Based on the yield platform of the sample under the condition of flat punch loading equivalent stress strain curve determination method
By constructing a power-hardening constitutive model and an energy density equivalent method, the problem of large material error in determining the yield plateau in planar punch tests was solved, and high-precision equivalent stress-strain curve determination was achieved, which is suitable for low-cost testing of precious metals and service components.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2026-04-17
- Publication Date
- 2026-06-05
AI Technical Summary
Existing planar punch test methods are difficult to accurately determine the equivalent stress-strain curve of power-hardened materials with yield plateaus, and the calculation errors of the yield point and yield plateau stage are large.
A constitutive equivalent stress-strain curve determination method based on the yield plateau of circular specimens under planar punch loading conditions was adopted. By constructing a power-hardening constitutive model, key constitutive parameters were extracted in stages, including the characteristics of the elastic, elastoplastic and power-hardening stages. Combined with the energy density equivalent method, the full-strain equivalent stress-strain curve of the material was obtained.
It enables accurate measurement of materials with yield plateaus, reduces calculation errors, and is suitable for small sample testing of precious metals and service components. It features high precision and low cost, and is suitable for micro-destructive sampling and quantitative evaluation of material safety performance.
Smart Images
Figure CN122150025A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of material mechanical property testing, specifically relating to a method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions. Background Technology
[0002] Stress-strain relationships, elastic modulus, and yield strength are the fundamental mechanical relationships and properties of materials for structural integrity analysis. Structural materials operating under long-term high temperature, high pressure, and corrosive environments suffer varying degrees of damage and performance degradation. Traditional destructive testing methods are difficult to apply to engineering structures and small-sized components. Micro-sample techniques, represented by the Small Punch Test (SPT), were initially used in the nuclear industry. Nuclear reactor shell materials operate under long-term neutron irradiation, and the fracture properties of these materials are evaluated through mechanical property testing of irradiation-monitored test blocks to assess the changes in temperature and irradiation dose. Later, SPT was extended to study the mechanical properties of materials.
[0003] Existing techniques, based on the equivalent energy principle and differential methods, determine the stress-strain relationship of materials through incremental spherical indentation tests and the DIC method. For stage III of the Ph curve of circular specimens of ductile materials, a theory related to the stress-strain relationship has been proposed based on the energy density equivalent method. However, further research is needed for materials without stage III. Building upon this, existing techniques propose a method for determining the stress-strain curve of materials using planar punch tests based on the Hollomon constitutive model and the energy density equivalent principle. This method solves for the Hollomon model parameters from the load-displacement test curves to obtain the material's stress-strain curve, but it fails to achieve a direct correlation between the load / displacement test points and the material's stress-strain curve. Summary of the Invention
[0004] The purpose of this invention is to address the aforementioned shortcomings in the prior art by providing a method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions. This method solves the problems of existing planar punch testing methods, which struggle to accurately determine the equivalent stress-strain curve of power-hardened materials with a yield plateau, and suffer from large errors in calculating the yield point and yield plateau stage.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions, comprising the following steps: S1. Perform a planar punch loading test on the circular sample to obtain the load-displacement curve of the circular sample; S2. Construct a power-hardening constitutive model with a yield plateau to describe the relationship between equivalent stress and equivalent strain of the material under test; S3. Perform staged feature extraction and analytical calculation on the load-displacement test curve to obtain key constitutive parameters describing the mechanical properties of the material under test; S4. Substitute the key constitutive parameters into the power-hardening constitutive model in S2 to obtain the full-segment equivalent stress-strain curve of the disc sample under planar punch loading conditions.
[0006] Furthermore, in S2, the power-hardening constitutive model is expressed as: In the formula, For equivalent stress, The elastic modulus of the material, For equivalent change, For yield stress, For yield strain, For the yield plateau length, , The strain hardening index is the power-law hardening index.
[0007] Furthermore, in step S3, the load-displacement test curve is subjected to staged feature extraction and analytical calculation to obtain key constitutive parameters describing the mechanical properties of the material under test, including: Elastic phase; based on the load-displacement curve data for the elastic phase, and combined with characteristic area and characteristic displacement, the elastic modulus of the material is calculated: In the formula, For load, For characteristic displacement, The coefficient of elastic deformation is 1. For the characteristic area, It is a purely elastic displacement.
[0008] Furthermore, in step S3, the load-displacement test curve is subjected to staged feature extraction and analytical calculation to obtain key constitutive parameters describing the mechanical properties of the material under test, including: Elastic-plastic stage; linear regression of the load-displacement curve in the elastoplastic stage yields the dimensionless load-displacement rate of change in the elastoplastic stage. G and elastoplastic dimensionless load-displacement intercept D And the elastoplastic dimensionless load-displacement change rate G and elastoplastic dimensionless load-displacement intercept D The yield stress is obtained by substituting it into the equivalent yield stress equation set calibrated by the finite element method.
[0009] Furthermore, the equivalent yield stress equations are expressed as follows: In the formula, Tangent modulus, , , , , , , , To solve for the transformation parameters of tangent modulus and yield stress.
[0010] Furthermore, in step S3, the load-displacement test curve undergoes staged feature extraction and analytical calculation, including: Power hardening stage: Substitute the power hardening stage data of the load-displacement curve into the power hardening equivalent stress-strain equation to obtain the real-time equivalent stress-strain relationship, and perform power-law fitting on the real-time equivalent stress-strain relationship to obtain the hardening parameters.
[0011] Furthermore, the power-hardening equivalent stress-strain equation is expressed as: In the formula, For equivalent plastic strain coefficient, For equivalent plastic strain index, For equivalent plastic stress coefficient, The equivalent plastic stress index, It is a purely plastic displacement. The equivalent stress of a representative volume element.
[0012] The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions provided by this invention has the following advantages: This invention proposes a formula based on the energy density equivalent method. The formula is simple in structure and easy to calibrate. It is applicable to power-hardening materials with yield plateaus. It can obtain equivalent stress-strain curves of various materials, perform micro-damage sampling on in-service components, and obtain results with high accuracy. It can quantitatively evaluate the safety performance of materials.
[0013] This invention overcomes the problem of large errors near the yield point and yield plateau stage when obtaining stress-strain based on the equivalent RO constitutive relation of energy density. This method has significant advantages for testing small sample materials such as precious metals and in-service components. Sample preparation, experimental principles, and data processing are all relatively simple. Researchers only need to perform simple data processing on the experimentally obtained Ph curve of the sample to obtain the equivalent stress-strain curve of the material. It has a sound theoretical basis, low experimental cost, and is easy to popularize and apply. Attached Figure Description
[0014] Figure 1 This is a flowchart illustrating the method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions, as described in this embodiment.
[0015] Figure 2 This is a schematic diagram of power hardening of the yield plateau in the embodiment.
[0016] Figure 3 The planar punch loading device is shown in the embodiment.
[0017] Figure 4 The disc sample configuration is shown in the example.
[0018] Figure 5 The example shows the line load-displacement curve of 42CrMo in the test.
[0019] Figure 6 The stress-strain relationship of 42CrMo obtained from the model in the example is compared with that of single tensile stress. Detailed Implementation
[0020] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0021] This embodiment provides a method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions, based on the energy density equivalence principle and a power-hardening constitutive model with a yield plateau. A model is established to describe the elastic modulus, yield stress, yield plateau, and the relationship between equivalent stress, strain, load, displacement, and geometry of the circular specimen under planar punch loading. A method suitable for determining the strain-stress relationship with a yield plateau using a planar punch is proposed, enabling the determination of the equivalent stress-strain relationship of the material through the load-displacement curve of a small punch. (Reference) Figure 1 Specifically, it includes the following: S1. Perform a planar punch loading test on the circular sample to obtain the load-displacement curve of the circular sample; refer to Figure 3 , Figure 4 The configuration of the disc sample is as follows Figure 4 As shown, the loading device consists of a thin circular sample held and fixed by two clamps, with the normal direction of the middle of the sample extending from the diameter... d f Loading is applied to a cylinder with a diameter of 1 mm. r The chamfer radius of the lower fixture is...d 1 represents the lower clamping hole diameter. d 2 represents the diameter of the upper clamping hole. B The thickness of the circular sample is given. For the characteristic area, Characteristic displacement; The corresponding feature dimensions and geometric parameters are given in Table 1: Table 1 Geometric Parameters A planar punch loading test was performed on the circular specimen to obtain the load-displacement curve. P - h , h For displacement.
[0022] The elastic modulus of the material can be obtained by regressing the elastic phase data of the load-displacement curves obtained from the experiment. E Linear regression in the elastoplastic stage yields the dimensionless load-displacement rate of change. G and elastoplastic dimensionless load-displacement intercept D Then, the yield stress can be obtained. y Substituting the data from the elastoplastic stage into the power-hardening equivalent stress-strain equation, we obtain... K L and N L Finally, we obtained L The detailed process is shown in the following steps.
[0023] S2. Construct a power-hardening constitutive model with a yield plateau to describe the relationship between equivalent stress and equivalent strain of the material under test; Yield plateau power hardening Figure 2 As shown, the power-hardening constitutive model is expressed as: In the formula, For equivalent stress, For equivalent strain For yield strain, For the yield plateau length, , The strain hardening index is the power-law hardening index.
[0024] S3. Perform staged feature extraction and analytical calculation on the load-displacement test curve to obtain key constitutive parameters describing the mechanical properties of the material under test; Equivalent strain eq and dimensionless effective deformation domain volume V eff / V* The dimensionless loading linear displacement of the planar punch specimen, respectively h / h * There is a functional relationship between them. V * Take as A * h * Then the relationship between the energy of the planar punch specimen and the material constitutive parameters, geometric dimensions, and displacement can be determined, as follows: Elastic phase; based on the load-displacement curve data for the elastic phase, and combined with characteristic area and characteristic displacement, the elastic modulus of the material is calculated: In the formula, For load, The elastic deformation coefficient is 0.187. It is a purely elastic displacement.
[0025] Elastic-plastic stage; linear regression of the load-displacement curve in the elastoplastic stage yields the dimensionless load-displacement rate of change in the elastoplastic stage. G and elastoplastic dimensionless load-displacement intercept D And the elastoplastic dimensionless load-displacement change rate G and elastoplastic dimensionless load-displacement intercept D The yield stress is obtained by substituting it into the equivalent yield stress equation set calibrated by the finite element method. The equivalent yield stress equations are expressed as follows: In the formula, Tangent modulus, , , , , , , , To solve for the transformation parameters of tangent modulus and yield stress, h The parameters in the equivalent yield stress equation system, ∈(0.05mm, 0.3mm), are obtained through finite element calibration. a 1~ a The three values are: 2.172, 111.369, and 0.104, respectively. m 1~ m The values for the four values are: 4.612, 5.612, -3.774, and -0.833. K e-2 and K ep-2The values are 0.0564 and 0.261, respectively.
[0026] Power-law hardening stage: Substituting the load-displacement curve data of the power-law hardening stage into the power-law hardening equivalent stress-strain equation, the real-time equivalent stress-strain relationship is obtained, and the hardening parameters are obtained by power-law fitting of the real-time equivalent stress-strain relationship. K L and N L ; The power-hardening equivalent stress-strain equation is expressed as: In the formula, For equivalent plastic strain coefficient, For equivalent plastic strain index, For equivalent plastic stress coefficient, The equivalent plastic stress index, It is a purely plastic displacement. The equivalent stress of the representative volume element is 5.521. 1.129 4.761 and 0.0292, This is a purely plastic displacement.
[0027] S4. Key constitutive parameters, including the material's elastic modulus. Yield stress Hardening parameters K L and N L Substituting into the power-hardening constitutive model in S2, the full-strain equivalent stress-strain curve of the disc specimen under planar punch loading conditions is obtained.
[0028] like Figure 5 The figure shows the load-displacement curves obtained from the 42CrMo small punch test. These curves were obtained through single-stretch test processing. E The Pa is 208.6 GPa. y The model prediction parameters are 300 MPa. E , y , K L and N L The values were 217.7 GPa, 299 MPa, 931.36 MPa and 0.2682, respectively. Figure 6 The stress-strain relationship obtained through the present invention is compared with that obtained under uniaxial tension.
[0029] In practical applications, its scope of application can be appropriately modified and broadened depending on the circumstances. For example, the method is equally applicable to test samples of different materials; simply substitute the load displacement into the formulas and steps in this embodiment for calculation.
[0030] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.
Claims
1. A method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions, characterized in that, Includes the following steps: S1. Perform a planar punch loading test on the circular sample to obtain the load-displacement curve of the circular sample; S2. Construct a power-hardening constitutive model with a yield plateau to describe the relationship between equivalent stress and equivalent strain of the material under test; S3. Perform staged feature extraction and analytical calculation on the load-displacement test curve to obtain key constitutive parameters describing the mechanical properties of the material under test; S4. Substitute the key constitutive parameters into the power-hardening constitutive model in S2 to obtain the full-segment equivalent stress-strain curve of the disc sample under planar punch loading conditions.
2. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 1, characterized in that, In S2, the power-hardening constitutive model is expressed as: In the formula, For equivalent stress, The elastic modulus of the material, For equivalent change, For yield stress, For yield strain, For the yield plateau length, , The strain hardening index is the power-law hardening index.
3. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 2, characterized in that, In step S3, the load-displacement test curve is subjected to staged feature extraction and analytical calculation to obtain key constitutive parameters describing the mechanical properties of the material under test, including: Elastic phase; based on the load-displacement curve data for the elastic phase, and combined with characteristic area and characteristic displacement, the elastic modulus of the material is calculated: In the formula, For load, For characteristic displacement, The coefficient of elastic deformation is . For the characteristic area, It is a purely elastic displacement.
4. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 3, characterized in that, In step S3, the load-displacement test curve is subjected to staged feature extraction and analytical calculation to obtain key constitutive parameters describing the mechanical properties of the material under test, including: Elastic-plastic stage; linear regression of the load-displacement curve in the elastoplastic stage yields the dimensionless load-displacement rate of change in the elastoplastic stage. G and elastoplastic dimensionless load-displacement intercept D And the elastoplastic dimensionless load-displacement change rate G and elastoplastic dimensionless load-displacement intercept D The yield stress is obtained by substituting it into the equivalent yield stress equation set calibrated by the finite element method.
5. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 4, characterized in that, The equivalent yield stress equations are expressed as follows: In the formula, Tangent modulus, , , , , , , , To solve for the transformation parameters of tangent modulus and yield stress.
6. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 4, characterized in that, In step S3, the load-displacement test curve is subjected to staged feature extraction and analytical calculation, including: Power hardening stage: Substitute the power hardening stage data of the load-displacement curve into the power hardening equivalent stress-strain equation to obtain the real-time equivalent stress-strain relationship, and perform power-law fitting on the real-time equivalent stress-strain relationship to obtain the hardening parameters.
7. The method for determining the constitutive equivalent stress-strain curve of a circular specimen under planar punch loading conditions according to claim 3, characterized in that, The power-hardening equivalent stress-strain equation is expressed as: In the formula, For equivalent plastic strain coefficient, For equivalent plastic strain index, For equivalent plastic stress coefficient, The equivalent plastic stress index, It is a purely plastic displacement. The equivalent stress of a representative volume element.