A method for predicting failure of composite materials based on mohr theory
The composite material failure prediction method constructed based on Mohr's theory uses three basic strength values to predict the failure envelope and fracture surface angle of composite materials, solving the problems of relying on empirical parameters and complex calculations in existing technologies, and achieving high-precision failure prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA AIRPLANT STRENGTH RES INST
- Filing Date
- 2026-05-21
- Publication Date
- 2026-06-19
AI Technical Summary
Existing composite matrix failure criteria rely on empirical parameters, have inconsistent expressions, are only applicable to brittle composites, and are computationally complex, making it difficult to accurately predict the failure modes and fracture surface angles of semi-brittle materials.
A composite material failure prediction method based on Mohr theory is adopted. The matrix failure function is constructed using three basic strength values: transverse tensile strength, transverse compressive strength and longitudinal shear strength. The failure is determined by the stress components on the potential fracture surface according to Mohr theory. It is applicable to brittle and semi-brittle composite materials and predicts the failure envelope and fracture surface angle.
It achieves high-precision failure prediction without the need for additional empirical parameters, simplifies the calculation process, is applicable to a variety of composite materials, improves prediction accuracy, and reduces testing costs and complexity.
Smart Images
Figure CN122245568A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of composite material mechanical property prediction technology, specifically to a composite material failure prediction method based on Mohr theory, which is particularly suitable for matrix failure prediction of unidirectional fiber reinforced composite materials under combined transverse tensile, compressive and shear stresses. Background Technology
[0002] Fiber-reinforced resin matrix composites are widely used in aerospace, marine engineering, transportation and other fields due to their excellent properties of being lightweight and having high strength. In actual service, composite structures inevitably bear complex loads, and matrix failure (i.e., inter-fiber failure) is one of the most common failure modes of composite materials. Accurately predicting the initiation of matrix failure and the angle of the fracture surface is crucial for the safe design of composite structures.
[0003] Failure theory and strength prediction methods have always been a key focus and challenge in the field of composite material research, with the core issue being the construction of failure criteria. Currently, researchers have proposed dozens of composite material failure criteria, such as the Hashin criterion, the Puck criterion, and the LaRC05 criterion. However, these existing techniques still have the following shortcomings:
[0004] First, existing composite matrix failure criteria that predict failure modes and fracture surface angles rely on empirical parameters. For example, the LaRC05 criterion requires the fracture surface angle under pure transverse compression as input, but this parameter is difficult to determine accurately through experiments, and most materials lack such experimental data; the Puck criterion requires additional tilt angle parameters, which increases the difficulty of use.
[0005] Second, the existing expressions for composite matrix failure criteria that predict failure modes and fracture surface angles are not uniform. They are generally divided into two independent formulas for tensile failure and compressive failure, which increases the computational complexity and makes them inconvenient to apply.
[0006] Third, existing matrix failure criteria for composite materials are mainly applicable to brittle thermosetting composite materials, and their prediction accuracy is poor for semi-brittle thermoplastic composite materials, lacking a unified prediction framework.
[0007] Therefore, there is an urgent need for a matrix failure prediction method that is simple in form, has readily available parameters, a unified expression, and is applicable to both brittle and semi-brittle composite materials. Summary of the Invention
[0008] The purpose of this invention is to overcome the shortcomings of existing composite matrix failure criteria, which rely on empirical parameters, have inconsistent expressions, and are only applicable to brittle composite materials. This invention provides a composite material failure prediction method based on Mohr's theory. This method only requires three basic strength values: transverse tensile strength, transverse compressive strength, and longitudinal shear strength. It does not require additional empirical parameters and can accurately predict the failure envelope and fracture surface angle under the combined stress of transverse tension, compression, and shear. It is applicable to both brittle thermosetting composite materials and semi-brittle thermoplastic composite materials.
[0009] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting composite material failure based on Mohr's theory includes the following steps: To obtain the three basic strength values of composite materials: transverse tensile strength Lateral compressive strength and longitudinal shear strength ; Constructing the matrix failure function The matrix failure function is based on Mohr's theory, assuming that matrix failure is determined by stress components on its potential fracture surface, and that the potential fracture surface is parallel to the fiber direction; the expression for the matrix failure function is:
[0010] in, The normal stress on the potential fracture surface, This represents the shear stress along the fiber direction on the potential fracture surface. This refers to the shear stress perpendicular to the fiber direction on the potential fracture surface. , , , These are coefficients to be determined; The undetermined coefficients are determined using the three basic strength values, wherein: Using the assumption of transverse isometric biaxial loading, which assumes that the composite material has a finite strength under transverse biaxial tension and an infinite strength under transverse biaxial compression, the following is derived: =0; Determined by longitudinal shear loading ; The coefficients were determined by lateral compressive loading and lateral tensile loading. and and according to The ratio distinguishes between brittle and semi-brittle materials: when When the material is determined to be a semi-brittle material, The material was determined to be brittle. For a given stress state, at the potential fracture surface angle The range of values Internal calculation of the matrix failure function The value of , and determine what makes Angle at maximum value The angle of the fracture surface is given; if the maximum value is reached, the composite material is determined to have experienced matrix failure.
[0011] Furthermore, the stress components on the potential fracture surface Calculate using the following formula:
[0012] in, For the transverse normal stress of the composite material, For longitudinal normal stress in composite materials, This refers to the in-plane transverse shear stress of the composite material. For the in-plane longitudinal shear stress of the composite material, For out-of-plane longitudinal shear stress in composite materials, The angle of the potential fracture surface.
[0013] Furthermore, the coefficient and Determine using the following formula:
[0014] in, For transverse tensile strength, This refers to the lateral compressive strength.
[0015] Furthermore, the final expression of the failure function is:
[0016] in, Longitudinal shear strength, The normal stress on the potential fracture surface, This represents the shear stress along the fiber direction on the potential fracture surface. This represents the shear stress perpendicular to the fiber direction on the potential fracture surface.
[0017] Furthermore, the fracture surface angle has analytical expressions under lateral tension and lateral compression, respectively: When stretched laterally:
[0018] During lateral compression:
[0019] in, The transverse tensile fracture angle, This is the transverse compression fracture angle.
[0020] Furthermore, the method is applicable to matrix failure prediction of brittle thermosetting composites and semi-brittle thermoplastic composites.
[0021] Furthermore, when predicting the failure envelope under combined transverse tensile, compressive, and shear stresses, the method obtains the failure boundary by calculating the maximum value of the matrix failure function under different stress ratios.
[0022] Furthermore, the three basic strength values were determined through standard mechanical tests: transverse tensile strength. The transverse compressive strength was determined by a transverse tensile test. The longitudinal shear strength was determined by transverse compression test. Determined by ±45° off-axis tensile or V-notch beam shear tests.
[0023] Furthermore, the method also includes: outputting prediction results, the prediction results including whether matrix failure has occurred, the critical stress state at failure, and the predicted fracture surface angle. .
[0024] Compared with the prior art, the present invention has at least the following beneficial effects: 1. This invention requires only three basic strength values (transverse tensile strength, transverse compressive strength, and longitudinal shear strength), eliminating the need for transverse shear strength or empirical parameters, thus reducing testing costs and time.
[0025] 2. This invention uses a unified matrix failure function expression, which does not distinguish between tensile failure and compressive failure, making calculation simple.
[0026] 3. This invention is achieved through... The ratio automatically distinguishes between brittle and semi-brittle materials, and is applicable to both thermosetting (brittle) and thermoplastic (semi-brittle) composite materials.
[0027] 4. Compared with existing methods such as the Puck criterion, the method described in this invention provides better agreement with experimental data on the predicted failure envelope and fracture surface angle, with smaller errors. Attached Figure Description
[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in 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.
[0029] Figure 1 This is a schematic diagram of stress components on the potential fracture surface of the matrix in an embodiment of the present invention; Figure 2 This is a comparison chart of the failure envelope of AS4 / 55A material under transverse tensile / compressive and shear conditions predicted by the method criteria described in the embodiments of the present invention and the Puck criterion. Figure 3 This is a comparison chart of the fracture surface angle of IM7 / 8552 material under off-axis compression predicted by the method criteria described in the embodiments of the present invention and the Puck criterion; Figure 4 This is a comparison chart of the failure envelope of AS4 / PEEK material under transverse tensile / compression and shear forces predicted by the method criteria described in the embodiments of the present invention and the Puck criterion. Detailed Implementation
[0030] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0031] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention 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 the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0032] Example 1 This invention provides a method for predicting composite material failure based on Mohr's theory, specifically including the following steps: Step 1: Obtain the basic strength parameters of the composite material To obtain the three basic strength values of composite materials: transverse tensile strength Lateral compressive strength and longitudinal shear strength These parameters can be determined through standard mechanical tests. For example, transverse tensile strength. The transverse compressive strength was determined by a transverse tensile test. The longitudinal shear strength was determined by transverse compression test. Determined by ±45° off-axis tensile or V-notch beam shear tests.
[0033] Step 2: Constructing a matrix failure function based on Mohr's theory The embodiments of the present invention are based on Mohr's theory (Mohr proposed that the failure of isotropic materials depends on the stress on the failure surface), which assumes that the failure of the composite matrix is determined by the stress components on its potential fracture surface, and that the potential fracture surface is parallel to the fiber direction. Figure 1 A schematic diagram of stress components on the potential fracture surface of the matrix is shown. In the figure, Indicates the angle of the potential fracture surface; This represents the principal stress along the material axis; directions 1, 2, and 3 are the principal directions of the material axis, where 1 represents the direction parallel to the fiber direction, and 2 and 3 represent the two directions perpendicular to the fiber direction. These represent the normal stresses on planes perpendicular to the principal axes 1, 2, and 3 of the material, respectively. This represents the shear stress in a plane perpendicular to the principal axis 1 of the material. This represents the shear stress in a plane perpendicular to the principal axis 2 of the material. This represents the shear stress on a plane perpendicular to the principal axis 3 of the material, and satisfies... .
[0034] like Figure 1 As shown, let the angle between the normal of the potential fracture surface and the transverse direction of the material (axis 2 in the figure) be . The stress components on the potential fracture surface include: normal stress. Shear stress (perpendicular to the fracture surface) and parallel to the fiber direction Shear stress perpendicular to the fiber direction The relationship between these stress components and the principal axial stresses of the material is as follows: (1) In equation (1), For the transverse normal stress of the composite material, For longitudinal normal stress in composite materials, This refers to the in-plane transverse shear stress of the composite material. For the in-plane longitudinal shear stress of the composite material, For out-of-plane longitudinal shear stress in composite materials, The angle of the potential fracture surface.
[0035] Construct a matrix failure function of the following form: (2) In equation (2) For matrix failure function, This indicates that the matrix has failed.
[0036] The failure function is usually expanded into a power series of stress components and terminated at the second-order term. Since positive and negative shear have the same effect on failure, the first-order term of shear stress should be eliminated. At this time, the failure function expression is as follows: (3) Among them, in equation (3) The normal stress on the potential fracture surface, This represents the shear stress along the fiber direction on the potential fracture surface. This refers to the shear stress perpendicular to the fiber direction on the potential fracture surface. , , , These are coefficients to be determined.
[0037] According to equations (1) and (3), the matrix failure function is... It's about angles A periodic function with period . Therefore, it is only necessary to Finding the matrix failure function within the range The angle at which the maximum value is reached is the fracture surface angle. When the substrate fails, it is determined to be defective.
[0038] The failure function defined by equation (3) is sufficiently smooth. Within one cycle, the maximum value is the maximum value. Therefore, when fracture occurs under a certain stress state, the following condition is satisfied: (4) In equation (4), The angle of the fracture surface.
[0039] Step 3: Determine the undetermined coefficients The embodiments of the present invention use three basic strength values: transverse tensile strength. Lateral compressive strength and longitudinal shear strength The undetermined coefficients are uniquely determined without any empirical parameters. The process for determining the undetermined coefficients is as follows: Lateral biaxial loading: The embodiments of this invention make the following assumptions regarding transverse isoaxial loading of the matrix: It is assumed that the composite material has a finite strength under transverse biaxial tension and an infinite strength under transverse biaxial compression. Based on this assumption, transverse isoaxial loading to failure (i.e., According to equation (1), the stress components on the potential fracture surface of the matrix are as follows: (5) In equation (5), It represents the normal stress during transverse biaxial failure.
[0040] Substituting equation (5) into equation (3), we get: (6) when hour, This indicates that the matrix has infinite strength under biaxial tensile load, but this is clearly unreasonable. When, equation (6) must have two real roots: (7) This means that the transverse biaxial tensile strength is The transverse biaxial compressive strength is This contradicts the assumption. Therefore, we can deduce that: (8) As can be seen from equation (8), this assumption is consistent with the physical understanding of the transverse properties of composite materials: the material is difficult to break under biaxial compression.
[0041] Longitudinal shear loading: This invention's embodiments consider longitudinal pure shear loading to material failure. According to equation (1), the stress components on the potential fracture surface of the matrix are as follows: (9) Substituting equation (9) into equation (3), we get: (10) when hour, When the maximum value is reached, the material fails. (11) Using the above condition for the potential fracture surface angle to reach an extreme value, we can obtain: (12) Lateral compression loading: Consider lateral compressive loading to material failure ( According to equation (1), the stress components on the potential fracture surface of the matrix are as follows: (13) Let the failure function be defined. exist hour( (For transverse compression fracture angle), reaching a maximum value of 1. Substituting equation (13) into equation (3), we can obtain the following from the condition in equation (4): (14) (15) (16) The transverse compressive fracture angle of general composite materials °. Therefore, equation (15) can be simplified to: (17) Substituting equation (17) into equations (14) and (16), we get: (18) (19) From this, we can deduce that... and The relationship.
[0042] Lateral stretching loading: This invention considers transverse tensile loading to material failure. According to equation (1), the stress components on the potential fracture surface of the matrix are as follows: (20) Let the failure function be defined. exist ( When the transverse tensile fracture angle is 1, the maximum value is reached. Substituting equation (20) into equation (3), we can obtain the following from the condition in equation (4): (twenty one) (twenty two) (twenty three) From equation (22), we can obtain: (twenty four) or: (25) when Then, equation (21) can be simplified to: (26) Therefore, it can be deduced that: (27) Substituting equation (27) into equation (18), we get: (28) Substituting equations (27) and (28) into equation (23), we get: (29) Therefore, we can conclude that: (30) Substituting equations (26) and (28) into equation (19), it can be seen that the condition for taking the maximum value during transverse compression fracture is strictly satisfied.
[0043] when At that time, that is: (31) At this point, equation (21) can be simplified to: (32) Solving equations (18) and (32) simultaneously yields: (33) Substituting equation (33) into equation (23), we get: (34) Therefore, we can conclude that: (35) In particular, When equations (24) and (25) are satisfied simultaneously, the undetermined coefficients are... , Since they have the same value, they can be used to distinguish between semi-brittle and brittle materials. Therefore, according to The ratio of the materials is used to classify materials into two categories in this embodiment of the invention: when At that time, the material is considered a semi-brittle material. At that time, the material is considered a brittle material.
[0044] Substituting equation (33) into equation (19), the condition for taking the maximum value during transverse compression fracture is also strictly satisfied.
[0045] Through the above derivation, the final expression of the failure function is obtained, and the failure prediction criterion of the method described in the embodiments of the present invention is determined: (36) Among them, coefficient and Determined by the following formula: (37) Step 4: Failure Prediction For a given stress state The angle range of the inclined plane is Calculate the included angles according to formula (1) Stress components on the inclined surface Substitute into the failure function (36) to find the cause. Angle that achieves the maximum value If the maximum value is ≥1, then the composite material is determined to have experienced matrix failure, and This is the predicted fracture surface angle.
[0046] The embodiments of the present invention also provide analytical expressions for the fracture surface angles under transverse tension and transverse compression: (38) Specifically, in equation (38), when hour, .
[0047] The final prediction result output of the method described in this embodiment of the invention includes whether matrix failure has occurred, the critical stress state at the time of failure, and the predicted fracture surface angle. .
[0048] The following examples of different composite materials illustrate the effectiveness of the failure prediction method established in this invention for predicting matrix failure of brittle thermosetting composites and semi-brittle thermoplastic composites.
[0049] Example 2 This embodiment uses the AS4 / 55A carbon fiber / epoxy resin composite material disclosed in the literature as an example to illustrate the effectiveness of the failure prediction method established in this invention for brittle thermosetting composite materials.
[0050] Material parameters: The basic mechanical properties of the AS4 / 55A composite material are shown in the table below:
[0051] Material type determination: calculate =94.7 / 26.7≈3.55>3, therefore this material belongs to the brittle material branch, and adopts formula (37) The formula is used to calculate the coefficients.
[0052] Calculation of undetermined coefficients:
[0053]
[0054]
[0055] Failure envelope prediction: The method described in this invention predicts the failure envelope under combined transverse tensile, compressive, and shear stresses by calculating the matrix failure function under different stress ratios. The maximum value is used to obtain the failure boundary.
[0056] Specifically, for a series of different stress ratios ,exist Searching within the range makes equation (36) Take the angle with the maximum value, set the maximum value to 1, solve for the corresponding critical stress value, and thus obtain the point on the failure envelope.
[0057] like Figure 2As shown, the failure envelope of AS4 / 55A material predicted by the criteria of this invention agrees well with the experimental data reported in the literature, and its prediction accuracy is significantly better than that of the Puck criterion. Especially in the region of combined transverse compression and shear stress, the prediction results of the criteria of this invention are closer to the experimental values.
[0058] Example 3 This embodiment uses IM7 / 8552 carbon fiber / epoxy resin composite material as an example to verify the predictive ability of the method described in this embodiment of the invention for fracture surface angle.
[0059] Material parameters: The basic mechanical properties of the IM7 / 8552 composite material are as follows:
[0060] Material type determination: calculate =253.7 / 62.3 ≈ 4.07>3, therefore this material belongs to the brittle materials category.
[0061] Fracture surface angle prediction: For off-axis compressive loading, the principal stress state of the material varies with the off-axis angle. This invention embodiment calculates the failure function at its maximum value under different off-axis angles. The curve of the fracture surface angle changing with the off-axis angle was obtained.
[0062] like Figure 3 As shown, the fracture surface angle of IM7 / 8552 material under off-axis compression predicted by the criteria of this invention is in high agreement with the experimental data, maintaining good prediction accuracy throughout the entire off-axis angle range. In contrast, the Puck criterion shows significant deviation in the off-axis angle range of approximately 30° to 60°.
[0063] Example 4 This embodiment uses AS4 / PEEK carbon fiber / polyetheretherketone thermoplastic composite material as an example to verify the applicability of the present invention to semi-brittle thermoplastic composite materials.
[0064] Material parameters: The basic mechanical properties of AS4 / PEEK composite materials are as follows:
[0065] Material type determination: calculate =205.9 / 93 ≈ 2.21 The range is such that the material belongs to the semi-brittle material branch, and the formula (37) is used. The formula is used to calculate the coefficients.
[0066] Calculation of undetermined coefficients:
[0067]
[0068]
[0069] Failure envelope prediction: like Figure 4 As shown, the failure envelope of AS4 / PEEK material predicted by the criteria of this invention agrees well with the experimental data reported in the literature. It is worth noting that the Puck criterion has a large deviation in predicting semi-brittle thermoplastic composites, while the criteria of this invention successfully achieves high-precision prediction of semi-brittle materials by adaptively adjusting the coefficient calculation formula.
[0070] In summary, the method described in this invention can effectively predict the failure envelope and fracture surface angle of composite materials, and can achieve high-precision prediction for brittle and semi-brittle materials. The failure prediction method provided in this invention can be embedded in the user material subroutine of finite element software (such as ABAQUS, ANSYS, etc.) to realize progressive damage analysis of composite material structures under complex loads.
[0071] 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, various modifications and variations can be made to the embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for predicting composite material failure based on Mohr's theory, characterized in that, Includes the following steps: To obtain the three basic strength values of composite materials: transverse tensile strength Lateral compressive strength and longitudinal shear strength ; Constructing the matrix failure function The matrix failure function is based on Mohr's theory, assuming that matrix failure is determined by stress components on its potential fracture surface, and that the potential fracture surface is parallel to the fiber direction; the expression for the matrix failure function is: in, The normal stress on the potential fracture surface, This represents the shear stress along the fiber direction on the potential fracture surface. This refers to the shear stress perpendicular to the fiber direction on the potential fracture surface. , , , These are coefficients to be determined; The undetermined coefficients are determined using the three basic strength values, wherein: Using the assumption of transverse isometric biaxial loading, it is assumed that the composite material has a finite strength under transverse biaxial tension and an infinite strength under transverse biaxial compression. From this, the following is derived: =0; Determined by longitudinal shear loading ; The coefficients were determined by lateral compressive loading and lateral tensile loading. and and according to The ratio distinguishes between brittle and semi-brittle materials: when When the material is determined to be a semi-brittle material, The material was determined to be brittle. For a given stress state, at the potential fracture surface angle The range of values Internal calculation of the matrix failure function The value of , and determine what makes Angle at maximum value The angle of the fracture surface is denoted as 1; if the maximum value is ≥1, the composite material is determined to have experienced matrix failure.
2. The method according to claim 1, characterized in that, Stress components on the potential fracture surface Calculate using the following formula: in, For the transverse normal stress of the composite material, For longitudinal normal stress in composite materials, This refers to the in-plane transverse shear stress of the composite material. For the in-plane longitudinal shear stress of the composite material, For out-of-plane longitudinal shear stress in composite materials, The angle of the potential fracture surface.
3. The method according to claim 1, characterized in that, The coefficient and Determine using the following formula: in, For transverse tensile strength, This refers to the lateral compressive strength.
4. The method according to claim 3, characterized in that, The final expression of the failure function is: in, Longitudinal shear strength, The normal stress on the potential fracture surface, This represents the shear stress along the fiber direction on the potential fracture surface. This represents the shear stress perpendicular to the fiber direction on the potential fracture surface.
5. The method according to claim 1, characterized in that, The fracture surface angle has analytical expressions under lateral tension and lateral compression, respectively: When stretched laterally: During lateral compression: in, The transverse tensile fracture angle, This is the transverse compression fracture angle.
6. The method according to claim 1, characterized in that, The method is applicable to matrix failure prediction of brittle thermosetting composites and semi-brittle thermoplastic composites.
7. The method according to claim 1, characterized in that, When predicting the failure envelope under combined transverse tensile, compressive, and shear stresses, the method obtains the failure boundary by calculating the maximum value of the matrix failure function under different stress ratios.
8. The method according to claim 1, characterized in that, The three basic strength values were determined through standard mechanical tests: transverse tensile strength. The transverse compressive strength was determined by a transverse tensile test. The longitudinal shear strength was determined by transverse compression test. Determined by ±45° off-axis tensile or V-notch beam shear tests.
9. The method according to claim 1, characterized in that, The method further includes: outputting prediction results, which include whether matrix failure has occurred, the critical stress state at the time of failure, and the predicted fracture surface angle. .