Multi-scale calculation method and system for mechanical properties of unidirectional fiber reinforced ceramic matrix composite

Abstract

The invention provides a multi-scale calculation method and system for mechanical properties of a unidirectional fiber reinforced ceramic matrix composite material. According to the method, a sequential multi-scale method is adopted, the surface energy of a matrix material is obtained through molecular dynamics on the nanoscale scale, and the molecular dynamics-discrete element coupled unidirectional fiber reinforced ceramic matrix composite material multi-scale calculation method and system are provided on the basis of the periodic damage characteristic of the material under the microscale. Compared with the prior art, the method has the advantages that the nanoscale damage behavior of the ceramic matrix composite matrix and the aggregation characteristic of the microcracks are fully considered, and the calculation precision of a microscopic result is remarkably improved. The method is suitable for component design, structure optimization and mechanical property prediction of the ceramic-based composite material in the aerospace field.

Description

Technical Field

[0001] The present invention belongs to the technical field of the mechanics of ceramic matrix composites, and particularly relates to a multi-scale calculation method and system for the mechanical properties of unidirectional fiber-reinforced ceramic matrix composites. Background Art

[0002] Fiber-reinforced ceramic matrix composites (hereinafter referred to as CMC materials) have become ideal multi-functional materials due to their characteristics such as low density, high fracture toughness, and excellent thermal stability, and have been widely used in the fields of aerospace and the like. However, due to factors such as the small size of the fiber filaments (differing by several orders of magnitude from the experimental sample size) and the unclear mechanical properties of the matrix, the numerical calculation of the mechanical properties of CMC materials faces great difficulties, which is also a hot issue in the current research field of CMC materials.

[0003] Regarding the tensile fracture behavior of unidirectional CMC materials, several literatures have proposed different numerical calculation methods based on the finite element method. The common feature of these methods is that the matrix is regarded as a brittle material with a random distribution of tensile strength, and the elastic-brittle constitutive relationship or failure criterion is used to describe the matrix and fibers, while the cohesive force constitutive model is used for the interface layer. However, there are obvious differences between the results obtained by the above methods and the experimental results, especially in terms of the tensile curve, lacking the progressive damage section unique to the classical tensile curve. This may be due to the lack of description of the mechanical behavior details of the matrix material at the nanoscale.

[0004] Molecular dynamics is considered to be an effective tool for exploring the mechanical behavior of materials at the nanoscale. The multi-scale calculation method based on molecular dynamics and the finite element method provides new ideas for the development of this field. Through molecular dynamics, the relationship between the opening displacement and the traction force at the crack tip of the interface can be extracted, and combined with the finite element method for calculation, the mechanical responses such as tension, compression, bending, and shear of the material at the microscopic level can be obtained. However, this method is applicable to continuous media such as epoxy resins, metals and other materials. For materials with internal enrichment of microcracks and non-continuous medium characteristics (such as ceramics, rocks, etc.), the finite element method fails to accurately capture the stress concentration phenomenon at the internal microcracks, resulting in a large deviation between its fracture mechanics response and the actual situation, and the calculation accuracy is also low. Therefore, it is urgent to further study and improve the relevant calculation methods. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-scale calculation method and system for the mechanical properties of unidirectional fiber-reinforced ceramic matrix composites, considering the nanoscale damage behavior of the matrix of CMC materials and the characteristics of enriched microcracks, so as to improve the calculation accuracy of microscopic results; in addition, this method is implemented through the commercial molecular dynamics software LAMMPS and the discrete element software PFC, and has strong versatility, and can solve large-scale engineering problems.

[0006] The technical solution for achieving the object of the present invention is as follows:

[0007] A multi-scale calculation method for the mechanical properties of a unidirectional fiber-reinforced ceramic matrix composite, comprising:

[0008] S1: Based on a unidirectional fiber-reinforced ceramic matrix composite sample, obtain the macroscopic mechanical parameters, microscopic structure parameters and nano-scale structure parameters of the sample, and determine the matrix composition; wherein the macroscopic mechanical parameters include the elastic modulus and tensile strength of the fiber, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer; the microscopic structure parameters include the fiber diameter and the average length ratio of the periodic damaged area to the non-damaged area; the nano-scale structure parameter is the matrix crystal plane spacing;

[0009] S2: Establish a discrete element representative volume element model;

[0010] S3: According to the macroscopic mechanical parameters obtained in S1, independently calibrate the particle bonding parameters of the fiber, matrix and interface, and determine the optimal combination of the particle bonding parameters of the matrix; the particle bonding parameters include the fiber bonding elastic modulus, fiber bonding tensile strength, matrix bonding elastic modulus, and matrix bonding tensile strength;

[0011] S4: Calibrate the bonding elastic modulus and bonding shear strength of the interface, and determine the optimal combination of the particle bonding parameters of the interface layer;

[0012] S5: Based on the matrix composition, establish a surface energy calculation model for the corresponding crystal, including selecting atomic species, establishing a molecular structure, inputting atomic potential functions, and setting periodic boundary conditions;

[0013] S6: Integrate the optimal combinations of the particle bonding parameters obtained in S3 - S5, including the bonding elastic modulus and bonding tensile strength of the fiber, the bonding elastic modulus, bonding tensile strength, and bonding softening coefficient of the matrix, and the bonding elastic modulus and bonding shear strength of the interface layer;

[0014] S7: Input the determined optimal combination of the particle bonding parameters into the discrete element representative volume element model, and input the bonding tensile strength of the matrix particle contact pairs in the non-damaged area; set the periodic boundary conditions; apply a tensile load to perform tensile along the fiber length direction on the model, and solve the tensile stress-strain curve of the unidirectional fiber-reinforced ceramic matrix composite.

[0015] A multi-scale calculation system for the mechanical properties of a unidirectional fiber-reinforced ceramic matrix composite, comprising:

[0016] A macroscopic mechanical parameter acquisition module: used to acquire the macroscopic mechanical parameters of the sample, including the elastic modulus and tensile strength of the fiber, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer;

[0017] Microstructure parameter acquisition module: used to acquire the cross-sectional microstructure of the sample, measure and calculate the fiber diameter and the average length ratio of the periodic damaged region to the non-damaged region in the sample microstructure parameters;

[0018] Nano-structure parameter acquisition module: used to acquire the nano-structure of the matrix, calculate the crystal plane spacing of the matrix according to the fast Fourier transform method, and determine the composition of the matrix;

[0019] Discrete element representative volume element modeling module: used to establish a discrete element representative volume element model;

[0020] Particle bonding parameter calibration module: used to independently calibrate the particle bonding parameters of the fiber, matrix and interface according to the macro-mechanical parameters obtained by the macro-mechanical parameter acquisition module, and determine the optimal combination of the particle bonding parameters of the matrix; the particle bonding parameters include the bonding elastic modulus, bonding tensile strength of the fiber and matrix, and the bonding elastic modulus and bonding shear strength of the interface;

[0021] Surface energy and bonding softening coefficient calculation module: based on the matrix nano-structure parameters obtained by the nano-structure parameter module, establish a molecular dynamics model of the matrix, and based on the first principles, obtain the surface energy of the matrix and the bonding softening coefficient of the matrix;

[0022] Mechanical property calculation module: used to input the particle bonding parameters determined by the particle bonding parameter calibration module and the surface energy and bonding softening coefficient calculation module into the discrete element representative volume element modeling module, and input the bonding tensile strength of the matrix particle contact pairs in the non-damaged area; set periodic boundary conditions; apply a tensile load to perform tensile along the fiber length direction on the model, and solve the tensile stress-strain curve of the unidirectional fiber reinforced ceramic matrix composite.

[0023] Compared with the prior art, the remarkable advantages of the present invention are:

[0024] (1) Through the method combining molecular dynamics and discrete element, the nano-micro transfer of the matrix damage evolution process of the ceramic matrix composite is realized.

[0025] (2) By considering the damage evolution characteristics of the matrix at the nano-scale and the periodic damage characteristics of the material at the micro-scale, the accuracy of the multi-scale calculation of the tensile mechanical properties of the unidirectional ceramic matrix composite is improved. Description of the drawings

[0026] Figure 1 It is a schematic flow chart of Embodiment 1 of the present invention.

[0027] Figure 2 It is a schematic diagram of the system composition of Embodiment 2 of the present invention. Detailed implementation manners

[0028] In order to enable those skilled in the art to have a clearer understanding and knowledge of the present invention, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described below are only used to explain the present invention for easy understanding. The technical solutions provided by the present invention are not limited to the technical solutions provided by the following embodiments, and the technical solutions provided by the embodiments should not limit the protection scope of the present invention.

[0029] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Therefore, only the components related to the present invention are shown in the diagrams, rather than being drawn according to the number, shape, and size of the components in actual implementation. The actual morphology, quantity, and proportion of each component during actual implementation can be regarded as an arbitrary change, and the component layout morphology may also be more complex.

[0030] Embodiment 1

[0031] As Figure 1 shown, this embodiment provides a multi-scale calculation method for the mechanical properties of unidirectional fiber-reinforced ceramic matrix composites. The design principle of this method is as follows: This method takes into account the nanoscale damage behavior of the matrix of unidirectional fiber-reinforced ceramic matrix composites and the characteristics of enriched microcracks. Compared with the traditional multi-scale calculation method combining macroscopic mechanical experiments and finite element methods, the calculation results have higher accuracy.

[0032] In this embodiment, the specific steps of a multi-scale calculation method for the mechanical properties of unidirectional fiber-reinforced ceramic matrix composites are as follows:

[0033] S1: Based on the unidirectional fiber-reinforced ceramic matrix composite sample, obtain the macroscopic mechanical parameters, microscopic structure parameters, and nanoscale structure parameters of the sample; among them, the macroscopic mechanical parameters include the elastic modulus and tensile strength of the fiber, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer; the microscopic structure parameters include the fiber diameter and the average length ratio of the periodic damage region to the non-damage region; the nanoscale structure parameter is the matrix crystal plane spacing; the specific steps include:

[0034] S1.1. According to the unidirectional fiber-reinforced ceramic matrix composite tensile spline, through a tensile test, obtain the tensile stress-strain curve of the sample; according to the slope of the second linear segment of the curve, identify the elastic modulus and tensile strength of the fiber in the sample; according to the slope of the first linear segment of the curve and the preset fiber volume fraction, identify the elastic modulus and tensile strength of the matrix in the sample;

[0035] S1.2. According to the unidirectional fiber-reinforced ceramic matrix composite thin sheet sample, through a fiber push-out experiment, obtain the indenter reaction force-displacement curve of the nano-indentation instrument; according to the slope of the first linear segment, identify the shear modulus of the interface layer; through the peak value of the reaction force, identify the shear strength of the interface layer;

[0036] S1.3. Obtain the microscopic structure of the sample cross-section through a scanning electron microscope experiment, measure the fiber diameter in the microscopic structure parameters of the sample according to the scale of the scanning electron microscope image, and calculate the average length ratio of the periodic damage region to the non-damage region;

[0037] S1.4. Obtain the nanoscale structure of the matrix through a transmission electron microscope experiment, and calculate the crystal plane spacing of the matrix by the fast Fourier transform method to determine the composition of the matrix;

[0038] S2: Based on the discrete element software PFC (Particle Flow Code), establish a discrete element representative volume element model, specifically including:

[0039] S2.1. Based on the fiber diameter R obtained in S1.3 and the preset fiber volume fraction V f , calculate the side length l of the discrete element representative volume element model:

[0040]

[0041] Particle radius r:

[0042]

[0043] S2.2. According to the side length l and the particle radius r, establish a homogeneous particle group cube model with side length l through the ball distribute command; according to the fiber diameter R, divide the particle model into a fiber particle group and a matrix particle group through the ball group command;

[0044] S2.3. Within the fiber particle group, create fiber particle contact pairs through the cmat apply command; within the matrix particle group, create matrix particle contact pairs through the cmat apply command; between the fiber particle group and the matrix particle group, create interface layer particle contact pairs through the cmatapply command; divide the matrix particle contact pairs into non-damaged-damaged-non-damaged regions of 0.5l1:l2:0.5l1 along the fiber length direction according to the damage region length ratio l1:l2 obtained in step S1.3, where l1 is the average length of the non-damaged region and l2 is the average length of the damaged region;

[0045] S3: According to the macroscopic mechanical parameters obtained in S1, independently calibrate the particle bonding parameters of the fiber, matrix, and interface; the particle bonding parameters include fiber bonding elastic modulus, fiber bonding tensile strength, matrix bonding elastic modulus, and matrix bonding tensile strength. The specific steps include:

[0046] S3.1. Set the bonding elastic modulus of the fiber-particle contact pair to the fiber elastic modulus in S1.1, and set the bonding tensile strength to the fiber tensile strength in S1.1; set the required bonding parameters of the matrix particle group and the interface particle group to 10 -9 ; Set the periodic boundary conditions and perform tensile loading to obtain the tensile stress-strain curve of the fiber;

[0047] S3.2. According to the tensile stress-strain curve of the fiber, identify the curve slope as the microscopic elastic modulus parameter of the fiber, and identify the stress peak as the microscopic tensile strength of the fiber; compare the microscopic elastic modulus and microscopic tensile strength of the fiber with the fiber elastic modulus and tensile strength in S1.1 respectively; adjust the bonding elastic modulus and bonding tensile strength of the fiber until the error between the obtained microscopic elastic modulus and tensile strength and the comparison result in S.1.1 is within 1%, and determine the optimal combination of the particle bonding parameters of the fiber;

[0048] S3.3. Set the bonding elastic modulus of the matrix-particle contact pair to the matrix elastic modulus in S1.1, and set the bonding tensile strength to the matrix tensile strength in S1.1; set the bonding parameters of the fiber-particle group and the interface particle group to 10 -9 ; Set the periodic boundary conditions model domain condition periodic and perform tensile loading to obtain the tensile stress-strain curve of the fiber;

[0049] S3.4. According to the tensile stress-strain curve of the matrix, calculate the curve slope as the microscopic elastic modulus parameter of the matrix, and calculate the stress peak as the microscopic tensile strength of the matrix; compare the microscopic elastic modulus and microscopic tensile strength of the matrix with the matrix elastic modulus and tensile strength in S1.1 respectively; adjust the bonding elastic modulus and bonding tensile strength of the matrix until the error between the obtained microscopic elastic modulus and tensile strength and the comparison result in S1.1 is within 1%, and determine the optimal combination of the particle bonding parameters of the matrix;

[0050] S4: Calibrate the bonding elastic modulus and bonding shear strength of the interface, specifically including:

[0051] S4.1. Based on the discrete element representative volume element model in S2.3, refer to the thickness dimension of the thin sheet sample used in the fiber push-out experiment and modify the model dimension in the fiber length direction; refer to the actual indenter shape, establish an indenter model for downward loading, and obtain the simulation reaction force-displacement curve of the indenter;

[0052] S4.2. Based on the simulated reaction force-displacement curve of the indenter, identify the peak reaction force, the displacement at which the reaction force reaches the peak, and the peak displacement; adjust the bonding elastic modulus and bonding shear strength of the interface layer until the error from the comparison result of the fiber push-out experiment in S1.2 is within 1%, and determine the optimal combination of particle bonding parameters of the interface layer;

[0053] S5: Based on the matrix nanoscale structure parameters obtained in S1.4, establish a molecular dynamics model of the matrix, and based on the first principles, obtain the surface energy of the matrix and the bonding softening coefficient ξ of the matrix, specifically including:

[0054] S5.1. Based on the matrix composition determined in S1.4, establish a surface energy calculation model of the corresponding crystal in the molecular dynamics software Lammps, including selecting atomic species, establishing molecular structures, inputting atomic potential functions, and setting periodic boundary conditions;

[0055] S5.2. Minimize the energy of the model based on the conjugate gradient method min_style cg to obtain the total energy E of the model bulk ; Insert a vacuum layer in the middle of the model, and minimize the energy again to obtain the total energy E of the model with the vacuum layer cut ;

[0056] S5.3. Based on the first principles, calculate the surface energy γ of the sample matrix:

[0057]

[0058] where A is the cross-sectional area of the vacuum layer.

[0059] S5.4: According to the tensile strength of the matrix obtained in S1, the surface energy γ obtained in S5.3, and the particle radius r in S2.1, calculate the bonding softening coefficient ξ of the matrix contact pair:

[0060]

[0061] where E m is the matrix elastic modulus determined in S1, σ m is the matrix tensile strength determined in S1, t1 is the particle spacing 2r of the contact pair, r is the particle radius calculated in S2.1, and t2 is the width 6nm of the crystal crack statistical region;

[0062] S6: Integrate the optimal combinations of particle bonding parameters obtained in S3 - S5, including the bonding elastic modulus and bonding tensile strength of the fiber, the bonding elastic modulus, bonding tensile strength, and bonding softening coefficient of the matrix, and the bonding elastic modulus and bonding shear strength of the interface layer;

[0063] S7: Input the optimal combination of the particle bonding parameters determined in S6 into the discrete element representative volume element model established in S2.3, where the bonding tensile strength of the matrix particle contact pairs in the non-damage zone is input as 10 9 GPa; Set the periodic boundary conditions; Apply a tensile load to perform tensile testing on the model along the fiber length direction to solve the tensile stress-strain curve of the unidirectional fiber-reinforced ceramic matrix composite material.

[0064] Example 2

[0065] As Figure 2 shown, this example provides a multi-scale calculation system for the mechanical properties of unidirectional fiber-reinforced ceramic matrix composites. The design principle of this method is as follows: This method takes into account the nano-scale damage behavior of the matrix of unidirectional fiber-reinforced ceramic matrix composites and the characteristics of enriched microcracks. Compared with the traditional multi-scale calculation method combining macroscopic mechanical experiments and finite element methods, its calculation results have higher accuracy; specifically, it includes:

[0066] Macroscopic mechanical parameter acquisition module: Based on samples of unidirectional fiber-reinforced ceramic matrix composites, obtain the macroscopic mechanical parameters of the samples, including the elastic modulus and tensile strength of the fibers, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer; The specific steps include:

[0067] S1.1 According to the experimental results of the tensile test of unidirectional fiber-reinforced ceramic matrix composites, obtain the tensile stress-strain curve of the sample; According to the slope of the second linear segment of the curve, identify the elastic modulus and tensile strength of the fibers in the sample; According to the slope of the first linear segment of the curve, identify the elastic modulus and tensile strength of the matrix in the sample;

[0068] S1.2 According to the experimental results of the fiber push-out test of unidirectional fiber-reinforced ceramic matrix composites, obtain the indenter reaction force-displacement curve of the nano-indentation instrument; According to the slope of the first linear segment, identify the shear modulus of the interface layer; Through the peak value of the reaction force, identify the shear strength of the interface layer;

[0069] Microscopic structure parameter acquisition module: Through the experimental results of scanning electron microscopy, obtain the cross-sectional microstructure of the sample, and measure the fiber diameter in the microscopic structure parameters of the sample according to the scale length of the scanning electron micrograph and calculate the average length ratio of the periodic non-damage region to the damage region;

[0070] Nano-scale structure parameter acquisition module: Through the experimental results of transmission electron microscopy, obtain the nano-scale structure of the matrix, and calculate the crystal plane spacing of the matrix according to the fast Fourier transform method to determine the matrix composition;

[0071] Discrete element representative volume element modeling module: Based on the discrete element software PFC (Particle Flow Code), a discrete element representative volume element model is established, specifically including:

[0072] S2.1. Based on the fiber diameter R obtained from the microstructure parameter module and the preset fiber volume fraction V f , the side length l of the discrete element representative volume element model is calculated as follows:

[0073]

[0074] Particle radius r:

[0075]

[0076] S2.2. According to the side length l and the particle radius r, a homogeneous particle group model with side length l is established through the ball distribute command; according to the fiber diameter R, the particle model is divided into fiber particle groups and matrix particle groups through the ball group command;

[0077] S2.3. Within the fiber particle group, fiber particle contact pairs are created through the cmat apply command; within the matrix particle group, matrix particle contact pairs are created through the cmat apply command; between the fiber particle group and the matrix particle group, interfacial layer particle contact pairs are created through the cmatapply command; the matrix particle contact pairs are divided into non-damaged - damaged - non-damaged regions of 0.5l1:l2:0.5l1 along the fiber length direction according to the damage region length ratio l1:l2 obtained in step S1.3, where l1 is the average length of the non-damaged region and l2 is the average length of the damaged region;

[0078] Particle bond parameter calibration module: According to the macroscopic mechanical parameters obtained by the macroscopic mechanical parameter acquisition module, the particle bond parameters of the fiber, matrix, and interface are independently calibrated; the particle bond parameters include the bond elastic modulus, bond tensile strength of the fiber and matrix, and the bond elastic modulus and bond shear strength of the interface. The specific steps are as follows:

[0079] S3.1. Set the bond elastic modulus of the fiber particle contact pair to the fiber elastic modulus of the macroscopic mechanical parameter acquisition module, and the bond tensile strength to the fiber tensile strength in the macroscopic mechanical parameter acquisition module; set the required bond parameters of the matrix particle group and the interface particle group to 10 -9 ; Set the periodic boundary conditions and perform tensile loading to obtain the tensile stress-strain curve of the fiber;

[0080] S3.2. Calculate the slope of the curve as the microscopic elastic modulus parameter of the fiber and the peak stress as the microscopic tensile strength of the fiber according to the tensile stress-strain curve of the fiber; compare the microscopic elastic modulus and microscopic tensile strength of the fiber with the fiber elastic modulus and tensile strength in the macroscopic mechanical parameter acquisition module respectively; adjust the bonding elastic modulus and bonding tensile strength of the fiber until the error between the obtained microscopic elastic modulus and tensile strength and the comparison result in the macroscopic mechanical parameter acquisition module is within 1%, and determine the optimal combination of the particle bonding parameters of the fiber.

[0081] S3.3. Set the bonding elastic modulus of the matrix particle contact pair to the fiber elastic modulus in the macroscopic mechanical parameter acquisition module and the bonding tensile strength to the fiber tensile strength in the macroscopic mechanical parameter acquisition module; set the bonding parameters of the fiber particle group and the interface particle group to 10 -9 ; Set the periodic boundary condition model domain condition periodic, perform tensile loading, and obtain the tensile stress-strain curve of the fiber.

[0082] S3.4. Calculate the slope of the curve as the microscopic elastic modulus parameter of the matrix and the peak stress as the microscopic tensile strength of the matrix according to the tensile stress-strain curve of the matrix; compare the microscopic elastic modulus and microscopic tensile strength of the matrix with the matrix elastic modulus and tensile strength in the macroscopic mechanical parameter acquisition module respectively; adjust the bonding elastic modulus and bonding tensile strength of the matrix until the error between the obtained microscopic elastic modulus and tensile strength and the comparison result in the macroscopic mechanical parameter acquisition module is within 1%, and determine the optimal combination of the particle bonding parameters of the matrix.

[0083] S3.5. Based on the discrete element representative volume element modeling module, modify the model size in the fiber length direction with reference to the thickness dimension of the thin sheet sample used in the fiber push-out experiment; establish a indenter model for downward loading with reference to the actual indenter shape, and obtain the simulation reaction force-displacement curve of the indenter.

[0084] S3.6. Based on the simulation reaction force-displacement curve of the indenter, identify the peak reaction force, the displacement when the reaction force reaches the peak, and the peak displacement; adjust the bonding elastic modulus and bonding shear strength of the interface layer until the error from the comparison result of the fiber push-out experiment in the macroscopic mechanical parameter acquisition module is within 1%, and determine the optimal combination of the particle bonding parameters of the interface layer.

[0085] Surface energy and bonding softening coefficient calculation module: Based on the matrix nanoscale structure parameters obtained by the nanoscale structure parameter module, establish a molecular dynamics model of the matrix, and based on the first principles, obtain the surface energy of the matrix and the bonding softening coefficient ξ of the matrix, specifically including:

[0086] S4.1. Based on the matrix composition determined by the nano-scale structure parameter module, a surface energy calculation model of the corresponding crystal is established in the molecular dynamics software Lammps, including selecting atomic species, establishing molecular structures, inputting atomic potential functions, and setting periodic boundary conditions;

[0087] S4.2. Based on the conjugate gradient method min_style cg, the total energy E of the model in the energy-minimized state is obtained bulk ; A vacuum layer is inserted in the middle of the model, and energy minimization is performed again to obtain the total energy E of the model with the vacuum layer cut ;

[0088] S4.3. Based on the first principles, calculate the surface energy γ of the sample matrix:

[0089]

[0090] where A is the cross-sectional area of the vacuum layer.

[0091] S4.4: According to the tensile strength of the matrix obtained from the macro-mechanical parameter module, the surface energy γ obtained in S4.3, and the particle radius r in the discrete element representative volume element modeling module, calculate the bond softening coefficient ξ of the matrix:

[0092]

[0093] where E m is the matrix elastic modulus determined in S1, σ m is the matrix tensile strength determined in S1, t1 is the particle spacing of the contact pair, and t2 is the width of the crystal crack statistical area, 6 nm;

[0094] Mechanical property calculation module: Input the particle bond parameters determined by the particle bond parameter calibration module, the surface energy, and the softening coefficient calculation module into the model established by the discrete element representative volume element modeling module, and replace the bond tensile strength of the matrix particle contact pairs in the non-damaged area with 10 9 GPa; Set periodic boundary conditions; Apply a tensile load to stretch the model along the fiber length direction to solve the tensile stress-strain curve of the unidirectional fiber-reinforced ceramic matrix composite;

[0095] It should be noted that the division of each module in the above system only represents a division of logical functions; in actual implementation, these modules can be fully or partially integrated into a physical entity, or separately implemented. They can be called in software by a processing element, or fully implemented in hardware form; for example, a certain module can exist as an independent processing unit, or be integrated in a certain chip in the device. In addition, the program code can also be stored in the memory of the device and called by a certain processing element to execute the functions of the module, and the implementation methods of other modules are similar. These modules can be fully or partially integrated, or can operate independently; the processing element mentioned here can be an integrated circuit with signal processing capabilities. In the implementation process, the steps or modules of the above method can be completed through the logical circuit or software instructions of the processor and related hardware.

[0096] For example, these modules can form one or more integrated circuits to execute the above method, including one or more application-specific integrated circuits, microprocessors, or field-programmable gate arrays, etc.; in addition, when a certain module is implemented by a processing element in the form of program code, the processing element can be a general-purpose processor, such as a central processing unit or other processors capable of calling program code; these modules can also be integrated together in the form of a system-on-chip.

Claims

1. A multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composites, characterized in that: include: S1: Based on the unidirectional fiber reinforced ceramic matrix composite sample, the macroscopic mechanical parameters, microstructural parameters and nanostructural parameters of the sample are obtained, and the matrix composition is determined; the macroscopic mechanical parameters include the elastic modulus and tensile strength of the fiber, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer; the microstructural parameters include the fiber diameter and the average length ratio of the periodic non-damaged area to the damaged area; the nanostructural parameter is the matrix crystal plane spacing; S2: Establish a discrete element representative volume unit model; S3: Based on the macroscopic mechanical parameters obtained in S1, the particle bonding parameters of the fiber, matrix and interface are independently calibrated to determine the optimal combination of particle bonding parameters of the matrix; the particle bonding parameters include fiber bonding elastic modulus, fiber bonding tensile strength, matrix bonding elastic modulus, and matrix bonding tensile strength; S4: calibrate the bonding elastic modulus and bonding shear strength of the interface, and determine the optimal combination of particle bonding parameters of the interface layer; S5: Based on the composition of the matrix, a surface energy calculation model of the corresponding crystal is established, including selecting atomic species, establishing molecular structure, inputting atomic potential functions, and setting periodic boundary conditions; S6: integrating the preferred combination of particle bonding parameters obtained in S3-S5, including bonding elastic modulus and bonding tensile strength of the fiber, bonding elastic modulus, bonding tensile strength and bonding softening coefficient of the matrix, and bonding elastic modulus and bonding shear strength of the interface layer; S7: inputting the determined optimal combination of particle bonding parameters into the discrete element representative volume unit model, and inputting the bonding tensile strength of the matrix particle contact pair in the damage-free zone; Set periodic boundary conditions; apply tensile load to stretch the model along the fiber length direction, and solve the tensile stress-strain curve of unidirectional fiber-reinforced ceramic matrix composites.

2. The multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 1, characterized in that: S1 specifically includes: S1.

1. According to the tensile test of the unidirectional fiber reinforced ceramic matrix composite tensile specimen, the tensile stress-strain curve of the sample is obtained; according to the slope of the second linear segment of the curve, the elastic modulus and tensile strength of the fiber in the sample are identified; according to the slope of the first linear segment of the curve and the preset fiber volume fraction, the elastic modulus and tensile strength of the matrix in the sample are identified; S1.

2. Based on the unidirectional fiber reinforced ceramic matrix composite sheet sample, the indenter reaction force-displacement curve of the nanoindenter is obtained through the fiber push-out experiment; the shear modulus of the interface layer is identified according to the slope of the first linear segment; the shear strength of the interface layer is identified through the reaction force peak value; S1.

3. Obtain the microstructure of the cross section of the sample, measure and calculate the fiber diameter and the damaged area length ratio among the microstructure parameters of the sample; S1.

4. The nanostructure of the matrix is ​​obtained through transmission electron microscopy experiments, and the interplanar spacing of the matrix is ​​calculated through the fast Fourier transform method to determine the composition of the matrix.

3. The multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 1, characterized in that: S2 specifically includes: S2.

1. Based on the obtained fiber diameter R and the preset fiber volume fraction V f , calculate the side length l of the discrete element representative volume unit model: Particle radius r: S2.

2. According to the side length l and the particle radius r, a cube model of a homogeneous particle group with a side length of l is established by using the ball distribute command; according to the fiber diameter R, the particle model is divided into a fiber particle group and a matrix particle group by using the ball group command; S2.

3. In the fiber particle group, create fiber-particle contact pairs through the cmat apply command; in the matrix particle group, create matrix-particle contact pairs through the cmat apply command; between the fiber particle group and the matrix particle group, create interface layer particle contact pairs through the cmatapply command; divide the matrix particle contact pairs into damage-free-damaged-damaged areas of 0.5l1:l2:0.5l1 along the fiber length direction according to the obtained damage area length ratio, where l1 is the average length of the damage-free area and l2 is the average length of the damaged area.

4. The multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 1, characterized in that: S3 specifically includes: S3.

1. Set the bonding elastic modulus of the fiber-particle contact pair to the fiber elastic modulus in S1, and the bonding tensile strength to the fiber tensile strength in S1; set the required bonding parameters of the matrix particle group and the interface particle group; set periodic boundary conditions, perform tensile loading, and obtain the tensile stress-strain curve of the fiber; S3.

2. According to the tensile stress-strain curve of the fiber, the slope of the curve is identified as the micro elastic modulus parameter of the fiber, and the stress peak is identified as the micro tensile strength of the fiber; the micro elastic modulus and micro tensile strength of the fiber are compared with the fiber elastic modulus and tensile strength in S1 respectively; the bonding elastic modulus and bonding tensile strength of the fiber are adjusted until the obtained micro elastic modulus and tensile strength are within the error range of the comparison results in S1, and the preferred combination of particle bonding parameters of the fiber is determined; S3.

3. Set the bonding elastic modulus of the matrix particle contact pair to the matrix elastic modulus in S1, and the bonding tensile strength to the matrix tensile strength in S1; set the bonding parameters of the fiber particle group and the interface particle group; set the periodic boundary conditions, perform tensile loading, and obtain the tensile stress-strain curve of the fiber; S3.

4. According to the tensile stress-strain curve of the matrix, calculate the slope of the curve as the microelastic modulus parameter of the matrix, and calculate the stress peak as the microtensile strength of the matrix; compare the microelastic modulus and microtensile strength of the matrix with the elastic modulus and tensile strength of the matrix in S1 respectively; adjust the bonding elastic modulus and bonding tensile strength of the matrix until the obtained microelastic modulus and tensile strength are within the error range of the comparison results with those in S1, and determine the preferred combination of particle bonding parameters of the matrix.

5. The multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 1, characterized in that: S4 specifically includes: S4.

1. Based on the discrete element representative volume unit model, refer to the thickness of the thin sheet sample used in the fiber push-out experiment, modify the model size in the fiber length direction; refer to the actual indenter shape, establish the indenter model for downward pressure loading, and obtain the simulated reaction force-displacement curve of the indenter; S4.

2. Based on the simulated reaction force-displacement curve of the pressure head, identify the reaction force peak, the displacement when the reaction force reaches the peak value, and the displacement peak; adjust the bonding elastic modulus and the bonding shear strength of the interface layer until the error of the comparison result with the fiber push-out test is within the range, and determine the optimal combination of particle bonding parameters of the interface layer.

6. The multi-scale calculation method for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 1, characterized in that: S5 specifically includes: S5.

1. Based on the matrix composition, a surface energy calculation model of the corresponding crystal is established in the molecular dynamics software Lammps, including selecting atomic species, establishing molecular structure, inputting atomic potential functions, and setting periodic boundary conditions; S5.

2. Minimize the energy of the model based on the conjugate gradient method to obtain the total energy E of the model bulk ; Insert a vacuum layer in the middle of the model and perform energy minimization again to obtain the total energy E of the model with the vacuum layer cut ; S5.

3. Calculate the surface energy γ of the sample matrix based on first principles: Where A is the cross-sectional area of ​​the vacuum layer; S5.4: Based on the tensile strength of the matrix, the surface energy γ and the particle radius r, calculate the bonding softening coefficient ξ of the matrix contact pair: Among them, E m is the matrix elastic modulus, σ m is the tensile strength of the matrix, t1 is the distance between contacting particles, and t2 is the width of the statistical area of ​​crystal cracks.

7. A multi-scale calculation system for mechanical properties of unidirectional fiber-reinforced ceramic matrix composite materials, characterized in that: include: Macro-mechanical parameter acquisition module: used to obtain the macro-mechanical parameters of the sample, including the elastic modulus and tensile strength of the fiber, the elastic modulus and tensile strength of the matrix, and the shear modulus and shear strength of the interface layer; Microstructure parameter acquisition module: used to obtain the microstructure of the sample cross section, measure and calculate the fiber diameter and the average length ratio of the periodic non-damaged area to the damaged area in the sample microstructure parameters; Nanostructure parameter acquisition module: used to obtain the nanostructure of the substrate, calculate the interplanar spacing of the substrate according to the fast Fourier transform method, and determine the composition of the substrate; Discrete element representative volume unit modeling module: used to establish discrete element representative volume unit model; Particle bonding parameter calibration module: used to independently calibrate the particle bonding parameters of the fiber, matrix and interface according to the macroscopic mechanical parameters obtained by the macroscopic mechanical parameter acquisition module, and determine the optimal combination of particle bonding parameters of the matrix; the particle bonding parameters include the bonding elastic modulus and bonding tensile strength of the fiber and matrix, and the bonding elastic modulus and bonding shear strength of the interface; Surface energy and bonding softening coefficient calculation module: Based on the nanostructure parameters of the matrix obtained by the nanostructure parameter module, a molecular dynamics model of the matrix is ​​established, and based on the first principles, the surface energy and bonding softening coefficient of the matrix are obtained; Mechanical properties calculation module: used to input the particle bonding parameters determined by the particle bonding parameter calibration module and the surface energy and softening coefficient calculation module into the model established by the discrete element representative volume unit modeling module, and input the bonding tensile strength of the matrix particle contact pair in the damage-free zone; Set periodic boundary conditions; apply tensile load to stretch the model along the fiber length direction, and solve the tensile stress-strain curve of unidirectional fiber-reinforced ceramic matrix composites.

8. The multi-scale calculation system for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 7, characterized in that: Establish a discrete element representative volume unit model, including: Based on the obtained fiber diameter R and the preset fiber volume fraction V f , calculate the side length l of the discrete element representative volume unit model: Particle radius r: According to the side length l and the particle radius r, the ball distribute command is used to establish a cube model of a homogeneous particle group with a side length of l; according to the fiber diameter R, the ball group command is used to divide the particle model into a fiber particle group and a matrix particle group; In the fiber particle group, the cmat apply command is used to create fiber-particle contact pairs; in the matrix particle group, the cmat apply command is used to create matrix-particle contact pairs; between the fiber particle group and the matrix particle group, the cmat apply command is used to create interface layer particle contact pairs; the matrix particle contact pairs are divided into damage-free-damaged-damaged areas of 0.5l1:l2:0.5l1 along the fiber length direction according to the obtained damage area length ratio, where l1 is the average length of the damage-free area and l2 is the average length of the damaged area.

9. The multi-scale calculation system for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 7, characterized in that: The processing of the particle bonding parameter calibration module includes: The bonding elastic modulus of the fiber-particle contact pair is set as the fiber elastic modulus of the macroscopic mechanical parameter acquisition module, and the bonding tensile strength is set as the fiber tensile strength in the macroscopic mechanical parameter acquisition module; the required bonding parameters of the matrix particle group and the interface particle group are set; the periodic boundary conditions are set, and tensile loading is performed to obtain the tensile stress-strain curve of the fiber; According to the tensile stress-strain curve of the fiber, the slope of the curve is calculated as the micro elastic modulus parameter of the fiber, and the stress peak is calculated as the micro tensile strength of the fiber; the micro elastic modulus and micro tensile strength of the fiber are respectively compared with the fiber elastic modulus and tensile strength in the macro mechanical parameter acquisition module; the bonding elastic modulus and bonding tensile strength of the fiber are adjusted until the error of the comparison result of the obtained micro elastic modulus and tensile strength and the macro mechanical parameter acquisition module is within the range, and the optimal combination of particle bonding parameters of the fiber is determined; The bonding elastic modulus of the matrix particle contact pair is set to the fiber elastic modulus in the macroscopic mechanical parameter acquisition module, and the bonding tensile strength is set to the fiber tensile strength in the macroscopic mechanical parameter acquisition module; the bonding parameters of the fiber particle group and the interface particle group are set to set periodic boundary conditions, and tensile loading is performed to obtain the tensile stress-strain curve of the fiber; According to the tensile stress-strain curve of the matrix, the slope of the curve is calculated as the micro elastic modulus parameter of the matrix, and the stress peak is calculated as the micro tensile strength of the matrix; the micro elastic modulus and micro tensile strength of the matrix are respectively compared with the elastic modulus and tensile strength of the matrix in the macro mechanical parameter acquisition module; the bonding elastic modulus and bonding tensile strength of the matrix are adjusted until the error of the comparison result of the obtained micro elastic modulus and tensile strength and the macro mechanical parameter acquisition module is within the range, and the optimal combination of particle bonding parameters of the matrix is ​​determined; Based on the discrete element modeling module, the model size in the fiber length direction is modified with reference to the thickness of the thin sheet sample used in the fiber push-out experiment; the indenter model is established with reference to the actual indenter shape for downward pressure loading to obtain the simulated reaction force-displacement curve of the indenter; Based on the simulated reaction force-displacement curve of the pressure head, the reaction force peak, the displacement when the reaction force reaches the peak value, and the displacement peak are identified; the bonding elastic modulus and the bonding shear strength of the interface layer are adjusted until the error of the fiber push-out experiment comparison result of the macroscopic mechanical parameter acquisition module is within the range, and the optimal combination of particle bonding parameters of the interface layer is determined.

10. The multi-scale calculation system for mechanical properties of unidirectional fiber reinforced ceramic matrix composite materials according to claim 7, characterized in that: The surface energy and bonding softening coefficient calculation module processing process specifically includes: Based on the matrix composition determined by the nanostructure parameter module, a surface energy calculation model of the corresponding crystal is established, including selecting atomic species, establishing molecular structure, inputting atomic potential functions, and setting periodic boundary conditions; Based on the conjugate gradient method, the total energy E of the model in the energy minimization state is obtained bulk ; Insert a vacuum layer in the middle of the model and perform energy minimization again to obtain the total energy E of the model with the vacuum layer cut ; Based on the first principles, the surface energy γ of the sample matrix is ​​calculated: Where A is the cross-sectional area of ​​the vacuum layer; According to the tensile strength and surface energy γ of the matrix obtained by the macroscopic mechanical parameter module and the particle radius r in the discrete element representative volume unit modeling module, the bonding softening coefficient ξ of the matrix is ​​calculated: Among them, E m is the matrix elastic modulus, σ m is the tensile strength of the matrix, t1 is the distance between the contacting particles, and t2 is the width of the crystal crack statistical area.

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