Mechanical property calculation method of whisker reinforced metal matrix composite

Abstract

The invention provides a mechanical property calculation method of a whisker reinforced metal matrix composite material. The method comprises the following steps: acquiring configuration parameters, geometric parameters of whiskers and geometric parameters of a matrix; judging whether a mesh configuration is generated or not; if the mesh configuration is generated, cell element walls are generated through cell element information based on geometric parameters of the matrix; if the netlike configuration is not generated, cell element walls are not generated; whiskers are generated according to geometric parameters of the whiskers, and conflict detection is carried out through partition, whisker projection and whisker distance; combining the whisker reinforcements and cutting the matrix; performing grid division and material attribute endowing, and setting calculation steps and boundary conditions; and performing finite element calculation, and outputting a tensile stress-strain curve result according to a calculation result. The method can be widely applied to structural modeling of the whisker reinforced metal-based composite material, and is particularly suitable for simulation and performance evaluation of large-scale whisker distribution.

Description

Technical Field

[0001] The invention relates to the technical field of finite element modeling of composite materials, and in particular to a method for calculating the mechanical properties of a whisker-reinforced metal-based composite material. Background Art

[0002] With the rapid development of industries such as transportation, aerospace, etc., the demand for metal matrix composites with excellent mechanical properties and high temperature resistance is increasing. Studies have shown that the stiffness and strength of composite materials can be effectively improved by optimizing the structural design. The mesh configuration is one of the typical configurations of metal matrix composites, which helps to improve the strength, plasticity and high temperature performance of the material. Optimizing the mesh configuration parameters (such as the volume fraction of the dispersed reinforcement, the aspect ratio and the network size, etc.) can help to further improve the mechanical properties.

[0003] In the actual material preparation process, it is very difficult and costly to accurately control the configuration parameters to understand their influence on mechanical properties. As a common computational material method, the finite element method (FEM) is widely used to establish the relationship between the structure and mechanical behavior of particles, whiskers and fiber-reinforced composites. Although there are methods based on Abaqus secondary development and RSA algorithm for model reconstruction of composite materials, these methods significantly increase the computational complexity of overlap detection when dealing with a large number of fine whiskers (such as filling thousands of whiskers). A more efficient modeling method is urgently needed to generate random distribution models of these configurations.

[0004] After searching, it was found that the Chinese invention patent with application publication number CN109829213A discloses a method for designing and predicting the mechanical properties of discontinuously reinforced metal matrix composite materials. Its operation process includes: constructing a three-dimensional geometric model of discontinuously reinforced composite materials based on the random distribution state of particles, short rods, and whisker-shaped reinforcements; meshing the three-dimensional model; correcting the strength of the metal matrix and reinforcements through formula calculation; assigning the mechanical properties of each component to the model; applying boundary conditions and loads to the model; and calculating the mechanical properties of the composite material through simulation technology. In the collision detection between spherical particles and other particles, this prior art performs distance detection according to the spherical geometric characteristics to prevent the reinforcements from overlapping, but for particles of other shapes, they are divided into several tetrahedrons, and vertex and tetrahedron coordinate determinant calculations are performed to determine the intersection, which is relatively complicated. Summary of the invention

[0005] In view of the defects in the prior art, an object of the present invention is to provide a method for calculating the mechanical properties of a whisker reinforced metal matrix composite material.

[0006] The present invention provides a method for calculating the mechanical properties of a whisker-reinforced metal matrix composite material, comprising:

[0007] Obtaining configuration parameters, geometric parameters of whiskers and geometric parameters of the matrix;

[0008] According to the configuration parameters, determining whether to generate a mesh configuration;

[0009] If a mesh configuration is generated, the cell wall is generated through the cell information based on the geometric parameters of the matrix; if a mesh configuration is not generated, the cell wall is not generated;

[0010] Generate whiskers according to their geometric parameters, and perform collision detection through partitioning, whisker projection and whisker distance;

[0011] Incorporating whisker reinforcements and cutting the matrix;

[0012] Perform meshing and material property assignment, and set calculation steps and boundary conditions;

[0013] Perform finite element calculation and output tensile stress-strain curve results based on the calculation results.

[0014] Further, the configuration parameters, geometric parameters of the whiskers and geometric parameters of the substrate are obtained, wherein: the geometric parameters of the whiskers include whether the whiskers are dual-size whiskers, the whisker diameter, the whisker aspect ratio, the whisker volume fraction, the representative volume unit size and the detection area size; the configuration includes a uniform configuration or a mesh configuration, and the parameters of the mesh configuration include the number of cell walls N on each side of the representative volume unit x , N y , N z and the cell wall thickness t x , t y , t z .

[0015] Further, generating a cell wall through cell information includes:

[0016] Use the Pyvoro library to generate Voronoi cell information, including cell number, cell vertex, and cell face;

[0017] Traverse the cell faces and vertex information of each cell, use the WirePolyLine command in Abaqus software to connect the cell edges, and then use the CoverEdges command to form the cell faces;

[0018] Each cell face forms a cell shell, and then the AddCells command is used to generate a cell entity;

[0019] The constructed cells are named Cell-0, Cell-1, ..., Cell-((N x +1)(N y +1)(N z +1)-1);

[0020] Each cell is displaced along the x, y, and z directions to generate a spatial structure for cutting the cell wall.

[0021] Further, the whiskers are generated according to the geometric parameters of the whiskers, and conflict detection is performed through partitioning, whisker projection and whisker distance, wherein the process of generating the whiskers includes:

[0022] It is determined whether the whisker configuration is a uniform configuration or a mesh configuration. If the whisker configuration is a uniform configuration, whisker 1 and whisker 2 are set, whisker 1 is generated first, and then whisker 2 is generated; if the whisker configuration is a mesh configuration, whisker 1 is distributed in the cell wall area, and whisker 2 is distributed in the cell area.

[0023] Further, the whiskers are generated according to the geometric parameters of the whiskers, and whisker conflict detection is performed through partitioning, whisker projection and whisker distance, wherein the whisker conflict detection includes:

[0024] The whiskers are randomly distributed in the representative volume unit by rotation and movement, and the detection area where the whiskers are located after rotation and movement is determined;

[0025] Project the new and old whiskers onto the corresponding axes to determine whether their axial projection intervals intersect;

[0026] If the projection intervals do not intersect, the whiskers do not intersect; if the projection intervals intersect, the closest distance between the two whiskers is calculated. If the closest distance is greater than the sum of the two whisker radii, it is judged that there is no intersection. Otherwise, the two whiskers intersect, and the new whisker is randomly rotated and moved to a new position until they do not intersect each other.

[0027] Determine whether the volume fraction of whiskers meets preset requirements;

[0028] If the volume fraction of the whiskers does not meet the preset requirements, new whiskers continue to be generated. When the preset volume fraction is reached, the whisker generation stops.

[0029] Further, the determining whether the axial projection intervals intersect includes:

[0030] The whiskers do not intersect if the intervals satisfy the following rules:

[0031]

[0032] Where d1 is the new whisker, d2 is the existing whisker diameter, represents the collision margin, C 1-top is the coordinate of the upper and lower surfaces of the new whisker, C 2-top is the coordinate of the upper and lower surfaces of the existing whiskers, C 1-bottom is the coordinate of the bottom surface of the new whisker, C 2-bottom is the coordinate of the bottom surface of the existing whisker, is the unit direction vector.

[0033] Further, the calculating the shortest distance between two whiskers comprises:

[0034] Determine whether two whiskers are parallel according to the following parallel judgment formula:

[0035]

[0036] If the parallel judgment formula is satisfied, the two whiskers are parallel, and the distance formula is:

[0037]

[0038] If the parallel judgment formula is not satisfied, the two whiskers are not parallel, and the distance formula is:

[0039]

[0040] In the above formula, | means taking the absolute value; ∥ means taking the Euclidean norm; d min is the shortest distance between the new whisker and the existing whisker.

[0041] Further, the determining whether the volume fraction of the whisker meets the preset requirements includes: determining whether the coordinates of the bottom surface of the whisker exceed the range of the representative volume unit; if so, cutting the whisker from the surface of the representative volume unit, and then determining whether the current volume fraction of the whisker meets the preset requirements.

[0042] Furthermore, the meshing and material attribute assignment are performed, wherein the material attribute assignment includes: the density, elastic modulus, Poisson's ratio, and brittle damage model of the whisker are assigned to Whiskers; the density, elastic modulus, Poisson's ratio, plastic constitutive model, and ductile fracture model of the matrix are assigned to Base-hole; and the cohesion model describing the interface behavior is assigned to Interface;

[0043] The setting of calculation steps and boundary conditions includes: creating an explicit dynamics calculation step, setting the calculation step length, setting a uniaxial stretching boundary condition, and binding the stretching surface to the reference point Rp-1; setting a reference point set RF, RF binding the stretching surface in the positive direction of the x-axis, the displacement boundary condition of RF is 0.05×L, L is the size of the representative volume unit, and the displacement degree of freedom of the fixed surface on the other side is set to zero.

[0044] Further, outputting the tensile stress-strain curve result according to the calculation result includes:

[0045] According to the calculation results, the reaction force and displacement data are extracted for stress-strain behavior and mechanical performance evaluation and analysis, which are defined as:

[0046] σ=RF1 / L 2 , ε=U1 / L;

[0047] Among them, σ is the tensile stress, ε is the strain, RF1 is the reaction force component of the reference point set RF, U1 is the displacement component of RF, and L is the size of the representative volume unit.

[0048] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0049] 1. Reduce time complexity and improve modeling efficiency: The present invention introduces spatial geometric information judgment, utilizes whisker geometric features, and adopts structural coordinates for conflict detection, which is simple and effective. The partition detection mechanism is introduced, and the newly added whisker is only detected for conflict with the whiskers in the current detection area, which can reduce the number of detections, that is, the number of detections is reduced from N-1 to M (less than N-1, depending on the number of partitions), and the time complexity is reduced from O(N) to M (less than N-1, depending on the number of partitions) in the unpartitioned method. 2 ) is reduced to O(N), which significantly improves the computational efficiency; especially for models with more than 100 whiskers, it has a high execution efficiency;

[0050] 2. Flexible mesh configuration generation: The present invention generates cell walls by inputting the model size L and the number of cells and cell wall thickness on the three sides of the x, y, and z directions, and performing displacement and cutting operations on the cells. The cell size and cell wall thickness can be freely controlled to control the whisker distribution area in the mesh configuration, and then control the mesh configuration distribution of the whiskers, providing strong support for the structural design of mesh configuration composite materials;

[0051] 3. Diversified configuration design: The present invention can generate RVE models of composite materials with various whisker sizes, volume fractions, uniform configurations or network configurations by inputting model size L, configuration type (uniform configuration or mesh configuration), number of sizes (single size or double size), whisker diameter and length, and whisker volume fraction, and then perform finite element calculations and obtain mechanical property data, providing strong support for configuration design optimization.

[0052] The method provided by the invention can be used for studying the tensile mechanical behavior of whisker-reinforced metal-based composite materials, and has a guiding role in the structural design of metal-based composite materials with whiskers having uniform random and mesh configuration distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0054] Figure 1 It is a schematic diagram of a flow chart of a method for calculating the mechanical properties of a whisker-reinforced metal matrix composite material in one embodiment of the present invention;

[0055] Figure 2 A model diagram of a single-size uniform TiB / Ti composite material with a volume fraction of 2.5 vol.% in one embodiment of the present invention;

[0056] Figure 3 Calculate the tensile stress-strain curve for a single-size uniform TiB / Ti composite material model with a volume fraction of 2.5 vol.% in one embodiment of the present invention;

[0057] Figure 4 Schematic diagram of the cell wall structure generation process in one embodiment of the present invention;

[0058] Figure 5 A model diagram of a dual-size network-structured TiB / Ti composite material with a volume fraction of 2.5 vol.% in one embodiment of the present invention;

[0059] Figure 6 Calculated tensile stress-strain curve and typical experimental curve for a dual-size network-structured TiB / Ti composite material model with a volume fraction of 2.5 vol.% in one embodiment of the present invention. DETAILED DESCRIPTION

[0060] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0061] The embodiment of the present invention provides a method for quickly constructing a metal matrix composite material model with uniform and mesh configurations containing a large number of randomly distributed whiskers and calculating its mechanical properties. The method is implemented based on a secondary development program of finite element software written in Python.

[0062] Reference Figure 1 A method for calculating the mechanical properties of a whisker-reinforced metal matrix composite material provided by an embodiment of the present invention comprises the following steps:

[0063] S1, obtaining configuration parameters, geometric parameters of whiskers and geometric parameters of the substrate;

[0064] S2. judging whether to generate a network configuration according to the configuration parameters, wherein the network configuration refers to the distribution of whiskers;

[0065] S3. If a mesh configuration is generated, a cell wall is generated based on the geometric parameters of the matrix and the cell information, which is used for subsequent judgment that the whisker is located in the cell wall / in the cell, and the cells and the cell walls form all areas of the matrix cube model; if a mesh configuration is not generated, the cell wall is not generated;

[0066] S4, generating whiskers according to the geometric parameters of the whiskers, and performing conflict detection through partitioning, whisker projection and whisker distance;

[0067] S5, merging the whisker reinforcement and cutting the matrix;

[0068] S6. Perform meshing and material property assignment, and set calculation steps and boundary conditions;

[0069] S7. Perform finite element calculation and output tensile stress-strain curve results according to the calculation results.

[0070] The embodiment of the present invention adopts the projection detection and distance detection method to optimize the intersection judgment algorithm between whiskers, and uses the geometric characteristics of the whisker rod to simplify the calculation process of intersection judgment. At the same time, the partition detection is used to reduce the number of conflict detections, that is, the number of detections is reduced from N-1 to M (less than N-1, depending on the number of partitions), and the time complexity is reduced from O(N) to M. 2 ) is reduced to O(N), where N is the Nth generated whisker, M is the number of whiskers in the detection area, and O is the Big O representation of the algorithm time complexity, thereby improving the efficiency of conflict detection. The embodiment of the present invention is suitable for generating a large number of randomly distributed whiskers, especially for a model with more than 100 whiskers, and has a high execution efficiency.

[0071] In the embodiment of the present invention, the cell wall is constructed to achieve a mesh distribution of whisker 1, and the cell limits the distribution area of ​​whisker 2. Partition detection is to divide the detection area within the entire L×L×L model area to reduce the number of whiskers that need to be detected for each conflict detection; through conflict detection, it is determined whether the whiskers with random orientations and positions inserted in sequence overlap with the inserted whiskers, thereby generating a composite material model with random whisker positions, orientation distributions, and no overlap; during conflict detection, it is first ensured that the whiskers do not intersect with the whiskers already inserted, and then it is determined whether the whiskers are located in the cell or in the cell wall. Under the default dual size, if whisker 1 is to be inserted into the cell wall, an intersection judgment is made with the cell wall, and the intersecting whiskers are retained; if whisker 2 is inserted into the cell, the whiskers that do not intersect with the cell wall are retained. Among them, whisker 1 and whisker 2 are descriptions of two whiskers of different sizes, which are distributed together in the composite material model. When it is a uniform configuration, the two sizes of whiskers are randomly distributed at any position in the model with the same probability, and do not intersect each other using conflict detection; when it is a mesh configuration, it is stipulated that whisker 1 is distributed on the cell wall and whisker 2 is distributed in the cell. Whisker 1 is distributed in a mesh pattern in the cell wall area, and whisker 2 is uniformly and randomly distributed in the cell (i.e., in the mesh space surrounded by whisker 1). The mesh configuration achieves that the two are randomly distributed at any position in their respective areas with the same probability.

[0072] In some embodiments, the geometric parameters of the whiskers include whether the whiskers are dual-size whiskers, the whisker diameter, the whisker aspect ratio, the whisker volume fraction, the representative volume element (RVE) size L, and the detection area size; through step S1, the whiskers are set to single-size / dual-size type; the diameter, aspect ratio and volume fraction of the whiskers are set; the size of the representative volume unit is determined; a whisker component and a base component Base are created (Base is the name of the base component, covering the entire geometric features of the base, and its edges are located in the range of 0 to L on each coordinate in the assembly, that is, the spatial position of the composite material matrix with a side length of L is located in the cube area between (0, 0, 0) and (L, L, L)); the detection area size grid-size is set to create a detection area.

[0073] The above configuration includes a configuration type, which includes a uniform configuration or a mesh configuration. If it is a mesh configuration, the number of cell walls and the cell wall thickness on the RVE edge need to be determined. The parameters of the mesh configuration include the number of cell walls N on each edge of the representative volume unit. x , N y , N z and the cell wall thickness t x , t y , t z , different parameters can be set in the three axes.

[0074] In some embodiments, in step S3, a matrix cube model is generated according to the geometric parameters of the matrix, and cells and cell walls are generated. Specifically, Voronoi geometric information is generated, and the generated Voronoi geometric information is used to construct a geometric structure for the cell wall; a representative volume unit model is constructed in Abaqus and the model is cut to obtain the cell wall and cells for controlling the distribution of the mesh configuration whiskers.

[0075] In the embodiment of the present invention, the cell wall is obtained by cutting the cube model of the substrate after a closed Voronoi cell model is opened along the positive direction of the XYZ axis. The side length of the Voronoi cell model before opening is determined by the Voronoi information, such as Figure 4 Determine the Voronoi information, including:

[0076] Calculate the edge length L of the Voronoi structure used for cell wall cutting Voroni , defined as:

[0077]

[0078] Generate a cell wall through cell information, including: generate Voronoi cell information using a Pyvoro library, the Voronoi cell information refers to the coordinate information of the points of a closed Voronoi cell model generated by the specified number of cells and the side length of the Voronoi cell model, the association information between the edges and points, the association information between the edges and faces, and the association information between each cell and face, including cell number, cell vertex, and cell face; traverse the cell faces and vertex information of each cell, use the WirePolyLine command in turn to connect the cell edges in the Abaqus software, and then use the CoverEdges command to form the cell face; each cell face forms a cell shell, and then use the AddCells command to generate a cell entity; and name the constructed cells as Cell-0, Cell-1, ..., Cell-((N x +1)(N y +1)(N z +1)-1); Each cell is displaced along the x, y, and z directions to generate a spatial structure for cutting the cell wall, that is, each cell after being pulled apart is ready to be cut with the Base of the cube to form a cell wall.

[0079] For Cell-i, the displacement is defined as follows (where [] indicates rounding down):

[0080]

[0081] Cut each cell with the Base and divide the Base into cell walls and other areas.

[0082] In the embodiment of the present invention, for the whisker distribution, a uniform random distribution of whiskers is generated in a representative volume unit according to random rotation and displacement, and collision detection is used to ensure that there is no intersection between whiskers. Specifically, after the whisker model is generated, it is placed in the Base through random rotation and displacement, and collision detection is performed. Before reaching the stop criterion of the preset volume fraction, the whisker generation and collision detection are continuously cycled.

[0083] The configuration types include single / double-size enhanced uniform / network configurations, wherein the network configuration includes setting a cell wall inside the RVE and filling whiskers 1, while whiskers 2 are filled in other areas outside the cell wall.

[0084] In some embodiments, in step S3, the process of generating whiskers includes: judging whether the whisker configuration is a uniform configuration or a mesh configuration, and the mesh configuration needs to define the size and content of whisker 1 and whisker 2, because whisker 1 only retains whiskers distributed in the cell wall, and whisker 2 retains whiskers distributed in the cell. Whisker 1 and whisker 2 can input the same size, that is, a mesh configuration composed of single-size whiskers. The uniform configuration can be that whiskers of two sizes are distributed in the model with uniform probability, rather than being distributed in a mesh. If the whisker configuration is a uniform configuration of two sizes, whisker 1 and whisker 2 are set, whisker 1 is generated first, and then whisker 2 is generated; both the mesh configuration and the uniform configuration are placed in a position that does not intersect with other whiskers by randomly rotating and displacing in the model, but the mesh model will retain whiskers that intersect with the cell wall by judging the position of the whisker and the cell wall. This judgment is not made for the uniform configuration; for the mesh configuration, whisker 1 is distributed in the cell wall area, and whisker 2 is distributed in the cell area. According to the volume fraction, a uniform random distribution is performed in the RVE to ensure the reasonable arrangement of the whiskers; for the mesh configuration, the cell wall is used for cutting operations to achieve the effective distribution of whisker 1 and whisker 2 in different areas.

[0085] In some embodiments, in step S4, whisker conflict detection includes:

[0086] S41. After randomly generating whiskers, the whiskers are randomly distributed in the representative volume unit by rotating and moving, and the detection area where the whiskers are located after rotation and movement is determined; specifically, the upper and lower bottom surface coordinates of the new whiskers are read: C 1-top , C 1-bottom , then the detection area number Grid-index that needs to be considered can be obtained by the following formula (where [] means rounding down, and {} means set):

[0087]

[0088] Then the existing whiskers in the detection area are traversed and collision detection is performed in turn;

[0089] S42, firstly, perform axial projection judgment, project the new and old whiskers to the corresponding axial direction, and judge whether their axial projection intervals intersect, that is, whether there is overlap; the new whisker represents the whisker newly inserted into the Base, and the old whisker represents the whisker inserted into the whisker for conflict detection; when performing conflict detection, after the newly inserted whisker detects its own position, the inserted whiskers in the detection area are retrieved for conflict judgment in sequence, and the old whisker is the inserted whisker for which the conflict judgment is performed in sequence;

[0090] S43, if the projection intervals do not intersect, the whiskers do not intersect; if the projection intervals intersect and the axial projection non-intersection condition is not met, the closest distance between the two whiskers is calculated, and if the closest distance is greater than the sum of the two whisker radii, it is determined that there is no intersection, otherwise the two whiskers intersect, and the new whisker is randomly rotated and moved to a new position again until they do not intersect each other;

[0091] S44, judging whether the volume fraction of whiskers meets the preset requirements;

[0092] S45. If the volume fraction of the whiskers does not meet the preset requirement, continue to generate new whiskers. When the preset volume fraction is reached, stop generating whiskers.

[0093] Specifically, in step S42, the bottom coordinates of the new whisker are subtracted to obtain a direction vector, and the direction vector is normalized to be defined as:

[0094]

[0095] in is the unit direction vector, C 1-top , C 1-bottom are the upper and lower bottom coordinates of the new whisker;

[0096] The projection interval of the new whisker is defined as:

[0097]

[0098] The projection interval of the existing whiskers can be written as:

[0099]

[0100] Among them C 2-top , C 2-bottom are the coordinates of the upper and lower bottom surfaces of the existing whisker, [] represents a closed interval;

[0101] The geometric meaning of this projection interval is that the four bottom surface coordinates of the two whiskers are mapped to a one-dimensional reference system in the three-dimensional coordinate system that passes through the origin and is along the direction of the new whiskers, indicating their coordinates starting from the origin;

[0102] In some embodiments, taking into account the whisker diameter, increasing The collision margin of is used to determine whether the axial projection intervals intersect, including: if the intervals meet the following rules, the whiskers do not intersect:

[0103]

[0104] Where d1 is the new whisker, d2 is the existing whisker diameter, represents the collision margin, C 1-top is the coordinate of the upper and lower surfaces of the new whisker, C 2-topis the coordinate of the upper and lower surfaces of the existing whiskers, C 1-bottom is the coordinate of the bottom surface of the new whisker, C 2-bottom is the coordinate of the bottom surface of the existing whisker, is the unit direction vector.

[0105] In some embodiments, calculating the shortest distance between two whiskers includes: determining whether the two whiskers are parallel according to the following parallel determination formula:

[0106]

[0107] If the parallel judgment formula is satisfied, the two whiskers are parallel, and the distance formula is:

[0108]

[0109] If the parallel judgment formula is not satisfied, the two whiskers are not parallel, and the distance formula is:

[0110]

[0111] In the above formula, | means taking the absolute value; ∥ means taking the Euclidean norm; d min is the shortest distance between the new whisker and the existing whisker; C 1-top is the coordinate of the upper and lower surfaces of the new whisker, C 2-top are the coordinates of the upper and lower surfaces of the existing whiskers.

[0112] If d min >(d1+d2) / 2, the two whiskers do not intersect; otherwise, the two whiskers intersect.

[0113] In some embodiments, determining whether the volume fraction of the whisker meets the preset requirements includes: detecting the RVE boundary and the cell boundary, determining whether the coordinates of the bottom surface of the whisker exceed the range of the representative volume unit, if exceeding the range, cutting the whisker and the surface of the representative volume unit, cutting off the excess part, updating the new whisker information (coordinates, diameter) in the whisker set in the detection area, calculating the volume fraction, and then determining whether the current volume fraction of the whisker meets the preset requirements. Repeat the above process until the specified volume fraction is reached.

[0114] In the above-mentioned embodiment of the present invention, the distribution of whiskers in the RVE adopts a partition detection mechanism, which reduces the number of conflict detections and improves the efficiency of whisker distribution generation by dividing the detection area into several partitions.

[0115] In some embodiments, the process of merging reinforcements and cutting the base includes: merging generated whiskers into instance Whiskers, and cutting the Base with the Whiskers to obtain a Base-hole.

[0116] In the embodiment of the present invention, according to the distribution of whiskers, the structural model of the reinforcement and the matrix is ​​established in the finite element software, the corresponding material properties are assigned, the finite element mesh is generated, the boundary conditions are set and the calculation is submitted to generate the mechanical property calculation results. Specifically, the generation of Voronoi geometric information, the cutting of cell walls, the random distribution of whiskers and the assignment of material properties are realized by using the finite element software secondary development program written in Python language.

[0117] In some embodiments, in step S6, the Whiskers and Base-hole instances are divided according to a given finite element mesh size; the surface of the Base-hole is traversed, and the internal interface is created as a set Surf-1; the unit faces on the Whiskers surface are traversed, and a zero-thickness interface layer Interface is created on the Whiskers surface; and the outer unit face Interface-Top of Interface is bound to Surf-1. Finite element meshing includes: dividing the reinforcement and the matrix according to a given mesh size; traversing the matrix and the reinforcement surface, and creating an interface set for tensile property calculation. Material property assignment includes: the density, elastic modulus, Poisson's ratio, and brittle damage model of the whiskers are assigned to Whiskers; the density, elastic modulus, Poisson's ratio, plastic constitutive model, and ductile fracture model of the matrix are assigned to the Base-hole; and the cohesion model describing the interface behavior is assigned to the Interface.

[0118] Setting the calculation step and boundary conditions includes: creating an explicit dynamic calculation step, setting the calculation step length, setting the uniaxial tensile boundary condition, binding the tensile surface to the reference point Rp-1; setting the reference point set RF, RF binding the tensile surface in the positive direction of the x-axis, and the displacement boundary condition of RF is 0.05×L, L is the size of the representative volume unit, and the fixed surface on the other side is set to zero displacement freedom. By setting the uniaxial tensile boundary condition, specifying the reference point and applying the displacement, the reaction force and displacement of the reference point are output to calculate the stress-strain behavior of the composite material.

[0119] In some embodiments, in step S7, the tensile stress-strain curve result is output according to the calculation result, including: generating an inp file and submitting a finite element task for calculation; according to the calculation result, extracting the reaction force and displacement data for stress-strain behavior and mechanical property evaluation analysis, which is defined as:

[0120] σ=RF1 / L 2 , ε=U1 / L;

[0121] Among them, σ is the tensile stress, ε is the strain, RF1 is the reaction force component of the reference point set RF, U1 is the displacement component of RF, and L is the size of the representative volume unit.

[0122] The above embodiment of the present invention optimizes the whisker conflict detection process by introducing spatial geometric information judgment and partition detection mechanism, reduces the number of detections, and significantly improves the calculation efficiency. At the same time, the cell wall is generated by displacement and cutting operations on the cell, and the cell size and cell wall thickness are flexibly controlled to control the whisker distribution area in the mesh configuration, providing strong support for the structural design of mesh configuration composite materials. The above embodiment of the present invention can be widely used in the structural modeling of whisker-reinforced metal matrix composites, and is particularly suitable for the simulation and performance evaluation of large-scale whisker distribution.

[0123] The following is a further explanation of the calculation method of the mechanical properties of the whisker-reinforced metal-based composite material by taking a fine titanium boride whisker-reinforced titanium-based composite material as an example.

[0124] Example 1

[0125] Single-size homogeneous TiB / Ti composite material model with a volume fraction of 2.5 vol.% (whisker 1 size: Φ0.3 μm×6 μm).

[0126] In this embodiment, step S1 specifically includes:

[0127] S11. Determine the geometric parameters of the whiskers and the substrate, wherein the whisker geometric parameters include: single-size whiskers, whisker 1 diameter of 0.3 μm, whisker 1 aspect ratio of 20, whisker 1 volume fraction of 2.5 vol.%, and RVE size of 15 μm, detection zone size of 15 μm.

[0128] S12, determining the configuration to be a uniform configuration;

[0129] S13, creating whiskers with a size of Φ0.3μm×6μm;

[0130] S14, establish a three-dimensional RVE with a side length of L = 15 μm and name it Base;

[0131] S15. Define a detection area. In this example, there is only one detection area, numbered (0,0,0).

[0132] In this embodiment, step S4 specifically includes:

[0133] S41, the whiskers are randomly distributed in the RVE area by random rotation and movement, and the newly added whiskers provide the upper and lower circular surface coordinates C after movement 1-top , C 1-bottom , then the detection area number Grid-index can be obtained by the following formula (where [] means rounding down, and {} means set):

[0134]

[0135] S42, calling the position information of the whiskers added in the area and the position information of the newly added whiskers to perform position conflict judgment, firstly perform axial projection judgment, that is, project the old and new whiskers into a one-dimensional reference system passing through the origin and along the direction of the new whiskers, and the one-dimensional coordinates of the axis of the new whiskers;

[0136] S43, subtracting the bottom coordinates of the new whisker to obtain a direction vector, and normalizing the direction vector, which is specifically defined as:

[0137]

[0138] in is the unit direction vector, C 1-top , C 1-bottom are the upper and lower bottom coordinates of the new whisker.

[0139] S44, the projection interval of new whiskers and existing whiskers can be written as:

[0140]

[0141] Among them C 2-top , C 2-bottom are the coordinates of the upper and lower bottom surfaces of the existing whisker;

[0142] S45. If the interval satisfies the following rules, the whiskers must not intersect (taking into account the whisker diameter, increase Collision margin):

[0143]

[0144] Where d1 and d2 are the diameters of the new whisker and the existing whisker respectively.

[0145] S46, if the axial projection judgment is not satisfied, continue to judge the closest distance between the two whiskers, first judge whether the two whiskers are parallel, that is, satisfy the following formula:

[0146]

[0147] If they are parallel, the distance formula is written as follows (| means taking the absolute value):

[0148]

[0149] If they are not parallel, the distance formula is written as follows (∥ means taking the Euclidean norm):

[0150]

[0151] d1 is the new whisker diameter, d2 is the existing whisker diameter; if d min >(d1+d2) / 2, the two whiskers do not intersect; otherwise, the two whiskers intersect.

[0152] S47, if the new whisker intersects with the existing whisker, the new whisker is randomly rotated and moved to a new position; if the new whiskers do not intersect with each other, the volume fraction is determined;

[0153] S48. If the coordinates of the bottom surface of the whisker exceed the range of the RVE, it means that the whisker has passed through the surface of the RVE. The whisker and the RVE surface are cut and the volume is calculated to determine the current volume fraction.

[0154] S49. If the specified volume fraction (2.5 vol.%) is not reached, new whiskers continue to be generated. When the specified volume fraction is reached, the generation of whiskers is stopped.

[0155] In this embodiment, step S5 specifically includes: merging whisker distributions into an instance Whiskers, and cutting Whiskers and Base to obtain a base instance Base-hole with a hole.

[0156] In this embodiment, step S6 specifically includes:

[0157] S61, Splitting examples Whiskers and Base-holes according to given finite element mesh size;

[0158] S62. Traverse the Base-hole surface. If the coordinates of the center of the surface are not on the RVE boundary, it is an internal interface. Create a set Surf-1 for the internal surface.

[0159] S63, traverse the Whiskers outer surface of the instance, and create a zero-thickness interface layer Interface according to the Whiskers outer surface unit information, whose bottom surface is bound to the Whiskers outer surface node, and the top surface is bound to the Surf-1 upper node;

[0160] S64. Assign the material properties of the matrix, reinforcement and interface to Base-hole, Whiskers and Interface respectively, including: density, elastic modulus, Poisson's ratio and brittle damage model of titanium boride whiskers; density, elastic modulus, Poisson's ratio, plastic constitutive model and ductile fracture model of titanium matrix; cohesion model of interface behavior;

[0161] S65, create a new explicit dynamics calculation step and specify the step size as 0.1;

[0162] S66, set uniaxial tensile boundary conditions, bind the tensile surface to the reference point Rp-1, and set the reference point to the set RF. Set the displacement boundary condition for RF, the distance is 0.05*L, and the fixed surface is set to zero displacement degree of freedom;

[0163] S67, output RF reaction force and displacement for tensile performance calculation.

[0164] In this embodiment, step S7 specifically includes:

[0165] S71, submitting the finite element task for calculation;

[0166] S72. After the calculation is completed, open odb, extract and process the reaction force component RF1 and displacement component U1 of RF as the data of stress-strain behavior, which are defined as:

[0167] σ=RF1 / L 2 , ε=U1 / L

[0168] S73. Draw the tensile stress-strain curve.

[0169] Figure 2 The figure shows a model diagram of a 2.5 vol.% single-size uniform TiB / Ti composite material, in which single-size whiskers are randomly distributed with uniform probability at any position in the model area and are randomly oriented, showing the effect of generating a whisker-reinforced composite material model according to an embodiment of the present invention.

[0170] Figure 3 is the tensile stress-strain curve of the model, where the finite element material property parameters are not described in detail. Figure 3 The results show that the model generated by the embodiment of the present invention can be successfully put into finite element analysis to obtain the calculation results of tensile mechanical behavior.

[0171] Example 2

[0172] Model of a dual-size network TiB / Ti composite material with a volume fraction of 2.5 vol.% (whisker 1: 0.4 vol.%, Φ0.3 μm×6 μm; whisker 2: 2.1 vol.%, Φ0.1 μm×2 μm)

[0173] In this embodiment, step S1 specifically includes:

[0174] S11. Determine the geometric parameters of the whisker and the substrate, wherein the whisker geometric parameters include: double-sized whiskers, whisker 1 diameter of 0.3 μm, whisker 1 aspect ratio of 20, whisker 1 volume fraction of 0.4 vol.%, whisker 2 diameter of 0.1 μm, whisker 2 aspect ratio of 20, whisker 2 volume fraction of 2.1 vol.%, RVE size of 15 μm, and detection zone size of 5 μm. In this example, there are 27 detection zones, numbered from (0,0,0) to (2,2,2).

[0175] S12, determine that the configuration is a mesh configuration, the number of cell walls N on each side of RVE is 1 μm, and the cell wall thickness t is 1 μm;

[0176] S13, creating a whisker 1 with a size of Φ0.3 μm×6 μm, and creating a whisker 2 with a size of Φ0.1 μm×2 μm;

[0177] S14. Establish a three-dimensional RVE with a side length of L = 15 μm and name it Base.

[0178] In this embodiment, step S3 specifically includes:

[0179] S31. Calculate the side length L of the Voronoi structure used for cell wall cutting Voronoi , defined as:

[0180] L Voronoi =LN*t=14μm

[0181] S32. Use the Pyvoro library to generate Voronoi cell information, including cell number, cell vertex, and cell face; traverse the cell face and vertex information of each cell, use the WirePolyLine command in Abaqus software to connect the cell edges, and then use the CoverEdges command to form the cell face; each cell face forms a cell shell, and then use the AddCells command to generate a cell entity; name the constructed cells Cell-0, Cell-1, ..., Cell-((N+1)) 3 -1); each cell is displaced along the (x, y, z) direction to generate a spatial structure for cutting the cell wall. For Cell-i, the displacement is defined as:

[0182]

[0183] S33, cutting each cell with the Base, and dividing the Base into cell walls and other areas.

[0184] Figure 4 Shown is a schematic diagram of the generated cell wall.

[0185] In this embodiment, step S4 specifically includes:

[0186] S41, first insert the whisker 1, and the conflict judgment method is the same as S41 to S47 of embodiment 1;

[0187] S42. If the coordinates of the bottom surface of the whisker exceed the range of the RVE, it means that the whisker has passed through the surface of the RVE, and the whisker and the RVE surface are cut; the whisker is cut using the cell wall to ensure that whisker 1 is within the cell wall; the volume is calculated after cutting to determine the current volume fraction.

[0188] S43. If the specified volume fraction (0.4 vol.%) is not reached, then the generation of new whiskers 1 continues. When the specified volume fraction is reached, the generation of whiskers 1 stops.

[0189] S44, inserting whisker 2, and the conflict determination method is the same as S41 to S47 of embodiment 1;

[0190] S45, if the coordinates of the bottom surface of the whisker exceed the range of the RVE, it means that the whisker has passed through the surface of the RVE, and the whisker and the RVE surface are cut; the whisker is cut using the cell wall to ensure that the whisker 2 is located at other positions outside the cell wall; the volume is calculated after cutting to determine the current volume fraction;

[0191] S46. If the specified volume fraction (2.1 vol.%) is not reached, then the generation of new whiskers 2 continues. When the specified volume fraction is reached, the generation of whiskers 2 is stopped.

[0192] In this embodiment, steps S5, S5 and S7 are the same as those in embodiment 1.

[0193] Figure 5 The generated 2.5 vol.% dual-size mesh TiB / Ti composite model is shown, in which the larger whiskers 1 are distributed in the cell wall area, and the smaller whiskers 2 are distributed in the cell, wherein the number of whiskers 2 is about 4000, indicating that the embodiment of the present invention has the ability to generate a huge number of randomly distributed whiskers. The distribution characteristics of the model whiskers are consistent with the various input parameters, showing the good effect of the embodiment of the present invention in generating the whisker-reinforced composite model.

[0194] Figure 6 The tensile stress-strain curve of the model and the comparison of typical experimental data of the same configuration are shown in Figure 1. The finite element material property parameters are not described in detail. The tensile stress-strain curve of the model shows that the model generated by the embodiment of the present invention can be smoothly put into finite element analysis to obtain the tensile mechanical behavior calculation results. The elastic stage and the plastic stage in the calculation results have a high consistency with the experimental data, which shows that the model generated by the embodiment of the present invention has a good effect in the calculation and analysis of composite material structure modeling.

[0195] The method provided by the above embodiment of the present invention introduces spatial geometric information judgment, utilizes whisker geometric features, and adopts structural coordinates for conflict detection, which is simple and effective; introduces a partition detection mechanism, and the newly added whiskers are only detected for conflict with the whiskers in the current detection area, which can reduce the number of detections, thereby reducing time complexity and improving modeling and calculation efficiency; especially for models with more than 100 whiskers, it has a higher execution efficiency; the above embodiment of the present invention performs displacement and cutting operations on cells to generate cell walls, and can flexibly control the cell size and cell wall thickness to control the whisker distribution area in the mesh configuration, and then control the mesh configuration distribution of whiskers, providing strong support for the structural design of mesh configuration composite materials. The above embodiment of the present invention can generate a variety of composite material RVE models with different whisker sizes, volume fractions, uniform configurations or mesh configurations through parameter input, realize diversified configuration design, and then perform finite element calculations and obtain mechanical performance data, providing strong support for configuration design optimization.

[0196] The method provided by the above embodiment of the present invention can be used to study the tensile mechanical behavior of whisker-reinforced metal-based composite materials, and has a guiding role in the structural design of metal-based composite materials with uniform, random, and network-shaped distribution of whiskers.

[0197] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various modifications or variations within the scope of the claims, which does not affect the essence of the present invention. The above preferred features can be used in any combination without conflicting with each other.

Claims

1. A method for calculating the mechanical properties of whisker reinforced metal matrix composites, characterized in that: include: Obtaining configuration parameters, geometric parameters of whiskers and geometric parameters of the matrix; According to the configuration parameters, determining whether to generate a mesh configuration; If a mesh configuration is generated, the cell wall is generated through the cell information based on the geometric parameters of the matrix; if a mesh configuration is not generated, the cell wall is not generated; Generate whiskers according to their geometric parameters, and perform collision detection through partitioning, whisker projection and whisker distance; Incorporating whisker reinforcements and cutting the matrix; Perform meshing and material property assignment, and set calculation steps and boundary conditions; Perform finite element calculation and output tensile stress-strain curve results based on the calculation results.

2. The method according to claim 1, characterized in that The configuration parameters, the geometric parameters of the whiskers and the geometric parameters of the substrate are obtained, wherein: the geometric parameters of the whiskers include whether the whiskers are double-sized whiskers, the whisker diameter, the whisker aspect ratio, the whisker volume fraction, the representative volume unit size and the detection area size; the configuration includes a uniform configuration or a mesh configuration, and the parameters of the mesh configuration include the number of cell walls N on each side of the representative volume unit x , N y , N z and the cell wall thickness t x , t y , t z .

3. The method according to claim 1, characterized in that: The step of generating a cell wall through cell information includes: Use the Pyvoro library to generate Voronoi cell information, including cell number, cell vertex, and cell face; Traverse the cell faces and vertex information of each cell, use the WirePolyLine command in Abaqus software to connect the cell edges, and then use the CoverEdges command to form the cell faces; Each cell face forms a cell shell, and then the AddCells command is used to generate a cell entity; The constructed cells are named Cell-0, Cell-1, ..., Cell-((N x +1)(N y +1)(N z +1)-1); Each cell is displaced along the x, y, and z directions to generate a spatial structure for cutting the cell wall.

4. The method according to claim 1, characterized in that: The whiskers are generated according to the geometric parameters of the whiskers, and conflict detection is performed through partitioning, whisker projection and whisker distance, wherein the process of generating the whiskers includes: It is determined whether the whisker configuration is a uniform configuration or a mesh configuration. If the whisker configuration is a uniform configuration, whisker 1 and whisker 2 are set, whisker 1 is generated first, and then whisker 2 is generated; if the whisker configuration is a mesh configuration, whisker 1 is distributed in the cell wall area, and whisker 2 is distributed in the cell area.

5. The method according to claim 1, characterized in that The whiskers are generated according to the geometric parameters of the whiskers, and whisker collision detection is performed through partitioning, whisker projection and whisker distance, wherein the whisker collision detection includes: The whiskers are randomly distributed in the representative volume unit by rotation and movement, and the detection area where the whiskers are located after rotation and movement is determined; Project the new and old whiskers onto the corresponding axes to determine whether their axial projection intervals intersect; If the projection intervals do not intersect, the whiskers do not intersect; if the projection intervals intersect, the closest distance between the two whiskers is calculated. If the closest distance is greater than the sum of the two whisker radii, it is judged that there is no intersection. Otherwise, the two whiskers intersect, and the new whisker is randomly rotated and moved to a new position until they do not intersect each other. Determine whether the volume fraction of whiskers meets preset requirements; If the volume fraction of the whiskers does not meet the preset requirements, new whiskers continue to be generated. When the preset volume fraction is reached, the whisker generation stops.

6. The method according to claim 5, characterized in that The determining whether the axial projection intervals intersect includes: The whiskers do not intersect if the intervals satisfy the following rules: Where d1 is the new whisker, d2 is the existing whisker diameter, represents the collision margin, C 1-top is the coordinate of the upper and lower surfaces of the new whisker, C 2-top is the coordinate of the upper and lower surfaces of the existing whiskers, C 1-bottom is the coordinate of the bottom surface of the new whisker, C 2-bottom is the coordinate of the bottom surface of the existing whisker, is the unit direction vector.

7. The method according to claim 5, characterized in that The calculation of the shortest distance between two whiskers comprises: Determine whether two whiskers are parallel according to the following parallel judgment formula: If the parallel judgment formula is satisfied, the two whiskers are parallel, and the distance formula is: If the parallel judgment formula is not satisfied, the two whiskers are not parallel, and the distance formula is: In the above formula, | means taking the absolute value; ∥ means taking the Euclidean norm; d min is the shortest distance between the new whisker and the existing whisker.

8. The method according to claim 5, characterized in that The determining whether the volume fraction of the whisker meets the preset requirements includes: determining whether the coordinates of the bottom surface of the whisker exceed the range of the representative volume unit; if so, cutting the whisker from the surface of the representative volume unit, and then determining whether the current volume fraction of the whisker meets the preset requirements.

9. The method according to claim 1, characterized in that: The meshing and material attribute assignment are performed, wherein the material attribute assignment includes: the density, elastic modulus, Poisson's ratio, and brittle damage model of the whisker, which are assigned to Whiskers; the density, elastic modulus, Poisson's ratio, plastic constitutive model, and ductile fracture model of the matrix, which are assigned to Base-hole; and the cohesion model describing the interface behavior, which is assigned to Interface; The setting of calculation steps and boundary conditions includes: creating an explicit dynamics calculation step, setting the calculation step length, setting a uniaxial stretching boundary condition, and binding the stretching surface to the reference point Rp-1; setting a reference point set RF, RF binding the stretching surface in the positive direction of the x-axis, the displacement boundary condition of RF is 0.05×L, L is the size of the representative volume unit, and the displacement degree of freedom of the fixed surface on the other side is set to zero.

10. The method according to claim 9, characterized in that The step of outputting the tensile stress-strain curve result according to the calculation result includes: According to the calculation results, the reaction force and displacement data are extracted for stress-strain behavior and mechanical performance evaluation and analysis, which are defined as: σ=RF1 / L 2 ,ε=U1 / L; Among them, σ is the tensile stress, ε is the strain, RF1 is the reaction force component of the reference point set RF, U1 is the displacement component of RF, and L is the size of the representative volume unit.

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