A method for predicting the surface morphology and dynamic behavior of materials under laser irradiation

Abstract

This invention discloses a method for predicting the surface morphology and dynamic behavior of materials under laser irradiation, belonging to the field of laser surface processing technology. The method includes: determining the parameters of the target material, the laser source parameters, and the geometric dimensions of the target material; determining the energy deposited onto the target material using Beer-Lambert's law; updating the thermodynamic state of free electrons using the generalized finite difference method based on a dual-temperature model; simulating the ablation and evaporation phase transition processes of the material using thermoelasticity governing equations; and simulating the flow and cooling solidification processes of the molten pool using fluid dynamics and nucleation kinetics equations, thereby achieving the prediction of the surface morphology and dynamic behavior of materials under laser irradiation. This invention uses the above method to construct a simulation model of the ablation and removal process of material surfaces under laser irradiation, providing theoretical support and computational tools for accurately predicting the surface morphology and dynamic behavior of materials.

Description

Technical Field

[0001] This invention relates to the field of laser surface processing technology, and in particular to a method for predicting the surface morphology and dynamic behavior of materials under laser irradiation. Background Technology

[0002] The discovery of laser-induced periodic surface structures dates back to the development of the first laser source. To date, this method of inducing periodic structures can be achieved on almost all types of materials, such as metals, semiconductors, and other dielectric materials. Depending on the thermodynamic and optical properties of the material, laser sources with different parameters can leave unique surface nanostructures on the material surface, which can control many fundamental surface properties. With the rapid development of laser technology, non-contact, large-area surface processing has become feasible and controllable, enabling entirely new industrial applications in fields such as medicine, optics, and biology.

[0003] Over the past two decades, research in the field of laser-induced periodic surface structures has been highly successful and in-depth, not only in terms of the processing precision of surface microstructures but also in terms of processing yield. For some micrometer-scale structures, current processes can even easily achieve this in a single step. However, from a theoretical perspective, whether this surface removal behavior stems from material recombination or electromagnetic effects remains highly controversial, and current simulation models are unable to accurately predict surface morphology and dynamic behavior. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the surface morphology and dynamic behavior of materials under laser irradiation. Based on the dual temperature equation and thermoelastic dynamic equation, combined with the ablation-evaporation phase transition model and fluid dynamic equation, a simulation model of the ablation removal process of material surface under laser irradiation is constructed using the generalized finite difference method and the level set method. This provides theoretical support and computational tools for accurately predicting the surface morphology and dynamic behavior of materials.

[0005] To achieve the above objectives, this invention provides a method for predicting the surface morphology and dynamic behavior of materials under laser irradiation, comprising the following steps:

[0006] S1. Determine the target material parameters, laser source parameters, and geometric dimensions of the target material. The target material parameters include the thermodynamic, mechanical, and optical parameters of the material, and the laser source parameters include the spatiotemporal distribution characteristics of the laser energy.

[0007] S2. Based on the optical parameters of the target material and the spatiotemporal distribution characteristics of the laser energy, the Beer-Lambert law is used to determine the energy of the laser deposited on the target material.

[0008] S3. Based on the obtained laser energy deposited onto the target material, electron-lattice heating is simulated according to the dual-temperature model, and the thermodynamic state of free electrons in the target material is updated using the generalized finite difference method.

[0009] S4. Based on the thermodynamic state of the target material, the thermoelastic mechanical control equation is used to simulate the ablation and evaporation phase change process of the target material;

[0010] S5. Based on the fluid dynamics governing equations and nucleation dynamics, the generalized finite difference method is applied to solve the dynamics and surface morphology evolution of the molten pool.

[0011] S6. Based on the fluid dynamics evolution of the molten pool, the horizontal set method is used to capture the interface of multiphase components, thereby enabling the prediction of the surface morphology and dynamic behavior of materials under laser irradiation.

[0012] Preferably, the thermodynamic parameters of the material in step S1 include density ρ and heat capacity c. p Thermal conductivity k, electronic heat capacity c e , lattice heat capacity c l Coefficient of linear expansion α L Electronic thermal conductivity k e lattice thermal conductivity k l Melting point T melt vaporization temperature T vapor Latent heat of fusion L melt and latent heat of vaporization L vapor The mechanical parameters of the material include Lamé constants λ and G, and temperature-dependent surface tension σ. sf Melt strength P s And melt viscosity μ; material optical parameters include the material's complex permittivity ε and complex refractive index. Reflectance coefficient The absorption coefficient α = 2kω / c, where ω is the angular frequency of the incident light source and c is the speed of sound.

[0013] Preferably, the spatiotemporal distribution characteristics of laser energy in step S1 include the laser flux F0 and the laser pulse width τ. p And the laser beam waist radius r0.

[0014] Preferably, in step S2, the energy of laser deposition onto the target material is determined using Beer-Lambert's law, expressed as:

[0015]

[0016] In the formula, S(r,z,t) is the laser source term, representing the spatiotemporal coordinates of the material, corresponding to the horizontal direction, depth direction, and time, respectively; R is the laser reflection coefficient; and α is the laser absorption coefficient.

[0017] Preferably, in step S3, based on the obtained laser deposition energy onto the target material, and according to the dual-temperature model, the electron-lattice heating is simulated by considering the two-step coupled thermodynamic process of electron-lattice. The expression for the dual-temperature model is:

[0018]

[0019] In the formula, the subscripts e and l represent electrons and lattice respectively, c is the specific heat capacity, and G e-ph c is the electron-phonon coupling coefficient. e =γT e For electronic heat capacity, k B n is the Boltzmann constant. e T represents the free electron number concentration. F Fermi temperature, electronic thermal conductivity A e and B e G are specific material constants that describe the electron-electron and electron-phonon collision rates, respectively. e-ph Represents the electron-phonon coupling coefficient. Speed ​​of sound m e For effective electron mass, τ e For the free electron relaxation time, Average electron velocity Z represents the charge state of the ion. Let lnΛ be the plasma frequency, and lnΛ be the Coulomb logarithm, expressed as: The maximum collision coefficient Minimum collision coefficient The specific heat capacity and thermal conductivity of the crystal lattice are considered constants, and S represents the energy source term of the laser effect.

[0020] Preferably, the thermodynamic state of the target material's free electrons updated using the generalized finite difference method is expressed as follows:

[0021]

[0022] k3=f e (T e -k1Δt+2k2Δt,T l ,t+Δt);

[0023]

[0024] In the formula, k1, k2, and k3 represent the three self-templates in the Runge-Kutta algorithm, f n+1 f represents the function value at time n+1. n f represents the function value at time n. eThe value represents the electron temperature at the current position, t represents time, and Δt represents the time increment step.

[0025] Preferably, in step S4, the heat conduction equation containing an internal heat source and thermoelasticity are used to describe the temperature and thermal deformation process of the material, and the expression is:

[0026]

[0027] In the formula, the first equation is the equation of motion in terms of stress, σ is the stress tensor, and X is the body force. The first equation represents the second derivative of the lattice displacement *u* with respect to time; the second equation is the thermoelastic constitutive equation expressed in terms of displacement *u*; the third equation is the lattice heat conduction equation considering thermal deformation, thermal convection, and melting and evaporation phase transitions, where *U* is the velocity of the melt, and *L* is the velocity of the melt. m and L v Latent heat of fusion and latent heat of vaporization, δ m and δ v These are the conditions for melting and evaporation, respectively, α L is the coefficient of linear expansion.

[0028] Preferably, the fluid dynamics equations are:

[0029]

[0030] In the formula, U is the fluid velocity, p is the fluid pressure, and μ is the fluid viscosity.

[0031] Preferably, in step S5, the nucleation kinetic model is expressed as:

[0032]

[0033] In the formula, v s R represents the nucleation rate, V0 represents the maximum interface velocity, and R represents the nucleation rate. g T represents the metal leaching constant. m T represents the melting point temperature. l,I This indicates the temperature at the fluid-solid interface.

[0034] Preferably, in step S6, the level set method is expressed as:

[0035]

[0036] In the formula, φ is the level set function.

[0037] Therefore, the present invention employs the above-mentioned method for predicting the surface morphology and dynamic behavior of materials under laser irradiation, which has the following beneficial effects:

[0038] (1) By analyzing the ablation and melting nucleation process of the material surface under given laser parameters and material thermodynamic and optical parameters, an analytical method is provided for the precise control of laser surface processing technology, which helps to promote the application of laser surface processing in the field of fine structure manufacturing.

[0039] (2) By constructing a simulation model of the ablation and removal process of material surface under laser action, the surface morphology and dynamics of material under laser action can be accurately predicted, providing theoretical support and calculation tools for understanding the surface processing effect under different laser parameters and material parameters.

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the solution process in an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram illustrating the discretization of the computational domain in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of laser energy deposition according to an embodiment of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0045] Example

[0046] This invention provides a method for predicting the surface morphology and dynamic behavior of materials under laser irradiation, such as... Figure 1 The diagram shown illustrates the solution method. The method steps include:

[0047] S1. Determine the target material parameters, laser source parameters, and geometric dimensions of the target material. The target material parameters include the thermodynamic, mechanical, and optical parameters of the material, and the laser source parameters include the spatiotemporal distribution characteristics of the laser energy.

[0048] Specifically, the thermodynamic parameters of a material include density ρ and heat capacity c. p Thermal conductivity k, electronic heat capacity c e , lattice heat capacity c l Coefficient of linear expansion α L Electronic thermal conductivity k e lattice thermal conductivity k l Melting point T melt vaporization temperature T vapor Latent heat of fusion L melt and latent heat of vaporization L vapor The mechanical parameters of the material include Lamé constants λ and G, and temperature-dependent surface tension σ. sf Melt strength P s And melt viscosity μ. Material optical parameters include the material's complex permittivity ε and complex refractive index. Reflectance coefficient The absorption coefficient α = 2kω / c, where ω is the angular frequency of the incident light source and c is the speed of sound. The spatiotemporal distribution characteristics of laser energy include the laser fluence F0 and the laser pulse width τ. p And the laser beam waist radius r0. The geometric dimensions include the target's thickness h and length l.

[0049] S2. Based on the optical parameters of the target material and the spatiotemporal distribution characteristics of the laser energy, the Beer-Lambert law is used to determine the energy of laser deposition onto the target material. A schematic diagram of laser energy deposition is shown below. Figure 3 As shown.

[0050] Specifically, Beer-Lambert's law describes the absorption of laser energy by materials. According to Beer-Lambert, the source term of laser loading can be expressed as:

[0051]

[0052] In the formula, S(r,z,t) is the laser source term, representing the spatiotemporal coordinates of the material, corresponding to the horizontal direction, depth direction, and time, respectively; R is the laser reflection coefficient; and α is the laser absorption coefficient.

[0053] S3. Based on the energy obtained from laser deposition onto the target material, electron-lattice heating is simulated according to a dual-temperature model, and the thermodynamic state of free electrons in the target material is updated using the generalized finite difference method.

[0054] Specifically, based on the two-temperature model, considering the electron-lattice two-step coupled thermodynamic process to simulate electron-lattice heating, the expression of the two-temperature model is:

[0055]

[0056] In the formula, the subscripts e and l represent electrons and lattice respectively, c is the specific heat capacity, and G e-ph c is the electron-phonon coupling coefficient. e =γT e For electronic heat capacity, k B n is the Boltzmann constant. e T represents the free electron number concentration. F Fermi temperature, electronic thermal conductivity A e and B e G are specific material constants that describe the electron-electron and electron-phonon collision rates, respectively. e-ph Represents the electron-phonon coupling coefficient. Speed ​​of sound m e For effective electron mass, τ e For the free electron relaxation time, Average electron velocity Z represents the charge state of the ion. Let lnΛ be the plasma frequency, and lnΛ be the Coulomb logarithm, expressed as: The maximum collision coefficient Minimum collision coefficient The specific heat capacity and thermal conductivity of the crystal lattice are considered constants, and S represents the energy source term of the laser effect.

[0057] The generalized finite difference method is a meshless method. This method first arranges discrete nodes throughout the entire computational domain, which is discrete as follows: Figure 2 As shown, assume U0 is the function value at the center point x0, U i Points near x0 i If the function value is zero, then the derivative of the unknown function at the center point x0 can be approximated by a linear combination of the function values ​​of its m neighboring nodes:

[0058]

[0059] In the formula, D U It consists of the derivatives of U0, i.e. U = [U1, U2, ..., U m ] T U0 = [U0, U0, ..., U0] T , W is composed of distance weight functions for each point. P is generated by U0 in x i The composition of Taylor expansion coefficients at each order at the point, i.e.

[0060]

[0061] The spatial derivatives of U0 can be obtained from the above matrix. Then, by combining the Runge-Kutta method for time advancement, the numerical solution of the differential equation is completed, and the thermodynamic state of the free electrons of the target material is updated as follows:

[0062]

[0063] k3=f e (T e -k1Δt+2k2Δt,T l ,t+Δt);

[0064]

[0065] In the formula, k1, k2, and k3 represent the three sub-templates in the Runge-Kutta algorithm, respectively, f n+1 f represents the function value at time n+1. n f represents the function value at time n. e The value represents the electron temperature at the current position, t represents time, and Δt represents the time increment step.

[0066] S4. Based on the thermodynamic state of the target material, the thermoelastic mechanical control equation is used to simulate the ablation and evaporation phase change process of the target material.

[0067] Specifically, the heat conduction equation containing an internal heat source and thermoelasticity are used to describe the temperature and thermal deformation process of the material, and the expression is:

[0068]

[0069] In the formula, the first equation is the equation of motion in terms of stress, σ is the stress tensor, and X is the body force. The first equation represents the second derivative of the lattice displacement *u* with respect to time; the second equation is the thermoelastic constitutive equation expressed in terms of displacement *u*; the third equation is the lattice heat conduction equation considering thermal deformation, thermal convection, and melting and evaporation phase transitions, where *U* is the velocity of the melt, and *L* is the velocity of the melt. m and L v Latent heat of fusion and latent heat of vaporization, δ m and δ v These are the conditions for melting and evaporation, respectively, α L is the coefficient of linear expansion.

[0070] S5. Based on the fluid dynamics governing equations and nucleation dynamics, the generalized finite difference method is applied to solve the dynamics and surface morphology evolution of the molten pool.

[0071] Specifically, the fluid dynamics equations are:

[0072]

[0073] In the formula, U is the fluid velocity, p is the fluid pressure, and μ is the fluid viscosity.

[0074] The nuclear kinetic model describes the process of surface micro / nanostructures forming during the cooling and solidification of a molten pool, where the growth rate of the interface can be expressed as:

[0075]

[0076] In the formula, v s R represents the nucleation rate, V0 represents the maximum interface velocity, and R represents the nucleation rate. g T represents the metal leaching constant. m T represents the melting point temperature. l,I This indicates the temperature at the fluid-solid interface.

[0077] S6. Based on the fluid dynamics evolution of the molten pool, the horizontal set method is used to capture the interface of multiphase components, thereby enabling the prediction of the surface morphology and dynamic behavior of materials under laser irradiation.

[0078] Specifically, the level set method can be used to track the position of the interface, as shown below:

[0079]

[0080] In the formula, φ is the level set function.

[0081] Therefore, the present invention adopts the above-mentioned method for predicting the surface morphology and dynamic behavior of materials under laser irradiation. By analyzing the ablation, melting and nucleation process of the material surface under given laser parameters and material thermodynamic and optical parameters, it provides an analytical method for accurately controlling laser surface processing technology, which helps to promote the application of laser surface processing in the field of fine structure manufacturing.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the surface morphology and kinetic behavior of a material under laser action, characterized by the steps of The method comprises the following steps: S1, determining target material parameters, laser light source parameters and geometric dimensions of the target material, the target material parameters including thermodynamic parameters, mechanical parameters and optical parameters of the material, and the laser light source parameters including time and space distribution characteristics of laser energy; S2, determining the energy of laser deposition to the target material according to the optical parameters of the target material and the time and space distribution characteristics of the laser energy by using Beer-Lambert law; S3, simulating electron-lattice heating according to a two-temperature model based on the obtained energy of laser deposition to the target material, and updating the thermodynamic state of free electrons of the target material by using a generalized finite difference method; S4, simulating the ablation and evaporation phase change process of the target material according to the thermodynamic state of the target material by using a thermoelasticity control equation, specifically: using a heat conduction equation containing an internal heat source and thermoelasticity to describe the temperature and thermal deformation process of the material, and the expression is as follows: ； ； ； where the first equation is the motion equation expressed in stress, is the stress tensor, is the body force, denotes the displacement of the crystal lattice is the second order derivative with respect to time; the second equation is the displacement denotes the thermo-elastic constitutive equation; the third equation is the heat conduction equation of the crystal lattice considering thermal deformation, thermal convection, and melting and evaporation phase change, where is the velocity of the melt, and are the latent heat of melting and evaporation, respectively, and are the occurrence conditions of melting and evaporation, respectively, is the linear expansion coefficient; S5, solving the dynamics and surface morphology evolution process of the molten pool by using a generalized finite difference method according to a fluid dynamics control equation and nucleation kinetics, wherein the nucleation kinetics model is expressed as: ； wherein, Vnrepresents the nucleation velocity, Vmaxrepresents the maximum interface velocity, Kmrepresents the metal leaching constant, Tmrepresents the melting point temperature, Tifrepresents the fluid-solid interface temperature; S6, capturing the interface of multi-phase components by using a level set method according to the fluid dynamics evolution process of the molten pool, and realizing the prediction of the material surface morphology and dynamic behavior under the action of laser.

2. The method for predicting the surface morphology and dynamic behavior of a material under laser action according to claim 1, characterized in that: The thermodynamic parameters of the material in step S1 include density , heat capacity , thermal conductivity , electronic heat capacity , lattice heat capacity , linear expansion coefficient , electronic thermal conductivity , lattice thermal conductivity , melting point , vaporization temperature , latent heat of fusion , and latent heat of evaporation ; the mechanical parameters of the material include Lame constants and , temperature-dependent surface tension , melt strength , and melt viscosity ; the optical parameters of the material include the complex dielectric constant , complex refractive index , reflection coefficient , and absorption coefficient , where is the angular frequency of the incident light source, is the sound velocity.

3. The method of claim 2, wherein the method further comprises: determining the surface morphology of the material under the laser action based on the laser fluence and the laser intensity. The spatio-temporal distribution characteristics of the laser energy in step S1 include the fluence of the laser , the laser pulse width , and the laser beam waist radius .

4. The method of claim 3, wherein the method further comprises: The determination of the energy of laser deposition to the target material in step S2 by using Beer-Lambert law is expressed as: ； In the formula, is the laser source term, and represents the spatial and temporal coordinates of the material, corresponding to the horizontal direction, the depth direction and the time, respectively, is the laser reflection coefficient, is the laser absorption coefficient.

5. The method of claim 4, wherein the method further comprises: determining the surface morphology of the material under the laser action based on the laser fluence and the laser intensity. In step S3, the electron-lattice heating is simulated according to a two-temperature model based on the obtained energy of laser deposition to the target material, and the two-temperature model is expressed as: ； ； where the subscripts and denote the electron and lattice, respectively, is the specific heat capacity, is the electron-phonon coupling coefficient, is the electronic heat capacity, , is the Boltzmann constant, is the free electron number density, is the Fermi temperature, the electronic thermal conductivity , and are specific material constants that describe the electron-electron and electron-phonon collision rates, respectively, denotes the electron-phonon coupling coefficient, , the speed of sound , is the effective electron mass, is the free electron relaxation time, , the electron average velocity , is the ion charge state, is the plasma frequency, is the Coulomb logarithm, denoted as where the maximum collision coefficient , the minimum collision coefficient , the specific heat capacity and thermal conductivity of the lattice are considered constant, and S denotes the energy source term of the laser action.

6. The method of claim 5, wherein the method further comprises: The updating of the thermodynamic state of free electrons of the target material by using a generalized finite difference method is expressed as: ； ； ； ； wherein , , represent three sub-templates in the Runge-Kutta algorithm, represent the function value at the time point, represent the function value at the time point, represent the function value at the time point, represent the function value at the time point, represent the electron temperature at the current position, t represents the time, represent the time increment step.

7. The method of claim 1, wherein the method further comprises: determining a laser fluence of the laser beam; and determining a laser intensity of the laser beam. In step S5, the fluid dynamics equation is: ； ； wherein is the velocity of the fluid, is the pressure of the fluid, is the viscosity of the fluid.

8. The method of claim 1, wherein the method further comprises: determining a laser fluence of the laser beam; and determining a laser intensity of the laser beam. In step S6, the level set method is expressed as: ； In the formula, is a level set function.

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