CN114818374B - Calculation method of composite material Tsai modulus - Google Patents
Calculation method of composite material Tsai modulus Download PDFInfo
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- 239000002131 composite material Substances 0.000 title claims abstract description 124
- 238000004364 calculation method Methods 0.000 title description 3
- 238000006243 chemical reaction Methods 0.000 claims abstract description 49
- 238000000034 method Methods 0.000 claims abstract description 30
- 238000005259 measurement Methods 0.000 claims abstract description 10
- 229920000049 Carbon (fiber) Polymers 0.000 claims abstract description 8
- 239000004917 carbon fiber Substances 0.000 claims abstract description 8
- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 claims abstract description 8
- 239000011159 matrix material Substances 0.000 claims description 9
- 230000001965 increasing effect Effects 0.000 claims description 4
- 229920001169 thermoplastic Polymers 0.000 claims description 4
- 229920001187 thermosetting polymer Polymers 0.000 claims description 4
- 239000004416 thermosoftening plastic Substances 0.000 claims description 4
- 239000000463 material Substances 0.000 description 6
- 239000010410 layer Substances 0.000 description 4
- 238000004804 winding Methods 0.000 description 3
- 230000006978 adaptation Effects 0.000 description 2
- 238000009864 tensile test Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000002708 enhancing effect Effects 0.000 description 1
- 239000011229 interlayer Substances 0.000 description 1
- 239000002356 single layer Substances 0.000 description 1
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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Abstract
The disclosure relates to a method for calculating a composite material Tsai modulus. The method comprises the following steps: determining the layering angle and the conversion coefficient of the composite material sample according to the longitudinal tensile modulus range based on a preset corresponding relation between the longitudinal tensile modulus of the composite material, the layering angle and the conversion coefficient, wherein the composite material is a carbon fiber composite material; preparing a sample of the composite material according to the determined layering angles and the positive layering angles; performing test measurement on the prepared sample to obtain the equivalent longitudinal tensile modulus of the sample; the Tsai modulus of the composite material was calculated from the equivalent longitudinal tensile modulus and the conversion coefficient of the test specimen. By the method for calculating the Tsai modulus of the composite material, the problem of large error of an original method can be solved, and a traditional method for analyzing the rigidity of the laminated structure of the composite material can be simplified.
Description
Technical Field
The disclosure relates to the technical field of aircraft composite material structural design and analysis, in particular to a calculation method of a composite material Tsai modulus.
Background
The Tsai Modulus is a new elastic constant, i.e. trace=q 11+Q22+2Q66, of the composite elastic matrix, proposed by professor of the university of stethomson, the national institute of engineering, "father of composite" Stephen w.tsai, 2014, which characterizes the overall stiffness properties of the composite, and is formally internationally named "Tsai's module", i.e. Tsai Modulus, for the purpose of commemorating the discovery of this elastic constant, while for the purpose of showing the historical contribution of Stephen w.tsai in the composite field.
According to the original theory of Stephen W.Tsai, the Tsai modulus of a certain material can be approximately obtained only through a 0-degree-paved unidirectional plate longitudinal tensile test, and the specific method is that the longitudinal tensile modulus E 1 of the material is obtained through the 0-degree-paved unidirectional plate longitudinal tensile test of the certain material, and then the Tsai modulus of the material can be approximately calculated through the following method:
0.88 of the method is obtained by statistics of mechanical properties of various carbon fiber composite materials. When the ply angle phi=0°, the normalized longitudinal tensile modulus of the different materials is still more dispersed, and therefore, when the Tsai modulus of the carbon fiber composite is calculated using the 0 ° laminate test, the error is relatively large.
Accordingly, there is a need to provide a new solution to ameliorate one or more of the problems presented in the above solutions.
It should be noted that the information disclosed in the above background section is only for enhancing understanding of the background of the present disclosure and thus may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
It is an object of the present disclosure to provide a method of calculating a composite Tsai modulus, which overcomes one or more of the problems due to the limitations and disadvantages of the related art, at least to some extent.
According to an embodiment of the disclosure, a method for calculating a Tsai modulus of a composite material includes:
Determining the layering angle and the conversion coefficient of a composite material sample according to the longitudinal tensile modulus range based on a preset corresponding relation between the longitudinal tensile modulus of the composite material, the layering angle and the conversion coefficient, wherein the composite material is a carbon fiber composite material;
Preparing a sample of the composite material according to the determined layering angles and the positive layering angles;
Performing test measurement on the prepared sample to obtain the equivalent longitudinal tensile modulus of the sample;
the Tsai modulus of the composite material is calculated from the equivalent longitudinal tensile modulus of the test specimen and the conversion coefficient.
In embodiments of the present disclosure, the specimen is a rectangular flat plate tensile specimen or a spiral wound round tube specimen.
In an embodiment of the disclosure, the ply angle and the conversion coefficient in the preset correspondence are statistically derived from a plurality of known composite elastic constants.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
The longitudinal tensile modulus, transverse tensile modulus, in-plane poisson's ratio, in-plane shear modulus of each known composite were counted and the elastic matrix coefficient of each composite was calculated according to classical laminate theory.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
the Tsai modulus of each known composite is calculated from the elastic matrix coefficients of each of the composites.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
Setting a virtual laminate consisting of two ply angles of the positive and negative ply angles, gradually increasing the ply angle from 0 DEG to 90 DEG, and calculating the equivalent longitudinal tensile modulus of the virtual laminate of any positive and negative ply angle according to the classical laminate theory.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
the normalized equivalent longitudinal tensile modulus is derived from the equivalent longitudinal tensile modulus of the virtual laminate and the Tsai modulus of the known composite.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
And respectively drawing a change curve of the equivalent longitudinal tensile modulus of the virtual laminate along with the ply angle and a change curve of the normalized equivalent longitudinal tensile modulus along with the ply angle according to the equivalent longitudinal tensile modulus of the virtual laminate, the normalized equivalent longitudinal tensile modulus and the ply angle.
In an embodiment of the disclosure, the step of obtaining the ply angle and the conversion coefficient in the preset correspondence through statistics of a plurality of known elastic constants of the composite material includes:
And obtaining an abscissa and an ordinate of the intensive intersection point according to the intensive intersection point in the curve of the normalized equivalent longitudinal tensile modulus along with the change of the ply angle, wherein the value corresponding to the abscissa is the ply angle, the value of the ordinate is the conversion coefficient, and correcting the obtained ply angle and the conversion coefficient.
In an embodiment of the present disclosure, the composite material is a thermoplastic composite material or a thermoset composite material.
The technical scheme provided by the embodiment of the disclosure can comprise the following beneficial effects:
In one embodiment of the disclosure, by the above method for calculating Tsai modulus of a composite material, a layup angle and a conversion coefficient of the composite material are determined according to a longitudinal tensile modulus range, a sample is prepared according to the layup angle, the prepared sample is subjected to test measurement to obtain an equivalent longitudinal tensile modulus, and the Tsai modulus of the composite material is obtained based on the equivalent longitudinal tensile modulus and the conversion coefficient. The method can solve the problem of large error of the original method, and can simplify the traditional method for analyzing the rigidity of the laminated structure of the composite material.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
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. It will be apparent to those of ordinary skill in the art that the drawings in the following description are merely examples of the disclosure and that other drawings may be derived from them without undue effort.
FIG. 1 schematically illustrates a flow chart of steps of a method of calculating a composite Tsai modulus in an exemplary embodiment of the disclosure;
FIG. 2 schematically illustrates a composite rectangular flat panel tensile specimen structure and loading schematic in an exemplary embodiment of the present disclosure;
FIG. 3 schematically illustrates a composite spiral wound round tube sample structure and loading schematic in an exemplary embodiment of the present disclosure;
FIG. 4 schematically illustrates an equivalent longitudinal tensile modulus E x of a virtual laminate as a function of ply angle phi in an exemplary embodiment of the present disclosure;
FIG. 5 schematically illustrates normalized equivalent longitudinal tensile modulus of a virtual laminate in an exemplary embodiment of the present disclosure A variation curve with ply angle phi.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments may be embodied in many 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 the 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.
As can be seen from fig. 4, when the ply angle phi=0°, the normalized longitudinal tensile modulus of the different materials is still more dispersed, and thus, when the Tsai modulus of the carbon fiber composite material is calculated using the 0 ° laminate test, the error is relatively large.
In this example embodiment, a method for calculating a Tsai modulus of a composite material is provided, and referring to fig. 1, the method may include:
Step S101: and determining the layering angle and the conversion coefficient of the composite material sample according to the longitudinal tensile modulus range based on a preset corresponding relation between the longitudinal tensile modulus of the composite material, the layering angle and the conversion coefficient, wherein the composite material is a carbon fiber composite material.
Step S102: and preparing a sample of the composite material according to the determined layering angles and the positive layering angles.
Step S103: and performing test measurement on the prepared sample to obtain the equivalent longitudinal tensile modulus of the sample.
Step S104: the Tsai modulus of the composite material is calculated from the equivalent longitudinal tensile modulus of the test specimen and the conversion coefficient.
By the method for calculating the Tsai modulus of the composite material, the layering angle and the conversion coefficient of the composite material are determined according to the longitudinal tensile modulus range, a sample is prepared according to the layering angle, the prepared sample is subjected to test measurement, the equivalent longitudinal tensile modulus is obtained, and the Tsai modulus of the composite material is obtained based on the equivalent longitudinal tensile modulus and the conversion coefficient. The method can solve the problem of large error of the original method, and can simplify the traditional method for analyzing the rigidity of the laminated structure of the composite material.
Next, each step of the above-described method in the present exemplary embodiment will be described in more detail with reference to fig. 1 to 5.
In step S101, the ply angle and the conversion coefficient of the composite sample are determined according to the longitudinal tensile modulus range based on the preset correspondence between the longitudinal tensile modulus of the composite material and the ply angle and the conversion coefficient, wherein the composite material is a carbon fiber composite material. Specifically, the preset correspondence between ply angle phi, conversion coefficient K and longitudinal tensile modulus E 1 of the composite is shown in table 1. The corresponding ply angle phi and conversion factor K are looked up by Table 1 based on the longitudinal tensile modulus E 1 range.
TABLE 1 preset correspondence between longitudinal tensile modulus E 1 and ply angle phi, conversion coefficient K of composite material
| Modulus of elongation in machine direction E 1 | Sample ply angle phi | Conversion coefficient K |
| 100GPa～120GPa | ±17° | 0.655 |
| 120GPa～150GPa | ±17° | 0.656 |
| 150GPa～200GPa | ±15° | 0.711 |
| 200GPa～250GPa | ±14° | 0.736 |
| 300GPa～350GPa | ±11° | 0.823 |
| Uncertainty of | ±14° | 0.731 |
In step S102, a sample of the composite material is prepared according to the determined ply angle and the positive and negative ply angles. Specifically, according to the determined size of the pavement angle, preparing a sample of the composite material according to the positive pavement angle plus or minus pavement angle phi, so that the sample corresponding to the size of the pavement angle is conveniently obtained, and the subsequent test measurement of the sample is conveniently carried out.
In step S103, the prepared test specimen is subjected to test measurement to obtain an equivalent longitudinal tensile modulus of the test specimen. Specifically, the equivalent longitudinal tensile modulus E x of the prepared composite material sample is obtained by performing test measurement on the prepared composite material sample.
In step S104, the Tsai modulus of the composite material is calculated from the equivalent longitudinal tensile modulus of the test specimen and the conversion coefficient. Specifically, the Tsai modulus of the composite material was calculated according to the following formula (1).
Alternatively, in some embodiments, the specimen is a rectangular flat plate tensile specimen or a spiral wound round tube specimen. Specifically, the rectangular flat tensile sample is prepared by paving a composite material at positive and negative layering angles + -phi, and the spiral winding round tube sample is prepared by spirally winding the composite material at positive and negative layering angles + -phi, wherein the rectangular flat tensile sample is shown in figure 2, and the spiral winding round tube sample is shown in figure 3.
Optionally, in some embodiments, the ply angle and the conversion factor in the preset correspondence are statistically derived from a plurality of known composite elastic constants. Specifically, the preset correspondence between the longitudinal tensile modulus, the ply angle and the conversion coefficient shown in table 1 is obtained through statistics of a large number of known elastic constants of the composite materials.
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
The longitudinal tensile modulus, transverse tensile modulus, in-plane poisson's ratio, in-plane shear modulus of each known composite were counted and the elastic matrix coefficient of each composite was calculated according to classical laminate theory. Specifically, the elastic matrix coefficient Q 11、Q22、Q12、Q66 and the like of each composite material were calculated according to classical laminate theory based on the longitudinal tensile modulus E 1, the transverse tensile modulus E 2, the in-plane poisson ratio μ 12, the in-plane shear modulus G 12 of each known composite material of statistics. Among them, classical laminate theory is based on the following 3 assumptions: (1) the interlayer deformation coincidence assumption: the single layers of the laminated board are firmly stuck, the deformation between the layers is consistent, and no relative displacement exists; (2) straight normal assumption: the straight line vertical to the middle surface of the plate before deformation is still vertical after deformation, and the length is unchanged; (3) plane stress state assumption: each individual layer in the laminate can be considered approximately in a planar stress state.
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
the Tsai modulus of each known composite is calculated from the elastic matrix coefficients of each of the composites. Specifically, the Tsai modulus of each known composite is calculated according to the following formula (2), wherein the Tsai modulus of each known composite is the trace of the elastic matrix of the composite.
Trace＝Q11+Q22+2Q66 (2)
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
Setting a virtual laminated board formed by two layers of + -phi, gradually increasing the layer angle from 0 DEG to 90 DEG, and calculating the equivalent longitudinal tensile modulus of the virtual laminated board with any + -phi according to the classical laminated board theory. Specifically, the virtual laminate is formed by layering two layering angles of +phi and-phi, and when the layering angle is gradually increased from 0 DEG to 90 DEG, the equivalent longitudinal tensile modulus E x of the virtual laminate with any + -phi is calculated according to the classical laminate theory.
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
The normalized equivalent longitudinal tensile modulus is derived from the equivalent longitudinal tensile modulus of the virtual laminate and the Tsai modulus of the known composite. Specifically, the resulting equivalent longitudinal tensile modulus E x is divided by the Tsai modulus of each known composite to give a normalized equivalent longitudinal tensile modulus
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
And respectively drawing a change curve of the equivalent longitudinal tensile modulus of the virtual laminate along with the ply angle and a change curve of the normalized equivalent longitudinal tensile modulus along with the ply angle according to the equivalent longitudinal tensile modulus of the virtual laminate, the normalized equivalent longitudinal tensile modulus and the ply angle. Specifically, the change in the equivalent longitudinal tensile modulus E x of the virtual laminate with the ply angle phi is plotted according to the relationship between the equivalent longitudinal tensile modulus E x of the virtual laminate and the ply angle phi, as shown in fig. 4. Normalized equivalent longitudinal tensile modulus according to virtual laminate Plotting normalized equivalent longitudinal tensile modulus of a virtual laminate as a function of ply angle phiThe variation with ply angle phi is shown in figure 5.
Optionally, in some embodiments, the step of statistically obtaining the ply angle and the conversion coefficient in the preset correspondence by a plurality of known elastic constants of the composite material includes:
And obtaining an abscissa and an ordinate of the intensive intersection point according to the intensive intersection point in the curve of the normalized equivalent longitudinal tensile modulus along with the change of the ply angle, wherein the value corresponding to the abscissa is the ply angle, the value of the ordinate is the conversion coefficient, and correcting the obtained ply angle and the conversion coefficient. Specifically, through FIG. 5, normalized equivalent longitudinal tensile modulus of various composite materials was found The dense intersection point A in the change curve along with the pavement angle phi can be called a focus, the numerical value corresponding to the abscissa of the dense intersection point A is the pavement angle phi, and the numerical value corresponding to the ordinate of the dense intersection point A is the conversion coefficient K. The ply angle phi and the conversion coefficient K obtained at this time can be corrected by a large number of sample data of the longitudinal tensile modulus, the transverse tensile modulus, the Poisson's ratio and the shear modulus of the composite material, respectively. The modified ply angle phi, conversion coefficient K and longitudinal tensile modulus E 1 form a predetermined correspondence between the ranges as shown in table 1.
Alternatively, in some embodiments, the composite is a thermoplastic composite or a thermoset composite. Specifically, the Tsai modulus can be calculated for either thermoplastic composites or thermoset composites.
By the method for calculating the Tsai modulus of the composite material, the layering angle and the conversion coefficient of the composite material are determined according to the longitudinal tensile modulus range, a sample is prepared according to the layering angle, the prepared sample is subjected to test measurement, the equivalent longitudinal tensile modulus is obtained, and the Tsai modulus of the composite material is obtained based on the equivalent longitudinal tensile modulus and the conversion coefficient. The method can solve the problem of large error of the original method, and can simplify the traditional method for analyzing the rigidity of the laminated structure of the composite material.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any adaptations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
Claims (3)
1. A method for calculating the Tsai modulus of a composite material, the method comprising:
Determining the layering angle and the conversion coefficient of a composite material sample according to the longitudinal tensile modulus range based on a preset corresponding relation between the longitudinal tensile modulus of the composite material, the layering angle and the conversion coefficient, wherein the composite material is a carbon fiber composite material;
Preparing a sample of the composite material according to the determined layering angles and the positive layering angles;
Performing test measurement on the prepared sample to obtain the equivalent longitudinal tensile modulus of the sample;
calculating the Tsai modulus of the composite material according to the equivalent longitudinal tensile modulus of the test sample and the conversion coefficient;
wherein the layering angle and the conversion coefficient in the preset corresponding relation are obtained through statistics of a plurality of known elastic constants of the composite materials;
the step of obtaining the ply angle and the conversion coefficient in the preset corresponding relation through statistics of a plurality of known elastic constants of the composite materials comprises the following steps:
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;
Calculating the Tsai modulus of each known composite material according to the elastic matrix coefficient of each composite material;
setting a virtual laminated board consisting of two kinds of ply angles of the positive and negative ply angles, gradually increasing the ply angle from 0 degree to 90 degrees, and calculating the equivalent longitudinal tensile modulus of the virtual laminated board of any positive and negative ply angle according to the classical laminated board theory;
Obtaining normalized equivalent longitudinal tensile modulus according to the equivalent longitudinal tensile modulus of the virtual laminate and the Tsai modulus of the known composite material;
Drawing a change curve of the equivalent longitudinal tensile modulus of the virtual laminate along with the ply angle and a change curve of the normalized equivalent longitudinal tensile modulus along with the ply angle according to the equivalent longitudinal tensile modulus of the virtual laminate, the normalized equivalent longitudinal tensile modulus and the ply angle respectively;
And obtaining an abscissa and an ordinate of the intensive intersection point according to the intensive intersection point in the curve of the normalized equivalent longitudinal tensile modulus along with the change of the ply angle, wherein the value corresponding to the abscissa is the ply angle, the value of the ordinate is the conversion coefficient, and correcting the obtained ply angle and the conversion coefficient.
2. A method of calculating the Tsai modulus of a composite material according to claim 1,
The sample is a rectangular flat plate tensile sample or a spiral wound round tube sample.
3. A method of calculating the Tsai modulus of a composite material according to claim 1,
The composite material is a thermoplastic composite material or a thermosetting composite material.
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