modulus and Poisson's ratio, and ε* for elastic strain;

[0102] The driving force (P-K force) of the dislocation i is the resultant force of the external stress and the interaction force between dislocations, which is expressed as:

[0103]

[0104] wherein n i represents the normal direction of the slip plane of the dislocation i, s i represents the slip direction of the slip system, and a represents the number of dislocations;

[0105] The average value of the driving force (P-K force) of all dislocations can be expressed as:

[0106]

[0107] According to the shear modulus, Poisson's ratio, Burgers vector and dislocation line length, the Piner force and dislocation proliferation strength of the analysis area 120 are calculated, and the Piner force in the area is expressed as:

[0108]

[0109] wherein,

[0110]

[0111] wherein ω represents the dislocation width, and d represents the distance between the slip planes

[0112] The dislocation source 150 is fixed on the initial slip system, and when the shear stress received is greater than the proliferation strength, the dislocation proliferates. In two-dimensional discrete dislocation dynamics, the main slip is proliferation, and the F-R dislocation source is the main proliferation mode. After the F-R dislocation source is stressed, it will release a pair of dislocations with opposite signs after a nucleation time. After the dislocations are released, it begins to shrink to a stable state, and the nucleation strength rises to wait for the next proliferation. Since a pair of dislocations with opposite signs are generated, the pair of dislocations with opposite signs must have a certain distance, otherwise annihilation will occur. The directions of the positive and negative dislocations are related to the P-K force, wherein the dislocation proliferation strength is expressed as:

[0113]

[0114] wherein L0 is the dislocation line length, generally taken as 10^4b, and in order to prevent multiple dislocation sources 150 from proliferating at the same time, the dislocation proliferation strength satisfies the normal distribution

[0115] wherein the distance between the dislocations with opposite signs formed by proliferation is expressed as:

[0116]

[0117] According to the driving force and resistance of each dislocation source 150, a corresponding dislocation source stress is obtained, and according to the stress, a movement speed of the dislocation along the slip system is obtained, which is represented as:

[0118]

[0119] Wherein, B g is a linear resistance coefficient, and for slip action, B g = 1000b;

[0120] According to the comparison between the stress and the multiplication strength, if the stress is greater than the multiplication strength, the dislocation continues to move along the slip system by overcoming the multiplication, otherwise, dislocation pile-up occurs, and at this time, the dislocation position is the final position of the dislocation;

[0121] According to the dislocation movement speed, a corresponding current position of the dislocation is obtained, and according to the distance between each dislocation, it is judged whether dislocation annihilation occurs, if the distance between positive and negative dislocations on the same slip system is less than 6b, dislocation annihilation occurs

[0122] According to the movement time, the current time dislocation movement position can be obtained, which is represented as:

[0123] X t+Δt = X t + VΔt

[0124] Wherein, X t is the position of the dislocation at the last time, X t+Δt is the position of the dislocation at the current time, and Δt is the movement time

[0125] According to the dislocation movement position, the crystal grain and unit where the dislocation moves to are judged, the number of dislocations in each unit and grain 160 is obtained, and it is particularly noted that when dislocation annihilation occurs, it should be removed, and the dislocation density in the unit is related to the size of the unit cell area, which is represented as:

[0126]

[0127] Wherein, n represents the number of geometrically necessary dislocations in the unit, A represents the area of the unit, and c and d are the length and width of the unit, the analysis region 120 is divided into a plurality of unit cells of the same size, so the unit area is the same;

[0128] In addition to the geometrically necessary dislocations, there are also statistical storage dislocations, and the corrected density calculation formula can be represented as:

[0129]

[0130] Where, E is Young's modulus, A is the initial yield stress, B is the strain hardening modulus, C is the strain rate sensitive parameter, n is the hardening exponent, ε is the plastic strain, is the reference strain rate, α is a dimensionless coefficient, generally taken as 0.5;

[0131] According to the dislocation density and grain size, the hardness of the machined surface is obtained and expressed as:

[0132]

[0133] Where D is the grain size, α and β are dimensionless constants, and ρ GND is the geometrically necessary dislocation density, ρ SSD In order to count the storage dislocation density, the dislocation density is considered as the effective value of the dislocation density that contributes to the hardening of the material during the calculation process, rather than simply adding the numbers, that is:

[0134]

Claims

1. A method for predicting the hardness of a machined surface based on an impact imprint nanoindentation experiment, characterized in that: The specific steps of the method are as follows: Obtaining in advance the basic material parameters and crystal parameters of the alloy workpiece to be processed, and selecting an analysis area on the alloy workpiece to be processed as a dislocation evolution area; Establishing a discrete dislocation dynamics model based on the basic material parameters and crystal parameters, wherein the model is used to simulate the dislocation evolution behavior in the area below the indenter; The dislocation density of the analysis area is calculated to obtain the surface hardness of the alloy workpiece to be processed.

2. The method according to claim 1, wherein the method comprises: The diamond indenter is fed at a certain speed toward the alloy workpiece to be processed and vibrates at a certain frequency.

3. The method according to claim 1, characterized in that The step of selecting an analysis area on the alloy workpiece to be processed as a dislocation evolution area comprises: According to the initial position of the stamping, an analysis area of ​​a certain size is selected on the alloy workpiece to be processed. The analysis area is a rectangular area with a certain length c and width d, directly below the initial position of the diamond indenter and with the indenter as the upper midpoint.

4. The method according to claim 1, wherein The material of the alloy workpiece to be processed includes any one of nickel-based alloy and titanium alloy, and the basic material parameters include any one of elastic modulus, Poisson's ratio and shear modulus.

5. The method according to claim 1, wherein The crystal parameters include any one or a combination of Burgers vector, number of dislocation sources, dislocation line length, dislocation barrier, dislocation multiplication time, and slip plane spacing.

6. The method according to claim 1, characterized in that The step of establishing the discrete dislocation dynamics model specifically includes: Establishing a crystal slip system according to the slip plane spacing and slip direction and the normal direction of the slip plane in the alloy workpiece to be processed, wherein the slip system directions of the crystal slip system include a 0° direction, a 60° direction and a 60° direction, selecting a suitable grain size to divide the grain boundary according to the size of the analysis area, and dividing the area into a plurality of units; According to the slip system, the intersection of slip systems in different directions is determined to obtain the position of the forest dislocation; Evenly distributing the dislocation sources and dislocation barriers in three slip systems and different grains to obtain initial dislocation source and dislocation barrier positions, wherein the dislocation barriers are distributed at both ends of the dislocation source along the slip system, and the number is 1.5 times that of the dislocation sources; According to the impact stamping speed and the depth of the processing area, the total predicted calculation time is obtained, and according to the crystal slip system, the positions of each dislocation source, and the positions of each dislocation obstacle, the discrete dislocation dynamics model is established based on discrete dislocation dynamics.

7. The method according to claim 1, characterized in that The dislocation evolution behavior includes any one or more of dislocation multiplication, dislocation accumulation, dislocation movement, and dislocation annihilation.

8. The method according to claim 6, characterized in that Calculating the predicted duration, and iteratively analyzing the dislocations in the region based on the discrete dislocation dynamics model to obtain the dislocation evolution steps include: Initialize dislocation-related factors such as dislocation source, dislocation barrier, and proliferation intensity; Obtain the external stress at the current time, and determine the shear force on the dislocation and the long-range stress between dislocations (inter-dislocation force) based on the position of the dislocation on the slip system at the current time, expressed as: Where, in, represents the normal stress in the x direction of dislocation j on dislocation i, represents the normal stress of dislocation j on dislocation i in the y direction, represents shear stress, G represents shear modulus, v represents Poisson's ratio, b represents Burgers vector, and x and y represent the distances between dislocation i and dislocation j in the x and y directions; In addition to the inter-dislocation forces, dislocations are also subject to external stress, which can be calculated using Hooke's law and expressed as: s ext =Le* Among them, L is the elastic stiffness matrix. For isotropic materials, it is only related to the elastic modulus and Poisson's ratio, ε * is the elastic strain; The driving force (PK force) on dislocation i is the resultant force of the external stress and the inter-dislocation force, which can be expressed as: Among them, n i represents the normal direction of the slip plane where dislocation i is located, s i represents the slip direction of the slip system, and a represents the number of dislocations; The average driving force (PK force) of all dislocations can be expressed as: According to the shear modulus, Poisson's ratio, Burgers vector and dislocation line length, the Paine force and dislocation multiplication strength of the analysis area are calculated. The Paine force in the area is expressed as: Where, Where, ω represents the dislocation width, d represents the slip plane spacing The dislocation multiplication intensity is expressed as: Where L0 is the length of the dislocation line. To prevent multiple dislocation sources from multiplying simultaneously, the dislocation multiplication intensity is made to satisfy the normal distribution. According to the driving force and resistance of each dislocation source, the corresponding dislocation source composite stress is obtained. According to the composite stress, the movement speed of the dislocation i along the slip system is obtained, which is expressed as: Among them, B g is the linear resistance coefficient. For slip action, B g =1000b; Comparing the magnitudes of the resultant stress and the proliferation strength, if the resultant stress is greater than the proliferation strength, the dislocation skips the proliferation and continues to move along the slip system; otherwise, dislocation pileup occurs, and the dislocation position at this time is the final position of the dislocation; According to the dislocation movement speed, the corresponding current position of the dislocation is obtained, and according to the distance between each dislocation, whether dislocation annihilation occurs is determined. If the distance between positive and negative dislocations in the same slip system is less than 6b, dislocation annihilation occurs. The current time dislocation motion position is expressed as: X t+Δt =X t +VΔt Among them, X t is the position of the dislocation at the previous moment, X t+Δt is the current time dislocation location, Δt is the movement time; The grain and unit where the dislocation moves are determined according to the dislocation movement position, and the number of dislocations in each unit and grain is obtained.

9. The method according to claim 1, wherein The steps of calculating the dislocation density of the analysis area and obtaining the surface hardness of the alloy workpiece to be processed are: The number of dislocations according to claim 8 is used to obtain the geometrically necessary dislocation density in the region, expressed as: in, n represents the number of geometrically necessary dislocations in the unit cell, A represents the area of ​​the unit cell, and c and d represent the length and width of the unit cell; In addition to geometrically necessary dislocations, there are also statistical storage dislocations, and the modified density calculation formula can be expressed as: Where, E is Young's modulus, A is the initial yield stress, B is the strain hardening modulus, C is the strain rate sensitive parameter, n is the hardening exponent, ε is the plastic strain, is the reference strain rate, α is a dimensionless coefficient, generally taken as 0.5; According to the dislocation density and grain size, the hardness of the machined surface is obtained and expressed as: Where D is the grain size, α and β are dimensionless constants, and ρ GND is the geometrically necessary dislocation density, ρ SSD is the statistical storage dislocation density.

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