CN111783255B - Design method of axis compression member based on microscale and axis compression member - Google Patents
Design method of axis compression member based on microscale and axis compression member Download PDFInfo
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- 239000000463 material Substances 0.000 claims abstract description 18
- 238000004364 calculation method Methods 0.000 claims abstract description 7
- 229910000831 Steel Inorganic materials 0.000 claims description 36
- 239000010959 steel Substances 0.000 claims description 36
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- 239000013589 supplement Substances 0.000 abstract description 2
- 239000011859 microparticle Substances 0.000 description 4
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- 241001131688 Coracias garrulus Species 0.000 description 2
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical group [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 description 2
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Abstract
The invention discloses a design method of an axle center compression member based on microscopic scale and the axle center compression member, firstly determining the size of macroscopic particles according to the actual type of materials and the external environment; then determining Morse potential function parameters; then establishing a microstructure model, establishing a microstructure model and establishing a macroscopic structure model; finally, obtaining the minimum value of the thickness of the axial compression member; the invention supplements the existing material strength calculation method, and essentially analyzes the reasons of material deformation and damage. The design based on the design method is more accurate, and the cost can be greatly saved.
Description
Technical Field
The invention belongs to the technical field of molecular dynamics analysis, relates to a design method of an axial tension member and the axial tension member, and in particular relates to a method for designing a pressed steel plate on the basis of researching the internal microstructure composition and the action effect of materials and the axial tension member.
Background
The existing steel structure design principle is obtained through experiments, and the adoption of the existing steel structure design principle is based on experience. The micro composition and performance of the material essence are not considered, the stability problem, the fatigue problem, the low-temperature cold embrittlement and the welding residual stress which are commonly encountered in the steel structure theory are not fully explained by the micro essence, the influence of the working environment factors is not considered, the structural design is not enough, and the design precision is far insufficient.
Although a model is proposed in the patent "a design method of pressed steel sheet based on multi-scale analysis" (ZL 2015 1 0565815.9), the interaction between microscopic unit bodies in the patent adopts L-J potential, however, the L-J potential is mainly used to describe the interaction force between molecules, and it is not reasonable to use it to simulate the interaction between iron atoms. The patent uses rollers to achieve shear slippage, but the displacement of the rollers is limited and does not simulate the elastoplastic and plastic phases well. The microscopic model built in this patent will undergo plastic deformation, i.e. roller movement, upon application of force. However, it is realistic that the crystal skeleton is plastically deformed after a certain stress state (e.g., yield stress) is reached, and it is not appropriate to simulate the plastic deformation by using a roller. The tensile or compressive strength of the macroscopic model established in this patent is not the same in all directions, however, the reality is that most materials are isotropic.
Disclosure of Invention
In order to solve the technical problems, the invention provides a design method of an axle center compression member based on a microscale and the axle center compression member, wherein the performance strength of a compression steel plate is researched from multiple layers, and the compression steel plate is subjected to simulation analysis and design on the basis.
The technical scheme adopted by the invention is as follows: a design method of an axle center compression member based on microscopic scale is characterized by comprising the following steps: establishing a microstructure model by using a Morse potential function to simulate interaction of atoms in the steel structure material;
the specific implementation method comprises the following steps:
step 1: determining the size of macro-particles according to the actual type of the material and the external environment;
step 2: determining Morse potential function parameters including the side length l (unit mm) of the cubic particles, and the interaction force f between the cubic particles ij (unit N), distance r between centers of two cubic particles ij (Unit) Balanced bond length r o (Unit->) Equilibrium binding energy ε (units eV), inverse length factor α (units +.>) Distance r between when the spring between two cubic particles reaches yield strength 1 (unit mm), distance r between when the spring between two cubic particles reaches its tensile strength 2 (unit mm), cubeDistance r between particles when attraction between particles reaches maximum m Elastic coefficient of spring between two cubic particles (unit mm)>(unit N/mm), the yield strength of the spring between two cube particles +.>(unit N/mm), the tensile strength of the spring between two cubic particles +.>Length of macroparticles a (unit N/mm), width of macroparticles b (unit mm), height of macroparticles c (unit mm), length of steel plate L (unit mm), width of steel plate W (unit mm), thickness of steel plate t (unit mm), load design value parallel to plate surface (unit N);
step 3: establishing a microstructure model;
the microstructure model consists of two microscopic particles, and interaction between the particles is simulated by a sliding block and a spring; the length of the particles is l, and the interaction between the particles adopts Morse potential, so that the interaction force between the particles is obtained as follows:
the parameter eta in the formula ij 、α 0 Is a dimensionless quantity;
α 0 ＝αr 0 ； (3)
defining the magnitude of the spring constant in the modelSince the elastic deformation amount of the metal crystal is small,the spring constant can be defined as the equilibrium position r 0 Slope at, i.e.:
let the inter-particle distance be r m When the attraction between the particles reaches the maximum, f ij ′(r m ) =0, obtained:
let r be 1 ＝β 1 r m When the spring between the two particles reaches the yield strengthThen:
let r be 2 ＝r 1 +β 2 When the spring between the two particles reaches the tensile strengthThen:
step 4: establishing a mesoscopic structure model;
the microstructure models are arranged in two mutually perpendicular directions by a plurality of microstructure models; the length, width and height of the mesoscopic structural model are respectively a, b and c;
in the plane formed by the length and the width, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
in the plane formed by the length and the height, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
in the plane formed by the width and the height, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
step 5: building up a macrostructure model (volume 1 mm) 3 ) The length, width and height are 1mm;
the macroscopic structure model consists of a plurality of microscopic structure models which are irregularly arranged; in each plane, the number of springs connected in parallel is as follows:
wherein, min { ab, ac, bc } is the minimum value of the three;
the tensile strength of the macrostructure model is:
step 6: obtaining the minimum value of the thickness of the axial compression member;
the length, width and thickness of the steel plate are known as L, W and t, respectively; when the load design value parallel to the middle surface of the plate end and the plate is Q, in order to ensure that the steel plate is not damaged in strength, the following requirements are met:
then, the axial compression member thickness t is:
in order to ensure that the steel plate is not unstable, the following conditions are satisfied:
namely:
wherein a represents the cross-sectional area of the plate; lambda represents slenderness ratio, and the calculation formula isi is the radius of gyration of the cross section.
The invention also provides an interaction simulation device between particles, which is characterized in that: comprises microscopic particles, springs and sliding blocks; the microscopic particles are an entity made up of a plurality of atoms; the number of the micro particles is two, and the two micro particles are connected with the sliding block through a spring.
The invention also provides an axle center compression member, which is characterized in that: the preparation method is characterized by comprising the following steps. Aiming at the prior art, the invention has the beneficial effects that:
1. based on the principle of molecular dynamics, a microstructure model is established to simulate the deformation and damage mechanism of the material under the action of external force, so that the material is designed more accurately, and the cost is greatly saved.
2. Supplement the existing macroscopic steel structure stability theory, and propose a new method for designing structural members.
3. And the microstructure and performance relationship of the material is established by utilizing microscopic, microscopic and macroscopic structural models, so that a better explanation is made on the degradation mechanism of the stress performance of the steel structure on a macroscopic scale.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic illustration of the creation of a microstructure model according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the dimensions of a mesostructured model according to an embodiment of the invention;
FIG. 4 is a schematic illustration of interactions between mesostructured models according to an embodiment of the invention;
FIG. 5 is a diagram of a macrostructure model of an embodiment of the present invention.
Detailed Description
In order to facilitate the understanding and practice of the invention, those of ordinary skill in the art will now make further details with reference to the drawings and examples, it being understood that the examples described herein are for the purpose of illustration and explanation only and are not intended to limit the invention thereto.
Referring to fig. 1, the invention provides a design method of an axial compression member based on a microscale, which adopts a Morse potential function to describe interaction of cubic particles in a steel structure material. Firstly, determining the size of macroscopic particles according to the actual type of the material and the external environment, and secondly, determining parameters related to a Morse potential function. The above relevant symbols and their meanings are shown in Table 1;
table 1 symbols and meanings
Based on the above definition, the calculation method of the present invention comprises the following steps:
step 1: a microstructure model is built, as shown in fig. 2, where 1 is a microscopic particle, 2 is a spring, and 3 is a slider. Microscopic particles can be considered as a whole made up of many atoms. The number of the micro particles 1 is two, and the two micro particles 1 are connected with the sliding block 3 through the spring 2. The slider 3 is composed of elements with a certain coefficient of friction damping, which can be actuated, i.e. plastically deformed, after the spring has reached a certain stress state.
Step 2: the microstructure model is arranged by a plurality of microstructure models in two mutually perpendicular directions, as shown in fig. 3; FIG. 4 is a schematic illustration of interactions between mesostructured models according to an embodiment of the invention
Step 3: building up a macrostructure model (volume 1 mm) 3 ) The length, width and height are all 1mm. As shown in fig. 5; the macrostructure model is composed of an irregular arrangement of a plurality of microstructure models.
Step 4: the length, width and thickness of the steel plate are known as L, W and t, respectively; when the load design value parallel to the middle plane of the plate at the plate end is Q, calculating the thickness t (unit mm) of the plate; thus, under the condition of building macroscopic external force, the minimum value of the thickness of the steel plate is obtained through the calculation steps.
The method is characterized in that when in specific implementation:
1. determining particle equilibrium radius r based on material quality and ambient temperature 0 The method comprises the steps of carrying out a first treatment on the surface of the The elastic coefficient of the springs between the particles can be calculated by using the formula (4)The maximum attractive force between particles can be calculated by using the formula (5)Inter-grain distance r m The method comprises the steps of carrying out a first treatment on the surface of the On the basis of this, the inter-particle distance r when the yield strength of the spring between the two particles is reached can be determined 1 Inter-particle distance r at which its compressive strength is reached 2 。
2. The yield strength of the two inter-particle springs can be determined by the formulas (6) and (7)And compressive Strength +.>
3. The length, width and height of the microstructure model are a, b and c respectively, and the microstructure model is formed by arranging a plurality of microstructure models in two mutually perpendicular directions, as shown in fig. 3. The number of springs and the compressive strength which are connected in parallel in each plane of the microstructure model can be obtained by the formulas (8) - (13).
4. The macrostructure model is composed of an irregular arrangement of a plurality of microstructure models, as shown in fig. 4. Based on the result in the step 3, the number of springs and the compressive strength of the macrostructure model which are connected in parallel in each plane can be obtained.
5. When the load design value parallel to the middle plane of the plate at the plate end is Q, the thickness can be obtained by using the formulas (17) and (19). Thus, under the condition of building macroscopic external force, the minimum value of the thickness of the steel plate is obtained through the calculation steps.
Compared with the existing steel structure design method, the invention has the advantages that:
the four-sided hinge steel plate of this example was a steel Q345, the ambient temperature was room temperature (20 ℃), and the plate end load design value parallel to the plate center plane was q=520×10 3 N, length l=5.0m, width w=400 mm, slenderness ratio 60, and plate thickness t was measured.
(1) Macroscopic design methods of the prior art;
at the ambient temperature of normal temperature (20 ℃), according to the elastic stability theory, the maximum stress (i.e. critical stress) that the plate can bear in a stable state is related to the shape, size, supporting condition, stress condition and the like of the plate, and the critical stress of the plate can be expressed by the following formula:
wherein χ is the elastic constraint coefficient of the plate edge; beta is the buckling coefficient; η is an elastic modulus reduction coefficient, and may be taken as:
η＝0.1013λ 2 (1-0.0248λ 2 f y /E)f y /E (21)；
since the plate is a four-sided hinged steel plate, the buckling coefficient β is 4 at this time. The elastic constraint coefficient χ=1.3 is desirable according to the test. Calculated η=0.475, so by:
the method can obtain:
t＞6.7mm(23)；
calculated from intensity:
the method can obtain:
t＞4.2mm (25)；
thus, the thickness t of the plate is more than 6.7mm.
(2) The design method of the invention;
it is known that: at the ambient temperature of normal temperature (20 ℃), the material is Fe with the equilibrium radius ofDissociation energy of ε= 0.4172eV, inverse length factor +.>The size of the macroscopic particle body is as follows: a=20 μm, b=10 μm and c=30 μm; coefficient beta related to yield and compressive strength of spring between two particles in microscopic particle model 1 And beta 2 The values are 0.8515 and 2.87 multiplied by 10 respectively -10 . Solving:
when the attraction between two particles reaches the maximum, the distance between the particles is as follows:
when the spring between two particles reaches its yield strength, the distance between the particles is:
r 1 ＝0.851r m ＝2.8474×10 -7 mm (27)；
when the spring between two particles reaches the compression strength, the distance between the particles is as follows:
r 2 ＝r 1 +2.87×10 -10 ＝2.8493×10 -7 mm(28)；
spring coefficient of spring between two particles:
the spring between the two particles reaches the compression strength
The compressive strength of the macrostructure model is:
the compressive strength here has a value that is greater than the yield strength of the Q345 steel in the first method. To ensure that the steel plate has sufficient strength, then:
in order to ensure that the steel plate does not lose stability, the following steps are:
thus, the thickness t of the plate is more than 2.3mm.
Comparing the two methods, the second design method is more accurate. Assuming that the accuracy is improved by δ, the calculation formula is as follows:
therefore, the second method has an improvement in accuracy of 65.7% compared to the first method.
The invention is affected by external factors:
(1) Most elastoplastic metal materials consist of a crystalline skeleton which, upon being subjected to a force, is elastically deformed, here by a spring to simulate the elastic deformation. The crystal skeleton can be subjected to plastic deformation immediately after reaching a certain stress state (such as yield stress), and the sliding block is used for simulating elastic deformation. When there are welding residual stress and fatigue cracks in the steel sheet, it can be simulated that the part of the spring between the fine grain bodies breaks, i.e., n will decrease, as seen from the formula (17), at which time the value of the sheet thickness t will increase.
(2) Considering external factors such as welding process, fatigue crack, low temperature and dynamic load, etc., the balance distance r between the particles is the actual fact,the values, the effect of the microstructure of the material such as yield strength, etc., thus macroscopically showing a more accurate explanation of the deterioration of the stress properties of the steel structure under the influence of the above-mentioned factors.
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the foregoing description of the preferred embodiment is not intended to limit the scope of the invention. Those skilled in the art can make substitutions and alterations without departing from the scope of the invention as defined by the appended claims, which are intended to be embraced by the claims.
Claims (2)
1. A design method of an axle center compression member based on microscopic scale is characterized by comprising the following steps: establishing a microstructure model by using a Morse potential function to simulate interaction of atoms in the steel structure material;
the specific implementation method comprises the following steps:
step 1: determining the size of macro-particles according to the actual type of the material and the external environment;
step 2: determining Morse potential function parameters, including the side length l of the cubic particles, and unit mm; interaction forces f between cubic particles ij Unit N; distance r between centers of two cubic particles ij Units ofBalance combined length r o Unit->Equilibrium binding energy ω, in eV; inverse length factor α, unit->Distance r between when the spring between two cubic particles reaches yield strength 1 Unit mm; distance r between the two cubic particles when the spring reaches its tensile strength 2 Unit mm; distance r between when attraction between cubic particles reaches maximum m Unit mm; spring coefficient of spring between two cubic particles +.>Unit N/mm; yield strength of spring between two cube particles +.>Unit N/mm; tensile Strength of spring between two cubic particles +.>Unit N/mm; the length a of the macro-particle body is in mm; the width b of the macro-particle body is unit mm; the height c of the macro-particle body is in mm; the length L of the steel plate is in mm; the width W of the steel plate is in mm; the thickness t of the steel plate is in mm; load design value parallel to the plate surface, unit N;
step 3: establishing a microstructure model;
the microstructure model consists of two microscopic particles, and interaction between the particles is simulated by a sliding block and a spring; the length of the particles is l, and the interaction between the particles adopts Morse potential, so that the interaction force between the particles is obtained as follows:
the parameter eta in the formula ij 、α 0 Is a dimensionless quantity;
α 0 ＝αr 0 ；
defining the magnitude of the spring constant in the modelDefining the spring constant as the equilibrium position r 0 Slope at, i.e.:
let the inter-particle distance be r m When the attraction between the particles reaches the maximum, f ij ′(r m ) =0, obtained:
let r be 1 ＝β 1 r m When the spring between the two particles reaches the yield strengthThen:
let r be 2 ＝r 1 +β 2 When the spring between the two particles reaches the tensile strengthThen:
wherein beta is 1 And beta 2 Is a coefficient related to the yield strength and compressive strength of the spring between two particles in the microscopic particle model;
step 4: establishing a mesoscopic structure model;
the microstructure models are arranged in two mutually perpendicular directions by a plurality of microstructure models; the length, width and height of the mesoscopic structural model are respectively a, b and c;
in the plane formed by the length and the width, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
in the plane formed by the length and the height, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
in the plane formed by the width and the height, the number of the springs connected in parallel is as follows:
the tensile strength in this plane is:
step 5: establishing a macroscopic structure model;
the macroscopic structure model consists of a plurality of microscopic structure models which are irregularly arranged; in each plane, the number of springs connected in parallel is as follows:
wherein, min { ab, ac, bc } is the minimum value of the three;
the tensile strength of the macrostructure model is:
step 6: obtaining the minimum value of the thickness of the axial compression member;
the length, width and thickness of the steel plate are known as L, W and t, respectively; when the load design value parallel to the middle surface of the plate end and the plate is Q, in order to ensure that the steel plate is not damaged in strength, the following requirements are met:
namely:
in order to ensure that the steel plate is not unstable, the following conditions are satisfied:
namely:
wherein a represents the cross-sectional area of the plate; lambda represents slenderness ratio, and the calculation formula isi is the radius of gyration of the cross section.
2. An axial compression member, characterized in that: is made by the method of claim 1.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH1153414A (en) * | 1997-08-01 | 1999-02-26 | Ii R C:Kk | Designing method for material and structure by combined analysis of molecule simulation method and homogenizing method |
| CN105046029A (en) * | 2015-09-08 | 2015-11-11 | 武汉大学 | Pressed steel plate design method based on multiscale analysis |
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| WO2017177233A2 (en) * | 2016-04-08 | 2017-10-12 | Northwestern University | Optimized gamma-prime strengthened austenitic trip steel and designing methods of same |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH1153414A (en) * | 1997-08-01 | 1999-02-26 | Ii R C:Kk | Designing method for material and structure by combined analysis of molecule simulation method and homogenizing method |
| CN105046029A (en) * | 2015-09-08 | 2015-11-11 | 武汉大学 | Pressed steel plate design method based on multiscale analysis |
Non-Patent Citations (2)
| Title |
|---|
| 摩擦界面微区受限颗粒体非稳态行为特性的研究;侯淑晴;基础科学;7 * |
| 铁电纳米复合材料的电畴结构和储能效率研究;朱道佩;工程科技I辑;全文 * |
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