Inversion analysis method and device of material mechanics constitutive and electronic equipment

Abstract

The invention relates to the technical field of material micro-area mechanical property testing, and discloses a material mechanical constitutive inversion analysis method and device and electronic device.The method comprises the steps that a nanoindentation test is conducted on a to-be-tested material, and an average load-depth curve is obtained; extracting inversion input parameters based on the average load-depth curve; constructing a dimensionless function based on dimensional analysis and a characteristic strain method, fitting the dimensionless function, and establishing a Ludwick constitutive inversion model; and on the basis of the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are solved, the multiple mechanical constitutive parameters of the material can be directly and uniquely inverted, and the experiment complexity and cost are remarkably reduced while the accuracy and uniqueness of the inversion result are guaranteed.

Description

Technical Field

[0001] This invention relates to the field of micro-region mechanical property testing technology for materials, specifically to inversion analysis methods, devices, and electronic equipment for material mechanical constitutive models. Background Technology

[0002] Ti2AlNb alloys combine the high thermal strength of nickel-based superalloys with the low density of titanium alloys, making them promising candidates for applications in high-temperature components such as aero-engine casings. In practical manufacturing, welding is often used to reduce forming difficulty. However, welded casings suffer from uneven microstructure and mechanical properties at the weld joint, leading to unreliable results for the overall elastic modulus and strength of the weld joint obtained using traditional testing methods (such as uniaxial tensile testing), thus affecting the strength evaluation of the casing. In other words, for advanced alloys like Ti2AlNb, especially their welded joints, the uneven microstructure results in insufficient reliability of traditional "integral" uniaxial tensile testing, failing to characterize micro-area properties.

[0003] While nanoindentation is suitable for micro-area testing, its inversion analysis presents challenges. Current mainstream research focuses on the Hollomon power-law hardening model with fewer parameters (only two), which cannot accurately describe complex materials (such as Ti2AlNb alloys). Although some studies have attempted to invert the Ludwick hardening model with more parameters (e.g., three), the methods employed (such as those based on spherical indenters and requiring extensive data point fitting) result in high experimental costs, complex procedures, large errors in the inversion results (>15%), and difficulty in guaranteeing uniqueness.

[0004] Therefore, there is an urgent need for an analytical method that can conveniently, accurately, and uniquely invert and obtain multiple plasticity parameters of the Ludwick hardening model of materials. Summary of the Invention

[0005] This invention provides a method, apparatus, and electronic device for inversion analysis of material mechanical constitutive models, in order to solve the problems of complex process, large error in inversion results, and difficulty in obtaining multiple plasticity parameters in the existing Ludwick hardening model inversion method.

[0006] In a first aspect, the present invention provides an inversion analysis method for the constitutive model of materials mechanics, the method comprising: Nanoindentation tests were performed on the test material to obtain the average load-depth curve; Based on the average load-depth curve, inversion input parameters are extracted; Based on dimensional analysis and characteristic strain method, a dimensionless function is constructed and fitted to establish the Ludwick constitutive inversion model. Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained by solving.

[0007] This invention provides an inversion analysis method for the constitutive model of materials. By combining dimensional analysis and the characteristic strain method, a closed dimensionless function system suitable for the three-parameter Ludwick hardening model is constructed. Only by obtaining the average load-depth curve through conventional nanoindentation tests and extracting a few key response parameters, multiple mechanical constitutive parameters of the material can be directly and uniquely inverted. While ensuring the accuracy and uniqueness of the inversion results, the experimental complexity and cost are significantly reduced. This solves the problems of complex process, large error in inversion results, and difficulty in obtaining multiple plasticity parameters in the existing Ludwick hardening model inversion methods.

[0008] In one optional implementation, nanoindentation testing is performed on the test material to obtain a load-depth profile, including: The material to be tested was made into a standard sample, and the changing trend of elastic modulus and hardness with the preset maximum indentation depth was obtained based on the nanoindentation continuous stiffness method. Select the maximum indentation load corresponding to the stable elastic modulus and hardness from the changing trends; Nanoindentation tests were conducted based on the maximum indentation load to obtain the average load-depth curve.

[0009] The present invention provides an inversion analysis method for the constitutive model of materials mechanics, which accurately determines the test load through the continuous stiffness method and obtains the average load-depth curve based on it, significantly improving the stability and repeatability of nanoindentation tests, thereby ensuring the reliability and representativeness of the input data on which the subsequent inversion analysis is based.

[0010] In one alternative implementation, a nanoindentation test is performed based on the maximum indentation load to obtain an average load-depth curve, including: Based on the maximum indentation load, a nanoindentation test was conducted using a conical indenter in an array matrix indentation method, resulting in multiple initial load-depth curves. During the nanoindentation test, the indentation spacing was a preset multiple of the preset maximum indentation depth. After removing outlier curves from multiple initial load-depth curves, the depth values ​​of the remaining initial load-depth curves under the same load are averaged to obtain the average load-depth curve.

[0011] The present invention provides an inversion analysis method for the constitutive model of materials mechanics. Multiple initial curves are obtained by pressing an array matrix, and then the average load-depth curve is obtained by screening and averaging. This design systematically improves the statistical representativeness and reliability of the data, effectively eliminates the interference of local inhomogeneity of materials and random test errors, and provides stable and reliable basic input data for subsequent inversion analysis.

[0012] In one alternative implementation, inversion input parameters are extracted based on the mean load-depth curve, including: Based on the average load-depth curve, the reduced elastic modulus is calculated using elastic modulus and hardness analysis, and the indentation work and actual maximum indentation depth are extracted. The reduced elastic modulus, indentation work, and actual maximum indentation depth are used as inversion input parameters.

[0013] This invention provides an inversion analysis method for material mechanics constitutive models. By accurately extracting three parameters with clear physical meaning from the average load-depth curve—reduced elastic modulus, indentation work, and actual maximum indentation depth—as inversion inputs, the complex indentation response curve is transformed into a set of simplified, quantified, and comprehensively characterizing key feature values. This provides a direct, reliable, and dimensionally matched input data foundation for subsequent dimensional analysis-based inversion calculations, ensuring the feasibility of the inversion process and the accuracy of the results.

[0014] In one alternative implementation, a dimensionless function is constructed based on dimensional analysis and the characteristic strain method, including: Based on a pre-set hardening model, multiple sets of pre-set material constitutive parameters are systematically combined, and finite element software is used to perform nanoindentation numerical simulation on each set of pre-set material constitutive parameters to obtain a simulation dataset. Based on a simulated dataset, a dimensionless function is constructed using dimensional analysis and the characteristic strain method.

[0015] This invention provides an inversion analysis method for constitutive models in materials mechanics. It constructs a dataset through systematic numerical simulation and builds dimensionless functions based on dimensional analysis and characteristic strain method, thereby transforming the complex constitutive inversion problem into a clear mathematical relationship. This method guarantees the uniqueness of the inversion results in principle and significantly reduces the dependence of traditional methods on a large amount of experimental data, thus improving the reliability and computational efficiency of the inversion process.

[0016] In one optional implementation, finite element software is used to perform nanoindentation numerical simulations on each set of preset material parameters to obtain a simulation dataset, including: The finite element method was used to perform nanoindentation numerical simulation on each set of preset material constitutive parameters, and multiple sets of simulation results were obtained. The corresponding nanoindentation response parameters were extracted from each set of simulation results. The pre-set material constitutive parameters and nanoindentation response parameters are matched to obtain the simulation dataset.

[0017] This invention provides an inversion analysis method for material mechanical constitutive parameters. Through finite element numerical simulation, it systematically constructs a dataset of precise correspondences between material constitutive parameters and nanoindentation response parameters. This provides a complete, pure, and widely covered data foundation for establishing a reliable inversion model, fundamentally avoiding the uncontrollable random errors and cost limitations in physical experiments, and ensuring the theoretical rigor and universality of the inversion method.

[0018] In one alternative implementation, based on a simulated dataset, a dimensionless function is constructed using dimensional analysis and the characteristic strain method, including: The preset material constitutive parameters and nanoindentation response parameters in the simulation dataset are combined to form multiple dimensionless numbers; Characteristic strain and characteristic stress are introduced as intermediate variables, and dimensionless numbers are used as data points. Numerical fitting method is used to fit and obtain dimensionless functions.

[0019] This invention provides an inversion analysis method for constitutive models in materials mechanics. By introducing characteristic strain and characteristic stress as intermediate variables, the multi-parameter inversion problem is cleverly transformed into a deterministic functional relationship between dimensionless numbers. Numerical fitting is used to directly obtain an explicit expression of this relationship from the system data. This theoretically ensures the directness, uniqueness, and mathematical closure of the mapping from finite indentation response to complete constitutive parameters, fundamentally overcoming the inherent defects of traditional methods that require a large amount of experimental data, repeated iterative fitting, and non-unique solutions.

[0020] In one alternative implementation, the mechanical constitutive parameters are obtained by solving based on the inversion input parameters and the Ludwick constitutive inversion model, including: Substituting the reduced elastic modulus, indentation work, and actual maximum indentation depth into the Ludwick constitutive inversion model yields the mechanical constitutive parameters, which include yield strength, hardening exponent, and hardening strength.

[0021] This invention provides an inversion analysis method for material mechanics constitutive models. The three key inversion input parameters extracted are directly substituted into the constructed Ludwick constitutive inversion model. By solving a closed set of mathematical equations, the three core mechanical constitutive parameters of yield strength, hardening index, and hardening strength are obtained simultaneously in one go. This achieves a direct, rapid, unique, and quantitative inversion from experimental data to material constitutive models, avoiding the problems of repeated iterations, fitting, or multiple solution uncertainties in traditional methods.

[0022] Secondly, the present invention provides an inversion analysis apparatus for constitutive properties of materials, the apparatus comprising: The nanoindentation testing module is used to perform nanoindentation tests on the test material to obtain the average load-depth curve; The inversion input parameter extraction module is used to extract inversion input parameters based on the mean load-depth curve. The Ludwick constitutive inversion model building module is used to construct a dimensionless function based on dimensional analysis and the characteristic strain method, and to fit the dimensionless function to build the Ludwick constitutive inversion model. The inversion analysis module is used to solve for the mechanical constitutive parameters based on the inversion input parameters and the Ludwick constitutive inversion model.

[0023] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the material mechanics constitutive inversion analysis method described in the first aspect or any corresponding embodiment thereof.

[0024] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to perform the inversion analysis method of the material mechanical constitutive model described in the first aspect or any corresponding embodiment thereof.

[0025] Fifthly, the present invention provides a computer program product, including computer instructions for causing a computer to execute the inversion analysis method of the material mechanics constitutive model described in the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0026] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram of an application scenario according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the first process of the inversion analysis method of the constitutive model of materials mechanics according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the second process of the inversion analysis method of the material mechanics constitutive model according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the third process of the inversion analysis method of the material mechanics constitutive model according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the mathematical descriptions of the Hollomon hardening model and the Ludwick hardening model; Figure 6 This is a schematic diagram comparing the load-depth curves obtained from nanoindentation experiments and simulations according to an embodiment of the present invention; Figure 7 This is a schematic diagram comparing the stress-strain curves obtained from the uniaxial tensile test and the inversion according to an embodiment of the present invention. Figure 8(a) is a schematic diagram of the initial stage of the indentation depth in a finite element simulation of the nanoindentation indentation process of the conical indenter according to an embodiment of the present invention; Figure 8(b) is a schematic diagram of the maximum indentation depth stage in the finite element simulation of the nanoindentation indentation process of the conical indenter according to an embodiment of the present invention; Figure 8(c) is a schematic diagram of the complete unloading stage in the finite element simulation of the nanoindentation pressing process of the conical indenter according to an embodiment of the present invention; Figure 8(d) is a schematic diagram of the indentation work and actual maximum indentation depth of the nanoindentation indentation process of the conical indenter according to an embodiment of the present invention; Figure 9 This is a structural block diagram of the inversion analysis device for the constitutive properties of materials according to an embodiment of the present invention; Figure 10 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0030] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0031] As an optional application scenario of this invention, such as Figure 1As shown, application 101 is installed in terminal device 110, and user 130 can interact with application 101 through terminal device 110 and / or access device of terminal device 110.

[0032] For example, application 101 can be any application that provides question-and-answer related services. For instance, application 101 could be a question-and-answer interactive application, such as a text-to-text application, an image-to-text application, etc. Figure 1 In the application scenario shown, if application 101 is active, the terminal device 110 can display the interface 102 of application 101. The interface 102 may include various pages that application 101 can provide, such as interactive pages, settings pages, query pages, etc.

[0033] In some embodiments, terminal device 110 is communicatively connected to server 120 to provide services to application 101. Terminal device 110 may be a mobile terminal, fixed terminal, or portable terminal, etc., including but not limited to mobile phones, desktop computers, laptop computers, multimedia tablets, e-book devices, gaming devices, or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some embodiments, terminal device 110 may also support any type of interface, and server 120 may be various types of computing systems or servers capable of providing computing power, including but not limited to mainframes, edge computing nodes, computing devices in cloud environments, etc.

[0034] It should be noted that, Figure 1 This is merely an example of an application scenario and does not limit the scope of protection of this invention.

[0035] The embodiments of the present invention will now be described with reference to the accompanying drawings. It should be understood that the pages shown in the drawings are merely examples, and various page designs are possible in practice. The various graphic elements on the page may have different arrangements and different visual representations; one or more elements may be omitted or replaced, and one or more other elements may also be present, without any limitation in the embodiments of the present invention. Furthermore, the embodiments described below primarily pertain to terminal device 110. It should be understood that the actions described relative to terminal device 110 can be performed by application 101 on terminal device 110, or can be performed by application 101 in conjunction with its server (e.g., server 120).

[0036] Currently, selecting a suitable mechanical constitutive model is the first step in inversion analysis based on nanoindentation experiments. For most metallic materials, the Hollomon hardening model and the Ludwick hardening model are commonly used. For example, [the two models are compared]. Figure 5As shown, current research on mechanical constitutive inversion analysis based on nanoindentation tests, both domestically and internationally, mostly focuses on the relatively simple Hollomon hardening model. Research on constitutive inversion of alloys like Ti2AlNb, which are suitable for the Ludwick hardening model, is less common. While related techniques exist for the Ludwick hardening model, they are costly, involve complex inversion processes, produce large errors in the results, and the spherical indenters used are not universally applicable compared to the more common conical indenters.

[0037] This invention provides an inversion analysis method for the constitutive model of materials mechanics. For the Ludwick hardening model, dimensional analysis is used in conjunction with the characteristic strain method to construct a general dimensionless function. This function is then fitted and solved using a dataset obtained from nanoindentation finite element simulation, establishing a nanoindentation constitutive inversion model suitable for the Ludwick hardening model. Finally, the mechanical constitutive parameters are obtained, achieving the effect of significantly reducing experimental complexity and cost while ensuring the accuracy and uniqueness of the inversion results.

[0038] According to an embodiment of the present invention, an embodiment of an inversion analysis method for constitutive models of materials mechanics is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0039] This embodiment provides an inversion analysis method for the constitutive properties of materials, which can be used in the aforementioned electronic devices or terminal devices. Figure 2 This is a flowchart of the inversion analysis method for the constitutive model of materials according to an embodiment of the present invention, such as... Figure 2 As shown, the process includes the following steps: Step S201: Perform nanoindentation test on the material to be tested to obtain the average load-depth curve.

[0040] Specifically, the material under test refers to a metallic material suitable for describing the mechanical behavior using the Ludwick hardening model, such as a Ti2AlNb alloy. The Ludwick hardening model is a method used to describe the stress (stress) in metallic materials during the plastic deformation stage. ) and strain ( ε Constitutive model of the relationship.

[0041] Nanoindentation is a non-destructive / micro-destructive testing technique that uses a computer-controlled, rigid indenter with a regular shape (such as a conical indenter) to continuously and controllably indent the material surface under ultra-low loads at the micro- and nano-scale, while simultaneously measuring the relationship between load and indentation depth with high precision. This test directly outputs load-depth curves (such as average load-depth curves), and based on these curves (e.g., using the Oliver-Pharr method), the elastic modulus and hardness of the material can be calculated. It is an experimental method for obtaining the mechanical property parameters of micro-regions of materials.

[0042] The average load-depth curve is a single standard curve that is statistically representative and used for subsequent inversion analysis. This is obtained by performing multiple nanoindentation tests (such as 4×4 array indentation) on the same micro-region of the material, removing outliers, and averaging the depth data of all valid test curves under the same load value.

[0043] Step S202: Extract the inversion input parameters based on the average load-depth curve.

[0044] Specifically, the inversion input parameters include, but are not limited to, the reduced elastic modulus calculated using the Oliver-Pharr method. Er and the extracted pressure work W t and actual maximum indentation depth h As input parameters for inversion.

[0045] Step S203: Based on dimensional analysis and characteristic strain method, construct a dimensionless function and fit the dimensionless function to establish the Ludwick constitutive inversion model.

[0046] Specifically, in dimensional analysis and the characteristic strain method, dimensional analysis is a mathematical method based on the fundamental principle that the units (dimensions) of physical quantities must be consistent. In this embodiment, the response of nanoindentation (such as indentation work) W t It depends on material properties (such as reduced elastic modulus E, stress) Hardening index n Hardening strength K ) and test scale (i.e., preset maximum indentation depth) h’ Dimensional analysis identifies several dimensional quantities, such as , and demonstrates that the true physical relationships between these quantities can be equivalently described by relationships between a set of dimensionless numbers composed of them. This significantly reduces the number of variables and provides a theoretical framework for establishing universal functional relationships.

[0047] The Ludwick constitutive inversion model is constructed based on nanoindentation test data through dimensional analysis and characteristic strain method. It is used to uniquely determine the three plasticity parameters (stress, stress, and strain) of the Ludwick hardening model of a material. Hardening index n Hardening strength K A closed system of mathematical equations and its solution system.

[0048] Step S204: Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained by solving.

[0049] Specifically, the three key inversion input parameters extracted (reduced elastic modulus E, indentation work) will be used to... W t Compared with the actual maximum indentation depth h By directly substituting the data into the pre-constructed Ludwick constitutive inversion model and solving the closed dimensionless function equations corresponding to the model, all mechanical constitutive parameters of the material, namely yield strength, hardening index and hardening strength, can be analyzed in one go and uniquely, thus realizing a direct, deterministic and efficient inversion from experimental data to material constitutives.

[0050] The material mechanics constitutive inversion analysis method provided in this embodiment constructs a closed dimensionless function system suitable for the three-parameter Ludwick hardening model by combining dimensional analysis and the characteristic strain method. It only requires obtaining the average load-depth curve through conventional nanoindentation tests and extracting a few key response parameters to directly and uniquely invert multiple mechanical constitutive parameters of the material. While ensuring the accuracy and uniqueness of the inversion results, it significantly reduces experimental complexity and cost, and solves the problems of complex process, large error in inversion results, and difficulty in obtaining multiple plasticity parameters in the existing Ludwick hardening model inversion methods.

[0051] This embodiment provides an inversion analysis method for the constitutive properties of materials, which can be used in the aforementioned electronic devices or terminal devices. Figure 3 This is a flowchart of the inversion analysis method for the constitutive model of materials according to an embodiment of the present invention, such as... Figure 3 As shown, the process includes the following steps: Step S301: Perform nanoindentation test on the material to be tested to obtain the average load-depth curve.

[0052] Specifically, step S301 includes: Step S3011: The material to be tested is made into a standard sample, and the trend of the elastic modulus and hardness increasing with the preset maximum indentation depth is obtained based on the nanoindentation continuous stiffness method.

[0053] Specifically, taking Ti2AlNb alloy as an example, the Ti2AlNb alloy was prepared by metallographic sampling and polished. The elastic modulus and hardness obtained by the nanoindentation continuous stiffness method were compared with the preset maximum indentation depth. h’The increasing trend of change (i.e., the size effect curve). This preset maximum indentation depth. h’ This serves as a reference target value for test planning and control before the formal array test. It is an expected or nominal value set during the test design phase. It is usually selected based on the size effect curve of previous continuous stiffness method tests or probe tests, corresponding to the depth at which performance tends to stabilize.

[0054] Step S3012: Select the maximum indentation load corresponding to the stable elastic modulus and hardness from the changing trends.

[0055] Specifically, based on the obtained size effect curve, the load values ​​corresponding to the elastic modulus and hardness entering the stable region are selected, and these load values ​​are taken as the maximum indentation load.

[0056] Step S3013: Perform a nanoindentation test based on the maximum indentation load to obtain the average load-depth curve.

[0057] In some optional implementations, step S3013 above includes: Step a1: Based on the maximum indentation load, a nanoindentation test is conducted using a conical indenter in an array matrix indentation method to obtain multiple initial load-depth curves. During the nanoindentation test, the indentation spacing is a preset multiple of the preset maximum indentation depth. Schematic diagrams of the initial indentation depth stage, the maximum indentation depth stage, and the complete unloading stage in the finite element simulation of the nanoindentation process using the conical indenter are shown in Figures 8(a), 8(b), and 8(c), respectively.

[0058] Specifically, a 4×4 array of tapered indenters is used to press the Ti2AlNb alloy surface to improve the reliability and repeatability of the average measurement. When performing nanoindentation tests, the indentation spacing is set to 20 times the preset maximum indentation depth to avoid interference between adjacent indentation tests.

[0059] Step a2: After removing abnormal curves from multiple initial load-depth curves, average the depth values ​​of the remaining initial load-depth curves under the same load to obtain the average load-depth curve.

[0060] Specifically, the 16 sets of nanoindentation load-depth curves were analyzed and screened. After removing obviously abnormal curves, the remaining load-depth curves were averaged at different depths under the same load (the indentation load and time are linearly related under load rate control) to obtain the average load-depth curve, which was then used as the inversion input curve. A schematic diagram comparing the load-depth curves obtained from nanoindentation experiments and simulations is shown below. Figure 6 As shown.

[0061] Step S302: Extract the inversion input parameters based on the average load-depth curve.

[0062] Specifically, step S302 includes: Step S3021: Based on the average load-depth curve, the reduced elastic modulus is calculated using the elastic modulus and hardness analysis method, and the indentation work and the actual maximum indentation depth are extracted.

[0063] Specifically, based on the average load-depth curve, the stiffness during the unloading phase is analyzed using the Oliver-Pharr method, and the reduced elastic modulus is calculated. Er The indentation work is obtained by integrating the area under the loading curve. W t The displacement value corresponding to the end point of loading is directly read from the average load-depth curve and used as the actual maximum indentation depth. h Actual maximum indentation depth h This is a measurement result directly read from the load-depth curve after a single nanoindentation or averaging, following the formal array test. It is a measured value. The data processing stage after the nanoindentation test is completed. Read from the x-axis of the obtained load-depth curve.

[0064] Figure 8(d) shows a schematic diagram of the indentation work and the actual maximum indentation depth during the nanoindentation process of the conical indenter.

[0065] Step S3022: The reduced elastic modulus, indentation work, and actual maximum indentation depth are used as inversion input parameters.

[0066] Specifically, the reduced elastic modulus Er Injection power W t and actual maximum indentation depth h The inversion input parameters required for this inversion method are determined, forming a set of quantitative data that can be directly substituted into the subsequent mathematical model.

[0067] Step S303: Based on dimensional analysis and the characteristic strain method, a dimensionless function is constructed, and the dimensionless function is fitted to establish the Ludwick constitutive inversion model. For details, please refer to [link to relevant documentation]. Figure 2 Step S203 of the illustrated embodiment will not be described again here.

[0068] Step S304: Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained. For details, please refer to [link to relevant documentation]. Figure 2 Step S204 of the illustrated embodiment will not be described again here.

[0069] The material mechanics constitutive inversion analysis method provided in this embodiment accurately determines the test load through the continuous stiffness method and obtains the average load-depth curve based on it, which significantly improves the stability and repeatability of nanoindentation tests. This ensures the reliability and representativeness of the input data used for subsequent inversion analysis. By accurately extracting three parameters with clear physical meaning from the average load-depth curve—reduced elastic modulus, indentation work, and actual maximum indentation depth—as inversion inputs, the complex indentation response curve is transformed into a set of simplified, quantified, and comprehensively characterizing key feature values. This provides a direct, reliable, and dimensionally matched input data foundation for subsequent inversion calculations based on dimensional analysis.

[0070] This embodiment provides an inversion analysis method for the constitutive properties of materials, which can be used in the aforementioned electronic devices or terminal devices. Figure 4 This is a flowchart of the inversion analysis method for the constitutive model of materials according to an embodiment of the present invention, such as... Figure 4 As shown, the process includes the following steps: Step S401: Perform nanoindentation testing on the material to be tested to obtain the average load-depth curve. For details, please refer to [link to relevant documentation]. Figure 3 Step S301 of the illustrated embodiment will not be described again here.

[0071] Step S402: Extract the inversion input parameters based on the mean load-depth curve. For details, please refer to [link to relevant documentation]. Figure 3 Step S302 of the illustrated embodiment will not be described again here.

[0072] Step S403: Based on dimensional analysis and characteristic strain method, construct a dimensionless function and fit the dimensionless function to establish the Ludwick constitutive inversion model.

[0073] Specifically, the constructed universal dimensionless function is fitted and solved using the dataset obtained from nanoindentation finite element simulation to establish the Ludwick constitutive inversion model. Step S403 includes: Step S4031: Based on the preset hardening model, systematically combine multiple sets of preset material constitutive parameters, and use finite element software to perform nanoindentation numerical simulation on each set of preset material constitutive parameters to obtain a simulation dataset.

[0074] In some optional implementations, step S4031 above includes: Step b1: Use finite element software to perform nanoindentation numerical simulation on each set of preset material constitutive parameters to obtain multiple sets of simulation results, and extract the corresponding nanoindentation response parameters from each set of simulation results.

[0075] Specifically, using finite element method (FEM) software, with preset constitutive parameters for each set of materials (including elastic modulus, yield strength, hardening index, and hardening strength) as input, numerical simulation of the entire nanoindentation process is performed to obtain the corresponding load-depth curves. Subsequently, preset nanoindentation response parameters, including at least the maximum indentation depth, are extracted from each simulation curve. h、 Indentation work W t and the reduced elastic modulus calculated based on the simulation curve. Er .

[0076] Step b2 involves matching the pre-set material constitutive parameters and nanoindentation response parameters for each set to obtain a simulation dataset.

[0077] Specifically, the preset material constitutive parameters input for each simulation are systematically correlated and paired with the corresponding nanoindentation response parameters extracted in step b1 to form a one-to-one data record, which is then integrated into a structured simulation dataset.

[0078] Step S4032: Based on the simulation dataset, a dimensionless function is constructed using dimensional analysis and the characteristic strain method.

[0079] In some optional implementations, step S4032 above includes: Step c1: Combine the preset material constitutive parameters and nanoindentation response parameters in the simulation dataset to form multiple dimensionless numbers.

[0080] Specifically, based on the principle of dimensional analysis, the material constitutive parameters and nanoindentation response parameters corresponding to each set in the simulation dataset are combined to form several independent dimensionless numbers (π terms). In particular, by multiplying and combining physical quantities containing basic dimensions by powers, their units are eliminated, thereby obtaining a set of dimensionless variables that characterize the essence of physical relationships.

[0081] Step c2 introduces characteristic strain and characteristic stress as intermediate variables, uses dimensionless numbers as data points, and employs numerical fitting to obtain a dimensionless function.

[0082] Introducing a fixed characteristic strain ε r As an intermediate variable, and based on this, the corresponding characteristic stress is defined according to the constitutive model. σ r Subsequently, using the dimensionless numbers generated in the first step as coordinate data points, a numerical fitting algorithm (such as nonlinear regression) is employed to determine the mathematical relationships between these dimensionless numbers, ultimately fitting an explicit dimensionless function expression connecting all key variables.

[0083] For example, the Ludwick constitutive inversion model established through step S403 above includes: (1); (2); (3); In equation (3), M1, M2, and M3 are... σ y / E r For functions of variables, the formulas are as follows: (4); (5); (6).

[0084] Equations (1), (2), and (3) are combined to obtain the Ludwick constitutive inversion model.

[0085] In step S402, the inversion input parameters are obtained, including the reduced elastic modulus. E r Injection power W t and actual maximum indentation depth h Characteristic strain of the conical indenter in the characteristic strain method ε r The characteristic stress is 0.033. σ r = σ y + Kε r n Therefore, equations (1), (2), and (3) only contain the yield strength. σ y Hardening index n and hardening strength K These three unknowns form a closed system of equations, which can be solved.

[0086] Step S404: Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained by solving.

[0087] Specifically, step S404 includes: Step a: Substitute the reduced elastic modulus, indentation work, and actual maximum indentation depth into the Ludwick constitutive inversion model to obtain the mechanical constitutive parameters, which include yield strength, hardening exponent, and hardening strength.

[0088] Based on the reduced elastic modulus obtained in step S402E r Injection power W t and actual maximum indentation depth h， Inversion analysis was performed using the Ludwick constitutive inversion model established in step S403 to calculate the mechanical constitutive parameters, including yield strength. σ y Hardening index n and hardening strength K This allows us to obtain the Ludwick mechanical constitutive curve.

[0089] The solution process is as follows: First, solve according to equation (1) to obtain the unique solution. σ r Then, combining equation (2) and... σ r = σ y + Kε r n Solving for a unique solution σ y numerical sum Kε r n The overall value is C1; finally, the simultaneous equations are... Kε r n = Solving C1 and equation (3) yields a unique solution. n Numerical and K Therefore, the Ludwick constitutive inversion model established in this embodiment has inversion uniqueness.

[0090] The material mechanics constitutive inversion analysis method provided in this embodiment directly substitutes the three key inversion input parameters extracted into the constructed Ludwick constitutive inversion model. By solving a closed set of mathematical equations, the three core mechanical constitutive parameters of yield strength, hardening index, and hardening strength are obtained simultaneously in one go. This achieves a direct, rapid, unique, and quantitative inversion from experimental data to material constitutive model, avoiding the problems of repeated iterations, fitting, or multiple solution uncertainties in traditional methods.

[0091] As one or more specific application embodiments of the present invention, combined with Figure 6Figure 8(c) further details the inversion analysis method for the material mechanics constitutive model provided by this invention. In this embodiment, dimensional analysis combined with the characteristic strain method is used for the Ludwick hardening model to construct a general dimensionless function. This function is then fitted and solved using a dataset obtained from nanoindentation finite element simulation, establishing a nanoindentation constitutive inversion method suitable for the Ludwick hardening model. Taking Ti2AlNb alloy as an example, the specific implementation steps are as follows: Step ①: Prepare a metallographic sample of the Ti2AlNb alloy and polish it. Based on the trend of the elastic modulus and hardness increasing with the maximum indentation depth obtained by the nanoindentation continuous stiffness method (i.e., size effect), select the maximum indentation load corresponding to the point where the elastic modulus and hardness tend to stabilize. Use a conical indenter to perform 4×4 matrix indentation on its surface to improve the reliability and repeatability of the average measurement. The indentation spacing is 20 times the maximum indentation depth to avoid interference between adjacent indentation tests.

[0092] Step 2: Analyze and screen the 16 sets of nanoindentation load-depth curves obtained in Step 1. After removing obviously abnormal curves, average the different depth values ​​of the remaining curves under the same load (the indentation load and time are linearly related under the load rate control) to obtain the average load-depth curve, which is used as the inversion input curve.

[0093] Step 3: Based on the average load-depth curve obtained in Step 2, calculate the reduced elastic modulus using the Oliver-Pharr method. E r and extract the pressurized power W t and actual maximum depth h As input parameters for inversion.

[0094] Step 4: Using the dataset obtained from nanoindentation finite element simulation, fit and solve the constructed universal dimensionless function to establish the Ludwick constitutive inversion model, specifically including: (1); (2); (3); In equation (3), M1, M2, and M3 are... σ y / E r For functions of variables, the formulas are as follows: (4); (5); (6).

[0095] Equations (1), (2), and (3) are combined to obtain the Ludwick constitutive inversion model.

[0096] In step S402, the inversion input parameters are obtained, including the reduced elastic modulus. E r Injection power W t and actual maximum indentation depth h Characteristic strain of the conical indenter in the characteristic strain method ε r The characteristic stress is 0.033. σ r = σ y + Kε r n Therefore, equations (1), (2), and (3) only contain the yield strength. σ y Hardening index n and hardening strength K These three unknowns form a closed system of equations, which can be solved.

[0097] Step 5: Based on the reduced elastic modulus obtained in step 3 E r Injection power W t and actual maximum indentation depth h， Inversion analysis was performed using the Ludwick constitutive inversion model established in step ④ to calculate the mechanical constitutive parameters, including yield strength. σ y Hardening index n and hardening strength K This allows us to obtain the Ludwick mechanical constitutive curve.

[0098] In this embodiment, nanoindentation experiments were conducted on Ti2AlNb alloys. The inversion model was verified by comparing the load-depth curves from the experiments and simulations. Figure 6 As shown, the curves of the two methods during the loading stage show a small deviation, which is superior to the micromechanical properties of hot-stamped martensite / bainite dual-phase structures based on nanoindentation inverse algorithm and the crystal material constant inversion method of laser repair layer based on nanoindentation in related technologies.

[0099] In this embodiment, a Ti2AlNb alloy uniaxial (i.e., Figure 7 (Physical example in the text) Tensile test, verifying the inversion model by comparing the test and the inverted stress-strain curves, such as Figure 7As shown, the deviation between the two plastic stage curves is 6.0%, which is within the acceptable error range for engineering and is superior to the micromechanical properties of hot-stamped martensitic / bainitic dual-phase microstructures based on nanoindentation inverse algorithm in related technologies.

[0100] Most related technologies are aimed at the relatively simple Hollomon hardening model, while the material mechanics constitutive inversion analysis method provided in this embodiment is a nanoindentation constitutive inversion analysis method applicable to the Ludwick hardening model. In this embodiment, a conical indenter is used, which is convenient for testing, has low experimental cost, is simple to calculate, has high accuracy, and ensures the uniqueness of the inversion results.

[0101] This embodiment also provides an inversion analysis apparatus for material mechanics constitutive models, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0102] This embodiment provides an inversion analysis device for the constitutive properties of materials mechanics, such as... Figure 9 As shown, it includes: The nanoindentation test module 901 is used to perform nanoindentation tests on the test material to obtain the average load-depth curve.

[0103] The inversion input parameter extraction module 902 is used to extract inversion input parameters based on the average load-depth curve.

[0104] The Ludwick constitutive inversion model building module 903 is used to construct a dimensionless function based on dimensional analysis and characteristic strain method, and to fit the dimensionless function to build the Ludwick constitutive inversion model.

[0105] The inversion analysis module 904 is used to solve for the mechanical constitutive parameters based on the inversion input parameters and the Ludwick constitutive inversion model.

[0106] In some alternative implementations, the nanoindentation testing module 901 includes: The size effect determination unit is used to prepare standard specimens of the material to be tested, and based on the nanoindentation continuous stiffness method, obtain the changing trend of elastic modulus and hardness as the preset maximum indentation depth increases.

[0107] The maximum indentation load determination unit is used to select the maximum indentation load corresponding to the stable elastic modulus and hardness from the changing trends.

[0108] The nanoindentation test unit is used to perform nanoindentation tests based on the maximum indentation load to obtain the average load-depth curve.

[0109] In some alternative implementations, the nanoindentation testing unit includes: The initial load-depth curve determination sub-unit is used to conduct nanoindentation tests using an array matrix indentation method with a conical indenter based on the maximum indentation load, and to obtain multiple initial load-depth curves; the indentation spacing is a preset multiple of the preset maximum indentation depth during the nanoindentation test.

[0110] The average load-depth curve determination sub-unit is used to eliminate abnormal curves in multiple initial load-depth curves, and then average the depth values ​​of the remaining initial load-depth curves under the same load to obtain the average load-depth curve.

[0111] In some optional implementations, the inversion input parameter extraction module 902 includes: The parameter calculation unit is used to calculate the reduced elastic modulus based on the average load-depth curve using elastic modulus and hardness analysis methods, and to extract the indentation work and the actual maximum indentation depth.

[0112] The inversion input parameter determination unit is used to take the reduced elastic modulus, indentation work, and actual maximum indentation depth as inversion input parameters.

[0113] In some alternative implementations, the Ludwick constitutive inversion model building module 903 includes: The simulation dataset determination unit is used to systematically combine multiple sets of preset material constitutive parameters based on a preset hardening model, and to perform nanoindentation numerical simulation on each set of preset material constitutive parameters using finite element software to obtain the simulation dataset.

[0114] Dimensionless function construction unit, used to construct dimensionless functions based on simulated datasets using dimensional analysis and characteristic strain method.

[0115] In some optional implementations, the simulation dataset determination unit includes: The numerical simulation and response parameter determination sub-unit is used to perform nanoindentation numerical simulation on each set of preset material constitutive parameters using finite element software, obtain multiple sets of simulation results, and extract the corresponding nanoindentation response parameters from each set of simulation results.

[0116] The matching sub-unit is used to match each set of preset material constitutive parameters and nanoindentation response parameters to obtain a simulation dataset.

[0117] In some alternative implementations, the dimensionless function building block includes: Dimensionless number forming sub-units are used to combine the preset material constitutive parameters and nanoindentation response parameters in the simulation dataset to form multiple dimensionless numbers.

[0118] The fitting sub-unit is used to introduce characteristic strain and characteristic stress as intermediate variables, and uses dimensionless numbers as data points. The numerical fitting method is used to fit the dimensionless function.

[0119] In some alternative implementations, the inversion analysis module 904 includes: The inversion analysis unit is used to substitute the reduced elastic modulus, indentation work, and actual maximum indentation depth into the Ludwick constitutive inversion model to obtain mechanical constitutive parameters, including yield strength, hardening index, and hardening strength.

[0120] The inversion analysis apparatus for material mechanics constitutive models provided in this invention can execute the inversion analysis method for material mechanics constitutive models provided in any embodiment of this invention, and has the corresponding functional modules and beneficial effects for executing the method. Further functional descriptions of the various modules and units described above are the same as in the corresponding embodiments described above, and will not be repeated here.

[0121] Figure 10 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0122] The following is a detailed reference. Figure 10 This diagram illustrates a suitable structural schematic for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from memory 1008 into random access memory (RAM) 1003. The RAM 1003 also stores various programs and data required for the operation of the electronic device. The processor 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0123] Typically, the following devices can be connected to the I / O interface 1005: input devices 1006 including, for example, a touchscreen, touchpad, keyboard, mouse, camera, microphone, accelerometer, gyroscope, etc.; output devices 1007 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; memory devices 1008 including, for example, magnetic tape, hard disk, etc.; and communication devices 1009. Communication device 1009 allows electronic devices to exchange data via wireless or wired communication with other devices. Although Figure 10Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0124] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 1009, or installed from a memory 1008, or installed from a ROM 1002. When the computer program is executed by the processor 1001, it performs the functions defined in the inversion analysis method of the constitutive model of materials according to embodiments of the present invention.

[0125] Figure 10 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0126] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the inversion analysis method of the material mechanics constitutive model shown in the above embodiments is implemented.

[0127] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0128] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. An inversion analysis method for constitutive models of materials, characterized in that, The method includes: Nanoindentation tests were performed on the test material to obtain the average load-depth curve; Based on the average load-depth curve, extract the inversion input parameters; Based on dimensional analysis and characteristic strain method, a dimensionless function is constructed, and the dimensionless function is fitted to establish the Ludwick constitutive inversion model. Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained by solving.

2. The inversion analysis method for constitutive models of materials according to claim 1, characterized in that, The nanoindentation test is performed on the material to be tested to obtain the load-depth curve, including: The material to be tested was made into a standard sample, and the changing trend of elastic modulus and hardness with the preset maximum indentation depth was obtained based on the nanoindentation continuous stiffness method. Select the maximum indentation load corresponding to the stable elastic modulus and hardness from the aforementioned trends; Nanoindentation tests were conducted based on the maximum indentation load to obtain the average load-depth curve.

3. The inversion analysis method for constitutive models of materials according to claim 2, characterized in that, Nanoindentation tests were conducted based on the maximum indentation load to obtain the average load-depth curve, including: Based on the maximum indentation load, a nanoindentation test was conducted using a conical indenter in an array matrix indentation method, resulting in multiple initial load-depth curves. During the nanoindentation test, the indentation spacing was a preset multiple of the preset maximum indentation depth. After removing the abnormal curves from the multiple initial load-depth curves, the depth values ​​of the remaining initial load-depth curves under the same load are averaged to obtain the average load-depth curve.

4. The inversion analysis method for constitutive models of materials according to claim 1, characterized in that, Based on the average load-depth curve, inversion input parameters are extracted, including: Based on the average load-depth curve, the reduced elastic modulus is calculated using elastic modulus and hardness analysis, and the indentation work and actual maximum indentation depth are extracted. The reduced elastic modulus, indentation work, and actual maximum indentation depth are used as inversion input parameters.

5. The inversion analysis method for constitutive models of materials according to claim 1, characterized in that, The construction of dimensionless functions based on dimensional analysis and characteristic strain method includes: Based on a pre-set hardening model, multiple sets of pre-set material constitutive parameters are systematically combined, and finite element software is used to perform nanoindentation numerical simulation on each set of pre-set material constitutive parameters to obtain a simulation dataset. Based on the simulated dataset, a dimensionless function is constructed using dimensional analysis and the characteristic strain method.

6. The inversion analysis method for constitutive models of materials according to claim 5, characterized in that, The finite element method (FEM) software was used to perform nanoindentation numerical simulations on each set of preset material parameters, resulting in a simulation dataset, including: The finite element method was used to perform nanoindentation numerical simulation on each set of preset material constitutive parameters, and multiple sets of simulation results were obtained. The corresponding nanoindentation response parameters were extracted from each set of simulation results. The pre-set material constitutive parameters and nanoindentation response parameters are matched to obtain the simulation dataset.

7. The inversion analysis method for constitutive models of materials according to claim 5, characterized in that, Based on the simulated dataset, a dimensionless function is constructed using dimensional analysis and the characteristic strain method, including: The preset material constitutive parameters and nanoindentation response parameters in the simulation dataset are combined to form multiple dimensionless numbers; Characteristic strain and characteristic stress are introduced as intermediate variables, and the dimensionless number is used as the data point. A numerical fitting method is used to fit and obtain the dimensionless function.

8. The inversion analysis method for constitutive models of materials according to claim 4, characterized in that, Based on the inversion input parameters and the Ludwick constitutive inversion model, the mechanical constitutive parameters are obtained by solving, including: Substituting the reduced elastic modulus, indentation work, and actual maximum indentation depth into the Ludwick constitutive inversion model yields mechanical constitutive parameters, including yield strength, hardening exponent, and hardening strength.

9. An inversion analysis device for constitutive models of materials mechanics, characterized in that, The device includes: The nanoindentation testing module is used to perform nanoindentation tests on the test material to obtain the average load-depth curve; The inversion input parameter extraction module is used to extract inversion input parameters based on the average load-depth curve; The Ludwick constitutive inversion model building module is used to construct a dimensionless function based on dimensional analysis and characteristic strain method, and to fit the dimensionless function to establish the Ludwick constitutive inversion model. The inversion analysis module is used to solve for the mechanical constitutive parameters based on the inversion input parameters and the Ludwick constitutive inversion model.

10. An electronic device, characterized in that, include: A memory and a processor are interconnected, the memory stores computer instructions, and the processor executes the computer instructions to perform the inversion analysis method of the material mechanics constitutive model according to any one of claims 1 to 8.

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