Method for predicting low-speed impact pit depth of aluminum alloy sheet

Abstract

The invention discloses a method for predicting the low-speed impact pit depth of an aluminum alloy sheet, and the method comprises the steps: setting an assumption, and simplifying the low-speed impact problem of the aluminum alloy sheet; a plastic failure mechanism is constructed and segmented; constructing a plastic dissipation power model, only considering the bending moment, of the aluminum alloy circular plate; and constructing an aluminum alloy sheet impact pit depth prediction model, inputting actual impact load data and structural parameters of the aluminum alloy sheet into an analysis model, and outputting the low-speed impact pit depth of the aluminum alloy sheet. The method has the advantages of being simple, convenient, practical and accurate in prediction, has important engineering application value, and particularly has important value for pit depth prediction and structural maintenance after impact of the aircraft aluminum alloy sheet component.

Description

Technical Field

[0001] The invention relates to the technical field of metal structure impact damage assessment, and in particular to a method for predicting the depth of a low-speed impact dent on an aluminum alloy sheet. Background Art

[0002] Aluminum alloy materials have always been the main material for aircraft fuselage structures in the aviation field due to their high specific strength and easy processing characteristics. Aircraft are prone to a large number of low-speed impact events (such as tool falling, debris impact, and bird strikes) during engineering operations, which cause permanent pitting deformation in the aluminum alloy fuselage structure and significantly reduce its static strength and fatigue performance. At present, in the field of aerospace engineering, most aircraft fuselage structures use aluminum alloy thin plate structures with a thickness of generally about 0.2 mm to 4 mm. Reliably evaluating the effect of low-speed impact loads on the permanent pitting deformation of aluminum alloy thin plates will provide an important basis for the impact pitting damage tolerance performance of aircraft aluminum alloy structures. The current aircraft aluminum alloy structure impact pitting damage assessment cannot accurately predict the depth of low-speed impact pits on aluminum alloy thin plates.

[0003] Therefore, the applicant has developed a method for predicting the depth of a low-speed impact dent on an aluminum alloy sheet to solve the above problem. Summary of the invention

[0004] The present invention proposes a method for predicting the depth of a low-speed impact dent on an aluminum alloy sheet, so as to solve the problem that the depth of a low-speed impact dent on an aluminum alloy sheet cannot be accurately predicted in the existing aircraft aluminum alloy structure impact dent damage assessment.

[0005] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0006] A method for predicting the depth of a low-speed impact dent on an aluminum alloy sheet, comprising:

[0007] Setting assumptions, wherein the assumptions include: assuming that the aluminum alloy thin plate is insensitive to strain rate, assuming that the aluminum alloy thin plate has ideal rigid-plastic properties, assuming that the external load power of the aluminum alloy thin plate is completely converted into plastic dissipation power, assuming that the initial impact energy of the aluminum alloy thin plate is completely dissipated by the plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy thin plate is simplified to a quasi-static problem in which the center of a peripherally clamped aluminum alloy circular plate is subjected to a load;

[0008] According to the small deformation assumption and the assumption conditions, the plastic failure mechanism of the aluminum alloy circular plate under load is constructed, and the plastic failure mechanism is divided into a plurality of fan-shaped rigid plates, each of which is connected by a ray-shaped plastic hinge line, and the angular velocity of each of the fan-shaped rigid plates is the same and the direction is respectively along the arc edge of the fan-shaped rigid plate;

[0009] Acquiring first information, wherein the first information includes the arc length of each of the fan-shaped rigid plates, the relative angular velocity between two adjacent fan-shaped rigid plates, and the structural parameters of the aluminum alloy circular plate;

[0010] According to the first information, based on simply supported boundary conditions and clamped supported boundary conditions, a plastic dissipation power model of the aluminum alloy circular plate is constructed that only considers the bending moment;

[0011] According to the plastic dissipation power model and based on the energy conservation equation, a prediction model for the impact pit depth of aluminum alloy thin plates is constructed;

[0012] Acquiring second information, wherein the second information includes actual impact load data and structural parameters of the aluminum alloy sheet;

[0013] The second information is input into the analysis model to output the depth of the low-speed impact dent on the aluminum alloy sheet.

[0014] Specifically, obtaining the first information includes:

[0015] Acquire structural parameters of the aluminum alloy circular plate, wherein the structural parameters include the radius and thickness of the aluminum alloy circular plate;

[0016] Calculating the arc length of the fan-shaped rigid plate according to the plastic hinge length of the fan-shaped rigid plate and the number of the fan-shaped rigid plates, wherein the plastic hinge length is the radius of the aluminum alloy circular plate;

[0017] The relative angular velocity between two adjacent sector-shaped rigid panels is calculated according to the angular velocity of the sector-shaped rigid panels and the number of the sector-shaped rigid panels.

[0018] Specifically, the calculation formulas for the arc length and the relative angular velocity are as follows:

[0019] The calculation formula of the arc length is:

[0020] (1)

[0021] The calculation formula of the relative angular velocity is:

[0022] (2) is the arc length of the fan-shaped rigid plate, is the length of the plastic hinge line, is the number of the fan-shaped rigid plates, is the relative angular velocity, is the angular velocity of the fan-shaped rigid plate.

[0023] Specifically, according to the first information, based on simply supported boundary conditions and clamped supported boundary conditions, a plastic dissipation power model of the aluminum alloy circular plate considering only the bending moment is constructed, including:

[0024] Under simply supported boundary conditions (b=1), only the plastic dissipation power of the bending moment is considered. The calculation formula is:

[0025] (3)

[0026] Under the fixed boundary condition (b=2), only the plastic dissipation power of the bending moment is considered. The calculation formula is: (4)

[0027] (5)

[0028] when When , the plastic dissipation power model of the aluminum alloy circular plate considering only the bending moment can be obtained, and its formula is:

[0029] (6)

[0030] in, is the plastic limit bending moment per unit width of the aluminum alloy circular plate, is the thickness of the aluminum alloy circular plate, is the yield stress of the aluminum alloy circular plate, b=1 represents the simply supported boundary condition, and b=2 represents the fixed supported boundary condition.

[0031] Specifically, according to the plastic dissipation power model and based on the energy conservation equation, a prediction model for the impact pit depth of an aluminum alloy sheet is constructed, including:

[0032] Calculate the external load of the aluminum alloy circular plate Power for

[0033] (7)

[0034] Ignoring the energy consumption caused by friction, it can be seen from the energy balance condition that the external load power of the aluminum alloy circular plate is completely converted into plastic dissipation power, that is,

[0035] (8)

[0036] Substituting equations (6) and (7) into equation (8), we can obtain the external load when only considering the plastic dissipation caused by the bending moment: for:

[0037] (9)

[0038] When the impact pit depth of the aluminum alloy sheet reaches The energy consumed for:

[0039] (10)

[0040] The plastic dissipation power of the aluminum alloy circular plate considering the combined action of bending moment and membrane force is for:

[0041] (11)

[0042] In the formula, is the membrane force factor, It depends only on the boundary conditions of the aluminum alloy circular plate and the dimensionless deflection during deformation. :

[0043] (12)

[0044] For the aluminum alloy circular plate with simple support and clamp support at the periphery, the film force factor for:

[0045] (13-a)

[0046] (13-b)

[0047] Substituting equations (7) and (11) into the energy balance equation, we can obtain the external load that considers the plastic dissipation caused by the combined action of bending moment and membrane force: for:

[0048] (14)

[0049] Therefore, when the impact pit depth of the aluminum alloy sheet reaches The energy consumed for:

[0050] (15)

[0051] Substituting equations (12) and (13) into equation (15), it can be obtained that the impact pit depth of the aluminum alloy sheet reaches The energy consumed for:

[0052] (16a)

[0053] (16b)

[0054] Assuming that the initial impact energy is completely dissipated by the plastic failure mechanism during the impact process, we have:

[0055] (17)

[0056] In the formula, is the initial impact energy;

[0057] Combining equations (16) and (17), the dimensionless deflection of the center of the aluminum alloy circular plate after the impact load can be solved. Under the fixed boundary condition (b = 1), the dimensionless deflection is The display expression is:

[0058] (18)

[0059] Substituting equations (5) and (12) into equation (18), we can obtain the predicted impact pit depth of aluminum alloy sheet under the fixed boundary condition (b = 2): The display expression of the impact pit depth prediction model of aluminum alloy sheet is:

[0060] (19).

[0061] The beneficial effects of the present invention are:

[0062] The method for predicting the depth of low-speed impact dents on aluminum alloy thin plates proposed in the present invention solves the problem that the depth of low-speed impact dents on aluminum alloy thin plates cannot be accurately predicted in existing aircraft aluminum alloy structure impact dent damage assessment. The method has the advantages of being simple, practical, and accurate in prediction, and has important engineering application value, especially for the prediction of dent depth after impact and structural repair of aircraft aluminum alloy thin plate components. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 A step diagram of a method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet in an embodiment of the present application;

[0064] Figure 2 This is a schematic diagram of the principle of a clamped aluminum alloy sheet subjected to a low-speed impact in an embodiment of the present application;

[0065] Figure 3 A schematic diagram of a plastic failure mechanism in an embodiment of the present application;

[0066] Figure 4 It is a schematic diagram of the depth of the central pit of the aluminum alloy thin plate component impacted in the embodiment of the present application. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0068] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0070] In the description of the present invention, it should be understood that the terms "upper", "lower", "inside", "outside", "left", "right", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, or are directions or positional relationships in which the product of the invention is usually placed when in use, or are directions or positional relationships commonly understood by those skilled in the art. These directions or positional relationships are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.

[0071] Furthermore, the terms “first”, “second”, etc. are merely used for distinguishing descriptions and should not be understood as indicating or implying relative importance.

[0072] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms such as "setting" and "connection" should be understood in a broad sense. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0073] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0074] like Figure 1 As shown, the steps of a method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet in an embodiment of the present application are as follows:

[0075] Step S100: Set up hypothetical conditions to simplify the low-speed impact problem of aluminum alloy sheet

[0076] The following simplified models are used for the mechanical problems of aluminum alloy thin plates under impact loads: i) It is assumed that aluminum alloy materials are insensitive to strain rate and the influence of strain rate is ignored; ii) It is assumed that the material properties of aluminum alloy plates are ideal rigid-plastic; iii) It is assumed that the external load power is completely converted into plastic dissipation power; iv) It is assumed that the initial impact energy is completely dissipated by the plastic failure mechanism; v) Figure 2 As shown in the figure, it is assumed that the low-velocity impact problem of aluminum alloy sheet can be simplified to a plate with a thickness of , the radius is The aluminum alloy circular plate is fixed around the periphery and the center is subjected to load Quasi-static problem of action.

[0077] Step S200: Construct and segment the plastic failure mechanism

[0078] like Figure 3 As shown, under load Under the action of the aluminum alloy circular plate, permanent plastic deformation occurs. Under the assumption of small deformation, the plastic failure mechanism of the aluminum alloy circular plate can be established on the basis of the initial configuration. Assume that its failure mechanism is The structure is composed of a number of small fan-shaped rigid plates, each of which is connected by a ray-shaped plastic hinge. From the deformation coordination condition, we can know that the angular velocity of each rigid plate is , and the directions are along the arc edges of the rigid plates.

[0079] Step S300: Constructing a plastic dissipation power model of an aluminum alloy circular plate considering only the bending moment

[0080] Depend on Figure 3 From the geometric relationship in , we can see that the plastic hinge length of each small sector plate is , arc length for:

[0081] (1)

[0082] The relative angular velocity between two adjacent small fan-shaped rigid plates for

[0083] (2)

[0084] Under simply supported boundary conditions (b = 1), the plastic dissipated power considering only the bending moment is

[0085] (3)

[0086] Under the clamped boundary condition (b=2), there is also a plastic hinge line on the clamped arc boundary. Therefore, the plastic dissipated power considering only the bending moment is:

[0087] (4)

[0088] In formula (3) and formula (4), is the plastic limit bending moment per unit width of the aluminum alloy circular plate

[0089] (5)

[0090] In the formula, is the yield stress of aluminum alloy circular plate material.

[0091] when When the aluminum alloy circular plate ( ) Considering only the plastic dissipation power of the bending moment,

[0092] (6)

[0093] Step S400: Constructing an aluminum alloy sheet impact pit depth prediction model

[0094] Aircraft aluminum alloy sheet components are subjected to low-speed impacts of different energies during service. Usually, due to limited time and cost, only low-speed impact tests with a certain energy are performed. However, the low-speed impacts suffered by aircraft in service are random, and it is difficult to determine the impact energy. Therefore, based on the energy conservation equation, a prediction model for the impact pit depth of aluminum alloy sheet is established.

[0095] External load at the center of aluminum alloy circular plate Power for:

[0096] (7)

[0097] Ignoring the energy consumption caused by friction, the energy balance condition shows that the external load power is completely converted into plastic dissipation power:

[0098] (8)

[0099] Substituting equations (6) and (7) into equation (8), we can obtain the external load when only considering the plastic dissipation caused by the bending moment: for:

[0100] (9)

[0101] Therefore, when the depth of the impact pit on the aluminum alloy sheet reaches The energy consumed is

[0102] (10)

[0103] If the low-speed impact causes a large deformation of the aluminum alloy circular plate, the energy consumed by the membrane force has a significant effect on the total plastic dissipation energy. Therefore, the plastic dissipation power considering the combined effect of the bending moment and the membrane force is:

[0104] (11)

[0105] In the formula, is the membrane force factor, which has nothing to do with the radius and external load of the aluminum alloy circular plate, and only depends on the boundary conditions of the aluminum alloy circular plate and the dimensionless deflection during the deformation process. :

[0106] (12)

[0107] For the aluminum alloy circular plate with simple support and clamp support, the membrane force factor is derived for:

[0108] (13-a)

[0109] (13-b)

[0110] Substituting equations (7) and (11) into the energy balance equation, we can obtain the external load that considers the plastic dissipation caused by the combined action of bending moment and membrane force: for:

[0111] (14)

[0112] Therefore, when the depth of the impact pit on the aluminum alloy sheet reaches The energy consumed is

[0113] (15)

[0114] Substituting equations (12) and (13) into equation (15), we can obtain that the impact pit depth of the aluminum alloy sheet reaches The energy consumed is

[0115] (16a)

[0116] (16b)

[0117] Assuming that the initial impact energy is completely dissipated by the plastic failure mechanism during the impact process, we have

[0118] (17)

[0119] In the formula, is the initial impact energy.

[0120] Combining equations (16) and (17), we can solve the dimensionless deflection of the center of the aluminum alloy circular plate after the impact load. Under the fixed boundary condition (b = 1), the dimensionless deflection The display expression is

[0121] (18)

[0122] Substituting equations (5) and (12) into equation (18), we can obtain that under the fixed support boundary condition (b = 2), the depth of the central pit is The display expression is

[0123] (19)

[0124] b=1 refers to simply supported boundary conditions, and b=2 refers to fixed supported boundary conditions.

[0125] Step S500: Input the actual impact load data and the structural parameters of the aluminum alloy sheet into the analysis model, and output the depth of the low-speed impact pit of the aluminum alloy sheet.

[0126] The actual impact load data , and aluminum alloy sheet parameters , Substituting into equation (19), we can obtain the depth of the central pit of the aircraft aluminum alloy sheet after impact: ,like Figure 4 shown.

[0127] The present invention also provides a device for predicting the depth of a low-speed impact pit on an aluminum alloy sheet, comprising:

[0128] A setting module, the setting module is used to set assumptions, the assumptions include: assuming that the aluminum alloy thin plate is insensitive to strain rate, assuming that the aluminum alloy thin plate has ideal rigid-plastic properties, assuming that the external load power of the aluminum alloy thin plate is completely converted into plastic dissipation power, assuming that the initial impact energy of the aluminum alloy thin plate is completely dissipated by the plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy thin plate is simplified to a quasi-static problem in which the center of a peripherally clamped aluminum alloy circular plate is subjected to a load;

[0129] A first construction module, wherein the first construction module is used to construct a plastic failure mechanism of the aluminum alloy circular plate under load according to a small deformation assumption and the assumption conditions, and divide the plastic failure mechanism into a plurality of fan-shaped rigid plates, wherein the fan-shaped rigid plates are connected by ray-shaped plastic hinges, and the angular velocities of the fan-shaped rigid plates are the same in magnitude and are respectively directed along the arc edges of the fan-shaped rigid plates;

[0130] A first acquisition module, the first acquisition module is used to acquire first information, the first information including the arc length of each of the fan-shaped rigid plates, the relative angular velocity between two adjacent fan-shaped rigid plates, and the structural parameters of the aluminum alloy circular plate;

[0131] A second construction module, wherein the second construction module is used to construct a plastic dissipation power model of the aluminum alloy circular plate considering only the bending moment based on the simply supported boundary condition and the clamped supported boundary condition according to the first information;

[0132] The third construction module is to construct an impact pit depth prediction model for aluminum alloy thin plates according to the plastic dissipation power model and based on the energy conservation equation;

[0133] Acquiring second information, wherein the second information includes actual impact load data and structural parameters of the aluminum alloy sheet;

[0134] The second information is input into the analysis model to output the depth of the low-speed impact dent on the aluminum alloy sheet.

[0135] The present invention also provides a device for predicting the depth of a low-speed impact pit on an aluminum alloy sheet, comprising:

[0136] Memory for storing computer programs;

[0137] A processor is used to implement the steps of the method for predicting the depth of a low-speed impact dent on an aluminum alloy sheet when executing the computer program.

[0138] The present invention also provides a readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method for predicting the depth of a low-speed impact pit of an aluminum alloy sheet are implemented. The readable storage medium can be a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other readable storage media that can store program codes.

[0139] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet, characterized in that: include: Setting assumptions, wherein the assumptions include: assuming that the aluminum alloy thin plate is insensitive to strain rate, assuming that the aluminum alloy thin plate has ideal rigid-plastic properties, assuming that the external load power of the aluminum alloy thin plate is completely converted into plastic dissipation power, assuming that the initial impact energy of the aluminum alloy thin plate is completely dissipated by the plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy thin plate is simplified to a quasi-static problem in which the center of a peripherally clamped aluminum alloy circular plate is subjected to a load; According to the small deformation assumption and the assumption conditions, the plastic failure mechanism of the aluminum alloy circular plate under load is constructed, and the plastic failure mechanism is divided into a plurality of fan-shaped rigid plates, each of which is connected by a ray-shaped plastic hinge line, and the angular velocity of each of the fan-shaped rigid plates is the same and the direction is respectively along the arc edge of the fan-shaped rigid plate; Acquiring first information, wherein the first information includes the arc length of each of the fan-shaped rigid plates, the relative angular velocity between two adjacent fan-shaped rigid plates, and the structural parameters of the aluminum alloy circular plate; According to the first information, based on simply supported boundary conditions and clamped supported boundary conditions, a plastic dissipation power model of the aluminum alloy circular plate is constructed that only considers the bending moment; According to the plastic dissipation power model and based on the energy conservation equation, a prediction model for the impact pit depth of aluminum alloy thin plates is constructed; Acquiring second information, wherein the second information includes actual impact load data and structural parameters of the aluminum alloy sheet; The second information is input into the aluminum alloy sheet impact dent depth prediction model to output the aluminum alloy sheet low-speed impact dent depth.

2. The method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet according to claim 1, characterized in that: Obtain the first information, including: Acquire structural parameters of the aluminum alloy circular plate, wherein the structural parameters include the radius and thickness of the aluminum alloy circular plate; Calculating the arc length of the fan-shaped rigid plate according to the plastic hinge length of the fan-shaped rigid plate and the number of the fan-shaped rigid plates, wherein the plastic hinge length is the radius of the aluminum alloy circular plate; The relative angular velocity between two adjacent sector-shaped rigid panels is calculated according to the angular velocity of the sector-shaped rigid panels and the number of the sector-shaped rigid panels.

3. The method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet according to claim 2, characterized in that: The calculation formulas for the arc length and the relative angular velocity are as follows: The calculation formula of the arc length is: （1） The calculation formula of the relative angular velocity is: （2） is the arc length of the fan-shaped rigid plate, is the length of the plastic hinge line, is the number of the fan-shaped rigid plates, is the relative angular velocity, is the angular velocity of the fan-shaped rigid plate.

4. The method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet according to claim 3, characterized in that: According to the first information, based on the simply supported boundary condition and the clamped boundary condition, a plastic dissipation power model of the aluminum alloy circular plate considering only the bending moment is constructed, including: Under simply supported boundary conditions (b=1), only the plastic dissipation power of the bending moment is considered. The calculation formula is: （3） Under the fixed boundary condition (b=2), only the plastic dissipation power of the bending moment is considered. The calculation formula is: （4） （5） when When , the plastic dissipation power model of the aluminum alloy circular plate considering only the bending moment can be obtained, and its formula is: （6） in, is the plastic limit bending moment per unit width of the aluminum alloy circular plate, is the thickness of the aluminum alloy circular plate, is the yield stress of the aluminum alloy circular plate, b=1 represents the simply supported boundary condition, and b=2 represents the fixed supported boundary condition.

5. The method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet according to claim 4, characterized in that: According to the plastic dissipation power model and based on the energy conservation equation, a prediction model for the impact pit depth of aluminum alloy thin plates is constructed, including: Calculate the external load of the aluminum alloy circular plate Power for （7） Ignoring the energy consumption caused by friction, it can be seen from the energy balance condition that the external load power of the aluminum alloy circular plate is completely converted into plastic dissipation power, that is, （8） Substituting equations (6) and (7) into equation (8), we can obtain the external load when only considering the plastic dissipation caused by the bending moment: for: （9） When the impact pit depth of the aluminum alloy sheet reaches The energy consumed for: （10） The plastic dissipation power of the aluminum alloy circular plate considering the combined action of bending moment and membrane force is for: （11） In the formula, is the membrane force factor, It depends only on the boundary conditions of the aluminum alloy circular plate and the dimensionless deflection during deformation. : （12） For the aluminum alloy circular plate with simple support and clamp support at the periphery, the film force factor for: （13-a） （13-b） Substituting equations (7) and (11) into the energy balance equation, we can obtain the external load that considers the plastic dissipation caused by the combined action of bending moment and membrane force: for: （14） Therefore, when the impact pit depth of the aluminum alloy sheet reaches The energy consumed for: （15） Substituting equations (12) and (13) into equation (15), it can be obtained that the impact pit depth of the aluminum alloy sheet reaches The energy consumed for: （16a） （16b） Assuming that the initial impact energy is completely dissipated by the plastic failure mechanism during the impact process, we have: （17） In the formula, is the initial impact energy; Combining equations (16) and (17), the dimensionless deflection of the center of the aluminum alloy circular plate after the impact load can be solved. Under the fixed boundary condition (b = 1), the dimensionless deflection is The display expression is: （18） Substituting equations (5) and (12) into equation (18), we can obtain the predicted impact pit depth of aluminum alloy sheet under the fixed boundary condition (b = 2): The display expression of the impact pit depth prediction model of aluminum alloy sheet is: （19）。

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