Annular sample, clamp and axial tension pure shear test method

Abstract

The invention provides an annular sample, a clamp and an axial tension pure shear test method, belongs to the field of material mechanical property test, and aims to thoroughly solve the problem of non-uniform pure shear stress field caused by necking phenomenon. Under axial tension, a sample global uniform pure shear stress field is achieved, the pure shear stress-strain relation of the hyperelastic material is directly solved according to force and displacement data of the sample, and the influence of tension displacement and strain is avoided. The mechanical property of the rubber material can be better evaluated. Through verification, an annular sample tensile test has good substitutability for a plane tensile test.

Description

Technical Field

[0001] This invention belongs to the field of material mechanical property testing, specifically relating to a pure shear test method for hyperelastic materials. Background Technology

[0002] Superelastic materials such as rubber are widely used in many fields, including automotive, aerospace, and machinery manufacturing, due to their excellent elasticity, wear resistance, and sealing properties. Accurately measuring the mechanical properties of rubber materials, especially their performance parameters under pure shear conditions, is crucial for evaluating product quality and optimizing product design.

[0003] Currently, planar tensile testing is often used instead of pure shear testing. This is because the rectangular specimen (PS) used in planar tensile testing has a length much larger than its width, making the central region approximately equivalent to a "pure shear" condition. However, PS specimens exhibit necking during tension, which intensifies with increasing tensile displacement and is also related to the type of rubber. The more pronounced the necking, the more uneven the stress field of the PS specimen, leading to inaccurate equivalent pure shear data.

[0004] To address this issue, patent CN 115630544 A obtains the true stress-strain curve during the material's plastic stage, uses the Swift and Hockett-Sherby equations for fitting and extrapolation, and then weights and integrates the results. After determining the weighting coefficients through finite element simulation, a simulation curve is generated. Patent CN 103940668A measures the actual deformation in the central region by etching a mesh on a PS (polystyrene) sample, and then derives the material's pure shear mechanical properties. All of these inventions are based on PS samples and do not completely solve the problem of uneven pure shear stress field caused by necking. Summary of the Invention

[0005] To completely solve the problem of non-uniform pure shear stress field caused by necking, this invention proposes a pure shear test method using a ring specimen, fixture, and axial tension. This invention uses a ring specimen, which does not have the necking phenomenon caused by free edges, and can achieve a uniform pure shear stress field throughout the entire range during axial tension. The pure shear stress-strain relationship of hyperelastic materials can be directly solved based on the force and displacement data of the specimen, without being affected by tensile displacement and strain.

[0006] The technical solution adopted in this invention is as follows: The annular specimen described in this invention has a radius and height that are much greater than its wall thickness, wherein the radius R ≥ 50 mm, the height H is 5 mm ~ 15 mm, and the wall thickness t is 0.5 mm ~ 3 mm; the upper and lower ends are provided with transition round edges for easy clamping, and the radius r of the transition round edges satisfies 5 mm ≤ r ≤ 10 mm.

[0007] The clamp for the annular sample consists of upper and lower clamping discs 1 and 5 and upper and lower clamping rings 2 and 4. The upper and lower clamping rings 2 and 4 are each assembled from three clamping ring assemblies. The circular groove formed by the clamping rings and clamping discs has a diameter controlled at 94-96% of the diameter of the upper and lower circular edges of the annular sample. An interference fit provides the clamping preload between the sample and the clamp. The upper clamping disc 1 and the upper clamping ring 2, as well as the lower clamping disc 5 and the lower clamping ring 4, are fixedly connected. The upper clamping disc 1 and the lower clamping disc 5 are connected to the displacement module 6 or the force measuring module 7 respectively through tooling.

[0008] Furthermore, the clamping ring assembly is provided with threaded holes for bolt connection, and the three clamping ring assemblies are connected and fixed by three sets of bolts.

[0009] Furthermore, the upper clamping plate 1 and the upper clamping ring 2, as well as the lower clamping plate 5 and the lower clamping ring 4, are fastened together by bolts through six sets of evenly distributed threaded holes.

[0010] After proper assembly, an annular space concentric with the edge of the sample will be formed between the clamping ring and the clamping plate, which can ensure the accurate installation and positioning of the sample on the fixture.

[0011] The present invention discloses a pure shear test method for axial tension of a ring-shaped specimen, the specific steps of which are as follows: (1) Accurately assemble the ring-shaped sample with the fixture and measure the distance between the upper and lower clamping plates 1 and 5. L 0; The lower clamping plate 5 is connected to the force measuring module 7 and the upper clamping plate 1 is connected to the displacement module 6 through the fixture tooling; the force measuring module 7 is used to obtain the tensile force of the annular sample and the displacement module 6 is used to obtain the displacement of the upper clamping plate 1. (2) The axial tensile direction of the annular specimen is defined as the first principal direction, the thickness direction as the second principal direction, and the circumferential direction as the third principal direction; Stress σ in the first direction 11 The force F measured by the force measuring module is divided by the cross-sectional area A of the annular specimen to obtain: (1) The cross-sectional area A of the annular specimen is calculated according to formula (2): (2) In formula (2), R is the outer diameter of the annular sample and t is the thickness of the arm of the annular sample; Strain ε in the first direction of the unit 11 The displacement L measured by the displacement module and the initial distance L0 between the upper and lower clamping plates are used to obtain the following: (3) Strain energy function W For the deformation gradient of the material For right Cauchy-Green deformable tensor C The function, , ; (3) The stress σ in the first direction under different tensile conditions was collected through experiments. 11 With strain ε 11 The data was analyzed using the nonlinear least squares method on the selected strain energy function. W By fitting parameters to a model (such as the Mooney-Rivlin model, Neo-Hookean model, etc.), the constitutive relation expression of the material can be determined.

[0012] The advantages of this invention are: (1) The pure shear test method proposed in this invention achieves a uniform pure shear stress field across the entire sample under axial tension through the synergistic effect of the annular sample and the multi-stage bolt clamping device. The pure shear stress-strain relationship of the hyperelastic material is directly solved based on the force and displacement data of the sample, without being affected by tensile displacement and strain. This method can better evaluate the mechanical properties of rubber materials.

[0013] (2) PS specimens exhibit necking during tension, which intensifies with increasing strain. Furthermore, the necking phenomenon varies significantly among different types of materials, making it difficult for some PS specimens to maintain a pure shear state during tension. Ring specimens completely avoid this situation.

[0014] (3) By conducting quasi-static tensile tests on annular specimens, the output experimental data can be fitted together with experimental data such as uniaxial tensile (UT) and iso-biaxial tensile (ET) to obtain hyperelastic constitutive model parameters that reflect the mechanical properties of rubber. Based on this constitutive model, a planar tensile simulation of PS specimens was conducted, and it was found that the simulation results were in good agreement with the experimental data. Therefore, the annular specimen tensile test has good substitutability for the planar tensile test. Attached Figure Description

[0015] Figure 1 Schematic diagram of the ring-shaped specimen structure; Figure 2 Schematic diagram of the ring-shaped sample clamp structure; Figure 3 Schematic diagram of the fit between the annular specimen and the fixture; Figure 4 Schematic diagram of the tensile direction of the annular specimen; Figure 5 Comparison of specimen deformation before and after tensile testing; Figure 6 Schematic diagram of unit stretching; Figure 7Displacement-load curves and experimentally measured PT tensile data; Figure 8 Comparison of theoretical curves of the Ogden model for mixtures of NR and SBR with simulation results of RS samples; Figure 9 Comparison of theoretical curves from polyurethane MR model with simulation results of RS samples; Reference numerals: 1-Upper clamping plate; 2-Upper clamping ring; 3-Annular specimen; 4-Lower clamping ring; 5-Lower clamping plate; 6-Displacement module; 7-Force measuring module; Detailed Implementation

[0016] The technical solution of the present invention will be further explained and described below with reference to specific embodiments.

[0017] (1) such as Figure 1 As shown, the annular specimen provided by this invention has a radius and height much greater than its wall thickness, with transition rounded edges at the top and bottom for easy clamping. This structure can form a uniform pure shear stress field during axial tension, avoiding the necking problem of traditional PS. Based on the stress uniformity requirements under pure shear conditions, the wall thickness needs to be controlled within 0.5mm ≤ t ≤ 3mm to ensure uniform radial stress distribution during tensioning and avoid stress concentration due to excessively thick or thin walls. The height of the tensile zone is designed to be 5mm ≤ H ≤ 15mm. This range ensures sufficient deformation of the specimen in the tensile test to obtain accurate mechanical data while avoiding overall stability issues caused by excessive height. The radius is designed to be R ≥ 50mm. This dimension ensures sufficient operating space for the clamping device during installation, avoiding clamping difficulties due to an excessively small radius. The transition arc radius at the top and bottom meets 5mm ≤ R ≤ 10mm. The smooth arc transition reduces stress concentration at the clamping area, ensuring uniform force transmission during tensioning and making the central region of the specimen closer to the ideal pure shear state.

[0018] The clamp for the annular sample in this invention, such as Figure 2 and Figure 3 As shown, it consists of upper and lower clamping discs 1 and 5 and upper and lower clamping rings 2 and 4. The upper and lower clamping rings 2 and 4 are each composed of three clamping ring assemblies. The circular groove formed by the clamping rings and clamping discs has a diameter controlled at 94~96% of the diameter of the upper and lower circular edges of the annular sample. It provides the clamping preload between the sample and the fixture through an interference fit. The upper clamping disc 1 and the upper clamping ring 2, as well as the lower clamping disc 5 and the lower clamping ring 4 are fixedly connected. The upper clamping disc 1 and the lower clamping disc 5 are connected to the displacement module 6 or the force measuring module 7 respectively through tooling.

[0019] The clamping ring assembly has threaded holes for bolt connection, and the three clamping ring assemblies are connected and fixed together by three sets of bolts. The upper clamping plate 1 and the upper clamping ring 2, as well as the lower clamping plate 5 and the lower clamping ring 4 are fastened together by bolts through six sets of evenly distributed threaded holes.

[0020] The assembly process of the annular sample and the fixture in this invention includes the following steps: (1) Connect the lower clamping plate 5 of the clamping fixture to the force measuring module 7, and connect the upper clamping plate 1 to the displacement module 6.

[0021] (2) Place the lower transition edge of the annular sample onto the lower clamping plate 5 to ensure that the lower transition edge of the sample fits into the semi-circular space of the clamping plate.

[0022] (3) Install three lower clamping ring assemblies and fix the lower clamping ring assemblies and the lower clamping plate 5 together with 6 sets of bolts. After ensuring that the circular space formed by the lower clamping ring 4 and the lower clamping plate 5 fits the lower transition circle edge of the annular specimen, use bolts to lock the three lower clamping plate assemblies to ensure the provision of clamping force at the bottom of the annular specimen during stretching.

[0023] (4) Lower the upper clamping plate 1 installed on the displacement module 6, and stop lowering after ensuring that the upper transition circle of the annular sample can fit tightly with the semi-circular space of the upper clamping plate 1.

[0024] (5) Install three upper clamping ring assemblies and fix the upper clamping ring 2 and the upper clamping plate 1 together with 6 sets of bolts. After ensuring that the circular space formed by the upper clamping ring 2 and the upper clamping plate 1 fits the transition circle above the annular sample, use bolts to lock the three upper clamping plate assemblies to ensure the provision of clamping force at the top of the sample during tensioning.

[0025] After proper assembly, an annular space concentric with the edge of the sample will be formed between the clamping ring and the clamping plate, which can ensure the accurate installation and positioning of the sample on the fixture.

[0026] The specific implementation method for the pure shear test of the axial tension of the annular specimen is as follows: (1) Operate displacement module 6, zero the initial force of force measuring module 7, and record the initial vertical distance L0 between upper and lower clamping plates 1 and 5 at this time.

[0027] (2) After ensuring the above steps are completed, begin the tensile test. The force measuring module 7 outputs the force F during the tensile process (e.g., ...). Figure 4 As shown), displacement module 6 outputs tensile displacement L.

[0028] (3) The axial tensile direction of the annular specimen is defined as the first principal direction, the thickness direction as the second principal direction, and the circumferential direction as the third principal direction; Figure 5The figure shows a comparison before and after stretching. As can be seen from the figure, when the unit cell on the annular sample is small enough, from the perspective of the local micro-element, the third direction can be approximated as the vertical direction. At this time, the curvature of the unit cell has a negligible effect on the analysis results. like Figure 6 As shown, the elongation rates in the three directions are respectively λ 1. λ 2. λ 3. When the axial tensile elongation λ 1= λ When the deformation in the thickness direction of the annular sample is ignored, that is... λ 2=1. Due to the incompressibility of rubber, the volume of the unit cell remains unchanged before and after stretching. λ 1 λ 2 λ 3=1, at this point the material deformation is considered as a pure shear condition; The stress-strain of the annular specimen is solved based on force-displacement data, where the stress σ in the first direction of the element is... 11 The force F measured by the force measuring module is divided by the cross-sectional area A of the annular specimen to obtain: (1) The cross-sectional area A of the annular specimen is calculated according to formula (2): (2) In formula (2), R is the outer diameter of the annular sample and t is the thickness of the arm of the annular sample; Strain ε in the first direction of the unit 11 The displacement L measured by the displacement module and the initial distance L0 between the upper and lower clamping plates are used to obtain the following: (3) (4) The data obtained from the mechanical testing of the rubber material of the ring sample are used as the stress and strain data under pure shear conditions. The strain energy function W is fitted and can be used as the mechanical parameters of the material.

[0029] To further verify the accuracy of the invention, a ring-shaped sample with R=50mm and t=1mm was selected in this embodiment. L 0=10mm, the material is natural rubber filled with silica, and the three-parameter MR strain energy density model is selected as the hyperelastic constitutive model of the material: The data obtained from the test of the annular specimen were used as the stress-strain data under pure shear conditions. Combined with uniaxial tensile and equal biaxial tensile data, the model parameter value C was obtained by fitting. 10 =0.9416, C 01 =-0.1933, C 11=0.0322; Based on this constitutive model, a simulation analysis of the tensile process of a planar tensile specimen was conducted. The obtained displacement-load curves and experimentally measured PT tensile data are shown below. Figure 7 As shown, the simulation results agree well with the experimental data, with the maximum error controlled within 10%, effectively verifying the reliability of the material parameters and the substitutability of the annular specimen for planar tension.

[0030] To verify this superiority, the constitutive parameters of two materials, a mixture of NR and SBR and polyurethane rubber, were selected for simulation of planar tension and annular tension. The stress-strain data after simulation were exported and compared with the stress-strain theoretical curves of the hyperelastic constitutive models of the two materials under pure shear conditions.

[0031] from Figure 8 , Figure 9 As can be seen, the theoretical curve and the RS sample simulation curve are basically consistent in the early stage. In the later stage, due to the difference between the simulation and the definition of rubber incompressibility in theory, there is a deviation, but the error is much smaller than that of the PS simulation curve. This verifies the superiority of the ring sample over the PS sample under some rubber material properties.

Claims

1. An annular test sample, characterized by, The radius and height are much greater than the wall thickness, wherein the radius R is greater than or equal to 50 mm, the height H is 5 mm to 15 mm, and the wall thickness t is 0.5 mm to 3 mm; the upper and lower ends are provided with transition round edges facilitating clamping, and the radius r of the transition round edges satisfies 5 mm≤ r ≤ 10 mm.

2. The ring specimen holder of claim 1, wherein The clamp is composed of upper and lower clamping discs (1, 5) and upper and lower clamping rings (2, 4), the upper and lower clamping rings (2, 4) are respectively composed of three clamping ring assemblies, a circular groove is formed between the clamping ring and the clamping disc, the diameter of the circular groove is controlled to be 94-96% of the diameter of the upper and lower round edges of the annular sample, and the clamping pre-tightening force between the sample and the clamp is provided through interference fit; the upper clamping disc (1) and the upper clamping ring (2), and the lower clamping disc (5) and the lower clamping ring (4) are fixedly connected; the upper clamping disc (1) and the lower clamping disc (5) are respectively connected with a displacement module (6) or a force measuring module (7) through a tool.

3. The ring specimen holder of claim 2, wherein The clamping ring assembly is provided with a threaded hole for bolt connection, and the three clamping ring assemblies are connected and fixed through three groups of bolts.

4. The ring specimen holder of claim 2, wherein The upper clamping disc (1) and the upper clamping ring (2), and the lower clamping disc (5) and the lower clamping ring (4) are connected and fixed through six groups of uniformly distributed threaded holes.

5. The method of claim 1, wherein the axial tension pure shear test method is for a ring specimen. The specific steps of the method are as follows: (1) The annular sample is accurately assembled with the fixture, and the distance between the upper and lower clamping discs (1, 5) is measured L 0; the lower clamping disc (5) is connected with the force module (7) and the upper clamping disc (1) is connected with the displacement module (6) through the fixture tooling; the force module (7) is used to obtain the tensile force of the annular sample, and the displacement module (6) obtains the displacement of the upper clamping disc (1); (2) The axial tensile direction of the annular sample is defined as the first principal direction, the thickness direction is the second principal direction, and the circumferential direction is the third principal direction; Stress σ in the first direction 11 Force F measured by the force module divided by the annular specimen cross-sectional area A gives: （1） The cross-sectional area A of the annular sample is calculated according to formula (2): （2） In formula (2), R is the outer diameter of the annular sample, and t is the arm thickness of the annular sample. Strain ε of the unit body in the first direction 11 The displacement L measured by the displacement module and the initial distance L0 between the upper and lower clamping discs are used to obtain: （3） Strain energy function W as a function of the deformation gradient F or the right Cauchy-Green deformation tensor C of the material, ， ； (3) The stress σ 11 and strain ε 11 data, the selected strain energy function W model is fitted by nonlinear least squares method, that is, the constitutive relationship expression of the material can be determined.

6. The axial tension pure shear test method of an annular specimen of claim 5, wherein, Strain energy function W The model is selected from one of a Mooney-Rivlin model, a Neo-Hookean model.

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