Method for inverting parameters of intrinsic strain model based on curing deformation of composite material

Abstract

The invention belongs to the technical field of composite material curing deformation prediction, and particularly discloses a method for inverting parameters of an intrinsic strain model based on composite material curing deformation, which is used for solving the problem that the intrinsic strain model lacks a method for accurately and simply acquiring input parameters when the intrinsic strain model is used for predicting PID (Proportion Integration Differentiation). Comprising the following steps: forming a flat plate piece and an L-shaped component by using a curing process period recommended by a manufacturer, and obtaining a deformation field of a curing forming piece; determining the rebound deformation of the L-shaped component by using a flange tangent included angle, and inverting the intrinsic strain of the single-layer composite material in the first direction and the third direction by combining a rebound deformation analytical formula of the L-shaped component; solving the mechanical properties of the composite material according to the self-consistent field mesomechanics model; and using a quadratic curve fitting curvature to determine the buckling deformation of the flat plate piece after curing molding, and inverting the intrinsic strain of the single-layer composite material in the direction 2 according to the buckling deformation result of the flat plate piece. The intrinsic strain model parameter acquisition method provided by the invention is simple and better in implementability.

Description

Technical Field

[0001] The present invention belongs to the technical field of composite material curing deformation prediction, and particularly relates to a method for inverse-inverting the parameters of the eigenstrain model based on the curing deformation of composite materials. Background Art

[0002] Composite material structures are widely used in the fields of aerospace and civil industries due to their excellent properties such as high modulus, high specific strength, corrosion resistance, and fatigue resistance. For thermosetting composite materials, during the curing process, due to the mismatch between the thermal expansion coefficient and the chemical shrinkage coefficient of the material, the interaction between the mold and the part, etc., residual stresses are generated and accumulated inside the material, causing the part to deform (such as warping and springback) after demolding. This kind of deformation is called process-induced deformation (PID) or curing deformation. The deformation of composite material parts will affect the assembly accuracy, thus forming assembly gaps, generating assembly stresses, and reducing the service life, performance, and reliability of composite material components. In order to reduce the PID of composite material parts and shorten the R & D cycle of composite material products, accurately and quickly predicting PID is one of the most important problems in the manufacturing process of composite material parts.

[0003] Traditional PID prediction methods can be divided into analytical methods and numerical methods. For the curing deformation of simple structures, the analytical method can be used for rapid prediction, mainly based on the classical laminate theory and the method based on the deformation mechanism, which is convenient for studying the influence of single parameters or coupling parameters of composite materials. The numerical method is the most widely used method for predicting the curing residual stress and PID of composite materials, especially suitable for structures with complex geometries, but it often requires a large amount of computing time. In recent years, algorithms for predicting PID using neural networks have emerged continuously. The advantage is that it can quickly obtain results when facing research that requires a large amount of calculation, but there are still limitations when facing complex structural parts. The finite element simulation analysis in the numerical method is currently the mainstream method for curing deformation prediction, and some researchers are working hard to reduce the time used to predict PID using the finite element analysis method. Using the eigenstrain model to describe the material stress-strain relationship in finite element analysis to predict PID is one of the effective solutions, but the eigenstrain model lacks an accurate and simple method to obtain input parameters. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for inverse-inverting the parameters of the eigenstrain model based on the curing deformation of composite materials, effectively solving the problem that the eigenstrain model lacks an accurate and simple method to obtain input parameters when using the eigenstrain model to predict PID.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for inverting the parameters of the eigenstrain model based on the curing deformation of composite materials, comprising the following steps: S1. Using the curing process cycle recommended by the manufacturer to mold flat components and L-shaped components, and obtaining the deformation field of the cured components; S2. Using the flange tangent angle to determine the springback deformation after the L-shaped component is cured and formed, and combining the springback deformation analysis formula of the L-shaped component to invert the eigenstrains in the 1-direction and 3-direction of the single-layer composite material, where the 1-direction is the fiber direction of the composite material and the 3-direction is the thickness direction of the composite material; S3. Solving the mechanical properties of the composite material according to the self-consistent field micromechanics model; S4. Using the quadratic curve fitting curvature to determine the warpage deformation after the flat component is cured and formed, and inverting the eigenstrain in the 2-direction of the single-layer composite material according to the warpage deformation result after the flat component is cured and formed, where the 2-direction is the direction perpendicular to the fiber direction of the composite material.

[0007] Further, in step S1, three L-shaped components with the flange direction as the fiber direction are molded using the curing process cycle recommended by the manufacturer, and a flat component with a ply of [907 / 07] is molded, and the surface of the component is obtained using a laser scanner.

[0008] Further, in step S2, first, calculate the springback angle according to the surface of the L-shaped component after curing and forming, and substitute the structural parameters of the three L-shaped components into the analysis formula:

[0009]

[0010] where

[0011] where Δθ t is the springback angle of the L-shaped component, is the non-mechanical strain in the thickness direction in the rubber state, v ZR is the Poisson's ratio in the flange direction, is the non-mechanical strain in the flange direction in the rubber state, θ is the fillet angle, is the in-plane thermal expansion coefficient in the glass state, is the thermal expansion coefficient in the thickness direction in the glass state, ΔT1 is the temperature difference in the glass state, G θR is the interlaminar shear modulus of the composite material in the rubber state, E θ is the elastic modulus in the flange direction of the composite material in the rubber state, R is the fillet radius, L is the flange length, and t is the thickness of the L-shaped component.

[0012] The fillet radius R, the fillet angle θ, the flange length L, and the thickness t of the L-shaped component are all known structural parameters.

[0013] Secondly, for the L-shaped component in step S1, assume ΔT1 = 1, m = G θR / Eθ , obtain:

[0014]

[0015] where ΔT2 is the pseudo temperature difference in the rubber state,

[0016] Solve the three sets of equations simultaneously to determine the eigenstrain α1 in the 1 direction of the single-layer composite material: and the eigenstrain α3 in the 3 direction:

[0017] Furthermore, in step S3, use the m value in step S2 to solve for the elastic modulus and shear modulus of the composite material in the rubber state. Assuming that the elastic modulus of the composite material in the rubber state is equal to that in the glass state, the elastic modulus and shear modulus of the composite material in the rubber state are obtained on the premise of satisfying the self-consistent field micromechanics model. Then, the matrix elastic modulus and matrix shear modulus values are obtained through the elastic modulus and shear modulus of the composite material in the rubber state. At the same time, all mechanical properties of the composite material in the rubber state and glass state are obtained through the self-consistent field micromechanics model.

[0018] The theoretical formula of the self-consistent field micromechanics model is:

[0019]

[0020] where E1, E2, and E3 are the elastic moduli in the 1, 2, and 3 directions of the composite material, respectively, G 12 , G 13 , G 23 are the shear moduli in the 1, 2, and 3 directions of the composite material, respectively, v 12 , v 13 , v 23 are the Poisson's ratios in the 1, 2, and 3 directions of the composite material, respectively, E 1f is the longitudinal elastic modulus of the fiber, V f is the fiber volume content percentage, E r is the matrix elastic modulus of the composite material, G r is the matrix shear modulus of the composite material, v r is the matrix Poisson's ratio of the composite material, v 12f is the fiber longitudinal and transverse Poisson's ratio, G 12f is the fiber longitudinal and transverse shear modulus, G 23f is the fiber transverse isotropic plane shear modulus.

[0021] Furthermore, since there is a proportional relationship between the warpage amount and the coefficient of thermal expansion after the flat component is cured and formed, a finite element model with a layup of [907 / 07] is established, and the eigenstrain is input into the finite element model as a pseudo-thermal strain parameter. Among them, the eigenstrain α2 in the 2 direction of the single-layer composite material is respectively taken as 0.8×α3, α3, and 1.2×α3 for simulation.

[0022] The deformation curvature is fitted by the quadratic function shown in the following formula, and the linear relationship between α2 and the deformation curvature is constructed. The eigenstrain α2 in the 2 direction of the single-layer composite material is solved according to the deformation curvature after the actual flat component is cured and formed:

[0023] z p = k1x p 2 + k2x p + b;

[0024]

[0025] where x p is the cross-sectional length of the flat component after curing and forming, z p is the warpage amount of the flat component after curing and forming, k1, k2, and b are all formula coefficients, and K c is the deformation curvature of the flat component after curing and forming.

[0026] Compared with the prior art, the beneficial technical effects of the present invention are:

[0027] (1) The eigenstrain model proposed by the present invention has a simple structure, reduces the number of parameters in the curing deformation simulation, and only needs to measure the mechanical properties of the fibers.

[0028] (2) The method for obtaining the eigenstrain model parameters proposed by the present invention is simple, only requires 3 L-shaped components and 1 flat component, and has better feasibility.

[0029] (3) The present invention inversely calculates the curing deformation parameters from the component scale, reduces the measurement error of obtaining parameters from the material scale, and improves the prediction accuracy of curing deformation.

[0030] (4) The constitutive model proposed by the present invention has higher calculation efficiency and lower requirements for computer hardware. Brief Description of the Drawings

[0031] Figure 1 is a flowchart of the present invention for inversely calculating the eigenstrain model parameters based on the curing deformation of the composite material.

[0032] Figure 2 is the curing process cycle recommended by the manufacturer.

[0033] Figure 3 is a schematic structural diagram of the L-shaped component (a) and the flat component (b).

[0034] Figure 4 It is a schematic diagram of the relationship between the eigenstrain in the 2 direction and the deformation curvature of the flat component with a ply of [907 / 07].

[0035] Figure 5 It is the analytical solution (a), numerical solution (b) of the springback of the L-shaped component and its error nephogram (c) when the diameter-thickness ratio and length-thickness ratio change.

[0036] Figure 6 It is a comparison chart of the experimental results and simulation results of the formed flat component when the ply angle, size, and number of layers change. Detailed implementation mode

[0037] Example 1: In this example, the CCF800H / AC531 material system is selected, and unidirectional composite materials are used to form L-shaped components and flat components, and the method of the present invention for inversely calculating the eigenstrain model parameters based on the curing deformation of composite materials is described in detail.

[0038] As Figure 1 shown, it includes the following steps: S1. Use the curing process cycle recommended by the manufacturer (as Figure 2 shown) to form three L-shaped components with the flange direction as the fiber direction (the flange length is 100 mm, the width is 10 mm, the thicknesses are 2 mm, 3 mm, and 4 mm respectively, the fillet angle is 90 degrees, and the radius of the R corner is 20 mm), and form a flat component (the ply is [907 / 07], and the size is 200 mm × 200 mm), as Figure 3 shown. Use a laser scanner to obtain the surface of the component.

[0039] S2. Use the included angle of the flange tangent to determine the springback deformation after the L-shaped component is cured and formed, and inversely calculate the eigenstrain parameters in the 1 direction and 3 direction of the single-layer composite material in combination with the analytical formula of the springback deformation of the L-shaped component, where the 1 direction is the fiber direction of the composite material, and the 3 direction is the thickness direction of the composite material.

[0040] The specific steps are as follows: First, calculate the springback angle according to the surface of the L-shaped component after curing and forming, substitute the structural parameters of the three L-shaped components into the analytical formula, and construct a system of equations. The analytical formula for the curing deformation of the L-shaped component is as follows:

[0041]

[0042] Among them,

[0043] Among them, Δθ t is the springback angle of the L-shaped component, is the non-mechanical strain in the thickness direction in the rubber state, v ZR is the Poisson's ratio in the flange direction, is the non-mechanical strain in the rubber flange direction, θ is the fillet angle, is the in-plane thermal expansion coefficient of the glass state, is the thermal expansion coefficient in the thickness direction of the glass state, ΔT1 is the temperature difference in the glass state, G θR is the interlaminar shear modulus of the composite material in the rubber state, E θ is the elastic modulus of the composite material in the flange direction when it is in the rubber state, R is the fillet radius, L is the flange length, and t is the thickness of the L-shaped component.

[0044] The known structural parameters are fillet radius R=20, fillet angle θ=90, flange length L=100 and L-shaped component thickness t of 2, 3 and 4 respectively.

[0045] Secondly, simplify the unknowns in the equations. For the L-shaped component in step S1,

[0046] Assumptions ΔT1=1,m=G θR / E θ Substituting each value into formula (1), we can get formula (2):

[0047]

[0048] Among them, ΔT2 is the pseudo temperature difference in the rubber state,

[0049] The unknowns in the analytical formula are simplified to m, and ΔT2, solve the three unknowns through the simultaneous equations: m = 37805, ΔT2 = 1.76. This step determines the intrinsic strain α1 in the 1 direction of the single-layer composite material: And the eigenstrain α3 in the 3-direction:

[0050] S3. Among the mechanical properties of the composite material, only the matrix elastic modulus and the matrix shear modulus are unknown. The matrix elastic modulus and the matrix shear modulus of the composite material are solved using the m value in step S2.

[0051] Formula m=G θR / E θ The shear modulus and elastic modulus in are the properties of the composite material in the rubber state, and their values ​​are difficult to calibrate. Assuming that the elastic modulus of the composite material in the rubber state is equal to that in the glassy state, the elastic modulus of the composite material in the rubber state can be obtained under the premise of satisfying the self-consistent field micromechanics model: θ =E1=170120.85MPa and shear modulus G θR =G 12= 4.50 MPa; then, the matrix elastic modulus E is obtained from the elastic modulus and shear modulus of the composite material in the rubber state r = 5908.00 MPa and the matrix shear modulus G r = 1.23 MPa. At the same time, all mechanical properties of the composite material in the rubber state and glass state are obtained through the self-consistent field micromechanics model.

[0052] The theoretical formula of the self-consistent field micromechanics model is:

[0053]

[0054] where E1, E2, and E3 are the elastic moduli of the composite material in the 1st, 2nd, and 3rd directions respectively, G 12 , G 13 , G 23 are the shear moduli of the composite material in the 1st, 2nd, and 3rd directions respectively, v 12 , v 13 , v 23 are the Poisson's ratios of the composite material in the 1st, 2nd, and 3rd directions respectively, E 1f is the longitudinal elastic modulus of the fiber, V f is the fiber volume content percentage, E r is the matrix elastic modulus of the composite material, G r is the matrix shear modulus of the composite material, v r is the matrix Poisson's ratio of the composite material, v 12f is the fiber longitudinal and transverse Poisson's ratio, G 12f is the fiber longitudinal and transverse shear modulus, G 23f is the fiber transverse isotropic plane shear modulus.

[0055] S4. Use the quadratic curve fitting curvature to determine the warping deformation of the flat component after curing and forming. According to the warping deformation result of the flat component after curing and forming, the eigenstrain α2 in the 2nd direction of the single-layer composite material is inversed, where the 2nd direction is the direction perpendicular to the composite material fiber.

[0056] Since there is a proportional relationship between the warping amount of the flat component after curing and forming and the thermal expansion coefficient, a finite element model with a layup of [907 / 07] is established, and the eigenstrain is input into the finite element model as a pseudo-thermal strain parameter, where α2 is taken as 0.8×α3, α3, and 1.2×α3 respectively for simulation.

[0057] Use the quadratic function shown in the following formula to fit the deformation curvature and construct a linear relationship between α2 and the deformation curvature, as Figure 4 shown. Solve the eigenstrain α2 in the 2nd direction of the single-layer composite material according to the actual deformation curvature of the flat component: α2 = 0.00508:

[0058] z p = k1xp 2 + k2x p + b;

[0059]

[0060] Wherein, x p is the cross-sectional length of the flat component after curing and forming, z p is the warpage amount of the flat component after curing and forming (as shown in the coordinate system of the flat component in Figure 6 ), k1, k2, and b are all formula coefficients, and K c is the deformation curvature of the flat component after curing and forming.

[0061] Using the eigenstrain model parameters obtained by inversion for curing simulation, with the diameter-to-thickness ratio length-to-thickness ratio of the L-shaped component with the flange direction as the fiber direction as variables respectively, calculate the analytical solution and numerical solution of springback. The results are as Figure 5 shown, and the error between the analytical solution and the numerical solution is within 10%. Change the ply angle, size, and number of layers to form flat components, measure the deformation curvature, and compare it with the simulation results. As Figure 6 shown, the error is within 6%.

[0062] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples either. Changes, modifications, additions, or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for inverting intrinsic strain model parameters based on composite material curing deformation, characterized in that: The following steps are involved: S1. Forming a flat plate component and an L-shaped component using a curing process cycle recommended by the manufacturer, and obtaining the deformation field of the cured molded component; S2. Use the flange tangent angle to determine the springback deformation of the L-shaped component after curing and forming, and combine the springback deformation analytical formula of the L-shaped component to invert the eigenstrain of the single-layer composite material in directions 1 and 3, where direction 1 is the fiber direction of the composite material and direction 3 is the thickness direction of the composite material; S3. Solve the mechanical properties of composite materials based on the self-consistent field micromechanics model; S4. Use a quadratic curve to fit the curvature to determine the warping deformation of the flat plate component after solidification, and invert the intrinsic strain of the single-layer composite material in two directions based on the warping deformation result after solidification of the flat plate component, wherein the two directions are perpendicular to the fiber direction of the composite material.

2. The method for inverting intrinsic strain model parameters based on composite material solidification deformation according to claim 1, characterized in that: In step S1, three L-shaped components with flange directions in the fiber direction are formed using the curing process cycle recommended by the manufacturer, a flat plate component with a ply of [907 / 07] is formed, and the component surface is obtained using a laser scanner.

3. The method for inverting intrinsic strain model parameters based on composite material solidification deformation according to claim 2, characterized in that: In step S2, first, the springback angle is calculated according to the profile of the L-shaped component after solidification, and the structural parameters of the three L-shaped components are substituted into the analytical formula: in, Among them, Δθ t is the springback angle of the L-shaped member, is the non-mechanical strain in the thickness direction of the rubber state, v ZR is the Poisson’s ratio in the flange direction, is the non-mechanical strain in the rubber flange direction, θ is the fillet angle, is the in-plane thermal expansion coefficient of the glass state, is the thermal expansion coefficient in the thickness direction of the glass state, ΔT1 is the temperature difference in the glass state, G θR is the interlaminar shear modulus of the composite material in the rubber state, E θ is the elastic modulus of the composite material in the flange direction when in the rubber state, R is the fillet radius, L is the flange length, and t is the thickness of the L-shaped component; The fillet radius R, fillet angle θ, flange length L and L-shaped component thickness t are all known structural parameters; Secondly, for the L-shaped component in step S1, Assumptions ΔT1=1,m=G θR / E θ ,get: Among them, ΔT2 is the pseudo temperature difference in the rubber state, The three equations are solved together to determine the eigenstrain α1 of the single-layer composite material in the 1 direction: And the eigenstrain α3 in the 3-direction:

4. The method for inverting intrinsic strain model parameters based on composite material solidification deformation according to claim 3, characterized in that: In step S3, the elastic modulus and shear modulus of the composite material in the rubber state are solved by using the m value of step S2. Assuming that the elastic modulus of the composite material in the rubber state is equal to the value of the glassy state, the elastic modulus and shear modulus of the composite material in the rubber state are obtained on the premise of satisfying the self-consistent field micromechanics model, and then the values ​​of the matrix elastic modulus and matrix shear modulus are obtained by the elastic modulus and shear modulus of the composite material in the rubber state, and all mechanical properties of the composite material in the rubber state and the glassy state are obtained by the self-consistent field micromechanics model. The theoretical formula of the self-consistent field micromechanics model is: Among them, E1, E2, and E3 are the elastic moduli of the composite material in directions 1, 2, and 3, respectively. 12 , G 13 , G 23 are the shear moduli of the composite material in directions 1, 2, and 3, respectively, and v 12 、v 13 、v 23 are the Poisson's ratios of the composite materials in directions 1, 2, and 3, respectively; E1f is the longitudinal elastic modulus of the fiber; V f is the fiber volume content percentage, E r is the elastic modulus of the composite matrix, G r is the composite matrix shear modulus, v r is the Poisson's ratio of the composite matrix, v 12 f is the fiber longitudinal Poisson's ratio, G 12 f is the longitudinal and transverse shear modulus of the fiber, G 23 f is the transverse isotropic shear modulus of the fiber.

5. The method for inverting intrinsic strain model parameters based on composite material solidification deformation according to claim 4, characterized in that: Since the warpage of the flat plate component after solidification is proportional to the thermal expansion coefficient, a finite element model with [907 / 07] ply is established, and the intrinsic strain is input into the finite element model as a pseudo-thermal strain parameter. The eigenstrain α2 of the single-layer composite material in two directions is taken as 0.8×α3, α3, and 1.2×α3 for simulation; The deformation curvature is fitted using the quadratic function shown in the following formula to construct a linear relationship between α2 and the deformation curvature. The eigenstrain α2 of the single-layer composite material in two directions is obtained according to the deformation curvature of the actual flat plate component after curing: z p =k1x p 2 +k2x p +b; Among them, x p is the section length of the flat plate component after solidification, z p is the warpage of the flat plate component after solidification, k1, k2 and b are formula coefficients, K c It is the deformation curvature of the flat plate component after solidification.

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