A simulation method for thermal straightening of composite rotary body based on deformation energy theory

Abstract

The application discloses a simulation method for thermal straightening of a composite material rotary body based on deformation energy theory, belongs to the field of structural composite materials and process technology, and is suitable for manufacturing of a composite material rotary body component. The application adopts a mesoscopic mechanics model to predict viscoelastic properties of the composite material as model material performance input conditions, performs straightening load design based on a functional principle through energy conservation of three energy increments, i.e., a deformation energy increment caused by the straightening load, a deformation energy increment caused by springback deformation after unloading of the straightening load, and a deformation energy increment between a final straightening state and an initial deformation state, simulates straightening springback and straightening residual deformation conditions, and guides deformation control of the composite material process.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of structural composites and processes, and relates to a composite material rotary body thermal straightening simulation method based on deformation energy theory. BACKGROUND

[0002] Carbon fiber reinforced resin matrix composites are widely used in aerospace, aviation, transportation and other fields due to their light weight, high strength, designability and other advantages. Composite material is an important development trend for the upgrading of aerospace equipment structures, and the amount of composite materials has gradually become an important symbol of whether an aerospace vehicle is advanced in performance. Facing the application requirements of a new generation of aerospace launch vehicle structures, composite material rotary body component structures are applied to launch vehicle structural sections due to their light weight, high load capacity, high structural efficiency, good structural stability and strong designability.

[0003] The force-thermal coupling service environment of the next generation of advanced launch vehicles is more demanding, and the system manufacturing precision and service reliability of composite material structure rotary body components with light weight, high strength and designability are also continuously improved. Composite material rotary body component structures have multiple complex structural properties, such as thin-walled skin, complex grid, variable cross-section transition zone, thickening zone, window, end frame, etc., and process curing deformation restricts the improvement of the system manufacturing precision of composite material rotary body components. In order to ensure the technical requirements of large composite material rotary body components such as internal density, high fiber volume fraction, low defect rate, and uniformity of fiber and resin, a grid pre-impregnated filament winding-skin layering whole curing process in a thermal pressure tank is generally used for manufacturing. However, due to the effects of multiple factors such as mismatched thermal expansion of process components, asymmetric multi-feature structures, and anisotropy of composite materials, large composite material rotary body component structures are prone to curing process deformation problems. Unlike the warping and twisting deformation characteristics that may occur in typical wing surface structures, the deformation of rotary body components is manifested as deviation of the roundness from the theoretical value.

[0004] At present, the traditional empirical method based on mold compensation for controlling the process deformation of large composite material rotary body components is no longer applicable, and the process deformation problem of composite material structure rotary body components needs to be fundamentally solved. In addition, in order to improve the process geometric dimension precision of composite material rotary body components, it is also necessary to convert from internal curing deformation to active thermal straightening. A composite material rotary body component thermal straightening simulation method based on the deformation energy theory of composite material viscoelastic micromechanics can be used to simulate the straightening springback and residual deformation, carry out thermal straightening process parameter design and straightening mold tooling scheme design, and guide the control of composite material process deformation. SUMMARY

[0005] The technical problem solved by the present application is to overcome the shortcomings of the prior art and provide a composite material rotary body thermal straightening simulation method based on deformation energy theory.

[0006] The technical scheme provided by the present application is as follows:

[0007] A composite material rotary body thermal straightening simulation method based on deformation energy theory comprises the following steps:

[0008] S1: Viscoelastic micromechanics modeling of the composite material is performed by the unit cell method to obtain a macroscopic stiffness matrix C of the unidirectional composite material * and a macroscopic compliance matrix S * ; wherein the composite material comprises a plurality of repeatable unit cells, each unit cell comprises four square-arranged subcells, one subcell represents a fiber, and the other three subcells represent viscoelastic matrix materials;

[0009] S2: Laplace transform is performed on one of the viscoelastic matrix materials in the subcell according to the linear viscoelastic basic equation of stress relaxation to obtain an image function; the stiffness matrix of the viscoelastic matrix material in the frequency domain is extracted from the image function ; the stiffness matrix of the viscoelastic matrix material in the time domain is obtained according to the stiffness matrix of the viscoelastic matrix material in the frequency domain ; the macroscopic compliance matrix S is obtained according to the macroscopic compliance matrix ; and the stiffness matrix of the viscoelastic matrix material in the time domain is obtained by applying Laplace inverse transform to the macroscopic compliance matrix ;

[0010] S3: S2 is 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;

[0011] S4: 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 to obtain a composite material viscoelastic micromechanics model;

[0012] S5: based on the composite material viscoelastic micromechanics model, thermal straightening of the composite material rotary body component is simulated, specifically comprising the following steps:

[0013] ①establishing a macro finite element model of the composite rotary body component structure, performing curing deformation simulation analysis of the composite rotary body component, obtaining the curing deformation condition and the initial thermal residual stress state, and the curing deformation condition includes the initial displacement load matrix δ of the composite rotary body component after curing deformation;

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

[0015] ③The initial thermal residual stress state of the macro finite element model of the composite rotary body component structure is input, the macroscopic stiffness matrix of the unidirectional composite material is assigned to the element integration point, the initial displacement load matrix δ of the composite rotary body component after curing deformation and the correction displacement load increment matrix Δδ of the composite rotary body component are input, and the deformation energy energy conservation is taken as the boundary condition to calculate the macroscopic stress field, strain field and displacement field;

[0016] ④According to the macroscopic strain field, the macroscopic strain is obtained;Then the macroscopic strain is input into the macro finite element model of the composite rotary body component structure as the boundary condition of the repeatable unit cell, and the stress-strain of the micro component is obtained;

[0017] ⑤According to the stress-strain of the micro component, the damage criterion of the micro component is used for damage judgment, if damage occurs, the calculation stops, the loading fails, the load is reduced, and the initial load is changed to restart the cycle;If no damage occurs, continue to increase the duration after the initial load is applied, return to step ③, and cycle calculation until the stiffness matrix obtained according to the composite viscoelastic micromechanics model no longer changes, the calculation is terminated, and the displacement load increment matrix δ of the composite rotary body component after correction is obtained according to the displacement field. ∞ And the correction residual stress obtained according to the macroscopic stress field.

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

[0019] (1) The present application first proposes a micromechanics model for predicting the viscoelastic properties of composite materials, which realizes the fine prediction of the viscoelastic properties of composite materials through the fiber and resin matrix constitutive model, composite viscoelastic micromechanics modeling, viscoelastic micromechanics model solving, composite viscoelastic constitutive relationship establishment, etc. As a basis, it effectively supports the prediction accuracy of the thermal correction simulation analysis of the composite rotary body component.

[0020] (2) The application firstly proposes an orthopaedic load multi-scale collaborative simulation design method based on the functional principle, breaks through the composite material rotating body component process deformation prediction technology considering material thermal / chemical / force coupling and structure multi-feature influence, and has important significance for improving the forming assembly, production flexibility and structural service reliability of the launch vehicle rotating body section. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 It is a schematic diagram of the one-way composite material unit cell model of the application: (a) extraction and evolution process (b) unit cell model

[0022] Figure 2 It is a schematic diagram of the end frame orthopaedic displacement load application of the rotating body component of the application: (a) composite material thermal orthopaedic loading form (b) thermal orthopaedic process

[0023] Figure 3 It is a schematic diagram of the high-temperature creep property of the double-mart resin at 210 degrees of the application;

[0024] Figure 4 It is a schematic diagram of the carbon fiber monofilament measuring device and modulus calculation parameter correction method of the application;

[0025] Figure 5 It is a program interface diagram of the composite material viscoelastic mesoscopic mechanics model of the application;

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

[0027] Figure 7 It is a rotating body of the embodiment of the application: (a) geometric model (b) boundary condition;

[0028] Figure 8 It is the curing deformation calculation result of the rotating body of the embodiment of the application: (a) longitudinal deformation cloud picture (b) transverse deformation cloud picture (c) roundness theoretical value, measured value and calculated value comparison;

[0029] Figure 9 It is a schematic diagram of the thermal correction load application of the embodiment of the application: (a) the position change value before and after the curing deformation after the orthopaedic displacement is applied to each orthopaedic point (b) the loading scheme diagram of 16 orthopaedic points in the model (c) the profile after the curing deformation of the rotating body and the orthopaedic displacement is applied;

[0030] Figure 10 It is a schematic diagram of the thermal correction effect of the embodiment of the application: (a) "curing deformation-thermal orthopaedic" profile diagram (b) whole process deformation energy change;

[0031] Figure 11Residual stress distribution nephogram of the embodiment of the present application: (a) S22 (b) maximum principal stress (c) S12 (d) S13. DETAILED DESCRIPTION

[0032] In order to make the objects, technical solutions and advantages of the present application clearer, the disclosed embodiments will be further described in detail below with reference to the drawings.

[0033] A composite material rotary body thermal straightening simulation method based on deformation energy theory, which adopts a mesoscopic mechanics model to predict composite material viscoelastic properties as model material performance input conditions, comprises the following steps:

[0034] (1) Composite material viscoelastic mesoscopic mechanics modeling

[0035] The Generalized Methods of Cells (GMC) assumes that the composite material is composed of repeatable cell units, and the composite material mesoscopic mechanics model established by extracting the repeatable cell units is a cell model. The fibers of the unidirectional composite material are arranged in the x1 direction, and the fibers are arranged in a square in the x2-x3 plane. The repeatable cell unit is a cell containing a fiber section, and the fiber section is equivalent to a rectangle. The cell model contains four subcells, one of which represents the fiber, and the other three represent the viscoelastic matrix material, as shown in Figure 1 .

[0036] (2.6)-(2.9) are the process of solving the volume of the cell model. From the geometric characteristics of the cell model, we can get the following relationships:

[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] In the formula, 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 DV, respectively, and d is the length of the unit cell in the fiber direction. The parameter factor λ is used to measure the magnitude of the effect of viscosity on the unit cell model under different loads. h is the fiber diameter.

[0042] The parameter factor λ is in the range of:

[0043] V f < λ < 1 / V f (2.10)

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

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

[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 by the following formula:

[0050]

[0051] Write the above formula in the incremental form as:

[0052]

[0053] In the formula, V and V α are the volume of the unit cell model and each sub-cell, respectively.

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

[0055]

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

[0057]

[0058] Write equations (2.17)-(2.22) in matrix form as:

[0059]

[0060] where dε α = [dε A , dε B , dε C , dε D , dε A , dε B , dε C , dε D ]Tare the strain increments of the subcells A, B, C and D, respectively; A G is a 13 x 24 matrix describing the geometry of the interior of the unit cell model; B G is a 13 x 6 matrix describing the geometry of the interior of the unit cell model. A G and B G are called geometry matrices.

[0061] Similarly, using the stress continuity conditions at the interfaces between the subcells and between the adjacent unit cell models, the following basic relations for the volume-averaged stresses of the subcells are obtained, which describe the relationship between the subcell strains and the macroscopic strain.

[0062] A M dε α = 0 (2.24)

[0063] where A M is an 11 x 24 matrix determined by the material constants of the subcells.

[0064] These equations obtained by applying the continuity conditions relate the subcell strains to the macroscopic strain of the composite material. By combining equations (2.23) and (2.24) and writing them in a more compact matrix form, we have:

[0065]

[0066] where

[0067]

[0068] To obtain the subcell strains expressed in terms of the volume-averaged macroscopic strain, equation (2.25) is solved to give:

[0069]

[0070] where

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

[0072] To obtain the specific form of the matrix R, the matrix is expressed in block form as:

[0073]

[0074] where is (A 11 )13x12 matrix.

[0075] Combining equations (2.11), (2.27) and (2.28), the following expression can be obtained:

[0076]

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

[0078]

[0079] where C * is the macroscopic stiffness matrix of the unidirectional composite, which is expressed as:

[0080]

[0081] where V is the volume of the unit cell; V α is the volume of the subcell α; α∈[A, B, C or D], A represents the region of the subcell as fiber, B~D represent the region of the subcell as viscoelastic matrix material; C α is the stiffness matrix of the subcell α; R α is the constant conversion matrix of the relationship between the strain component of the subcell α and the strain component of the unit cell.

[0082] (2.34) is obtained by calculating the volume of the composite unit cell and the macroscopic stiffness matrix of the composite. The macroscopic compliance matrix S * of the unidirectional composite is expressed as:

[0083]

[0084] (2) Viscoelastic micromechanics model to solve the viscoelastic matrix material changes with time

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

[0086]

[0087] where C ijkl is the stiffness matrix of the material. σ ij is the stress of the material, σ ij is the strain of the material, τ is the relaxation time, and t is the reduced time of the Maxwell unit.

[0088] Taking Laplace transform of equation (2.35), the image function can be obtained as follows:

[0089]

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

[0091]

[0092] The basic equation of the composite material in frequency domain is obtained by the micromechanics model. By converting the material constants in it into the corresponding material constant expressions in frequency domain, these equations can be directly used.

[0093]

[0094] Here is the macroscopic compliance matrix of the unidirectional composite material in frequency domain, which can be calculated by equation (2.34).

[0095] By comparing the form of equation (2.39), the corresponding stiffness matrix of the viscoelastic matrix material in frequency domain can be obtained:

[0096]

[0097]

[0098] By using the inverse Laplace transform, the stiffness matrix of the viscoelastic matrix material in time domain can be obtained.

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

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

[0101] According to the stress and strain of the unit cell, as well as the geometric parameters of the unit cell, the boundary conditions of the unit cell and the 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, which is the basic data of the viscoelastic micromechanics model for the calculation of the composite material laminated plate and structure. 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, and the viscoelastic micromechanics model of the composite material is obtained.

[0102] Using a viscoelastic micromechanical model of composite materials, the viscoelastic properties of the composite material can be calculated. The viscoelastic property is the variation of stiffness with time (or temperature). The micromechanical model is written as a FORTRAN program for easy integration with other finite element software for composite material and structural analysis. The subroutine includes three parts: component property assignment, unit cell creation, and subcell stress / strain calculation.

[0103] A simulation method for thermal straightening of composite rotating bodies based on deformation energy theory, based on the functional principle, designs the straightening load by conserving the energy of three factors: the deformation energy increment caused by the straightening load, the deformation energy increment caused by the springback deformation after the straightening load is unloaded, and the deformation energy increment between the final straightened state and the initial deformation state. The method simulates the straightening springback and residual deformation, and includes the following steps:

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

[0105] 2. Design the corrective displacement load.

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

[0107] Under corrective loading, temperature rise and temperature plateau cause creep / stress relaxation in the rotating component, generating additional irreversible deformation energy E in the rotating component. cr ;

[0108] After unloading, the deformation energy of the driving rotating component during springback is the elastic deformation energy E. el This includes both ordinary elastic deformation energy and high elastic deformation energy.

[0109] Assume that the corrective displacement load is applied to n points on the end frame of the rotating component, each point having two degrees of freedom in a plane perpendicular to the axis. Based on the principle of "method of exhaustion," the more loading points there are, the smaller the corrective displacement applied to each point, and the closer the final shape will be to a circle. The corrective scheme can be designed based on the roundness values ​​in various directions, including the corrective points and displacements. Figure 3 As shown. The load application and evolution process is shown in [reference needed]. Figure 2 Figures a and b.

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

[0111]

[0112] The increment of the displacement load of the final orthopedic state of the rotating body member can be written as:

[0113]

[0114] dE tot , dE el , dE cr are respectively the increment of the deformation energy caused by the orthopedic load, the increment of the deformation energy caused by the rebound deformation after the unloading of the orthopedic load, and the increment of the deformation energy between the final orthopedic state and the initial deformation state. The increment of the deformation energy and the orthopedic displacement load have the following relationship:

[0115] dE tot = [C] [δ] (2.47)

[0116] dE cr = [C cr ] [△δ] (2.48)

[0117] dE el = [C cr ] [δ ∞ ] (2.49)

[0118] Wherein, [C] and [C cr ] are respectively the stiffness of the composite material before the initial load is applied and the stiffness after the initial load is unloaded, and are calculated according to the viscoelastic micromechanics model of the composite material; δ is the initial displacement load matrix of the rotating body member of the composite material after the curing deformation; Δδ is the increment of the orthopedic displacement load applied to the rotating body member of the composite material, and δ ∞ is the increment of the displacement load of the rotating body member of the composite material after the orthopedic treatment.

[0119] 3. Simulation of rebound strain after orthopedic treatment and orthopedic residual stress

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

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

[0122] The relationship formula of the deformation energy energy conservation is used to simulate the rebound displacement results and the orthopedic residual stress of the rotating body member of the composite material after the orthopedic treatment. The specific calculation iteration steps are as follows:

[0123] ①establishing a macro finite element model of the composite body of revolution component structure, performing curing deformation simulation analysis of the composite body of revolution component, obtaining the curing deformation condition and initial thermal residual stress state, and the curing deformation condition including the initial displacement load matrix δ of the composite body of revolution component after curing deformation;

[0124] ②applying the initial load to the composite repeatable unit cell according to the composite viscoelastic micromechanics model, and calculating the macro stiffness matrix of the unidirectional composite material;

[0125] ③inputting the initial thermal residual stress state to the macro finite element model of the composite body of revolution component structure, assigning the macro stiffness matrix of the unidirectional composite material to the element integration point, inputting the initial displacement load matrix δ of the composite body of revolution component after curing deformation and the correction displacement load increment matrix Δδ of the composite body of revolution component, taking the deformation energy energy conservation as the boundary condition, and calculating the macro stress field, strain field and displacement field;

[0126] ④obtaining the macro strain according to the macro strain field; then inputting the macro strain as the boundary condition of the repeatable unit cell to the macro finite element model of the composite body of revolution component structure, and obtaining the stress-strain of the micromechanical component;

[0127] ⑤judging the damage according to the stress-strain of the micromechanical component by using the micromechanical component failure criterion, if the damage occurs, the calculation stops, the loading fails, the load is reduced, and the initial load is changed to restart the cycle; if the damage does not occur, the duration after the initial load is increased, and the cycle calculation is returned to step ③ until the stiffness matrix obtained according to the composite viscoelastic micromechanics model no longer changes, the calculation is terminated, the displacement load increment matrix δ∞ of the composite body of revolution component after correction is obtained according to the displacement field, and the correction residual stress is obtained according to the macro stress field.

[0128] Example 1

[0129] The following further detailed description of the composite body of revolution thermal correction simulation method provided by the embodiment of the application is made in combination with the drawings of the specification, and the specific implementation mode can include:

[0130] TG800 / 802 carbon fiber reinforced bismaleimide composite grid body of revolution structure thermal correction simulation

[0131] (1) Using the micromechanics model to predict the composite viscoelastic properties as the model material performance input condition

[0132] (1) Composite viscoelastic micromechanics modeling

[0133] Most polymer matrices used in composite materials exhibit viscoelastic behavior, which is a superposition of elasticity and viscosity. In micromechanical simulations, the polymer matrix behavior is generally considered to be linear viscoelastic, and the constants in the viscoelastic equation of the material are assumed to be independent of temperature. The relaxation modulus of the resin is defined using the Prony series:

[0134]

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

[0136] Poisson's ratio υ of the material m It is considered a constant and is 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°C is as follows: Figure 3 As shown. Initial stresses of 38 MPa, 30 MPa, and 22 MPa were selected. Creep / stress relaxation occurred in the resin at high temperature. At 210℃, creep equilibrium was basically reached within 2 hours, and strain changed with time after unloading. The essential molecular chain motion of polymer creep manifested sequentially at different time scales. After unloading, both elastic deformation ε1 and high-elastic deformation ε2 recovered, but viscous flow deformation strain ε3 remained. At the instant of unloading, elastic deformation ε1 disappeared, while high-elastic deformation ε2 basically recovered after 10 minutes, and the curve region was flat. Residual strain at the same time and temperature increased with the application of initial stress. Ten minutes after creep unloading, the residual strains corresponding to initial stresses of 38 MPa, 30 MPa, and 22 MPa were 0.7%, 0.44%, and 0.25%, respectively.

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

[0140]

[0141] Represented in vector form as follows:

[0142]

[0143] In the formula, <·> represents the average value of the components, and C ijkl(t) is the total stiffness matrix of the heterogeneous material, which is a 6x6 matrix. For transversely isotropic materials, there are only 5 independent parameters in this matrix. The tensile modulus and strength of carbon fiber are tested by a single fiber strength tester, and the carbon fiber single fiber measuring device and the modulus calculation parameter correction method are shown in Figure 4

[0144] 70 single fiber samples of each carbon fiber are prepared, the failure mode is recorded during the tensile process, and it is observed whether the carbon fiber single fiber in the gauge length section is broken, that is, the abnormal failure sample data is immediately removed, and the normal failure sample strength-displacement curve is recorded. It is generally believed that the tensile strength of carbon fiber single fiber satisfies Weibull distribution, and the expression is:

[0145]

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

[0147] Table 1 Weibull fitting of TG800 single fiber tensile strength

[0148]

[0149] The modulus of the single fiber needs to be corrected by different gauge lengths. The transmission error between the upper and lower clamps causes the elongation test error. For different gauges of 20-40 mm, 10 samples of each sample are prepared, and the effective samples are taken to calculate the tensile modulus of TG800, which is 294.11 GPa.

[0150] (2) Solution of viscoelastic micromechanics model

[0151] Using the micromechanics model, the time (or temperature) variation law of the viscoelastic material properties of the elastic parameters of the composite material can be calculated. The micromechanics model is written into a FORTRAN program, which is convenient for calling when analyzing the composite material and structure with other finite element software. The subroutine includes three parts of component attribute assignment, unit cell establishment and unit cell stress / strain solution, and the subroutine interface is as follows Figure 5 .

[0152] (3) Establishment of viscoelastic constitutive relation of composite material

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

[0154] ​​(II) Based on the functional principle, the orthotic load is designed by the energy conservation of the deformation energy increment caused by the orthotic load, the deformation energy increment caused by the rebound deformation after the unloading of the orthotic load, and the deformation energy increment between the final orthotic state and the initial deformation state. The orthotic rebound and the orthotic residual deformation are simulated.

[0155] (1) The curing deformation simulation analysis of the composite rotating body component is performed to obtain the curing deformation condition.

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

[0157]

[0158] In the 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 respectively represent the strain caused by mechanical stress, thermal strain and curing shrinkage.

[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 holding platform stage can be expressed as

[0164]

[0165] For continuous fiber reinforced composite materials, due to the constraint effect of fibers, 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 during the cooling stage and the curing shrinkage during the holding platform is a constant value, denoted as s, which is measured by the fiber grating experiment.

[0166]

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

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

[0169] Δσ = [C] ΔE e (2.63)

[0170] The cure distortion prediction for the TG800 / 802 composite 1.7m rotor includes the skin, upper and lower end frames, grid stringers (circumferential and ±45°), and the thickened area, as shown in Figure 7 (a). The specific plies are shown in Table 2.

[0171] Table 2. Grid rotor plies

[0172]

[0173] The boundary conditions for the distortion prediction model are that the axial distortion at the end frame bottom is 0, as shown in Figure 7 (b).

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

[0175] Table 3. 1.7m rotor cure distortion experimental values

[0176]

[0177] (2) Perform orthotic displacement load design

[0178] The orthotic displacement load loading method is shown in Figure 9 (a), in which the numbers represent the position change values before and after the cure distortion after the orthotic displacement is applied at each orthotic point, and the overall profile is elliptical. The vertical major axis b of the ellipse is greater than the horizontal major axis a, so the orthotic displacement value applied at 90° and 270° is about +7mm, and the orthotic displacement value applied at 0° and 180° is about -5mm. The orthotic displacement values of the remaining orthotic points are adjusted according to the internal stress and the distortion energy. The orthotic displacement load loading in the finite element model is shown in Figure 9 (b). The final profile and orthotic displacement size are shown in Figure 9 (c).

[0179] (3) Simulate the orthotic results and orthotic stress conditions

[0180] According to the orthotic scheme and the strain energy theory, the "cure distortion-thermal orthotic" profile is fitted and obtained, as shown in Figure 10 (a). After the cure distortion, the structure is elliptical, with the horizontal major axis a being greater than the vertical minor axis b. After the orthotic displacement is applied, the vertical axis b of the ellipse becomes the major axis. Finally, the rotor structure profile rebounds to a circle, with a residual distortion of 0.9mm<1mm. During the entire process, as shown in Figure 10(b) as shown, the deformation energy of the three stages meets the balance relationship when loaded at room temperature, under the action of orthopedic load, and after unloading.

[0181] The contour of the rotary body is an ellipse with the horizontal axis as the long axis after curing deformation, the contour changes to an ellipse with the vertical axis as the long axis after applying the orthopedic displacement, and the contour becomes a circle after unloading and rebounding. During the whole process, the orthopedic deformation energy theory is met, and the change of the end frame roundness of the rotary body before and after orthopedic changes from 3.22 mm to 0.87 mm. The residual contour roundness experimental result is 0.9 m, the rotary body deformation prediction error is 3.3%, and the model reliability is verified.

[0182] The rotary body residual stress calculation result is shown in Figure 11 a, b, c and d. The maximum value of the transverse tensile stress S22 on the second layer of the layer is about 42.6 MPa, the maximum value is located at the bending part of the front frame and the end frame, and reaches 72.3% of the transverse tensile strength; the resin tensile damage is easy to occur. The longitudinal tensile stress is 406 MPa, which is 16.4% of the tensile strength; the maximum value of the in-plane shear stress S12 is about 30.8 MPa, which is 30.5% of the shear strength; the maximum value of the out-of-plane shear stress S13 is 25.9 MPa, which is 25.6% of the shear strength. The stress values of the unit where the maximum value of the transverse tensile stress S22 are substituted into the Hashin and Puck failure criteria to judge that the internal stress does not reach the failure condition, and the rotary body structure does not damage.

[0183] The contents not described in detail in the specification of the present application are the known technology of those skilled in the art.

[0184] The present application is described in detail in combination with the specific embodiments and exemplary examples, but these descriptions cannot be understood as limitations of the present application. Those skilled in the art understand that various equivalent replacements, modifications or improvements can be made to the technical solutions and embodiments of the present application without departing from the spirit and scope of the present application, and these all fall within the scope of the present application. The protection scope of the present application is subject to the appended claims.

Claims

1. A method for simulating thermal straightening of a composite material revolution body based on deformation energy theory, characterized by, Comprise: S1: Viscoelastic micromechanics modeling of the composite material by unit cell method, obtaining the macroscopic stiffness matrix C of the unidirectional composite material * Expression and macroscopic compliance matrix S * Expression; wherein the composite material comprises a plurality of repeatable unit cells, and each unit cell comprises four sub-cells arranged in a square, one of which represents a fiber, and the other three represent viscoelastic matrix material; S2: Laplace transform is made to one of the viscoelastic matrix materials of the subcell according to linear viscoelastic basic equation of stress relaxation, an image function is obtained, and a stiffness matrix of the viscoelastic matrix material in a frequency domain is extracted from the image function a stiffness matrix of the viscoelastic matrix material is obtained according to the stiffness matrix of the viscoelastic matrix material a macroscopic flexibility matrix is obtained a stiffness matrix of the viscoelastic matrix material in a time domain is obtained according to the macroscopic flexibility matrix by using Laplace inverse transform a stiffness matrix of the viscoelastic matrix material in a time domain is obtained according to the macroscopic flexibility matrix by using Laplace inverse transform S3: repeat S2, obtain the stiffness matrix of each viscoelastic matrix material in the time domain, and determine the stiffness matrix of the fiber according to the material of the fiber; S4: the stiffness matrix in the time domain of the viscoelastic matrix material 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 micromechanics model of the composite material is obtained; S5: based on the composite material viscoelastic micromechanics model, the composite material rotary body component thermal straightening is simulated, specifically including: ①The macroscopic finite element model of composite material rotary body component structure is established, the curing deformation simulation analysis of composite material rotary body component is carried out, the curing deformation condition and initial thermal residual stress state are obtained, the curing deformation condition includes the initial displacement load matrix δ of composite material rotary body component after curing deformation; ②According to the composite material viscoelastic micromechanics model, the initial load is applied to the composite material repeatable unit cell, and the macroscopic stiffness matrix of unidirectional composite material is calculated; ③The initial thermal residual stress state is input to the macroscopic finite element model of composite material rotary body component structure, the macroscopic stiffness matrix of unidirectional composite material is assigned to the element integral point, the initial displacement load matrix δ of composite material rotary body component after curing deformation and the straightening displacement load increment matrix Δδ of composite material rotary body component are input, and the deformation energy energy conservation is taken as the boundary condition to calculate the macroscopic stress field, strain field and displacement field; ④According to the macroscopic strain field, the macroscopic strain is obtained; then the macroscopic strain is input to the macroscopic finite element model of composite material rotary body component structure as the boundary condition of repeatable unit cell, and the stress-strain of micromechanical component is obtained. ⑤According to the stress-strain of the meso-component, the damage is judged by the failure criterion of the meso-component, if damage occurs, the calculation stops, the loading fails, the load is reduced, and the initial load is changed to return to step ② and recirculate; if no damage occurs, continue to increase the duration after the initial load is applied, return to step ③, and circulate calculation until the stiffness matrix obtained at this time according to the viscoelastic mesoscopic mechanics model of the composite material no longer changes, the calculation is terminated, and the displacement load increment matrix δ of the composite material after the orthopedic rotation body member is obtained according to the displacement field ∞ And the residual stress obtained according to the macroscopic stress field after orthopedic correction.

2. The method according to claim 1, wherein: The initial load is applied on the n points of the end frame at the edge position of the composite material rotary body component, and each point has two degrees of freedom in the plane perpendicular to the axis of the composite material rotary body component.

3. The method according to claim 1, wherein, The deformation energy energy conservation is: dE tot = dE el + dE cr ; At room temperature loading, the total work done by the initial load is entirely converted into composite body of revolution component deformation energy E tot ; under the action of the initial load, the temperature rise and temperature plateau cause the composite body of revolution component to creep / stress relax, forming additional composite body of revolution component irrecoverable deformation energy E cr ; The deformation energy of the composite material rotary body member to rebound after unloading the initial load is elastic deformation energy E el .

4. The method according to claim 3, wherein, The dE tot = [C] [delta], dE cr = [C cr ][△δ], dE el = [C cr ][δ ∞ ], wherein [C] and [C cr ] are the stiffness of the composite before the initial load is applied and the stiffness of the composite after the initial load is removed, respectively, and are calculated according to the viscoelastic micromechanics model of the composite; δ is the initial displacement load matrix of the composite after the curing deformation of the composite body of revolution; Δδ is the increment matrix of the displacement load of the composite body of revolution after the correction, and δ ∞ is the increment matrix of the displacement load of the composite body of revolution after the correction.

5. The method of claim 1, wherein, In the S1, the viscoelastic micromechanics modeling of the composite material is carried out by the cell method to obtain the macroscopic stiffness matrix C of the unidirectional composite material * Expression and macroscopic compliance matrix S * Expression, comprising: Using homogenization theory, the volume average stress of each unit cell is obtained; According to the volume average stress of each unit cell, and using the interface displacement continuity condition, the relationship between the macroscopic strain of the composite material and the volume average strain of each unit cell is obtained; According to the relationship between the macroscopic strain of the composite material and the volume average strain of each unit cell, the stress continuity condition of the interface between the unit cells and the adjacent unit cells is used to obtain the basic relationship of the volume average stress of the unit cell; According to the volume average stress basic relation of the sub-cells, the macroscopic stiffness matrix C of the unidirectional composite material is obtained * The expression is obtained according to the macroscopic stiffness matrix C of the unidirectional composite material * The expression is obtained according to the macroscopic stiffness matrix C of the unidirectional composite material * The expression is obtained according to the macroscopic stiffness matrix C of the unidirectional composite material 6. The method according to claim 5, wherein, The volume average stress of each cell should be: where V α is the volume of the cell; a e [A, B, C or D], A indicating that the cell is a fiber region, B-D indicating that the cell is a viscoelastic matrix material region; is the stress increment of the cell; V is the volume of the cell; σ ij is the stress increment of the cell.

7. The method according to claim 6, wherein The relationship between the macroscopic strain of the composite material and the volume average strain of each unit cell is: Where, dε α =[dε A ,dε B ,dε C ,dε D ], dε A ,dε B ,dε C and dε D These represent 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 features of the unit cell model.

8. The method according to claim 7, wherein, The volumetric average stress of the sub-cell is substantially related to the formula A M dε α =0 where A M is a matrix determined by the material constants of each subcell; dε α is the strain increment of subcell α.

9. The method of claim 1, wherein, The macroscopic stiffness matrix C of the unidirectional composite * The expression is: where V is the volume of the unit cell; V α is the volume of the unit cell α; α ∈ [A, B, C or D], A represents the region of the unit cell being fiber, B-D represent the region of the unit cell being viscoelastic matrix material; C α is the stiffness matrix of the unit cell α; R α is the constant conversion matrix of the relationship between the strain component of the unit cell α and the strain component of the unit cell; λ is a parameter factor.

10. The method of claim 9, wherein the method is characterized by: The macroscopic flexibility matrix S * The expression is: S * (λ) = [C * (λ)] -1 .

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