Finite element modeling and analysis method for nanosecond pulse laser target material

Abstract

The invention belongs to the field of laser processing and numerical simulation, and particularly relates to a finite element modeling and analysis method for a nanosecond pulse laser target material. The method comprises the following steps: establishing and loading a laser heat source model; establishing a target material finite element model and carrying out grid division; establishing and solving a transient heat conduction equation; carrying out multi-cycle iterative solution and post-processing; and performing model verification and parameter analysis. According to the method, the laser heat source model is established, the adaptive grid encryption strategy for temperature gradient optimization is adopted, and the transient solution algorithm is combined, so that compared with a traditional simplified analysis model or general commercial software simulation, the prediction precision of the target material temperature field spatio-temporal evolution law under the nanosecond pulse laser effect is remarkably improved. The method can accurately predict the temperature distribution and evolution law of the target material under the action of laser, has the advantages of high modeling precision, good calculation efficiency, wide application range and the like, and is suitable for engineering applications such as laser processing and damage evaluation of optical materials and composite materials.

Description

Technical Field

[0001] This invention belongs to the field of laser processing and numerical simulation, and in particular relates to a finite element modeling and analysis method for nanosecond pulse laser target impact materials. Background Technology

[0002] Nanosecond pulsed lasers, due to their high peak power and short interaction time, are widely used in materials processing, surface treatment, and medical devices. Accurate prediction of the temperature field during laser-material interaction is crucial for controlling processing quality and avoiding thermal damage. Traditional analysis methods, mostly based on analytical solutions or simplified numerical models, struggle to accurately reflect the spatial distribution and temporal characteristics of the laser, as well as changes in the thermal properties of the material. This is especially true for non-homogeneous materials such as composites and optical materials, where existing methods fall short in terms of modeling accuracy and computational efficiency. Furthermore, existing research on simulating the thermal accumulation effect under repetitive frequency pulsed lasers lacks systematic analysis schemes and efficient solution strategies. Therefore, a high-precision, high-efficiency finite element modeling and analysis method is urgently needed to support temperature field prediction and optimization design under nanosecond pulsed laser irradiation, addressing issues such as coarse modeling, inaccurate temperature rise prediction, and limited applicability in existing technologies. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention provides a finite element modeling and analysis method for nanosecond pulse laser target impact materials, comprising the following steps: Step 1: Establishment and Loading of Laser Heat Source Model: Establish a laser heat source model, calculate the peak power density based on the single pulse energy, spot radius, pulse width and absorption coefficient of the laser, and simulate the heat flow input of the nanosecond pulse laser using a Gaussian or rectangular time distribution function. The laser pulse period is the time period during which laser energy is output, and the pulse interval is the time period during which no laser energy is output. The laser heat source model is loaded onto the target surface region corresponding to the finite element model in the form of boundary conditions. Step 2: Establishment and mesh generation of the finite element model of the target material: Construct a finite element model of the target material and refine the local spatial mesh in the laser spot action area and the depth direction of the target material; Step 3: Establishment and solution of transient heat conduction equation: During the laser pulse, a time step smaller than the pulse width is used to simulate rapid temperature rise, and during the pulse interval, a time step larger than the pulse duration is used to improve computational efficiency. By solving the transient heat conduction equation, the transient temperature field distribution is output. Step 4: Multi-cycle iterative solution and post-processing: Set the repetition frequency of the laser, perform multi-cycle iterative calculations, and use the temperature field at the end of the previous pulse cycle as the initial condition for the next cycle to simulate the thermal accumulation effect under repeated laser irradiation. Step 5: Model Validation and Parameter Analysis: Compare the simulation results with the benchmark data to verify the accuracy of the model and analyze the influence of laser process parameters on the temperature field evolution.

[0004] The principle of this invention lies in establishing a surface heat source model that accurately describes the spatiotemporal energy distribution of laser light. In the finite element model of the target material, a non-uniform mesh is refined in both the horizontal and depth directions of the laser-affected region. The transient heat conduction equation is solved using a combination of the finite element method and the finite difference method. Furthermore, the heat accumulation effect is simulated through multi-period iterative calculations, ultimately achieving high-precision and high-efficiency simulation of the temperature field under nanosecond pulsed laser light. Specifically, this method is implemented through five steps: establishing and loading the laser heat source model; establishing and meshing the finite element model of the target material; establishing and solving the transient heat conduction equation; multi-period iterative solution and post-processing; and model verification and parameter analysis.

[0005] The beneficial effects of this invention are as follows: By establishing a laser heat source model, employing an adaptive mesh refinement strategy optimized for temperature gradients, and combining it with a transient solution algorithm, this invention significantly improves the prediction accuracy of the spatiotemporal evolution of the target temperature field under nanosecond pulsed laser irradiation compared to traditional simplified analytical models or general commercial software simulations. Simultaneously, by optimizing the calculation process, computational efficiency is improved while maintaining accuracy, providing a practical tool for rapid optimization of laser process parameters and thermal damage assessment. This invention has significant application value in engineering applications such as laser processing and damage assessment of optical materials and composite materials, as well as related engineering fields. Attached Figure Description

[0006] The above and other features, advantages, and aspects of embodiments of the present invention will become clearer with reference to the accompanying drawings and the following detailed description. The drawings are intended to aid in understanding the invention and are not intended to limit the invention. Identical or similar reference numerals represent identical or similar elements, wherein: Figure 1 This is a flowchart of the finite element modeling and analysis method for nanosecond pulse laser target impact materials according to the present invention; Figure 2 This is a schematic diagram of the laser heat source model of the present invention; Figure 3 This is a time distribution diagram of the laser power density of the present invention; Figure 4 This is a schematic diagram of the finite element model of the target material and the mesh refinement of the present invention; Figure 5 This is a schematic diagram of the multi-period temperature field evolution of the present invention; Figure 6 This is a graph showing the distribution of the highest temperature of the present invention over a period of time. Figure 7 This is a comparison chart showing the effect of pulsed laser duty cycle on temperature rise in this invention. Detailed Implementation

[0007] To enable those skilled in the art to better understand the technical solutions and advantages of the present invention, the present application will be described in detail below with reference to the accompanying drawings, but this is not intended to limit the scope of protection of the present invention.

[0008] This invention uses the temperature field analysis of a silicon target blank under the action of a 1064nm nanosecond pulsed laser as an example for illustration, but the method described in this invention is also applicable to other optical materials, composite materials and cases with different laser parameters.

[0009] This invention provides a finite element modeling and analysis method for nanosecond pulsed laser target impact materials, such as... Figure 1 As shown, it includes the following steps: Step 1: Establishment and loading of the laser heat source model.

[0010] This step aims to accurately describe the temporal and spatial energy distribution of the pulsed laser. The laser heat source is simplified to a surface heat source acting on the target surface, such as... Figure 2 As shown, its heat flux density From the spatial distribution function and time distribution function Multiplying them together, we get the expression: (1) in, The distance to the center of the light spot. For time, The absorption coefficient of the target material to the laser; It is a single pulse energy; The laser spot radius; The laser pulse width; Let be the spatial distribution function; for a uniform light spot, it is 1; for a Gaussian light spot, it is expressed as . ; It is a time distribution function; In expression (1) The normalization coefficient is used to ensure that the energy of a single pulse is normalized. The light spot area and pulse duration are correctly allocated according to the selected spatial and temporal distribution functions; for rectangular pulses, the normalization coefficients in... The value is 1 within the pulse width and 0 otherwise; a more accurate model can use a Gaussian time distribution. ,in, The pulse center time, The relationship with pulse width is At this time, the normalized coefficients in The laser heat source model is applied as boundary conditions to the target surface region corresponding to the finite element model. Figure 3 The distribution of output pulsed laser power density over time is shown, indicating that the pulsed laser was correctly applied.

[0011] Step 2: Establishment of the finite element model of the target material and mesh generation.

[0012] This step is crucial for ensuring both computational accuracy and efficiency. For example... Figure 4 As shown, firstly, based on the actual size of the target material, preferably a silicon wafer with a diameter of 50mm and a thickness of 10mm, a three-dimensional geometric model is established in CAD software or a finite element preprocessing module; then, meshing is performed. To improve computational efficiency and ensure the accuracy of key areas, a partitioned meshing densification technique is adopted, including densification of the laser action area, densification of the depth direction, and densification of the outer area.

[0013] Laser-affected area refinement: In the horizontal direction within the laser spot's effective area, the element size gradually increases from the center of the spot outwards. Specifically, a circular region with a size 2-3 times the spot diameter is defined on the horizontal plane, preferably with the spot center as the origin. This region is then meshed. The element type can be an eight-node hexahedral thermal conductivity element DC3D8, and the mesh size in this region is controlled between 10-50 μm.

[0014] Depth-direction densification: In the depth direction of the target material, the unit size gradually increases from the top surface to the interior. Since the laser energy decays exponentially along the depth direction, the temperature gradient is extremely large. Therefore, non-uniform densification must be performed along the thickness direction. Preferably, at least 20 or more units can be set in the thickness direction, and the layer thickness gradually increases from the surface to the bottom to ensure that the maximum temperature gradient on the surface can be captured.

[0015] Enhancing the outer area: For areas far from the laser's effect area, a sparser grid is used to save computational resources. Preferably, the grid size can be set to 5-10 times that of the laser's effect area.

[0016] Step 3: Establishment and solution of the transient heat conduction equation.

[0017] The transient temperature field distribution during laser heating follows the transient heat conduction control equation, namely: (2) in, For density, For specific heat capacity, Thermal conductivity, For temperature, For time, As a heat source, in this embodiment The value is 0, and the heat source is applied as a boundary condition; The partial differential equation (2) above is discretized in space using the Galerkin weighted residual method to obtain the finite element equation for transient heat conduction: (3) in, This is the heat capacity matrix; This is the heat conduction matrix; The temperature load array is mainly contributed by surface heat flow; and These are the nodal temperature vectors and their derivatives with respect to time, respectively. The time domain is discretized using the finite difference method. This embodiment uses the backward difference method (implicit Euler method) in the direct integration method, and its expression is: (4) Among them, superscript and Indicates the first and Each time step For time step; Step 4: Multi-cycle iterative solution and post-processing.

[0018] Nanosecond pulsed lasers typically operate at a certain repetition frequency, preferably 100 Hz. Therefore, multi-cycle iterative calculations are required to simulate the cumulative effect of heat, including the following steps: Set calculation parameters: Total number of calculation cycles (e.g., 20 cycles), the time step of the pulse phase (laser pulse duration) within each laser pulse cycle. Time step of the non-pulse phase (pulse interval) To calculate the temperature rise and cooling process during the pulsed and non-pulsed phases; the time step during the laser pulse is set to be less than 1 / 10 of the pulse width, and the time step during the pulse interval is dynamically adjusted according to the temperature change rate, which can be increased to 1 / 10 of the non-pulsed interval.

[0019] Initial conditions: Set the initial temperature field for the entire model.

[0020] Iterative solution: At each time step, assemble the matrix. , and Solving the system of linear equations yields the temperature field at that moment. .

[0021] Periodic loop: The temperature field at the end of one pulse cycle is used as the initial condition for the next cycle, and so on until the set total number of cycles is reached.

[0022] Results extraction and post-processing: The program outputs the node temperature at each time step, and can generate temperature cloud maps, feature point temperature rise curves, and maximum temperature-cycle number curves.

[0023] Temperature cloud map, such as Figure 5 As shown in the figure, the temperature distribution within the target material at specific moments, namely the last moment of the pulse and the last moment of the non-pulse.

[0024] The feature point temperature rise curve records the temperature change of a point on the surface or inside the laser-acted center point throughout the entire time history.

[0025] Maximum temperature-cycle number curve, such as Figure 6 As shown, the highest temperature reached within each pulse cycle is recorded to observe the cumulative trend of temperature rise.

[0026] Step 5: Model Validation and Parameter Analysis.

[0027] Model Validation: Comparison with simulation results from commercial software. Identical geometric and physical models were established, and simulation calculations were performed in the commercial software Abaqus with identical laser parameters, material properties, initial and boundary conditions. The temperature field distributions obtained from both methods were compared. The results show that the temperature deviation between the method of this invention and the Abaqus calculation results is less than 3% over the entire time history, fully validating the accuracy and reliability of the method of this invention.

[0028] Parameter Analysis: Laser Duty Cycle Influence Analysis. Using a validated model, the impact of key laser process parameters (such as pulse duty cycle) on the processing effect is analyzed. Figure 7 As shown, the influence of the duration of the non-pulse phase on the target cooling effect was analyzed by adjusting the non-pulse phase time (i.e., changing the pulse duty cycle). Simulation results show that as the non-pulse time increases, the temperature drop of the target first increases rapidly, and then gradually levels off. Quantitative analysis shows that when the non-pulse time exceeds 1 ms, further extending the cooling time has less than a 2% effect on improving the maximum temperature drop. This calculation result provides a clear quantitative basis for optimizing pulsed laser parameters (such as frequency and pulse duty cycle) to achieve efficient thermal management and control. Specifically, to balance processing efficiency and thermal control, the non-pulse time can preferably be set to within 1 ms.

[0029] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made to the present invention should be included within the scope of protection of the present invention.

Claims

1. A finite element modeling and analysis method for nanosecond pulse laser target impact materials, characterized in that, Includes the following steps: Step 1: Establishment and Loading of Laser Heat Source Model: Establish a laser heat source model, calculate the peak power density based on the single pulse energy, spot radius, pulse width and absorption coefficient of the laser, and simulate the heat flow input of the nanosecond pulse laser using a Gaussian or rectangular time distribution function. The laser pulse period is the time period during which laser energy is output, and the pulse interval is the time period during which no laser energy is output. The laser heat source model is loaded onto the target surface region corresponding to the finite element model in the form of boundary conditions. Step 2: Establishment and mesh generation of the finite element model of the target material: Construct a finite element model of the target material and refine the local spatial mesh in the laser spot action area and the depth direction of the target material; Step 3: Establishment and solution of transient heat conduction equation: During the laser pulse, a time step smaller than the pulse width is used to simulate rapid temperature rise, and during the pulse interval, a time step larger than the pulse duration is used to improve computational efficiency. By solving the transient heat conduction equation, the transient temperature field distribution is output. Step 4: Multi-cycle iterative solution and post-processing: Set the repetition frequency of the laser, perform multi-cycle iterative calculations, and use the temperature field at the end of the previous pulse cycle as the initial condition for the next cycle to simulate the thermal accumulation effect under repeated laser irradiation. Step 5: Model Validation and Parameter Analysis: Compare the simulation results with the benchmark data to verify the accuracy of the model and analyze the influence of laser process parameters on the temperature field evolution.

2. The method according to claim 1, characterized in that: The formula used to establish the laser heat source model in step one is: ； in, For heat flux density, Indicates the distance to the center of the light spot. Indicates time, The absorption coefficient of the target material to the laser; It is a single pulse energy; The laser spot radius; The laser pulse width; Let be the spatial distribution function. For a uniform light spot, it is 1; for a Gaussian light spot, it is expressed as: ; For a rectangular pulse, the time distribution function is 1 during the pulse duration and 0 during the pulse interval. In the above formula The normalization coefficients are those used when the time distribution function is a rectangular pulse. When the time distribution function is a Gaussian impulse, the normalization coefficients in .

3. The method according to claim 1, characterized in that: The local spatial mesh refinement described in step two is performed in the horizontal direction of the laser spot's action area and in the depth direction of the target material.

4. The method according to claim 3, characterized in that: The local spatial mesh refinement described in step two adopts a non-uniform refinement strategy, specifically: in the horizontal direction of the laser spot's action area, the unit size gradually increases from the center of the spot to the periphery; in the depth direction of the target material, the unit size gradually increases from the upper surface to the interior.

5. The method according to claim 1, characterized in that: In step three, the transient temperature field distribution is obtained by solving the following transient heat conduction equation: ； in, For density, For specific heat capacity, Thermal conductivity, For temperature, For time, It serves as a heat source for the body.

6. The method according to claim 1, characterized in that: The specific process of the multi-cycle iterative calculation in step four is as follows: the temperature field at the end of the nth pulse cycle is used as the initial temperature field condition for the (n+1)th pulse cycle for solution, where n is an integer greater than or equal to 1, and the iteration continues until all the set pulse cycles are completed.

7. The method according to claim 6, characterized in that: In the multi-cycle iterative calculation, within each laser pulse cycle, the temperature rise and cooling process during the pulse period and the non-pulse period are calculated by setting the time step of the laser pulse action period and the time step of the pulse interval period.

8. The method according to claim 7, characterized in that: The time step of the laser pulse action period is less than the pulse width, and the time step of the pulse interval period is dynamically adjusted according to the temperature change rate.

9. The method according to claim 1, characterized in that: The benchmark data mentioned in step five is the result of commercial software simulation; the laser process parameters include the pulse duty cycle.

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