Correction method for measuring elasticity modulus of non-uniform section sample by contact extensometer

Abstract

The invention provides a method for measuring the elasticity modulus of a non-uniform section sample by correcting a contact type extensometer, which comprises the following steps of: firstly, acquiring the stress, strain and deformation of the non-uniform section sample under the action of an external load in the measuring range of the extensometer; the variable cross section of the non-uniform-section sample is decomposed into a series of tiny sections, each section has a constant cross section area, the stress and strain of each tiny section are obtained, and the total strain of the non-uniform-section sample is obtained based on the obtained stress and strain of each tiny section; the total deformation amount of the sample is obtained based on the total strain of the non-uniform-section sample, and finally the elastic modulus of the sample is solved through the external force acting on the non-uniform-section sample and the total deformation amount of the non-uniform-section sample. The method is reasonable in conception, and can accurately measure the elastic modulus of the non-national standard part, thereby providing a powerful guarantee for the precision and the service life of the part in the use process.

Description

Technical Field

[0001] The present invention relates to the technical field of material mechanics, and in particular to a correction method for measuring the elastic modulus of a sample with a non-uniform cross-section by a contact extensometer. Background Art

[0002] The elastic modulus plays a vital role in the part design process, especially in stiffness calculation, deformation prediction, vibration analysis, structural stability and stress analysis. It is a core parameter in the design process. When designing non-national standard parts (such as guide rails and spindles), it is particularly important to accurately calculate the elastic modulus in order to ensure its accuracy and service life during use. However, under certain special test conditions, the measured sample cannot be processed into a uniform cross-section. For example, for composite material samples, the sample may be cut directly from the actual part, and due to limited size, it is impossible to make a specimen with a uniform cross-section. In addition, some parts cannot be subjected to destructive testing and must be calibrated directly for the elastic modulus. Therefore, it is crucial for the design and application of parts to develop an accurate elastic modulus calculation method for these non-uniform cross-section specimens. Summary of the invention

[0003] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a correction method for measuring the elastic modulus of non-uniform cross-section specimens using a contact extensometer. The method has a reasonable design and can accurately obtain the elastic modulus of non-national standard parts, thus providing a guarantee for the accuracy and service life of the parts during use.

[0004] In order to solve the above technical problems, the present invention provides a correction method for measuring the elastic modulus of a non-uniform cross-section sample by a contact extensometer. Within the measurement range of the extensometer, the stress, strain and deformation of the non-uniform cross-section sample under the action of an external load are first obtained, and then the variable cross-section of the non-uniform cross-section sample is decomposed into a series of small segments and each segment has a constant cross-sectional area, and then the stress and strain of each small segment are obtained, and the total strain of the non-uniform cross-section sample is obtained based on the obtained stress and strain of each small segment, and then the total deformation of the sample is obtained based on the total strain of the non-uniform cross-section sample, and finally the elastic modulus of the sample is solved by the external force acting on the non-uniform cross-section sample and the total deformation of the non-uniform cross-section sample.

[0005] The correction method for measuring the elastic modulus of non-uniform cross-section specimens by a contact extensometer, wherein the specific process of obtaining the stress and strain of each micro-segment is as follows: selecting a non-uniform cross-section specimen and defining its x-axis direction, with the y-axis direction perpendicular to the x-axis direction; the external force acting on the non-uniform cross-section specimen is F, and the outer contour of the non-uniform cross-section specimen, i.e., the cross-sectional area f(x), is expressed as a function of x; on this basis, each micro-segment length dx of the specimen is intercepted, and Hooke's law is used to calculate its stress σ(x) and strain ∈(x), wherein the expressions of stress σ(x) and strain ∈(x) can be expressed as:

[0006]

[0007] In the above formula (2), E is the elastic modulus of the non-uniform cross-section specimen.

[0008] The correction method for measuring the elastic modulus of non-uniform cross-section specimens by a contact extensometer, wherein: the total deformation ΔL of the non-uniform cross-section specimen is obtained by integrating the stress σ(x) and strain ∈(x) of each micro-segment of the non-uniform cross-section specimen; the total deformation ΔL of the non-uniform cross-section specimen can be expressed as the integration result of the stress and strain of each micro-segment along the x direction of the non-uniform cross-section specimen, so as to accurately reflect the total deformation of the entire non-uniform cross-section specimen under the action of the external force F.

[0009] The correction method for measuring the elastic modulus of a non-uniform cross-section sample by a contact extensometer, wherein the total deformation ΔL of the non-uniform cross-section sample is obtained by the following formula (3):

[0010]

[0011] In the above formula (3), L represents the total length of the non-uniform cross-section specimen.

[0012] The correction method for measuring the elastic modulus of a non-uniform cross-section sample by a contact extensometer, wherein the elastic modulus E of the non-uniform cross-section sample is expressed as:

[0013]

[0014] Since the external force F and the total deformation ΔL of the non-uniform cross-section specimen are known, and f(x) is a function of x, Extract it:

[0015]

[0016] The elastic modulus of the non-uniform cross-section specimen can be obtained from the above formula (5).

[0017] By adopting the above technical solution, the present invention has the following beneficial effects:

[0018] The present invention is not limited to measuring national standard samples, but can also accurately measure the elastic modulus of non-national standard parts, especially for samples with complex shapes, non-equal cross-sections, and no gauge length sections, which are difficult to handle with traditional measurement methods. Through the correction method, the measurement accuracy of the contact extensometer is effectively improved, so that in complex shape parts, its material properties can be more accurately reflected to ensure the reliability of the experimental results. Accurately measuring the elastic modulus can provide more reliable data support for part design and manufacturing, help optimize the structural design of parts, reduce material waste, and improve manufacturing efficiency. By accurately measuring the elastic modulus of non-equal cross-section samples, the stress conditions of parts in actual use can be better estimated, and damage to parts caused by material property errors can be avoided, thereby extending their service life. For application scenarios requiring high precision and high reliability (such as aerospace, precision machinery manufacturing, etc.), the present invention can provide more accurate material performance data to ensure the safety and stability of parts under harsh conditions. Through this correction method, the scrap rate caused by non-standard samples during the measurement process can be reduced, the experimental cost can be reduced, and the subsequent debugging and rework caused by inaccurate data can be reduced. In summary, this invention provides an efficient and accurate elastic modulus measurement solution, which can solve the problem of difficult measurement of material properties of complex parts, and bring significant technical advantages and economic benefits to improving the design optimization, manufacturing accuracy, and service life of parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 A non-uniform cross-sectional diagram of a contact extensometer measuring non-uniform cross-sectional specimens involved in a correction method for measuring elastic modulus of a non-uniform cross-sectional specimen using a contact extensometer of the present invention;

[0021] Figure 2 A schematic diagram of calculating the elastic modulus involved in the correction method for measuring the elastic modulus of a sample with a non-uniform cross-section by a contact extensometer of the present invention;

[0022] Figure 3 A schematic diagram of non-uniform cross-sectional dimensions involved in the correction method for measuring elastic modulus of non-uniform cross-sectional specimens by a contact extensometer of the present invention;

[0023] Figure 4 The present invention is a static simulation analysis diagram of non-uniform cross-sections in SolidWorks involved in the correction method for measuring the elastic modulus of non-uniform cross-section specimens using a contact extensometer. DETAILED DESCRIPTION

[0024] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] The present invention is further explained below in conjunction with specific implementation modes.

[0026] like Figure 1 As shown, the present embodiment provides a correction method for measuring the elastic modulus of a sample with non-uniform cross-section using a contact extensometer, specifically:

[0027] When the cross-sectional area of ​​the specimen within the measuring range of the extensometer is not constant, the calculation of its stress, strain and deformation under the action of external loads requires consideration of the change in cross-sectional area. For the analysis of the cross-sectional area of ​​non-uniform cross-sectional specimens, it can be decomposed into a series of tiny segments, each with a constant cross-sectional area. Then, for each microelement, Hooke's law can be used to calculate its stress and strain, and the total strain can be solved by integral calculation.

[0028] In this embodiment, it is assumed that there is a cylindrical specimen with non-uniform cross-section subjected to force along the axial direction, and the clamping range of the extensometer is the red framed area, such as Figure 1 shown.

[0029] For the convenience of analysis, the external loads are equal in magnitude and opposite in direction. When analyzing, a section of the variable cross-section cylindrical specimen is selected for analysis. The axial direction of the non-uniform cross-section cylindrical specimen is taken as the direction of the x-axis coordinate axis, and the direction perpendicular to the x-axis in the variable cross-section is taken as the y-axis direction, such as Figure 2 .

[0030] The external force acting on the non-uniform cross-section cylindrical specimen is F, and the outer contour of the non-uniform cross-section cylindrical specimen, i.e., the cross-sectional area f(x), is a function of the coordinate x. For each micro-segment, Hooke's law can be used to calculate the stress σ(x) and strain ∈(x). For the intercepted micro-segment dx, the stress σ(x) and strain ∈(x) can be expressed as:

[0031]

[0032] In the above formula, E is the elastic modulus of the non-uniform cross-section cylindrical specimen.

[0033] The total deformation ΔL of the non-uniform cross-section cylindrical specimen can be obtained by integrating the strain; for the entire non-uniform cross-section cylindrical specimen, L represents the total length of the non-uniform cross-section cylindrical specimen, and the total deformation ΔL of the non-uniform cross-section cylindrical specimen can be expressed as:

[0034]

[0035] Since F and ΔL are known quantities, and f(x) is a function of x, we can Extract it:

[0036]

[0037] The solution for the elastic modulus E can be obtained.

[0038] By summarizing the above process, when the load F applied to the non-uniform cross-section cylindrical specimen, the length L of the specimen, the total deformation ΔL of the non-uniform cross-section cylindrical specimen measured by the extensometer, and the cross-sectional area function f(x) of the external contour of the non-uniform cross-section cylindrical specimen are known, its elastic modulus E can be solved.

[0039] The following specific examples are used to verify the accuracy of the elastic modulus calculation results:

[0040] In order to verify the accuracy of the calculation results, a static simulation analysis is carried out on a cylindrical specimen with non-uniform cross-section. The dimensions of the cylindrical specimen with non-uniform cross-section are as follows: Figure 3 , as shown (unit: mm), a force load F = 500N is applied to it along the axial direction.

[0041] The outer contour of the non-uniform cross-section cylindrical specimen is a semicircle with a radius of R = 43 mm, the minimum radius of the variable cross-section is r0 = 2.585 mm, and the length of the variable cross-section is L = 37.96 mm. Figure 4 ) The total deformation of the non-uniform cross-section cylindrical specimen with variable cross-section is ΔL = 4.906 × 10 -3 mm. (Note: To calculate the elastic modulus, the following calculation process converts the above units into international standard units, size: m, load: N).

[0042] The above data in Figure 2 Calculate in the diagram to obtain the outer contour of the non-uniform cross-section cylindrical specimen, i.e. the cross-sectional area f(x):

[0043]

[0044] Substituting F=500N into formula (1), we obtain:

[0045]

[0046] Substituting formula (7) into formula (4) yields:

[0047]

[0048] The elastic modulus E1 is obtained as 9.9926×10 10 N / m 2 The simulation gives E2 = 1.048003 × 10 11 N / m 2 The error is only 4.65%, which shows that this calculation result can be used to solve the elastic modulus of non-uniform cross-section specimens.

[0049] The invention has a reasonable conception and can accurately obtain the elastic modulus of non-national standard parts, such as non-uniform cross-section and non-gauge length section specimens, thereby providing a guarantee for the accuracy and service life of the parts during use.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A correction method for measuring the elastic modulus of non-uniform cross-section specimens using a contact extensometer, characterized in that: Within the measurement range of the extensometer, the stress, strain and deformation of the non-uniform cross-section specimen under the action of external load are first obtained, and then the variable cross-section of the non-uniform cross-section specimen is decomposed into a series of small segments and each segment has a constant cross-sectional area, and then the stress and strain of each small segment are obtained, and the total strain of the non-uniform cross-section specimen is obtained based on the obtained stress and strain of each small segment, and then the total deformation of the specimen is obtained based on the total strain of the non-uniform cross-section specimen, and finally the elastic modulus of the specimen is solved by the external force acting on the non-uniform cross-section specimen and the total deformation of the non-uniform cross-section specimen.

2. The correction method for measuring the elastic modulus of non-uniform cross-section specimens by a contact extensometer according to claim 1, characterized in that: The specific process of obtaining the stress and strain of each micro segment is as follows: select a non-uniform cross-section sample and define its x-axis direction, and define the y-axis direction perpendicular to the x-axis direction; define the external force acting on the non-uniform cross-section sample as F, and express the outer contour of the non-uniform cross-section sample, i.e., the cross-sectional area f(x), as a function of x; on this basis, cut off each micro segment length dx of the sample, and use Hooke's law to calculate its stress σ(x) and strain ∈(x), wherein the expressions of stress σ(x) and strain ∈(x) can be expressed as: In the above formula (2), E is the elastic modulus of the non-uniform cross-section specimen.

3. The correction method for measuring the elastic modulus of non-uniform cross-section specimens by a contact extensometer according to claim 2, characterized in that: The total deformation ΔL of the non-uniform cross-section specimen is obtained by integrating the stress σ(x) and strain ∈(x) of each micro-segment of the non-uniform cross-section specimen; the total deformation ΔL of the non-uniform cross-section specimen can be expressed as the integral result of the stress and strain of each micro-segment along the x direction of the non-uniform cross-section specimen, so as to accurately reflect the total deformation of the entire non-uniform cross-section specimen under the action of the external force F.

4. The correction method for measuring the elastic modulus of non-uniform cross-section specimens by a contact extensometer according to claim 2, characterized in that: The total deformation ΔL of the non-uniform cross-section specimen is obtained by the following formula (3): In the above formula (3), L represents the total length of the non-uniform cross-section specimen.

5. The correction method for measuring elastic modulus of non-uniform cross-section specimens by a contact extensometer according to claim 4, characterized in that: The elastic modulus E of the non-uniform cross-section specimen is expressed as: Since the external force F and the total deformation ΔL of the non-uniform cross-section specimen are known, and f(x) is a function of x, Extract it: The elastic modulus of the non-uniform cross-section specimen can be obtained from the above formula (5).

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