A method for microstructure evolution prediction in selective laser sintering additive manufacturing process

Abstract

The application discloses a microstructure evolution prediction method in a selective laser sintering additive manufacturing process, according to the microstructure evolution characteristics of the selective laser sintering additive manufacturing, starting from the free energy density functional of the system, the time and space evolution expressions of temperature, conservative order parameter and non-conservative order parameter are derived in thermodynamic self-consistency, the Cahn-Hilliard equation containing temperature gradient driven diffusion and the determination method of model parameters are given, and numerical calculation is realized through finite element programming. Combined with powder bed laying and finite element calculation, the non-isothermal phase field model can simulate the sintering neck, grain boundary migration and other microstructure evolution in the selective laser sintering additive manufacturing process, simulate the influence of the huge temperature gradient in the selective laser sintering additive manufacturing, optimize the process parameters of the selective laser sintering additive manufacturing, reveal the influence law of the process parameters of the selective laser sintering additive manufacturing on the microstructure evolution and the final microstructure, and improve the design efficiency of the selective laser sintering additive manufacturing.

Description

Technical Field

[0001] This invention relates to the field of aerospace materials and manufacturing, and in particular to a method for predicting the microstructure evolution during selective laser sintering additive manufacturing. Background Technology

[0002] Compared with traditional manufacturing processes, laser additive manufacturing technology produces structural components with advantages such as lightweight, integrated design, and structural-functional integration, which is expected to make the manufactured aerospace vehicles more advanced, lighter, and more maneuverable.

[0003] Microstructure evolution plays a crucial role in the obtained material and structural properties. However, it is difficult to measure the real-time evolution of microstructure through experiments, making computational simulation an indispensable research tool.

[0004] Currently, the microstructure simulation of the selective laser sintering additive manufacturing process is based on isothermal models, which cannot account for the huge temperature gradients in the process. Therefore, it is necessary to develop non-isothermal phase field models and establish mature methods for predicting the evolution of microstructures in selective laser sintering additive manufacturing. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a method for predicting the microstructure evolution in the selective laser sintering additive manufacturing process. This method can predict the microstructure characteristics and evolution behavior in selective laser sintering additive manufacturing, providing a technical approach for optimizing the process parameters of selective laser sintering additive manufacturing to achieve controllable microstructure.

[0006] Technical solution: This invention provides a method for predicting the microstructure evolution during selective laser sintering additive manufacturing, comprising the following steps:

[0007] (1) Establish a non-isothermal phase field model and obtain the energy expression. From the perspective of thermodynamic self-consistency, obtain the expressions for the changes of temperature, conservative order parameter, and non-conservative order parameter with time and space.

[0008] (2) Based on the non-isothermal phase field model, the expression relating the model parameters to the experimental parameters is obtained. Combined with the experimental parameters, the parameters of the non-isothermal phase field model are solved and fitted.

[0009] (3) The expressions of temperature, conservative order parameter and non-conservative order parameter as a function of time and space are discretized using the finite element method to obtain the residual and iteration matrix, and a finite element program is written.

[0010] (4) Establish an ideal sintering model of two particles and perform numerical calculations to obtain the relevant mechanism of microstructure evolution during selective laser sintering additive manufacturing;

[0011] (5) Discrete element simulation is used to simulate the powder bed laying of selective laser sintering additive manufacturing to obtain the initial distribution of powder particles;

[0012] (6) In the finite element program, the relevant mechanism, powder bed laying, residual error and iterative matrix, non-isothermal phase field model parameters are combined to calculate the influence of selective laser sintering additive manufacturing process parameters on microstructure evolution and final microstructure, including sintering neck, grain boundary migration, porosity, surface morphology, grain shape and density of microstructure characteristics, and the selected process parameters are summarized.

[0013] Further, in step (1), the non-isothermal phase field model comprises the following steps:

[0014] (1.1) In the phase field model, the conserved order parameter p represents the material (p = 1) and the pore / gas region (p = 0), the non-conserved order parameter η J (J = 1, 2, … N) represents the grain with different crystal orientation, and the grain boundary energy is represented as The free energy density f of the non-isothermal phase field model is defined as:

[0015]

[0016] Where, f a , f b represent the thermal contribution of different phases, f ht (T) = Φ(p)f a + [1-Φ(p)]f b , W c (T) and W d (T) are temperature-dependent potential barrier heights, κ ρ (T) and κ η (T) are gradient term coefficients, and Φ(p) is an interpolation function, which is as follows:

[0017] Φ(p) = φ 3 (10-15φ+6φ 2 )

[0018] (1.2) The internal energy density e is represented as:

[0019]

[0020] (1.3) For the grain surface energy, a one-dimensional case is considered, in which p = η = 1 in the grain, η1 = η in the atmosphere / vacuum, and η2 = 0, the interface is located at x = 0, and the related free energy density is:

[0021]

[0022] (1.4) The evolution equation of the conserved order parameter at any time point t and space point r is:

[0023]

[0024] where is the time derivative of p, is the chemical potential of the conserved order parameter, Q is the transport heat of the vacancy, where the second term on the right hand side represents the diffusion driven by the temperature gradient, is an important feature of selective laser sintering additive manufacturing, V m is the molar volume, D is the diffusion coefficient, which is composed of four parts, expressed as: ss D at D sf D gb

[0025] D = Φ ss D ss + Φ at D at + Φ sf D sf + Φ gb D gb

[0026] where the interpolation function is:

[0027] Φ ss = p 3 (10-15p+6p 2 ), Φ at = 1- Φ ss ,

[0028] Φ sf = 16p 2 (1-p) 2 ,

[0029] (1.5) The non-conserved order parameter at any time point and space point is expressed as:

[0030]

[0031] where L(T) is the interface moving parameter, is the chemical potential of the non-conserved order parameter;

[0032] (1.6) The kinetic equation of temperature is expressed as:

[0033]

[0034] is the time derivative of T, k is the thermal conductivity, q(r) is the external heat source, which is used to represent the heat source input of selective laser sintering additive manufacturing.​

[0035] Further, in step (2), the following steps are included:

[0036] (2.1) According to the characteristics of the non-isothermal phase field model, the expression of the correlation between the model parameters and the experimental parameters is derived;

[0037] (2.2) Obtain the temperature-dependent experimental parameters of different material systems;

[0038] (2.3) According to the obtained experimental parameters, the non-isothermal phase field model parameters in the simulation process are obtained.

[0039] Further, in step (3), the following steps are included:

[0040] (3.1) According to the time and space evolution expressions of temperature, conservative order parameters and non-conservative order parameters obtained in step 1, the residual and iterative matrix after finite element discretization is derived, which includes stiffness matrix and damping matrix;

[0041] (3.2) Write the obtained residual and iterative matrix into the finite element program and compile it.

[0042] Further, in step (4), the following steps are included:

[0043] (4.1) Set the non-conservative order parameters of the non-isothermal phase field model to (η1, η2) to obtain a two-particle ideal model, and simulate the sintering process of the two particles;

[0044] (4.2) Analyze the simulation results to obtain the general mechanism of microstructure evolution in the selective laser sintering additive manufacturing process.

[0045] Further, in step (6), the following steps are included:

[0046] (6.1) By adjusting the sintering parameters generated during sintering, observe the microstructure evolution during the sintering process of the powder bed, including sintering neck, grain boundary migration, porosity, surface topography, grain shape, and density of the microstructure characteristics;

[0047] (6.2) According to the process of microstructure evolution, the influence of microstructure in the sintering process is obtained.

[0048] Beneficial effects: compared with the prior art, the present application has the remarkable characteristics that, by means of a non-isothermal phase field model and an energy expression, the time and space evolution expressions of temperature, conservative order parameters and non-conservative order parameters are derived from the thermodynamic point of view, the mechanism of microstructure evolution in selective laser sintering additive manufacturing is revealed by taking a two-particle ideal sintering model as an example, and the non-isothermal phase field model can predict the microstructure characteristics of selective laser sintering additive manufacturing, better simulate the microstructure evolution law in the selective laser sintering additive manufacturing process, thereby optimizing the process parameters of selective laser sintering additive manufacturing, revealing the influence law of the process parameters of selective laser sintering additive manufacturing on the microstructure evolution and the final microstructure, and finally providing effective technical means for obtaining a structure with better performance and improving the design efficiency of selective laser sintering additive manufacturing. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a flowchart of the present application;

[0050] Figure 2 is a schematic diagram of the change of sintering neck in two-dimensional 316L two-particle sintering in the present application;

[0051] Figure 3 is a sintering simulation schematic diagram of the present application with a single scanning laser power of 10W and a scanning speed of 1m / s;

[0052] Figure 4 is a sintering simulation schematic diagram of the present application with a single scanning laser power of 20W and a scanning speed of 1m / s;

[0053] Figure 5 is a sintering simulation schematic diagram of the present application with a double scanning laser power of 20W and a scanning speed of 1m / s. DETAILED DESCRIPTION

[0054] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0055] EMBODIMENT

[0056] The present application provides a microstructure evolution prediction method in a selective laser sintering additive manufacturing process, wherein a non-isothermal phase field calculation framework is built in an open source code MOOSE, and a finite element program is written on the MOOSE platform. MOOSE is an object-oriented multi-physical finite element library developed by the Idaho National Laboratory in the United States, and all the codes are open source. In this embodiment, a two-dimensional 316L single-layer powder bed is used. Please refer to Figure 1 , which comprises the following steps:

[0057] (1) Obtain free energy expression, from the perspective of thermodynamic self-consistency, obtain the expression of temperature, conservative order parameter, non-conservative order parameter with time and space variation, and establish the non-isothermal phase field model according to the expression.

[0058] (1.1) In the phase field model, the conservative order parameter ρ is used to represent the material (ρ = 1) and the pore / gas region (ρ = 0). A set of non-conservative order parameters η J (J = 1, 2, … N) represent grains with different crystal orientations. The grain boundary energy can be expressed as The free energy density of the non-isothermal phase field model is defined as:

[0059]

[0060] Where, f a , f b represent the thermal contribution of different phases, f ht (T) = Φ(ρ) f a + [1-Φ(ρ)] f b , W c (T) and W d (T) are temperature-dependent potential barrier heights, κ ρ (T) and κ η (T) are gradient term coefficients, Φ(ρ) is an interpolation function, and the formula is as follows:

[0061] Φ(ρ) = φ 3 (10-15φ+6φ 2 )

[0062] (1.2) The internal energy density e can be expressed as:

[0063]

[0064] (1.3) For the grain surface energy, a one-dimensional case is considered, where ρ = η = 1 in the grain, η1 = η2 = 0 in the atmosphere / vacuum, and the interface is located at x = 0. The related free energy density is:

[0065]

[0066] (1.4) The evolution equation of the conservative order parameter at any time point t and space point r is:

[0067]

[0068] Where is the time derivative of ρ, Chemical potential, Q is the transport heat of empty sites, where the second term on the right represents temperature gradient driven diffusion (thermophoresis), which is an important feature of selective laser sintering additive manufacturing. V mFor the molar volume, D is the diffusion coefficient, which is the diffusion coefficient D in the material ss , the diffusion coefficient D in air at , the diffusion coefficient D of the surface sf , the diffusion coefficient D of the grain boundary gb Four parts, the expression is:

[0069] D = Φ ss D ss + Φ at D at + Φ sf D sf + Φ gb D gb

[0070] Where the interpolation function is

[0071] Φ ss = ρ 3 (10-15ρ+6ρ 2 ), Φ at =1-Φ ss ,

[0072] Φ sf =16ρ 2 (1-ρ) 2 ,

[0073] (1.5) Non-conservative order parameter at any time point space point is represented as:

[0074]

[0075] Where L(T) is the interface moving parameter.

[0076] (1.6) The kinetic equation of temperature is represented as:

[0077]

[0078] The time derivative of T is k, the thermal conductivity, q(r) is the external heat source, which can be used to represent the heat source input of selective laser sintering additive manufacturing.

[0079] (2) According to the non-isothermal phase field model, the expression of the correlation between the model parameters and the experimental parameters is obtained, and the non-isothermal phase field model parameters are solved and fitted by combining the experimental parameters.

[0080] (2.1) According to the characteristics of the non-isothermal phase field model, the expression of the correlation between the model parameters and the experimental parameters is derived;

[0081] (2.2) Obtain the temperature-related experimental parameters of different material systems;

[0082] (2.3) According to the obtained experimental parameters, the non-isothermal phase field model parameters in the simulation process are obtained.

[0083] (3) The finite element is used to discretize the expression of the conservative order parameter and the non-conservative order parameter changing with time and space to obtain the residual and iteration matrix.

[0084] (3.1) According to the time and space evolution expressions of temperature, conservative order parameter and non-conservative order parameter obtained in step 1, the residual and iteration matrix after finite element discretization is derived, which includes stiffness matrix and damping matrix;

[0085] (3.2) The obtained residual and iteration matrix are written into the finite element program and compiled.

[0086] (4) An ideal sintering model of double particles is established and numerical calculation is carried out to obtain the related mechanism of microstructure evolution in the selective laser sintering additive manufacturing process, wherein the change of sintering neck is as shown in Figure 2 .

[0087] (4.1) The non-conservative order parameter of the above non-isothermal phase field model is set to 2 (η1, η2), and then the double-particle ideal model can be obtained and the simulation of the double-particle sintering process can be carried out;

[0088] (4.2) The simulation results are analyzed to obtain that in the selective laser sintering process, the sintering neck is slowly formed at the beginning and rapidly increases in the middle of sintering, and due to the migration of the grain boundary, the sintering neck gradually moves from the high-temperature end to the low-temperature end, and finally the particles at the high-temperature end swallow the particles at the low-temperature end, and the obvious swallow phenomenon appears, which is caused by the temperature gradient. The isothermal phase field model cannot predict this phenomenon.

[0089] (5) The powder bed laying simulation can be carried out for the powder bed of selective laser sintering additive manufacturing, and the single-layer and multi-layer powder laying simulation can be carried out.

[0090] (6) In the finite element program, the related mechanism, powder bed laying, residual and iteration matrix, non-isothermal phase field model parameters are combined to calculate the influence law of the process parameters of selective laser sintering additive manufacturing on the microstructure evolution and the final microstructure (sintering neck, grain boundary migration, porosity, surface topography, grain shape, density, etc. Microstructure characteristics), and the process parameters that can be selected are summarized.

[0091] (6.1) In this embodiment, a two-dimensional 316L single-layer powder bed is laid, the sintering parameters in the selective laser sintering process are adjusted, the microstructure evolution in the powder bed sintering process is observed, and the laser scanning speed is set to 1 m / s. The single-scan laser power is 10W, and the sintering result is as shown in Figure 3 ; the single-scan laser power is 20W, and the sintering result is as shown inFigure 4 The double scanning laser power is 20 W, and the sintering result is shown in Fig. 6. Figure 5 The double scanning laser power is 20 W, and the sintering result is shown in Fig. 6.

[0092] (6.2) According to the process of microstructure evolution, the influence law of microstructure in selective laser sintering additive manufacturing process is analyzed. With the increase of laser power, the porosity of sintering product gradually decreases.

Claims

1. A method of microstructure evolution prediction in a selective laser sintering additive manufacturing process, characterized by, Comprising the following steps: (1) Establish a non-isothermal phase field model and obtain an energy expression, from the perspective of thermodynamic self-consistency, obtain the expressions of temperature, conservative order parameter, and non-conservative order parameter varying with time and space; (2) According to the non-isothermal phase field model, obtain the expression of the correlation between the model parameters and the experimental parameters, combine the experimental parameters to solve and fit the parameters of the non-isothermal phase field model; (3) Discretize the expressions of temperature, conservative order parameter, and non-conservative order parameter varying with time and space using finite elements, obtain the residual and iteration matrix, and write a finite element program; (4) Establish an ideal sintering model of double particles and perform numerical calculation to obtain the related mechanism of microstructure evolution in the selective laser sintering additive manufacturing process; (5) Use discrete element simulation to simulate the powder bed laying of selective laser sintering additive manufacturing to obtain the initial distribution of powder particles; (6) In the finite element program, combine the relevant mechanism, powder bed laying, residual and iteration matrix, non-isothermal phase field model parameters, calculate the influence of selective laser sintering additive manufacturing process parameters on microstructure evolution and the final microstructure, including sintering neck, grain boundary migration, porosity, surface topography, grain shape, and density of microstructure characteristics, and summarize the process parameters that can be selected; In step (1), establishing a non-isothermal phase field model comprises the following steps: (1.1) In the phase field model, a conserved order parameter represents the material ( = 1) and the pore / gas region ( = 0), and non-conserved order parameters (J = 1, 2, … N) represent grains with different crystal orientations, where the grain boundary energy is represented as , and the free energy density of the non-isothermal phase field model is defined as: wherein represents the thermal contribution of the different phases, , is the temperature dependent barrier height, and is the gradient term coefficient, is the interpolation function, which is given by the formula: (1.2) inner energy density is represented as: (1.3) For the grain surface energy, consider the one-dimensional case, where in the grain , in the atmosphere / vacuum , the interface is located , the relevant free energy density is: (1.4) arbitrary point in time and spatial points The evolution equation for the conserved quantity of the spatial points is where is the time derivative of the chemical potential of the conserved order parameter, is the chemical potential of the conserved order parameter, is the transport heat of the vacancies, where the second term on the right represents the temperature gradient driven diffusion, is an important feature of selective laser sintering additive manufacturing, is the molar volume, , is the diffusion coefficient, which is composed of four parts in the material, in the air, on the surface, at the grain boundary, and the expression is: Where the interpolation function is: (1.5) The non-conservative order parameter at any time point and space point is represented as: wherein is an interfacial mobility parameter, is a chemical potential of the non-conserved order parameter; (1.6) The kinetic equation of temperature is represented as: for The time derivative, where k is the thermal conductivity. This is an external heat source used to represent the heat source input for selective laser sintering additive manufacturing.

2. The method of microstructure evolution prediction in selective laser sintering additive manufacturing process according to claim 1, characterized in that, In step (2), it comprises the following steps: (2.1) According to the characteristics of the non-isothermal phase field model, derive the expression of the correlation between the model parameters and the experimental parameters; (2.2) Obtain the temperature-related experimental parameters of different material systems; (2.3) According to the obtained experimental parameters, obtain the non-isothermal phase field model parameters in the simulation process.

3. The method of microstructure evolution prediction in selective laser sintering additive manufacturing process according to claim 1, characterized in that, In step (3), it comprises the following steps: (3.1) According to the time and space evolution expressions of temperature, conservative order parameter, and non-conservative order parameter obtained in step 1, derive the residual and iteration matrix after finite element discretization, which includes stiffness matrix and damping matrix; (3.2) Write the obtained residual and iteration matrix into the finite element program and compile it.

4. The method of microstructure evolution prediction in selective laser sintering additive manufacturing process according to claim 1, characterized in that, In step (4), it comprises the following steps: (4.1) Set the non-conservative order parameter of the non-isothermal phase field model to ( We obtained an ideal model of two particles and simulated the sintering process of two particles. (4.2) Analyze the simulation results to obtain the general mechanism of microstructure evolution in the selective laser sintering additive manufacturing process.

5. The method of microstructure evolution prediction in selective laser sintering additive manufacturing process according to claim 1, wherein, In step (6), it comprises the following steps: (6.1) By adjusting the parameters in the selective laser sintering additive manufacturing process, observe the microstructure evolution in the powder bed sintering process, including sintering neck, grain boundary migration, porosity, surface topography, grain shape, and density of microstructure characteristics; (6.2) According to the process of microstructure evolution, obtain the factors affecting the microstructure in the selective laser sintering additive manufacturing process.

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