Method for forecasting surface topography and dynamic behaviors of material under action of laser

Abstract

The invention discloses a method for forecasting surface topography and dynamic behaviors of a material under the action of laser, which belongs to the technical field of laser surface processing and comprises the following steps of: determining target material parameters, laser light source parameters and geometric dimensions of the target material; determining the energy deposited on the target material by adopting a Beer-Lambert law; according to the double-temperature model, the thermodynamic state of the free electrons is updated through a generalized finite difference method; adopting a thermoelastic mechanical control equation to simulate the ablation and evaporation phase change process of the material; a fluid dynamic equation and a nucleation dynamic equation are adopted to simulate the flowing and cooling solidification process of a molten pool, and forecasting of the surface morphology and dynamic behaviors of the material under the action of laser is achieved. According to the method, the simulation model of the material surface ablation removal process under the laser effect is constructed, and theoretical support and a calculation tool are provided for accurately predicting the material surface morphology and dynamic behaviors.

Description

Technical Field

[0001] The invention relates to the technical field of laser surface processing, and in particular to a method for predicting the surface morphology and dynamic behavior of a material under the action of laser. Background Art

[0002] The discovery of laser-induced periodic surface structures can be traced back to when the first laser light source was developed. To date, this periodic structure induction method 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 light sources with different parameters can leave unique surface nanostructures on the surface of the material, and these surface nanostructures can control many basic surface properties. With the rapid development of laser technology, non-contact large-area surface processing has become feasible and controllable, which has made new industrial applications in fields such as medicine, optics, and biology possible.

[0003] In the past two decades, research in the field of laser-induced periodic surface structures has been very successful and in-depth, which is reflected not only in the processing accuracy of surface microstructures, but also in the processing yield. For some micron-level structures, the current process can even be easily achieved through a single-step process. However, from a theoretical point of view, there is still a lot of controversy as to whether this surface removal behavior is caused by material reorganization or electromagnetic effects, and the current simulation model cannot accurately predict the surface morphology and dynamic behavior. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the surface morphology and dynamic behavior of materials under the action of laser. Based on the dual temperature equation and the thermoelastic dynamic equation, combined with the ablation evaporation phase change model and the fluid dynamics equation, the generalized finite difference method and the level set method are used to construct a simulation model of the ablation removal process of the material surface under the action of laser, providing theoretical support and calculation tools for accurately predicting the surface morphology and dynamic behavior of materials.

[0005] To achieve the above object, the present invention provides a method for predicting the surface morphology and dynamic behavior of a material under the action of a laser, the steps comprising:

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

[0007] S2. According to 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 deposited by the laser on the target material;

[0008] S3, based on the energy obtained by laser deposition onto the target material, simulating electron-lattice heating according to a dual-temperature model, and updating the thermodynamic state of free electrons in the target material using a generalized finite difference method;

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

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

[0011] S6. According to the fluid dynamics evolution of the molten pool, the level set method is used to capture the interface of multiphase components to predict the surface morphology and dynamic behavior of the material under the action of laser.

[0012] Preferably, the thermodynamic parameters of the material in step S1 include density ρ, heat capacity c p , thermal conductivity k, electronic heat capacity c e , lattice heat capacity c l 、Linear expansion coefficient α L , electronic thermal conductivity k e , lattice thermal conductivity k l , melting point T melt , gasification temperature T vapor , latent heat of fusion L melt and latent heat of evaporation L vapor ; The mechanical parameters of the material include the Lame constant λ and G, the temperature-dependent surface tension σ sf , melt strength P s and melt viscosity μ; the material optical parameters include the material's complex dielectric constant ε, complex refractive index Reflection coefficient And 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 the laser energy in step S1 include the laser fluence F0, the laser pulse width τ p and the laser beam waist radius r0.

[0014] Preferably, in step S2, the Beer-Lambert law is used to determine the energy of laser deposition on the target material, which is expressed as:

[0015]

[0016] Where S(r,z,t) is the laser source term, which represents the space-time 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 energy of the laser deposition on the target material, according to the dual-temperature model, the electron-lattice two-step coupled thermodynamic process is considered to simulate the electron-lattice heating, and the dual-temperature model expression is:

[0018]

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

[0020] Preferably, the generalized finite difference method is used to update the thermodynamic state of the free electrons of the target material 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, respectively, and f n+1 represents the function value at time n+1, f n represents the function value at time n, f erepresents the electron temperature at the current position, t represents the time, and Δt represents the time increment step.

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

[0026]

[0027] Where the first equation is the equation of motion expressed in terms of stress, σ is the stress tensor, X is the volume force, represents the second derivative of the lattice displacement u with respect to time; the second equation is the thermoelastic constitutive equation represented by the 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, L m and L v are the latent heat of melting and evaporation, δ m and δ v are the conditions for melting and evaporation, respectively, L is the linear expansion coefficient.

[0028] Preferably, the fluid dynamics equation is:

[0029]

[0030] Where U is the velocity of the fluid, p is the pressure of the fluid, and μ is the viscosity of the fluid.

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

[0032]

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

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

[0035]

[0036] Where φ is the level set function.

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

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

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

[0040] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a solution flow chart of an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the discrete calculation domain of an embodiment of the present invention;

[0043] Figure 3 Schematic diagram of laser energy deposition according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] Example

[0046] The present invention provides a method for predicting the surface morphology and dynamic behavior of materials under the action of laser. Figure 1 As shown, it is a schematic diagram of the method solution, and the method steps include: the steps include:

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

[0048] Specifically, the thermodynamic parameters of the material include density ρ, heat capacity c p , thermal conductivity k, electronic heat capacity c e , lattice heat capacity c l 、Linear expansion coefficient α L , electronic thermal conductivity k e , lattice thermal conductivity k l , melting point T melt , gasification temperature T vapor , latent heat of fusion L melt and latent heat of evaporation L vapor The mechanical parameters of the material include the Lame constant λ and G, the temperature-dependent surface tension σ sf , melt strength P s and melt viscosity μ. The optical parameters of the material include the complex dielectric constant ε, complex refractive index Reflection coefficient And 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 flux F0, the laser pulse width τ p and the laser beam waist radius r0. The geometric dimensions include the thickness h and length l of the target.

[0049] S2. According to 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. The schematic diagram of laser energy deposition is shown in Figure 3 shown.

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

[0051]

[0052] Where S(r,z,t) is the laser source term, which represents the space-time 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 of laser deposition onto the target material, the electron-lattice heating is simulated according to the dual-temperature model, and the thermodynamic state of the free electrons of the target material is updated using the generalized finite difference method.

[0054] Specifically, according to the dual-temperature model, the electron-lattice two-step coupled thermodynamic process is considered to simulate the electron-lattice heating. The dual-temperature model expression is:

[0055]

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

[0057] The generalized finite difference method is a meshless method. In this method, discrete nodes are arranged in the entire computational domain. The computational domain is discrete as follows: Figure 2 As shown, assuming that U0 is the function value at the center point x0, U i is a point x near x0 i , 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 adjacent nodes:

[0058]

[0059] Where D U It is composed of various derivatives of U0, that is, U=[U1,U2,…,U m ] T ,U0=[U0,U0,…,U0] T , W is composed of the distance weight function of each point, P is formed by U0 at x i The Taylor expansion coefficients of various orders at the point are composed of

[0060]

[0061] The spatial derivatives of U0 of various orders can be obtained through the above matrix, and then the Runge-Kutta method is combined for time advancement to complete the numerical solution of the differential equation, 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, and f n+1 represents the function value at time n+1, f n represents the function value at time n, f e represents the electron temperature at the current position, t represents the time, and Δt represents the time increment step.

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

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

[0068]

[0069] Where the first equation is the equation of motion expressed in terms of stress, σ is the stress tensor, X is the volume force, represents the second derivative of the lattice displacement u with respect to time; the second equation is the thermoelastic constitutive equation represented by the 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, L m and L v are the latent heat of melting and evaporation, δ m and δ v are the conditions for melting and evaporation, respectively, L is the linear expansion coefficient.

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

[0071] Specifically, the fluid dynamics equation is:

[0072]

[0073] Where U is the velocity of the fluid, p is the pressure of the fluid, and μ is the viscosity of the fluid.

[0074] The nuclear dynamics model describes the process of the formation of surface micro-nanostructures during the cooling and solidification of the molten pool, in which the growth rate of the interface can be expressed as:

[0075]

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

[0077] S6. According to the fluid dynamics evolution of the molten pool, the level set method is used to capture the interface of multiphase components to predict the surface morphology and dynamic behavior of the material under the action of laser.

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

[0079]

[0080] Where 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 the action of laser. By analyzing the ablation, melting and nucleation process of the material surface under given laser parameters and material thermodynamic and optical parameters, an analysis method is provided for precisely controlling the laser surface processing technology, which helps to promote the application of laser surface processing in the field of fine structure production and manufacturing.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the surface morphology and dynamic behavior of a material under the action of a laser, characterized in that the steps include: S1. Determine the target material parameters, laser light source parameters and geometric dimensions of the target material. The target material parameters include the thermodynamic parameters, mechanical parameters and optical parameters of the material. The laser light source parameters include the spatiotemporal distribution characteristics of the laser energy. S2. According to 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 deposited by the laser on the target material; S3, based on the energy obtained by laser deposition onto the target material, simulating electron-lattice heating according to a dual-temperature model, and updating the thermodynamic state of free electrons in the target material using a generalized finite difference method; S4. According to the thermodynamic state of the target material, the thermoelastic control equation is used to simulate the ablation and evaporation phase change process of the target material; S5. Based on the governing equations of fluid dynamics and nucleation dynamics, the generalized finite difference method is used to solve the dynamics and surface morphology evolution of the molten pool; S6. According to the fluid dynamics evolution of the molten pool, the level set method is used to capture the interface of multiphase components to predict the surface morphology and dynamic behavior of the material under the action of laser.

2. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 1, characterized in that: The thermodynamic parameters of the material in step S1 include density ρ, heat capacity c p , thermal conductivity k, electronic heat capacity c e , lattice heat capacity c l 、Linear expansion coefficient α L , electronic thermal conductivity k e , lattice thermal conductivity k l , melting point T melt , gasification temperature T vapor , latent heat of fusion L melt and latent heat of evaporation L vapor ; The mechanical parameters of the material include the Lame constant λ and G, the temperature-dependent surface tension σ sf , melt strength P s and melt viscosity μ; the material optical parameters include the material's complex dielectric constant ε, complex refractive index Reflection coefficient And the absorption coefficient α = 2kω / c, where ω is the angular frequency of the incident light source and c is the speed of sound.

3. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 2, characterized in that: The spatiotemporal distribution characteristics of the laser energy in step S1 include the laser flux F0, the laser pulse width τ p and the laser beam waist radius r0.

4. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 3, characterized in that: In step S2, the Beer-Lambert law is used to determine the energy of laser deposition on the target material, which is expressed as: Where S(r,z,t) is the laser source term, which represents the space-time 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.

5. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 4, characterized in that: In step S3, based on the energy of the laser deposition on the target material, according to the dual-temperature model, the electron-lattice two-step coupled thermodynamic process is considered to simulate the electron-lattice heating. The dual-temperature model expression is: In the formula, the subscripts e and l represent electrons and lattices respectively, c is the specific heat capacity, and G e-ph is the electron-phonon coupling coefficient, c e =γT e is the electron heat capacity, k B is the Boltzmann constant, n e is the free electron number concentration, T F is the Fermi temperature, the electronic thermal conductivity A e and B e are material-specific constants that describe the electron-electron and electron-phonon collision rates, respectively, G e-ph represents the electron-phonon coupling coefficient, Speed ​​of sound m e is the effective electron mass, τ e is the free electron relaxation time, Average electron speed Z is the charge state of the ion, is the plasma frequency, lnΛ is the Coulomb logarithm, expressed as The maximum collision coefficient Minimum collision coefficient The specific heat capacity and thermal conductivity of the lattice are considered as constants, and S represents the energy source term of the laser action.

6. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 5, characterized in that: The thermodynamic state of the free electrons of the target material updated by the generalized finite difference method is expressed as: k3=f e (T e -k1Δt+2k2Δt,T l ,t+Δt); In the formula, k1, k2, and k3 represent the three sub-templates in the Runge-Kutta algorithm, respectively, and f n+1 represents the function value at time n+1, f n represents the function value at time n, f e represents the electron temperature at the current position, t represents the time, and Δt represents the time increment step.

7. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 6, characterized in that: In step S4, the heat conduction equation with internal heat source and thermoelastic mechanics are used to describe the temperature and thermal deformation process of the material, and the expression is: Where the first equation is the equation of motion expressed in terms of stress, σ is the stress tensor, X is the volume force, represents the second derivative of the lattice displacement u with respect to time; the second equation is the thermoelastic constitutive equation represented by the 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, L m and L v are the latent heat of melting and evaporation, δ m and δ v are the conditions for melting and evaporation, respectively, L is the linear expansion coefficient.

8. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 1, characterized in that: In step S5, the fluid dynamics equation is: Where U is the velocity of the fluid, p is the pressure of the fluid, and μ is the viscosity of the fluid.

9. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 1, characterized in that: In step S5, the nucleation kinetic model is expressed as: In the formula, v s represents the nucleation rate, V0 represents the maximum interface velocity, R g is the metal leaching constant, T m Indicates the melting point temperature, T l,I represents the fluid-solid interface temperature.

10. The method for predicting the surface morphology and dynamic behavior of a material under the action of laser according to claim 1, characterized in that: In step S6, the level set method is expressed as: Where φ is the level set function.

Images