2.5-dimensional automatic tape laying woven composite material microstructure optimization design method

Abstract

The invention discloses a 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method, and relates to the technical field of composite material optimization design. According to the method, whether a delamination layer is expanded or not can be judged according to a criterion established by fracture mechanics, and if the energy release rate of the crack tip is greater than or equal to the critical energy release rate, the delamination layer is expanded; the energy release rate of delamination in a novel woven composite material beam structure is solved through an energy method based on a beam theory, and the value of the energy release rate can be reduced for verifying the rigidity design of a laminated plate, so that delamination expansion is delayed or slowed down. The energy release rate of delamination in the three-point bending beam model can be affected by material combination and the number of parts divided under the same length, the interlayer energy release rate is reduced by changing the microstructure, delamination extension is delayed, and microstructure optimization design is carried out.

Description

Technical Field

[0001] The invention relates to the technical field of composite material optimization design, and in particular to a 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method. Background Art

[0002] The existing commonly used mechanical models for predicting the mechanical properties of automated tape laying woven composites mainly include laminate theory model and finite element model. The research on the optimization design of woven composites mainly focuses on the optimization design of microstructure.

[0003] (1) Laminated plate theory model, assuming that the woven fabric structural unit is a combination of multiple unidirectional plies, and each unidirectional ply has the same fiber volume fraction, and then the stiffness matrix of each ply is integrated into the overall stiffness matrix. This type of model is based on the classical laminate theory and uses the averaging method to calculate the in-plane elastic constants of the woven composite material.

[0004] (2) Finite element analysis model: Analyze the microscopic geometric model of woven fabrics. Use a unit cell model or a representative volume unit model to study the spatial arrangement of fiber bundles, consider factors such as the non-circular cross-sectional shape of the yarn and the buckling of the fiber bundles, and predict the mechanical properties of the fabric such as tension, compression, and post-impact compression.

[0005] (3) Microstructure optimization design, comprehensively considering factors such as material stiffness, unit cell width, unit cell length and weaving depth. By optimizing the material size and weaving process parameters, the material weight, strength, stability, frequency and specific damping capacity are optimized, and multiple homogenized stiffness calculations are performed to finally obtain a micro-skeleton structure with all indicators meeting the design requirements.

[0006] At present, in the field of composite materials, most technologies carry out micro-structure modeling methods for existing structures, and carry out calculation and simulation methods for equivalent elastic modulus, equivalent stiffness and equivalent thermal expansion coefficient of specific structures, but fail to carry out optimization design for achieving specific goals of the structure. Based on the above reasons, the present invention proposes a micro-structure optimization design method for 2.5-dimensional automatic tape laying woven composite materials. Summary of the invention

[0007] 1. Technical issues to be resolved

[0008] In view of the shortcomings of the prior art, the present invention can determine whether a delamination will expand through the criteria established by fracture mechanics. If the energy release rate at the crack tip is greater than or equal to the critical energy release rate, the delamination will expand; the energy release rate of the delamination in the new woven composite beam structure is solved by the energy method based on beam theory, in order to verify that the stiffness design of the laminate can reduce the value of the energy release rate and thus delay or slow down the delamination expansion, and the combination of materials and the number of parts of equal length can affect the energy release rate of the delamination in the three-point bending beam model. The present invention reduces the interlayer energy release rate by changing the mesostructure, thereby delaying the delamination expansion and optimizing the mesostructure design.

[0009] (II) Technical solution

[0010] To achieve the above object, the present invention provides the following technical solution: a 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method, comprising the following steps:

[0011] S1: Determination of material properties of different parts of the composite material to obtain delamination across different sub-laminates in a simple woven composite;

[0012] S2: After determining the material properties, it is also necessary to determine the generalized forces of each part after delamination, which are calculated based on the minimum complementary energy principle and Lagrange number multiplication;

[0013] S3: Calculate the energy release rates at the left and right ends of the delamination based on the generalized force and material stiffness. After obtaining the energy release rates at both ends of the crack, the criterion established by fracture mechanics can be used to determine whether the delamination will expand.

[0014] S4: Optimize the design of 2.5D automated tape laying woven composite laminates based on the combination of materials and the effect of the number of portions of equal length on the woven composite.

[0015] Preferably, the determination of the material properties of the composite material in step S1 includes the neutral axis of each part of the structure containing the matrix and the tensile, bending and shear stiffness, determining the new neutral line NA2 of the sub-laminate area, the neutral line NA1 of the triangular matrix and woven tape area, the neutral line NA of the entire structure and the bending stiffness EI of any part, and the calculation method of the shear deformation stiffness is the same as the calculation method of the tensile stiffness, only needing to replace EA with GA.

[0016] Preferably, the calculation of the generalized force of each part after delamination in step S2 includes the following steps:

[0017] S11: Calculate the complementary energy of the delaminated beam. Delamination divides the three different materials into six parts. x1 is the left axial position of the delaminated beam, x2 is the right axial position of the delaminated beam, and the transition points between different materials are e1 and e2. The neutral lines of the six sub-beams are different. The distances from the neutral lines of the three upper sub-beams to the neutral lines of the three lower sub-beams are c1, c2, and c3 respectively.

[0018] S12: Under the continuous conditions at the positions x=x1, x=e1, x=e2 and x=x2, determine the constraints of the Lagrange multiplier method, and the number of the constraints is the same as the number of Lagrange multiplier factors, and the Lagrange multiplier factors are λ1, λ2, λ3, λ4, λ5 and λ6;

[0019] S13: Differentiate the Lagrange equation with respect to N;

[0020] S14: The Lagrange equation is differentiated for each bending moment and solved to obtain the generalized forces in the delaminated beam.

[0021] Preferably, the objective function of calculating the minimum energy of the delaminated sub-beam by the Lagrange multiplier method in step S11 is:

[0022]

[0023]

[0024] Preferably, the calculation formulas for the energy release rates at the left and right ends of the delamination in step S3 are:

[0025]

[0026] Preferably, the step S4 of optimizing the design of the 2.5-dimensional automatic tape laying woven composite laminate comprises the following steps:

[0027] S21: Establish a model of a woven composite laminate;

[0028] S22: The problem scope of 2.5D woven composite structure optimization is narrowed down to satisfying two objectives under constraints using genetic algorithm;

[0029] S23: Optimizing the weaving method of the 2.5-dimensional woven composite material to meet the constraints based on material properties and dimensions.

[0030] Preferably, in step S21, it is assumed that the influence of the matrix on the material properties of the entire structure is negligible, and a unidirectional woven composite laminate model is established. For a simple woven composite material with a ply sequence of [02 / 45 / -45 / (02w / 902f) / 0]s, the materials of the two main parts are traditional composite laminates with ply sequences of [02 / 45 / -45 / 02 / 902 / 0]s and [02 / 45 / -45 / 902 / 02 / 0]s.

[0031] Preferably, the two constraints in step S22 include:

[0032] (1) Use the same fiber belt;

[0033] (2) The tensile stiffness of the composite laminate is maximum under the constraint of a certain thickness, the bending stiffness of the two main laminate materials that make up the woven composite material is twice that of the other, and the two laminates can be connected using a woven layer.

[0034] (III) Beneficial effects

[0035] Compared with the prior art, the present invention provides a 2.5-dimensional automatic tape-laying woven composite microstructure optimization design method, which has the following beneficial effects: the present invention can determine whether a delamination will expand through the criteria established by fracture mechanics, and if the energy release rate at the crack tip is greater than or equal to the critical energy release rate, then the delamination will expand; the energy release rate of the delamination in the new woven composite beam structure is solved by the energy method based on beam theory, and the stiffness design of the laminate can reduce the value of the energy release rate to delay or slow down the delamination expansion, and the combination of materials and the number of parts with equal length can affect the energy release rate of the delamination in the three-point bending beam model. The present invention reduces the interlayer energy release rate by changing the mesostructure, thereby delaying the delamination expansion and performing mesostructure optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention is an optimization design method flow chart;

[0037] Figure 2 The structural diagram of the present invention includes the substrate region;

[0038] Figure 3 To decouple the bending moment and axial force for the present invention, a new neutral line diagram is established;

[0039] Figure 4 The axial force, shear force and bending moment analysis diagram of different parts after delamination occurs in the present invention;

[0040] Figure 5 A diagram showing the location of delamination in a 2.5-dimensional automated tape-laying woven composite laminate optimized by the present invention;

[0041] Figure 6 Comparison of the analytical energy release rate of delamination in the 2.5D automated tape-laying woven composite laminate optimized by the present invention with the finite element results Figure 1 ;

[0042] Figure 7 Comparison of the analytical energy release rate of delamination in the 2.5D automated tape-laying woven composite laminate optimized by the present invention with the finite element results Figure 2 . DETAILED DESCRIPTION

[0043] In order to better understand the purpose, structure and function of the present invention, in order to achieve structural optimization of 2.5-dimensional automatic tape laying woven composite materials, the present invention can determine whether a delamination will expand through the criteria established by fracture mechanics. If the energy release rate at the crack tip is greater than or equal to the critical energy release rate, then the delamination will expand; the energy release rate of the delamination in the new woven composite beam structure is solved by the energy method based on beam theory, in order to verify that the stiffness design of the laminate can reduce the value of the energy release rate and thus delay or slow down the delamination expansion, and the combination of materials and the number of parts of equal length can affect the energy release rate of the delamination in the three-point bending beam model. The present invention reduces the interlayer energy release rate by changing the microstructure, so as to delay the delamination expansion and perform microstructure optimization design. A 2.5-dimensional automatic tape laying woven composite mesostructure optimization design method of the present invention is further described in detail.

[0044] Example 1: Reference Figure 1-4 The present invention: A 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method, comprising the following steps:

[0045] S1: Determination of material properties of different parts of the composite material to obtain delamination across different sub-laminates in a simple woven composite;

[0046] Furthermore, the material properties of the composite material are determined, including the neutral axis of each part of the structure containing the matrix and the tensile, bending and shear stiffness, the new neutral line NA2 of the sub-laminate area, the neutral line NA1 of the triangular matrix and woven belt area, the neutral line NA of the entire structure and the bending stiffness EI of any part, and the calculation method of shear deformation stiffness is the same as that of tensile stiffness, just replace EA with GA;

[0047] Specifically, in order to decouple the bending moment and axial force in the complementary energy expression, a new neutral line needs to be established, such as Figure 2 As shown in Figure 2, after the neutral line is repositioned, the axial force contributes to the bending moment. The distance from the original neutral line to the new neutral line is t. dTherefore, the complementary energy formula is

[0048]

[0049] N and M are force and bending moment respectively, a 11 and b 11 are the elements in the flexibility matrix abd (abd flexibility matrix is ​​the inverse matrix of ABD stiffness matrix), decoupling, so that d 11 Mn d +b 11 MN is zero, so we get

[0050]

[0051] The new tensile stiffness is: The bending stiffness is:

[0052] The neutral line of the entire structure is represented by NA. The neutral line of the entire structure is calculated as follows: Where E is the tensile modulus of the material, A is the area of ​​the cross section, and y is the distance from the bottom position to the neutral line;

[0053] The bending stiffness of any part can be expressed as:

[0054] EI=Σ(EI) i , (EI) i is the bending stiffness of the ith section and is calculated as follows:

[0055] Among them I c is the moment of inertia about the centerline, d i is the distance from the centerline to the i-th section. The tensile stiffness of the matrix region is the sum of the tensile stiffness of the woven tape, the triangle region, and the sublaminate region with a layup of [0 / 90 / 05 / 905].

[0056] S2: After determining the material properties, it is also necessary to determine the generalized forces of each part after delamination, which are calculated based on the minimum complementary energy principle and Lagrange number multiplication;

[0057] Furthermore, the calculation of the generalized forces of each part after delamination includes the following steps:

[0058] S11: Calculate the complementary energy of the delaminated beam. Delamination divides the three different materials into six parts. x1 is the left axial position of the delaminated beam, x2 is the right axial position of the delaminated beam, and the transition points between different materials are e1 and e2. The neutral lines of the six sub-beams are different. The distances from the neutral lines of the three upper sub-beams to the neutral lines of the three lower sub-beams are c1, c2, and c3 respectively.

[0059] Specifically, the axial force, shear force and bending moment analysis of different parts are as follows: Figure 4 As shown. From the equilibrium equation in the x direction, we can conclude that:

[0060]

[0061] The objective function of calculating the minimum energy of the delaminated sub-beam by the Lagrange multiplier method is:

[0062]

[0063] S12: Under the continuous conditions at the positions x=x1, x=e1, x=e2 and x=x2, determine the constraints of the Lagrange multiplier method, and the number of the constraints is the same as the number of Lagrange multiplier factors, and the Lagrange multiplier factors are λ1, λ2, λ3, λ4, λ5 and λ6;

[0064] Specifically, the constraints of the Lagrange multiplier method are:

[0065] S13: Differentiate the Lagrange equation with respect to N,

[0066]

[0067] S14: Lagrange equations are differentiated for each bending moment and solved to obtain the generalized forces in the delaminated beam;

[0068]

[0069] The constants are:

[0070]

[0071] S3: Calculate the energy release rates at the left and right ends of the delamination based on the generalized force and material stiffness. After obtaining the energy release rates at both ends of the crack, the criterion established by fracture mechanics can be used to determine whether the delamination will expand.

[0072] Specifically, the calculation formulas for the energy release rates at the left and right ends of the delamination are:

[0073]

[0074] S4: Optimize the design of 2.5D automated tape laying woven composite laminates based on the combination of materials and the effect of the number of portions of equal length on the woven composites.

[0075] Specifically, the optimization design of the 2.5D automatic tape laying woven composite laminate includes the following steps:

[0076] S21: Establish a woven composite laminate model, assuming that the influence of the matrix on the material properties of the entire structure can be ignored, and establish a unidirectional woven composite laminate model. For a simple woven composite material with a ply sequence of [02 / 45 / -45 / (02w / 902f) / 0]s, the materials of the two main parts are traditional composite laminates with plies of [02 / 45 / -45 / 02 / 902 / 0]s and [02 / 45 / -45 / 902 / 02 / 0]s;

[0077] S22: The problem scope of 2.5D woven composite structure optimization is narrowed down to satisfying two objectives under constraints using genetic algorithm;

[0078] More specifically, the two constraints include:

[0079] (1) Use the same fiber belt;

[0080] (2) The tensile stiffness of the composite laminate is maximum under the constraint of a certain thickness, the bending stiffness of the two main laminate materials that make up the woven composite material is twice that of the other, and the two laminates can be connected using a woven layer.

[0081] S23: Optimizing the weaving method of the 2.5-dimensional woven composite material to meet the constraints based on material properties and dimensions.

[0082] Example 2, the present invention provides a 2.5-dimensional automatic tape laying woven composite material micro-structure optimization design method, and establishes an optimized automatic tape laying woven composite material [(902 / 45) f / (02 / -45 / 02) w / 02] s , according to the above process, the delamination energy release rate of the optimized analytical model is determined and compared with the delamination energy release rate of the finite element method;

[0083] The length of the woven composite laminate beam model is L = 60 mm, the thickness is t = 3 mm, the position of the delamination in the thickness is t1 / t = 2 / 5, t1 is the thickness of the upper sublayer, and the axial position of the left end of the delamination is x1 = 0.1L;

[0084] In the analytical model, the matrix region is neglected and two conventional composite laminates [902 / 45 / 02 / -45 / 04] s and [02 / -45 / 02 / 902 / 45 / 02] s The delamination of different lengths in the optimized automatic tape laying woven composite laminate [(902 / 45) f / (02 / -45 / 02) w / 02]s The position in the structure is Figure 5 As shown;

[0085] The comparison of the delamination energy release rate in the analytical model and the delamination energy release rate in the finite element model is shown in Figure 2. Figure 6 and Figure 7 As shown in the figure, the difference at the peak of the energy release rate at the left end of the delamination is 22.4%, and the difference at the maximum value of the energy release rate at the right end is 14.3%. Generally speaking, the energy release rate obtained by the analytical method is slightly smaller than that obtained by the finite element model.

[0086] In summary, compared with traditional plies, cracks propagate faster without changing direction. The optimized structure can force cracks to change their propagation direction and delay or slow down crack propagation.

[0087] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method, characterized in that: The steps include: S1: Determination of material properties of different parts of the composite material to obtain delamination across different sub-laminates in a simple woven composite; S2: After determining the material properties, it is also necessary to determine the generalized forces of each part after delamination, which are calculated based on the minimum complementary energy principle and Lagrange number multiplication; S3: Calculate the energy release rates at the left and right ends of the delamination based on the generalized force and material stiffness. After obtaining the energy release rates at both ends of the crack, the criterion established by fracture mechanics can be used to determine whether the delamination will expand. S4: Optimize the design of 2.5D automated tape laying woven composite laminates based on the combination of materials and the effect of the number of portions of equal length on the woven composite.

2. The method for optimizing the microstructure of a 2.5-dimensional automatic tape laying woven composite material according to claim 1, characterized in that: The material properties of the composite material in step S1 are determined, including the neutral axis of each part of the structure containing the matrix and the tensile, bending and shear stiffness, determining the new neutral line NA2 of the sub-laminate area, the neutral line NA1 of the triangular matrix and woven belt area, the neutral line NA of the entire structure and the bending stiffness EI of any part, and the calculation method of the shear deformation stiffness is the same as the calculation method of the tensile stiffness, only needing to replace EA with GA.

3. A 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method according to claim 2, characterized in that: The calculation of the generalized force of each part after delamination in step S2 includes the following steps: S11: Calculate the complementary energy of the delaminated beam. Delamination divides the three different materials into six parts. x1 is the left axial position of the delaminated beam, x2 is the right axial position of the delaminated beam, and the transition points between different materials are e1 and e2. The neutral lines of the six sub-beams are different. The distances from the neutral lines of the three upper sub-beams to the neutral lines of the three lower sub-beams are c1, c2, and c3 respectively. S12: Under the continuous conditions at the positions x=x1, x=e1, x=e2 and x=x2, determine the constraints of the Lagrange multiplier method, and the number of the constraints is the same as the number of Lagrange multiplier factors, and the Lagrange multiplier factors are λ1, λ2, λ3, λ4, λ5 and λ6; S13: Differentiate the Lagrange equation with respect to N; S14: The Lagrange equation is differentiated for each bending moment and solved to obtain the generalized forces in the delaminated beam.

4. A 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method according to claim 3, characterized in that: The objective function of calculating the minimum energy of the delaminated sub-beam by the Lagrange multiplier method in step S11 is:

5. The method for optimizing the microstructure of a 2.5-dimensional automatic tape laying woven composite material according to claim 1, characterized in that: The calculation formulas for the energy release rates at the left and right ends of the delamination in step S3 are:

6. The method for optimizing the microstructure of a 2.5-dimensional automatic tape laying woven composite material according to claim 1, characterized in that: The step S4 includes optimizing the design of the 2.5-dimensional automatic tape laying woven composite laminate, and includes the following steps: S21: Establish a model of a woven composite laminate; S22: The problem scope of 2.5D woven composite structure optimization is narrowed down to satisfying two objectives under constraints using genetic algorithm; S23: Optimizing the weaving method of the 2.5-dimensional woven composite material to meet the constraints based on material properties and dimensions.

7. A 2.5-dimensional automatic tape laying woven composite material microstructure optimization design method according to claim 6, characterized in that: In step S21, it is assumed that the influence of the matrix on the material properties of the entire structure is negligible, and a unidirectional woven composite laminate model is established. For a simple woven composite material with a ply sequence of [02 / 45 / -45 / (02w / 902f) / 0]s, the materials of the two main parts are traditional composite laminates with ply sequences of [02 / 45 / -45 / 02 / 902 / 0]s and [02 / 45 / -45 / 902 / 02 / 0]s.

8. The method for optimizing the microstructure of a 2.5-dimensional automatic tape laying woven composite material according to claim 6, characterized in that: The two constraints in step S22 include: (1) Use the same fiber belt; (2) The tensile stiffness of the composite laminate is maximum under the constraint of a certain thickness, the bending stiffness of the two main laminate materials that make up the woven composite material is twice that of the other, and the two laminates can be connected using a woven layer.

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