Method and System for Fitting Stress-Strain Curves in Multiple Temperature Zones of Materials for Nuclear Fusion Devices

Abstract

This invention discloses a method and system for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices, relating to the field of material performance characterization technology. The method includes: determining the fundamental performance parameters of the nuclear fusion device material at at least one target temperature within a preset temperature range, wherein the fundamental performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters; for each target temperature, based on the yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters at the target temperature, establishing a monotonic constitutive model based on yield point and limit point constraints, and using the monotonic constitutive model to fit a monotonic stress-strain curve at the target temperature. Therefore, by precisely controlling the yield point and limit point constraints, temperature-related stress-strain curves can be generated, solving the problems of scarce data and inconsistent fitting of materials in multiple temperature zones of nuclear fusion devices, and improving the accuracy and design reliability of finite element simulation.

Description

Technical Field

[0001] This invention relates to the field of material property characterization technology, and in particular to a method and system for fitting stress-strain curves in multiple temperature zones of materials for nuclear fusion devices. Background Technology

[0002] With the increasing scale of nuclear fusion devices such as tokamaks, their key components need to operate for extended periods in an ultra-wide temperature range of 4K to 1500K. The mechanical properties of materials are highly sensitive to temperature, but existing nuclear engineering specifications typically only provide limited strength parameters, which cannot meet the requirements of complete stress-strain curves in actual finite element simulations.

[0003] Currently, obtaining material stress-strain curves mainly relies on scattered literature data, manual processing of limited experimental points, or empirical models, which suffers from systemic problems such as insufficient temperature coverage, fragmented processing methods, and non-standardized conversion and fitting. Especially for the ultra-low temperature (4K, 80K) and high temperature (welding zone) conditions unique to nuclear fusion devices, experimental data is scarce, forcing designers to rely on empirical estimations, which cannot accurately reflect the yielding and hardening behavior of materials.

[0004] Existing constitutive characterization techniques are mostly geared towards single temperature points or specific material systems, lacking systematic solutions for the multi-material and ultra-wide temperature range characteristics of nuclear fusion devices. Furthermore, existing methods have significant shortcomings in cross-temperature extrapolation capabilities, automated processing, and closed-loop update mechanisms, which limit simulation accuracy and design efficiency.

[0005] Therefore, there is an urgent need to develop a standardized method that can systematically process the mechanical properties of materials for nuclear fusion devices at multiple temperatures and automatically generate stress-strain curves that meet constraints based on key engineering parameters, so as to improve design reliability and simulation analysis accuracy. Summary of the Invention

[0006] The purpose of this invention is to propose a method and system for fitting stress-strain curves of materials in multiple temperature zones of nuclear fusion devices, so as to solve the problems of scarce data and inconsistent fitting of materials in multiple temperature zones of nuclear fusion devices, and improve the accuracy of finite element simulation and design reliability.

[0007] In a first aspect, embodiments of the present invention propose a method for fitting stress-strain curves of materials for nuclear fusion devices in multiple temperature zones. The method includes: determining the basic performance parameters of the materials for nuclear fusion devices at at least one target temperature within a preset temperature range, wherein the basic performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters; for each target temperature, establishing a monotonic constitutive model based on yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters at the target temperature, and using the monotonic constitutive model to fit a monotonic stress-strain curve at the target temperature.

[0008] In some embodiments, determining the basic performance parameters of the nuclear fusion device material at at least one target temperature within a preset temperature range includes: determining whether the target temperature is a preset specification temperature; if it is the preset specification temperature, then obtaining the basic performance parameters at the target temperature from a preset memory; if it is not the preset specification temperature, then obtaining the two preset specification temperatures with the smallest difference from the target temperature from the preset memory, and using an interpolation method based on the basic performance parameters at the two preset specification temperatures to obtain the basic performance parameters at the target temperature.

[0009] In some embodiments, when the target temperature is not a preset specification temperature, the basic performance parameters of the target temperature are obtained by the following formula:

[0010]

[0011] in, , for target temperature The following are the basic performance parameters; Target temperature The yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters are given. Preset standard temperature The following are the basic performance parameters. Preset standard temperature The following are the basic performance parameters. In and between.

[0012] In some embodiments, the monotonic constitutive model is expressed by the following equation:

[0013]

[0014] in, To respond realistically, For actual stress, Target temperature The elastic modulus below, Target temperature Yield strength below; Target temperature The strain coefficient is set to 0.002. , Target temperature The strain hardening index is below; Target temperature The plastic reference strain parameters are as follows: Target temperature The ultimate strength below.

[0015] In some embodiments, generating a monotonic stress-strain curve at the target temperature using the monotonic constitutive model includes: generating multiple true strains within a predetermined strain range; solving for the true stress corresponding to each true strain using the monotonic constitutive model based on yield point and limit point constraints; and fitting a monotonic true stress-strain curve at the target temperature based on the multiple true stresses and their corresponding multiple true strains.

[0016] In some embodiments, generating the monotonic stress-strain curve at the target temperature using the monotonic constitutive model further includes: calculating multiple engineering stresses and their corresponding multiple engineering strains based on multiple real strains and their corresponding multiple real stresses; and fitting the monotonic engineering stress-strain curve at the target temperature based on the multiple engineering stresses and their corresponding multiple engineering strains.

[0017] In some embodiments, the method further includes: acquiring a plurality of measured stresses and their corresponding plurality of measured strains at the target temperature; and calculating the fitting error at the target temperature based on the plurality of measured stresses and their corresponding plurality of measured strains using the following formula:

[0018]

[0019] in, Target temperature The fitting error is as follows. The quantity of the measured stress, To utilize the monotonic constitutive model based on the target temperature The j-th measured strain The obtained fitted stress, Target temperature The j-th measured stress; adjust parameters , , At least one of them, to minimize the fitting error, to obtain the corrected monotonic true stress-strain curve at the target temperature.

[0020] In some embodiments, the basic performance parameter further includes Poisson's ratio; the method further includes: generating an elastic matrix based on the Poisson's ratio and the elastic modulus; and using the elastic matrix, combined with the yield strength and the plastic hardening law extracted from the monotonic constitutive model, establishing an elastoplastic constitutive model for three-dimensional finite element simulation.

[0021] In some embodiments, the method is implemented using Matlab.

[0022] Secondly, embodiments of the present invention propose a multi-temperature-zone stress-strain curve fitting system for materials used in nuclear fusion devices. The system includes: a determination module, used to determine the basic performance parameters of the materials used in nuclear fusion devices at at least one target temperature within a preset temperature range, wherein the basic performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters; and a fitting module, used for establishing a monotonic constitutive model based on yield point and ultimate point constraints for each target temperature, based on the yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters at the target temperature, and using the monotonic constitutive model to fit a monotonic stress-strain curve at the target temperature.

[0023] The present invention discloses a method and system for fitting stress-strain curves of materials for nuclear fusion devices in multiple temperature zones. First, it determines the fundamental performance parameters of the materials for the nuclear fusion device at at least one target temperature within a preset temperature range. These fundamental performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters. Then, for each target temperature, based on the yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters at the target temperature, a monotonic constitutive model based on yield point and limit point constraints is established. The monotonic stress-strain curve at the target temperature is then fitted using this monotonic constitutive model. Therefore, by precisely controlling the yield point and limit point constraints, temperature-dependent stress-strain curves are generated, which solves the problems of scarce data and inconsistent fitting for materials in multiple temperature zones of nuclear fusion devices, improving the accuracy of finite element simulation and the reliability of the design. Attached Figure Description

[0024] Figure 1 This is a flowchart of the multi-temperature zone stress-strain curve fitting method for materials in nuclear fusion devices according to an embodiment of the present invention;

[0025] Figure 2 This is a flowchart of a method for fitting stress-strain curves of materials in a nuclear fusion device across multiple temperature zones, according to a specific embodiment of the present invention.

[0026] Figure 3 This is a structural block diagram of the stress-strain curve fitting system for multi-temperature zones of materials in a nuclear fusion device according to an embodiment of the present invention. Detailed Implementation

[0027] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0028] This invention addresses the constitutive modeling requirements of key structural materials in nuclear fusion devices over an ultra-wide temperature range (approximately 4K to 1500K), as well as the problems in existing technologies such as fragmented acquisition of stress-strain curves across multiple temperature regions, inconsistent fitting methods, and low coupling with engineering specifications and simulation tools. The core technical problems to be solved mainly include the following aspects:

[0029] (1) Technical problem of lack of unified acquisition and fitting mechanism for real stress-strain curves in multiple temperature regions

[0030] In current engineering practice, the sources of stress and strain data for materials at different temperatures (such as 4K, 80K, 293K, 500K, and near the high temperature of welding) are scattered. Existing standards mainly provide scattered parameters such as ultimate strength and allowable stress, and test data are mostly stored independently for single temperature and single project. There is a lack of a unified data structure and processing flow, making it difficult to build a complete multi-temperature real stress and strain curve library.

[0031] The first type of technical problem that this invention aims to solve is: how to integrate ASME and other standard parameters with multi-source test data under a unified data framework, automatically complete the conversion and fitting from engineering stress and strain to real stress and strain, and form standardized curves that can be directly used for finite element simulation at multiple typical temperature points.

[0032] (2) Technical problems of insufficient accuracy in modeling the evolution of material parameters with temperature and extrapolating across temperatures.

[0033] For temperature points that have not been tested, current methods mostly rely on linear interpolation or empirical extrapolation, which cannot reasonably reflect the nonlinear evolution of yield strength, ultimate strength, hardening parameters, etc. with temperature. This can easily lead to large errors in extremely low temperatures and high welding temperatures, affecting safety assessments.

[0034] The second type of technical problem to be solved by this invention is: how to establish a unified function / model for the change of key mechanical parameters of materials with temperature on the Matlab platform, so that stress-strain curves at multiple temperature points in the range of 4K to 1500K can be obtained by interpolation and extrapolation based on a limited number of experimental temperature points, while the extrapolation error can be evaluated in a controllable manner.

[0035] (3) Technical problems of single stress-strain curve fitting model and strong reliance on manual intervention.

[0036] Existing curve fitting methods mostly use a single constitutive form (such as ideal elastoplastic or simple Ramberg–Osgood models), which lacks a flexible description of the yield plateau, strain hardening, and even phase transformation behavior of materials at different temperatures. At the same time, the model selection, parameter initialization, and outlier removal in the fitting process are highly dependent on human experience, resulting in inconsistent and untraceable results.

[0037] The third type of technical problem to be solved by this invention is: how to build a configurable multi-model fitting framework in Matlab (supporting ideal elastoplastic, multilinear reinforcement, Ramberg-Osgood type and its variants, etc.), and use automated parameter identification and error evaluation algorithms to reduce human subjectivity and improve the robustness and uniformity of the fitting.

[0038] (4) Technical problem of lacking an automatic feedback correction and incremental update mechanism for newly added experimental / measured data

[0039] Throughout the entire lifespan of a nuclear fusion device, with the introduction of new batches of materials, the conduct of new temperature point experiments, and the accumulation of service measurement data, existing practices make it difficult to update the existing constitutive database in a timely manner. Often, it is necessary to reorganize and fit all the data, which is labor-intensive and prone to errors.

[0040] The fourth type of technical problem to be solved by this invention is: how to design a multi-temperature zone material stress-strain fitting system with "feedback correction" and "incremental update" capabilities, so that new data can automatically participate in the refitting and parameter correction of existing models, and dynamically improve the accuracy of extrapolation curves in different temperature ranges.

[0041] (5) Technical issues related to loose coupling with engineering specifications and finite element simulation environment

[0042] Existing methods often only focus on experimental data processing or academic analysis, lacking standardized interfaces with specifications such as ASME BPVC VIII-2 and finite element software such as Abaqus / ANSYS. This results in a large amount of manual processing and format conversion required when importing material curves into simulations, which is not conducive to batch analysis and archiving of results in engineering projects.

[0043] The fifth type of technical problem to be solved by this invention is: how to achieve automatic mapping and export between Matlab and engineering specification parameter formats and finite element material card formats, forming a multi-temperature zone material database that can be directly used in simulation models, and supporting visual inspection and automatic report generation.

[0044] To address this, this invention proposes a method and system for fitting stress-strain curves across multiple temperature zones for materials used in nuclear fusion devices. This technique does not rely on complete tensile test curves; instead, it constructs a monotonic stress-strain curve model conforming to the ASME BPVC VIII-2 standard based solely on temperature-dependent fundamental performance parameters such as yield strength, ultimate strength, elastic modulus, and Poisson's ratio. The model automatically generates stress-strain data for multiple temperature zones from 4K to 1500K in the Matlab environment for finite element simulation and strength assessment. When necessary, a small number of measured stress-strain points are used to provide feedback correction to the model.

[0045] ASME VIII-2, in Annex 3-D, provides a recommended model for constructing stress-strain curves based on yield strength and ultimate strength, and offers a parameter table for fitting, which can serve as a reference basis for stress-strain curve models. This invention draws upon its approach of "constructing stress-strain curves using yield strength + ultimate strength + a small number of fitting parameters," and proposes a set of analytical model derivation and multi-temperature-zone fitting procedures for the Ramberg-Osgood type, which are easy to implement and extend in Matlab.

[0046] The following description, with reference to the accompanying drawings, illustrates a method and system for fitting stress-strain curves of materials in a nuclear fusion device across multiple temperature zones, according to embodiments of the present invention.

[0047] Figure 1 This is a flowchart of a method for fitting stress-strain curves of materials in a nuclear fusion device across multiple temperature zones, according to an embodiment of the present invention.

[0048] In this embodiment, the method for fitting the stress-strain curves of materials in multiple temperature zones of a nuclear fusion device can be implemented using Matlab. For example... Figure 1 As shown, the method for fitting stress-strain curves of materials in multiple temperature zones of nuclear fusion devices includes:

[0049] S11, determine the basic performance parameters of the nuclear fusion device material at at least one target temperature within a preset temperature range, wherein the basic performance parameters include yield strength, ultimate strength, elastic modulus and plastic reference strain parameter.

[0050] In this embodiment, the preset temperature range can be 4K to 1500K, and the target temperature can be a preset standard temperature (such as obtained from ASME standards), or other typical or critical point temperatures determined according to actual needs, in K.

[0051] S12. For each target temperature, based on the yield strength, ultimate strength, elastic modulus and plastic reference strain parameters at the target temperature, a monotonic constitutive model based on yield point and ultimate point constraints is established, and the monotonic stress-strain curve at the target temperature is obtained by fitting the monotonic constitutive model.

[0052] This method generates temperature-dependent stress-strain curves by precisely controlling the yield point and limit point constraints, which can solve the problems of scarce material data and inconsistent fitting in multiple temperature zones of nuclear fusion devices, and improve the accuracy of finite element simulation and design reliability.

[0053] In some embodiments of the present invention, determining the basic performance parameters at the target temperature includes: determining whether the target temperature is a preset specification temperature; if it is a preset specification temperature, obtaining the basic performance parameters at the target temperature from a preset memory; if it is not a preset specification temperature, obtaining the two preset specification temperatures with the smallest difference between the target temperature and the two preset specification temperatures from the preset memory, and using an interpolation method based on the basic performance parameters at the two preset specification temperatures to obtain the basic performance parameters at the target temperature.

[0054] Specifically, step S11 involves the collection and processing of basic material parameters for multiple temperature zones, including:

[0055] (1) Obtain temperature-related strength and elastic parameters from ASME standards

[0056] 1) Find the yield strength of the material at each preset specification temperature in ASME BPVC Section II, Part D. With ultimate strength ;

[0057] 2) Find the elastic modulus of the material at various temperatures in Annex 3-E or relevant property tables. ;

[0058] 3) Obtain Poisson's ratio from ASME or material handbooks and literature. For materials whose temperature variations are not significant across multiple temperature zones, Poisson's ratio can be taken as a constant value. .

[0059] (2) Introducing plastic reference strain parameters

[0060] Table 3-D.1 of Annex 3-D provides the stress-strain curve parameters for different materials, including a strain parameter representing the material in the "macroscopic plastic region". It is used to control the "length and steepness" of the plastic strengthening section.

[0061] This invention will Considered as "the target value of plastic strain at the ultimate strength", denoted as If left as a default value, a default value can be provided based on the material type, and manual modification in Matlab or recalibration using a small number of measured points is supported.

[0062] (3) Establish a set of temperature points

[0063] A temperature list is generated based on various preset standard temperatures:

[0064]

[0065] in,

[0066] For the first Temperature points, in K; The total number of temperature points is dimensionless.

[0067] Matlab will use the above , , , , Used as basic input and stored.

[0068] Based on this, if the target temperature is within the aforementioned set of temperature points, the basic performance parameters at the target temperature can be obtained directly from the stored data.

[0069] For example, when the target temperature is not the preset specification temperature, the basic performance parameters of the target temperature are obtained by the following formula:

[0070] (1)

[0071] in, , for target temperature The following are the basic performance parameters; Target temperature The yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters are given. Preset standard temperature The following are the basic performance parameters. Preset standard temperature The following are the basic performance parameters. In and between.

[0072] Specifically, ASME tables typically only provide discrete temperature points. , , This invention performs multi-temperature-zone parameter interpolation and extrapolation on these parameters in Matlab, thereby achieving arbitrary target temperatures within the range of 4K to 1500K. Rapidly generate stress-strain curves. Includes:

[0073] (1) Linear interpolation of basic parameters with temperature

[0074] For a certain parameter At adjacent known temperatures Linear interpolation can be performed using the above formula (1).

[0075] (2) Extrapolation to 4K and 1500K

[0076] For points slightly exceeding the preset temperature range (such as 4K or manufacturing processes approaching 1500K), linear or low-order polynomial extrapolation can be appropriately used, provided that the parameter change trend is reasonable. A "physical rationality check" should be set in the system to prevent the generation of non-physical curves.

[0077] The physical rationality check involves verifying the key characteristics of the generated curve, including: whether the elastic modulus and strength parameters remain positive and change continuously; whether the yield strength and ultimate strength satisfy the temperature correlation of monotonically decreasing (high temperature) or increasing (low temperature); and whether the plastic hardening trend conforms to the behavior of typical metallic materials. If the extrapolation result violates any of the above criteria, an alarm can be triggered, prompting manual intervention for correction. This expands the temperature coverage range while fundamentally eliminating the risk of generating non-physical curves due to over-extrapolation, ensuring the rigor and safety of engineering analysis.

[0078] In some implementations, the temperature list may also include typical temperatures of nuclear fusion devices (4K, 80K, 293K, 500K, and welding high temperature 1500K), and the basic performance parameters corresponding to these typical temperatures may be stored in advance for recall when needed.

[0079] Therefore, by pre-setting and storing typical temperature points of nuclear fusion devices such as 4K, 80K, 293K, 500K, and the welding high temperature of 1500K, system coverage of key operating conditions over an ultra-wide temperature range can be achieved. This design can directly correlate material properties at each characteristic temperature, providing clear engineering anchors for the establishment and extrapolation of temperature-related constitutive models, effectively supporting the simulation accuracy of the entire process from the low-temperature service of superconducting magnets to the high-temperature welding in vacuum chambers.

[0080] In some embodiments of the present invention, the monotonic constitutive model is expressed by the following equation:

[0081] (2)

[0082] in, The true strain is dimensionless. This represents the true stress, measured in MPa. Target temperature The elastic modulus at 100°, in MPa; Target temperature Yield strength at 0.2% specified plastic strain (0.2% specified plastic strain yield), unit MPa; Target temperature The strain coefficient under the yield is usually related to the "0.2% offset strain" in the yield definition, and has a value of 0.002, which is dimensionless; , Target temperature The strain hardening exponent is dimensionless. Target temperature The plastic reference strain parameters are as follows: Target temperature The ultimate strength below.

[0083] Specifically, the monotonic constitutive model can adopt a uniaxial Ramberg–Osgood type real stress-strain model, as shown in equation (2) above, which serves as the basis for the monotonic constitutive model. In equation (2) above, the first term... It is linear elastic strain, item 2. It is plastic additional strain. As long as it is determined... and The Ramberg–Osgood type real stress-strain model can then be used to generate the stress-strain curve for the entire process at that temperature.

[0084] Regarding parameters The derivation can be based on the "0.2% offset yield". Yield strength in ASME Typically defined as a 0.2% offset, meaning when the total strain reaches: hour, ,in, Represents the plastic strain components. (The engineering strain or the actual strain is approximately the same).

[0085] In the Ramberg–Osgood model of this invention, when At that time, we have the following formula (3):

[0086] (3)

[0087] Corresponding this to the total strain defined by a 0.2% offset, we obtain the following equation (4):

[0088] (4)

[0089] In other words, under the 0.2% offset yield definition, You can directly take 0.002, and it is independent of temperature and material (unless other offset standards are used).

[0090] Physical meaning: The curve constructed in this way corresponds to the "plastic strain initiation offset at the yield point" and is consistent with the 0.2% offset yield in the specification. This curve matches the ASME yield definition near the yield point.

[0091] Regarding the hardening index The derivation can be based on the ultimate strength. With plastic reference strain parameters Proceed accordingly. Refer to Annex 3-D Table 3-D.1 or engineering experience, at the ultimate strength... At this point, its plastic strain reaches the predetermined target value. .

[0092] (1) Define the total strain and plastic strain at the limit point

[0093] exist At that time, the total strain given by the Ramberg–Osgood model is:

[0094] (5)

[0095] in, The total true strain at the ultimate strength is dimensionless. For temperature The ultimate strength of the engineering structure, in MPa.

[0096] The corresponding plastic strain is defined as:

[0097] (6)

[0098] Combining the total strain given by the Ramberg–Osgood model, we can obtain:

[0099] (7)

[0100] (2) Set constraints

[0101] Let the limit point plastic strain equal the target plastic strain, as follows:

[0102] (8)

[0103] That is, at the ultimate strength, the plastic strain is equal to the reference strain of the "macroscopic plastic zone" selected in advance or recommended by the specification. Therefore, we can obtain:

[0104] (9)

[0105] Taking the natural logarithm of both sides, we get:

[0106] (10)

[0107] Solve the hardening index :

[0108] (11)

[0109] in, For temperature The target value of plastic strain at the selected limit point is dimensionless; This is the offset strain coefficient, typically 0.002; For the strength ratio , dimensionless. Decide "at which point do we begin to clearly yield" Determines "how high the stress a material can withstand". It determines "approximately how much plastic deformation has accumulated when the ultimate strength is reached".

[0110] Based on satisfying both the 0.2% offset definition of the yield point and ensuring that the plastic strain at the limit point reaches the expected level, the hardening index is... It's calculated automatically.

[0111] In some embodiments of the present invention, generating a monotonic stress-strain curve at a target temperature using a monotonic constitutive model includes: generating multiple true strains within a predetermined strain range; solving for the true stress corresponding to each true strain using a monotonic constitutive model based on yield point and limit point constraints; and obtaining a monotonic true stress-strain curve at the target temperature by fitting multiple true stresses and their corresponding multiple true strains.

[0112] Specifically, after obtaining the temperature Below , , , , Then, the monotonic stress-strain curves at this temperature were generated in Matlab using a Ramberg–Osgood type true stress-strain model. This included:

[0113] (1) Take several strain sampling points

[0114] Within the predetermined strain range Internally generated series of real strains: .in, For the first A real response, dimensionless; The number of actual strains is dimensionless.

[0115] (2) Solve for the corresponding true stress using the Ramberg–Osgood type true stress-strain model.

[0116] Since stress appears in the exponential term in the Ramberg–Osgood model, numerical methods (such as Newton–Raphson) are generally required for solving it.

[0117] (12)

[0118] For each Iterative solution To obtain the true stress-strain point series .

[0119] (3) Based on the actual stress-strain point series The monotonic stress-strain curve was obtained by fitting.

[0120] For example, generating a monotonic stress-strain curve at a target temperature using a monotonic constitutive model further includes: calculating multiple engineering stresses and their corresponding multiple engineering strains based on multiple real strains and their corresponding multiple real stresses; and generating a monotonic engineering stress-strain curve at the target temperature based on the multiple engineering stresses and their corresponding multiple engineering strains.

[0121] Specifically, in obtaining the stress-strain point series Then, according to the engineering form required by the finite element software, it is converted into an engineering stress-strain point series using the following formula (13):

[0122] (13)

[0123] in, For the first Each engineering stress is expressed in MPa. For the first The strain of an engineering sample, under the assumption of small deformation, is approximately the same as the actual strain and is dimensionless.

[0124] Subsequently, based on the engineering stress-strain point series The monotonic stress-strain curve was obtained by fitting.

[0125] The discrete points (i.e., the stress-strain point column) generated above can be directly exported as a multi-point stress-strain table required by software such as Abaqus and ANSYS.

[0126] In some embodiments of the present invention, the method for fitting stress-strain curves of materials in nuclear fusion devices across multiple temperature zones further includes: acquiring multiple measured stresses and their corresponding multiple measured strains at a target temperature; calculating the fitting error at the target temperature based on the multiple measured stresses and their corresponding multiple measured strains; and adjusting parameters. , , At least one of them is used to minimize the fitting error and obtain the corrected monotonic true stress-strain curve at the target temperature.

[0127] Specifically, although the basic model of this invention can rely entirely on , , , , However, to further improve the accuracy of key temperature points, this invention introduces a feedback correction mechanism:

[0128] (1) At the target temperature If a small number of measured stress-strain data points are obtained Error functions can be defined in Matlab:

[0129]

[0130] in, Target temperature Fitting error under; The quantity of the measured stress is dimensionless. To utilize the Ramberg–Osgood model based on the target temperature The j-th measured strain The fitted stress is obtained in MPa; Target temperature The j-th measured stress, in MPa.

[0131] (2) with , , At least one of them is a parameter to be tuned, which is minimized under constraints using an optimization algorithm in Matlab (such as fminsearch or lsqnonlin). This allows the temperature to be automatically corrected. The monotonic stress-strain curve.

[0132] It should be noted that if new measured data are available for the same material at multiple temperature points, the data can be analyzed along the temperature dimension. , Perform a smooth fit to make the overall parameters more consistent with actual temperature changes, and provide a more reliable extrapolation curve for untested temperature points.

[0133] In some embodiments of the present invention, the basic performance parameters also include Poisson's ratio; the method further includes: generating an elastic matrix based on Poisson's ratio and elastic modulus; and using the elastic matrix, combined with the yield strength and the plastic hardening law extracted from the monotonic constitutive model, establishing an elastoplastic constitutive model for three-dimensional finite element simulation.

[0134] Specifically, although uniaxial stress-strain curves only require the elastic modulus... However, in three-dimensional finite element simulation, an elasticity matrix is ​​also required. This invention utilizes Poisson's ratio. The shear modulus and bulk modulus are generated using the following formulas for easy integration with FE programs:

[0135] (14)

[0136] (15)

[0137] in, For temperature Lower shear modulus, in MPa; For temperature Lower bulk modulus, in MPa; For temperature Poisson's ratio is dimensionless.

[0138] The elasticity matrix is ​​obtained through the following formula.

[0139] (16)

[0140] The shear modulus appears directly in the last three diagonal elements of the matrix and uniquely controls the relationship between all shear stress components and their corresponding engineering shear strain components. The bulk modulus, in combination with the shear modulus, appears in the first three diagonal and off-diagonal elements of the matrix, jointly controlling the relationship between all normal stress components and normal strain components. This combination reflects that normal strain causes both volume changes (contributed by the bulk modulus) and shape changes (contributed by the shear modulus).

[0141] It can automatically output temperature-related elastic constants compatible with various finite element software in Matlab, realizing a one-stop conversion from "parameter table" to "material card".

[0142] The method of this invention can use Matlab as the core computing and management platform, and may include, but is not limited to, the following functional modules:

[0143] ① Parameter Import Module: Import parameters from ASME standard forms, material manuals, or user-defined files. , , , , Data, etc.

[0144] ② Model parameter determination module: based on the offset strain coefficient Derivation of formula and hardening index The derived formula automatically calculates the temperature points. and ;

[0145] ③ Curve generation module: Generates stress-strain data points at various temperatures by discretizing according to the Ramberg–Osgood model, and can choose to output in real or engineering form;

[0146] ④ Multi-temperature zone interpolation and extrapolation module: Performs temperature interpolation and extrapolation on parameters, and quickly generates curves at any temperature within the range of 4K to 1500K;

[0147] ⑤ Feedback Correction Module: Performs fitting error analysis on a small number of measured points and automatically adjusts the settings. , Parameters such as these enable incremental updates of the model;

[0148] ⑥ Material Library and Interface Module: Store multi-temperature zone stress-strain curves and material parameters into the database, and export them with one click to the material cards or input fragments required by software such as Abaqus and ANSYS.

[0149] Through the above steps and modules, this invention can construct multi-temperature stress-strain curves that conform to engineering specifications using existing basic data such as temperature-related yield strength, ultimate strength, and elastic modulus in the ASME standard without the need for complete experimental curves. This enables efficient constitutive modeling of key materials for nuclear fusion devices in the range of 4K to 1500K, while retaining the ability to make feedback corrections through limited experimental points, thus significantly improving the accuracy, uniformity, and maintainability of simulation input data.

[0150] In some embodiments of the present invention, the method further includes: simultaneously calling multiple candidate constitutive models (which can be obtained based on the monotonic constitutive model described above) at the same target temperature, performing parallel fitting based on the same basic material performance parameters to obtain the fitted stress-strain curves corresponding to each candidate constitutive model; automatically screening and scoring each fitted stress-strain curve based on a preset set of physical rationality criteria, wherein the set of physical rationality criteria includes at least: the fitted curve has a positive slope in the elastic stage, maintains strain monotonicity and stress non-negativity in the plastic stage, the yield strength ratio is within a preset reasonable range, and the predicted hardening behavior meets the material constitutive convexity requirements; comprehensively ranking each candidate constitutive model according to the goodness-of-fit index and physical rationality score results; automatically selecting the optimal candidate constitutive model as the final model at the target temperature based on the ranking results, and automatically marking or removing non-physical behavior curves appearing in the fitting results.

[0151] Specifically, by adding a constitutive model automatic selection and physical constraint screening module to the Matlab platform, the Ramberg–Osgood model, the multilinear hardening model, and other candidate constitutive forms can be simultaneously fitted in parallel at the same temperature point. Based on physical rationality criteria such as fitting error, yield strength ratio constraint, strain monotonicity, and stress-strain curve convexity, different models are automatically scored and ranked to select the constitutive model that best fits the characteristics of the material and temperature range. At the same time, when a candidate model exhibits non-physical problems such as "stress drop" or "abnormal increase in stiffness" in a local strain range, it can be automatically marked and eliminated. Thus, multi-model automatic selection and curve quality control can be completed without manual intervention, further improving the intelligence and engineering reliability of the fitting process.

[0152] In some embodiments of the present invention, the method further includes: treating the basic performance parameters as random input variables with preset statistical distribution characteristics; generating multiple sets of material parameter samples based on the random input variables using Latin hypercube sampling or Monte Carlo simulation methods; automatically calling a monotonic constitutive model for each set of material parameter samples to generate corresponding stress-strain curves in batches; statistically analyzing the set of stress-strain curves generated in batches to obtain the confidence interval of stress response within the key strain range; and calculating the sensitivity index of each random input variable based on the batch generation results to generate a constitutive model with intervals and parameter sensitivity ranking for safety margin assessment.

[0153] Specifically, by introducing uncertainty and sensitivity analysis functions at the material parameter input end, yield strength, ultimate strength, elastic modulus, and reference plastic strain can be treated as random variables with statistical fluctuations. Multiple sets of parameter samples can be generated in Matlab using Latin hypercube sampling or Monte Carlo methods, and a corresponding stress-strain curve can be automatically constructed for each set of samples. The confidence interval and sensitivity ranking results of stress response within the key strain range can be statistically obtained, thus providing "range-based" constitutive input for the safety margin assessment of key components of nuclear fusion devices. In terms of implementation, this function only requires extending the existing participation curve generation module, which can significantly improve the robustness and innovation of material constitutive modeling against batch differences and measurement errors.

[0154] The method of the present invention is described below through three system embodiments, and the method of the present invention can be used in these systems:

[0155] Example 1: Multi-temperature zone stress-strain curve fitting method based on standard parameters

[0156] This embodiment provides a specific implementation method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices. It focuses on how to generate stress-strain curve data that can be directly used for finite element simulation at multiple temperature points without relying on complete tensile test curves, using only parameters such as yield strength, ultimate strength, elastic modulus, Poisson's ratio, and plastic reference strain given in the specifications.

[0157] 1.1 System Operating Environment

[0158] The system in this embodiment runs on a general-purpose computer or engineering workstation and includes:

[0159] The processor is used to execute Matlab program code; the memory is used to store material parameter tables, fitting results, and generated stress-strain data files; the display is used to show curve graphs, parameter tables, and export settings interfaces; the operating system can be a general desktop operating system; and the Matlab software platform is used to realize data reading, parameter calculation, curve generation, and result export.

[0160] The system can be implemented as a Matlab script or a graphical interface based on Matlab App Designer, allowing users to import parameters, set fitting parameters, and export results through the interface.

[0161] 1.2 Import and management of basic material parameters (implemented by the basic material parameters module)

[0162] In this embodiment, the user first establishes a "material basic parameter table" for key materials of a nuclear fusion device in the system.

[0163] Based on ASME standards and material handbooks, users compiled basic material parameters at multiple temperature points, including:

[0164] Yield strength parameter, ultimate strength parameter, elastic modulus parameter, Poisson's ratio parameter, and plastic reference strain parameter for each temperature (these can be referenced from the recommended values ​​in the specifications or provided by engineering experience).

[0165] Users can import the above data in the following ways:

[0166] Enter tables directly in the Matlab interface; import from external table files, such as comma-separated text files or spreadsheet files; retrieve existing material parameter records from an existing project database.

[0167] After importing, the system will automatically check the temperature list to ensure that the temperature values ​​are arranged in ascending order, and check whether there are any missing or unreasonable values ​​for each physical property parameter, such as a negative elastic modulus or a yield strength greater than the ultimate strength. If any abnormalities are found, the system will prompt the user to make corrections.

[0168] After importation, the system saves the material's "temperature list" and "corresponding basic parameters" in a structured format, serving as a unified data source for subsequent fitting.

[0169] 1.3 Procedure for obtaining constitutive parameters at a single temperature point (implemented by the single-temperature constitutive parameter determination module)

[0170] In this embodiment, the system uses a target temperature as an example to illustrate the process of obtaining single-temperature constitutive parameters.

[0171] The user selects the target temperature in the interface. If the target temperature already exists in the basic parameter table, the corresponding yield strength, ultimate strength, elastic modulus, Poisson's ratio, and plastic reference strain parameters are used directly. If the target temperature is between two preset specification temperature points, the system will interpolate the parameters of the two adjacent temperature points to obtain the basic parameters for the current temperature. The interpolation method can be selected by the user; the default is linear interpolation.

[0172] The system uses these basic parameters and a preset analytical constitutive model to constrain the strain levels near the yield and the limit, so that the yield point corresponds to the offset strain specified in the specification and the limit point corresponds to the expected plastic deformation level.

[0173] The system internally solves for the constitutive model parameters, such as determining the boundary between the elastic and plastic segments and the strengthening morphology of the plastic segment, and stores these constitutive parameters in a "single-temperature constitutive parameter table" for use in curve generation at that temperature.

[0174] In this process, users do not need to manually derive the expressions; they only need to provide the basic parameters for each temperature point, and the system will automatically obtain the constitutive parameters for each temperature.

[0175] 1.4 Generation and visualization of single-temperature stress-strain curves (implemented by the curve generation module)

[0176] After obtaining the constitutive parameters for a single temperature, the system in this embodiment continues to generate stress-strain curve data at that temperature. Based on the strain range and step size set by the user, the system generates a set of strain sampling points within that range, for example, from zero strain to a certain maximum strain limit. For each strain sampling point, the system calls the aforementioned constitutive parameters to calculate the corresponding stress value, thereby forming a set of paired strain and stress data.

[0177] The system automatically plots the stress-strain curve at that temperature, which users can view on the interface: whether the overall shape of the curve is reasonable, whether there is an obvious yield inflection point near the yield point, and whether the expected strengthening trend is reflected near the ultimate strength.

[0178] Users can zoom in, zoom out, and shift the curve, and view the stress and strain values ​​of any data point on the graph for engineering judgment. If users believe that the plastic deformation range is too long or too short, they can appropriately adjust the plastic reference strain parameter or related settings at that temperature. The system will immediately regenerate a new curve to quickly compare the impact of different settings on the curve shape.

[0179] The generated curve data can be saved either in the form of "true stress – true strain" or converted to the form of "engineering stress – engineering strain" according to the requirements of the finite element software and then saved.

[0180] 1.5 Automatic generation of multi-temperature zones and batch export of curves

[0181] After implementing the single-temperature curve generation process, this embodiment further realizes the batch processing capability of multiple temperature points.

[0182] Users can select multiple target temperatures in the interface, such as typical temperature points of nuclear fusion devices, including superconducting magnet operating temperature, cold screen operating temperature, room temperature structure temperature, vacuum chamber baking temperature, and welding manufacturing temperature, etc., or they can select all temperature points in the specification table to generate the full range.

[0183] The system sequentially performs the following for each target temperature: automatically acquires or interpolates the basic parameters at that temperature, automatically calculates the constitutive model parameters, automatically generates stress and strain data at that temperature, and automatically plots and saves the curve image.

[0184] Once generated, the system will display the status of each temperature point in a list on the interface, including: whether a curve has been generated; whether it has passed basic rationality checks, such as whether the yield strength and ultimate strength are correctly ordered; and the save paths for the curve file and image file.

[0185] Users can choose one or more export formats, such as: a text input fragment compatible with a specific finite element software; a universal comma-separated data file for use by other programs; or a summary file containing all temperature point curves for easy reuse in subsequent projects.

[0186] 1.6 Basic Implementation of Feedback Correction Function

[0187] In this embodiment, the system also provides a basic feedback correction function, which is used to introduce a small amount of measured data at key temperature points to fine-tune the curve.

[0188] When a user obtains a limited number of measured stress-strain data points at a specific temperature, they can import this data into the system in tabular form. The system will compare the curve generated by the current model with these measured data, calculate the error metric between the two, and graphically display the position of the measured points relative to the model curve.

[0189] Within the user-permitted range, the system can automatically adjust some control parameters at that temperature point, such as parameters related to the plastic reference strain or strengthening mode, to make the corrected curve closer to the measured data, while keeping the yield strength and ultimate strength unchanged. After the correction is completed, the system updates the constitutive parameters and curve data at that temperature point and records the comparison results before and after the correction for easy tracking and review.

[0190] 1.7 Integration of Material Library and Finite Element Interface

[0191] This embodiment manages the above-mentioned multi-temperature zone stress-strain curves in a unified manner in the form of a "material library" and provides an external interface.

[0192] In the material library, each material corresponds to an independent entry, which records: material grade and description, temperature list and basic parameters at each temperature, constitutive model type and parameters at each temperature, stress and strain data file path at each temperature, and whether there is a feedback correction record.

[0193] The system provides a one-click export function, allowing users to: export a single material card file for a specific material and temperature; export a complete set of multi-temperature zone material cards for a specific material for direct use by finite element software; and back up the material library as a universal data file for restoration and use in other projects or on other computers.

[0194] When used in conjunction with finite element software, users only need to select the corresponding material and temperature before simulation, and the exported material card can be directly embedded into the simulation model without having to manually edit the stress and strain points.

[0195] Through the above steps, this embodiment achieves full automation from standard parameters to multi-temperature stress-strain curves. It is applicable to multi-temperature baseline modeling of vacuum chambers, cold shields, Dewars, support structures, and superconducting magnet-related structural components in nuclear fusion devices, providing a unified and maintainable material input basis for subsequent strength analysis, fatigue assessment, and welding simulation.

[0196] Example 2: A system with automatic constitutive model selection and physical screening functions

[0197] Based on Example 1, this embodiment further integrates the "automatic constitutive model selection and physical screening function", which is used to automatically compare multiple candidate constitutive models at the same temperature point, and automatically select the most suitable stress-strain curve model based on the fitting quality and physical rationality, thereby reducing human subjective judgment and improving curve quality and engineering reliability.

[0198] 2.1 Functional Module Structure

[0199] In addition to the existing modules in Example 1, this example adds the following functional modules: constitutive model candidate library module, constitutive fitting and scoring module, physical constraint screening module, and model optimization and result management module.

[0200] The above modules work together with the "material basic parameter module", "single temperature constitutive parameter calculation module" and "curve generation module" in Example 1. By adding automatic judgment and screening steps, intelligent selection of constitutive models is achieved.

[0201] 2.2 Design of Constitutive Model Candidate Library

[0202] In this embodiment, the system incorporates several typical constitutive models (i.e., the aforementioned candidate constitutive models) applicable to pressure vessels and nuclear fusion structural materials: a continuous smooth curve model with yield strength and ultimate strength as control points; a piecewise linear hardening model with obvious elastic segments and yield plateaus; a smooth hardening model suitable for high-strength steel or materials with obvious hardening; and a simplified hardening model suitable for materials with shorter plastic regions.

[0203] Each type of model has a unified description in the system, including: required input parameters, applicable temperature range, and adjustable internal parameters during fitting. Users can select the types of models to be included in the comparison in the interface, or select only a subset of models for selection.

[0204] 2.3 Parallel Fitting and Scoring Process for Multiple Models

[0205] At a target temperature, the system first obtains the basic parameters for that temperature from the standard parameter table according to the method in Example 1, and then enters the multi-model fitting process: the system sequentially calls each model type in the candidate library, uses the same set of basic parameters, and generates a stress-strain curve at this temperature; for each model type, the system generates a set of stress-strain discrete data according to a unified strain sampling point, and calculates the deviation between the data and the benchmark reference data or the preset target shape; the system calculates a "fit score" for each model.

[0206] The scoring can take into account the following factors: the degree of fit between the curve at the yield point and the limit point, the overall smoothness and monotonicity of the curve, and whether the slope change of the curve within the strain range of engineering concern is reasonable.

[0207] The fit score is recorded in numerical form and presented on the interface as a bar chart or table, allowing users to view the merits of different models.

[0208] In the absence of actual measurement data, this embodiment can use standard parameters and engineering experience as a reference; if there are a small number of actual measurement points, the deviations of these actual measurement points can also be included in the scoring calculation, so that the model that is closer to the actual measurement points can get a higher score.

[0209] 2.4 Physical Constraint Screening Mechanism

[0210] To avoid curves that are "mathematically well-fitted but physically unreasonable," this embodiment adds a physical constraint screening module to automatically check the curves generated by each candidate model.

[0211] Physical constraints include, but are not limited to: stress increasing monotonically with strain without significant stress drop; the slope of the elastic segment should be basically consistent with the input elastic modulus, with deviations within acceptable limits; no obvious plastic plateau should appear before the yield point; the ultimate strength should be greater than the yield strength; and the stiffness variation in different strain ranges should not show abnormal increases or negative stiffness phenomena.

[0212] When a curve generated by a model violates any of the above constraints, the system will automatically mark the model as "fail" and remove it or significantly reduce its weight during the scoring stage. The interface will display the specific "reason for failure," such as "stress drop occurs in the limit segment" or "excessive nonlinearity of the curve before yielding," to facilitate understanding and confirmation by engineers.

[0213] 2.5 Model Optimization and Result Consolidation

[0214] After scoring and physical screening of all candidate models, the system enters the optimization stage: the system automatically selects the model with the highest score and that passes the physical screening as the "recommended constitutive model" for that temperature point; if the user needs, they can also manually select one of the "highly scored and screened" models as the final model, and the system records the user's selection; the final selected model type and corresponding parameters are uniformly stored in the material database and used for the generation and export of subsequent stress-strain curves at that temperature point.

[0215] Through the above process, this embodiment realizes automatic comparison of multiple models and screening of physical rationality, avoids relying on a single model, reduces the influence of human experience, and makes the generated stress-strain curves more robust, safe and traceable.

[0216] Example 3: A system with material parameter uncertainty and sensitivity analysis capabilities

[0217] This embodiment, based on Embodiment 1, incorporates the aforementioned "better" solution by introducing a material parameter uncertainty and sensitivity analysis function. The aim is to provide the variation range of the stress-strain curve at a certain confidence level through automatic statistical analysis methods, especially when there are batch differences, measurement errors, or differences in literature regarding the basic material parameters. It also identifies the sensitive parameters that have the greatest impact on the curve, providing a reference for safety margin assessment and parameter control.

[0218] 3.1 Uncertainty Modeling Module

[0219] This embodiment introduces uncertainty descriptions at the level of fundamental material parameters. Taking a certain material as an example, statistical characteristics are introduced for the following parameters: the possible fluctuation range of yield strength at a certain temperature, the possible fluctuation range of ultimate strength at a certain temperature, the measurement dispersion of elastic modulus at a certain temperature, the upper and lower limits of the engineering-acceptable range of plastic reference strain, and the dispersion range of Poisson's ratio between different test results.

[0220] The system allows users to specify a simple probability distribution type for each of the above parameters in the interface, such as a uniform distribution or a normal distribution, and to set the mean and fluctuation range. For scenarios without clear statistical data, users can also use engineering experience to provide upper and lower limit intervals, and the system will automatically construct a reasonable distribution hypothesis.

[0221] 3.2 Sampling and Batch Curve Generation Process

[0222] After completing the parameter uncertainty modeling, the system in this embodiment generates multiple sets of "virtual material parameter samples" through sampling methods, and constructs corresponding stress-strain curves for each set of samples: the user sets the number of samples in the interface, for example, selecting to generate several sets of parameter samples; based on the distribution assumptions of each parameter, the system uses Latin hypercube sampling or simplified Monte Carlo sampling methods to randomly generate multiple combinations of parameters such as yield strength, ultimate strength, elastic modulus, and plastic reference strain; for each set of parameter combinations, the system calls the constitutive parameter calculation and curve generation process in Embodiment 1 to generate corresponding stress-strain curves at the target temperature point or multiple temperature points; after the above iteration, the system will obtain a set of "curve families", that is, multiple different stress-strain curves generated at the same temperature point due to the uncertainty of material parameters.

[0223] Once generated, the system can overlay these curves on the interface and distinguish different samples by color or transparency, comparing their differences before yielding, after yielding, and in the near-limit region.

[0224] 3.3 Statistical Intervals and Sensitivity Analysis

[0225] After obtaining multiple stress-strain curves, this embodiment performs statistical analysis on key strain ranges: users can specify one or more strain ranges of engineering interest, such as the vicinity of yield, strain ranges commonly used in fatigue assessment, and plastic strain ranges commonly used in welding residual stress analysis; the system statistically analyzes the stress values ​​of all sample curves at the specified strain points, calculates their average value, standard deviation, and upper and lower limits at several confidence levels, such as the 5th and 95th percentiles; the system displays these statistical results in the form of "stress versus strain intervals," that is, plots an average curve on the graph and plots banded areas on both sides to represent the range of uncertainty; users can intuitively see the possible range of changes in the stress-strain curve within the fluctuation range of material parameters, providing a basis for conservative design or safety margin assessment.

[0226] For sensitivity analysis, this embodiment further ranks the parameters by comparing the magnitude of the influence of different parameter disturbances on the curve change, and obtains: which parameter has the greatest influence on the stress level near the yield, which parameter has the greatest influence on the stress or elongation at the end of the plastic zone, and which parameter has the most significant influence on the overall curve stiffness.

[0227] The system can output sensitivity ranking results in the form of a list or bar chart, prompting engineers to focus on which parameters during material acceptance, parameter control, and experimental design.

[0228] 3.4 Correlation between Uncertainty Results and Material Library

[0229] This embodiment links uncertainty analysis with the material library. For each material, the system adds sub-entries for "Parameter Uncertainty Configuration" and "Sensitivity Analysis Results" under the material library entry. When the user selects this material in a subsequent simulation project, they can choose to: use only the basic curve for normal qualitative analysis; export a "conservative curve," such as the curve corresponding to the upper limit of the statistical interval, for extreme condition evaluation; and, based on the sensitivity analysis results, determine the parameters that need to be more closely monitored in testing and quality control.

[0230] Through this mechanism, this embodiment not only provides a single "nominal curve" but also provides extended information with "uncertainty awareness," enabling simulation and design personnel to better understand the impact of material parameter fluctuations on structural response.

[0231] 3.5 Examples of Engineering Application Scenarios

[0232] In nuclear fusion devices, this embodiment can be applied to the following scenarios: when performing multi-temperature constitutive modeling on materials in the welding area of ​​the vacuum chamber, considering the differences in yield strength and ultimate strength of different batches of materials, the range of welding residual stress is obtained through uncertainty analysis; when performing low-temperature strength analysis on materials for cold shields and Dewar structures, the most unfavorable stress level under extreme low-temperature conditions is assessed by combining the material parameter dispersion; when performing fatigue evaluation on superconducting magnet support structures, the results of sensitivity analysis are used to determine the material parameters that should be focused on in subsequent tests and monitoring to improve the overall safety of the device.

[0233] Through Example 3, the present invention further expands the dimensions of "parameter uncertainty" and "sensitivity analysis" based on Example 1, so that the stress-strain curves of the multi-temperature zone are no longer single fixed values, but interval information with statistical meaning, thereby providing richer, more innovative and practical data support for the safety margin assessment and risk decision-making of nuclear fusion devices.

[0234] Figure 2 This is a flowchart of a method for fitting stress-strain curves in multiple temperature zones of materials for a nuclear fusion device according to a specific embodiment of the present invention.

[0235] like Figure 2 As shown, the method for fitting stress-strain curves of materials in multiple temperature zones of nuclear fusion devices includes:

[0236] S21, determine the target material and the temperature range to be covered, and select the typical operating temperature point in the nuclear fusion device;

[0237] S22, import parameters such as yield strength, ultimate strength, elastic modulus, Poisson's ratio and plastic reference strain parameters at each temperature point from the specifications and material handbook;

[0238] S23, Parameter completeness and rationality verification: Check whether the parameters at each temperature point are complete and whether the numerical relationships are reasonable;

[0239] If yes, proceed to step S24; otherwise, return to step S22.

[0240] S24: Organize the basic parameters for the target temperature point. If they already exist, use them directly. If they are between adjacent temperatures, interpolate to obtain the complete parameters for that temperature.

[0241] S25, based on the yield strength, ultimate strength, elastic modulus and plastic reference strain at this temperature, the system automatically obtains the constitutive control parameters describing the elastic segment and the plastic segment;

[0242] S26, generate a series of strain points within the preset strain range, calculate the corresponding stress using constitutive control parameters, obtain complete stress-strain data for the temperature and plot the curve;

[0243] S27, check whether the curve is monotonically reasonable, and whether the shape near the yield and limit conforms to engineering experience;

[0244] If yes, proceed to step S28; otherwise, return to step S25.

[0245] S28, determine whether the constitutive model automatic optimization function needs to be enabled for the current material and temperature;

[0246] If yes, proceed to step S29; otherwise, proceed to step S210.

[0247] S29, generate curves in parallel for multiple candidate constitutive models at the same temperature, calculate the fit score for each model and perform physical constraint checks;

[0248] S210: Select models with higher scores and those that pass physical screening as recommended models, and write the model type and control parameters into the material database.

[0249] S211 performs parameter processing, constitutive determination and curve generation on multiple temperature points in batches to form a multi-temperature zone stress-strain curve library and display it in chart form.

[0250] S212, engineers manually review the curves of key temperature points and, if necessary, fine-tune the control parameters of individual temperature points to conform to project experience.

[0251] S213, determine whether a small amount of actual measurement has been obtained for key temperature points, and whether it is needed for feedback correction;

[0252] If yes, proceed to step S214; otherwise, proceed to step S215.

[0253] S214: Import the measured data for the corresponding temperature, compare the current model curve with the measured points, and automatically fine-tune the control parameters to make the curve closer to the measured results.

[0254] After step S214, return to step S211.

[0255] S215, determine whether the current project needs to consider material parameter fluctuations and batch differences;

[0256] If yes, proceed to step S216; otherwise, proceed to step S219.

[0257] S216 sets the fluctuation range and distribution form for parameters such as yield strength, ultimate strength, elastic modulus and plastic reference strain, and generates multiple sets of parameter samples in the system;

[0258] S217 generates corresponding stress-strain curves for each set of parameter samples, statistically analyzes the average level and range of stress in the key strain interval, and displays them in the form of a curve band area.

[0259] S218 analyzes the impact of different parameter variations on the curves and key stress levels, and provides a ranking of parameter sensitivity and recommendations for engineering considerations.

[0260] S219 writes the multi-temperature zone basic curves, optimized model information, feedback correction records, and uncertainty analysis results into the material library, and exports them as material data files that can be directly called by finite element software as needed.

[0261] The multi-temperature region stress-strain curve fitting method for nuclear fusion device materials according to embodiments of the present invention can achieve the following beneficial effects:

[0262] ① It uses yield strength, ultimate strength, elastic modulus, Poisson's ratio, and plastic reference strain as inputs, without relying on the complete tensile test curve;

[0263] ② By using two types of constraints, namely "the yield point should meet the definition of offset yield" and "the limit point should meet the specified level of plastic deformation", the strengthening mode of the plastic segment is deduced, so that the generated curve is consistent with the specification parameters and engineering experience near both the yield and the limit.

[0264] ③ By organizing and interpolating the yield strength, ultimate strength, elastic modulus and plastic reference strain at different temperatures, a correspondence between temperature and constitutive control parameters is formed, which can quickly generate the corresponding monotonic stress-strain curve at any temperature in the range of 4K to 1500K.

[0265] ④ Using Matlab as the core platform, the entire process from parameter import, automatic parameter calculation, curve generation, visualization inspection to data export is integrated. Curves and constitutive parameters of multiple materials and multiple temperature zones are uniformly managed as a material library, facilitating cross-project reuse and maintenance;

[0266] ⑤ At a single temperature point, multiple constitutive models generate curves in parallel, and automatically score and sort them according to fitting quality and engineering rationality. At the same time, unreasonable curves such as stress drop and stiffness anomaly are automatically eliminated, and the most suitable model is recommended, which can reduce human subjective judgment.

[0267] ⑥ By importing a small amount of measured or inverted stress-strain data at key temperature points and comparing the differences with the model curve, and by automatically fine-tuning the morphology of the plastic segment while keeping the yield strength and ultimate strength unchanged, the curve can be made closer to the actual material behavior.

[0268] ⑦ By treating yield strength, ultimate strength, elastic modulus and plastic reference strain as fluctuating parameters, multiple families of curves are generated through sampling, the stress range of key strain regions is statistically analyzed, and the most sensitive parameters that have the greatest impact on the curves are given, which can provide a reference for safety margin and quality control.

[0269] ⑧ Automatically converts multi-temperature zone stress-strain discrete points or equivalent constitutive parameters into material card or data file formats that can be directly called by mainstream finite element software. This reduces manual processing and repetitive data entry, ensuring the consistency and traceability of material input.

[0270] Figure 3 This is a structural block diagram of the stress-strain curve fitting system for multi-temperature zones of materials in a nuclear fusion device according to an embodiment of the present invention.

[0271] like Figure 3 As shown, the multi-temperature zone stress-strain curve fitting system 100 for nuclear fusion device materials includes: a determination module 10 and a fitting module 20.

[0272] The determination module is used to determine the basic performance parameters of the nuclear fusion device material at at least one target temperature within a preset temperature range. The basic performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters. The fitting module is used to establish a monotonic constitutive model based on yield point and ultimate point constraints for each target temperature, based on the yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters at the target temperature, and to use the monotonic constitutive model to fit the monotonic stress-strain curve at the target temperature.

[0273] It should be noted that for other specific embodiments of the stress-strain curve fitting system 100 for multi-temperature zones of nuclear fusion device materials in the present invention, please refer to the specific embodiments of the stress-strain curve fitting method for multi-temperature zones of nuclear fusion device materials in the above embodiments.

[0274] In summary, the stress-strain curve fitting method and system for multi-temperature zones of nuclear fusion device materials according to the embodiments of the present invention have the following outstanding advantages compared with existing technical solutions that mainly rely on complete tensile test curves, constitutive fitting at a single temperature point, or are only applicable to general engineering materials:

[0275] (1) Significantly reduces reliance on experiments and lowers construction costs.

[0276] This invention only requires the yield strength, ultimate strength, elastic modulus, Poisson's ratio, and a small number of plastic reference strain parameters already given in the specifications and material handbooks to construct stress-strain curves for multiple temperature zones. It does not require additional complete tensile tests for each temperature point, making it particularly suitable for the challenging and costly conditions of nuclear fusion devices, such as low temperature, high temperature, and high welding temperature tests.

[0277] (2) Achieve continuous constitutive modeling in an ultrawide temperature range of 4K–1500K

[0278] Compared to existing technologies that mostly target room temperature or a few high-temperature points, this invention establishes a unified multi-temperature zone curve generation method based on typical operating temperatures such as superconducting magnets, cold shields, Dewars, vacuum chamber baking, and high-temperature welding. It can quickly obtain stress-strain curves at any temperature within the range of 4K–1500K, providing continuous and reliable material input for the full life cycle simulation of nuclear fusion devices.

[0279] (3) Automatically satisfies the standard yield and limit constraints, resulting in good engineering consistency.

[0280] This invention simultaneously satisfies the definition of yield strength and the requirement of ultimate strength in the specifications during model construction, ensuring that the generated curves are consistent with specifications such as ASME at the yield point and ultimate point. This avoids deviations caused by manually splicing curves based on experience, and improves the consistency and traceability between the model construction and strength and fatigue assessment.

[0281] (4) The integrated system based on Matlab is efficient and easy to promote.

[0282] Compared to scattered scripts or manual processing, this invention integrates functions such as parameter import, constitutive parameter calculation, curve generation, graphic inspection, material library management, and finite element interface export within the Matlab platform. It can complete batch processing of multiple materials and multiple temperature points with one click, greatly reducing the workload of manual data entry and repeated data processing, and is suitable for standardized promotion within engineering units.

[0283] (5) Automatic selection and physical screening of constitutive models reduce human subjective intervention.

[0284] Existing technologies often rely on engineers to subjectively select constitutive models. This invention generates multiple candidate models in parallel, scores and checks their physical rationality, automatically eliminates non-physical curves, and recommends the optimal model, achieving "automatic modeling + automatic quality control." This improves the consistency and reliability of results when used by multiple personnel and projects.

[0285] (6) It has feedback and correction capabilities and can gradually become more accurate as the project progresses.

[0286] This invention supports importing a small amount of measured or inverted data at key temperature points, automatically fine-tuning the morphology of the plastic segment without changing key indicators such as yield strength and ultimate strength, and writing it back to the material library to form a closed-loop correction mechanism. As experimental and operational data accumulate, the material curve can gradually approximate the actual behavior, which is significantly better than the traditional approach of fixing it once and for all and making it difficult to update.

[0287] (7) Introduce parameter uncertainty and sensitivity analysis to support safety margin assessment

[0288] This scheme can treat yield strength, ultimate strength, elastic modulus, etc. as fluctuating parameters, generate a family of curves, and give the stress range and sensitive parameter ranking of the key strain zone. It provides a quantitative basis for safety margin assessment of key components of nuclear fusion device, material batch control and test scheme design, which is difficult to achieve with the traditional single "nominal curve" method.

[0289] (8) Standardized interfaces for finite element software to reduce errors and repetitive work.

[0290] This invention can directly output material cards or data files usable by mainstream finite element software, avoiding errors introduced by manual copying and format conversion, simplifying the entire chain from standard parameters to simulation models, and improving the overall efficiency and reliability of engineering analysis.

[0291] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0292] Furthermore, 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 at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0293] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0294] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices, characterized in that, The method includes: Determine the basic performance parameters of materials for nuclear fusion devices at at least one target temperature within a preset temperature range, wherein the basic performance parameters include yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters; For each target temperature, a monotonic constitutive model based on yield strength, ultimate strength, elastic modulus and plastic reference strain parameters at the target temperature is established, and the monotonic stress-strain curve at the target temperature is generated using the monotonic constitutive model. The determination of the basic performance parameters of the materials for the nuclear fusion device at at least one target temperature within a preset temperature range includes: Determine whether the target temperature is a preset standard temperature; if it is the preset standard temperature, retrieve the basic performance parameters at the target temperature from the preset memory; if it is not the preset standard temperature, retrieve the two preset standard temperatures with the smallest difference from the target temperature from the preset memory, and use interpolation based on the basic performance parameters at the two preset standard temperatures to obtain the basic performance parameters at the target temperature.

2. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 1, characterized in that, When the target temperature is not a preset standard temperature, the basic performance parameters of the target temperature are obtained by the following formula: in, , for target temperature The following are the basic performance parameters; Target temperature The yield strength, ultimate strength, elastic modulus, and plastic reference strain parameters are given. Preset standard temperature The following are the basic performance parameters. Preset standard temperature The following are the basic performance parameters. In and between.

3. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 1, characterized in that, The monotonic constitutive model is expressed by the following equation: in, To respond realistically, For actual stress, Target temperature The elastic modulus below, Target temperature Yield strength below; Target temperature The strain coefficient is set to 0.

002. , Target temperature The strain hardening index is below; Target temperature The plastic reference strain parameters are as follows: Target temperature The ultimate strength below.

4. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 3, characterized in that, The step of generating the monotonic stress-strain curve at the target temperature using the monotonic constitutive model includes: Generate multiple real strains within a predetermined strain range; Using the monotone constitutive model based on yield point and limit point constraints, the true stress corresponding to each true strain is solved; The monotonic real stress-strain curve at the target temperature is obtained by fitting multiple real stresses and their corresponding real strains.

5. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 4, characterized in that, The step of generating the monotonic stress-strain curve at the target temperature using the monotonic constitutive model further includes: Based on the multiple real strains and their corresponding multiple real stresses, multiple engineering stresses and their corresponding multiple engineering strains are calculated. The monotonic engineering stress-strain curve at the target temperature is obtained by fitting multiple engineering stresses and their corresponding multiple engineering strains.

6. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 4, characterized in that, The method further includes: Obtain multiple measured stresses and their corresponding multiple measured strains at the target temperature; The fitting error at the target temperature is calculated using the following formula based on the multiple measured stresses and their corresponding multiple measured strains: in, Target temperature The fitting error is as follows. The quantity of the measured stress, To utilize the monotonic constitutive model based on the target temperature The j-th measured strain The obtained fitted stress, Target temperature The j-th measured stress; Adjust parameters , , At least one of them, to minimize the fitting error, to obtain the corrected monotonic true stress-strain curve at the target temperature.

7. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to claim 4, characterized in that, The basic performance parameter also includes Poisson's ratio; the method further includes: An elasticity matrix is ​​generated based on the Poisson's ratio and the elastic modulus; Using the elastic matrix, combined with the yield strength and the plastic hardening law extracted from the monotonic constitutive model, an elastoplastic constitutive model for three-dimensional finite element simulation is established.

8. The method for fitting stress-strain curves of materials in multiple temperature zones for nuclear fusion devices according to any one of claims 1-7, characterized in that, The method is implemented using Matlab.

9. A multi-temperature zone stress-strain curve fitting system for materials used in nuclear fusion devices, characterized in that, The system includes: The determination module is used to determine the basic performance parameters of the materials of the nuclear fusion device at at least one target temperature within a preset temperature range, wherein the basic performance parameters include yield strength, ultimate strength, elastic modulus and plastic reference strain parameters; The fitting module is used to establish a monotonic constitutive model based on yield strength and ultimate strength, elastic modulus and plastic reference strain parameters at each target temperature, and to fit the monotonic stress-strain curve at the target temperature using the monotonic constitutive model. The determination of the basic performance parameters of the materials for the nuclear fusion device at at least one target temperature within a preset temperature range includes: Determine whether the target temperature is a preset standard temperature; if it is the preset standard temperature, retrieve the basic performance parameters at the target temperature from the preset memory; if it is not the preset standard temperature, retrieve the two preset standard temperatures with the smallest difference from the target temperature from the preset memory, and use interpolation based on the basic performance parameters at the two preset standard temperatures to obtain the basic performance parameters at the target temperature.

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