Shear modulus measurement method based on Rayleigh-Taylor instability

Abstract

The invention belongs to the field of material mechanical property testing, and particularly discloses a Rayleigh-Taylor instability-based shear modulus measuring method, which comprises the following steps: S1, filling a cylindrical mold with a to-be-measured material; s2, the mold is placed in a centrifugal machine loading bin, the free surface faces the centrifugal force direction, and the rotating speed is gradually increased; s3, surface deformation of the material is captured in real time through a camera, and when periodic wrinkles or interface instability is observed, the critical rotating speed is recorded; s4, converting the critical rotating speed into a supergravity value, and calculating a shear modulus by using a constant obtained by Rayleigh-Taylor linear stability analysis; the to-be-measured material is placed in the centrifugal machine, the rotating speed is gradually increased until Rayleigh-Taylor instability occurs on the free surface of the material, the critical rotating speed is recorded and converted into the supergravity value, the shear modulus is calculated in combination with a theoretical formula, equipment is simple, cost is low, and the method is particularly suitable for accurate measurement of the small shear modulus.

Description

Technical Field

[0001] The invention belongs to the field of material mechanical property testing, and particularly relates to a shear modulus measurement method based on Rayleigh-Taylor instability. Background Art

[0002] The shear modulus of a material is a key parameter that characterizes its ability to resist shear deformation. For soft materials (e.g., μ<1kPa), existing measurement methods have significant limitations:

[0003] Nanoindenter: The equipment is expensive and is prone to errors due to substrate effects for small modulus materials;

[0004] Rheometer: The noise interference is large during low-frequency measurement, resulting in insufficient resolution of small moduli;

[0005] Tension / compression method: Soft materials are prone to plastic deformation or slip, making it difficult to obtain accurate data.

[0006] Rayleigh-Taylor instability is a phenomenon in which the interface between two fluids of different densities becomes unstable in an acceleration field. Its critical condition is related to the elastic modulus of the material (Phys. Rev. Lett. 2010, 105, 204301). Summary of the Invention

[0007] The purpose of the present invention is to provide a shear modulus measurement method based on Rayleigh-Taylor instability, which can achieve low-cost and high-precision measurement of shear modulus by inducing instability in a hypergravity environment, so as to solve the problems raised in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A shear modulus measurement method based on Rayleigh-Taylor instability, comprising:

[0010] S1. Fill the material to be tested into a cylindrical mold, ensuring that the sides and lower surface fit tightly with the mold, while the upper surface remains free.

[0011] S2. Place the mold in the centrifuge loading chamber with the free surface facing the direction of centrifugal force and gradually increase the rotation speed;

[0012] S3. Use a camera to capture the material surface deformation in real time. When periodic wrinkles or interface instability are observed, it indicates instability and the critical speed is recorded.

[0013] S4. After converting the critical speed into a supergravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis.

[0014] Preferably, the centrifuge loading chamber gradually increases the rotation speed to 0-5000 rpm, corresponding to a hypergravity acceleration of 1-100 g.

[0015] Preferably, the critical speed is converted into the supergravity value Ng using the following formula:

[0016] Ng

[0017] N=Rω 2 / g

[0018] Where R is the centrifugal radius, ω is the critical speed, g = 9.8m / s 2 is the acceleration due to gravity on the Earth's surface.

[0019] Preferably, after converting the critical speed into a high gravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis, and the formula is as follows:

[0020]

[0021] Where: μ is the shear modulus, unit is Pa, ρ is the material density, unit is kg / m 3 , h is the material thickness in m, 6.22 is the constant obtained from the Rayleigh-Taylor linear stability analysis, and Ng is the supergravity value.

[0022] The shear modulus formula is obtained as follows:

[0023]

[0024] is the stress under the updated Lagrangian description, and its constitutive relation is expressed as:

[0025]

[0026] in, is the incremental perturbation of the hydrostatic pressure, and A0 is the instantaneous elastic modulus tensor.

[0027] The displacement solution obtained is as follows:

[0028]

[0029] Then we get the critical characteristic equation:

[0030]

[0031] For different R / H, there is an m that minimizes α, that is:

[0032]

[0033] Right now:

[0034]

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention places the material to be tested in a centrifuge, gradually increases the rotation speed until Rayleigh-Taylor instability occurs on the free surface of the material, records the critical speed and converts it into a hypergravity value, and calculates the shear modulus using a formula. Only a centrifuge and a camera are required, and the equipment is simple and low-cost. It is particularly suitable for accurate measurement of small shear moduli, thereby achieving low-cost, high-precision measurement of the shear modulus. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0038] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0040] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0041] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0042] As attached Figure 1 As shown:

[0043] Embodiment 1: This embodiment provides a shear modulus measurement method based on Rayleigh-Taylor instability, comprising:

[0044] S1. Fill the material to be tested into a cylindrical mold, ensuring that the sides and bottom surface are tightly fitted to the mold and the top surface remains free. The mold radius is 3 cm and the thickness is 0.7 cm.

[0045] S2. Place the mold in the centrifuge loading chamber with the free surface facing the direction of centrifugal force and gradually increase the rotation speed;

[0046] The centrifuge loading chamber gradually increases its speed from 0 to 5000 rpm, corresponding to a hypergravity acceleration of 1 to 100 g.

[0047] S3. Use a camera to capture the material surface deformation in real time. When periodic wrinkles or interface instability are observed, it indicates instability and the critical speed is recorded.

[0048] S4. After converting the critical speed into a supergravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis.

[0049] The critical speed is converted into the supergravity value Ng, the formula is as follows:

[0050] Ng

[0051] N=Rω 2 / g

[0052] Where R is the centrifugal radius, ω is the critical speed, g = 9.8m / s 2 is the acceleration due to gravity on the Earth's surface.

[0053] After converting the critical speed into a supergravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis, as follows:

[0054]

[0055] Where: μ is the shear modulus, unit is Pa, ρ is the material density, unit is kg / m 3 , h is the material thickness in m, 6.22 is the constant obtained from the Rayleigh-Taylor linear stability analysis, and Ng is the supergravity value.

[0056] Three sets of data were obtained using the method of Example 1 and the traditional rheometer measurement method, and the comparison is as follows:

[0057] Group 1 2 3 Instability hypergravity (9.8g / m2) 6.32 6.09 5.87 Shear modulus (instability method) 69.7 67.1 64.7 Shear modulus (rheometer) 66.7 66.7 63.1

[0058] Results: The method of Example 1 has a clear criterion for the critical point of instability, and the small modulus measurement error is ≤5%, which meets the requirements. The measurable modulus range is 0.1Pa-1kPa, covering ultra-soft materials such as biological soft tissues, and is particularly suitable for the mechanical characterization of low modulus materials such as biomaterials, hydrogels, and polymer gels.

[0059] It is important to note that the construction and arrangement of the present application shown in a number of different exemplary embodiments are merely illustrative. Although only a few embodiments are described in detail in this disclosure, it should be readily understood by those who refer to this disclosure that many modifications are possible (e.g., the size, scale, structure, shape and proportion of various elements, as well as parameter values ​​(e.g., temperature, pressure, etc.), mounting arrangements, use of materials, color, directional changes, etc.) without departing substantially from the novel teachings and advantages of the subject matter described in this application. For example, an element shown as integrally formed may be composed of multiple parts or elements, the position of the element may be inverted or otherwise changed, and the nature or number or position of the discrete elements may be altered or changed. Therefore, all such modifications are intended to be included within the scope of the present invention. The order or sequence of any process or method steps may be changed or reordered according to alternative embodiments. In the claims, any "means plus function" clause is intended to cover the structure described herein that performs the function, and is not only structurally equivalent but also equivalent structures. Other replacements, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the exemplary embodiments without departing from the scope of the present invention. Therefore, the invention is not limited to the specific embodiments, but extends to various modifications that still fall within the scope of the appended claims.

[0060] Additionally, in order to provide a concise description of exemplary embodiments, all features of an actual embodiment (i.e., those features that are not relevant to the best mode presently contemplated for carrying out the invention or those that are not relevant to implementing the invention) may not be described.

[0061] It will be appreciated that in the development of any actual embodiment, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort may be complex and time-consuming, but will, for those of ordinary skill having the benefit of this disclosure, be a routine undertaking of design, fabrication, and production without undue experimentation.

[0062] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A shear modulus measurement method based on Rayleigh-Taylor instability, characterized in that: include: S1. Fill the material to be tested into a cylindrical mold, ensuring that the sides and lower surface fit tightly with the mold, while the upper surface remains free. S2. Place the mold in the centrifuge loading chamber with the free surface facing the direction of centrifugal force and gradually increase the rotation speed; S3. Use a camera to capture the material surface deformation in real time. When periodic wrinkles or interface instability are observed, it indicates instability and the critical speed is recorded. S4. After converting the critical speed into a supergravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis.

2. The shear modulus measurement method based on Rayleigh-Taylor instability according to claim 1, characterized in that: The centrifuge loading chamber gradually increases the rotation speed to 0-5000 rpm, corresponding to a hypergravity acceleration of 1-100 g.

3. The shear modulus measurement method based on Rayleigh-Taylor instability according to claim 1, characterized in that: The formula for converting the critical speed into the supergravity value Ng is as follows: Ng N=Rω 2 / g Where R is the centrifugal radius, ω is the critical speed, g = 9.8m / s 2 is the acceleration due to gravity on the Earth's surface.

4. The shear modulus measurement method based on Rayleigh-Taylor instability according to claim 1, characterized in that: After converting the critical speed into a supergravity value, the shear modulus is calculated using the constants obtained from the Rayleigh-Taylor linear stability analysis, and the formula is as follows: Where: μ is the shear modulus, unit is Pa, ρ is the material density, unit is kg / m 3 , h is the material thickness in m, 6.22 is the constant obtained from the Rayleigh-Taylor linear stability analysis, and Ng is the supergravity value.

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