Method for testing bending fatigue of small sample based on notched cantilever beam
By subjecting a small notched cantilever beam specimen to low-frequency bending symmetrical cyclic loading and establishing the stress-strain relationship using the energy method, combined with the Manson-Coffin model, the problem that traditional methods are difficult to detect bending fatigue performance is solved, and accurate material bending fatigue performance detection and life prediction are achieved.
Patent Information
- Application Number
- CN202510738736.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-04
- Publication Date
- 2025-09-23
AI Technical Summary
Traditional fatigue test methods are difficult to directly detect the stress and strain at the most unfavorable point of a bending load-bearing component, especially for non-uniform and non-isotropic materials, which makes it difficult to detect bending fatigue performance.
A small notched cantilever beam specimen was subjected to low-frequency bending symmetrical cyclic loading. The load-displacement and fatigue source RVE stress-strain relationships were established using the energy method. Combined with the Manson-Coffin fatigue life estimation model, the cyclic stress-strain relationship and fatigue life of the material were obtained.
It realizes accurate detection of bending fatigue performance, solves the problem of obtaining bending fatigue performance of small structural parts and welding materials and residual life detection of micro-damage sampling of active structures, and is suitable for fields such as micro-electromechanical systems, aviation, energy systems and biomedicine.
Smart Images
Figure CN120685473A_ABST
Abstract
Description
Technical Field
[0001] This proposal relates to the field of material testing, and specifically to a bending fatigue testing method for a small specimen based on a notched cantilever beam. Background Art
[0002] The fatigue mechanical properties of materials are fundamental to the safety assessment of material structures and are of great significance to engineering safety analysis. The low-cycle fatigue performance of materials is primarily characterized by low-cycle stress-strain relationships and fatigue life curves. Low-cycle stress-strain relationships describe the essential physical relationship of a material's mechanical behavior under elastic-plastic fatigue loading and are crucial for strength analysis of structures in service under cyclic loading. Fatigue life curves are essential for life and safety assessment of materials or structures. In practical engineering, numerous mechanisms and components are subjected to long-term cyclic loading, such as temperature and pressure. Their fatigue mechanical properties are essential for system safety assessment and failure analysis. However, traditional fatigue testing methods primarily utilize cyclic axial tension and compression loading on round rods to generate fatigue life curves (ε-N or σ-N curves), which have significant limitations. Furthermore, traditional methods are difficult to directly test for commonly encountered bending components. The fundamental reason is that the stress and strain at the worst point in bending components cannot be directly measured. Typically, surface stress can only be derived through simple moment conversion, but this approach is completely inapplicable under plastic deformation conditions and cannot be effectively applied to inhomogeneous and non-isotropic materials. Summary of the Invention
[0003] The present invention aims to provide a bending fatigue testing method for a small specimen based on a notched cantilever beam, so as to establish a theoretical connection between the load-displacement relationship at the end of the cantilever beam and the stress-strain relationship at the root of the arc notch (fatigue source RVE), thereby establishing a fatigue life estimation model and obtaining the fatigue performance of the material.
[0004] To achieve the above object, the present invention adopts the following technical solutions: a bending fatigue test method based on a small specimen of a notched cantilever beam, S1, a low-frequency bending symmetrical cyclic loading test is performed on the specimen to obtain the end load-displacement curve, the specimen is a cantilever beam with a circular arc notch, and the circular arc notch is set on the bending surface of the cantilever beam; S2, the load-displacement and fatigue source RVE true strain amplitude ε are established by the energy method m , stress amplitude σ m The corresponding relationship; S3, according to ε m and σ m Establish a fatigue life estimation model to obtain material fatigue properties.
[0005] Beneficial effects: 1. By setting a notch on the sample, the stress of the sample is concentrated and controllable during the bending process.
[0006] 2. This scheme makes the bending position of the sample controllable by subjecting the arc notch cantilever beam specimen to symmetrical cyclic loading of tension and compression, obtains the number of cycles under each load level and the load and displacement peak-valley values of each cycle, and predicts the cyclic stress-strain relationship of the material through the load-displacement hysteresis curve of each cyclic stability (Nf / 2), and establishes the ε eq (Average strain amplitude)-ε m (true stress amplitude) and ε eq (Average strain amplitude)-σ m (stress amplitude) relationship, completes the Manson-Coffin fatigue life prediction, overcomes the traditional empirical method of replacing bending fatigue performance with tensile fatigue equivalent, and further provides a test method for detecting the bending fatigue performance of materials, so as to accurately obtain the cyclic stress-strain relationship of materials and predict the bending fatigue life of materials; solves the key technical problems of obtaining the bending fatigue performance of small structural parts and welding materials and detecting the remaining life of micro-damage sampling of in-service bending-resistant structures; has important significance for obtaining the bending fatigue mechanical properties of bending-resistant component materials and detecting the remaining life of micro-damage sampling of in-service structures in key projects such as micro-electromechanical systems, aviation, energy systems, and biomedicine.
[0007] Furthermore, the S1 medium and low frequency bending symmetrical cyclic loading test also includes a rigid fixture, which includes a lower chuck of a fixed support and a movable upper chuck; an arc notch is set on the cantilever beam and divides the cantilever beam into a fixed section and a bending section, the fixed section is fixedly connected to the lower chuck of the fixed support, and the movable upper chuck includes an upper chuck body and two roller columns, the two roller columns are rotatably set on the upper chuck body, and the end of the bending section is set between the two roller columns and can move up and down under the push of the two rollers, thereby repeatedly bending the sample at the notch.
[0008] Furthermore, the fixed support lower clamp includes a lower clamp body and a cover plate. The lower clamp body is provided with a fixing groove. The cover plate covers the space above the fixing groove and is detachably connected to the lower clamp body.
[0009] Furthermore, the notch is arc-shaped.
[0010] Furthermore, the notches are symmetrically arranged on the bending surface.
[0011] Furthermore, S2 is used to establish the load-displacement and fatigue source RVE true strain amplitude ε by the energy method. m , stress amplitude σ m In the corresponding relationship, including S21, the elastic section of the cyclic load-displacement curve is linearly fitted, and the plastic section is fitted by power law to obtain the slope S and loading curvature C, respectively.
[0012] Where: he is the elastic displacement at the end, h is the total displacement at the end, and P is the load at the end; S21, substitute S and C obtained in S21 into the following formula:
[0013] Where: E is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening exponent, k0, k1 and k2 are constants, R is the characteristic length of the specimen, A * represents the characteristic area; S23, substituting E, K, and n obtained in step S22 into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material;
[0014] Where: ε is the total strain, ε e is the elastic strain, ε p is the plastic strain.
[0015] Furthermore, k0, k1 and k2 are obtained through finite element calibration.
[0016] Furthermore, the relationship between k0, k1 and k2 is as follows:
[0017] Where a1, a2 and a3, b1, b2 and b3, and c1, c2 and c3 are all constants, and λ is the geometric factor.
[0018] Furthermore, in S3, the Manson-Coffin fatigue life estimation model is adopted.
[0019] Beneficial effects: 1. This scheme fits the linear segment of the curve with a straight line and the purely plastic part with a power law to obtain the Ramberg-Osgood constitutive model parameters E, σy, and n; the obtained E, K, and n are substituted into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material.
[0020] 2. The method of the present invention overcomes the traditional empirical method of replacing bending fatigue performance with tensile fatigue equivalent, and provides a test method for detecting the bending fatigue performance of materials, which includes a specimen, a test device and a stress amplitude and strain amplitude acquisition method, so as to accurately obtain the cyclic stress-strain relationship of the material and predict the bending fatigue life of the material; the present invention is of great significance for the acquisition of bending fatigue mechanical properties of bending-resistant component materials that are widely present in key engineering fields such as micro-electromechanical systems, aviation, energy systems, and biomedicine, and for the remaining life detection of micro-damage sampling of in-service structures. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Figure 1This is a schematic diagram of the separate structure of the sample and the test equipment of the present invention; Figure 2 An assembly diagram of the sample and experimental equipment of the present invention from one perspective; Figure 3 This is an assembly diagram of the sample and experimental equipment of the present invention from another perspective.
[0022] The reference numerals in the drawings of the specification include: lower chuck body 11, slot 111, cover plate 12, clamping body 21, roller column 22, connector 23, test specimen 3, fixing section 31, notch 32, bending section 33, first mounting block 41, and second mounting block 42. DETAILED DESCRIPTION
[0023] The following is further described in detail through specific implementation methods: Example The embodiment is basically as follows Figure 1 As shown, Figure 1 The method for testing the bending fatigue of a small specimen of a notched cantilever beam shown in the figure comprises the following steps: S1, obtaining the end load-displacement curve by a low-frequency bending symmetrical cyclic loading test; S2, establishing the load-displacement and fatigue source RVE true strain amplitude ε by the energy method. m , stress amplitude σ m The corresponding relationship; S3, according to ε m and σ m Establish a fatigue life estimation model to obtain material fatigue properties.
[0024] S1 medium and low frequency bending symmetrical cyclic loading test includes specimens and test equipment, such as Figure 1 As shown, the sample is a cantilever beam sample provided with a notch 32 . The notch 32 is provided on the curved surface of the cantilever beam and divides the cantilever beam sample into a fixed section 31 and a bent section 33 .
[0025] The clamping unit includes a movable upper clamp and a fixed support lower clamp. The movable upper clamp includes a clamping body 21. A connecting head 23 and a first mounting block 41 are fixedly provided on the clamping body 21. In this embodiment, the connecting head 23 and the first mounting block 41 are both welded to the clamping body 21. The connecting head 23 is used to be fixedly connected to the output shaft of the micro-force test loading device. A clamping assembly is provided on the clamping body 21. The clamping assembly includes two roller columns 22. The two roller columns 22 are rotatably provided on the clamping body 21.
[0026] The fixed support lower chuck includes a lower chuck body 11 and a cover plate 12. A second mounting block 42 is welded to the lower chuck body 11. The lower chuck body 11 is fixed to the test bench by bolts. A sample slot 111 is provided on the lower chuck body 11. The cover plate 12 is fixedly connected to the fixed body by bolts, thereby covering the slot 111 and fixing the sample in the sample slot 111.
[0027] During the test, if Figure 2 、 Figure 3 As shown, first, the fixed section 31 of the test sample 3 is placed in the fixed slot 111 so that the edge of the notch 31 is flush with the open side of the sample slot 111, and the cover plate 12 is covered on the fixed slot 111 by bolts, so that the fixed section 31 is fixed to the lower clamp of the fixed support, thereby ensuring that the bending position of the sample is determined, so that the stress during the bending process is concentrated, and thus the accuracy of the measurement is ensured. Subsequently, the end of the bending section 33 is fixed between the two roller columns 22. When the upper clamp moves up and down, the roller column 22 rotates, thereby eliminating the influence of the horizontal tension on the sample and ensuring the test accuracy. At the same time, The movable upper chuck is connected to the micro-force test loading device through the connector 23; at the same time, the displacement sensor is fixed between the first mounting block 41 and the second mounting block 42. The displacement sensor can be a capacitive displacement sensor or a magnetostrictive displacement sensor. In this embodiment, the displacement sensor is a magnetostrictive displacement sensor; then, the micro-force test loading device is turned on, and a symmetrical cyclic loading of tension and compression is applied to the movable upper chuck through the micro-force test loading device, so that the number of cycles under load, the load of the cycle and the peak and valley values of the displacement are obtained through the displacement detector until the sample breaks, and then the load applied by the micro-force test loading is changed.
[0028] Repeat several times to obtain the number of cycles under each load level and the load and displacement peak and valley values of each cycle, thereby obtaining the load-displacement curve.
[0029] Then, the load-displacement and fatigue source RVE true strain amplitude ε are established by the energy method. m , stress amplitude σ m In the corresponding relationship, including S21, the elastic section of the cyclic load-displacement curve is linearly fitted, and the plastic section is fitted by power law to obtain the slope S and loading curvature C, respectively.
[0030] Where: h e is the elastic displacement at the end, h is the total displacement at the end, and P is the load at the end; S22, substitute S and C obtained in S21 into the following formula:
[0031] Where: E is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening exponent, k0, k1 and k2 are constants, R is the characteristic length of the specimen, A * Represents the characteristic area; Figure 1 As shown, it is assumed that the characteristic length h*=R, R represents the radius of the gap 32; the characteristic volume V * =h * A * , A * Represents the characteristic area A * =(2w-πR)t, w is the specimen thickness, t is the specimen width.
[0032] k0, k1, and k2 are obtained through finite element calibration. The relationship between k0, k1, and k2 is as follows:
[0033] Where a1, a2 and a3, b1, b2 and b3, and c1, c2 and c3 are all constants, and λ is the geometric factor.
[0034] S23, substituting E, K, and n obtained in step S22 into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material;
[0035] Where: ε is the total strain, ε e is the elastic strain, ε p is the plastic strain.
[0036] S3, according to ε m and σ m Establish a fatigue life estimation model to obtain the fatigue performance of the material. Specifically, the strain amplitude-life curve is the basic curve used for fatigue life evaluation of materials or structures. Existing standards have provided methods for obtaining it. The key is to obtain the true strain amplitude and stress amplitude of the fatigue source RVE (Representative Volume Element, material representative volume element). Based on the material cyclic stress-strain relationship as the material property, a simple finite element elastic-plastic calculation is performed to establish the true strain amplitude ε of the fatigue source RVE. m , stress amplitude σ m and the average strain amplitude ε eq According to the relationship of ε m and σ m Establish the fatigue life Manson-Coffin estimation model, complete life prediction, and obtain material fatigue performance.
[0037] The above is only an embodiment of the present invention, and common knowledge such as the specific technical solutions and / or characteristics in the solution are not described in detail here. It should be pointed out that the technical means for solving the problems in the above-mentioned embodiments of the present invention can be used in combination to solve multiple technical problems at the same time. For those skilled in the art, without departing from the technical solution of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.
Claims
1. A bending fatigue test method for small specimens based on a notched cantilever beam, characterized by: The method comprises the following steps: S1, performing a low-frequency bending symmetrical cyclic loading test on a specimen to obtain a terminal load-displacement curve, wherein the specimen is a cantilever beam provided with a circular arc notch, and the circular arc notch is provided on the curved surface of the cantilever beam; S2, establishing the load-displacement and fatigue source RVE true strain amplitude ε by the energy method m , stress amplitude σ m The corresponding relationship; S3, according to ε m and σ m Establish a fatigue life estimation model to obtain material fatigue properties.
2. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 1, characterized in that: The S1 medium and low frequency bending symmetrical cyclic loading test also includes a rigid fixture, which includes a fixed support lower chuck and a movable upper chuck; an arc notch is set on the cantilever beam and divides the cantilever beam into a fixed section and a bending section, the fixed section is fixedly connected to the fixed support lower chuck, and the movable upper chuck includes an upper chuck body and two roller columns, the two roller columns are rotatably set on the upper chuck body, and the end of the bending section is set between the two roller columns and can move up and down under the push of the two rollers, thereby repeatedly bending the sample at the notch.
3. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 2, characterized in that: The fixed support lower clamp comprises a lower clamp body and a cover plate. The lower clamp body is provided with a fixing groove. The cover plate covers the space above the fixing groove and is detachably connected to the lower clamp body.
4. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 3, characterized in that: The notches are symmetrically arranged above and below the bending line.
5. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 1, characterized in that: S2, establish the load-displacement and fatigue source RVE true strain amplitude ε by energy method m , stress amplitude σ m In the corresponding relationship, including S21, the elastic section of the cyclic load-displacement curve is linearly fitted, and the plastic section is fitted by power law to obtain the slope S and loading curvature C, respectively. Where: he is the elastic displacement at the end, h is the total displacement at the end, and P is the load at the end; S22, substitute S and C obtained in S21 into the following formula: Where: E is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening exponent, k0, k1 and k2 are constants, R is the notch radius length in the specimen, A * represents the characteristic area; S23, substituting E, K, and n obtained in step S22 into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material; Where: ε is the total strain, ε e is the elastic strain, ε p is the plastic strain.
6. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 5, characterized in that: k0, k1 and k2 are obtained through finite element calibration.
7. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 6, characterized in that: The relationship between k0, k1 and k2 is as follows: Where a1, a2 and a3, b1, b2 and b3, and c1, c2 and c3 are all constants, and λ is the geometric factor.
8. The method for testing bending fatigue of a small specimen based on a notched cantilever beam according to claim 1, characterized in that: In S3, the Manson-Coffin fatigue life estimation model is adopted.