1. A microscopic scale fine modeling simulation method of a hollow sphere-metal matrix three-phase composite material is characterized by comprising the following steps:

firstly, a single cell structure of an equivalent body-centered cubic homogenization model is reproduced, and a mapping relation between the single cell structure and a target hollow sphere-metal matrix three-phase composite material structure is established, wherein the specific method comprises the following steps:

(1) according to the geometric parameters and the target porosity of each composition phase of the hollow sphere-metal matrix three-phase composite material, a single cell structure of the equivalent body-centered cubic homogenization model is reproduced:

arranging a ball base of the hollow ball-metal matrix three-phase composite material in an equivalent homogenized body-centered cubic form, and reducing the body-centered cubic stacking porosity by increasing the distance between the hollow balls to obtain a cell structure which is extremely similar to that of a real hollow ball-metal matrix three-phase composite material; extracting an equivalent core cubic unit cell structure from the integral model, wherein the cubic unit cell structure and the hollow sphere-metal matrix three-phase material have the same porosity and are as follows:

wherein, V_dIs the volume of a cubic cell in mm³；V_dmIs the matrix volume of a cubic cell element in mm³；V_dsThe volume of the hollow ball is cubic cell element and is in mm³；V_dhIs the volume of the pores of the cubic cell in mm³；

The side length of the single cubic unit cell is:

wherein a is the side length of a cubic cell element and the unit is mm; r is the external radius of the hollow ball, and the unit is mm; t is the wall thickness of the hollow sphere in mm;

(2) establishing a mapping relation between a single cell structure and a target hollow sphere-metal matrix three-phase composite structure;

assuming that the target structure model is a cuboid, the target model is placed under a Cartesian coordinate system, and in order to eliminate the boundary effect of the hollow sphere-metal matrix three-phase composite material, the number of the hollow spheres and the number of the single cell elements in any direction of the simulation model meet the following requirements:

N_dmin＝N_min-1 (6)

wherein N is_dminThe minimum value of the number of single cells in any direction of the target model is used for eliminating the boundary effect; n is a radical of_minThe minimum value of the number of the hollow spheres in any direction of the target model is used for eliminating the boundary effect;

the geometric parameters of the model are then:

L_x＝m·a(N_dmin≤m≤m_max) (7)

L_y＝n·a(N_dmin≤n≤n_max) (8)

L_z＝p·a(N_dmin≤p≤p_max) (9)

wherein L is_xThe length of the target model in the x direction is unit mm; l is_yThe length of the target model in the y direction is unit mm; l is_zThe length of the target model in the z direction is unit mm; m is the number of single cubic cell elements in the x direction of the target model; n is the number of single cubic cell elements in the y direction of the target model; p is the number of single cubic cell elements in the z direction of the target model; m is_maxThe maximum value of the number of single cubic cell elements in the x direction of the target model; n is_maxThe maximum value of the number of single cubic cell elements in the y direction of the target model; p is a radical of_maxThe maximum value of the number of single cubic cell elements in the z direction of the target model;

namely, establishing the quantity and geometric mapping relation between a single cell structure and a target hollow sphere-metal matrix three-phase composite material structure;

secondly, creating a target structure geometric model according to the overall dimension of the target hollow sphere-metal matrix three-phase composite material structure, the ball base distribution rule of the hollow sphere-metal matrix three-phase composite material and the topological structure relationship among the ball bases, wherein the target structure geometric model specifically comprises the following steps:

(1) in a Cartesian coordinate system, the values are (0, 0, 0) and (L)_x，0，0)、(0，L_y，0)、(0，0，L_z) Creating a target sample geometric entity for the base point;

(2) creating a first layer of hollow sphere coordinate points in the X-O-Z plane where y is 0, namely:

P_i,j,k＝(ia,ja,ka)(i＝0,1,···,m,k＝0,1,···,p,j＝0) (10)

(3) in thatCreates a second layer of hollow sphere coordinate points, namely:

(4) linearly copying the two layers of coordinate points into arrays along the positive direction of the Y axis, wherein the number of the arrays is n, the array interval is a, and the unit is mm; linearly copying the first layer of coordinate points into an array along the positive direction of the Y axis, wherein the array number is 2, the array pitch is na, and the unit mm is obtained, and finally obtaining the coordinate points of the spherical center positions of the hollow spheres;

(5) creating a solid sphere at the sphere center coordinate point of the hollow sphere, wherein the sphere radius is the internal radius r of the hollow sphere:

r＝R-t (12)

removing a spherical entity with radius r created at a sphere center coordinate point in the sample entity through Boolean subtraction operation to obtain a porous entity model;

(6) creating a curved surface of the outer wall of the hollow ball at the position of the position coordinate of the center of the ball generated in the step (4), wherein the radius of the curved surface is the same as the size of the outer radius of the hollow ball; cutting the solid body through a curved surface, and cutting the porous solid body model obtained in the step (5) by using the curved surface of the outer wall of the hollow ball;

obtaining a hollow sphere with the wall thickness of (R-R) and a porous matrix through cutting, wherein the topological state of the curved surfaces between the hollow sphere and the porous matrix is a shared curved surface, and a 2D grid is created by taking the shared curved surface as a target surface to obtain a geometric model of the hollow sphere-metal matrix three-phase composite material structure;

and thirdly, endowing material properties and node constraint conditions for discrete units of the hollow sphere-metal matrix three-phase composite material:

(1) dispersing the geometric model of the hollow sphere-metal matrix three-phase composite material structure into various units, and performing displacement interpolation on the dispersed unit nodes;

the change relation between the position and the time of each part node of the geometric model of the hollow sphere-metal matrix three-phase composite material structure is expressed by the coordinate interpolation value of the discrete unit node as follows:

wherein, i is 1,2,3 is a space coordinate index; 1,2, n represents a finite element node; wherein mu_iIRepresenting the displacement of the ith node of the unit in the I direction; n is a radical of_I(x, y, z) is the Lagrangian interpolation function of the I node;

triangular two-dimensional unit surface mesh processing is carried out on the hollow sphere-metal matrix three-phase composite material, so that the surface mesh is consistent with the attribute of a complex geometric surface and meets the following requirements:

p≤t (14)

wherein p is the two-dimensional grid size; t is the wall thickness of the hollow sphere;

selecting a hollow sphere-metal matrix three-phase composite material geometric model generated in the second step of ten-node tetrahedral unit dispersion, automatically generating smaller grid units in a compact structure area, keeping the consistency of the grid surface and the target structure geometric model generated in the second step to the maximum extent, and ensuring that the tetrahedral grid and the two-dimensional grid have correlation when dispersing entities, and meeting the following requirements:

p′≤t (15)

wherein p' is the size of a ten-node tetrahedral unit; t is the wall thickness of the hollow sphere;

obtaining hollow sphere-metal matrix three-phase composite discrete units after dispersion, wherein the hollow sphere-metal matrix three-phase composite discrete units comprise hollow sphere discrete units obtained by dispersing a hollow sphere geometric structure and solid matrix discrete units obtained by dispersing a porous matrix geometric structure;

(2) giving material properties and node constraint conditions to the hollow sphere-metal matrix three-phase composite discrete units; the method comprises the following specific steps:

(a) setting a yield criterion, material parameters and a failure criterion for the hollow sphere discrete units and the solid matrix discrete units;

the hollow sphere and the matrix material are all made of isotropic ideal elastic-plastic metal materials, and the Young modulus, the yield strength, the mass density, the Poisson ratio, the tangent modulus, the failure parameters and the equivalent stress-strain curve of the materials are respectively defined for the hollow sphere discrete unit and the solid matrix discrete unit;

the discrete units of the hollow sphere and the solid matrix define material failure indexes according to effective plastic strain and minimum time step when the material fails, and when the equivalent plastic strain of the discrete units reaches an invalid value, the discrete units fail;

setting discrete unit attributes and cross section attributes, creating ten-node tetrahedral entity unit attributes and endowing the ten-node tetrahedral entity unit attributes to the hollow sphere and the solid matrix discrete unit;

(b) endowing node constraint conditions for the hollow sphere-metal matrix three-phase composite discrete unit nodes, namely establishing contact constraint at the hollow sphere-metal matrix three-phase composite discrete unit nodes;

the contact friction coefficient between the hollow ball and the discrete unit node of the solid matrix is determined by a plurality of groups of parameters:

wherein, mu_cIs the contact friction coefficient; FD is a dynamic friction factor; FS is the static friction factor; DC is an exponential decay coefficient; v. of_relIs the contact surface relative speed;

meanwhile, in view of the failure mode of the hollow sphere and the matrix composition phase, binding contact with failure criteria is required to be defined when the contact relation between the two unit nodes is simulated; when the binding contact failure is achieved after the contact failure criterion is met, the contact type between the hollow ball and the base unit node is converted into common contact;

when the contact surface units reach the interface limit separation distance, the contact points are completely damaged, the interface between the hollow sphere and the matrix is completely separated, and the brittle intermetallic phase between the hollow sphere and the matrix is completely damaged and fails to form a micro-crack on the outer side of the sphere wall;

obtaining a microscopic scale fine simulation model of the hollow sphere-metal matrix three-phase composite material through the three steps; and calculating the mechanical response and damage mode of the material under the target working condition, establishing a simulation model crack observation section of the material, and obtaining the interface failure and crack form of the hollow sphere-metal matrix three-phase composite material under the microscopic scale by observing the crack distribution of the section.

2. The hollow sphere-metal matrix three-phase composite material microscopic scale fine modeling simulation method according to claim 1, wherein in the step (2) (a) according to claim 1, isotropic Von Mises yield criterion is given to both the hollow sphere discrete units and the solid matrix discrete units, and the Von Mises yield criterion in a principal coordinate system is as follows:

wherein σ₁、σ₂、σ₃Is the principal stress of a unit in X, Y, Z directions under a Cartesian coordinate system_sIs the unit yield stress; the physical meaning of the method is that when the elastic modulus of the volume shape change of the hollow sphere and the solid matrix discrete unit reaches a certain constant, the unit mass point yields.

3. The hollow sphere-metal matrix three-phase composite material microscopic scale fine modeling simulation method according to claim 1 or 2, wherein in the step (2) (b), the contact failure criterion is as follows:

wherein σ_nAnd σ_sRespectively the normal stress and the shear stress of the contact surface in MPa; NFLS and SFLS are the corresponding contact surface failure normal stress and contact surface failure shear stress, respectively.

Background

The hollow sphere-metal matrix three-phase composite material is an advanced porous material, consists of the hollow metal spheres with the cell size, shape and wall thickness as set values and a solid metal matrix, and has high strength, high rigidity and excellent sound absorption performance, so that the hollow sphere-metal matrix three-phase composite material has wide application prospects in the fields of automobiles, aerospace, energy engineering, medical appliances and the like. Compared with the traditional foam metal material, the hollow sphere-metal matrix three-phase composite material has a uniformly distributed cell structure and firm sphere matrix bonding strength. Therefore, it has higher strength, rigidity and energy absorption capacity as an isotropic material. However, the microscopic structure and the mechanical property of the hollow sphere-metal matrix three-phase composite material are very complex, and a refined modeling simulation method of the composite material is the basis for researching the deformation mode and the damage mechanism of the material and is also the research focus in the field at present.

The modeling analysis of the hollow sphere-metal matrix three-phase composite material can be divided into two methods based on a macro scale and a micro scale, and the two methods respectively define and illustrate the material characteristics of the hollow sphere-metal matrix three-phase composite material from different angles. The modeling method on the macro scale ignores the influence of the hollow metal ball, is mainly based on the stress-strain curve of the hollow ball-metal matrix three-phase composite material under various strain rates, and is equivalent to the metal matrix three-phase composite material with complex material properties by adopting a homogenization method. Although the method can reflect the mechanical characteristics of the material under the target working condition on a macroscopic scale, the microscopic structure and the deformation damage mechanism of each composition phase of the material cannot be accurately represented. The material difference between the hollow sphere and the base material is ignored in the micro-scale modeling method, and a simulation model of the hollow sphere-metal matrix three-phase composite material non-spherical wall is established mainly based on the base material linear elastic stress strain curve. The method can reflect the deformation condition of the metal pores under given working conditions to a certain extent, but neglects the supporting and connecting action of the hollow sphere wall on the base material, so that the failure behavior of each composition phase cannot be given, namely the micro processes such as the connection failure between the base body and the hollow sphere interface, the crack propagation path of the base material and the like cannot be defined.

In 2019, Afsaneh Rabeii et al published "Ballistic performance of Composite metal foam against large ceramic three-phase composites Structures", the hollow ball-metal matrix three-phase Composite material is equivalent to a hollow ball-metal matrix three-phase Composite material with complex material properties by a homogenization method based on stress strain curves of the hollow ball-metal matrix three-phase Composite material under various strain rates, neglecting the influence of a hollow metal ball and a porous structure. Although the method can reflect the mechanical properties of the material under the target working condition on a macroscopic scale, the method has the defect that the microscopic structure and the deformation damage mechanism of each component phase of the material cannot be accurately represented. Therefore, in order to research the hollow sphere-metal matrix three-phase composite material, it is urgently needed to establish a microscopic scale model capable of reflecting the structural distribution and damage evolution of each component phase under different porosities, and the microscopic scale model is used for researching the connection failure between a substrate and a hollow sphere interface and the crack expansion path of the substrate material, namely, the microscopic scale model of the hollow sphere-metal matrix three-phase composite material is established by an equivalent body-centered cubic homogenization method.

Disclosure of Invention

The invention provides a microscopic scale fine modeling simulation method of a hollow sphere-metal matrix three-phase composite material, which is used for establishing an equivalent body-centered cubic homogenization microscopic scale model of a hollow sphere wall and a solid metal matrix composite material. The model can accurately reproduce the structural distribution of each component phase of the hollow sphere-metal matrix three-phase composite material, is used for researching the micro processes such as the connection failure between the interface of the matrix and the hollow sphere and the crack expansion path of the matrix material, and has profound significance for improving the accuracy of numerical simulation of the metal matrix three-phase composite material.

In order to achieve the purpose, the invention adopts the technical scheme that:

a microscopic scale fine modeling simulation method of a hollow sphere-metal matrix three-phase composite material comprises the steps of firstly, according to geometric parameters and target porosity of each composition phase of the hollow sphere-metal matrix three-phase composite material, reproducing a single cell structure of an equivalent body-centered cubic homogenization model, and establishing a mapping relation between the single cell structure and the target hollow sphere-metal matrix three-phase composite material structure; secondly, creating a target structure geometric model according to the overall dimension of the target hollow sphere-metal matrix three-phase composite material structure, the sphere base distribution rule of the hollow sphere-metal matrix three-phase composite material and the topological structure relationship among the sphere bases; and finally, dispersing the geometric model of the hollow sphere-metal matrix three-phase composite material structure into various units, and performing displacement interpolation on discrete unit nodes to endow material properties and node constraint conditions for the discrete units. The method comprises the following specific steps:

firstly, a single cell structure of an equivalent body-centered cubic homogenization model is reproduced according to the geometric parameters and the target porosity of each component phase of the hollow sphere-metal matrix three-phase composite material, and a mapping relation between the single cell structure and the target hollow sphere-metal matrix three-phase composite material structure is established, wherein the specific method comprises the following steps:

(1) according to the geometric parameters and the target porosity of each composition phase of the hollow sphere-metal matrix three-phase composite material, a single cell structure of the equivalent body-centered cubic homogenization model is reproduced:

the porosity of the hollow sphere-metal matrix three-phase composite material is between the body-centered cubic stacking porosity and the simple cubic stacking porosity, and the position distribution of the hollow spheres in the base material on the microscopic scale is consistent with the body-centered cubic stacking mode, so that the sphere bases of the hollow sphere-metal matrix three-phase composite material are distributed in an equivalent homogenized body-centered cubic mode, the body-centered cubic stacking porosity is reduced by increasing the distance between the hollow spheres, and a cell structure extremely similar to that of a real hollow sphere-metal matrix three-phase composite material is obtained.

The porosity of the hollow sphere-metal matrix three-phase composite material is as follows:

wherein V is the volume of the target hollow sphere-metal matrix three-phase composite material and has unit mm³；V_mIs the volume of the matrix material of the hollow sphere-metal matrix three-phase composite material, and the unit is mm³；V_sThe volume of the hollow ball is the hollow ball volume of the hollow ball-metal matrix three-phase composite material, and the unit is mm³；V_hIs the volume of the pores of the hollow sphere-metal matrix three-phase composite material in mm³。

Since the mesoscopic model of the hollow sphere-metal matrix three-phase material is an equivalent body-centered cubic homogenization model, an equivalent body-centered cubic unit cell structure is extracted from the integral model, and the cubic unit cell structure and the hollow sphere-metal matrix three-phase material have the same porosity:

wherein, V_dIs the volume of a cubic cell in mm³；V_dmIs the matrix volume of a cubic cell element in mm³；V_dsThe volume of the hollow ball is cubic cell element and is in mm³；V_dhIs the volume of the pores of the cubic cell in mm³。

The cubic unit cell volume is:

V_d＝a³ (3)

wherein a is the side length of the cubic cell in mm.

The volume of the pores in the cubic cell was:

wherein R is the external radius of the hollow ball, and the unit is mm; t is the wall thickness of the hollow sphere in mm.

Furthermore, from the equations (2), (3) and (4), it can be deduced that the side length of a single cubic unit cell is:

the side length of a single cubic cell can be calculated through the target porosity of the hollow sphere-metal matrix three-phase composite material, the outer diameter size of the hollow sphere and the wall thickness of the hollow sphere.

(2) And establishing a mapping relation between the single cell structure and the target hollow sphere-metal matrix three-phase composite material structure.

Assuming that the target structure model is a cuboid, the target model is placed under a Cartesian coordinate system, and in order to eliminate the boundary effect of the hollow sphere-metal matrix three-phase composite material, the number of the hollow spheres and the number of the single cell elements in any direction of the simulation model meet the following requirements:

N_dmin＝N_min-1 (6)

wherein N is_dminThe minimum value of the number of single cells in any direction of the target model is used for eliminating the boundary effect; n is a radical of_minThe minimum value of the number of the hollow spheres in any direction of the target model is used for eliminating the boundary effect.

The geometric parameters of the model are then:

L_x＝m·a(N_dmin≤m≤m_max) (7)

L_y＝n·a(N_dmin≤n≤n_max) (8)

L_z＝p·a(N_dmin≤p≤p_max) (9)

wherein L is_xThe length of the target model in the x direction is unit mm; l is_yThe length of the target model in the y direction is unit mm; l is_zThe length of the target model in the z direction is unit mm; m is the number of single cubic cell elements in the x direction of the target model; n is the number of single cubic cell elements in the y direction of the target model; p is the number of single cubic cell elements in the z direction of the target model; m is_maxThe maximum value of the number of single cubic cell elements in the x direction of the target model; n is_maxThe maximum value of the number of single cubic cell elements in the y direction of the target model; p is a radical of_maxThe maximum value of the number of the single cubic cells in the z direction of the target model.

Namely, the number and the geometric mapping relation between the single cell structure and the target hollow sphere-metal matrix three-phase composite material structure is established.

Secondly, creating a target structure geometric model according to the overall dimension of the target hollow sphere-metal matrix three-phase composite material structure, the ball base distribution rule of the hollow sphere-metal matrix three-phase composite material and the topological structure relationship among the ball bases, wherein the target structure geometric model specifically comprises the following steps:

(1) in a Cartesian coordinate system, the values are (0, 0, 0) and (L)_x，0，0)、(0，L_y，0)、(0，0，L_z) Creating a target sample geometric entity for the base point;

(2) creating a first layer of hollow sphere coordinate points in the X-O-Z plane where y is 0, namely:

P_i,j,k＝(ia,ja,ka) (i＝0,1,···,m,k＝0,1,···,p,j＝0) (10)

(3) in thatCreates a second layer of hollow sphere coordinate points, namely:

(4) linearly copying the two layers of coordinate points into arrays along the positive direction of the Y axis, wherein the number of the arrays is n, the array interval is a, and the unit is mm; and linearly copying the first layer of coordinate points into an array along the positive direction of the Y axis, wherein the array number is 2, the array pitch is na, and the unit mm is obtained, and finally obtaining the coordinate points of the spherical center positions of the hollow spheres.

(5) Creating a solid sphere at the sphere center coordinate point of the hollow sphere, wherein the sphere radius is the internal radius r of the hollow sphere:

r＝R-t (12)

and removing the spherical entity with the radius r created at the sphere center coordinate point in the sample entity through Boolean subtraction operation to obtain the porous entity model.

(6) Due to the topological structure relationship between the matrix and the hollow spheres, the grid nodes of the two parts need to be fitted with each other and transfer node force. Therefore, firstly, a hollow ball outer wall curved surface is created at the position of the position coordinate of the spherical center generated in the step (4), and the radius of the curved surface is the same as the size of the outer radius of the hollow ball; and cutting the solid body through a curved surface, and cutting the porous solid model obtained in the step (5) by using the curved surface of the outer wall of the hollow ball.

Hollow spheres with the wall thickness of (R-R) and a porous matrix can be obtained through cutting, the topological state of the curved surfaces between the hollow spheres and the porous matrix is a shared curved surface, and the 2D meshes created by taking the shared curved surface as a target surface can realize one-to-one correspondence of mesh nodes so as to be used for next accurate mesh division. According to the method, the geometric model of the hollow sphere-metal matrix three-phase composite material structure can be obtained.

And thirdly, dispersing the geometric model of the hollow sphere-metal matrix three-phase composite material structure into various units, and performing displacement interpolation on discrete unit nodes to endow material properties and node constraint conditions for the discrete units. The method specifically comprises the following steps:

(1) and dispersing the geometric model of the hollow sphere-metal matrix three-phase composite material structure into various units, and performing displacement interpolation on the dispersed unit nodes.

The change relation between the position and the time of each part node of the geometric model of the hollow sphere-metal matrix three-phase composite material structure is expressed by the coordinate interpolation value of the discrete unit node as follows:

whereinI is 1,2 and 3, which are indexes of space coordinates; 1,2, n represents a finite element node; wherein mu_iIRepresenting the displacement of the ith node of the unit in the I direction; n is a radical of_I(x, y, z) is the Lagrangian interpolation function for the I-th node.

Because the hollow sphere wall and the sphere interval are in narrow size, in order to prevent local stress concentration, the hollow sphere-metal matrix three-phase composite material is subjected to triangular two-dimensional unit surface mesh treatment, so that the surface mesh is consistent with the complex geometric surface attribute and meets the following requirements:

p≤t (14)

wherein p is the two-dimensional grid size; t is the wall thickness of the hollow sphere.

In order to ensure the calculation precision, a hollow sphere-metal matrix three-phase composite material geometric model generated in the second step of dispersing ten-node tetrahedral units is selected, smaller grid units are automatically generated in a compact structure region (wherein the region between the hollow sphere wall and the hollow sphere is the compact structure region), the consistency of the grid surface and the target structure geometric model generated in the second step is kept to the maximum extent, and the tetrahedral grid and the two-dimensional grid are ensured to have correlation when dispersing entities and meet the following conditions:

p’≤t (15)

wherein p' is the size of a ten-node tetrahedral unit; t is the wall thickness of the hollow sphere.

After the dispersion, the hollow sphere-metal matrix three-phase composite discrete unit can be obtained, wherein the hollow sphere discrete unit obtained by the dispersion of the hollow sphere geometric structure and the solid matrix discrete unit obtained by the dispersion of the porous matrix geometric structure are included.

(2) And giving material properties and node constraint conditions to the hollow sphere-metal matrix three-phase composite discrete units. The method comprises the following specific steps:

(a) and setting a yield criterion, a material parameter and a failure criterion for the hollow sphere discrete units and the solid matrix discrete units.

As the hollow spheres and the matrix material are all isotropic materials, the isotropic Von Mises yield criterion is followed, so that the isotropic Von Mises yield criterion is given to the hollow sphere discrete units and the solid matrix discrete units, namelyA second invariant J 'of the amount of stress deflection at a point within the deformable body, regardless of stress state'₂When a certain value is reached, the point is changed from the elastic state to the plastic state. The Von Mises yield criterion in the main coordinate system is as follows:

wherein σ₁、σ₂、σ₃Is the principal stress of a unit in X, Y, Z directions under a Cartesian coordinate system_sIs the unit yield stress. The physical meaning of the method is that when the elastic modulus of the volume shape change of the hollow sphere and the solid matrix discrete unit reaches a certain constant, the unit mass point yields.

The hollow sphere and the matrix material are all isotropic ideal elastic-plastic metal materials, and the Young modulus, the yield strength, the mass density, the Poisson ratio, the tangent modulus, the failure parameters and the equivalent stress-strain curve of the material are respectively defined for the hollow sphere discrete unit and the solid matrix discrete unit.

The discrete units of the hollow sphere and the solid matrix define material failure indexes according to effective plastic strain and minimum time step when the material fails, and when the equivalent plastic strain of the discrete units reaches failure values, the discrete units fail.

Setting the discrete unit attribute and the section attribute, creating the ten-node tetrahedral entity unit attribute and endowing the ten-node tetrahedral entity unit attribute to the hollow sphere and the solid matrix discrete unit.

(b) And (3) endowing node constraint conditions for the hollow sphere-metal matrix three-phase composite discrete unit nodes, namely establishing contact constraint at the hollow sphere-metal matrix three-phase composite discrete unit nodes.

The hollow sphere-metal matrix three-phase composite material has complex contact characteristics among the phases, so that the contact friction coefficient between the hollow sphere and discrete unit nodes of the solid matrix is determined by multiple groups of parameters:

wherein, mu_cIs the contact friction coefficient; FD is a dynamic friction factor; FS is the static friction factor; DC is an exponential decay coefficient; v. of_relIs the contact surface relative velocity.

Meanwhile, in view of the failure mode of the hollow sphere and the matrix composition phase, binding contact with failure criteria needs to be defined when the contact relation between the two unit nodes is simulated. The binding contact is based on a contact algorithm of a penalty function, compressive stress and tensile stress are transferred among discrete unit nodes of a contact phase, contact force is applied to a non-penetrating slave node to enable the penetrating distance between the slave node and a main surface section to be zero, the binding contact fails after a contact failure criterion is reached, and the contact type between the hollow ball and the base unit node is converted into common contact. The contact failure criteria were:

wherein σ_nAnd σ_sRespectively the normal stress and the shear stress of the contact surface in MPa; NFLS and SFLS are the corresponding contact surface failure normal stress and contact surface failure shear stress, respectively.

When the contact surface units reach the limit separation distance of the interface, the contact points are completely destroyed, the interface between the hollow sphere and the matrix is completely separated, and the brittle intermetallic phase between the hollow sphere and the matrix is completely damaged and fails to form microcracks outside the spherical wall.

The microscopic scale fine simulation model of the hollow sphere-metal matrix three-phase composite material can be obtained through the three steps.

Calculating the mechanical response and damage mode of the material under the target working condition by an explicit solving method, establishing a simulation model crack observation section of the material, observing the crack distribution of the section by an equivalent stress, an equivalent strain and a maximum shear stress cloud chart, and obtaining the interface failure and crack form of the hollow sphere-metal matrix three-phase composite material under the mesoscale so as to obtain the mechanical numerical solution of the mesoscale simulation model of the hollow sphere-metal matrix three-phase composite material.

The invention has the beneficial effects that:

(1) describing the spherical base arrangement of the hollow sphere-metal base three-phase composite material by adopting an equivalent homogenized body-centered cubic arrangement mode, and establishing a hollow sphere wall and solid matrix mesoscale model; the body-centered cubic stacking porosity is reduced by increasing the distance between the hollow spheres, a cell structure which is very similar to that of a real hollow sphere-metal matrix three-phase composite material is obtained, and the structural model can accurately reproduce the structural distribution of each component phase of the hollow sphere composite metal foam material.

(2) The influence of the connection mode between the hollow metal ball and the metal matrix is considered, the contact characteristics and the material difference of the hollow ball-matrix connection part are simulated, and the micro changes such as connection failure between the solid metal matrix and the hollow ball interface, crack expansion of the matrix material and the like can be researched.

Drawings

FIG. 1 is a simplified diagram of a single cell structure of an equivalent body-centered cubic homogenization model according to the present invention; fig. 1(a) is a side view of a single cell structure; figure 1(b) is an isometric view of a single cell structure.

FIG. 2 is a mapping relation diagram of the unit cell structure and the target hollow sphere-metal matrix three-phase composite material structure.

FIG. 3 is a circle center coordinate distribution diagram of the single-layer hollow sphere according to the present invention; fig. 3(a) is a coordinate distribution diagram of a first layer of hollow spheres on an X-O-Z plane with y being 0; FIG. 3(b) isThe coordinate distribution diagram of the second layer of hollow spheres on the X-O-Z plane.

FIG. 4 is an isometric view of a geometric model of a target substrate structure according to the present invention.

FIG. 5 is an isometric view of a geometric model of a hollow sphere-metal matrix three-phase composite structure according to the present invention.

FIG. 6 is a diagram of discrete units of a hollow sphere-metal matrix three-phase composite model according to the present invention.

FIG. 7 is a distribution diagram of interfacial failure and stress distribution cracks of a hollow sphere-metal matrix three-phase composite material under a microscopic scale according to the present invention;

FIG. 7(a) is a graph of model bulk interface failure, stress distribution and crack distribution; FIGS. 7(b) and (c) are the interface failure, stress distribution and crack distribution diagram of different stages of the observed cross section of the simulated model crack.

Detailed Description

The structural and operational principles of the present invention are explained in detail below with reference to the accompanying drawings and examples.

A microscopic scale fine modeling simulation method of a hollow sphere-metal matrix three-phase composite material is characterized by comprising the following steps:

the basic variables of the invention comprise the porosity of the hollow sphere-metal matrix three-phase composite material, the external radius of the hollow sphere, the wall thickness of the hollow sphere, the size of a target geometric structure, a reference coordinate and three-phase composite material parameters; referring to fig. 5, the porosity of the hollow sphere-metal matrix three-phase composite material selected in the present invention is f ═ 0.39; the external radius R of the hollow ball is 1 mm; the wall t of the hollow sphere is 0.1 mm; target geometry dimension L_x＝7.5mm、L_y＝22.5mm、L_z7.5 mm; the reference coordinates are (0, 0, 0); the hollow ball material in the hollow ball-metal matrix three-phase composite material is stainless steel 316L, and the matrix material is AL 7075. The calculation of the relevant parameters of the specific hollow sphere-metal matrix three-phase material equivalent body-centered cubic homogenization model is as follows:

(1) referring to FIG. 1, the pore volume V in the single cell structure of the Equivalent body centered cubic homogenization model_dh：

The volume V of the cubic unit cell is calculated from the porosity f 0.39_d：

Side length a of a cubic single cell structure:

(2) referring to fig. 2, a mapping relationship between a single cell structure and a target hollow sphere-metal matrix three-phase composite structure is established.

The number m of the single cubic cell elements in the x direction of the target geometric model is as follows:

the number n of the single cubic cell elements in the y direction of the target geometric model is as follows:

the number p of the single cubic cell elements in the z direction of the target geometric model is as follows:

(3) referring to fig. 3, a three-dimensional geometric model of the target structure in a cartesian coordinate system is created according to the sphere base distribution rule of the hollow sphere-metal matrix three-phase composite material.

And (3) creating a target structure geometric model by taking (0, 0, 0), (2.5, 0, 0), (0, 22.5, 0) and (0, 0, 2.5) as basic points under a Cartesian coordinate system.

Creating a first layer of hollow sphere coordinate points in the X-O-Z plane where y is 0, namely:

P_i,j,k＝(2.5i,2.5j,2.5k)

(i＝0,1,···,m,k＝0,1,···,p,j＝0) (7)

creating a second layer of hollow sphere coordinate points in the X-O-Z plane where y is 1.25, namely:

linearly copying the two layers of coordinate points along the positive direction of the Y axis to obtain an array, wherein the number of the arrays is n-9, the array interval is 2.5, and the unit is mm; and linearly copying the first layer of coordinate points into an array along the positive direction of the Y axis, wherein the array number is 2, the array pitch is 22.5, and the unit mm is obtained, and finally obtaining the coordinate points of the spherical center positions of the hollow spheres.

(4) Referring to fig. 4, a solid sphere is created at the coordinates of the sphere center of the hollow sphere, the radius of the sphere being the inner radius r of the hollow sphere:

r＝R-t＝1-0.1＝0.9mm (9)

and removing the spherical entity with the radius of 0.9mm created at the sphere center coordinate point in the sample entity through Boolean subtraction operation to obtain the geometric model of the porous entity.

(5) Referring to fig. 5, according to the topological structure relationship between the substrate and the hollow sphere, a hollow sphere outer wall curved surface is created at the sphere center position coordinate generated in (3), and the radius of the curved surface is 1 mm; and cutting the solid body through a curved surface, and cutting the porous solid model obtained in the step (4) by using the curved surface of the outer wall of the hollow ball.

The cutting can obtain the hollow sphere with the wall thickness t being 0.1mm and a porous matrix, namely a geometric model of the hollow sphere-metal matrix three-phase composite material structure.

(6) Referring to fig. 6, the geometric model of the hollow sphere-metal matrix three-phase composite structure generated in (5) is discretized into various units, a ten-node tetrahedral unit discretization hollow sphere-metal matrix three-phase composite model is selected, and the unit size p:

p≤0.1 (10)

(7) the hollow sphere-metal matrix three-phase composite discrete unit endows material properties and node constraint conditions, the hollow sphere and the matrix are all made of isotropic ideal elastic-plastic metal materials, the hollow sphere is made of stainless steel 316L, and the matrix is AL 7075.

TABLE 1 hollow sphere-metal matrix three-phase composite model Material Properties

The discrete units of the hollow sphere and the solid matrix define material failure indexes according to effective plastic strain and minimum time step when the material fails, and when the equivalent plastic strain of the discrete units reaches failure values, the discrete units fail.

The contact relation between the hollow ball and the discrete unit node of the metal matrix is defined as binding contact with a failure criterion. When the contact surface units reach the limit separation distance of the interface, the contact points are completely destroyed, the interface between the hollow sphere and the matrix is completely separated, and the brittle intermetallic phase between the hollow sphere and the matrix is completely damaged and fails to form microcracks outside the spherical wall.

(8) Referring to fig. 7, the mechanical response and the damage mode of the three-phase material under the target working condition are obtained, the simulation model crack observation section of the material is obtained, and the interface failure and the crack form of the hollow sphere-metal matrix three-phase composite material are observed under the microscopic scale.

The above-mentioned embodiments only express the embodiments of the present invention, but not should be understood as the limitation of the scope of the invention patent, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the concept of the present invention, and these all fall into the protection scope of the present invention.