A test method, storage medium and device for obtaining stress-strain relationship of linearly hardening elastic-plastic material
By employing micro-destructive indentation tests and finite element-assisted testing methods, the challenge of obtaining the stress-strain relationship of linearly reinforced elasto-plastic materials in pressurized water reactor pipelines was solved, achieving an efficient and low-loss testing method that ensures equipment safety and testing accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SUZHOU NUCLEAR POWER RES INST CO LTD
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies cannot effectively obtain the stress-strain relationship of linearly reinforced elasto-plastic materials in the primary loop of pressurized water reactors, especially since the material toughness decreases under long-term high-temperature conditions and standard samples cannot be obtained from the in-service materials.
The displacement-load curve of the indenter loading on the surface of the specimen or component is obtained by micro-destructive indentation test. Combined with the finite element auxiliary test method, the load-displacement model is established and fitted to obtain the stress-strain relationship of the linearly strengthened elasto-plastic material.
It enables high-throughput testing of linearly reinforced elastoplastic materials, reduces material and equipment wear, and ensures testing accuracy and equipment safety.
Smart Images
Figure CN122149989A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of materials measurement technology, and in particular to a testing method, storage medium, and device for obtaining the stress-strain relationship of linearly reinforced elastoplastic materials. Background Technology
[0002] The primary loop piping of a pressurized water reactor (PWR) is a crucial barrier for nuclear power plants. Through the definition and screening of SSCs (Safety Management System Components), it was determined that the primary loop piping falls within the scope of Aging Management Review (AMR). Its material has a high elongation rate and is classified as a linearly strengthened elasto-plastic material. Under long-term high-temperature operation, it will undergo thermal aging, with the ferrite phase becoming embrittled, leading to a decrease in material toughness. Currently, it is not possible to obtain standard samples from in-service materials to obtain their stress-strain relationships. Summary of the Invention
[0003] The technical problem to be solved by the present invention is to provide a testing method, storage medium and device for obtaining the stress-strain relationship of linearly reinforced elasto-plastic materials.
[0004] The technical solution adopted by this invention to solve its technical problem is: a test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials, comprising the following steps: Obtain test blocks or components with smooth surfaces; The indentation test was used to obtain the indenter loading displacement h-load P curve on the surface of the specimen or component. Based on the relationship between the total strain energy of the material of the test block or the component and the strain energy density and the effective deformation domain volume, a load P-displacement h model is established. Based on the finite element-assisted testing method, the key parameters of the load P-displacement h model were calibrated. The stress-strain relationship of the linearly reinforced elastoplastic material is obtained by fitting the displacement h-load P curve of the indenter with the load P-displacement h model.
[0005] Optionally, the elongation of the test block or the component must be greater than or equal to 30%; the stress-strain relationship of the material should satisfy the following formula: In the formula, It is the elastic modulus; Tangent modulus; For yield strain; It is the yield stress, and has = ; For stress, In response to the situation.
[0006] Optionally, the indentation depth of the micro-damage indentation test is not less than 0.5 mm.
[0007] Optionally, the test block or the component includes a test micro-region, which is uniform and isotropic.
[0008] Optionally, the surface finish of the test block or the component is not less than 0.6.
[0009] Optionally, the specimen size of the test block is greater than or equal to 20 mm × 20 mm × 10 mm.
[0010] Optionally, a load-displacement h model is established to establish the relationship between the total strain energy of the material of the test block or the component and the strain energy density and the effective deformation domain volume, including: Based on the relationship between the total strain energy of the material, the strain energy density, and the volume of the effective deformation domain, the load P-displacement h model is obtained by using the integral mean value theorem.
[0011] Optionally, the key parameters include dimensionless model parameters calculated based on the dimensionless constant of the effective deformation domain volume and the dimensionless constant of the equivalent strain during the compression process, as well as the strain energy density compensation constant of the strain energy density; the load P-displacement h model is as follows: In the formula, C is the loading coefficient of the load-displacement curve, m is the loading exponent, h is the loading depth of the indenter, D is the diameter of the indenter, and E is the elastic modulus. Tangent modulus, and These are the parameters of the dimensionless model; ~ is the strain energy density compensation constant.
[0012] A computer-readable storage medium storing a computer program adapted for loading by a processor to perform the steps of any of the test methods described above for obtaining the stress-strain relationship of a linearly strengthened elastoplastic material.
[0013] A computer device, including a memory and a processor; The memory contains computer programs; The processor executes the steps of any of the test methods described above for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials by calling the computer program stored in the memory.
[0014] The implementation of this invention has the following beneficial effects: This invention tests linearly reinforced elastoplastic materials through a low-destruction indentation test, thereby obtaining the stress-strain relationship of the linearly reinforced elastoplastic materials, reducing the wear and tear on materials and service equipment, and thus achieving the purpose of high-throughput testing. Attached Figure Description
[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of a test method for obtaining the stress-strain relationship of a linearly strengthened elastoplastic material in one embodiment; Figure 2 This is a schematic diagram of a planar indentation finite element auxiliary test mesh in one embodiment; Figure 3 This is a comparison diagram of stress-strain curves of austenitic stainless steel material in one embodiment. Detailed Implementation
[0016] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0017] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.
[0018] This invention provides a testing method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials, such as... Figure 1 As shown, it includes the following steps: Obtain test blocks or components with smooth surfaces.
[0019] Using test blocks or components with smooth surfaces ensures the accuracy and consistency of subsequent experimental results, avoiding any contamination or impurities that could affect measurement precision.
[0020] The indentation test is used to obtain the indenter displacement h-load P curve on the surface of the test block or component.
[0021] When obtaining the indenter displacement h-load P curve on the surface of the test block or component, the indenter is perpendicular to the plane of the test block or component surface.
[0022] In some scenarios, the indentation device is equipped with the function of acquiring the indenter displacement h-load P curve, and the indenter is a flat-headed cylindrical indenter. At the tip of the indenter, the chamfer radius r is 0.005 mm, and the indenter diameter D is 0.3 mm. The indenter displacement h-load P curve is recorded throughout the test.
[0023] Based on the relationship between the total strain energy of the material of the test block or component and the strain energy density and the volume of the effective deformation domain, a load P-displacement h model is established.
[0024] Based on the finite element-assisted testing method, the parameters of the load P-displacement h model are calibrated.
[0025] Based on the finite element-assisted testing method, the load-displacement model curve corresponding to the load P-displacement h model is obtained, thereby calibrating the parameters of the load P-displacement h model.
[0026] By fitting the indenter displacement h-load P curve with the load P-displacement h model, the stress-strain relationship of the linearly strengthened elasto-plastic material is obtained.
[0027] Based on the indenter displacement h-load P curve obtained through micro-damage indentation test, the load-displacement model curve of load P-displacement h model is fitted to determine the specific data of material parameters in load P-displacement h model, thereby determining the stress-strain relationship of linearly strengthened elastoplastic material.
[0028] This invention utilizes a minimally invasive indentation test to examine linearly reinforced elasto-plastic materials, thereby obtaining their stress-strain relationships. This reduces wear and tear on materials and in-service equipment, achieving high-throughput testing. It enables effective evaluation of in-service equipment, ensuring orderly production and improving the safety and reliability of equipment operation.
[0029] In some embodiments, the elongation of the specimen or component must be greater than or equal to 30%; the stress-strain relationship of the material should satisfy the following formula: In the formula, It is the elastic modulus; Tangent modulus; For yield strain; It is the yield stress, and has = ; For stress, In response to the situation.
[0030] The elongation of the specimen or component should not be less than 30% to ensure that the material has sufficient plastic deformation capacity during indentation or loading, avoiding local necking, cracking, or premature failure before reaching the target indentation depth, thus obtaining a complete and stable load-displacement response curve. A higher elongation allows the material to enter a fully developed plastic stage, significantly improving the accuracy and sensitivity of identifying elasto-plastic parameters (such as yield strength and hardening modulus) and reducing calibration errors caused by insufficient deformation. Simultaneously, the large deformation capacity reduces experimental dispersion, making the matching between finite element simulation and experimental data more reliable, ensuring that the calibrated model parameters have good stability and engineering applicability.
[0031] In some embodiments, the indentation depth of the micro-damage indentation test is no greater than 0.5 mm.
[0032] By strictly controlling the indentation depth of the micro-destructive indentation test to within 0.5 mm, the impact of the test on the tested material or structure can be minimized. This shallow indentation method not only effectively reduces potential damage to the material's surface and internal structure but also maintains the material's original mechanical properties and integrity while ensuring test accuracy. Therefore, it reduces damage to in-service equipment during testing.
[0033] In some embodiments, the test block or component includes a test micro-region, which is uniform and isotropic.
[0034] The test micro-area is the region measured using a micro-damage indentation test.
[0035] By defining the test micro-region of the specimen or component as homogeneous and isotropic, the mechanical response law of the specimen or component is ensured to be simple, unique, and highly repeatable. This effectively reduces the complexity of the mechanical model and numerical analysis, significantly reduces the number of parameters to be calibrated, and improves the stability and uniqueness of parameter identification. Simultaneously, the experimental data exhibits low dispersion and good consistency, effectively improving the model calibration accuracy; the finite element modeling and solution process is more stable and reliable, and simulation results are easily matched with experimental results, thus ensuring the credibility of the analysis results.
[0036] In some embodiments, the surface finish of the test block or component is not less than 0.6.
[0037] Understandably, limiting the surface finish of the test block or component to no less than 0.6 μm is equivalent to a surface roughness Ra ≤ 0.6 μm. This technical feature ensures sufficient flatness and smoothness of the sample surface, reducing the impact of microscopic surface unevenness on the indentation test results. A smooth surface ensures stable and uniform contact between the indenter and the sample, avoiding localized stress concentration or unstable contact caused by surface roughness, thus ensuring the accuracy and reliability of the indenter loading displacement h-load P curve. This requirement effectively reduces the dispersion of test data, improves the accuracy and stability of subsequent finite element auxiliary parameter calibration, and conforms to the basic specifications for material mechanical property testing and indentation testing.
[0038] In some embodiments, the specimen size of the test block is greater than or equal to 20 mm × 20 mm × 10 mm.
[0039] In some scenarios, test blocks are standardized specimens made from the base material or welds that make up the components.
[0040] Furthermore, if the surface of the test block or the structure is flat or curved, the surface must first be ground flat with a grinding wheel, and then polished with fine sandpaper. During the test, the loading head must be perpendicular to the structural plane.
[0041] In some embodiments, a load-displacement h model is established based on the relationship between the total strain energy of the material of the specimen or component and the strain energy density and the effective deformation domain volume, including: Based on the relationship between the total strain energy of the material, the strain energy density, and the effective deformation domain volume, the load P-displacement h model is obtained by using the integral mean value theorem.
[0042] According to the mean value theorem for integrals, there must exist a point M within the effective deformation domain of the material such that the total strain energy of the material is... The table shows the strain energy density of a representative volume element. With effective deformation domain volume The product of these is: In the formula, The total strain energy of the material; Strain energy density; For the effective deformation domain volume.
[0043] For a representative volume element of the material at point M, its strain energy density can be further expressed as: In the formula, Let be the strain tensor of a representative volume element of the material at any point; Let be the stress tensor of a representative volume element of the material at any point; The equivalent strain is given by the equivalent strain of a representative volume element of the material at any point. Let be the equivalent stress of a representative volume element of the material at any point; Let M be the strain tensor; Equivalent strain at point M; Let be the strain energy density.
[0044] From the above, we can see the strain energy density of a representative volume element in a compressive material: In the formula, Strain energy density; ; It is the elastic modulus; Tangent modulus; For yield strain.
[0045] Based on the test conditions of the micro-damage indentation test, the equivalent elastic-plastic strain of the linearly reinforced elastoplastic material can be obtained. Much greater than the yield strain ,but We can obtain: In the above formula Let it be denoted as a function , The strain energy density of the compressive material can be expressed as: Therefore, the total strain energy of the compressive material is: Furthermore, based on the power-law relationship between the effective deformation domain volume of the compressed material, the equivalent strain, and the dimensionless displacement, we can obtain: In the formula, h is the indenter loading depth, and D is the indenter diameter. and Let be the dimensionless constant of the effective deformation domain volume during the compression process. and It is an equivalent variable dimensionless constant.
[0046] There are other functions and as follows: In the formula, k5~k10 are strain energy density compensation constants.
[0047] According to mathematical principles, there must exist another separating function. AND function Equivalently, we can obtain: In the formula, h is the indenter loading depth; D is the indenter diameter.
[0048] Combining the above formulas, we can obtain: In some embodiments, key parameters include dimensionless model parameters calculated based on the dimensionless constant of the effective deformation domain volume and the dimensionless constant of the equivalent strain during the compression process, as well as the strain energy density compensation constant of the strain energy density.
[0049] To simplify the above equation, let's denote... = , = , = , = , = , = , = , = ,Right now: The load P-displacement h model is as follows: In the formula, C is the loading coefficient of the load-displacement curve, m is the loading exponent, h is the loading depth of the indenter, D is the diameter of the indenter, and E is the elastic modulus. Tangent modulus, and These are the parameters of the dimensionless model; ~ is the strain energy density compensation constant.
[0050] Specifically, will Substitute Thus, the load P-displacement h model is obtained.
[0051] In one embodiment, the material yield strength is initially determined based on finite element-assisted testing technology. The range is 200~1000MPa, and the strengthening modulus is... The load-displacement curves were obtained within the range of 800 MPa to 4800 MPa, thereby extracting the loading coefficient C and loading exponent m. Specifically, the finite element auxiliary test mesh curves were indented, as shown below. Figure 2 As shown.
[0052] Furthermore, the key parameters of the planar indentation model for linearly strengthened elasto-plastic materials can be determined using formulas, i.e., based on different strengthening moduli. and different yield strengths The finite element analysis results can be used to calibrate and obtain model parameters. and ~ The specific value.
[0053] Based on the indenter loading displacement h-load P curve obtained from the micro-damage indentation test, this curve is fitted to the curve of the plane indentation theory model based on the linear strengthening elastoplastic assumption. Then, through numerical inversion and parameter fitting methods, the stress-strain relationship of the material is derived, thereby effectively obtaining the constitutive model parameters of the linear strengthening elastoplastic material. A comparison of stress-strain curves for various austenitic stainless steel materials is shown below. Figure 3 As shown.
[0054] The present invention provides a computer-readable storage medium storing a computer program adapted for loading by a processor to perform the steps of any of the above-mentioned test methods for obtaining the stress-strain relationship of a linearly strengthened elasto-plastic material.
[0055] This invention provides a computer device, including a memory and a processor; The memory contains computer programs; The processor executes the steps of any of the above test methods for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials by calling computer programs stored in memory.
[0056] The above embodiments only illustrate preferred embodiments of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can freely combine the above technical features without departing from the concept of the present invention, and can also make several modifications and improvements, all of which fall within the protection scope of the present invention. Therefore, all equivalent transformations and modifications made with respect to the scope of the claims of the present invention should fall within the scope of the claims of the present invention.
Claims
1. A test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials, characterized in that, Includes the following steps: Obtain test blocks or components with smooth surfaces; The indentation test was used to obtain the indenter loading displacement h-load P curve on the surface of the specimen or component. Based on the relationship between the total strain energy of the material of the test block or the component and the strain energy density and the effective deformation domain volume, a load P-displacement h model is established. Based on the finite element-assisted testing method, the key parameters of the load P-displacement h model were calibrated. The stress-strain relationship of the linearly strengthened elasto-plastic material is obtained by fitting the displacement h-load P curve of the indenter with the load P-displacement h model.
2. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 1, characterized in that, The elongation of the test block or component must be greater than or equal to 30%; the stress-strain relationship of the material should satisfy the following formula: In the formula, It is the elastic modulus; Tangent modulus; For yield strain; It is the yield stress, and has = ; For stress, In response to the situation.
3. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 1, characterized in that, The indentation depth of the micro-damage indentation test shall not be less than 0.5 mm.
4. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 3, characterized in that, The test block or the component includes a test micro-region, which is uniform and isotropic.
5. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 1, characterized in that, The surface finish of the test block or the component is not less than 0.
6.
6. The test method for obtaining the stress-strain relationship of linearly reinforced elastoplastic materials according to claim 5, wherein the specimen size of the test block is greater than or equal to 20 mm × 20 mm × 10 mm.
7. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 1, characterized in that, The relationship between the total strain energy of the material of the test block or the component and the strain energy density and the effective deformation domain volume is established using a load P-displacement h model, including: Based on the relationship between the total strain energy of the material, the strain energy density, and the volume of the effective deformation domain, the load P-displacement h model is obtained by using the integral mean value theorem.
8. The test method for obtaining the stress-strain relationship of linearly strengthened elasto-plastic materials according to claim 7, characterized in that, The key parameters include dimensionless model parameters calculated based on the dimensionless constant of the effective deformation domain volume and the dimensionless constant of the equivalent strain during the compression process, as well as the strain energy density compensation constant of the strain energy density. The load P-displacement h model is as follows: In the formula, C is the loading coefficient of the load-displacement curve, m is the loading exponent, h is the loading depth of the indenter, D is the diameter of the indenter, and E is the elastic modulus. Tangent modulus, and These are the parameters of the dimensionless model; ~ is the strain energy density compensation constant.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted for loading by a processor to perform the steps of the test method for obtaining the stress-strain relationship of a linearly strengthened elasto-plastic material as described in any one of claims 1 to 8.
10. A computer device, characterized in that, Including memory and processor; The memory stores computer programs; The processor executes the steps of the test method for obtaining the stress-strain relationship of a linearly strengthened elasto-plastic material as described in any one of claims 1 to 8 by calling the computer program stored in the memory.