A method for predicting springback angle of bending corner in laser-assisted automatic placement of composite materials

Abstract

The present invention relates to a method for predicting the springback angle of a bend corner of a laser-assisted automatic placement composite material, comprising the following steps: Step 1: obtaining the properties of the fiber and the resin matrix by experiment or by consulting data; Step 2: fitting the material properties obtained in Step 1 into a function; Step 3: establishing a representative volume element at a microscopic scale. Step 4: performing equivalent processing on the uniaxial deformation results of the representative volume element. Step 5: establishing a mesoscale finite element model. Step 6: equivalent processing of the axial compression behavior of the mesoscale finite element. Step 7: establishing a finite element model of the temperature field of the bend corner forming at a macroscopic scale. Step 8: establishing a finite element model of the springback deformation of the bend corner forming at a macroscopic scale. In the present invention, a multi-scale finite element method is used to simulate the equivalent bending properties of the composite material, so as to realize the prediction of the springback deformation of the composite material during automatic placement forming.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical simulation and relates to a method for predicting the springback angle of a bending corner in laser-assisted automatic placement of composite materials. Background Art

[0002] Continuous fiber reinforced resin matrix composites have great application prospects in aerospace, transportation and other fields due to their high specific strength and good heat resistance. As the demand for composite parts in the aerospace industry continues to grow, the demand for automated forming processes for fiber reinforced composites continues to increase. One of the representative processes of automated forming is the automatic placement process, as shown in the schematic diagram Figure 1 As shown, the process has a high degree of automation and is not limited by processing site, part size and shape, and has great potential in saving time and reducing labor costs.

[0003] When using laser-assisted automatic placement to prepare continuous fiber reinforced composite angle structures, bending rebound occurs, resulting in large angle errors in the product. Forming rate, laser power, and roller pressure have a significant impact on the springback angle of the angle forming.

[0004] The bending rebound phenomenon is caused by the existence of residual stress after bending deformation. When the composite material is bent, the inner side of the bend is compressed, resulting in fiber kinking and resin deformation. The inner material has a certain plastic deformation, but some stress still exists. After unloading, the residual stress is released and the sample rebounds.

[0005] At present, the prediction method for the rebound deformation of automatic placement is only the empirical formula summarized by experiments, and there is a lack of numerical simulation prediction methods. The process of measuring the bending properties of fiber-reinforced composite materials is cumbersome, which not only requires complex experimental equipment and a lot of time, but also has the problem of high cost. The numerical simulation method can predict the rebound deformation of composite materials with different resin matrices and different volume fractions. Compared with the method of summarizing empirical formulas by experiments, the method of numerical simulation has the advantages of high convenience and low cost. Summary of the invention

[0006] The present invention provides a method for predicting the springback angle of a composite material bend during laser-assisted automatic placement, aiming at predicting the angle error caused by the springback deformation of the composite material bend structure.

[0007] The present invention adopts a multi-scale finite element method to first calculate the equivalent performance of the material and then predict the springback deformation of the corner structure. The specific technical solution is as follows:

[0008] Step 1: Obtain the properties of the fiber and resin matrix, including:

[0009] (1) The Young's modulus E1 (50-600 GPa), density ρ1 (1.5-3.0 g / cm³) and thermal conductivity λ1 (0.01-1000 W / (m·K)) of fiber materials vary greatly depending on the specific parameters of the fiber materials. The parameters of the fiber materials are simplified to be temperature-invariant.

[0010] (2) Temperature-dependent Young’s modulus E2 (0.5-5 GPa), density ρ2 (0.5-1.5 g / cm³), thermal expansion coefficient α (40-150 ppm / °C), and thermal conductivity λ2 (0.1-0.5 W / (m·K)) of the resin matrix material;

[0011] (3) Plastic deformation stress-strain curves of resin matrix materials at different temperatures and deformation rates.

[0012] Step 2: Fit the plastic deformation stress curve obtained in step 1 (3) into a function.

[0013] The stress curve after plastic yield of the resin matrix is ​​fitted into a function to establish the equivalent plastic strain , temperature T, equivalent plastic strain rate The relationship function between the three and the yield stress .

[0014] Step 3: Establish a representative volume element at the microscopic scale.

[0015] A representative volume element is established, the material parameters obtained in step 1 and the plastic stress function obtained in step 2 are written into the unit of the volume element, periodic boundary conditions are set for the volume element, and uniaxial strain is applied.

[0016] Step 4: Perform equivalent processing on the uniaxial deformation results of representative volume elements.

[0017] The uniaxial stress in six directions (positive directions of x, y, and z and shear directions of xy, yz, and zx) and the uniaxial strain in six directions as well as the equivalent plastic strain and unit volume of each unit in each frame are extracted. The uniaxial stress, uniaxial strain and equivalent plastic strain of each frame are weighted averaged according to the unit volume to obtain the elastic modulus in six directions at different temperatures.

[0018] The uniaxial stress yield criterion in the reference direction is fitted using the uniaxial stress variation curve in the reference direction. Then, the anisotropy of the material's plasticity is equivalent to the yield stress in the six directions of the volume element at the reference temperature.

[0019] Step 5: Establish the mesoscale finite element model.

[0020] A finite element two-dimensional mesoscale model of the composite material is established, an initial deflection angle is set, and a horizontal pressure is applied. Furthermore, the material properties and anisotropic plastic behaviors obtained in step 4 are written into the units of the mesoscale model.

[0021] Step 6: Equivalent treatment of the mesoscale finite element axial compression behavior.

[0022] According to the stress-strain curve in the horizontal direction, the yield stress of the sample in step 5 is fitted piecewise to obtain the axial equivalent compression behavior of the bending sample.

[0023] Step 7: Establish a finite element model of the temperature field of macro-scale bending forming.

[0024] The sequential coupling method is used to establish a thermal-mechanical coupling model, and the finite element calculation of the temperature field is performed to calculate the temperature field to ensure that the boundaries of the composite material units gradually fit the boundaries of the mold model.

[0025] Step 8: Establish a macro-scale bending angle forming springback deformation finite element model.

[0026] A finite element model of springback deformation during corner forming is established. The model is a pure mechanical analysis model. The temperature field in step 7 is imported into the composite material unit to predict the final springback of the composite material. The predicted springback deformation results are highly consistent with the actual situation.

[0027] The present invention uses a multi-scale finite element method to simulate the equivalent bending performance of composite materials and realize the prediction of the springback deformation of composite materials during automatic placement and forming, which has great market prospects and value. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of the automatic fiber placement process. The composite material is deformed by the pressure of the roller and the heating of the laser.

[0029] Figure 2 The figure is a schematic diagram of a representative volume element of the present invention. The figure is a stress cloud diagram calculated by a representative volume element model established in the finite element software Abaqus. The middle cylinder and four 1 / 4 cylinders are fibers, and the remaining units are resins.

[0030] Figure 3 This is the equivalent effect diagram of the yield stress in the reference direction of the volume element in step 4 of the present invention. The circle in the figure is the extracted average stress, and the surface is the fitted stress function surface. The average stress is all located on the surface after the resin matrix yields, reflecting the accuracy of the surface fitting. In the embodiment of the present invention, it is the zx shear direction.

[0031] Figure 4The figure is a schematic diagram of the mesoscale model of the present invention. The figure is a schematic diagram of the mesoscale model established in the finite element software Abaqus. The model is a two-dimensional model, the unit is a triangular unit, and can only be sheared and deformed. The model is squeezed in the horizontal direction.

[0032] Figure 5 This is the equivalent yield stress result diagram of the mesoscale model of the present invention. The circles in the figure are Figure 4 The average stress in the horizontal direction extracted by the mesoscale model, the ordinate is stress, and the abscissa is the average yield strain of the unit. The surface is the stress function surface obtained by fitting, and the surface fitting is accurate.

[0033] Figure 6 The figure is a macroscopic temperature finite element model diagram of the present invention. The figure is a macroscopic temperature finite element model established in the finite element software Abaqus, a two-dimensional model, which consists of three parts: a pressure roller on the upper left, a composite material in the middle, and a mold at the bottom.

[0034] Figure 7 The finite element result diagram of the macroscopic springback deformation of the present invention is shown in the figure. The stress cloud diagram of the finite element software Abaqus is shown in the figure. The roller moves from left to right, and then the pressure is unloaded. The shape of the composite material after springback deformation is shown in the figure. Figure 7 shown.

[0035] Figure 8 This is a comparison chart between the prediction results of the present invention and the experimental results. DETAILED DESCRIPTION

[0036] The following is a further explanation using carbon fiber reinforced polyetheretherketone composite material (CF / PEEK) as an example.

[0037] Step 1: Obtain the properties of the fiber and resin matrix through experiments or literature, including:

[0038] (1) Young's modulus, density and thermal conductivity of AS4 12k carbon fiber;

[0039] (2) Young’s modulus, density, thermal expansion coefficient and thermal conductivity of VICTREX™ PEEK450G resin

[0040] (3) Plastic yield stress of VICTREX™ PEEK450G resin at different temperatures and deformation rates. The resin parameters of this example are from the literature: Zhuang Jingdong, Huang Zhigao, Zhou Huamin. Research and modeling of mechanical behavior of PEEK under thermoforming conditions. Plastics Industry, 2015, 43(7): 73-77).

[0041] Step 2: Fit the plastic deformation stress obtained in step 1 (3) into a function. The plastic yield stress of the resin matrix is ​​fitted into the Johnson-Cook yield formula, as shown in Formula 1. The specific values ​​are shown in Table 1, T rThe reference temperature is 165°C, T m The melting point is 343°C.

[0042] (1)

[0043] Table 1 Elastic-plastic parameters of VICTREX™ PEEK450G

[0044]

[0045] Step 3: Establish a representative volume element at the microscopic scale

[0046] Representative volume element diagrams are shown in Figure 2 As shown, it consists of complete carbon fiber in the center and 1 / 4 carbon fiber in the four corners. No cohesive force unit and contact are set for the interface. Both fiber and resin units are C3D8 units. A uniaxial strain of -0.1 in six directions is applied to the surface. Periodic boundary conditions are applied to the corresponding surfaces. The implicit analysis module Abaqusstandard is used for calculation.

[0047] Step 4: Perform equivalent processing on the uniaxial deformation results of representative volume elements.

[0048] Use Python to write a script for extracting stress, extract the uniaxial stress in 6 directions (x, y, z positive directions and xy, yz, zx shear directions), uniaxial strain in 6 directions, equivalent plastic strain and unit volume of each unit in each frame, and perform weighted average of the uniaxial stress, uniaxial strain and equivalent plastic strain of each frame according to the unit volume. Obtain the elastic modulus in 6 directions at different temperatures.

[0049] The uniaxial stress change curve in the zx direction of Abaqus is used as the reference direction to fit the uniaxial stress yield criterion in this direction (Formula (2)). The fitting effect at 165°C is shown in Figure 3 Then, the anisotropic plasticity of the material is equivalent to the yield stress in the six directions at the reference temperature (Formula (3), Formula (4)). The specific values ​​are shown in Table 2. In Table 2, E1 represents the Young's modulus in the x direction, G 31 represents the shear modulus in the zx direction, R 11 is the anisotropic plastic parameter in formula (4), and the last 7 rows in Table 2 are the plastic parameters of formula (2).

[0050] (2)

[0051] (3)

[0052] (4)

[0053] Table 2 Equivalent parameters of representative volume element results

[0054]

[0055] Step 5: Establish the mesoscale finite element model.

[0056] Establish a finite element two-dimensional mesoscale model of the composite material, such as Figure 4 As shown, the initial deflection angle is set to 2° and horizontal pressure is applied. Furthermore, the material properties and anisotropic plastic behaviors obtained in step 4 are written into the triangular unit CPS3. Four calculations are performed, and the experimental groups are shown in Table 3.

[0057] Table 3 Mesoscale model experimental group

[0058]

[0059] Step 6: Equivalent treatment of the mesoscale finite element axial compression behavior.

[0060] For the stress-strain curve in the horizontal direction, the yield stress of the sample in step 5 is segmentedly fitted to obtain the axial equivalent compression behavior of the bending sample. The fitting effect of the yield stress at 165°C is shown in Figure 5 , the fitting surface expression is shown in formula (5), and the parameters are shown in Table 4

[0061] (5)

[0062] Table 5 Mesoscale equivalent yield criterion parameters

[0063]

[0064] Step 7: Establish a finite element model of the temperature field of macro-scale bending forming.

[0065] Using the sequential coupling method, a thermo-mechanical coupling model is established, such as Figure 6 As shown, the temperature field finite element calculation is performed to calculate the temperature field to ensure that the deformation of the sample is roughly in line with the actual situation. The contact thermal resistance h between the composite material and the mold and the pressure roller is set to 1650 W / m 2 K. Use Gaussian heat source to simulate the effect of Gaussian laser on the material. The heat source is realized by heat flux. The synchronous movement of the laser is simulated. The speed on the horizontal plane is consistent with the speed along the inclined plane. The heat flux is applied to the upper boundary of the composite material, and the heat flux in the vertical direction remains unchanged. Use the abaqus subroutine vdflux to realize the application of the moving heat source and the calculation of the complex changing temperature field.

[0066] Step 8: Establish a macro-scale bending angle forming springback deformation finite element model.

[0067] Establishing the finite element model of springback deformation during bending is a dynamic mechanical analysis. The time-varying temperature field calculated in step 7 is imported to simulate the springback deformation of the composite material. The die and roller are modeled using analytical rigid bodies, and the friction coefficient between the material and the die is 0.2. Figure 7 is the sample after bending and rebound. The comparison between the predicted results and the experimental results is shown in Figure 8 , the error between the predicted results and the actual experimental results is within 1°.

Claims

1. A method for predicting the springback angle of a curved corner of a composite material during laser-assisted automatic placement, firstly calculating the equivalent performance of the material, and then predicting the springback deformation of the curved corner structure; the steps are as follows: Step 1: Obtain the properties of the fiber and resin matrix, including: (1) The Young's modulus of the fiber material is E1 = 50-600 GPa, and the density is ρ1 = 1.5-3.0 g / cm 3 and thermal conductivity λ1=0.01-1000W / (m·K), which varies greatly according to the different parameters of the specific fiber material, and the parameters of the fiber material are simplified to be invariant with temperature; (2) The Young's modulus of the resin matrix material that changes with temperature is E2 = 0.5-5 GPa, and the density is ρ2 = 0.5-1.5 g / cm 3 , thermal expansion coefficient α = 40-150ppm / ℃ and thermal conductivity λ2 = 0.1-0.5W / (m·K); (3) Plastic deformation stress-strain curves of resin matrix materials at different temperatures and deformation rates; Step 2: Fit the plastic deformation stress curve obtained in step 1 (3) into a function; The stress curve after plastic yield of the resin matrix is ​​fitted into a function, and the relationship function σ=f(ε,T,ε') among the equivalent plastic strain ε, temperature T, equivalent plastic strain rate ε' and yield stress is established; Step 3: Establish a representative volume element at the microscopic scale; Establish a representative volume element, write the material parameters obtained in step 1 and the plastic stress function obtained in step 2 into the unit of the volume element, set periodic boundary conditions for the volume element, and apply uniaxial strain; Step 4: Perform equivalent processing on the uniaxial deformation results of representative volume elements; The uniaxial stress in six directions, the uniaxial strain in six directions, the equivalent plastic strain and the unit volume of each unit in each frame are extracted, and the uniaxial stress, uniaxial strain and equivalent plastic strain of each frame are weighted averaged according to the unit volume to obtain the elastic modulus in six directions at different temperatures; among them, the six directions are the positive directions of x, y, z and the shear directions of xy, yz and zx; The uniaxial stress change curve in the reference direction is used to fit the uniaxial stress yield criterion σ=f(ε,T,ε') in this direction, and then the anisotropy of the plasticity of the material is equivalent to the yield stress in the six directions of the volume element at the reference temperature; Step 5: Establish a mesoscale finite element model; Establish a finite element two-dimensional mesoscale model within the plane of the composite material, set the initial deflection angle, and apply horizontal pressure; further, write the material properties and various anisotropic plastic behaviors obtained in step 4 into the units of the mesoscale model; Step 6: Equivalent treatment of the axial compression behavior of the mesoscale finite element; For the stress-strain curve in the horizontal direction, the yield stress of the sample in step 5 is fitted piecewise to obtain the axial equivalent compression behavior of the bending sample; Step 7: Establish a finite element model of the temperature field of the macro-scale bending angle forming; Use the sequential coupling method to establish a thermal-mechanical coupling model, perform finite element calculation of the temperature field, calculate the temperature field, and ensure that the boundaries of the composite unit gradually fit the boundaries of the mold model; Step 8: Establish a macro-scale bending angle forming springback deformation finite element model; A finite element model of springback deformation during corner forming is established. The model is a pure mechanical analysis model. The temperature field in step 7 is imported into the composite material unit to predict the final springback of the composite material. The predicted springback deformation results are highly consistent with the actual situation.

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