An additive manufacturing gradient composition optimization method for materials with property differences based on thermodynamics and solidification models

Abstract

This invention discloses a gradient composition optimization method for additive manufacturing of materials with different physical properties based on thermodynamics and solidification models, belonging to the field of additive manufacturing and gradient material design. This method aims to solve the technical problems of excessive brittle phase formation and thermal stress cracking that often occur in existing empirical gradient composition designs. The method includes: determining the basic parameters of the starting and ending materials; calculating the volume fraction of the brittle phase using thermodynamic software, and using the brittle phase volume fraction as the core constraint to determine the initial composition range and candidate compositions; constructing a non-equilibrium solidification model, calculating the solidification characteristic parameters of the candidate compositions, and selecting a step-like gradient composition sequence based on parameter matching principles. By combining thermodynamic calculations with solidification theory models, this invention suppresses brittle phases at the source and ensures the continuity of solidification behavior, significantly reducing fabrication defects and providing scientific and reliable design guidance for gradient additive manufacturing of materials with different physical properties.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing technology and gradient material design, specifically involving a gradient composition optimization method for additive manufacturing of materials with different physical properties based on thermodynamic and solidification models. Background Technology

[0002] Additive manufacturing technology (also known as 3D printing technology), with its advantages of rapid prototyping, strong ability to manufacture complex structures, and high material utilization, has become one of the core technologies in the field of advanced manufacturing, and is widely used in aerospace, medical devices, and high-end equipment. Gradient materials, as a new type of functional material with continuous or stepwise changes in composition, structure, and properties, can achieve complementary advantages of different functional materials, effectively solving the problem that single materials cannot meet the comprehensive performance requirements under complex working conditions. Among them, the gradient combination of materials with large differences in physical properties can enable materials to possess multiple excellent properties such as high strength, high temperature resistance, high electrical conductivity, and high thermal conductivity, which has significant engineering application value.

[0003] However, materials with significant differences in core physical properties such as melting point, coefficient of thermal expansion, and elastic modulus are prone to a series of manufacturing defects during additive manufacturing gradient bonding, severely restricting their engineering applications. The main problems include: First, the uneven distribution of temperature and concentration fields in different composition regions during solidification easily induces the formation of a large number of brittle intermetallic compounds, leading to a sharp decrease in material toughness and even brittle fracture; second, the significant difference between the coefficient of thermal expansion and solidification shrinkage characteristics easily triggers uncontrollable thermal stress, resulting in stress concentration and subsequent defects such as cracks; third, current gradient composition design largely relies on empirical linear or exponential gradient settings, failing to fully integrate solidification theory and thermodynamic laws for scientific optimization, resulting in low manufacturing efficiency, poor yield, and difficulty in achieving stable engineering production.

[0004] In existing technologies, gradient composition design methods have significant shortcomings: some schemes only use simple composition gradient presets without considering the phase transformation characteristics and brittle phase precipitation rules during solidification, and cannot fundamentally avoid the excessive generation of brittle phases; many more schemes use experimental trial and error methods to conduct a large number of composition gradient design experiments across the entire range, which greatly increases the experimental cost and experimental cycle. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a gradient composition optimization method for additive manufacturing of materials with different physical properties based on thermodynamics and solidification models, so as to solve the problem that it is difficult to avoid the excessive generation of brittle phases in the design of gradient material composition in the prior art.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A gradient composition optimization method for additive manufacturing of materials with different physical properties based on thermodynamics and solidification models includes the following steps: S1. Based on the actual engineering application scenario, confirm the core performance indicators of the gradient material, and then determine the starting material and the ending material and the corresponding basic performance parameters; the starting material and the ending material are two or more metallic materials with a large difference in at least one performance parameter, including melting point, coefficient of linear expansion and elastic modulus. S2, using thermodynamic software, simultaneously performs equilibrium solidification calculations on the starting and ending materials to obtain phase equilibrium and solidification-related parameters; performs non-equilibrium solidification calculations to obtain the brittle phase volume fractions of the starting and ending materials with different proportions; uses the brittle phase volume fraction as the core constraint condition, combined with the composition undercooling auxiliary constraint condition, to obtain the preliminary composition design range, and then obtains candidate compositions. S3, based on solidification theory, constructs a non-equilibrium solidification model, combines phase equilibrium and solidification-related parameters, calculates solidification characteristic parameters, and uses solidification characteristic parameters as the basis for judgment to screen out a step-gradient component sequence with matching solidification characteristics from candidate components. S4. The verified gradient component sequence and the corresponding additive manufacturing process parameters are organized into a gradient component design scheme. In the gradient component design scheme, the content of the starting material gradually decreases from the starting material to the ending material in the gradient material.

[0007] A further improvement of the present invention is that: Preferably, the basic performance parameters include chemical composition, melting point, coefficient of thermal expansion, elastic modulus, density, and liquid phase density.

[0008] Preferably, in S2, the specific process of obtaining phase equilibrium and solidification-related parameters by performing equilibrium solidification calculations on the starting and ending materials using thermodynamic software is as follows: select an appropriate thermodynamic database according to the type of the target material system, and obtain phase equilibrium and solidification-related parameters by calculating using Thermo-Calc. The phase equilibrium and solidification-related parameters include the input element type, temperature range, and working pressure parameters.

[0009] Preferably, the temperature range is based on the melting point of the material with the highest melting point in the system, extending upwards by 100°C to 300°C to cover the liquid phase region, and downwards to room temperature.

[0010] Preferably, the non-equilibrium calculation process is as follows: the non-equilibrium solidification calculation uses the Scheil-Gulliver module, sets the additive manufacturing cooling rate, and obtains the phase precipitation sequence, the variation law of brittle phase formation with temperature and composition, and the degree of composition supercooling during the actual solidification process.

[0011] Preferably, the core constraint condition for the brittle phase volume fraction is that the brittle phase volume fraction is ≤5%; In the process of obtaining the preliminary composition design range, the brittle phase volume fraction data is superimposed with the composition undercooling data, and the composition points that do not meet the constraints are eliminated. Finally, the feasible composition range at each temperature is determined, and the preliminary composition design range is obtained.

[0012] Preferably, the non-equilibrium solidification model is a non-equilibrium solidification model based on the Scheil equation, which describes the dynamic change law of solute redistribution and solid fraction through the relationship between solid fraction and temperature.

[0013] Preferably, the solidification characteristic parameters include the solid fraction curve, solidification shrinkage rate, and solid-liquid two-phase region width; the solid fraction curve is obtained by numerically solving the solidification model by inputting phase equilibrium and solidification-related parameters; the solidification shrinkage rate is calculated based on the solid fraction curve and material density data; the solid-liquid two-phase region width is calculated by the difference between the liquidus temperature and the solidus temperature.

[0014] Preferably, the number of gradient layers in the stepped gradient component sequence is 5 to 15, the gradient of the main element content change between adjacent layers is 5% to 15%, and a small gradient change of 5% to 8% is used in the brittle phase sensitive range.

[0015] Preferably, between S3 and S4, the solidification characteristic matching degree of the selected step gradient component sequence is verified. If the preset matching standard is met, the optimized gradient component sequence is output; if not, the process returns to S3 to adjust the number of gradient layers or component gradients and then recombines them for verification.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a gradient composition optimization method for additive manufacturing of materials with significant property differences, based on thermodynamics and solidification models. This method is a gradient composition design approach for additive manufacturing of materials with large property differences, based on solidification theory, models, and thermodynamic calculations. Using solidification theory as its core and combining Thermo-Calc thermodynamic calculation technology, it accurately determines the composition range without a large amount of brittle phase. By establishing a solidification model and optimizing and screening composition sequences with matching solidification characteristics, it achieves the scientific gradient design of materials with large property differences. This theoretically solves the problems of excessive brittle phase formation and stress concentration, improving the preparation quality and yield of gradient materials, and providing a reliable design basis for additive manufacturing experiments and engineering applications. This method is applicable to the preparation of gradient materials in metallic material systems with large property differences and can be widely used in aerospace, electronic packaging, high-end equipment, and other fields with high requirements for comprehensive material performance. This method can precisely control the formation of brittle phases and match solidification characteristics to reduce stress concentration, providing scientific guidance for the additive manufacturing of materials with large property differences. The method of this invention has the following advantages: (1) Achieve synergistic optimization of solidification theory and thermodynamic calculation: Taking solidification theory as the core and combining it with Thermo-Calc high-precision thermodynamic calculation, accurately control the precipitation law of brittle phase and solidification characteristic parameters, realize the scientific design of gradient composition from the theoretical level. Compared with the existing empirical design methods, it significantly improves the scientificity and reliability of the design and effectively avoids the cost waste caused by blind experimentation.

[0017] (2) Precise control of preparation defects: Thermo-Calc calculations clearly define the composition range without a large amount of brittle phase, suppressing the excessive generation of brittle phase from the source; the composition sequence with matching solidification characteristics is optimized and screened through solidification model, which increases the consideration of transition continuity. It ensures that the solidification behavior (shrinkage rate, size of solidified paste area) of each layer is smoothly transitioned in the process of printing gradient material from A to B, rather than abruptly, ensuring the continuity of solidification shrinkage and two-phase area width during gradient transition, reducing thermal stress concentration, avoiding defects such as cracks, and greatly improving the preparation quality and yield of gradient material.

[0018] (3) It is highly versatile and provides excellent guidance: It is applicable to a variety of metal material systems with large differences in physical properties. It clarifies the specific parameters and operation procedures for thermodynamic calculation and solidification model construction. The output design scheme includes detailed composition sequence and process parameters, which can directly guide additive manufacturing experiments and engineering applications, reduce R&D cycle and production costs, and has broad promotion value. Attached Figure Description

[0019] Figure 1 This is an overall flowchart of the gradient composition design method for additive manufacturing of materials with large physical property differences based on thermodynamic calculations and solidification models, as presented in this invention. Figure 2 The Thermo-Calc phase diagram of the Ti-Ni system (TC4-IN625) in Example 1 is shown. The horizontal axis represents the mass fraction of Ni (wt%), and the vertical axis represents the temperature (°C).

[0020] Figure 3 The Thermo-Calc phase diagram for the Ti-Cu system (TC4-Cu) is shown. The horizontal axis represents the mass fraction of Cu (wt%), and the vertical axis represents the temperature (°C).

[0021] Figure 4 The graph shows the volume fraction of precipitated phases in TC4 materials with 20%-50% Cu added, calculated based on the Scheil equation, as a function of temperature. The horizontal axis represents temperature (°C), and the vertical axis represents the volume fraction of precipitated phases, illustrating the variation of different precipitated phases with temperature.

[0022] Figure 5A schematic diagram of the gradient material composition is provided, with each gradient layer having different compositions and process parameters, providing an intuitive structural reference for additive manufacturing experiments. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings: To enable those skilled in the art to understand the features and effects of the present invention, the terms and expressions used in the specification and claims are explained and defined in general below. Unless otherwise specified, all technical and scientific terms used herein have the ordinary meaning understood by those skilled in the art regarding the present invention, and in case of conflict, the definitions in this specification shall prevail.

[0024] In this article, unless otherwise specified, “contains,” “includes,” “contains,” “has,” or similar terms cover the meanings of “composed of” and “mainly composed of”. For example, “A contains a” covers the meanings of “A contains a and others” and “A contains only a”.

[0025] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0026] The following examples use instruments and equipment conventional in the art. Experimental methods in the following examples, unless otherwise specified, are generally performed under conventional conditions or as recommended by the manufacturer. All raw materials used in the following examples are conventional commercially available products with specifications conventional in the art. In this specification and the following examples, unless otherwise specified, "%" refers to weight percentage, "parts" refers to parts by weight, and "ratio" refers to weight proportion.

[0027] A gradient composition design method for additive manufacturing of materials with large property differences based on thermodynamic calculations and solidification models includes the following steps: S1, Define the application requirement parameters and determine the basic information of the gradient system. First, based on the actual engineering application scenario, the core performance indicators that the gradient materials must meet are clearly defined, including but not limited to mechanical strength, temperature resistance, electrical conductivity, and corrosion resistance. Simultaneously, the starting and ending materials of the gradient transition range are determined, limiting them to two or more metallic materials where at least one performance parameter difference exceeds a set threshold. These performance parameters include melting point, coefficient of linear expansion, and elastic modulus. The performance parameter difference between the starting and ending materials is defined as a melting point difference ≥ 300℃ and a coefficient of linear expansion difference ≥ 5 × 10⁻⁶. -6At least one of the following conditions must be significantly different: / ℃, elastic modulus difference ≥50GPa. Comprehensive collection of basic performance parameters of the starting and ending materials, including specific chemical composition, melting point, coefficient of thermal expansion, elastic modulus, density, and liquid phase density, is required to provide fundamental data support for subsequent thermodynamic and solidification model calculations.

[0028] S2, Determination of the composition range of the absence of a large number of brittle phases based on thermodynamic calculations. A refined thermodynamic analysis of the target material system was conducted using the thermodynamic calculation software Thermo-Calc. This accurately obtained phase equilibrium and solidification-related parameters, clarified the compositional range without a large amount of brittle phases, and provided reliable thermodynamic data support for subsequent solidification model optimization. The specific process is as follows: (1) Database selection: Based on the type of the target material system, select a high-precision thermodynamic database that is compatible with Thermo-Calc software to ensure that the database contains the interaction parameters and phase equilibrium data of all elements in the system. The phase diagram calculation accuracy error is ≤5℃, which can accurately characterize the phase equilibrium relationship of different material systems and ensure the reliability and accuracy of the calculation results.

[0029] (2) Calculation parameter setting: The calculation parameters include the specific element types, temperature range, and working pressure of the material. The input element types are the main alloying elements and trace impurity elements of the starting and ending materials. The starting material is set as material A and the ending material is set as material B. The mass fraction range of each element in the two types of materials is specified, and impurity elements (O, N, etc.) with a mass fraction ≤0.05% are also included. The thermodynamic parameters of the impurity elements are directly retrieved from the database. The temperature range is based on the melting point of the material with the highest melting point in the system, and is extended upward by 100°C to 300°C to cover the complete liquid phase region, and downward to room temperature (25°C) to include the room temperature equilibrium phase, ensuring complete coverage of the temperature range of the entire solidification process. The pressure setting adopts standard atmospheric pressure (101.325 kPa), which is consistent with the environmental pressure of conventional additive manufacturing (such as laser selective melting and electron beam melting) to avoid the influence of pressure on phase equilibrium.

[0030] (3) Equilibrium and non-equilibrium solidification calculations: Specifically, in the equilibrium solidification calculation process, the compositions of materials A and B are first input, and the equilibrium calculation module of Thermo-Calc is used with the calculation step size set to 10℃. By solving the Gibbs free energy minimization equation, the equilibrium phase diagram, liquidus temperature TL, solidus temperature TS, eutectic reaction temperature TE, and phase composition and content at each temperature of the material system are obtained, clarifying the basic phase transformation law of the system and providing basic parameters for the subsequent solidification model.

[0031] Furthermore, during the solution process, when calculating the equilibrium phase diagram, the principal elements in materials A and B are selected to draw the binary phase diagram, where the principal elements are elements with a percentage content > 50% in the materials; even further, if there are ≥ 2 principal elements in the materials, then a ternary phase diagram or a quaternary phase diagram can be drawn according to the content of the principal elements in the two materials.

[0032] Specifically, in the non-equilibrium solidification calculation process, the Scheil-Gulliver module is used. This module assumes that the solid phase has no diffusion and the liquid phase has limited diffusion, which is consistent with the rapid cooling process characteristics of additive manufacturing. During the calculation, all elements are considered, and a typical laser additive manufacturing cooling rate is set to obtain the phase precipitation sequence, the variation law of brittle phase formation with temperature and composition, and the degree of compositional supercooling in the actual solidification process. The focus is on calculating the evolution curve of the volume fraction of brittle phase with temperature under different material A and material B ratios.

[0033] (4) Screening of feasible components, using core constraints as auxiliary constraints as common screening conditions.

[0034] Specifically, the core constraint is that the volume fraction of brittle phase is ≤5% during thermodynamic calculations, which is controlled within an acceptable range for engineering applications.

[0035] The process of determining the auxiliary constraints is as follows: combining the requirements for compositional undercooling stability, and using the formula... calculate( The slope of the liquidus line is calculated using Thermo-Calc. As the initial components; This is the solute partition coefficient; (For liquid-phase equilibrium composition), undercooling of the composition >150℃ can easily lead to dendritic segregation and solidification cracks. Therefore, the undercooling of the composition is limited to a reasonable range to avoid solidification defects.

[0036] The brittle phase volume fraction data obtained from non-equilibrium solidification calculations are superimposed with the composition undercooling data. Composition points that do not meet the constraints are eliminated, and finally, the feasible composition range at each temperature is determined, forming a preliminary composition design interval and obtaining candidate compositions.

[0037] S3, Based on solidification theory, a model was established to optimize and screen component sequences that match solidification characteristics. A non-equilibrium solidification model is constructed based on the Scheil equation, combined with the thermodynamic parameters obtained in step S2 ( , , (etc.), quantitatively calculate the solidification characteristic parameters of each candidate component, and screen the gradient component sequence through solidification characteristic matching criteria to ensure the continuity of solidification behavior during the gradient transition and reduce the generation of thermal stress. The specific process is as follows: A non-equilibrium solidification model is established based on solidification theory. Using the thermodynamic parameters obtained in step S2, the solidification characteristics of candidate components within the initial composition range are analyzed to screen out gradient component sequences with matching solidification characteristics. The specific process is as follows: (1) Solidification Model Construction: A non-equilibrium solidification model based on the core equation of solidification theory is adopted. This model can accurately describe the dynamic changes in solute redistribution and solid fraction during the rapid cooling process of additive manufacturing. Its core calculation formula is:

[0038] in, The solid fraction, The instantaneous temperature during the solidification process. The solute partition coefficient (obtained from the thermodynamic calculations in step S2, calculated using the Phase Equilibrium module of Thermo-Calc based on the composition ratio of the solid and liquid phases in the phase diagram). Liquidus temperature The solidus temperature is denoted as α. The core advantage of this formula is that it can accurately predict the evolution of the solid fraction under rapid cooling conditions, which is highly consistent with the actual solidification behavior of additive manufacturing.

[0039] (2) Calculation of solidification characteristic parameters, including solid fraction curve, solidification shrinkage rate and solid-liquid two-phase region width.

[0040] Specifically, the solid fraction curve is calculated by taking the solid fraction curves of each candidate component obtained in step S2. , , Inputting parameters such as values ​​into the solidification model, the solid fractions corresponding to different candidate components are obtained through numerical solutions. With temperature The curve shows the change in solidification rate; the slope of the curve reflects the solidification rate, and the larger the slope, the faster the solidification. Calculation of solidification shrinkage rate: based on - The curve and the density data of the material are expressed through the formula. Calculate the solidification shrinkage rate, where For liquid phase volume, For solid volume, , ( For material quality, The density of the liquid phase is... The solid density was calculated using the Density module of Thermo-Calc. Calculation of the width of the solid-liquid two-phase region: through Calculations show that the width of the two-phase region directly affects the stability of the solidification process. An excessively wide two-phase region can easily lead to the accumulation of solidification stress, while an excessively narrow region can easily lead to insufficient solidification of the liquid phase. It is a key indicator for matching solidification characteristics.

[0041] (3) After calculating and obtaining the solidification characteristic parameters, the component sequence is screened: the solidification characteristic matching criteria are based on the fact that the difference in solidification shrinkage rate and the difference in the width of the solid-liquid two-phase region between adjacent gradient layers simultaneously meet the preset matching range. This ensures that the solidification characteristics are controlled within the preset matching range. Component points that meet the conditions are screened from the preliminary component intervals to form a stepped gradient component sequence. It should be understood that in the stepped gradient component sequence, from material A to material B, the content of material A gradually decreases, and the content of material B gradually increases.

[0042] The number of gradient layers is set to 5-15 layers according to actual application needs and performance requirements, and the gradient of the main element content change between adjacent layers is controlled at 5%-15%. For the sensitive range of brittle phase, a small gradient change of 5%-8% is adopted to further reduce the risk of brittle phase formation and improve the continuity and stability of gradient transition.

[0043] Furthermore, in this process, if during the solidification simulation, it is found that the candidate component has a risk of local brittle phase aggregation and is prone to precipitation of brittle phase, then the corresponding candidate component is removed.

[0044] In this process, when forming a stepped gradient component sequence, the solidification characteristic matching criteria for each layer are to be determined by using the difference in solidification shrinkage rate and the difference in solid-liquid two-phase region width between adjacent gradient layers as the same as the preset matching range. During the component selection process, each layer has several candidate components to choose from.

[0045] Generally, the selection and judgment of the component sequence is carried out layer by layer from one material to another. If a certain layer partially meets the requirements during the selection process, the selection and adjustment of the components in the first 2 to 5 layers are carried out again. For example, during the selection process, it is difficult for the components in the Nth layer and the (N-1)th layer to meet the two requirements at the same time. Therefore, the selection of the components in the N-5th layer is carried out again starting from the (N-5)th layer. The component change gradient from the (N-6)th layer to the (N-5)th layer is adjusted, the components in the N-5th layer are changed, and then the components in the N-4th layer and so on are changed.

[0046] Furthermore, a comprehensive verification of the solidification property matching degree is performed on all gradient component sequences obtained in step S3. The difference in solidification shrinkage rate and the difference in solid-liquid two-phase region width between adjacent gradient layers are checked one by one to ensure they meet the judgment criteria. The process is then reconfirmed to confirm whether any steps in the above process were incorrectly adjusted. If any adjacent layer does not meet the matching requirements, step S3 is returned to adjust the selection of candidate components or the gradient interval (e.g., increasing the number of gradient layers or decreasing the gradient of component change between adjacent layers), and the solidification property parameters are recalculated and screened. If all adjacent layers meet the matching requirements, the component sequence is determined to be an optimized feasible gradient component sequence. This verification and optimization step ensures the continuity of solidification properties during the gradient transition, fundamentally reducing thermal stress concentration caused by abrupt changes in solidification properties.

[0047] Step S5: Design scheme for output gradient components The optimized gradient composition sequence and corresponding additive manufacturing process parameters were compiled into a complete gradient composition design scheme. The process parameters include laser power, scanning speed, layer thickness, and scanning strategy, and must be optimized synchronously according to the compositional characteristics of each gradient layer—higher laser power is used in high-melting-point component regions to ensure sufficient melting, while moderate scanning speeds are used in component regions near the brittle phase-sensitive area to control the cooling rate and avoid excessive formation of brittle phases. The number of gradient layers, the specific chemical composition of each layer (mass fraction of each element), and the corresponding process parameters for each layer were standardized and organized to form a design scheme that can directly guide experimental and engineering applications.

[0048] Figure 1The overall flowchart of the method clearly presents the complete logical link and step connection relationship of the method of the present invention. The specific description of each step is as follows: First, step S1 is started to clarify the application requirements and basic information of the gradient system, and to comprehensively collect basic parameters such as chemical composition, melting point, and density of the starting and ending materials to provide data support for subsequent calculations. After completing S1, step S2 thermodynamic calculation is started. This step is divided into four progressive sub-steps: First, an appropriate database is selected, and different high-precision databases are selected according to the material system; then, element, temperature, and pressure parameters are set, alloy element and impurity content are accurately entered, and the temperature range and standard atmospheric pressure covering the complete solidification range are set; then, equilibrium and non-equilibrium solidification calculations are performed, and basic parameters such as equilibrium phase diagrams are obtained through the Equilibrium module, and the phase precipitation law under rapid cooling conditions of additive manufacturing is simulated through the Scheil-Gulliver module; finally, the range of components without a large amount of brittle phase is screened, and the preliminary feasible composition range is determined based on constraints such as the volume fraction of brittle phase. After step S2 is completed, proceed to step S3. Optimize and screen the solidification model by calculating solidification shrinkage rate, two-phase region width, etc., quantify solidification characteristic parameters, and select gradient sequences with matching solidification characteristics between adjacent layers. Step S4 verifies the component sequence matching degree. Each selected sequence is checked individually. If all adjacent layers meet the matching requirements, proceed to step S5 to output the gradient component design scheme; otherwise, return to S3 to recalculate and optimize. Step S5 outputs a complete scheme including the number of gradient layers, the composition of each layer, and supporting process parameters, ultimately used to guide additive manufacturing experiments and engineering applications.

[0049] The following description, in conjunction with specific embodiments, provides further details.

[0050] Example 1: Gradient composition design of Ti-Ni system (TC4-IN625) This embodiment focuses on a Ti-Ni gradient material for aero-engine blades. This material needs to combine the high strength of TC4 with the high-temperature resistance of IN625. The starting and ending materials are TC4 titanium alloy (composition: Ti-6Al-4V, mass fraction) and IN625 nickel-based superalloy (composition: Ni-21Cr-9Mo-3.6Nb, mass fraction). The differences in their physical properties are: melting point difference of approximately 370℃ and linear expansion coefficient difference of approximately 6.2 × 10⁻⁶. -6 The temperature difference is approximately 55°C, and the elastic modulus difference is about 55 GPa, classifying it as a typical material with large property differences. The gradient composition design method of this invention is performed using the following specific steps: S1. Define application requirements and basic information: Core performance indicators are room temperature tensile strength ≥800MPa, high temperature (600℃) tensile strength ≥500MPa, and fracture toughness ≥40MPa·m. 1 / 2The gradient transition range was determined to be TC4→IN625, and basic performance parameters were collected: TC4 melting point 1660℃, solid density 4.5 g / cm³. 3 The liquid phase density is 4.1 g / cm³. 3 Elastic modulus 110 GPa; IN625 melting point 1290℃, solid density 8.4 g / cm³ 3 The liquid phase density is 7.9 g / cm³. 3 The elastic modulus is 165 GPa, providing data support for subsequent calculations.

[0051] S2. Thermo-Calc thermodynamic calculations: In this embodiment, a refined thermodynamic analysis was performed using Thermo-Calc software. The specific operation procedure is as follows: S21. The TTNi8 database of Thermo-Calc software is selected. This database contains complete thermodynamic parameters of elements such as Ti, Ni, Al, V, Cr, Mo, and Nb, which can accurately calculate the phase equilibrium and solidification characteristics of the Ti-Ni system.

[0052] S22. Input elements and parameters: The main elements are Ti, Al, V, Ni, Cr, Mo, and Nb. The mass fraction of each element matches the composition range of TC4 and IN625, specifically Ti (90%-31.4%), Al (6%), V (4%), Ni (0%-58%), Cr (0%-21%), Mo (0%-9%), and Nb (0%-3.6%). The mass fraction of impurity elements O and N is ≤0.05%. Set the temperature range (25℃-1860℃) covering the complete solidification range and the environmental pressure of conventional additive manufacturing, and set a reasonable calculation step size.

[0053] S23. Equilibrium and Non-equilibrium Calculations: ① Equilibrium Calculations: Obtain the equilibrium phase diagram of the Ti-Ni system using the Equilibrium module ( Figure 2 ), and the fitting yielded the relationship between Ni content and , Relationship equation: ( (Ni mass fraction) Eutectic reaction temperature ≈984℃, corresponding to a eutectic composition of Ni: 49%; ② Non-equilibrium calculation: Using the Scheil-Gulliver module, a typical additive manufacturing cooling rate was set to obtain the curves showing the change in the amount of brittle phases such as Ti2Ni as a function of Ni content. Based on the obtained data ( Figure 2 Determine a feasible range of compositions that do not contain a large amount of brittle phases.

[0054] Specifically, the feasible composition range for the TC4 side is a Ni mass fraction of 0%-22%; the feasible composition range for the IN625 side is a Ni mass fraction of 45%-58%; and a Ni content of 22%-45% is a brittle phase sensitive region.

[0055] S24. Screening feasible composition range: Combining the constraints of brittle phase and compositional undercooling, the feasible composition range covering TC4 to IN625 is calculated, and the core feasible range and transitional feasible range are divided.

[0056] Among these, when the Ni mass fraction is between 0% and 22%, the brittle phase (Ti₂Ni) volume fraction is <3%, and the compositional undercooling is <120℃, fully satisfying both constraints, constituting core feasible region 1, where a conventional compositional gradient of 8% to 15% can be used. When the Ni mass fraction is between 22% and 45%, the brittle phase volume fraction is 5% to 25%, and the compositional undercooling is 150℃ to 280℃, exceeding the constraint critical value, belonging to the transitional feasible region, requiring a minimal gradient of 5% to 8%. Among these, when the Ni mass fraction is between 30% and 40%, the Ti₂Ni phase volume fraction reaches as high as 25%, and the compositional undercooling reaches 276℃, belonging to the high-risk core sensitive region, requiring a minimum gradient transition. When the Ni mass fraction is between 45% and 58%, the brittle phase volume fraction is <4%, and the compositional undercooling is <130℃, fully satisfying both constraints, constituting core feasible region 2, where a conventional compositional gradient of 8% to 15% can be used.

[0057] S3. Solidification model optimization and screening: S31. Construct a non-equilibrium solidification model based on the Scheil equation. The core calculation formula is as follows:

[0058] Input the thermodynamic parameters such as solute partition coefficient obtained from Thermo-Calc calculation.

[0059] S32. Calculate solidification characteristic parameters: Input the thermodynamic parameters of multiple candidate components within the feasible composition range into the solidification model for calculation, obtain the solid fraction variation curve with temperature through numerical solution, and calculate the solidification shrinkage rate and solid-liquid two-phase region width of each candidate component based on the curve and material density data.

[0060] The solid-liquid two-phase region width of the key candidate components ranged from 35℃ to 138℃, with solidification shrinkage rates ranging from 7.2% to 10.1%. Specifically, for Ni mass fractions of 0%, 10%, 20%, 27%, 33%, 38%, 43%, 50%, 54%, and 58%, the solid-liquid two-phase region width ΔT was 40℃, 52℃, 65℃, 88℃, 125℃, 138℃, 92℃, 55℃, 45℃, and 35℃, respectively, and the solidification shrinkage rates ΔV were 7.2%, 7.6%, 8.1%, 8.7%, 9.8%, 10.1%, 9.3%, 8.3%, 7.9%, and 7.5%, respectively.

[0061] S33. Screening of Component Sequences: The matching criteria were set as follows: the difference in solidification shrinkage rate between adjacent layers ≤2% and the difference in the width of the solid-liquid two-phase region ≤50℃. Combined with the matching rules of solidification characteristics, a step-gradient component sequence was screened and determined layer by layer from the core feasible region of Ni mass fraction 0%~22% and 45%~58% and the brittle phase sensitive region of 22%~45%. Smaller gradient changes were used in the brittle phase sensitive region to improve transition stability. Specifically, a conventional component gradient of 5%~15% was used in the core feasible region, and a smaller gradient change of 5%~8% was used in the brittle phase sensitive region. Finally, 10 gradient sequences with Ni mass fractions of 0%, 10%, 20%, 27%, 33%, 38%, 43%, 50%, 54%, and 58% were obtained. The parameter differences between all adjacent layers met the matching criteria, thus improving the gradient transition stability.

[0062] Specifically, the differences in the solid-liquid two-phase region widths of all adjacent layers are 12℃, 13℃, 23℃, 37℃, 13℃, 46℃, 37℃, 10℃, and 10℃, respectively, and the differences in solidification shrinkage rates of adjacent layers are 0.4%, 0.5%, 0.6%, 1.1%, 0.3%, 0.8%, 1.0%, 0.4%, and 0.4%, respectively.

[0063] S4. Matching verification: Check the matching of adjacent layers one by one. If all adjacent layers meet the matching criteria, the sequence is determined to be a feasible gradient component sequence.

[0064] S5. Output Design Scheme: Clearly define the number of gradient layers and the specific components of each layer (mass fraction of each element), forming a structure as follows: Figure 5The layered gradient material structure design shown optimizes the additive manufacturing process parameters according to the composition characteristics of each gradient layer. For example, in the TC4 region: laser power 155W, scanning speed 1200mm / s; in the low-to-medium Ni625 region: power 180W, speed 1100mm / s; in the high-IN625 region: power 205W, speed 1000mm / s; and in the pure IN625 region: power 225W, speed 1000mm / s. The layer thickness is 30μm, the scanning spacing is 80μm, and the scanning strategy adopts strip scanning with interlayer rotation of 66.7° to ensure uniform forming.

[0065] The design scheme was used to conduct experimental verification of selective laser melting (SLM) additive manufacturing. The prepared Ti-Ni gradient material must meet relevant requirements, such as the volume fraction of the brittle phase of Ti2Ni, tensile strength, and absence of defects such as cracks, so as to fully meet the application requirements of aero-engine blades.

[0066] Example 2: Gradient composition design of Ti-Cu system (TC4-Cu) This embodiment targets Ti-Cu thermally conductive gradient materials for electronic packaging, requiring the combination of the high strength of TC4 and the high thermal conductivity of pure Cu. The starting and ending materials are TC4 titanium alloy and pure Cu, with the following differences in physical properties: melting point difference of approximately 680℃ and linear expansion coefficient difference of approximately 12.5 × 10⁻⁶. -6 The temperature difference is approximately 80 GPa, indicating a large difference in elastic modulus, classifying it as a material with significant property variations. The method of this invention is used to design gradient compositions, with the following steps: S1. Application Requirements and Basic Information: Core performance indicators are: room temperature thermal conductivity ≥150W / (m·K), tensile strength ≥600MPa, and no obvious brittle phase; gradient transition range TC4→pure Cu; basic parameters: TC4 melting point 1660℃, solid density 4.5g / cm³. 3 The liquid phase density is 4.1 g / cm³. 3 Thermal conductivity 6.7 W / (m·K); pure Cu melting point 980℃, solid density 8.9 g / cm³ 3 The liquid phase density is 8.5 g / cm³. 3 Thermal conductivity 401 W / (m·K).

[0067] S2. Thermo-Calc thermodynamic calculations: The TTTi6 database was selected, with input elements Ti, Al, V, and Cu, and impurity elements O and N ≤ 0.05%. A temperature range covering the entire solidification range was set. Equilibrium and non-equilibrium calculations were performed. Figure 3 , Figure 4 The main brittle phases are TiCu and Ti2Cu, and their formation rules are clarified. Feasible composition ranges without a large number of brittle phases are screened out, and the core feasible range and transitional feasible range are divided.

[0068] Similar to Example 1, in this system, the core feasible region is 0%-15% and 85%-100% Cu by mass, and the transition feasible region is 15%-85% Cu by mass.

[0069] S3. Solidification model optimization and screening: A solidification model based on the Scheil equation is constructed, and its core calculation formula is as follows:

[0070] Input the thermodynamic parameters, such as the solute partition coefficient, obtained from Thermo-Calc calculations. Combine with... Figure 3 , Figure 4 The evolution law of solid fraction of each candidate component is calculated, and then the solidification shrinkage rate and solid-liquid two-phase region width are obtained. According to the relevant solidification characteristic matching requirements, the step gradient component sequence that meets the conditions is screened out. Smaller gradient changes are used in the brittle phase sensitive region to improve stability.

[0071] Similar to Example 1, a stepwise gradient composition sequence with Cu mass fractions of 0%, 10%, 18%, 25%, 32%, 40%, 50%, 65%, 80%, and 100% was selected, with matching requirements of a solidification shrinkage rate difference of ≤2% between adjacent layers and a solid-liquid two-phase region width difference of ≤50℃. Small gradient changes of 5% to 8% were used in the brittle phase sensitive range of 15% to 85% Cu mass fraction to improve gradient transition stability. Specifically, the solid-liquid two-phase region width difference between adjacent layers was 17℃, 33℃, 43℃, 24℃, 8℃, 25℃, 43℃, 34℃, and 30℃ for Cu mass fractions of 0%, 10%, 18%, 25%, 32%, 40%, 50%, 65%, 80%, and 100%, respectively, and the shrinkage rate difference between adjacent layers was 0.5%, 0.8%, 1.1%, 1.3%, 0.3%, 0.6%, 1.1%, 1.3%, and 0.7%, respectively.

[0072] S4. Matching verification: Check the matching of adjacent layers one by one, and continuously adjust the relevant parameters to ensure that all adjacent layers meet the solidification characteristic matching standard.

[0073] S5. Output Scheme: Forming as follows Figure 5The layered gradient material structure shown clearly defines the composition sequence of each layer. Based on the composition characteristics of each gradient layer, the matching additive manufacturing process parameters are optimized (TC4 region: laser power 155W, speed 1200mm / s; low Cu region: power 175W, speed 900mm / s; medium Cu region: power 225W, speed 800mm / s; high copper region: power 300W, speed 600mm / s; pure Cu region: power 350W, speed 400mm / s; layer thickness is 20μm, scanning spacing is 80μm, the scanning strategy for high Cu and pure Cu regions adopts checkerboard scanning, and other regions adopt strip scanning with interlayer rotation of 66.7° to ensure uniform forming).

[0074] Experiments have verified that the prepared Ti-Cu gradient material meets the relevant performance indicators and can satisfy application requirements.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for additive manufacturing gradient composition optimization of materials with property differences based on thermodynamics and solidification models, characterized in that, Includes the following steps: S1. Based on the actual engineering application scenario, confirm the core performance indicators of the gradient material, and then determine the starting material and the ending material and the corresponding basic performance parameters; the starting material and the ending material are two or more metallic materials with a large difference in at least one performance parameter, including melting point, coefficient of linear expansion and elastic modulus. S2, using thermodynamic software, simultaneously performs equilibrium solidification calculations on the starting and ending materials to obtain phase equilibrium and solidification-related parameters; performs non-equilibrium solidification calculations to obtain the brittle phase volume fractions of the starting and ending materials with different proportions; uses the brittle phase volume fraction as the core constraint condition, combined with the composition undercooling auxiliary constraint condition, to obtain the preliminary composition design range, and then obtains candidate compositions. S3, based on solidification theory, constructs a non-equilibrium solidification model, combines phase equilibrium and solidification-related parameters, calculates solidification characteristic parameters, and uses solidification characteristic parameters as the basis for judgment to screen out a step-gradient component sequence with matching solidification characteristics from candidate components. S4. The verified gradient component sequence and the corresponding additive manufacturing process parameters are organized into a gradient component design scheme. In the gradient component design scheme, the content of the starting material gradually decreases from the starting material to the ending material in the gradient material.

2. The method according to claim 1, characterized in that, Basic performance parameters include chemical composition, melting point, coefficient of thermal expansion, elastic modulus, density, and liquid phase density.

3. The method according to claim 1, characterized in that, In S2, the specific process of obtaining phase equilibrium and solidification related parameters by performing equilibrium solidification calculations on the starting and ending materials using thermodynamic software is as follows: Select an appropriate thermodynamic database according to the type of the target material system, and obtain phase equilibrium and solidification related parameters by calculating Thermo-Calc. The phase equilibrium and solidification related parameters include the type of input element, temperature range, and working pressure parameters.

4. The method according to claim 3, characterized in that, The temperature range is based on the melting point of the material with the highest melting point in the system, extending upwards by 100°C to 300°C to cover the complete liquid phase region, and downwards to room temperature.

5. The method according to claim 3, characterized in that, The non-equilibrium calculation process is as follows: the non-equilibrium solidification calculation uses the Scheil-Gulliver module, sets the additive manufacturing cooling rate, and obtains the phase precipitation sequence, the variation law of brittle phase formation with temperature and composition, and the degree of composition supercooling during the actual solidification process.

6. The method according to claim 1, characterized in that, The core constraint for the volume fraction of the brittle phase is that the volume fraction of the brittle phase is ≤5%. In the process of obtaining the preliminary composition design range, the brittle phase volume fraction data is superimposed with the composition undercooling data, and the composition points that do not meet the constraints are eliminated. Finally, the feasible composition range at each temperature is determined, and the preliminary composition design range is obtained.

7. The method according to claim 1, characterized in that, The non-equilibrium solidification model is based on the Scheil equation and describes the dynamic changes of solute redistribution and solid fraction through the relationship between solid fraction and temperature.

8. The method according to claim 1, characterized in that, Solidification characteristic parameters include solid fraction curve, solidification shrinkage rate, and solid-liquid two-phase region width; the solid fraction curve is obtained by numerically solving the solidification model by inputting phase equilibrium and solidification-related parameters; the solidification shrinkage rate is calculated based on the solid fraction curve and material density data; the solid-liquid two-phase region width is calculated by the difference between the liquidus temperature and the solidus temperature.

9. The method according to claim 1, characterized in that, The stepped gradient component sequence has 5 to 15 gradient layers, with the main element content of adjacent layers varying by 5% to 15%, and a small gradient variation of 5% to 8% used in the brittle phase sensitive region.

10. The method according to claim 1, characterized in that, Between S3 and S4, the solidification characteristic matching degree of the selected step gradient component sequence is verified. If the preset matching standard is met, the optimized gradient component sequence is output; otherwise, the process returns to S3 to adjust the number of gradient layers or component gradients and then recombines them for verification.

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