A method for measuring the tensile and compressive elastic moduli based on a four-point beam bending test, taking into account the dual elastic modulus properties of materials

Abstract

The present invention provides a method for measuring tensile and compressive elastic moduli based on a four-point beam bending test, taking into account the dual-modulus properties of materials. Solution: A four-point bending beam specimen with a height-to-span ratio of less than 1 / 6 is used, with both ends simply supported. A symmetrical longitudinal concentrated load is applied, placing the middle section in a state of pure bending stress. Strain gauges are attached to the top and bottom surfaces of the middle section of the specimen, or strain is measured using DIC technology. The position of the neutral layer is determined from the strain on the top and bottom surfaces, and the horizontal stress distribution at the central cross section is then described. The maximum horizontal compressive stress and tensile stress on the top and bottom surfaces are calculated using force equilibrium and moment equilibrium equations. Finally, the compressive and tensile moduli of the material are inverted from the measured compressive and tensile strains. This method allows for simultaneous measurement of the tensile and compressive moduli, is simple to operate, and has high measurement accuracy.

Description

[Technical Field]

[0001] The present invention relates to the technical field of material mechanical performance testing, and in particular to a method for measuring tensile and compressive elastic moduli taking into account the dual elastic modulus characteristics of a material based on a four-point vertical beam bending test. [Background technology]

[0002] In actual construction, many materials, such as ceramics, fiberglass, plastics, reinforced concrete, graphite, powder metallurgy materials, polymer materials, and fiber-reinforced composites, exhibit different tensile and compressive elastic modulus characteristics to different degrees. Not only do the tensile and compressive strengths of these materials vary greatly, but their tensile and compressive elastic moduli also vary. With the rapid development of science and technology, the demand for research into the mechanical properties of materials is increasing, and the development of new materials and the exploration of the potential properties of materials themselves have become new research trends.

[0003] Due to the lack of a constitutive equation that reasonably takes into account the dual-modulus properties of materials and a simple and reliable method for measuring tensile elastic parameters, previous researchers have ignored the dual-modulus properties of materials and simplified them to single-modulus materials when using numerical methods to study the tensile deformation performance of materials. Therefore, there is currently a strong demand for a method for measuring the tensile and compressive elastic moduli of materials that can measure the tensile and compressive elastic moduli of materials and that can improve the efficiency, simplicity, and accuracy of measuring the tensile and compressive elastic moduli of materials. Summary of the Invention [Problem to be solved by the invention]

[0004] In order to solve the above-mentioned problems of the prior art, the present invention proposes a method for measuring tensile and compressive elastic moduli that takes into account the dual elastic modulus characteristics of materials based on a four-point vertical beam bending test. [Means for solving the problem]

[0005] To achieve the above object, the present invention provides a method for measuring tensile and compressive elastic moduli based on a four-point vertical beam bending test, taking into account the dual elastic modulus characteristics of a material, The test material is used as a test piece, and both ends are Simple and applying a symmetrical longitudinal concentrated load to the beam specimen to form a four-point bending load structure. measuring strains on the top and bottom surfaces of the beam specimen at a midpoint of the beam specimen; determining the position of the neutral layer based on the absolute value of compressive strain on the upper surface of the beam and the absolute value of tensile strain on the lower surface; Describing the stress distribution of horizontal stress at the central cross section of the beam specimen using a mathematical formula based on the position of the neutral layer; A step of calculating the maximum horizontal compressive stress and the maximum horizontal tensile stress on the upper and lower surfaces of the beam from the force equilibrium equation and the moment equilibrium equation at the central cross section in the beam axial direction; and synchronously inverting the compressive and tensile moduli of the material by measuring the compressive and tensile strains at the upper and lower surfaces of the central cross section in the axial direction of the beam.

[0006] Preferably, the beam specimen is a four-point bending beam specimen having a height-to-span ratio of 1 / 6 or less.

[0007] Preferably, measuring the strain on the top and bottom surfaces of the beam specimen involves attaching strain gauges to the top and bottom surfaces of the middle section of the specimen or using DIC measurement techniques.

[0008] Preferably, the equation for the position of the neutral layer is:

[0009]

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[0010] Preferably, the stress distribution formula of the horizontal stress is the following formula:

[0011]

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[0012] Preferably, the distribution gradient of the horizontal compression region and the distribution gradient of the horizontal tension region are expressed as follows:

[0013]

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[0014]

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[0015]

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[0016] Preferably, the synchronous inversion equation is:

[0017]

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[0018] The present invention also provides a computer apparatus, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to perform the steps of the method.

[0019] The present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program performing the steps of the method when executed by a processor.

[0020] The present invention also provides a computer program product, comprising a computer program for implementing the steps of the method when the computer program is executed by a processor. [Effects of the Invention]

[0021] Compared with existing technologies, the present invention has the following advantages and technical effects:

[0022] The proposed method for measuring the tensile and compressive elastic moduli of a material based on a four-point vertical beam bending test, which takes into account the dual elastic modulus characteristics of the material, can measure the tensile and compressive elastic moduli of the material simultaneously, and is characterized by its simple operation and high measurement accuracy. [Brief explanation of the drawings]

[0023] The drawings, which form a part of this application, are intended to provide a further understanding of the present application, and the illustrative embodiments and their description are intended to be illustrative of the present application and are not to be construed as unduly limiting the present application. [Figure 1] FIG. 1 is a schematic diagram of a four-point bending beam specimen having a height-to-span ratio of 1 / 6 according to an embodiment of the present invention. [Figure 2] 1 is a schematic diagram of the stress distribution in a four-point bending beam according to an embodiment of the present invention; [Figure 3] 1 is a schematic diagram of compressive stress and tensile stress distribution in a central cross section in the beam axis direction of an embodiment of the present invention. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0024] In addition, the embodiments and features of the embodiments of the present application can be combined with each other if there is no conflict. The present application will be described in detail below by combining the embodiments with reference to the drawings.

[0025] It should be noted that the steps shown in the flowcharts of the figures may be performed by a computer system, such as a set of computer-executable instructions, and that although shown in a logical order in the flowcharts, the steps may in some cases be performed in a different order than shown or described herein.

[0026] Example 1

[0027] In this example, a method for measuring the tensile and compressive elastic moduli taking into account the dual elastic modulus characteristics of materials based on a four-point vertical beam bending test is provided. The steps are as follows: 1) The test material is prepared as a specimen with a height-to-span ratio of 1 / 6 or less, and both ends are simply supported. A symmetrical longitudinal concentrated load is applied to the beam specimen to form a four-point bending load structure, placing the middle section of the four-point bending beam in a pure bending stress state; 2) Strain gauges are attached to the upper and lower surfaces of the middle section of the specimen, or DIC measurement technology is used to measure the strains on the upper and lower surfaces; and 3) The absolute value of the compressive strain |ε on the upper surface of the beam is calculated. c xx | and the absolute value of the tensile strain on the lower surface |ε t xx | Determine the position z0 of the neutral layer, and 4) calculate the horizontal stress σ at the central cross section of the beam specimen using the mathematical formula xx 5) From the equations of equilibrium of the force and the equations of equilibrium of the moment at the central cross section in the axial direction of the beam, the maximum horizontal compressive stress (σ c xx ) max and maximum horizontal tensile stress (σ t xx ) max6) Finally, by measuring the compressive and tensile strains on the upper and lower surfaces of the central cross section in the beam axial direction, the compressive and tensile moduli of the material can be synchronously inverted.

[0028] To achieve the objectives of the present invention, the four-point bending beam specimen must be appropriately dimensioned. To avoid the influence of shear stress, the present invention uses a four-point bending beam specimen with a height-to-span ratio of 1 / 6 or less, so that the middle section of the four-point bending beam is under pure bending stress.

[0029] Furthermore, strain gauges are attached to the upper and lower surfaces of the middle section of the test piece, or DIC measurement technology is used to measure the strain on the upper and lower surfaces.

[0030] Furthermore, the position z0 of the neutral layer is determined. Observing the results of the numerical calculation, E t changes, and E c , v c , v t If there is no change in the horizontal strain ε xx still has the same gradient dε xx Based on this conclusion, the absolute value of compressive strain |ε on the upper surface of the beam is c xx | and the absolute value of the tensile strain on the lower surface |ε t xx The position of the neutral layer can be determined from |, and the formula is

[0031]

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[0032] where ε c xx is the maximum compressive strain at the central cross section in the beam axial direction, i.e., the strain value at (x=0, z=H / 2), and ε t xx is the maximum tensile strain at the central cross section in the beam axial direction, i.e., the strain value at (x=0, z=-H / 2), and z0 is σ at the central cross section x=0. xx =0 and ε xx Indicates the position of E = 0.c =E t = 60 GPa, v c =v t = 0.25, |ε t xx |=|ε c xx |, z0 = 0.0m. (Note that the position of the neutral layer is related to the coordinate system. Here, z0 = 0.0m indicates that it is at half the height of the beam.)

[0033] Furthermore, the horizontal stress σ at the central cross section of the beam specimen was calculated using the mathematical formula xx From the results of numerical calculations, the horizontal stress σ at the central cross section in the beam axis direction under different conditions is xx and horizontal strain ε xx It can be seen that follows a linear or bilinear distribution characteristic. Therefore, using equation (2), σ xx The vertical distribution pattern of

[0034]

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[0035] where b1 is the horizontal compression area σ xx is the gradient of the horizontal tension region σ xx is the gradient of σ c xx is the compressive stress at any height in the compression zone at the central cross section (x=0m), and σ t xx is the tensile stress at any height in the tension region at the central cross section (x=0m), and z0 is σ at the central cross section x=0 xx =0 and ε xx =0 position.

[0036] Furthermore, from the force equilibrium equation and moment equilibrium equation at the central cross section in the beam axial direction, the maximum horizontal compressive stress (σ c xx ) max and maximum horizontal tensile stress (σ t xx ) maxBased on the load characteristics of a four-point bending beam, the horizontal resultant force F at the central cross section in the beam axial direction is 0, and the formula is as follows:

[0037]

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[0038] Furthermore, since only a counterclockwise bending moment M around the y-axis (perpendicular to the xy plane and passing through the coordinate origin) acts on the central cross section (x=0m), we establish the bending moment equation (clockwise is positive) shown in equation (4):

[0039]

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[0040] Here, B is the thickness of the beam. Solving equations (3) and (4) gives the following equation:

[0041]

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[0042]

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[0043] In a four-point straight beam bending test, the bending moment M at the central cross section of the beam is indirectly generated by the upper load F, and the following equation holds (L1 is the distance between the two support points on the lower surface of the beam specimen, and L3 is the distance between the two load points on the upper surface of the beam specimen).

[0044]

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[0045]

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[0046] Furthermore, by measuring the compressive and tensile strains on the upper and lower surfaces of the central cross section in the beam axial direction, the compressive and tensile moduli of the material can be synchronously reversed. The applied load F and the compressive strain ε at (x=0m, z=H / 2) on the central cross section of the beam can be calculated as c xx and tensile strain ε at (x=0m,z=-H / 2) t xx After obtaining the above, the tensile and compressive moduli of the material can be obtained by synchronous inversion, and the inversion formula is as follows: do. In this embodiment, "inversion" means that the compressive and tensile moduli of the material are calculated inversely based on the measured values ​​of compressive strain and tensile strain on the upper and lower surfaces of the central cross section in the beam axis direction, and "synchronization" means that the compressive and tensile moduli are calculated simultaneously.

[0047]

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[0048] In this example, the following experiment is also carried out.

[0049] In Figure 1, to ensure the standardization and consistency of the test conditions and the accuracy of the test results, a four-point bending beam specimen must first be prepared. The length of the specimen is L2, the thickness is B, the height is H, the distance between the two support points on the lower surface of the beam specimen is L1, the distance between the two load points on the upper surface of the beam specimen is L3, and the height-to-span ratio H / L1 is 1 / 6.

[0050] In Figure 1, the beam specimen is simply supported at both ends and subjected to a symmetrical longitudinal concentrated load. The distance between the two load points is L3, forming a four-point bending load structure, placing the middle section of the four-point bending beam under pure bending stress. Two resistance strain gauges are attached to the centers of the upper and lower surfaces of the specimen, respectively. In addition to using strain gauges to measure the strain on the upper and lower surfaces of the specimen, DIC measurement technology can also be used to measure the strain on the upper and lower surfaces of the specimen. This method requires the installation of a DIC camera at an appropriate position to monitor the full-field deformation of the specimen.

[0051] Figure 2 is a schematic diagram of the stress distribution within the beam specimen.

[0052] In Figure 3, first, the maximum compressive strain absolute value |ε c xx | and the absolute value of maximum tensile strain |ε t xx | into analytical equation (1) to calculate the position z0 of the neutral layer, and then use equation (7) to calculate the maximum horizontal compressive stress (σ c xx ) max and maximum horizontal tensile stress (σ t xx ) max Finally, by measuring the compressive and tensile strains at the top and bottom surfaces of the axial central cross section of the beam specimen and substituting them into analytical equation (8), the compressive and tensile moduli of the material can be synchronously inverted.

[0053] A specific example adopts a numerical test: the length of the beam specimen model is L2=650mm, the thickness is B=30mm, the height is H=100mm, the distance between the two support points on the lower surface of the beam specimen model is L1=600mm, and the distance between the two load points on the upper surface of the beam specimen model is L3=400mm. Other related parameters and results are shown in the table below:

[0054] [Table 1]

[0055] εc xx , ε t xx are the strain values ​​measured at (x=0m, z=±H / 2) in the numerical test, and (σ c xx ) max is the compressive stress value at (x=0m, z=H / 2) obtained from equation (7), (σ t xx ) max is the tensile stress value at (x=0m, z=-H / 2) obtained from Eq. (7), and E c ' , E t ' are the compressive and tensile moduli of the material measured using this method. From the above table, it can be seen that the elastic modulus of the material obtained based on the measurement method proposed by the present invention is relatively close to the elastic modulus input in the numerical test, with a small relative error, and the measurement method proposed by the present invention has relatively good reliability.

[0056] The above are only preferred specific embodiments of the present application, but the scope of protection of the present application is not limited thereto, and any changes or substitutions that a person skilled in the art can easily conceive within the technical scope disclosed in the present application should be included within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be governed by the claims.

Claims

1. A method for measuring tensile and compressive elastic moduli taking into account the dual elastic modulus characteristics of a material based on a four-point vertical beam bending test, comprising: The test material is used as a test specimen, both ends of which are simply supported, and a symmetrical longitudinal concentrated load is applied to the beam test specimen to form a four-point bending load structure; measuring strains on the top and bottom surfaces of the beam specimen at a midpoint of the beam specimen; determining the position of the neutral layer based on the absolute value of compressive strain on the upper surface of the beam and the absolute value of tensile strain on the lower surface; Describing the stress distribution of horizontal stress at the central cross section of the beam specimen using a mathematical formula based on the position of the neutral layer; A step of calculating the maximum horizontal compressive stress and the maximum horizontal tensile stress on the upper and lower surfaces of the beam from the force equilibrium equation and the moment equilibrium equation at the central cross section in the beam axial direction; By measuring the compressive strain and tensile strain on the top and bottom surfaces of the central cross section in the beam axial direction, A method for measuring tensile and compressive elastic moduli that takes into account the dual elastic modulus characteristics of a material based on a four-point straight beam bending test, characterized in that it includes a step of simultaneously determining the compression and tensile moduli of the material by back-calculating them based on the measured values ​​of compressive strain and tensile strain.

2. 2. The method of claim 1, wherein the beam specimen is a four-point bending beam specimen having a height-to-span ratio of 1 / 6 or less.

3. 10. The method of claim 1, wherein measuring the strain on the upper and lower surfaces of the beam specimen includes attaching strain gauges to the upper and lower surfaces of the middle section of the specimen or measuring using DIC measurement techniques.

4. The equation for the position of the neutral layer is: [Equation 1] where ε ｃ ｘｘ is the maximum compressive strain at the central cross section in the beam axial direction, ε ｔ ｘｘ The method according to claim 1, wherein σ is the maximum tensile strain at the central cross section in the beam axial direction, and H is the height of the beam test specimen.

5. The stress distribution formula for horizontal stress is as follows: [Equation 2] Here, b １ is the horizontal compression region σ ｘｘ is the distribution gradient of b ２ is the horizontal tension region σ ｘｘ is the distribution gradient of σ ｃ ｘｘ is the compressive stress at any height within the compressed region on the central cross section, and σ ｔ ｘｘ is the tensile stress at any height in the tensile region on the central cross section, and z ０ 2. The method of claim 1, wherein σ represents the position of the neutral layer, and z represents an arbitrary height in the central cross section of the beam specimen.

6. The distribution gradient of the horizontal compression region and the distribution gradient of the horizontal tension region are expressed as follows: [Equation 3] [Equation 4] [Equation 5] Here, B is the thickness of the beam, L １ is the distance between the two support points on the lower surface of the beam specimen, L ３ 6. The method according to claim 5, wherein F is the distance between two load points on the upper surface of the beam test specimen, and F is the horizontal resultant force at the central cross section in the axial direction of the beam.

7. The synchronous inversion equation is: [Equation 6] where ε ｃ ｘｘ is the maximum compressive strain at the central cross section in the beam axial direction, ε ｔ ｘｘ is the maximum tensile strain at the central cross section in the beam axial direction, σ ｃ ｘｘ is the compressive stress at any height within the compressed region on the central cross section, σ ｔ ｘｘ 2. The method of claim 1, wherein σ is the tensile stress at any height within the tensile region on the central cross section.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, the computer program implementing the steps of the method according to any one of claims 1 to 7 when executed by a processor.

10. A computer program product comprising a computer program, the computer program implementing the steps of the method according to any one of claims 1 to 7 when said computer program is executed by a processor.

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