A multi-scale prediction method for microstructure and performance of laser hardened layer

Abstract

The application belongs to the technical field of laser quenching, and specifically discloses a multi-scale prediction method for the microstructure performance of a laser quenching hardened layer, which comprises the following steps: constructing a phase change dynamics model considering the influence of a heating rate and constructing a mechanical response mathematical model; based on the phase change dynamics model, the mechanical response mathematical model and a finite element geometric model of a sample, performing finite element simulation on a laser quenching process to obtain a temperature field, the volume fraction of each phase and residual stress; based on the austenite nucleation and growth coarsening mechanism and the martensite nucleation and growth mechanism, obtaining a cellular automaton simulation model through cellular automaton transformation rules; cellularizing the initial microstructure and adopting the cellular automaton simulation model to obtain microstructure evolution and grain size; and adopting a hardness calculation hybrid rule and combining the relationship between hardness and grain size to obtain the hardness prediction value of the hardened layer. Through the application, the volume fraction distribution of the sample surface and the surface performance can be accurately predicted.

Description

Technical Field

[0001] This application belongs to the field of laser hardening technology, and more specifically, relates to a multi-scale prediction method for the microstructure and properties of laser hardened layers. Background Technology

[0002] Laser hardening technology, as a highly efficient surface strengthening method, has been widely used in the surface hardening of metallic materials. The laser hardening process uses a high-energy laser beam to rapidly heat the metal surface, creating localized high-temperature zones that cause austenitization. During the subsequent rapid cooling process, a martensitic phase transformation occurs, thereby improving the material's surface hardness, wear resistance, and fatigue life.

[0003] However, relying solely on parameter tuning and trial-and-error methods to optimize laser quenching process parameters is not only inefficient but also costly. Current numerical simulation models for laser surface quenching typically only consider the influence of laser process parameters on surface temperature evolution, failing to couple the austenite, martensite, and tempered martensite phase transformation models. This results in their inability to accurately predict the phase volume fraction distribution and surface properties of the surface.

[0004] Establishing a multi-field coupled thermo-mechanical-structural model to study the phase transformation dynamics, heat transfer, and stress-strain evolution mechanism during laser quenching, and to predict surface properties, has significant engineering application value. For quasi-laser quenching, accurately predicting the phase volume fraction distribution and surface properties of the sample surface is a pressing technical problem to be solved in this field. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this application is to provide a multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers, thereby solving the problem that existing technologies cannot accurately predict the phase volume fraction distribution and surface properties of sample surfaces.

[0006] To achieve the above objectives, this application provides a multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers, the method comprising: A phase transformation kinetic model considering the effect of heating rate and a mechanical response mathematical model are constructed. The phase transformation kinetic model is used to obtain the volume fractions of austenite, martensite, and tempered martensite (volume fractions of each phase). The mechanical response mathematical model is used to obtain the total strain increment, including elastic strain increment, plastic strain increment, volumetric strain increment, and phase transformation-induced plastic strain increment. Based on the phase transformation dynamics model, the mechanical response mathematical model, and the finite element geometric model of the sample, a finite element simulation of the laser quenching process was performed to obtain the temperature field, the volume fraction of each phase, and the residual stress. Based on the austenite nucleation and growth coarsening mechanism and the martensite nucleation and growth mechanism, a cellular automata simulation model for the laser quenching process is obtained through cellular automata transformation rules. Based on the temperature field, the initial microstructure is cellularized, and a cellular automata simulation model is used to obtain the microstructure evolution and grain size during the laser quenching process. Based on the volume fraction of each phase and the grain size, the hardness prediction value of the laser-quenched hardened layer is obtained by using the hardness calculation mixing rule and combining the relationship between hardness and grain size.

[0007] In one possible implementation, the phase transition dynamics model is specifically used for: The volume fraction of austenite during the heating process was obtained based on the JMAK diffusion phase transformation model. Based on the Koistinen-Marburger equation, the volume fraction of martensite during the cooling process was obtained; Based on the JMAK diffusion phase transformation model, the volume fraction of tempered martensite during the tempering process was obtained. Specifically, for non-isothermal processes with non-fixed heating rates during laser quenching, the non-isothermal transformation process is described as an isothermal process with multiple incremental steps, and the phase transformation volume fraction of each phase under the non-isothermal process is obtained.

[0008] In one possible implementation, the austenite volume fraction is calculated using the following formula: ; in, Indicates the volume fraction of austenite; This represents the temperature-dependent austenitizing kinetic coefficient; Indicates isothermal time; This represents the Avrami index used for austenite.

[0009] In one possible implementation, the martensite volume fraction is calculated using the following formula: ; in, Indicates the volume fraction of martensite; Indicates the volume fraction of austenite; Represents a constant; This indicates the temperature at which martensite begins to transform; This indicates the temperature at the current time step.

[0010] In one possible implementation, the volume fraction of tempered martensite is calculated using the following formula: ; in, This indicates the volume fraction of tempered martensite. This represents the temperature-dependent kinetic coefficient of tempered martensite; Indicates isothermal time; This represents the Avrami index used for tempered martensite.

[0011] In one possible implementation, in the incremental step The volume fraction of the time-transformation phase is calculated using the following formula: ; Equivalent time: ; Indicates incremental step Time Phase volume fraction; Indicates the first related to temperature Phase transition kinetic coefficients; Indicates equivalent time; Indicates the first The Avrami index of the phase; Indicates the number of increment steps before the current increment. Phase transition volume fraction.

[0012] In one possible implementation, the mathematical model of the mechanical response is determined by the following formula: ; in, Indicates the total strain increment; Indicates the increment of elastic strain; Indicates the increment of plastic strain; Indicates the volumetric strain increment; This represents the increment of plastic strain induced by phase transformation.

[0013] In one possible implementation, the above-mentioned finite element simulation of the laser quenching process includes: Based on the finite element geometric model, the temperature field of laser quenching is simulated and calculated to obtain the temperature field of the specimen throughout the laser quenching process. At each incremental step, the phase transformation kinetic model is invoked, and the volume fraction of each phase is used as the field variable to calculate the volume fraction of austenite, martensite, and tempered martensite. Based on the mathematical model of volume fraction and mechanical response of each phase, the volume fraction increment caused by phase transformation-induced volume fraction change and density difference of each phase is calculated in each increment step, and stress-strain calculation is performed to obtain residual stress. The finite element simulation uses a flat-top Gaussian heat source, and the expression for the heat flux of the light spot of the flat-top Gaussian heat source is as follows: ; Indicates laser heat flux; This indicates the material's absorption rate of laser light; Indicates laser power; Indicates the area of ​​the laser spot; This represents the coordinate values ​​with the center of the light spot as the origin; This indicates the width of the laser spot.

[0014] In one possible implementation, the cellular automata simulation model is used for: Based on the degree of overheating, the austenite nucleation density is obtained through the austenite grain nucleation model, and the nucleation is determined according to the austenite nucleation transformation rules. Based on the cell mobility at grain boundaries, a transformation rule is used to control the grain growth direction and obtain the austenite growth and coarsening results. Based on the martensite volume fraction, a martensite nucleation and growth model is used to obtain the martensite nucleation rate, and nucleation and growth are carried out according to the martensite transformation rules. The austenite nucleation rate, extended to non-isothermal processes, is obtained using the following formula: ; This represents the austenite nucleation rate extended to non-isothermal processes (the combined austenite nucleation rate). Parameters indicating the effect of pearlite on the nucleation rate of austenite; Indicates the correlation coefficient of pearlite structure; Represents the temperature gradient; Indicates the activation energy of austenite nucleation; Represents the Boltzmann constant; Indicates overheating.

[0015] In one possible implementation, the hybrid rule for hardness calculation is determined by the following formula: ; in, The calculated hardness value represents the current phase structure distribution; Indicates the volume fraction of martensite; Indicates the hardness of martensite; Indicates the volume fraction of ferrite; Indicates the hardness of ferrite; This indicates the hardness contribution value of dissolved carbides; This indicates the hardness of undissolved carbides during laser surface hardening; The relationship between hardness and grain size is determined by the following formula: ; in, This indicates the contribution of grain size to hardness. This represents a constant hardness value that is independent of grain size. Indicates the preset coefficient; Indicates grain size.

[0016] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art.

[0017] (1) This application establishes a phase transformation dynamics model that considers the influence of heating rate, and constructs an austenitic phase transformation dynamics model based on the JMAK diffusion phase transformation model, a martensitic phase transformation dynamics model based on the Koistinen-Marburger equation, and a martensitic tempering process dynamics model, respectively. The classical JMAK equation is extended to non-isothermal processes through the Scheil superposition principle, so as to adapt to the phase transformation calculation under non-fixed heating rate conditions during laser quenching. In the finite element simulation, the above phase transformation dynamics model is embedded into the calculation of each incremental step through the USDFLD subroutine of ABAQUS, and the volume fraction evolution of each phase (pearlite, austenite, martensite, tempered martensite) is calculated in real time in combination with temperature field information, thereby realizing the accurate prediction of the phase volume fraction distribution on the sample surface during laser quenching.

[0018] (2) This application uses a hybrid hardness calculation method based on phase composition and hardness of each phase, combined with the volume fraction of each phase obtained from finite element simulation and the grain size obtained from cellular automata simulation, to correct the hardness calculation value using the relationship between hardness and grain size (Hall-Petch formula), thereby achieving accurate prediction of the surface hardness of the laser-quenched hardened layer; at the same time, this application couples phase transformation-induced plasticity effect with multiphase thermal strain, which can accurately predict the distribution transformation law of residual compressive / tensile stress in the depth direction from the hardened layer to the matrix. Therefore, this application can accurately predict the surface properties (hardness, residual stress) of the sample during laser quenching. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers provided in the embodiments of this application. Figure 2 These are schematic diagrams of the laser quenching finite element model and the flat-top Gaussian heat source model provided in the embodiments of this application; Figure 3 This is a comparison diagram of the cross-sectional morphology of the hardened layer and the simulated temperature field provided in the embodiments of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0021] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0022] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0023] First, the technical terms used in the embodiments of this application will be introduced.

[0024] The Avrami exponent is a key parameter in the JMAK equation, reflecting the nucleation and growth mechanisms of phase transitions.

[0025] The flat-top Gaussian heat source is a heat source model constructed based on the actual energy distribution law of fiber laser spot: the energy distribution in the central region of the spot is uniform (flat-top), and the energy at the edge gradually decays in the form of a high-order Gaussian function.

[0026] The JMAK model (Johnson-Mehl-Avrami-Kolmogorov model) is a classical equation describing the kinetics of diffusion-type solid-state phase transformations. The JMAK model assumes a uniform distribution of nucleation sites and that the nucleation rate is independent of time, and can describe the S-shaped transformation kinetics of most diffusion-type phase transformations (such as austenitization and bainitic transformation).

[0027] The Koistinen-Marburger (KM) equation is an empirical equation describing the relationship between the volume fraction of diffusionless martensitic phase transformation and temperature.

[0028] ABAQUS is a finite element analysis software used in engineering simulation fields such as structural mechanics, thermal analysis, and fluid-structure interaction.

[0029] The USDFLD subroutine is a user-defined field subroutine interface provided by ABAQUS, which allows users to write custom code in Fortran to calculate and update user-defined field variables at each integration point in each increment step.

[0030] The UEXPAN subroutine is a user-defined expansion interface provided by ABAQUS, which allows users to customize the calculation logic for thermal strain (including thermal expansion and phase transformation volumetric strain) of materials.

[0031] The DISP subroutine is a user-defined displacement (boundary condition) subroutine interface provided by ABAQUS, which is typically used to implement complex boundary conditions that vary over time.

[0032] The Stefan-Boltzmann law is a fundamental physical law describing thermal radiation: the radiative power (radiative heat flux density) per unit area of ​​an ideal blackbody is proportional to the fourth power of its absolute surface temperature.

[0033] The embodiments of this application are described below with reference to the accompanying drawings.

[0034] Example 1.

[0035] The technical solution adopted in this application is a multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers, such as... Figure 1 As shown, please follow these steps: Step 1: Establish a phase transition kinetic model that considers the effect of heating rate; Step 2: Establish a mathematical model of the mechanical response; Step 3: Establish a finite element geometric model, perform mesh generation and refinement, set boundary conditions, and input material property parameters; Step 4: Perform finite element simulation of temperature, phase volume fraction, and residual stress during the laser quenching process; Step 5: Establish the austenite nucleation and growth coarsening model, the martensite nucleation and growth model, and the transformation rule model in the laser quenching cellular automata simulation process. Step 6: Perform initial cellularization of the structure and simulate the laser quenching cellular automata based on the temperature field information from the finite element simulation. Step 7: Perform hardness prediction based on phase composition and grain size.

[0036] This application establishes a phase transformation kinetic model that considers the influence of heating rate. It constructs an austenitic phase transformation kinetic model based on the JMAK diffusion phase transformation model, a martensitic phase transformation kinetic model based on the Koistinen-Marburger equation, and a martensitic tempering process kinetic model. The classical JMAK equation is extended to non-isothermal processes through the Scheil superposition principle, thus adapting to phase transformation calculations under non-fixed heating rate conditions during laser quenching. In the finite element simulation, the above phase transformation kinetic models are embedded into the calculation of each incremental step through the USDFLD subroutine of ABAQUS. Combined with temperature field information, the volume fraction evolution of each phase (pearlite, austenite, martensite, and tempered martensite) is calculated in real time, thereby achieving accurate prediction of the phase volume fraction distribution on the sample surface during laser quenching.

[0037] This application employs a hybrid hardness calculation method based on phase composition and the hardness of each phase, combined with the phase volume fraction obtained from finite element simulation and the grain size obtained from cellular automata simulation. It then uses the relationship between hardness and grain size (Hall-Petch formula) to correct the calculated hardness value, thereby achieving accurate prediction of the surface hardness of the laser-quenched hardened layer. Simultaneously, this application couples phase transformation-induced plasticity with multiphase thermal strain, enabling accurate prediction of the residual compressive / tensile stress distribution transformation law in the depth direction from the hardened layer to the substrate. Therefore, this application can accurately predict the surface properties (hardness, residual stress) of samples during laser quenching.

[0038] Furthermore, this application overcomes the limitations of traditional single macroscopic temperature field simulation. It simulates the temperature field, phase volume fraction distribution, and residual stress field during laser quenching on a macroscopic scale using the finite element method. Simultaneously, it simulates the grain evolution behaviors such as nucleation, growth, and coarsening of austenite and martensite on a mesoscopic scale using the cellular automata method and obtains the grain size. Finally, it combines the phase volume fraction on a macroscopic scale with the grain size on a mesoscopic scale to predict hardness, thus achieving cross-scale coupling from macroscopic thermo-mechanical field to mesoscopic grain evolution and completing multi-scale prediction.

[0039] Step 1: Establish a phase transition kinetic model that considers the effect of heating rate. Step 1 specifically includes the following steps 1.1 to 1.4.

[0040] Step 1.1: Establishment of the dynamic model of austenite phase transformation.

[0041] The austenitic phase transformation during heating is a diffusion phase transformation. Based on the JMAK diffusion phase transformation model, assuming that nucleation and growth are independent of time, the austenite volume fraction (JMAK equation) is: (1); Parameter explanation: Austenite volume fraction; Temperature-dependent austenitizing kinetic coefficients; Isothermal time; Avrami index.

[0042] The austenite kinetic coefficients (Arrhenius equation) are: (2); Parameter explanation: Temperature-dependent austenitizing kinetic coefficients; A coefficient determined by the material and the type of phase transition; Activation energy for austenitic phase transformation; Gas constant; Temperature (K).

[0043] Phase transition activation energy Evaluation using the Kissinger equation: (3); Parameter explanation: Heating rate; : Temperature at maximum phase change rate (temperature at 50% phase change volume fraction); Activation energy for austenitic phase transformation; Gas constant; : The intercept constant of the Kissinger equation.

[0044] The elongation of the material as a function of temperature under different heating rates was obtained through thermal expansion tests. The austenite volume fraction as a function of temperature under different heating rates was calculated using the lever law. (4); Parameter explanation: Austenite volume fraction; The initial length of the sample; : The length of the sample when it retains its initial structure; : Length of the sample when it is pure austenite.

[0045] By fitting different heating rates and The value of is used to obtain the slope of the fitted curve, which is the activation energy of the austenite phase transformation. The ratio of the gas constant R to the austenite phase transformation activation energy is obtained.

[0046] Taking the logarithm twice on both sides of the JMAK formula (linearizing the JMAK equation), it can be transformed into: (5); Parameter explanation: : Austenite transformation fraction; Avrami index of austenitic phase transformation; A coefficient determined by the material and the type of phase transition; : Temperature-dependent austenitizing kinetic coefficient.

[0047] in The approximate value is: (6); Parameter explanation: : Austenitizing kinetic coefficient; A coefficient determined by the material and the type of phase transition; : Current step temperature change; Heating rate; Total steps; Phase transition activation energy; Gas constant; : No. The temperature of the step.

[0048] Will As the independent variable, The calculated data is used as the dependent variable, and a curve is fitted to the calculated data values. The slope of the resulting fitted curve is then calculated. Value, intercept is value.

[0049] Step 1.2: Establishment of the dynamic model of martensitic phase transformation.

[0050] The martensitic phase transformation process is a diffusionless phase transformation, and its volume fraction can be described by the Koistinen-Marburger equation (KM equation): (7); Parameter explanation: Martensite volume fraction; Austenite volume fraction; : constant (e.g., 0.02); The temperature at which martensite begins to transform; : Current time step temperature.

[0051] Step 1.3: Establishment of the kinetic model of the martensitic tempering process.

[0052] The martensitic tempering process is a diffusion phase transformation, and the JMAK diffusion phase transformation model (JMAK equation) is also used for calculation: (8); Parameter explanation: Volume fraction of tempered martensite; : Temperature-dependent kinetic coefficients of tempered martensite; Isothermal time; Avrami index (tempered martensite).

[0053] The kinetic coefficients follow the modified Arrhenius equation: (9); Parameter explanation: : Temperature-dependent kinetic coefficients of tempered martensite; : A constant determined by the material; Activation energy for tempering martensitic phase transformation (J / mol); Gas constant; Temperature (K).

[0054] The curves of material hardness versus tempering time at different temperatures were obtained using JmatPro, and the curves of tempered martensite volume fraction versus time were obtained using the following formula: (10); Parameter explanation: Volume fraction of tempered martensite; Initial hardness (untempered martensite); Current hardness; Hardness in the fully tempered state.

[0055] The method for determining parameters in the JMAK equations is similar to that in the austenitic model.

[0056] Step 1.4, extension of non-isothermal process.

[0057] Since the classical JMAK equations only apply to isothermal phase transitions at fixed heating rates, they are not suitable for simulating laser surface hardening processes. Therefore, the Scheil superposition principle is used to extend these equations, making them applicable to calculating the phase transition volume fraction for processes with non-fixed heating rates. Based on Scheil's additivity rule, the non-isothermal transformation process is described as an isothermal process consisting of multiple small increment steps. Based on the calculated phase transition volume at the current heating rate, the equivalent time at which the phase transition occurs is obtained. Then, the volume increment at the time step is calculated using the JMAK equation at the current temperature. The volume fraction of the transformed phase at increment step p is: (11); Equivalent time: ; Parameter explanation: Incremental steps Time Phase volume fraction; The first temperature-related factor Phase transition kinetic coefficients; Equivalent time (a time parameter that converts non-isothermal conditions into isothermal conditions); : No. The Avrami index of the phase; The first increment step before the current increment step Phase transition volume fraction.

[0058] Incremental steps Time The phase transition rate of the phase is: (12); Parameter explanation: : No. The Avrami index of the phase; The first temperature-related factor Phase transition kinetic coefficients; Equivalent time.

[0059] The phase transition volume increment of the i-th phase at increment step p is: (13); Parameter explanation: Incremental steps Time The volume increment of the phase transition; Time step; Phase transition rate (in equivalent time) (The value at that location).

[0060] Integrating the phase transition increments in each increment step yields the phase transition volume at the current increment step p. .

[0061] Step 2: Establish a mathematical model of mechanical response.

[0062] The total strain increment is represented by the superposition of multiple components: (14); Parameter explanation: Total strain increment; Elastic strain increment; : Increment of plastic strain; Volumetric strain increment (considering phase transformation and temperature change); : Phase transformation induced plastic strain increment.

[0063] The volumetric strain increment is dominated by the density difference caused by phase type and temperature change, and is modeled using a linear mixing rule: (15); Parameter explanation: Volumetric strain increment (considering phase transformation and temperature change); : No. Phase volume fraction; : No. Phase density; : No. The differential increment of phase density; : Identity matrix.

[0064] The total volumetric strain increment is the sum of the volumetric strain increments of pearlite, austenite, martensite, and tempered martensite. During diffusionless phase transformation, externally induced stress generates additional phase transformation-induced plastic strain. The phase transformation-induced plastic strain increases linearly with increasing stress. To accurately obtain the phase transformation-induced plastic strain increment during laser surface hardening, a linear model is used for modeling: (16); Parameter explanation: Phase transformation induced plastic strain; : Constants related to phase transition type and material; : Diffusion phase transition rate; :stress.

[0065] Step 3: Establish the finite element geometric model and set the boundary conditions. Step 3 specifically includes the following steps 3.1 to 3.3.

[0066] Step 3.1: Establishment of finite element geometric model and mesh generation.

[0067] Based on the ABAQUS software platform, a finite element geometric model of the specimen was established. The simplified finite element geometric model is as follows: Figure 2 As shown, the mesh is refined on the sample surface; below the refined region, the mesh size increases with increasing depth and distance from the plane of symmetry.

[0068] Figure 2 This is a schematic diagram of the laser quenching finite element model and the flat-top Gaussian heat source model of this application. Figure 2As shown, the figure is arranged horizontally: the left side is the three-dimensional finite element mesh geometric model of the sample, which is a thin plate-shaped cuboid. A flat-topped Gaussian heat source energy distribution surface, rising from the inside out in a hill-like pattern, is superimposed on the center of its upper surface. This surface is flat at the top and gradually decreases in energy at the edges, represented by a color gradient from red, orange, yellow, green, blue to purple, indicating the gradual decrease in heat source energy from the center to the edges. Below the model on the left, a localized mesh refinement area is outlined with a red dashed line, extending to the right side. The right side is an enlarged view of this locally refined area, showing the mesh further refined below the sample surface, with the mesh size increasing with depth below the refined area. This figure characterizes the meshing method of the finite element geometric model and the energy distribution characteristics of the flat-topped Gaussian heat source, which exhibits uniform energy at the center and gradually decreasing energy at the edges.

[0069] Numerical simulations of thermo-mechanical-structural multi-field coupling were performed using a sequential coupling approach. In the temperature field numerical simulation, a heat transfer analysis step was used, with the billet set as a rigid body and the element type being a three-dimensional heat transfer tetrahedral element (C3D8T). In the thermo-mechanical coupling numerical simulation, a static general analysis step was used, with the billet set as a plastic body and the element type being a three-dimensional stress tetrahedral element (C3D8).

[0070] A flat-top Gaussian heat source is constructed based on the energy distribution pattern of a fiber laser spot, and its motion control is implemented using a DISP subroutine. The heat transfer coefficient at the workpiece-air interface is set to... The ambient temperature is maintained at 25°C. The energy distribution is uniform at the center of the light spot and gradually decreases at the edges. The expression for the heat flux of the light spot is: (17); Parameter explanation: Laser heat flux; The absorption rate of laser light by the material; Laser power; Laser spot area; : Coordinates with the center of the light spot as the origin; This represents the x-coordinate value with the center of the light spot as the origin; This represents the ordinate value with the center of the light spot as the origin; : Laser spot width.

[0071] Step 3.2: Setting thermal property parameters.

[0072] The specific heat capacity and thermal conductivity of the sample are obtained by using a laser thermal conductivity meter, and the relationship between temperature and these values ​​is then input into the material properties of the finite element model to improve accuracy.

[0073] Step 3.3: Set heat transfer boundary conditions.

[0074] The heat transfer process in laser surface hardening follows the law of conservation of energy, and the temperature field exhibits typical transient nonlinear changes. The main heat transfer phenomena include absorption of the laser beam upon impact with the sample surface, radiative heat transfer from the sample surface to the surrounding environment, and heat transfer within the material. As the sample temperature rises, the surface emits radiative energy to the environment. According to the Stefan-Boltzmann law, the heat flux density from the sample surface to the environment through radiation is: (18); Parameter explanation: Radiative heat flux density ( ); : The blackness coefficient of the sample (e.g., take 0.35); Stefan-Boltzmann constant; Real-time surface temperature of the object.

[0075] Simultaneously, the surface of the sample (excluding the bottom surface) undergoes convective heat transfer with the air or cooling medium. In the numerical model, it is assumed that the initial temperature of the sample is uniform and equal to the ambient temperature. A convective boundary condition is applied to the surface of the sample in contact with the air, while thermal conduction occurs between the bottom surface of the sample and the substrate. During laser surface hardening, the heat transfer process of the sample is primarily controlled by the heat conduction equation. The coupling equations of the heat conduction model are: (19); Parameter explanation: : A temperature function representing the change of temperature at different locations with time t; Material density; Specific heat capacity of the material; Thermal conductivity; Phase change latent heat (internal heat source term).

[0076] In local surface heat treatment processes with high heating rates, the latent heat of phase transformation has a relatively small effect on the overall temperature increase. The heat change caused by the latent heat of phase transformation is ignored in the numerical simulation of the austenitizing process.

[0077] Step 4: Perform finite element simulation of temperature, phase volume fraction, and residual stress during the laser quenching process.

[0078] The laser quenching temperature field was simulated and calculated using ABAQUS. The volume fraction of each phase was calculated using custom field variables in the USDFLD subroutine, with the initial pearlite volume fraction set to 1. The USDFLD subroutine can store custom variables, allowing for the calculation of the volume fraction of each phase at each increment step. The phase transformation-induced volume fraction change (phase transformation-induced plastic strain increment) and the volume fraction increment caused by the density difference of each phase (volume strain increment) were calculated at each increment step using the UEXPAN subroutine. Stress and strain were then calculated using the constitutive model built into ABAQUS.

[0079] Specifically, step 4 uses the USDFLD user-defined field variable subroutine in the ABAQUS software to call the phase transformation dynamics model established in step 1: the austenitic phase transformation dynamics model (JMAK equation), the martensitic phase transformation dynamics model (Koistinen-Marburger equation), the tempered martensitic phase transformation dynamics model, and the non-isothermal process phase transformation calculation model extended by the Scheil superposition principle established in step 1 are written into the USDFLD subroutine. In each incremental step of the finite element simulation, the subroutine reads the temperature and time information of the current integration point, substitutes it into the above phase transformation dynamics model to calculate the volume fraction of each phase, and stores the results in the form of user-defined field variables. The initial state is set to pearlite volume fraction of 1, so that the volume fraction of each phase of pearlite, austenite, martensite, and tempered martensite is updated and calculated in real time in each incremental step.

[0080] Further, step 4 uses the UEXPAN user-defined thermal expansion subroutine in the ABAQUS software to call the mechanical response mathematical model established in step 2: the total strain increment in step 2 is decomposed into the superposition relationship of elastic strain increment, plastic strain increment, volumetric strain increment, and phase transformation-induced plastic strain increment, and written into the UEXPAN subroutine. In each increment step, the subroutine calculates the volumetric strain increment caused by the density difference of the four phases (pearlite, austenite, martensite, and tempered martensite) based on the volume fraction of each phase calculated by the USDFLD subroutine, and uses the linear mixing rule to calculate the phase transformation-induced plastic strain increment (phase transformation-induced volume fraction change) determined by the diffusion phase transformation rate and the current stress. These strain increments are then passed to the constitutive model built into ABAQUS for stress-strain solution, thereby realizing the calculation of residual stress.

[0081] This section provides an illustrative example of the process of obtaining the temperature field through finite element simulation in step 4. In step 4, the temperature field is simulated using a sequential coupling method in ABAQUS software. First, a finite element geometric model of the sample is established and the mesh is generated and refined. In the numerical simulation stage of the temperature field, a heat transfer analysis step is used. The billet is set as a rigid body, and a three-dimensional heat transfer tetrahedral element (C3D8T) is used. A flat-top Gaussian heat source is constructed based on the energy distribution mode of the fiber laser spot, and the movement of the heat source is controlled by the DISP subroutine. The heat transfer coefficient of the workpiece-air interface, the ambient temperature, and the Stefan-Boltzmann radiation boundary conditions are set. By solving the heat conduction coupling equation, the temperature field distribution of different positions inside the sample during laser quenching is obtained. The temperature is highest at the center of the spot, and the temperature gradually decreases as the distance from the center of the spot increases.

[0082] This section provides an illustrative example of the process of obtaining the volume fraction of each phase through finite element simulation in step 4. A custom field variable is defined in the finite element model to store the volume fraction of each phase. The initial state is set with pearlite volume fraction as 1 and the volume fraction of the other phases as 0. In each increment step of the temperature field simulation, the USDFLD subroutine reads the temperature and time information of the current integration point, calls the phase transformation kinetic model established in step 1 (including the non-isothermal JMAK equation extended by the Scheil superposition principle to calculate the volume fraction of austenite and tempered martensite, and the Koistinen-Marburger equation to calculate the volume fraction of martensite), calculates the phase transformation volume increment of each phase in the current increment step, integrates and accumulates, and obtains the volume fraction distribution of the four phases of pearlite, austenite, martensite, and tempered martensite at the integration point.

[0083] Here, we provide an illustrative explanation of the process of obtaining residual stress through finite element simulation in step 4. After obtaining the temperature field and the volume fraction of each phase, step 4 enters the thermo-mechanical coupling numerical simulation stage. The static general analysis step is adopted, the billet is set as a plastic body, and a three-dimensional stress tetrahedral element (C3D8) is used. The UEXPAN subroutine calculates the volumetric strain increment caused by phase transformation and temperature change (based on the linear mixing law of the density difference of each phase) and the phase transformation-induced plastic strain increment determined by the diffusion phase transformation rate and the current stress (based on the linear model) in each incremental step. The above strain increment is superimposed with the elastic strain increment and the plastic strain increment to obtain the total strain increment, which is passed to the constitutive model built into ABAQUS for stress-strain solution, thereby obtaining the residual stress distribution from the laser-hardened layer to the depth of the matrix.

[0084] Step 5: Establish the austenite nucleation and growth coarsening model, the martensite nucleation and growth model, and the transformation rule model in the laser quenching cellular automata simulation process. Step 5 specifically includes the following steps 5.1 to 5.3.

[0085] Step 5.1: Establishment of the austenite grain nucleation model.

[0086] Calculation of austenite nucleation density during isothermal process: (20); Parameter explanation: austenite nucleation density; : Parameters reflecting the influence of pearlite on the nucleation rate of austenite (e.g., taking...) ); : Austenitic nucleation activation energy (e.g., taking ); Boltzmann constant; Overheating.

[0087] Extending to non-isothermal processes, the nucleation rate per cell is: (twenty one); Parameter explanation: Non-isothermal nucleation rate (number of nuclei formed per unit time); : A constant related to the interlamellar spacing and grain size of pearlite; : Current cell temperature gradient (heating rate); Nucleation density; Pearlite volume fraction in the initial tissue; : Total area of ​​cellular automata.

[0088] Because laser quenching involves a large temperature gradient, it rapidly reaches a high degree of superheat during the heating phase. The nucleation rate is calculated by combining the above formulas: (twenty two); Parameter explanation: : The nucleation rate of austenite after merging; Parameters that influence the nucleation rate of austenite; : Correlation coefficient of pearlite structure (taken as 2.5); Temperature gradient (heating rate); : Austenite nucleation activation energy; Boltzmann constant; Overheating.

[0089] The above formula enables static nucleation at grain boundaries and within grains, as well as dynamic austenite nucleation related to temperature gradients.

[0090] Austenite nucleation transformation rule: First, search all cells. If it is a ferrite grain, the austenite nucleation rate is 0; if it is a pearlite grain boundary, the austenite nucleation rate is 0%. If it is inside the pearlite, then the nucleation rate is... A random number between 0 and 1 is generated using the `random` function in Python and compared with the nucleation rate. If the random number is less than the nucleation rate, austenite nucleation occurs in that cell, assigning a random initial orientation value to the nucleated austenite. , range .

[0091] Step 5.2: Establishment of the austenite growth and coarsening model.

[0092] Austenite growth and coarsening transformation rules: Since austenite grain growth occurs at grain boundaries, a grain boundary mask is first created, assigning the grain boundary state to the cells of all grain boundaries after the previous step. This process iterates through all grains; growth and coarsening only occur when the mask state is a grain boundary. Then, transformation rules 1-5 are applied sequentially, and austenite growth and coarsening occurs if any rule is met.

[0093] Transformation Rule 1: Grain boundary migration of austenite requires overcoming an energy barrier to begin; that is, the cell at the grain boundary needs to exceed the austenite migration activation threshold for migration to occur. Furthermore, the higher the temperature, the higher the probability of migration. The migration rate of austenite grains is: (twenty three); Parameter explanation: : Austenite grain migration probability (growth probability); : Coefficients related to material properties (calculated by assuming that surface migration must occur at the melting point); Current temperature; The temperature at which austenite begins to transform; Melting point; Activation energy for austenite migration (taken as 159 kJ / mol); : Gas constant.

[0094] During grain growth, curved grain boundaries tend to straighten, growing towards the direction with the lowest surface area and reducing the total surface energy. By controlling the grain growth direction through transformation rules 2-4, grain boundaries can preferentially grow towards the straight direction.

[0095] Transition Rule 2: If there are 5 or more cells in the Moore neighborhood of the current cell that are in the same state, the current cell state will be updated to that state in the next time step.

[0096] Transition Rule 3: If there are 3 or more cells in the Moore neighborhood of the current cell that are in the same state, the current cell state will be updated to that state in the next time step.

[0097] Transition Rule 4: If there are 3 or more cells in the Moore neighborhood of the current cell that are in the same state, the current cell state will be updated to that state in the next time step.

[0098] Transition Rule 5: The current cell randomly obtains the states of its surrounding neighbors, calculates the grain boundary energy before the transformation and the grain boundary interface energy after the transformation of the current cell respectively. If the increment of the grain boundary interface energy is less than 0, the cell is updated to the state of its neighbors.

[0099] Step 5.3: Establishment of the Martensitic nucleomorphic growth model.

[0100] The relationship between the number of martensite nucleation sites and the martensite volume fraction is as follows: (twenty four); Parameter explanation: Number of martensitic nuclei; : Current martensite volume fraction; Martensite grain width-to-length ratio.

[0101] Martensite volume fraction: (25); Parameter explanation: Martensite volume fraction; Austenite volume fraction; : constant (taken as 0.02); The temperature at which martensite begins to transform; : Current time step temperature.

[0102] Nucleation rate at current time step t: (26); Parameter explanation: : Probability of martensitic nucleation at the current time step t; : The number of martensitic nucleation points at the current time step t; : The number of martensitic nuclei in the previous time step; : The total number of cells in the current cellular automaton.

[0103] When the temperature drops below the martensitic transformation temperature, martensitic nucleation and growth occur. First, all cells are traversed, and then, according to transformation rule 1, the martensitic nucleation state of all cells in the austenitic grain state is updated.

[0104] Transformation Rule 1: Calculate the martensitic nucleation rate of the cell, generate a random number and use the nucleation rate to determine nucleation, and assign a random initial orientation value to the current cell. , range .

[0105] After the nucleation traversal is completed, all cells are traversed again to update the martensitic state using transformation rule 2.

[0106] Transformation Rule 2: When the cell state is martensite nucleation, a martensite growth state update is performed. The martensite grain growth direction is randomly selected, and then growth is carried out along the length direction until the grain state is non-austenite. The current martensite grain width is calculated based on the martensite aspect ratio, and growth is carried out along the width direction.

[0107] Step 6: Perform initial tissue cellularization and laser quenching cellular automata simulation.

[0108] First, the initial microstructure (ferrite and pearlite) is cellularized. Then, the nucleation, growth and coarsening process of austenite during laser surface quenching is simulated by deriving the finite element simulation temperature evolution curve of laser surface quenching. Finally, the microstructure evolution during the cooling stage is predicted.

[0109] Specifically, step 6 first involves cellularizing the initial tissue (ferrite and pearlite) using a certain number (e.g., 1600 × 400) of square cells to form a predetermined size (e.g., The size of a single cell is The cellular space of pearlite is defined as a Moore neighborhood. During the heating stage, based on the temperature evolution curve derived from the finite element method, the nucleation transformation rules established in step 5 are used to determine the nucleation of pearlite grain boundaries and intragranular cells and assign random orientation values. Subsequently, the growth and coarsening of austenite grains are simulated according to the growth and coarsening transformation rules (including grain boundary migration barrier rules, Moore neighborhood majority state rules, and surface energy reduction rules). During the cooling stage, when the temperature drops below the martensite transformation temperature (210℃), the nucleation transformation rules are used to determine the nucleation of pearlite grains and assign random orientation values. Subsequently, needle-like growth is carried out along random directions in length and width according to the martensite growth transformation rules. Finally, by statistically analyzing the number and distribution of cells of each grain in the simulation results, the microstructure evolution law and the relationship between grain size and depth at different depths are obtained.

[0110] This section explains how step 6 specifically uses the temperature field obtained from the finite element simulation in step 4: Step 6 derives the temperature-time evolution curve at a specific depth location from the finite element simulation in step 4, using it as the time-dependent input condition for the cellular automata simulation. At each time step of the cellular automata simulation, the temperature value of the current cell is obtained based on the derived temperature evolution curve, and then parameters such as superheat and temperature gradient of the current cell are calculated. These parameters directly drive the austenite nucleation model (calculating the nucleation rate through superheat), the austenite growth and coarsening model (calculating grain boundary mobility through temperature), and the martensite nucleation and growth model (determining whether the temperature is below the martensite transformation temperature) established in step 5. This allows the finite element macroscopic temperature field information to be mapped into the mesoscopic tissue evolution simulation of cellular automata.

[0111] Step 7: Perform hardness prediction based on phase composition and grain size.

[0112] Based on phase composition and the hardness of each phase, the hardness value of the current phase structure distribution is calculated using the mixing rule for hardness calculation. : (27); Parameter explanation: : Calculated hardness value of the current phase structure distribution; Martensite volume fraction; Martensitic hardness; Ferrite volume fraction; Ferrite hardness; : Hardness contribution value of dissolved carbides; Hardness of undissolved carbides during laser surface hardening.

[0113] Martensitic hardness Calculated using the following formula: (28); Parameter explanation: Martensitic hardness; Carbon content (%) in the martensitic phase.

[0114] The hardness of dissolved carbides is determined by the following formula: (29); Parameter explanation: : Hardness contribution value of dissolved carbides; Carbon content in the phase (%).

[0115] The Hall-Petch formula describes the relationship between hardness and grain size; the hardness of martensitic material is proportional to the reciprocal of the square root of the grain diameter. (30); Parameter explanation: : The contribution of grain size to hardness; Hardness value is a constant term independent of grain size; : Preset coefficient (Hall-Petch enhancement coefficient); Grain size.

[0116] Considering the influence of grain size, the calculated hardness value is corrected by combining simulation results with the Hall-Petch formula to obtain the final predicted hardness value.

[0117] Here, we will explain how to use the volume fractions of each phase obtained from the finite element simulation in step 4 in step 7: In step 7, the volume fractions of each phase obtained from the finite element simulation in step 4 are directly substituted into the hardness calculation mixing rule formula (the above formula (27)), where the martensite volume fraction is... and ferrite volume fraction The hardness of each phase (martensite hardness is calculated empirically using carbon content, and dissolved carbide hardness is calculated using the logarithmic relationship of carbon content) is taken directly from the simulation results in step 4 as known parameters. The hardness calculation value based on the phase structure distribution is then calculated and used as the benchmark value for subsequent Hall-Petch formula correction.

[0118] This section explains the specific implementation method of correcting the calculated hardness value by combining simulation results and the Hall-Petch formula in step 7, and explains the contribution of grain size to hardness refinement and strengthening. ) superimposed on the hardness calculation value based on phase composition ( This process corrects the calculated hardness value, resulting in a final predicted hardness value that considers both phase composition and grain size. ,in These are the weighting coefficients.

[0119] Example 2.

[0120] This embodiment takes 7CrSiMnMoV steel as the object and implements it according to the aforementioned steps 1 to 7. The specific parameter values ​​and numerical simulation results for 7CrSiMnMoV steel in each step are given.

[0121] Step 1 of this embodiment: Determining the parameters of the phase transition dynamics model.

[0122] In the austenitic phase transformation kinetic model in step 1.1, the gas constant R is taken as... By fitting relevant data values ​​at different heating rates, the slope of the fitted curve is obtained as the ratio of the austenite phase transformation activation energy to the gas constant R. Therefore, the austenite phase transformation activation energy of 7CrSiMnMoV steel is... .

[0123] Because the heating rate varies widely, averaging the kinetic parameters reduces the predictive power of the kinetic model. Therefore, fitting the kinetic parameter values ​​to the heating rate yields the kinetic parameters for austenite phase transformation. and The variation with heating rate is as follows: (31); Parameter explanation: Avrami index of austenitic phase transformation; Heating rate.

[0124] (32); Parameter explanation: Avrami index of austenitic phase transformation; A coefficient determined by the material and the type of phase transition; The parameter combination corresponding to the intercept obtained from curve fitting; Heating rate.

[0125] In the martensitic phase transformation kinetic model in step 1.2, the constant in formula (7) Take 0.02.

[0126] In the kinetic model of the martensitic tempering process in step 1.3, the hardness of 7CrSiMnMoV steel at different temperatures as a function of tempering time was obtained using JmatPro. The hardness of 30 HRC after tempering at 550℃ for 36000 s was taken as the fully tempered hardness of 7CrSiMnMoV steel. The activation energy of the tempering martensitic phase transformation was obtained through curve fitting. for Material-related constants It is 10.34; take the values ​​at four tempering temperatures. and The average values ​​of 0.40 and -7.93 were used to calculate the volume fraction of tempered martensite phase transformation.

[0127] Step 3 of this embodiment: Finite element geometric model and boundary condition parameters.

[0128] In step 3.1, the sample size is set to... The mesh is further refined to a depth of 2.5 mm below the surface, resulting in a unit size of [missing value]. Below the refinement region, the mesh size increases with increasing depth and distance from the plane of symmetry.

[0129] In step 3.3, the heat transfer boundary conditions, the emissivity coefficient of the sample in formula (18) Take 0.35. In step 3.2, the specific heat capacity and thermal conductivity of 7CrSiMnMoV cold work die steel as a function of temperature are obtained by laser thermal conductivity meter, and then input into the material properties of the finite element model to improve accuracy.

[0130] Step 4 of this embodiment: Finite element simulation results.

[0131] The finite element simulation results for laser quenching temperature field calculation using ABAQUS at a laser power of 2000W and a scanning speed of 4mm / s are as follows: Figure 3 As shown, the highest temperature is obtained at the center of the light spot, and the temperature gradually decreases as the distance from the center of the light spot increases. The volume fraction of each phase is calculated by custom field variables in the USDFLD subroutine, with the initial pearlite volume fraction being 1. The phase transformation-induced volume fraction change and the volume fraction increment caused by the density difference of each phase are calculated in each increment step by the UEXPAN subroutine, and the stress and strain are calculated by the constitutive model provided by ABAQUS.

[0132] Figure 3This is a comparison diagram of the cross-sectional morphology of the hardened layer and the simulated temperature field in an embodiment of this application. For example... Figure 3 As shown, the image uses a left-right stitching comparison method: the left half is a metallographic morphology photograph of the actual cross-section of the sample's hardened layer, showing a lighter-colored hardened area on the surface and a darker-colored matrix area below. The lower left corner of the photograph is marked with a length scale bar "1mm". The right half is a finite element simulation temperature field cloud map of the corresponding location, using a color gradient from red, orange, yellow, green, blue to gray to represent the temperature distribution that gradually decreases from the surface to the interior. The right side of the cloud map is accompanied by a temperature legend (labeled with temperature (TEMP), Avg: 75%), with the legend values ​​from top to bottom being approximately 1341.5, 1277.1, 1212.7, 1148.4, 1084.0, 1019.6, 955.2, 890.8, 826.4, 762.0, and 27.8 (unit: °C). Both the left and right sections are marked with a red arc-shaped dashed line to indicate the boundary outline of the hardened layer (high temperature affected zone), which is used to compare the actual cross-sectional hardened layer morphology with the high temperature area predicted by the simulated temperature site. The outlines of the two are consistent with each other.

[0133] This is for Figure 3 The meaning of Avg is explained below. Avg represents the average threshold in the Abaqus post-processed contour plot. When displaying a contour plot in Abaqus, a node is typically shared by multiple cells. Each neighboring cell may extrapolate a temperature value near that node. To make the contour plot display smoother, Abaqus averages the node values ​​given by these neighboring cells. When the difference between the extrapolated results from neighboring cells at the same node does not exceed a set threshold, Abaqus will average them for display; if the difference is too large, averaging is not performed to preserve abrupt changes. Figure 3 The value of Avg is 75%.

[0134] Step 5 of this embodiment: Cellular automata model parameters.

[0135] In step 5.1, the austenite grain nucleation model, the parameters of formula (20) Pick Activation energy of austenitic nucleation Pick The correlation coefficient of pearlite structure in formula (22) Take 2.5.

[0136] In step 5.2, the austenite growth and roughening model, the correlation coefficient between formula (23) and material properties is... Take 38791.3, austenite migration activation energy Take 159 kJ / mol.

[0137] In step 5.3, the martensitic nucleation growth model, the constant of formula (25) Take 0.02; when the temperature drops below the martensitic transformation temperature of 210℃, martensitic nucleation and growth occur.

[0138] Step 6 of this embodiment: Initial tissue cellularization parameters.

[0139] First, the initial structure was cellularized, with each cell measuring 0.5 μm and using Moore neighborhood. To obtain the evolution of grain size with depth, a 1600 × 400 square cell space was used, with an actual size of [missing information]. Subsequently, by deriving the finite element simulation temperature evolution curve of laser surface quenching, the nucleation, growth and coarsening process of austenite during laser surface quenching was simulated, and the microstructure evolution during the cooling stage was predicted.

[0140] Step 7 of this embodiment: Hardness prediction parameters.

[0141] In step 7, the hardness prediction based on phase composition and grain size, the strengthening coefficient of formula (30) We set the value to 113.2. Considering the influence of grain size, we combined the simulation results with the Hall-Petch formula to correct the hardness calculation value based on phase composition, thus obtaining the final predicted hardness value.

[0142] In summary, the beneficial effects of this application are as follows.

[0143] (1) This application proposes a multi-scale prediction method based on the microstructure and properties of laser-quenched hardened layers, which breaks the limitations of traditional single macroscopic temperature field simulation. It can realize the coupling from macroscopic thermo-mechanical field to mesoscopic grain evolution, and can realize the simulation of phase transformation volume fraction, microstructure and spatiotemporal evolution of temperature field during laser quenching.

[0144] (2) The finite element-cellular automata coupled model constructed in this application can intuitively output the microstructure evolution behavior and law of austenite and martensite grains at different depths during laser quenching, obtain the relationship between grain size and depth, and have a more intuitive understanding of the microstructure evolution law under rapid laser heating and cooling.

[0145] (3) The model constructed in this application integrates the phase transformation induced plasticity effect and multiphase thermal strain, which can accurately predict the distribution transformation law of residual compressive / tensile stress in the direction of depth from the hardened layer to the matrix. It also considers the influence of grain size and can accurately predict the hardness of the hardened layer, providing a reliable theoretical basis for optimizing laser quenching process parameters.

[0146] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0147] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers, characterized in that, include: A phase transformation kinetic model considering the effect of heating rate and a mechanical response mathematical model are constructed. The phase transformation kinetic model is used to obtain the volume fractions of austenite, martensite, and tempered martensite. The mechanical response mathematical model is used to obtain the total strain increment, including elastic strain increment, plastic strain increment, volumetric strain increment, and phase transformation-induced plastic strain increment. The volumetric strain increment is dominated by the density difference caused by phase type and temperature change, and is modeled using a linear mixing rule. Based on the phase transformation dynamics model, the mechanical response mathematical model, and the finite element geometric model of the sample, a finite element simulation of the laser quenching process was performed to obtain the temperature field, the volume fraction of each phase, and the residual stress. Based on the austenite nucleation and growth coarsening mechanism and the martensite nucleation and growth mechanism, a cellular automata simulation model for the laser quenching process is obtained through cellular automata transformation rules. Based on the temperature field, the initial microstructure is cellularized, and a cellular automata simulation model is used to obtain the microstructure evolution and grain size during the laser quenching process. Based on the volume fraction of each phase and the grain size, the hardness prediction value of the laser-quenched hardened layer is obtained by using the hardness calculation mixing rule and combining the relationship between hardness and grain size. The phase transition dynamics model is specifically used for: The volume fraction of austenite during the heating process was obtained based on the JMAK diffusion phase transformation model. Based on the Koistinen-Marburger equation, the volume fraction of martensite during the cooling process was obtained; Based on the JMAK diffusion phase transformation model, the volume fraction of tempered martensite during the tempering process was obtained. Among them, for the non-isothermal process with a non-fixed heating rate during laser quenching, the non-isothermal transformation process is described as an isothermal process with multiple incremental steps, and the phase transformation volume fraction of each phase under the non-isothermal process is obtained. The volume fraction of austenite is calculated using the following formula: ； in, Indicates the volume fraction of austenite; This represents the temperature-dependent austenitizing kinetic coefficient; Indicates isothermal time; Indicates the Avrami index used for austenite; The finite element simulation of the laser quenching process includes: Based on the finite element geometric model, the temperature field of laser quenching is simulated and calculated to obtain the temperature field of the specimen throughout the laser quenching process. At each incremental step, the phase transformation kinetic model is invoked, and the volume fraction of each phase is used as the field variable to calculate the volume fraction of austenite, martensite, and tempered martensite. Based on the mathematical model of volume fraction and mechanical response of each phase, the volume fraction increment caused by phase transformation-induced volume fraction change and density difference of each phase is calculated in each increment step, and stress-strain calculation is performed to obtain residual stress. The finite element simulation uses a flat-top Gaussian heat source, and the expression for the heat flux of the light spot of the flat-top Gaussian heat source is as follows: ； Indicates laser heat flux; This indicates the material's absorption rate of laser light; Indicates laser power; Indicates the area of ​​the laser spot; This represents the coordinate values ​​with the center of the light spot as the origin; Indicates the width of the laser spot; The hardness calculation hybrid rule is determined by the following formula: ； in, The calculated hardness value represents the current phase structure distribution; Indicates the volume fraction of martensite; Indicates the hardness of martensite; Indicates the volume fraction of ferrite; Indicates the hardness of ferrite; This indicates the hardness contribution value of dissolved carbides; This indicates the hardness of undissolved carbides during laser surface hardening; The relationship between hardness and grain size is determined by the following formula: ； in, This indicates the contribution of grain size to hardness. This represents a constant hardness value that is independent of grain size. Indicates the preset coefficient; Indicates grain size.

2. The multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers according to claim 1, characterized in that, The martensite volume fraction is calculated using the following formula: ； in, Indicates the volume fraction of martensite; Indicates the volume fraction of austenite; Represents a constant; This indicates the temperature at which martensite begins to transform; This indicates the temperature at the current time step.

3. The multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers according to claim 1, characterized in that, The volume fraction of tempered martensite is calculated using the following formula: ； in, This indicates the volume fraction of tempered martensite. This represents the temperature-dependent kinetic coefficient of tempered martensite; Indicates isothermal time; This represents the Avrami index used for tempered martensite.

4. The multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers according to claim 1, characterized in that, In incremental steps The volume fraction of the time-transformation phase is calculated using the following formula: ； Equivalent time: ; Indicates incremental step Time Phase volume fraction; Indicates the first related to temperature Phase transition kinetic coefficients; Indicates equivalent time; Indicates the first The Avrami index of the phase; Indicates the number of increment steps before the current increment. Phase transition volume fraction.

5. The multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers according to claim 1, characterized in that, The mathematical model of mechanical response is determined by the following formula: ； in, Indicates the total strain increment; Indicates the increment of elastic strain; Indicates the increment of plastic strain; Indicates the volumetric strain increment; This represents the increment of plastic strain induced by phase transformation.

6. The multi-scale prediction method for the microstructure and properties of laser-quenched hardened layers according to claim 1, characterized in that, Cellular automata simulation models are used for: Based on the degree of overheating, the austenite nucleation density is obtained through the austenite grain nucleation model, and the nucleation is determined according to the austenite nucleation transformation rules. Based on the cell mobility at grain boundaries, a transformation rule is used to control the grain growth direction and obtain the austenite growth and coarsening results. Based on the martensite volume fraction, a martensite nucleation and growth model is used to obtain the martensite nucleation rate, and nucleation and growth are carried out according to the martensite transformation rules. The austenite nucleation rate, extended to non-isothermal processes, is obtained using the following formula: ； This represents the austenite nucleation rate extended to non-isothermal processes; Parameters indicating the effect of pearlite on the nucleation rate of austenite; Indicates the correlation coefficient of pearlite structure; Represents the temperature gradient; Indicates the activation energy of austenite nucleation; Represents the Boltzmann constant; Indicates overheating.

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