Macroscopic finite element simulation analysis method and device considering plastic deformation of seals

Abstract

The present application provides a macroscopic finite element simulation analysis method and device for seals considering plastic deformation, which belongs to the field of seal design. The method includes: obtaining the engineering stress-strain curve of the plastic material under compression; converting the engineering stress-strain curve into a true stress-strain curve; determining the yield limit, and using the strain point corresponding to the yield limit as the dividing point between elastic and plastic deformation; extracting the elastic section of the true stress-strain curve, calculating the elastic modulus, and obtaining the Poisson's ratio by measuring the axial and lateral strains in the uniaxial compression test; extracting the plastic section of the true stress-strain curve, and establishing a multilinear isotropic hardening model; constructing a complete elastic-plastic constitutive model covering the elastic deformation zone and the plastic deformation zone; simulating the stress distribution, strain response and contact performance of plastic seals under compression deformation. The method and device provided in the present application can solve the problem that the existing seal simulation only uses the elastic modulus and Poisson's ratio, resulting in results that are inconsistent with reality.

Description

Technical Field

[0001] The present application relates to the technical field of seal design, and in particular to a macroscopic finite element simulation analysis method and device for seals taking plastic deformation into consideration. Background Art

[0002] In aerospace, hydraulic machinery, and other fields, the performance of rubber and plastic seals is crucial to system reliability and safety. Plastic components, such as polytetrafluoroethylene (PTFE) slip rings, are widely used in aviation hydraulic sealing applications. Plastic materials exhibit significant nonlinear properties under compressive loads, including complex mechanical responses such as elastic and plastic deformations and hardening behavior. Therefore, high-precision simulation analysis is required to guide design. However, traditional simulation methods have significant shortcomings in analyzing these seals.

[0003] Currently, macroscopic finite element simulations of rubber and plastic seals used in aviation hydraulics generally use only elastic modulus and Poisson's ratio to characterize the plastic material properties, simplifying the model to a linear elastic model. This method obtains the engineering stress-strain curve from a uniaxial compression test, extracts only the elastic phase data, and ignores the nonlinear behavior during the plastic deformation phase. The linear elastic model is then imported into the finite element software and simulated based on the seal structure and loading conditions. This simplification fails to fully reflect the material's true mechanical properties.

[0004] The existing technology has many defects due to ignoring the plastic deformation characteristics of plastic materials. The description of material properties is distorted, and the linear elastic model cannot characterize the nonlinear behavior of the material after entering the plastic deformation stage, resulting in significant deviations from the actual simulation stress calculation results. Specifically, when the material stress exceeds the yield limit, the linear elastic model still derives the stress according to the linear relationship of the elastic stage, causing the calculated stress value to be significantly higher than the actual stress of the material; at the same time, the simplified method of calculating the engineering strain based on the initial length does not reflect the cumulative effect of plastic deformation, and objectively underestimates the actual plastic strain degree of the material, ultimately resulting in serious discrepancies between the simulation results and the actual working conditions; on the other hand, the simulation results deviate significantly from the actual working conditions, which will overestimate the stress in the plastic zone of the seal and misjudge the contact performance; in addition, the existing technology lacks the ability to model the entire elastic-plastic stage, cannot simulate the continuous mechanical behavior of the material from elasticity to plasticity, and is difficult to evaluate the failure mode of the seal under the extreme load. Summary of the Invention

[0005] In view of this, the present application provides a macroscopic finite element simulation analysis method and device for seals taking plastic deformation into consideration, so as to solve the problem in the existing macroscopic finite element simulation analysis of rubber and plastic seals for aviation hydraulics, in which only elastic modulus and Poisson's ratio are used to characterize the properties of plastic materials, resulting in serious discrepancies between the simulation results and the actual working conditions.

[0006] Specifically, this application is implemented through the following technical solutions:

[0007] In a first aspect, the present application provides a macroscopic finite element simulation analysis method for a seal considering plastic deformation, the method comprising:

[0008] Obtain the engineering stress-strain curve of plastic materials under compression;

[0009] converting the engineering stress-strain curve into a true stress-strain curve;

[0010] Determining the yield limit based on a comparison between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and using the strain point corresponding to the yield limit as the dividing point between elastic and plastic deformation;

[0011] Extracting the elastic section of the true stress-strain curve before the demarcation point, calculating the elastic modulus based on the stress-strain linear relationship, and obtaining the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test;

[0012] extracting the plastic section of the true stress-strain curve after the dividing point, and establishing a multilinear isotropic hardening model based on the data of the plastic section;

[0013] Integrating the elastic modulus, Poisson's ratio and multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering elastic deformation zone and plastic deformation zone;

[0014] The complete elastic-plastic constitutive model is imported into finite element simulation analysis software, and the seal structure model and loading boundary conditions are combined to simulate the strain performance of the plastic seal under the compression deformation state.

[0015] A second aspect of the present application provides a macroscopic finite element simulation and analysis device for a seal considering plastic deformation, the device comprising an acquisition module, a conversion module, a determination module, a calculation module, an establishment module, and a simulation module;

[0016] Wherein, the acquisition module is used to obtain the engineering stress-strain curve of the plastic material under compression;

[0017] The conversion module is used to convert the engineering stress-strain curve into a real stress-strain curve;

[0018] The determination module is configured to determine a yield limit based on a comparison between a true stress-strain curve and an engineering stress-strain curve of the plastic material, and use a strain point corresponding to the yield limit as a dividing point between elastic and plastic deformation;

[0019] The calculation module is used to extract the elastic section of the true stress-strain curve before the demarcation point, calculate the elastic modulus based on the stress-strain linear relationship, and obtain the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test;

[0020] The establishment module is used to extract the plastic section of the true stress-strain curve after the dividing point, and establish a multilinear isotropic hardening model based on the data of the plastic section;

[0021] The establishment module is further used to integrate the elastic modulus, Poisson's ratio and multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering the elastic deformation zone and the plastic deformation zone;

[0022] The simulation module is used to import the complete elastic-plastic constitutive model into finite element simulation analysis software, combine the seal structure model with the loading boundary conditions, and simulate the strain performance of the plastic seal under the compression deformation state.

[0023] The macroscopic finite element simulation analysis method and device for seals taking plastic deformation into consideration provided in this application solves the problem of the lack of description of nonlinear material behavior caused by existing simulations using only elastic parameters by introducing real stress-strain curves and elastic-plastic constitutive models. It can accurately distinguish between the elastic and plastic deformation stages of the material, and avoid the stress and strain calculation deviation caused by ignoring the cross-sectional area change and deformation accumulation effect in the engineering stress-strain curve during the plastic stage. In addition, by integrating elastic parameters and multilinear hardening models, a continuous simulation of the mechanical response of the seal from elastic deformation to plastic deformation is achieved, so that the simulation results can truly reflect the stress distribution, strain field and contact pressure distribution of the seal under compressive load, improve the accuracy of sealing performance evaluation, provide reliable data support for the structural design and material selection of seals in scenarios such as aviation hydraulics, and reduce the R&D costs and cycle losses caused by traditional trial and error methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A schematic diagram of the stress-strain curve of the plastic material of the rubber-plastic seal for aviation hydraulics provided in this application;

[0025] Figure 2 This is a flow chart of Example 1 of the macroscopic finite element simulation analysis method for a seal considering plastic deformation provided by this application;

[0026] Figure 3 A comparison diagram of the engineering stress-strain curve and the true stress-strain curve of a certain plastic material shown in this application;

[0027] Figure 4 This is a simulation analysis result diagram of the plastic material of a certain aviation hydraulic rubber-plastic seal shown in this application under two conditions: considering only elasticity and considering plasticity;

[0028] Figure 5 Another simulation analysis result diagram of the plastic material of a certain aviation hydraulic rubber-plastic seal shown in this application under two conditions: considering only elasticity and considering plasticity;

[0029] Figure 6 This is a structural schematic diagram of Example 2 of the macroscopic finite element simulation and analysis device for sealing components taking plastic deformation into consideration provided in this application. DETAILED DESCRIPTION

[0030] Exemplary embodiments are described in detail herein, with examples illustrated in the accompanying drawings. When the following description refers to the drawings, identical numerals in different drawings represent identical or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with this application.

[0031] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms "a," "the," and "the" used in this application are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0032] It should be understood that although the terms first, second, third, etc. may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from each other. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0033] Specific embodiments are given below to introduce the technical solutions of the present application in detail.

[0034] Before introducing the specific embodiments of the present application, an overall introduction to the solution of the present application is first given. Figure 1 For the stress-strain curve diagram of the plastic material of the rubber-plastic seal for aviation hydraulics provided in this application, please refer to Figure 1 In the stress-strain curve of the plastic material used in aviation hydraulic rubber-plastic seals, segment OA represents the elastic deformation stage (linear characteristics, characterized by the elastic modulus and Poisson's ratio). Point A represents the yield limit, after which the material enters the plastic deformation stage (nonlinear characteristics, with the total strain consisting of elastic strain OA' and plastic strain OB'). However, when modeling using only elastic parameters, the stress path deviates to point C, which is seriously inconsistent with reality. Therefore, it is necessary to introduce the stress-strain curve of segments AB in the plastic section to accurately characterize the material properties.

[0035] Example 1

[0036] Figure 2This is a flow chart of the first embodiment of the macroscopic finite element simulation analysis method for the seal considering plastic deformation provided by this application. Figure 2 The method provided in this embodiment may include:

[0037] S201. Obtain an engineering stress-strain curve of a plastic material under compression.

[0038] It should be noted that the plastic materials used in rubber-plastic seals for aviation hydraulics primarily bear compressive loads in practice, and their mechanical properties directly impact the sealing effectiveness and service life. By obtaining engineering stress-strain curves under compression, the entire process of elastic and plastic deformation of the material under pressure can be intuitively reflected, providing critical data support for accurate modeling.

[0039] Specifically, obtaining the engineering stress-strain curve of the plastic material under compression includes:

[0040] (1) The standard uniaxial compression test method is used to apply axial compression load to the plastic material specimen.

[0041] It should be noted that the standard uniaxial compression test method is a standardized test method that applies a compressive load to the specimen along a single axial direction (usually the axial direction of the specimen) in material mechanics testing to obtain the mechanical performance parameters of the material. It can standardize and accurately test the mechanical response of the material under compression conditions.

[0042] The specific operation process involves commissioning a universal materials testing machine (this is only an example; a servo-hydraulic testing system can also be used for loading), clamping the plastic material specimen to the testing machine's compression fixture, setting test parameters such as the loading rate (which must comply with material testing standards or be reasonably set based on actual needs to ensure a stable and reproducible loading process), and then controlling the testing machine to slowly apply a compressive load along the specimen's axial direction. By applying an axial load to the specimen, the compressive stress environment that the seal plastic material may experience in actual operation can be simulated, allowing the material's mechanical response to be determined.

[0043] (2) Real-time measurement of the axial deformation of the specimen and the applied load.

[0044] It should be noted that the physical properties of sensors (e.g., strain gauge force sensors based on the strain effect, and displacement sensors based on electromagnetic induction or optical principles) can be utilized to convert mechanical quantities into measurable and recordable electrical signals, thus achieving electrical measurement conversion of non-electrical quantities. Specifically, displacement sensors obtain axial deformation by sensing the relative displacement between the ends of a specimen, while force sensors obtain load by sensing the reaction force exerted by the tooling on the specimen. Both convert physical signals into electrical signals, which are then processed (e.g., by a data acquisition system) and transmitted to a computer for recording.

[0045] (3) Calculate the ratio of the axial deformation to the initial length as the engineering strain.

[0046] Based on the definition of engineering strain, relative deformation is used to simplify the characterization of material deformation, facilitating comparative analysis of deformation results for specimens of different sizes. This is a common method for quantifying deformation in material mechanics testing. Specifically, based on the engineering strain calculation formula, engineering strain value = axial deformation value / initial length, the axial deformation value measured in step (2) and the known initial length of the specimen are substituted into the calculation to obtain the engineering strain value.

[0047] Optionally, if the effect of temperature changes on the length of the specimen during compression is considered (e.g., high-temperature compression testing), a temperature correction factor can be introduced during the calculation to compensate for the initial length before calculation. This is not described in detail here.

[0048] (4) Calculate the ratio of the applied load to the initial cross-sectional area of ​​the specimen as the engineering stress.

[0049] It should be noted that, under the simplified premise of not considering the change in cross-sectional area caused by plastic deformation of the material (engineering stress assumes that the cross-sectional area remains unchanged), using the ratio of load to initial cross-sectional area to quickly characterize the material stress state is a basic method for obtaining stress data in material mechanics testing. Specifically, based on the engineering stress calculation formula, that is, engineering stress value = applied load / initial cross-sectional area of ​​the specimen, the load measured in step (2) and the known initial cross-sectional area of ​​the specimen are substituted to calculate the engineering stress value.

[0050] (5) Record the corresponding engineering stress-strain data to form a complete engineering stress-strain curve.

[0051] It should be noted that converting discrete stress-strain data into a continuous curve through data correlation and visualization facilitates intuitive analysis of material mechanical properties (such as elastic modulus, yield strength, and plastic deformation capacity), and is a standard method for presenting material mechanical test results. Specifically, the engineering stress and strain data corresponding to each moment in the loading sequence are mapped one-to-one and stored in a data table (such as an Excel spreadsheet). Drawing software is then used to plot a continuous curve, i.e., the engineering stress-strain curve, with engineering strain as the horizontal axis and engineering stress as the vertical axis.

[0052] S202: Convert the engineering stress-strain curve into a true stress-strain curve.

[0053] It should be noted that when the plastic components of rubber-plastic seals used in aviation hydraulics are operating, the stress often exceeds the yield limit and enters the plastic deformation stage. At this time, the engineering stress-strain curve cannot reflect the true mechanical behavior because it "assumes that the material cross-sectional area remains unchanged." In short, the engineering curve is disconnected from the true mechanical behavior of the material in the plastic stage. If used directly for seal simulation, key results such as stress, strain, and contact pressure will be severely distorted. Therefore, it is necessary to convert the engineering stress-strain curve into a true stress-strain curve. Among them, the true stress-strain curve can accurately reflect the nature of the material's plastic deformation through physical correction (taking into account the change in cross-sectional area and using logarithmic strain to describe the accumulated deformation).

[0054] Specifically, converting the engineering stress-strain curve into a true stress-strain curve includes:

[0055] (1) Perform natural logarithm transformation on the engineering strain and calculate the true strain.

[0056] It should be noted that the natural logarithm transformation is a mathematical transformation method that uses the natural logarithm function (with e as the base, e≈2.71828) to process the engineering strain and convert the linear strain description based on the initial length into the true strain calculation that reflects the cumulative effect of deformation (that is, converting the linear deformation description based on the initial length into a nonlinear description that reflects the cumulative deformation). The formula is ε 真实 =ln(1+ε 工程 ), where ε 真实 is the true strain, ε 工程 is the engineering strain. Specifically, each engineering strain data is substituted into the calculation one by one according to the conversion formula between true strain and engineering strain. For example, if the engineering strain at a certain moment is ε 工程 =0.2, then the true strain ε 真实 =ln(1+0.2)≈0.1823.

[0057] (2) Based on the change in cross-sectional area during the compression process of the plastic material, the engineering stress is corrected and the true stress is calculated.

[0058] It should be noted that cross-sectional area change information refers to the pattern of cross-sectional area changes with deformation due to plastic deformation during the compression process of plastic materials. Based on the principle of conservation of mass (the material volume remains approximately unchanged during plastic deformation, i.e., the initial volume V0 = A0L0, and the instantaneous volume V = AL, so A = A0L0 / L, where A0 is the initial cross-sectional area, L0 is the initial length, A is the instantaneous cross-sectional area, and L is the instantaneous length), the cross-sectional area change can be deduced from the engineering strain, and then the engineering stress can be corrected to obtain the true stress.

[0059] Specifically, according to the mass conservation law A0L0=AL, and L=L0(1+ε 工程), we can get the instantaneous cross-sectional area A=A0 / (1+ε 工程 ). Furthermore, the true stress σ 真实 is the ratio of the instantaneous load F to the instantaneous cross-sectional area A, and the engineering stress σ 工程 =F / A0, and we can get σ 真实 =σ 工程 (1+ε 工程 ). Combine each engineering stress data with the corresponding engineering strain and calculate the true stress point by point. For example, the engineering stress σ 工程 =50Mpa, engineering strain ε 工程 = 0.2, the true stress σ 真实 =50(1+0.2)=60Mpa. Essentially, this process corrects the cross-sectional area based on the conservation of mass, allowing the stress calculation to adapt to the actual changes in the material's load-bearing area and resolving the engineering stress error caused by "assuming a constant area."

[0060] (3) Using the true stress and true strain as the horizontal and vertical coordinates, draw a true stress-strain curve.

[0061] Specifically, with the true strain as the horizontal coordinate (X axis) and the true stress as the vertical coordinate (Y axis), the corresponding data points are arranged in sequence and fitted into a continuous curve using the drawing tool. For example, each group (ε 真实 , σ 真实 ) data as coordinate points, which are connected to form a complete true stress-strain curve, which can intuitively present the true mechanical behavior of the material from elastic deformation to plastic deformation.

[0062] Through the above three steps, the scientific conversion of engineering stress-strain curve to real curve is achieved, solving the core data distortion problem of seal plastic deformation simulation.

[0063] S203 : Determine a yield limit based on a comparison between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and use a strain point corresponding to the yield limit as a dividing point between elastic and plastic deformation.

[0064] It should be noted that the yield limit, also known as yield strength, is one of the mechanical property indicators of materials. It refers to the critical stress value at which the material transitions from the elastic deformation stage to the plastic deformation stage. When the stress reaches the yield limit, the material will retain some plastic deformation even if it is unloaded. It is a key parameter for judging the boundary between elastic and plastic deformation of the material. Among them, elastic deformation refers to the deformation of the material under the action of external force. When the external force is removed, the deformation completely disappears. During the deformation process, the stress and strain of the material are linearly related (in accordance with Hooke's law). In essence, it is the elastic displacement between atoms. Plastic deformation refers to the deformation of the material under the action of external force. After the external force is removed, the deformation cannot completely disappear and remains. During the deformation process, the stress and strain are nonlinear. In essence, it is the dislocation movement within the crystal or the sliding between grains.

[0065] Figure 3 This application presents a comparison of the engineering stress-strain curve and the true stress-strain curve for a plastic material. Specifically, the engineering stress-strain curve and the true stress-strain curve are plotted in the same coordinate system (strain on the abscissa, stress on the ordinate) to observe the curve morphology. The engineering curve is linear in the elastic phase, with a slope corresponding to the elastic modulus. After entering the plastic phase, the slope of the curve does not change significantly due to the lack of correction for cross-sectional area, but it gradually diverges from the true curve. The true curve overlaps with the engineering curve in the elastic phase (because the cross-sectional area changes minimally during elastic deformation, the engineering stress and strain are approximately equal to the true values). After reaching the yield limit, the slope of the curve decreases (plastic deformation begins).

[0066] In specific implementation, the yield limit can be determined by finding the intersection of the linear segment in the elastic stage and the nonlinear segment in the plastic stage in the true stress-strain curve. The corresponding stress value is the yield limit σ s , the strain ε corresponding to the intersection point s For example, by fitting a straight line (σ=Eε, E is the elastic modulus) to the elastic segment of the true curve and a nonlinear curve (such as the power hardening model σ=Kε) to the plastic segment, n K is the hardening coefficient, a constant related to the material's inherent properties. It reflects the material's ability to harden during plastic deformation. Its units are the same as those of stress. Larger K values ​​indicate a faster increase in stress with strain during plastic deformation, meaning the material has a higher degree of hardening. Different plastic materials have different K values. n is the hardening exponent, also a dimensionless property inherent to the material, reflecting the change in the hardening rate during plastic deformation. n ranges from 0 to 1. The closer n is to 1, the more linear the stress-strain increase during plastic deformation (resulting in a relatively stable hardening rate). The closer n is to 0, the faster the hardening rate and the more rapid the stress increase. Find the intersection of the two fitted curves to determine the yield limit.

[0067] In addition, the yield limit can be determined by extending the linear segment of the engineering curve in the elastic phase and using the intersection of the true curve in the plastic phase as a reference for the yield limit (because the linear characteristics of the elastic phase of the engineering curve are more obvious, it is convenient to quickly identify the elastic phase range). For example, if the slope of the elastic phase of the engineering curve is M, the stress at the intersection of the extended linear segment and the true curve is the yield limit (the principle is that the engineering stress and strain in the elastic phase are close to the true value, while the true curve deviates from the engineering curve due to the change in cross-sectional area in the plastic phase. The intersection corresponds to the material's transition from elastic to plastic).

[0068] Preferably, the yield limit is determined based on the comparison relationship between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and the strain point corresponding to the yield limit is used as the dividing point between elastic and plastic deformation, including:

[0069] (1) Calculate the relative stress error between the true stress-strain curve and the engineering stress-strain curve at each corresponding strain point.

[0070] It should be noted that the relative error of stress is an indicator that truly reflects the degree of deviation between the actual stress and the engineering stress. The calculation formula is δ=|(σ 真实 -σ 工程 ) / σ 真实 |×100%, where σ 真实 is the true stress, σ 工程 is the engineering stress. The relative stress error is used to quantify the stress difference between two curves at the same strain and to determine the transition between material deformation stages.

[0071] Specifically, for each strain point, substitute the stress relative error calculation formula to calculate the relative error sequence under the strain. The principle is to use the error to quantify the degree of deviation between the two curves. In the elastic deformation stage, due to the small change in cross-sectional area, σ 真实 ≈σ 工程 , the relative error is small; in the plastic deformation stage, due to the significant change in cross-sectional area, σ 真实 and σ 工程 The larger the deviation, the larger the relative error. The relative error series reflects the degree of stress difference between the two curves under different strains.

[0072] (2) Setting an error threshold based on the characteristics of the plastic material. When the relative error exceeds the threshold for the first time, the corresponding strain point is determined to be the yield limit.

[0073] It's important to note that the error threshold here is a pre-set relative error threshold based on the physical properties of the plastic material (such as elastic deformation limit and plastic deformation sensitivity). When the relative stress error exceeds this value, the material is considered to have transitioned from elastic to plastic deformation dominance. The threshold is determined based on material test data, engineering experience, or industry standards. For example, for rubber-plastic seals used in aviation hydraulics, the threshold may be set at 5%-10% due to the stringent sealing requirements.

[0074] Specifically, the relative error sequence is traversed to find the first strain point that satisfies the relative error sequence greater than the error threshold. The corresponding true stress at this time is the yield limit.

[0075] Preferably, in addition to a fixed threshold (such as 5%), a dynamic threshold can also be used, that is, it is automatically adjusted based on the maximum error of the elastic segment. For example, the average relative error δ of the elastic segment (assuming the first 10 strain points) is calculated. 弹性平均 , set the threshold to δ 阈值 =δ 弹性平均 ×2 (or other multiples) to adapt the threshold to the elastic error characteristics of the material itself. This approach avoids the inaccurate recognition problem caused by material differences when using a fixed threshold and is suitable for yield point recognition of various types of plastic materials (such as polytetrafluoroethylene and filled modified plastics).

[0076] Preferably, strain energy error can be incorporated to aid in the judgment process, incorporating strain energy relative error into the calculation of stress relative error (the specific formula is not shown here; please refer to the related art). The yield limit is determined only when both the stress relative error and the strain energy relative error exceed their respective thresholds. This approach, utilizing the dual criteria of "stress error + energy error," improves the reliability of yield limit identification and is suitable for aviation hydraulic applications (such as high-pressure and vibration conditions) where seal reliability is extremely critical, avoiding the risk of misjudgment associated with a single stress error criterion.

[0077] (3) Taking the yield limit as the boundary, the true stress-strain curve is divided into an elastic section and a plastic section.

[0078] Specifically, the strain ε is less than or equal to the yield strain ε s The section with the elastic property is the elastic section, and the section with the plastic property is the plastic section.

[0079] It should be noted that in this step, numerical errors replace subjective judgments to improve the objectivity and accuracy of yield limit determination. For example, for plastic materials used in aviation hydraulic seals, the error threshold method can identify the "elastic-plastic transition critical point" missed by traditional methods, making the simulation more consistent with the actual mechanical behavior of the material. In addition, after clarifying the elastic and plastic sections, the finite element model can adopt different constitutive relations (Hooke's law in the elastic section, hardening model in the plastic section) in a targeted manner, solving the problem of confusing elasticity and plasticity in existing simulations and significantly improving the accuracy of calculations such as stress distribution and contact pressure. Accurate yield limits and stage divisions provide a quantitative basis for seal structure design (such as adjusting the thickness of slip rings) and material selection (such as comparing the yield characteristics of different plastics), which can help optimize the sealing performance and improve the reliability of aviation hydraulic systems.

[0080] S204, extracting the elastic section of the true stress-strain curve before the dividing point, calculating the elastic modulus based on the stress-strain linear relationship, and obtaining the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test.

[0081] Specifically, the elastic modulus is calculated based on the linear relationship between stress and strain, and the Poisson's ratio is obtained by measuring the axial and transverse strains in the uniaxial compression test, including:

[0082] (1) Extracting the elastic section data before the yield limit in the true stress-strain curve.

[0083] It should be noted that the material complies with Hooke's law (linearity) during the elastic deformation phase, while the plastic deformation phase is nonlinear due to the hardening effect. The yield limit determined by S203 can accurately capture the data segment of pure elastic deformation.

[0084] (2) Perform linear fitting on the elastic segment data to obtain the slope of stress versus strain as the value of the elastic modulus.

[0085] It should be noted that the elastic modulus describes the linear correlation strength between stress and strain in the elastic deformation stage of the material, and reflects the material's ability to resist elastic deformation.

[0086] Specifically, the least squares fitting method can be used to eliminate the test noise and extract the slope that best reflects the elastic properties of the material.

[0087] (3) In the uniaxial compression test, the axial strain and lateral strain of the seal are measured.

[0088] Specifically, strain gauges can be attached to the specimen axially (to measure axial strain) and transversely (to measure transverse strain). Alternatively, a DIC (digital image correlation) system can be used to capture surface speckle patterns for non-contact strain measurement. Furthermore, loading is performed at a low rate (ensuring the specimen is in the elastic phase and load is less than the yield limit), and the axial load, axial strain, and transverse strain are recorded in real time.

[0089] (4) Calculate the Poisson's ratio based on the ratio of the measured lateral strain to the axial strain.

[0090] It should be noted that Poisson's ratio is the absolute value of the ratio of lateral strain to axial strain when the material is elastically deformed. It reflects the Poisson effect of "axial elongation and lateral contraction" or "axial compression and lateral expansion" when the material is deformed. It is dimensionless and is used to describe the volume change characteristics of the material during elastic deformation.

[0091] S205 , extracting the plastic section of the true stress-strain curve after the dividing point, and establishing a multilinear isotropic hardening model based on the data of the plastic section.

[0092] It should be noted that the multilinear isotropic hardening model is a classic model used in finite element simulation to describe the hardening behavior of materials during plastic deformation. Its core concept is that after a material enters plastic deformation, the stress-strain relationship exhibits nonlinear hardening characteristics. By "piecewise linearizing" the true stress-strain curve, the material's hardening behavior, whereby the more it deforms, the harder it becomes to deform, is simulated. For seals, the multilinear isotropic hardening model accurately captures the plastic deformation and contact pressure changes of plastic components under high pressure.

[0093] Specifically, a multilinear isotropic hardening model is established based on the data of the plastic section, including:

[0094] (1) Segmenting the extracted plastic section of the true stress-strain curve.

[0095] Specifically, the strain range or stress range of the plastic section can be divided into several equidistant intervals, each interval corresponding to a linear segment.

[0096] (2) Fit the stress-strain relationship in segments to form a multilinear data table.

[0097] Specifically, the original data points are divided into several subsets at the nodes, with each subset corresponding to a linear segment. Then, a least-squares method is used to fit a straight line to each subset. Finally, the fitted stress values ​​are calculated at the nodes, ensuring continuity between adjacent segments at the nodes (i.e., the stress value at a node must satisfy the fitting equations for both the left and right segments). For example, if the segmented interval is ε∈[0.04, 0.06], corresponding to the original data points (0.04, 50 MPa), (0.05, 60 MPa), and (0.06, 70 MPa), the fitted line σ=1000ε+10 is obtained. The stress corresponding to any strain ε within the interval can then be calculated using this equation.

[0098] Furthermore, the linear parameters of each segment are organized into a table as input data for the finite element software. The table must include the strain nodes and the corresponding true stress values.

[0099] (3) The fitting data in the multilinear data table is used as the input curve of the multilinear isotropic hardening model.

[0100] In addition, it should be noted that before segmenting the extracted plastic section of the true stress-strain curve, the following steps are included:

[0101] (1) Extract the minimum strain value and the maximum strain value of the plastic section in the true stress-strain curve and calculate the total strain span.

[0102] Specifically, from the plastic section of the true stress-strain curve (strain > yield limit corresponding strain ε s ), extract the minimum strain ε min and the maximum strain ε max , calculate the total strain span: .

[0103] (2) Determine the number of segments based on the preset single-segment strain width or error tolerance.

[0104] The method of presetting the single-segment strain width is to presetting the single-segment maximum allowable strain width (such as 0.02), the formula for calculating the number of segments is: ,in To round up, ensure that each width .For example, , ,but part.

[0105] It should be noted that the error tolerance segmentation method is to preset the stress fitting error tolerance δσ (e.g., 5% of the true stress) and iteratively increase the number of segments n until the linear fitting error of each segment is less than δσ. For specific implementation methods, please refer to the description of related technologies.

[0106] (3) Generate equally spaced strain nodes based on the number of segments, and perform linear interpolation between adjacent nodes to form a multilinear stress-strain data table.

[0107] The multilinear stress-strain data table includes at least the strain point, the true stress value corresponding to the strain point, and the segmented interval where the strain point is located.

[0108] S206. Integrate the elastic modulus, Poisson's ratio and multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering the elastic deformation zone and the plastic deformation zone.

[0109] It should be noted that the elastoplastic constitutive model is a mathematical framework that describes the mechanical behavior of a material throughout its entire deformation phase, from elastic deformation (reversible) to plastic deformation (irreversible). Specifically, the elastic modulus and Poisson's ratio calculated based on the elastic section are used to describe the material's elastic deformation behavior; a multilinear isotropic hardening model established based on the plastic section is used to describe the material's plastic deformation behavior. By integrating these elastic modulus, Poisson's ratio, and multilinear hardening model, a continuous elastoplastic constitutive relationship covering both the elastic and plastic sections is formed. This complete constitutive model is then imported into finite element simulation software to simulate the seal's elastoplastic response under compressive loads.

[0110] It is important to note that by integrating elastic parameters with a multilinear hardening model, an elastic-plastic constitutive model covering the seal's full deformation stage was constructed, resolving the core issues of traditional simulations, namely the separation of elasticity and plasticity and distortion of constitutive parameters. This model not only accurately describes the mechanical behavior of the material but, through deep coupling with finite element technology, provides a reliable digital twin foundation for the design, analysis, and optimization of aviation hydraulic seals.

[0111] S207, importing the complete elastic-plastic constitutive model into finite element simulation analysis software, combining the seal structure model with the loading boundary conditions, and simulating the strain performance of the plastic seal under the compression deformation state.

[0112] It should be noted that the strain performance may at least include stress distribution, strain response and contact performance.

[0113] Specifically, the simulation of the strain performance of the plastic seal under the compressive deformation state includes: importing the constructed elastic-plastic constitutive model into the finite element simulation analysis software as material properties; establishing a geometric structure model of the seal and applying boundary conditions and compression loads; running the finite element simulation solution process to obtain the overall stress distribution and strain field of the seal under compression loading; extracting the contact pressure distribution in the sealing surface area, analyzing the contact state and sealing performance, and outputting the stress, strain and contact performance results.

[0114] It should be noted that boundary conditions refer to the constraints imposed on the model during finite element simulation, used to simulate the structural constraints encountered in real-world scenarios. A compressive load refers to the external force applied to a seal to cause it to compress and deform. This can be applied through displacement control (specified compression, such as a 10%-30% compression ratio) or pressure loading (hydraulic pressure applied within the seal cavity, such as 20 MPa or 35 MPa) to simulate the stresses experienced by the seal in actual operation. Stress distribution refers to the distribution of stress magnitude and direction within the seal under compressive load. This can be visualized through a stress contour map, useful for analyzing weak points and assessing structural strength. The strain field refers to the distribution of deformation across the seal under load, reflecting the material's deformation state. Correlated with the stress distribution, it helps understand the seal's deformation trends and determine whether excessive deformation or failure risks are imminent. The contact pressure distribution refers to the distribution of pressure magnitude within the contact area between the seal and its mating surface (such as the piston rod or cylinder barrel), and is a key indicator for evaluating sealing performance. The minimum contact pressure must be greater than the sealing medium pressure to effectively prevent leakage; the uniformity of contact pressure distribution will also affect the sealing reliability and friction power consumption.

[0115] Specifically, the previously constructed elastic-plastic constitutive model (including elastic parameters such as the elastic modulus and Poisson's ratio, as well as the plastic properties described by the multilinear isotropic hardening model) is imported into the material property definition module of the finite element simulation analysis software. This creates a complete material property card, which informs the software of the material's deformation patterns at different stress stages. Next, based on the actual shape and size of the seal, a two-dimensional axisymmetric model (for simple shapes like O-rings) or a three-dimensional solid model (accounting for complex cross-sections and groove structures) is constructed in the finite element software. Boundary conditions are then applied to the model, fixing the relevant parts of the seal groove to simulate the installed and fixed state. Finally, a compressive load is applied to simulate the forces acting on the seal during assembly and operation. Furthermore, solution parameters are set (such as enabling the large deformation option to handle geometric nonlinearity, using adaptive step size control to ensure contact convergence, and setting a sufficient number of substeps to resolve contact pressure jumps). The simulation is then started. The software discretizes the seal into numerous small elements using the finite element method and solves the equations for each element to obtain the overall stress and strain field of the seal under compressive loading. Finally, the contact pressure distribution data of the sealing surface area is extracted from the simulation results. By analyzing indicators such as minimum contact pressure, contact width, and stress concentration factor, the contact state and sealing performance are evaluated. Finally, the result data such as stress, strain, and contact performance and visual charts are output.

[0116] This process accurately simulates the stress, strain, and contact pressure distribution of seals under actual operating conditions, avoiding errors caused by empirical estimates in traditional designs. It guides design optimization of seal groove dimensions, seal shape, and other factors, resulting in more reliable sealing performance. Simulations can also compare the performance of different materials, analyzing their hardening behavior and plastic deformation capacity, selecting the sealing material most suitable for specific operating conditions, or guiding improvements to material formulations, such as determining the optimal content of filler particles to enhance the overall performance of the seal. Furthermore, simulations can predict seal performance and potential failure modes (such as extrusion and cracking) in advance, allowing optimization to be implemented directly during the design phase, reducing R&D cycles and costs.

[0117] It should also be noted that after simulating the stress distribution, strain response and contact performance of plastic seals in a compressive deformation state, the following steps are performed: identifying stress or strain areas in the simulation results that are higher than a preset threshold, and evaluating the potential failure location of the seal under extreme load; analyzing the sealing uniformity and contact integrity of the sealing surface based on the simulated contact pressure distribution; adjusting the sealing structure parameters or material parameters according to the simulation feedback results; and re-executing the simulation analysis to verify the optimized sealing performance, thereby forming a data-driven simulation optimization closed loop.

[0118] Specifically, first, in the post-processing of finite element simulation, set stress or strain thresholds (such as marking areas exceeding the threshold through the software's threshold screening function); the software automatically generates cloud maps of high-risk areas (such as stress concentration areas marked in red), and combines material failure criteria (such as maximum principal stress exceeding the strength limit, equivalent plastic strain exceeding the fracture strain) to determine potential failure locations (such as the root of the seal, lip corners). Secondly, extract the contact pressure distribution data of the sealing surface and generate a pressure curve or cloud map; calculate indicators such as the standard deviation and uniformity coefficient of the contact pressure to evaluate uniformity; check whether there are gaps (areas with zero contact pressure) or pressure mutation points in the contact area to determine contact integrity. Furthermore, modify the geometric dimensions of the seal (such as the lip corner radius, groove depth, and compression ratio) to improve stress concentration or contact pressure distribution; adjust the material's elastic-plastic constitutive parameters (such as elastic modulus, hardening coefficient, and Poisson's ratio) to enhance the material's deformation resistance or sealing adaptability. Finally, the adjusted parameters are imported into the finite element model, the mesh is re-divided and boundary conditions are applied; the simulation solution is run to compare the stress, strain, contact pressure and other results before and after optimization; if the requirements are still not met, the above steps are repeated until they are met, forming a cyclic optimization.

[0119] In the above steps, through threshold screening and failure assessment, failure risks can be identified in advance during the design phase, reducing design risks; through automatic parameter adjustment through simulation closed loop, reliance on manual experience can be reduced, reducing trial and error costs and R&D costs.

[0120] The method provided in this embodiment solves the problem that existing seal simulations only use elastic modulus and Poisson's ratio, resulting in results that are inconsistent with reality. It can accurately capture the mechanical behavior of materials in all stages from elasticity to plasticity, avoid problems such as stress overestimation and misjudgment of contact performance caused by ignoring plastic deformation, and improve the accuracy of seal stress distribution, strain response and contact pressure calculations. It provides a quantitative basis for sealing structure parameter optimization and material selection, reduces the trial and error cost of physical prototypes, shortens the R&D cycle, and enhances the reliability and efficiency of seal design in harsh scenarios such as aviation hydraulics.

[0121] Experimental verification:

[0122] Figure 4 This is a simulation analysis result diagram of the plastic material of a certain aviation hydraulic rubber-plastic seal shown in this application under two conditions: considering only elasticity and considering plasticity. Figure 5 This is another simulation analysis result diagram of the plastic material of a certain aviation hydraulic rubber-plastic seal shown in this application under two conditions: considering only elasticity and considering plasticity. Please also refer to Figure 4 and Figure 5 Under the working pressure of 35MPa, the maximum stress and strain of the L-shaped plastic slip ring of the model considering only elasticity both appear at the sealing lip, which are 409.75MPa and 0.2mm / mm respectively. The maximum contact pressure at the main sealing surface reaches 669.23MPa. The effective contact area with a pressure higher than 35MPa is only 0.3mm; in contrast, the maximum stress of the L-shaped plastic slip ring of the model considering plasticity is only 54.55MPa, and the maximum stress and strain at the sealing lip are 45.7MPa and 0.475mm / mm respectively. The maximum contact pressure at the main sealing surface is only 117.2MPa, but the effective contact area is as high as 0.604mm; it is obvious that the stress, strain, contact pressure and contact area of ​​the plastic material after considering plastic deformation are more reasonable and more in line with the actual situation.

[0123] Example 2

[0124] Corresponding to the aforementioned embodiment of a macroscopic finite element simulation analysis method for a seal taking plastic deformation into consideration, the present application also provides an embodiment of a macroscopic finite element simulation analysis device for a seal taking plastic deformation into consideration.

[0125] Figure 6 This is a schematic diagram of the structure of the second embodiment of the macro finite element simulation analysis device for the seal considering plastic deformation provided by this application. Figure 6 The device provided in this embodiment includes an acquisition module 610, a conversion module 620, a determination module 630, a calculation module 640, an establishment module 650 and a simulation module 660;

[0126] Wherein, the acquisition module 610 is used to obtain the engineering stress-strain curve of the plastic material under compression;

[0127] The conversion module 620 is used to convert the engineering stress-strain curve into a real stress-strain curve;

[0128] The determination module 630 is configured to determine a yield limit based on a comparison between a true stress-strain curve and an engineering stress-strain curve of the plastic material, and use a strain point corresponding to the yield limit as a dividing point between elastic and plastic deformation;

[0129] The calculation module 640 is used to extract the elastic section of the true stress-strain curve before the demarcation point, calculate the elastic modulus based on the stress-strain linear relationship, and obtain the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test;

[0130] The establishment module 650 is used to extract the plastic section of the true stress-strain curve after the dividing point, and establish a multilinear isotropic hardening model based on the data of the plastic section;

[0131] The establishment module 650 is further used to integrate the elastic modulus, Poisson's ratio and the multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering the elastic deformation zone and the plastic deformation zone;

[0132] The simulation module 660 is used to import the complete elastic-plastic constitutive model into finite element simulation analysis software, and simulate the strain performance of the plastic seal under compression deformation state by combining the seal structure model and loading boundary conditions.

[0133] The device of this embodiment can be used to perform Figure 1 The steps, specific implementation principles and implementation processes of the method embodiment shown are similar and will not be repeated here.

[0134] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0135] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0136] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A macroscopic finite element simulation analysis method for seals considering plastic deformation, characterized in that: The method comprises: Obtain the engineering stress-strain curve of plastic materials under compression; converting the engineering stress-strain curve into a true stress-strain curve; Determining the yield limit based on a comparison between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and using the strain point corresponding to the yield limit as the dividing point between elastic and plastic deformation; Extracting the elastic section of the true stress-strain curve before the demarcation point, calculating the elastic modulus based on the stress-strain linear relationship, and obtaining the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test; extracting the plastic section of the true stress-strain curve after the dividing point, and establishing a multilinear isotropic hardening model based on the data of the plastic section; Integrating the elastic modulus, Poisson's ratio and multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering elastic deformation zone and plastic deformation zone; Importing the complete elastic-plastic constitutive model into finite element simulation analysis software, combining the seal structure model with the loading boundary conditions, and simulating the strain performance of the plastic seal under a compressive deformation state; the strain performance includes at least stress distribution, strain response, and contact performance; The method of determining the yield limit based on the comparison between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and using the strain point corresponding to the yield limit as the dividing point between elastic deformation and plastic deformation, includes: Calculating the relative stress error between the true stress-strain curve and the engineering stress-strain curve at each corresponding strain point; Setting an error threshold based on the characteristics of the plastic material, and determining the corresponding strain point as the yield limit when the relative error exceeds the threshold for the first time; The true stress-strain curve is divided into an elastic section and a plastic section with the yield limit as the boundary.

2. The method according to claim 1, characterized in that The converting the engineering stress-strain curve into a true stress-strain curve comprises: Perform natural logarithm transformation on engineering strain to calculate true strain; Correct the engineering stress based on the change in cross-sectional area during the compression process of the plastic material and calculate the true stress; The true stress and true strain are used as horizontal and vertical coordinates to draw a true stress-strain curve.

3. The method according to claim 1, characterized in that The multilinear isotropic hardening model is established based on the data of the plastic section, comprising: Segmenting the extracted plastic section of the true stress-strain curve; Segment-wise fitting of stress-strain relationships to form a multi-linear data table; The fitting data in the multilinear data table is used as the input curve of the multilinear isotropic hardening model.

4. The method according to claim 3, characterized in that Before segmenting the extracted plastic section of the true stress-strain curve, the method includes: Extracting the minimum strain value and the maximum strain value of the plastic section in the true stress-strain curve and calculating the total strain span; Determine the number of segments based on the preset single-segment strain width or error tolerance; Equally spaced strain nodes are generated based on the number of segments, and linear interpolation is performed between adjacent nodes to form a multi-linear stress-strain data table.

5. The method according to claim 1, wherein The elastic modulus is calculated based on the stress-strain linear relationship, and the Poisson's ratio is obtained by measuring the axial and transverse strains in the uniaxial compression test, including: Extracting elastic section data before the yield limit in the true stress-strain curve; Performing a linear fit on the elastic segment data to obtain the slope of stress versus strain as the value of the elastic modulus; In the uniaxial compression test, the axial strain and transverse strain of the seal are measured; The Poisson's ratio was calculated based on the ratio of the measured transverse strain to the axial strain.

6. The method according to claim 1, characterized in that The obtaining of the engineering stress-strain curve of the plastic material under compression comprises: A standard uniaxial compression test method is used to apply axial compression load to the plastic material specimen; Real-time measurement of the specimen's axial deformation and applied load; The ratio of the axial deformation to the initial length was calculated as the engineering strain; Calculate the ratio of the applied load to the initial cross-sectional area of ​​the specimen as the engineering stress; Record the corresponding engineering stress-strain data to form a complete engineering stress-strain curve.

7. The method according to claim 1, characterized in that The strain performance of the simulated plastic seal under compression deformation state includes: Import the constructed elastic-plastic constitutive model into the finite element simulation analysis software as material properties; Establish the seal geometry model and apply boundary conditions and compression loads; Run the finite element simulation solution process to obtain the overall stress distribution and strain field of the seal under compression loading; Extract the contact pressure distribution in the sealing surface area, analyze the contact state and sealing performance, and output stress, strain and contact performance results.

8. The method according to claim 1, characterized in that The simulation of the stress distribution, strain response and contact performance of the plastic seal under the compression deformation state includes: Identify stress or strain areas above a preset threshold in the simulation results and assess potential failure locations of seals under extreme loads. Analyze the sealing uniformity and contact integrity of the sealing surface based on simulated contact pressure distribution; Adjust the sealing structure parameters or material parameters according to the simulation feedback results; Re-execute simulation analysis to verify the optimized sealing performance, forming a data-driven simulation optimization closed loop.

9. A macroscopic finite element simulation analysis device for sealing components taking plastic deformation into consideration, characterized in that: The device includes an acquisition module, a conversion module, a determination module, a calculation module, a creation module and a simulation module; Wherein, the acquisition module is used to obtain the engineering stress-strain curve of the plastic material under compression; The conversion module is used to convert the engineering stress-strain curve into a real stress-strain curve; The determination module is configured to determine a yield limit based on a comparison between a true stress-strain curve and an engineering stress-strain curve of the plastic material, and use a strain point corresponding to the yield limit as a dividing point between elastic and plastic deformation; The calculation module is used to extract the elastic section of the true stress-strain curve before the demarcation point, calculate the elastic modulus based on the stress-strain linear relationship, and obtain the Poisson's ratio by measuring the axial and transverse strains in the uniaxial compression test; The establishment module is used to extract the plastic section of the true stress-strain curve after the dividing point, and establish a multilinear isotropic hardening model based on the data of the plastic section; The establishment module is further used to integrate the elastic modulus, Poisson's ratio and multilinear isotropic hardening model to construct a complete elastic-plastic constitutive model covering the elastic deformation zone and the plastic deformation zone; The simulation module is used to import the complete elastic-plastic constitutive model into finite element simulation analysis software, and combine the seal structure model with the loading boundary conditions to simulate the strain performance of the plastic seal under the compressive deformation state; the strain performance includes at least stress distribution, strain response and contact performance; The method of determining the yield limit based on the comparison between the true stress-strain curve and the engineering stress-strain curve of the plastic material, and using the strain point corresponding to the yield limit as the dividing point between elastic deformation and plastic deformation, includes: Calculating the relative stress error between the true stress-strain curve and the engineering stress-strain curve at each corresponding strain point; Setting an error threshold based on the characteristics of the plastic material, and determining the corresponding strain point as the yield limit when the relative error exceeds the threshold for the first time; The true stress-strain curve is divided into an elastic section and a plastic section with the yield limit as the boundary.

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