Particle reinforced composite material crack characterization quantification method
Through CT scanning and finite element analysis, three-dimensional particle and crack models are constructed and equivalent material properties are calculated, which solves the problem of difficulty in quantifying crack parameters of particle-enhanced composite materials in the prior art, and realizes accurate quantification of cracks and prediction of material properties.
Patent Information
- Application Number
- CN202510620252.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-14
- Publication Date
- 2025-08-08
AI Technical Summary
The prior art is difficult to accurately extract and quantify crack key parameters in particle-reinforced composite materials, especially in material designs of different morphology and damage degrees.
Material slice images were obtained through CT scans, three-dimensional reconstruction and threshold segmentation were performed, three-dimensional particle and crack models were constructed, equivalent length and width were calculated, and the matrix finite element model was converted into an octahedral model, and the equivalent material properties were calculated. Abaqus finite element software was used for analysis, periodic boundary conditions were applied, and the equivalent elastic modulus, Poisson's ratio and shear modulus were calculated.
The precise quantification of cracks in particle-reinforced composite materials is achieved, and new data support is provided, which can simulate the expansion process of cracks in the material, predict the mechanical properties of the material, and solve the problem of lack of quantitative evaluation methods in the prior art.
Smart Images
Figure CN120451411A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of process optimization design, and more particularly to a method for characterizing and quantifying cracks in particle-reinforced composite materials. Background Art
[0002] Particle-reinforced composites (or PRCs) are macroscopically composed of two or more materials with different properties. Due to their unique characteristics, such as particle type, particle volume fraction, matrix type, and anisotropic mechanical properties, PRCs are highly designable and widely used in areas such as building concrete, aerospace metal-based materials, and solid propellants for solid rocket engines. However, due to the complex preparation process, PRCs contain numerous cracks, which are an unavoidable defect. When PRCs are subjected to tensile loads, the interface between the particles and the matrix is damaged, and cracks within the matrix gradually expand into large cracks, ultimately causing the material to fracture and fail.
[0003] Clarifying the characterization method of cracks in particle-reinforced composite materials and proposing a calculation method for the equivalent stiffness parameters of the finite element model of the cracked matrix, and determining the material properties of the finite element model containing cracks, are of great practical significance for the study of the mechanical properties of particle-reinforced composite materials and for guiding process design.
[0004] However, existing technologies have certain limitations in crack characterization and quantification, making it difficult to accurately extract and quantify the key parameters of material cracks. Especially in the field of material design with different morphologies and damage degrees, there is a lack of an effective and universal evaluation method. Summary of the Invention
[0005] To solve the problem that the above-mentioned prior art is difficult to accurately extract and quantify the key parameters of material cracks, the present invention proposes a method for characterizing and quantifying cracks in particle-reinforced composite materials, which includes: Obtaining slice images of the material taken by a CT instrument; Performing three-dimensional reconstruction based on the slice images within the slice range to obtain a three-dimensional reconstructed model; performing threshold segmentation on the three-dimensional reconstructed model to obtain a three-dimensional particle model and a three-dimensional crack model; obtaining the equivalent length and equivalent width of all cracks in the three-dimensional crack model; Equivalently converting the three-dimensional crack model into an octahedron model includes: determining the value range of the edge length and the value range of the center plane side length of the octahedron model based on the numerical range of the equivalent length and the equivalent width of multiple cracks in the three-dimensional crack model measured by image analysis software; determining the upper and lower vertex coordinates of the octahedron model based on the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model, and constructing the octahedron model; Constructing a matrix finite element model, wherein the matrix finite element model includes a plurality of octahedral models of different volumes at this stage, and the sum of the volumes of all the octahedral models is the total volume content of the crack model calculated after threshold segmentation of the three-dimensional model; Determining equivalent material properties of the matrix finite element model, wherein the material properties include an equivalent elastic modulus, an equivalent Poisson's ratio, and an equivalent shear modulus, and then obtaining the stiffness of the matrix finite element model based on the equivalent material properties; Determine a three-dimensional particle finite element mesh model, wherein the three-dimensional particle finite element mesh model includes establishing a hexahedral mesh model including particles and a matrix based on a three-dimensional reconstruction model of the particles after threshold segmentation; wherein the material properties of the matrix are the values calculated based on the above-mentioned matrix finite element model containing crack properties; calculate the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the three-dimensional particle finite element mesh model containing equivalent crack properties.
[0006] Based on the above-mentioned crack characterization and crack parameter quantification methods of particle-reinforced composite materials, the present invention further establishes a high-fidelity real structure finite element mesh model of the scanned test section material through an image processing algorithm, and calculates the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the material containing crack properties in the Abaqus finite element software. The method of importing the finite element mesh model into the Abaqus finite element software includes two steps. The first step is to write an algorithm in the software Matlab to realize the processing of the scanned images of two types of structures, particles and matrix, and save them as binary files. The second step is to use the Python language to write an algorithm to process the binary file completed in the first step, import it into the Abaqus finite element software for analysis, and establish a three-dimensional finite element mesh model. The corresponding material property values are assigned to the particles, and the material properties of the matrix are calculated using the above-mentioned matrix finite element model; then the model is assembled, the analysis step is set, and general periodic boundary conditions are applied to obtain the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the particle-reinforced composite material.
[0007] Preferably, the method for determining the slicing range includes: Determine the slicing range in the initial stage as .
[0008] Among them, 0< b - a < N ,and a 、 b All are preset values. N is the number of CT slice images corresponding to the material at the initial stage.
[0009] Preferably, performing threshold segmentation on the three-dimensional reconstructed model to obtain a three-dimensional particle model and a three-dimensional crack model includes: Determine the threshold range, which includes: drawing a grayscale histogram of the three-dimensional reconstructed model, and determining the first peak of the grayscale histogram as the crack threshold; determining the crack threshold range as: [0, θ ],in θ is the crack threshold; the grayscale corresponding to the second peak m is the matrix threshold, and the crack threshold range is determined as: [ θ , m]; the third peak and the nth peak correspond to the thresholds of different particles, and the corresponding threshold ranges are determined respectively, and the maximum threshold value is 255.
[0010] The three-dimensional reconstructed model is threshold segmented according to the crack threshold range to obtain a three-dimensional crack model and a three-dimensional particle model.
[0011] Preferably, a Zhang Zhidi b Zhang's slice images are superimposed to obtain the reconstructed model including: For the first a Zhang Zhidi b Zhang's slice images were superimposed to obtain a three-dimensional reconstructed model; The parts other than the material in the three-dimensional reconstructed model are cut to obtain a reconstructed model, and the reconstructed model is a cuboid.
[0012] Preferably, obtaining the equivalent length and equivalent width of the three-dimensional crack model includes: Obtaining a first projection surface of the three-dimensional crack model on a first preset plane, and obtaining a maximum length of the first projection surface in a first preset direction and a maximum width in a second preset direction, wherein the first preset direction is perpendicular to the second preset direction; Obtaining a second projection surface of the three-dimensional crack model on a second preset plane, and obtaining a maximum length of the second projection surface in a second preset direction and a maximum width in a third preset direction, wherein the second preset plane is perpendicular to the third preset plane; Obtaining a third projection surface of the three-dimensional crack model on a third preset plane, and obtaining a maximum length of the third projection surface in a third preset direction and a maximum width in the first preset direction, wherein the third preset plane is perpendicular to the first preset plane; Determine the equivalent length of all cracks in the three-dimensional crack model as , where L1 is the minimum length of the three-dimensional crack model in the first preset direction on the first projection surface, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; L2 is the maximum length of the three-dimensional crack model in the first preset direction on the first projection surface, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; the equivalent width of all cracks in the three-dimensional crack model is determined as w=max(W1,W2), where W1 is the minimum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; W2 is the maximum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; at the same time, the value requirement is to satisfy w1<w2<L1<L2.
[0013] Preferably, determining the coordinates of the upper and lower vertices of the octahedron model based on the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model includes: randomly generating the side length of the center plane of the octahedron, the side length is taken as the equivalent width of all the cracks, and calculating the upper and lower vertices based on the determined side length and edge length; randomly generating the edge length of the octahedron, the edge length is taken as the equivalent length of all the cracks; and at the same time judging that any two octahedron models do not interfere with each other, and the judgment condition is that the distance between the centers of any two octahedron models is greater than twice L2.
[0014] Preferably, determining the edge length of the octahedron model according to the equivalent length and equivalent width of the three-dimensional crack model includes: Generate the edge length of the octahedron model according to the random function R : Using Python, we write an algorithm to build a matrix finite element model containing an octahedron and save it in .py format. We generate the octahedron model by writing code and running it in the finite element software Abaqus. We call the random function random.uniform to generate the edge length R of the octahedron model: ; in k 1 and k 2 are coefficients of preset size and 0< k 1<1< k 2, L1, L2 Take the equivalent length of all cracks as w is the equivalent width, random.uniform is a random function.
[0015] Preferably, the method further includes determining the center coordinates of the octahedron model, including: The matrix finite element model is equivalent to a cube, the side length of the cube is L, and the value is n times L2, where L2 is the maximum equivalent length of the crack; the random function random.uniform is called again to generate the center coordinates of the center plane of the octahedron model, where: ; ; ; in and are all random coefficients, and 0< < <L / 2, random.uniform is a random function, the center coordinates are ( x , y , z ).
[0016] Preferably, the calculation method of the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix material includes: The octahedron model with a certain volume content is equivalent to a matrix finite element model. A matrix finite element model with a certain crack volume is established using Python and saved as a .py file format. In the file menu of the Abaqus software, select Run .py file. The second step is to define the material properties. The equivalent material properties of the octahedron model are: Density: 1.29 kg / m 3 , the elastic modulus is m times that of the matrix, m>1, and the Poisson's ratio is 0.01; the rest is given the cross-sectional properties of the matrix material; the octahedron model and the matrix model are assembled; the analysis step is created as a static analysis step; the octahedron model and the matrix model are divided into tetrahedral meshes, general periodic boundary conditions are applied, and the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model are calculated by the homogenization method; the crack volume is the sum of the volumes of all the octahedron models.
[0017] Preferably, it also includes: writing algorithms in Matlab and Python languages to process slice images, reconstructing a material finite element mesh model, including a particle finite element mesh model and a matrix finite element mesh model; calculating the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the material finite element mesh model, and the material properties of the matrix finite element mesh model are the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model; and applying general periodic boundary conditions to the three-dimensional particle finite element mesh model again, and calculating the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the particle finite element mesh model by a homogenization method.
[0018] The beneficial effects of the present invention are: 1. This method can accurately extract and quantify key parameters of material cracks, providing new data support for further analysis and research of cracks. The method can be effectively applied to different types of particle-reinforced composite materials and quantitatively evaluate parameters such as different crack morphologies and volumes.
[0019] 2. The present invention calculates the equivalent stiffness of the material, providing a reliable numerical model for predicting the mechanical properties of an equivalent finite element model of a particle-reinforced composite material containing a certain crack under a damaged state, and can effectively simulate the mechanical properties of the crack propagation process in the material.
[0020] 3. The present invention solves the current lack of quantitative research methods for cracks in different composite materials. It proposes a method for establishing a finite element model of a cracked matrix and an equivalent stiffness calculation algorithm, as well as a method for establishing a real mesh finite element model of a composite material. Using a finite element model of a matrix with different crack parameters as input, the present invention calculates the effect of crack damage on the equivalent stiffness of the composite material, thereby achieving more accurate material performance prediction. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood by reading the following detailed description with reference to the accompanying drawings. In the accompanying drawings, several embodiments of the present invention are shown in an illustrative and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein: Figure 1 is a flowchart schematically illustrating the steps of a method for characterizing and quantifying cracks in a particle-reinforced composite material according to an embodiment of the present invention; Figure 2 is a schematic diagram of a three-dimensional crack model according to an embodiment of the present invention; Figure 3 is a schematic diagram of a finite element matrix and an octahedron model according to an embodiment of the present invention; Figure 4 is a schematic diagram of a finite element model obtained based on a finite element matrix and an octahedron model according to an embodiment of the present invention; Figure 5 It is to establish a three-dimensional finite element mesh model of the scanning test section material Figure 6 is a schematic diagram of stress distribution of ammonium perchlorate (AP) particles according to an embodiment of the present invention; Figure 7 is a schematic diagram of stress distribution of aluminum (AL) particles according to an embodiment of the present invention; Figure 8 is a schematic diagram of crack stress distribution according to an embodiment of the present invention; Figure 9 Schematic diagram of matrix stress distribution according to an embodiment of the present invention. DETAILED DESCRIPTION
[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work shall fall within the scope of protection of the present invention.
[0023] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0024] Figure 1 The figure schematically shows a flowchart of the steps of a method for characterizing and quantifying cracks in a particle-reinforced composite material according to an embodiment of the present invention.
[0025] like Figure 1 As shown, a method for characterizing and quantifying cracks in a particle-reinforced composite material includes steps S1 to S8.
[0026] Step S1: Obtaining a slice image of a material captured by a CT device.
[0027] Step S2: Perform three-dimensional reconstruction based on the slice images within the slice range to obtain a three-dimensional reconstructed model.
[0028] In one embodiment, the method for determining the slicing range includes: determining the slicing range in the initial stage as .
[0029] Among them, 0< b - a < N ,and a 、 b All are preset values. N is the number of CT slice images of the material.
[0030] In one embodiment, the initial stage a Zhang Zhidi b The slice images of the first stage are superimposed to obtain the reconstructed model, including: a Zhang Zhidi b The slice images of Zhang are superimposed to obtain a three-dimensional reconstructed model; the parts other than the material in the three-dimensional reconstructed model are cut to obtain a reconstructed model, and the reconstructed model is a cuboid.
[0031] Step S3: performing threshold segmentation on the three-dimensional reconstructed model to obtain a three-dimensional particle model and a three-dimensional crack model.
[0032] In one embodiment, performing threshold segmentation on a three-dimensional model to obtain three-dimensional particle models and three-dimensional crack models at each stage includes: determining a threshold range, which includes: drawing a grayscale histogram of the three-dimensional reconstructed model and determining the first peak of the grayscale histogram as the crack threshold; determining the crack threshold range as: [0, θ ],in θ is the crack threshold; the grayscale corresponding to the second peak m is the matrix threshold, and the crack threshold range is determined as: [ θ , m]; The third peak and the nth peak correspond to the thresholds of different particles, and the corresponding threshold ranges are determined respectively, with the maximum threshold value being 255. According to the crack threshold range, the three-dimensional model is threshold segmented to obtain a three-dimensional crack model and a three-dimensional particle model. In this embodiment, the threshold segmentation command Interactive thresholding is created in the Avizo software to perform threshold segmentation on the three-dimensional model, and the threshold range is determined to be: [0, θ ], a crack reconstruction model is obtained, and different particles correspond to different threshold ranges. The reconstruction model includes a three-dimensional crack model and a three-dimensional particle model corresponding to different particles.
[0033] It should be noted that the grayscale values are extracted from the three-dimensional model in the initial stage. By plotting the grayscale histogram of these values, the distribution of different grayscale intervals can be observed. In this case, the first peak of the histogram usually corresponds to the crack area (the crack area usually has a large difference in grayscale value from the surrounding particle area). According to the histogram, the first peak is determined as the crack threshold (θ). This threshold is the upper limit of the grayscale value range of the crack area. The grayscale value of the crack area is usually low and is significantly different from other areas (such as the particle area). The crack threshold range is determined to be: [0, θ ], that is, it contains all regions with grayscale values lower than or equal to θ. These regions are marked as crack regions in the subsequent segmentation process.
[0034] like Figure 2 As shown in Figure 1, 3D crack models in a material's 3D model often have multiple different shapes and sizes. Crack geometries can have different starting locations, propagation paths, and complex geometric features, so a single 3D crack model may not fully describe the actual situation.
[0035] Step S4: Obtain the equivalent length and equivalent width of all cracks in the three-dimensional crack model.
[0036] In one embodiment, obtaining the equivalent length and equivalent width of the three-dimensional crack model includes: obtaining a first projection surface of the three-dimensional crack model on a first preset plane, and obtaining the maximum length of the first projection surface in the first preset direction and the maximum width in the second preset direction, wherein the first preset direction is perpendicular to the second preset direction; obtaining a second projection surface of the three-dimensional crack model on a second preset plane, and obtaining the maximum length of the second projection surface in the second preset direction and the maximum width in the third preset direction, wherein the second preset plane is perpendicular to the third preset plane; obtaining a third projection surface of the three-dimensional crack model on a third preset plane, and obtaining the maximum length of the third projection surface in the third preset direction and the maximum width in the first preset direction, wherein the third preset plane is perpendicular to the first preset plane; determining the equivalent length of the three-dimensional crack model as l=max(L1,L2), wherein L1 is the maximum length of the three-dimensional crack model on the first projection surface The minimum length of the length in the first preset direction, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; L2 is the maximum length of the three-dimensional crack model in the first preset direction on the first projection surface, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; the equivalent width of all cracks in the three-dimensional crack model is determined as w=max(W1,W2), where W1 is the minimum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; W2 is the maximum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; and the values are required to satisfy w1<w2<L1<L2. In this embodiment, the first preset plane is the plane where the x and y axes are located, the second preset plane is the plane where the y and z axes are located, and the third preset plane is the plane where the z and x axes are located.
[0037] It should be noted that since the three-dimensional crack model is relatively complex, it is necessary to convert the three-dimensional crack model into an equivalent octahedron to facilitate the subsequent calculation of the crack characteristics of the material. This step is to quantify the size of the three-dimensional crack model in order to construct the equivalent octahedron.
[0038] Step S5: Equivalent the three-dimensional crack model to an octahedron model.
[0039] Among them, equating the three-dimensional crack model to an octahedron model includes: determining the numerical range of the equivalent length and equivalent width of multiple cracks in the three-dimensional crack model obtained by measuring with image analysis software, determining the value range of the edge length and the value range of the center plane side length of the octahedron model according to the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model, and constructing the octahedron model.
[0040] In one embodiment, determining the edge length of the octahedron model according to the equivalent length and equivalent width of the three-dimensional crack model includes: generating the edge length of the octahedron model according to the random function R : Using Python, we write an algorithm to build a matrix finite element model containing an octahedron and save it in .py format. We generate the octahedron model by writing code and running it in the finite element software Abaqus. We call the random function random.uniform to generate the edge length R of the octahedron model: ; in k 1 and k 2 are coefficients of preset size and 0< k 1<1< k 2, L1, L2 Take the equivalent length of all cracks as w is the equivalent width, random.uniform is a random function.
[0041] In one embodiment, determining the upper and lower vertex coordinates of the octahedron model based on the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model includes: randomly generating the side length of the center plane of the octahedron, and the side length is taken as the equivalent width of all the cracks; randomly generating the edge length of the octahedron, and the edge length is taken as the equivalent length of all the cracks; and simultaneously judging that any two octahedron models do not interfere with each other, and the judgment condition is that the distance between the centers of any two octahedron models is greater than twice L2.
[0042] The distance between the center coordinate and the vertex, half of the side length of the center plane, and the edge length of the octahedron model can form a right triangle. Repeat this step to obtain the upper and lower vertices.
[0043] It should be noted that the random.uniform function is provided by the Python random module and is used to generate random floating-point numbers within a specified range. This function accepts two parameters, representing the range of random numbers to be generated, and returns a floating-point number that is uniformly distributed within that range.
[0044] Step S6: constructing a matrix finite element model.
[0045] The matrix finite element model includes multiple octahedral models of different volumes at this stage, and the sum of the volumes of all octahedral models is the total volume content of the crack model calculated after threshold segmentation of the three-dimensional model.
[0046] In one embodiment, the process of establishing a matrix finite element model containing multiple cracks is written in Python and saved in a .py file format. The .py file can be run in the menu file of the finite element software Abaqus to establish a matrix finite element model with multiple cracks. Figure 3 As shown, the base finite element model in this embodiment is a cube model, which includes multiple octahedron models inside.
[0047] Step S7: determining the equivalent material properties of the matrix finite element model; and then obtaining the stiffness of the matrix finite element model based on the equivalent material properties.
[0048] Among them, the equivalent material properties include equivalent elastic modulus, equivalent Poisson's ratio, and equivalent shear modulus.
[0049] In one embodiment, a method for calculating the equivalent elastic modulus, equivalent Poisson's ratio, and equivalent shear modulus of the matrix material includes: The octahedron model with a certain volume content is equivalent to a matrix finite element model. A matrix finite element model with a certain crack volume is established using Python and saved as a .py file format. In the file menu of the Abaqus software, select Run .py file. The second step is to define the material properties. The equivalent material properties of the octahedron model are: Density: 1.29 kg / m 3 , the elastic modulus is m times that of the matrix, m>1, and the Poisson's ratio is 0.01; the rest is given the cross-sectional properties of the matrix material; the octahedron model and the matrix model are assembled; the analysis step is created as a static analysis step; the octahedron model and the matrix model are divided into tetrahedral meshes, general periodic boundary conditions are applied, and the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model are calculated by the homogenization method; the crack volume is the sum of the volumes of all the octahedron models.
[0050] In one embodiment, the assembly operation is completed in the finite element software Abaqus, divided into tetrahedral meshes, general periodic boundary conditions are applied, and the stiffness homogenization calculation method is applied to obtain the equivalent stiffness value of the matrix finite element model with equivalent cracks as follows: Figure 4 As shown. In the present invention, an algorithm is written in Python to implement a method for calculating equivalent elastic property values. The characteristic angles, characteristic edges, and characteristic faces of hexahedral elements are defined, and the equivalent elastic modulus, equivalent Poisson's ratio, and equivalent shear modulus of all tetrahedral mesh elements within the hexahedral model are obtained. Finally, the homogenization method is applied to calculate the equivalent stiffness properties of the entire material model. Figure 4On the right side, the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model containing a certain crack are obtained by applying the algorithm of the present invention. For example, the equivalent elastic modulus is: (E1 is 11.289 MPa, E2 is 11.247 MPa, and E3 is 11.312 MPa).
[0051] In one embodiment, the feature angle (Vertex) is the coordinates of all vertices of the finite element model (hexahedron). The feature edge (Edge) is the vector (length and direction) of all strips of the finite element model. The feature face (Face) is the normal vector and area of all faces of the finite element model. In one embodiment, the stiffness E of the matrix finite element model is obtained based on the equivalent material properties of the matrix finite element model. m , Poisson's ratio V m and shear modulus G m ;.
[0052] For the i A finite element model with a stiffness of E i =f c,i E c + f m,i E m , f c,i is the ratio of the volume of the octahedron model to the volume of the finite element model; E c is the stiffness of the octahedron model; E m is the stiffness of the matrix finite element model; f m,i is the ratio of the volume of the part of the finite element model that belongs to the matrix finite element model to the volume of the finite element model. i The Poisson's ratio of the finite element model is V i ( V i =f p,i V p +f m,i V m ) and the shear modulus is G i ( G i =f p,i G p +f m,i G m ). V p is the Poisson's ratio of the octahedral model, V m is the Poisson's ratio of the matrix finite element model; G pis the shear modulus of the octahedron model, G m is the shear modulus of the matrix finite element model; f p,i It represents the ratio of the volume of the part of the finite element model belonging to the particle finite element model to the volume of the finite element model.
[0053] Step S8: Determine a three-dimensional particle finite element mesh model.
[0054] The three-dimensional particle finite element grid model includes establishing a hexahedral grid model containing particles and a matrix based on a three-dimensional reconstruction model of the particles after threshold segmentation; wherein the material properties of the matrix are the values calculated based on the above-mentioned matrix finite element model containing crack properties; and calculating the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the three-dimensional particle finite element grid model containing equivalent crack properties.
[0055] In one embodiment, determining the center coordinates of the octahedron model further includes: The matrix finite element model is equivalent to a cube, the side length of the cube is L, and the value is n times L2, where L2 is the maximum equivalent length of the crack; the random function random.uniform is called again to generate the center coordinates of the center plane of the octahedron model, where: ; ; ; in and are all random coefficients, and 0< < <L / 2, random.uniform is a random function, the center coordinates are ( x , y , z ).
[0056] In one embodiment, it also includes: processing slice images using algorithms written in Matlab and Python languages, reconstructing a material finite element mesh model, including a particle finite element mesh model and a matrix finite element mesh model; calculating the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the material finite element mesh model, and the material properties of the matrix finite element mesh model are the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model; and applying general periodic boundary conditions to the three-dimensional particle finite element mesh model again, and calculating the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the particle finite element mesh model through a homogenization method.
[0057] In one embodiment, a particle-reinforced composite material comprises two structures: particles and a matrix. Building on the methods for characterizing cracks and quantifying crack parameters in the particle-reinforced composite material described in S1, the present invention further utilizes an image processing algorithm to establish a high-fidelity finite element mesh model of the scanned test section material. The equivalent elastic modulus, equivalent Poisson's ratio, and equivalent shear modulus of the crack-containing properties are calculated using the finite element software Abaqus. The calculation method is consistent with that described in S7.
[0058] In one embodiment, a method for importing a real-geometry mesh finite element model of a material into the finite element software Abaqus includes two steps. The first step is to write an algorithm in Matlab to process scanned slice images of both the particle and matrix structures and save them as binary files. The second step is to write an algorithm in Python to process the binary file completed in the first step, import it into the finite element software Abaqus for analysis, and establish a three-dimensional mesh finite element model. The particle material properties are assigned corresponding numerical values, and the matrix material properties are calculated using S7 to predict the matrix finite element model. The model is then assembled, the analysis steps are set, and general periodic boundary conditions are applied to obtain the equivalent stiffness of the particle-reinforced composite material.
[0059] In one embodiment, the steps for establishing a scanned image processing method using Matlab include: ① creating a new file and importing the three-dimensional raw format CT image files obtained from the first step of reconstruction, namely the particle.raw file for the particles and the matrix.raw file for the matrix. Defining the image reading function imread to read the corresponding slice images along the scanning direction from the two imported raw files, skipping the image if it is empty, and looping to convert each slice image into a grayscale image. ② defining the threshold analysis function graythresh to calculate the image threshold; defining the function imbinarize to perform binarization processing on the image, and looping to save the binarized image. Defining three-dimensional arrays arrgrid1 and arrgrid2 to store the binary values of the corresponding slices in each raw file, respectively. Using the unique() statement to calculate the distribution of the binary values, the values are updated in a loop and stored in the three-dimensional arrays arrgrid1 and arrgrid2. ③ Based on the maximum geometric dimensions of the particle.raw file and the matrix.raw file for the matrix, the geometric dimensions of the new cube array arrgrid3 are defined. Define the volshow statement to display the processed images in the three-dimensional arrays arrgrid1 and arrgrid2. Place the arrgrid1 and arrgrid2 arrays into the arrgrid3 array. Define the image scaling value, define the slice function to display slices at different angles, and apply a custom color map. Save the file as new.raw in the uint8 format.
[0060] The second step is to use Python language to write an algorithm to process the mesh model completed in the first step, and import it into the finite element software Abaqus for analysis. The steps of the algorithm include: ① Setting parameters: defining the size of the three-dimensional geometric model, the path of the 3D image folder and the image data type, defining the function np.fromfile to read the raw file and determine whether the data is empty, defining the function array, creating a new model and naming it. Create a component, and draw a rectangle by sketching and stretching it along the depth direction to form a solid unit. ② Divide the component into grids, define three arrays to store the particle, matrix, and crack solid units respectively, create materials and assign them to the particle, crack, and matrix units, create a mechanical analysis step, apply general periodic boundary conditions, and apply the homogenization method, which is similar to the analysis step method described in S7. The equivalent stiffness of the particle reinforced composite material can be obtained. For the first i A finite element mesh model with a stiffness of E i =f p,i E p + f m,i E m , fp,i is the ratio of the volume of the particle model to the volume of the finite element mesh model in the finite element model; E p is the stiffness of the particle model; E m is the stiffness of the matrix finite element model; f m,i is the ratio of the volume of the part of the finite element model belonging to the matrix finite element model to the volume of the finite element mesh model. i The Poisson's ratio of the finite element model is V i ( V i =f p,i V p +f m,i V m ) and the shear modulus is G i ( G i =f p,i G p +f m,i G m ). V c is the Poisson's ratio of the particle model, V m is the Poisson's ratio of the matrix finite element model; G p is the shear modulus of the particle model, G m is the shear modulus of the matrix finite element model.
[0061] The finite element mesh model of the particles and matrix is completed by the method of realizing the above-mentioned real finite element mesh model. The general periodic boundary conditions are applied to the particle reinforced composite material with crack properties as follows Figure 5 After applying the general periodic boundary conditions, setting the analysis step to statics and applying the tensile load at the main node, the mechanical response of different particles and matrices can be obtained. The results are shown in Figure 6 , Figure 7 , Figure 8 and Figure 9 .
[0062] Based on this, the present invention combines general periodic boundary conditions with multi-scale modeling technology to accurately capture the crack damage parameters of particle-reinforced composite materials and predict the mechanical properties of the calculated materials.
[0063] While several embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Numerous modifications, variations, and alternatives will occur to those skilled in the art without departing from the concept and spirit of the present invention. It should be understood that various alternatives to the embodiments of the present invention described herein may be employed in practicing the present invention.
Claims
1. A method for characterizing and quantifying cracks in particle-reinforced composite materials, characterized in that: include: Obtaining slice images of the material taken by a CT instrument; Performing three-dimensional reconstruction according to the slice images within the slice range to obtain a three-dimensional reconstructed model; Performing threshold segmentation on the 3D reconstructed model to obtain a 3D particle model and a 3D crack model; Obtain the equivalent length and equivalent width of all cracks in the three-dimensional crack model; Equivalently converting the three-dimensional crack model into an octahedron model includes: determining the value range of the edge length and the value range of the center plane side length of the octahedron model based on the numerical range of the equivalent length and the equivalent width of multiple cracks in the three-dimensional crack model measured by image analysis software; determining the upper and lower vertex coordinates of the octahedron model based on the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model, and constructing the octahedron model; Constructing a matrix finite element model, wherein the matrix finite element model includes a plurality of octahedral models of different volumes at this stage, and the sum of the volumes of all the octahedral models is the total volume content of the crack model calculated after threshold segmentation of the three-dimensional model; Determining equivalent material properties of the matrix finite element model, wherein the material properties include an equivalent elastic modulus, an equivalent Poisson's ratio, and an equivalent shear modulus; and then obtaining the stiffness of the matrix finite element model based on the equivalent material properties; Determine a three-dimensional particle finite element mesh model, wherein the three-dimensional particle finite element mesh model includes establishing a hexahedral mesh model including particles and a matrix based on a three-dimensional reconstruction model of the particles after threshold segmentation; wherein the material properties of the matrix are the values calculated based on the above-mentioned matrix finite element model containing crack properties; calculate the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the three-dimensional particle finite element mesh model containing equivalent crack properties.
2. A particle-reinforced composite material crack characterization and quantification method according to claim 1, characterized in that: Methods for determining the slice range include: Determine the slicing range in the initial stage as .
3. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: Threshold segmentation is performed on the 3D reconstructed model to obtain a 3D particle model and a 3D crack model, including: Determine the threshold range, which includes: drawing a grayscale histogram of the three-dimensional reconstructed model, and determining the first peak of the grayscale histogram as the crack threshold; determining the crack threshold range as: [0, θ ],in θ is the crack threshold; the grayscale corresponding to the second peak m is the matrix threshold, and the crack threshold range is determined as: [ θ , m]; the third peak and the nth peak correspond to the thresholds of different particles, and the corresponding threshold ranges are determined respectively, and the maximum threshold value is 255; The three-dimensional reconstructed model is threshold segmented according to the crack threshold range to obtain a three-dimensional crack model and a three-dimensional particle model.
4. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: For the first a Zhang Zhidi b Zhang's slice images are superimposed to obtain the reconstructed model including: For the first a Zhang Zhidi b Zhang's slice images were superimposed to obtain a three-dimensional reconstructed model; The parts other than the material in the three-dimensional reconstructed model are cut to obtain a reconstructed model, and the reconstructed model is a cuboid.
5. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: Obtaining the equivalent length and equivalent width of a 3D crack model includes: Obtaining a first projection surface of the three-dimensional crack model on a first preset plane, and obtaining a maximum length of the first projection surface in a first preset direction and a maximum width in a second preset direction, wherein the first preset direction is perpendicular to the second preset direction; Obtaining a second projection surface of the three-dimensional crack model on a second preset plane, and obtaining a maximum length of the second projection surface in a second preset direction and a maximum width in a third preset direction, wherein the second preset plane is perpendicular to the third preset plane; Obtaining a third projection surface of the three-dimensional crack model on a third preset plane, and obtaining a maximum length of the third projection surface in a third preset direction and a maximum width in the first preset direction, wherein the third preset plane is perpendicular to the first preset plane; Determine the equivalent length of all cracks in the three-dimensional crack model as , where L1 is the minimum length of the three-dimensional crack model in the first preset direction on the first projection surface, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; L2 is the maximum length of the three-dimensional crack model in the first preset direction on the first projection surface, the length in the second preset direction on the second projection surface, and the length in the third preset direction on the third projection surface; the equivalent width of all cracks in the three-dimensional crack model is determined as w =max(W1,W2), where W1 is the minimum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; W2 is the maximum width of the three-dimensional crack model in the second preset direction on the first projection surface, the width in the third preset direction on the second projection surface, and the width in the first preset direction on the third projection surface; at the same time, the value requirement is to satisfy w1<w2<L1<L2.
6. A particle-reinforced composite material crack characterization and quantification method according to claim 5, characterized in that: The coordinates of the upper and lower vertices of the octahedron model are determined based on the center coordinates of the center plane of the three-dimensional crack model and the edge length of the octahedron model. The side length of the octahedron center plane is randomly generated, and the side length is taken as the equivalent width of all the cracks; the edge length of the octahedron is randomly generated, and the edge length is taken as the equivalent length of all the cracks; at the same time, it is judged that any two octahedron models do not interfere with each other, and the judgment condition is that the distance between the centers of any two octahedron models is greater than twice L2.
7. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: Determining the edge length of the octahedron model according to the equivalent length and equivalent width of the three-dimensional crack model includes: Generate the edge length of the octahedron model according to the random function R : Using Python, we write an algorithm to build a matrix finite element model containing an octahedron and save it in .py format. We generate the octahedron model by writing code and running it in the finite element software Abaqus. We call the random function random.uniform to generate the edge length R of the octahedron model: ； in k 1 and k 2 are coefficients of preset size and 0< k 1<1< k 2, L1, L2 Take the equivalent length of all cracks as random.uniform is a random function.
8. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: It also includes determining the center coordinates of the octahedron model: The matrix finite element model is equivalent to a cube, the side length of the cube is L, and the value is n times L2, where L2 is the maximum equivalent length of the crack; the random function random.uniform is called again to generate the center coordinates of the center plane of the octahedron model, where: ； ； ； in a 1 and a 2 are random coefficients, and 0 <a1<a2<L / 2,, random.uniform is a random function, the center coordinates are ( x , y , z ).
9. The method for characterizing and quantifying cracks in a particle-reinforced composite material according to claim 1, wherein: The calculation methods of the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix material include: The octahedron model with a certain volume content is equivalent to a matrix finite element model. A matrix finite element model with a certain crack volume is established using Python and saved as a .py file format. In the file menu of the Abaqus software, select Run .py file. The second step is to define the material properties. The equivalent material properties of the octahedron model are: Density: 1.29 kg / m 3 , the elastic modulus is m times that of the matrix, m>1, and the Poisson's ratio is 0.01; the rest is given the cross-sectional properties of the matrix material; the octahedron model and the matrix model are assembled; the analysis step is created as a static analysis step; the octahedron model and the matrix model are divided into tetrahedral meshes, general periodic boundary conditions are applied, and the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model are calculated by the homogenization method; the crack volume is the sum of the volumes of all the octahedron models.
10. The method for characterizing and quantifying cracks in particle-reinforced composite materials according to claim 1, characterized in that: Also includes: Using Matlab and Python to write algorithms to process slice images, reconstruct the material finite element mesh model, including the particle finite element mesh model and the matrix finite element mesh model; The equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the material finite element mesh model are calculated, and the material properties of the matrix finite element mesh model are the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the matrix finite element model; general periodic boundary conditions are again applied to the three-dimensional particle finite element mesh model, and the equivalent elastic modulus, equivalent Poisson's ratio and equivalent shear modulus of the particle finite element mesh model are calculated by the homogenization method.