A high-temperature creep deformation prediction method based on honeycomb structure characteristics

Abstract

The present invention discloses a method for predicting high-temperature creep deformation based on honeycomb structure characteristics, which includes the following steps: S1. Combining the high-temperature creep experiment of the initial honeycomb core and the initial constitutive model, fitting to obtain a unified high-temperature creep constitutive model; S2. Measuring the structural characteristic parameters of the initial honeycomb core and calculating the stress conversion factor; S3. Measuring the structural characteristic parameters of the honeycomb core to be measured; S4. Constructing a simulation model of the honeycomb core to be measured in simulation software; S5. Applying loads to the simulation model of the honeycomb core to be measured, setting analysis steps, introducing the stress conversion factor, and embedding the unified high-temperature creep constitutive model; S6. Submitting the job to predict the high-temperature creep deformation of the honeycomb core to be measured. The present invention has high accuracy, reduces experimental costs, reduces experimental risks, saves manpower, and the simulation prediction method is faster than the experimental method. It can also predict in advance the types of honeycomb cores that cannot be produced by existing processes.

Description

Technical Field

[0001] The present invention belongs to the technical field of honeycomb composite materials, and particularly relates to a method for predicting high-temperature creep deformation based on honeycomb structure characteristics. Background Art

[0002] The honeycomb sandwich structure is mainly composed of a honeycomb core, upper and lower skins, and is bonded by an adhesive film. According to its application form, the honeycomb sandwich structure is mainly divided into two application structures: the honeycomb sandwich panel structure and the full-height honeycomb sandwich structure. The full-height honeycomb sandwich structure is widely used in the structures such as aircraft control surfaces due to its high stiffness and strength characteristics. In the full-height honeycomb sandwich structure, the upper and lower surfaces of the honeycomb core directly form the aerodynamic surface of the aircraft, that is, the aerodynamic shape accuracy of the aircraft directly determines the forming accuracy of the full-height honeycomb sandwich structure. According to "Aerodynamic Outer Edge Tolerances for Civil Aircraft" (HB 7086-2023), for an aircraft with a cruise speed ≥ 600 km / h in category I, it is stipulated that the concave-convex amount error of its control surface (rudder) is controlled within 0.5 mm, and the profile value error in the leading edge area of the wing is within 0.8 mm. For commonly used domestic military aircraft, the basic profile value tolerance is (-0.5, +1.0) mm, and the limit deviation is (-0.6, +1.2) mm. For high-precision satellites, the limit deviation of its honeycomb sandwich structure is even more stringent. If the dimensional accuracy of the honeycomb sandwich structure parts does not meet the standard, it will not only affect the overall aerodynamic shape of the aircraft, but may seriously affect the safety performance of the entire aircraft.

[0003] However, the honeycomb sandwich structure will undergo permanent shrinkage during the forming process, which makes it difficult for the formed honeycomb sandwich structure parts to meet the thickness tolerance standard. At the same time, according to the patent document CN119348280A, a forming method for a honeycomb sandwich structure based on allowance compensation, among the non-recoverable deformations that occur during the forming process of the honeycomb sandwich structure, the creep deformation that occurs to the honeycomb core under high temperature and high pressure is the most difficult to measure, and the creep deformation highly coincides with the non-recoverable deformation of the honeycomb core.

[0004] In current industrial production, due to the differences in the thickness of aramid paper, impregnation process, and honeycomb manufacturing process, the structural characteristics of the manufactured honeycomb cores are variable (wall thickness d, expansion angle θ, wall length h and l, or different honeycomb cell types), resulting in different creep deformations of the honeycomb cores during the forming process. If we measure the high-temperature creep deformation of the honeycomb cores under each different structural characteristic, it will inevitably waste a large amount of manpower and material resources. That is to say, the existing methods are difficult to meet the prediction and verification of the high-temperature creep deformation of honeycomb cores with different structural characteristics.

[0005] Therefore, it is necessary to design a new method for predicting high-temperature creep deformation based on honeycomb structure characteristics. Summary of the Invention

[0006] The object of the present invention is to provide a high-temperature creep deformation prediction method based on honeycomb structure characteristics, so as to solve the problem that the existing methods in the background technology are difficult to meet the prediction and verification of high-temperature creep deformation of honeycomb cores with different structural characteristics.

[0007] To achieve the above object, the present invention provides a high-temperature creep deformation prediction method based on honeycomb structure characteristics, including the following steps:

[0008] S1. Combine the high-temperature creep experiment of the initial honeycomb core and the initial constitutive model applicable to creep to fit and obtain the unified high-temperature creep constitutive model of the honeycomb core;

[0009] S2. Measure the structural characteristic parameters of the initial honeycomb core and calculate the stress conversion factor;

[0010] S3. Measure the structural characteristic parameters of the honeycomb core to be measured;

[0011] S4. Build a simulation model of the honeycomb core to be measured in the simulation software according to the structural characteristic parameters of the honeycomb core to be measured;

[0012] S5. Apply loads and set analysis steps to the simulation model of the honeycomb core to be measured, introduce the stress conversion factor, and embed the unified high-temperature creep constitutive model of the honeycomb core obtained by fitting into the simulation model of the honeycomb core to be measured;

[0013] S6. Submit the job to predict the high-temperature creep deformation of the honeycomb core to be measured.

[0014] In a specific embodiment, the initial constitutive model applicable to creep is the Findley constitutive model.

[0015] In a specific embodiment, in step S1, the nonlinear surface fitting method in Matlab is used for fitting.

[0016] In a specific embodiment, during the fitting process, time and the nominal stress received by the honeycomb core are set as independent variables and do not participate in the fitting; the time-creep deformation data is the dependent variable and does not need to be fitted either; the variables to be fitted include the initial creep deformation, creep parameters, stress dependence index, and time index; the nominal stress = load / nominal area, and the nominal area is the overall area of the honeycomb core;

[0017] Input the formula of the initial constitutive model into the fitting software, and input the time-creep deformation data of the initial honeycomb core under different temperatures and pressures in the high-temperature creep experiment of the initial honeycomb core into the fitting software together, and finally fit out the variables to be fitted.

[0018] In a specific embodiment, the structural characteristic parameters include the straight wall length, inclined wall length, expansion angle, wall thickness of the honeycomb core cell, and the length, width, and height of the overall size of the honeycomb core.

[0019] In a specific embodiment, the simulation software is Abaqus simulation software; in combination with FORTRAN and Visual Studio development environment, the fitted high-temperature creep unified constitutive model of the honeycomb core is embedded into the simulation software by combining the CREEP subroutine interface of the Abaqus simulation software's secondary development.

[0020] In a specific implementation, the stress conversion factor I=A1 / A2, A1 is the cross-sectional area of ​​the initial honeycomb core, and A2 is the nominal area of ​​the initial honeycomb core.

[0021] In a specific implementation, in step S1, the initial high-temperature creep experiment of the honeycomb core is performed using a creep machine with a planar compression creep assembly.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention provides a high-temperature creep deformation prediction method based on honeycomb structure characteristics, which is not only highly accurate, but also reduces experimental costs, reduces experimental risks, saves manpower, and the simulation prediction method is faster than the experimental method. It can also predict in advance the types of honeycomb cores that cannot be produced by existing processes, which provides solid technical support for the performance prediction and optimization design of composite materials under extreme environmental conditions.

[0024] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention is further described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0026] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0027] Figure 2 This is a fitting result diagram of an embodiment of the present invention at 120°C and 0.2-0.5MPa;

[0028] Figure 3 This is a fitting result diagram of an embodiment of the present invention at 180°C and 0.2-0.5MPa;

[0029] Figure 4 It is a diagram of the overall size and structural characteristic parameters of a honeycomb core of an embodiment of the present invention;

[0030] Figure 5 It is a schematic cross - sectional view of a hexagonal honeycomb core;

[0031] Figure 6 It is a schematic cross - sectional view of an over - expanded honeycomb core;

[0032] Figure 7 It is a comparison chart of the simulated creep prediction deformation and experimental results of honeycomb cores with different structural features in an embodiment of the present invention;

[0033] Figure 8 It is a schematic view of a honeycomb sandwich structure; wherein, 1, honeycomb core; 2, adhesive film; 3, upper skin; 4, lower skin. Specific implementation manners

[0034] The following is a detailed description of the embodiments of the present invention. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0035] Embodiment 1

[0036] A method for predicting high - temperature creep deformation based on honeycomb structural features of the present invention includes the following steps:

[0037] S1. Combining the initial honeycomb core high - temperature creep experiment and the initial constitutive model applicable to creep, a unified high - temperature creep constitutive model of the honeycomb core is obtained by fitting.

[0038] The initial constitutive model applicable to creep is the Findley constitutive model, and its expression is:

[0039] ,

[0040] wherein, ε \(\varepsilon(t)\) is the creep deformation at creep time \(t\), ε \(\varepsilon_0\) is the initial creep strain, \(A\) is the creep parameter, and the creep parameter is affected by temperature and material properties, σ \(\sigma\) is the applied stress, \(n\) is the stress - dependent exponent, and \(m\) is the time exponent.

[0041] In the initial honeycomb core high - temperature creep experiment, the initial honeycomb core selected is a hexagonal honeycomb core. The overall dimensions of the hexagonal honeycomb core are: \(W\times L\times T = 35\mathrm{mm}\times35\mathrm{mm}\times20\mathrm{mm}\). The structural feature parameters of its honeycomb core cells are: \(h = 1.99\mathrm{mm}\), l \(b = 2.02\mathrm{mm}\), \(d = 0.05\mathrm{mm}\), \(\theta = 30^{\circ}\). The temperature conditions are: \(120^{\circ}C\) and \(180^{\circ}C\), the nominal stress conditions are: \(0.2\mathrm{MPa}-0.5\mathrm{MPa}\), nominal stress = load / nominal area, nominal area = \(W\times L\), and the creep time is: \(35\mathrm{h}\).

[0042] In the step S1, a creep testing machine with a plane compression creep assembly is used for the high-temperature creep experiment of the initial honeycomb core to conduct the high-temperature creep of the honeycomb core under multiple common experimental conditions, laying a foundation for the subsequent establishment of a unified constitutive model.

[0043] The plane compression creep assembly includes a tensile conduction compression die, an upper plane compression die, and a lower plane compression die; the tensile conduction compression die includes a first pressing block and a second pressing block, and a spacing for installing a specimen is maintained between the first pressing block and the second pressing block along the tensile direction of the creep testing machine, and the value of this spacing can be adjusted. When the spacing becomes smaller, it is used to provide creep compression loading operation for the specimen, and when the spacing becomes larger, it is used to remove the specimen; a first threaded hole is provided on the second pressing block, and the axis line of the first threaded hole is the same as the tensile direction of the creep testing machine. A first through hole coaxial with the first threaded hole is provided on the first pressing block; the upper plane compression die includes an upper cylindrical rod, an external thread end, and an upper circular plate. One end of the upper cylindrical rod is fixedly connected to the external thread end, and one side plate surface of the upper circular plate is fixedly connected to the other end of the upper cylindrical rod. The external thread end and the upper circular plate are coaxially arranged with the upper cylindrical rod; the external thread end is fitted on the first threaded hole; the lower plane compression die includes a lower cylindrical rod, a cylindrical base, a pin, and a lower circular plate. The cylindrical base is plate-shaped, one end of the pin is fixedly connected to one side surface of the cylindrical base, the other side surface of the cylindrical base is fixedly connected to one end of the lower cylindrical rod, and the lower circular plate is fixedly arranged at the other end of the lower cylindrical rod. The pin and the lower circular plate are coaxially arranged with the lower cylindrical rod. The surface of the cylindrical base close to the pin is perpendicular to the axis line of the lower cylindrical rod, and the surface of the lower circular plate far from the pin is parallel to the surface of the cylindrical base close to the pin; the pin is fitted on the first through hole. Preferably, the adopted plane compression creep assembly has the same structure as that disclosed in the patent document CN202410785728.3.

[0044] In the step S1, the nonlinear surface fitting method in Matlab is used for fitting.

[0045] During the fitting process, the creep time t and the nominal stress σ received by the honeycomb core are set as independent variables and do not participate in the fitting. The creep time t is the independent variable, and the nominal stress σ received by the honeycomb core is the environmental variable, which changes with the change of the experimental applied load; the time-creep deformation data ε (t) is the dependent variable and does not need to be fitted either; the variables to be fitted include the initial creep deformation ε 0, the creep parameter A, the stress dependence index n, and the time index m; the nominal stress = load / nominal area, and the nominal area is the overall area of the honeycomb core;

[0046] Input the initial constitutive model formula into the fitting software, and also input the time-creep deformation data of the initial honeycomb core at different temperatures and pressures in the initial honeycomb core high-temperature creep experiment into the fitting software, and finally fit the variables to be fitted.

[0047] S2. Measure the structural characteristic parameters of the initial honeycomb core and calculate the stress conversion factor.

[0048] Under the same experimental conditions (temperature and load), when the structural characteristics in the honeycomb core change (cell wall thickness, cell size, wall length or cell type), it will inevitably cause a change in the equivalent stress inside the honeycomb core (the equivalent stress is the stress received by each tiny unit in the honeycomb core, different from the nominal stress. The nominal stress refers to the pressure received by the whole honeycomb core, often equal to the experimental pressure). Once the equivalent stress inside the honeycomb core changes, this equivalent stress is then converted into the nominal stress in the unified constitutive model through the stress conversion factor, and finally the creep deformation prediction simulation of the honeycomb core under different structural characteristics is realized.

[0049] The stress conversion factor is a constant, mainly used to convert the equivalent stress of the honeycomb core used in the experiment into the nominal stress required in the unified creep constitutive model. σ This factor is determined by the ratio of the cross-sectional area of the initial honeycomb core to the nominal area.

[0050] Determination of the stress conversion factor:

[0051] First, measure the structural characteristic parameters of the initial honeycomb core. The structural characteristic parameters include the straight wall length, inclined wall length, expansion angle, wall thickness of the honeycomb core cells, and the length, width and height of the overall size of the honeycomb core.

[0052] Then calculate the cross-sectional area A1 of the initial honeycomb core according to the structural characteristic parameters. The cross-sectional area is the area directly borne by the honeycomb core. The area of the hollow in the middle of the honeycomb core hexagon is not, that is to say, the area occupied by the solid material.

[0053] Taking the external experimental pressure condition σ 1 as an example, assuming the nominal area of the honeycomb core = A2, the force F applied to the surface of the honeycomb core can be calculated according to the pressure formula as σ 1×A2 (Note: The cross-sectional area of the honeycomb core and the nominal area are not the same concept).

[0054] In the simulation, when the experimental conditions are applied, the stress received by the internal units of the honeycomb core can be obtained, assumed to be σ 2 = F / A1. And the stress σ in the unified constitutive model σ is equal to σ2 Stress converted to the constitutive model σ 1. Also, because

[0055] σ 2 = F / A1, F = σ 1 × A2

[0056] It is deduced that:

[0057] σ 2 * A1 / A2 = σ 1

[0058] Therefore, A1 / A2 is defined as a new constant I, that is, the stress conversion factor, to convert the creep stress output in the simulation model to the nominal stress in the constitutive model. The creep stress output in the simulation model is the equivalent stress, which is the stress suffered by the internal units of the honeycomb core during the creep process.

[0059] Then calculate the nominal area of the initial honeycomb core. The nominal area A2 = W × L. The nominal area is the overall area of the honeycomb core, which is Figure 4 W × L in

[0060] Finally, calculate the stress conversion factor I = A1 / A2, where A1 is the cross-sectional area of the initial honeycomb core and A2 is the nominal area of the initial honeycomb core. The stress conversion factor is used to convert the creep stress output in the simulation model to the nominal stress in the constitutive model σ .

[0061] S3. Measure the structural characteristic parameters of the honeycomb core to be measured.

[0062] S4. Construct a simulation model of the honeycomb core to be measured according to the structural characteristic parameters of the honeycomb core to be measured in the simulation software. The single-layer orthotropic method is used for modeling in the simulation software, and the aramid paper and phenolic resin are equivalent to a unified solid element.

[0063] S5. Apply loads and set analysis steps to the simulation model of the honeycomb core to be measured, introduce the stress conversion factor, and embed the unified constitutive model of high-temperature creep of the honeycomb core obtained by fitting into the simulation model of the honeycomb core to be measured;

[0064] Apply load F, where load = experimental pressure condition (nominal stress) × W × L.

[0065] The simulation software is Abaqus 2023 simulation software; combined with the FORTRAN 2020 and Visual Studio 2019 development environments, the constitutive model is compiled and embedded. The unified constitutive model of high-temperature creep of the honeycomb core obtained by fitting is embedded into the simulation software through the CREEP subroutine interface with the secondary development provided by the Abaqus simulation software to realize the high-temperature creep simulation of the honeycomb core.

[0066] During the compilation process, the stress conversion factor I is introduced to predict the creep deformation of honeycomb cores with different structural features in the subsequent steps.

[0067] During the compilation process, the Findley model is divided into two analysis steps and embedded step by step.

[0068] Findley constitutive model: 。

[0069] During the creep simulation of the honeycomb core, two viscous analysis steps are set. The Findley constitutive model is separated. That is, it is embedded in the first viscous analysis step ε 0, and embedded in the second viscous analysis step 。Since the function in the second analysis step is a continuous function, normal calculation can be carried out. While the first viscous analysis step ε 0 is a step function, and because ε 0 is a fixed constant, a linear increment method is adopted to calculate ε 0 through multiple fixed increment steps. The purpose is to convert the ε 0 step function into a linear continuous function to achieve the purpose of calculation convergence. Example: Use n fixed increment steps to smooth ε 0, and deform ε 0 / n respectively under each fixed increment step, where n is determined by multiple simulation trials until the calculation converges.

[0070] S6. Submit the job to predict the high-temperature creep deformation of the honeycomb core to be tested.

[0071] Experimental verification:

[0072] Verification 1. Compare the creep deformation prediction with the experimental results of the same honeycomb core under different pressures.

[0073] Experimental materials: Hexagonal honeycomb cores with the same structural features (structural features: h = 1.99 mm, l = 2.02 mm, d = 0.05 mm, θ = 30°), the same as the initial honeycomb core, overall dimensions: W×L×T = 35 mm×35 mm×20 mm.

[0074] Experimental conditions: 180 °C, 0.6 MPa, 35 h (the unified constitutive model is established under 0.2 - 0.5 MPa, so the applicability of the model under different pressure conditions is verified).

[0075] Experimental equipment: The same creep machine with a plane compression creep assembly.

[0076] Verification 2. Compare the creep deformation prediction with the experimental results of honeycomb cores with different structural features.

[0077] Experimental materials: Over-expanded honeycomb cores with different structural features (structural parameters: h = 1.77 mm, l = 3.85 mm, d = 0.085 mm, θ = 11°), overall dimensions: W×L×T = 35 mm×35 mm×20 mm.

[0078] Experimental conditions: 180 °C, 0.6 MPa, 35 h.

[0079] Experimental equipment: A creep testing machine with the same planar compression creep assembly.

[0080] Verification results: Under the same experimental conditions, in terms of the prediction of the final creep deformation, the simulation prediction accuracy of the hexagonal honeycomb core is 98%, and for the over-expanded honeycomb cores with different structural features, the simulation prediction accuracy is also as high as 97.1%. This shows that the simulation prediction method provided by the present invention can achieve the prediction of the out-of-plane compression creep deformation of honeycomb cores with different nominal stresses and different structural features, and has a high prediction accuracy, proving the feasibility of this method. This provides a solid technical support for the performance prediction and optimal design of honeycomb composites under extreme environmental conditions.

[0081] A high-temperature creep deformation prediction method based on the honeycomb structural features provided by the present invention can be used to predict in advance the creep deformation of honeycomb cores with different structural features, and then, while milling the honeycomb cores, add the allowance of the honeycomb cores to compensate for the shrinkage deformation that occurs during the forming process of the honeycomb sandwich structure, and finally achieve the purpose of precise forming of the honeycomb sandwich structure.

[0082] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions and substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A high temperature creep deformation prediction method based on honeycomb structure characteristics, characterized in that: The steps include: S1. Combining the initial honeycomb core high temperature creep experiment and the initial constitutive model suitable for creep, a unified constitutive model of high temperature creep of the honeycomb core is fitted; the initial honeycomb core high temperature creep experiment uses a creep machine with a plane compression creep assembly to carry out the honeycomb core high temperature creep experiment; the initial constitutive model suitable for creep is the Findley constitutive model; the nonlinear surface fitting method in Matlab is used for fitting; During the fitting process, time and nominal stress of the honeycomb core are set as independent variables and do not participate in the fitting; time-creep deformation data is the dependent variable and does not need to be fitted; the variables to be fitted include the initial creep deformation, creep parameters, stress dependence index and time index of the Findley constitutive model; the nominal stress = load / nominal area, and the nominal area is the overall area of ​​the honeycomb core; The initial constitutive model formula is input into the fitting software, and the time-creep deformation data of the initial honeycomb core at different temperatures and pressures in the initial honeycomb core high temperature creep experiment are also input into the fitting software, and finally the variables to be fitted are fitted; S2, measuring the structural characteristic parameters of the initial honeycomb core and calculating the stress conversion factor; the stress conversion factor I=A1 / A2, A1 is the cross-sectional area of ​​the initial honeycomb core, and A2 is the nominal area of ​​the initial honeycomb core; S3, measuring the structural characteristic parameters of the honeycomb core to be tested; S4. constructing a simulation model of the honeycomb core to be tested according to the structural characteristic parameters of the honeycomb core to be tested in the simulation software; S5, applying load to the honeycomb core simulation model to be tested, setting analysis steps, introducing stress conversion factors, and embedding the fitted high-temperature creep unified constitutive model of the honeycomb core into the honeycomb core simulation model to be tested; S6. Submit the work to predict the high temperature creep deformation of the honeycomb core to be tested.

2. The high temperature creep deformation prediction method based on honeycomb structure characteristics according to claim 1 is characterized in that: The structural characteristic parameters include the straight wall length, inclined wall length, expansion angle, wall thickness of the honeycomb core cell, and the length, width and height of the overall size of the honeycomb core.

3. The high temperature creep deformation prediction method based on honeycomb structure characteristics according to claim 1, characterized in that: The simulation software is Abaqus simulation software; combining FORTRAN and Visual Studio development environment, the high-temperature creep unified constitutive model of the honeycomb core obtained by fitting is embedded into the simulation software by combining the CREEP subroutine interface of the Abaqus simulation software with secondary development.

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