Method for determining critical wrinkling stress-strain of bimetallic clad plate

Abstract

The present application relates to a kind of for bimetal composite plate critical wrinkle stress strain determination method, it includes the following steps, step 1: obtain the plate material performance parameter of bimetal composite plate;Step 2: utilize mixed rule to establish the stress strain relationship of each metal layer;Step 3: the stress neutral layer position of bimetal composite plate is determined by finite element analysis method;Step 4: according to stress neutral layer position determines the critical wrinkle stress strain of bimetal composite plate.The present application is by collecting the strain path diagram of each metal layer, obtains the strain path bifurcation time of each metal layer, then by normal stress along the thickness direction variation curve and composite plate thick displacement with time variation diagram determines the position of composite plate stress neutral layer, the strain path bifurcation time of the metal layer where stress neutral layer is located is determined as the critical wrinkle time of composite plate, accurately predict the stress strain of composite plate wrinkling instability time, for establishing composite plate critical wrinkle determination line and widely used in engineering practice lay a solid foundation.

Description

Technical Field

[0001] This application relates to the field of sheet metal forming, and specifically to a method for determining the critical wrinkling stress-strain of bimetallic composite plates. Background Technology

[0002] With the development of modern industry, people have increasingly higher requirements for the special properties of materials, such as resistance to high and low temperatures, wear resistance, corrosion resistance, and high strength. Materials with single properties are difficult to meet the needs of modern industry. The emergence of composite materials has greatly satisfied the demand for composite performance. Metal matrix composites have the potential to integrate the excellent properties of each component material. While maintaining the characteristics of each component metal or alloy, they have a "complementary effect," which can make up for their respective deficiencies. With proper combination, excellent comprehensive performance can be obtained. At present, researchers have conducted extensive and in-depth practical exploration and theoretical research on the preparation and forming technologies of metal matrix composites, and have formed relatively mature preparation methods. However, plastic instability problems still exist in the actual forming process of metal composites, and there are few reports on wrinkling judgment criteria and model establishment for metal composites, both domestically and internationally. There are many influencing factors among metal composites, and the coupling effect between different factors will affect the forming of metal composites. The critical wrinkling instability moment and wrinkling morphology of metal composites are difficult to predict and determine. Therefore, correctly determining the wrinkling stress and strain of parts in the plastic forming process of metal composites has become one of the research hotspots in this field. By determining the critical wrinkling moment of metal composite panels and identifying the critical wrinkling stress-strain, a critical wrinkling criterion line can be established. Furthermore, accurate prediction of wrinkles can improve the plastic forming limit of the composite panel, thereby expanding the processing window of the metal composite panel. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention obtains the strain path bifurcation time of each metal layer by collecting strain path diagrams of each metal layer. Then, it determines the position of the stress neutral layer of the composite plate by combining the change curve of the normal stress along the thickness direction of the cross section and the change diagram of the thickness displacement of the composite plate over time. The strain path bifurcation time of the metal layer where the stress neutral layer is located is defined as the critical wrinkling time of the bimetallic composite plate. This accurately predicts the wrinkling instability time of the composite plate and determines the critical wrinkling stress and strain, laying a solid foundation for the subsequent establishment of the critical wrinkling judgment line of the composite plate and its widespread application in engineering practice.

[0004] To achieve the above objectives, the solution adopted by the present invention is: a method for determining the critical wrinkling stress-strain of bimetallic composite plates, comprising the following steps:

[0005] Step 1: Obtain the material performance parameters of the bimetallic composite panel;

[0006] A uniaxial tensile test was conducted on the bimetallic composite plate to obtain the overall stress σ of the bimetallic composite plate. m and strain ε m Microhardness tests were performed on the bimetallic composite plate to accurately obtain the hardness HV of the first metal layer by observing the distribution of hardness along the thickness direction. I The hardness of the second metal layer is HV. II and the hardness HV of the mixed metal layer I-II ;

[0007] Step 2: Establish the stress-strain relationship between the first metal layer, the second metal layer, and the hybrid metal layer using the mixing principle;

[0008] The stresses of the first metal layer, the second metal layer, and the hybrid metal layer are determined according to the mixing principle, as shown below:

[0009]

[0010] Where: σ I σ represents the stress in the first metal layer. II Indicates the stress in the second metal layer; σ I-II HV represents the stress in the hybrid metal layer; F represents the total load on the bimetallic composite plate; HV I HV indicates the hardness of the first metal layer. II Indicates the hardness of the second metal layer; HV I-II Indicates the hardness of the mixed metal layer; A I A represents the cross-sectional area of ​​the first metal layer; II A represents the cross-sectional area of ​​the second metal layer; I-II This represents the cross-sectional area of ​​the mixed metal layer;

[0011] Since the tensile strain of each layer in the composite plate is consistent, the strain of the overall mixed material and each heterogeneous layer of the bimetallic composite plate satisfies the identity equation, as shown below:

[0012] ε m =ε I =ε I-II =ε II ;

[0013] Where: ε m ε represents the overall strain of the bimetallic composite plate. I ε represents the strain of the first metallic layer. II ε represents the strain of the second metal layer. I-II Indicates the strain of the hybrid metal layer;

[0014] The stress-strain relationship of the first metal layer, the second metal layer, and the hybrid metal layer can all be expressed by the following formula:

[0015] σ=σ0+Kε;

[0016] In the formula: σ represents the stress of the metallic material; σ0 represents the yield stress of the metallic material; K represents the strength coefficient of the metallic material; ε represents the strain of the metallic material;

[0017] Step 3: Determine the location of the stress neutral layer in the bimetallic composite plate using finite element analysis.

[0018] Step 31: Design a tensile wrinkling test for bimetallic composite plates;

[0019] Step 32: Establish a finite element analysis simulation model based on the tensile wrinkling test conditions of bimetallic composite plates;

[0020] Step 33: Compare the finite element simulation results with the experimental results to verify the accuracy of the finite element simulation;

[0021] Step 34: Draw the strain path of each metal layer based on the finite element simulation results; extract the first principal strain ε1 and the second principal strain ε2 of each layer material integration point in the thickness direction of the buckling element of the bimetallic composite plate, draw the strain path diagram, and record the bifurcation time t1, t2, t3 of the strain path of each metal layer.

[0022] Step 35: Determine the location of the stress neutral layer based on the finite element simulation results; determine the location P of the stress neutral layer by combining the curve of the in-plane normal stress perpendicular to the ridge direction along the thickness direction and the graph of the thickness displacement of the composite plate over time. α Record the bifurcation time t of the strain path in the metal layer containing the stress neutral layer. α ;

[0023] Step 4: Determine the critical wrinkling stress-strain result of the bimetallic composite plate based on the location of the stress neutral layer;

[0024] Step 41: Based on the bifurcation time t of the strain path in the metal layer where the stress neutral layer is located α Determine the critical wrinkling time t of the integral bimetallic composite plate CA The details are as follows:

[0025] t CA =t α ;

[0026] In the formula: t CA Indicates the critical wrinkling moment of the integral bimetallic composite panel; t α Indicates the moment when the strain path of the metal layer containing the stress neutral layer bifurcates;

[0027] Step 42: Based on the critical wrinkling time t of the overall bimetallic composite plate CA Extract the stress σ′ of the bimetallic composite plate at this time. m and strain ε′ mThe critical wrinkling stress-strain results of the bimetallic composite plate were obtained.

[0028] Preferably, the material performance parameters of the bimetallic composite plate in step 1 include: the overall stress σ of the bimetallic composite plate. m The overall strain ε of the bimetallic composite plate m First metal layer HV I Second metal layer HV II and the hardness HV of the mixed metal layer I-II .

[0029] Preferably, the determination of the stresses of the first metal layer, the second metal layer, and the mixed metal layer according to the mixing rule in step 2 is specifically as follows:

[0030] The delamination stress-strain relationship is calculated based on the uniaxial tensile stress in the thickness direction of the bimetallic composite plate. During the tensile process of the bimetallic composite plate, the total load F on the bimetallic composite plate satisfies the following equation:

[0031] F = σ m A m =σ I A I +σ I-II A I-II +σ II A II ;

[0032] Where: σ m Indicates the stress experienced by the bimetallic composite plate; A m This represents the cross-sectional area subjected to by the bimetallic composite plate;

[0033] The bimetallic composite plate is subjected to a cross-sectional area A m The cross-sectional area A of the first metal layer I The cross-sectional area A of the second metal layer II and the cross-sectional area A of the mixed metal layer I-II The following relationship is satisfied:

[0034] A m =A I +A I-II +A II ;

[0035] Based on the relationship between microhardness and stress in metallic materials, the stress and microhardness of each heterogeneous layer in a heterogeneous metal layered composite plate satisfy the following equation:

[0036]

[0037] If we set the ratio in the above equation as a proportionality constant k, then the above equation can be transformed into:

[0038]

[0039] In the formula: k represents the microhardness of the metallic material as a function of stress;

[0040] In summary, the formula for calculating the proportionality constant k is as follows:

[0041]

[0042] Further analysis can yield the stresses of the first metal layer, the second metal layer, and the hybrid metal layer.

[0043] Preferably, in step 32, a finite element analysis simulation model is established based on the tensile wrinkling test conditions of the bimetallic composite plate, specifically as follows:

[0044] Step 321: Based on the finite element mesh type, select the type of bimetallic composite plate, select continuous shell element for calculation, and create a three-dimensional solid of bimetallic composite plate;

[0045] Step 322: Set the material parameters of the bimetallic composite plate in the property module, and obtain the material parameters of the first metal layer, the second metal layer and the mixed metal layer determined in step 2 for material setting;

[0046] Step 323: Select Composite Layup for rapid modeling, and set the layer thickness, material selection, layup direction, and number of integration points for each layer of the bimetallic composite panel;

[0047] Step 324: Select the finite element mesh type according to the finite element mesh type. For continuous shell elements, the SC8R mesh type should be selected.

[0048] Step 325: Set up the analysis step. Set the continuous shell element Buckle-dynamic with initial defects as the analysis step of the finite element algorithm and establish the finite element simulation model.

[0049] Preferably, step 33, which involves comparing the finite element simulation results with experimental results to verify the accuracy of the finite element simulation, specifically includes:

[0050] Thickness displacement contour maps of bimetallic composite plates from experiments and simulations were extracted to verify consistency in wrinkle type and wrinkle quantity at the same location in both methods. Furthermore, the thickness displacement curves along the measurement path of the bimetallic composite plates at different times in the experiments and simulations were compared. α and x β It was found that the thickness displacements of both materials along the measurement path during the entire forming process of the bimetallic composite plate were similar, and their displacement errors Δx satisfied the following relationship:

[0051]

[0052] In the formula: Δx represents the thickness displacement error of the bimetallic composite plate along the measurement path throughout the entire forming process; x α This represents the thickness displacement curves of the bimetallic composite plate along the measurement path at different times during the experiment; x β This represents the thickness displacement curves of the bimetallic composite plate along the measurement path at different times during the simulation. In other words, the wrinkling process in the experiment and the simulation are consistent, and the wrinkle development law is consistent. Therefore, the finite element simulation can accurately reflect the real experimental results.

[0053] Preferably, in step 35, the position of the stress neutral layer is determined by the curve of the change of in-plane normal stress perpendicular to the ridge direction along the thickness direction and the graph of the thickness displacement of the composite plate over time. Specifically, the determination is as follows: at the critical buckling moment of each critical metal layer, the data of the entire composite plate is extracted, and the stress values ​​at the integration points of each metal layer are compared. When the following formula is satisfied, it is determined that the stress neutral layer is located in that metal layer.

[0054]

[0055] Where: σ x This represents the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate. This represents the derivative of the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate along the thickness direction.

[0056] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0057] (1) The present invention obtains the strain path bifurcation time of each metal layer by collecting the strain path diagram of each metal layer, and then determines the position of the stress neutral layer of the composite plate by the curve of the change of in-plane normal stress along the thickness direction perpendicular to the ridge direction and the curve of the thickness displacement of the composite plate with time. The strain path bifurcation time of the metal layer where the stress neutral layer is located is defined as the critical wrinkling time of the bimetallic composite plate.

[0058] (2) The present invention has a clear concept, detailed calculations, and intuitive process. The results accurately predict the moment of wrinkling instability of composite board and determine the critical wrinkling stress and strain, laying a solid foundation for the subsequent establishment of the critical wrinkling judgment line of composite board and its widespread application in engineering practice. Attached Figure Description

[0059] Figure 1 This is a flowchart of a method for determining the critical wrinkling stress and strain of a bimetallic composite plate according to an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of the copper-aluminum composite plate under uniaxial tensile stress according to an embodiment of the present invention;

[0061] Figure 3This is a diagram showing the actual stress-strain curve of the copper layer in an embodiment of the present invention.

[0062] Figure 4 This is a graph showing the actual stress-strain curve of the aluminum layer in an embodiment of the present invention;

[0063] Figure 5 This is a diagram showing the actual stress-strain curve of the metallurgical bonding layer in an embodiment of the present invention.

[0064] Figure 6 The following are assembly drawings and actual drawings of the tensile wrinkling test mold according to an embodiment of the present invention;

[0065] Figure 7 A flowchart is established for the composite layup rapid modeling method of this invention.

[0066] Figure 8 This is a distribution diagram of the integration points in the thickness direction of the composite plate in a finite element simulation according to an embodiment of the present invention.

[0067] Figure 9 This is a finite element simulation diagram of the strain path of the copper layer metal in the ridge region of the composite plate according to an embodiment of the present invention.

[0068] Figure 10 This is a finite element simulation diagram of the metallographic bonding layer in the ridge region of the composite plate according to an embodiment of the present invention;

[0069] Figure 11 This is a finite element simulation diagram of the strain path of the aluminum layer in the ridge region of the composite plate according to an embodiment of the present invention.

[0070] Figure 12 This is a diagram showing the distribution of in-plane normal stress along the thickness direction perpendicular to the ridge direction at each bifurcation moment in an embodiment of the present invention.

[0071] Figure 13 This is a graph showing the change of the thickness displacement of the composite plate over time in an embodiment of the present invention;

[0072] Figure 14 This is a comparison between the determination line obtained by simulation in an embodiment of the present invention and the theoretical critical wrinkling determination line. Detailed Implementation

[0073] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0074] In this invention, copper-aluminum composite plates were tested and analyzed. By collecting strain path diagrams of each metal layer, the bifurcation time of the strain path for each metal layer was obtained. Then, the location of the stress-neutral layer in the composite plate was determined by combining the in-plane normal stress variation curve perpendicular to the wrinkle direction along the thickness direction and the thickness displacement of the composite plate over time. The bifurcation time of the strain path of the metal layer containing the stress-neutral layer was defined as the critical wrinkling time of the bimetallic composite plate. The results accurately predicted the wrinkling instability time of the composite plate and determined the critical wrinkling stress-strain, laying a solid foundation for the subsequent establishment of a critical wrinkling judgment line for composite plates and its widespread application in engineering practice. Figure 1 The diagram shows a flowchart of the method for determining the critical wrinkling stress and strain of bimetallic composite plates according to an embodiment of the present invention.

[0075] This invention provides a method for determining the critical wrinkling stress-strain of bimetallic composite plates. To demonstrate the applicability of this invention, it is applied to an example, specifically including the following steps:

[0076] S1: Obtain the material performance parameters of the bimetallic composite panel.

[0077] The performance parameters of bimetallic composite panels include: the overall stress σ of the bimetallic composite panel. m The overall strain ε of the bimetallic composite plate m The hardness of the first metal layer is HV. Cu The hardness of the second metal layer is HV. Al and the hardness HV of the mixed metal layer Al-Cu .

[0078] A uniaxial tensile test was conducted on the copper-aluminum composite plate to obtain the overall stress σ of the copper-aluminum composite plate. m and strain ε m Microhardness tests were conducted on copper-aluminum composite plates to accurately obtain the hardness HV of the first metal layer by observing the distribution of hardness along the thickness direction. Cu The hardness of the second metal layer is HV. Al and the hardness HV of the mixed metal layer Al-Cu .

[0079] S2: Establish the stress-strain relationship between the first metal layer, the second metal layer, and the mixed metal layer using the mixing principle.

[0080] The stresses of the first metal layer, the second metal layer, and the hybrid metal layer are determined according to the mixing principle, specifically as follows:

[0081] Calculate the delamination stress-strain relationship based on the uniaxial tensile stress in the thickness direction of the bimetallic composite plate, such as... Figure 2 The diagram shown is a schematic representation of the uniaxial tensile stress on a copper-aluminum composite plate according to an embodiment of the present invention. During the tensile process of the bimetallic composite plate, the total load F on the bimetallic composite plate satisfies the following equation:

[0082] F = σ m A m =σ Cu A Cu +σ Al-Cu A Al-Cu +σ Al A Al ;

[0083] Where: σ m Indicates the stress experienced by the bimetallic composite plate; A m This represents the cross-sectional area of ​​the bimetallic composite plate.

[0084] The cross-sectional area A of the bimetallic composite plate m The cross-sectional area A of the first metal layer Cu The cross-sectional area A of the second metal layer Al and the cross-sectional area A of the mixed metal layer Al-Cu The following relationship is satisfied:

[0085] A m =A Cu +A Al-Cu +A Al ;

[0086] Based on the relationship between microhardness and stress in metallic materials, the stress and microhardness of each heterogeneous layer in a heterogeneous metal layered composite plate satisfy the following equation:

[0087]

[0088] If we set the ratio in the above equation as a proportionality constant k, then the above equation can be transformed into:

[0089]

[0090] In the formula: k represents the microhardness of the metallic material as a function of stress;

[0091] In summary, the formula for calculating the proportionality constant k is as follows:

[0092]

[0093] Further analysis yields the stresses in the first metal layer, the second metal layer, and the hybrid metal layer, as shown below:

[0094]

[0095] Where: σ Cu σ represents the stress in the first metal layer. Al Indicates the stress in the second metal layer; σ Al-Cu HV represents the stress in the hybrid metal layer; F represents the total load on the bimetallic composite plate; HVCu HV indicates the hardness of the first metal layer. Al Indicates the hardness of the second metal layer; HV Al-Cu Indicates the hardness of the mixed metal layer; A Cu A represents the cross-sectional area of ​​the first metal layer; Al A represents the cross-sectional area of ​​the second metal layer; Al-Cu This represents the cross-sectional area of ​​the mixed metal layer.

[0096] Since the tensile strain of each layer in the composite plate is consistent, the strain of the overall mixed material and each heterogeneous layer of the bimetallic composite plate satisfies the identity equation, as shown below:

[0097] ε m =ε Al =ε Al-Cu =ε Cu ;

[0098] Where: ε m ε represents the overall strain of the bimetallic composite plate. Cu ε represents the strain of the first metallic layer. Al ε represents the strain of the second metal layer. Al-Cu This represents the strain of the hybrid metal layer.

[0099] The stress-strain relationship of the first metal layer, the second metal layer, and the hybrid metal layer can all be expressed by the following formula:

[0100] σ=σ0+Kε;

[0101] In the formula: σ represents the stress of the metallic material; σ0 represents the yield stress of the metallic material; K represents the strength coefficient of the metallic material; ε represents the strain of the metallic material;

[0102] like Figure 3 The figure shown is a real stress-strain curve of the copper layer in the embodiment of the present invention, corresponding to the first metal layer; as shown Figure 4 The figure shown is a true stress-strain curve of the aluminum layer in the embodiment of the present invention, corresponding to the second metal layer; as shown Figure 5 The figure shown is a true stress-strain curve of the metallurgical bonding layer of the present invention, corresponding to the mixed metal layer; the constitutive equations of the materials of each layer are shown in Table 1.

[0103] Table 1 Constitutive Equation Parameters for Layered Materials

[0104]

[0105] S3: Determine the location of the stress neutral layer of the bimetallic composite plate using the finite element analysis method.

[0106] S31: Design of a tensile wrinkling test for bimetallic composite plates, details of which include: The wedge-shaped component of a copper-aluminum composite plate can slide within support grooves on both sides. The angle between the two support sliders is adjusted to accommodate different deformation zones. The normal direction of the wedge is constrained by a transparent acrylic plate to control the wrinkling height. The transparent acrylic plate is used to facilitate DIC (Digital Interpreter) imaging of the wrinkling development process of the wedge under normal constraint. The gap between the two acrylic plates is controlled by a slender strip located above the bolt holes of the acrylic plates. The gap distance is adjusted by changing strips of different thicknesses. Since the acrylic plates are not fixedly constrained in the normal direction, they will tilt as the specimen buckles. To maintain the consistency of the constraint gap in the deformation zone of the specimen, a normal constraint buckle is designed. The buckle is fixed on both sides of the wedge angle without obstructing the position of the specimen, thus limiting the tilting behavior of the acrylic plate. Figure 6 The diagram shown is an assembly drawing and a physical drawing of the mold for the tensile wrinkling test according to an embodiment of the present invention.

[0107] S32: Establish a finite element analysis simulation model based on the tensile wrinkling test conditions of bimetallic composite plates. For example... Figure 7 The diagram shown is a flowchart of the composite layup rapid modeling method according to an embodiment of the present invention.

[0108] S321: Based on the finite element mesh type, select the type of bimetallic composite plate, select continuous shell element for calculation, and create a three-dimensional solid of bimetallic composite plate.

[0109] S322: Set the material parameters of the bimetallic composite plate in the attribute module, and obtain the material parameters of the first metal layer, the second metal layer and the mixed metal layer determined in step 2 for material setting.

[0110] S323: Select Composite layup for rapid modeling, and set the layer thickness, material selection, layup direction, and number of integration points for each layer of the bimetallic composite panel.

[0111] S324: Select the finite element mesh type according to the finite element mesh element type. For continuous shell elements, the SC8R mesh type should be selected.

[0112] S325: Set the analysis step. Set the continuous shell element Buckle-dynamic with initial defects as the analysis step of the finite element algorithm to establish the finite element simulation model.

[0113] S33: Compare the finite element simulation results with the experimental results to verify the accuracy of the finite element simulation; extract the thickness displacement contour maps of the bimetallic composite plate from the experiment and simulation, and check whether the wrinkle type and the number of wrinkles in the bimetallic composite plate at the same location are consistent; then compare the thickness displacement curves x of the bimetallic composite plate along the measurement path at different times in the experiment and simulation. α and x β It was found that the thickness displacements of both materials along the measurement path during the entire forming process of the bimetallic composite plate were similar, and their displacement errors Δx satisfied the following relationship:

[0114]

[0115] In the formula: Δx represents the thickness displacement error of the bimetallic composite plate along the measurement path throughout the entire forming process; x α This represents the thickness displacement curves of the bimetallic composite plate along the measurement path at different times during the experiment; x β This represents the thickness displacement curves of the bimetallic composite plate along the measurement path at different times during the simulation.

[0116] The wrinkling process and wrinkle development patterns are consistent between the experimental and simulated methods, thus the finite element simulation can accurately reflect the actual experimental results.

[0117] S34: Draw the strain paths of each metal layer based on the finite element simulation results; set 5 integration points for the three layers of the composite plate at equal thickness intervals along their respective thickness directions, such as... Figure 8 The figure shown is a distribution diagram of the integration points along the thickness direction of the composite plate in a finite element simulation according to an embodiment of the present invention. Taking a copper-aluminum composite plate with a copper layer ratio of 15% and an overall thickness of 1 mm as an example, the first principal strain ε1 and the second principal strain ε2 of each layer material integration point in the thickness direction of the buckling element of the bimetallic composite plate are extracted respectively, and a strain path diagram is plotted. At the same time, the bifurcation times t1, t2, and t3 of the strain path of each metal layer are recorded; as shown... Figure 9 The diagram shown is a finite element simulation of the strain path of the copper layer metal in the ridge region of the composite plate according to an embodiment of the present invention, used to illustrate the strain path of the copper layer metal; as shown... Figure 10 The diagram shown is a finite element simulation of the metallurgical bonding layer in the ridge region of the composite plate according to an embodiment of the present invention, used to illustrate the metallurgical bonding layer strain path in the ridge region of the composite plate; as shown... Figure 11 The diagram shown is a finite element simulation of the strain path of the aluminum layer metal in the ridge region of the composite plate according to an embodiment of the present invention, used to illustrate the strain path of the aluminum layer metal.

[0118] S35: Determine the location of the stress neutral layer based on the finite element simulation results; determine the location P of the stress neutral layer by combining the curve of the in-plane normal stress along the thickness direction perpendicular to the ridge direction and the graph of the thickness displacement of the composite plate over time. α Record the bifurcation time t of the strain path in the metal layer containing the stress neutral layer.α The location of the stress neutral layer is determined by the curve of the change of normal stress along the thickness direction of the section perpendicular to the ridge direction. The specific determination principle is as follows: at the critical buckling moment of each critical metal layer, the data of the whole composite plate is extracted and the stress values ​​at the integration point of each metal layer are compared. When the following formula is satisfied, it is determined that the stress neutral layer is located in that metal layer.

[0119]

[0120] Where: σ x This represents the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate. This represents the derivative of the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate along the thickness direction.

[0121] S4: Determine the critical wrinkling stress-strain result of the bimetallic composite plate based on the location of the stress neutral layer.

[0122] S41: Based on the bifurcation time t of the strain path of the metal layer where the stress neutral layer is located. α Determine the critical wrinkling time t of the integral bimetallic composite plate CA The method for determining the critical wrinkling moment of a monolithic bimetallic composite panel is as follows:

[0123] The stress paths of each layer in the bimetallic composite plate reveal that the strain paths always diverge and develop after bifurcation in the metal layer containing the stress-neutral layer, while the strain paths of other metal layers develop in parallel after bifurcation. Simultaneously, the change in thickness displacement of the bimetallic composite plate over time indicates that the metal layer containing the stress-neutral layer is also the first to begin bifurcation and separation, at which point thickness displacement begins to appear in the bimetallic composite plate. If the bifurcation moment of other metal layers is taken as the critical wrinkling moment, wrinkling has already occurred in the metal layer containing the stress-neutral layer, and this is the moment when wrinkles continue to grow, which cannot achieve the function of predicting and determining the critical wrinkling moment. Therefore, the bifurcation moment of the strain path in the metal layer containing the stress-neutral layer is the critical wrinkling moment t of the entire bimetallic composite plate. CA The details are as follows:

[0124] t CA =t α ;

[0125] In the formula: t CA Indicates the critical wrinkling moment of the integral bimetallic composite panel; t α This indicates the moment when the strain path of the metal layer containing the stress-neutral layer bifurcates.

[0126] Let t1 be the time when the aluminum layer bifurcates, t2 be the time when the copper layer bifurcates, and t3 be the time when the metallurgical bonding layer bifurcates. The time sequence from earliest to latest is t1, t2, t3. Figure 12The diagram shows the distribution of in-plane normal stress along the thickness direction perpendicular to the ridge direction at each bifurcation moment in an embodiment of the present invention. From the distribution of in-plane normal stress along the thickness direction of the composite plate at each bifurcation moment, it can be seen that at times t1, t2, and t3, the copper layer and the metallurgical bonding layer are under compressive stress as a whole. The outermost layer of the aluminum layer is under tension, and the inner side is under compression, but both the compressive and tensile stresses are very small. The neutral layer, i.e., the position where the normal stress is 0, is located within the aluminum layer.

[0127] S42: Based on the critical wrinkling time t of the integral bimetallic composite plate CA Extract the stress σ′ of the bimetallic composite plate at this time. m and strain ε′ m This represents the critical wrinkling stress-strain result of the bimetallic composite plate. Analysis of the stress paths in each layer of the composite plate reveals that the strain paths always diverge and develop separately after bifurcation in the neutral metal layer, while the strain paths in other metal layers develop in parallel after bifurcation. Furthermore, from... Figure 13 As shown in the graph illustrating the change in thickness displacement of the composite plate in this embodiment of the invention over time, the metal layer containing the neutral layer and the aluminum layer are also the first to begin bifurcation and separation, at which point the specimen begins to exhibit thickness displacement. If the bifurcation moment of other metal layers is taken as the critical wrinkling moment, the metal layer containing the neutral layer has already begun to wrinkle, and this is the moment when wrinkles continue to grow, which cannot achieve the function of predicting and determining the critical wrinkling moment. Therefore, the bifurcation moment of the strain path of the metal layer containing the stress neutral layer is defined as the critical wrinkling moment of the entire composite plate. Figure 14 As shown, the stress and strain of the composite plate at this point were extracted, and a critical wrinkling criterion line was plotted. Compared with the theoretical wrinkling criterion line, the two curves basically coincide. This further demonstrates the correctness and scientific validity of the critical wrinkling stress and strain obtained through simulation.

[0128] In summary, the simulation results of bimetallic composite plates can vary depending on the method used to establish the finite element analysis model. Furthermore, the strain paths of each metal layer in the composite plate are different, and the selection of the bifurcation time of the strain path of different metal layers as the critical wrinkling time of the entire composite plate also varies, ultimately leading to differences in the determined critical wrinkling stress and strain.

[0129] Therefore, to more accurately obtain the critical wrinkling stress and strain of bimetallic composite plates, the assembly conditions corresponding to the experiment must be set when establishing the finite element simulation model of the composite plate. Composite layup is used for rapid modeling, and the Buckle-dynamic finite element algorithm with introduced initial defects is selected. The strain paths of each metal layer are extracted from the simulation results, and the location of the stress-neutral layer is found. The bifurcation time of the strain path of the metal layer where the stress-neutral layer is located is the critical wrinkling time of the entire composite plate. Finally, the stress and strain at the critical wrinkling time of the entire composite plate are extracted, which is the critical wrinkling stress and strain of the bimetallic composite plate. This method for determining the critical wrinkling stress and strain of bimetallic composite plates is well-suited for obtaining the stress and strain values ​​at the critical wrinkling time of the composite plate wrinkling instability problem in the actual forming process, and it has guiding significance for the subsequent establishment of the WLD (Warranty Layout Design) for the actual forming process of composite plates.

[0130] In summary, the prediction results of the flowchart used in this case study to determine the critical wrinkling stress and strain of bimetallic composite plates demonstrate its excellent effectiveness.

[0131] (1) In this embodiment of the invention, copper-aluminum composite plate is taken as the research object. By collecting the strain path diagram of each metal layer, the bifurcation time of the strain path of each metal layer is obtained. Then, the position of the stress neutral layer of the composite plate is determined by the curve of the change of in-plane normal stress along the thickness direction perpendicular to the ridge direction and the curve of the thickness displacement of the composite plate with time. The bifurcation time of the strain path of the metal layer where the stress neutral layer is located is defined as the critical wrinkling time of the bimetallic composite plate. This illustrates the characteristics of this method in predicting the critical wrinkling stress and strain of the composite plate.

[0132] (2) The embodiments of the present invention have a clear idea, detailed calculation, and intuitive process. The results accurately predict the moment of wrinkling instability of composite board and determine the critical wrinkling stress and strain. This lays a solid foundation for the subsequent establishment of the critical wrinkling judgment line of composite board and its widespread application in engineering practice. The embodiments further prove that the present invention can better meet the actual application needs.

[0133] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for determining the critical wrinkling stress-strain of bimetallic composite plates, characterized in that, It includes the following steps: Step 1: Obtain the material performance parameters of the bimetallic composite panel; A uniaxial tensile test was performed on the bimetallic composite plate to obtain the overall stress of the bimetallic composite plate. and strain Microhardness tests were performed on the bimetallic composite plate to accurately determine the hardness of the first metal layer by observing the distribution of hardness along the thickness direction. Hardness of the second metal layer and the hardness of the mixed metal layer ; The material performance parameters of the bimetallic composite panel in step 1 include: the overall stress of the bimetallic composite panel. Overall strain of bimetallic composite plate Hardness of the first metal layer Hardness of the second metal layer and the hardness of the mixed metal layer ; Step 2: Establish the stress-strain relationship between the first metal layer, the second metal layer, and the hybrid metal layer using the mixing principle; The stresses of the first metal layer, the second metal layer, and the hybrid metal layer are determined according to the mixing principle, as shown below: ； In the formula: This indicates the stress in the first metal layer; This indicates the stress in the second metal layer; Indicates the stress in the hybrid metal layer; This indicates the total load on the bimetallic composite plate; Indicates the hardness of the first metal layer; Indicates the hardness of the second metal layer; Indicates the hardness of the mixed metal layer; This represents the cross-sectional area of ​​the first metal layer; This represents the cross-sectional area of ​​the second metal layer; This represents the cross-sectional area of ​​the mixed metal layer; Since the tensile strain of each layer in the composite plate is consistent, the strain of the overall mixed material and each heterogeneous layer of the bimetallic composite plate satisfies the identity equation, as shown below: ； In the formula: This represents the overall strain of the bimetallic composite plate. This represents the strain of the first metal layer; This indicates the strain in the second metal layer; Indicates the strain of the hybrid metal layer; The stress-strain relationship of the first metal layer, the second metal layer, and the hybrid metal layer can all be expressed by the following formula: In the formula: Indicates stress in metallic materials; Indicates the yield stress of metallic materials; Indicates the strength coefficient of metallic materials; Indicates strain in metallic materials; The determination of the stresses of the first metal layer, the second metal layer, and the hybrid metal layer according to the mixing principle in step 2 is specifically as follows: The delamination stress-strain relationship is calculated based on the uniaxial tensile stress in the thickness direction of the bimetallic composite plate. During the tensile process of the bimetallic composite plate, the total load F on the bimetallic composite plate satisfies the following equation: ； In the formula: This indicates the stress experienced by the bimetallic composite plate; This represents the cross-sectional area subjected to by the bimetallic composite plate; The bimetallic composite plate is subjected to a cross-sectional area Cross-sectional area of ​​the first metal layer Cross-sectional area of ​​the second metal layer and the cross-sectional area of ​​the mixed metal layer The following relationship is satisfied: ； Based on the relationship between microhardness and stress in metallic materials, the stress and microhardness of each heterogeneous layer in a heterogeneous metal layered composite plate satisfy the following equation: ； If we set the ratio in the above equation as a proportionality constant k, then the above equation can be transformed into: ； In the formula: k represents the microhardness of the metallic material as a function of stress; In summary, the formula for calculating the proportionality constant k is as follows: ； The stress in the first metal layer, the second metal layer, and the hybrid metal layer can be obtained by sorting. Step 3: Determine the location of the stress neutral layer in the bimetallic composite plate using finite element analysis. Step 31: Design a tensile wrinkling test for bimetallic composite plates; Step 32: Establish a finite element analysis simulation model based on the tensile wrinkling test conditions of bimetallic composite plates; Step 33: Compare the finite element simulation results with the experimental results to verify the accuracy of the finite element simulation; Step 34: Draw the strain path of each metal layer based on the finite element simulation results; extract the first principal strain of the material integration points of each metal layer in the thickness direction of the buckling element of the bimetallic composite plate. Second principal strain Plot the strain path diagram and record the bifurcation time of the strain path in each metal layer. ; Step 35: Determine the location of the stress neutral layer based on the finite element simulation results; the location of the stress neutral layer is determined by the curve of the in-plane normal stress perpendicular to the ridge direction along the thickness direction and the graph of the thickness displacement of the composite plate over time. Record the bifurcation time of the strain path in the metal layer containing the stress neutral layer. ; Step 4: Determine the critical wrinkling stress-strain result of the bimetallic composite plate based on the location of the stress neutral layer; Step 41: Based on the bifurcation time of the strain path in the metal layer containing the stress neutral layer Determine the critical wrinkling moment of the integral bimetallic composite panel The details are as follows: ； In the formula: This indicates the critical wrinkling moment of the overall bimetallic composite panel; Indicates the moment when the strain path of the metal layer containing the stress neutral layer bifurcates; Step 42: Based on the critical wrinkling moment of the overall bimetallic composite panel Extract the stress of the bimetallic composite plate at this time. and strain The critical wrinkling stress-strain results of the bimetallic composite plate were obtained.

2. The method for determining the critical wrinkling stress-strain of bimetallic composite plates according to claim 1, characterized in that, In step 32, a finite element analysis simulation model is established based on the tensile wrinkling test conditions of the bimetallic composite plate. Specifically: Step 321: Based on the finite element mesh type, select the type of bimetallic composite plate, select continuous shell element for calculation, and create a three-dimensional solid of bimetallic composite plate; Step 322: Set the material parameters of the bimetallic composite plate in the property module, and obtain the material parameters of the first metal layer, the second metal layer and the mixed metal layer determined in step 2 for material setting; Step 323: Select Composite Layup for rapid modeling, and set the layer thickness, material selection, layup direction, and number of integration points for each layer of the bimetallic composite panel; Step 324: Select the finite element mesh type according to the finite element mesh type. For continuous shell elements, the SC8R mesh type should be selected. Step 325: Set up the analysis step. Set the continuous shell element Buckle-dynamic with initial defects as the analysis step of the finite element algorithm and establish the finite element simulation model.

3. The method for determining the critical wrinkling stress-strain of bimetallic composite plates according to claim 1, characterized in that, Step 33, which compares the finite element simulation results with the experimental results to verify the accuracy of the finite element simulation, specifically involves: Thickness displacement contour maps of bimetallic composite plates from experiments and simulations were extracted to verify that the wrinkle type and wrinkle number at the same location were consistent in both. Then, the thickness displacement curves of the bimetallic composite plates along the measurement path at different times in the experiments and simulations were compared. and The results showed that the thickness displacement of both materials along the measurement path was similar during the entire forming process of the bimetallic composite plate, and their displacement errors were similar. The following relationship is satisfied: In the formula: This indicates the thickness displacement error of the bimetallic composite plate along the measurement path throughout the entire forming process. The thickness displacement curves of the bimetallic composite plate along the measurement path are shown at different times during the test. This represents the thickness displacement curves of the bimetallic composite plate along the measurement path at different times during the simulation.

4. The method for determining the critical wrinkling stress-strain of bimetallic composite plates according to claim 1, characterized in that, In step 35, the position of the stress neutral layer is determined by the curve of the change of in-plane normal stress perpendicular to the ridge direction along the thickness direction and the graph of the thickness displacement of the composite plate over time. Specifically, the determination is as follows: at the critical buckling moment of each critical metal layer, the data of the entire composite plate is extracted and the stress values ​​at the integration points of each metal layer are compared. When the following formula is satisfied, it is determined that the stress neutral layer is located in that metal layer. ； In the formula: This represents the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate. This represents the derivative of the in-plane normal stress perpendicular to the ridge direction of the bimetallic composite plate along the thickness direction.

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