Composite multi-scale analysis method considering manufacturing defects and application

Abstract

The application discloses a kind of composite material multiscale analysis method and application considering manufacturing defect, belong to composite material performance analysis technical field.The method is by constructing microcosmic, mesoscopic and macro scale model introducing manufacturing defect;Damage model of each scale model is constructed, the damage model includes the constitutive relation of describing material linear elastic behavior, initial failure criterion judging damage initiation, and damage evolution criterion describing stiffness degradation after damage occurs;Through bridging model, the stress, strain and damage information between microcosmic and mesoscopic scale are bidirectionally transferred, and the equivalent performance of composite material is obtained;Equivalent performance is endowed to macro scale model for structure analysis.The application can be applied to performance prediction, defect tolerance evaluation and structure design optimization of composite material by multiscale coupling and defect introduction, accurately predicts the mechanical properties and failure mechanism of composite material containing manufacturing defect.

Description

Technical Field

[0001] This invention relates to the field of composite material performance analysis technology, and more specifically, to a multi-scale analysis method for composite materials that takes into account manufacturing defects, and the application of this method in predicting the mechanical properties of composite materials, assessing manufacturing defect tolerance, and optimizing structural design. Background Technology

[0002] Composite materials, due to their lightweight, high strength, and designability, are widely used in aerospace, shipbuilding, and automotive engineering. While composite materials possess high designability, various manufacturing defects, such as fiber misalignment, porosity, and thickness variations, are inevitably introduced during the manufacturing process due to factors such as raw material properties and molding process parameter control. These defects severely affect the strength, stiffness, and durability of composite materials, are difficult to observe, and exhibit complex failure modes and mechanisms. Furthermore, multi-scale effects on performance and damage transmission exist at both micro and macro scales, along with the coupling and interaction of different failure modes. Current knowledge and research on composite mechanics still cannot fully reveal the highly nonlinear behavior, complex coupled failure mechanisms, multi-scale effects, and the adverse effects of random manufacturing defects. Most existing multi-scale analysis methods neglect the impact of manufacturing defects or only consider some defects at a single scale, lacking a comprehensive introduction of manufacturing defects at different scales and effective information transmission and coupling across scales. Moreover, a universal method is lacking to assess the impact of complex manufacturing processes on composite material failure modes. Therefore, developing a model that combines multi-scale analysis and defect impact assessment is of great significance. Therefore, it is necessary to explore the microscopic damage failure mechanism of composite materials containing manufacturing defects, and further reveal the failure mechanism of composite materials containing manufacturing defects.

[0003] Establishing representative manufacturing defect models and accurately developing multi-scale or cross-scale damage models capable of reproducing composite materials are crucial for understanding the failure mechanisms of composite materials containing manufacturing defects and form the foundation for research on these mechanisms. In recent years, representative volume elements (RVEs) have been widely used in the microscopic mechanical property analysis of defective composite materials, yielding accurate failure responses and mechanical properties. However, due to the information transmission and coupling processes between different scales influencing the performance of composite structures by manufacturing defects, microscopic-scale studies alone cannot effectively reveal the impact of defects on the failure mechanisms of composite structures. Therefore, it is necessary to develop a multi-scale analysis method for composite materials that considers manufacturing defects to accurately predict the actual performance of composite materials and provide optimization design references. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-scale analysis method and application for composite materials that takes into account manufacturing defects, so as to accurately predict the mechanical properties and failure mechanisms of composite materials containing manufacturing defects.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A multi-scale analysis method for composite materials that takes into account manufacturing defects includes the following steps: Step A: Construct microscale models, mesoscale models, and macroscale models, and introduce manufacturing defects into each model; The microscale model is a representative volumetric unit model that includes fibers and a matrix, and fiber positional deviation defects and / or porosity defects are introduced into the model. The microscale model is a representative volumetric unit model that includes fiber bundles, matrix and the interface between the two, and introduces porosity defects and / or fiber bundle alignment deviation defects into the model. The macroscopic model is a finite element model constructed based on the geometric dimensions of the component, and thickness deviation defects are introduced into the model; Step B: Construct damage models for each scale. The damage models include constitutive relations describing the linear elastic behavior of materials, initial failure criteria for determining the onset of damage, and damage evolution criteria describing stiffness degradation after damage occurs. Step C: Achieve bidirectional transmission of stress, strain, and damage information between the microscale model and the mesoscale model through a bridging model, and obtain the equivalent properties of the composite material considering manufacturing defects. Step D: Assign the equivalent properties of the composite material as homogenized mechanical property parameters to the macroscopic scale model, and perform finite element analysis of the macroscopic structural properties.

[0006] In a preferred embodiment of the present invention, the microscale model and / or mesoscale model employs periodic boundary conditions. By employing periodic boundary conditions, the periodic microstructure of composite materials can be accurately simulated, ensuring that the displacement and stress of adjacent element boundary surfaces are continuous when representative volume elements are subjected to external loads, thereby obtaining a more accurate local stress-strain field. The constraint equations of the periodic boundary conditions are: ; in, The average strain tensor of a representative volume element; and These represent the displacement components of the boundary surface corresponding to the representative solid element; and The coordinates of any point on the boundary surface; superscript and Representing along The positive and negative directions of the axis; This is the periodic displacement correction amount.

[0007] In another preferred embodiment of the present invention, the initial failure criterion of the macroscopic model is the maximum stress failure criterion, which is used to distinguish five failure modes: longitudinal tensile failure, longitudinal compressive failure, transverse tensile failure, transverse compressive failure, and shear failure. This criterion is simple in form and has a clear physical meaning, and can intuitively determine the main failure stress of the material, thereby effectively capturing the onset of damage.

[0008] As a further preferred embodiment of the present invention, in step C, the bridging model is implemented through a bridging matrix. The internal stress of the fibers in the microscale model is related to the stress field calculated from the mesoscale model. Internal stress of the matrix The relation is: Bridge matrix The introduction of this method enables precise solutions from mesoscale stress to microscale material internal stress, serving as a crucial bridge connecting mechanical fields at different scales. Its specific elemental expression can be determined based on the micromechanical theory of composite materials, combined with the material properties and geometric characteristics of the fibers and matrix.

[0009] As a further preferred embodiment of the present invention, the bridging model is also used to convert the damage information of the fiber and the matrix into equivalent damage of the fiber bundle, thereby realizing the reverse transmission of damage information. Among them, the longitudinal damage variable of fiber bundles and transverse damage variables They are determined by the following formulas respectively: ; ; In the above formula, and These are the longitudinal Young's modulus and transverse Young's modulus of the fiber bundle obtained in step C under the undamaged state, respectively. and These represent the longitudinal and transverse Young's moduli, respectively, considering the reduction in fiber bundle size after damage. Through this reverse transmission mechanism, the damage accumulation of micro-components can be accurately reflected in the performance degradation of the meso-fiber bundles, thus realistically simulating the progressive failure process of materials from micro-damage to macro-failure.

[0010] In another preferred embodiment of the present invention, in step D, the stiffness parameter is transferred between the microscale model and the macroscale model through a microstructure performance prediction formula that does not consider porosity and / or a microstructure performance prediction formula that considers porosity, and / or the strength parameter is transferred through a strength prediction theory formula. These theoretical formulas provide an efficient and reliable method for homogenizing the calculation of equivalent macrostructure performance.

[0011] In another preferred embodiment of the present invention, step E, which involves cross-scale information feedback and iterative optimization, is included after step D: Information on localized high-stress regions or early failure regions identified in the macro-scale analysis is fed back to the meso-scale and / or micro-scale models. The defect parameters of the corresponding regions are adjusted for reanalysis, and the homogenized mechanical property parameters passed to the macro-scale model are updated based on the reanalysis results. This process is repeated until the preset accuracy requirements are met. This feedback iteration mechanism fully considers the dependence of macroscopic failure on local microstructures, achieving closed-loop optimization of multi-scale analysis and significantly improving prediction accuracy.

[0012] In another preferred embodiment of the present invention, the matrix in the microscale model adopts the following formula as the initial failure criterion, the expression of which is: ; in, The failure factor of the fiber bundle outer matrix; For the von Mises stress of the matrix; This is the first stress invariant of the matrix; These are bridging parameters; and These represent the tensile strength and compressive strength of the matrix, respectively. This criterion comprehensively considers the response of the polymer matrix material under different stresses, and more accurately predicts the damage initiation of the matrix.

[0013] In another preferred embodiment of the present invention, the method further includes the step of establishing an interlaminar failure model. This model uses the traction-separation rule to describe its linear elastic behavior, employs a second nominal stress criterion as the initial damage criterion, and uses the BK criterion based on fracture energy as the damage evolution criterion to simulate interlaminar debonding or delamination. This model can effectively capture common delamination failure modes in composite laminates, further improving the simulation capability for the overall failure behavior of composite materials.

[0014] Compared with the prior art, the present invention has the following beneficial effects: (1) By comprehensively introducing manufacturing defects such as fiber position deviation, pores, fiber bundle arrangement deviation, and thickness deviation into the multi-scale model, the problem of large prediction deviation caused by neglecting manufacturing defects in traditional methods is solved.

[0015] (2) A bridging model is adopted to realize the bidirectional transmission of stress, strain and damage information between the micro and meso scales, and a feedback iteration mechanism from macro to micro is established, which truly reflects the multi-scale coupling failure mechanism of composite materials.

[0016] (3) A complete damage model system containing multiple failure criteria and evolution criteria has been constructed, which can accurately predict the entire process from the initiation of micro-damage to the destruction of macro-structure.

[0017] (4) The method of the present invention is highly versatile and can be widely applied to the performance prediction, defect tolerance assessment and structural design optimization of various composite materials, and has significant engineering application value. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A schematic diagram illustrating a multi-scale analysis method for composite materials that takes manufacturing defects into account, provided by the present invention. Figure 2 A flowchart illustrating the implementation of a multi-scale analysis method for composite materials that takes manufacturing defects into account, provided by this invention. Figure 3 This is a schematic diagram of the microscale and mesoscale finite element models of the present invention; Figure 4 This is a schematic diagram of the macroscopic finite element model of the present invention; Figure 5 This is a schematic diagram illustrating defects at different scales and their characterization methods according to the present invention. Figure 6 This is a schematic diagram of the bridging model theory of the present invention; Figure 7 Figure (a) shows the load-time curves of the experiment and simulation, and Figure (b) shows the damage morphology comparison between the experimental and simulation results. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] Example 1 This embodiment provides a multi-scale analysis method for composite materials that takes into account manufacturing defects, and its flowchart is shown below. Figure 1 and Figure 2 As shown, the specific steps include: Step A: Construct finite element models at the micro, meso, and macro scales, and introduce manufacturing defects.

[0021] First, a microscale model is constructed. This microscale model is a representative volumetric element (RVE) model containing both fibers and the matrix, typically at the micrometer (μm) scale, such as... Figure 3 As shown on the left. This model introduces fiber positional deviation defects and / or porosity defects. Specifically, fiber positional deviation defects include axial and radial deviations, which can be achieved by applying random perturbations to the fiber centerline coordinates during modeling; porosity defects are generated in the matrix using a random distribution algorithm based on the volume fraction, shape, and size range that may occur during actual manufacturing.

[0022] Secondly, a mesoscale model is constructed. This mesoscale model is a representative volumetric element (RVE) model comprising fiber bundles, the matrix, and the interface between the two, typically at the millimeter (mm) scale. Figure 3 As shown on the right. This model introduces porosity defects and / or fiber bundle alignment deviations.

[0023] Finally, a macro-scale model is constructed. This macro-scale model is a finite element model built based on the geometric dimensions of the component, typically with a scale ranging from centimeters to meters (cm to m). Figure 4 As shown, a thickness deviation defect is introduced into this model. The thickness deviation defect can be determined by setting the thickness parameters of different regions in the macroscopic model based on the actual measurement data or statistical laws of the thickness deviation at different positions of the component during the manufacturing process.

[0024] Step B: Assign material properties to models at each scale and construct damage models.

[0025] First, initial material properties are assigned to models at each scale. Among them, some material properties of the macro-scale model (such as the stiffness and strength of fiber bundles) are obtained from the simulation results of the micro-scale model through a homogenization method.

[0026] Then, damage models for each scale are constructed. Each damage model consists of three parts: a constitutive relation describing the linear elastic behavior of the material, an initial failure criterion for determining the onset of damage, and a damage evolution criterion describing the stiffness degradation after damage occurs.

[0027] (I) Macroscale Damage Model For macroscopic models, composite materials exhibit linear elastic behavior during the initial loading stage, and their elastic constitutive relation can be expressed as (taking plane stress as an example): ; The subscripts 11, 22, and 12 represent the longitudinal, transverse, and shear directions, respectively. , , This represents the strain in the corresponding direction; , , This refers to the stress in the corresponding direction; and This represents the elastic modulus in the corresponding direction; It is the in-plane shear modulus; and This refers to the Poisson's ratio in the corresponding direction; For longitudinal damage variables; For lateral damage variables; This represents the in-plane shear damage variable. Damage variable and Between 0 and 1, d=0 indicates that the material is intact, and d=1 indicates that the material is completely ineffective.

[0028] and Further defined by the following formula: ; in, For longitudinal tensile damage variables; For longitudinal compression damage variables; For transverse tensile damage variables; These are transverse compression damage variables. By introducing these damage variables, it is possible to distinguish the damage evolution behavior under different loading modes of tension and compression, making the model more consistent with the actual failure characteristics of composite materials.

[0029] The initial failure criterion of the macroscopic-scale model distinguishes five failure modes: longitudinal tensile failure, longitudinal compressive failure, transverse tensile failure, transverse compressive failure, and shear failure. This criterion considers multi-stress coupling effects and can more accurately characterize the anisotropic failure features of composite materials, as described below: Longitudinal tensile failure: ; Longitudinal compression failure: ; Lateral tensile failure: ; Lateral compression failure: ; Shear failure: in , , These are the effective stresses in the longitudinal, transverse, and shear directions, respectively. For longitudinal tensile strength, Longitudinal compressive strength; It is the transverse tensile strength; Transverse compressive strength; It is the in-plane shear strength; It is the longitudinal tensile failure factor; It is the longitudinal compression failure factor; It is the failure factor for transverse tensile stress; It is the lateral compression failure factor; This is the in-plane shear failure factor. When the failure factor reaches 1, the material begins to be damaged and enters the damage evolution stage. The tension-shear coupling coefficient has a value of [value missing]. .

[0030] Once damage begins, the material's stiffness degrades. The macroscopic damage model of this invention employs an asymptotic damage evolution criterion based on a stiffness reduction method. After damage begins, the material's reduced stiffness matrix... It can be obtained by inverting the elastic constitutive relation, and its expression is: ; in This represents the in-plane shear modulus. By introducing this reduced stiffness matrix, the stiffness degradation behavior after material damage can be accurately described, thus more realistically simulating the progressive failure process of macroscopic structures.

[0031] The progressive damage evolution model introduces damage variables. ( i= 1T, 1C, 2T, 2C, and 12 represent the degree of material damage. 1T, 1C, 2T, 2C, and 12 represent longitudinal tension, longitudinal compression, transverse tension, transverse compression, and shear, respectively. At that time, the material was not damaged; when At that time, the material was partially damaged. At that time, the material was completely damaged, among which This represents the maximum damage variable. Based on the five failure modes considered in the initial failure criterion, the corresponding damage evolution criteria are defined as follows: ; in This refers to the elastic properties of the corresponding material; This corresponds to the fracture energy of the material. The feature length of the unit; The shear response parameters used for calibration; The variable representing the maximum damage caused by shearing; The damage threshold, Damage weight; and The calculation formula is as follows: ; ; in t The current time; It is a time variable; For 0~ t Failure factors within a time period; Effective stress; To respond effectively.

[0032] (II) Microscale Damage Model For the mesoscale model, composite fiber bundles are treated as transversely isotropic materials, and their damage also includes elastic deformation, initial failure, and damage evolution stages. The three-dimensional elastic constitutive relations of the fiber bundles are as follows: ; The superscript fb indicates a fiber bundle; For the mesoscale strain tensor in different directions of the fiber bundle; For the mesoscale stress tensor in different directions of the fiber bundle; The fourth-order stiffness tensor of the fiber bundle reduction has a Voigt form 6×6 block matrix expression as follows: ; The expressions for each component of the stiffness tensor including damage are: ; ; ; ; ; ; ; ; in This is a simplified term in the denominator of the stiffness tensor; These are the initial stiffness matrix elements of the fiber bundle; These represent Young's moduli in different directions within the fiber bundle; For the shear modulus in different directions within the fiber bundle; Poisson's ratio in different directions within the fiber bundle; For longitudinal damage variables of fiber bundles; , For transverse damage variables of fiber bundles; This represents the fiber shear damage variable. , , It can be obtained from the following formula: ; in , , , These are the variables for longitudinal tensile damage, longitudinal compressive damage, transverse tensile damage, and transverse compressive damage of the fiber bundle, respectively.

[0033] The initial failure of fiber bundles is classified into five damage modes: longitudinal tension, longitudinal compression, transverse tension, transverse compression, and shear. Their specific expressions are as follows: Longitudinal tensile failure : ; Longitudinal compression failure : ; Lateral tensile failure : ; Lateral compression failure : ; In-plane shear failure : ; in, , , , , These are the failure factors for longitudinal tension, longitudinal compression, transverse tension, transverse compression, and in-plane shear of the fiber bundle, respectively. , , These are the axial and two transverse normal stress components of the fiber bundle, respectively; , , These are the shear stress components in the three-dimensional space of the fiber bundle; is the tension-shear coupling coefficient, used to characterize the contribution of shear stress to fiber tensile failure; , , , These are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, and transverse compressive strength of the fiber bundle, respectively. , , These represent the in-plane shear strength of the fiber bundle in three-dimensional space. When any failure factor reaches 1, the material begins to damage and enters the damage evolution stage.

[0034] The mesoscale matrix outside the composite fiber bundle is considered an isotropic material with equal material properties in different directions. Its three-dimensional elastic constitutive relation is described as follows: ; The superscript 'm' indicates the mesoscale matrix outside the fiber bundle; This represents the mesoscale stress vector; It is the mesoscale strain tensor (components include the 11, 22, 33, 12, 13, and 23 directions). This is the stiffness tensor reduced by the matrix.

[0035] Based on Lamé constant The expression containing damage is as follows: ; Its Voigt form 6×6 block matrix is: ; in It is a second-order unit tensor; It is a fourth-order symmetric unit tensor; For the damage variable of the outer matrix of the fiber bundle; , The Lamé constant of the matrix is ​​calculated using the following formula: ; in The Young's modulus of the outer matrix of the fiber bundle; The shear modulus of the outer matrix of the fiber bundle; is the Poisson's ratio of the outer matrix of the fiber bundle.

[0036] The initial damage failure of the fiber bundle outer matrix is ​​calculated as follows: ; in The failure factor of the fiber bundle outer matrix; and The tensile and compressive strength of the fiber bundle outer matrix; It is the first invariant of stress; Von-Mises stress in the outer matrix of the fiber bundle; This is the tension-compression asymmetry coefficient. and The calculation formula is as follows: ; Once damage to the fiber bundles or matrix begins, the material immediately undergoes stiffness degradation. Among these factors, the fiber bundle damage variable... Determined by the following formula: ; in, The damage variable is the one corresponding to the fiber bundle in the direction of the damage. This represents the equivalent displacement of the fiber bundle at the initial damage in the corresponding direction. This represents the equivalent displacement when the fiber bundle is completely damaged in the corresponding direction. This represents the equivalent displacement of the fiber bundle in different directions.

[0037] ; in This represents the fracture energy in the corresponding direction of the fiber bundle; The equivalent stress at the initial damage of the fiber bundle; is the length of the fiber bundle characteristic unit.

[0038] The outer matrix of the fiber bundle is a brittle material. The damage evolution criterion of the direct reduction method is used to predict its damage degradation, and its expression is as follows: ; in is the reduction factor for the stiffness matrix of the fiber bundle outer matrix, and its value is determined by model debugging; Let be the initial stiffness tensor of the matrix.

[0039] (III) Microscale damage model For the microscale model, damage models for fibers and the matrix are constructed separately. Since the matrix inside and outside the fiber bundle is the same material, the elastic constitutive model of the fiber bundle matrix in the microscale damage model is consistent with the elastic constitutive model of the fiber bundle matrix in the mesoscale damage model.

[0040] The stress tensor and strain tensor of the fibers (filaments) within the fiber bundle satisfy the fourth-order tensor constitutive relation: ; in For fiber stress tensor; For fiber strain tensor; The fourth-order stiffness tensor of the fiber has a 6×6 block matrix in Voigt form as follows: Its stiffness matrix components are directly expressed by the elastic constants as follows: ; in The axial elastic modulus of the fiber; The transverse elastic modulus of the fiber; , Poisson's ratio; , Shear modulus; This is a simplified term in the stiffness denominator.

[0041] Since the transverse dimension of the fiber is extremely small, considering only longitudinal damage, the initial failure criterion is as follows: Fiber tensile failure : ; Fiber compression failure : ; in, and These are the fiber tensile failure factor and the fiber compressive failure factor, respectively. The tensile failure strength of the fiber filament; The compressive failure strength of the fiber filament; , , The stress in the three longitudinal directions of the fiber; , As a shear contribution factor; This represents the shear strength of the fiber filament.

[0042] After fiber filament damage occurs, the direct reduction damage evolution criterion is used to simulate the brittle fracture damage of the fiber filament, and the damage variables are... The calculation formula is as follows: ; In the formula: i = T or C, corresponding to tension and compression respectively; This is the reduction factor (constant); This is the damage evolution index.

[0043] The initial microscopic failure of the matrix within the fiber bundle is predicted using the following formula: ; In the formula: ; ; ; ; ; ; It is the failure factor of the matrix within the fiber bundle; , The strength tensor coefficient of the matrix within the fiber bundle; The stress concentration factor; , , There are three principal stress components; , , represents the three shear stress components; represents the shear strength of the matrix within the fiber bundle.

[0044] The microscopic damage evolution criterion for the matrix within the fiber bundle can be either the direct reduction damage evolution criterion or the progressive damage evolution criterion, with the following formulas: Directly reduce damage: ; Progressive damage evolution damage: ; in, For matrix damage variables within fiber bundles; This is the matrix reduction factor (constant); The matrix damage evolution index; This is a factor used to control material damage reduction; For the elastic properties of the matrix; This represents the fracture energy of the matrix.

[0045] As a preferred improvement of the present invention, the scale considering interlayer failure adopts the following interlayer failure model: Interlayer failure modes can be broadly categorized into three stages: linear elastic deformation, initial damage, and progressive damage evolution. Figure 5 As shown. OA represents the linear elastic deformation stage, and according to the linear elastic constitutive relation: ; ; In the formula: For normal traction stress, and There are two tangential stresses; , , For different stiffness coefficients; For normal displacement, , There are two tangential displacements; For interface damage variables; , , For the three current traction stresses.

[0046] As the interfacial traction stress increases, i.e., after the stress value reaches point A, initial damage will occur at the interface. The initial interfacial damage can be described using the second nominal stress: ; In the formula: For the normal interface strength, and The strengths are the two tangential interfaces.

[0047] After the initial damage criterion is met, degumming or stratification occurs at the interface, significantly reducing the load-bearing capacity. This process is simulated using linear or nonlinear damage evolution criteria, and the calculations are shown below: Linear damage evolution criteria: ; In the formula: This represents the maximum damage displacement during the interface damage process. This represents the initial damage displacement of the interface. This represents the current damage displacement of the interface.

[0048] Nonlinear damage evolution criteria: ; In the formula: For effective traction stress, The initial damage elastic properties of the interface, This represents the current elasticity of the interface.

[0049] The criteria for judging the state of interface damage are: when and When, the interface is undamaged; when and At that time, the interface was partially damaged; when and At that time, the interface was completely damaged.

[0050] The interface damage behavior is defined based on the mixed-mode fracture energy, meaning that a certain energy level is required for complete debinding and delamination of the interface. Its expression is as follows: The α here differs from the previous definition and needs to be represented by a different character. In the formula: This represents the fracture energy in the corresponding direction. This refers to the critical fracture energy in the corresponding direction. , , This represents the work done by stress in the normal and two tangential directions at the corresponding displacement; This is a viscosity parameter.

[0051] Step C: Set boundary conditions and transfer information between micro and mesoscale levels.

[0052] For microscale and mesoscale models, since they are representative volumetric units, periodic boundary conditions are required to simulate the periodic repeating structure of composite materials. The constraint equations for these periodic boundary conditions are: ; in, The average strain tensor of a representative volume element; and These represent the displacement components of the boundary surface corresponding to the representative solid element; and The coordinates of any point on the boundary surface; superscript and Representing along The positive and negative directions of the axis; This is the periodic displacement correction amount.

[0053] Based on this, a bridging model is used to achieve bidirectional transmission of stress, strain, and damage information between the microscale model and the mesoscale model.

[0054] To more intuitively demonstrate the principle of information transfer between the micro and mesoscales in the bridging model, such as... Figure 6 As shown, the present invention uses a bridging matrix Establish the relationship between the internal stress of the fiber and the matrix. Figure 6 This demonstrates the average stress of fiber bundles at the mesoscale, through the bridging matrix. The internal stress of the microscale fiber and matrix is ​​calculated, and the damage variables of the microscale components are then transmitted in reverse to obtain a two-way information transmission path for the equivalent damage properties of the microscale fiber bundle.

[0055] Specifically, the bridging model uses non-singular matrices The internal stress of the fiber Internal stress of the matrix They are related, and their relationship is as follows: Based on this, combined with fiber volume fraction and matrix volume fraction This model can calculate the average stress and average strain of fiber bundles, thus achieving accurate solutions from mesoscale stress to the internal stress of microscopic material components. Simultaneously, it supports the reverse transfer of damage information, that is, converting damage variables of fibers and the matrix into longitudinal damage variables of the fiber bundles. and transverse damage variables This allows for a realistic simulation of the progressive failure process of materials, from microscopic damage to macroscopic failure. Figure 6The direction of the middle arrow clearly shows the path of this two-way information transmission, demonstrating the bridging model's role as a core bridge connecting the microscopic and mesoscopic scales.

[0056] The bridging model uses a bridging matrix. The relationship between the stress field in the mesoscale model and the internal stress of the fibers in the microscale model is established. Internal stress of the matrix The relation is: ; According to the fundamental equation, the average stress and average strain of the fiber bundle satisfy the following: ; in, This represents the fiber volume fraction. This represents the volume fraction of the matrix. ; and These represent the average stress and average strain corresponding to the fiber bundle, respectively. It is an identity matrix.

[0057] Bridge matrix The elements can be determined by the material properties and geometric characteristics of the fiber bundle, fibers, and matrix, and their expression is: ; in, , , Let be the flexibility tensor of the fiber, matrix, and fiber bundle. The flexibility tensor is the inverse matrix of the stiffness tensor, i.e. .

[0058] After calculating the bridging matrix, the internal stresses of the fiber and matrix are obtained through fiber bundle stress. The cross-scale stress transfer is expressed component by component as follows: ; After obtaining the internal stresses of the fiber and matrix, initial damage is determined using their initial failure criteria. Then, through cross-scale damage propagation, the reverse transmission of microscopic damage information to the mesoscale is achieved, simulating macroscopic fracture caused by the accumulation of microscopic damage. First, the corresponding failure factors are calculated using the initial failure criteria of the fiber and matrix, and then the damage variables are obtained. and The damage information of micro-components is equivalently converted into the damage of fiber bundles. The expression for this conversion is as follows: ; in For longitudinal damage variables of fiber bundles; For transverse damage variables of fiber bundles; The longitudinal Young's modulus of the fiber bundle; The transverse Young's modulus of the fiber bundle; The longitudinal Young's modulus of the fiber bundle reduction; Let be the transverse Young's modulus of the fiber bundle. Based on the bridging model, the formula for calculating the equivalent stiffness tensor of the fiber bundle with damage is as follows: ; in The equivalent stiffness tensor of the fiber bundle with damage; The bridge matrix contains damage; The stiffness tensor of the fiber filaments is reduced. This is the stiffness tensor reduced by the matrix.

[0059] The formula for calculating the reduced fiber modulus component is as follows: ; in , The transverse and longitudinal moduli of the fiber filaments are reduced. The flexibility tensor of the fiber filaments is reduced. The Poisson's ratio of the matrix within the fiber bundle; , , These represent the variables for fiber tension, compression, and shear damage, respectively.

[0060] Through this bidirectional transmission mechanism, the accumulation of damage at the microscale can be accurately reflected in the performance degradation of the mesoscopic fiber bundles, thus realistically simulating the gradual failure process of materials from the microscopic to the mesoscopic.

[0061] Finally, the equivalent properties of the composite material, such as the equivalent stiffness matrix and strength parameters, are obtained by homogenization methods to account for manufacturing defects. These equivalent properties will serve as input parameters for the macroscale model in step D.

[0062] Step D: Macroscale analysis.

[0063] The equivalent properties of the composite material obtained in step C are used as homogenized mechanical property parameters and assigned to the macroscopic model. During this process, the microscopic and macroscopic models can be compared and verified using theoretical models to predict stiffness and strength, serving as a basis for simulation results.

[0064] For example, the theoretical formula for homogenizing material properties without considering the influence of porosity is: ; ; ; ; ; in, This represents the fiber volume fraction. , , , , is the elastic constant of the fiber; , , The elastic constants of the matrix; It is the transverse shear modulus; This represents the transverse shear modulus of the fiber.

[0065] When calculating the properties of homogenized materials considering the influence of pores in the matrix, the pores in the matrix are approximated as spherical, and the modulus and Poisson's ratio of the pores are assumed to be zero. The elastic modulus of the porous matrix is... Compared to Poisson The calculation is as follows: ; ; in, and The bulk modulus and shear modulus of the porous matrix are respectively calculated by the following formula: , ; in, It represents the percentage of pores in the total volume of the fiber and matrix.

[0066] The strength parameters of the fiber bundle can be predicted using the following theoretical formula: ; ; ; ; ; ; in, , These are the axial tensile and compressive strengths of the fiber bundle, respectively. , These are the transverse tensile and compressive strengths of the fiber bundle, respectively. , The shear strength of the fiber bundle; , These represent the axial tensile and compressive strengths of a single fiber, respectively. , , These represent the tensile, compressive, and shear strengths of the matrix, respectively.

[0067] After assigning material properties, loads and boundary conditions are applied to the macroscopic model, and finite element analysis is performed to calculate the stress and strain distribution and damage evolution process of the macroscopic structure until structural failure.

[0068] Step E: Cross-scale information feedback and iterative optimization.

[0069] After completing the initial macroscale analysis, step E involves cross-scale information feedback and iterative optimization. Specifically, information about local high-stress regions or early failure regions identified in the macroscale analysis (such as the coordinates and stress values ​​of stress concentration areas) is fed back to the mesoscale model and / or microscale model. For these key regions, the corresponding defect parameters are adjusted (e.g., increasing the porosity or fiber deviation in the region) for a more refined reanalysis to explore the sensitivity of defects to local performance. Then, the homogenized mechanical property parameters passed to the macroscale model are updated based on the reanalysis results, and the macroscale analysis is performed again. This process is repeated until the preset accuracy requirements are met (e.g., the difference between the two analysis results is less than 5%). This feedback iterative mechanism fully considers the dependence of macroscale failure on local microstructure, achieves closed-loop optimization of multi-scale analysis, and significantly improves the overall prediction accuracy.

[0070] Furthermore, to comprehensively simulate the failure behavior of composite laminates, the method of this invention also includes establishing an interlaminar failure model. The failure modes of the interlaminar failure model can be broadly divided into a linear elastic deformation stage, an initial damage stage, and a progressive damage evolution stage. The linear elastic deformation stage is described according to the traction-separation law: ; ; in, Normal traction stress; and There are two tangential stresses; , , This is the corresponding stiffness coefficient; For normal displacement, and There are two tangential displacements; This is a variable representing interface damage, ranging between 0 and 1; , , The elastic traction stress is not considered when damage occurs.

[0071] As the interfacial traction stress increases, i.e., after the stress value reaches point A, initial damage will occur at the interface. The initial interfacial damage can be described using the second nominal stress: ; In the formula: For the normal interface strength, and The strengths are the two tangential interfaces.

[0072] After the initial damage criterion of the interface is met, delamination or separation begins to occur at the adhesive interface, such as... Figure 5 As shown. At this point, the load-bearing capacity of the adhesive interface is greatly reduced. The damage evolution model for this interface adopts either a linear damage evolution criterion or a nonlinear damage evolution criterion, as shown below: Linear damage evolution criteria: ; In the formula: This represents the maximum damage displacement during the interface damage process. This represents the initial damage displacement of the interface. The displacement represents complete damage to the interface.

[0073] Nonlinear damage evolution criteria: ; In the formula: For effective traction stress; This represents the total fracture energy at the interface. For interfacial elastic properties.

[0074] when and At that time, the interface was not damaged; and The interface was partially damaged at that time. and The interface was completely damaged at that time.

[0075] The interface damage behavior is defined based on the hybrid mode fracture energy, meaning that a certain energy level is required for complete debinding and delamination of the interface. Its expression is as follows: ; In the formula: This represents the fracture energy in the corresponding direction. The critical fracture energy; , , This represents the work done by stress in the normal and two tangential directions at the corresponding displacement; The parameters are viscous. By introducing an interlaminar failure model, the common delamination failure modes of composite laminates can be effectively captured, further improving the simulation capability of the overall failure behavior of composite materials.

[0076] To verify the correctness and feasibility of the model established in this invention, the simulation results were compared with experimental data, such as... Figure 7 As shown. Figure 7The figure shows a comparison between the simulation results and experimental data of the stress-strain curves of T700 / epoxy resin composite laminates under uniaxial tensile load. As can be seen from the figure, the simulated curves and experimental curves show a high degree of agreement in the initial linear stage, damage initiation point, and nonlinear softening stage. The prediction error of the peak stress is less than 5%, indicating that the established multi-scale analysis model can accurately predict the mechanical behavior of composite materials containing manufacturing defects, thus verifying the correctness and feasibility of the invention.

[0077] In summary, by establishing a multi-scale analysis framework, introducing manufacturing defects, constructing a complete damage model system, and realizing bidirectional transmission and iterative optimization of cross-scale information, this invention can accurately predict the mechanical properties and failure mechanisms of composite materials containing manufacturing defects, providing important theoretical basis and technical support for the structural design, process optimization, and defect tolerance assessment of composite materials.

[0078] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made without departing from the principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-scale analysis method for composite materials considering manufacturing defects, characterized in that, Includes the following steps: Step A: Construct microscale models, mesoscale models, and macroscale models, and introduce manufacturing defects into each model; The microscale model is a representative volumetric unit model that includes fibers and a matrix, and fiber positional deviation defects and / or porosity defects are introduced into the microscale model. The microscale model is a representative volumetric unit model that includes fiber bundles, matrix and the interface between the two, and introduces porosity defects and / or fiber bundle alignment deviation defects into the microscale model. The macroscopic model is a finite element model constructed based on the geometric dimensions of the component, and thickness deviation defects are introduced into this macroscopic model; Step B: Construct damage models for each scale. The damage models include constitutive relations describing the linear elastic behavior of materials, initial failure criteria for determining the onset of damage, and damage evolution criteria describing stiffness degradation after damage occurs. Step C: Achieve bidirectional transmission of stress, strain, and damage information between the microscale model and the mesoscale model through a bridging model, and obtain the equivalent properties of the composite material considering manufacturing defects. Step D: Assign the equivalent properties of the composite material as homogenized mechanical property parameters to the macroscopic scale model, and perform finite element analysis of the macroscopic structural properties.

2. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, The microscale model and / or mesoscale model employs periodic boundary conditions, and the constraint equations for the periodic boundary conditions are as follows: ； in, The average strain tensor of a representative volume element; and These represent the displacement components of the boundary surface corresponding to the representative solid element; and The coordinates of any point on the boundary surface; superscript and Representing along The positive and negative directions of the axis; This is the periodic displacement correction amount.

3. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, The initial failure criterion of the macroscopic scale model is the maximum stress failure criterion, which is used to distinguish five failure modes: longitudinal tensile failure, longitudinal compressive failure, transverse tensile failure, transverse compressive failure, and shear failure.

4. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, In step C, the bridging model is implemented through a bridging matrix. The relationship between the stress field in the mesoscale model and the internal stress of the fibers in the microscale model is established. and the internal stress of the matrix The relation is: .

5. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 4, characterized in that, The bridging model is also used to convert the damage information of fibers and matrix into equivalent damage of fiber bundles, thereby realizing the reverse transmission of damage information. Among them, the longitudinal damage variable of fiber bundles and transverse damage variables They are determined by the following formulas respectively: ； In the above formula, and These are the longitudinal Young's modulus and transverse Young's modulus of the fiber bundle obtained in step C under the undamaged state, respectively. and These are the longitudinal Young's modulus and the transverse Young's modulus, respectively, taking into account the reduction of fiber bundles after damage.

6. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, In step D, the microscale model and the macroscale model transfer stiffness parameters through mechanical performance theory prediction model and / or transfer strength parameters through strength prediction theory model.

7. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, Step D is followed by step E, which involves cross-scale information feedback and iterative optimization. Information on local high-stress areas or early failure areas identified in the macro-scale analysis is fed back to the meso-scale model and / or micro-scale model. The defect parameters of the corresponding areas are adjusted for reanalysis, and the homogenized mechanical property parameters passed to the macro-scale model are updated based on the reanalysis results. This process is repeated until the preset accuracy requirements are met.

8. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, The initial failure calculation of the matrix in the mesoscale model is as follows: ； in, The failure factor of the fiber bundle outer matrix; For the von Mises stress of the matrix; This is the first stress invariant of the matrix; These are bridging parameters; and These represent the tensile strength and compressive strength of the matrix, respectively.

9. The multi-scale analysis method for composite materials considering manufacturing defects according to claim 1, characterized in that, The method further includes the step of establishing an interlaminar failure model, wherein the interlaminar failure model uses the traction-separation rule to describe its linear elastic behavior, adopts the second nominal stress criterion as the initial damage criterion, and adopts the BK criterion based on fracture energy as the damage evolution criterion to simulate interlaminar debonding or delamination.

10. An application of a multi-scale analysis method for composite materials considering manufacturing defects as described in any one of claims 1 to 9, characterized in that, The method described above is applied to simulate and analyze composite materials containing manufacturing defects to obtain their mechanical property parameters.

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