A method for predicting failure of a composite matrix without empirical parameters based on a fracture surface theory

Abstract

This application provides a method for predicting matrix failure of composite materials without empirical parameters based on fracture surface theory, belonging to the field of materials mechanics. The method includes: constructing a quadratic polynomial containing undetermined coefficients for the failure function of a unidirectional composite material; establishing failure functions under tensile and compressive states based on the quadratic polynomial of the failure function, according to the sign of the normal stress; determining the undetermined coefficients in the failure functions under tensile and compressive states using basic strength parameters, based on assumptions of macroscopic homogeneity, transverse isotropy, and smooth failure surface, thus obtaining a matrix failure criterion; verifying the matrix failure criterion through tensile tests, compressive tests, and combined stress tests; and predicting the transverse shear strength using transverse tensile strength and transverse compressive strength based on the matrix failure criterion. This method offers higher prediction accuracy, significantly reduces experimental costs, improves design efficiency, and provides reliable evaluation results.

Description

Technical Field

[0001] This application relates to the field of materials mechanics, and in particular to a method for predicting failure of composite matrix without empirical parameters based on fracture surface theory. Background Technology

[0002] Composite materials, with their superior specific strength, specific stiffness, and design freedom, have become core supporting materials in the aerospace and high-end manufacturing fields of the 21st century. However, their significant anisotropy and complex multimode failure mechanisms pose a huge challenge to the high-precision assessment of structural strength. Existing composite material strength evaluation methods have obvious limitations in engineering applications: First, traditional macroscopic failure criteria (such as Tsai-Wu and Hashiin) lack clear physical mechanism support, limiting their prediction accuracy when dealing with complex multiaxial stress states; second, although criteria such as Puck introduce fracture surface theory, their models still rely on multiple empirical coefficients that are difficult to measure directly through physical experiments, resulting in highly subjective parameter values, reducing the model's universality and reliability, and increasing its uncertainty and subjectivity. This situation of "mechanism ambiguity" and "parameter dependence on experience" forces engineering designs to adopt extremely conservative safety factors and rely on large-scale destructive tests to compensate for the uncertainty of simulation predictions. This not only causes serious structural redundancy but also greatly increases research and development costs and time. Therefore, establishing a failure criterion whose parameters are entirely derived from standard measurable basic strength values, has clear physical connotations, and can accurately determine the damage initiation point is of vital engineering value for breaking through the bottleneck of weight reduction in composite materials and realizing high-fidelity digital design.

[0003] Furthermore, due to the unreliability of simulation predictions, the product development process relies heavily on numerous full-scale or component-level destructive tests. This not only generates enormous material and human resource costs but also significantly extends the design-to-delivery cycle, limiting the rapid iteration of new technologies. Summary of the Invention

[0004] In view of this, the present application provides a method for predicting matrix failure of composite materials without empirical parameters based on fracture surface theory. This method at least partially solves the problem that existing composite material in-layer failure criteria (such as the Puck criterion) require the introduction of empirical coefficients that cannot be directly measured by standard mechanical tests when constructing matrix failure criteria. This leads to difficulties in obtaining model parameter values, insufficient reliability of prediction results, and consequently, excessive reliance on destructive testing in engineering design.

[0005] This application provides a method for predicting the failure of composite material matrices without empirical parameters based on fracture surface theory, including:

[0006] Construct a quadratic polynomial for the failure function of unidirectional composite materials containing undetermined coefficients; Based on the quadratic polynomial of the failure function, failure functions under tensile and compressive states are established according to the sign of the normal stress. Using basic strength parameters, and based on the assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface, the undetermined coefficients in the failure functions under tensile and compressive states are determined, thus obtaining the matrix failure criterion. The matrix failure criteria were verified through tensile tests, compression tests, and combined stress tests. Based on the matrix failure criterion, the transverse tensile strength and transverse compressive strength are used to predict the transverse shear strength.

[0007] According to a specific implementation of an embodiment of this application, the construction of a quadratic polynomial containing undetermined coefficients of a failure function for a unidirectional composite material includes: The matrix failure of unidirectional composite materials depends on the stress on the fracture surface, and the failure function can be expressed as a quadratic polynomial of stress: ; Since the effects of positive and negative shear stress on material failure are the same, the quadratic polynomial of the stress function is simplified to obtain the simplified quadratic polynomial of the failure function: , Where F is the failure function, and A1, A2, B1, B2, C1, C2, D1, D2, and D3 are the first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth undetermined coefficients, respectively. , and These are the normal stress, transverse shear stress, and longitudinal shear stress acting on the fracture surface of the matrix, respectively.

[0008] According to a specific implementation of this application, the expressions for the failure functions in the tensile state and the compressive state are respectively: , , Among them, F t F is the failure function under tension. c The failure function under compression. This is the first undetermined coefficient under normal tensile stress state. This is the first undetermined coefficient under normal compressive stress state. This is the second undetermined coefficient under normal tensile stress state. This is the second undetermined coefficient under normal compressive stress state.

[0009] According to a specific implementation of an embodiment of this application, the step of using basic strength parameters and determining the undetermined coefficients in the failure function under tensile and compressive states based on assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface to obtain the matrix failure criterion includes: Step 31: Based on the fact that only longitudinal shear stress exists on the inclined section under pure shear stress, determine the sixth undetermined coefficient. The expression; Step 32: Under the isobiaxial stress state, only normal compressive stress exists on any oblique section parallel to the fiber. Since normal compressive stress inhibits failure, Hashin's assumption... Determine the second undetermined coefficient under normal compressive stress state. , =0, where, It is equal biaxial transverse compressive strength; Step 33: Under the transverse compressive stress state, obtain the first undetermined coefficients under the normal compressive stress state based on relevant assumptions and equations. The relevant equations; Step 34: Under the transverse tensile stress state, obtain the first undetermined coefficients under the normal tensile stress state based on relevant assumptions and equations. The second undetermined coefficient under normal tensile stress state The related equations for the fourth undetermined coefficient B2; Step 35: Based on the assumption of smoothness of the failure surface, obtain the first undetermined coefficient under normal tensile stress state. The first undetermined coefficient under normal compressive stress state The relevant equations; Step 36: Solve the simultaneous equations obtained in steps 31, 32, 33, 34, and 35 to find the undetermined coefficients. , , , B2 and C2 are used to obtain the matrix failure criteria.

[0010] According to a specific implementation of an embodiment of this application, the sixth undetermined coefficient The expression: , Among them, S 21 This represents the longitudinal shear strength of a unidirectional composite plate.

[0011] According to a specific implementation of an embodiment of this application, the first undetermined coefficient under the normal compressive stress state... The relevant equations are: , Among them, Y C This refers to the lateral compressive strength.

[0012] According to a specific implementation of an embodiment of this application, the first undetermined coefficient under the normal tensile stress state... The second undetermined coefficient under normal tensile stress state The relevant equation for the fourth undetermined coefficient B2 is: , , Among them, Y T This refers to the transverse tensile strength.

[0013] According to a specific implementation of an embodiment of this application, the first undetermined coefficient under the normal tensile stress state... The first undetermined coefficient under normal compressive stress state The relevant equations are: .

[0014] According to a specific implementation of an embodiment of this application, the expression for the matrix failure criterion is: .

[0015] According to a specific implementation of this application, the prediction equation for the transverse shear strength is: , Among them, S 23 This refers to the transverse shear strength.

[0016] Beneficial effects: The matrix failure prediction method for composite materials based on fracture surface theory in this application presents an innovative matrix failure criterion applicable to brittle composite materials that does not require additional empirical parameters. Compared with traditional matrix failure criteria, the matrix failure criterion of this invention has the advantage of not including any empirical parameters, thereby avoiding errors caused by the use of empirical parameters, and thus providing more accurate prediction results. The prediction accuracy is higher, greatly reducing test costs, improving design efficiency, and ensuring that the evaluation results are true and reliable. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a method for predicting failure of composite matrix without empirical parameters based on fracture surface theory according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the failure surface of a composite material according to an embodiment of the present invention; Figure 3 According to an embodiment of the present invention, σ 22 -τ 21 Failure envelope under stress, (a) for E-glass / LY556 composite material, (b) for IM7 / 8552 composite material. Detailed Implementation

[0019] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0020] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0022] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0023] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0024] This application provides a novel matrix failure prediction method for brittle composite materials based on fracture surface theory, without empirical parameters. The undetermined coefficients in this method only need to be determined through the basic strength, thus avoiding the dependence of previous matrix failure criteria on biaxial test data or empirical parameters. Furthermore, the transverse tensile strength Y is derived. T Transverse compressive strength Y C and transverse shear strength S 23 The relationship between them is described in detail below with reference to the attached diagram.

[0025] In one embodiment, an empirical parameter-free composite matrix failure prediction method based on fracture surface theory is provided, referring to... Figure 1 This includes the following steps: Step 1: Construct a quadratic polynomial for the failure function of unidirectional composite materials containing undetermined coefficients; Step 2: Based on the quadratic polynomial of the failure function, establish the failure functions for the tensile and compressive states according to the sign of the normal stress. Step 3: Using basic strength parameters, based on the assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface, determine the undetermined coefficients in the failure function under tensile and compressive states to obtain the matrix failure criterion. Step 4: Verify the matrix failure criteria through tensile tests, compression tests, and combined stress tests; Step 5: Based on the matrix failure criterion, the transverse tensile strength and transverse compressive strength are used to predict the transverse shear strength.

[0026] According to a specific implementation of an embodiment of this application, the construction of a quadratic polynomial containing undetermined coefficients of a failure function for a unidirectional composite material includes: The matrix failure of unidirectional composite materials depends on the stress on the fracture surface, and the failure function can be expressed as a quadratic polynomial of stress: ; Since the effects of positive and negative shear stress on material failure are the same, the quadratic polynomial of the stress function is simplified to obtain the simplified quadratic polynomial of the failure function: , Where F is the failure function, and A1, A2, B1, B2, C1, C2, D1, D2, and D3 are the first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth undetermined coefficients, respectively. , and These are the normal stress, transverse shear stress, and longitudinal shear stress acting on the fracture surface of the matrix, respectively.

[0027] Specifically, matrix failure of unidirectional composite materials depends on the stress on the fracture surface. , and ,like Figure 2 As shown, where , and It can be calculated using equation (1): (1), in, For the stress in the 2-2 direction of the composite material, For the stress in the 3-3 direction of the composite material, For the shear stress in the 2-1 direction of the composite material, For the shear stress in the 2-3 directions of the composite material, For the shear stress in the 3-1 direction of the composite material, The angle of the fracture surface. The failure function is expressed as a quadratic polynomial of stress: (2), Since the effects of positive and negative shear stress on material failure are the same, the linear term of shear stress should disappear, and equation (2) simplifies to .

[0028] Furthermore, since the effects of normal tensile stress and normal compressive stress on material failure are different on the fracture surface—normal tensile stress promotes failure while normal compressive stress inhibits failure—the expressions for the failure functions under tensile and compressive states are respectively: (3), (4), Among them, F t F is the failure function under tension. c The failure function under compression. This is the first undetermined coefficient under normal tensile stress state. This is the first undetermined coefficient under normal compressive stress state. This is the second undetermined coefficient under normal tensile stress state. This is the second undetermined coefficient under normal compressive stress state.

[0029] Furthermore, the six undetermined coefficients are determined using the basic strength and assumptions based on macroscopic homogeneity, transverse isotropy, and the convexity and smoothness of the failure surface / line. The final matrix failure criterion is then obtained: (5).

[0030] The proposed matrix failure criterion was verified through various tensile / compression tests and combined stress tests. Equation (5) in the plane stress state is as follows: (6), Among them, S 21 This represents the longitudinal shear strength of a unidirectional composite plate.

[0031] like Figure 3 As shown, E-glass / LY556 (Y T =40, Y C =137.4, S 21 =61.2) and IM7 / 8552 (Y T =76.4, Y C =288, S 21 =89) Composite materials in σ 22 -τ 21 The figure shows a comparison between the failure envelope under stress and the experimental results. The "current criterion" in the figure is the method of this application. It can be seen that the prediction results of this application are in good agreement with the experimental data.

[0032] Furthermore, by employing basic strength parameters and based on assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface, the undetermined coefficients in the failure functions under tensile and compressive states are determined to obtain the matrix failure criterion, including: Step 31: Based on the fact that only longitudinal shear stress exists on the inclined section under pure shear stress, determine the sixth undetermined coefficient. The expression; Step 32: Under the isobiaxial stress state, only normal compressive stress exists on any oblique section parallel to the fiber. Since normal compressive stress inhibits failure, Hashin's assumption... Determine the second undetermined coefficient under normal compressive stress state. , =0, where, It is equal biaxial transverse compressive strength; Step 33: Under the transverse compressive stress state, obtain the first undetermined coefficients under the normal compressive stress state based on relevant assumptions and equations. The relevant equations; Step 34: Under the transverse tensile stress state, obtain the first undetermined coefficients under the normal tensile stress state based on relevant assumptions and equations. The second undetermined coefficient under normal tensile stress state The related equations for the fourth undetermined coefficient B2; Step 35: Based on the assumption of smoothness of the failure surface, obtain the first undetermined coefficient under normal tensile stress state. The first undetermined coefficient under normal compressive stress state The relevant equations; Step 36: Solve the simultaneous equations obtained in steps 31, 32, 33, 34, and 35 to find the undetermined coefficients. , , , B2 and C2 are used to obtain the matrix failure criteria.

[0033] Furthermore, the sixth undetermined coefficient The expression: .

[0034] Furthermore, the first undetermined coefficient under the normal compressive stress state The relevant equations are: , Among them, Y C This refers to the lateral compressive strength.

[0035] Furthermore, the first undetermined coefficient under the normal tensile stress state The second undetermined coefficient under normal tensile stress state The relevant equation for the fourth undetermined coefficient B2 is: , , Among them, Y T This refers to the transverse tensile strength.

[0036] Furthermore, the first undetermined coefficient under the normal tensile stress state The first undetermined coefficient under normal compressive stress state The relevant equations are: .

[0037] Furthermore, the expression for the matrix failure criterion is as follows: .

[0038] In practice, step 3 includes the following: Step 31: Based on the fact that only longitudinal shear stress exists on the inclined section under pure shear stress, determine the sixth undetermined coefficient. The expression; Specifically, according to equation (1), under pure shear stress, only longitudinal shear stress exists on the inclined section: (7), exist On the inclined section, When the stress reaches its maximum value, material failure occurs. The failure stress ( =S 21 Substituting the values, we get: (8).

[0039] Step 32: Under the isobiaxial stress state, only normal compressive stress exists on any oblique section parallel to the fiber. Since normal compressive stress inhibits failure, Hashin's assumption... Determine the second undetermined coefficient under normal compressive stress state. , =0, where, It is equal biaxial transverse compressive strength; Specifically, equal biaxial transverse compressive stress ( = =- Substituting <0 into equation (1), we get: (9), In the formula, The biaxial transverse compressive strength is given. Substituting equation (9) into equation (4) yields: (10), Equation (10) can be solved to obtain: (11); Under isoaxial transverse compressive stress, only normal compressive stress exists on any oblique section parallel to the fiber. Since normal compressive stress inhibits failure, the Hashin hypothesis is followed. Substituting it into equation (11) yields: (12).

[0040] Step 33: Under the transverse compressive stress state, obtain the first undetermined coefficients under the normal compressive stress state based on relevant assumptions and equations. The relevant equations; Specifically, the transverse compressive stress state will be determined by the transverse compressive stress ( =-Y C Substituting into equation (1), we get: (13), Substituting equation (13) into equation (4), we get: (14), definition This is the transverse compression fracture angle. When At that time, failure function Therefore, when the maximum value is reached, we have: (15), (16), because Solving equation (16) yields: (17), Solving equations (15) and (17) simultaneously, we get: (18).

[0041] Due to the transverse shear stress acting on the fracture surface This promotes material failure, therefore the failure functions in equations (3) and (4) It must be greater than 0, therefore From equation (18), we can obtain: (19), Substituting equation (17) into the first term of the above equation, we get: (20), Since the first term of equation (19) is not equal to 0, the equation can be simplified to: (twenty one), Equation (21) can be simplified to: (twenty two), Substituting equation (22) into equation (17) and solving, we get: (twenty three).

[0042] Step 34: Under the transverse tensile stress state, obtain the first undetermined coefficients under the normal tensile stress state based on relevant assumptions and equations. The second undetermined coefficient under normal tensile stress state The related equations for the fourth undetermined coefficient B2; Specifically, the transverse tensile stress state will be determined by the transverse tensile stress ( =Y T Substituting into equation (1), we get: (twenty four), Substituting equation (24) into the failure function equation (3), we get: (25), definition This is the transverse tensile fracture angle. When... At that time, failure function Therefore, when the maximum value is reached, we have: (26), (27), Solving equation (27) yields: (28), or (29), Based on the magnitude of the transverse tensile fracture angle, composite materials can be classified into brittle materials and ductile materials. For brittle materials, substituting equation (28) into equation (26) yields: (30), For ductile materials, equation (29) holds. In the limiting case of ductile materials, i.e. when... and At that time, equation (29) still holds, therefore we have: (31), Solving equation (31) yields: (32)

[0043] Step 35: Based on the assumption of smoothness of the failure surface, obtain the first undetermined coefficient under normal tensile stress state. The first undetermined coefficient under normal compressive stress state The relevant equations; Specifically, for plastic materials, .like If the plastic material is brittle, then it can be approximated as a brittle material. Therefore, equation (32) applies to brittle materials. Since the failure envelope is in If the area at =0 is smooth, then: (33), Substituting equations (3) and (4) into equation (33), we get: (34).

[0044] Step 36: Solve the system of equations obtained in steps 31, 32, 33, 34 and 35 simultaneously, i.e., simultaneous equations (8), (12), (22), (30), (32) and (34), to solve for the undetermined coefficients. , , , B2 and C2 are used to obtain the matrix failure criteria.

[0045] Furthermore, the prediction equation for the transverse shear strength is: , Among them, S 23 This refers to the transverse shear strength.

[0046] Specifically, this embodiment proposes Y T Y C and S 23 The mathematical relationship between them will be explained in detail below.

[0047] Under transverse shear stress ( =S 23 The stress components on the inclined section can be given by equation (1): (35), At this point, the failure occurs On the inclined section with ≥0. Substituting equation (35) into equation (6) In the case where ≥0, the failure function F is obtained. t : (36), The failure function reaches its maximum value at the fracture angle, therefore: (37), (38), In the formula The transverse shear fracture angle is given. Equation (38) can be simplified to: (39), From equation (39), we can obtain: (40), or (41), When the material meets At that time, only normal stress exists on the fracture surface. ,and Therefore, the failure is entirely due to the normal stress. This leads to, and thus: (42), When the material meets At that time, the fracture angle is given by equation (41). Solving equations (37) and (41), we get: (43), We can solve this from equation (43): (44), Substituting B2 from equation (5) into equation (44) further, we get: (45)

[0048] The embodiments provided by the present invention have the following advantages: This invention eliminates empirical parameters in the Puck matrix failure equation, improving the objectivity of the model. The matrix failure criterion proposed in this invention is derived based on three-dimensional fracture surface theory, and all parameters involved are material strength values ​​that can be directly measured through standard mechanical tests. Compared with existing criteria such as Puck, it does not require the introduction of any empirical coefficients, fundamentally eliminating the subjectivity and uncertainty of parameter values.

[0049] Reduce reliance on testing and shorten R&D cycles. Since model parameters can be directly obtained through standard experiments, simulation prediction results are more reliable, effectively reducing the dependence on numerous destructive tests in engineering R&D, lowering material and labor costs, and accelerating product development iteration.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting failure of composite matrix without empirical parameters based on fracture surface theory, characterized in that, include: Construct a quadratic polynomial for the failure function of unidirectional composite materials containing undetermined coefficients; Based on the quadratic polynomial of the failure function, failure functions under tensile and compressive states are established according to the sign of the normal stress. Using basic strength parameters, and based on the assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface, the undetermined coefficients in the failure functions under tensile and compressive states are determined, thus obtaining the matrix failure criterion. The matrix failure criteria were verified through tensile tests, compression tests, and combined stress tests. Based on the matrix failure criterion, the transverse tensile strength and transverse compressive strength are used to predict the transverse shear strength; The construction of the quadratic polynomial containing the failure function with undetermined coefficients in the unidirectional composite material includes: The matrix failure of unidirectional composite materials depends on the stress on the fracture surface, and the failure function can be expressed as a quadratic polynomial of stress: ； Since the effects of positive and negative shear stress on material failure are the same, the quadratic polynomial of the stress function is simplified to obtain the simplified quadratic polynomial of the failure function: ， Where F is the failure function, and A1, A2, B1, B2, C1, C2, D1, D2, and D3 are the first, second, third, fourth, fifth, sixth, seventh, eighth, and ninth undetermined coefficients, respectively. , and These are the normal stress, transverse shear stress, and longitudinal shear stress acting on the fracture surface of the matrix, respectively. The expressions for the failure functions under tensile and compressive states are as follows: ， ， Among them, F t F is the failure function under tension. c The failure function under compression. This is the first undetermined coefficient under normal tensile stress state. This is the first undetermined coefficient under normal compressive stress state. This is the second undetermined coefficient under normal tensile stress state. This is the second undetermined coefficient under normal compressive stress state; The expression for the matrix failure criterion is as follows: ， Among them, Y T Y represents the transverse tensile strength. C For transverse compressive strength, S 21 This represents the longitudinal shear strength of a unidirectional composite plate.

2. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 1, characterized in that, The method employs basic strength parameters and, based on assumptions of macroscopic homogeneity, transverse isotropy, and smoothness of the failure surface, determines the undetermined coefficients in the failure functions under tensile and compressive states to obtain matrix failure criteria, including: Step 31: Based on the fact that only longitudinal shear stress exists on the inclined section under pure shear stress, determine the sixth undetermined coefficient. The expression; Step 32: Under the isobiaxial stress state, only normal compressive stress exists on any oblique section parallel to the fiber. Since normal compressive stress inhibits failure, Hashin's assumption... Determine the second undetermined coefficient under normal compressive stress state. , =0, where, It is equal biaxial transverse compressive strength; Step 33: Under the transverse compressive stress state, obtain the first undetermined coefficients under the normal compressive stress state based on relevant assumptions and equations. The relevant equations; Step 34: Under the transverse tensile stress state, obtain the first undetermined coefficients under the normal tensile stress state based on relevant assumptions and equations. The second undetermined coefficient under normal tensile stress state The related equations for the fourth undetermined coefficient B2; Step 35: Based on the assumption of smoothness of the failure surface, obtain the first undetermined coefficient under normal tensile stress state. The first undetermined coefficient under normal compressive stress state The relevant equations; Step 36: Solve the simultaneous equations obtained in steps 31, 32, 33, 34, and 35 to find the undetermined coefficients. , , , B2 and C2 are used to obtain the matrix failure criteria.

3. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 2, characterized in that, The sixth undetermined coefficient The expression: 。 4. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 3, characterized in that, The first undetermined coefficient under the normal compressive stress state The relevant equations are: 。 5. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 4, characterized in that, The first undetermined coefficient under the normal tensile stress state The second undetermined coefficient under normal tensile stress state The relevant equation for the fourth undetermined coefficient B2 is: ， 。 6. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 2, characterized in that, The first undetermined coefficient under the normal tensile stress state The first undetermined coefficient under normal compressive stress state The relevant equations are: 。 7. The method for predicting failure of composite material matrices without empirical parameters based on fracture surface theory according to claim 1, characterized in that, The prediction equation for the transverse shear strength is: ， Among them, S 23 This refers to the transverse shear strength.

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