A numerical simulation method for the influence of process parameters on temperature field of laser directed energy deposition of inconel 718

Abstract

The present application belongs to the technical field of numerical simulation of laser directed energy deposition, and relates to a numerical simulation method for the influence of process parameters on the temperature field of laser directed energy deposition of Inconel 718. When calculating the transient temperature field distribution in the process of laser directed energy deposition, the present application needs to complete the definition of material properties, the establishment of a geometric model and mesh division, the establishment of a transient temperature field control equation, the application of a heat source, the application of initial conditions and boundary conditions, the discrete processing of a transient temperature field finite element equation set, latent heat processing, and iterative solving of several parts of work. The numerical simulation method of the present application studies the temperature distribution law in the process of laser directed energy deposition of Inconel 718 material, analyzes the influence of process parameters on the temperature field, establishes and perfects the theoretical basis of laser directed energy deposition of Inconel 718 material, and guides the formulation of process parameters, which has important scientific research significance and engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of laser directed energy deposition, specifically relating to a numerical simulation method for the influence of process parameters on the temperature field of Inconel 718 laser directed energy deposition. Background Technology

[0002] Inconel 718 nickel-based alloys possess advantages such as high strength, oxidation resistance, radiation resistance, and good hot workability, making them widely used in turbine disks, turbine rotor blades, and other fastening structural components of aero-engines. With the rapid development of high-end manufacturing, parts are increasingly becoming more integrated and complex, placing new demands on the manufacturing processes and product quality of Inconel 718 nickel-based alloy parts. However, traditional casting and forging processes for Inconel 718 nickel-based alloy parts are time-consuming and costly. Furthermore, the high hardness of Inconel 718 alloy accelerates tool wear, leading to poor surface integrity and making it difficult to produce complex parts. Therefore, traditional Inconel 718 nickel-based alloy manufacturing processes can no longer meet the needs of modern manufacturing. Laser-directed energy deposition (LDED) technology overcomes the limitations of traditional manufacturing processes, enabling the efficient production of parts with uniform microstructure and excellent performance. It has broad application prospects in the fabrication of Inconel 718 alloy parts and provides possibilities for achieving freedom in the manufacturing and design of complex structures.

[0003] However, laser-directed energy deposition (LDED) is a forming process with high energy input and repeated cycles of rapid heating and cooling. Its process parameters directly affect the temperature distribution during forming, thus impacting the quality of the formed part. When inappropriate process parameters are used, typical defects are easily generated during forming, such as weak layer-to-layer bonding, "spheroidization," cracking, and warping. These defects can range from low part quality and poor overall mechanical properties to excessive deformation during forming, leading to process interruption. Therefore, to select suitable process parameters and reduce defects in LDED, it is essential to study the evolution of the temperature field during LDED and the influence of process parameters on it.

[0004] The temperature field changes rapidly during laser-directed energy deposition (LDED) and is influenced by many factors. Therefore, it is difficult to monitor the temperature field distribution in real time using existing experimental equipment. Numerical simulation is a convenient and effective method for studying the evolution of the temperature field during LDED. Numerical simulation techniques often obtain the characteristics and corresponding numerical values ​​of the physical process by solving mathematical models, and these results can be used to study the relationship between process parameters and time, space, and other varying factors. Currently, there are few quantitative studies on the temperature field under different process parameters during Inconel 718 LDED, both domestically and internationally. Exploring the influence mechanism of process parameters on the temperature field during Inconel 718 LDED, and subsequently optimizing process parameters to achieve high-precision LDED, is crucial.

[0005] This invention takes Inconel 718 material as the research object and establishes a finite element model of the temperature field of laser directional energy deposition using ANSYS software as the platform. Numerical simulations of the temperature field under different laser powers (800W, 1200W, 1600W) and different scanning speeds (10mm / s, 12mm / s, 14mm / s) are carried out. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] A numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 includes the following steps:

[0009] Step 1: Define material properties;

[0010] Step 2: Establish the geometric model and generate the mesh;

[0011] Step 3: Establish the governing equations for the transient temperature field;

[0012] Step 4: Apply a heat source;

[0013] Step 5: Apply initial and boundary conditions;

[0014] Step 6: Discretize the finite element equations of the transient temperature field. Discretize the equations from Step 3 in both the spatial and time domains.

[0015] Step 7: Latent heat treatment, iterative solution.

[0016] Furthermore, the parameters related to the numerical simulation of the temperature field in step 1 include thermal conductivity, density, and specific heat capacity. The thermal properties of Inconel 718 material vary with temperature as shown in Table 1.

[0017] Table 1. Thermophysical properties of Inconel 718 material.

[0018]

[0019] Furthermore, in step 2, UG software is used to perform geometric modeling for laser directional energy deposition, wherein the size of the substrate is 40mm×40mm×3mm and the size of the part to be formed is 20mm×20mm×6mm.

[0020] Furthermore, in step 2, the geometric model is divided into Cartesian meshes, with a total of 103,754 mesh cells and 42,440 nodes.

[0021] Furthermore, in step 3, during the laser-directed energy deposition process, the thermal conductivity temperature distribution of Inconel 718 satisfies the following equation:

[0022]

[0023] Where Q is the heat input, T is the temperature field distribution function, and t is time, a constant. This is called the material's heat release coefficient.

[0024] Furthermore, in step 4, a double ellipsoidal heat source model is used to simulate the energy distribution of the laser. The heat flux density distribution expressions for the front and rear halves of the ellipsoid are as follows:

[0025]

[0026]

[0027] In the formula, q f q r , respectively, represent the heat flux density distribution functions of the front and rear halves of the ellipsoid; b is the width of the molten pool; d is the depth of the molten pool; a f a is the length of the front half-axis; r Where is the length of the rear half-shaft; Q is the effective power of the thermal input; f f f r These are the heat flux distribution coefficients for the front and rear halves of the ellipsoid, respectively, f. f +f r =2.

[0028] Furthermore, step 5 involves the third type of boundary condition, with the following formula:

[0029]

[0030] Where h is the surface convective heat transfer coefficient; T is the surface temperature of the object boundary; T0 is the temperature of the surrounding medium, i.e., the initial temperature, set to 25℃; σ is the Stephan-Boltzmann constant, approximately 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ); ε is the emissivity, which is between 0 and 1.

[0031] Furthermore, in step 6, the discretization of the spatial domain involves discretizing the spatial volume, dividing the model into multiple finite element meshes. The temperature equation within each mesh can be expressed as:

[0032]

[0033] Where [K] is the heat conduction matrix; [C] is the heat capacity matrix; {P} is the temperature load vector; and {T} is the temperature vector of the global finite element node.

[0034] Furthermore, in step 6, the time domain is expanded using the finite difference method, and the equation is:

[0035] [A(T)]{T}={B(T)}.

[0036] Furthermore, the formula in step 7 is:

[0037]

[0038] The coefficient matrix on the left side of the equation and the load vector on the right side can be expressed as follows:

[0039]

[0040]

[0041] H0 is obtained from the initial temperature value T0, and H is obtained through iteration. t and T t .

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows.

[0043] The laser-directed energy deposition (LDED) process of Inconel 718 involves highly complex non-equilibrium physical metallurgical and thermophysical processes. Current finite element modeling for temperature field analysis neglects the laser's penetration of the metal, the stretching effect of the molten pool during motion, and the influence of latent heat of phase transformation. The finite element model established in this invention uses a double ellipsoidal heat source to simulate the laser energy distribution and incorporates latent heat treatment, thus more accurately reflecting the rapidly changing real-world processing scenario. Therefore, using the numerical simulation method of this invention to study the temperature distribution during the LDED process of Inconel 718 and analyze the influence of process parameters on the temperature field has significant scientific research value and engineering application value for establishing and improving the theoretical foundation of LDED of Inconel 718 and guiding the formulation of process parameters. Attached Figure Description

[0044] Figure 1 The present invention provides a numerical simulation process for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718.

[0045] Figure 2 This invention provides a numerical simulation geometric model.

[0046] Figure 3 The mesh generation result of the geometric model of this invention.

[0047] Figure 4 This invention relates to a double ellipsoidal heat source model.

[0048] Figure 5 Numerical simulations and experiments at different laser powers show temperature variations over time.

[0049] Figure 6 Temperature variation curves over time in numerical simulations and experiments at different scanning speeds. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments in this specification clearer, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, not all embodiments. Based on the embodiments in the specification, those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0051] Numerical simulation of the effect of temperature field on laser-directed energy deposition in Inconel 718.

[0052] Calculating the transient temperature field distribution during laser-directed energy deposition (LDED) requires several steps: defining material properties; establishing a geometric model and meshing; establishing the governing equations for the transient temperature field; applying a heat source; applying initial and boundary conditions; discretizing the finite element equations for the transient temperature field; handling latent heat; and iteratively solving the problem. The numerical simulation process for the temperature field during LDED is as follows: Figure 1 As shown.

[0053] Step 1: Define material properties

[0054] Material properties have a significant impact on the accuracy of numerical simulations of the temperature field in laser-directed energy deposition. Parameters relevant to temperature field simulations include thermal conductivity, density, and specific heat capacity. Table 1 shows the variation of the thermal properties of Inconel 718 material with temperature.

[0055] Step 2: Establish geometric model and mesh generation

[0056] This paper selects UG software for geometric modeling of laser directional energy deposition, such as... Figure 2 As shown. The dimensions of the substrate are 40mm×40mm×3mm, and the dimensions of the part to be formed are 20mm×20mm×6mm.

[0057] After the geometric model and element type are determined, mesh generation is required before converting it into a finite element model for solution. This geometric model uses a Cartesian mesh, such as... Figure 3 As shown, the total number of grid cells and nodes is 103,754 and 42,440, respectively.

[0058] Step 3: Establish the governing equations for the transient temperature field

[0059] During laser-directed energy deposition, the heat conduction temperature distribution satisfies the following equation:

[0060]

[0061] Where, k x k y k z The values ​​represent the thermal conductivity of anisotropic materials in different directions, where Q is the heat input, ρ is the density of the material, c is the specific heat capacity of the material, T is the temperature field distribution function, and t is time.

[0062] For Inconel 718, the thermal conductivity is basically the same in all three directions, i.e., kJ / m². x =k y =k z Therefore, equation (1-1) can be simplified to:

[0063]

[0064] Where, constant This is called the material's heat release coefficient.

[0065] Step 4: Apply a heat source

[0066] In current numerical simulations, the Gaussian surface heat source is the most widely used heat source model. However, traditional heat source models cannot accurately simulate the actual energy distribution, neglecting the laser's penetrating effect on the material and the tensile effect during the molten pool's movement. Therefore, this invention employs a double ellipsoidal heat source model to simulate the laser's energy distribution, such as... Figure 4 As shown, the heat flux density distribution expressions for the front and rear halves of the ellipsoid are as follows:

[0067]

[0068]

[0069] In the formula, q f q r , respectively, represent the heat flux density distribution functions of the front and rear halves of the ellipsoid; b is the width of the molten pool; d is the depth of the molten pool; a f a is the length of the front half-axis; r Where is the length of the rear half-shaft; Q is the effective power of the thermal input; f f f r These are the heat flux distribution coefficients for the front and rear halves of the ellipsoid, respectively, f. f +f r =2.

[0070] The parameters of the double ellipsoidal heat source model are shown in Table 2.

[0071] Table 2. Parameters of the double ellipsoidal heat source model.

[0072]

[0073] Step 5: Apply initial and boundary conditions

[0074] When solving equation (1-2) using the finite element method, initial and boundary conditions need to be applied. For laser-directed energy deposition, heat dissipation to the surrounding air is mainly achieved through convection and radiation, i.e., the third type of boundary condition, as shown in the formula:

[0075] q t =q conv +q rad =h(T-T0)+σε(T0) 4 -T 4 (1-4)

[0076] Where h is the surface convective heat transfer coefficient; T is the surface temperature of the object boundary; T0 is the temperature of the surrounding medium, i.e., the initial temperature, set to 25℃; σ is the Stephan-Boltzmann constant, approximately 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ); ε is the emissivity, which is between 0 and 1.

[0077] Step Six: Discretization of the Finite Element Equations for the Transient Temperature Field

[0078] To obtain the transient temperature field distribution during laser directional energy deposition, the heat conduction control equation (1-2) needs to be discretized in both the spatial and temporal domains.

[0079] 1) Discretization of the spatial domain

[0080] First, the spatial volume is discretized, and the model is divided into multiple finite element meshes. The temperature equation inside each element can be expressed as:

[0081] T (x,y,z,t) =[N (x,y,z) ] e {T t} e (1-5)

[0082] Among them, T (x,y,z,t) Represents the temperature value at any point within the unit; [N (x,y,z) ] e Represents a set of unit shape functions; {T t} e This indicates the temperature of the nodes inside the cell.

[0083] The following equation is obtained using the weighted residual method:

[0084]

[0085] In the formula,

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] {P1} i =∫ Ω NT QdΩ (1-13)

[0093] {P2} i =∫ Γ N T qdΓ (1-14)

[0094] {P3} i =∫ Γ N T αT α dΓ (1-15)

[0095] Where [K] is the heat conduction matrix; [C] is the heat capacity matrix; {P} is the temperature load vector; {T} is the global finite element nodal temperature vector; q is the heat flux density; N e The number of units.

[0096] Considering the nonlinear relationship between material and temperature during laser-directed energy deposition, equation (1-6) can be modified as follows:

[0097]

[0098] 2) Discretization in the time domain

[0099] When solving transient temperature fields, the initial temperature distribution and boundary conditions are usually known. Since {T} is an unknown term, solving for it using equation (1-16) is quite difficult. Therefore, we expand it using the finite difference method and discretize it in the time domain. Within each time step of interval Δt, we establish a difference scheme for the point (t+Δt), where θ is the weighting coefficient (0≤θ≤1).

[0100] From the Taylor series expansion, we can obtain:

[0101] T (t+θ△t) =θT t+△t +(1-θ)T (t) +o(△t 2 (1-17)

[0102]

[0103] Substituting the above two equations into (1-16), and performing the same treatment on P, we obtain...

[0104]

[0105] In the formula, the superscript θ represents the matrix; C θ K θ The result is obtained by substituting the temperature at time t+θΔt. After the above processing, the nonlinear differential equation is transformed into a system of nonlinear algebraic equations.

[0106] In equation (1-19), θ is taken as 2 / 3.

[0107] After the above discretization of the time domain, the equation can finally be written as:

[0108] [A(T)]{T}={B(T)}(1-20)

[0109] Step 7: Latent heat treatment, iterative solution

[0110] When metallic materials are subjected to external heat, they undergo a process where the temperature remains constant for a period of time, but the liquid phase continuously increases. This is due to the latent heat of phase transition present in the material. In transient temperature field calculations, the latent heat of the metallic material must be fully considered to ensure that the simulated temperature distribution conforms to objective physical laws. This invention uses the enthalpy method to establish the relationship between temperature and enthalpy, as shown in the following equation:

[0111]

[0112] Where: ρ - density value, kg / m³ 3

[0113] c - Specific heat capacity, J / (kg·K)

[0114] L - Latent heat, J / kg

[0115] T L -Liquidus temperature, °C

[0116] T S - Solidus temperature, °C

[0117] Using enthalpy to correct for temperature, formula (1-16) can be expressed as:

[0118]

[0119] Simultaneously, by performing time-domain difference discretization on the above equation, we can obtain:

[0120]

[0121] If we ignore the unit transformation between solid and liquid, then we have:

[0122] H t+△t -H t =T t+△t -T t (1-24)

[0123] Substituting it into equation (1-23) yields:

[0124]

[0125] Therefore, the above formula can be rearranged as:

[0126]

[0127] The coefficient matrix on the left side of the equation and the load vector on the right side can be expressed as follows:

[0128]

[0129]

[0130] Therefore, H0 can be obtained from the initial temperature value T0, and H can be obtained through iteration. t and T t .

[0131] 2. Numerical simulation and experimental verification of the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718.

[0132] K-type thermocouples were used to measure temperature during laser directional energy deposition. The corresponding node position was selected in the numerical model, and the temperature change of the node over time was recorded during the numerical simulation.

[0133] like Figure 5 The six temperature curves shown represent the temperature changes over time during numerical simulations and experiments, respectively, under the conditions of a constant scanning speed of 10 mm / s and laser powers of 800 W, 1200 W, and 1600 W. Figure 6 The six temperature curves shown represent the temperature changes over time during numerical simulations and experiments, respectively, under the conditions of constant laser power of 1400W and scanning speeds of 10mm / s, 12mm / s, and 14mm / s.

[0134] according to Figure 5 and Figure 6 It is evident that each temperature curve exhibits fluctuations during the heating process, indicating a significant heat input from the formation of each layer during laser-directed energy deposition, thus causing a gradual increase in temperature at that node. (Comparison follows.) Figure 5 and Figure 6 The temperature curves from the numerical simulation and experiments show that the temperature obtained from the numerical simulation and the temperature obtained from the thermocouple have the same trend.

[0135] according to Figure 5 It can be seen that as the laser power gradually increases from 800W, 1200W to 1600W, the highest values ​​of the temperature curves obtained from numerical simulation also gradually increase, reaching 1683℃, 2467℃, and 3647℃ respectively. Compared with the data obtained from thermocouple measurements, the errors in the highest temperatures are 4.2%, 1.5%, and 3.6%, respectively. Similarly, according to... Figure 6It can be seen that as the scanning speed gradually increases from 10 mm / s, 12 mm / s, and 14 mm / s, the time for the temperature curve obtained from the numerical simulation to reach its maximum point decreases, and the maximum temperature also shows a downward trend, reaching 3589℃, 3168℃, and 2836℃ respectively. Compared with the data obtained from thermocouple measurements, the errors in the maximum temperature are 1.7%, 3.8%, and 7.6%, respectively. The above analysis shows that the error in the maximum temperature obtained from the numerical simulation is within 8%, which is within a reasonable error range, and the temperature data obtained from the numerical simulation under different process parameters shows a consistent variation pattern with the temperature data obtained from the thermocouple measurements.

Claims

1. A method of numerical simulation of the influence of process parameters on the temperature field of laser directed energy deposition of Inconel 718, characterized in that, Includes the following steps: Step 1: Define material properties; Step 2: Establish the geometric model and generate the mesh; Step 3: Establish the governing equations for the transient temperature field; Step 4: Apply a heat source; Step 5: Apply initial and boundary conditions; Step 6: Discretize the finite element equations of the transient temperature field. Discretize the equations from Step 3 in both the spatial and time domains. Step 7: Latent heat treatment, iterative solution; In step 3, during the laser-directed energy deposition process, the thermal conductivity temperature distribution of Inconel 718 satisfies the following equation: Where Q is the heat input, T is the temperature field distribution function, and t is time, a constant. This is called the material's heat transfer coefficient; In step 4, a double ellipsoidal heat source model is used to simulate the energy distribution of the laser. The heat flux density distribution expressions for the front and rear halves of the ellipsoid are as follows: , In the formula, q f q r The heat flux density distribution functions for the front and rear halves of the ellipsoid are respectively; b is the width of the molten pool; d is the depth of the molten pool; a f a is the length of the front half-axis; r Where is the length of the rear half-shaft; Q is the effective power of the thermal input; f f f r These are the heat flux density distribution coefficients for the front and rear halves of the ellipsoid, respectively. The boundary condition formula in step 5 is: Where h is the surface convective heat transfer coefficient; T is the boundary surface temperature of the object; T0 is the ambient medium temperature; and σ is the Stephan-Boltzmann constant, approximately 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ); ε is the emissivity, which is between 0 and 1.

2. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, In step 1, the parameters related to the numerical simulation of the temperature field include thermal conductivity, density, and specific heat capacity. The changes of the thermal properties of Inconel 718 material with temperature are shown in the table below: Table of thermophysical properties of Inconel 718 material 。 3. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, In step 2, UG software is used to perform geometric modeling for laser directional energy deposition, wherein the size of the substrate is 40mm×40mm×3mm and the size of the part to be formed is 20mm×20mm×6mm.

4. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, In step 2, the geometric model is divided into Cartesian meshes, with a total of 103,754 mesh cells and 42,440 nodes.

5. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, In step 6, the discretization of the spatial domain involves discretizing the spatial volume, dividing the model into multiple finite element meshes. The internal temperature equation of each element can be expressed as: ;in, This is the heat conduction matrix; This is the heat capacity matrix; This is the temperature load vector; This represents the temperature vector at each node of the overall finite element unit.

6. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, In step 6, the time domain is discretized using the finite difference method, and the equation is: 。 7. The numerical simulation method for the influence of process parameters on the temperature field of laser-directed energy deposition Inconel 718 as described in claim 1, characterized in that, The formula in step 7 is: （1-26） The coefficient matrix on the left side of the equation and the load vector on the right side can be expressed as follows: , H0 is obtained from the initial temperature value T0, and H is obtained through iteration. t and T t .

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