Method for determining stress-strain curve of sample under complex stress state

Abstract

The application discloses a method for determining stress-strain curve of a sample under complex stress state, and belongs to the field of experimental mechanics and computational mechanics. The method comprises the following steps: firstly, uniaxial tension test is carried out to obtain the true stress-plastic strain curve of the material; then, mechanical test is carried out on the non-uniaxial loading sample to obtain the load-displacement curve, and a corresponding finite element model is established, and numerical simulation is carried out by using the true stress-plastic strain curve; then, the experimental result is compared with the numerical simulation result, the true stress-plastic strain curve is corrected according to the error between the two, and reverse iterative analysis is carried out until the error is less than a preset threshold; finally, based on the corrected numerical simulation result, the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading area is extracted. The application can overcome the problems in the prior art that the stress-strain under complex stress state is difficult to directly measure, different stress components are difficult to separate, and the true stress-strain curve is difficult to obtain.

Description

Technical Field

[0001] This invention belongs to the fields of experimental mechanics and computational mechanics, and specifically relates to a method for determining the stress-strain curve of a specimen under complex stress conditions. Background Technology

[0002] In engineering fields such as aerospace, transportation, and high-end equipment manufacturing, structural materials typically endure multiple loads, including tension, compression, and shear, during service, resulting in complex stress states within the materials. Accurately obtaining the stress-strain response of materials under complex stress states is crucial for structural strength assessment, structural modeling, and life prediction.

[0003] Currently, the testing methods for the mechanical properties of materials mainly rely on uniaxial tensile and compression test standards. By measuring the force and displacement or strain along the gauge length of the specimen, the engineering stress-strain curve of the material is calculated, and then converted into a true stress-true strain curve. This method assumes that the specimen is under a uniform uniaxial stress state, and can accurately reflect the mechanical behavior of the material under simple stress states. Building upon this, researchers have introduced concepts such as equivalent stress and equivalent strain to extrapolate uniaxial test results to multiaxial stress states, which is used to calibrate various constitutive models and fracture criteria.

[0004] However, existing technologies still have certain limitations. First, stress and strain are difficult to measure directly. Under complex stress conditions, the stress and strain fields inside the specimen exhibit significant non-uniform distribution, with large differences in stress states at different locations. It is difficult to obtain full-field stress and strain data of a local area of ​​the specimen directly and accurately using traditional experimental methods such as strain gauges and extensometers. Second, it is difficult to separate different stress components. The macroscopic mechanical response obtained solely from experimental testing is a comprehensive result of the overall response of the specimen, and it is impossible to effectively separate the independent contributions of tensile stress, compressive stress, and shear stress to material deformation and failure, resulting in a lack of in-depth understanding of the mechanical behavior of materials under multiaxial loads. Finally, it is difficult to obtain the true stress-strain curve for calibration. Due to the aforementioned difficulties in measurement and separation, existing methods cannot directly provide the true stress-strain curve of materials under complex stress conditions. This makes it difficult to obtain direct and reliable data support for the parameter calibration of high-precision constitutive models and the establishment of fracture criteria, thus restricting the accuracy of refined simulation analysis of engineering structures.

[0005] Therefore, this invention proposes a method for determining the stress-strain curve of a specimen under complex stress conditions, which can meet the needs of engineering and scientific research for characterizing the multiaxial mechanical properties of materials, and has important engineering application value and scientific research significance. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the stress-strain curve of a specimen under complex stress conditions, which can overcome the problems in the prior art that stress and strain are difficult to measure directly under complex stress conditions, different stress components are difficult to separate, and the true stress-strain curve is difficult to obtain.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is: a method for determining the stress-strain curve of a specimen under complex stress conditions, comprising the following steps: S1. Conduct uniaxial tensile tests to obtain the true stress-plastic strain curve of the material; S2. Conduct mechanical tests on the non-uniaxially loaded specimen, obtain the load-displacement curve, establish the finite element model of the non-uniaxially loaded specimen, and perform numerical simulation using the true stress-plastic strain curve. S3. Compare the load-displacement curve obtained from the experiment with the numerical simulation results, correct the true stress-plastic strain curve based on the error between the two, and perform reverse iterative analysis until the error is less than the preset threshold. S4. Based on the numerical simulation results where the error meets the preset threshold, extract the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading region.

[0008] Furthermore, the non-uniaxial loading specimen includes tensile shear specimens, compression shear specimens, biaxial compression specimens, triaxial compression specimens, biaxial tensile specimens, or equivalent loading forms.

[0009] Furthermore, in step S1, the uniaxial tensile test uses a smooth round bar specimen, and the true stress-plastic strain curve is obtained from the experimental measurement results after geometric correction.

[0010] Furthermore, the finite element model established in step S2 includes the actual geometry of the specimen, the loading method, and the boundary conditions, and uses the true stress-plastic strain curve to describe the constitutive behavior of the material.

[0011] Further, step S3 specifically involves discretizing the true stress-plastic strain curve into several control points, using the stress value corresponding to the control point as the variable to be optimized, adjusting the stress value of the control point according to the error, and re-inputting the adjusted true stress-plastic strain curve as the material constitutive parameter into the finite element model for numerical simulation. Through multiple iterations, the error is gradually reduced until it is less than a preset threshold.

[0012] Furthermore, the error is the sum of the squares of the differences between the experimental load and the simulated load, and the preset threshold is set to be less than 10% according to the experimental accuracy requirements.

[0013] Furthermore, the non-uniaxial loading region is the tensile-shear region or the combined loading region where the specimen undergoes major plastic deformation.

[0014] Further, step S4 specifically involves extracting the equivalent stress and equivalent plastic strain corresponding to all elements or integration points within the non-uniaxial loading region based on the finite element numerical simulation results after the error meets a preset threshold, and performing arithmetic averaging on the equivalent stress and equivalent plastic strain to obtain the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading region.

[0015] The beneficial effects of the above technical solution are as follows: 1. This invention effectively reduces the difficulty of experimental implementation, eliminating the need for direct measurement of internal stress and strain under complex stress states. Specifically, this invention does not rely on direct measurement of the internal stress and strain fields of the specimen under complex stress states. Instead, it employs a technical approach combining experimental testing and numerical simulation. By obtaining easily measurable load-displacement curves and combining them with finite element simulation, the stress-strain relationship of the material is inverted. This method effectively avoids the technical difficulty of directly obtaining local stress-strain data under complex stress states using strain gauges, extensometers, and other means in traditional methods, thereby reducing the difficulty of experimental implementation and hardware requirements.

[0016] 2. This invention significantly improves the accuracy and stability of the equivalent stress-equivalent plastic strain curve. Specifically, this invention uses inverse iterative analysis, with the error between experimental results and numerical simulation results as the convergence criterion, to successively correct the true stress-plastic strain curve input to the simulation until the error meets a preset condition. This closed-loop correction mechanism ensures a high degree of consistency between the numerical simulation results and experimental results, overcoming the bias caused by relying solely on theoretical extrapolation or empirical formulas in traditional methods, thereby improving the accuracy and stability of the equivalent stress-equivalent plastic strain curve of materials under complex stress states.

[0017] 3. This invention possesses excellent versatility and can be applied to various non-uniaxial loading conditions. Specifically, it is not only applicable to simple stress states such as uniaxial tension and compression, but also to specimen structures that generate complex stress states, such as tension-shear specimens, compression-shear specimens, biaxial compression specimens, triaxial compression specimens, and biaxial tension specimens. Furthermore, it can be extended to quasi-static and dynamic tests under room temperature and high temperature conditions, as well as combined tests under these conditions. This method has excellent versatility and scalability, providing reliable mechanical parameter support for parameter calibration of material constitutive models under complex stress states, establishment of fracture criteria, and refined simulation analysis of engineering structures. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 A schematic diagram of the structure of a smooth round bar specimen used in a uniaxial tensile test; Figure 3This is a schematic diagram of the tensile shear specimen. Figure 4 A schematic diagram of the true stress-plastic strain curve of a smooth round bar specimen; Figure 5 This is a schematic diagram of the load-displacement curve of a tensile-shear specimen. Figure 6 This is a schematic diagram of the mesh generation for the finite element model of the tension-shear specimen. Figure 7 This is a schematic diagram comparing the load-displacement curves obtained from experiments and numerical simulations. Figure 8 This is a schematic diagram of the average equivalent stress-average equivalent plastic strain curve in the tension-shear zone, extracted based on numerical simulation results. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0020] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0021] To address the challenges of accurately obtaining material constitutive relations under complex stress states and the inability to directly apply true stress-plastic strain curves determined by traditional uniaxial tensile tests to multiaxial stress conditions, this invention proposes a method for determining the stress-strain curve of a specimen under complex stress states, such as... Figure 1 As shown, it includes the following steps: S1. Conduct uniaxial tensile tests to obtain the true stress-plastic strain curve of the material.

[0022] Specifically, a smooth round bar tensile specimen is prepared from the material to be tested, and a uniaxial tensile test is performed on a material testing machine at a predetermined loading rate. The load and displacement data of the tensile specimen during the tensile process are recorded. The structure of the smooth round bar tensile specimen is as follows: Figure 2 As shown, the diameter of the clamping sections at both ends is 10mm and the length is 20mm, the diameter of the working section in the middle is 4mm, and the sample is transitioned by a circular arc with a radius of 3mm. The total length of the sample is 68mm.

[0023] Based on the load and displacement data, combined with the initial geometry of the tensile specimen, the engineering stress-engineering strain curve of the material is calculated, and then further converted to obtain the true stress-true strain curve.

[0024] Based on this, by subtracting the elastic strain component, the true stress-plastic strain curve of the material under uniaxial tensile conditions is obtained, as shown in the figure. Figure 4 As shown, it can be used as the initial material constitutive relation for subsequent numerical simulations.

[0025] S2. Conduct mechanical tests on the non-uniaxially loaded specimen to obtain the load-displacement curve, establish the finite element model of the non-uniaxially loaded specimen, and perform numerical simulation using the true stress-plastic strain curve.

[0026] Among them, non-uniaxial loading specimens include tensile shear specimens, compression shear specimens, biaxial compression specimens, triaxial compression specimens, biaxial tensile specimens, or loading forms equivalent to the above specimens.

[0027] Specifically, a tensile-shear specimen is prepared and a tensile load is applied to it on a material testing machine. Load and displacement data are collected in real time during the test to obtain the load-displacement curve of the tensile-shear specimen. The tensile-shear specimen can convert the tensile load at both ends into tensile and shear stresses in the gauge length region, thereby achieving combined tensile-shear loading. The tensile-shear specimen structure is as follows: Figure 3 As shown, its total length is 40mm, with circular clamping heads at both ends, each 10mm in diameter and 14mm in length. The middle section is a rectangular plate, 8mm wide and 4mm thick, with a slanted shear notch in the center. The shear section width is 2mm, and the normal direction of this shear surface forms a 15° angle with the sample axis. The load-displacement curve is shown below. Figure 5 As shown.

[0028] Based on the geometry of the tensile-shear specimen and the experimental loading conditions, a corresponding finite element model of the tensile-shear specimen is established, and its mesh generation is as follows: Figure 6 As shown. In the finite element model of the tensile-shear specimen, the loading method and boundary conditions are consistent with the tensile-shear test process.

[0029] Using the true stress-plastic strain curve of the smooth round bar specimen obtained in step S1 as the material constitutive input parameter, the mechanical response of the tensile-shear specimen is numerically simulated to obtain the corresponding load-displacement numerical results.

[0030] S3. Compare the load-displacement curve obtained from the experiment with the numerical simulation results, correct the true stress-plastic strain curve based on the error between the two, and perform reverse iterative analysis until the error is less than a preset threshold.

[0031] Specifically, the load-displacement curves obtained from the tensile-shear test in step S2 are compared and analyzed with the numerical simulation results, and an error function is constructed. The comparison graph of load-displacement curves obtained from experiments and numerical simulations is shown below. Figure 7 As shown, the error function The expression is: In the formula, The total number of data points. Let i be the test load value for the i-th data point. Let be the simulated load value for the i-th data point.

[0032] The true stress-plastic strain curve obtained in step S1 is discretized into several control points, and the stress value of the control points is used as the variable to be optimized.

[0033] When the error exceeds a preset threshold, the stress value of the control point is adjusted according to the error, and the adjusted true stress-plastic strain curve is re-input into the finite element model as the material constitutive parameter for numerical simulation. The preset threshold is preferably an error function value of less than 10%.

[0034] Through multiple rounds of iterative calculations, the error is gradually reduced until the error between the experimental load-displacement curve and the numerical simulation result is less than a preset threshold.

[0035] S4. Based on the numerical simulation results where the error meets the preset threshold, extract the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading region.

[0036] Specifically, based on the finite element numerical simulation results after the error in step S3 meets the preset threshold, the equivalent stress and equivalent plastic strain corresponding to all elements or integration points in the tension-shear zone are extracted, and the equivalent stress and equivalent plastic strain are arithmetically averaged to obtain the average equivalent stress-average equivalent plastic strain curve of the tension-shear zone, as shown below. Figure 8 As shown.

[0037] The average equivalent stress-average equivalent plastic strain curve characterizes the macroscopic mechanical response of the material under tensile and shear stress, and can be used as the basic data for the calibration of material constitutive parameters and analysis of mechanical properties under non-uniaxial loading conditions.

[0038] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for determining the stress-strain curve of a specimen under complex stress conditions, characterized in that, Includes the following steps: S1. Conduct uniaxial tensile tests to obtain the true stress-plastic strain curve of the material; S2. Conduct mechanical tests on the non-uniaxially loaded specimen, obtain the load-displacement curve, establish the finite element model of the non-uniaxially loaded specimen, and perform numerical simulation using the true stress-plastic strain curve. S3. Compare the load-displacement curve obtained from the experiment with the numerical simulation results, correct the true stress-plastic strain curve based on the error between the two, and perform reverse iterative analysis until the error is less than the preset threshold. S4. Based on the numerical simulation results where the error meets the preset threshold, extract the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading region.

2. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, The non-uniaxial loading specimens include tensile shear specimens, compression shear specimens, biaxial compression specimens, triaxial compression specimens, biaxial tensile specimens, or equivalent loading forms.

3. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, In step S1, the uniaxial tensile test uses a smooth round bar specimen, and the true stress-plastic strain curve is obtained from the experimental measurement results after geometric correction.

4. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, The finite element model established in step S2 includes the actual geometry of the specimen, the loading method, and the boundary conditions, and uses the true stress-plastic strain curve to describe the constitutive behavior of the material.

5. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, Step S3 specifically involves discretizing the true stress-plastic strain curve into several control points, using the stress values ​​corresponding to the control points as variables to be optimized, adjusting the stress values ​​of the control points according to the error, and then re-inputting the adjusted true stress-plastic strain curve as material constitutive parameters into the finite element model for numerical simulation. Through multiple iterations, the error is gradually reduced until it is less than a preset threshold.

6. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1 or 5, characterized in that, The error is the sum of the squares of the differences between the experimental load and the simulated load, and the preset threshold is set to be less than 10% according to the experimental accuracy requirements.

7. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, The non-uniaxial loading region is the tensile-shear zone or the combined loading zone where the specimen undergoes major plastic deformation.

8. The method for determining the stress-strain curve of a specimen under complex stress state according to claim 1, characterized in that, Specifically, step S4 involves extracting the equivalent stress and equivalent plastic strain corresponding to all elements or integration points within the non-uniaxial loading region based on the finite element numerical simulation results after the error meets a preset threshold, and performing an arithmetic average on the equivalent stress and equivalent plastic strain to obtain the average equivalent stress-average equivalent plastic strain curve of the non-uniaxial loading region.

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