Thermal correction simulation method for composite material rotary body based on deformation energy theory

Abstract

The invention discloses a thermal correction simulation method for a composite material rotary body based on a deformation energy theory, belongs to the technical field of structural composite materials and processes, and is suitable for manufacturing composite material rotary body components. According to the method disclosed by the invention, the viscoelastic properties of the composite material are forecasted by adopting the mesomechanical model as a model material performance input condition; the shape righting load is designed through energy conservation of deformation energy increment caused by the shape righting load, deformation energy increment caused by rebound deformation after the shape righting load is unloaded and deformation energy increment between a final shape righting state and an initial deformation state, shape righting rebound and shape righting residual deformation conditions are simulated, and composite material process deformation control is guided.

Description

Technical Field

[0001] The present application belongs to the field of structural composite materials and process technology, and relates to a composite material rotating body thermal correction simulation method based on deformation energy theory. Background Art

[0002] Carbon fiber reinforced resin-based composite materials are widely used in aerospace, aviation, transportation and other fields due to their advantages such as light weight, high strength and designability. Composite materials are an important development trend in the structural upgrade of aerospace equipment, and the amount of composite materials used has gradually become an important indicator of whether the performance of aerospace vehicles is advanced. Facing the structural application needs of the new generation of space launch vehicles, composite rotating body component structures are used in launch vehicle structural sections due to their excellent characteristics such as light weight, strong load-bearing capacity, high structural efficiency, good structural stability and strong designability.

[0003] The future generation of advanced launch vehicles will have a more demanding service environment for mechanical-thermal coupling, and the requirements for the system manufacturing accuracy and service reliability of lightweight, high-strength, and designable composite structural rotating body components are also increasing. Composite rotating body component structures present multi-feature complex structural properties, such as thin-walled skins, complex grids, variable-section transition zones, thickened zones, windows, end frames, etc. Process curing deformation restricts the improvement of the system manufacturing accuracy of composite rotating body components. In order to ensure the technical requirements of internal density, high fiber volume fraction, low defect rate, fiber and resin uniformity of large composite rotating body components, the autoclave overall co-curing process of grid prepreg winding-skin layer is generally used for manufacturing. However, due to the influence of multiple factors such as thermal expansion mismatch of components in the curing process, asymmetric multi-feature structures, and anisotropy of composite materials, large composite rotating body component structures are prone to curing process deformation problems. Different from the deformation characteristics of warping and twisting that occur in typical wing structures, the deformation of rotating body components is manifested as roundness deviation from theoretical values.

[0004] At present, the traditional qualitative control based on experience such as mold compensation is no longer applicable to the process deformation of large composite rotating body components. It is necessary to fundamentally solve the problem of process deformation of composite structural rotating body components. In addition, in order to improve the process geometric dimensional accuracy of composite rotating body components, it is also necessary to switch from "intrinsic" curing deformation to "active" thermal correction. The thermal correction simulation method of composite rotating body components based on the viscoelastic micromechanical deformation energy theory of composite materials can be used to simulate correction rebound and correction residual deformation, carry out thermal correction process parameter design, correction mold tooling scheme design, and guide composite material process deformation control. Summary of the invention

[0005] The technical problem solved by the present application is: to overcome the shortcomings of the prior art and provide a thermal correction simulation method for composite rotating bodies based on deformation energy theory. By adopting a microscopic mechanical model to predict the viscoelastic properties of the composite material as the input condition of the model material performance, based on the functional principle, the orthopedic load is designed through the conservation of energy of the deformation energy increment caused by the orthopedic load, the deformation energy increment caused by the rebound deformation after the orthopedic load is unloaded, and the deformation energy increment between the final orthopedic state and the initial deformation state. The orthopedic rebound and orthopedic residual deformation are simulated, and the thermal correction process parameter design and orthopedic mold tooling scheme design are carried out to guide the process deformation control of the composite material and improve the molding quality and precision of the composite rotating body components.

[0006] The technical solutions provided by this application are as follows:

[0007] A composite material rotating body thermal correction simulation method based on deformation energy theory, comprising:

[0008] S1: Viscoelastic micromechanical modeling of composite materials is performed by unit cell method to obtain the macroscopic stiffness matrix C of unidirectional composite materials * Expression and macro flexibility matrix S * Expression; wherein the composite material includes a plurality of repeatable unit cells, each unit cell includes four sub-cells arranged in a square cross section, one sub-cell represents the fiber, and the remaining three sub-cells represent the viscoelastic matrix material;

[0009] S2: For one of the viscoelastic matrix materials of the daughter cell, Laplace transform is performed according to the linear viscoelastic basic equation of stress relaxation to obtain the image function; the stiffness matrix of the viscoelastic matrix material in the frequency domain is extracted from the image function According to the stiffness matrix of the viscoelastic matrix material Obtaining the macroscopic flexibility matrix Using the inverse Laplace transform, we can get the macro flexibility matrix Obtain the stiffness matrix of the viscoelastic matrix material in the time domain;

[0010] S3: repeat S2 to obtain the stiffness matrix of each viscoelastic matrix material in the subcell in the time domain, and determine the stiffness matrix of the fiber according to the material of the fiber;

[0011] S4: The stiffness matrix of the viscoelastic matrix material in the time domain and the stiffness matrix of the fiber are introduced into the macroscopic stiffness matrix C of the unidirectional composite material. * In the expression, the viscoelastic micromechanical model of the composite material is obtained;

[0012] S5: Based on the viscoelastic micromechanical model of composite materials, the thermal correction of composite rotating body components is simulated, including:

[0013] ① Establish a macroscopic finite element model of the composite rotating body component structure, conduct a simulation analysis of the curing deformation of the composite rotating body component, and obtain the curing deformation and initial thermal residual stress state. The curing deformation includes the initial displacement load matrix δ of the composite rotating body component after curing deformation;

[0014] ② According to the viscoelastic micromechanical model of composite materials, the initial load is applied to the repeatable unit cell of the composite material to calculate the macroscopic stiffness matrix of the unidirectional composite material;

[0015] ③ Input the initial thermal residual stress state to the macroscopic finite element model of the composite body of revolution component structure, assign the macroscopic stiffness matrix of the unidirectional composite material to the unit integration point, input the initial displacement load matrix δ of the composite body of revolution component after curing deformation and the orthopedic displacement load increment matrix Δδ applied by the composite body of revolution component, and calculate the macroscopic stress field, strain field and displacement field with the conservation of deformation energy as the boundary condition;

[0016] ④ Obtain the macroscopic strain according to the macroscopic strain field; then input the macroscopic strain into the macroscopic finite element model of the composite material rotation body component structure as the boundary condition of the repeatable unit cell to obtain the stress-strain of the microscopic component;

[0017] ⑤ According to the stress-strain of the micro-component, the failure criterion of the micro-component is used to judge the damage. If damage occurs, the calculation stops, the loading fails, the load is reduced, and the step ② is returned to change the initial load and the cycle is repeated; if no damage occurs, the duration after the initial load is applied is continued to increase, and the step ③ is returned to the cycle until the stiffness matrix obtained according to the viscoelastic micro-mechanical model of the composite material no longer changes, the calculation is terminated, and the displacement load increment matrix δ of the composite rotating body component after correction obtained according to the displacement field is obtained. ∞ and the orthopedic residual stress obtained based on the macroscopic stress field.

[0018] In summary, this application at least includes the following beneficial technical effects:

[0019] (1) The present invention proposes for the first time a method for predicting the viscoelastic properties of composite materials using a micromechanical model. Through the fiber and resin matrix constitutive model, composite viscoelastic micromechanical modeling, viscoelastic micromechanical model solution, and composite viscoelastic constitutive relationship establishment, the present invention achieves a precise prediction of the viscoelastic properties of composite materials, which can effectively support the prediction accuracy of thermal orthopedic simulation analysis of composite rotating body components as a basic input.

[0020] (2) The present invention proposes for the first time a multi-scale collaborative simulation design method for orthopedic loads based on functional principles, which breaks through the process deformation prediction technology of composite rotating body components that considers the thermal / chemical / mechanical coupling of materials and the influence of multiple structural characteristics. It is of great significance to improving the forming and assembly of the rotating body sections of launch vehicles, production flexibility and structural service reliability. The simulation design method of the invention and the process orthopedic control method in engineering can be effectively combined, iteratively optimized, and directly applied to the production and preparation of the rotating body components of launch vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the unit cell model of the unidirectional composite material of the present invention: (a) extraction and evolution process (b) unit cell model

[0022] Figure 2 Schematic diagram of the application of displacement load for the end frame correction of the rotating body component of the present invention: (a) thermal correction loading form of composite materials (b) thermal correction process;

[0023] Figure 3 It is a schematic diagram of the creep characteristics of the bismaleimide resin of the present invention at a high temperature of 210°;

[0024] Figure 4 A schematic diagram of a carbon fiber monofilament measuring device and a modulus calculation parameter correction method of the present invention;

[0025] Figure 5 This is a program interface diagram of the viscoelastic micromechanical model of the composite material of the present invention;

[0026] Figure 6 is the calculation result of the viscoelastic constitutive relation of the composite material of the present invention;

[0027] Figure 7 The body of revolution of the embodiment of the present invention: (a) geometric model (b) boundary conditions;

[0028] Figure 8 The calculation results of the solidification deformation of the rotating body of the embodiment of the present invention are as follows: (a) longitudinal deformation cloud map (b) transverse deformation cloud map (c) comparison of the theoretical value, measured value and calculated value of roundness;

[0029] Fig. 9 Schematic diagram of the application of thermal correction loads in an embodiment of the present invention: (a) the front-to-back position change value of each correction point after correction displacement and curing deformation (b) the schematic diagram of the loading scheme of 16 correction points in the model (c) the contour of the rotating body after curing deformation and after correction displacement;

[0030] Fig.10 Schematic diagram of the thermal correction effect of the embodiment of the present invention: (a) "curing deformation-thermal correction" profile diagram (b) deformation energy change during the whole process;

[0031] Fig.11The residual stress distribution cloud diagram of the embodiment of the present invention: (a) S22 (b) maximum principal stress (c) S12 (d) S13. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0033] A composite material rotation body thermal orthopedic simulation method based on deformation energy theory uses a micromechanical model to predict the viscoelastic properties of the composite material as the input condition of the model material performance, including the following steps:

[0034] (1) Viscoelastic micromechanical modeling of composite materials

[0035] The Generalized Methods of Cells (GMC) assumes that the composite material is composed of repeatable unit cells. The composite micromechanical model established by extracting the repeatable unit cells is the unit cell model. The fibers of the unidirectional composite material are arranged in a square along the x1 direction in the x2-x3 plane. The repeatable unit cell is 1 / 4 of the unit cell containing the fiber cross section, and the fiber cross section is equivalent to a rectangle. The unit cell model contains 4 subcells, one subcell represents the fiber, and the other three subcells represent the viscoelastic matrix material, see Figure 1 .

[0036] (2.6)-(2.9) is the process of solving the volume of the unit cell model. From the geometric characteristics of the unit cell model, we can obtain the following relationship:

[0037] V A =V 11 =λh 2 d (2.6)

[0038] V B =V 21 =h(1-λh)d (2.7)

[0039] V C =V 12 =λh(1-h)d (2.8)

[0040] V D =V 22 =(1-h)(1-λh)d (2.9)

[0041] Where A represents the fiber area, B~D represent the resin area (i.e., the viscoelastic matrix material area), V A ,V B ,V C and V DRepresent the volume of each sub-region, d is the length of the unit cell along the fiber direction. The parameter factor λ is used to measure the effect of viscosity on the unit cell model under different loads. h is the fiber diameter.

[0042] The value range of parameter factor λ is:

[0043] V f <λ<1 / V f (2.10)

[0044] Where V f is the fiber volume fraction.

[0045] (2.11)-(2.33) is the process of solving the macroscopic stiffness matrix of the composite material through the unit cell model. According to the generalized Hooke's law, the basic equation of each sub-region is expressed in the following incremental form:

[0046]

[0047] In the formula, is the stiffness matrix of each sub-region, A represents the fiber region, B~D represents the resin, dσ ij and Respectively represent the stress and strain increments of each sub-region, and their expressions are:

[0048]

[0049] Using the homogenization theory, the volume average stress of each unit cell can be solved as follows:

[0050]

[0051] The above formula can be written in incremental form as:

[0052]

[0053] Where V and V α are the volumes of the unit cell model and each subcell respectively.

[0054] Similarly, the strain increment of the unit cell can be expressed as:

[0055]

[0056] Using the condition of interface displacement continuity, the relationship between the macroscopic strain of the composite material and the average strain of each subcell volume can be obtained:

[0057]

[0058] Equations (2.17)-(2.22) can be written in matrix form as:

[0059]

[0060] Where, dε α =[dε A , dε B , dε C , dε D ],dε A , dε B , dε C and dε D are the strain increments of daughter cells A, B, C and D respectively; A G is a 13×24 matrix that describes the internal geometric features of the unit cell model; B G It is a 13×6 matrix that describes the geometric features inside the unit cell model. Also called A G and B G is a geometric matrix.

[0061] Similarly, by using the stress continuity conditions between sub-cells and the interfaces between adjacent unit cell models, we can obtain the following basic relationship between the volume average stress of the sub-cell, which describes the relationship between the sub-cell strain and the macroscopic strain.

[0062] A M dε α =0(2.24)

[0063] In the formula, A M It is a 11×24-order matrix determined by the material constants of each subcell.

[0064] These equations obtained by imposing continuity conditions relate the relationship between the subcell strain and the macroscopic strain of the composite material. Equations (2.23) and (2.24) are combined and written in a more concise matrix form:

[0065]

[0066] In the formula,

[0067]

[0068] In order to obtain the subcell strain represented by the volume average macroscopic strain, solve equation (2.25) to obtain:

[0069]

[0070] In the formula,

[0071] R=A -1 B(2.28)

[0072] In order to obtain the specific form of the matrix R, the matrix is ​​represented as follows:

[0073]

[0074] In the formula, (A 11 )13×12 matrix.

[0075] Combining formulas (2.11), (2.27) and (2.28), we can get the following expression:

[0076]

[0077] Substituting equation (2.27) into (2.11), the average stress of the unit cell can be obtained as:

[0078]

[0079] In the formula, C * is the macroscopic stiffness matrix of the unidirectional composite material, expressed as:

[0080]

[0081] Where V is the volume of the unit cell; V α is the volume of daughter cell α; α∈[A, B, C or D], A represents the area where the daughter cell is fiber, B~D represents the area where the daughter cell is viscoelastic matrix material; C α is the stiffness matrix of subcell α; R α It is the constant conversion matrix between the strain components of subcell α and the strain components of unit cell.

[0082] (2.34) is the process of solving the macroscopic flexibility matrix of the composite material, which is calculated from the composite unit cell volume and the composite macroscopic stiffness matrix. The macroscopic flexibility matrix S of the unidirectional composite material * It is expressed as:

[0083]

[0084] (2) Solving the viscoelastic micromechanical model - obtaining the change of the viscoelastic matrix material over time

[0085] Based on the Boltzmann superposition principle, under the assumption of small deformation, the linear viscoelastic basic equation for stress relaxation of viscoelastic matrix materials is usually expressed in the following integral form:

[0086]

[0087] In the formula, C ijkl is the material stiffness matrix. ij is the stress of the material, σ ij is the material strain, τ is the relaxation time, and t is the reduction time of the Maxwell element.

[0088] By performing Laplace transform on equation (2.35), we can obtain the image function, as follows:

[0089]

[0090] In the frequency domain, the transformed viscoelastic material equation is Equivalent to the stiffness matrix of the viscoelastic matrix material

[0091]

[0092] The basic equations of composite materials in the frequency domain are obtained through the micromechanical model. By converting the material constants into the corresponding material constant expressions in the frequency domain, these equations can be directly used.

[0093]

[0094] here It is the macroscopic flexibility matrix of the unidirectional composite material in the frequency domain, which can be calculated by formula (2.34).

[0095] Comparing the form of equation (2.39), we can obtain the corresponding stiffness matrix of the viscoelastic matrix material in the frequency domain:

[0096]

[0097]

[0098] By applying the inverse Laplace transform, we can obtain the stiffness matrix of the viscoelastic matrix material in the time domain.

[0099] Through the above steps of (2), the stiffness matrix of one of the viscoelastic matrix materials of the subcell in the time domain is solved; the above steps are repeated to obtain the stiffness matrix of each viscoelastic matrix material in the subcell in the time domain, and the stiffness matrix of the fiber is determined according to the material of the fiber.

[0100] (3) Establishment of viscoelastic constitutive relationship of composite materials

[0101] Based on the unit cell stress and strain, unit cell geometric parameters, unit cell boundary conditions and unit cell model, the macroscopic viscoelastic constitutive equation of the composite material is established, and the viscoelastic stiffness matrix of the composite material is solved as the basic data of the viscoelastic micromechanical model for composite laminate and structural calculation. That is, the stiffness matrix of the viscoelastic matrix material in the time domain and the stiffness matrix of the fiber are brought into the macroscopic stiffness matrix C of the unidirectional composite material. * In the expression, the viscoelastic micromechanical model of the composite material is obtained.

[0102] Using the viscoelastic micromechanical model of composite materials, the viscoelastic properties of composite materials can be calculated. The viscoelastic properties are the law of stiffness changing with time (or temperature). The micromechanical model is written as a FORTRAN program, which is convenient for calling other finite element software for composite material and structural analysis. The subroutine includes three parts: component attribute assignment, unit cell establishment, and subcell stress / strain solution.

[0103] A thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory is based on the functional principle. The orthopedic load is designed by the energy conservation of the deformation energy increment caused by the orthopedic load, the deformation energy increment caused by the rebound deformation after the orthopedic load is unloaded, and the deformation energy increment between the final orthopedic state and the initial deformation state. The orthopedic rebound and orthopedic residual deformation are simulated, and the steps are as follows:

[0104] 1. Establish a macroscopic finite element model of the composite rotating body component structure, conduct a simulation analysis of the curing deformation of the composite rotating body component, and obtain the curing deformation and initial thermal residual stress state. The curing deformation includes the initial displacement load matrix δ of the composite rotating body component after curing deformation.

[0105] 2. Carry out orthopedic displacement load design.

[0106] When loaded at room temperature, the total work done by the orthopedic load is completely converted into the deformation energy E of the rotating body component. tot ;

[0107] Under the action of orthopedic load, the temperature rise and temperature plateau cause the rotation component to creep / stress relaxation, forming additional irreversible deformation energy E of the rotation component. cr ;

[0108] After unloading, the deformation energy that drives the rotating body component to rebound is the elastic deformation energy E el , including general elastic deformation energy and high elastic deformation energy.

[0109] Assume that the orthopedic displacement load is applied to n points of the end frame of the rotating body component, and each point has two degrees of freedom in the plane perpendicular to the axis. According to the idea of ​​"circle cutting", the more loading points there are, the smaller the orthopedic displacement added to each loading point, and the closer the final shape is to a circle. The orthopedic scheme can be designed based on the roundness values ​​in each direction, such as Figure 3 The load application and evolution process are shown in Figure 2 Figure a and b of .

[0110] The orthopedic displacement load δ can be written in the following matrix form:

[0111]

[0112] The displacement load increment Δδ of the final rotation component in the corrected state can be written as:

[0113]

[0114] dE tot ,dE el ,dE cr They are the deformation energy increment caused by the orthopedic load, the deformation energy increment caused by the rebound deformation after the orthopedic load is unloaded, and the deformation energy increment between the final orthopedic state and the initial deformation state. The relationship between the deformation energy increment and the orthopedic displacement load is as follows:

[0115] dE tot =[C][δ] (2.47)

[0116] dE cr =[C cr ][△δ] (2.48)

[0117] dE el =[C cr ][δ ∞ ] (2.49)

[0118] Among them, [C] and [C cr ] are the stiffness of the composite material before the initial load is applied and the stiffness after the initial load is unloaded, both of which are calculated according to the viscoelastic micromechanics model of the composite material; δ is the initial displacement load matrix of the composite rotating body component after solidification deformation; Δδ is the orthopedic displacement load increment matrix applied by the composite rotating body component, δ ∞ It is the displacement load increment matrix of the composite rotating body component after correction.

[0119] 3. Simulate the rebound strain and residual stress after orthopedic surgery

[0120] dE tot ,dE el ,dE cr The relationship between the three deformation energy increments is:

[0121] dE tot =dE el +dE cr (2.64)

[0122] The relationship of deformation energy conservation is used to simulate the springback displacement and residual stress of composite rotating body components after correction. The specific calculation iterative steps are as follows:

[0123] ① Establish a macroscopic finite element model of the composite rotating body component structure, conduct a simulation analysis of the curing deformation of the composite rotating body component, and obtain the curing deformation and initial thermal residual stress state. The curing deformation includes the initial displacement load matrix δ of the composite rotating body component after curing deformation;

[0124] ② According to the viscoelastic micromechanical model of composite materials, the initial load is applied to the repeatable unit cell of the composite material to calculate the macroscopic stiffness matrix of the unidirectional composite material;

[0125] ③ Input the initial thermal residual stress state to the macroscopic finite element model of the composite body of revolution component structure, assign the macroscopic stiffness matrix of the unidirectional composite material to the unit integration point, input the initial displacement load matrix δ of the composite body of revolution component after curing deformation and the orthopedic displacement load increment matrix Δδ applied by the composite body of revolution component, and calculate the macroscopic stress field, strain field and displacement field with the conservation of deformation energy as the boundary condition;

[0126] ④ Obtain the macroscopic strain according to the macroscopic strain field; then input the macroscopic strain into the macroscopic finite element model of the composite material rotation body component structure as the boundary condition of the repeatable unit cell to obtain the stress-strain of the microscopic component;

[0127] ⑤ According to the stress-strain of the meso-component, the failure criterion of the meso-component is used to judge the damage. If damage occurs, the calculation stops, the loading fails, the load is reduced, and the process returns to step ② and changes the initial load to recycle. If no damage occurs, the duration after applying the initial load continues to increase, and the process returns to step ③ and the calculation is repeated until the stiffness matrix obtained according to the viscoelastic mesomechanical model of the composite material no longer changes. The calculation is terminated, and the displacement load increment matrix δ∞ of the composite rotating body component after correction obtained according to the displacement field and the correction residual stress obtained according to the macroscopic stress field are obtained.

[0128] Example 1

[0129] The following is a further detailed description of a composite material rotating body thermal correction simulation method based on deformation energy theory provided by an embodiment of the present invention in conjunction with the accompanying drawings of the specification. The specific implementation method may include:

[0130] Thermal orthopedic simulation of TG800 / 802 carbon fiber reinforced bismuth composite grid rotation structure

[0131] (I) Using micromechanical models to predict the viscoelastic properties of composite materials as input conditions for model material performance

[0132] (1) Viscoelastic micromechanical modeling of composite materials

[0133] Most polymer matrices used as composite materials conform to viscoelastic behavior, which is the superposition of elasticity and viscosity. In micromechanical simulations, the behavior of polymer matrices is generally considered to conform to linear viscoelasticity, and the constants in the viscoelastic equations of the material are considered to be invariant with temperature. The resin relaxation modulus is defined in the form of a Prony series:

[0134]

[0135] In the formula, τ i is the relaxation time, E ∞ is the modulus after complete relaxation, E 0 is the unrelaxed modulus, W i and t are the weight factor and reduction time of the Maxwell unit, respectively.

[0136] Poisson's ratio of the material m is considered to be a constant and independent of the relaxation time. The shear modulus of the linear elastic matrix material is:

[0137]

[0138] The creep relationship of 802 bismaleimide resin at 210° high temperature is as follows Figure 3 As shown. The initial stresses were 38MPa, 30MPa and 22MPa. Creep / stress relaxation occurs at high temperatures in the resin. At a high temperature of 210°C, the creep equilibrium state is basically reached within 2 hours, and the strain changes with time after unloading. The molecular chain movement of the polymer creep essence is manifested successively on different time scales; after unloading, both the general elastic deformation ε1 and the high elastic deformation ε2 can be recovered, but the viscous flow deformation strain ε3 remains. At the moment of unloading, the general elastic deformation ε1 disappears, the high elastic deformation ε2 is basically restored in 10 minutes, and the curve area is flat. At the same time and temperature, the residual strain increases with the application of the initial stress. After 10 minutes of creep unloading, the residual strains corresponding to the initial stresses of 38MPa, 30MPa and 22MPa are 0.7%, 0.44% and 0.25%, respectively.

[0139] Fibers are usually considered to be transversely isotropic materials. Therefore, they can be expressed by a generalized Hooke's law. Under the assumption of small deformation, the basic linear viscoelastic equation for predicting the stress relaxation behavior of composite materials can be expressed in the following integral form:

[0140]

[0141] It is expressed in vector form as follows:

[0142]

[0143] In the formula, <·> represents the average value of the components, C ijkl(t) is the overall stiffness matrix of the heterogeneous material, which is a 6-order square matrix. For transversely isotropic materials, the matrix has only 5 independent parameters. The tensile modulus and strength of carbon fiber are tested by a single-filament strength machine, a single-filament carbon fiber measuring device, and a modulus calculation parameter correction method. Figure 4 As shown, the test standard refers to ISO 11566.

[0144] 70 single-filament samples of each type of carbon fiber were prepared, and the failure mode was recorded during the stretching process to observe whether the carbon fiber single-filament was broken in the gauge section. The abnormal failure sample data was immediately eliminated, and the strength-displacement curve of the normal failure sample was recorded. It is generally believed that the tensile strength of the carbon fiber single-filament satisfies the Weibull distribution, and the expression is:

[0145]

[0146] For the two-parameter Weibull distribution (location parameter σu=0), the above equation is simplified and the logarithms of both sides are obtained: The shape parameter m and scale parameter σ0 can be obtained by linear fitting.

[0147] Table 1 TG800 single filament tensile strength Weibull fitting

[0148]

[0149] The single-filament modulus needs to be corrected by different gauge lengths. The transmission error of the upper and lower chuck gap leads to the elongation test error. For different gauge lengths of 20-40mm, 10 samples of each type are prepared, and the effective samples are taken for calculation to obtain the TG800 tensile modulus of 294.11GPa.

[0150] (2) Solution of viscoelastic micromechanical model

[0151] Using the micromechanical model, the viscoelastic material properties of the composite material's elastic parameters can be calculated to determine how they change over time (or temperature). The micromechanical model is written as a FORTRAN program, which is convenient for calling other finite element software for composite material and structural analysis. The subroutine includes three parts: component attribute assignment, unit cell establishment, and subcell stress / strain solution. The subroutine interface is as follows: Figure 5 .

[0152] (3) Establishment of viscoelastic constitutive relationship of composite materials

[0153] According to the stress and strain of the subcell, the geometric parameters of the unit cell, the boundary conditions of the unit cell and the subcell interface model, the macroscopic viscoelastic constitutive equation of the composite unit cell is established, and the viscoelastic stiffness matrix of the composite material is solved. Figure 6 Shown are the prediction results of relaxation modulus of TG800 / 802 composite materials.

[0154] (ii) Based on the functional principle, the orthopedic load is designed by conserving the energy of the deformation energy increment caused by the orthopedic load, the deformation energy increment caused by the rebound deformation after the orthopedic load is unloaded, and the deformation energy increment between the final orthopedic state and the initial deformation state to simulate the orthopedic rebound and orthopedic residual deformation.

[0155] (1) Carry out a simulation analysis of the curing deformation of composite rotating body components to obtain the curing deformation situation.

[0156] During autoclave molding, the composite material has completed the curing and cross-linking reaction at the high temperature platform stage. Assuming that the mechanical properties of the composite material do not change during the cooling stage, the mechanical property stiffness matrix of the composite material used in the simulation is:

[0157]

[0158] In numerical simulation, the strain increment of the element can be expressed as

[0159] Δε=Δε e +Δε th +Δε sh (2.59)

[0160] ε e , Δε th , Δε sh They represent the strain caused by mechanical stress, thermal strain and curing shrinkage strain respectively.

[0161] The thermal deformation of the composite material during the cooling stage is expressed by the average thermal expansion coefficient and the temperature drop.

[0162]

[0163] The curing shrinkage of the composite material during the insulation platform stage can be expressed as

[0164]

[0165] For continuous fiber reinforced composites, due to the constraint of the fiber, the thermal expansion and curing shrinkage in the fiber direction are very small values. In addition, according to the symmetry of the composite material, it can be assumed that the ratio of the thermal shrinkage in the cooling stage and the curing shrinkage on the insulation platform is a constant value, denoted as s, which is measured by the fiber Bragg grating experiment.

[0166]

[0167] Δε=Δε e +Δε th +Δε sh =Δε e +(1+s)·Δε th

[0168] The stress-strain relationship in incremental form is:

[0169] Δσ=[C]Δε e (2.63)

[0170] The prediction of the curing deformation of the TG800 / 802 composite 1.7m rotating body includes the skin, upper and lower end frames, grid ribs (circumferential and ±45°) and thickened areas, such as Figure 7 (a) is shown. The specific layers are shown in Table 2.

[0171] Table 2 Grid rotation body ply

[0172]

[0173] The boundary condition adopted by the deformation prediction model is: the axial deformation of the bottom end of the end frame is 0, such as Figure 7 (b) as shown.

[0174] The total deformation calculation results are shown in Figure 8 a, b, c and shown in Table 3.

[0175] Table 3 Experimental values ​​of solidification deformation of 1.7m rotating body

[0176]

[0177] (2) Design of orthopedic displacement load

[0178] Orthopedic displacement load loading method Fig. 9 As shown in (a), the numbers in the figure represent the change in the front and rear positions of each orthopedic point after the orthopedic displacement is applied and the solidification deformation. The overall contour is an ellipse. The vertical major axis b of the ellipse is greater than the horizontal major axis a. Therefore, the orthopedic displacement values ​​applied at 90° and 270° are approximately +7mm, and the orthopedic displacement values ​​applied at 0° and 180° are approximately -5mm. The orthopedic displacement values ​​of the remaining orthopedic points can be fine-tuned according to the internal stress and deformation. The orthopedic displacement load loading in the finite element model is as follows Fig. 9 (b) The final contour and correction displacement are shown in Fig. 9 (c) as shown.

[0179] (3) Simulation of orthopedic results and orthopedic stress

[0180] According to the correction scheme combined with strain energy theory, the "curing deformation-thermal correction" profile is fitted as follows Fig.10 As shown in (a), after solidification deformation, the structure is elliptical, and the horizontal major axis a of the ellipse is larger than the vertical minor axis b. After the orthopedic displacement is applied, the vertical axis b of the ellipse becomes the major axis. Finally, the contour of the rotating body structure rebounds to a circle, and the residual deformation roundness value is 0.9mm<1mm. During the whole process, Fig.10As shown in (b), the deformation in the three stages, namely, loading at room temperature, under orthopedic load, and after unloading, can satisfy the equilibrium relationship.

[0181] The contour of the rotating body changes from an ellipse with the horizontal axis as the major axis after solidification deformation to an ellipse with the vertical axis as the major axis after the orthopedic displacement is applied, and finally the contour becomes a circle after unloading and rebounding. The whole process conforms to the orthopedic deformation energy theory. The roundness change of the rotating body end frame before and after correction is reduced from 3.22mm to 0.87mm. The residual contour roundness experimental result is 0.9m, and the prediction error of the rotating body deformation is 3.3%, which verifies the reliability of the model.

[0182] The calculation results of residual stress of rotating body are shown in Fig.11 a, b, c and d. The transverse tensile stress S22 on the second layer of the laminate reaches a maximum value of about 42.6MPa, and the maximum value is located at the junction of the front frame flange and the end frame, reaching 72.3% of the transverse tensile strength; resin tensile damage is prone to occur. The longitudinal tensile stress is 406MPa, which is 16.4% of the tensile strength; the maximum value of the in-plane shear stress S12 is about 30.8MPa, which is 30.5% of the shear strength; the maximum value of the out-of-plane shear stress S13 is 25.9MPa, which is 25.6% of the shear strength. Substituting the remaining stress values ​​of the unit where the maximum value of the S22 transverse tensile stress is located into the Hashin and Puck failure criteria, it is judged that the internal stress has not reached the failure condition and the rotating body structure has not been damaged.

[0183] The contents not described in detail in this application specification belong to the common knowledge of those skilled in the art.

[0184] The present application is described in detail above in conjunction with specific implementation methods and exemplary examples, but these descriptions cannot be understood as limiting the present application. Those skilled in the art understand that, without departing from the spirit and scope of the present application, a variety of equivalent replacements, modifications or improvements can be made to the technical solution of the present application and its implementation methods, all of which fall within the scope of the present application. The scope of protection of the present application shall be subject to the attached claims.

Claims

1. A composite material rotating body thermal correction simulation method based on deformation energy theory, characterized in that: include: S1: Viscoelastic micromechanical modeling of composite materials is performed by unit cell method to obtain the macroscopic stiffness matrix C of unidirectional composite materials * Expression and macro flexibility matrix S * Expression; wherein the composite material includes a plurality of repeatable unit cells, each unit cell includes four sub-cells arranged in a square cross section, one sub-cell represents the fiber, and the remaining three sub-cells represent the viscoelastic matrix material; S2: For one of the viscoelastic matrix materials of the daughter cell, Laplace transform is performed according to the linear viscoelastic basic equation of stress relaxation to obtain the image function; the stiffness matrix of the viscoelastic matrix material in the frequency domain is extracted from the image function According to the stiffness matrix of the viscoelastic matrix material Obtaining the macroscopic flexibility matrix Using the inverse Laplace transform, we can get the macro flexibility matrix Obtain the stiffness matrix of the viscoelastic matrix material in the time domain; S3: repeat S2 to obtain the stiffness matrix of each viscoelastic matrix material in the subcell in the time domain, and determine the stiffness matrix of the fiber according to the material of the fiber; S4: The stiffness matrix of the viscoelastic matrix material in the time domain and the stiffness matrix of the fiber are introduced into the macroscopic stiffness matrix C of the unidirectional composite material. * In the expression, the viscoelastic micromechanical model of the composite material is obtained; S5: Based on the viscoelastic micromechanical model of composite materials, the thermal correction of composite rotating body components is simulated, including: ① Establish a macroscopic finite element model of the composite rotating body component structure, conduct a simulation analysis of the curing deformation of the composite rotating body component, and obtain the curing deformation and initial thermal residual stress state. The curing deformation includes the initial displacement load matrix δ of the composite rotating body component after curing deformation; ② According to the viscoelastic micromechanical model of composite materials, the initial load is applied to the repeatable unit cell of the composite material to calculate the macroscopic stiffness matrix of the unidirectional composite material; ③ Input the initial thermal residual stress state to the macroscopic finite element model of the composite body of revolution component structure, assign the macroscopic stiffness matrix of the unidirectional composite material to the unit integration point, input the initial displacement load matrix δ of the composite body of revolution component after curing deformation and the orthopedic displacement load increment matrix Δδ applied by the composite body of revolution component, and calculate the macroscopic stress field, strain field and displacement field with the conservation of deformation energy as the boundary condition; ④ Obtain the macroscopic strain according to the macroscopic strain field; then input the macroscopic strain into the macroscopic finite element model of the composite material rotation body component structure as the boundary condition of the repeatable unit cell to obtain the stress-strain of the microscopic component; ⑤ According to the stress-strain of the micro-component, the failure criterion of the micro-component is used to judge the damage. If damage occurs, the calculation stops, the loading fails, the load is reduced, and the step ② is returned to change the initial load and the cycle is repeated; if no damage occurs, the duration after the initial load is applied is continued to increase, and the step ③ is returned to the cycle until the stiffness matrix obtained according to the viscoelastic micro-mechanical model of the composite material no longer changes, the calculation is terminated, and the displacement load increment matrix δ of the composite rotating body component after correction obtained according to the displacement field is obtained. ∞ and the orthopedic residual stress obtained based on the macroscopic stress field.

2. The thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory according to claim 1 is characterized by: The initial load is applied to n points of the end frame at the edge of the composite material rotating body component, and each point has two degrees of freedom in a plane perpendicular to the axis of the composite material rotating body component.

3. The thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory according to claim 1 is characterized in that: The deformation energy conservation is: of tot =dE el +dE cr ; When loaded at room temperature, the total work done by the initial load is completely converted into the deformation energy E of the composite rotating body component. tot ; Under the action of the initial load, the temperature rise and temperature platform cause the composite rotating body component to undergo creep / stress relaxation, forming additional irreversible deformation energy E of the composite rotating body component cr ; After unloading the initial load, the deformation energy that drives the composite rotating body component to rebound is the elastic deformation energy E el .

4. The thermal orthopedic simulation method for composite material rotating body based on deformation energy theory according to claim 3 is characterized in that: The dE tot =[C][δ], of cr =[C cr ][△δ], of el =[C cr ][δ ∞ ], Among them, [C] and [C cr ] are the stiffness of the composite material before the initial load is applied and the stiffness after the initial load is unloaded, both of which are calculated based on the viscoelastic micromechanics model of the composite material; δ is the initial displacement load matrix of the composite rotating body component after solidification deformation; Δδ is the orthopedic displacement load increment matrix applied by the composite rotating body component, δ ∞ It is the displacement load increment matrix of the composite rotating body component after correction.

5. The thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory according to claim 1 is characterized in that: In S1, the viscoelastic micromechanical modeling of the composite material is performed by the unit cell method to obtain the macroscopic stiffness matrix C of the unidirectional composite material. * Expression and macro flexibility matrix S * Expressions, including: Using homogenization theory, the volume average stress of each unit cell is obtained; According to the volume average stress of each unit cell and the condition of interface displacement continuity, the relationship between the macroscopic strain of the composite material and the volume average strain of each subcell can be obtained; According to the relationship between the macroscopic strain of the composite material and the volume average strain of each subcell, the basic relationship of the volume average stress of the subcell is obtained by using the stress continuity conditions of the interface between subcells and adjacent unit cells. According to the basic relationship of the volume average stress of the subcell, the macroscopic stiffness matrix C of the unidirectional composite material is obtained: * Expression (i.e., Formula 2.33), according to the macroscopic stiffness matrix C of the unidirectional composite material * The macro flexibility matrix S is obtained by the expression * expression.

6. The thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory according to claim 5 is characterized in that: The volume average stress of each unit cell is: Among them, V α is the volume of daughter cell α; α∈[A, B, C or D], A represents the region where the daughter cell is fiber, and B~D represents the region where the daughter cell is viscoelastic matrix material; is the stress increment of subcell α; V is the volume of the unit cell; σ ij is the stress increment of the unit cell.

7. The thermal orthopedic simulation method for composite rotating bodies based on deformation energy theory according to claim 6 is characterized in that: The relationship between the macroscopic strain of the composite material and the average strain of each subcell volume is: Among them, dε α =[dε A , dε B , dε C , dε D ],dε A , dε B , dε C and dε D are the strain increments of daughter cells A, B, C and D respectively; A G and B G It is a matrix that describes the internal geometric characteristics of the unit cell model.

8. The thermal orthopedic simulation method for composite material rotating body based on deformation energy theory according to claim 7, characterized in that: The basic relationship between the volume average stress of the daughter cell is: M dε α =0 Among them, A M is a matrix determined by the material constants of each subcell; dε α is the strain increment of daughter cell α.

9. The thermal orthopedic simulation method for composite material rotating body based on deformation energy theory according to claim 1, characterized in that: The macroscopic stiffness matrix C of the unidirectional composite material * The expression is: Where V is the volume of the unit cell; V α is the volume of daughter cell α; α∈[A, B, C or D], A represents the area where the daughter cell is fiber, B~D represents the area where the daughter cell is viscoelastic matrix material; C α is the stiffness matrix of subcell α; R α It is the constant conversion matrix between the strain components of subcell α and the strain components of unit cell.

10. The thermal orthopedic simulation method for composite material rotating body based on deformation energy theory according to claim 1, characterized in that: The macroscopic flexibility matrix S * The expression is: * (λ)=[C * (λ)] -1 .

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