Poisson's ratio measuring method for solid propellant

Abstract

The invention discloses a Poisson's ratio measurement method for a solid propellant. The invention relates to a Poisson's ratio measurement method. The method comprises the following steps: applying a load to a cross-shaped sample; measuring the thickness change percentage delta d of the central point of the thinned area in the middle of the sample and the strain value epsilon of the sample in the plane stretching direction; and calculating the Poisson's ratio of the sample based on the thickness change percentage delta d of the central point of the thinned area in the middle of the sample and the strain value epsilon of the sample in the plane stretching direction. The invention provides a method for measuring the Poisson's ratio of a sample, which comprises the following steps: biaxially stretching a cross-shaped sample to obtain the thickness change percentage delta d of the central point of a thinned area in the middle of the sample and the strain value epsilon of the sample in the plane stretching direction, and then calculating to obtain the Poisson's ratio of the sample. The method provided by the invention is based on the biaxial tensile test, combines a contact measurement method and a non-contact measurement method, and improves the test precision.

Description

Technical Field

[0001] The invention belongs to the field of testing technology, and tests or analyzes materials by measuring the physical properties of incompressible materials, especially those with a Poisson's ratio close to 0.5, and specifically relates to a method for measuring the Poisson's ratio of solid propellants. Background Art

[0002] Poisson's ratio refers to the ratio of the transverse normal strain to the axial normal strain when the material is subjected to unidirectional tension or compression. It is an important elastic constant that characterizes the mechanical properties of the material. The accuracy of Poisson's ratio measurement directly affects the reliability of subsequent mechanical analysis.

[0003] The Poisson's ratio measurement of materials includes two categories: contact measurement and non-contact measurement. Contact measurement includes electrical measurement (strain gauge method), and non-contact method essentially calculates the required data by external observation of sample deformation, including video extensometry.

[0004] At present, non-contact measurement based on uniaxial tension has distortion in transverse strain. Due to the size characteristics of uniaxial specimens, the testable transverse gauge length is much shorter than the longitudinal one. According to the definition of strain ε=Δx / Li(i=x,y), for the same △x error, since Lx>Ly, the transverse strain error is large. For large deformation processes, the distortion is more serious due to the reduction of the transverse effective section.

[0005] Patent document 1 discloses a method and system for measuring the Poisson's ratio of solid propellant, which is used to test the Poisson's ratio of solid propellant. The method includes a preparation stage and a test stage, wherein the preparation stage includes: making a propellant sample; determining the size of the sample; measuring the proportional limit of the sample; calibrating a flexible sensor for measuring the width direction strain of the sample; installing the flexible sensor on the sample; detecting the parallelism and verticality of the flexible sensor; and the test stage includes: applying a load and collecting data.

[0006] Patent document 2 discloses a method for measuring the Poisson's ratio of a material based on a biaxial tensile test, the method comprising the following steps: pasting a strain gauge along a certain tensile direction of the biaxial test piece and connecting it to a strain gauge, fastening the biaxial test piece to a biaxial test device, operating the biaxial test device, elastically loading and unloading according to a given loading trajectory, obtaining a curve of the strain gauge strain value changing with time, determining its zero point and the corresponding position of the loading curve at that moment, and calculating the Poisson's ratio of the material according to the formula based on the position value.

[0007] In addition, Zhang Yue et al. also analyzed the characteristics of different measurement schemes in detail in "Comparison of strain and Poisson's ratio measurement accuracy of contact and non-contact extensometers", Experimental Mechanics, February 2018, Vol. 33, No. 1.

[0008] Patent Document 1:

[0009] Publication number: CN113820214A; Applicant: Beijing Institute of Technology; Classification number: G01N3 / 08.

[0010] Patent Document 2:

[0011] Publication number: CN109187180A; Applicant: Southeast University; Classification number: G01N3 / 08. Summary of the invention

[0012] Based on the inventor's research and practical experience in this field, the following improved technical solution is proposed here.

[0013] A method for measuring Poisson's ratio, the method comprising:

[0014] Apply load to the cross-shaped specimen;

[0015] Measure the thickness change percentage Δd at the center point of the thinning zone in the middle of the specimen and the strain value ε of the specimen in the plane tensile direction;

[0016] The Poisson's ratio of the sample is calculated based on the thickness change percentage Δd of the center point of the thinning zone in the middle of the sample and the strain value ε of the sample in the plane tensile direction.

[0017] According to one aspect of the present invention, the Poisson's ratio v of the sample is calculated by the following formula:

[0018]

[0019] The thickness change percentage is Where d0 is the initial thickness at the center of the specimen, and d is the thickness at the center of the specimen after the test.

[0020] According to one aspect of the present invention, the sample is a solid propellant. The material has an incompressible property with a Poisson's ratio close to 0.5.

[0021] According to one aspect of the present invention, the percentage change Δd of the thickness at the center point of the thinning zone in the middle of the sample is obtained by a contact displacement measuring device.

[0022] According to one aspect of the present invention, the strain value ε of the sample in the plane tensile direction is obtained by an image measuring device.

[0023] As can be seen from the above, the present invention provides a method for measuring the Poisson's ratio of a sample, by biaxially stretching the cross-shaped sample to obtain the thickness change percentage Δd of the center point of the thinning zone in the middle of the sample and the strain value ε of the sample in the plane stretching direction, and then the Poisson's ratio of the sample can be obtained by calculation. The method of the present invention is based on a biaxial tensile test, combines contact measurement and non-contact measurement methods, and improves the test accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Exemplary embodiments of the present invention are described with reference to the accompanying drawings, in which:

[0025] Figure 1 A schematic diagram showing a measuring device used in the Poisson's ratio measuring method of the present invention. DETAILED DESCRIPTION

[0026] The specific implementation of the present invention is described below with reference to the accompanying drawings.

[0027] The applicant has found through research that the Poisson's ratio of the sample can be obtained by measuring the thickness change and strain value of the sample. The measurement method proposed by the present invention combines contact and non-contact methods.

[0028] Specifically, Figure 1 As shown in FIG. 1 , in the measuring device used in the method for measuring Poisson's ratio of the present invention, the sample 1 has two parts perpendicular to each other, so that the whole is in the shape of a cross. There is a thinned portion in the middle of the sample 1. As an example, the thinned portion has a circular shape. Figure 1 , and its thickness is less than other parts of the sample 1. The measuring device includes an image measuring device 2, which can be a camera, preferably a high-precision camera, to capture the deformation of the sample 1 during the test. In addition, the measuring device also includes a displacement measuring device 2, preferably a contact displacement measuring device, preferably with an accuracy of measuring 1 micron displacement. The displacement measuring device 2 is in direct contact with the thinned area of ​​the sample 1 to facilitate the measurement of the deformation of the thinned area of ​​the sample 1 during the test. More preferably, the displacement measuring device 2 is in direct contact with the central part of the thinned area of ​​the sample 1.

[0029] Therefore, during the test, when the sample 1 is stretched, the strain value ε of the sample 1 in the plane stretching direction can be obtained by the image measuring device 2, and the thickness change percentage Δd at the center point of the sample can be measured by the displacement measuring device 2 to obtain the Poisson's ratio of the sample.

[0030] Specifically, the present invention is based on the following considerations.

[0031] Theoretically, the Poisson's ratio of composite solid propellant is close to 0.5, and it is incompressible in volume, that is, the cross section of the sample is significantly thinned during the stretching process, which affects the accuracy of stress measurement. At the same time, the study found that the Poisson's ratio of solid propellant under ignition and pressure buildup conditions may have numerical changes. Therefore, the deformation law of solid propellant during ignition is affected by both incompressibility and Poisson's ratio.

[0032] For the convenience of calculation, the elastic body assumption is made for the solid propellant material, which does not affect the reflection of the macroscopic deformation law. According to the elastic theory, the three-dimensional stress and strain follow the following constitutive relationship:

[0033]

[0034] Where σ is the second-order stress tensor, ε is the second-order strain tensor, G is the bulk modulus, K is the shear modulus, and I is the second-order unit tensor. and are the deviatoric strain tensor and static strain respectively, and their calculation formulas are as follows:

[0035]

[0036] Where E is the elastic modulus and v is Poisson's ratio. Considering the equibiaxial tensile conditions and the axial symmetry of the specimen, the stress and strain in the two orthogonal tensile directions are equal, and the thickness-to-width ratio of the plane biaxial tensile specimen is small, the stress along the thickness direction is approximately 0, that is:

[0037]

[0038] Combining (0.1), (0.2), and (0.3), we can get:

[0039]

[0040] Furthermore, the center thickness d and the unit strain ε along the thickness z direction are i The relationship is as follows:

[0041]

[0042] Where d0 is the initial thickness of the specimen center. Considering that the thickness of biaxial specimens is generally small, it is assumed that the unit strains in the thickness direction are equal, and the relationship between the thickness and strain value after stretching is as follows:

[0043]

[0044] The thickness change percentage Δd is defined as follows:

[0045]

[0046] Combining (0.4), (0.6), and (0.7), we can get:

[0047]

[0048] Further we get the expression of Poisson's ratio:

[0049]

[0050] Therefore, that is to say, by measuring the strain value ε of the sample 1 in the plane tensile direction and the percentage change Δd of the thickness at the center point of the sample, the Poisson's ratio of the sample can be obtained. Among them, the strain value ε and the percentage Δd can be observed and calculated by relevant experimental equipment.

[0051] The above description is merely an exemplary embodiment of the spirit and principle of the present invention. It will be appreciated by those skilled in the art that various changes may be made to the described examples without departing from the spirit and principle, and these changes and their various equivalents are all anticipated by the inventors and fall within the scope defined by the claims of the present invention.

Claims

1. A method for measuring Poisson's ratio, characterized in that: The method comprises: Apply load to the cross-shaped specimen; Measure the thickness change percentage Δd at the center point of the thinning zone in the middle of the specimen and the strain value ε of the specimen in the plane tensile direction; The Poisson's ratio of the sample is calculated based on the thickness change percentage Δd of the center point of the thinning zone in the middle of the sample and the strain value ε of the sample in the plane tensile direction.

2. The method for measuring Poisson's ratio according to claim 1, characterized in that: The Poisson's ratio v of the sample is calculated by the following formula: The thickness change percentage is Where d0 is the initial thickness at the center of the specimen, and d is the thickness at the center of the specimen after the test.

3. The Poisson's ratio measurement method according to claim 1 or 2, characterized in that: The sample is a solid propellant.

4. The method for measuring Poisson's ratio according to claim 1 or 2, characterized in that: The percentage change Δd of the thickness at the center point of the thinning zone in the middle of the sample is obtained by a contact displacement measuring device.

5. The method for measuring Poisson's ratio according to claim 1 or 2, characterized in that: The strain value ε of the sample in the plane tensile direction is obtained by an image measuring device.

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