Mesoscopic RVE determination method for needled ceramic matrix composite material

Abstract

The invention discloses a method for determining microcosmic RVE of an acupuncture ceramic matrix composite material, and belongs to the field of composite material design. According to the method, a CT projection image of the microstructure of the material is obtained by cutting a sample and performing CT scanning. Secondly, recognizing the geometric dimension (side length and height) of the RVE in the image, and counting the volume distribution of the RVE; then, fitting an exponential distribution function through a volume distribution histogram, and defining an integral range of a characteristic length, which is a core index for representing the statistical uniformity of the material, on the basis of the function; and finally, calculating the average height of the RVE in combination with the integral range, and determining the side length of the RVE as a volume constraint, thereby establishing a mesoscopic RVE model with statistical representativeness. According to the method, the size of the RVE is determined from the aspect of probability by quantifying the volume distribution and the feature length.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of composite material design, and particularly relates to a kind of micro RVE determination method of needle-punched ceramic matrix composite. BACKGROUND

[0002] Ceramic matrix composites, especially continuous fiber reinforced ceramic matrix composites, have become key candidate materials for hot end components in the field of aerospace due to their excellent high-temperature performance, high specific strength and damage resistance. Among the many reinforcement configurations, needle-punched ceramic matrix composites have a periodic microstructure compared to laminated materials and woven materials due to the unique needle-punching process. During the needle-punching process, the barbs on the needle repeatedly penetrate the fiber preform, introducing in-plane fibers into the thickness direction to form Z-direction reinforcement. Although this mechanical action enhances the interlaminar performance of the material, it also disrupts the regular distribution of fibers and introduces a high degree of non-uniformity and randomness. Therefore, the micro-morphology of needle-punched ceramic matrix composites is complex, and it is difficult to find an accurate representative volume element to describe the overall performance of the material.

[0003] Currently, the RVE determination method for needle-punched ceramic matrix composites is mostly based on optical microscopic observation and SEM images, and a model with corresponding geometric structure characteristics is constructed based on the micro-morphology. However, the statistical representativeness of the micro RVE determination method has not been fully demonstrated. For typical non-homogeneous materials such as needle-punched ceramic matrix composites, the internal relationship between micro volume and prediction accuracy must be considered in the prediction of macro mechanical properties, i.e. within a predetermined error limit, the constructed RVE model should accurately reflect the probability mean of the true material performance. Currently, there is no complete statistical method for determining the micro RVE of needle-punched ceramic matrix composites.

[0004] Therefore, it is necessary to propose a micro RVE determination method for needle-punched ceramic matrix composites to more accurately reflect the material performance of the real material from a probabilistic perspective. SUMMARY

[0005] The technical problem to be solved is: In order to avoid the shortcomings of the prior art, the present application provides a micro RVE determination method for needle-punched ceramic matrix composites, which quantifies the RVE size from a statistical perspective through CT scanning, volume distribution fitting and integral range calculation, solving the problem of RVE determination for non-periodic materials.

[0006] The technical scheme of the present application is: a micro RVE determination method for needle-punched ceramic matrix composites, comprising the following steps: Step 1, sample preparation and CT scanning: a standard sample is cut from the needle-punched ceramic matrix composite material, and an X-ray computed tomography (CT) technique is used to scan the sample to obtain a series of two-dimensional projection images reflecting the microstructure of the material inside; Step 2, needle-punched area identification and volume statistics: from the two-dimensional projection images obtained in step 1, identify the area with typical needle-punched features, measure the geometric dimensions of each needle-punched area, and calculate the volume of each needle-punched area based on the geometric dimensions to obtain a volume statistical sample of the needle-punched area; Step 3, volume distribution function fitting: perform distribution analysis on the volume statistical sample obtained in step 2, draw a volume distribution histogram, and use a mathematical function to fit the volume distribution to obtain a probability distribution function of the volume of the needle-punched area; Step 4, integral range calculation: based on the probability distribution function obtained in step 3, calculate the ratio of the second moment to the mean of the volume of the needle-punched area, and define this ratio as the integral range A3 of the characteristic length representing the statistical uniformity of the material; Step 5, RVE size determination: based on the integral range A3 determined in step 4, take it as the volume of the RVE; at the same time, statistically analyze the height values of all needle-punched areas in step 2, and calculate the average height; combine the volume and average height of the RVE to calculate the characteristic side length of the RVE in the plane, and finally determine the mesoscopic RVE size of the needle-punched ceramic matrix composite material. A further technical solution of the present application is that in step 1, the size of the standard sample is a cuboid of 9mm×9mm×3mm; the cumulative rotation angle of the CT scanning is 360°, and the scanning resolution is sufficient to clearly distinguish the fiber and pore structure inside the composite material.

[0007] A further technical solution of the present application is that in step 2, the two-dimensional projection images are processed using ImageJ image processing software, the most prominent needle-punched feature and the largest cross-sectional area are selected, and the needle-punched area in the image is identified and sized.

[0008] A further technical solution of the present application is that in step 2, the geometric dimensions of the needle-punched area include the projected side length and height of the area in the two-dimensional image; the volume is calculated from the projected side length and height, wherein based on the assumption that the needle-punched area is approximately symmetric in the plane direction, the three-dimensional volume is estimated from the two-dimensional cross-sectional size.

[0009] A further technical solution of the present application is that in step 3, the mathematical function used to fit the volume distribution is an exponential distribution function.

[0010] A further technical solution of the present application is that in step 4, the integral range A3 is calculated by the following formula:

[0011] wherein, is the second moment of the volume of the needled region, is the mean of the volume of the needled region, V is the volume of the needled region, and the subscript 3 indicates a three-dimensional space material.

[0012] A further technical solution of the present application is that in step 5, the characteristic side length of the RVE in the plane is calculated by the following formula:

[0013] wherein, S is the cross-sectional area of the RVE; V is the volume of the RVE, that is, the integral range A3; is the average height of the RVE.

[0014] A further technical solution of the present application is that the RVE model determined in step 5 is used for finite element prediction or multi-scale analysis of the macroscopic equivalent mechanical properties of the needled ceramic matrix composite material.

[0015] A method for determining a mesoscopic representative volume element (RVE) of a heterogeneous material, comprising: obtaining a microstructure image of the material by CT scanning; statistically analyzing the volume distribution of a characteristic region and fitting a distribution function thereof; and calculating an integral range to determine the size of the RVE; wherein the heterogeneous material includes, but is not limited to, a non-periodic composite material, a porous material or a particle reinforced composite material with random microstructure.

[0016] A system for determining a mesoscopic RVE of a needled ceramic matrix composite material, comprising: an image acquisition module configured to perform CT scanning on a needled ceramic matrix composite material sample to obtain a series of two-dimensional projection images; an image processing module connected to the image acquisition module and configured to identify a needled region from the two-dimensional projection images and measure the geometric size of each needled region; a volume statistical module connected to the image processing module and configured to calculate the volume of each needled region based on the geometric size to obtain a volume statistical sample of the needled region; a distribution fitting module connected to the volume statistical module and configured to perform distribution analysis on the volume statistical sample to fit a probability distribution function of the volume of the needled region; an integral range calculation module connected to the distribution fitting module and configured to calculate the ratio of the second moment to the mean of the volume of the needled region based on the probability distribution function to obtain an integral range representing the statistical uniformity of the material; The RVE determining module, connected with the integral range calculating module, is used for taking the numerical value of the integral range as the volume of the mesoscopic RVE, and calculating the characteristic size of the RVE in combination with the average height of the needling area.

[0017] Advantages The method of the present application is a mesoscopic RVE determining method for a typical heterogeneous material, i.e., a needled ceramic matrix composite material, and the size of the material mesoscopic RVE that can predict the macroscopic mechanical properties of the material is ascertained from the perspective of probability, thereby overcoming the limitations of the traditional optical or microscopic observation method for establishing a mesoscopic RVE model. 1. The present application first proposes a RVE determining method based on the theory of probability statistics, and by introducing the "integral range" as a core quantitative criterion, it is ensured that the determined RVE can represent the macroscopic properties of the whole material at a given confidence level, thereby fundamentally overcoming the limitations of the traditional method that relies on subjective experience and lacks statistical representativeness.

[0018] 2. The present application obtains a large amount of data through CT scanning, and based on strict volume distribution fitting and integral range calculation, it provides a clear mathematical basis and objective standard for the determination of the RVE size. This greatly reduces the dispersion and error in the prediction of macroscopic mechanical properties (such as elastic modulus and strength), making the simulation results more reliable and laying a solid foundation for the precise design and safety evaluation of materials.

[0019] 3. The present application provides a standardized operation process, which avoids the large amount of time and computing resources consumed by the traditional "trial and error method" for repeatedly constructing and verifying RVE models of different sizes. Engineers can quickly determine a statistically reliable RVE size according to the present application, and directly use it for subsequent finite element analysis or multiscale simulation, significantly shortening the period from material design to performance evaluation and reducing research and development costs.

[0020] The method proposed in the present application can be extended to the determination of mesoscopic RVE models for other heterogeneous materials. For composite materials with complex microstructure and non-periodic microstructure distribution, this method can provide a way to establish a mesoscopic RVE for composite materials from the perspective of probability statistics. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 CT scan image of the needled ceramic matrix composite material obtained in the embodiment of the present application; Figure 2 Statistical RVE region size diagram in the embodiment of the present application; Figure 3 Volume distribution histogram of the mesoscopic RVE of the needled ceramic matrix composite material in the embodiment of the present application; Figure 4A height distribution histogram of a micro RVE of a needled ceramic matrix composite material in an embodiment of the present application. DETAILED DESCRIPTION

[0022] The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0023] Currently, the accurate prediction of the macroscopic mechanical properties of composite materials relies heavily on representative volume elements (RVEs) that can represent the microstructure characteristics of the composite materials. In the prior art, the determination methods of RVEs are mainly divided into two categories: Method for periodic structure: As described in patents CN110688790B and CN113761763B, for woven, laminated or honeycomb composite materials with obvious periodicity, the unit cell can be directly selected as the RVE, and periodic boundary conditions are applied for homogenization calculation. This method is obviously not suitable for needled materials with random structure.

[0024] Empirical method based on image observation: As pointed out in the disclosure, for needled composite materials, the geometric model is currently constructed based on the micro morphology of optical microscope or scanning electron microscope (SEM) images, which is subjective and empirical. Although this method reflects the geometric characteristics of the material to some extent, its statistical representativeness has not been fully demonstrated. Whether the size of the constructed RVE is sufficient to represent the overall macroscopic performance of the material in a statistical sense is still unknown, resulting in a large uncertainty and randomness in the prediction of macroscopic performance.

[0025] In addition, although patent CN114741744B provides a micro modeling method for needled composite materials, its focus is on “how to perform multi-scale analysis on the known needled region”, and its premise is that the geometric model of the needled region has been obtained, and it does not solve the fundamental problem of “how to statistically determine the size of a representative needled region RVE”.

[0026] Based on the above problems, the present application provides a method for determining the micro RVE of a needled ceramic matrix composite material, comprising the following steps: Step 1, sample preparation and CT scanning: cutting a standard sample from a needled ceramic matrix composite material, and scanning the sample using X-ray computed tomography (CT) technology to obtain a series of two-dimensional projection images reflecting the internal microstructure of the material; Step 2, needled region identification and volume statistics: identifying the region with typical needling characteristics from the two-dimensional projection images obtained in step 1, and measuring the geometric size of each needled region, and calculating the volume of each needled region based on the geometric size, thereby obtaining the volume statistical sample of the needled region; Step 3, volume distribution function fitting: the volume statistics sample obtained in step 2 is subjected to distribution analysis, a volume distribution histogram is drawn, and a mathematical function is used to fit the volume distribution to obtain a probability distribution function of the needling region volume; Step 4, integral range calculation: based on the probability distribution function obtained in step 3, the ratio of the second moment to the mean of the needling region volume is calculated, and the ratio is defined as the integral range A3 of the characteristic length representing the statistical uniformity of the material; Step 5, RVE size determination: based on the integral range A3 determined in step 4, the volume of the RVE is determined; at the same time, the height values of all the needling regions in step 2 are counted, and the average height is calculated; combining the volume of the RVE and the average height, the characteristic side length of the RVE in the plane is calculated, and finally the mesoscopic RVE size of the needled ceramic matrix composite material is determined. Specifically, in step 4, the integral range A3 is calculated by the following formula:

[0027] Wherein, is the second moment of the needling region volume, is the mean of the needling region volume, V is the needling region volume, and the subscript 3 represents a three-dimensional material.

[0028] Specifically, in step 5, the characteristic side length of the RVE in the plane is calculated by the following formula:

[0029] Wherein, S is the cross-sectional area of the RVE; V is the volume of the RVE, that is, the integral range A3; is the average height of the RVE; considering that the RVE in the plane is a figure, the area is the square of the side length .

[0030] The application also provides a method for determining a mesoscopic representative volume element (RVE) of a heterogeneous material, which comprises the following steps: obtaining a material microstructure image through CT scanning, counting the volume distribution of a characteristic region and fitting a distribution function, and then calculating an integral range to determine the RVE size.

[0031] The application also provides a system for determining a mesoscopic RVE of a needled ceramic matrix composite material, which comprises: An image acquisition module is configured to perform CT scanning on a needled ceramic matrix composite material sample to obtain a series of two-dimensional projection images. An image processing module is connected with the image acquisition module, and is used for identifying a needling area from the two-dimensional projection image and measuring a geometric size of each needling area; A volume statistics module is connected with the image processing module, and is used for calculating a volume of each needling area based on the geometric size, and obtaining a volume statistical sample of the needling area; A distribution fitting module is connected with the volume statistics module, and is used for performing distribution analysis on the volume statistical sample, and fitting to obtain a probability distribution function of the needling area volume; An integral range calculation module is connected with the distribution fitting module, and is used for calculating a ratio of a second moment to a mean value of the needling area volume based on the probability distribution function, and obtaining an integral range representing material statistical uniformity; An RVE determination module is connected with the integral range calculation module, and is used for taking a value of the integral range as a volume of a mesoscopic RVE, and combining the average height of the needling area to calculate a characteristic size of the RVE.

[0032] The above technical solutions are further analyzed in combination with the drawings and examples as follows: In one embodiment, a method for determining a mesoscopic RVE of a needled ceramic matrix composite material includes the following steps: 1) Obtain a micro-morphology image of the needled ceramic matrix composite material, cut a 9mm×9mm×3mm cuboid CT scanning sample from the object material, record and obtain a series of projection images of the sample on different angle scanning sections by using a detector; 2) According to the CT scanning image of the needled ceramic matrix composite material obtained in step 1), identify the size of a representative volume element (RVE) model of a typical needling area in each image, including the side length and height of the needling area, and further calculate the volume of the needling area for statistics; 3) Based on the RVE size and volume data obtained in step 2), perform a drawing visualization operation on the volume data of the RVE model, obtain a volume distribution histogram of the RVE model, perform an exponential curve fitting, and obtain a volume distribution function of the RVE model; 4) Based on the volume distribution function of the RVE model obtained in step 3), determine an integral range (A n ) that can represent the statistical uniformity of the microstructure of the needled ceramic matrix composite material and is a core quantitative index for defining a representative volume element (RVE); 5) Based on the integral range A n determined in step 4), statistically analyze the height distribution of the RVE model, calculate the average height of the model, take the integral range as the side length of the RVE volume to calculate the model, and finally determine the size of the RVE model.

[0033] Further, in step 1), CT image scanning test is carried out to obtain a series of cross-sectional images of the needle-punched ceramic matrix composite material. To analyze the microstructure of the tensile needle-punched C / SiC composite material at room temperature, a cuboid sample with a size of 9mmx9mmx3mm is cut from the clamping section of the sample, and the sample is placed on the rotating sample stage between the X-ray beam source and the detector. The sample stage rotates at a constant angular velocity, and the cumulative rotation is 360°. During the process of X-ray penetrating the material, the intensity of the ray attenuates exponentially through the ray attenuation coefficient, which reflects the influence of material density and the absorption capacity of the material to the ray. Based on the principle that X-ray has different attenuation rates when penetrating different components of the sample, when the X-ray beam hits the sample, the detector records and obtains a series of images of the sample in the thickness direction scanning section, ensuring that the resolution is sufficient to show the fibers and pores of the composite material.

[0034] Further, in step 2), based on the obtained CT scanning images in the thickness direction of the material, the ImageJ image processing software is used to screen out the images with the most significant needle-punched area characteristics and the largest cross-sectional area from the large number of images obtained by the Micro-CT test piece, and then accurately measure the size of the needle-punched area. Thus, the volume of different mesoscopic RVE of the needle-punched ceramic matrix composite material is calculated.

[0035] Further, in step 3), the volume distribution of the RVE model obtained by calculation is used to draw the volume distribution histogram of the RVE, visualize the volume distribution of the RVE model, and perform curve fitting on the RVE volume distribution to obtain the RVE distribution function of the needle-punched ceramic matrix composite material. Further, in step 4), based on the obtained RVE volume distribution function, the ratio of the second moment of the RVE area volume to its mean value is calculated as the integral range, which is the mesoscopic RVE volume of the needle-punched area of the needle-punched ceramic matrix composite material that can represent the overall macroscopic mechanical properties of the area from a statistical perspective.

[0036] (1) Basic theory for determining the size of RVE of random materials: The RVE model of heterogeneous materials should ensure that the given volume V The effective properties obtained by spatial averaging of stress field, strain field or energy field can meet the preset accuracy requirements. When the volume V is small, the same accuracy can be achieved by statistical averaging of multiple independent microstructures, that is, to ensure the representativeness of the model from a statistical point of view. The following briefly describes the theoretical method for determining the size of the RVE of heterogeneous materials in combination with the linear elasticity theory.

[0037] (a) Boundary conditions When predicting the macroscopic mechanical properties of materials, the boundary conditions of non-homogeneous materials must be fully considered, including a volume element made of a non-homogeneous material. V On its boundary On point x Apply displacement u The following conditions must be met: (1) in, E It is a position x An independent symmetric second-order tensor. Its definition is: (2) symbol The left-hand side defines the parameter; the macroscopic stress tensor can be similarly defined by spatial averaging. (3) When a static uniform boundary condition is applied to the boundary of a representative volume element, the traction vector on the boundary can be defined as follows: (4) It is a with x Unrelated symmetric second-order tensors n Indicates boundary At point x If the normal vector is at a certain point, then we have: (5) Then the macroscopic strain tensor can be defined as the spatial average value, and thus we have (6) For periodic boundary conditions, the entire representative volume element V The displacement field on can be expressed as (7) in, It indicates periodic fluctuations. Its volume... V The same value is taken at two points of the same origin on opposite surfaces. And the traction vector... exist V The opposite values ​​are taken at two points of the same origin on opposite surfaces.

[0038] When the mechanical behavior of a component can be described by linear elastic equations, a unique solution exists for three micromechanical boundary conditions—kinematic homogeneity, static homogeneity, and periodicity. For static homogeneity and periodicity boundary conditions, a fourth-order lumped tensor field necessarily exists. Then there is (8) For kinematically uniform boundary problems, there exists a fourth-order stress tensor field. Then we have (9) For the static homogeneous boundary value problem, according to equation (3) and equation (6), the tensor field can be expressed as (10) where A fourth order identity tensor acting on the symmetric second order tensor space.

[0039] (b) Apparent and effective moduli Let and be the fourth order tensor fields describing the elastic stiffness and compliance in the inhomogeneous material volume V , respectively. Then we have (11) For the kinematic homogeneous boundary value problem, we have (12) For the static homogeneous boundary value problem, we have (13) Equation (12) and equation (13) define the apparent stiffness V and apparent compliance which are uniquely determined on a given volume . The above relations show that the apparent mechanical properties cannot be obtained by simple mixing rules in the general sense, but need to be calculated by a more complex homogenization process.

[0040] The definition of the apparent modulus can also be given based on the strain energy e : (14) For the kinematic homogeneous boundary value problem, we have (15) For the static homogeneous boundary value problem. The symbol “T” denotes the transpose. From this, the following definition of the apparent modulus can be obtained: (16) The explicit formula makes the symmetry of the apparent modulus more intuitive. However, according to the so-called Hill-Mandel lemma, these two definitions are essentially equivalent. In fact, for a sufficiently large volume V , the apparent modulus no longer depends on the type of boundary conditions and is consistent with the target effective properties of the medium, then we have: (17) For a medium volume V , only the following bound inequalities need to be satisfied: (18) (2) Statistical description of random heterogeneous materials The RVE model of heterogeneous materials needs to contain two types of features, one is to describe the microstructure characteristics of the material, and the other is the accuracy of predicting the macroscopic performance of the material. First of all, based on morphological tools, the microstructure of the material is analyzed, and the geometric characteristics of the heterogeneous material are quantitatively characterized, and the RVE size that can describe the geometric characteristics of the microstructure of the material is determined. Then, based on the strength effective performance as the evaluation object, the sample size with strength performance representative is determined, and the relationship between the sample volume and the material inherent integral range is established. Among them, the integral range is defined as follows To further improve the statistical representativeness of the above "range", kanit proposed the concept of "integral range" to characterize the volume size of the measured parameters within the volume. A range can be defined to characterize the structure size of the measured parameters within the volume. The range is called the integral range. In space, the definition of the integral range is: (19) is a core parameter representing the statistical characteristics of the heterogeneous microstructure, and the definition is of great significance for predicting the variability of material performance with structure size.

[0041] For heterogeneous materials, the relationship between the covariance function of the structure and the covariance can be related by the following formula: (20) Substituting the above formula into the integral range solving formula, we get: (21)Calculate the above formula: (22) Equation (22) gives the integral range A3, which represents the RVE size that can represent the microstructure characteristics of the material in three-dimensional space from a geometric point of view, that is, the size of the RVE in the series model in Bazant's theory. Further, in step 5), the RVE model height when calculating the volume of the above RVE model is statistically determined. Due to the symmetry of the in-plane needle region, the micro RVE size of the needle ceramic matrix composite material can be determined.

[0042] In one embodiment, taking the micro RVE of the needle ceramic matrix composite material tensile specimen at room temperature as an example, the specific implementation process is as follows:

[0043] Step 1: Cut a 9 mm x 9 mm x 3 mm cuboid sample from the clamping section of the needle-punched ceramic matrix composite room temperature tensile specimen, place the sample on the rotating sample holder between the X-ray beam source and the detector, and perform CT scanning on the thickness direction of the sample. The detector records and acquires a series of images on the scanning section of the side of the sample, as shown in FIG. 1, ensuring that the resolution of the images is sufficient to display the geometric structure characteristics of the fiber and pores of the needle-punched ceramic matrix composite. Select images with typical needle-punched region shapes from all CT scan images. Figure 1

[0044] Step 2: Use ImageJ image processing software to perform three-dimensional volume statistics on the needle-punched region of the needle-punched C / SiC composite material. Identify and process the images selected in Step 1, filter out the images with the most prominent needle-punched region characteristics and the largest cross-sectional area, and then accurately measure the size of the needle-punched region. A total of 60 representative needle-punched region RVE models are obtained. Some example images are shown in FIG. 2, which clearly show the microscopic morphological features of fiber deflection and fracture in the needle-punched region. Further analysis shows that under the same needle-punching path, the needle-punched fiber presents an expandable structure of "single layer of 0° non-woven cloth - single layer of mesh - single layer of 90° non-woven cloth - single layer of mesh" stacked alternately along the thickness direction. Therefore, this region can be regarded as the RVE model of the needle-punched region. However, the size distribution of each needle-punched region is obviously discrete. For example, the width and height of Example 1 are about 1.231 mm and 0.944 mm, respectively. The corresponding dimensions of Example 2 are about 1.380 mm and 1.076 mm, respectively. Since the needle-punched C / SiC composite material studied uses a 0° / 90° alternating non-woven cloth structure, the geometric dimensions of the preform in the width and length directions of the needle-punching hole are basically the same, so the volume of the needle-punched region RVE can be directly estimated from the two-dimensional cross-sectional images. Figure 2

[0045] Step 3: After calculating the volume of the RVE model in a large number of images, the statistical results can obtain the frequency distribution of 60 RVE volumes, as shown in FIG. 3. Among them, there are 4 in the volume interval 0-1 mm³, 37 in the interval 1-2 mm³, 13 in the interval 2-3 mm³, 4 in the interval 3-4 mm³, 1 in the interval 4-5 mm³, and 1 in the interval 5-6 mm³. Based on the above statistical results, the RVE volume distribution is curve-fitted to obtain the following expression: Figure 3 (23) where y is the RVE volume distribution, x and n is the number of RVEs under the distribution.

[0046] ​​​Step 4: After obtaining the RVE volume distribution function, the integral range of the needled C / SiC composite material can be solved. In Kanit's theory, the integral solution of formula (19) can be approximately expressed as the ratio of the second moment of the area volume to the mean value thereof, which can be expressed as: (24) Through the volume statistical analysis of 60 groups of needled area RVE, it can be known that the volume mean of the needled C / SiC composite material is about 1.948mm 3 , and the second moment of the volume is about 5.376mm 3 . Therefore, by substituting formula (24), the volume integral range of the C / SiC composite material studied in the present subject is about 2.76mm 3 , that is, when the RVE volume of the needled area reaches 2.76mm 3 , the overall macroscopic mechanical properties of the area can be represented.

[0047] Step 5: Based on the above RVE integral range, the length, width and height of the needled area RVE are further determined. First, the height of 60 groups of RVE images is statistically analyzed, and the result is shown in Figure 4 . It can be seen that the height of the needled area RVE is mainly concentrated between 0.8mm and 1.2mm, and the calculated height mean is about 1.06mm. Considering that the volume of the needled area RVE is 2.76mm, the length and width thereof are about 1.50mm. Thus, the micro RVE size of the needled ceramic matrix composite material is obtained by the method proposed in the present application.

[0048] Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A method for determining the microscopic relative velocity (RVE) of needle-punched ceramic matrix composites, characterized in that, Includes the following steps: Step 1, Sample preparation and CT scan: A standard sample is cut from the needle-punched ceramic matrix composite material, and the sample is scanned using X-ray computed tomography (CT) technology to obtain a series of two-dimensional projection images reflecting the internal microstructure of the material. Step 2, Acupuncture Area Identification and Volume Statistics: From the two-dimensional projection image obtained in Step 1, identify areas with typical acupuncture features, measure the geometric dimensions of each acupuncture area, and calculate the volume of each acupuncture area based on the geometric dimensions, thereby obtaining a statistical sample of the volume of the acupuncture areas. Step 3, volume distribution function fitting: Perform distribution analysis on the volume statistical samples obtained in Step 2, draw a volume distribution histogram, and use a mathematical function to fit the volume distribution to obtain the probability distribution function of the acupuncture area volume; Step 4, Calculation of integration range: Based on the probability distribution function obtained in Step 3, calculate the ratio of the second moment of the volume of the needle-punched region to the mean, and define this ratio as the integration range A3 of the characteristic length characterizing the statistical homogeneity of the material. Step 5, RVE size determination: Based on the integration range A3 determined in Step 4, it is taken as the volume of the RVE; at the same time, the height values ​​of all needled areas in Step 2 are counted, and their average height is calculated; combined with the volume and average height of the RVE, the characteristic side length of the RVE in the plane is calculated, and finally the microscopic RVE size of the needled ceramic matrix composite material is determined.

2. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 1, the standard sample is a cuboid with dimensions of 9mm × 9mm × 3mm; the cumulative rotation angle of the CT scan is 360°, and the scanning resolution is sufficient to clearly distinguish the fiber and pore structure inside the composite material.

3. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 2, the two-dimensional projection image is processed using ImageJ image processing software to select the image with the most significant needle puncture features and the largest cross-sectional area, and the needle puncture area in the image is identified and its size is measured.

4. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 2, the geometric dimensions of the acupuncture area include the projected side length and height of the area on the two-dimensional image; the volume is calculated using the projected side length and height, wherein the three-dimensional volume is estimated by using the two-dimensional cross-sectional dimensions based on the assumption that the acupuncture area is approximately symmetrical in the in-plane direction.

5. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 3, the mathematical function used to fit the volume distribution is an exponential distribution function.

6. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 4, the integration range A3 is calculated using the following formula: in, Let be the second moment of the volume of the acupuncture region. This represents the average volume of the acupuncture area. V The volume represents the needle-punched area, and the subscript 3 indicates the material in three-dimensional space.

7. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: In step 5, the feature edge length of RVE in the plane Calculated using the following formula: Where S is the cross-sectional area of ​​RVE; V is the volume of RVE, which is the integration range A3; This represents the average height of the RVE.

8. The method for determining the microscopic RVE of needle-punched ceramic matrix composites according to claim 1, characterized in that: The RVE model determined in step 5 is used for finite element prediction or multi-scale analysis of the macroscopic equivalent mechanical properties of needled ceramic matrix composites.

9. A method for determining the representative volume element (RVE) at the mesoscopic level of a heterogeneous material, characterized in that, The method employs the method described in any one of claims 1 to 8, acquiring material microstructure images through CT scanning, statistically analyzing the volume distribution of feature regions and fitting their distribution functions, and then calculating the integral range to determine the RVE size; the heterogeneous material includes, but is not limited to, non-periodic composite materials with randomly distributed microstructures, porous materials, or particle-reinforced composite materials.

10. A system for determining the microscopic relative velocity (RVE) of needle-punched ceramic matrix composites, used to perform the method according to any one of claims 1-9, characterized in that, include: The image acquisition module is used to perform CT scans on needle-punched ceramic matrix composite material samples to acquire a series of two-dimensional projection images. An image processing module, connected to the image acquisition module, is used to identify acupuncture areas from the two-dimensional projection image and measure the geometric dimensions of each acupuncture area; A volume statistics module, connected to the image processing module, is used to calculate the volume of each acupuncture region based on the geometric dimensions, and obtain a volume statistics sample of the acupuncture region. The distribution fitting module, connected to the volume statistics module, is used to perform distribution analysis on the volume statistics sample and fit the probability distribution function of the acupuncture area volume. The integral range calculation module, connected to the distribution fitting module, is used to calculate the ratio of the second moment to the mean of the acupuncture area volume based on the probability distribution function, so as to obtain the integral range characterizing the statistical uniformity of the material. The RVE determination module, connected to the integration range calculation module, is used to use the value of the integration range as the volume of the microscopic RVE and to calculate the feature size of the RVE in combination with the average height of the needle-punched area.

Images