A prediction method for mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates
By designing and manufacturing carbon fiber reinforced composite laminate samples and establishing a finite element model, the Type II fracture toughness at any interface angle is solved, and an efficient prediction method is achieved.
Patent Information
- Application Number
- CN202211077732.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-05
- Publication Date
- 2025-08-19
- Estimated Expiration
- 2042-09-05
AI Technical Summary
The prior art is difficult to exhaustively determine the fracture toughness of the type II layer at any interface of the composite layer plate through experimental means, resulting in high test costs and resource-consuming and lack of effective prediction models.
The carbon fiber reinforced composite layered panel samples with typical interfaces were designed and manufactured, and the end notch bending device was used for testing, a finite element model was established, and the user's subprogram was written. The crack tip stress field was analyzed through ABAQUS software, and a theoretical model with the interface angle as the independent variable was established to predict the type II fracture toughness at any interface angle.
It significantly shortens the test cycle, reduces the test cost, and shows that the predicted results are consistent with the test results through verification, and is suitable for engineering applications.
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Figure CN115410669B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of prediction of mode II interlaminar fracture toughness of fiber reinforced composite materials, and in particular to a method for predicting the delamination fracture toughness of carbon fiber reinforced composite laminates at arbitrary interface angles. Background Art
[0002] Composite materials are renowned for their high specific modulus and specific strength, making them useful in many engineering applications where both weight and quality are crucial. The aerospace industry is increasingly using composite components to meet its lighter weight requirements and reduce fuel consumption. Carbon fiber composites offer superior vibration resistance, fatigue resistance, and design flexibility. One indicator of the advancement of modern aircraft is the proportion of composite materials used. my country's large passenger aircraft, the C919, uses approximately 12% composite materials. Compared to advanced foreign aircraft, which use over half, composite research in my country needs further strengthening. Another important area of composite application in aviation is aircraft engine fan blades. Compared to metal fan blades, blades made of composite materials offer numerous advantages. Blades made from composite materials have a higher damage tolerance. Traditional metal or alloy blades typically develop cracks of various shapes at the root over time. Further crack propagation can significantly compromise blade safety. Through specific layup and structural design, composite blades are less likely to propagate even when notched. The demand for high-performance aircraft structures is growing, and research on the fracture and damage behavior of composite materials supports this development goal.
[0003] Components made of composite materials are generally laminate structures. Taking advantage of the designability of composite structures, it is generally necessary to optimize the layup angle. Composite laminates are made by laying unidirectional fiber layers in a designed order and angle, and then undergoing a series of bonding and curing processes. Composite laminates have obvious advantages over single-layer composite materials. This is mainly manifested in two aspects. The first is that the stable value of the fracture toughness of the laminate is much higher than that of the unidirectional plate; the second is that a reasonable layup design can significantly improve the laminate's ability to resist delamination and expansion. Therefore, composite laminate structures are used in most practical applications.
[0004] Sensitivity to delamination is a major design issue for many advanced multilayer composite structures. Delamination limits the toughness and ductility of multiphase composites, significantly impacting their stiffness and strength. Delamination often leads to irreversible catastrophic failure without prior evidence, prompting extensive research in both academia and industry on composite interface failure. Among the most common delamination propagation behaviors, Type III accounts for the lowest proportion, with research primarily focused on Types I, II, and I / II composites. Studying the static delamination propagation behavior of Type II provides important theoretical insights for material selection, layup design, and structural optimization in composite laminates subjected to relevant loading regimes. Accurately determining Mode II fracture toughness is crucial for the design of composite structures. While various testing methods have been established, such as end-notched bending (ENF), end-loaded splitting (ELS), and four-point ENF (4ENF) testing, research on Type II delamination remains limited, primarily focusing on unidirectional laminates. Furthermore, multidirectional laminates, while more widely used in practical engineering, are less studied than unidirectional laminates. Most researchers have analyzed the mode II delamination propagation behavior of multidirectional laminates from a qualitative perspective without quantitatively considering the relationship between mode II fracture toughness and interface angle.
[0005] Extensive experimental research has demonstrated that interface angle significantly influences the fracture toughness of composite laminates. Delamination can occur at any interface, and experimentally determining the fracture toughness of composite materials at all interfaces would be prohibitively expensive and impossible to exhaustively explore. By measuring the delamination fracture toughness at a limited number of specific interface angles, it would be ideal to develop a theoretical model that can predict the interlaminar fracture toughness at other interface angles. Therefore, it is necessary to develop a predictive model for type II interlaminar fracture toughness that is readily applicable in engineering applications. Summary of the Invention
[0006] The technical problem addressed by this invention is to provide a method for predicting the Mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates. The proposed theoretical formula for the Mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates, using the interface angle as the independent variable, can be used to predict the Mode II fracture toughness of carbon fiber reinforced composite laminates at any other interface angle, using the fracture toughness test results of carbon fiber reinforced composite laminates with two typical interfaces. This significantly shortens the testing cycle and reduces testing costs.
[0007] The present invention solves the above technical problems by adopting a technical solution: a method for predicting the mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates, comprising the following steps:
[0008] Step 1, designing and manufacturing carbon fiber reinforced composite laminate specimens with delamination interfaces of 0° / 0°, 22.5° / -22.5°, 45° / -45°, 90° / 90°, 0° / 45°, and 0° / 90°;
[0009] Step 2: Conducting a Mode II delamination test on the composite laminate specimen using an end notch bending (ENF) apparatus, and using beam theory to process the recorded load, displacement, and delamination length data to obtain a test value of Mode II interlaminar fracture toughness.
[0010] Step 3: A three-dimensional finite element model of the ENF test was established using ABAQUS software. Singular elements were used at the crack tip to accurately capture the stress field at the crack tip. A user-defined subroutine was written to define the material failure criterion and obtain the crack tip damage zone for specimens with different interface angles. Based on the damage zone size and crack tip stress field analysis, a theoretical model for the mode II fracture toughness of composite laminates was proposed.
[0011] Step 4: The fracture toughness G of the 0° / 0° interface specimen obtained from the test is IIC Fracture toughness G of (0°, 0°) and 0° / 90° interface specimens IIC Substitute (0°, 90°) into the theoretical model and calculate the model parameters B1 and B2;
[0012] In step 5, the obtained B1 and B2 data and the theoretical model of mode II fracture toughness of composite laminates in step 3 are used to predict the mode II fracture toughness of any other θ1 / θ2 interface specimens. The validity of the theoretical model is verified by comparing the predicted values with the test results.
[0013] Furthermore, the carbon fiber reinforced composite laminate can be made of different material systems, such as unidirectional tape prepregs combined with different resins such as T300, T700, T800, and T1000;
[0014] Furthermore, the specific calculation formula for the mode II interlaminar fracture toughness in step 2 is:
[0015]
[0016] Where P and δ are the load and displacement applied to the specimen, a and B are the effective delamination length and width of the specimen, and L is the span;
[0017] Furthermore, in step 3, the modified maximum stress failure criterion is used to evaluate the damage zone at the crack tip; according to the modified maximum stress failure criterion, considering the transverse isotropy of the composite laminate, the matrix cracking is determined by the maximum principal stress following the Mohr circle theory, and the maximum principal stress and matrix cracking angle Respectively expressed as:
[0018]
[0019]
[0020] Among them, σ 22 , σ 23 , σ 33 is the stress component in the principal axis coordinate system in the transverse plane of a single layer. According to the modified maximum stress failure criterion, when the maximum principal stress exceeds the in-plane shear strength of the unidirectional laminate, the matrix in the adjacent laminate cracks, and the matrix crack angle is perpendicular to the direction of the maximum principal stress. To assess the damage depth of the plies adjacent to the delamination interface during delamination, the numerical calculation step when the energy release rate is equal to the delamination fracture toughness is selected as the "reference moment". Therefore, the criterion for evaluating the damage of the plies adjacent to the delamination interface during delamination propagation can be expressed as:
[0021]
[0022] Where f is the failure index of intralayer damage, is the in-plane in-situ shear strength of the laminate; the modified maximum stress failure criterion is implemented in ABAQUS via the user subroutine UVARM, and the failure exponent f is defined as an element output quantity.
[0023] Furthermore, in step 3, the mode II delamination fracture toughness of a multidirectional laminate with any interface is divided into three parts: one part is the fracture work independent of the interface, the second part is the matrix damage related to the two adjacent plies at the interface, and the third part is the matrix damage caused by the interaction between the two plies. Under mode II loading, the in-plane stress perpendicular to the fiber direction will cause intralaminar damage and transverse cracking. This stress is a sinusoidal function related to the interface angle. Based on the analysis of the width of the damage zone and the stress field at the crack tip, a theoretical model for the mode II fracture toughness of composite laminates is derived. The specific expression of the theoretical model is as follows:
[0024] G IIC (θ1,θ2)=G0+B1(sin|θ1|+sin|θ2|)+B2sin(2|θ1+θ2|)
[0025] Among them, G IIC (θ1,θ2) represents the mode II fracture toughness of any specimen with θ1 / θ2 interface, and the value of G0 is equal to the fracture toughness G of the specimen with 0° / 0° interface. IIC (0°, 0°), with B1 and B2 being model parameters. This model provides an analytical formula for the Mode II delamination fracture toughness at any delamination interface angle. This formula uses the angle of the plies adjacent to the delamination interface as the independent variable and fully reflects the delamination interface angle dependence of the Mode II fracture toughness.
[0026] The advantages of the present invention compared with the prior art are:
[0027] (1) The present invention addresses the problem that existing research cannot predict the mode II fracture toughness of carbon fiber reinforced composite laminates at any interface, and proposes a prediction method that is convenient for engineering application.
[0028] (2) The present invention can predict the mode I fracture toughness of carbon fiber reinforced composite laminates at any interface angle by testing the delamination fracture toughness of the laminates at typical interface angles, thereby significantly reducing the workload of the test and lowering the test cost.
[0029] (3) The prediction results of the present invention have been verified by experiments, and the predicted values are well consistent with the experimental measured values, indicating that the prediction method of the present invention has good applicability. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 It is an implementation flow chart of the present invention;
[0031] Figure 2 is a schematic diagram of the ENF specimen configuration and geometric dimensions (unit: mm);
[0032] Figure 3 It is the schematic diagram and actual picture of ENF specimen loading;
[0033] Figure 4 It is the finite element model of the ENF specimen and the crack tip mesh;
[0034] Figure 5 It is an analysis of matrix cracking within a layer based on stress state;
[0035] Figure 6 It is the state of the damage zone in the crack tip layer of samples with different interfaces. DETAILED DESCRIPTION
[0036] The present invention will be further described in detail below with reference to the embodiments.
[0037] The present invention provides a method for predicting the mode II interlaminar fracture toughness of a carbon fiber reinforced composite laminate, and the specific implementation steps are as follows:
[0038] Step 1: Design and manufacture carbon fiber reinforced composite laminate specimens with 0° / 0°, 22.5° / -22.5°, 45° / -45°, 90° / 90°, 0° / 45°, and 0° / 90° delamination interfaces according to ASTM standard D7905 / D7905M-14. All interface specimens are Figure 2The same configuration and geometric dimensions as shown. Carbon fiber reinforced composite laminates can be made from unidirectional carbon fiber / resin prepregs such as T300, T700, T800, and T1000. For example, using T800 / X850 carbon fiber epoxy composite prepreg as an example, a prefabricated crack is created by placing a polytetrafluoroethylene (PTFE) film or equivalent film on the mid-surface of one end of the specimen. The film must be flat and less than 0.015 mm thick.
[0039] Step 2: Conduct Type II static delamination extension test, Figure 3 Schematic diagram of the test setup. The contact surfaces between the loading head and support and the specimen should be cylindrical. The loading head and support radii should be 5.0 ± 0.1 mm, the span 2L between the supports should be 100 mm, and the effective crack length a should be 25 mm. The loading mode should be displacement-controlled, with a low loading rate (1-2 mm / min) to ensure slow and steady delamination growth. The applied load, displacement, and delamination growth length should be recorded in real time during the test. The number of valid specimens for each delamination interface should not be less than three.
[0040] The step 2 uses a beam theory-based method to calculate the mode II delamination fracture toughness G IIC , the specific calculation formula is:
[0041]
[0042] Where P and δ are the load and displacement applied to the specimen, a and B are the effective delamination length and width of the specimen, and L is the span. The measured mode II fracture toughness results of six different interface specimens are listed in Table 1.
[0043] Table 1 Comparison between experimental and predicted values of type II delamination fracture toughness
[0044]
[0045] Step 3: Use ABAQUS software to establish Figure 4 The three-dimensional finite element model of the ENF specimen is shown, in which singular elements are used at the crack tip to accurately capture the crack tip stress field; a user-defined subroutine is written to define the material failure criterion and obtain the crack tip damage area of specimens with different interfaces.
[0046] The step 3 uses the modified maximum stress failure criterion to evaluate the damaged area at the crack tip; according to the modified maximum stress failure criterion, considering the transverse isotropy of the composite laminate, the matrix cracking is determined by the maximum principal stress following the Mohr circle theory, and the maximum principal stress and matrix cracking angle Respectively expressed as:
[0047]
[0048]
[0049] Among them, σ 22 , σ 23 , σ 33 is the stress component in the principal axis coordinate system in the transverse plane of a single layer; according to the modified maximum stress failure criterion, when the maximum principal stress exceeds the in-plane shear strength of the unidirectional laminate, the matrix in the adjacent laminate will crack, and the matrix crack angle is perpendicular to the maximum principal stress direction, such as Figure 5 As shown in the figure, in order to evaluate the damage depth of the plies near the delamination interface during delamination, the numerical calculation step when the energy release rate is equal to the delamination fracture toughness is selected as the "reference moment". Therefore, the criterion for evaluating the damage of the plies near the delamination interface during the delamination extension process can be expressed as:
[0050]
[0051] Where f is the failure index of intralayer damage, is the in-plane in-situ shear strength of the laminate; the modified maximum stress failure criterion is implemented in ABAQUS through the user subroutine UVARM, and the failure index f is defined as the unit output; the calculated state of the damage zone in the crack tip layer is as follows Figure 6 shown.
[0052] During the type II delamination expansion process of a multi-directional laminate, the expansion path around the delamination interface is not straight. The crack does not expand on the interface between the two plies, but expands within the two plies near the interface. Therefore, the measured fracture toughness must take into account the angle of the ply where the crack expands, and the differences caused by the symmetry and asymmetry of the two plies adjacent to the interface. Step 3 divides the type II delamination fracture toughness of a multi-directional laminate with any interface into three parts: one part is the fracture work independent of the interface, the second part is the matrix damage related to the two adjacent plies at the interface, and the third part is the matrix damage caused by the interaction between the two plies; under type II load, the in-plane stress perpendicular to the fiber direction will cause intra-layer damage and transverse cracking. This stress is a sine function related to the interface angle; based on the analysis of the width of the damage zone and the stress field at the crack tip, a theoretical model for the type II fracture toughness of composite laminates is proposed. The specific expression of the theoretical model is as follows:
[0053] G IIC (θ1,θ2)=G0+B1(sin|θ1|+sin|θ2|)+B2sin(2|θ1+θ2|)
[0054] Among them, G IIC (θ1,θ2) represents the mode II fracture toughness of any specimen with θ1 / θ2 interface, and the value of G0 is equal to the fracture toughness G of the specimen with 0° / 0° interface. IIC(0°, 0°), B1 and B2 are model parameters; this model is an analytical formula for the mode II delamination fracture toughness under any delamination interface angle of the laminate. This formula uses the angle of the plies adjacent to the delamination interface as the independent variable and can fully reflect the delamination interface angle dependence of the mode II fracture toughness;
[0055] Step 4: The fracture toughness G of the 0° / 0° interface specimen obtained from the test IIC Fracture toughness G of (0°, 0°) and 0° / 90° interface specimens IIC Substituting (0°, 90°) into the theoretical model proposed in step 3, the values of model parameters B1 and B2 are determined to be 543.97 J / m 2 and 1504.94 J / m 2 ;
[0056] Step 5: Using the B1 and B2 data obtained in the previous step as basic parameters, the following fracture toughness prediction formula with the delamination interface angle as the independent variable was used to predict the mode II fracture toughness of the other interface specimens. The prediction results are listed in Table 1. The relative error between the predicted results and the experimental results is less than 7.5%, indicating good agreement. This validates the applicability of the proposed method for predicting the mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates.
[0057] Some parts of the present invention are well known to those skilled in the art and are not described in detail.
[0058] The above description is only part of the specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person familiar with the art within the technical scope disclosed in the present invention should be covered by the protection scope of the present invention.
Claims
1. A method for predicting the mode II interlaminar fracture toughness of carbon fiber reinforced composite laminates, characterized in that The following steps are involved: Step 1, designing and manufacturing carbon fiber reinforced composite laminate specimens with delamination interfaces of 0° / 0°, 22.5° / -22.5°, 45° / -45°, 90° / 90°, 0° / 45°, and 0° / 90°; The carbon fiber reinforced composite material laminate in step 1 is made of unidirectional tape prepreg combined with carbon fiber and resin; Step 2: Conducting a Mode II delamination test on the composite laminate specimen using an end notch bending (ENF) apparatus, and using beam theory to process the recorded load, displacement, and delamination length data to obtain a test value of Mode II interlaminar fracture toughness. The specific calculation formula for the mode II interlaminar fracture toughness in step 2 is: Where P and δ are the load and displacement applied to the specimen, a and B are the effective delamination length and width of the specimen, and L is the span; Step 3: A three-dimensional finite element model of the ENF test was established using ABAQUS software. Singular elements were used at the crack tip to accurately capture the stress field at the crack tip. A user-defined subroutine was written to define the material failure criterion and obtain the crack tip damage zone for specimens with different interface angles. Based on the damage zone size and the crack tip stress field analysis, a theoretical model for the mode II fracture toughness of composite laminates was proposed. The step 3 uses the modified maximum stress failure criterion to evaluate the damaged area at the crack tip; according to the modified maximum stress failure criterion, considering the transverse isotropy of the composite laminate, the matrix cracking is determined by the maximum principal stress following the Mohr circle theory, and the maximum principal stress and matrix cracking angle Respectively expressed as: Among them, σ 22 , σ 23 , σ 33 is the stress component in the principal axis coordinate system in the transverse plane of a single layer. According to the modified maximum stress failure criterion, when the maximum principal stress exceeds the in-plane shear strength of the unidirectional laminate, the matrix in the adjacent laminate cracks, and the matrix crack angle is perpendicular to the direction of the maximum principal stress. To assess the damage depth of the plies adjacent to the delamination interface during delamination, the numerical calculation step where the energy release rate is equal to the delamination fracture toughness is selected as the "reference moment". Therefore, the criterion for evaluating the damage of the plies adjacent to the delamination interface during delamination propagation can be expressed as: Where f is the failure index of intralayer damage, is the in-plane in-situ shear strength of the laminate; the modified maximum stress failure criterion is implemented in ABAQUS via the user subroutine UVARM, and the failure exponent f is defined as an element output quantity; In step 3, the mode II delamination fracture toughness of a multi-directional laminate with any interface is divided into three parts: one part is the fracture work independent of the interface, the second part is the matrix damage related to the two adjacent plies at the interface, and the third part is the matrix damage caused by the interaction between the two plies. Under mode II loading, the in-plane stress perpendicular to the fiber direction will cause intralaminar damage and transverse cracking. This stress is a sine function related to the interface angle. Based on the analysis of the width of the damage zone and the stress field at the crack tip, a theoretical model for the mode II fracture toughness of composite laminates is proposed. The specific expression of the theoretical model is as follows: G IIC (θ1,θ2)=G0+B1(sin|θ1|+sin|θ2|)+B2sin(2|θ1+θ2|) Among them, G IIC (θ1,θ2) represents the mode II fracture toughness of any specimen with θ1 / θ2 interface, and the value of G0 is equal to the fracture toughness G of the specimen with 0° / 0° interface. IIC (0°, 0°), B1 and B2 are model parameters; this model is an analytical formula for the mode II fracture toughness under any delamination interface angle of the laminate. This formula uses the angle of the plies adjacent to the delamination interface as the independent variable and can fully reflect the delamination interface angle dependence of the mode II fracture toughness; Step 4: The fracture toughness G of the 0° / 0° interface specimen obtained from the test is IIC Fracture toughness G of (0°, 0°) and 0° / 90° interface specimens IIC Substitute (0°, 90°) into the theoretical model and calculate the model parameters B1 and B2; In step 5, the obtained B1 and B2 data and the theoretical model of mode II fracture toughness of composite laminates in step 3 are used to predict the mode II fracture toughness of any other θ1 / θ2 interface specimens. The validity of the theoretical model is verified by comparing the predicted values with the test results.