CN114818372A - A Calculation Method of Tsai Modulus of Composite Materials - Google Patents

Abstract

The disclosure relates to a method for calculating the Tsai modulus of a composite material. The method comprises the following steps: determining the ply angle and the normalized stiffness coefficient of the composite material sample according to the longitudinal tensile modulus range based on the preset corresponding relation among the longitudinal tensile modulus, the ply angle and the normalized stiffness coefficient of the composite material; preparing a sample of the composite material according to the determined ply angle and the positive and negative ply angles; performing tensile test measurement on the prepared sample to obtain longitudinal strain of the sample under the action of tensile load, and determining the in-plane longitudinal stiffness of the sample according to the longitudinal strain and the width of the sample; determining the normalized stiffness of the composite material according to the in-plane longitudinal stiffness of the sample and the thickness of the sample; the Tsai modulus of the composite material is determined based on the normalized stiffness and the normalized stiffness coefficient of the composite material. Through the calculation method of the composite material Tsai modulus, the problem of large error of an original method can be solved, and the traditional composite material laminated structure rigidity analysis method can be simplified.

Description

A Calculation Method of Tsai Modulus of Composite Materials

technical field

The present disclosure relates to the technical field of aircraft composite material structure design and analysis, and in particular, to a method for calculating the Tsai modulus of composite materials.

Background technique

The Tsai modulus is a new elastic constant proposed by Stephen W. Tsai, a professor at Stanford University, an academician of the National Academy of Engineering, and the "father of composite materials" in 2014, to characterize the overall stiffness performance of composite materials, that is, the trace of the elastic matrix of composite materials (Trace). =Q ₁₁ +Q ₂₂ +2Q ₆₆ ), in 2020, in order to commemorate the discovery of the elastic constant, and in recognition of Stephen W. Tsai's historical contribution in the field of composite materials, the elastic constant was officially named "Tsai's Modulus" internationally. , which is the Tsai modulus.

According to Stephen W.Tsai's original theory, the Tsai modulus of a certain material can be approximated by only the longitudinal tensile test of a 0° layered unidirectional plate. The longitudinal tensile modulus E ₁ of the material is obtained by the longitudinal tensile test of the plate, and then the Tsai modulus of the material can be approximately calculated by the following method:

0.88 in the above method is obtained from the statistics of the mechanical properties of various carbon fiber composite materials. However, when the layup angle φ=0°, the normalized stiffness coefficients of different materials are still widely dispersed. Therefore, when the Tsai modulus of carbon fiber composites is calculated by the 0° laminate test, the error will be relatively large.

Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

It should be noted that the information disclosed in the above Background section is only for enhancement of understanding of the background of the present disclosure, and therefore may contain information that does not form the prior art that is already known to a person of ordinary skill in the art.

SUMMARY OF THE INVENTION

The purpose of the present disclosure is to provide a method for calculating the Tsai modulus of a composite material, so as to at least to a certain extent overcome one or more problems caused by limitations and defects of the related art.

Based on the preset correspondence between the longitudinal tensile modulus of the composite material, the layup angle, and the normalized stiffness coefficient, the layup angle and normalization of the composite material sample are determined according to the longitudinal tensile modulus range stiffness coefficient, wherein the composite material is a carbon fiber composite material;

According to the determined layup angle, the sample preparation of the composite material is carried out according to the positive and negative layup angles;

Perform a tensile test on the prepared sample to obtain the longitudinal strain of the sample under tensile load, and determine the in-plane longitudinal stiffness of the sample according to the longitudinal strain and the width of the sample ;

determining a normalized stiffness of the composite material from the in-plane longitudinal stiffness of the specimen and the thickness of the specimen;

The Tsai modulus of the composite material is determined based on the normalized stiffness and normalized stiffness coefficient of the composite material.

In the embodiment of the present disclosure, the sample is a rectangular flat plate tensile sample or a helically wound round tube sample.

In the embodiment of the present disclosure, the layup angle and the normalized stiffness coefficient in the preset corresponding relationship are statistically obtained from a plurality of known elastic constants of composite materials.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The longitudinal tensile modulus, transverse tensile modulus, in-plane Poisson's ratio, and in-plane shear modulus of each known composite were counted, and the elastic matrix coefficients of each composite were calculated according to classical laminate theory.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The Tsai modulus of each known composite was calculated from the elastic matrix coefficients of each of the composites.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

Set a virtual laminate composed of two layers of the positive and negative layup angles, gradually increase the layup angle from 0° to 90°, and calculate any of the positive and negative layup angles according to the classical laminate theory The in-plane longitudinal stiffness of the virtual laminate.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The normalized stiffness coefficient is derived from the thickness of the virtual laminate, the in-plane longitudinal stiffness, and the Tsai modulus of the composite.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The normalized stiffness coefficient is plotted according to the layup angle of the virtual laminate as a function of the layup angle.

In the embodiment of the present disclosure, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

According to the dense intersection point in the variation curve of the normalized stiffness coefficient with the ply angle, the abscissa and the ordinate of the dense intersection point are obtained, and the value corresponding to the abscissa is the ply angle, The value of the ordinate is the normalized stiffness coefficient, and the obtained layup angle and the normalized stiffness coefficient are corrected.

In the embodiments of the present disclosure, the composite material is a thermoplastic composite material or a thermosetting composite material.

The technical solutions provided by the embodiments of the present disclosure may include the following beneficial effects:

In an embodiment of the present disclosure, by the above method, the layup angle and the normalized stiffness coefficient of the composite material are determined according to the range of the longitudinal tensile modulus, the sample is prepared according to the layup angle, and the prepared sample is subjected to The tensile test is determined to obtain the longitudinal strain under the tensile load, the in-plane longitudinal stiffness of the specimen is determined based on the longitudinal strain and the specimen width, the normalized stiffness is determined by the in-plane longitudinal stiffness and the specimen thickness, and the normalized stiffness is determined based on the in-plane longitudinal stiffness and specimen thickness. The normalized stiffness and the normalized stiffness coefficient were used to obtain the Tsai modulus of the composite. This method can solve the problem of large error of the original method, and can simplify the traditional stiffness analysis method of composite laminated structure.

It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure.

Description of drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description serve to explain the principles of the disclosure. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort.

FIG. 1 schematically shows a flow chart of steps of a method for calculating the Tsai modulus of a composite material in an exemplary embodiment of the present disclosure;

FIG. 2 schematically shows the structure and loading schematic diagram of the composite rectangular flat plate tensile specimen in the exemplary embodiment of the present disclosure;

FIG. 3 schematically shows the structure and loading schematic diagram of the composite material helically wound round tube sample in the exemplary embodiment of the present disclosure;

随铺层角φ的变化曲线。FIG. 4 schematically illustrates the normalized stiffness coefficients of virtual laminates in an exemplary embodiment of the present disclosure

Variation curve with ply angle φ.

Detailed ways

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments, however, can be embodied in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

Furthermore, the drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repeated descriptions will be omitted. Some of the block diagrams shown in the figures are functional entities that do not necessarily necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, or in one or more hardware modules or integrated circuits, or in different networks and/or processor devices and/or microcontroller devices.

However, it can be seen from Figure 4 that when the layup angle φ=0°, the normalized stiffness coefficients of different materials are still widely dispersed. Therefore, when the Tsai modulus of carbon fiber composites is calculated by the 0° laminate test, the error will be larger.

This example embodiment provides a method for calculating the Tsai modulus of a composite material. Referring to Figure 1, the method may include:

Step S101: Based on the preset correspondence between the longitudinal tensile modulus of the composite material, the layup angle, and the normalized stiffness coefficient, determine the layup angle and Normalized stiffness coefficient, wherein the composite material is a carbon fiber composite material.

Step S102: According to the determined layup angle, the sample preparation of the composite material is performed according to the positive and negative layup angles.

Step S103 : perform a tensile test on the prepared sample, obtain the longitudinal strain of the sample under the action of the tensile load, and determine the surface of the sample according to the longitudinal strain and the width of the sample Inner longitudinal stiffness.

Step S104: Determine the normalized stiffness of the composite material according to the in-plane longitudinal stiffness of the sample and the thickness of the sample.

Step S105: Determine the Tsai modulus of the composite material based on the normalized stiffness and the normalized stiffness coefficient of the composite material.

By the above method, the layup angle and normalized stiffness coefficient of the composite material are determined according to the range of longitudinal tensile modulus, the sample is prepared according to the layup angle, and the prepared sample is subjected to tensile test measurement to obtain the tensile load. The longitudinal strain under the action, the in-plane longitudinal stiffness of the specimen is determined based on the longitudinal strain and the specimen width, the normalized stiffness is determined by the in-plane longitudinal stiffness and the specimen thickness, and is obtained based on the normalized stiffness and the normalized stiffness coefficient Tsai modulus of composites. This method can solve the problem of large error of the original method, and can simplify the traditional stiffness analysis method of composite laminated structure.

Hereinafter, each step of the above method in this example embodiment will be described in more detail with reference to FIGS. 1 to 4 .

与复合材料的纵向拉伸模量E₁之间的预设对应关系如表1所示。根据纵向拉伸模量E₁范围通过表1查找对应的铺层角φ和归一化刚度系数

In step S101, based on the preset correspondence between the longitudinal tensile modulus of the composite material, the layup angle, and the normalized stiffness coefficient, the layup of the composite material sample is determined according to the longitudinal tensile modulus range angle and normalized stiffness coefficient, wherein the composite material is a carbon fiber composite material. Specifically, the layup angle φ, normalized stiffness coefficient

The preset correspondence with the longitudinal tensile modulus E1 of the composites is shown in Table ₁ . According to the range of longitudinal tensile modulus E1, look up the corresponding ply angle φ and normalized stiffness coefficient through Table ₁

之间的预设对应关系Table ₁ Longitudinal tensile modulus E1 of composites versus ply angle φ, normalized stiffness coefficient

preset correspondence between

In step S102, the sample preparation of the composite material is performed according to the determined layup angles according to the positive and negative layup angles. Specifically, according to the size of the layup angle determined by the preset corresponding relationship in Table 1, the sample preparation of the composite material is carried out according to the positive and negative layup angles ±φ two kinds of layup angles, so that it is convenient to obtain a sample with a size corresponding to the layup angle. The sample is convenient for subsequent testing and measurement of the sample.

In step S103, a tensile test is performed on the prepared sample to obtain the longitudinal strain of the sample under the action of the tensile load, and the sample is determined according to the longitudinal strain and the width of the sample in-plane longitudinal stiffness. Specifically, after the sample is prepared according to the determined layup angle, when the sample is subjected to tensile sample measurement, one end of the sample is fixed, and the other end is subjected to a tensile load F to ensure that the sample is under the current load. No damage of any kind occurred in the laminate, and the longitudinal strain ε ₀ of the sample laminate under tensile load F was determined experimentally. The in-plane longitudinal stiffness of the specimen is then calculated from the longitudinal strain and the specimen width. Specifically, it is calculated according to the following formula (1).

In step S104, the normalized stiffness of the composite material is determined according to the in-plane longitudinal stiffness of the sample and the thickness of the sample. Specifically, the normalized stiffness of the specimen is calculated according to the following formula (2)

In step S105, the Tsai modulus of the composite material is determined based on the normalized stiffness and the normalized stiffness coefficient of the composite material. Specifically, the Tsai modulus of the composite material was calculated according to the following formula (3).

Optionally, in some embodiments, the sample is a rectangular flat plate tensile sample or a helically wound round tube sample. Specifically, the rectangular flat plate tensile specimen is prepared by laying the composite material at the positive and negative layup angles ±φ, and the spirally wound round tube sample is the composite material with the positive and negative layup angles ±φ. The seed ply corners are prepared by spiral winding. The rectangular flat plate tensile sample is shown in Figure 2, where L represents the length of the sample, and the spiral wound round tube sample is shown in Figure 3.

Optionally, in some embodiments, the layup angle and the normalized stiffness coefficient in the preset correspondence are obtained by statistics of a plurality of known elastic constants of composite materials. Specifically, the preset corresponding relationship between the longitudinal tensile modulus, the layup angle, and the normalized stiffness coefficient as shown in Table 1 is obtained through statistics of a large number of known elastic constants of composite materials.

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The longitudinal tensile modulus, transverse tensile modulus, in-plane Poisson's ratio, and in-plane shear modulus of each known composite were counted, and the elastic matrix coefficients of each composite were calculated according to classical laminate theory. Specifically, the longitudinal tensile modulus E ₁ , the transverse tensile modulus E ₂ , the in-plane Poisson’s ratio μ ₁₂ , and the in-plane shear modulus G ₁₂ of each known composite material are calculated according to the classical laminate theory. The elastic matrix coefficients Q ₁₁ , Q ₂₂ , Q ₁₂ , Q ₆₆ , etc. of each composite material. Among them, the classical laminate theory is based on the following 3 assumptions: (1) The interlayer deformation consistency hypothesis: the single layers of the laminate are sticky and firm, the interlayer deformation is consistent, and there is no relative displacement; (2) The straight normal line assumption: deformation The straight line perpendicular to the middle surface of the board remains vertical after deformation, and its length remains unchanged; (3) Assumption of plane stress state: each single layer in the laminate can be approximately considered to be in a plane stress state.

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

The Tsai modulus of each known composite was calculated from the elastic matrix coefficients of each of the composites. Specifically, the Tsai modulus of each known composite material is calculated according to the following formula (4), wherein the Tsai modulus of each composite material is the trace of the elastic matrix of the composite material.

Trace=Q ₁₁ +Q ₂₂ +2Q ₆₆ (4)

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

Set a virtual laminate composed of two layers of the positive and negative layup angles, gradually increase the layup angle from 0° to 90°, and calculate any of the positive and negative layup angles according to the classical laminate theory The in-plane longitudinal stiffness A ₁₁ of the virtual laminate. Specifically, the virtual laminate is formed by laying up two ply angles of +φ and -φ. When the ply angle gradually increases from 0° to 90°, the virtual laminate of any ±φ is calculated according to the classical laminate theory. In-plane longitudinal stiffness A ₁₁ .

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

然后再根据得到的归一化纵向刚度和复合材料的Tsai模量得到归一化刚度系数

The normalized stiffness coefficient is derived from the thickness of the virtual laminate, the in-plane longitudinal stiffness, and the Tsai modulus of the composite. Specifically, the normalized longitudinal stiffness is obtained by calculating the in-plane longitudinal stiffness A ₁₁ and the thickness h of the virtual laminate

The normalized stiffness coefficient is then obtained based on the obtained normalized longitudinal stiffness and the Tsai modulus of the composite

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

与铺层角φ的关系绘制虚拟层压板的归一化刚度系数

随铺层角φ的变化曲线，如图4所示。The normalized stiffness coefficient as a function of the layup angle is plotted according to the layup angle of the virtual laminate. Specifically, the normalized stiffness coefficient of the virtual laminate

Normalized stiffness coefficients for virtual laminates plotted as a function of ply angle φ

The variation curve with the layup angle φ is shown in Figure 4.

Optionally, in some embodiments, the step of statistically obtaining the layup angle and the normalized stiffness coefficient in the preset correspondence relationship through a plurality of known elastic constants of composite materials includes:

随铺层角φ的变化曲线中的密集交汇点A，该密集交汇点A可称为焦点A，密集交汇点A的横坐标对应的数值即为铺层角φ，密集交汇点A的纵坐标对应的数值即为归一化刚度系数

此时得到的铺层角φ和归一化刚度系数

分别可以通过大量复合材料纵向拉伸模量、横向拉伸模量、泊松比及剪切模量的样本数据进行修正。修正后的铺层角φ、归一化刚度系数

和纵向拉伸模量E₁范围之间形成预设对应关系，如表1所示。The abscissa and ordinate of the dense junction are obtained according to the dense junction in the variation curve of the normalized stiffness coefficient with the ply angle, and the value corresponding to the abscissa is the ply angle, so The value of the ordinate is the normalized stiffness coefficient, and the obtained layup angle and the normalized stiffness coefficient are corrected. Specifically, through Figure 4, find the normalized stiffness coefficients of various composite materials

The dense junction A in the curve with the change of the ply angle φ, the dense junction A can be called the focus A, the value corresponding to the abscissa of the dense junction A is the ply angle φ, and the ordinate of the dense junction A The corresponding value is the normalized stiffness coefficient

The ply angle φ and normalized stiffness coefficient obtained at this time

It can be corrected by a large number of sample data of longitudinal tensile modulus, transverse tensile modulus, Poisson's ratio and shear modulus of composite materials, respectively. Corrected ply angle φ, normalized stiffness coefficient

A preset correspondence is formed between the range of the longitudinal tensile modulus E1, as shown in Table ₁ .

Optionally, in some embodiments, the composite material is a thermoplastic composite material or a thermosetting composite material. Specifically, whether it is a thermoplastic composite material or a thermosetting composite material, its Tsai modulus can be calculated.

Through the above method, the layup angle and normalized stiffness coefficient of the composite material are determined according to the range of longitudinal tensile modulus, the samples are prepared according to the layup angle, and the prepared samples are tested and measured to obtain the equivalent longitudinal tensile force. Modulus, the normalized stiffness of the composite material is obtained based on the equivalent longitudinal tensile modulus, specimen width and specimen thickness, and then the Tsai modulus of the composite material is obtained by the normalized stiffness and normalized stiffness coefficient. This method can solve the problem of large error of the original method, and can simplify the traditional stiffness analysis method of composite laminated structure.

Other embodiments of the present disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or techniques in the technical field not disclosed by the present disclosure . The specification and examples are to be regarded as exemplary only, with the true scope and spirit of the disclosure being indicated by the appended claims.

Claims (10)

1. A method for calculating a composite material Tsai modulus is characterized by comprising the following steps:

determining a ply angle and a normalized stiffness coefficient of a composite material sample according to the longitudinal tensile modulus range based on a preset corresponding relation among the longitudinal tensile modulus, the ply angle and the normalized stiffness coefficient of the composite material, wherein the composite material is a carbon fiber composite material;

preparing a sample of the composite material according to the determined ply angle and the positive and negative ply angles;

performing tensile test measurement on the prepared sample to obtain longitudinal strain of the sample under the action of tensile load, and determining the in-plane longitudinal stiffness of the sample according to the longitudinal strain and the width of the sample;

determining the normalized stiffness of the composite material according to the in-plane longitudinal stiffness of the sample and the thickness of the sample;

determining a Tsai modulus for the composite material based on the normalized stiffness and the normalized stiffness coefficient for the composite material.

2. The method for calculating the Tsai modulus of the composite material according to claim 1,

the test sample is a rectangular flat plate tensile test sample or a spiral winding round pipe test sample.

3. The method for calculating the Tsai modulus of the composite material according to claim 1,

the ply angle and the normalized stiffness coefficient in the preset corresponding relation are obtained through statistics of a plurality of known elastic constants of the composite material.

4. The method for calculating the Tsai modulus of the composite material according to claim 3, characterized in that,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

and counting the longitudinal tensile modulus, the transverse tensile modulus, the in-plane Poisson ratio and the in-plane shear modulus of each known composite material, and calculating the elastic matrix coefficient of each composite material according to the classical laminate theory.

5. The method for calculating the Tsai modulus of the composite material according to claim 4,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

the Tsai modulus for each known composite was calculated from the elastic matrix coefficients for each of the composites.

6. The method for calculating the Tsai modulus of the composite material according to claim 5,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

setting a virtual laminated board consisting of the positive and negative ply angles, gradually increasing the ply angle from 0 degrees to 90 degrees, and calculating the in-plane longitudinal stiffness of the virtual laminated board with any positive and negative ply angle according to a classical laminated board theory.

7. The method for calculating the Tsai modulus of the composite material according to claim 6,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

and obtaining the normalized stiffness coefficient according to the thickness and in-plane longitudinal stiffness of the virtual laminated plate and the Tsai modulus of the composite material.

8. The method for calculating the Tsai modulus of the composite material according to claim 7, characterized in that,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

and drawing a variation curve of the normalized stiffness coefficient along with the ply angle according to the ply angle of the virtual laminated board.

9. The method for calculating the Tsai modulus of the composite material according to claim 8,

the step of obtaining the ply angle and the normalized stiffness coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite material comprises the following steps:

and obtaining an abscissa and an ordinate of the dense intersection point according to the dense intersection point in the variation curve of the normalized stiffness coefficient along with the ply angle, wherein the numerical value corresponding to the abscissa is the ply angle, and the numerical value of the ordinate is the normalized stiffness coefficient, and correcting the obtained ply angle and the normalized stiffness coefficient.

10. The method for calculating the Tsai modulus of the composite material according to claim 1, wherein the composite material is a thermoplastic composite material or a thermosetting composite material.

Images