Construction method of in-plane mechanical isotropic size effect prediction model of two-dimensional three-way woven composite material
By constructing a two-dimensional triaxial woven composite material in-plane mechanical isotropic size effect prediction model, and combining elasticity and analytical geometry methods, the problem of neglecting boundary effects in traditional models is solved, and accurate prediction of TWF tensile stiffness under finite size is achieved, which is applicable to the material design of aerospace deployable structures.
Patent Information
- Application Number
- CN202511425701.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-30
- Publication Date
- 2025-12-16
AI Technical Summary
Existing technologies struggle to accurately predict the size effect of tensile stiffness in two-dimensional triaxial woven fabrics under finite dimensions, and traditional unit cell models neglect boundary effects, leading to inaccurate predictions.
A predictive model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials was constructed. Combining elasticity and analytical geometry methods, the deformation response of fiber bundles under different boundary conditions was analyzed, and the functional relationship between the tensile stiffness of TWF and its size and angle was established.
It accurately describes the relationship between sample size, tensile modulus and loading angle with an error of less than 5%, providing a theoretical tool for the material and size coordination design of deployable aerospace structures.
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Figure CN121145481A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method and theoretical framework for predicting the size effect of in-plane mechanical isotropy in two-dimensional triaxial woven composite materials. Background Technology
[0002] Two-dimensional triaxial woven fabrics (TWFs) possess advantages such as in-plane quasi-isotropy, light weight, and high dimensional stability, making them ideal materials for spatially deployable structures. However, the quasi-isotropic behavior of these materials exhibits significant size dependence characteristics within finite dimensions, posing a challenge to accurate prediction using traditional unit cell models.
[0003] TWF is a planar triaxial fabric composed of yarns interwoven in three different directions at 0°, 60°, and -60°. By combining it with resin, TWF composite materials with unique mechanical properties can be obtained, such as... Figure 1 As shown. Compared to biaxial woven fabrics, the equal-angle weaving method and periodically distributed hexagonal holes of TWF give it equal 0° and ±60° yarn components on its mid-surface, resulting in macroscopic in-plane quasi-isotropic mechanical properties. This makes it widely used in space-deployable structures such as satellite antenna reflectors. However, this quasi-isotropy is derived under the premise of ideal infinitely large dimensions and is not applicable to TWFs with finite dimensions. For example, in tensile tests, when the dimensions of the TWF tensile specimen change, a size effect in tensile stiffness will appear. Therefore, accurately evaluating the size effect of the mechanical properties of TWF and its composites from both theoretical and experimental perspectives is of great significance. Summary of the Invention
[0004] This invention provides a method for constructing a prediction model of in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials. The model constructed by this method can overcome the limitation of typical volume element analysis methods that ignore boundary effects, and provides a theoretical tool for the material and size coordination design of aerospace deployable structures such as space deployable antennas.
[0005] The objective of this invention is achieved through the following technical solution:
[0006] A method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials includes the following steps:
[0007] Step 1: Define the length of the TWF fabric as... Width is The distance between the central axes of adjacent fiber bundles is The weaving angle is Construct a geometric model for the tensile test TWF;
[0008] Step 2: For finite-size TWF tensile testing, assuming that the fiber bundles can independently respond to deformation applied to the entire fabric, the tensile stiffness of the fabric is the sum of the resistance provided by each yarn to the deformation applied to it. Therefore, by quantifying the fiber bundles under different boundary conditions, a functional relationship between TWF tensile stiffness and size and tensile angle is constructed. The specific steps are as follows:
[0009] Step Two: Analyze the structure of the finite-size TWF fabric, with the fiber bundle at a 0° angle to the horizontal. At that time, the number of fiber bundles at 0° of the tensile specimen was obtained according to the geometric relationship. -60° fiber bundle number Number of 60° fiber bundles Number of fiber bundle intersections ,in:
[0010]
[0011]
[0012] ,
[0013] ,
[0014]
[0015] In the formula, L and W are the length and width of the TWF unit cell;
[0016] Step 2: Analyze the relationship between the number of fiber bundles with both ends clamped in the tensile test of a finite-size TWF tensile specimen and the specimen size and tensile direction. Based on geometric relationships, obtain the number of 0° fiber bundles with both ends clamped. -60° fiber bundle number and the number of 60° fiber bundles The functional relationship between the tensile specimen's geometry and the geometric dimensions, where:
[0017]
[0018]
[0019] ,
[0020] ,
[0021] Step 3: For finite-size TWF tensile stiffness, assuming that the fiber bundles can independently respond to deformation applied to the entire fabric, the tensile stiffness of the fabric is the sum of the resistance provided by each yarn to the deformation applied to it. Therefore, a functional relationship between the number of TWF fiber bundles and the tensile stiffness is constructed, as follows:
[0022] Step 3: Analyze any single fiber bundle of TWF under tensile load. Tensile elongation occurs under the action With rotational displacement, the fiber bundle is subjected to force as The component of the fiber bundle in the tensile direction is The fiber bundle elongation is The tensile modulus of the fiber bundle is The cross-sectional area of the fiber bundle is The angle between the fiber bundle and the stretching direction is , ,in:
[0023]
[0024]
[0025]
[0026] Step 3.2: Establish the relationship between the tensile load displacement of the TWF and the single fiber bundle, and equate the cross-sectional shape of the TWF in the tensile direction to a length of... Thickness is A rectangular cross-section with a cross-sectional area of ;Stretch and deform TWF Equivalent to the minimum deformation in fiber bundles at 0°, 60°, and -60° with both ends clamped under tension; TWF tensile load This is equivalent to the sum of the resultant force of each fiber bundle held at both ends in the tensile direction and the resistance of the braided structure to the tensile deformation of the TWF; where:
[0027]
[0028]
[0029]
[0030] In the formula, To characterize the reinforcing factor of the braided cross structure on the tensile stiffness of the TWF;
[0031] Step 3: Based on the definition of tensile modulus, obtain the TWF tensile stiffness. and tensile modulus The relationship is:
[0032]
[0033] This leads to the expression for the tensile modulus of TWF fabrics of arbitrary size at arbitrary angles:
[0034]
[0035] in:
[0036]
[0037]
[0038] In the formula, Characterizing TWF in The direction of the fiber bundle that plays a major role during directional stretching. As a correction factor, The number of fiber bundles held at both ends during TWF stretching and the contribution of fiber bundle cross-weaving to the tensile stiffness of TWF are characterized for a selected TWF material. N / HT characterizes the size effect of TWF tensile stiffness;
[0039] Steps three and four, in When the length H of the clamping section of the tensile specimen is equal to the length P of the tensile section, then... When the angle is doubled, the size effect is constant and independent of the angle, so:
[0040]
[0041]
[0042] In the formula, The ratio of the tensile stiffness of the TWF fabric to that of the fiber bundle.
[0043] Compared with the prior art, the present invention has the following advantages:
[0044] This invention explores the size effect of the tensile properties of a TWF system under different loading directions. By combining elasticity theory with analytical geometry, a novel mechanical model is established to quantitatively describe the relationship between specimen size, tensile modulus, and loading angle. This model clarifies how the reinforcement effect of local fiber bundle constraint and braided structure influences macroscopic mechanical behavior. The theoretical derivation reveals a three-stage size effect in the mechanical response and defines two key aspect ratio thresholds (…). and The study found that the in-plane isotropic properties of TWF fabrics and their composite material TWFC are closely related to the boundary conditions and the geometry of the specimen, and exhibit specific patterns. Specifically, for rectangular TWF fabric specimens clamped at opposite sides, the in-plane isotropic properties, within a certain aspect ratio... At this point, the in-plane isotropic properties are almost lost because the tensile modulus at 30° is nearly zero, resulting in fiber bundle pull-out during stretching, and the end-to-end fiber bundle full load force transmission is lost; at aspect ratio At that time, with The anisotropy gradually decreases with increasing in-plane tensile modulus, and... When it is reduced to the minimum; in aspect ratio At this point, the in-plane anisotropic properties remain almost constant. The fundamental reason for these properties is that, under boundary conditions of opposite sides clamping, the main load-bearing fiber bundles change with geometric dimensions. After TWF fabric is composited with a low-modulus flexible matrix to form TWFC, the in-plane isotropic properties still follow similar rules; the difference lies in the aspect ratio. At that time, in-plane anisotropy will still follow The in-plane quasi-isotropic property gradually decreases as the fiber bundle cross structure increases, approaching quasi-isotropy. Therefore, in practical engineering applications, the use of in-plane quasi-isotropy in TWFs must be approached with extreme caution, especially when dealing with low-modulus matrices such as silicone rubber. Furthermore, uniaxial tensile tests and finite element simulations verified the model's accuracy, with an error of less than 5%. This model overcomes the limitation of typical volume element analysis methods that neglect boundary effects, providing a theoretical tool for the material and dimensional coordination design of aerospace deployable structures such as space deployable antennas. Attached Figure Description
[0045] Figure 1 Models were established for TWF stretching at different specifications and angles;
[0046] Figure 2 A flowchart for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials;
[0047] Figure 3 The TWF geometric model is used for tensile testing. Detailed Implementation
[0048] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.
[0049] This invention provides a method for constructing a prediction model of the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials, such as... Figure 2As shown, the method takes the macroscopic braided structure of TWF as the starting point, and uses elasticity and analytical geometry methods to analyze the size effect of TWF tensile stiffness. It constructs a quantitative predictive mechanical model between TWF tensile stiffness and sample size, predicts the tensile stiffness of TWF under different tensile angles, and verifies it through tensile experiments.
[0050] Finite-size TWF tensile test geometry model, such as Figure 3 As shown, the length of the TWF fabric is (Clamping section), width is (Tension segment) Figure 3 (a) is stretching in the 0° direction, i.e., stretching along the fiber bundle direction. Figure 3 (b) is Angular stretching, i.e., the angle between the fiber bundle and 0° is... Directional stretching, the TWF braided structure is periodically symmetrical about 60°, therefore it is set Define the distance between the central axes of adjacent fiber bundles as k, and the braiding angle as... A geometric model of the tensile test TWF was constructed. From Figure 3 As can be seen, for finite-size TWF tensile tests, there are fiber bundles whose ends are not clamped, i.e., there are edge-free fiber bundles. The contribution of these fiber bundles to the TWF tensile stiffness is only related to the bending stiffness, torsional stiffness, and friction between the fiber bundles. Assuming that the fiber bundles can independently respond to deformation applied to the entire fabric, the tensile stiffness of the fabric is the sum of the resistance provided by each yarn to the deformation applied to it. Therefore, the functional relationship between TWF tensile stiffness and size and tensile angle can be constructed by quantifying fiber bundles under different boundary conditions.
[0051] analyze Figure 2 The finite-size TWF fabric structure in the middle, with the fiber bundle at a 0° angle to the horizontal is At that time, the number of fiber bundles at 0° of the tensile specimen can be obtained according to the geometric relationship. -60° fiber bundle number Number of 60° fiber bundles Number of fiber bundle intersections By subscript To represent the number of fiber bundles The number of fiber bundle intersections can be represented by the following geometric relationships:
[0052]
[0053]
[0054] ,
[0055] ,
[0056]
[0057] Where L and W are the length and width of a TWF unit cell. This represents the distance between the central axes of adjacent fiber bundles.
[0058] Furthermore, the relationship between the number of fiber bundles with both ends clamped in the tensile test of a finite-size TWF tensile specimen and the specimen size and tensile direction was analyzed. Based on geometric relationships, the number of 0° fiber bundles with both ends clamped can be obtained. -60° fiber bundle number and the number of 60° fiber bundles The functional relationship between the tensile specimen's geometry and the number of fiber bundles held at both ends is expressed by the subscript eff, and the calculation formula is shown below:
[0059]
[0060]
[0061] ,
[0062] ,
[0063] For the tensile stiffness of finite-size TWF, assuming that the fiber bundles can independently respond to deformation applied to the entire fabric, the tensile stiffness of the fabric is the sum of the resistances provided by each yarn to the deformation applied to it. Therefore, a functional relationship between the number of TWF fiber bundles and the tensile stiffness can be constructed. Based on this assumption, an analysis is performed on an arbitrary single fiber bundle of TWF, and the fiber bundle under tensile load... Tensile elongation occurs under the action With rotational displacement, the fiber bundle is subjected to force as The component of the fiber bundle in the tensile direction is The fiber bundle elongation is The tensile modulus of the fiber bundle is The cross-sectional area of the fiber bundle is The angle between the fiber bundle and the stretching direction is Furthermore, due to the TWF periodic weaving structure, The range of values is .
[0064] Based on the force balance and geometric relationships of the fiber bundle, we can obtain:
[0065]
[0066]
[0067]
[0068] Establish the correlation between the tensile load displacement of the TWF and a single fiber bundle, and equate the cross-sectional shape of the TWF in the tensile direction to its length. ,thickness A rectangular cross-section with a cross-sectional area of TWF tensile deformation Equivalent to the minimum deformation in fiber bundles at 0°, 60°, and -60° with both ends clamped in the tensile direction; TWF tensile load It is equivalent to the sum of the resultant force of each fiber bundle held at both ends in the tensile direction and the resistance of the braided structure to the tensile deformation of the TWF.
[0069]
[0070]
[0071]
[0072] in: To characterize the reinforcing factor of the braided cross structure on the tensile stiffness of the TWF, it can be measured by the TWF in... Determined by tensile test in the 0° direction.
[0073] Based on the definition of tensile modulus, the tensile stiffness of TWF can be obtained. and tensile modulus The relationship is:
[0074]
[0075] This leads to the expression for the tensile modulus of TWF fabrics of arbitrary size at arbitrary angles:
[0076]
[0077] in:
[0078]
[0079]
[0080] in, Characterizes TWF in The fiber bundle orientation that plays a major role in directional stretching is independent of the size of the TWF stretched sample, characterizing the performance differences of TWF in different stretching directions, i.e., isotropic deviation. To account for deviations in weaving techniques, material damage, and material consistency, correction factors are introduced, which can be achieved through TWF. Determined by tensile test in the 0° direction. The number of fiber bundles held at both ends during TWF stretching and the contribution of fiber bundle cross-weaving to the tensile stiffness of TWF were characterized. Therefore, for a selected TWF material, N / HT characterizes the size effect of TWF tensile stiffness.
[0081] Based on the above analysis, When the length H of the clamping section of the tensile specimen is equal to the length P of the tensile section, then... When the angle is doubled, the size effect is constant and independent of the angle, so:
[0082]
[0083]
[0084] in The ratio of the tensile stiffness of the TWF fabric to that of the fiber bundle.
[0085] verify:
[0086] TWF tensile specimens were prepared according to ASTM D3039M. The TWF fabric used in the experiment was woven from TG300A-1K carbon fiber. The specimens were divided into three categories (A / B / C), with specimens A and B having dimensions according to... The specimens were prepared with H values of 69.3 mm and 34.7 mm, respectively. The C specimen was a standard ASTM D3039M specimen with H of 25 mm and P of 100 mm. Based on theoretical analysis, the TWF tensile stiffness has a period of 60° and is symmetrical about 30°. The tensile angles of the specimens were set to 0°, 15°, and 30°. Uniaxial tensile tests were performed using an INSTRON universal tensile testing machine at a tensile rate of 1 mm / min. The load and displacement during the tensile test were automatically recorded.
[0087]
[0088] The overall deviation is less than 5%, which proves the accuracy and applicability of the model proposed in this invention.
Claims
1. A method for constructing a prediction model for the in-plane mechanical isotropic size effect of a two-dimensional triaxial woven composite material, characterized in that... The method includes the following steps: Step 1: Define the length of the TWF fabric as... Width is The distance between the central axes of adjacent fiber bundles is The weaving angle is Construct a geometric model for the tensile test TWF; Step 2: For finite-size TWF tensile tests, it is assumed that the fiber bundles can independently respond to the deformation applied to the entire fabric, and the tensile stiffness of the fabric is the sum of the resistance provided by each yarn to the deformation applied to it. Thus, by quantifying the fiber bundles under different boundary conditions, a functional relationship between TWF tensile stiffness and size and tensile angle is constructed. Step 3: For finite-size TWF tensile stiffness, it is assumed that the fiber bundles can independently respond to deformations applied to the entire fabric. The tensile stiffness of the fabric is the sum of the resistances provided by each yarn to the deformations applied to it. Thus, a functional relationship between the number of TWF fiber bundles and tensile stiffness is constructed.
2. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 1, characterized in that... The specific steps of step two are as follows: Step Two: Analyze the structure of the finite-size TWF fabric, with the fiber bundle at a 0° angle to the horizontal. At that time, the number of fiber bundles at 0° of the tensile specimen was obtained according to the geometric relationship. -60° fiber bundle number Number of 60° fiber bundles Number of fiber bundle intersections ; Step 2: Analyze the relationship between the number of fiber bundles with both ends clamped in the tensile test of a finite-size TWF tensile specimen and the specimen size and tensile direction. Based on geometric relationships, obtain the number of 0° fiber bundles with both ends clamped. -60° fiber bundle number and the number of 60° fiber bundles The functional relationship between the geometric dimensions of the stretched sample and the sample.
3. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 2, characterized in that... In step two, , , and The formula is: ， ， In the formula, L and W are the length and width of the TWF unit cell.
4. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 1, characterized in that... In step two, , and The formula is: ， ， 。 5. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 1, characterized in that... The specific steps of step three are as follows: Step 3: Analyze any single fiber bundle of TWF under tensile load. Tensile elongation occurs under the action With rotational displacement, the fiber bundle is subjected to force as The component of the fiber bundle in the tensile direction is The fiber bundle elongation is The tensile modulus of the fiber bundle is The cross-sectional area of the fiber bundle is The angle between the fiber bundle and the stretching direction is , ; Step 3.2: Establish the relationship between the tensile load displacement of the TWF and the single fiber bundle, and equate the cross-sectional shape of the TWF in the tensile direction to a length of... Thickness is A rectangular cross-section with a cross-sectional area of ; TWF stretching deformation Equivalent to the minimum deformation in fiber bundles at 0°, 60°, and -60° with both ends clamped under tension; TWF tensile load It is equivalent to the sum of the resultant force of each fiber bundle held at both ends in the tensile direction and the resistance of the braided structure to the tensile deformation of the TWF. Step 3: Based on the definition of tensile modulus, obtain the TWF tensile stiffness. and tensile modulus The relationship is: This leads to the expression for the tensile modulus of TWF fabrics of arbitrary size at arbitrary angles: In the formula, Characterizing TWF in The direction of the fiber bundle that plays a major role during directional stretching. The number of fiber bundles held at both ends during TWF stretching and the contribution of fiber bundle cross-weaving to the tensile stiffness of TWF are characterized for a selected TWF material. N / HT characterizes the size effect of TWF tensile stiffness; Steps three and four, in At that time, that is, the length of the clamping section of the stretched sample. H It is the length of the stretching section. P of When the angle is doubled, the size effect is constant and independent of the angle, so: In the formula, The ratio of the tensile stiffness of the TWF fabric to that of the fiber bundle.
6. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 5, characterized in that... In step three, , The formula is: 。 7. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 5, characterized in that... In step three two, , , The formula is: In the formula, This is a factor characterizing the enhancement of the tensile stiffness of the TWF by the braided cross structure.
8. The method for constructing a prediction model for the in-plane mechanical isotropic size effect of two-dimensional triaxial woven composite materials according to claim 5, characterized in that... In step three: In the formula, This is a correction factor.