A method for constructing and predicting a plastic mechanics model of CFRP reinforced thin-walled square tube

Abstract

The present application relates to the technical field of rail transit materials, in particular to a CFRP reinforced thin-walled square tube plastic mechanics model construction and prediction method, the construction method comprising the following steps: step 1: a mixed square tube is composed of a CFRP square tube and a steel square tube; step 2: a plastic mechanics model of the CFRP reinforced thin-walled square tube under end constraint boundary conditions is established. The prediction method comprises the following steps: S1: size data and material parameters of the mixed square tube are obtained; S2: a suitable plastic mechanics model is selected; S3: data is input into the model to predict the plastic mechanics and energy absorption response of the mixed square tube under end constraint conditions. The present application proposes a plastic mechanics theoretical prediction model construction method for the CFRP reinforced thin-walled square tube. An expression between bending load and deflection of the mixed square tube under end constraint conditions and an energy absorption theoretical prediction model are constructed. The accurate prediction of the influence law of the energy absorption mechanism of the CFRP reinforced thin-walled square tube with changes in various structural parameters is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rail transit materials, and particularly relates to a CFRP reinforced thin-walled square tube plastic mechanics model construction and prediction method. BACKGROUND

[0002] Metro collision accidents often occur in the end area of the metro head car, and the end anti-collision structure is the most important structure for absorbing energy and transmitting impact load when the metro collides. If the end anti-collision structure is damaged by foreign matter, it will threaten the safety of the driver and passengers. Carbon fiber composite materials (CFRP) can significantly reduce the weight of rail vehicles, helping to reduce carbon emissions and energy consumption of vehicles, and conforming to the concept of sustainable transportation. Although CFRP performs well in mechanical properties, its economic cost is much higher than that of traditional metal materials such as aluminum alloy and steel, which limits its application range to some extent. In addition, from the perspective of structural performance, CFRP may exhibit local buckling and brittle fracture failure under transient impact load, resulting in a significant decrease in crashworthiness. In order to pursue lightweight structures while considering economic cost and crashworthiness, a feasible method is to introduce low-cost, high-ductility, and stable deformation metal materials into CFRP with high specific strength and high specific stiffness, so as 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 through axial deformation and bending deformation of the thin-walled structure. At present, some good results have been achieved in the study of crashworthiness of thin-walled structures under axial load conditions. Previous studies 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, and their two ends are usually connected to other structural components to form a complete energy absorption system, such as the two ends of the end anti-collision structure of a metro vehicle being fixed by a rocker beam and a chassis. When the anti-collision structure collides with external large objects, it can be regarded as a bending loading behavior under end constraint conditions. Since three-point bending conditions or pure bending conditions ignore the axial force, this may cause the design scheme to deviate from the actual situation or be difficult to apply in engineering. The bending loading behavior of thin-walled structures under end constraint conditions is much more complex, and when plastic large 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 its application in metro end anti-collision structures. SUMMARY

[0004] In view of the technical defects in the background art, the present application proposes a CFRP reinforced thin-walled square tube plastic mechanics model construction and prediction method, which solves the above technical problems and meets the actual needs, and the specific technical scheme is as follows:

[0005] A CFRP reinforced thin-walled square tube plastic mechanics model construction method, comprising the following steps:

[0006] Step 1: CFRP reinforced thin-walled square tube is used, that is, a mixed square tube composed of CFRP square tube and Steel square tube through inner and outer tube combination;

[0007] Step 2: CFRP reinforced thin-walled square tube plastic mechanics model under end constraint boundary conditions is established, wherein CFRP square tube and Steel square tube are simplified as ideal rigid-plastic model;

[0008] Step 2.1: the expressions of full plastic axial force N p and full plastic bending moment M p of the cross section of the mixed square tube in step 1 are determined;

[0009] Step 2.2: the relationship between load P and bending deflection W0 of the mixed square tube in step 1 is determined, the calculation expression of large deflection analytical solution of the mixed square tube under end constraint boundary conditions is derived, and the relationship between plastic deformation energy E and bending deflection W0 of the mixed square tube is determined 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 energy is accumulated to obtain the calculation expression of plastic deformation energy E of the mixed square tube under end constraint boundary conditions, and the CFRP reinforced thin-walled square tube plastic mechanics model is obtained.

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

[0012] Step 2.1.1: it is assumed that the cross section of the mixed square tube is subjected to full plastic stress distribution, the mixed square tube is an elongated tube and its shear force is ignored, 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, the axial force N i and bending moment M i (i=sc or cs) of the cross section of the mixed square tube under different conditions are calculated, and the expressions of full plastic axial force N p and full plastic bending moment M p are determined;

[0014] Step 2.1.3: Based on the full plastic axial force Np and the full plastic bending moment Mp of the 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 hybrid square tube cross section.

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

[0016] Step 2.2.1: In the mid-span loading condition, assuming that the slender hybrid square tube is rigid except for the mid-span position and the end clamping part, the global deformation occurs in a whole manner, and the local deformation effect at the loading position is ignored, to obtain the relationship expression between the load P acting on the mid-span and the bending deflection W0 of the hybrid square tube;

[0017] Step 2.2.2: Based on the yield criterion of the hybrid square tube cross section, 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 large deflection analytical solution of the hybrid square tube under the end constraint boundary condition is derived;

[0018] Step 2.2.3: The P-W0 curve of the load P and the bending deflection W0 in the step 2.2.1 is integrated to obtain the relationship between the plastic deformation energy E of the hybrid square tube and the bending deflection W0.

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

[0020] As a further technical solution of the present application, the end constraint boundary of the slender hybrid square tube composed of the CFRP square tube and the Steel square tube under the quasi-static transverse loading is that both left and right ends of the hybrid square tube are completely constrained, and the shear force of the hybrid square tube is ignored under large deflection.

[0021] As a further technical solution of the present application, in the step 2, the material yield stress σ mSubject to the ideal rigid-plasticity criterion, i.e., the tensile and compressive properties of the Steel square tube are considered to be the same, the stress σ m Strain ε is linear, the stress of the CFRP square tube is considered to be σ c , the stress of the CFRP square tube is considered to be σ c Strain ε is linear, the CFRP square tube and the Steel square tube are simplified as ideal rigid-plasticity models.

[0022] As a further technical solution of the application, the axial force N i and the bending moment M i (i = sc or cs) are divided into three cases according to the position of the plastic neutral surface, including that the plastic neutral surface is located entirely in the outer tube, that the plastic neutral surface is mostly located in the inner tube and a small part is located in the outer tube, and that the plastic neutral surface is located between the upper and lower surfaces of the inner tube.

[0023] A CFRP-reinforced thin-walled square tube plastic mechanics model prediction method, comprising the following steps:

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

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

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

[0027] The application has the beneficial effects that:

[0028] The application proposes a CFRP-reinforced thin-walled square tube plastic mechanics theoretical prediction model construction method. The quantitative relationship between the strain, bending stress and axial stress of the mixed square tube under the combined action of the axial force and the bending moment is disclosed. The mathematical expression between the bending load and the deflection of the mixed square tube under the end constraint condition and the energy absorption theoretical prediction model are constructed. The accurate prediction of the influence law of the structural parameter change on the energy absorption mechanism of the CFRP-reinforced thin-walled square tube is realized. BRIEF DESCRIPTION OF DRAWINGS

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

[0030] Figure 2 It is a schematic diagram of the mixed square tube under the action of the transverse load: (a) boundary condition details; (b) cross section of the mixed square tube.

[0031] Figure 3 Simplified stress-strain curves: (a) Steel material; (b) CFRP material.

[0032] Figure 4 Schematic diagram of the neutral surface position in the cross section of the Steel / CFRP hybrid square tube according to the present application.

[0033] Figure 5 Stress and strain distribution in the cross section of the Steel / CFRP hybrid square tube according to the present application in the first case.

[0034] Figure 6 Stress and strain distribution in the cross section of the Steel / CFRP hybrid square tube according to the present application in the second case.

[0035] Figure 7 Stress and strain distribution in the cross section of the Steel / CFRP hybrid square tube according to the present application in the third case.

[0036] Figure 8 Schematic diagram of the lateral profile of the hybrid square tube under the end-restrained boundary according to the present application.

[0037] Figure 9 Diagram of the free-body analysis of the left side of the hybrid square tube under the end-restrained boundary according to the present application.

[0038] Figure 10 Load-displacement curve of the CFRP / Steel hybrid square tube according to the experimental results of the present application.

[0039] Figure 11 Bending loading deformation process diagram of the CFRP / Steel hybrid square tube according to the experimental results of the present application.

[0040] Figure 12 Load-displacement curve of the Steel / CFRP hybrid square tube according to the experimental results of the present application.

[0041] Figure 13 Bending loading deformation process diagram of the Steel / CFRP hybrid square tube according to the experimental results of the present application.

[0042] Figure 14 Load-displacement curve of the CFRP / Steel hybrid square tube according to the theoretical prediction and the experimental results of the present application.

[0043] Figure 15 Energy-displacement curve of the CFRP / Steel hybrid square tube according to the theoretical prediction and the experimental results of the present application.

[0044] Figure 16 Load-displacement curve of the Steel / CFRP hybrid square tube according to the theoretical prediction and the experimental results of the present application.

[0045] Figure 17 Figure 1 is an energy-displacement curve diagram of the Steel / CFRP hybrid square tube according to the present application. DETAILED DESCRIPTION

[0046] The embodiments of the present application will be described in relation to the drawings appended hereto. Figures 1-17 The embodiments of the present application are described in relation to the following examples, and the embodiments of the present application are not limited to the following examples, and the present application relates to the necessary components in the technical field, which should be regarded as the known technology in the technical field, and is known and mastered by the person skilled in the art.

[0047] The present application provides a CFRP reinforced thin-walled square tube plastic mechanics model construction method, comprising the following steps: step 1: using a CFRP reinforced thin-walled square tube, that is, a hybrid square tube composed of a CFRP square tube and a Steel square tube through internal and external tube combination; step 2: establishing a plastic mechanics model of the CFRP reinforced thin-walled square tube under end constraint boundary conditions, wherein the CFRP square tube and the Steel square tube are simplified as ideal rigid-plastic models; step 2.1: determining the expressions of the full plastic axial force N p and the full plastic bending moment M p of the cross section of the hybrid square tube in step 1; step 2.2: determining the relationship between the load P and the bending deflection W0 of the hybrid square tube in step 1, deriving the calculation expression of the large deflection analytical solution of the hybrid square tube under the end constraint boundary conditions, and determining the relationship between the plastic deformation energy E and the bending deflection W0 of the hybrid square tube by integrating the P-W0 curve; step 2.3: based on step 2.1 and step 2.2, integrating and accumulating the energy of the load-displacement curve of each interval stage to obtain the calculation expression of the plastic deformation energy E of the hybrid square tube under the end constraint boundary conditions, and obtaining the plastic mechanics model of the CFRP reinforced thin-walled square tube.

[0048] and a prediction method thereof, comprising the following steps:

[0049] S1: obtaining the size data and material parameters of the hybrid square tube; S2: determining whether the hybrid square tube is a Steel / CFRP hybrid square tube or a CFRP / Steel hybrid square tube, and selecting a suitable plastic mechanics model; S3: inputting the size 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 the end constraint condition.

[0050] The application proposes a method for constructing a plastic mechanics theoretical prediction model of a CFRP reinforced thin-walled square tube. The quantitative relationship between the strain, bending stress and axial stress of the hybrid square tube under the combined action of axial force and bending moment is revealed. The mathematical expression between the bending load and deflection of the hybrid square tube under end constraint conditions and the energy absorption theoretical prediction model are constructed. The accurate prediction of the influence law of the energy absorption mechanism of the CFRP reinforced thin-walled square tube with various structural parameters is realized.

[0051] In the professional standard of ASME RT-2-2014 Collision Safety for Rail Transit Vehicles, strict crashworthiness design checks are made for the end crash structure of the subway vehicle under the middle crash column loading scenario and the corner crash column loading scenario, aiming to ensure the structural safety of the carrying vehicle under extreme collision conditions, reduce the 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, i.e. the high toughness of metal and the high strength and low mass of CFRP. This combination can significantly improve the performance of thin-walled structures, including increasing their carrying 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 the energy consumption of transportation tools, improving fuel efficiency and reducing greenhouse gas emissions. CFRP reinforced hybrid structures have great application potential in improving carrying capacity, lightweight and crashworthiness performance.

[0053] In actual engineering structures, thin-walled structures are not independent, their two ends are usually connected with other structural components, thus forming a complete energy absorption system. For example, in side collision conditions, the B-pillar of a car is fixed by the rocker beam and roof longitudinal beam; in foreign object intrusion conditions, the two ends of the end crash structure of the subway vehicle are fixed by the rocker beam and the underframe, which can be simplified as bending loading behavior under end constraint conditions. At present, scholars at home and abroad have carried out a lot of research on bending loading behavior under end constraint conditions.

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

[0055] At present, the research on the crashworthiness of the end crash structure of the subway head car under the new standard ASME RT-2-2014 mainly focuses on structure design, test verification and optimization design under single loading scenario. For the end crash structure of the subway, there is no report on the design of crashworthiness enhancement using light-weight high-performance materials and the optimization design of the structure under multiple loading scenarios.

[0056] In the background art, there is also a mention that the current research on the bending behavior of Steel / CFRP hybrid thin-walled structures under end constraints and its application in subway end anti-collision structures are rarely reported. For the next generation of subway trains, the design requirements of lightweight, green, and safe integration are more prominent, such as Figure 1 Therefore, the present application couples the advantages of Steel and CFRP materials, develops a theoretical model that can quickly reflect the plastic mechanical response of CFRP reinforced thin-walled square tube, explores the bending mechanical behavior of Steel / CFRP hybrid square tube under end constraints, reveals the evolution law of each structural parameter on the bending response, and further improves the survival space of the driver and passengers, which has important research value and engineering significance for improving the passive safety of subway vehicles.

[0057] The following is an embodiment of the present application.

[0058] Embodiment 1

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

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

[0061] Step 1: a CFRP reinforced thin-walled square tube is used, i.e. a hybrid square tube composed of a CFRP square tube and a Steel square tube through the combination of inner and outer tubes; the elongated hybrid square tube composed of the CFRP square tube and the Steel square tube in step 1 has an end constraint boundary under quasi-static transverse loading, and the left and right ends of the hybrid square tube are completely constrained, and the shear force of the hybrid square tube under large deflection is ignored.

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

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

[0064] Step 2: Establish the plastic mechanics model of the CFRP reinforced thin-walled square tube under end constraint boundary conditions, where the CFRP square tube and the Steel square tube are simplified as ideal rigid-plastic models. It is assumed 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 the energy absorption is mainly dominated by the plastic behavior. Therefore, the elastic behavior of the material is ignored in the theoretical analysis, and only the range considering plastic deformation is retained.

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

[0066] Step 2.1: Determine the expressions of the full plastic axial force N p and the full plastic bending moment M p of the cross section of the hybrid square tube in step 1; the hybrid square tube is divided into Steel / CFRP hybrid square tube and CFRP / Steel hybrid square tube according to whether the Steel square tube is located outside or inside, the axial force of the Steel / CFRP hybrid square tube is N sc , the bending moment is M sc , the full plastic axial force is Full plastic moment is Axial force of Steel / CFRP hybrid square tube is N cs Bending moment is M cs Full plastic axial force is Full plastic 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 slender 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 Steel / CFRP hybrid square tube) According to the change of the position of the plastic neutral surface of the hybrid square tube, the axial force N sc and bending moment M sc of the cross-section of the hybrid square tube under different conditions are calculated, and the expressions of full plastic axial force and full plastic moment are determined.

[0069] For the structure of the hybrid square tube, the geometric neutral surface and the plastic neutral surface do not necessarily coincide. The schematic diagram of the plastic neutral surface position of the hybrid square tube is shown in Figure 4 . Figure 4 In the left side of the figure, the plastic neutral surface is entirely located inside the Steel tube; Figure 4 In the middle of the figure, the plastic neutral surface is mostly located in the CFRP tube, and the remaining part is distributed inside the Steel tube; Figure 4 In the right side of the figure, the plastic neutral surface is located between the upper and lower surfaces of the CFRP inner tube. Among them, t m is the thickness of the Steel layer located outside the hybrid square tube, and t c is the thickness of the CFRP layer located inside.

[0070] According to the change of the position of the plastic neutral surface, the axial force and the 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 the action of the mid-span load is depicted. The plastic neutral surface is defined as measured from the bottom panel of the hybrid square tube. The distance of the plastic neutral surface from 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 );

[0072] At this point, the entire plastic neutral plane lies within the bottom panel of the Steel tube. The stress and strain distribution diagrams of the Steel / CFRP hybrid square tube cross-section under axial force and bending moment are shown below. Figure 5 As shown. The corresponding axial force N of the cross section. sc and bending moment M sc The calculation expressions are shown in equations (1-1) and (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 plane moves upward, the stress and strain distribution diagram of the cross-section of the Steel / CFRP hybrid square tube is as follows: Figure 6 As shown. Therefore, the axial force N in the cross-section of the Steel / CFRP hybrid square tube is... sc and bending moment M sc The expressions are shown in equations (1-3) and (1-4).

[0077]

[0078]

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

[0080] from Figure 7 As can be seen, the plastic neutral plane continues to move upward as the stress state changes. The stress and strain distribution diagram under this state is as follows: Figure 7 As shown. Axial force N in the cross-section of the steel / CFRP hybrid square tube. sc and bending moment M sc The expressions for are shown in equations (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 final results of the axial force N sc and the bending moment M sc of the Steel / CFRP hybrid square tube with different ξ values can be expressed as:

[0084]

[0085] When ξ = 0, the full plastic axial force of the Steel / CFRP hybrid square tube can be obtained by substituting equation (1-1) as: When ξ = 1 / 2, the full plastic bending moment of the Steel / CFRP hybrid square tube can be obtained by substituting equation (1-6) as: For the Steel / CFRP hybrid square tube, the expressions of the full plastic axial force N and the full plastic bending moment M are shown in equations (1-9) and (1-10), respectively.

[0086]

[0087] Step 2.1.3: Based on the full plastic axial force N and the full plastic bending moment M of step 2.1.2, 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 hybrid square tube cross-section are further obtained.

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

[0089]

[0090]

[0091] To obtain the yield criterion of the Steel / CFRP hybrid square tube, the simultaneous equations (1-11) and (1-12) are used to eliminate the parameter ξ from the two equations, and the yield criterion expression of the Steel / CFRP hybrid square tube cross section is obtained as shown in equation (1-13)

[0092]

[0093] wherein 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 hybrid square tube in step 1, derive the calculation expression of the large deflection analytical solution of the hybrid 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 hybrid square tube by integrating the P-W0 curve;

[0096] Step 2.2.1: The energy generated during the bending deformation process of the hybrid square tube structure is mainly absorbed by the hybrid plastic hinge. Under the cross loading condition, it is assumed that the slender hybrid square tube is rigid except for the cross position and the end clamping position, and the global deformation occurs in a whole manner, and the local deformation effect at the loading position is ignored. Therefore, the simplified schematic diagram of the neutral axis large deflection response of the hybrid square tube under the transverse cross loading is as shown in Figure 8 From Figure 8 it can be seen that the span of the hybrid square tube is L, and the cross position of the hybrid square tube has a global deformation of bending deflection W0 under the action of the external concentrated load P, and the angles of the left and right ends of the hybrid square tube are ψ.

[0097] The free body on the left side of the hybrid square tube is taken for separate force analysis, as shown in Figure 9 Therefore, the moment balance equation can be defined as:

[0098]

[0099] In the formula, F is approximately equal to the axial force N, that is, F = N. Considering the symmetry of the whole structure about the geometric center, the bending moments acting on the left clamping end and the loading end are M = M m Therefore, by converting equation (1-23), the relationship expression between the load P acting on the cross and the bending deflection W0 of the hybrid square tube can be obtained as shown in equation (1-24).

[0100]

[0101] Assuming that the total elongation e of the left half of the hybrid square tube free body is L The related calculation expression is shown in equation (1-25).

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

[0103] where e L1 and e L2 denote the axial elongation at the left clamped end and the loading end, respectively. For e L1 and e L2 , it can be considered that e L1 = e L2 . In addition, according to the geometric relationship in Figure 8 and 9 , the total elongation e L of the left free body and the rotation angle ψ can be obtained by equations (1-26) and (1-27).

[0104]

[0105] The ratio of the axial elongation and the curvature at the left clamped end and the loading end of the hybrid square tube can be obtained by combining equations (1-25), (1-26) and (1-27), and the relationship expression of the ratio with the bending deflection W0 can be represented by equation (2-28).

[0106]

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

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

[0109]

[0110] The partial differential equation of equation (1-13) is solved, and the result of the partial differential equation is brought into equation (1-29), to obtain the relationship expression of the ratio of the axial elongation and the curvature at the left clamped end and the loading end of the hybrid square tube with the dimensionless axial force n, which can be represented by equation (1-30).

[0111]

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

[0113]

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

[0115]

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

[0117] Integrating the P-W0 curve, the relationship expression between the plastic deformation energy E and the bending deflection W0 of the hybrid square tube can be obtained, as shown in equation (1-34).

[0118]

[0119] 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-restrained boundary condition, and the plastic mechanics model of the CFRP reinforced thin-walled square tube is obtained.

[0120] Substituting equation (1-33) into equation (1-34) and integrating and accumulating the energy of the load-displacement curve of each interval stage, the calculation expression of the plastic deformation energy E of the Steel / CFRP hybrid square tube under the end-restrained boundary condition can be obtained, as shown in equation (1-35).

[0121]

[0122] At the same time, the modeling method of the CFRP / Steel hybrid square tube plastic mechanics model is similar to that of the Steel / CFRP hybrid square tube. The modeling process of the lateral force analysis and the plastic mechanics behavior of the CFRP / Steel hybrid square tube is not 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 equation (1-36).

[0123]

[0124] The expressions of the full-plastic axial force and full-plastic bending moment of the CFRP / Steel hybrid square tube are shown in Equations (1-37) and (1-38), respectively.

[0125]

[0126] Substitute Equation (1-36) into Equation (1-34) and integrate and accumulate the energy for the load-displacement curve of each interval stage, thus 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 Equation (1-39).

[0127]

[0128] A CFRP-reinforced thin-walled square tube plastic mechanics model prediction method, comprising the following steps:

[0129] S1: obtaining the size data and material parameters of the hybrid square tube;

[0130] S2: determining whether the hybrid square tube is a Steel / CFRP hybrid square tube or a CFRP / Steel hybrid square tube, and selecting a suitable plastic mechanics model;

[0131] S3: inputting the size 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 the end constraint condition.

[0132] The following CFRP-reinforced thin-walled square tube plastic mechanics model experiment verification.

[0133] The layering sequence of the CFRP tube in the two types of hybrid square tubes is [0° / 90° / 45° / -45°] alternating layering. In order to improve the reliability of the test data and reduce the test error, two repeated test pieces are 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, it may cause differences in the bending performance of the structure. Table 1-1 records the detailed geometric parameter information of the test specimens of the two types of hybrid square tubes.

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

[0135]

[0136] In order to systematically evaluate the crashworthiness performance of the crashworthiness structure during the bending loading process, several key crashworthiness indicators are predetermined in this section, namely energy absorption (EA), peak force (PCF), average force (MCF), specific energy absorption (SEA), crush 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): is obtained by integrating the load-displacement curve formed during the bending loading process, which is widely used to evaluate the ability of energy absorption during structural deformation, which 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 in the loading stage.

[0140] (2) Peak Crushing Force (PCF): represents the maximum crushing force generated during the deformation of the structure. Excessive PCF can lead to a decrease in the survival rate of the driver and passengers, which can be expressed as:

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

[0142] (3) Mean Crushing Force (MCF): is the average value of the force of the structure during the entire bending loading stage, which can be defined by equation (2-3).

[0143]

[0144] (4) Specific Energy Absorption (SEA): is defined as the ability of a structure to absorb unit mass energy, which is an important evaluation index for lightweight structures, and its calculation method is as follows:

[0145]

[0146] (5) Crushing Force Efficiency (CFE): 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. An ideal energy-absorbing structure always pursues high CFE, and its calculation expression is shown in equation (2-5).

[0147]

[0148] (6) Final intrusion (D lmax ): After the indenter is completely unloaded, the final deformation of the structure after elastic recovery. Excessive intrusion is not desirable, and the intrusion after crushing of the structure should be minimized.

[0149] (7) Intrusion area (S inv ): Under the action of bending load, the crash structure not only needs to have excellent plastic mechanics performance, but also should have certain elastic recovery ability, and after bending crushing, it can release a certain intrusion space to protect the safety space of the cab. Therefore, the intrusion area S invThe parameter is selected as the evaluation index, which is defined as the area swept by the position before and after the structure bending and crushing. The smaller the intrusion area, the better the elastic recovery performance of the structure.

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

[0151] In addition, from the load-displacement curve, it can be seen 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, as the loading proceeds, when the displacement reaches about 3mm, the load appears a small range of decline. This is due to the fracture of the fibers in the outer CFRP tube, which causes a temporary decline in its carrying capacity.

[0152] The Figure 11 corresponding deformation mode can be seen that at this time, the outer CFRP tube has obvious fiber radial fracture phenomenon. With the further loading of the indenter, due to the action of the axial force, the load curve appears a smooth upward trend. The reason is that the outer CFRP tube of the CFRP / Steel hybrid square tube and the inner Steel tube produce interactive effect, the inner Steel tube plays its carrying role, thereby further improving 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 smooth upward trend.

[0153] The third stage is the elastic recovery stage, from Figure 11 the deformation mode of the third stage in , it can be seen that after the indenter is loaded downward to the maximum displacement, it starts to unload upward. At this time, the load-displacement curve starts to decline. With the complete release of the elastic deformation energy of the CFRP / Steel hybrid square tube, the lateral displacement gradually recovers to the final deformation mode.

[0154] The quasi-static bending loading experimental results of the Steel / CFRP hybrid square tube under the end constraint boundary condition are shown in Figures 2-17 and Figure 12The load-displacement curves of the two repeated tests are very similar. Like the CFRP / Steel hybrid square tube, the whole test process is also divided into three stages. In the elastic loading stage, the load-displacement curve tends to be linear. When the displacement reaches about 2.5 mm, the load-displacement curve drops instantaneously, and the Steel / CFRP hybrid square tube enters the plastic deformation stage. Compared with the CFRP / Steel hybrid square tube, the load-displacement curve of the Steel / CFRP hybrid square tube is more stable and has less fluctuation, showing stronger bearing capacity. Combined with the deformation mode of each stage, it can be seen that the Steel / CFRP hybrid square tube, like the CFRP / Steel hybrid square tube, has a certain degree of local indentation at the loading point. However, overall, the final deformation of both types of hybrid tubes presents a global deformation mode. Figure 13

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

[0156] From Figure 14 and Figure 16 , it can be seen that at the initial stage 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, only retaining the range of considering plastic deformation. With the increase of loading displacement, the load-displacement theoretical prediction curves of the CFRP / Steel hybrid square tube and the Steel / CFRP hybrid square tube are highly consistent with the experimental curves.

[0157] From Figure 15 and Figure 17 ​​The comparison of the theoretical prediction and the experimental energy-displacement curve can find that the energy absorption is slightly different in the initial loading stage, but most of the energy is absorbed in the later stage of bending loading. From the overall effect of the energy-displacement curve of the two types of mixed variational theory prediction and experiment, the trend of the theoretical prediction curve is basically consistent with that of the experimental curve, which shows that the derived mixed variational theory prediction model has high reliability. As shown in Tables 1-2, the relative error of the energy absorption of the two types of mixed variational theory prediction and experimental results is not more than 3%, which shows that the theoretical prediction model can be used for further research.

[0158] Table 1-2 Comparison of energy absorption of two types of mixed variational theory prediction and experimental results

[0159]

[0160] The above only describes the preferred embodiments of the present application, and it should be noted that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.

Claims

1. A method for constructing a plastic mechanical model of CFRP-reinforced thin-walled square tube, characterized in that, The method comprises the following steps: Step 1: CFRP reinforced thin-walled square tube is formed by combining CFRP square tube and steel square tube into a hybrid square tube through inner and outer tube combination; Step 2: a plastic mechanics model of the CFRP reinforced thin-walled square tube under end constraint boundary condition is established, wherein the CFRP square tube and the steel square tube are simplified into ideal rigid-plastic models; Step 2.1: Determining the expressions for the total plastic axial force N and the total plastic bending moment M of the cross section of the pipe in the step 1 mixture p of the pipe in the step 1 mixture p ​ Step 2.2: the relationship between the load P and the bending deflection W0 of the hybrid square tube in step 1 is determined, the calculation expression of the large deflection analytical solution of the hybrid square tube under the end constraint boundary condition is derived, and the relationship between the plastic deformation energy E and the bending deflection W0 of the hybrid square tube is determined by integrating the P-W0 curve; 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; 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 is rigid except the positions of the mid-span and the end clamping, the global deformation occurs in an integral manner, and the local deformation effect at the loading position is ignored, and the relationship expression between the load P acting 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 expressions of the dimensionless axial force n and the dimensionless moment m with the bending deflection W0 are derived, and the calculation expression of the large deflection analytical solution of the hybrid square tube under the end constraint boundary condition is derived; Step 2.2.3: the P-W0 curve of the load P and the bending deflection W0 in step 2.2.1 is integrated to obtain the relationship between the plastic deformation energy E and the bending deflection W0 of the hybrid square tube.

2. The CFRP-reinforced thin-walled square tube plastic mechanics model construction method according to claim 1, characterized in that, The step 2.1 comprises the following steps: Step 2.1.1: it is assumed 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 the shear force is ignored, and the full plastic stress distribution of the cross section of the hybrid square tube is composed of axial force and bending moment; Step 2.1.2: Calculate the axial force of the cross section of the hybrid pipe under different conditions according to the change of the position of the plastic neutral surface of the mixed pipe and bending moment where i = sc or cs, and determine the expression of the full plastic axial force N p and full plastic bending moment M p ; Step 2.1.3: Total plastic axial force N based on the step 2.1.2 p and total plastic bending moment M p , further obtaining 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 hybrid square tube cross section.

3. The CFRP-reinforced thin-walled square tube plastic mechanics model construction method according to claim 1, characterized in that, The mixed square tube according to Steel square tube is located outside or inside, and is divided into Steel / CFRP mixed square tube and CFRP / Steel mixed square tube, the axial force N sc , the bending moment is M sc , the full plastic axial force is , the full plastic bending moment is , the axial force of the CFRP / Steel mixed square tube is N cs , the bending moment is M cs , the full plastic axial force is , the full plastic bending moment is .

4. The CFRP-reinforced thin-walled square tube plastic mechanics model construction method according to claim 1, characterized in that, The end constraint boundary of the slender hybrid square tube composed of the CFRP square tube and the steel square tube under the quasi-static transverse loading, the left and right ends of the hybrid square tube are completely constrained, and the shear force of the hybrid square tube under large deflection is ignored.

5. The CFRP-reinforced thin-walled square tube plastic mechanics model construction method according to claim 1, characterized in that, The material yield stress of the Steel square tube is assumed in step 2 The stress of the Steel square tube is assumed to be linear with strain The stress of the CFRP square tube is assumed to be linear with strain The CFRP square tube and the Steel square tube are simplified to ideal rigid-plastic models.​​​ 6. The CFRP-reinforced thin-walled square tube plastic mechanics model construction method according to claim 2, characterized in that, The axial force of the mixed square pipe cross section in step 2.1.2 And bending moment Where i = sc or cs, according to the location of the plastic neutral surface, there are three cases including the plastic neutral surface is located in the outer tube, the plastic neutral surface is mostly 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.

7. A CFRP-reinforced thin-walled square tube plastic mechanics model prediction method, characterized by, The method comprises the following steps: S1: obtaining the size data and material parameters of the hybrid square tube; S2: determining whether the hybrid square tube is a steel / CFRP hybrid square tube or a CFRP / steel hybrid square tube, and constructing the plastic mechanics model according to the plastic mechanics model construction method of the CFRP reinforced thin-walled square tube in any one of claims 1 to 6; S3: inputting the size 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 the end constraint condition.

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