A method for predicting the microstructure morphology of molten deposited layers in laser metal additive manufacturing

Abstract

The present invention provides a method for predicting the microstructure morphology of a molten deposit layer manufactured by laser metal additive manufacturing, which belongs to the field of laser metal additive manufacturing. In order to solve the problem that the existing methods for numerical simulation in the additive manufacturing process mainly focus on analyzing the temperature field, stress field and melt flow field near the molten pool to analyze the molten pool solidification process and the causes of defects, there is a lack of numerical simulation methods for predicting the microstructure morphology and size of the molten deposit layer manufactured by additive manufacturing. The present invention constructs a geometric model of the molten deposit layer manufactured by laser metal additive manufacturing, and constructs a numerical model including a laser heat source model, a molten pool surface dynamic tracking model, a phase change heat transfer model and a liquid metal flow model, solves the transient temperature field distribution cross section of the molten pool of the molten deposit layer, and further calculates the morphological parameters and cooling rate to predict the microstructure morphology and size of the molten deposit layer. The present invention can quickly predict the microstructure morphology and size distribution of the molten deposit layer under different process parameters.

Description

Technical Field

[0001] The present invention relates to the field of laser metal additive manufacturing, and in particular to a method for predicting the microstructure morphology of a molten deposited layer in laser metal additive manufacturing. Background Art

[0002] Metal additive manufacturing refers to a forming technology that uses metal powder or wire as raw materials, combined with computer-aided design and laser processing technologies, to achieve three-dimensional structure manufacturing through layer-by-layer accumulation. Compared with traditional forming processes such as casting, additive manufacturing does not require expensive molds, so it can greatly shorten the R&D cycle and production costs. Laser metal additive manufacturing technology using powder as material (such as selective laser melting technology and direct energy deposition technology) can manufacture high-density, low-defect complex parts and is considered to be one of the most promising advanced manufacturing technologies in the 21st century.

[0003] Thanks to the rapid development of computer technology, more and more numerical simulation models and methods have been widely used in the analysis and research of temperature field, stress field and flow field in the molten pool during additive manufacturing, and the simulation results are highly consistent with the experimental results. On the other hand, the mechanical properties of additively manufactured products (such as tensile strength, elongation after fracture, hardness, etc.) are closely related to the grain morphology and grain size of the internal microstructure of the deposited layer. In general, fine equiaxed crystals can bring higher strength, hardness, plasticity and toughness, and coarse columnar crystals often bring poor mechanical performance. At present, the numerical simulation of the additive manufacturing process mainly focuses on the analysis of the temperature field, stress field and melt flow field near the molten pool to help researchers better understand the molten pool solidification process and the causes of defects. There is a lack of numerical simulation methods specifically for the prediction of the microstructure morphology and size of the molten deposited layer in additive manufacturing.

[0004] In the process of laser metal additive manufacturing, the temperature gradient G and solidification rate R in the molten pool are the key parameters affecting the solidification behavior of the melt in the molten pool. The influence of temperature gradient G and solidification rate R on the microstructure and size of the molten deposit layer is as follows: Figure 2 As shown in the figure, the microstructure morphology of the molten deposited layer is affected by the combined parameter morphological parameter (G / R) of G and R. The smaller the morphological parameter, the transformation of the microstructure morphology from planar crystal to cellular crystal, columnar crystal and equiaxed crystal. The microstructure size of the molten deposited layer is affected by the combined parameter cooling rate (G×R) of G and R. The larger the cooling rate, the smaller the microstructure size.

[0005] In order to solve the current lack of numerical simulation prediction methods for microstructure morphology and size of laser metal additive manufacturing, a method for predicting the microstructure morphology of the molten deposited layer in laser metal additive manufacturing is urgently needed to predict the morphology and size of the microstructure of the molten deposited layer based on the morphological parameters G / R and the cooling rate G×R. Summary of the invention

[0006] The technical problems to be solved by the present invention are:

[0007] Existing methods for numerical simulation of additive manufacturing processes mainly focus on analyzing the temperature field, stress field and melt flow field near the molten pool to analyze the molten pool solidification process and the causes of defects. There is a lack of numerical simulation methods specifically for predicting the microstructure morphology and size of the molten deposited layer in additive manufacturing.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] The present invention provides a method for predicting the microstructure morphology of a molten deposited layer produced by laser metal additive manufacturing, comprising the following steps:

[0010] Step 1: Construct a geometric model of the molten deposition layer of laser metal additive manufacturing, and mesh the processing area and non-processing area respectively;

[0011] Step 2: construct a numerical model and control equations, wherein the numerical model includes a laser heat source model, a molten pool surface dynamic tracking model, a phase change heat transfer model, and a liquid metal flow model;

[0012] Step 3: Set the thermophysical parameters of the model metal;

[0013] Step 4, solving the temperature field of the molten pool of the molten deposition layer, and performing a section of the temperature field parallel to the laser scanning direction to obtain multiple transient temperature field distribution sections of the molten deposition layer molten pool;

[0014] Step 5: Based on the transient temperature field distribution section, extract the liquidus line corresponding to each section, and calculate the temperature gradient G and the solidification rate R according to the liquidus line;

[0015] Step 6: Project the obtained temperature gradient G and solidification rate R of each cross section onto the same cross section perpendicular to the laser scanning direction to obtain a cloud diagram of the temperature gradient G and solidification rate R inside the molten pool during the entire solidification process;

[0016] Step 7: Obtain the two-dimensional cross-sectional projection cloud map of the morphological parameter G / R and the cooling rate G×R to predict the microstructure morphology and grain size of the molten deposit layer.

[0017] Furthermore, the laser heat source model described in step 2 approximates the heat source density distribution to a Gauss heat source model that conforms to a normal distribution, and the laser heat source satisfies the following conditions at the gas / liquid interface:

[0018]

[0019] Where, q——heat flux distribution J / m 2 .s, P——Laser power (W), ηl ——Laser energy absorption coefficient, r——Spot radius (m), v——Scanning speed (m / s), x, y——Distance from the center of the laser beam (m), h——Convection heat transfer coefficient (W / (m 2 ·K)), T——processing temperature (K), T0——ambient temperature (K), σ b ——Boltzmann constant, ε——material absorptivity.

[0020] Furthermore, the dynamic tracking model of the molten pool surface in step 2 uses a moving mesh method to simulate the deposition process of the molten deposit layer on the molten pool surface. The interface movement velocity V caused by the mass addition is p for:

[0021]

[0022] Where M p ——Powder feeding rate (mg / min), η p ——Powder capture efficiency, ρ p ——Powder density (kg / m 3 ), r p ——Radius of powder flow (m), z——unit vector in the direction of lift.

[0023] Furthermore, the phase change heat transfer model described in step 2 takes into account the influence of the phase change latent heat caused by the solid / liquid phase change during the heat transfer process, and the energy conservation equation is:

[0024]

[0025] Where, ρ is density (kg / m 3 ), c p ——Specific heat (J / (kg·K)), u i ——velocity component in the i-th direction (m / s), k——thermal conductivity (W / (m·K)), ΔH——melting latent enthalpy capacity (J / kg);

[0026] in,

[0027] ΔH=Lf l

[0028] Where, L is the latent heat of fusion (J / kg), f l ——Liquid phase mass fraction;

[0029] in,

[0030]

[0031] Wherein, the subscripts s and l represent the solid phase and the liquid phase.

[0032] Furthermore, the liquid metal flow model described in step 2 uses the incompressible Navior-Stokes equation to describe the liquid metal in the molten pool, taking into account the convective momentum dissipation caused by the solidification of dendrites in the mushy zone, and considering the volume force caused by the liquid expansion and the surface tension caused by the Marangoni effect in the melt, the mass conservation and momentum conservation equations are:

[0033]

[0034]

[0035] In the formula, μ is the viscosity (Pa·s), p is the pressure (Pa), K0 is the constant that characterizes the morphology of the porous medium, B is the decimal set in the viscous dissipation term to avoid the denominator being zero, and F is the combined effect of body force, gravity, and melt surface tension (N / m 3 );

[0036] in,

[0037]

[0038] In the formula, g is the acceleration due to gravity (m / s 2 ), β——metal thermal expansion coefficient (1 / K), γ——surface tension temperature coefficient (N / (K·m)), σ——surface tension (N / m), κ——interface curvature (1 / m 2 ).

[0039] Furthermore, the thermophysical parameters in step three include powder density, thermal conductivity, specific heat, viscosity, and enthalpy, and a temperature variation curve of each thermophysical parameter of the substrate and the powder is set.

[0040] Furthermore, the temperature variation curve of the thermophysical property parameter is obtained by using the mixing rate formula:

[0041]

[0042] In the formula, P is the thermal physical parameter of the composite material, P1 is the thermal physical parameter of the base material, P2 is the thermal physical parameter of the reinforced material, ——volume fraction of base material, ——Volume fraction of reinforcing material.

[0043] Furthermore, the solidification rate R in step 5 is expressed as:

[0044] R=v·cosθ

[0045] Where, θ is the angle between the normal vector of the solid / liquid interface of the molten pool and the laser scanning direction,

[0046] The temperature gradient G is expressed as:

[0047]

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention discloses a method for predicting the microstructure morphology of a molten deposited layer in laser metal additive manufacturing. The method innovatively proposes the use of transient temperature field data obtained by numerical simulation for laser metal additive manufacturing, and uses the transient temperature field data to calculate morphological parameters and cooling rate, thereby predicting the microstructure morphology and size of the molten deposited layer. The method of the present invention can help researchers quickly predict the microstructure morphology and size distribution of the molten deposited layer under different process parameters, reduce the time cost and economic cost caused by a large number of preliminary process parameter exploration experiments, and greatly reduce the laser metal additive manufacturing process optimization process. At the same time, the present invention can provide an effective technical reference for the design of metal laser additive manufacturing process parameters for obtaining parts with expected mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of a method for predicting the microstructure morphology of a molten deposited layer in laser metal additive manufacturing according to an embodiment of the present invention;

[0051] Figure 2 This is a diagram showing the influence of G and R on microstructure morphology and size mentioned in the background technology of the present invention;

[0052] Figure 3 It is a geometric model and mesh drawing for numerical simulation of laser metal additive manufacturing in an embodiment of the present invention;

[0053] Figure 4 This is a temperature field diagram of the molten pool of the molten deposition layer in an embodiment of the present invention;

[0054] Figure 5 It is a two-dimensional cross-sectional projection cloud diagram of temperature gradient G and solidification rate R in an embodiment of the present invention;

[0055] Figure 6 It is a two-dimensional cross-sectional projection cloud diagram of the morphological parameter G / R and the cooling rate G×R in an embodiment of the present invention;

[0056] Figure 7 This is a comparison chart of the numerical simulation morphological parameter G / R in the embodiment of the present invention and the experimental verification results of the laser additive manufacturing AlSi10Mg molten deposition layer. DETAILED DESCRIPTION

[0057] In the description of the present invention, it should be noted that the terms "first", "second", and "third" mentioned in the embodiments of the present invention are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second", and "third" may explicitly or implicitly include one or more of the features.

[0058] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0059] like Figure 1 As shown, the present invention provides a method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing, comprising the following steps:

[0060] Step 1: Figure 3 As shown, a geometric model of the laser metal additive manufacturing molten deposition layer is constructed, and the processing area and non-processing area are meshed separately.

[0061] In order to save computing power and computer memory, the geometric model of the molten deposition layer of laser metal additive manufacturing is half of the entire molten deposition layer, and the calculation results of the other half of the model are obtained by setting symmetric boundary conditions. The overall size of the geometric model is 12mm×4mm×6mm, and the processing area is a small cuboid with a size of 12mm×1.8mm×1.3mm. The substrate in the processing area has changes such as fluid heat transfer, solid / liquid phase change, and surface growth. It is the focus of numerical simulation. The mesh is divided into a conventional free tetrahedron mesh for fluid dynamics, and the mesh of the processing area is refined. There is only solid heat transfer in the non-processing area. In order to save computing power, the mesh of the non-processing area is divided into a coarsened free tetrahedron mesh of ordinary physics.

[0062] Step 2: construct a numerical model and control equations, wherein the numerical model includes a laser heat source model, a molten pool surface dynamic tracking model, a phase change heat transfer model and a liquid metal flow model.

[0063] ①Laser heat source model

[0064] During the laser metal additive manufacturing process, the laser spot is irradiated to the substrate surface, and the energy density at the center of the spot is obviously higher than that around it. The heat source density distribution is approximated to the Gauss heat source model that conforms to the normal distribution. The laser heat source satisfies the boundary on the gas / liquid interface:

[0065]

[0066] Where, q——heat flux distribution J / m 2 .s, P——Laser power (W), η l——Laser energy absorption coefficient, r——spot radius (m), v——scanning speed (m / s), x, y——distance from the center of the laser beam (m), h——convective heat transfer coefficient (W / (m 2 ·K)), T——processing temperature (K), T0——ambient temperature (K), σ b ——Boltzmann constant, ε——material absorptivity.

[0067] ②Dynamic tracking of the molten pool surface

[0068] The moving mesh method is used to simulate the deposition process of the molten deposit layer on the molten pool surface, which is mainly due to the interface movement velocity V caused by mass addition. p for:

[0069]

[0070] Where M p ——Powder feeding rate (mg / min), η p ——Powder capture efficiency, ρ p ——Powder density (kg / m 3 ), r p ——Radius of powder flow (m), z——unit vector in the direction of lift.

[0071] ③Phase change heat transfer model

[0072] In the process of laser additive manufacturing, heat transfer is generated due to the input of laser energy. In addition, due to the existence of solid / liquid phase change, the influence of phase change latent heat must be considered in the heat transfer equation. The energy conservation equation is:

[0073]

[0074] Where, ρ is density (kg / m 3 ), c p ——Specific heat (J / (kg·K)), u i ——velocity component in the i-th direction (m / s), k——thermal conductivity (W / (m·K)), ΔH——melting latent enthalpy capacity (J / kg);

[0075] in,

[0076] ΔH=Lf l

[0077] Where, L is the latent heat of fusion (J / kg), f l ——Liquid phase mass fraction;

[0078] in,

[0079]

[0080] Wherein, the subscripts s and l represent the solid phase and the liquid phase.

[0081] The relevant material thermophysical parameters are:

[0082] C p =f s C ps +f l c pl

[0083] ρ=V s ρ s +V l ρ l

[0084]

[0085] Where V is the volume fraction.

[0086] ④Liquid metal flow model

[0087] The incompressible Navior-Stokes equation is used to describe the liquid metal in the molten pool. Considering the convective momentum dissipation caused by the solidification of dendrites in the mushy zone, the volume force caused by the liquid expansion and the surface tension caused by the Marangoni effect in the melt, the mass conservation and momentum conservation equations are:

[0088]

[0089]

[0090] In the formula, μ is the viscosity (Pa·s), p is the pressure (Pa), K0 is the constant that characterizes the morphology of the porous medium, B is the decimal set in the viscous dissipation term to avoid the denominator being zero, and F is the combined effect of body force, gravity, and melt surface tension (N / m 3 );

[0091] in,

[0092]

[0093] In the formula, g is the acceleration due to gravity (m / s 2 ), β——metal thermal expansion coefficient (1 / K), γ——surface tension temperature coefficient (N / (K·m)), σ——surface tension (N / m), κ——interface curvature (1 / m 2 ).

[0094] Step 3: Set the thermophysical parameters of the model metal.

[0095] The temperature variation curves of the thermophysical parameters of the substrate and powder are set respectively. According to the constituent elements and element contents of the target alloy, the temperature variation curves of the thermophysical parameters density, thermal conductivity, specific heat, viscosity, and enthalpy are obtained using the mixing rate formula:

[0096]

[0097] In the formula, P is the thermal physical parameter of the composite material, P1 is the thermal physical parameter of the substrate, P2 is the thermal physical parameter of the reinforcement material, ——volume fraction of substrate, ——Volume fraction of reinforcing material.

[0098] Step 4: Solve the temperature field of the molten pool of the molten deposition layer, and perform a section on the temperature field parallel to the laser scanning direction to obtain multiple transient temperature field distribution sections of the molten deposition layer molten pool.

[0099] The target process parameters (laser power of 2000W, scanning rate of 420mm / min, powder feeding rate of 2.0g / min) were set, and the model was initialized and solved to obtain the following Figure 4 The three-dimensional molten pool temperature field of the molten deposition layer shown in (a) is obtained as Figure 4 (b) is the cross section of transient temperature field distribution in the molten pool.

[0100] Step 5: Based on the transient temperature field distribution section, extract the liquidus line corresponding to each section, and calculate the temperature gradient G and solidification rate R according to the liquidus line.

[0101] like Figure 4 As shown in (b), according to the shape of the molten pool on the cross section of the transient temperature field distribution of the molten pool, the isotherms of the alloy melting point temperature on the cross section of the molten pool temperature field distribution are the liquidus lines corresponding to each cross section. The liquidus line profile is fitted with a function to obtain the liquidus line fitting function curve. The solidification rate R is calculated through the function curve. The solidification rate represents the advancement speed of the solid / liquid interface of the molten pool along the normal direction, which is expressed as:

[0102] R=v·cosθ

[0103] Where, θ is the angle between the normal vector of the solid / liquid interface of the molten pool (i.e., the normal direction of the edge of the liquidus line) and the laser scanning direction;

[0104] The temperature gradient G is the normal temperature gradient of the solid / liquid interface and is expressed as:

[0105]

[0106] Step 6: Figure 5As shown, the obtained temperature gradient G and solidification rate R of each cross section are projected onto the same cross section perpendicular to the laser scanning direction, and a cloud diagram of the temperature gradient G and solidification rate R inside the molten pool during the entire solidification process is obtained.

[0107] Step 7: Figure 6 As shown, the two-dimensional cross-sectional projection cloud map of the morphological parameter G / R and the cooling rate G×R is obtained to predict the microstructure morphology and grain size of the molten deposited layer.

[0108] like Figure 7 As shown in Figure 2, the target process parameters in this embodiment are used to perform laser additive manufacturing of AlSi10Mg molten deposition layer experiments to verify the method of the present invention. Figure 6 By comparing the G / R and G×R projection cloud map results of the numerical simulation of the present invention, it can be seen that the morphological parameter G / R at the top of the molten deposit layer is low and the cooling rate G×R is high, so the microstructure at the top of the molten deposit layer is mainly fine equiaxed crystals; the morphological parameter G / R at the bottom of the molten deposit layer is high and the cooling rate G×R is low, so the microstructure at the bottom of the molten deposit layer is mainly coarse dendrites; in the middle of the molten deposit layer, the microstructure transitions from fine equiaxed crystals at the top to coarse dendrites at the bottom. The prediction results of the method of the present invention are consistent with the experimental verification results, which fully proves the accuracy of the method of the present invention.

[0109] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for predicting the microstructure morphology of a molten deposited layer in laser metal additive manufacturing, characterized in that The steps include: Step 1: Construct a geometric model of the molten deposition layer of laser metal additive manufacturing, and mesh the processing area and non-processing area respectively; Step 2: construct a numerical model and control equations, wherein the numerical model includes a laser heat source model, a molten pool surface dynamic tracking model, a phase change heat transfer model, and a liquid metal flow model; Step 3: Set the thermophysical parameters of the model metal; Step 4, solving the temperature field of the molten pool of the molten deposition layer, and performing a section of the temperature field parallel to the laser scanning direction to obtain multiple transient temperature field distribution sections of the molten deposition layer molten pool; Step 5: Based on the transient temperature field distribution section, extract the liquidus line corresponding to each section, and calculate the temperature gradient G and the solidification rate R according to the liquidus line; Step 6: Project the obtained temperature gradient G and solidification rate R of each cross section onto the same cross section perpendicular to the laser scanning direction to obtain a cloud diagram of the temperature gradient G and solidification rate R inside the molten pool during the entire solidification process; Step 7: Obtain the two-dimensional cross-sectional projection cloud map of the morphological parameter G / R and the cooling rate G×R to predict the microstructure morphology and grain size of the molten deposit layer.

2. The method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing according to claim 1, characterized in that The laser heat source model described in step 2 approximates the heat source density distribution to the Gauss heat source model that conforms to the normal distribution. The laser heat source satisfies the following conditions at the gas / liquid interface: Where, q——heat flux distribution J / m 2 .s, P——Laser power (W), η l ——Laser energy absorption coefficient, r——Spot radius (m), v——Scanning speed (m / s), x, y——Distance from the center of the laser beam (m), h——Convection heat transfer coefficient (W / (m 2 ·K)), T——processing temperature (K), T0——ambient temperature (K), σ b ——Boltzmann constant, ε——material absorptivity.

3. The method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing according to claim 2, characterized in that The dynamic tracking model of the molten pool surface in step 2 uses a moving mesh method to simulate the deposition process of the molten deposit layer on the molten pool surface. The interface movement velocity V caused by mass addition is p for: Where M p ——Powder feeding rate (mg / min), η p ——Powder capture efficiency, ρ p ——Powder density (kg / m 3 ), r p ——Radius of powder flow (m), z——unit vector in the direction of lift.

4. The method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing according to claim 3, characterized in that The phase change heat transfer model described in step 2 considers the influence of the phase change latent heat caused by the solid / liquid phase change during the heat transfer process, and the energy conservation equation is: Where, ρ is density (kg / m 3 ), c p ——Specific heat (J / (kg·K)), u i ——velocity component in the i-th direction (m / s), k——thermal conductivity (W / (m·K)), ΔH——melting latent enthalpy capacity (J / kg); in, ΔH=Lf l Where, L is the latent heat of fusion (J / kg), f l ——Liquid phase mass fraction; in, Wherein, the subscripts s and l represent the solid phase and the liquid phase.

5. The method for predicting the microstructure morphology of a molten deposited layer produced by laser metal additive manufacturing according to claim 4, characterized in that The liquid metal flow model described in step 2 uses the incompressible Navior-Stokes equation to describe the liquid metal in the molten pool, taking into account the convective momentum dissipation caused by the solidification of dendrites in the mushy zone, and considering the volume force caused by the liquid expansion and the surface tension caused by the Marangoni effect in the melt. The mass conservation and momentum conservation equations are: In the formula, μ is the viscosity (Pa·s), p is the pressure (Pa), K0 is the constant that characterizes the morphology of the porous medium, B is the decimal set in the viscous dissipation term to avoid the denominator being zero, and F is the combined effect of body force, gravity, and melt surface tension (N / m 3 ); in, In the formula, g is the acceleration due to gravity (m / s 2 ), β——metal thermal expansion coefficient (1 / K), γ——surface tension temperature coefficient (N / (K·m)), σ——surface tension (N / m), κ——interface curvature (1 / m 2 ).

6. The method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing according to claim 1, characterized in that The thermophysical parameters described in step three include powder density, thermal conductivity, specific heat, viscosity, and enthalpy, and a temperature variation curve of each thermophysical parameter of the substrate and the powder is set.

7. The method for predicting the microstructure morphology of a molten deposited layer produced by laser metal additive manufacturing according to claim 6, characterized in that The thermophysical property parameter versus temperature curve is obtained using the mixing rate formula: In the formula, P is the thermal physical parameter of the composite material, P1 is the thermal physical parameter of the base material, P2 is the thermal physical parameter of the reinforced material, ——volume fraction of base material, ——Volume fraction of reinforcing material.

8. The method for predicting the microstructure morphology of a molten deposited layer by laser metal additive manufacturing according to claim 1, characterized in that The solidification rate R in step 5 is expressed as: R=v·cosθ Where, θ is the angle between the normal vector of the solid / liquid interface of the molten pool and the laser scanning direction, The temperature gradient G is expressed as:

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