CN106126802A - Investigation on Mechanical Properties of Hollow Integrated Sandwich Composites forecast system - Google Patents

Abstract

The invention relates to a system for predicting the mechanical properties of an integral hollow sandwich composite material, which combines the microscopic unit cell model of the integral hollow sandwich composite material, establishes a graphical user interface based on the GUI module of MATLAB, embeds a mechanical property predicting program, and passes the yarn specification, yarn Input variables such as density, panel thickness, core material height, yarn type, and resin type, etc., call the function to obtain output variables: the stiffness and strength of the overall hollow sandwich composite material in the longitudinal and latitude directions under the side tension (compression) condition, flat tension ( Strength under compression) condition, bending stiffness and strength per unit width in warp and latitude under four-point bending condition. The invention has simple operation, can quickly predict various mechanical properties of the integral hollow interlayer composite material, has high prediction accuracy, can effectively shorten the material design cycle, and reduce test time and cost.

Description

Prediction System of Mechanical Properties of Integral Hollow Sandwich Composite Materials

Technical field:

The invention belongs to the technical field of resin-based composite materials, and in particular relates to a system for predicting the mechanical properties of an integral hollow sandwich composite material, which is used for the working conditions of the integral hollow sandwich composite material in side tension, side compression, flat tension, flat compression, and four-point bending. Prediction of mechanical properties.

Background technique:

The overall hollow sandwich composite material is a new type of sandwich structure material. Compared with traditional sandwich materials, it has the advantages of light weight, delamination resistance, and impact resistance. Wide application prospects. Therefore, it is of great practical significance to accurately predict its mechanical properties.

At present, the prediction of the mechanical properties of the overall hollow sandwich composite material is mainly through the establishment of the material unit cell model, and then the finite element simulation is used to obtain the mechanical properties of the material (see "Mojtaba Sadighi. Finite element simulation and experimental study on mechanical behavior of 3D woven glass fiber composite sandwich panels [J]. Composites Part B, 2013, 55:158-166.”). The three-dimensional solid finite element model can describe the mesoscopic structure and stress distribution of textile composites in detail, but its disadvantages are heavy modeling workload, long calculation time, and inconvenient parameter analysis. Moreover, the structure of the overall hollow sandwich composite material is complex, and there are many parameters to be considered. Therefore, the prediction tool for the mechanical properties of the material is very necessary in the design stage of the material structure.

Invention content:

The purpose of the present invention is to provide a system for predicting mechanical properties of integral hollow sandwich composite materials, which is simple to operate and can more conveniently predict various mechanical properties of integral hollow sandwich composite materials with different structural parameters and material components.

The present invention adopts the following technical solutions: a system for predicting the mechanical properties of an integral hollow sandwich composite material, including a mechanical property forecast model and a visual forecast module; establishing a cellular unit cell model of an integral hollow sandwich composite material, and establishing mechanical properties in MATLAB using an analytical method Prediction model; based on the GUI module of MATLAB, a graphical user interface is established, and the program of the mechanical performance prediction model is embedded in it, and the mechanical performance of the overall hollow sandwich composite material under various working conditions is predicted by function calls, forming a visual prediction system ;

The mechanical performance prediction model includes: on the basis of the mesoscopic unit cell model of the overall hollow sandwich composite material, determine the yarn specification, yarn density, panel thickness, core material height, yarn type and resin type as the mechanical performance prediction The input variables of the system, the stiffness and strength in the latitude and longitude direction under the lateral tension (compression) condition, the strength under the flat tension (compression) condition, and the bending stiffness and strength per unit width in the latitude and longitude direction under the four-point bending condition are the output variables. Forecast models include:

(1) Stiffness performance

Calculate the engineering elastic constant of the unidirectional fiber bundle according to the basic mechanical property parameters of the fiber and resin, and obtain its flexibility matrix from the engineering elastic constant of the unidirectional fiber bundle, and then obtain the stiffness matrix of the unidirectional fiber bundle in the local coordinate system:

C=S ^-1 (1)

Since the material local coordinate system and the overall coordinate system of most yarns inside the material do not coincide, it is an off-axis problem, which needs to be converted to the overall coordinate system through the rotation axis formula:

C _i =TCT' (2)

where T is the transformation matrix, and T' is the transpose of T. According to the respective directions and inclination angles of warp fibers, weft fibers, and pile warps inside the overall hollow sandwich composite material, the stiffness matrix of each group of fiber bundles in the global coordinate system is obtained by using formula (2);

Then according to the geometric structure parameters, the stiffness matrix of each group of fiber bundles is integrated according to the method of volume averaging to obtain the total stiffness matrix of the unit body:

C _g ＝∑λ _i C _i (3)

Finally, the total stiffness matrix is inverted to obtain the total flexibility matrix of the unit body, and then the lateral tensile (compressive) stiffness of the overall hollow sandwich material is obtained.

If only the stiffness properties of the panel part or the core material part of the overall hollow sandwich composite are considered, the above steps can also be used for calculation similarly.

The bending stiffness of the integral hollow sandwich composite is calculated on the basis of the required panel stiffness or core material stiffness. According to the geometric structure parameters of the fabric, the ratio of the bending moment borne by the panel to the total bending moment in pure bending is deduced by using the sandwich beam theory. On this basis, the relationship between the macroscopic bending stiffness of the material and the bending stiffness of the panel can be derived:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Where E _t is the stiffness of the panel, I _t is the moment of inertia of the panel, α is the ratio of the stiffness of the panel to the stiffness of the core material, and β is the ratio of the moment of inertia of the panel to the moment of inertia of the core material.

(2) Side pull, flat pull and bending strength

On the basis of the above material stiffness prediction, the embedded strength criterion is used to predict the lateral tension, flat tension and bending strength of the overall hollow sandwich composite. The failure mode of the material under these three working conditions is mainly the failure of the fiber bundle. The tensile fracture of the fiber bundle is considered in the side tension and flat tension conditions, and the compression failure of the upper panel is considered in the bending condition. Cai-Wu strength can be used. Criteria for strength prediction.

Assuming that the material is subjected to the force σ under the corresponding working condition, the strain of the material in the global coordinate system is obtained by combining the above flexibility matrix:

[ε] _overall = [S] [σ] (5)

Then use the rotation axis formula to obtain the strain of the main load-bearing yarn bundle in the local coordinate system, and then combine the flexibility matrix of the yarn bundle in the local coordinate system to obtain the stress component in the direction of the main axis of the yarn bundle, and finally calculate the stress component Bring in the Cai-Wu strength criterion:

FI＝F ₁ σ ₁ +F ₂ σ ₁ +F ₁₁ σ ₁ ² +F ₂₂ σ ₂ ² +F ₆₆ σ ₁₂ ² +2F ₁₂ σ ₁ σ ₁ ＝1 (6)

in,

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 66</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}}<span\; class="notranslate">\; ,</span>$

X _t , X _c , Y _t , Y _c , and S are the longitudinal tensile strength, longitudinal tensile compressive strength, transverse tensile strength, transverse compressive strength, and shear strength of the fiber bundle, respectively.

Solve equation (6) to get the unknown quantity σ, which is the strength of the corresponding working condition.

(3) Lateral pressure, flat pressure strength

Different from working conditions such as side pull and flat pull, the failure mode of the material under lateral pressure is mainly the instability of the panel, and the failure mode of the material under flat pressure is mainly the instability of the core material, so the strength of these two working conditions can be adopted Criterion for pressure bar instability prediction. On the basis of the aforementioned panel stiffness and core material stiffness predictions, the lateral compression and flat compression strengths are predicted by embedding the compression bar instability criterion. For the instability of the compression bar, Euler's formula can be used to calculate the ultimate load, and then the failure strength can be obtained according to the cross-sectional area of the material's stressed surface. The obtained lateral pressure and flat compressive strength calculation formulas are as follows:

Lateral pressure strength:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; F\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Where E is the stiffness of the panel, t is the thickness of the panel, and L is the height of the panel;

Flat compressive strength:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; c</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Where E _Z is the rigidity of the core material, I is the moment of inertia of the core material, h is the height of the core material, and c is the density of the fleece.

The construction of the visual prediction module includes: establishing a graphical user interface based on the GUI module of MATLAB, embedding the program of the mechanical performance prediction model in it, and predicting the mechanical properties of the overall hollow sandwich composite material under various working conditions through function calls .

The present invention has following beneficial effect:

1. The operation is simple, and the mechanical properties of the overall hollow sandwich composite can be predicted conveniently;

2. The accuracy of the forecast results is high, which can save test time and cost, and shorten the design cycle of materials;

3. Through parametric calculation, the influence trend of different structural parameters on the mechanical properties of materials can be obtained, which can provide certain theoretical guidance for further optimized design of materials.

Description of drawings:

Figure 1 is the flow chart of the algorithm for the mechanical performance prediction model.

Fig. 2 is the parameter input interface of the mechanical performance prediction system of the integral hollow sandwich composite material.

Fig. 3 is the prediction interface of the lateral tension and lateral pressure conditions of the overall hollow sandwich composite material mechanical performance prediction system.

Fig. 4 is the prediction interface of the mechanical performance prediction system of the integral hollow sandwich composite material under the flat tension and flat compression conditions.

Fig. 5 is the prediction interface of the four-point bending condition of the overall hollow sandwich composite material mechanical performance prediction system.

detailed description:

The system for predicting the mechanical properties of the integral hollow sandwich composite material of the present invention includes a mechanical property forecast model and a visual forecast module; the microscopic unit cell model of the integral hollow sandwich composite material is established, and the mechanical property forecast model is established by using the analytical method in MATLAB; the GUI module based on MATLAB A graphical user interface is established, and the program of the mechanical performance prediction model is embedded in it, and the mechanical performance of the overall hollow sandwich composite material under various working conditions is predicted by calling the function, forming a visual prediction system.

The mechanical performance prediction model mainly includes: on the basis of the mesoscopic unit cell model of the overall hollow sandwich composite material, determine the yarn specification, yarn density, panel thickness, core material height, yarn type and resin type as the mechanical performance prediction model. The input variables of the system, the stiffness and strength in the latitude and longitude direction under the lateral tension (compression) condition, the strength under the flat tension (compression) condition, and the bending stiffness and strength per unit width in the longitudinal and weft direction under the four-point bending condition are the output variables. The implementation of the forecasting model is as follows:

(1) Stiffness performance

The calculation of the stiffness performance of the overall hollow sandwich composite material under different working conditions is carried out according to the process shown in Figure 1, and the specific steps for calculating the lateral tension (compression) stiffness are as follows:

Calculate the engineering elastic constant of the unidirectional fiber bundle according to the basic mechanical property parameters of the fiber and resin, and obtain its flexibility matrix from the engineering elastic constant of the unidirectional fiber bundle, and then obtain the stiffness matrix of the unidirectional fiber bundle in the local coordinate system:

C=S ^-1 (1)

Since the material local coordinate system and the overall coordinate system of most yarns inside the material do not coincide, it is an off-axis problem, which needs to be converted to the overall coordinate system through the rotation axis formula:

C _i =TCT' (2)

Where T is the transformation matrix and T' is the transpose of T. According to the respective directions and inclination angles of warp fibers, weft fibers, and pile warps inside the overall hollow sandwich composite material, the stiffness matrix of each group of fiber bundles in the global coordinate system is obtained by using formula (2);

Then according to the geometric structure parameters, the stiffness matrix of each group of fiber bundles is integrated according to the method of volume averaging to obtain the total stiffness matrix of the unit body:

C _g ＝∑λ _i C _i (3)

Finally, the total stiffness matrix is inverted to obtain the total flexibility matrix of the unit body, and then the lateral tensile (compressive) stiffness of the overall hollow sandwich material is obtained.

If only the stiffness properties of the panel part or the core material part of the overall hollow sandwich composite are considered, the above steps can also be used for calculation similarly.

The bending stiffness of the integral hollow sandwich composite is calculated on the basis of the required panel stiffness or core material stiffness. According to the geometric structure parameters of the fabric, the ratio of the bending moment borne by the panel to the total bending moment in pure bending is deduced by using the sandwich beam theory. On this basis, the relationship between the macroscopic bending stiffness of the material and the bending stiffness of the panel can be derived:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Where E _t is the stiffness of the panel, I _t is the moment of inertia of the panel, α is the ratio of the stiffness of the panel to the stiffness of the core material, and β is the ratio of the moment of inertia of the panel to the moment of inertia of the core material.

(2) Side pull, flat pull and bending strength

According to the process shown in Figure 1, on the basis of the above material stiffness prediction, the embedded strength criterion is used to predict the lateral tension, flat tension and bending strength of the overall hollow sandwich composite. The failure mode of the material under these three working conditions is mainly the failure of the fiber bundle. The tensile fracture of the fiber bundle is considered in the side tension and flat tension conditions, and the compression failure of the upper panel is considered in the bending condition. Cai-Wu strength can be used. Criteria for strength prediction.

Assuming that the material is subjected to the force σ under the corresponding working condition, the strain of the material in the global coordinate system is obtained by combining the above flexibility matrix:

[ε] _overall = [S] [σ] (5)

Then use the rotation axis formula to obtain the strain of the main load-bearing yarn bundle in the local coordinate system, and then combine the flexibility matrix of the yarn bundle in the local coordinate system to obtain the stress component in the direction of the main axis of the yarn bundle, and finally calculate the stress component Bring in the Cai-Wu strength criterion:

FI＝F ₁ σ ₁ +F ₂ σ ₁ +F ₁₁ σ ₁ ² +F ₂₂ σ ₂ ² +F ₆₆ σ ₁₂ ² +2F ₁₂ σ ₁ σ ₁ ＝1 (6)

in,

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 66</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}}<span\; class="notranslate">\; ,</span>$

X _t , X _c , Y _t , Y _c , and S are the longitudinal tensile strength, longitudinal tensile compressive strength, transverse tensile strength, transverse compressive strength, and shear strength of the fiber bundle, respectively.

Solve equation (6) to get the unknown quantity σ, which is the strength of the corresponding working condition.

(3) Lateral pressure, flat pressure strength

Different from the working conditions such as side pull and flat pull, the failure mode of the material under lateral pressure is mainly the instability of the panel, and the failure mode of the material under flat pressure is mainly the instability of the core material, so the strength of these two working conditions can be adopted Criterion for pressure bar instability prediction. According to the process shown in Figure 1, on the basis of the aforementioned panel stiffness and core material stiffness prediction, the lateral pressure and flat compression strength are predicted by embedding the pressure bar instability judgment criterion. For the instability of the compression bar, Euler's formula can be used to calculate the ultimate load, and then the failure strength can be obtained according to the cross-sectional area of the material's stressed surface. The obtained lateral pressure and flat compressive strength calculation formulas are as follows:

Lateral pressure strength:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Where E is the stiffness of the panel, t is the thickness of the panel, and L is the height of the panel;

Flat compressive strength:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; c</span>}}{{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Where E _Z is the rigidity of the core material, I is the moment of inertia of the core material, h is the height of the core material, and c is the density of the fleece.

The process of constructing the visual prediction module includes: firstly, based on the GUI module of MATLAB, a graphical user interface is established, and then the program of the mechanical performance prediction model is embedded in it, and the mechanical properties of the overall hollow sandwich composite material under various working conditions are analyzed through function calls. performance forecast.

The present invention adopts MATLAB language and the integral hollow interlayer composite material mechanical performance prediction program written by its GUI module to perform performance prediction: input the yarn specification, yarn density, panel thickness, core material height, and yarn in the overall hollow interlayer composite material Type and resin type, according to the input parameters, the performance prediction model calculates the corresponding stiffness and strength of the overall hollow sandwich composite material under the working conditions of side tension, side compression, flat tension, flat compression and four-point bending, and then through visual prediction The module displays the forecast results and gives the force schematic diagrams of various working conditions.

The present invention realizes the steps of predicting the mechanical properties of the integral hollow sandwich composite material as follows:

1. In the parameter input interface (as shown in Figure 2), input the specifications and densities of the warp, weft and pile warp, select the corresponding fiber and resin type, and then input the panel thickness and core material height of the material;

2. Click the "Calculate" button to enter the parameter pre-output interface (as shown in Figure 3-5), click the "Display" button to get the mechanical performance parameters of the material;

3. Select the working condition selection button in the upper right corner of the parameter output interface to switch to different working conditions for viewing.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, some improvements can also be made without departing from the principle of the present invention, and these improvements should also be regarded as the invention. protected range.

Claims (1)

1. A system for forecasting the mechanical property of an integral hollow interlayer composite material is characterized in that: the system comprises a mechanical property forecasting model and a visual forecasting module; establishing an integral hollow interlayer composite material mesomonas model, and establishing a mechanical property forecasting model in MATLAB by using an analytical method; establishing a graphical user interface based on a GUI module of MATLAB, embedding a program of a mechanical property forecasting model into the graphical user interface, and forecasting the mechanical property of the integral hollow interlayer composite material under various working conditions through function calling to form a visual forecasting system;

the mechanical property forecasting model comprises: on the basis of a mesoscopic unit cell model of the integral hollow interlayer composite material, determining the yarn specification, the yarn density, the panel thickness, the core material height, the yarn type and the resin type as input variables of a mechanical property forecasting system, taking the rigidity and the strength of the warp and weft directions under the side pulling (pressing) working condition, the strength under the horizontal pulling (pressing) working condition and the bending rigidity and the strength of the warp and weft unit width under the four-point bending working condition as output variables, wherein the forecasting model comprises the following steps:

(1) stiffness properties

Calculating the engineering elastic constant of the unidirectional fiber bundle according to the basic mechanical property parameters of the fiber and the resin, obtaining a flexibility matrix of the unidirectional fiber bundle according to the engineering elastic constant of the unidirectional fiber bundle, and further obtaining a rigidity matrix of the unidirectional fiber bundle under a local coordinate system:

C＝S^-1(1)

because the material local coordinate system and the overall coordinate system of most of the yarns in the material are not coincident, the problem of off-axis exists, and the yarns need to be converted into the overall coordinate system through a rotating shaft formula:

C_i＝TCT’ (2)

wherein T is a conversion matrix, T' is the transposition of T, and the rigidity matrix of each group of fiber bundles under the overall coordinate system is obtained by using the formula (2) according to the respective directions and inclination angles of the warp fibers, the weft fibers and the pile warps in the integral hollow interlayer composite material;

then according to the geometric structure parameters, integrating the rigidity matrix of each group of fiber bundles according to a volume averaging method to obtain a total rigidity matrix of the unit body:

C_g＝∑λ_iC_i(3)

finally, inverting the total stiffness matrix to obtain a unit body total flexibility matrix, and further obtaining the side pulling (pressing) stiffness of the integral hollow interlayer material;

calculating the bending rigidity of the integral hollow sandwich composite material on the basis of the rigidity of the panel or the rigidity of the core material, deducing the proportion of the bending moment borne by the panel in pure bending to the total bending moment by using a sandwich beam theory according to the geometric structure parameters of the fabric, and deducing a relational expression of the macroscopic bending rigidity of the material and the bending rigidity of the panel on the basis:

$E_{eq}=\frac{(1+\mathrm{\&alpha;}\mathrm{\&beta;})E_t{I}_t}{\mathrm{\&alpha;}\mathrm{\&beta;}}---\left(4\right)$

wherein E_tFor panel stiffness, I_tPanel moment of inertia, α the ratio of panel stiffness to core stiffness, β the ratio of panel moment of inertia to core stiffness;

(2) side pull, flat pull and bending strength

On the basis of the prediction of the rigidity of the material, the strength criterion is embedded to predict the strength of the integral hollow interlayer composite material by side pulling, horizontal pulling and bending, the failure mode of the material under the three working conditions is mainly the failure of the fiber bundle, wherein the tensile fracture of the fiber bundle is considered under the side pulling and horizontal pulling working conditions, the compression failure of the upper panel is considered under the bending working condition, and the strength prediction can be carried out by adopting the Chua-Wu strength criterion;

and (3) if the stress of the material is sigma under the corresponding working condition, calculating the strain of the material under a general coordinate system by combining the flexibility matrix:

[]_{general of}＝[S]·[σ](5)

And then obtaining the strain of the yarn bundle mainly bearing force under a local coordinate system by using a rotating shaft formula, then solving the stress component of the yarn bundle in the main shaft direction by combining the flexibility matrix of the yarn bundle under the local coordinate system, and finally bringing the obtained stress component into a Cai-Wu strength criterion:

wherein,

$F_1=\frac{1}{X_t}-\frac{1}{X_c},F_2=\frac{1}{Y_t}-\frac{1}{Y_c},F_{11}=\frac{1}{X_t{X}_c},F_{22}=\frac{1}{Y_t{Y}_c},$

$F_{66}=\frac{1}{S^2},F_{12}=\frac{-1}{2\sqrt{X_t{X}_c{Y}_t{Y}_c}},$

X_t、X_c、Y_t、Y_cs is respectively the longitudinal tensile strength, the longitudinal tensile compression strength, the transverse tensile strength, the transverse compression strength and the shear strength of the fiber bundle, and an unknown quantity sigma is obtained by solving an equation (6), namely the strength of the corresponding working condition;

(3) lateral pressure and flat pressure strength

Different from working conditions such as side pulling and horizontal pulling, the failure mode of the material during side pressure is mainly the instability of a panel, the failure mode of the material during horizontal pressing is mainly the instability of a core material, therefore, the strength of the two working conditions can be predicted by adopting a compression bar instability judgment criterion, the compression bar instability judgment criterion is embedded to predict the side pressure and the horizontal pressure strength on the basis of the prediction of the panel rigidity and the core material rigidity, the limit load of the compression bar instability can be solved by adopting an Euler formula, the failure strength can be obtained according to the sectional area of a material stress surface, and the calculation formulas of the obtained side pressure and the horizontal pressure strength are as follows:

side pressure strength:

${\mathrm{\&sigma;}}_{cy}=\frac{{\mathrm{E\&pi;}}^2{t}^2}{6L^2}---\left(7\right)$

wherein E is the panel stiffness, t is the panel thickness, and L is the panel height;

flat pressing strength:

${\mathrm{\&sigma;}}_{pl}=\frac{4E_z{\mathrm{\&pi;}}^{2}Ic}{h^2}---\left(8\right)$

wherein E_ZThe rigidity of the core material is shown, I is the inertia moment of the core material, h is the height of the core material, and c is the density of the pile warp;

the construction of the visual forecasting module comprises the following steps: and establishing a graphical user interface based on a GUI module of the MATLAB, embedding a program of a mechanical property forecasting model into the graphical user interface, and forecasting the mechanical properties of the integral hollow interlayer composite material under various working conditions through calling of functions.