Consideration of the interfacial diffusion in the calculation of fracture energy of composites

Abstract

The application discloses a composite material fracture energy calculation method considering reinforcement-matrix interface dispersion, and comprises the following steps: S1, a matrix crack fracture energy model is established; S2, a reinforcement-matrix interface fracture energy model is established; S3, a composite material fracture control equation model is established; S4, a composite material critical energy release rate is modified; S5, the interface phase field, the displacement field and the crack phase field in the composite material fracture control equation are discretized by using the finite element method, and an incremental iteration is carried out, so that the crack propagation in the composite material considering the interface dispersion is calculated. Through the adoption of the phase field model, the advantages of realizing the micro-to-macro multi-scale simulation are utilized, the properties of the interface in the composite material are associated with the properties of the matrix, that is, the interface crack propagation and other fracture properties of the composite material under the action of the load are dispersed to the surrounding matrix in the form of a continuous exponential function, and a mechanical model for more accurately predicting the mechanical behavior and fracture evolution of the composite material is established.

Description

Technical Field

[0001] This invention belongs to the field of composite material technology, specifically relating to a method for calculating the fracture energy of composite materials considering the dispersion at the reinforcement-matrix interface. Background Technology

[0002] Composite materials, as highly discrete multi-interface and multi-phase materials, exhibit highly complex mechanical behavior and strength evolution under load. This necessitates the development of refined fracture analysis methods to reveal their intrinsic response mechanisms and evolutionary patterns. Currently, research on composite material mechanical models largely relies on homogeneous theory, simplifying complex multiphase media into homogeneous equivalent media, and then utilizing continuum mechanics methods for analysis and calculation. This approach has significantly advanced our understanding of the mechanical deformation characteristics of composite materials at a macroscopic phenomenological scale and has greatly facilitated corresponding composite material engineering design. However, with further research, some limitations have gradually emerged: Damage to composite materials under load is a progressive, multi-scale process involving the evolution from microcracks to macrocracks. Traditional elastoplastic models are mainly applicable to local contact responses and are difficult to accurately simulate cross-scale damage evolution. The interaction between the reinforcement-matrix interface and the reinforcement and matrix in composite materials has a significant impact on the overall mechanical behavior, but homogeneous theory is difficult to effectively describe these interface effects. The theory of continuum mechanics is difficult to capture the dynamic development of damage such as crack initiation and propagation at the reinforcement-matrix interface inside composite materials under load, and it cannot reflect the influence of these microscopic damage evolutions on macroscopic mechanical behavior.

[0003] Current research has conducted triaxial-industrial CT combined tests on composite unit specimens. During the tests, the deformation characteristics of the specimens at each stage were obtained through CT scans. The results show that composite failure is a progressive process, typically beginning with crack initiation at the microscale. These microcracks then gradually propagate and connect, eventually forming a macroscale failure surface. Because the strength of the reinforcement within the composite material is significantly higher than that of the matrix, deformation and failure mainly consist of three parts: matrix cracking, shear debonding at the reinforcement-matrix interface, and the interaction between the two. How to simultaneously describe the progressive damage and failure of both the reinforcement-matrix interface and the composite matrix from a cross-scale perspective, as well as their interaction, has become a pressing challenge in current mechanical modeling research. Summary of the Invention

[0004] To address the aforementioned problems, embodiments of the present invention propose a method for calculating the fracture energy of composite materials that considers the dispersion at the reinforcement-matrix interface.

[0005] The present invention provides a method for calculating the fracture energy of composite materials considering the dispersion at the reinforcement-matrix interface, comprising the following steps:

[0006] S1. Establish a fracture energy model for cracks within the matrix;

[0007] S2. Establish a fracture energy model for the reinforcement-matrix interface;

[0008] S3. Establish a fracture control equation model for composite materials;

[0009] S4. Correction of the critical energy release rate of composite materials;

[0010] S5. Finite element discretization of the interface phase field, displacement field, and crack phase field control equations in the fracture control equations of composite materials, followed by incremental iteration, enables the calculation of crack propagation in composite materials considering interface dispersion.

[0011] The fracture energy model for intramatrix cracks is as follows:

[0012]

[0013] In the formula, Let Crack density be a function of the matrix. For the crack phase field, Let be the spatial variation rate of the crack phase field, and its expression is: , The x-axis is... Let be the dissipation function. It captures the crack phase field Contribution to the crack density function, Parameters for controlling the degree of crack dispersion within the matrix, The contribution of the crack surface gradient within the matrix was captured. To ensure dimensional consistency, , is the normalization constant used to ensure that the total integral equals 1. The denominator is used to guarantee the crack density function within the matrix. The volume integral is a dimensionless number.

[0014] The fracture energy model at the reinforcement-matrix interface is as follows:

[0015]

[0016] In the formula, Let be a functional of the interface area. In order to be in There exists an interface with zero thickness. For the interface phase field, Let be the spatial rate of change of the phase field at the interface, and its expression is: , The x-axis is denoted by , while This indicates the transition state between the user interface and non-user interface. It is a parameter characteristic value that controls the degree of dispersion of interface fracture properties. To find the solution domain.

[0017] The total potential energy of the composite material system is:

[0018]

[0019] In the formula, The total potential energy of the composite material system, It is a degenerate function. The elastic strain energy density of the composite material. For displacement field, The critical energy release rate of the interface. The critical energy release rate of the matrix. It is a force vector. For forces acting on the boundary Surface force vector on, Parameters for controlling the degree of crack dispersion within the matrix, For the crack phase field, The spatial variation rate of the crack phase field. For the interface phase field, The spatial rate of change of the phase field at the interface. The total area under the action of the boundary forces. It is a parameter characteristic value that controls the degree of dispersion of interface fracture properties. To find the solution domain.

[0020] In a given crack phase field and interface phase field Under these conditions, the equilibrium equations for the displacement field are obtained as follows:

[0021]

[0022] In the formula, The Cauchy stress tensor of a complete composite material is expressed as follows: , denoted as the elastic strain energy density of the composite material.

[0023] Under the given displacement field conditions, the governing equations of the composite material phase field are obtained as follows:

[0024]

[0025] In the formula, Let be the spatial variation rate of the crack phase field, and its expression is: , The x-axis is... Let be the spatial rate of change of the phase field at the interface, and its expression is: , The x-axis is... The Laplace equation for the crack phase field states that the value at each point within the crack phase field is equal to the average value of the surrounding area, expressed as: , The x-axis is... The Laplace equation for the interface phase field states that the value at every point within the interface phase field is equal to the average value of the surrounding area, and its expression is: , The x-axis is... The degenerate function with respect to the crack phase field The derivative, The elastic strain energy density of the composite material. Let be the outward normal vector of the boundary.

[0026] The corrected formula for the critical energy release rate of the composite material is:

[0027]

[0028] In the formula, This represents the critical energy release rate of the equivalent region. and This corresponds to the critical energy release rate of the interface and the matrix. To ensure a monotonically continuous variation of the interface phase field-related function between the interface and the matrix.

[0029] The weak form of the interface phase field control equation in the fracture control equation of the composite material is:

[0030]

[0031] In the formula, the interface phase field weight function It needs to satisfy the homogeneous essential boundary conditions, that is, in superior, , The spatial rate of change of the interface phase field weighting function.

[0032] The weak form of the displacement field control equation in the fracture control equation of the composite material is:

[0033]

[0034] In the formula, the displacement field weight function At the displacement boundary The above satisfies , Let be the spatial rate of change of the displacement field weighting function.

[0035] The weak form of the crack phase field governing equation in the fracture governing equation of the composite material is:

[0036]

[0037] In the formula, For the crack phase field weighting function, Let be the spatial rate of change of the crack phase field weighting function.

[0038] The core of this invention lies in proposing a calculation method for the fracture behavior of composite materials that considers the dispersion at the reinforcement-matrix interface. By introducing a phase field model, it achieves accurate simulation of the multi-scale damage evolution process of composite materials under load, from micro to macro.

[0039] The beneficial effects of this invention are:

[0040] 1. This application adopts a phase-field model, which leverages its advantage in enabling multi-scale simulation from micro to macro to correlate the properties of the interface with the properties of the matrix in composite materials. In other words, the damage properties such as interface crack propagation in composite materials under load are diffused into the surrounding matrix in the form of a continuous exponential function, thereby establishing a more accurate mechanical model for predicting the mechanical behavior and damage evolution of composite materials.

[0041] 2. This application introduces crack phase field and interface phase field respectively to normalize the material properties at discrete cracks and reinforcement-matrix interfaces, eliminate the discontinuity between cracks and interfaces and the matrix, and diffuse the fracture properties of cracks and interfaces into the matrix region, thereby constructing a new solution domain with continuous material properties.

[0042] 3. This application is conducive to a comprehensive and in-depth understanding of the multi-scale damage evolution mechanism and strength failure mechanism of composite materials, expands the research methods of composite material mechanics theory, provides a reliable theoretical basis and numerical analysis tools for the safety evaluation and toughness assessment of composite materials, and helps the smooth implementation of major national strategic projects. Attached Figure Description

[0043] Figure 1 This is the mechanical model of the microscopic deformation and failure of the composite material unit of the present invention.

[0044] Figure 2 This invention relates to the microscopic discrete model and phase field dispersion model of the composite material.

[0045] Figure 3 These are the discrete model and phase field dispersion model of the interface of this invention.

[0046] Figure 4 This invention relates to the geometric dimensions and stress models of composite materials with different reinforcement contents.

[0047] Figure 5 This describes the interfacial dispersion of composite materials with different reinforcement contents according to the present invention.

[0048] Figure 6 This invention describes the crack propagation characteristics of composite materials with different reinforcement contents.

[0049] Figure 7 This describes the variation law of displacement-load curves for composite materials with different reinforcement contents according to the present invention.

[0050] Figure 8 This describes the variation law of elastic strain energy of composite materials with different reinforcement contents under load.

[0051] Figure 9 This describes the variation of fracture energy of composite materials with different reinforcement contents under load according to the present invention. Detailed Implementation

[0052] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0053] This invention considers composite material units as multiphase materials composed of reinforcement, matrix, and reinforcement-matrix interfaces, such as... Figure 1 As shown, since the strength of the reinforcement is significantly higher than that of the matrix material, the reinforcement remains basically intact under load. The deformation and failure process of the composite element mainly manifests as matrix cracking, interfacial debonding, and the interaction between these two fracture mechanisms.

[0054] The present invention provides a method for calculating the fracture energy of composite materials considering the dispersion at the reinforcement-matrix interface, comprising the following steps:

[0055] S1. Establish a fracture energy model for cracks within the matrix;

[0056] Solution domain of composite element like Figure 2 As shown, the main components include microcracks at the reinforcement-matrix interface and within the matrix, considering body force vectors. and surface force vector Its function.

[0057] Crack phase field Similarly, the dispersion of cracks within the matrix is ​​achieved by using the interfacial phase field. After the internal cracks and interfacial fracture properties of the matrix disperse, both the reinforced structural region and the dispersed equivalent region become subdomains of the composite material. The force boundary in the element is... The displacement boundary is The phase field of the diffuse cracks within the matrix is:

[0058]

[0059] In the formula, For the crack phase field, Parameters for controlling the degree of crack dispersion within the matrix, The x-axis is denoted by .

[0060] In the crack phase-field model, after the crack is dispersed, the fracture energy of the crack within the matrix is... Density function of cracks within the matrix Related, the expression is:

[0061]

[0062] In the formula, This represents the fracture energy of an intramatrix crack. The critical energy release rate of the matrix. This is the crack density function within the matrix.

[0063] Since the crack is a two-dimensional surface, its surface area is described by geometric measures. In a simplified one-dimensional model, this is achieved through the crack density function within the matrix. To approximate the Dirac measure of the crack. To ensure that this dispersion representation is equivalent to a unit sharp crack in an energy sense, the normalization condition is:

[0064]

[0065] In-matrix crack density function It should rely on the crack phase field The sum is the spatial variation rate of the crack phase field. The more severe the material fracture, The larger the value, the greater its contribution to the crack density function within the matrix. A crack is the interface between the intact material and the fractured region. The steeper the interface, the greater the contribution to the crack density function. The larger the value, the more concentrated the interface, and the more effective crack surfaces are contained within a unit volume. This application uses a most general isotropic quadratic form to represent the crack density function within the matrix:

[0066]

[0067] In the formula, Let Crack density be a function of the matrix. For the crack phase field, Let be the spatial variation rate of the crack phase field, and its expression is: , The x-axis is... Let be the dissipation function. It captures the crack phase field Contribution to the crack density function, Parameters for controlling the degree of crack dispersion within the matrix, The contribution of the crack surface gradient within the matrix was captured. This ensures that the dimensions are consistent. is an undetermined normalization constant used to ensure that the total integral equals 1. The denominator is used to guarantee the crack density function within the matrix. The volume integral is a dimensionless number.

[0068] Without any external driving force, the crack should be determined by minimizing its own surface energy. That is, the crack phase field... This should be an extreme point of the crack density function within the matrix. Mathematically, this is described by the Euler-Lagrange equations:

[0069]

[0070] In the formula, For the first derivative of the crack phase field, The x-axis is denoted by .

[0071] According to equation (5), the following can be calculated:

[0072]

[0073] In the formula, Let be the derivative of the dissipation function with respect to the phase field. is the second derivative of the crack phase field.

[0074] Substituting equation (6) into equation (5), we get:

[0075]

[0076] because Substituting this into equation (7) yields:

[0077]

[0078] This is about dissipation functions. The differential equation can be solved by integration:

[0079]

[0080] In the formula, is the integration constant.

[0081] When the composite material is in good condition Dissipation function ,therefore Thus, the form of the dissipation function is obtained as:

[0082]

[0083] When dissipation function After that, the constants also need to be determined. This is to ensure that the crack density function within the matrix can accurately measure the fracture energy.

[0084] Substituting equations (1) and (10) into equation (4), we get:

[0085]

[0086] Substituting equation (11) into equation (3), we get:

[0087]

[0088] It can be seen from equation (12) that .

[0089] S2. Establish a fracture energy model for the reinforcement-matrix interface;

[0090] To clearly demonstrate the diffusion process of the phase-field model on the fracture properties of the reinforcement-matrix interface, the problem is analyzed based on a one-dimensional rod model. For example... Figure 3 As shown in (a), in There exists an interface with zero thickness. This interface can be described using a strongly discontinuous function, that is:

[0091]

[0092] In the formula, Let be the strongly discontinuous scalar field function of the interface. The x-axis is... This refers to the location of the interface.

[0093] At the interface Non-interface areas .

[0094] Using the strongly discontinuous scalar field function of equation (13) to describe the interface brings considerable difficulties to the calculation of conventional phase field models. Introducing the interface phase field... The interface fracture properties are described by the interface phase field, such as Figure 3 As shown in (b), the interface phase field expression is:

[0095]

[0096] In the formula, For the interface phase field, It is a parameter characteristic value that controls the degree of dispersion of interface fracture properties. The x-axis is... This refers to the location of the interface.

[0097] At the interface Non-interface areas ,and This represents the transition state between the interface and the non-interface. In the interface phase field of equation (14), These are characteristic values ​​of parameters that control the degree of dispersion of fracture properties at the interface, such as... Figure 3 As shown in (b), when the eigenvalue When it approaches 0, the dispersion of the interface fracture properties is infinitely close to the strongly discontinuous scalar field function form of equation (13).

[0098] interface phase field Based on Euler's variational principle, the distribution law of the phase field at the interface can be derived:

[0099]

[0100] In the formula, These are the boundary conditions for the interface. It is a functional of the interface area.

[0101]

[0102] In the formula, Let be a functional of the interface area. In order to be in There exists an interface with zero thickness. For the interface phase field, Let be the spatial rate of change of the phase field at the interface, and its expression is: , The x-axis is denoted by , while This indicates the transition state between the user interface and non-user interface. It is a parameter characteristic value that controls the degree of dispersion of interface fracture properties. To find the solution domain.

[0103] S3. Establish a fracture control equation model for composite materials;

[0104] like Figure 1 As shown, the overall potential energy of a composite material under load includes not only strain potential energy and external force potential energy, but also the fracture energy dissipated at the crack surface. Specifically, the release of elastic strain energy drives crack propagation, the dissipation of fracture energy resists crack propagation, and the external force potential energy is mainly composed of the material's body force vector. and acting on the force boundary Surface force vector This causes [the problem]. Therefore, the total potential energy of the composite material system can be written as:

[0105] (17);

[0106] In the formula, The total potential energy of the composite material system, It is a degenerate function. The elastic strain energy density of the composite material. For displacement field, The critical energy release rate of the interface. The critical energy release rate of the matrix. It is a force vector. For forces acting on the boundary Surface force vector on, Parameters for controlling the degree of crack dispersion within the matrix, For the crack phase field, The spatial variation rate of the crack phase field. For the interface phase field, The spatial rate of change of the phase field at the interface. The total area under the action of the boundary forces. It is a parameter characteristic value that controls the degree of dispersion of interface fracture properties. To find the solution domain. Let be the degradation function, describing the degradation process of a composite material from its intact state to its fractured state. Its expression is:

[0107]

[0108] In the formula, This is a numerical stability factor used to ensure the stability of numerical calculations. .

[0109] As can be seen from equation (17), in the total potential energy of the composite material system, fracture weakens the stiffness of the material, which is achieved through a degradation function. This is achieved through elastic strain energy density. For linear elastic materials, the elastic strain energy density... The expression is:

[0110]

[0111] In the formula, It is the elastic stiffness tensor of the material. For the strain tensor, and , It represents the spatial rate of change of the material displacement field.

[0112] First, it is necessary to determine the system in a given crack phase field. and interface phase field The mechanical equilibrium state under the condition that the total potential energy of the composite material system is related to the displacement field. The first variation of is zero, that is:

[0113] In the formula, The first variation of the total potential energy of the composite material system with respect to the displacement field is given by... Let be the displacement field weight function. Let be the spatial rate of change of the displacement field weighting function.

[0114] Applying the divergence theorem to equation (20) yields the equilibrium equation for the displacement field as follows:

[0115]

[0116] In the formula, The Cauchy stress tensor of a complete composite material is expressed as follows: , denoted as the elastic strain energy density of the composite material.

[0117] Secondly, given a displacement field, determine the equilibrium state of the crack phase field and the interface phase field. Similarly, the total potential energy of the composite material system with respect to the crack phase field... and interface phase field The first variation of is zero, that is:

[0118] (twenty two);

[0119] In the formula, The first-order variation of the total potential energy of the composite material system with respect to the crack phase field and the interface phase field is given by... For the crack phase field weighting function, Let be the spatial rate of change of the crack phase field weighting function. For the interface phase field weight function, The spatial rate of change of the interface phase field weighting function.

[0120] Applying the divergence theorem to equation (22), the equilibrium equations for the crack phase field and the interface phase field are obtained as follows:

[0121] In the formula, Let be the spatial variation rate of the crack phase field, and its expression is: , The x-axis is... Let be the spatial rate of change of the phase field at the interface, and its expression is: , The x-axis is... The Laplace equation for the crack phase field states that the value at each point within the crack phase field is equal to the average value of the surrounding area, expressed as: , The x-axis is... The Laplace equation for the interface phase field states that the value at every point within the interface phase field is equal to the average value of the surrounding area, and its expression is: , The x-axis is... The degenerate function with respect to the crack phase field The derivative, The elastic strain energy density of the composite material. Let be the outward normal vector of the boundary.

[0122] S4. Correction of the critical energy release rate of composite materials;

[0123] After obtaining the interfacial phase field distribution, the material properties of the interface and matrix can be fused using an interpolation function to form a continuous equivalent field. After the interfacial phase field disperses the interfacial fracture properties, the equivalent material parameters of the dispersed region consist of the material parameters of the matrix and the interface. Therefore, any equivalent material parameter of the dispersed region can be expressed as:

[0124]

[0125] In the formula, This represents the critical energy release rate of the equivalent region. and This corresponds to the critical energy release rate of the interface and the matrix.

[0126] function This ensures a monotonous and continuous change between the interface and the matrix, while satisfying... , , This application adopts Equation (24) ensures that in the matrix region , . The critical energy release rate of the matrix in the interfacial region , In the transition zone, exist and Smooth transition between them.

[0127] S5. Finite element discretization of the interface phase field, displacement field, and crack phase field in the phase field fracture control equation of composite materials, and incremental iteration, can calculate the crack propagation in composite materials considering interface dispersion.

[0128] The governing equations of the model in this application are strongly coupled and nonlinear. To solve them efficiently and stably, the finite element method is used for spatial discretization, and an alternating solution scheme is employed to decompose the problem. The Galerkin method is needed to transform the governing equations into a weak integral form, which is the basis of finite element discretization.

[0129] For the interface phase field The governing equations are static linear Helmholtz equations. To derive their weak form, an interface phase field weighting function is introduced. According to the Galerkin method, the interface phase field weighting function It needs to satisfy the homogeneous essential boundary conditions, that is, in superior, This is because in superior, The value of is fixed at 1, and its variation is zero. The residuals of the interface governing equations require that they be within the solution domain. The weighted inner integral is zero, therefore we can obtain:

[0130]

[0131] In the formula, The interface phase field weighting function.

[0132] For equation (25) Applying the divergence theorem, we can obtain:

[0133]

[0134] In the formula, The spatial rate of change of the interface phase field weighting function.

[0135] Moreover, due to the natural boundaries Above And at the essential boundary superior Therefore, the entire boundary integral term is zero. Equation (25) can be transformed into:

[0136]

[0137] Equation (27) is the weak form of the interface phase field control equation.

[0138] For displacement field The governing equations are used to introduce displacement field weighting functions. It is at the displacement boundary The above satisfies The residuals of the displacement field governing equations require that they lie in the solution domain. The weighted inner integral is zero, therefore we can obtain:

[0139]

[0140] In the formula, This is the displacement field weighting function.

[0141] right Applying the divergence theorem, we can obtain:

[0142]

[0143] Because in superior ,exist superior Therefore, the boundary integral simplifies to:

[0144]

[0145] Substituting equations (29) and (30) into equation (28), we obtain the weak form of the displacement field as follows:

[0146]

[0147] In the formula, Let be the spatial rate of change of the displacement field weighting function.

[0148] Equation (31) is the weak form of the displacement field control equation.

[0149] For the crack phase field The governing equations are used to introduce the crack phase field weighting function. The residuals of the crack phase field governing equations require that they be within the solution domain. The weighted inner integral is zero, therefore we can obtain:

[0150]

[0151] right Applying the divergence theorem, we can obtain:

[0152]

[0153] because exist The boundary integral term is zero, and substituting equation (33) into equation (32), the weak form of the crack phase field is:

[0154]

[0155] Equation (34) is the weak form of the crack phase field control equation.

[0156] Finite element discretization of equations (27), (31) and (34) and incremental iteration can be used to calculate the interfacial phase field and the crack propagation in the composite material.

[0157] Example

[0158] Composite material geometry and stress model with different reinforcement contents, as follows: Figure 4 As shown, Figure 4In the model, a, b, and c represent the geometric dimensions and stress models of composite materials with reinforcement contents of 30%, 45%, and 60%, respectively. The parameters of the three models are the same: the elastic modulus of the reinforcement in the model is 40 GPa, the Poisson's ratio is 0.33, and the critical energy release rate is 0.5 N / mm; the elastic modulus of the matrix is ​​4 GPa, the Poisson's ratio is 0.4, the critical energy release rate is 0.25 N / mm; and the critical energy release rate of the reinforcement-matrix interface is 0.05 N / mm. Figure 5 As the model demonstrates the dispersion of the interfacial phase field, it can be seen that the model can diffuse the fracture properties of the reinforcement-matrix interface in the composite material into the surrounding matrix.

[0159] Figure 6 The effect of reinforcement content on crack propagation path is shown. It can be seen that when the reinforcement content is 30%, the crack propagation path is relatively straight. When encountering reinforcement particles, the crack tends to bypass the particles directly or cause debonding between the particles and the matrix interface. Low reinforcement content has a weaker deflection and pinning effect on cracks. When the reinforcement content is 45%, the crack propagation path is the most tortuous. The crack frequently encounters reinforcement during propagation and is strongly deflected and bypassed. This means that more energy is required to propel the crack forward. A moderate reinforcement content achieves the best synergistic effect, effectively hindering crack propagation while maintaining good interfacial bonding and preventing premature interfacial failure. When the reinforcement content is 60%, the crack path becomes relatively direct again, but there is a tendency for it to penetrate along the reinforcement particles, and reinforcement fracture may even occur due to excessive reinforcement density. Excessively high reinforcement content leads to excessively close distances between reinforcement particles, severe stress concentration, and a tendency to form interconnected crack channels. At the same time, insufficient matrix material cannot effectively transfer and disperse stress, causing the interface to become a weak link.

[0160] Figure 7 To investigate the effect of reinforcement content on the macroscopic mechanical properties of composite materials, when the reinforcement content is 30%, the curve peak is low and the displacement is small. Because there is too little reinforcement, the strengthening effect is limited, crack propagation resistance is low, and the material fails rapidly. The composite material exhibits the lowest strength and toughness. When the reinforcement content is 45%, the curve shows the highest peak load and the largest fracture displacement. The area formed by the curve and the x-axis is the largest, indicating the best material toughness. When the reinforcement content is 60%, the curve has a high peak value, but it quickly drops sharply with small displacement, indicating that the material is brittle. Due to premature internal damage and through cracks, its load-bearing capacity is lower than that of the composite material with a reinforcement content of 45%.

[0161] Figure 8The variation of elastic strain energy of composite materials with different reinforcement contents under load shows that the elastic strain energy increases significantly when the reinforcement content increases from 30% to 45%, because the reinforcement is usually harder than the matrix. Increasing the content of hard reinforcement significantly improves the overall stiffness of the composite material. Under the same load, high-stiffness materials can store more elastic strain energy. When the reinforcement content increases from 45% to 60%, the elastic strain energy may remain at its peak or decrease slightly. This is because when the reinforcement content is too high, defects may appear inside the material, such as reinforcement agglomeration and porosity. These defects become stress concentration points, causing the material to yield locally or develop microcracks before reaching the theoretical elastic energy storage limit, thus reducing the effectively stored elastic strain energy.

[0162] Figure 9 The variation of fracture energy of composite materials with different reinforcement contents under load shows that the fracture energy increases as the reinforcement content increases from 30% to 60%. Furthermore, the fracture energy of the material with 60% reinforcement content is consumed significantly earlier than that of the materials with 30% and 45% reinforcement content. This is because the crack deflects around the reinforcement, making the path more tortuous and greatly increasing the surface area for crack propagation, thus consuming more energy.

[0163] Although the above embodiments have been shown and described, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions and variations made to the above embodiments by those skilled in the art are within the protection scope of the present invention.

Claims

1. A method for calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion, characterized in that, The method comprises the following steps: S1. establishing a matrix crack fracture energy model; S2. establishing a reinforcing body-matrix interface fracture energy model; S3. establishing a composite material fracture control equation model; The total potential energy of the composite material system is: where, is the total potential energy of the composite system, is a degradation function, is the elastic strain energy density of the composite, is the displacement field, is the critical energy release rate of the interface, is the critical energy release rate of the matrix, is the body force vector, is the surface force vector acting on the force boundary , is a parameter that controls the degree of dispersion of the matrix crack, is the crack phase field, is the spatial variation rate of the crack phase field, is the interface phase field, is the spatial variation rate of the interface phase field, is the total area of the boundary force action, is a parameter characteristic value that controls the degree of dispersion of the interface fracture property, is the solution domain; S4. correction of the critical energy release rate of the composite material; S5. finite element discretization is performed on the interface phase field, displacement field and crack phase field in the composite material fracture control equation, and an incremental iteration is performed, so that the crack propagation in the composite material considering the interface dispersion is calculated.

2. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The matrix crack density function is: where, is the crack density function in the matrix, is the crack phase field, is the spatial rate of change of the crack phase field, which is expressed as , is the horizontal coordinate, is the dissipation function, which captures the contribution of the crack phase field to the crack density function, is a parameter that controls the degree of dispersion of the cracks in the matrix, captures the contribution of the crack face gradient in the matrix, is made dimensionally consistent, is a normalization constant used to ensure that the total integral is equal to 1, in the denominator to ensure that the volume integral of the crack density function in the matrix is a dimensionless number.

3. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The reinforcing body-matrix interface fracture energy model is: where, is the functional of the interface area, is the interface phase field, is the interface with zero thickness at is the interface phase field, is the spatial variation rate of the interface phase field, which is expressed as , is the horizontal coordinate, and represents the transition state between the interface and the non-interface, is the eigenvalue of the parameter characteristic of the control interface fracture property dispersion, is the solution domain.

4. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, Under the condition of given crack phase field and interface phase field η, the equilibrium equation of displacement field is obtained as where denotes the Cauchy stress tensor of the complete composite, expressed as , is the elastic strain energy density of the composite, is the strain tensor, is the outward normal vector of the boundary.

5. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, Under the condition of a given displacement field, the composite material phase field control equation is obtained as: where is the spatial rate of change of the crack phase field, which is expressed as , is the horizontal coordinate, is the spatial rate of change of the interface phase field, which is expressed as , is the horizontal coordinate, is the Laplace equation of the crack phase field, which indicates that the value of each point in the crack phase field is equal to the average value of the surrounding, which is expressed as , is the horizontal coordinate, is the Laplace equation of the interface phase field, which indicates that the value of each point in the interface phase field is equal to the average value of the surrounding, which is expressed as , is the horizontal coordinate, is the derivative of the degenerate function with respect to the crack phase field , is the elastic strain energy density of the composite material, is the outward normal vector of the boundary.

6. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The correction formula of the critical energy release rate of the composite material is: wherein, Gc, the critical energy release rate of the equivalent zone, and Gc, the critical energy release rate of the equivalent zone, Gc, the critical energy release rate of the equivalent zone, is a function related to the interface phase field that ensures monotonic continuous variation between the interface and the matrix.

7. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The weak form of the interface phase field control equation in the composite material fracture control equation is: where the interfacial phase field potential function The homogeneous essential boundary condition needs to be satisfied, i.e. on , , is the spatial rate of change of the interfacial phase field potential function.

8. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The weak form of the displacement field control equation in the composite material fracture control equation is: where the displacement field weight function At the displacement boundary satisfies , is the spatial variation rate of the displacement field weight function.

9. The method of calculating the fracture energy of a composite material taking into account the reinforcement-matrix interface dispersion according to claim 1, characterized in that, The weak form of the crack phase field control equation in the composite material fracture control equation is: wherein is the crack phase field potential function, is the spatial rate of change of the crack phase field potential function.

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