Method for constructing and predicting plastic mechanical model of CFRP (carbon fiber reinforced plastic) reinforced thin-wall square tube

Abstract

The invention relates to the technical field of rail transit materials, in particular to a CFRP reinforced thin-wall square tube plastic mechanical model construction and prediction method, and the construction method comprises the steps: 1, forming a mixed square tube by a CFRP square tube and a Steel square tube; 2, establishing a plastic mechanical model of the CFRP reinforced thin-wall square tube under the end constraint boundary condition; the prediction method comprises the following steps: S1, obtaining size data and material parameters of the mixed square tube; s2, selecting a proper plastic mechanical model; and S3, inputting the data into the model, and predicting the plastic mechanics and energy absorption response of the hybrid square tube under the end constraint condition. The invention provides a method for constructing a plastic mechanics theoretical prediction model of a CFRP reinforced thin-wall square tube. And an expression between the bending load and the deflection of the hybrid square tube under the end constraint condition and an energy absorption theoretical prediction model are constructed. The method achieves the accurate prediction of the influence rule of the change of each structure parameter on the energy absorption mechanism of the CFRP reinforced thin-wall square tube.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit materials, and in particular to a CFRP reinforced thin-walled square tube plastic mechanics model construction and prediction method. Background Art

[0002] Subway collision accidents often occur in the end area of ​​subway head cars, and the end anti-collision structure is the most important structure for absorbing energy and transmitting impact loads during subway collisions. If the end anti-collision structure is damaged by foreign objects, it will threaten the life safety of drivers and passengers. Carbon fiber composite materials (CFRP for short) can significantly reduce the dead weight of rail vehicles, help reduce vehicle carbon emissions and energy consumption, and conform to the concept of sustainable transportation. Although CFRP has excellent mechanical properties, its economic cost is much higher than that of traditional metal materials such as aluminum alloy and steel, which limits its application scope to a certain extent. In addition, from the perspective of structural performance, CFRP may experience unstable deformations such as local buckling and brittle fracture failure when subjected to transient impact loads, resulting in a significant decrease in its crashworthiness. In order to consider economic costs and crashworthiness while pursuing structural lightweighting, a feasible method is to introduce low-cost, high-ductility, and stable deformation metal materials into lightweight, high-specific strength, and high-specific stiffness CFRP to guide the deformation and failure process of the material in a more effective way.

[0003] Most of the collision energy generated in a collision accident is often absorbed by the axial deformation and bending deformation of the thin-walled structure. At present, some good results have been achieved in the research on the crashworthiness of thin-walled structures under axial load conditions. In the past, the research on crashworthiness under bending load conditions mainly focused on three-point bending conditions or pure bending conditions. However, in actual engineering structures, thin-walled structures do not exist independently. Their two ends are usually connected to other structural components to form a complete energy absorption system. For example, the two ends of the end anti-collision structure of a subway vehicle are fixed by the sill beam and the chassis. When the anti-collision structure collides with a large external object, it can be regarded as a bending loading behavior under end constraint conditions. Since the three-point bending condition or pure bending condition ignores the axial force, this may cause the design scheme to deviate from reality or be difficult to apply in engineering. The bending loading behavior of thin-walled structures under end constraint conditions is much more complicated. When large plastic deformation occurs under this boundary condition, axial force, bending moment and shear force often participate together. However, there are few reports on the bending behavior of Steel / CFRP hybrid thin-walled structures under end constraint conditions and their application in subway end anti-collision structures. Summary of the invention

[0004] In view of the technical defects existing in the background technology, the present invention proposes a CFRP reinforced thin-walled square tube plastic mechanical model construction and prediction method, which solves the above technical problems and meets the actual needs. The specific technical solution is as follows:

[0005] A method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube comprises the following steps:

[0006] Step 1: Use CFRP to reinforce the thin-walled square tube, that is, a mixed square tube is formed by combining the CFRP square tube and the Steel square tube through the inner and outer tube combination;

[0007] Step 2: Establish a plastic mechanical model of CFRP reinforced thin-walled square tube under end constraint boundary conditions, where the CFRP square tube and Steel square tube are simplified to ideal rigid-plastic models;

[0008] Step 2.1: Determine the full plastic axial force N of the cross section of the mixed square tube in step 1 p and the fully plastic bending moment M p Expression of

[0009] Step 2.2: Determine the relationship between the load P and the bending deflection W0 of the mixed square tube in step 1, derive the calculation expression of the analytical solution of the large deflection of the mixed square tube under the end constraint boundary condition, and determine the relationship between the plastic deformation energy E and the bending deflection W0 of the mixed square tube by integrating the P-W0 curve;

[0010] Step 2.3: Based on step 2.1 and step 2.2, the load-displacement curve of each interval stage is integrated and the energy is accumulated to obtain the calculation expression of the plastic deformation energy E of the hybrid square tube under the end constraint boundary condition, and the plastic mechanics model of the CFRP reinforced thin-walled square tube is obtained.

[0011] As a further technical solution of the present invention, the step 2.1 comprises the following steps:

[0012] Step 2.1.1: Assume that the cross section of the mixed square tube is subjected to full plastic stress distribution, the mixed square tube is a slender tube and its shear force is negligible, and the full plastic stress distribution of the cross section of the mixed square tube is composed of axial force and bending moment;

[0013] Step 2.1.2: According to the position change of the plastic neutral surface of the mixed square tube, calculate the axial force N of the cross section of the mixed square tube under different conditions. i and bending moment M i (i=sc or cs), and determine the fully plastic axial force N p and the fully plastic bending moment M p Expression of

[0014] Step 2.1.3: Based on the fully plastic axial force Np and fully plastic bending moment Mp of step 2.1.2, further obtain the calculation expression of the dimensionless axial force n, the calculation expression of the dimensionless bending moment m and the yield criterion expression of the cross section of the mixed square tube.

[0015] As a further technical solution of the present invention, the step 2.2 comprises the following steps:

[0016] Step 2.2.1: Under the mid-span loading condition, it is assumed that the slender hybrid square tube except the mid-span position and the end clamping position is rigid and deforms globally in an integral manner, and the local deformation effect at the loading position is ignored, and the relationship expression between the load P acting transversely on the mid-span and the bending deflection W0 of the hybrid square tube is obtained;

[0017] Step 2.2.2: Based on the yield criterion of the cross section of the hybrid square tube, the relationship between the dimensionless axial force n and the dimensionless moment m and the bending deflection W0 is derived, and then the calculation expression of the analytical solution of the large deflection of the hybrid square tube under the end constraint boundary condition is derived;

[0018] Step 2.2.3: Integrate the P-W0 curve formed by the load P and the bending deflection W0 in step 2.2.1 to obtain the relationship between the plastic deformation energy E of the mixed square tube and the bending deflection W0.

[0019] As a further technical solution of the present invention, the mixed square tube is divided into a Steel / CFRP mixed square tube and a CFRP / Steel mixed square tube according to whether the Steel square tube is located outside or inside. The axial force of the Steel / CFRP mixed square tube is N sc , bending moment is M sc , the fully plastic axial force is The fully plastic bending moment is The axial force of the CFRP / Steel mixed square tube is N cs , bending moment is M cs , the fully plastic axial force is The fully plastic bending moment is

[0020] As a further technical solution of the present invention, in step 1, the slender mixed square tube composed of the CFRP square tube and the Steel square tube has an end constraint boundary under quasi-static lateral loading, and both left and right ends of the mixed square tube are fully constrained, and the shear force of the mixed square tube is negligible under large deflection.

[0021] As a further technical solution of the present invention, in step 2, it is assumed that the material yield stress σ of the Steel square tube mObeying the ideal rigid-plastic criterion, the tensile and compressive properties of the Steel square tube are considered to be the same, and the stress σ of the Steel square tube m - strain ε is linear, and the stress of the CFRP square tube in tension and compression is considered as σ c , the stress σ of the CFRP square tube c - The strain ε is linear, and the CFRP square tube and Steel square tube are simplified to an ideal rigid-plastic model.

[0022] As a further technical solution of the present invention, the axial force N of the cross section of the mixed square tube in step 2.1.2 i and bending moment M i (i=sc or cs) According to the position of the plastic neutral surface, it is divided into three situations, including that the plastic neutral surface is completely located in the outer tube, most of the plastic neutral surface is located in the inner tube and a small part is located in the outer tube, and the plastic neutral surface is located between the upper and lower surfaces of the inner tube.

[0023] A method for predicting a plastic mechanical model of a CFRP reinforced thin-walled square tube comprises the following steps:

[0024] S1: Obtain the size data and material parameters of the mixed square tube;

[0025] S2: Determine whether the mixed square tube is a Steel / CFRP mixed square tube or a CFRP / Steel mixed square tube, and select a suitable plastic mechanics model;

[0026] S3: Input the dimensional data and material parameters of S1 into the plastic mechanics model of S2 to predict the plastic mechanics and energy absorption response of the hybrid square tube under end constraint conditions.

[0027] The beneficial effects of the present invention are:

[0028] The present invention proposes a method for constructing a theoretical prediction model of plastic mechanics for CFRP-reinforced thin-walled square tubes. The method reveals the quantitative relationship between the strain, bending stress, and axial stress of a hybrid square tube under the combined action of axial force and bending moment. The mathematical expression between the bending load and deflection of a hybrid square tube under end constraint conditions and a theoretical prediction model for energy absorption are constructed. The method achieves an accurate prediction of the influence of changes in various structural parameters on the energy absorption mechanism of CFRP-reinforced thin-walled square tubes. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is the framework diagram of the bending load and energy absorption coupling requirements of the subway end anti-collision structure.

[0030] Figure 2 Schematic diagram of the hybrid square tube of the present invention under lateral load: (a) boundary condition details; (b) cross section of the hybrid square tube.

[0031] Figure 3 Simplified schematic diagram of stress-strain curve: (a) Steel material; (b) CFRP material.

[0032] Figure 4 It is a schematic diagram of the position of the neutral plane of the cross section of the Steel / CFRP hybrid square tube of the present invention.

[0033] Figure 5 This is the stress and strain distribution diagram of the first case of the cross section of the Steel / CFRP hybrid square tube of the present invention.

[0034] Figure 6 This is the stress and strain distribution diagram of the second case of the cross section of the Steel / CFRP hybrid square tube of the present invention.

[0035] Figure 7 This is the stress and strain distribution diagram of the third case of the cross section of the Steel / CFRP hybrid square tube of the present invention.

[0036] Figure 8 It is a schematic diagram of the transverse cross-sectional profile of the mixed square tube under the end constraint boundary of the present invention.

[0037] Fig. 9 This is a separate force analysis diagram for the free body on the left side of the mixed square tube under the end constraint boundary of the present invention.

[0038] Fig.10 The load-displacement curve of the CFRP / Steel mixed square tube of the experimental results of the present invention.

[0039] Fig.11 This is the bending loading deformation process diagram of the CFRP / Steel hybrid square tube according to the experimental results of the present invention.

[0040] Fig.12 The load-displacement curve of the Steel / CFRP hybrid square tube of the experimental results of the present invention.

[0041] Fig.13 This is the bending loading deformation process diagram of the Steel / CFRP hybrid square tube according to the experimental results of the present invention.

[0042] Fig.14 The load-displacement curve diagram of the theoretical prediction and experimental results of the CFRP / Steel hybrid formula of the present invention.

[0043] Fig.15 The energy-displacement curve diagram of the theoretical prediction and experimental results of the CFRP / Steel hybrid formula of the present invention.

[0044] Fig.16 The load-displacement curve diagram of the theoretical prediction and experimental results of the Steel / CFRP hybrid tube of the present invention.

[0045] Fig.17 The energy-displacement curve diagram of the theoretical prediction and experimental results of the Steel / CFRP hybrid solution of the present invention. DETAILED DESCRIPTION

[0046] The following is combined with Figures 1 to 17 The implementation modes of the present invention are described with relevant embodiments, but the implementation modes of the present invention are not limited to the following embodiments, and the present invention relates to relevant necessary components in this technical field, which should be regarded as the known technology in this technical field and can be known and mastered by the technicians in this technical field.

[0047] The present invention provides a method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube, comprising the following steps: step 1: using a CFRP reinforced thin-walled square tube, that is, a mixed square tube is formed by combining a CFRP square tube and a Steel square tube by combining an inner and outer tube; step 2: establishing a plastic mechanics model of a CFRP reinforced thin-walled square tube under an end constraint boundary condition, wherein the CFRP square tube and the Steel square tube are simplified to an ideal rigid-plastic model; step 2.1: determining the full plastic axial force N of the cross section of the mixed square tube in step 1 p and the fully plastic bending moment M p Expression; Step 2.2: Determine the relationship between the load P and the bending deflection W0 of the mixed square tube in step 1, derive the calculation expression of the analytical solution of the large deflection of the mixed square tube under the end constraint boundary condition, and determine the relationship between the plastic deformation energy E of the mixed square tube and the bending deflection W0 by integrating the P-W0 curve; Step 2.3: Based on steps 2.1 and 2.2, integrate and accumulate the energy of the load-displacement curve of each interval stage, obtain the calculation expression of the plastic deformation energy E of the mixed square tube under the end constraint boundary condition, and obtain the plastic mechanics model of CFRP reinforced thin-walled square tube.

[0048] And its prediction method, comprising the following steps:

[0049] S1: Obtain the dimensional data and material parameters of the hybrid square tube; S2: Determine whether the hybrid square tube is a Steel / CFRP hybrid square tube or a CFRP / Steel hybrid square tube, and select a suitable plastic mechanics model; S3: Input the dimensional data and material parameters of S1 into the plastic mechanics model of S2 to predict the plastic mechanics and energy absorption response of the hybrid square tube under end constraint conditions.

[0050] The present invention proposes a method for constructing a theoretical prediction model of plastic mechanics for CFRP-reinforced thin-walled square tubes. The method reveals the quantitative relationship between the strain, bending stress, and axial stress of a hybrid square tube under the combined action of axial force and bending moment. The mathematical expression between the bending load and deflection of a hybrid square tube under end constraint conditions and a theoretical prediction model for energy absorption are constructed. The method achieves an accurate prediction of the influence of changes in various structural parameters on the energy absorption mechanism of CFRP-reinforced thin-walled square tubes.

[0051] In the professional standard ASME RT-2-2014 for collision safety of rail transit vehicles, strict crashworthiness design assessments have been formulated for the end anti-collision structure of subway vehicles under the middle anti-collision column loading scenario and the corner anti-collision column loading scenario, aiming to ensure the structural safety of the transport vehicle under extreme collision conditions, reduce deformation after collision, and ensure the survival space of the driver and passengers.

[0052] The mixed use of metal materials and CFRP materials can combine the advantages of both materials, namely the high toughness of metals and the high strength and low mass of CFRP. This combination can significantly improve the performance of thin-walled structures, including improving their load-bearing capacity, durability and impact resistance, enabling the structure to work in more demanding environments and application conditions. The lightweight characteristics of CFRP-reinforced thin-walled structures are of great significance for reducing energy consumption, improving fuel efficiency and reducing greenhouse gas emissions in transportation vehicles. CFRP-reinforced hybrid structures have great application potential in improving load-bearing capacity, lightweight and crash resistance.

[0053] In actual engineering structures, thin-walled structures do not exist independently. Their two ends are usually connected to other structural components to form a complete energy absorption system. For example, in side collision conditions, the B-pillar of a car is fixed by the door sill beam and the roof longitudinal beam; in foreign body intrusion conditions, the two ends of the end anti-collision structure of a subway vehicle are fixed by the door sill beam and the chassis. These structures can be simplified as bending loading behaviors under end constraint conditions. At present, domestic and foreign scholars have conducted a lot of research on bending loading behaviors under end constraint conditions.

[0054] It is concluded that there is great potential research value in introducing low-cost, high-ductility metal materials into lightweight, high-specific strength and high-specific stiffness CFRP. Therefore, it is urgent to carry out research on the design strategy and regulation of the bending resistance and energy absorption coupling of CFRP-reinforced hybrid structures under end constraint conditions.

[0055] At present, the research on the crashworthiness of the end anti-collision structure of the subway head car under the new standard ASME RT-2-2014 mainly focuses on structural design, test verification and optimization design under a single loading scenario. For the end anti-collision structure of the subway, there are no reports on the use of lightweight high-performance materials to enhance the crashworthiness design and the structural optimization design research considering multiple loading scenarios.

[0056] It is also mentioned in the background technology that there are few reports on the bending behavior of Steel / CFRP hybrid thin-walled structures under end constraint conditions and their application in subway end anti-collision structures. For the next generation of subway trains, the demand for lightweight, green, and safe integrated design is more significant, such as Figure 1 To this end, this application couples the advantages of Steel materials and CFRP materials, develops a theoretical model that can quickly reflect the plastic mechanical response of CFRP-reinforced thin-walled square tubes, explores the bending mechanical behavior of Steel / CFRP hybrid square tubes under end constraint conditions, and reveals the evolution law of bending response of various structural parameters, so as to further improve the living space of drivers and passengers, which has important research value and engineering significance for improving the passive safety of subway vehicles.

[0057] The following are examples of the present invention.

[0058] Example 1

[0059] For Steel / CFRP hybrid square tubes and CFRP / Steel hybrid square tubes, since the theoretical analysis methods of the two are similar, this paper takes Steel / CFRP hybrid square tubes as an example to explore the plastic mechanical response of the hybrid square tubes, and proposes a plastic mechanical analytical model construction method and prediction method for the hybrid square tubes.

[0060] A method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube comprises the following steps:

[0061] Step 1: Use CFRP to reinforce the thin-walled square tube, that is, a hybrid square tube is formed by combining the CFRP square tube and the Steel square tube by combining the inner and outer tubes; in step 1, the end constraint boundary of the slender hybrid square tube composed of the CFRP square tube and the Steel square tube under quasi-static lateral loading, the left and right ends of the hybrid square tube are fully constrained, and the shear force of the hybrid square tube is negligible under large deflection.

[0062] The schematic diagram of the slender hybrid square tube composed of CFRP square tube and Steel square tube under mid-span loading is shown in Figure 2 shown. Figure 2 (a) shows the end constraint boundary of the hybrid square tube under quasi-static lateral loading. It can be found that the left and right ends of the hybrid square tube are fully constrained, and the cylindrical indenter is transversely loaded in the span of the tube, where the span is L.

[0063] Assuming that the radius of the pressure head is much smaller than the span of the mixed square tube, the load on the pressure head can be regarded as concentrated at the center point of the mixed square tube. For the analysis of lateral loading of slender tubes, when the deflection is small, the shear force plays a leading role in the early deformation stage, but under large deflection, the influence of the shear force is almost negligible compared with the bending moment and axial force. Therefore, the invention mainly considers axial tension, bending and the interaction between the two. Figure 2 (b) is a schematic diagram of the cross-section of two different configurations of the Steel / CFRP hybrid square tube and the CFRP / Steel hybrid square tube, where b is the cross-sectional width, t m and t c are the thickness of Steel tube and CFRP tube respectively.

[0064] Step 2: Establish a plastic mechanics model of CFRP reinforced thin-walled square tube under end constraint boundary conditions, in which the CFRP square tube and Steel square tube are simplified to an ideal rigid-plastic model. Assume that the contact surface between the Steel square tube and the CFRP square tube is ideally bonded. When the hybrid square tube undergoes large deflection bending deformation, the energy dissipated by the elastic deformation of the Steel square tube and the CFRP square tube is relatively small, and its energy absorption is mainly dominated by plastic behavior. Therefore, the elastic behavior of the material is ignored in the theoretical analysis, and only the range of plastic deformation is retained.

[0065] In order to simplify the analytical model of energy absorption, it is assumed that the material yield stress σ of the Steel square tube m Obeying the ideal rigid-plastic criterion, the tensile and compressive properties of the Steel square tube are considered to be the same, and the stress σ of the Steel square tube m - strain ε is linear, and its simplified stress-strain diagram is as follows Figure 3 (a) As shown in Figure 2, CFRP is an anisotropic material. Its asymmetric properties of tension and compression are not considered here. Its stress in both tension and compression states is considered as σ c , the stress σ of CFRP square tube c - strain ε is linear, and its simplified stress-strain diagram is as follows Figure 3 As shown in (b), the CFRP square tube and Steel square tube are simplified to the ideal rigid-plastic model.

[0066] Step 2.1: Determine the fully plastic axial force N of the cross section of the mixed square tube in step 1 p and the fully plastic bending moment M p The expression of; the mixed square tube is divided into Steel / CFRP mixed square tube and CFRP / Steel mixed square tube according to whether the Steel square tube is located outside or inside. The axial force of the Steel / CFRP mixed square tube is N sc , bending moment is M sc , the fully plastic axial force is The fully plastic bending moment is The axial force of the CFRP / Steel mixed square tube is N cs , bending moment is M cs , the fully plastic axial force is The fully plastic bending moment is

[0067] Step 2.1.1: Assume that the cross section of the hybrid square tube is subjected to full plastic stress distribution. The hybrid square tube is a slender tube and its shear force is negligible. The full plastic stress distribution of the cross section of the hybrid square tube is composed of axial force and bending moment.

[0068] Step 2.1.2: (This implementation is for Steel / CFRP hybrid square tube) According to the position change of the plastic neutral surface of the hybrid square tube, calculate the axial force N of the cross section of the hybrid square tube under different conditions sc and bending moment M sc , and determine the fully plastic axial force and the fully plastic bending moment expression.

[0069] For the mixed square tube structure, its geometric neutral surface and plastic neutral surface do not necessarily coincide. The schematic diagram of the location of the plastic neutral surface of the mixed square tube is as follows: Figure 4 shown. Figure 4 In the left figure, the plastic neutral surface is entirely inside the Steel tube; Figure 4 In the middle figure, most of the plastic neutral surface is located in the CFRP tube, and the rest is distributed inside the Steel tube; Figure 4 In the figure on the right, the physical neutral plane is located between the upper and lower surfaces of the CFRP inner tube. m is the thickness of the Steel layer on the outside of the mixed square tube, t c is the thickness of the CFRP layer placed inside.

[0070] According to the change of the position of the plastic neutral surface, the axial force and bending moment can also be divided into three cases. Figure 4 The stress and strain distribution of the cross section of the Steel / CFRP hybrid square tube under mid-span load is depicted. The plastic neutral surface is defined as the distance from the bottom panel of the hybrid square tube. The distance from the plastic neutral surface to the bottom panel can be expressed as h = ξ(c + 2t m +2t c ), where ξ∈[0,1].

[0071] (1) When 0≤ξ≤t m / (c+2t m +2t c )hour;

[0072] At this time, the plastic neutral surface is completely located in the bottom panel of the Steel tube. Under the action of axial force and bending moment, the stress and strain distribution diagram of the cross section of the Steel / CFRP hybrid square tube is as follows: Figure 5 As shown. The corresponding cross-sectional axial force N sc and bending moment M sc The calculation expressions of are shown in formula (1-1) and formula (1-2).

[0073]

[0074] M sc =∫ A σzdA=σ m b(c+2t c +2t m ) 2 ξ(1-ξ) (1-2)

[0075] (2) When t m / (c+2t m +2t c )≤ξ≤(t m +t c ) / (c+2t m +2t c )hour;

[0076] As the plastic neutral surface moves upward, the stress and strain distribution diagrams of the cross section of the Steel / CFRP hybrid square tube are shown in Figure 2. Figure 6 Therefore, the axial force N sc and bending moment M sc The expressions are shown in formulas (1-3) and (1-4).

[0077]

[0078]

[0079] (3) When (t m +t c ) / (c+2t m +2t c )≤ξ≤1 / 2;

[0080] from Figure 7 As can be seen from the figure, the plastic neutral surface will continue to move upward as the stress state changes. At this time, the stress and strain distribution diagram under this state is as follows: Figure 7 As shown. Axial force in the cross section of Steel / CFRP mixed square tube N sc and bending moment M sc The expressions of are shown in formulas (1-5) and (1-6).

[0081] N sc =∫ A σdA=(σ m t m +σ c t c )(c+2t c +2t m )(2-4ξ) (1-5)

[0082]

[0083] In summary, the axial force N of Steel / CFRP hybrid square tube under different ξ values sc and bending moment M sc The final result can be expressed as:

[0084]

[0085] When ξ=0, substituting into formula (1-1) we can get the full plastic axial force of Steel / CFRP hybrid square tube: When ξ=1 / 2, substituting into formula (1-6), the full plastic bending moment of Steel / CFRP hybrid square tube can be obtained: For Steel / CFRP hybrid square tube, full plastic axial force and the fully plastic bending moment The expressions of are shown in formula (1-9) and formula (1-10) respectively.

[0086]

[0087] Step 2.1.3: Full plastic axial force based on step 2.1.2 and the fully plastic bending moment The calculation expressions of dimensionless axial force n, dimensionless bending moment m and yield criterion of the cross section of the mixed square tube are further obtained.

[0088] Combining equations (1-7) and (1-9), we can further obtain the calculation expression of the dimensionless axial force n, as shown in equation (1-11). Combining equations (1-8) and (1-10), we can further obtain the calculation expression of the dimensionless bending moment m, as shown in equation (1-12).

[0089]

[0090]

[0091] In order to obtain the yield criterion of the Steel / CFRP hybrid square tube, equations (1-11) and (1-12) are combined, and the parameter ξ is eliminated from the two formulas to obtain the yield criterion expression of the cross section of the Steel / CFRP hybrid square tube, as shown in equation (1-13):

[0092]

[0093] The constants are given by equations (1-14) to (1-22):

[0094]

[0095] Step 2.2: Determine the relationship between the load P and the bending deflection W0 of the mixed square tube in step 1, derive the calculation expression of the analytical solution of the large deflection of the mixed square tube under the end constraint boundary condition, and determine the relationship between the plastic deformation energy E and the bending deflection W0 of the mixed square tube by integrating the P-W0 curve;

[0096] Step 2.2.1: The energy generated during the bending deformation of the hybrid square tube structure is mainly absorbed by the hybrid plastic hinge. Under the mid-span loading condition, it is assumed that the slender hybrid square tube, except for the mid-span position and the end clamping position, is rigid and deforms globally in an integral manner, and the local deformation effect at the loading position is ignored. Therefore, the simplified schematic diagram of the large deflection response of the neutral axis of the hybrid square tube under the transverse mid-span load is as follows: Figure 8 As shown. Figure 8 It can be seen that the span of the mixed square tube is L. Under the action of the external concentrated load P, the mixed square tube has an overall deformation of bending deflection W0 at the mid-span position. At this time, the angles at both ends of the mixed square tube are ψ.

[0097] Take the free body on the left side of the mixed square tube for separate force analysis, such as Fig. 9 As shown. Therefore, the equilibrium equation of the moment can be defined as:

[0098]

[0099] Where F is approximately equal to the axial force N, that is, considering that the entire structure is symmetrical about the geometric center, the bending moment acting on the left clamping end and the loading end is M = M m Therefore, by transforming formula (1-23), we can obtain the relationship expression between the load P acting on the mid-span and the bending deflection W0 of the mixed square tube, as shown in formula (1-24).

[0100]

[0101] Assume that the total elongation of the free body of the left half of the mixed square tube is e L , the relevant calculation expression is shown in formula (1-25).

[0102] e L =e L1 +e L2 (1-25)

[0103] Where e L1 and e L2 Respectively represent the axial extension of the left clamping end and the loading end. L1 and e L2 , which can be regarded as e L1 =e L2 In addition, according to Figure 8 and 9 The geometric relationship in the figure shows that the total extension of the free body on the left is e L and the rotation angle ψ can be obtained by equations (1-26) and (1-27).

[0104]

[0105] Combining equations (1-25), (1-26) and (1-27), the axial elongation of the left clamping end and the loading end of the mixed square tube is obtained: and curvature The relationship expression between the ratio and the bending deflection W0 can be expressed by formula (2-28).

[0106]

[0107] Step 2.2.2: Based on the yield criterion of the cross section of the hybrid square tube, the relationship between the dimensionless axial force n and the dimensionless moment m and the bending deflection W0 is derived, and then the calculation expression of the analytical solution of the large deflection of the hybrid square tube under the end constraint boundary condition is derived.

[0108] Based on the relevant flow law of the plastic yield criterion, equation (1-29) can be obtained.

[0109]

[0110] Solve the partial differential equation for equation (1-13), and substitute the result of the partial differential equation into equation (1-29) to obtain the axial elongation of the left clamping end and the loading end of the mixed square tube. and curvature The relationship between the ratio and the dimensionless axial force n can be expressed by formula (1-30).

[0111]

[0112] Based on equations (1-28) and (1-30), the relationship between the dimensionless axial force n and the dimensionless moment m and the bending deflection W0 can be derived, as shown in equations (1-31) and (1-32), respectively.

[0113]

[0114] Substituting equations (1-9), (1-10), (1-31) and (1-32) into equation (1-24), the calculation expression of the analytical solution of the large deflection of the Steel / CFRP hybrid square tube under the end constraint boundary conditions can be derived, as shown in equation (1-33).

[0115]

[0116] Step 2.2.3: Integrate the P-W0 curve formed by the load P and the bending deflection W0 in step 2.2.1 to obtain the relationship between the plastic deformation energy E of the mixed square tube and the bending deflection W0.

[0117] By integrating the P-W0 curve, we can obtain the relationship expression between the plastic deformation energy E of the mixed square tube and the bending deflection W0, as shown in formula (1-34).

[0118]

[0119] Step 2.3: Based on steps 2.1 and 2.2, the load-displacement curve of each interval stage is integrated and the energy is accumulated to obtain the calculation expression of the plastic deformation energy E of the hybrid square tube under the end constraint boundary condition, and the plastic mechanics model of the CFRP reinforced thin-walled square tube is obtained.

[0120] Substitute formula (1-33) into formula (1-34), integrate the load-displacement curve in each interval stage and accumulate the energy. Therefore, the calculation expression of the plastic deformation energy E of the Steel / CFRP hybrid square tube under the end constraint boundary conditions can be obtained, as shown in formula (1-35).

[0121]

[0122] At the same time, the modeling method of the plastic mechanics model of the CFRP / Steel hybrid square tube is similar to that of the Steel / CFRP hybrid square tube. The modeling process of the lateral force analysis and plastic mechanics behavior of the CFRP / Steel hybrid square tube is no longer described in detail, and the relationship between the load and the deflection is directly given. The relationship expression between the load Pcs and the deflection W0 of the CFRP / Steel hybrid square tube is shown in formula (1-36).

[0123]

[0124] For CFRP / Steel mixed square tube, its full plastic axial force and the fully plastic bending moment The expressions are shown in formulas (1-37) and (1-38) respectively.

[0125]

[0126] Substitute formula (1-36) into formula (1-34), integrate the load-displacement curve in each interval stage and accumulate the energy. Therefore, the calculation expression of the plastic deformation energy E of the CFRP / Steel hybrid square tube under the end constraint boundary condition can be obtained, as shown in formula (1-39).

[0127]

[0128] A method for predicting a plastic mechanical model of a CFRP reinforced thin-walled square tube comprises the following steps:

[0129] S1: Obtain the size data and material parameters of the mixed square tube;

[0130] S2: Determine whether the mixed square tube is a Steel / CFRP mixed square tube or a CFRP / Steel mixed square tube, and select a suitable plastic mechanics model;

[0131] S3: Input the dimensional data and material parameters of S1 into the plastic mechanics model of S2 to predict the plastic mechanics and energy absorption response of the hybrid square tube under end constraint conditions.

[0132] The following CFRP reinforced thin-walled square tube plastic mechanics model is experimentally verified.

[0133] The plying sequence of the CFRP tubes in both types of hybrid square tubes is [0° / 90° / 45° / -45°] alternating plying. In order to improve the reliability of the test data and reduce the test error, two repeated specimens were prepared for each test condition. It is worth noting that due to the different material configuration sequences of the CFRP / Steel hybrid square tube and the Steel / CFRP hybrid square tube, this may lead to differences in the bending performance of the structure. Table 1-1 records the detailed geometric parameter information of the two types of hybrid square tube test specimens.

[0134] Table 2-1 Summary of geometric parameters of mixed square tubes

[0135]

[0136] In order to systematically evaluate the crashworthiness of the crashworthy structure during bending loading, several key crashworthiness indices are pre-determined in this section, namely, energy absorption (EA), peak force (PCF), mean force (MCF), specific energy absorption (SEA), crushing force efficiency (CFE), maximum intrusion (Dlmax ) and the intrusion area (S inv ). The definitions of these parameters are as follows:

[0137] (1) Energy absorption (EA): It is obtained by integrating the load-displacement curve formed during bending loading. It is widely used to evaluate the ability of a structure to absorb energy during deformation and can be expressed as:

[0138]

[0139] Where F(s) represents the crushing force when the loading displacement is D, and D represents the displacement of the indenter during the loading stage.

[0140] (2) Peak force (PCF): It indicates the maximum crushing force generated during the structural deformation process. Too high PCF may reduce the survival rate of drivers and passengers, which can be expressed as:

[0141] PCF=max(F(s)) (2-2)

[0142] (3) Mean force (MCF): It is the average value of the force of the structure during the entire bending loading stage and can be defined by formula (2-3).

[0143]

[0144] (4) Specific energy absorption (SEA): It is defined as the ability of a structure to absorb energy per unit mass and is an important evaluation index for structural lightweighting. Its calculation method is as follows:

[0145]

[0146] (5) Crushing force efficiency (CFE): It is the ratio of the average crushing force to the peak crushing force. It is usually used to evaluate the stability of the structure during the crushing process. The ideal energy-absorbing structure always pursues a high CFE, and its calculation expression is shown in formula (2-5).

[0147]

[0148] (6) Final intrusion volume (D lmax ): The final deformation of the rear surface of the structure after elastic recovery after the pressure head is completely unloaded. Excessive intrusion is not desirable, and the intrusion after the structure is crushed should be minimized.

[0149] (7) Invasion area (S inv ): Under the action of bending load, the anti-collision structure not only needs to have excellent plastic mechanical properties, but also should have a certain elastic recovery ability, and be able to release a certain intrusion space after bending and crushing to protect the safety space of the cab]. Therefore, the intrusion area S invIt is selected as the evaluation index. This parameter is defined as the area swept by the structure before and after bending and crushing. The smaller the intrusion area, the better the elastic recovery performance of the structure.

[0150] The quasi-static bending loading test results of CFRP / Steel hybrid square tube under end constraint boundary conditions are shown in Fig.10 and 11 As shown. Fig.10 It can be seen from the load-displacement curves during the loading process that the results of the two repeated experiments are relatively similar, indicating that the experimental results have relatively high reliability.

[0151] In addition, the load-displacement curve shows that the entire experimental stage can be divided into three stages: the first stage is the elastic loading stage, in which the load increases linearly with the displacement; the second stage is the plastic deformation stage, and as the loading progresses, when the displacement reaches about 3mm, the load decreases slightly. This is because the fibers in the outer layer of the CFRP tube break, resulting in a temporary decrease in its load-bearing capacity.

[0152] combine Fig.11 The corresponding deformation mode shows that at this time, the outer CFRP tube has obvious radial fiber fracture. As the pressure head is further loaded downward, due to the action of the axial force, the load curve shows a steady upward growth trend. The reason is that the outer CFRP tube and the inner Steel tube of the CFRP / Steel hybrid square tube have an interactive effect, and the inner Steel tube plays its bearing role, thereby further enhancing the plastic energy absorption potential of the CFRP / Steel hybrid square tube. Therefore, for the entire plastic deformation stage, the load-displacement curve basically maintains a steady upward trend.

[0153] The third stage is the elastic recovery stage. Fig.11 It can be seen from the deformation mode of the third stage that the pressure head loads downward and then reaches the maximum displacement and then begins to unload upward. At this time, the load-displacement curve begins to show a downward trend. With the complete release of the elastic deformation energy of the CFRP / Steel hybrid square tube, the lateral displacement gradually returns to the final deformation mode.

[0154] The quasi-static bending loading test results of Steel / CFRP hybrid square tubes under end restraint boundary conditions are shown in Figure 2-17 As shown. Fig.12It can be seen from the load-displacement curve during the loading process that the load-displacement curve trends of the two repetitive experiments are very similar. Like the CFRP / Steel mixed square tube, the entire experimental process is also divided into three stages. In the elastic loading stage, the load-displacement curve tends to be a linear relationship. When the displacement reaches about 2.5mm, the load-displacement curve drops instantly, and the Steel / CFRP mixed square tube enters the plastic deformation stage. Compared with the CFRP / Steel mixed square tube, the load-displacement curve of the Steel / CFRP mixed square tube in this process is smoother and has smaller fluctuations, showing a stronger load-bearing capacity. Combined with Fig.13 From the deformation modes at each stage, it can be seen that the Steel / CFRP hybrid square tube and the CFRP / Steel hybrid square tube have a certain degree of local depression at the pressure head loading point. However, from the overall point of view, the final deformation of the two types of hybrid tubes presents a global deformation mode.

[0155] The span of the CFRP / Steel mixed square tube is L=300mm, and the thickness of the outer CFRP layer is t c =1mm, inner layer steel thickness t m =1mm, the cross-sectional span b = 28mm, and the outer layer steel thickness of the Steel / CFRP hybrid square tube is t m =1mm, inner layer steel thickness t c =1mm, other geometric parameters are the same as those of CFRP / Steel mixed square tube. Material mechanical properties parameters σ m =240Mpa,σ c =70Mpa, and the relevant geometric parameters are substituted into the analytical solution of large deflection of hybrid square tube. The comparison of force-displacement and energy-displacement curves between theoretical prediction and experimental results of CFRP / Steel hybrid square tube and Steel / CFRP hybrid square tube are shown in Figure 2. Figure 14 to Figure 17 shown.

[0156] from Fig.14 and Fig.16 It can be seen that at the beginning of bending loading, there is a certain deviation between the load-displacement theoretical prediction curve and the experimental curve. This is because in the theoretical analysis, the Steel and CFRP material models are assumed to be ideal rigid-plastic models, ignoring the elastic behavior of the material and only retaining the range of plastic deformation. With the increase of loading displacement, the load-displacement theoretical prediction curves of CFRP / Steel mixed square tubes and Steel / CFRP mixed square tubes maintain a high degree of consistency with the experimental curves.

[0157] from Fig.15 and Fig.17Comparison of the energy-displacement curves of the theoretical prediction and the experiment shows that there is a small error in the energy absorption at the initial stage of loading, but most of the energy is absorbed in the later stage of bending loading. From the overall effect of the energy-displacement curves of the theoretical prediction and experiment of the two types of mixed formulas, the trend of the theoretical prediction curve is basically consistent with the experimental curve, indicating that the derived mixed formula theoretical prediction model has a high reliability. As can be seen from Table 1-2, the relative error of the energy absorption between the theoretical prediction and experimental results of the two types of mixed formulas does not exceed 3%, indicating that the theoretical prediction model can be used for further research.

[0158] Table 1-2 Comparison of energy absorption between theoretical prediction and experimental results of two types of mixed formulas

[0159]

[0160] The above is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube, characterized in that: The following steps are involved: Step 1: Use CFRP to reinforce the thin-walled square tube, that is, a mixed square tube is formed by combining the CFRP square tube and the Steel square tube through the inner and outer tube combination; Step 2: Establish a plastic mechanical model of CFRP reinforced thin-walled square tube under end constraint boundary conditions, where the CFRP square tube and Steel square tube are simplified to ideal rigid-plastic models; Step 2.1: Determine the full plastic axial force N of the cross section of the mixed square tube in step 1 p and the fully plastic bending moment M p Expression of Step 2.2: Determine the relationship between the load P and the bending deflection W0 of the mixed square tube in step 1, derive the calculation expression of the analytical solution of the large deflection of the mixed square tube under the end constraint boundary condition, and determine the relationship between the plastic deformation energy E and the bending deflection W0 of the mixed square tube by integrating the P-W0 curve; Step 2.3: Based on step 2.1 and step 2.2, the load-displacement curve of each interval stage is integrated and the energy is accumulated to obtain the calculation expression of the plastic deformation energy E of the hybrid square tube under the end constraint boundary condition, and the plastic mechanics model of the CFRP reinforced thin-walled square tube is obtained.

2. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 1, characterized in that: The step 2.1 comprises the following steps: Step 2.1.1: Assume that the cross section of the mixed square tube is subjected to full plastic stress distribution, the mixed square tube is a slender tube and its shear force is negligible, and the full plastic stress distribution of the cross section of the mixed square tube is composed of axial force and bending moment; Step 2.1.2: According to the position change of the plastic neutral surface of the mixed square tube, calculate the axial force N of the cross section of the mixed square tube under different conditions. i and bending moment M i (i=sc or cs), and determine the fully plastic axial force N p and the fully plastic bending moment M p Expression of Step 2.1.3: Based on the fully plastic axial force Np and fully plastic bending moment Mp of step 2.1.2, further obtain the calculation expression of the dimensionless axial force n, the calculation expression of the dimensionless bending moment m and the yield criterion expression of the cross section of the mixed square tube.

3. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 1, characterized in that: The step 2.2 comprises the following steps: Step 2.2.1: Under the mid-span loading condition, it is assumed that the slender hybrid square tube except the mid-span position and the end clamping position is rigid and deforms globally in an integral manner, and the local deformation effect at the loading position is ignored, and the relationship expression between the load P acting transversely on the mid-span and the bending deflection W0 of the hybrid square tube is obtained; Step 2.2.2: Based on the yield criterion of the cross section of the hybrid square tube, the relationship between the dimensionless axial force n and the dimensionless moment m and the bending deflection W0 is derived, and then the calculation expression of the analytical solution of the large deflection of the hybrid square tube under the end constraint boundary condition is derived; Step 2.2.3: Integrate the P-W0 curve formed by the load P and the bending deflection W0 in step 2.2.1 to obtain the relationship between the plastic deformation energy E of the mixed square tube and the bending deflection W0.

4. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 1, characterized in that: The mixed square tube is divided into Steel / CFRP mixed square tube and CFRP / Steel mixed square tube according to whether the Steel square tube is located outside or inside. The axial force N sc , bending moment is M sc , the fully plastic axial force is The fully plastic bending moment is The axial force of the CFRP / Steel mixed square tube is N cs , bending moment is M cs , the fully plastic axial force is The fully plastic bending moment is 5. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 1, characterized in that: In the step 1, the end constraint boundary of the slender mixed square tube composed of the CFRP square tube and the Steel square tube under quasi-static lateral loading, the left and right ends of the mixed square tube are fully constrained, and the shear force of the mixed square tube is negligible under large deflection.

6. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 1, characterized in that: In step 2, it is assumed that the material yield stress σ of the Steel square tube m Obeying the ideal rigid-plastic criterion, the tensile and compressive properties of the Steel square tube are considered to be the same, and the stress σ of the Steel square tube m - strain ε is linear, and the stress of the CFRP square tube in tension and compression is considered as σ c , the stress σ of the CFRP square tube c - The strain ε is linear, and the CFRP square tube and Steel square tube are simplified to an ideal rigid-plastic model.

7. The method for constructing a plastic mechanics model of a CFRP reinforced thin-walled square tube according to claim 2, characterized in that: The axial force N of the cross section of the mixed square tube in step 2.1.2 i and bending moment M i (i=sc or cs) According to the position of the plastic neutral surface, it is divided into three situations, including that the plastic neutral surface is completely located in the outer tube, most of the plastic neutral surface is located in the inner tube and a small part is located in the outer tube, and the plastic neutral surface is located between the upper and lower surfaces of the inner tube.

8. A plastic mechanics model prediction method for CFRP reinforced thin-walled square tube, characterized in that: The following steps are involved: S1: Obtain the size data and material parameters of the mixed square tube; S2: Determine whether the mixed square tube is a Steel / CFRP mixed square tube or a CFRP / Steel mixed square tube, and select a suitable plastic mechanics model; S3: Input the dimensional data and material parameters of S1 into the plastic mechanics model of S2 to predict the plastic mechanics and energy absorption response of the hybrid square tube under end constraint conditions.

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