Prediction Method for Bending Performance of Steel / CFRP Hybrid Square Tubes Based on Different Loading Positions

Abstract

The present invention provides a method for predicting the bending performance of a Steel / CFRP hybrid square tube based on different loading positions, comprising the following steps: Step 1: Conduct experimental research on the Steel / CFRP hybrid square tube under offset loading through arranging offset loading experiments, form a comparison of final deformations, and realize the comparison of the mechanical properties of the Steel / CFRP hybrid square tube under different loading positions; Step 2: Construct a finite element model of the Steel / CFRP hybrid square tube under offset loading; Step 3: Construct a theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading, and obtain the influence of the offset distance on the theoretically predicted energy absorption; Step 4: Analyze the multi-parameter coupling effect under offset loading; Step 5: Analyze the influencing factors of bending characteristics; including the influence of different ply angles, the influence of different CFRP wrapping lengths, and the influence of different indenter shapes.

Description

Technical Field

[0001] The present invention relates to the technical field of research on the bending characteristics of Steel / CFRP hybrid square tubes, and particularly to a method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions. Background Art

[0002] Urban underground transportation systems, especially subways, have become an effective means to solve urban traffic congestion. As the backbone of urban public transportation, the operation safety of subways is of crucial importance. Due to the high speed and high passenger capacity characteristics of subways, once a collision accident occurs, it may lead to significant casualties and property losses. The severity of this problem has attracted extensive attention from all sectors of society. Especially in the context of rapid technological progress and high safety requirements, subway safety has become even more prominent. Subway collision accidents mostly occur in the end area of the subway head car, 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, the lives of the drivers and passengers will be threatened.

[0003] Carbon fiber reinforced polymer (referred to as CFRP) is an advanced material with lightweight, high specific strength, and high specific stiffness. It can significantly reduce the self-weight of rail vehicles, contribute to reducing vehicle carbon emissions and energy consumption, and conforms to the concept of sustainable transportation. CFRP materials also have excellent durability and corrosion resistance, which can extend the service life of vehicles and reduce maintenance costs. In addition, CFRP materials have good design flexibility and formability, enabling them to be used to manufacture various complex-shaped structural components to meet the requirements of different train models and car body designs. Therefore, more and more rail transit vehicles are applying carbon fiber materials to improve train performance and reduce energy consumption. For example: The driver's cab structure of the British Intercity 125 train uses CFRP materials, with a weight reduction of 30% - 35% compared to the steel structure; The car body of the French TGV double-decker passenger train uses CFRP materials formed by the vacuum curing bag process and a large number of honeycomb sandwich structures, with a weight reduction of 25% compared to the aluminum car body. The N700 series vehicles released in Japan are installed with carbon fiber composite material roofs and have achieved good weight reduction effects. The TTX train put into operation in South Korea uses CFRP roofs, side walls, and end wall structures, with a mass reduction of 28% compared to the stainless steel car body. In addition, the next-generation subway vehicle "CETROVO" proposed by CRRC in 2018 has the largest proportion of CFRP materials and the overall mass is reduced by about 30%.

[0004] However, although CFRP exhibits excellent mechanical properties, its economic cost is much higher than that of traditional metal materials such as aluminum alloy and steel, which to a certain extent limits its application scope. 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 decline in its crashworthiness. In order to consider economic cost and crashworthiness while pursuing structural lightweighting, a feasible method is to introduce metal materials with low cost, high ductility, and stable deformation into CFRP with lightweight, high specific strength, and high specific stiffness, so as to more effectively guide the deformation and failure process of the materials.

[0005] Most of the collision energy generated in a collision accident is often absorbed through the axial deformation and bending deformation of thin-walled structures. Some good achievements have been made in the current research on the crashworthiness of thin-walled structures under axial load conditions. Previous research on the 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. For example, the two ends of the anti-collision structure at the end of a subway vehicle are fixed by the sill beam and the underframe. When the anti-collision structure collides with a large object outside, 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 lead to the design scheme deviating from the actual situation or being difficult to apply in engineering. The bending loading behavior of thin-walled structures under end constraint conditions is much more complex. When large plastic deformations occur under this boundary condition, axial force, bending moment, and shear force often participate together. However, there are few reports on the bending behavior research of Steel / CFRP hybrid thin-walled structures under end constraint conditions and their application in subway end anti-collision structures.

[0006] The end structure of a subway vehicle usually plays an important protective role during a collision. Strengthening the load-bearing energy absorption of the subway end anti-collision structure as much as possible, reducing the structural mass, and at the same time reducing the deformation degree after crushing to improve the living space of the driver and passengers have important research value and engineering significance for improving the collision safety performance of subway vehicles, alleviating environmental pollution caused by emissions, and achieving lightweighting. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide a method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions, clarifying the matching relationship of multiple parameters under offset loading conditions, and characterizing the influence mechanism of ply angle, CFRP wrapping length, and indenter shape on the evolution of bending characteristics under offset loading.

[0008] To achieve the above object, the present invention adopts the following technical solutions: A method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions, comprising the following steps:

[0009] Step 1: Conduct experimental research on Steel / CFRP hybrid square tubes under offset loading through arranging offset loading experiments, form a comparison of final deformations, and achieve the comparison of the mechanical properties of Steel / CFRP hybrid square tubes under different loading positions;

[0010] Step 2: Construct a finite element model of the Steel / CFRP hybrid square tube under offset loading;

[0011] Step 3: Construct a theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading, and obtain the influence of the offset distance on the theoretically predicted energy absorption;

[0012] Step 4: Analyze the multi-parameter coupling effect under offset loading;

[0013] Step 5: Analyze the influencing factors of bending characteristics; including the influence of different ply angles, the influence of different CFRP wrapping lengths, and the influence of different indenter shapes.

[0014] In a preferred embodiment, in the step 1: The quasi-static bending experiment of the Steel / CFRP hybrid square tube under offset loading is carried out on an MTS-322 hydraulic servo control testing machine. The two ends of the specimen are locked and fixed by the upper and lower clamping devices of the U-support frame. It also includes rectangular clamping blocks. By adjusting the relative position relationship between the rectangular clamping blocks and the U-shaped fixture, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions are studied. Different loading position test scenarios are set by adjusting different effective spans.

[0015] In a preferred embodiment, in the step 2: The geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimen in the experiment. The degrees of freedom on its left and right sides are both constrained. The loading speed of the indenter is set to 1000 mm / s, and the downward compression displacement is set to 22 mm. The mesh sizes of the specimen and the indenter are set to 2 mm and 5 mm respectively; Set the offset distance ΔD of the indenter loading, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube; The effective span of the Steel / CFRP hybrid square tube is 300 mm. The offset distances ΔD for the 1 / 3 span loading condition and the 1 / 4 span loading condition are set to 50 mm and 75 mm respectively.

[0016] In a preferred embodiment, step 3 includes the analytical solution of large deflections of Steel / CFRP hybrid square tubes under offset loading; under the offset loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored; it is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and undergo global deformation as a whole; three hybrid plastic hinges are developed at the loading position and the end supports of the Steel / CFRP hybrid square tube respectively; the span of the hybrid square tube is L, the loading point is located at a distance L1 from the left support end, and the offset distance between the loading point and the center line of the span of the hybrid square tube is ΔD; under the action of the external concentrated load P b the maximum deflection W of the hybrid square tube occurs b ;

[0017] The moment equilibrium equation is obtained, as shown in Equation (1)

[0018]

[0019] where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b = M bm ; Equation (1) is transformed to obtain the relational expression between the concentrated load P b and the lateral displacement W b of the loading point, as shown in Equation (2)

[0020]

[0021] Assume that the total elongation of the left free body with a length of L1 is a L , and its calculation expression is as shown in Equation (3)

[0022] a L = a L1 + a L2 (3)

[0023] where a L1 and a L2 are the axial elongations at the ends of the left free body respectively;

[0024]

[0025] Combining Equation (3) and Equation (4) can be further simplified to obtain Equation (5)

[0026]

[0027] According to the geometric relationship, the left rotation angle ψ LThe calculation expression of is shown in formula (6):

[0028]

[0029] Similarly, assume that the total extension of the right free body with length L2 is b R , its calculation expression is shown in formula (7)

[0030] b R =b R1 +b R2 (7)

[0031] where b R1 and b R2 are the axial extensions of the left free body end respectively; according to the geometric relationship, formula (8)

[0032]

[0033] Combining equation (7) and equation (8) to further simplify equation (9)

[0034]

[0035] According to the geometric relationship, the right rotation angle ψ R The calculation expression of is shown in formula (10):

[0036]

[0037] The ratio of axial elongation to curvature and bending deflection W in the left and right free bodies b The relational expression of is shown in formula (11):

[0038]

[0039] On the other hand, the relevant flow rule for the plastic yield criterion is expressed as follows:

[0040]

[0041]

[0042] Combining equations (11), (12) and (13), we can obtain the expression of the bending deflection of the Steel / CFRP hybrid square tube under offset loading:

[0043]

[0044] Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 are expressed by the relationship between the offset distance and the span:

[0045] L1 = L / 2 + ΔD (15)

[0046] L2 = L / 2 - ΔD (16)

[0047] Substitute Equation (11), Equation (15), and Equation (16) into Equation (1) to obtain the calculation expression of the analytical solution for the large deflection of the Steel / CFRP hybrid square tube under offset loading, as shown in Equation (17);

[0048]

[0049] where, t m represents the thickness of Steel, t c represents the thickness of CFRP, P b1 , P b2 , P b3 , P b4 are the loading loads under different bending deflections Wb, σ m represents the material yield stress of the Steel square tube, σ c represents the stress of the Steel square tube in the tensile and compressive states;

[0050] Integrate and accumulate the energy of the P b -W b curve for each interval stage in Equation (17). Therefore, the relationship expression between the plastic bending deformation energy E b of the Steel / CFRP hybrid square tube under offset loading and the deflection W b is obtained, as shown in Equation (18);

[0051]

[0052] In a preferred embodiment, in step 4: Analyze the correlation between the Steel thickness, CFRP thickness, cross-sectional width, and offset distance, and find the main effects of the correlation between the Steel thickness, CFRP thickness, cross-sectional width, and offset distance on the response; Use a linear regression model to calculate the linear effects after normalizing the design parameters, where the value ranges of the normalized design parameters are all mapped to between [0, 1]; The calculation expression of the linear effect value between each design parameter x and the output response quantity f(x) is as shown in Equation (19)

[0053] f(x) = b0 + b1x (19)

[0054] In the linear regression model, the slope b1 of the line represents the degree of influence of the design parameter on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameter has little influence on the output response; if the line tends to be more vertical, it means that the design parameter has a greater influence on the output response; a positive slope of the line indicates a positive correlation between the design parameter and the output response, while a negative slope indicates a negative correlation between the design parameter and the output response.

[0055] In a preferred embodiment, in step 5: parametric analysis is used to study the effects of ply angle, CFRP wrapping length, and indenter shape on the bending characteristics of Steel / CFRP hybrid square tubes under offset loading conditions; the default boundary conditions of the 1 / 3-span loading condition are adopted, and the following geometric parameters of the Steel / CFRP hybrid square tube are set as default values: the span is set to 300 mm, the cross-sectional width is 28 mm, the Steel thickness is 1 mm, the CFRP thickness is 1 mm, the thickness of each layer of CFRP is 0.1 mm, the stacking sequence of the ply angle is [0° / 90° / 45° / -45°], the indenter diameter is 25 mm, and the indenter offset distance is 50 mm; when one influencing factor changes, the other factors remain at their default values.

[0056] Compared with the prior art, the present invention has the following beneficial effects: The present invention takes the Steel / CFRP hybrid square tube as the research object, and reveals the bending performance of the Steel / CFRP hybrid square tube under different loading positions based on experimental methods. A finite element model and a theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading are constructed and verified, and the influence of the offset distance on the bending energy absorption mechanism is revealed based on the theoretical prediction model. The influence of the simultaneous change of multiple parameter domains on the bending characteristics under offset loading is discussed. In addition, the influence of ply angle, CFRP wrapping length, and indenter shape on the bending characteristics is also explored. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Offset loading at different positions of the preferred embodiment of the present invention, wherein, (a) is 1 / 3-span loading; (b) is 1 / 4-span loading; (c) is the test specimen;

[0058] Figure 2 Experimental results of the Steel / CFRP hybrid square tube with 1 / 3-span loading of the preferred embodiment of the present invention, wherein, (a) is the load-displacement history curve of 1 / 3-span loading, (b) is the deformation process of 1 / 3-span loading;

[0059] Figure 3 Experimental results of the Steel / CFRP hybrid square tube with 1 / 4-span loading of the preferred embodiment of the present invention, wherein, (a) is the load-displacement history curve of 1 / 4-span loading, (b) is the deformation process of 1 / 4-span loading;

[0060] Figure 4 The final deformed shapes of the Steel / CFRP hybrid square tubes under different loading positions in the preferred embodiment of the present invention;

[0061] Figure 5 Comparison of the final intrusion displacement measurement results of the Steel / CFRP hybrid square tubes under different loading positions in the preferred embodiment of the present invention;

[0062] Figure 6 Comparison of the mechanical properties of the Steel / CFRP hybrid square tubes under different loading positions in the preferred embodiment of the present invention, where (a) is the comparison of the load-displacement curves under different loading conditions, and (b) is the comparison of the energy-displacement curves under different loading conditions;

[0063] Figure 7 Comparison of the crashworthiness of the Steel / CFRP hybrid square tubes under different loading positions in the preferred embodiment of the present invention, where (a) is the comparison of the EA and S of the tubes with different material configurations inv comparison, (b) is the comparison of the PCF and SEA of the tubes with different material configurations, and (c) is the comparison of the D lmax and MCF;

[0064] Figure 8 The finite element model of the Steel / CFRP hybrid square tube under offset loading in the preferred embodiment of the present invention;

[0065] Figure 9 Comparison of the experimental and simulation final deformation modes in the preferred embodiment of the present invention, where (a) is the 1 / 3 span loading condition; (b) is the 1 / 4 span loading condition;

[0066] Figure 10 Comparison of the experimental and simulation results of the Steel / CFRP hybrid square tubes under different offset loading conditions in the preferred embodiment of the present invention;

[0067] Figure 11 Comparison of the final intrusion displacements of the Steel / CFRP hybrid square tubes between simulation and experiment under different offset loading conditions in the preferred embodiment of the present invention;

[0068] Figure 12 Schematic diagram of the overall bending deformation mode of the plastic neutral axis of the Steel / CFRP hybrid square tube under offset loading in the preferred embodiment of the present invention, where (a) is the transverse cross-sectional profile under offset loading, and (b) is the axial force and moment acting on the free body;

[0069] Figure 13Mechanical property comparison between experimental results and theoretical predictions of Steel / CFRP hybrid square tubes under the 1 / 3 span loading condition of the preferred embodiment of the present invention. Among them, (a) is the load-displacement curve of experimental results and theoretical predictions, and (b) is the energy-displacement curve of experimental results and theoretical predictions;

[0070] Figure 14 Mechanical property comparison between experimental results and theoretical predictions of Steel / CFRP hybrid square tubes under the 1 / 4 span loading condition of the preferred embodiment of the present invention. Among them, (a) is the load-displacement curve of experimental results and theoretical predictions, and (b) is the energy-displacement curve of experimental results and theoretical predictions;

[0071] Figure 15 Comparison between theoretical predictions and simulation results of Steel / CFRP hybrid square tubes under offset loading of the preferred embodiment of the present invention;

[0072] Figure 16 Comparison between theoretical prediction EA and simulation results of Steel / CFRP hybrid square tubes at different offset distances of the preferred embodiment of the present invention;

[0073] Figure 17 Deformation modes of Steel / CFRP hybrid square tubes at different offset distances of the preferred embodiment of the present invention. Among them, (a) is the indenter offset distance ΔD = 25 mm, and (b) is the indenter offset distance ΔD = 100 mm;

[0074] Figure 18 Main effect analysis of each design parameter on the response of the preferred embodiment of the present invention. Among them, (a) is the main effect analysis of each parameter on EA, (b) is the main effect analysis of each parameter on S inv The main effect analysis of, (c) is the main effect analysis of each parameter on SEA, (d) is the main effect analysis of each parameter on PCF, (e) is the main effect analysis of each parameter on MCF, and (f) is the main effect analysis of each parameter on D lmax The main effect analysis;

[0075] Figure 19 Variation laws of each response under the coupling action of multiple parameters of the preferred embodiment of the present invention. Among them, (a) is the relationship between EA and t m 、t c The relationship between, (b) is EA and b, ΔD, (c) is S inv The relationship between and t m 、t c The relationship between, (d) is S inv The relationship between and b, ΔD, (e) is the relationship between SEA and t m 、t c The relationship between, (f) is the relationship between SEA and b, ΔD, (g) is the relationship between PCF and t m 、tc The relationship of (h) is between the PCF and b, ΔD, and (i) is between the MCF and t m and t c The relationship of (j) is between the MCF and b, ΔD, and (k) is for D lmax The relationship with ΔD, b, and (l) is for D lmax The relationship with t m and t c The relationship;

[0076] Figure 20 Comparison of load-displacement curves of Steel / CFRP hybrid square tubes with different ply angles in the preferred embodiment of the present invention;

[0077] Figure 21 Comparison of the final intrusion displacements of Steel / CFRP hybrid square tubes with different ply angles in the preferred embodiment of the present invention;

[0078] Figure 22 Comparison of crashworthiness indexes of Steel / CFRP hybrid square tubes with different ply angles in the preferred embodiment of the present invention. Among them, (a) is the comparison of S inv and EA, (b) is the comparison of PCF, SEA with different ply angles, and (c) is D with different ply angles lmax and MCF comparison;

[0079] Figure 23 Schematic diagram of the layout of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths in the preferred embodiment of the present invention;

[0080] Figure 24 Final deformation modes of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths in the preferred embodiment of the present invention;

[0081] Figure 25 Comparison of load-displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths in the preferred embodiment of the present invention;

[0082] Figure 26 Comparison of the final intrusion displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths in the preferred embodiment of the present invention;

[0083] Figure 27 Comparison of crashworthiness indexes of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths in the preferred embodiment of the present invention. Among them, (a) is the comparison of S inv and EA, (b) is the comparison of PCF, SEA with different CFRP wrapping lengths, and (c) is D with different CFRP wrapping lengths lmax, Comparison with MCF;

[0084] Figure 28 It is a schematic cross - sectional view of different indenter heads in the preferred embodiment of the present invention. Among them, (a) is conical, (b) is circular, (c) is trapezoidal, and (d) is square.

[0085] Figure 29 It is the final deformation mode of the Steel / CFRP hybrid square tube under offset loading of different - shaped indenter heads in the preferred embodiment of the present invention. Among them, (a) is offset loading with a conical indenter head, (b) is offset loading with a circular indenter head, (c) is offset loading with a trapezoidal indenter head, and (d) is offset loading with a square indenter head;

[0086] Figure 30 It is the comparison of the load - displacement curves of the Steel / CFRP hybrid square tube under offset loading of different - shaped indenter heads in the preferred embodiment of the present invention;

[0087] Figure 31 It is the comparison of the final intrusion displacement curves of the Steel / CFRP hybrid square tube under offset loading of different - shaped indenter heads in the preferred embodiment of the present invention;

[0088] Figure 32 It is the comparison of the crashworthiness indexes of the Steel / CFRP hybrid square tube under offset loading of different indenter - head shapes in the preferred embodiment of the present invention. Among them, (a) is the comparison of S inv , EA, (b) is the comparison of PCF, SEA of different indenter - head shapes, and (c) is the comparison of D lmax , MCF. Detailed implementation mode

[0089] The present invention will be further described below with reference to the drawings and embodiments.

[0090] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0091] It should be noted that the terms used herein are only for describing the specific implementation mode and are not intended to limit the exemplary implementation mode according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "include" and / or "comprise" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or their combinations.

[0092] This embodiment includes the following steps:

[0093] Step 1: Mechanical Property Analysis of Steel / CFRP Hybrid Square Tubes under Different Loading Positions

[0094] Step 11: Experimental Arrangement of Offset Loading

[0095] The quasi-static bending experiment of the Steel / CFRP hybrid square tube under offset loading was carried out on an MTS-322 hydraulic servo control testing machine. The details of the experimental device arrangement for the offset loading condition are as Figure 1 shown. As can be seen from Figure 1 , the two ends of the specimen were locked and fixed by the upper and lower clamping devices of the U-shaped support frame. In addition, by adjusting the relative position relationship between the rectangular clamp block and the U-shaped fixture, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions were studied. Figure 1 (a) in is the 1 / 3-span loading test scenario, with an effective span of 300 mm, a circular indenter diameter of 25 mm, and the distance from the indenter loading point to the left side of the U-shaped support frame being 100 mm, which is 1 / 3 of the effective span. Figure 1 (b) in is the 1 / 4-span loading test scenario, with the distance from the indenter loading point to the left side of the U-shaped support frame being 75 mm, which is 1 / 4 of the effective span. Figure 1 (c) in is the test specimen, and the lengths of both specimens are 380 mm. The Steel / CFRP hybrid square tube was prepared based on the vacuum bag molding process introduced in Chapter 3, and the carbon fiber prepreg was attached and coupled to the inner surface of the Steel tube in the form of alternating layers of [0° / 90° / 45° / -45°].

[0096] In addition, the circular indenter moved vertically downward at a loading speed of 2 mm / min, and the maximum loading displacement of the indenter was set to 22 mm, that is, when the indenter reached the maximum displacement, the downward loading was stopped. After the loading was completed, the indenter moved upward at a speed of 4 mm / min to unload the load. Table 1 records the detailed information of the Steel / CFRP hybrid square tube samples under two offset loading positions.

[0097] Table 1 Summary of Geometric Parameters of Steel / CFRP Hybrid Square Tubes

[0098]

[0099]

[0100] Step 12: Experimental Study of Steel / CFRP Hybrid Square Tubes under Offset Loading

[0101] The experimental results of the 1 / 3-span loading and 1 / 4-span loading of the Steel / CFRP hybrid square tube under the end constraint boundary condition are respectively as Figure 2 and Figure 3 shown. As can be seen from Figure 2(a) and Figure 3 From the load-displacement curves during the loading process of (a), it can be seen that the load-displacement curves of the two offset loading conditions show similar growth trends. In addition, similar to the mid-span loading, the load-displacement curves under the two offset loading conditions can also be divided into three stages: elastic loading, plastic deformation, and elastic recovery. In the elastic loading stage, the load and displacement almost show a monotonically increasing trend; as the load increases, it enters the initial plastic deformation stage. Due to the failure behavior of the internal CFRP tube, the bearing capacity under the two offset conditions decreases to a certain extent. With the further participation of the axial force, the load curve gradually rises; as the unloading displacement increases, the elastic deformation energy of the Steel / CFRP hybrid square tube gradually begins to be released until it returns to the final deformation state. From Figure 2 (b) and Figure 3 From the deformation process of (b), it can be seen that the Steel / CFRP hybrid square tube under the 1 / 3 span and 1 / 4 span loading undergoes overall bending deformation accompanied by the formation of local indentations. The indentations increase with the increase of the indenter displacement until they reach the maximum value during the entire quasi-static bending loading. As the indenter starts to unload upward until it returns to the initial position, it marks the end of the elastic recovery stage.

[0102] Step 13: Final deformation comparison

[0103] The final deformation shapes of the Steel / CFRP hybrid square tube at three different loading positions are as Figure 4 shown. From Figure 4It can be observed that local buckling occurred in the indenter loading area and the end restraint areas on both sides of the specimens under the three different loading positions, and three fixed plastic hinges were formed. It can also be seen that overall bending deformation occurred in the specimens under the three loading positions, and a certain degree of local deformation occurred in the indenter loading area. The indenter indentation area formed by the upper surface profile was the smallest under the 1 / 2 span loading. When the loading position was closer to the restraint end, the local deformation in the indenter loading area was greater. In addition, a careful observation of the indenter loading area revealed that the Steel / CFRP hybrid square tube under the 1 / 2 span loading produced a symmetric plastic deformation mode, and the indenter indentation and the indentation in the end restraint area were almost symmetric about the mid-span. However, the Steel / CFRP hybrid square tube under the 1 / 3 span and 1 / 4 span loadings showed an asymmetric plastic deformation mode in the indenter loading area. The indentations in the indenter loading area under the two offset loading conditions were inclined to the right to a certain extent, and the area of the plastic deformation region on the left side was significantly larger than that on the right side, mainly caused by the uneven axial forces acting on the left and right sides of the pipe fittings. The inclination degree of the indenter indentation in the loading area of the Steel / CFRP hybrid square tube under the 1 / 4 span loading was more obvious than that of the specimen under the 1 / 3 span loading. This was because the indenter loading position under the 1 / 4 span loading was closer to the restraint end, resulting in a greater shear force and more obvious asymmetry of the indenter indentation. As can be seen from Figure 4 (a), for the Steel / CFRP hybrid square tube under the mid-span loading, almost no obvious plastic deformation occurred at the two restraint ends on both sides; as can be seen from Figure 4 (b) and Figure 4 (c), obvious local depression occurred in the left clamping area of the Steel / CFRP hybrid square tube near the loading end, and the depression degree of the specimen under the 1 / 4 span loading was the most serious. Almost no plastic deformation occurred in the right clamping area of the specimen, which was caused by the uneven shear forces generated at both ends of the specimen under the offset loading.

[0104] After the indenter was completely unloaded, the final deformation amount at the midpoint of the bottom cross-section of the specimen needed to be measured. The left clamping end was regarded as the measurement starting point, and the measurements were taken sequentially to the right one by one, with the interval between each measurement point set at 30 mm. In the indenter loading area with a length of 70 mm, the interval between the measurement points was densified to 10 mm. The test results of the final intrusion displacements of the Steel / CFRP hybrid square tube under the three loading positions were summarized as shown in Figure 5 . Due to the accuracy of the ruler and the measurement error, the final cumulative error was limited within ±1 mm.

[0105] As can be seen from Figure 5It can be observed that, compared with the symmetric pattern presented by the maximum intrusion displacement under mid-span loading, the maximum intrusion displacement of the Steel / CFRP hybrid square tube under 1 / 3-span loading and 1 / 4-span loading does not occur at the center of the indenter loading, but on the right side of the center of the indenter loading. The above results of the final deformation also reveal this feature. In addition, it can also be seen that the bending deflection of the lower surface profile of the specimen is the largest under 1 / 2-span loading, while the bending deflection of the lower surface profile of the specimen is the smallest under 1 / 4-span loading. Compared with the loading at the mid-span position, when the loading position is closer to the constrained end, the overall deformation of the Steel / CFRP hybrid square tube is smaller, and the contribution degrees of the overall and local deformations to the final deformation also change.

[0106] Step 14: Performance comparison of Steel / CFRP hybrid square tubes under different loading positions

[0107] The load-displacement and energy-displacement curves of the Steel / CFRP hybrid square tubes at three different loading positions are as Figure 6 shown. From Figure 6 the load-displacement curve in (a), it can be seen that the load curves at three different loading positions gradually increase with the increase of the loading displacement. When just entering the plastic stage, the load-carrying capacities all show a certain degree of decline. Subsequently, under the action of the axial force, the load-carrying capacities all show a certain degree of increase. When the loading displacement reaches the set 22 mm, the indenter starts to unload upward. In addition, it can also be seen that the load-carrying capacities of the Steel / CFRP hybrid square tubes under 1 / 3-span loading and 1 / 4-span loading are both greater than that under mid-span loading. In addition, from Figure 6 the energy-displacement curve in (b), it can be clearly seen that the energy absorption of the Steel / CFRP hybrid square tube under 1 / 4-span loading is the largest, while the energy absorption of the Steel / CFRP hybrid square tube under mid-span loading is the smallest. This is because the closer the loading position is to the constrained end, the higher the participation degree of the axial force. Therefore, the load-carrying capacity increases accordingly, and the energy absorption also increases.

[0108] To quantitatively analyze the crashworthiness of the Steel / CFRP hybrid square tube under different loading conditions, the crashworthiness indexes in the load-displacement and final intrusion displacement curves are extracted and summarized in Table 2. It can be seen from Table 2 that the EAs of the Steel / CFRP hybrid square tubes under the 1 / 3-span loading condition and the 1 / 4-span loading condition are 233.22 J and 259.35 J respectively, and the S inv are 21.24 cm 2 and 20.69 cm 2 respectively, the PCFs are 11.74 kN and 13.27 kN respectively, the SEAs are 0.648 J / g and 0.719 J / g respectively, and the D lmaxThey are 12.78 mm and 12.64 mm respectively, and the corresponding MCFs are 10.60 kN and 11.79 kN respectively.

[0109] Table 2 Crashworthiness indexes of Steel / CFRP hybrid square tubes under different loading positions

[0110]

[0111] To observe the law change more intuitively, Figure 7 The line chart of... compares the crashworthiness performance of Steel / CFRP hybrid square tubes under different loading positions. From Figure 7 The comparison of the crashworthiness performance shows that under the 1 / 3-span loading, the crashworthiness performance indexes of the Steel / CFRP hybrid square tube are all between those under the 1 / 2-span loading and the 1 / 4-span loading. The closer the loading position is to the constrained end, the larger the EA is, and the corresponding SEA is also larger, while D lmax and the corresponding S inv are smaller. The EA of the Steel / CFRP hybrid square tube under the 1 / 3-span loading condition and the 1 / 4-span loading condition is increased by 14.62% and 27.46% respectively compared with that under the 1 / 2-span loading condition, the S inv is reduced by 0.84% and 3.41% respectively, the PCF is increased by 7.51% and 21.52% respectively, the SEA is increased by 13.88% and 26.36% respectively, and D lmax is reduced by 1.54% and 2.62% respectively.

[0112] Step 2: Finite element modeling and verification of Steel / CFRP hybrid square tube under offset loading

[0113] Step 21: Finite element modeling of Steel / CFRP hybrid square tube under offset loading

[0114] The finite element model of the Steel / CFRP hybrid square tube under offset loading is as shown in Figure 8 ... The geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimens in the experiment. The degrees of freedom on both the left and right sides are constrained. The loading speed of the indenter is set to 1000 mm / s, and the downward compression displacement is set to 22 mm. The mesh sizes of the specimen and the indenter are set to 2 mm and 5 mm respectively. In addition, to simulate the offset loading condition, an offset distance ΔD of the indenter loading is set, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube. The effective span of the Steel / CFRP hybrid square tube is 300 mm, and the offset distances ΔD under the 1 / 3-span loading condition and the 1 / 4-span loading condition are set to 50 mm and 75 mm respectively.

[0115] Step 22: Simulation and experimental verification

[0116] Figure 9 The final deformation modes of the Steel / CFRP hybrid square tubes under the 1 / 3 span loading condition and the 1 / 4 span loading condition were compared, which is an important criterion for verifying the correctness of the finite element model. From Figure 9 the finite element simulation results, local indentation in the indenter loading area and local buckling near the constrained end of the Steel / CFRP hybrid square tube can be observed. As expected, both the finite element model and the Steel / CFRP hybrid square tube in the experiment produced an asymmetric plastic deformation mode in the indenter loading area, indicating that the finite element model established in this chapter under offset loading can effectively predict the three plastic hinge mode of the Steel / CFRP hybrid square tube.

[0117] The comparisons of the force-displacement curves and energy-displacement curves between the simulation and the experiment under the 1 / 3 span loading condition and the 1 / 4 span loading condition are as Figure 10 shown. By Figure 10 it can be found that for both the experiment and the finite element simulation, the force-displacement curves of the Steel / CFRP hybrid square tube all experienced three stages: elastic loading, plastic deformation, and elastic recovery. And the load-displacement curves in each stage are in good agreement. In addition, for the two offset loading conditions, it can be seen that the energy-displacement curves in the simulation are in good agreement with the experimental results.

[0118] The comparisons of the final intrusion displacements between the simulation and the experiment of the Steel / CFRP hybrid square tube under different offset loading conditions are as Figure 11 shown. From Figure 11 it can be seen that the final intrusion displacements measured by the simulation and the experiment are in high agreement, indicating that the measurement results of the lower surface deformation of the finite element model are reliable. The crashworthiness indexes of the Steel / CFRP hybrid square tube in the simulation and the experiment under the two loading conditions are listed in Table 3. It can be seen from Table 3 that the error values of EA, PCF, and S inv under the 1 / 3 span loading are 4.17%, 1.70%, and 1.51% respectively; the error values of EA, PCF, and S inv under the 1 / 4 span loading are 2.84%, 2.94%, and 1.40% respectively. The maximum errors of the crashworthiness indexes under the two offset conditions are both less than 5%, indicating that the finite element model established in this chapter under offset loading can accurately predict the bending response and mechanical behavior of the Steel / CFRP hybrid square tube under the end constraint boundary condition.

[0119] Table 3 Comparison of crashworthiness indexes between the simulation and the experiment of the Steel / CFRP hybrid square tube under different offset loading conditions

[0120]

[0121] Step 3: Theoretical Prediction Model of Steel / CFRP Hybrid Square Tube under Offset Loading

[0122] Step 31: Analytical Solution of Large Deflection of Steel / CFRP Hybrid Square Tube under Offset Loading

[0123] Under the offset loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored. It is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and undergo global deformation in an overall manner. Therefore, a simplified schematic diagram of the large deflection response of the neutral axis of the Steel / CFRP hybrid square tube under lateral offset loading is as shown Figure 12 in. From Figure 12 it can be seen that three hybrid plastic hinges are developed at the loading position and the end supports of the Steel / CFRP hybrid square tube respectively. The span of the hybrid square tube is L, and the loading point is located at L1 from the left support end, which can be regarded as the offset distance ΔD between the loading point and the center line of the span of the hybrid square tube. Under the action of the external concentrated load P b , the maximum deflection W b of the hybrid square tube occurs.

[0124] According to Figure 12 the axial forces and moments distributed on the free body in (b), the moment equilibrium equation can be obtained as shown in Equation (1).

[0125]

[0126] where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b = M bm . Therefore, by transforming Equation (1), the relationship expression between the concentrated load P b and the lateral displacement W b at the loading point is obtained as shown in Equation (2).

[0127]

[0128] Assume that the total elongation of the left free body with a length of L1 is a L , and its calculation expression is as shown in Equation (3).

[0129] a L = a L1 + a L2 (3)

[0130] where a L1 and a L2are the axial elongation amounts at the free end of the left side respectively. According to Figure 12 the geometric relationships in

[0131]

[0132] Equation (4) can be obtained by combining Equation (3) and Equation (4).

[0133]

[0134] According to the geometric relationship, the calculation expression of the left rotation angle ψ L is shown in Equation (6).

[0135]

[0136] Similarly, assume that the total elongation amount of the right free body with length L2 is b R , and its calculation expression is shown in Equation (7).

[0137] b R = b R1 + b R2 (7)

[0138] where b R1 and b R2 are the axial elongation amounts at the free end of the left side respectively. Equation (8) can be obtained according to the geometric relationship.

[0139]

[0140] Equation (9) can be further simplified by combining Equation (7) and Equation (8).

[0141]

[0142] According to the geometric relationship, the calculation expression of the right rotation angle ψ R is shown in Equation (10).

[0143]

[0144] The relational expression between the ratio of the axial elongation rate to the curvature and the bending deflection W b in the left and right free bodies is shown in Equation (11).

[0145]

[0146] On the other hand, the associated flow rule of the plastic yield criterion can be expressed as follows:

[0147]

[0148] By combining Equation (11), Equation (12) and Equation (13), the expression of the bending deflection of the Steel / CFRP hybrid square tube under offset loading can be obtained.

[0149]

[0150] Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 can be expressed by the relationship between the offset distance and the span:

[0151] L1 = L / 2 + ΔD (15)

[0152] L2 = L / 2 - ΔD (16)

[0153] Substitute Equation (11), Equation (15), and Equation (16) into Equation (1) to obtain the calculation expression of the analytical solution of the large deflection of the Steel / CFRP hybrid square tube under offset loading, as shown in Equation (17).

[0154]

[0155] Integrate and accumulate the energy of the P b -W b curve in each interval stage of Equation (17). P b1 、P b2 、P b3 、P b4 are the loading loads at different bending deflections Wb, and σ m represents the material yield stress of the Steel square tube, and σ c represents the stress of the Steel square tube in the tensile and compressive states. Therefore, the relationship expression between the plastic bending deformation energy E b of the Steel / CFRP hybrid square tube and the deflection W b can be obtained, as shown in Equation (18).

[0156]

[0157] Step 32: Verification of the theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading

[0158] In the experiment, the span L of the Steel / CFRP hybrid square tube is 300 mm, the thickness t c of the outer CFRP is 1 mm, the thickness t m of the inner Steel is 1 mm, the cross-sectional width b is 28 mm, σ m = 240 MPa, σ c= 70 MPa. In addition, the indenter offset distance ΔD for the 1 / 3 span loading condition is 50 mm, and the indenter offset distance ΔD for the 1 / 4 span loading condition is 75 mm. To verify the effectiveness of the theoretical prediction model for the Steel / CFRP hybrid square tube under offset loading and substitute the relevant geometric parameters into the large deflection analytical solutions of the hybrid square tube in Equations (17) and (18), the mechanical property comparison diagrams between the experimental results and theoretical predictions of the Steel / CFRP hybrid square tube under the 1 / 3 span and 1 / 4 span loading conditions can be obtained, as shown respectively in Figure 13 and Figure 14 shown.

[0159] From Figure 13 (a) of Figure 14 and Figure 13 (a) of Figure 14 , it can be seen that for the Steel / CFRP hybrid square tube under different offset loading conditions, except for the initial elastic loading stage where the theoretical model cannot accurately predict the bending response of the Steel / CFRP hybrid square tube, the overall trend of the force-displacement curve calculated by the theoretical model in other stages is in good agreement with the experimental results. From (b) of

[0160] and (b) of

[0161] , it can be seen that the energy-displacement curves predicted by the theoretical models for the two offset loading conditions are in good agreement with the experimental results. The absorbed energies of the theoretical predictions and experimental results of the Steel / CFRP hybrid square tube under different loading conditions are summarized in Table 4. From the perspective of the absorbed energy, the maximum errors between the theoretical predictions and experimental results for the 1 / 3 span and 1 / 4 span loading conditions are 0.04% and 6.54% respectively, and this error is within the controllable range, indicating that the theoretical model of the Steel / CFRP hybrid square tube under offset loading can effectively predict the experimental results.

[0160] Table 4 Comparison of the absorbed energies of the theoretical predictions and experimental results of the Steel / CFRP hybrid square tube under different loading conditions

[0161]

[0162] To further verify the accuracy of the theoretical model under offset loading, the predicted results of the theoretical model of Steel / CFRP hybrid square tubes with different spans, cross-sectional widths, thicknesses, and offset distances were compared with the simulation results. In addition, for convenience of description, Steel / CFRP hybrid square tubes with different geometric dimensions and indenter offset distances were named according to the specific meanings represented by the geometric parameters. For example: If the span L of the Steel / CFRP hybrid square tube is 300 mm, the cross-sectional width b is 28 mm, the thickness t is 2 mm, and the indenter offset distance ΔD is 25 mm, then this pipe fitting is named St / CF-L300b28t2ΔD25. It should be noted that for Steel / CFRP hybrid square tubes with different geometric parameters, the outer Steel thickness and the inner CFRP thickness are both configured in a 1:1 ratio.

[0163] Comparison of the force-displacement curves predicted by the theoretical model of Steel / CFRP hybrid square tubes with the simulation results, as Figure 15 shown. As Figure 15 can be seen, the force-displacement curves predicted theoretically are in good agreement with the simulation results. The comparison of the energy absorption of the theoretical models and finite element simulations of Steel / CFRP hybrid square tubes with different geometric parameters is shown in Table 5. As can be seen from Table 5, the maximum error between the theoretical results and the simulation results of the bending energy absorption of Steel / CFRP square tubes under offset loading is 6.16%, which is less than 10%, indicating that this error is within the controllable range. In addition, considering comprehensively the degree of agreement of the force-displacement curves and the accuracy of the calculation of the bending energy absorption, the theoretical model can accurately predict the change trend of the force-displacement curves and the bending energy absorption of Steel / CFRP hybrid square tubes with different geometric parameters during offset loading in most cases.

[0164] Table 5 Comparison of energy absorption of Steel / CFRP hybrid square tubes with different geometric parameters

[0165]

[0166] Step 33: Influence of offset distance on the theoretically predicted energy absorption

[0167] To further explore the influence of different offset distances ΔD on the energy absorption performance of Steel / CFRP hybrid square tubes under offset loading. For this purpose, the following geometric parameters of the Steel / CFRP hybrid square tube were set as default values: span of 300 mm, indenter diameter of 25 mm, cross-sectional width of 28 mm, CFRP thickness of 1 mm, thickness of each layer of CFRP of 0.1 mm, and Steel thickness of 1 mm.

[0168] The theoretically predicted EA and the simulation results under different offset distances ΔD were compared, as Figure 16 shown. As Figure 16It can be seen that the theoretically predicted EA value increases with the increase of the offset distance ΔD. However, when the offset distance ΔD is greater than 80 mm, the gap between the simulated EA value and the theoretically predicted value gradually increases. This is mainly caused by the excessive shear force borne by the end of the Steel / CFRP hybrid square tube. As the offset distance increases, the shear force also gradually increases. When the shear force is too large to be ignored, dents will not only appear in the loading area under the indenter, but also spread to other areas of the hybrid square tube, such as Figure 17 as shown. From Figure 17 (a) of Figure 17 , it can be seen that the Steel / CFRP hybrid square tube with an offset distance of 25 mm almost shows an overall bending deformation mode; from

[0169] (b) of

[0170] , it can be seen that at the position near the left constraint end, serious local dents appear on the Steel / CFRP hybrid square tube, thus significantly reducing the EA of the pipe fitting under offset loading.

[0169] In summary, when the offset distance is less than 80 mm, EA will increase with the increase of the offset distance, as theoretically predicted. However, if the offset distance is too large, the participation of the shear force will significantly reduce the EA of the Steel / CFRP hybrid square tube.

[0170] Step 4: Analysis of multi-parameter coupling effect under offset loading

[0171] Step 41: Main effect analysis

[0172] Keeping the span unchanged, explore the changes in the bending behavior response of the Steel / CFRP hybrid square tube under multi-parameter combinations when the Steel thickness, CFRP thickness, cross-sectional width, and offset distance change simultaneously, and study the influence of the simultaneous change of multi-parameters in the offset loading domain on the bending characteristics. In order to scientifically statistically analyze and effectively analyze the influence degree of each design parameter, four design parameters selected in this study are given a certain change range according to the actual conditions. The initial values and change ranges of each design parameter are shown in Table 6. In this study, for the above four design parameters, a full-factor experimental design is used for sampling, and each design parameter takes five parameter levels.

[0173] Table 6 Change ranges of each design parameter of Steel / CFRP hybrid square tube under offset loading

[0174]

[0175]

[0176] In the interpretation of the bending characteristics and multi-parameter interaction relationships of Steel / CFRP hybrid square tubes under offset loading, an important analysis method is to determine the correlations between parameters and find the main effects of each design parameter on the response. The main effect is the influence of a single design parameter on the response, which can be expressed in the form of a linear effect. In this study, a linear regression model was used to calculate the linear effect after normalizing the design parameters, where the value ranges of the normalized design parameters were all mapped to between [0, 1]. The calculation expression for the linear effect value between each design parameter x and the output response quantity f(x) is shown in Equation (19).

[0177] f(x) = b0 + b1x (19)

[0178] In the linear regression model, the slope b1 of the line represents the degree of influence of the design parameter on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameter has little influence on the output response; if the line is more vertical, it means that the design parameter has a greater influence on the output response. A positive slope of the line indicates a positive correlation between the design parameter and the output response, while a negative slope indicates a negative correlation between the design parameter and the output response. The analysis of the main effects of each design parameter on the response is as Figure 18 shown. As can be seen from Figure 18 the main effect diagram of

[0179] (1) The thickness t of Steel m has the most significant influence on the responses EA, PCF, and MCF. The order of influence from large to small is: the thickness t of Steel m > offset distance ΔD > thickness t of CFRP c > cross-sectional width b. Among them, the thickness t of Steel m , offset distance ΔD, thickness t of CFRP c , and cross-sectional width b all have a positive correlation with EA, PCF, and MCF.

[0180] (2) The influence of each design variable on the responses S inv and D lmax is relatively complex. The order of influence from large to small is: the thickness t of Steel m > cross-sectional width b > offset distance ΔD > thickness t of CFRP c . Among them, S inv , D lmax and the thickness t of Steel m are all positively correlated, and are all negatively correlated with the cross-sectional width b, offset distance ΔD, and thickness t of CFRP c .

[0181] (3) The influence of the offset distance ΔD on the SEA is the most significant, and the influence of the cross-sectional width b on the SEA is the smallest. The order from the largest to the smallest influence degree is: offset distance ΔD > CFRP thickness t c > Steel thickness t m > cross-sectional width b. Among them, SEA is negatively correlated with the Steel thickness t m and is positively correlated with the offset distance ΔD, CFRP thickness t c , and cross-sectional width b.

[0182] Step 42: Multi-parameter coupling effect analysis

[0183] Figure 19 The variation laws of each response under the multi-parameter coupling action are plotted. It can be intuitively seen that as the Steel thickness t m gradually increases, EA, PCF, MCF, S inv , D lmax all show a monotonically increasing trend, while SEA shows a monotonically decreasing trend. Although increasing the Steel thickness t m can increase the energy absorption and load-bearing capacity, it also increases the intrusion amount and intrusion area, and has a negative effect on the specific energy absorption. The increase in the CFRP thickness t c has a relatively small increase in each response. However, increasing the CFRP thickness t c is beneficial to reducing the intrusion amount and intrusion area and improving the specific energy absorption. Therefore, selecting appropriate Steel and CFRP thicknesses is beneficial to improving the bending performance of the hybrid square tube. As the offset distance ΔD increases, EA, PCF, and MCF all show a monotonically increasing trend, and SEA shows a monotonically decreasing trend. As the cross-sectional width b increases, EA, PCF, and MCF all show a monotonically increasing trend, and S inv and D lmax show a monotonically decreasing trend, and have a small influence on SEA.

[0184] To sum up, from the multi-parameter coupling effect, it can be found that the Steel thickness t inv has the greatest influence on EA, PCF, MCF, S lmax , and D m ; the offset distance ΔD has the greatest influence on SEA. This is because the closer the loading position is to the constrained end, the higher the participation degree of the axial force, and thus a greater load-bearing capacity and energy absorption are obtained, and a greater SEA is generated without changing the mass.

[0185] Step 5: Analysis of influencing factors of bending characteristics

[0186] Parametric analysis was adopted to study the effects of ply angle, CFRP wrapping length, and indenter shape on the bending characteristics of Steel / CFRP hybrid square tubes under offset loading conditions. In this section, the default boundary conditions of the 1 / 3 span loading condition were adopted, and the following geometric parameters of the Steel / CFRP hybrid square tube were set as default values: the span was set to 300 mm, the cross-sectional width was 28 mm, the Steel thickness was 1 mm, the CFRP thickness was 1 mm, the thickness of each layer of CFRP was 0.1 mm, the stacking sequence of ply angles was [0° / 90° / 45° / -45°], the indenter diameter was 25 mm, and the indenter offset distance was 50 mm. When one influencing factor changed, the other factors remained at their default values.

[0187] Step 51: Effects of different ply angles

[0188] Under the end constraint boundary conditions, the bending characteristics of the Steel / CFRP hybrid square tube are directly related to the ply angle. To gain a deeper understanding of the bending collapse mechanism, parametric analysis was carried out on Steel / CFRP hybrid square tubes with different ply angles under the 1 / 3 span loading condition.

[0189] Figure 20 The comparison of the load-displacement curves of four Steel / CFRP hybrid square tubes with different ply angles is given while other parameters remain unchanged. From Figure 20 It can be seen that after the load-displacement of the Steel / CFRP hybrid square tubes with ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] enters the plastic deformation stage from the elastic loading stage, the bearing capacity will decrease significantly. While the load-displacement curve of the Steel / CFRP hybrid square tube with ply angles of [45° / -45°] is relatively stable. This is because fiber breakage occurs in the CFRP tube with 90° fiber plies, which leads to a decrease in load. While the CFRP tube with 45° fiber plies mainly bears shear force during the bending loading process, so its load curve shows a relatively stable state.

[0190] In addition, the final intrusion displacements of each measurement point are plotted in Figure 21 . From Figure 21 It can be seen that the Steel / CFRP hybrid square tube with a ply angle of [0° / 90°] produces the largest intrusion amount; while the Steel / CFRP hybrid square tube with ply angles of [45° / -45°] produces the smallest intrusion amount.

[0191] In addition, the crashworthiness indexes extracted from the load-displacement and final intrusion displacement curves are summarized in Table 7. To more intuitively observe the regular changes, Figure 22The histogram compares the crashworthiness of Steel / CFRP hybrid square tubes with different ply angles. Figure 22 As can be seen from (a), the EA and S of the hybrid square tube with 90° fiber layup inv The EA and S of the hybrid square tube with 45° fiber layup are relatively large. inv It can be seen from Table 7 that the EA of Steel / CFRP hybrid square tubes with ply angles of [0° / 90° / 45° / -45°], [0° / 90°] and [45° / -45°] are 223.49 J, 218.47 J and 203.25 J, respectively. inv 20.92cm respectively 2 、21.82cm 2 and 17.63cm 2 The EA of the Steel / CFRP hybrid square tube with the ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] is 9.96% and 7.49% higher than that of the Steel / CFRP hybrid square tube with the ply angle of [45° / -45°], respectively. inv An increase of 18.66% and 23.77% respectively.

[0192] from Figure 22 From (b), it can be seen that the Steel / CFRP hybrid square tube with a ply angle of [0° / 90° / 45° / -45°] produces the highest SEA, the Steel / CFRP hybrid square tube with a ply angle of [0° / 90°] produces the highest PCF, and the hybrid square tube with a ply angle of [45° / -45°] has the lowest SEA and PCF. Figure 22 (c) shows that the Steel / CFRP hybrid square tube with a ply angle of [0° / 90° / 45° / -45°] produces the highest MCF, the Steel / CFRP hybrid square tube with a ply angle of [0° / 90°] produces the highest PCF, and the hybrid square tube with a ply angle of [45° / -45°] has the lowest SEA and PCF. The PCF of the Steel / CFRP hybrid square tube with ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] are 13.82% and 14.97% higher than that of the Steel / CFRP hybrid square tube with a ply angle of [45° / -45°], respectively. lmax An increase of 11.89% and 16.96% respectively.

[0193] In general, the hybrid square tube with 90° fiber layup exhibited higher crashworthiness performance indicators in terms of EA, PCF, and SEA, while the hybrid square tube with 45° fiber layup had a lower S inv and D lmaxexhibits relatively high crashworthiness performance indicators. This is mainly because different fiber ply angles cause different failure characteristics in the inner CFRP tube of the Steel / CFRP hybrid square tube, thus changing the relative resistance to bending and indentation. In summary, the Steel / CFRP hybrid square tube with ply angles of [0° / 90° / 45° / -45°] exhibits relatively good crashworthiness under offset loading. Therefore, in subsequent studies, the Steel / CFRP hybrid square tube is based on the n ply angle for development.

[0194] Table 7 Crashworthiness indicators of Steel / CFRP hybrid square tubes with different ply angles

[0195]

[0196] Step 52: Influence of different CFRP wrapping lengths

[0197] To explore the influence of CFRP wrapping length on the bending characteristics of Steel / CFRP hybrid square tubes under end-constrained boundaries, parametric analysis will be carried out on Steel / CFRP hybrid square tubes with different CFRP wrapping lengths. The layout diagram of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths is as Figure 23 shown. According to Figure 23 the layout diagram, the CFRP wrapping length is defined as L w = 80, 180, 280, 380 mm, and other parameters remain unchanged.

[0198] The final deformation modes of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are as Figure 24 shown. It can be seen from Figure 24 that three plastic hinges are generated in all Steel / CFRP hybrid square tubes with four CFRP wrapping lengths. It can be seen from Figure 24 (a) that relatively severe local buckling occurs at both the left and right end constraints of the Steel / CFRP hybrid square tube with a CFRP wrapping length of 80 mm. In addition, it can be observed from Figure 24 (b) and Figure 24 (c) that obvious local buckling also occurs at the end constraints of the Steel / CFRP hybrid square tube without CFRP wrapping. For the Steel / CFRP hybrid square tube strengthened with CFRP, this phenomenon is not obvious. This is because shear force is easily generated at the end constraints under offset loading, and the wall thickness of the Steel / CFRP hybrid square tube without CFRP wrapping is relatively thin, and its shear resistance is relatively weak. Therefore, severe local buckling will occur at the end without CFRP wrapping, resulting in a decrease in the load-bearing capacity of the Steel / CFRP hybrid square tube.

[0199] The load-displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are as Figure 25 shown. It can be seen from Figure 25 that as the CFRP wrapping length increases, the load-bearing capacity of the hybrid square tube also increases accordingly. The final intrusion displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are as Figure 26 shown. It can be seen from Figure 26 that when the CFRP wrapping length is 380 mm, the maximum intrusion amount D lmax of the lower surface profile of the Steel / CFRP hybrid square tube is the smallest. When the CFRP wrapping length is 80 mm, the maximum intrusion amount D lmax of the hybrid square tube is the largest. The maximum intrusion amounts D lmax of the hybrid square tubes with CFRP wrapping lengths of 180 mm and 280 mm do not differ much.

[0200] In addition, the crashworthiness indexes extracted from the load-displacement and final intrusion displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are summarized in Table 8. To more intuitively observe the regular changes, Figure 27 the histograms of Figure 27 compare the crashworthiness performance of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths. It can be seen from inv the (a) of inv that the Steel / CFRP hybrid square tube with a CFRP wrapping length of 380 mm generates the highest EA and the smallest S inv . While the Steel / CFRP hybrid square tube with a CFRP wrapping length of 380 mm has the lowest EA and the largest S 2 . The EAs of the Steel / CFRP hybrid square tubes with CFRP wrapping lengths of 80 mm and 380 mm are 190.36 kJ and 223.49 kJ respectively, and the corresponding S 2 are 25.01 cm inv and 20.92 cm inv respectively. The EAs of the Steel / CFRP hybrid square tubes with CFRP wrapping lengths of 280 mm and 380 mm are increased by 11.69% and 17.40% respectively compared with the Steel / CFRP hybrid square tube with a CFRP wrapping length of 80 mm, while the S

[0201] decreases by 10.20% and 16.35% respectively. It is speculated that the reason for the decrease in SFigure 27 of (b) and Figure 27 As can be seen from (c), both the PCF and SEA of the Steel / CFRP hybrid square tube increase with the increase of the CFRP wrapping length, while D lmax decreases with the increase of the CFRP wrapping length. The PCF of the Steel / CFRP hybrid square tubes with CFRP wrapping lengths of 280 mm and 380 mm is increased by 16.60% and 23.96% respectively compared with that of the Steel / CFRP hybrid square tube with a CFRP wrapping length of 80 mm, and the SEA is increased by 3.5% and 4.9% respectively, while D lmax decreases by 8.48% and 14.55% respectively.

[0202] In summary, for the bending loading conditions, especially the offset bending loading conditions, under the end constraint boundary conditions, it is necessary to appropriately strengthen the thickness of the clamped part and the loading area at the end of the hybrid square tube to increase the axial force and its ability to resist shear failure.

[0203] Table 8 Crashworthiness indexes of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths

[0204]

[0205] Step 53: Influence of different indenter shapes

[0206] In actual foreign object intrusion cases, the shape and size of foreign objects are usually uncertain. To study the influence of different indenter shapes on the bending characteristics of Steel / CFRP hybrid square tubes under quasi-static loading, four different-shaped indenters are designed in this section. According to the cross-sectional shape, they are circular indenter, conical indenter, trapezoidal indenter and square indenter. The schematic diagrams of the cross-sectional shapes and detailed dimensions of the indenters are as Figure 28 shown. As can be seen from Figure 28 that the maximum cross-sectional size of the four indenters is 25 mm, and the shape of the indenter at the end facing the Steel / CFRP hybrid square tube gradually transitions from sharp to gentle.

[0207] After the indenter is completely unloaded, the final deformation modes of the Steel / CFRP hybrid square tubes under offset loading with different-shaped indenters are as Figure 29 shown. Since the shape of the indenter at the end facing the Steel / CFRP hybrid square tube gradually transitions from sharp to gentle, as can be seen from Figure 29It can be seen that after the conical indenter is unloaded, the plastic deformation area formed on the Steel / CFRP hybrid square tube is small; after the square indenter is unloaded, the plastic deformation area formed on the Steel / CFRP hybrid square tube is large; the plastic deformation areas formed after the conical indenter and trapezoidal indenter are unloaded are between the two. Under the offset loading of the conical and circular indenters, the local indentation of the specimen is funnel-shaped and the overall deformation is small. When the trapezoidal and square indenters are used to offset load the specimen, it is observed that the width of the local indentation is large and the overall deformation is relatively large. The indentations produced by different-shaped indenters all exhibit an asymmetric plastic deformation mode, which is due to the uneven distribution of axial forces on the left and right sides of the Steel / CFRP hybrid square tube caused by the offset loading.

[0208] The load-displacement curves of the Steel / CFRP hybrid square tube under the offset loading of different-shaped indenters are as Figure 30 shown. From Figure 30 it can be seen that the load response curves produced by different-shaped indenters show similar trends. The load on the specimen under the offset loading of the conical indenter is smaller than that of the other three-shaped indenters, and as the shape of the indenter gradually changes from sharp to gentle, the corresponding bearing capacity and peak force gradually increase.

[0209] To quantitatively analyze the intrusion area of the Steel / CFRP hybrid square tube under the offset loading of different-shaped indenters, the final intrusion displacements of each measurement point are plotted in Figure 31 . From Figure 31 it can be seen that the maximum intrusion amount produced after the square indenter is unloaded is the largest, while the maximum intrusion amount produced after the conical indenter is unloaded is relatively small. This is because the contact area between the square indenter and the specimen is much larger than that of the conical indenter, and the plastic deformation energy generated is also relatively larger, resulting in a corresponding increase in the ability of the Steel / CFRP hybrid square tube to resist bending deformation, so the maximum intrusion amount produced is also larger.

[0210] In addition, the crashworthiness indexes extracted from the load-displacement and final intrusion displacement curves under the offset loading of different-shaped indenters are summarized in Table 9. To more intuitively observe the regular changes, Figure 32 the histograms of Figure 32 compare the crashworthiness performance of the Steel / CFRP hybrid square tube under the offset loading of different-shaped indenters. From Figure 32 the comparison of the crashworthiness performance, it can be found that EA, PCF, SEA, D lmax , MCF and S invAll increase gradually as the indenter shape flattens. The EAs obtained by the Steel / CFRP hybrid square tube under offset loading with conical, circular, trapezoidal, and square indenters are 176.47 J, 223.49 J, 247.19 J, and 265.47 J, respectively. Compared with the loading with a conical indenter, the EAs and SEAs obtained by the loading with indenters of other shapes increase by 26.64%, 40.07%, and 50.43%, respectively. The S inv under the offset loading with circular, trapezoidal, and square indenters is increased by 10.11%, 32.00%, and 46.74%, respectively, compared with that under the loading with a conical indenter. The PCFs are increased by 31.21%, 7.36%, and 53.63%, respectively, and the D lmax is increased by 7.02%, 26.51%, and 40.72%, respectively. The Steel / CFRP hybrid square tube under the offset loading with a square indenter exhibits higher energy absorption and greater peak force because the contact area between the square indenter and the specimen is large, which results in more energy dissipation. Since the overall deformation of the Steel / CFRP hybrid square tube under the offset loading with a square indenter is larger, the maximum intrusion amount and intrusion area of the specimen increase. Therefore, from the perspective of collision safety, when designing a bending-resistant structure, the boundary value of a relatively large intruding foreign object should be considered, that is, a relatively large safety factor should be adopted.

[0211] Table 9 Crashworthiness indexes of Steel / CFRP hybrid square tube under offset loading with indenters of different shapes

[0212]

[0213] The present invention takes the Steel / CFRP hybrid square tube as the research object and reveals the bending performance of the Steel / CFRP hybrid square tube under different loading positions based on experimental methods. A finite element model and a theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading are constructed and verified, and the influence of the offset distance on the bending energy absorption mechanism is revealed based on the theoretical prediction model. The influence of the simultaneous change of multi-parameter domains on the bending characteristics under offset loading is discussed. In addition, the influence of the ply angle, CFRP wrapping length, and indenter shape on the bending characteristics is also explored.

[0214] (1) All the crashworthiness performances of the Steel / CFRP hybrid square tube under mid-span loading are less than those under 1 / 3-span loading and 1 / 4-span loading. The EAs of the Steel / CFRP hybrid square tube under 1 / 3-span loading and 1 / 4-span loading are increased by 14.62% and 27.46%, respectively, compared with that under mid-span loading. The S invThey were reduced by 0.84% and 3.41% respectively, the PCF was increased by 7.51% and 21.52% respectively, and the SEA was increased by 13.88% and 26.36% respectively. The closer the loading position is to the constrained end, the larger the EA, and the corresponding SEA is also larger, while D lmax and the corresponding S inv are smaller. This is because the closer the loading position is to the constrained end, the higher the participation degree of the axial force, which in turn increases the bearing capacity, the energy absorption, and reduces the intrusion area.

[0215] (2) An energy absorption theoretical model of the Steel / CFRP hybrid square tube under offset loading was established and compared with the experimental results of the 1 / 3 span and 1 / 4 span loading conditions. The maximum errors were 0.08% and 6.49% respectively, indicating that the theoretical model of the Steel / CFRP hybrid square tube under offset loading can effectively predict the experimental results. The influence of different offset distances was studied. When the offset distance is less than 80 mm, the EA will increase with the increase of the offset distance. However, if the offset distance is too large, the participation of the shear force will significantly reduce the EA of the Steel / CFRP hybrid square tube. From the analysis of the multi-parameter coupling effect, it can be found that the Steel thickness has the greatest influence on EA, PCF, MCF, S inv , D lmax . The offset distance ΔD has the greatest influence on SEA.

[0216] (3) The hybrid square tube with 90° fiber ply shows higher crashworthiness performance indicators in terms of EA, PCF and SEA, while the hybrid square tube with 45° fiber ply shows higher crashworthiness performance indicators in S inv and D lmax . This is mainly because different fiber ply angles cause different failure characteristics of the CFRP tube in the inner layer of the Steel / CFRP hybrid square tube, thus changing the relative resistance of bending and indentation. The Steel / CFRP hybrid square tube with full CFRP wrapping shows better bending performance. For the bending loading condition under the end constraint boundary condition, especially the offset bending loading condition, it is necessary to appropriately strengthen the thickness of the clamping part and the loading area at the end of the hybrid square tube to increase the energy absorption and the ability to resist shear failure of the structure. The Steel / CFRP hybrid square tube under the offset loading of the square indenter shows relatively large energy absorption and overall deformation. As the shape of the indenter at one end facing the Steel / CFRP hybrid square tube gradually changes from sharp to gentle, the crashworthiness indicators all show an upward trend.

Claims

1. A method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions, characterized in that The following steps are involved: Step 1: Conduct an experimental study on the Steel / CFRP hybrid square tube under offset loading by arranging an offset loading experiment to form a final deformation comparison and analyze the mechanical properties of the Steel / CFRP hybrid square tube under different loading positions; Step 2: Construct a finite element model of the Steel / CFRP hybrid square tube under offset loading; Step 3: Construct a theoretical prediction model for Steel / CFRP hybrid square tubes under offset loading to obtain the effect of offset distance on the theoretically predicted energy absorption; Step 4: Analyze the multi-parameter coupling effect under bias loading; Step 5: Analyze the factors affecting the bending characteristics; including the influence of different ply angles, the influence of different CFRP wrapping lengths, and the influence of different indenter shapes.

2. The bending property prediction method of the Steel / CFRP hybrid square tube based on different loading positions according to claim 1, wherein In the step 1: the quasi-static bending test of the Steel / CFRP hybrid square tube under offset loading is carried out on an MTS-322 hydraulic servo control testing machine, and both ends of the specimen are locked and fixed by the upper and lower clamping devices of the U-support frame, and also include a rectangular clamp block. By adjusting the relative position relationship between the rectangular clamp block and the U-shaped clamp, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions are studied, and different loading position test scenarios are set by adjusting different effective spans.

3. The bending property prediction method of the Steel / CFRP hybrid square tube based on different loading positions according to claim 1, characterized in that In the step 2: the geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimen in the experiment, the degrees of freedom on both sides are constrained, the loading speed of the pressure head is set to 1000 mm / s, the downward compression displacement is set to 22 mm, and the grid sizes of the specimen and the pressure head are set to 2 mm and 5 mm, respectively; the offset distance ΔD of the pressure head loading is set, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube; the effective span of the Steel / CFRP hybrid square tube is 300 mm, and the offset distances ΔD of the 1 / 3 span loading condition and the 1 / 4 span loading condition are set to 50 mm and 75 mm, respectively.

4. The bending performance prediction method of the Steel / CFRP hybrid square tube based on different loading positions according to claim 1, characterized in that Step 3 includes the analytical solution of large deflection of Steel / CFRP hybrid square tubes under eccentric loading; under the eccentric loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored; it is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and undergo global deformation in an overall manner; three hybrid plastic hinges are developed at the loading position and the end supports of the Steel / CFRP hybrid square tube respectively; the span of the hybrid square tube is L, the loading point is located at a distance L1 from the left support end, and the eccentric distance between the loading point and the center line of the span of the hybrid square tube is regarded as ΔD; under the action of the external concentrated load P b , the maximum deflection W of the hybrid square tube occurs b . The equilibrium equation of the moment is obtained, as shown in formula (1): where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b = M bm ; Transform Equation (1) to obtain the relationship expression between the concentrated load P b and the bending deflection W b as shown in Equation (2) Suppose the total elongation of the left free body with length L1 is a L , and its calculation expression is shown in Equation (3). a L = a L1 + a L2 (3) where a L1 and a L2 are respectively the axial elongation amounts of the left free body end; Combining equation (3) and equation (4) can further simplify equation (5) According to the geometric relationship, the left rotation angle ψ L is calculated by the expression shown in Equation (6). Similarly, assume that the total elongation of the right free body with a length of L2 is b R , and its calculation expression is as shown in Equation (7) b R = b R1 + b R2 (7) where b R1 and b R2 are respectively the axial elongation of the left free body end; Equation (8) is obtained according to the geometric relationship Combining equation (7) and equation (8) to further simplify equation (9) According to the geometric relationship, the right rotation angle ψ R is calculated by the expression shown in Equation (10). The relationship expression between the ratio of the axial elongation rate to the curvature and the bending deflection W in the left and right free bodies is as shown in Equation (11). b as shown in Equation (11). On the other hand, the relevant flow rule for the plastic yield criterion is expressed as follows: Combining equations (11), (12) and (13), we can obtain the expression of the bending deflection of the Steel / CFRP hybrid square tube under offset loading: Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 are expressed by the relationship between the offset distance and the span: L1=L / 2+ΔD (15) L2=L / 2-ΔD (16) Substituting equations (11), (15), and (16) into equation (1), the calculation expression of the analytical solution of the large deflection of the Steel / CFRP hybrid square tube under offset loading is obtained, as shown in equation (17); Among them, t m represents the thickness of Steel, t c represents the thickness of CFRP, P b1 、P b2 、P b3 、P b4 are the loading loads under different bending deflections W b , σ m represents the material yield stress of the Steel square tube, σ c represents the stress of the Steel square tube in the tensile and compressive states; Integrate and accumulate the energy of the P curve for each interval stage in Equation (17). Therefore, the plastic bending deformation energy E of the Steel / CFRP hybrid square tube under bias loading is obtained. b -W b The relationship expression between the deflection W is shown in Equation (18); b and the deflection W b is as shown in Equation (18).

5. The bending property prediction method of the Steel / CFRP hybrid square tube based on different loading positions according to claim 1, characterized in that In step 4: Analyze the correlations among the Steel thickness, CFRP thickness, cross-sectional width, and offset distance, and find the main effects of the correlations among the Steel thickness, CFRP thickness, cross-sectional width, and offset distance on the response. Use a linear regression model to calculate the linear effects of the normalized design parameters. The value ranges of the normalized design parameters are all mapped to the range of [0, 1]. The calculation expression for the linear effect value between each design parameter x and the output response quantity f(x) is shown in Equation (19). f(x) = b0 + b1x (19) In the linear regression model, the slope b1 of the line represents the degree of influence of the design parameter on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameter has little influence on the output response. If the line is more inclined to be vertical, it means that the design parameter has a greater influence on the output response. A positive slope of the line indicates a positive correlation between the design parameter and the output response, while a negative slope indicates a negative correlation between the design parameter and the output response.

6. The bending performance prediction method of the Steel / CFRP hybrid square tube based on different loading positions according to claim 1, characterized in that In step 5: Use parametric analysis to study the effects of the ply angle, CFRP wrapping length, and indenter shape on the bending characteristics of the Steel / CFRP hybrid square tube under the offset loading condition. Adopt the default boundary conditions of the 1 / 3-span loading condition, and set the following geometric parameters of the Steel / CFRP hybrid square tube as default values: the span is set to 300 mm, the cross-sectional width is 28 mm, the Steel thickness is 1 mm, the CFRP thickness is 1 mm, the thickness of each CFRP layer is 0.1 mm, the stacking sequence of the ply angle is [0° / 90° / 45° / -45°], the indenter diameter is 25 mm, and the indenter offset distance is 50 mm. When one influencing factor changes, the other factors remain at their default values.

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