A method for predicting dent depth of aluminum alloy sheet under low speed impact

Abstract

The application discloses a kind of aluminum alloy sheet low-speed impact pit depth prediction method, comprising: setting hypothesis, the low-speed impact problem of aluminum alloy sheet is simplified;Plastic failure mechanism is constructed and segmented;The plastic dissipation power model of only considering bending moment of aluminum alloy round plate is constructed;Aluminum alloy sheet impact pit depth prediction model is constructed, actual impact load data and the structure parameters of aluminum alloy sheet are input into analysis model, and the low-speed impact pit depth of aluminum alloy sheet is output.The application has the advantages of simple, practical, accurate prediction, and has important engineering application value, especially for the pit depth prediction and structure maintenance of aircraft aluminum alloy sheet component after impact has important value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of impact damage evaluation of metal structures, and in particular to a method for predicting the dent depth of an aluminum alloy sheet under low-speed impact. BACKGROUND

[0002] Aluminum alloy materials have been the main material for aircraft body structures in the aviation field due to their high specific strength and easy processing characteristics. Aircrafts are prone to suffer a large number of low-speed impact events (such as tool falling, debris impact, bird strike) in engineering operation, which causes permanent dent deformation of the aluminum alloy body structure and significantly reduces its static strength and fatigue performance. At present, in the field of aviation engineering, most aircraft body structures adopt aluminum alloy sheet structures with a thickness of about 0.2 mm to 4 mm. Reliably evaluating the influence of low-speed impact load on the permanent dent deformation of aluminum alloy sheets will provide an important basis for the impact dent damage tolerance performance of aircraft aluminum alloy structures. The current impact dent damage evaluation of aircraft aluminum alloy structures cannot accurately predict the dent depth of aluminum alloy sheets under low-speed impact.

[0003] Therefore, the present applicant has developed a method for predicting the dent depth of an aluminum alloy sheet under low-speed impact to solve the above problems. SUMMARY

[0004] The present application proposes a method for predicting the dent depth of an aluminum alloy sheet under low-speed impact to solve the problem that the current impact dent damage evaluation of aircraft aluminum alloy structures cannot accurately predict the dent depth of aluminum alloy sheets under low-speed impact.

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

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

[0007] setting a hypothetical condition, the hypothetical condition including: assuming that the aluminum alloy sheet is not sensitive to strain rate, assuming that the performance of the aluminum alloy sheet is ideal rigid-plasticity, assuming that the power of the external load of the aluminum alloy sheet is completely converted into plastic dissipation power, assuming that the initial impact energy of the aluminum alloy sheet is completely dissipated by a plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy sheet is simplified into a quasi-static problem of a circular aluminum alloy plate with a fixed periphery subjected to a load at the center;

[0008] constructing a plastic failure mechanism of the aluminum alloy circular plate under the load according to the small deformation assumption and the hypothetical condition, dividing the plastic failure mechanism into a plurality of sector-shaped rigid plate blocks, linking each sector-shaped rigid plate block with a radial plastic hinge line, and the angular velocity of each sector-shaped rigid plate block being the same in size and the direction being along the circular arc edge of the sector-shaped rigid plate block, respectively;

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

[0010] constructing a plastic dissipation power model of the aluminum alloy circular plate only considering bending moment based on the first information, simple support boundary condition and fixed support boundary condition;

[0011] constructing an impact dent depth prediction model of the aluminum alloy thin plate based on an energy conservation equation according to the plastic dissipation power model;

[0012] obtaining second information, the second information comprising actual impact load data and structural parameters of the aluminum alloy thin plate;

[0013] inputting the second information into the analysis model to output low-speed impact dent depth of the aluminum alloy thin plate.

[0014] Specifically, the first information is obtained, comprising:

[0015] obtaining structural parameters of the aluminum alloy circular plate, the structural parameters comprising radius and thickness of the aluminum alloy circular plate;

[0016] calculating the arc length of each of the fan-shaped rigid blocks according to plastic hinge length of the fan-shaped rigid blocks and number of the fan-shaped rigid blocks, the plastic hinge length being the radius of the aluminum alloy circular plate;

[0017] calculating the relative angular velocity between two adjacent fan-shaped rigid blocks according to angular velocity of the fan-shaped rigid blocks and number of the fan-shaped rigid blocks.

[0018] Specifically, the calculation formulas of 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)

[0023] the arc length of each of the fan-shaped rigid blocks, the plastic hinge length, n being the number of the fan-shaped rigid blocks, the relative angular velocity, the angular velocity of each of the fan-shaped rigid blocks.

[0024] Specifically, according to the first information, a plastic dissipation power model of the aluminum alloy round plate only considering bending moment is constructed based on a simply supported boundary condition and a clamped boundary condition, including:

[0025] In the simply supported boundary condition (b = 1), the plastic dissipation power of the aluminum alloy round plate only considering bending moment is The calculation formula is:

[0026] (3)

[0027] In the clamped boundary condition (b = 2), the plastic dissipation power of the aluminum alloy round plate only considering bending moment is The calculation formula is:

[0028] (4)

[0029] In the formula (3) and the formula (4), is the plastic limit bending moment per unit width of the aluminum alloy round plate;

[0030] (5)

[0031] When , the plastic dissipation power model of the aluminum alloy round plate only considering bending moment can be obtained, and the formula is:

[0032] (6)

[0033] Wherein, is the plastic limit bending moment per unit width of the aluminum alloy round plate, h is the thickness of the aluminum alloy round plate, is the yield stress of the aluminum alloy round plate, b = 1 refers to the simply supported boundary condition, and b = 2 refers to the clamped boundary condition.

[0034] Specifically, according to the plastic dissipation power model, an impact dent depth prediction model of the aluminum alloy thin plate is constructed based on an energy conservation equation, including:

[0035] The power of the external load P of the aluminum alloy round plate is calculated as

[0036] (7)

[0037] Ignoring the energy consumption caused by friction, according to the energy balance condition, the external load power of the aluminum alloy round plate is all converted into plastic dissipation power, that is

[0038] (8)

[0039] Substituting the formula (6) and (7) into the formula (8), the external load under the condition of plastic dissipation caused only by bending moment can be obtained​ is:

[0040] (9)

[0041] When the impact dent depth of the aluminum alloy sheet reaches Δ, the energy consumed is:

[0042] (10)

[0043] The plastic dissipation power of the aluminum alloy circular plate considering the combined action of bending moment and membrane force is:

[0044] (11)

[0045] wherein, is the membrane force factor, only depends on the boundary conditions of the aluminum alloy circular plate and the dimensionless deflection in the deformation process :

[0046] (12)

[0047] For the aluminum alloy circular plate with simply supported and clamped periphery, the membrane force factor is:

[0048] (13-a)

[0049] (13-b)

[0050] Substituting formula (7), formula (11) into the energy balance equation, the external load considering the plastic dissipation caused by the combined action of bending moment and membrane force is:

[0051] (14)

[0052] Therefore, when the impact dent depth of the aluminum alloy sheet reaches Δ, the energy consumed is:

[0053] (15)

[0054] Substituting formula (12) and (13) into formula (15), the energy consumed when the impact dent depth of the aluminum alloy sheet reaches Δ is:

[0055] (16a)

[0056] (16b)

[0057] Assuming that the initial impact energy is completely dissipated by the plastic failure mechanism during the impact process, there is:

[0058] (17)

[0059] wherein, is the initial impact energy;

[0060] Combining formula (16) and (17), the dimensionless deflection of the center of the aluminum alloy circular plate after bearing the impact load can be solved, and the dimensionless deflection of the center of the aluminum alloy circular plate under the clamped boundary condition (b = 1) is The display expression is:

[0061] (18)

[0062] By substituting formula (5) and formula (12) into formula (18), the display expression of the aluminum alloy thin plate impact dent depth prediction model for predicting the impact dent depth Δ of the aluminum alloy thin plate under the clamped boundary condition (b = 2) can be obtained:

[0063] (19).

[0064] The beneficial effects of the present application are:

[0065] The prediction method for the low-speed impact dent depth of the aluminum alloy thin plate provided by the present application solves the problem that the low-speed impact dent depth of the aluminum alloy thin plate cannot be accurately predicted in the existing impact dent damage evaluation of the aircraft aluminum alloy structure, has the advantages of being simple, practical, and accurate in prediction, and has important engineering application value, especially for the impact dent depth prediction and structure maintenance of the aircraft aluminum alloy thin plate component. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 is a step diagram of the prediction method for the low-speed impact dent depth of the aluminum alloy thin plate in the embodiment of the present application;

[0067] Figure 2 is a schematic diagram of the principle of the clamped aluminum alloy thin plate subjected to low-speed impact in the embodiment of the present application;

[0068] Figure 3 is a schematic diagram of the plastic failure mechanism in the embodiment of the present application;

[0069] Figure 4 is a schematic diagram of the impact center dent depth of the aluminum alloy thin plate component in the embodiment of the present application. DETAILED DESCRIPTION

[0070] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will be combined with the accompanying drawings to make a clear and complete description of the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0071] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0072] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0073] In the description of the present application, it should be understood that the terms "upper", "lower", "inner", "outer", "left", "right" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship commonly understood by those skilled in the art, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0074] In addition, the terms "first", "second" and the like are only used to distinguish description, and cannot be understood as indicating or implying relative importance.

[0075] In the description of the present application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "provided", "connected" and the like should be understood broadly, for example, "connected" can be fixedly connected, or detachably connected, or integrally connected; can be mechanically connected, or electrically connected; can be directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0076] The specific embodiments of the present application will be described in detail below in combination with the accompanying drawings.

[0077] As Figure 1 shown, the steps of a method for predicting low-speed impact dent depth of an aluminum alloy sheet in an embodiment of the present application are as follows:

[0078] Step S100: Set the hypothetical condition to simplify the low-velocity impact problem of the aluminum alloy sheet.

[0079] The following model simplifications are made for the mechanical problem of the aluminum alloy sheet under impact load: i) Assume that the aluminum alloy material is not sensitive to strain rate, and ignore the effect of strain rate; ii) Assume that the material properties of the aluminum alloy sheet are ideal rigid-plastic; iii) Assume that the power of the external load is completely converted into plastic dissipation power; iv) Assume that the initial impact energy is completely dissipated by the plastic failure mechanism; v) As shown in Figure 2 , assume that the low-velocity impact problem of the aluminum alloy sheet can be simplified into a quasi-static problem of a circular aluminum alloy plate with a thickness of h and a circumference of , which is fixedly supported at the periphery, and the center of which is subjected to a load P.

[0080] Step S200: Construct and segment the plastic failure mechanism.

[0081] As shown in Figure 3 , under the action of the load P, the aluminum alloy circular plate undergoes permanent plastic deformation, and if the small deformation assumption condition is met, the plastic failure mechanism of the aluminum alloy circular plate can be established on the basis of the initial configuration. It is assumed that the failure mechanism is composed of n small fan-shaped rigid plate blocks, and the fan-shaped plate blocks are linked by ray-shaped plastic hinge lines. According to the deformation compatibility condition, the angular velocity of each rigid plate block is , and the direction is along the circular arc edge of the rigid plate block.

[0082] Step S300: Construct a plastic dissipation power model of the aluminum alloy circular plate considering only bending moment.

[0083] From the geometric relationship in Figure 3 , the plastic hinge line length of each small fan-shaped plate is , and the circular arc length is:

[0084] (1)

[0085] The relative angular velocity between the adjacent two small fan-shaped plate rigid plate blocks is

[0086] (2)

[0087] Under the simply supported boundary condition (b=1), the plastic dissipation power considering only the bending moment is

[0088] (3)

[0089] Under the fixed boundary condition (b=2), the plastic hinge line also exists on the fixed circular arc boundary, so the plastic dissipation power considering only the bending moment is:

[0090] (4)

[0091] In formula (3) and formula (4), is the plastic limit bending moment per unit width of the aluminum alloy round plate;

[0092] (5)

[0093] In the formula, is the yield stress of the aluminum alloy round plate material.

[0094] When , the plastic dissipation power of the aluminum alloy round plate (M) caused by the bending moment can be obtained as:

[0095] (6)

[0096] Step S400: Constructing an aluminum alloy sheet impact dent depth prediction model.

[0097] The aircraft aluminum alloy sheet component is subjected to low-speed impact under different energies during service. However, due to the limited time and cost, low-speed impact tests under a certain specified energy are usually carried out. However, the low-speed impact suffered by the aircraft in service is random, and it is difficult to determine the impact energy. Therefore, based on the energy conservation equation, an aluminum alloy sheet impact dent depth prediction model is established.

[0098] The power of the external load P at the center of the aluminum alloy round plate is:

[0099] (7)

[0100] Ignoring the energy consumption caused by friction, it can be known from the energy balance condition that the external load power is completely converted into plastic dissipation power:

[0101] (8)

[0102] Substituting formula (6) and (7) into formula (8), the external load P under the condition of considering only the plastic dissipation caused by the bending moment can be obtained as:

[0103] (9)

[0104] Therefore, when the impact dent depth of the aluminum alloy sheet reaches Δ, the energy consumed is:

[0105] (10)

[0106] ​​​If the low velocity impact results in large deformation of the aluminum alloy circular plate, the energy consumed by membrane force has a significant effect on the total plastic dissipation energy, thus the plastic dissipation power considering the combined action of bending moment and membrane force is

[0107] (11)

[0108] wherein, is the membrane force factor, which is independent of 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 in the deformation process :

[0109] (12)

[0110] For the aluminum alloy circular plate with simply supported and clamped periphery, the membrane force factor is derived as :

[0111] (13-a)

[0112] (13-b)

[0113] Substituting formula (7) and formula (11) into the energy balance equation, the external load resulting in plastic dissipation considering the combined action of bending moment and membrane force is :

[0114] (14)

[0115] Therefore, when the impact pit depth of the aluminum alloy thin plate reaches Δ, the consumed energy is

[0116] (15)

[0117] Substituting formula (12) and (13) into formula (15), the consumed energy when the impact pit depth of the aluminum alloy thin plate reaches Δ is

[0118] (16a)

[0119] (16b)

[0120] Assuming that the initial impact energy is completely dissipated by the plastic failure mechanism during the impact process, there is

[0121] (17)

[0122] wherein, is the initial impact energy.

[0123] Combining equations (16) and (17), the dimensionless deflection of the center of the aluminum alloy circular plate under the impact load can be solved. The expression is shown as

[0124] (18)

[0125] Substituting equation (5) and equation (12) into equation (18), the expression of the center dent depth Δ under the fixed boundary condition (b=2) is

[0126] (19)

[0127] b=1 represents a simply supported boundary condition, and b=2 represents a fixed boundary condition.

[0128] Step S500: inputting actual impact load data and structure parameters of the aluminum alloy thin plate into the analysis model, and outputting the low-speed impact dent depth of the aluminum alloy thin plate.

[0129] Substituting the actual impact load data and the aluminum alloy thin plate parameters h into equation (19), the center dent depth Δ of the aluminum alloy thin plate after impact can be obtained, as shown in Figure 4 .

[0130] The application further provides a device for predicting the low-speed impact dent depth of an aluminum alloy thin plate, which comprises:

[0131] A setting module is configured to set a hypothetical condition, wherein the hypothetical condition comprises: assuming that the aluminum alloy thin plate is not sensitive to strain rate, assuming that the performance of the aluminum alloy thin plate is ideal rigid-plasticity, assuming that the power of the external load 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 a plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy thin plate is simplified into a quasi-static problem in which the center of a peripherally fixed aluminum alloy circular plate is subjected to a load.

[0132] A first construction module is configured to construct a plastic failure mechanism of the aluminum alloy circular plate under the action of a load according to a small deformation hypothesis and the hypothetical condition, and divide the plastic failure mechanism into a plurality of sector-shaped rigid plate blocks, wherein the sector-shaped rigid plate blocks are linked by ray-shaped plastic hinge lines, and the angular velocities of the sector-shaped rigid plate blocks are the same in size and respectively along the circular arc edges of the sector-shaped rigid plate blocks.

[0133] The first acquisition module is used for acquiring first information, and the first information includes the arc length of each fan-shaped rigid slab, the relative angular velocity between two adjacent fan-shaped rigid slabs, and the structural parameters of the aluminum alloy circular plate.

[0134] The second construction module is used for constructing a plastic dissipation power model of the aluminum alloy circular plate only considering bending moment based on the first information, a simply supported boundary condition and a clamped boundary condition.

[0135] The third construction module is used for constructing an aluminum alloy thin plate impact dent depth prediction model based on an energy conservation equation according to the plastic dissipation power model.

[0136] The second information is acquired, and the second information includes actual impact load data and the structural parameters of the aluminum alloy thin plate.

[0137] The second information is input into the analysis model, and the aluminum alloy thin plate low-speed impact dent depth is output.

[0138] The application further provides a kind of aluminum alloy thin plate low-speed impact dent depth prediction equipment, comprising:

[0139] The memory is used for storing computer programs.

[0140] The processor is used for executing the computer program to realize the steps of the aluminum alloy thin plate low-speed impact dent depth prediction method.

[0141] The application further provides a readable storage medium, and the readable storage medium stores computer programs, and the computer programs are executed by the processor to realize the steps of the aluminum alloy thin plate low-speed impact dent depth prediction method. The readable storage medium can be U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk and various readable storage media that can store program codes.

[0142] The above only is the preferred embodiment of the application, and it should be pointed out that, for ordinary skilled in the art, without departing from the technical principles of the application, a number of improvements and refinements can be made, and these improvements and refinements should be regarded as the protection scope of the application.

Claims

1. A method for predicting the depth of a low-speed impact pit on an aluminum alloy sheet, characterized in that: include: Assumptions are set, including: assuming that the aluminum alloy sheet is insensitive to strain rate, assuming that the aluminum alloy sheet has ideal rigid-plastic properties, assuming that all external load power of the aluminum alloy sheet is converted into plastic dissipation power, assuming that the initial impact energy of the aluminum alloy sheet is completely dissipated by the plastic failure mechanism, and assuming that the low-speed impact problem of the aluminum alloy sheet is simplified to a quasi-static problem in which a peripherally clamped aluminum alloy circular plate is subjected to a load at its center; A plastic failure mechanism of the aluminum alloy circular plate under load is constructed based on the small deformation hypothesis and the hypothetical conditions. The plastic failure mechanism is divided into a plurality of sector-shaped rigid plates. The sector-shaped rigid plates are connected by ray-shaped plastic hinges. The angular velocities of the sector-shaped rigid plates are the same in magnitude and are directed along the arc edges of the sector-shaped rigid plates. Acquiring first information, the first information including the arc length of each of the sector-shaped rigid plates, the relative angular velocity between two adjacent sector-shaped rigid plates, and structural parameters of the aluminum alloy circular plate; According to the first information, based on simply supported boundary conditions and clamped boundary conditions, constructing a plastic dissipation power model of the aluminum alloy circular plate that only considers 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, the second information including 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 low-speed impact dent depth of the aluminum alloy sheet.

2. The method for predicting the depth of a low-velocity impact pit on an aluminum alloy sheet according to claim 1, wherein: Obtaining 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 sector-shaped rigid plate according to the plastic hinge length of the sector-shaped rigid plate and the number of the sector-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-velocity impact pit on an aluminum alloy sheet according to claim 2, wherein: 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, 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-velocity impact pit on an aluminum alloy sheet according to claim 3, wherein: According to the first information, based on simply supported boundary conditions and clamped boundary conditions, 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 clamped boundary condition.

5. The method for predicting the depth of a low-velocity impact pit on an aluminum alloy sheet according to claim 4, wherein: According to the plastic dissipation power model and based on the energy conservation equation, a prediction model for the impact dent 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 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） Where, is the membrane force factor, It only depends 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 clamped support, 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), we can obtain 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） Where, 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 expression of the prediction model of impact pit depth of aluminum alloy sheet is shown as follows: （19）。

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