CN112800553B - Multi-stage controllable progressive energy-absorbing lattice structure - Google Patents
Multi-stage controllable progressive energy-absorbing lattice structure Download PDFInfo
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Abstract
The invention provides a multistage controllable progressive energy-absorbing lattice structure, which comprises a spliced rod piece, wherein the spliced rod piece comprises two X-shaped orthogonal connected diagonal rods, vertical rods for connecting the two diagonal rods are respectively arranged at two sides of the horizontal direction of the connecting point of the two diagonal rods, and the connecting positions of the two vertical rods are mutually corresponding and mutually parallel; the unit cell structure is formed by connecting points of two spliced rod pieces in an orthogonal interlocking assembly mode; the lattice structure is formed by mutually connecting a plurality of unit cell structures on a plane through adjacent diagonal rod endpoints, and interlocking positions of the unit cell structures are fixed by vacuum brazing. According to the invention, the mechanical property of multistage progressive energy absorption of the light structure is realized through the lattice structure, and a butterfly-type lattice configuration with gradually rising stress-strain curve and multistage controllable is provided according to the transformation of the configuration in the compression process of the lattice structure.
Description
Technical Field
The invention relates to the field of structural energy absorption, in particular to a multi-stage controllable progressive energy absorption lattice structure.
Background
Energy absorption of impact loads has a wide application requirement in various fields of automobiles, helmets, packaging and the like, and is always the focus of research and application of traditional light porous structures. In the design of energy absorbing structures, the most often desirable energy absorbing means is to stably absorb energy (CEA) at a constant peak load. In the lightweight porous structure, the foam material is always regarded as an ideal energy absorbing material, and the foam material has lower initial rigidity and initial strength due to the fact that a relatively stable yield platform exists in the loading process and the deformation characteristic of the foam material leading to bending, so that the damage to the protected object in the initial impact process is effectively reduced.
However, the random disordered pore structure inside the foam material makes the mechanical properties of the foam material not accurately designed and controlled, and the relative density is generally higher, so that the energy absorption efficiency is lower. In contrast, lattice structures are also often used as an object of investigation for impact protection because of their highly programmable nature of periodically distributed lattice units and unit bars, the initial strength and stiffness of which can be accurately predicted and designed.
In addition to the energy absorption and stable deformation energy absorption process, the design of the energy absorption structure also reduces the damage to the protected object as much as possible. In the actual situation, the collision speed faced by the energy-absorbing structure and the protected target are often various, but the energy-absorbing strategy of CEA is adopted, so that effective protection cannot be provided for different impact speeds and different targets, and the more efficient energy-absorbing device needs to have better suitability for different speeds and different protection targets, namely, the damage caused by too high peak load can be completely restrained when the low-speed collision occurs, and the kinetic energy caused by the impact is absorbed as much as possible at the higher collision speed, so that the damage is reduced as much as possible.
The high initial strength and rigidity of the tension-compression dominant lattice structure can lead the protected object to be easily damaged due to the fact that the load is too high at a low speed. In order to increase the safety factor of the energy absorbing device, it is desirable to reduce the initial strength and stiffness of the energy absorbing structure as much as possible, and in CEA energy absorbing strategies, there is often a contradiction between lower initial peak load and higher energy absorption.
Disclosure of Invention
The invention aims to provide a multi-stage controllable progressive energy-absorbing lattice structure.
In particular, the invention provides a multi-stage controllable progressive energy-absorbing lattice structure, which comprises,
the splicing rod piece comprises two X-shaped orthogonal connecting diagonal rods, vertical rods for connecting the two diagonal rods are respectively arranged on two sides of the horizontal direction of the connecting point of the two diagonal rods, and the connecting positions of the two vertical rods are mutually corresponding and mutually parallel;
the unit cell structure is formed by connecting points of two spliced rod pieces in an orthogonal interlocking assembly mode;
the lattice structure is formed by mutually connecting a plurality of unit cell structures on a plane through adjacent diagonal rod endpoints, and interlocking positions of the unit cell structures are fixed by vacuum brazing.
According to the invention, the mechanical property of light structure gradual energy absorption is realized through a lattice structure, a butterfly-type lattice structure with gradually rising stress strain curves and multiple controllable stages is provided according to the transformation of the configuration in the compression process of the lattice structure, two butterfly-type lattice structures with different densities are prepared by adopting cutting-interlocking assembly and vacuum brazing process design, and the parent metal of the lattice structure is 304 stainless steel with better plastic deformation.
Through the established theoretical model under the transformation of the two density butterfly type lattice structure configurations, theoretical prediction of each stage of a multi-level stress-strain curve is realized, experiments and numerical simulation researches under out-of-plane compression loads of the two types of lattice structures are carried out, and feasibility of realizing gradual rising and gradual energy absorption of the stress-strain curve through the configuration transformation and applicability of the theoretical model are verified. The invention is determined that the transformation stability of the compact lattice structure configuration adopted by the invention is stronger. In addition, the amplitude and the length of each level of stress platform in the energy absorption curve can be adjusted and controlled by changing the length of the vertical rod in the lattice structure.
Drawings
FIG. 1 is a schematic view of a spliced rod according to one embodiment of the present invention;
FIG. 2 is a schematic diagram of interlocking assembly and cutting assembly of a lattice structure and a dense lattice structure according to one embodiment of the present invention, wherein (a) and (c) are the cutting and assembly processes of the lattice structure, respectively, and (b) and (d) are the assembly processes of the dense lattice structure, respectively;
FIG. 3 is a schematic diagram of a configuration transition and multi-stage progressive stress-strain curve of a lattice cell compression process in accordance with one embodiment of the present invention; wherein, (a) is a rod end free boundary configuration transition schematic, (b) is a rod end directional sliding boundary configuration transition schematic, (c) is a rod end directional sliding boundary stress-strain curve;
FIG. 4 is a first stage force analysis model of an out-of-plane compressive load of a lattice structure in accordance with one embodiment of the present invention; wherein, (a) is a quarter lattice cell, (b) is a rod end free boundary condition, (c) is a rod end sliding boundary condition, and (d) is bending moment distribution at two ends of a vertical rod;
FIG. 5 is a schematic diagram of a force analysis of a second stage sub-configuration under an out-of-plane compressive load of a lattice structure in accordance with one embodiment of the present invention; wherein, (a) is a quarter sub-configuration, (b) is the bending distribution relation of the rod piece at the plastic hinge, and (c) is the stress of the vertical rod;
FIG. 6 is a geometric relationship of rods when stress densification of a lattice structure in accordance with an embodiment of the invention occurs;
FIG. 7 is a graph showing the transformation of a configuration under an off-plane compressive load of lattice unit cells having a relative density of 1.63% in accordance with one embodiment of the present invention; wherein, (a) is an experimental result, and (b) is a numerical simulation result under the equivalent strain condition;
FIG. 8 is the out-of-plane compressive stress strain line of FIG. 7;
FIG. 9 is a schematic representation of the mode of configuration transformation during out-of-plane compression of lattice structures with a relative density of 1.63% under experimental and numerical modeling conditions in accordance with one embodiment of the present invention;
FIG. 10 is a graph of the out-of-plane compressive stress strain of FIG. 9;
FIG. 11 is a graph showing the results of a configuration transformation experiment and numerical simulation under an out-of-plane compressive load of a dense lattice structure having a relative density of 2.69% in accordance with one embodiment of the present invention;
FIG. 12 is a graph of the out-of-plane compressive pressure strain of FIG. 11;
FIG. 13 is a schematic view of lattice units of three different vertical rod lengths according to one embodiment of the present invention;
FIG. 14 is a graph showing the results of a transformation experiment and numerical simulation under an out-of-plane compressive load of a dense lattice structure with a vertical rod length of 10.6mm in accordance with one embodiment of the present invention;
FIG. 15 is a graph of the out-of-plane compressive stress strain of FIG. 14;
FIG. 16 is a graph showing the results of a transformation experiment and numerical simulation of the configuration of a compact lattice structure with a vertical rod length of 16.6mm under an out-of-plane compressive load in accordance with one embodiment of the present invention;
FIG. 17 is an out-of-plane compressive stress strain graph of FIG. 16;
FIG. 18 is a graph of out-of-plane compressive stress strain for dense lattice structures of differing vertical rod lengths according to one embodiment of the present invention;
FIG. 19 is a graph showing the specific energy absorption versus strain for dense lattice structures of varying montant lengths in accordance with one embodiment of the present invention.
Detailed Description
Specific structures and implementation procedures of the present solution are described in detail below through specific embodiments and drawings.
In one embodiment of the invention, as shown in FIG. 1, a multi-stage controllable progressive energy absorbing lattice structure is disclosed, comprising, spliced poles, and unit cell structures and lattice structures formed by the spliced poles.
The splicing rod piece comprises two X-shaped orthogonal connecting diagonal rods, wherein vertical rods for connecting the two diagonal rods are respectively arranged at two opposite sides of the horizontal direction of the connecting point of the two diagonal rods, and the connecting positions of the two vertical rods are mutually corresponding and mutually parallel; namely, the vertical rods are only symmetrically arranged on two opposite sides of the diagonal rods, and the overall shape of the vertical rods is a butterfly-shaped two-dimensional pattern.
The unit cell structure is formed by mutually interlocking connection points of two diagonal rods of two spliced rod pieces in an orthogonal mode, the end parts of the diagonal rods on the same side of the two spliced rod pieces after interlocking are bottom supporting points, the end parts of the diagonal rods on the opposite side are top supporting points, and four vertical rods are perpendicular to the upper supporting points and the lower supporting points; the unit cell structure is only used as a description object for convenience of description and understanding, but in implementation and use, the following lattice structure is adopted.
The lattice structure is formed by connecting a plurality of unit cell structures with each other through adjacent diagonal rod endpoints, a lattice structure layer which can extend to any direction on a plane is finally formed, and interlocking positions of the unit cell structures are fixed by vacuum brazing.
The structure of the interlocking lock is as follows: the joint of the spliced rod pieces is provided with a clamping groove which is concave towards the direction of the joint, and the two spliced rod pieces are mutually inserted through the clamping groove and then connected to form a single cell structure.
In order to realize the transformation from the initial lattice configuration to the sub-configuration during the loading process, the spliced rod material forming the lattice structure needs to have better plastic deformation capability. In the embodiment, 304 stainless steel is selected as a base material, and a butterfly-type lattice structure is prepared by combining preparation processes of interlocking assembly and vacuum brazing.
As shown in fig. 2 (a) (c), wherein (a) and (c) are the cutting and assembling processes of the lattice structure, respectively.
The preparation steps mainly comprise three steps. First, a 304 stainless steel plate 1.45mm thick was cut into butterfly-type splice bars using laser cutting. Each spliced rod piece can form a structure which is mutually connected through the end parts of the inclined rods in the width direction of the stainless steel plates, the spliced rod piece has only one shape, and the end parts of the inclined rods are provided with horizontal support sections which are used for being in contact with the surface layers of the closed lattice structure, so that the support sections are simultaneously used as connecting sections of the end parts of the two inclined rods.
And the second step is to orthogonally splice the spliced rod pieces after cutting along the clamping grooves on the central axis of the cell to form a lattice structure. Wherein n is 1 And n 2 The number of cells of the first butterfly lattice along the X and Y directions, respectively.
And thirdly, carrying out vacuum brazing on the spliced lattice structure. The specific brazing steps are as follows:
step 100, uniformly coating Ni-7Gr-4.5Si-3.1B-3Fe brazing solder) on all the joint points of the clamping grooves of the lattice structure;
namely, ni-7Gr-4.5Si-3.1B-3Fe brazing solder (Nicrobraz 31) is uniformly smeared at all the joint points of the clamping grooves of the lattice structure.
Step 200, placing the lattice structure into a vacuum brazing furnace, heating to 950 ℃ at a heating speed of 15 ℃/min, maintaining the temperature for 30-60 min to uniformly heat the whole lattice structure, heating to 1050 ℃ at a heating speed of 20 ℃/min, and heating to 2X 10 2 Maintaining the pressure of Pa for 6-10min, and naturally cooling to room temperature;
and 300, applying a preset load on the upper and lower surfaces of the lattice structure in the brazing process so as to ensure the welding quality and reduce the warping phenomenon caused by thermal stress.
The specific preset load is determined according to parameters such as the diameter and the sectional area of the spliced rod piece.
According to the embodiment, the mechanical property of light structure gradual energy absorption is realized through the lattice structure, a butterfly-type lattice structure with gradually rising stress strain curves and multiple controllable stages is provided according to the transformation of the configuration in the compression process of the lattice structure, the lattice structure is prepared by adopting cutting-interlocking assembly and vacuum brazing process design, and a base material of the lattice structure adopts 304 stainless steel with better plastic deformation.
In one embodiment of the present invention, the lattice structure further includes a compact lattice structure, which further increases the number of spliced rods based on the lattice structure, thereby increasing the density of the entire lattice structure and further increasing the bearing effect, and the shape and structure of the spliced rods adopted by the compact lattice structure and the lattice structure are completely identical, but have a slight difference in the interlocking structure, and the shape of the interlocking structure will be described in detail later.
The specific compact lattice structure comprises two complementary unit cell structures formed by complementary rod pieces consistent with the spliced rod pieces, the complementary unit cell structures are respectively connected with the end points of the oblique rod pieces of the lattice structure in a interlocking manner through the end points of the oblique rod pieces on two sides, the connecting angle of the complementary unit cell structures is the middle included angle of the spliced rod pieces orthogonal to the original, namely, the angle of 45 degrees, so that all the oblique rod pieces of the whole connecting point are mutually separated by 45 degrees. The connection point positions forming the complementary unit cell structure are located at the center surrounded by the diagonal connection points of the four lattice structures at the periphery, namely between the two connection points of the lattice structures.
The complementary unit cell structure in this embodiment is completely identical to the unit cell structure of the lattice structure, and the assembling process shown in fig. 2 (b) and (d) is only that the positions of the complementary unit cell structure and the lattice structure after final assembling are mutually staggered, and the specific manufacturing process and the mounting process are the same as those of the lattice structure, and are not repeated here. For the purposes of description only, the dot matrix structure is used.
In the embodiment, a compact butterfly lattice structure is formed by inserting new rods between lattice structures, the rod cutting process of the compact lattice structure is shown in fig. 2 (b), two rods with two shapes are shared, and two-dimensional cells are connectedThe two notch forms of penetration and semi-penetration are arranged at the position to facilitate the splicing. Fig. 2 (c) and fig. 2 (d) show the assembling process of the lattice structure and the compact lattice structure, respectively, and since the compact lattice is assembled on the basis of the lattice structure, the number of cycles of the compact lattice structure along the X and Y directions is the same as that of the lattice structure. The cross sections of all spliced rods in the lattice structure and the compact lattice structure are square, t=w=1.45 mm, and the prepared sample cell cycle number n is equal to the sum of the total number of the cells in the lattice structure and the compact lattice structure 1 ＝n 2 The relative densities of the two lattice structures were 1.63% and 2.69%, respectively, =3.
The interlocking structure in the compact lattice structure is as follows: clamping grooves which are opened towards the top supporting point are respectively arranged at the connecting points of the supplementing rod pieces and the diagonal rod at the top supporting point; the width of the clamping groove is generally the same as the width of the spliced pole.
The two spliced rod pieces are connected with each other and serve as the inclined rod connection point of the bottom supporting point, a clamping groove which is opened towards the direction of the top supporting point is formed in the position, corresponding to the clamping groove, of the inclined rods of the two spliced rod pieces, the inclined rods of the two spliced rod pieces are of a disconnection structure, and the disconnection distance is the same as the diameter of the complementary rod pieces.
When the lattice structure is installed, the spliced rods connected into a row are respectively inserted from the disconnecting structures at the upper parts of the spliced rods in a mutually perpendicular manner, the clamping grooves at the connecting positions of the diagonal rods at the bottom of the supplementing rods are inserted into the clamping grooves at the connecting points of the two diagonal rods at the bottom supporting points of the spliced rods from top to bottom, the diagonal rod connecting points (without the clamping grooves) at the upper ends of the supplementing rods are positioned in the disconnecting structures at the top supporting points of the spliced rods, and the spliced rods are mutually perpendicular to the supplementing rods after being spliced.
The fixed position and the corresponding length of the vertical rod and the inclined rod are adjusted, so that the forming position of the plastic hinge of the lattice structure after being stressed can be changed, and finally the aim of adjusting the stress-strain curve of the lattice structure is achieved. Specific effects are described in the following specific examples.
The stress variation effect explanation which can be achieved by the density of the lattice structure and the compact lattice structure is given by the calculation formula. It should be noted that in the following description, the lattice structure and the compact lattice structure have identical effects on the relevant mechanical performance, and the differences are only specific effect parameters, so in the following calculation process, the compact lattice effect will be changed differently unless the same conditions are used, and all the cases are described by taking the lattice structure as an illustration.
1. With respect to relative density.
Relative density of lattice structureThe definition is that the density of the lattice structure divided by the density of the lattice structure parent material is equal to the volume occupied by the lattice structure parent material divided by the volume of the lattice structure. FIG. 5 defines the unit cell configuration of the lattice structure and the geometric parameters of the spliced rod, the relative density of the lattice structure +.>Can be expressed as:
wherein the inclination angle omega=45° of the diagonal rod, the spliced rod pieces are square sections, t is the width of the clamping groove, w is the width of the spliced rod pieces, t=w, b is the length of the supporting section,is the height of the clamping groove, h tab The height of the supporting section is higher than w; l is the distance between the connecting point of the diagonal rod and the supporting section, l 2 Is the length of the vertical rod; />Is the thickness of the bottom of the clamping groove.
In an embodiment, the oblique rod inclination ω=45°, all the spliced rods are square in cross-section, with t=w. Substitution into formula (1) can be simplified as:
neglecting the effect of node volume, the following formula is obtained for an ideal lattice structure:
from the cell distribution of the lattice structure and the dense lattice structure, it can be determined that the relative density for the dense lattice structure is related to the number of cycles of the lattice structure, then:
in the method, in the process of the invention,n 1 ,n 2 the number of cell periods of the compact lattice structure along the X and Y directions is respectively that when n 1 ，n 2 When > 1, ">The number of dot matrix periods prepared and studied in this embodiment is n 1 ＝n 2 =3, therefore:
2. with respect to the transformation of lattice configuration versus multi-level progression curve.
Under out-of-plane compressive loading, the lattice structure will undergo a transformation from its original configuration to its sub-configuration, the configuration transformation process and its corresponding stress-strain curve being shown in fig. 3. Fig. 3 (a) and 3 (b) are schematic diagrams of configuration transformation during out-of-plane compression when the lattice cell rod ends are free boundary conditions and directional sliding boundary conditions, respectively. Under the action of out-of-plane compression load, the lattice structure with dominant bending can undergo configuration transformation under the action of plastic hinges, so that the stress-strain curve of the lattice structure is gradually increased. For the free boundary condition of the rod end, under the action of out-of-plane compression load, a plastic hinge is formed at the intersection position of the vertical rod and the inclined rod of the lattice structure. The lattice structure with the rod end as the directional sliding boundary condition forms a plastic hinge at the interface of the rod end, the vertical rod and the inclined rod.
At this time, the stress-strain curve of the lattice structure reaches the first peak value sigma 1 pk . Because of the characteristic of bending dominant deformation, the post-peak stress of the lattice structure is basically unchanged before a new lattice substructure is formed, and the stress-strain curve of the lattice structure is a stable yield platform. When the macroscopic strain of the lattice structure is epsilon 1 And when the lattice structure is converted into a compact lattice structure, the equivalent stress of the lattice structure starts to increase again until a new plastic hinge is formed at the middle position of the vertical rod, and a second stress platform is reached. Then, the upper and lower rod ends of the lattice structure of the free boundary are contacted with each other to form a third bearing substructure, the stress rises along with the stress until reaching a third stress platform, while the unit rod ends of the directional sliding boundary cannot be bent downwards to form a substructure similar to the unit cells of the free end rod members due to the constraint of the other unit rod ends, so that the stress is maintained at a second stage stress platform until the densification of the structure begins, and the densification is changed into epsilon D As shown in fig. 3 (c). Since the third carrier structure in the lattice structure with the rod end as the free boundary has poor stability, and the boundary condition of the rod end is mainly the sliding boundary in the multi-cell lattice structure, the following two-stage progressive stress strain curve only aiming at the sliding boundary gives a corresponding theoretical model.
3. Theoretical solutions are related to the multi-stage progressive stress-strain curve.
Firstly, establishing theoretical solutions for parameters of each stage in a stress-strain curve of the lattice structure in the configuration transformation process of the lattice structure, and further providing theoretical support for quantitatively regulating and controlling the energy absorption performance of the lattice structure.
The stress analysis is performed by taking a quarter symmetrical spliced rod piece of a unit cell structure, as shown in fig. 4 (a), wherein (a) is a quarter lattice cell, (b) is a rod end free boundary condition, (c) is a rod end sliding boundary condition, and (d) is bending moment distribution at two ends of a vertical rod. There may be two forms of boundary conditions of the node C in the lattice structure, one is the node located at the outermost side, the boundary condition is a free boundary condition as shown in fig. 4 (b), and the second is the node located inside the point, belonging to the directional sliding boundary condition as shown in fig. 4 (C).
In this embodiment, according to the connection state of the diagonal rods on one side in the lattice structure, the side is divided into a free side which is not connected with other diagonal rods and a closed side which is connected with other diagonal rods;
1) Equivalent compressive modulus at theoretical solution of the first stage stress strain curve:
when one side of the lattice structure is a free side, the equivalent stiffness is calculated as follows:
wherein A is cell ＝(2l cos ω+b+t) 2 Representing the cross-sectional area of the lattice structure, l 1 Is the distance between the vertical rod connecting point and the inclined rod end point on the inclined rod, H is the distance between the top supporting point and the bottom supporting point, F 1 Is a pressure applied vertically to the lattice structure;
when one side of the lattice structure is a closed side, the equivalent stiffness is calculated as follows:
for lattice structure, there are:
wherein the method comprises the steps ofN 2 ＝1-N 1 The method comprises the steps of carrying out a first treatment on the surface of the Among the lattice samples prepared in this embodiment are/>
The compressive stiffness equal to the compact lattice structure is:
wherein the method comprises the steps ofN 4 ＝2(1-N 3 ). The lattice sample prepared in this embodiment includes
2) Equivalent compressive strength under theoretical solution of first stage stress strain curve:
the equivalent compressive strength of the lattice structure is the linear superposition of the strength corresponding to the free side and the closed side respectively, and the calculation formula is as follows:
when n is 1 ＝n 2 When the number of the samples is =3,
the equivalent compressive strength calculation formula of the compact lattice structure is as follows:
when n is 1 ＝n 2 When the number of the samples is =3,
the strain at the end of the first phase is:
3) Equivalent compressive modulus at theoretical solution of second-stage stress strain curve:
wherein the method comprises the steps of
4) Equivalent compressive strength at theoretical solution of second stage stress strain curve: wherein,
the lattice structure shown in fig. 5 is a schematic diagram for analyzing the stress after forming the second bearing substructure, wherein (a) is a quarter sub-configuration, (b) is a bending distribution relationship of the rod pieces at the plastic hinge, and (c) is the stress of the vertical rods. The compressive strength calculation formula of the second stage of the lattice structure is as follows:
the equivalent compressive strength calculation formula of the second stage of the compact lattice structure is as follows:
wherein the method comprises the steps of
5) Densification strain under theoretical solution of third stage stress strain curve: wherein,
fig. 6 shows the geometric relationship of the spliced rod when densification of the lattice structure occurs, theoretically, when the BE rod and the DE rod formed after bending the vertical rod BD are completely folded in half, that is, parallel to each other, the lattice structure is completely compacted, but in practice, it is found by combining the results of the experiment and the numerical simulation that the structural equivalent stress increases sharply before the lattice structure is completely compacted, so it is assumed that when the rod BE and the diagonal rod AB are parallel to each other, the structural equivalent stress of the lattice structure starts to increase in densification, and the strain at the beginning of densification is:
4. with respect to the out-of-plane compression mechanical behavior of the lattice structure.
In order to verify the mechanical properties of multi-level controllable energy absorption of the lattice structure, the repeatability of configuration transformation in lattice compression is verified by adopting numerical simulation, and finally, the multi-level controllable energy absorption curve obtained by experiment is compared with a numerical simulation result and a theoretical prediction result.
1) With respect to lattice structures.
The compression experiment of the unit cell structure adopts a displacement loading mode, and the loading speed is 2mm/min. The numerical simulation adopts commercial finite element software ABAQUS/Explicit, the constitutive model adopts a linear hardening model, a hexahedral sweeping unit (C3D 48R) is adopted to carry out grid division on a lattice structure, the grid number of the spliced rod piece in the thickness direction is 5, the grid division number of the lattice unit is 22250, the lattice structure and a loading panel are made of the same material, and the friction coefficient is 0.3. FIG. 7 is a graph showing the transformation of the configuration under the action of the compressive load outside the lattice unit cell surface with the relative density of 1.63%, wherein (a) is an experimental result, and (b) is a numerical simulation result diagram under the condition of equivalent strain; FIG. 8 shows out-of-plane compressive stress strain lines for unit cells having a relative density of 1.63%, where the solid line experimental results, the large density dashed line is a numerical simulation result, and the small density dashed line is a theoretical prediction result.
As can be seen from fig. 7, the unit cell structure has three typical configurations before the complete densification deformation, and the experiment is consistent with the numerical simulation of the lattice compression deformation form, so that the repeatability of the configuration transformation in the lattice compression process is verified. Numerical simulation gives a change of equivalent plastic strain in the rod in the lattice compression process, from which it can be seen that when compression begins, the rod first forms a plastic hinge at the junction of the vertical rod and the diagonal rod, the stress strain curve reaches an initial peak at this time, the diagonal rod is slowly bent around the plastic hinge as the macroscopic equivalent strain increases, the macroscopic equivalent stress remains relatively stable in this process until the plastic hinge on the diagonal rod contacts the loading surface to form a second lattice substructure similar to BCC-Z, the macroscopic equivalent stress of the lattice structure begins to rise as compression proceeds further, when the middle position of the vertical rod in the lattice structure begins to form a new plastic hinge, the stress strain curve reaches a second peak, the vertical rod is symmetrically bent inward along the plastic hinge, the stress has no obvious weakening phenomenon in the process, and a next oval bearing substructure is formed when the upper and lower surfaces of the rod ends contact.
It is noted that this oval lattice substructure is not stable in experiments, because the rod ends of the rods on the upper and lower sides are not completely symmetrical in deformation as in simulation due to errors in the fabrication of the lattice structure, and the upper and lower rod ends are not always in contact during deformation, and show a small increase in stress-strain curve, i.e., a small decrease in stress, and remain on a relatively smooth stress platform until the stress densifies. In the simulation, the structure is relatively stable, the stress is obviously increased after the substructure is formed and a third stress peak appears in the stress-strain curve obtained by simulation, the structure starts to densify along with the mutual contact of the bent vertical rods and the inclined rods, the stress starts to rapidly increase, and finally the vertical rods are completely folded, and the lattice structure is completely compacted.
In numerical simulation, the stress-strain curve shows three-stage step growth, and the obtained stress-strain curve obtained through experiments shows two-stage step growth before densification. Because the stress analysis of the third elliptic bearing substructure is complex and the structure only appears in a single-cell structure with a free rod end, the theoretical analysis does not consider the substructure, and the theoretical solution only gives a theoretical solution of a two-stage stress platform, which has better coincidence with an experimental value in the later stage of the second stage and has larger difference with a numerical simulation result.
Fig. 9 shows the pattern of configuration transition during out-of-plane compression of a lattice structure of 3 x 3 cells with a relative density of 1.63% under experimental and numerical simulation conditions, wherein the left side is the experimental result and the right side is the numerical simulation result.
Numerical simulations give the distribution of equivalent plastic strains in different configurations of rods. It can be seen from fig. 9 that the experimental and numerical simulations result in a configuration transition pattern that is substantially identical. In the initial compression state, the boundary conditions of the rod piece at the outermost side and the compression process of the single cell lattice structure are the same, and are free boundary conditions, the maximum bending moment is formed at the node position of the end part of the vertical rod, and a plastic hinge is formed, while the boundary condition of the rod end at the inner side of a cell is a sliding boundary condition, and two plastic hinges are formed at the end part of the vertical rod and the end part of the inclined rod at the same time. This is due to the fact that the bars of the sliding boundary condition have the same bending moment at both ends of the bars and reach the maximum bending moment simultaneously during compression. The rod piece rotates around the plastic hinge until a second bearing configuration is formed, the plastic hinge is formed at the middle part of the vertical rod along with the continuous loading, and the multi-cell lattice structure has no elliptic sub-configuration formed by the mutual contact of the upper rod end and the lower rod end except the outermost rod piece due to the mutual constraint action of the rod pieces among cells unlike the single cell lattice compression process.
The bending of the rod member can bring the lattice structure cells to move to the periphery, and the periphery cells except the central cell generate out-of-plane bending deformation after the second substructure is formed. An out-of-plane compressive stress strain curve of the lattice structure with a relative density of 1.63% is shown in fig. 10, wherein black is realized as experimental results, blue dense dotted lines are numerical simulation results, and red sparse dotted lines are theoretical prediction results.
It can be seen from fig. 10 that the experimental, simulated and theoretical predicted values differ significantly in the second stress plateau section, and the theoretical predicted second peak height is significantly greater than the second peak height measured by the experimental and numerical simulations, because the out-of-plane rod bending deformation occurs after the lattice structure forms the second substructure during the experimental and numerical simulations, and the peak strength of the second stage obtained by theoretical analysis is based on the in-plane bending deformation of the vertical rod.
2) With respect to dense lattice structures.
The compact lattice structure can theoretically increase the stability of the rod deformation in the lattice compression process, reduce the out-of-plane deformation of the rod of the outer cell in the second stage, and fig. 11 shows the results of the configuration transformation experiment and numerical simulation under the action of the out-of-plane compression load of the compact lattice structure of 3×3 cells with the relative density of 2.69%, wherein the left side is the experimental result, and the right side is the numerical simulation result. From the transformation mode of the configuration in the compression process and the deformation graph after the compression loading is completed, the out-of-plane deformation of the vertical rods of the cells outside the compact lattice structure is obviously inhibited, but the connection nodes of the upper and lower rod ends are in large deformation and stress concentration in the compression process, so that part of brazing nodes are broken and fall off.
Fig. 12 shows an out-of-plane compressive stress strain curve of a dense lattice structure with a relative density of 2.69%, wherein the solid line is an experimental result, the broken line with a large density is a numerical simulation result, and the broken line with a small density is a theoretical prediction result. As can be seen from fig. 12, the numerical simulation and theoretical prediction results are better matched with the experimentally measured stress-strain curve in the first stage, the theoretical value can also better predict the experimentally measured platform height in the second stage, the stress-strain curve obtained by numerical simulation does not present an obvious stress platform in the second stage, and the equivalent compression stiffness in the theoretical prediction in the second stage is obviously higher than the experimental value, because the vertical rod is assumed to be not deformed when the bearing configuration in the second stage is theoretically analyzed, but actually in the compression process, when the end node of the vertical rod contacts with the loading surface to form the second bearing sub-configuration, the vertical rod generates micro-bending in the surface, which greatly reduces the equivalent stiffness in the second stage. In the latter half of the second stage of the stress-strain curve, the experimental value is relatively close to the rising trend of numerical simulation, while theoretical prediction simplifies the analysis model, and the theoretical value is far away from the experimental and numerical simulation results in the latter half of the second stage because the stress remains unchanged from the formation of plastic hinges in the center of the vertical rods to the densification of the structure.
3) The analysis of the lattice structure and the compact lattice structure can show that the position of the plastic hinge plays a vital role in the transformation of the butterfly lattice structure configuration, the forming position of the plastic hinge on the diagonal rod can be changed within a certain range by changing the length of the vertical rod in the butterfly lattice structure, and then the length and the height of each stage of stress platform of the stress-strain curve are changed, so that the multi-stage controllable mechanical behavior of the stress-strain curve of the butterfly lattice structure with bending dominant is realized.
As shown in fig. 13, based on the compact lattice structure, three kinds of vertical rod lengths of 10.6mm,13.6mm and 16.6mm were selected, and the relative densities were 2.55%,2.69% and 2.85%, respectively. The out-of-plane compression response of a dense lattice structure with a relative density of 2.69% has been given above, and the out-of-plane compression response of two other sets of lattice structures with relative densities are analyzed below.
Fig. 14 and 15 show the transformation process of the configuration and the equivalent stress strain curve under the action of the compressive load outside the plane of the compact lattice structure with the length of the vertical rod of 10.6mm respectively, and it can be seen from fig. 14 that the transformation mode of the configuration obtained by the lattice structure experiment and the numerical simulation is consistent, the transformation of the configuration is stable, the forming position of the plastic hinge on the diagonal rod moves downwards along with the reduction of the length of the vertical rod, the stroke required by the transformation of the compact lattice structure from the initial configuration to the next bearing sub-configuration is obviously increased, and the second bearing configuration is formed when the strain is 0.5. As can be seen from fig. 15, the stress-strain curves obtained by the experiment have two stress platforms in total and rise step by step, the first stress platform has a longer length, about 0.45 compressive strain, the stress of the platform is smaller, about 0.65MPa, the second stress platform has a shorter length, about 0.07, and the stress of the platform is larger, about 0.58MPa. The stress-strain curve obtained through simulation is relatively similar to the experimental result in both numerical value and ascending trend, the stress-strain curve predicted by theory is basically consistent with the experimental and numerical simulation results in the first-stage stress platform section, but the second-stage stress platform height of the theoretical predicted value is obviously smaller than the experimental and simulation results, and the length of the second-stage stress platform predicted by theory is longer.
4) Fig. 16 and 17 show the transformation process of the configuration and the equivalent stress strain curve under the action of the compressive load outside the plane of the compact lattice structure with the length of the vertical rod of 16.6mm respectively, and it can be seen from fig. 16 that the deformation modes obtained by the experiment and numerical simulation of the compact lattice structure are basically consistent, the transformation of the configuration becomes insignificant, and the vertical rod starts to bend before the plastic hinge on the diagonal rod contacts with the loading surface, so that the lattice structure does not form an obvious second carrier structure. As can be seen from FIG. 16, the rod member is deformed to a greater extent, and a part of the soldered joint of the diagonal rod is detached, because the length of the vertical rod is increased, the instability of the in-plane deformation of the lattice rod member is increased, and a higher stress value is generated at the rod end joint, so that the soldered joint is more easily damaged.
As can be seen from fig. 17, the experimentally obtained stress-strain curve has only a long stress plateau, with a plateau height of about 1.2MPa and a length of about 0.7, before densification occurs. The initial peak height of the simulated stress-strain curve is slightly higher than the experimental value, and the stress gradually rises after the strain is greater than 0.4, and the difference between the stress-strain curve and the experimental value gradually becomes larger. The theoretical predicted stress-strain curve is consistent with the experimental value in the platform height and length.
5) Fig. 18 shows the experimental results of the out-of-plane compressive stress strain curves of the compact lattice structures with three different vertical rod lengths, and it can be seen from the figure that the lengths of the vertical rods play a critical role in the heights and the lengths of the first-stage stress platform and the second-stage stress platform, the stress of the first-stage stress platform becomes smaller along with the decrease of the vertical rod length, the stress of the second-stage stress platform becomes larger along with the decrease of the vertical rod length, the smaller the vertical rod length is in a certain range, the larger the height difference between the two-stage stress platforms is, and conversely, when the vertical rod length increases to a certain extent, the height difference between the two-stage stress platforms gradually disappears, and becomes a longer stress platform. The length of the first-stage stress platform is increased along with the reduction of the length of the vertical rod, and the change rule of the length of the second-stage stress platform is opposite.
Fig. 19 shows the specific energy absorption change during compression of a lattice structure for three different vertical rod lengths. It can be seen from the graph that the lattice structure with the lengths of the vertical rods of 10.6mm and 13.6mm has two sections of approximately constant energy absorption rate (slope) compared with the energy absorption curve, and the energy absorption rate of the first section is obviously lower than that of the second section. And the specific energy absorption of the lattice structure with the length of the vertical rods being 16.6mm is increased linearly at an approximately constant energy absorption rate. The energy absorption rate is linearly related to the height of the stress platform, and the higher the amplitude of the stress platform is, the greater the energy absorption rate is, and the multistage stress platform corresponds to a plurality of energy absorption rates. The lattice structure ratio energy absorption of the vertical rod length of 16.6mm is maximum when the compressive strain is smaller than 0.48, and the lattice structure ratio energy absorption of the vertical rod length of 13.6mm is maximum when the strain is larger than 0.48.
According to the analysis of the embodiments, the amplitude and the length of each stage of stress platform in the multistage progressive energy absorption curve can be quantitatively regulated and controlled by reasonably setting the length of the vertical rods in the bending dominant lattice structure.
According to the embodiment, theoretical prediction of each stage of a multi-level stress-strain curve can be realized through the established butterfly-type lattice structure configurations with two densities, experiments and numerical simulation researches under out-of-plane compression loads of the two types of lattice structures are carried out, and feasibility of realizing gradual rising and gradual energy absorption of the stress-strain curve through configuration transformation and applicability of a theoretical model are verified. The method is determined to have stronger stability in transformation of the compact lattice structure configuration. In addition, the amplitude and the length of each level of stress platform in the energy absorption curve can be adjusted and controlled by changing the length of the vertical rod in the lattice structure.
By now it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been shown and described herein in detail, many other variations or modifications of the invention consistent with the principles of the invention may be directly ascertained or inferred from the present disclosure without departing from the spirit and scope of the invention. Accordingly, the scope of the present invention should be understood and deemed to cover all such other variations or modifications.
Claims (6)
1. The multi-stage controllable progressive energy-absorbing lattice structure is characterized by comprising,
the splicing rod piece comprises two X-shaped orthogonal connecting diagonal rods, vertical rods for connecting the two diagonal rods are respectively arranged on two sides of the horizontal direction of the connecting point of the two diagonal rods, and the connecting positions of the two vertical rods are mutually corresponding and mutually parallel;
the unit cell structure is formed by connecting points of two spliced rod pieces in an orthogonal interlocking assembly mode;
the lattice structure is formed by mutually connecting a plurality of unit cell structures on a plane through adjacent diagonal rod endpoints, and interlocking positions of the unit cell structures are fixed by vacuum brazing;
the density of the lattice structure needs to satisfy the following conditions:
the relative density of the lattice structureDividing the density of the lattice structure by the density of the matrix material of the lattice structure,
wherein the inclination angle omega=45° of the diagonal rods, all the spliced rod pieces are square sections, t is the width of the clamping groove, w is the width of the spliced rod pieces, t=w, b is the length of the supporting section,h is the height of the clamping groove tab A height w above the support section; l is the distance from the connecting point of the diagonal rod to the supporting section, l 2 Length of the vertical rod; />The thickness of the bottom of the clamping groove is the thickness;
further simplified into:
neglecting the effect of node volume, the following formula is obtained for an ideal lattice structure:
the relative density of a dense lattice structure is related to the number of periods of the lattice structure, then:
in the method, in the process of the invention,n 1 ,n 2 the number of cell periods of the compact lattice structure along the X and Y directions is respectively that when n 1 ，n 2 When > 1, ">
According to the connection state of the inclined rods on one side of the lattice structure, the side edge is divided into a free side which is not connected with other inclined rods and a closed side which is connected with other inclined rods; after the lattice structure receives pressure on a plane, the integral stress curve change is divided into three stages, wherein the strain calculation formula in the first stage is as follows:
first, the lattice structure equivalent stiffness in this state is calculated:
when one side of the lattice structure is a free side, the equivalent stiffness is calculated as follows:
wherein A is cell ＝(2l cosω+b+t) 2 Representing the cross-sectional area of the lattice structure, l 1 Is the distance between the vertical rod connecting point and the inclined rod end point on the inclined rod, H is the distance between the top supporting point and the bottom supporting point, F 1 Is a pressure applied vertically to the lattice structure;
when one side of the lattice structure is a closed side, the equivalent stiffness is calculated as follows:
the lattice structure is subjected to an equivalent stiffness of:
wherein the method comprises the steps ofN 2 ＝1-N 1 ；
The equivalent rigidity suffered by the compact lattice structure is as follows:
wherein the method comprises the steps ofN 4 ＝2(1-N 3 )；
The equivalent compressive strength of the lattice structure in the first stage is calculated as follows:
the equivalent compressive strength of the lattice structure is the linear superposition of the strength corresponding to the free side and the closed side respectively, and the calculation formula is as follows:
the equivalent compressive strength calculation formula of the compact lattice structure is as follows:
the strain at the end of the first phase is:
the equivalent stiffness of the lattice structure in the second stage is calculated as follows:
wherein the method comprises the steps of
The equivalent compressive strength of the lattice structure is calculated as follows:
the equivalent compressive strength of the compact lattice structure is calculated as follows:
wherein the method comprises the steps of
2. The multi-stage controllable progressive energy absorbing lattice structure of claim 1,
the single-cell structure is connected with the inclined rod end points of the lattice structure in an interlocking manner through the end points of the inclined rods on two sides, and the connecting points of the single-cell structure are located at the center surrounded by the inclined rods of the four lattice structures.
3. The multi-stage controllable progressive energy absorbing lattice structure of claim 2,
the splicing rod pieces are formed by directly cutting stainless steel plates through laser, the splicing rod pieces in the same row are directly connected together through the end parts of the diagonal rods, the cross sections of the diagonal rods and the vertical rods are square with the same area, and horizontal supporting sections are arranged at the end parts of the diagonal rods.
4. The multi-stage controllable progressive energy absorbing lattice structure of claim 3,
the structure of the interlocking lock is as follows: a clamping groove recessed towards the direction of the connecting point is formed in the connecting point of the spliced rod pieces, and the two spliced rod pieces are mutually inserted in opposite mode through the clamping groove and then connected to form the unit cell structure;
in the compact lattice structure, clamping grooves which are opened towards the top supporting point are respectively arranged at the connecting points of the complementary rod pieces and the inclined rod connecting points at the top supporting point;
the two spliced rod pieces are connected with each other and serve as inclined rod connection points of bottom supporting points, clamping grooves which are opened towards the direction of top supporting points are formed in the positions, corresponding to the clamping grooves, of the inclined rods of the two spliced rod pieces, the inclined rods of the two spliced rod pieces are of a disconnection structure, and the disconnection distance is the same as the diameter of the supplementary rod pieces.
5. The multi-stage controllable progressive energy absorbing lattice structure of claim 1, wherein the step of vacuum brazing is as follows:
step 100, uniformly coating Ni-7Gr-4.5Si-3.1B-3Fe brazing solder) on all the joint points of the clamping grooves of the lattice structure;
step 200, placing the lattice structure into a vacuum brazing furnace, heating to 950 ℃ at a heating speed of 15 ℃/min, maintaining the temperature of 950 ℃ for 30-60 min to uniformly heat the whole lattice structure, heating to 1050 ℃ at a heating speed of 20 ℃/min, and heating to 2X 10 2 Maintaining the pressure of Pa for 6-10min, and naturally cooling to room temperature;
and 300, applying a preset load on the upper and lower surfaces of the lattice structure in the brazing process so as to ensure the welding quality and reduce the warping phenomenon caused by thermal stress.
6. The multi-stage controllable progressive energy absorbing lattice structure of claim 1,
the fixed position and the length of the vertical rod are adjusted according to the preset stress requirement, and the forming position of the plastic hinge of the lattice structure after being stressed is changed by adjusting the fixed position and the corresponding length of the vertical rod and the inclined rod, so that the aim of adjusting the stress-strain curve of the lattice structure is finally achieved.
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