Multi-scale simulation and forward design method and system for interlaminar fracture toughness of particle toughened composite

Abstract

The application provides a kind of particle toughening composite interlaminar fracture toughness multiscale simulation and forward design method and system, belongs to the electric digital data processing technical field.The application is by constructing three-dimensional representative volume element (RVE) model containing random distribution spherical particle, and is endowed with its elastic-plastic constitutive and progressive damage model, combines periodic boundary condition, accurately characterizes mesoscopic toughening mechanism;Establish a macro double cantilever beam (DCB) model integrating mesoscopic characteristics, use extended finite element (XFEM) method to simulate crack initiation and propagation, realize the cross-scale forward prediction from mesoscopic parameters to macro I interlaminar fracture toughness.The application overcomes the problems of long development cycle, high cost of traditional trial-and-error method, and existing simulation model simplification distortion, scale disconnection, etc., can optimize the design by adjusting the particle size, volume fraction and other parameters, and provides a reliable theoretical tool and design system for interlaminar toughening design of high-performance composite materials.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of electric digital data processing, relates to computer-aided design, relates to a method using finite elements, relates to design optimization, verification or simulation, and in particular relates to a multi-scale simulation and forward design method and system for interlaminar fracture toughness of particle toughened composite materials. BACKGROUND

[0002] Composite materials refer to new type of multiphase materials composed of two or more than two substances with different physical or chemical properties combined through a composite process, and the structure usually includes a continuous phase and a dispersed phase. Carbon fiber reinforced resin matrix composite (CFRPC) has high specific strength, high specific modulus and excellent designability, and plays a crucial role in the field of high-end equipment manufacturing such as aerospace. Since the last century, the aviation industry has generally taken the amount of composite materials as one of the key indicators to measure the advancement of aircraft structures.

[0003] To meet the demand of large-scale and high-efficiency manufacturing of aerospace structures, the industry widely adopts prepreg-thermal compression molding process to prepare CFRPC components. However, this manufacturing process based on lamination also leads to a significant weakening of the material performance in the thickness direction compared to the in-plane performance, i.e., the interlaminar performance becomes the structural short board. In actual service process, the component is prone to internal interlaminar delamination damage due to low-speed impact events such as tool drop and runway stone impact. Such damage is often difficult to be found in time through visual detection, but it is easy to expand under subsequent load, eventually causing a sharp drop in structural load-carrying capacity, premature failure, and even a catastrophic accident.

[0004] In the structural design of aviation composite materials, interlaminar fracture toughness is a key performance indicator for evaluating its resistance to delamination damage. To improve the interlaminar performance, existing technologies mainly focus on two types of methods: one is the physical Z-direction reinforcement technology, such as three-dimensional weaving, stitching and Z-pin technology, which introduces fibers in the thickness direction to improve interlaminar toughness, but this method damages the continuity of the fibers in the layer, which adversely affects the in-plane performance of the composite material; the other is the interlaminar toughening technology, such as inserting a thermoplastic film or dispersing toughening particles between the layers. Among them, the interlaminar particle toughening technology shows good application prospects due to its flexible process and basically no damage to the in-plane performance. However, the further development of this technology is severely limited by the "trial and error" research and development mode, and the fundamental reason is that the influence mechanism of particle size, distribution pattern and volume fraction on macroscopic fracture toughness is not clear, and there is a lack of effective theoretical prediction means.

[0005] At the same time, existing simulation analysis tools also have obvious limitations:

[0006] (1) Most studies use two-dimensional representative volume element models, which cannot truly reflect the stress field and damage evolution of particles in three-dimensional space. Moreover, researches are mostly limited to using mesoscopic models to obtain homogenized elastic parameters, and have not effectively linked the model to macroscopic crack propagation behavior. In macroscopic fracture simulation, the toughening layer is usually considered as a homogeneous material, which cannot reflect the mesoscopic toughening mechanism of particles, leading to a large deviation between the predicted results and experimental data.

[0007] (2) Inaccurate model: Most studies use two-dimensional representative volume element models, which cannot truly reflect the stress field and damage evolution of particles in three-dimensional space.

[0008] (3) Scale disconnection: Most studies are limited to using mesoscopic models to obtain homogenized elastic parameters, and have not effectively linked the model to macroscopic crack propagation behavior.

[0009] (4) Insufficient prediction accuracy: In macroscopic fracture simulation, the toughening layer is usually considered as a homogeneous material, which cannot reflect the mesoscopic toughening mechanism of particles, leading to a large deviation between the predicted results and experimental data.

[0010] In the field of mechanical property research of particle toughened composites, existing technologies have proposed various models and methods from different angles:

[0011] (1) The paper “Shang Chenyang, Mechanical Engineering. Modeling of particle reinforced composites and its mechanical properties and damage simulation [D]. Henan Polytechnic University [2026-01-14].” discloses a method of constructing a representative volume element (RVE) model of particle reinforced composites based on programming language and predicting its macroscopic equivalent mechanical parameters. Although it reveals the basic technical path of analyzing the influence of particle morphology, size and volume fraction through RVE, its research focuses on the prediction of material homogenization elastic properties, and does not involve the application of optimized mesoscopic parameters to specific macroscopic fracture behavior simulation, especially the lack of cross-scale verification links directly related to interlaminar fracture toughness (such as mode I).

[0012] (2) The paper “Tian W, Qi L, Chao X, et al. Periodic boundary condition and its numerical implementation algorithm for the evaluation of effective mechanical properties of the composites with complicated micro-structures [J]. Composites, 2019, 162, 1-10. DOI: 10.1016 / j.compositesb.2018.10.053” discloses a numerical algorithm for implementing RVE periodic boundary conditions in finite element software through a script interface. Although this method provides key technical support for accurately obtaining the equivalent elastoplastic response of composites, it is itself a general boundary condition processing tool and does not discuss how to further use the RVE analysis results to guide or construct a specific structural form of fracture model.

[0013] (3) The paper “Elbana Abdalla, Khennane Amar, Hazell paul J. Multiscale modelling of particulate composites with spherical inclusions [J]. Engineering with Computers, 2024, 40, 3087-3113. DOI:10.1007 / s00366-024-01954-8” discloses an automated process for generating a three-dimensional periodic RVE and conducting mesh convergence and size sensitivity analysis. Although it reflects the general considerations for model reliability and computational efficiency in multiscale modeling, its technical endpoint still stops at the level of material performance prediction and does not extend to structural scale failure analysis. It also does not disclose how to embed a mesoscopic model containing random particles into a macroscopic fracture model as a component.

[0014] (4) The paper “Bansal M, Sarkar S, Singh I V. An XFEM-Strain Gradient Damage Model for Efficient Modeling of Materials with Reinforcement Particles[J]. Engineering Fracture Mechanics, 2022, 271, 108667. DOI:10.1016 / j.engfracmech.2022.108667.” discloses a method of damage simulation of materials with reinforcement particles using extended finite element method (XFEM). Although this method avoids the difficulty of meshing complex particle geometry and provides an effective means for simulating the failure of heterogeneous materials, its application scenarios are focused on the damage evolution of materials themselves, and it is not combined with the interlaminar fracture problem of macroscopic laminated plate structure, nor does it involve the whole process design from mesoscopic parameter optimization to macroscopic fracture prediction.

[0015] (5) The paper “Sharma P, Mali H S, Dixit A. Mode-I interlaminar fracture modeling of DCB composite laminate using finite element techniques[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2023, 45(10), 1-31. DOI:10.1007 / s40430-023-04427-z.” discloses the use of XFEM and other methods to simulate the I-type interlaminar fracture of composite laminated plate. Although it confirms the applicability of XFEM in simulating the crack propagation of bonded interfaces, the material in its model is considered as a macroscopic homogeneous body, and the mesoscopic inhomogeneity of particle distribution in the interlaminar toughening region and its influence on crack propagation path and resistance are not considered.

[0016] (6) Chinese patent application CN111566164A and Chinese patent application CN119550705A disclose a method of setting specific chemically active particles between the interlayers of composite materials to improve the interlaminar toughness. Although both patent applications provide toughening solutions from the perspective of material design and preparation, they completely rely on experimental means for performance optimization and verification, and do not disclose any method of pre-quantitative guidance of particle parameter selection and high-precision prediction of fracture performance through multi-scale numerical simulation means.

[0017] Although the existing interlaminar toughening technology has made progress, there are still significant deficiencies in practical application and design, mainly in the following two aspects:

[0018] (1) Blindness in the design process: Before the material preparation stage, there is a lack of reliable means to quantitatively predict the final effect of the toughening scheme. It is difficult to accurately assess the influence of changes in particle parameters (such as size and volume fraction) on macroscopic fracture toughness, resulting in an optimization design that relies on trial and error, significantly lengthening the research and development cycle and increasing development costs.

[0019] (2) Distortion of simulation model: Existing numerical methods usually oversimplify the microstructure of the toughened layer, and the established simulation model cannot truly reproduce the key physical mechanisms of "pinning" and "bridging" of crack propagation by toughening particles in three-dimensional space. This disconnection between the model and physical reality results in insufficient credibility of the simulation results, making it difficult to effectively guide actual structural design and process optimization.

[0020] In summary, how to effectively improve the interlaminar fracture toughness of composite materials has become one of the core technical challenges in expanding their range of aerospace applications and ensuring the safety of aircraft. SUMMARY

[0021] The present application is to solve the above problems, and aims to provide a multi-scale simulation and forward design method and system for the interlaminar fracture toughness of particle toughened composite materials.

[0022] The present application provides a multi-scale simulation and forward design method for the interlaminar fracture toughness of particle toughened composite materials, which includes a laminate and a particle toughened layer disposed therein. The particle toughened layer includes a resin matrix and toughening particles distributed therein, and has the following characteristics, including the following steps: S10, batch modeling to generate a plurality of RVE models of the particle toughened layer, the particle diameters and volume fractions of the toughening particles in the plurality of RVE models are different; S20, the resin matrix and the toughening particles in the RVE model are given corresponding plastic yield functions, the elastic-plastic constitutive model is , and the material stress tensor is , and the total damage variable is , the progressive damage model, wherein is the plastic potential defined by the Mises equivalent stress, and its expression is , , , , , , , , , Represents equivalent plastic strain. This represents the stress-strain hardening function obtained from actual experiments. Represents the effective stress tensor, when This indicates that the material has completely lost its load-bearing capacity and the unit has been deleted. Represents the total damage variable. Represents the characteristic length of the element and the critical equivalent plastic displacement. , The fracture energy per unit area of ​​the material. The stress value at the onset of damage. Represents the equivalent plastic displacement, when time Equivalent plastic strain at the onset of material failure It is stress triaxiality and equivalent plastic strain rate The function, , , It is compressive stress. For equivalent stress; S30, the nodal displacement constraint equation applied to the RVE model is as follows: The periodic boundary conditions, where, , , Represents the spatial coordinates of any point within a unit cell. Indicates the displacement direction index. Corresponding to , , direction, This indicates the coordinate axis direction index corresponding to the unit cell boundary surface. Indicates perpendicular to , , Opposite faces of the axis Indices representing the components of the strain and displacement tensor. This represents the unit cell mean strain of the RVE model. Represents the coordinates of any point within a unit cell, indicated by the superscript. and They represent along The positive and negative directions of the axis. This represents the periodic displacement correction amount. In the given In the case of the cubic unit cell of the RVE model, in each set of parallel faces is a constant and S40, Perform mesh convergence analysis on the RVE model in finite element software to determine the mesh size that balances computational efficiency and accuracy; S50, Perform finite element simulation calculations on several RVE models to determine the particle diameter and volume fraction of the toughening particles under the optimal mechanical property parameters, and use them as parameters for the final designed particle-toughened composite material; S60, After modeling the cross-scale DCB model of the particle-toughened composite material, divide the DCB model into a pre-cracked region, a mesoscale region, and an equivalent region, and then assign the RVE model with the optimal parameters set and selected in steps S10~S50 to the corresponding DCB model. The particle-toughened layer in the mesoscopic region of the model; S70, firstly, the pre-cracked region, mesoscopic region and equivalent region are all defined as XFEM crack propagation regions, and the crack initiation and propagation criteria of this region are defined using the XFEM method. Then, the DCB model is simulated for type I interlaminar fracture toughness to obtain the simulated load-displacement response curve of the particle-toughened composite material. Subsequently, test specimens corresponding to the DCB model are prepared and subjected to type I interlaminar fracture toughness tests to obtain their actual load-displacement response curves. Finally, the simulated load-displacement response curves and the actual load-displacement response curves are compared and verified to confirm the design success.

[0023] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials provided by the present invention may also have the following features: In step S10, parametric modeling is performed using Python language, and the toughening particles are regarded as regular spheres of uniform size and randomly distributed in the resin matrix to obtain a 3D finite element model, which is used as the RVE model. The adjacent unit cell boundaries of the RVE model satisfy the conditions of deformation compatibility and stress compatibility.

[0024] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials provided by this invention may also have the following features: wherein, in step S20, the definition and assignment method of the elastoplastic constitutive model includes the following steps: S21, obtaining the initial yield stress of the resin matrix and the toughening particles respectively through actual experiments. and stress-strain hardening function S22, consider the definition of Mises equivalent stress and its expression as follows: of Plastic potential S23, uses an isotropic yielding model to simulate the mechanical behavior of the subsequent RVE model and expresses its plastic yield function in the form of equivalent plastic strain. S24, use the defined isotropic yield model as the elastoplastic constitutive model and assign it to the RVE model.

[0025] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials provided by the present invention may also have the following features: in step S21, the actual test includes: after preparing standard specimens of resin matrix and toughening particles respectively, tensile specimens are performed to obtain stress-strain curves of the two materials.

[0026] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials provided by this invention may also have the following features: wherein, in step S20, the definition and assignment method of the progressive damage model includes the following steps: S25, the equivalent plastic strain at the onset of material failure is... Considered as stress triaxiality and equivalent plastic strain rate The function; S26, using the scalar failure equation to represent the stress tensor of the material. S27 defines the total damage variable as follows: S28, The relationships defined in steps S25 to S27 are used as a progressive damage model and applied to the RVE model.

[0027] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials provided by this invention may also have the following feature: Step S30 includes the following sub-steps: S31, for a cubic unit cell with parallel opposing boundary surfaces in the RVE model, its periodic displacement field is denoted as: , S32, from step S31, we can obtain: S33, for each set of parallel faces of a cubic unit cell, It is a constant, once given but Since the constant is constant, the formula in step S32 is rewritten to obtain the nodal displacement constraint equation. This condition was then applied as a periodic boundary condition to the RVE model.

[0028] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials provided by the present invention may also have the following features: In step S40, the mesh convergence analysis is performed by applying a uniaxial tensile load to the RVE model to extract the stress-strain curves of the RVE model under different mesh densities.

[0029] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials provided by the present invention may also have the following features: In step S50, finite element simulation calculations are performed on several RVE models to determine the variation law of mechanical property parameters of particle-toughened composite materials with particle diameter and volume fraction of toughening particles, so that, given a particle diameter, the volume fraction that can make the mechanical property parameters optimal is selected. The mechanical property parameters include tensile modulus, compressive modulus, tensile strength and compressive strength.

[0030] The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials provided by the present invention may also have the following features: In step S70, the initial failure of the resin matrix and toughening particles in the DCB model is defined by the maximum stress criterion, the secondary stress criterion is used as the crack initiation criterion for the XFEM crack propagation region, and the crack propagation evolution law of the XFEM crack propagation region is defined by the linear evolution method based on the fracture energy definition.

[0031] This invention also provides a multi-scale simulation and forward design system for the interlaminar fracture toughness of particle-toughened composite materials. This system utilizes any of the aforementioned methods for multi-scale simulation and forward design of the interlaminar fracture toughness of particle-toughened composite materials, including: a modeling module for batch generating several RVE models of the particle-toughened layer, supporting adjustments to the particle diameter and volume fraction of the toughening particles; a material property assignment module for assigning elastoplastic constitutive models and progressive damage models to the resin matrix and toughening particles in the RVE models; a boundary condition application module for applying periodic boundary conditions to the RVE models; and a mesh convergence analysis module for performing mesh convergence analysis on the RVE models in finite element software. The E-model and DCB model are used for mesh convergence analysis to determine the optimal mesh size; the optimization analysis module is used to perform finite element simulations on multiple RVE models to analyze the relationship between mechanical property parameters and particle diameter and volume fraction, and to determine the optimal combination of particle diameter and volume fraction; the multi-scale modeling module is used to build a DCB model of particle-toughened composite material and divide it into pre-cracked region, mesoregion and equivalent region, and assign the mesoregion to the RVE model; and the fracture simulation and verification module is used to perform type I interlaminar fracture toughness simulation on the DCB model using the XFEM method, obtain the simulated load-displacement response curve, and compare and verify it with the real experimental results.

[0032] The beneficial effects of this invention are:

[0033] (1) It solves three core problems in existing design and simulation: 1. The problem of "blindness" in interlayer particle toughening design: Existing technology cannot accurately predict the influence of different toughening schemes (such as particle size, distribution and volume fraction) on macroscopic interlayer fracture toughness before material preparation, resulting in R&D relying on the trial and error cycle of "preparation-testing", which is costly and time-consuming; 2. It solves the problem of "inaccuracy" and "distortion" in existing simulation models: Existing simulation methods mostly use simplified two-dimensional models or homogenization assumptions, which cannot truly reflect the stress field, damage evolution and key mechanisms such as "pinning" and "bridging" of toughening particles in three-dimensional space, resulting in low credibility of simulation results and difficulty in effectively guiding design; 3. It solves the problem of "disconnection" between microscopic and macroscopic mechanical properties: Existing research often separates microscopic modeling from macroscopic fracture analysis, fails to establish an effective cross-scale method, and cannot directly and accurately apply the calculation results of microscopic RVE model to predict the initiation and propagation behavior of macroscopic cracks.

[0034] (2) Provides innovative simulation and design methods: 1. Provides a highly predictive simulation method: An integrated computational framework has been established, which can accurately simulate mechanical behavior from the micro-particle scale to the macro-structural scale, and realize reliable prediction from micro-parameters to macro-performance; 2. Realizes forward design of composite material performance: Changes the traditional R&D model that relies on "trial and error", and accurately predicts macro-interlaminar fracture toughness (such as type I fracture toughness GIC) by adjusting micro-design parameters (such as particle size, volume fraction, and distribution form), thereby guiding the selection of the optimal toughening scheme; 3. Reveals the essence of toughening from the mechanism level: Not only matches the macro-response, but also reveals the micro-toughening mechanisms such as "particle bridging", "crack pinning" and "interface debonding" through simulation visualization and data analysis, providing in-depth theoretical guidance for material design; 4. Forms a set of design systems and models that can be promoted: Constructs a forward design model, method and process applicable to the interlaminar toughening technology of domestic carbon fiber composite materials, and provides core tools and theoretical support for improving the technical maturity and independent design capability of domestic aerospace composite materials.

[0035] (3) It has extremely high technical advantages: 1. High-fidelity three-dimensional micromechanical model: It adopts a three-dimensional representative volume element model containing randomly distributed spherical particles and applies strict periodic boundary conditions, which breaks through the simplification limitations of traditional two-dimensional models and truly simulates the three-dimensional stress field distribution and damage initiation behavior of the interlayer toughening layer; 2. Mechanism-driven material and fracture modeling strategy: By giving the resin matrix and toughening particles an elastoplastic constitutive relationship and a progressive damage model, and using the XFEM method to simulate crack propagation, it reproduces the core toughening phenomena such as "particle bridging" and "crack deflection" from the physical mechanism level. 1. Achieving a leap from phenomenon fitting to mechanism reproduction; 2. Quantitative analysis and optimization of toughening parameters: By constructing parameterized RVE models with different particle diameters and volume fractions, the influence of key microscopic parameters on the macroscopic mechanical properties of the toughened layer is systematically explored, and the parameter combination for achieving the optimal toughening effect is clarified; 3. Construction of cross-scale fracture toughness prediction model: A macroscopic type I interlaminar fracture toughness prediction model integrating microscopic particle characteristics is established, combining the particle composition at the microscopic scale with the macroscopic double cantilever beam sample model to achieve accurate simulation and toughness prediction of the entire process from damage initiation to crack stable propagation.

[0036] (4) It can bring significant engineering benefits: 1. Achieve optimal design of the mechanical properties of the toughened layer: By optimizing the combination of parameters, the optimal design of the mechanical properties of the toughened layer can be achieved; 2. Accurately predict the interlaminar fracture toughness: The macro-micro combined model can accurately predict the interlaminar fracture toughness; 3. Significantly reduce R&D costs and cycle: Reduce the number of experiments, reduce R&D costs, and shorten the development cycle.

[0037] (5) This invention combines particle parameter optimization at the mesoscale with fracture behavior simulation at the macroscale to construct a full-process, multi-scale prediction method from material composition properties to structural failure behavior. This method can not only quantitatively guide the optimization of the diameter and volume content of interlaminar toughening particles based on representative volume element (RVE) simulation, but also achieve a more refined simulation of the crack propagation path and mechanical response in heterogeneous toughened layers by embedding a mesoscale model containing randomly distributed particles into a macroscale double cantilever beam (DCB) fracture model. Compared with traditional single-scale or homogenized models, this cross-scale coupling method significantly improves the accuracy of predicting the type I interlaminar fracture toughness of interlaminar toughened composite materials, providing a more reliable numerical analysis tool for the design and performance evaluation of similar composite materials.

[0038] (6) The multi-scale simulation and forward design method and system for interlaminar fracture toughness of particle-toughened composite materials of the present invention has broad application prospects in high-end equipment manufacturing fields such as aerospace composite structural parts and lightweight automotive components. The multi-scale simulation method provided by the present invention can accurately determine the key parameters of the toughening process, significantly improve interlaminar toughness, effectively solve the problems of high cost and long cycle of traditional trial and error methods, and realize accurate prediction of the mechanical properties of toughened layers. It has important engineering application value and broad market prospects. Attached Figure Description

[0039] Figure 1 This is a flowchart of a multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials according to an embodiment of the present invention.

[0040] Figure 2 This is an illustration of the RVE model in step S11 of an embodiment of the present invention, wherein (a) is a unit cell model of the RVE model and (b) is a particle model of the RVE model.

[0041] Figure 3 This is an illustration of several RVE models of the particle toughening layer in step S12 of an embodiment of the present invention, wherein (a) is a geometric model and (b) is a mesh model.

[0042] Figure 4 This is a schematic diagram of different grid densities in step S40 of an embodiment of the present invention.

[0043] Figure 5 The calculation results of the RVE model under different grid densities in step S40 of the embodiment of the present invention are shown. Part (a) is the stress-strain curve under different grid sizes under tensile load, and part (b) is the predicted tensile strength under different grid densities.

[0044] Figure 6 This is a parameter analysis of the toughening particles in the particle toughening layer of step S50 in an embodiment of the present invention.

[0045] Figure 7 This is a schematic diagram of the cross-scale DCB model in step S60 of an embodiment of the present invention.

[0046] Figure 8 This is a schematic diagram of the mesh of the fine region in the DCB model in step S70 of an embodiment of the present invention.

[0047] Figure 9 This is a schematic diagram comparing the simulated load-displacement response curve and the actual load-displacement response curve obtained in steps S72 and S73 of an embodiment of the present invention.

[0048] Figure 10This is a comparison between the interlaminar fracture cloud map of the DCB model in an embodiment of the present invention and the experimental sample.

[0049] Figure 11 This is a schematic diagram of the damage in the fine-grained region of the DCB model according to an embodiment of the present invention.

[0050] Figure 12 This is an architecture diagram of a multi-scale simulation and forward design system for interlaminar fracture toughness of particle-toughened composite materials according to an embodiment of the present invention.

[0051] Figure 13 This is a comparative schematic diagram of a macroscopic DCB two-dimensional model based on the XFEM method of the present invention.

[0052] Figure 14 This invention compares the simulated load-displacement response curve of the macroscopic DCB two-dimensional model with its actual load-displacement response curve. Detailed Implementation

[0053] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate a multi-scale simulation and forward design method and system for interlaminar fracture toughness of particle-toughened composite materials.

[0054] Example

[0055] This embodiment provides a multi-scale simulation and forward design method for the interlaminar fracture toughness of particle-toughened composite materials.

[0056] The particle-toughened composite material includes a laminate and a particle-toughening layer disposed therein, wherein the particle-toughening layer includes a resin matrix and toughening particles distributed therein.

[0057] Figure 1 This is a flowchart of a multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials according to an embodiment of the present invention.

[0058] like Figure 1 As shown, the multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials in this embodiment includes the following steps:

[0059] S10, Batch modeling of RVE model for particle toughened layer:

[0060] Because the true microstructure of the particle-toughened layer in composite materials is often very complex, a simplified approach is typically taken when studying the overall material properties. It is usually assumed that the entire material is composed of periodically distributed micro-units with point-like microstructures, known as representative volume elements (RVEs). The scale of these representative volume elements is generally much smaller than the macroscopic scale of the material, but must be large enough to encompass the main microstructural features of the composite material. For particle-toughened composites, by establishing a microscopic RVE model of the particle-toughened layer, and combining this with subsequent periodic boundary conditions and constitutive models of the corresponding component materials, the macroscopic homogeneous properties of the overall material can be obtained.

[0061] Specifically, in this embodiment, the batch modeling of the RVE model for the particle toughening layer in step S10 includes the following sub-steps S11 and S12:

[0062] S11, To facilitate subsequent finite element modeling, the toughening particles are considered as uniformly sized regular spheres, randomly distributed within the resin matrix. To generate a 3D finite element model of the randomly distributed particles and use it as the RVE model, parametric modeling is performed using Python. For ease of subsequent finite element calculations, this embodiment uses tetrahedral elements C3D4 for mesh generation, with RVE dimensions of 30μm × 30μm × 30μm. Figure 2 As shown. When using periodic microstructures to simulate material properties, applying periodic boundary conditions appropriately is the key to accurately obtaining material properties. For the RVE model, two conditions should be satisfied at the boundaries of adjacent unit cells: (1) deformation compatibility; (2) stress compatibility.

[0063] S12, In this embodiment, to further investigate the influence of the particle diameter and volume fraction of the toughening particles in the particle-toughened layer on the mechanical properties of the particle-toughened layer, RVE models of random particles with different diameters (5μm, 7μm, 10μm) and different volume fractions (20%, 25%, 30%) were generated in batches. Their geometric models and mesh models are as follows: Figure 3 As shown.

[0064] S20, Assign the corresponding material properties to the RVE model, including the following sub-steps S21~S28:

[0065] S21, the initial yield stress of the resin matrix and toughening particles was obtained through actual experiments. and stress-strain hardening function .in, It represents the equivalent plastic strain.

[0066] Specifically in this embodiment:

[0067] (1) Tensile specimens of resin matrix and toughened particles were prepared according to GB / T 2567 standard. Tensile tests were carried out on a universal testing machine. The stress-strain curves and basic mechanical property parameters of the two materials were obtained by strain gauges as shown in Table 1.

[0068] Table 1 (Mechanical properties of resin matrix and toughening particles)

[0069]

[0070] In Table 1 above, Indicates modulus, Represents Poisson's ratio. Indicates tensile strength. This indicates the rate of energy release during fracture.

[0071] (2) Hardening function in this embodiment As shown in Table 2 below:

[0072] Table 2 (Hardening Function)

[0073]

[0074] S22, consider the definition of equivalent stress through Mises and its expression as follows: of Plastic potential .

[0075] in, , , , , , These represent the six stress components.

[0076] S23. The stress-strain curve of the resin matrix exhibits significant nonlinearity, and fully determining its plastic constitutive parameters requires complex experimental design. Isotropic yield models are widely used in constitutive models of composite materials due to their simple expression and ease of deducing plastic parameters from experimental results. In this embodiment, to obtain the mechanical properties of the RVE model, an isotropic yield model is used as an elastoplastic constitutive model to simulate the mechanical properties of the resin and particles, in conjunction with the stress-strain experimental curve. Considering the plastic deformation of the resin matrix and toughening particles, the plastic yield function is expressed in the form of equivalent plastic strain. .

[0077] S24 uses the defined isotropic yield model as the elastoplastic constitutive model and assigns it to the RVE model.

[0078] S25, when the components of the toughened particulate layer reach the set failure criterion, the mechanical properties will decrease. This embodiment uses a toughness failure criterion as the initial damage criterion for the resin matrix and toughening particles. In the toughness failure criterion, material failure is considered to have occurred when the equivalent plastic strain of the material is equal to or greater than a critical value. This criterion assumes the equivalent plastic strain at the onset of material failure. It is stress triaxiality and equivalent plastic strain rate The function.

[0079] in, , It is compressive stress. This is the equivalent stress.

[0080] S26, when using the progressive damage method to describe the rate of material performance weakening after satisfying the failure criterion, the stress tensor of the material can be expressed by a scalar failure equation: .

[0081] in, Represents the effective stress tensor, when This indicates that the material has completely lost its load-bearing capacity and the unit has been deleted.

[0082] S27 defines the total damage variable as .

[0083] in, Represents the total damage variable. Represents the characteristic length of the element and the critical equivalent plastic displacement. , The fracture energy per unit area of ​​the material. The stress value at the onset of damage. Represents the equivalent plastic displacement, when time .

[0084] S28. The relationships defined in steps S25 to S27 are applied to the RVE model as a progressive damage model.

[0085] S30, Apply periodic boundary conditions to the RVE model, including the following sub-steps S31~S33:

[0086] S31, for a cubic unit cell with parallel opposing boundary surfaces in the RVE model, its periodic displacement field is denoted as: , .

[0087] in, Indicates the displacement direction index. This indicates the coordinate axis direction index corresponding to the unit cell boundary surface. Indices representing the components of the strain and displacement tensor. This represents the unit cell mean strain of the RVE model. Represents the coordinates of any point within a unit cell, indicated by the superscript. and They represent along The positive and negative directions of the axis. This represents the periodic displacement correction amount.

[0088] S32, from step S31, we can obtain: .

[0089] S33, for each set of parallel faces of a cubic unit cell, It is a constant, once given but Since the constant is constant, the formula in step S32 is rewritten to obtain the nodal displacement constraint equation. This condition was then applied as a periodic boundary condition to the RVE model.

[0090] in, Represents the spatial coordinates of any point within a unit cell. Corresponding to , , direction, Indicates perpendicular to , , Opposite faces of the axis.

[0091] In displacement-based finite element analysis, stress boundary conditions (second-type boundary conditions) are automatically satisfied through the principle of minimum potential energy. These are natural boundary conditions, so achieving periodic boundary conditions only requires applying periodic displacement boundary conditions to guarantee the unique determinism of the obtained results. The application of periodic displacement boundary conditions is achieved by establishing linear constraint equations at the corresponding mesh nodes on the parallel opposing surfaces of the unit cell. Step S30 above provides the constraint equations required to implement the periodic boundary conditions of step S33 on the corresponding face nodes, edge nodes, and corner nodes of the RVE unit cell model, and uses a Python script to implement the application of the periodic boundary equations.

[0092] S40, Mesh Convergence Analysis:

[0093] In finite element method (FEM) calculations, mesh size has a non-negligible impact on the results; that is, the smaller the mesh size, the better.

[0094] The calculation results converge to a certain value. Therefore, before calculating the RVE model of the particle-toughened layer in this embodiment, the mesh convergence of the elastic modulus and strength of the RVE model of the particle-toughened layer was analyzed, and the test model is as follows.Figure 4 As shown, the particle diameter is 12 μm and the particle volume content is 30%. The model is discretized using a tetrahedral C3D4 mesh with mesh sizes of 2 μm, 1.5 μm, 1 μm, 0.75 μm and 0.5 μm, and the corresponding mesh numbers are 27014, 55742, 177161, 352647 and 1117763, respectively. A uniaxial tensile load is applied to the RVE model, and the stress-strain curves of the RVE model under different mesh densities are extracted.

[0095] Figure 5 The calculation results of the RVE model under different grid densities in step S40 of the embodiment of the present invention are shown. Part (a) is the stress-strain curve under different grid sizes under tensile load, and part (b) is the predicted tensile strength under different grid densities.

[0096] like Figure 5 As shown, the initial segments of the stress-strain curves almost overlap. The mesh size has no effect on the predicted value of the elastic modulus, while the tensile strength gradually converges to a certain value as the mesh size decreases. Taking the tensile strength predicted by a mesh size of 0.50 μm as the baseline, the tensile strength changes predicted by models with mesh sizes of 0.75 μm, 1.00 μm, 1.50 μm, and 2.00 μm are -0.63%, +2.12%, +4.28%, and +8.99%, respectively. The strength prediction results increase with increasing mesh size, while the computational efficiency decreases with decreasing mesh size. To balance computational efficiency and accuracy, this embodiment uses a 1 μm mesh size discrete geometric model to predict the corresponding mechanical properties when performing subsequent calculations and analyses of the RVE model for the particle-toughened layer.

[0097] S50, optimization analysis of particle diameter and volume fraction:

[0098] Finite element simulations were performed on several RVE models to determine the variation of the mechanical property parameters (tensile modulus, compressive modulus, tensile strength, and compressive strength) of the toughened layer with respect to the particle diameter and volume fraction of the toughened particles. This allowed for the selection of the volume fraction that optimizes the mechanical property parameters given a particle diameter.

[0099] Figure 6 This is a parameter analysis of the toughening particles in the particle toughening layer of step S50 in an embodiment of the present invention.

[0100] like Figure 6 As shown, simulation calculations were performed on the RVE model for different particle diameters and volume fractions. Figure 6 Part (a) gives the case where the particle diameter is constant ( =10μm), the volume fraction (vol%, i.e., the subsequent...) of toughening particles. The effect on tensile and compressive properties. Figure 6 Part (b) is under the condition that the volume fraction of toughening particles is constant. =30%), the effect of particle diameter on tensile and compressive properties.

[0101] in, Figure 6 In the diagram, D represents the particle diameter, and D5, D7, and D10 represent particle diameters of 5μm, 7μm, and 10μm, respectively. The suffixes T and C represent tensile and compression tests, respectively.

[0102] from Figure 6 As shown in part (a), the tensile and compressive properties of the particle-toughened layer improve with increasing volume fraction, including tensile / compressive modulus and tensile / compressive strength. These properties then stabilize, with the interlayer toughness reaching its optimum at a particle volume fraction of approximately 30%. Figure 7 As shown in part (b), under a constant volume fraction, the tensile / compressive properties of the particulate toughening layer first decrease and then increase with the particle diameter. Therefore, for particulate toughening layers, different particle diameters require a suitable volume fraction of resin matrix to achieve optimal mechanical properties. Therefore, specifically in this embodiment, for the particulate toughening composite material, the parameter for a given toughening particle should be the particle diameter. =10μm, volume fraction =30%.

[0103] S60, cross-scale DCB modeling:

[0104] After obtaining the multi-scale DCB model of the particle-toughened composite material, the DCB model is divided into a pre-cracked region, a mesoscale region, and an equivalent region. Then, the RVE model, after setting and selecting the optimal parameters in steps S10 to S50, is assigned to the particle-toughened layer in the mesoscale region of the DCB model.

[0105] Specifically, in this embodiment, a method combining mesoscopic (RVE model) and macroscopic (DCB model) model is adopted. Considering the composition of the toughening particles at the mesoscopic scale, the mechanical behavior of the DCB specimen of the particle-toughened composite material under load is analyzed. A schematic diagram of the model is shown below. Figure 8As shown in the figure. To investigate the influence of particles on the toughness of type I interlaminar fracture, a 10 mm mesophyll region was established in the DCB model. This region contained a randomly distributed toughening layer of particles with a diameter of 10 µm, and the thickness of the toughening layer was assumed to be 20 µm. The entire pre-crack region, mesophyll region, and equivalent region were all defined as the XFEM crack propagation region, and a pre-crack of 70 mm in length was defined. The initial failure was defined using the maximum stress criterion for both the toughening particles and the resin matrix. Crack propagation was based on an energy-based criterion, and the plasticity of the toughening particles and the resin matrix was not considered. The model parameters are shown in Tables 3 and 4. Interlaminar failure was defined using XFEM, the crack initiation criterion was the secondary stress criterion, and the crack propagation process adopted a linear evolution method based on fracture energy.

[0106] Table 3 (Model parameters of laminates in the DCB model)

[0107]

[0108] Table 4 (XFEM region model parameters in the DCB model)

[0109]

[0110] In Tables 3 and 4 above, Indicates the longitudinal elastic modulus. This represents the transverse elastic modulus. This represents the Poisson's ratio in the 1-2 direction. This refers to the shear modulus in the 1-2 plane, i.e., the in-plane shear modulus. This represents the shear modulus in the 2-3 plane.

[0111] S70, Fracture Simulation and Verification, including the following sub-steps S71~S74:

[0112] S71 defines the pre-cracked region, the micro-region, and the equivalent region as the XFEM crack propagation region and uses the XFEM method to define the crack initiation and propagation criteria in this region.

[0113] Specifically, in this embodiment, a quadrilateral mesh is used to divide the DCB model, and a two-dimensional pixel mesh is used to discretize the mesoscopic regions in the DCB model. The cell type is CPE4R, and the mesh size is 1µm × 4µm. The mesh model of the mesoscopic region is as follows: Figure 9 As shown in the figure. In this embodiment, both the toughening particles and the resin matrix are defined as XFEM failure regions.

[0114] S72, simulate the type I interlaminar fracture toughness of the DCB model to obtain the simulated load-displacement response curve of the particle-toughened composite material.

[0115] S73, after preparing test specimens corresponding to the DCB model, conduct type I interlaminar fracture toughness tests to obtain their actual load-displacement response curves.

[0116] S74 compares and verifies the simulated load-displacement response curve with the actual load-displacement response curve to confirm the design success.

[0117] Figure 9 This is a schematic diagram comparing the simulated load-displacement response curve and the actual load-displacement response curve obtained in steps S72 and S73 of an embodiment of the present invention.

[0118] like Figure 10 As shown, "Simulation" represents the simulated load-displacement response curve (multi-scale DCB simulation), and "Experiment-1, Experiment-2, Experiment-3, Experiment-4, Experiment-5, and Experiment-6" represent the actual load-displacement response curves from six actual experiments. In this embodiment, the predicted peak load of the DCB model of the particle-toughened composite material designed using the multi-scale simulation and forward design method for interlaminar fracture toughness is 58.66 N, while the average measured peak load is 58.72 N, with an error of 0.10% for the peak load.

[0119] Figure 10 This is a comparison between the interlaminar fracture cloud map of the DCB model in an embodiment of the present invention and the experimental sample.

[0120] like Figure 11 As shown, this embodiment compares the loading conditions of the DCB model under actual experiments and simulation tests under different crack propagation lengths, including the opening of DCB specimens with crack lengths a of 60mm, 70mm, 80mm and 100mm. It can be seen that the deformation simulated by the DCB model under different crack propagation lengths is close to the actual experimental results, which proves the reliability of the numerical model established in this embodiment.

[0121] Figure 11 This is a schematic diagram of the damage in the fine-grained region of the DCB model according to an embodiment of the present invention.

[0122] like Figure 12 As shown, during crack propagation, in the region containing toughening particles, both the resin matrix and the toughening particles are damaged. Furthermore, since the loading direction of the DCB model is basically perpendicular to the crack propagation direction, the fracture plane of the entire interlayer directly penetrates the matrix and particles and propagates in a straight line.

[0123] Figure 12This is an architecture diagram of a multi-scale simulation and forward design system for interlaminar fracture toughness of particle-toughened composite materials according to an embodiment of the present invention.

[0124] like Figure 14 As shown, this embodiment also provides a multi-scale simulation and forward design system for interlaminar fracture toughness of particle-toughened composite materials. It uses the multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials in this embodiment, including a modeling module 10, a material property assignment module 20, a boundary condition application module 30, a mesh convergence analysis module 40, an optimization analysis module 50, a multi-scale modeling module 60, and a fracture simulation and verification module 70.

[0125] The modeling module 10 is used to generate several RVE models of the particle toughening layer in batches according to the method of step S10, and supports the adjustment of the particle diameter and volume fraction of the toughening particles.

[0126] The material property assignment module 20 is used to assign an elastoplastic constitutive model and a progressive damage model to the resin matrix and toughening particles in the RVE model according to the method in step S20.

[0127] The boundary condition application module 30 is used to apply periodic boundary conditions to the RVE model according to the method in step S30.

[0128] The mesh convergence analysis module 40 is used to perform mesh convergence analysis on the RVE model and DCB model in the finite element software according to the method in step S40, and to determine the optimal mesh size.

[0129] The optimization analysis module 50 is used to perform finite element simulations on multiple RVE models according to the method in step S50, analyze the relationship between mechanical performance parameters and particle diameter and volume fraction, and determine the optimal combination of particle diameter and volume fraction.

[0130] The multi-scale modeling module 60 is used to establish a DCB model of the particle-toughened composite material according to the method of step S60, and divide it into a pre-cracked region, a meso-region and an equivalent region, and assign the RVE model to the meso-region.

[0131] The fracture simulation and verification module 70 is used to perform type I interlaminar fracture toughness simulation on the DCB model using the XFEM method according to the method in step S70, obtain the simulated load-displacement response curve, and compare and verify it with the real test results obtained and input by the experimental operator.

[0132] This embodiment also provides the application of the aforementioned multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials.

[0133] The specific application areas are as follows:

[0134] (1) Aerospace: Provides high interlaminar toughness of composite materials for aerospace structural components.

[0135] (2) Automotive industry: Manufacturing structural components with greater stiffness to improve the collision safety performance of automobiles.

[0136] (3) Protective equipment: Used to make protective equipment and materials with high impact performance.

[0137] (4) Sports equipment: Provide high-strength, high-toughness, and impact-resistant sports equipment components.

[0138] Comparative Example

[0139] This comparative example refers to the macroscopic DCB two-dimensional simulation model of the particle-toughened composite material in the embodiment: the DCB model is divided into a pre-cracked region and an interlaminar interface region. The interlaminar interface region is divided using macroscopic mesh elements to construct the macroscopic DCB model, as shown in Figure 13. Subsequently, the optimal mechanical properties of the RVE model after setting and selecting the optimal parameters in steps S10~S50 of the embodiment are assigned to the interlaminar interface elements, and then simulation is performed.

[0140] Figure 14 This invention compares the simulated load-displacement response curve of the macroscopic DCB two-dimensional model with its actual load-displacement response curve.

[0141] like Figure 9 As shown, "Simulation" represents the simulated load-displacement response curve (macroscopic DCB simulation), and "Experiment-1, Experiment-2, Experiment-3, Experiment-4, Experiment-5, and Experiment-6" represent the actual load-displacement response curves from six actual experiments. A comparison of the macroscopic DCB model load curves with the DCB experimental test results shows that the predicted load-displacement curves are very close to the experimental results. The simulated predicted peak load is 67.13 N, while the average peak load measured in the experiment is 58.72 N, with a peak error of 14.3%.

[0142] like Figure 14 and ​ As shown, the multi-scale simulation and forward design method and system for interlaminar fracture toughness of particle-toughened composite materials in the embodiments of the present invention have better predictive capabilities.

[0143] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A multi-scale simulation and forward design method for interlaminar fracture toughness of a particle-toughened composite material, wherein the particle-toughened composite material comprises a laminate and a particle-toughening layer disposed therein, the particle-toughening layer comprising a resin matrix and toughening particles distributed therein, characterized in that, Includes the following steps: S10, batch modeling generates several RVE models of the toughening layer, wherein the toughening particles in the several RVE models have different particle diameters and volume fractions. S20, assign corresponding plastic yield functions to both the resin matrix and the toughening particles in the RVE model. The elastoplastic constitutive model and the material stress tensor are And the total damage variable is The progressive damage model, in, Defined by Mises equivalent stress Plastic potential, its form is as follows , , , , , , These represent the six stress components. Indicates the initial yield stress. Represents equivalent plastic strain. This represents the stress-strain hardening function obtained from actual experiments. Represents the effective stress tensor, when This indicates that the material has completely lost its load-bearing capacity and the unit has been deleted. Represents the total damage variable. Represents the characteristic length of the element and the critical equivalent plastic displacement. , The fracture energy per unit area of ​​the material. The stress value at the onset of damage. Represents the equivalent plastic displacement, when time Equivalent plastic strain at the onset of material failure It is stress triaxiality and equivalent plastic strain rate The function, , , It is compressive stress. Equivalent stress; S30, the nodal displacement constraint equation is applied to the RVE model as follows: The periodic boundary conditions, in, , , Represents the spatial coordinates of any point within a unit cell. Indicates the displacement direction index. Corresponding to , , direction, This indicates the coordinate axis direction index corresponding to the unit cell boundary surface. Indicates perpendicular to , , Opposite faces of the axis Indices representing the components of the strain and displacement tensor. This represents the unit cell mean strain of the RVE model. Represents the coordinates of any point within a unit cell, with superscript. and They represent along The positive and negative directions of the axis. This represents the periodic displacement correction amount. In the given In the case of the cubic unit cell of the RVE model, in each set of parallel faces is a constant and ; S40, Perform mesh convergence analysis on the RVE model in finite element software to determine the mesh size that balances computational efficiency and accuracy; S50, perform finite element simulation calculations on several RVE models to determine the particle diameter and volume fraction of the toughening particles under the optimal mechanical performance parameters, and use them as parameters for the final designed particle toughened composite material. S60, after modeling to obtain the cross-scale DCB model of the particle-toughened composite material, the DCB model is divided into a pre-cracked region, a meso-region and an equivalent region. Then, the RVE model after setting and selecting the optimal parameters in steps S10 to S50 is assigned to the particle-toughened layer in the meso-region of the DCB model. S70, firstly, the pre-cracked region, the micro-region, and the equivalent region are all defined as XFEM crack propagation regions, and the crack initiation and propagation criteria of this region are defined using the XFEM method. Next, the DCB model is used to simulate the type I interlaminar fracture toughness to obtain the simulated load-displacement response curve of the particle-toughened composite material. Subsequently, test specimens corresponding to the DCB model were prepared and subjected to type I interlaminar fracture toughness tests to obtain their actual load-displacement response curves. Finally, the simulated load-displacement response curve is compared with the actual load-displacement response curve to verify the successful design.

2. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, In step S10, parametric modeling is performed using Python. The toughening particles are treated as uniformly sized regular spheres randomly distributed in the resin matrix to obtain a 3D finite element model, which is then used as the RVE model. The RVE model satisfies the conditions for deformation compatibility and stress compatibility at the boundaries of adjacent unit cells.

3. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, In step S20, the definition and assignment method of the elastoplastic constitutive model includes the following steps: S21, Obtain the initial yield stress of the resin matrix and the toughening particles through actual experiments. and stress-strain hardening function ; S22, consider the definition of equivalent stress through Mises and its expression as follows: of Plastic potential ; S23, The mechanical behavior of the RVE model described later is simulated using an isotropic yielding model, and its plastic yield function is expressed in the form of equivalent plastic strain. ; S24, use the defined isotropic yield model as the elastoplastic constitutive model and assign it to the RVE model.

4. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 3, characterized in that: in, In step S21, the actual test includes: after preparing standard specimens of the resin matrix and the toughening particles respectively, tensile specimens are tested to obtain stress-strain curves of the two materials.

5. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, In step S20, the definition and assignment method of the progressive damage model includes the following steps: S25 represents the equivalent plastic strain at the onset of material failure. Considered as stress triaxiality and equivalent plastic strain rate The function; S26, Using the scalar failure equation to represent the stress tensor of the material. ; S27 defines the total damage variable as ; S28, The relationships defined in steps S25 to S27 are assigned to the RVE model as a progressive damage model.

6. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, Step S30 includes the following sub-steps: S31, for the cubic unit cell of the RVE model with parallel opposing boundary surfaces, its periodic displacement field is denoted as: 、 ； S32, from step S31, we can obtain: ； S33, for each set of parallel faces of the cubic unit cell, It is a constant, once given but Since the constant is constant, the formula in step S32 is rewritten to obtain the nodal displacement constraint equation. This is then applied as a periodic boundary condition to the RVE model.

7. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, In step S40, the mesh convergence analysis is performed by applying a uniaxial tensile load to the RVE model to extract the stress-strain curves of the RVE model under different mesh densities.

8. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-reinforced composite materials according to claim 1, characterized in that: in, In step S50, finite element simulation calculations are performed on several RVE models to determine the variation laws of the mechanical property parameters of the particle-toughened composite material with the particle diameter and volume fraction of the toughening particles, respectively. Thus, given the particle diameter, the volume fraction that optimizes the mechanical property parameters is selected. The mechanical property parameters include tensile modulus, compressive modulus, tensile strength, and compressive strength.

9. The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials according to claim 1, characterized in that: in, In step S70, the initial failure of the resin matrix and the toughening particles in the DCB model is defined using the maximum stress criterion. The secondary stress criterion was adopted as the crack initiation criterion in the crack propagation region of the XFEM. The crack propagation evolution law of the XFEM crack propagation region is defined by a linear evolution method based on the definition of fracture energy.

10. A multi-scale simulation and forward design system for interlaminar fracture toughness of particle-reinforced composite materials, characterized in that, The multi-scale simulation and forward design method for interlaminar fracture toughness of particle-toughened composite materials according to any one of claims 1 to 9 is used, including: The modeling module is used to generate several RVE models of the toughened particle layer in batches, and supports the adjustment of the particle diameter and volume fraction of the toughening particles. The material property assignment module is used to assign an elastoplastic constitutive model and a progressive damage model to the resin matrix and toughening particles in the RVE model. A boundary condition application module is used to apply periodic boundary conditions to the RVE model; The mesh convergence analysis module is used to perform mesh convergence analysis on the RVE model and the DCB model in finite element software to determine the optimal mesh size; The optimization analysis module is used to perform finite element simulations on multiple RVE models, analyze the relationship between mechanical performance parameters and particle diameter and volume fraction, and determine the optimal combination of particle diameter and volume fraction. A multi-scale modeling module is used to establish a DCB model of the particle-toughened composite material, divide it into a pre-cracked region, a mesoscopic region, and an equivalent region, and assign the RVE model to the mesoscopic region; and The fracture simulation and verification module is used to perform type I interlaminar fracture toughness simulation on the DCB model using the XFEM method, obtain the simulated load-displacement response curve, and compare and verify it with the actual test results.

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