An analytical method for calculating mode i initial fracture toughness considering fiber ply angle

Abstract

The application discloses a kind of I type initial fracture toughness analytical calculation method considering fiber layer angle, belong to composite material fracture mechanics technical field, including: carrying out DCB experiment;The data obtained by experiment is calculated I type interlaminar fracture toughness-crack length data, and is drawn into R curve;Observing the crack propagation path of sample in experiment, crack propagation mechanism model is established according to observation result;According to the crack propagation mechanism model obtained, the I type delamination initial fracture toughness analytical calculation method considering the influence of fiber layer angle is established;The initial fracture toughness of sample of different fiber layer angle is predicted.The application uses the above-mentioned I type initial fracture toughness analytical calculation method considering fiber layer angle, provides a new, based on the prediction tool of physical mechanism for the fracture analysis of composite material, so that in design stage can more accurately predict the fracture behavior of material under different layer configuration, to avoid the influence of experimental error.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of composite fracture mechanics, and particularly relates to an I-type initial fracture toughness analytical calculation method considering fiber layer angle. BACKGROUND

[0002] Carbon fiber reinforced resin matrix composite is widely used in aerospace and shipbuilding fields due to its high specific strength, high specific modulus, high temperature resistance, corrosion resistance and design freedom and other advantages. However, due to the fact that the interlaminar performance of the laminated plate structure is significantly weaker than the in-plane performance, delamination damage becomes one of the most common and dangerous failure modes. Among them, I-type delamination seriously threatens the structural integrity and service safety because it easily causes stiffness and strength loss, which makes the delamination initiation and propagation mechanism under complex conditions attract much attention. The ASTM D5528 international standard formulated by the American Society for Testing and Materials (ASTM) is the I-type static delamination experiment specification, which is originally designed for 0° interlaminar interface unidirectional laminated plate, but the method has been extended to the I-type delamination behavior characterization and fracture toughness determination of composite laminated plates with interface angle [0 n-1 / θ / / 0 n ]. In view of the universality of the multi-angle layer design application of the composite material and the significant influence of the interlaminar fiber angle on the delamination behavior, the static delamination experiment research on the multi-directional laminated plate has key significance to guarantee the structural safety and reliability.

[0003] Current research shows that the crack tip damage of the I-type delamination of the composite laminated plate is caused by two dominant mechanisms: one is the interlaminar matrix crack related to the fracture energy of the cured polymer matrix; the other is the fiber / matrix interface separation containing continuous and alternating fiber / matrix debonding, and the fiber / matrix interface strength is significantly weaker than the matrix cracking strength. It is worth noting that the delamination front jumping phenomenon caused by the alternating fiber / matrix interface debonding can form fiber bridging. The failure mechanism of the multi-directional laminated plate of the composite material is very complex, which is significantly affected by parameters such as thickness, interlaminar fiber angle, environmental factors and loading mode. Among them, the interlaminar fiber angle as a key influencing factor, its mechanical behavior is closely related to the relative orientation of the fiber layer adjacent to the delamination surface. In recent decades, a large number of researchers have carried out a large number of experimental researches on the delamination behavior of the multi-directional laminated plate, and the research focuses mainly on the influence of the delamination interface fiber layer angle on the delamination path and R curve. Among them, the initial fracture toughness, the steady-state fracture toughness and the evolution mechanism of the crack propagation behavior are all affected by the fiber layer angle. At present, the influence of the fiber layer angle on the delamination path morphology and energy dissipation mechanism has been widely recognized by researchers, but the research on the influence of the fiber layer angle on the initial fracture toughness G INI calculation has not reached a consensus. SUMMARY

[0004] The purpose of the present application is to provide a method for analyzing and calculating the initial mode I fracture toughness considering the fiber layer angle, which provides a new physical mechanism-based prediction tool for the fracture analysis of composite materials, so that the fracture behavior of the material under different layer configurations can be more accurately predicted at the design stage, thereby avoiding the influence of experimental errors.

[0005] To achieve the above-mentioned purpose, the present application provides a method for analyzing and calculating the initial mode I fracture toughness considering the fiber layer angle, comprising the following steps:

[0006] S1, designing and preparing a multi-directional layer angle DCB sample, and carrying out a DCB experiment;

[0007] S2, calculating the mode I interlaminar fracture toughness-crack length data of the DCB sample with different interlaminar layer angles obtained in S1, and drawing an R curve;

[0008] S3, observing the crack propagation path of the sample in S1 experiment, characterizing the fracture surface of the sample after failure by SEM, and establishing a crack propagation mechanism model according to the observation results;

[0009] S4, establishing a method for analyzing and calculating the initial mode I delamination fracture toughness considering the influence of the fiber layer angle according to the crack propagation mechanism model obtained in S3;

[0010] S5, predicting the initial fracture toughness of the sample with different fiber layer angles by the method for analyzing and calculating the initial mode I delamination fracture toughness considering the influence of the fiber layer angle, and verifying the accuracy of the method for analyzing and calculating the initial mode I delamination fracture toughness considering the influence of the fiber layer angle.

[0011] Preferably, in S1, the DCB sample layer design is: [0 12 / / θ / 0 13 ], wherein θ=0°, 30°, 45°, 60° and 90°, the symbol / / represents the position where the prefabricated crack is introduced in the preparation, a 13 μm thick polytetrafluoroethylene film is artificially laid as a pre-crack in the middle of the 12 layers / / 13 layers of the sample, the laminated plate is cut into 180 mm long, 25 mm wide, 4.8 mm thick, and the pre-set effective crack length a0=30 mm.

[0012] Preferably, in S1, when carrying out the DCB experiment, a double cantilever beam sample is used to carry out the mode I delamination experiment on a universal testing machine, the universal testing machine records the displacement-load data of the quasi-static delamination expansion in real time, and the corresponding crack propagation length is recorded by a digital camera system.

[0013] Preferably, in S2, the interlaminar fracture toughness is calculated by the modified beam theory method, and the formula is as follows:

[0014]

[0015] where P is the load, δ is the applied displacement, b is the specimen width, a is the delamination length, Δ is the correction factor for the crack tip delamination length, and its characteristic value is obtained by the least square method of the cubic root of the compliance C to the delamination length a, and the compliance C is the ratio of the loading point displacement and the applied load: δ / P.

[0016] Preferably, in S3, the crack propagation paths of the samples with different interlaminar fiber ply angles are observed during the static experiment, the differences between the 0 / / 0 and 0 / / θ samples are compared, the cross sections of the damaged samples are observed by SEM, the micro characteristics of the fractured matrix and bare fibers are analyzed, and a mechanism model for explaining the influence of different fiber ply angles on the crack propagation path is established based on the results, including a tangential crack propagation path model and an arc crack propagation path model.

[0017] Preferably, in S4, the initial fracture toughness G INI is determined according to the crack propagation mechanism model in S3.

[0018] G INI = G I-MC + G I-FD + G I-FB ;

[0019] where G INI represents the initial fracture toughness of crack propagation, G I-MC represents the fracture toughness of matrix cracking damage in the crack propagation formation process, G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, and G I-FB is obtained by fitting the experimental data, representing the fracture toughness of the alternating matrix / fiber separation-caused fiber bridging damage.

[0020] In the 0 / / 0 interface DCB sample, the delamination path does not deviate, and according to the complex damage types of the composite delamination, the initial fracture toughness of the 0 / / 0 sample is set as:

[0021]

[0022] where G I-MC-0 / / 0 represents the matrix cracking fracture toughness of the 0 / / 0 ply, G I-FD-0 / / 0 represents the continuous fiber / matrix separation fracture toughness of the 0 / / 0 ply, G I-FB-0 / / 0 represents the alternating fiber / matrix separation fracture toughness of the 0 / / 0 ply, and Δa -FD is taken as a reference value for defining the area of the matrix / fiber separation release fracture energy relative to the 0 / / 0 ply, and the value does not affect the calculation result.

[0023] The influence of 30 degrees, 45 degrees, 60 degrees and 90 degrees fiber orientation angles on the crack propagation path is considered, and initial fracture toughness prediction calculation formulae of 0 / / 30, 0 / / 45, 0 / / 60 and 0 / / 90 samples along the tangential and arc crack propagation paths are established.

[0024] Preferably, in S4, the initial fracture toughness prediction calculation formula along the tangential crack propagation path is:

[0025]

[0026] Wherein, is the included angle between the tangent and the x direction, G INI-0 / / θ-TAN is the initial fracture toughness calculated along the tangential crack propagation path, is a function related to θ, G I-FB-0 / / θ is the 0 / / θ layer alternating fiber / matrix separation fracture toughness;

[0027] The initial fracture toughness prediction calculation formula along the arc crack propagation path is:

[0028]

[0029] Wherein, G INI-0 / / θ-ARC is the initial fracture toughness calculated along the arc crack propagation path.

[0030] Preferably, in S5, by changing only the interlayer fiber layer angle of the DCB sample, the initial fracture toughness of the DCB sample with any other layer angle is derived from the initial fracture toughness of two groups of fiber layer angle samples, and the reliability of the method is verified by calculation based on the proposed tangential crack propagation path model and arc crack propagation path model and experimental results.

[0031] Preferably, the specific operation of S5 is: based on the tangential crack propagation path model and the arc crack propagation path model, the tangential path most easily expanding point is determined by fitting a curve based on the initial fracture toughness data, the initial fracture toughness of the sample with different fiber layer angles is predicted, and the prediction result is compared with the experimental data to verify the accuracy and reliability of the method in predicting the initial fracture toughness of the sample with different fiber layer angles.

[0032] Therefore, the I-type initial fracture toughness analytical calculation method considering the fiber layer angle has the following beneficial effects:

[0033] (1) It provides a new, physical mechanism-based prediction tool for composite material fracture analysis, which can more accurately predict the fracture behavior of materials under different layer configurations at the design stage, thereby avoiding the influence of experimental errors.

[0034] (2) It deepens the understanding of the damage and fracture mechanism of composite materials, and provides an effective calculation tool for composite material design and manufacturing, which helps to improve the structural performance and reliability of materials. In addition, the normalization introduced provides a flexible and universal theoretical framework for composite material fracture analysis, supporting researchers to adjust the material layer design according to specific application requirements.

[0035] The technical solutions of the present application will be further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is the DCB sample and DCB experiment schematic diagram of the present application;

[0037] Figure 2 is the load-displacement curve of the DCB sample with different interlaminar fiber layer angles of the present application;

[0038] Figure 3 is the R curve of the DCB sample with different interlaminar fiber layer angles of the present application;

[0039] Figure 4 is the delamination propagation path of the static test sample of the DCB sample with different interlaminar fiber layer angles of the present application;

[0040] Figure 5 is the fracture surface morphology and crack propagation mechanism model of the different interlaminar fiber layer samples of the present application;

[0041] Figure 6 is the schematic diagram of the two typical delamination propagation paths affected by the fiber orientation angle of the present application;

[0042] Figure 7 is the cross-sectional schematic diagram of the crack propagation direction of the interface angle of the present application;

[0043] Figure 8 is the confirmation function graph of the tangential crack propagation path model to the tangential propagation angle of the present application. DETAILED DESCRIPTION

[0044] The technical solutions of the present application will be further described in detail below through the accompanying drawings and examples.

[0045] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meaning understood by those skilled in the art to which the present application belongs.

[0046] The application provides an analytical calculation method for mode I initial fracture toughness considering fiber ply angle, comprising the following steps:

[0047] S1, a multi-directional ply angle DCB sample is designed and prepared, wherein the ply design of the DCB sample is: [0 12 / / θ / 0 13 ], wherein θ = 0°, 30°, 45°, 60° and 90°, the symbol / / represents a position where a prefabricated crack is introduced in preparation, a 13 μm thick polytetrafluoroethylene film is artificially laid in the middle of the 12th layer and the 13th layer as a pre-crack during preparation, the laminated plate is cut into a length of 180 mm, a width of 25 mm, a thickness of 4.8 mm, and the pre-crack length a0 is 30 mm. The DCB experiment is carried out, and when the DCB experiment is carried out, the mode I delamination experiment is carried out on the universal testing machine by using the double cantilever beam sample, the displacement-load data of the quasi-static delamination expansion are recorded in real time by the universal testing machine, and the corresponding crack propagation length is recorded by a digital camera system.

[0048] S2, the data obtained in S1 are calculated to obtain the mode I interlaminar fracture toughness-crack length data of the DCB sample with different interlaminar ply angles, and are plotted into R curves, and the interlaminar fracture toughness is calculated by the modified beam theory method, and the formula is as follows:

[0049]

[0050] , wherein P is the load, δ is the applied displacement, b is the width of the sample, a is the delamination length, and Δ is the crack tip delamination length correction coefficient, the characteristic value of which is obtained by the least square method graph of the cube root of the compliance C with respect to the delamination length a, and the compliance C is the ratio of the loading point displacement and the applied load: δ / P.

[0051] S3, the crack propagation path of the sample in S1 experiment is observed, the cross section of the sample after failure is characterized by SEM, and a crack propagation mechanism model is established according to the observation results, and the specific operation is as follows: the crack propagation path of the sample with different interlaminar fiber ply angles during the static experiment is observed, the differences between the 0 / / 0 sample and the 0 / / θ sample are compared, the cross section of the sample after failure is observed by SEM, the micro characteristics of the fracture matrix and the exposed fiber are analyzed, and a mechanism model explaining the influence of different fiber ply angles on the crack propagation path is established based on the results, including a tangential crack propagation path model and an arc crack propagation path model.

[0052] S4, an analytical calculation method for mode I delamination initial fracture toughness considering the influence of fiber ply angle is established according to the crack propagation mechanism model obtained in S3, and the specific operation is as follows:

[0053] According to the crack propagation mechanism model of S3, the mode I delamination initial fracture toughness G INI is determined, which is composed of three different toughening mechanisms, that is:

[0054] G INI = G I-MC + G I-FD + G I-FB ;

[0055] where G INI represents the initial fracture toughness of crack propagation, G I-MC represents the fracture toughness of matrix cracking damage in the process of crack propagation, G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, G I-FB represents the fracture toughness of alternating matrix / fiber separation-fiber bridging damage, which is obtained by fitting experimental data.

[0056] In the 0 / / 0 interface DCB specimen, the delamination path does not deviate, according to the complex damage type of composite delamination, the initial fracture toughness of the 0 / / 0 specimen is set as:

[0057]

[0058] where G I-MC-0 / / 0 represents the matrix cracking fracture toughness of the 0 / / 0 layer, G I-FD-0 / / 0 represents the continuous fiber / matrix separation fracture toughness of the 0 / / 0 layer, G I-FB-0 / / 0 represents the alternating fiber / matrix separation fracture toughness of the 0 / / 0 layer, and Δa -FD is a reference value used to define the area of the relative 0 / / 0 layer when the matrix / fiber separation releases the fracture energy, and the value does not affect the calculation result.

[0059] Considering the influence of 30°, 45°, 60° and 90° fiber orientation angles on the crack propagation path, the initial fracture toughness prediction calculation formula of the 0 / / 30, 0 / / 45, 0 / / 60 and 0 / / 90 specimens along the tangential and arc crack propagation paths is established.

[0060] The initial fracture toughness prediction calculation formula along the tangential crack propagation path is:

[0061]

[0062] where, is the included angle between the tangent and the x direction, G INI-0 / / θ-TAN is the initial fracture toughness calculated along the tangential crack propagation path, is a function related to θ, G I-FB-0 / / θ is the alternating fiber / matrix separation fracture toughness of the 0 / / θ layer.

[0063] The initial fracture toughness prediction calculation formula along the arc crack propagation path is:

[0064]

[0065] wherein G INI-0 / / θ-ARC is the initial fracture toughness calculated along the arc crack propagation path.

[0066] S5, the initial fracture toughness of the sample with different fiber layer angle is predicted by the I-type delamination initial fracture toughness analytical method considering the influence of fiber layer angle, and the accuracy of the I-type delamination initial fracture toughness analytical method considering the influence of fiber layer angle is verified.

[0067] In the case of only changing the interlaminar fiber layer angle of the DCB sample, the initial fracture toughness of the DCB sample with any other layer angle is derived by the known initial fracture toughness of two groups of fiber layer angle samples, the reliability of the method is verified based on the proposed tangential crack propagation path model and the arc crack propagation path model, and the experimental results are calculated, and the specific operation is as follows: based on the tangential crack propagation path model and the arc crack propagation path model, the initial fracture toughness data is combined, the most easily expanded point of the tangential path is determined by fitting the curve, the initial fracture toughness of the sample with different fiber layer angle is predicted, and the prediction result is compared with the experimental data to verify, and the same operation is performed on the arc crack propagation path model, and the accuracy and reliability of the method in predicting the initial fracture toughness of the sample with different fiber layer angle are verified.

[0068] Embodiment 1

[0069] The application provides an I-type initial fracture toughness analytical calculation method considering the fiber layer angle, which comprises the following steps:

[0070] S1, a multi-directional layer angle DCB sample is designed and prepared, and a DCB experiment is carried out. The 24-layer T700 unidirectional carbon fiber / epoxy resin prepreg (EV201-35%-12KHF30F-U-200gsm-1000, Hengshen) CFRP laminated plate DCB sample is prepared by manual lamination and then using a hot press curing process, and the basic mechanical properties are as shown in Table 1. In order to deeply explore the expansion behavior of the I-type delamination of the composite material, five groups of DCB samples with different interlaminar layer directions are designed, and the DCB sample layer design is as follows: [0 12 / / θ / 0 13 ], wherein θ=0°, 30°, 45°, 60° and 90°, and the symbol / / represents the position where the prefabricated crack is introduced in preparation, and the specific layering mode is as shown in Figure 1 (c). In the sample 12 layer / / 13 layer, a 13μm thick polytetrafluoroethylene film is manually laid in the middle as a pre-crack. The laminated plate is cut into 180mm long, 25mm wide and 4.8mm thick, the pre-crack length a0 is 30mm, and the geometric size is as shown in Figure 1 (d).

[0071] Table 1 Mechanical properties of composite laminates

[0072] Module Value E 11 / GPa 117 E 22 / GPa 7.47 E 33 / GPa 7.47 G 12 / GPa 4.07 G 13 / GPa 4.07 G 23 / GPa 2.31 12 ]]> ​ 0.33 13 ]]> ​ 0.33 23 ]]> ​ 0.3

[0073] Note: E - Elastic modulus; G - Shear modulus; v - Poisson's ratio; 1 - fiber direction; 2 - matrix direction; 3 - thickness direction of the ply.

[0074] Type I delamination tests were performed on a WANCE TSE 254C universal testing machine using double cantilever beam (DCB) specimens based on ASTM D5528 standard. The test setup is shown in Fig. Figure 1 (a). The pre-cracks and specimen defects were inspected by non-destructive ultrasonic C-scan, and a specimen without any obvious defects was selected. A 20 mm hinge was bonded to the front end of the specimen, and both sides were sprayed with thin white paint to improve the visibility of the delamination surface, and a scale paper strip was attached to help monitor the crack propagation length as shown in Fig. Figure 1 (b). The specimen was fixed in the machine clamp through a pair of separable hinges, one end of the metal plate was bonded to the specimen by 3M adhesive, and the other plate was clamped on the equipment. During the test, the quasi-static delamination propagation was recorded by the displacement-load data of the testing machine in real time and the corresponding crack propagation length was recorded by a digital camera system (Charge Coupled Device camera, CCD camera). The loading mode was displacement control, and the quasi-static loading rate was set to 0.5 mm / min. All tests were carried out at room temperature and laboratory environmental conditions (20°C, 50% RH).

[0075] S2, the interlaminar fracture toughness was provided by the Modified Beam Theory (MBT) of DCB test standard ASTM D5528, the formula is as follows:

[0076]

[0077] Where P is the load, δ is the applied displacement, b is the specimen width, a is the delamination length, and Δ is the crack tip delamination length correction coefficient, whose characteristic value is obtained by least squares graph of compliance C versus effective delamination length a, and the compliance C is the ratio of loading point displacement and applied load: δ / P.

[0078] S3, the load-displacement curves of five groups of DCB specimens with different interlaminar fiber ply angles are shown in Fig. Figure 2(a), (b), (c), (d), (e) respectively represent the DCB specimens of θ = 0°, 30°, 45°, 60° and 90°, and it can be observed from the figure that the load-displacement curves of three specimens with the same interlaminar fiber angle in each group all show similar change trend with good consistency. In terms of initial damage load, after all the specimens reach the maximum load, the load-displacement curves decrease rapidly, which is caused by the fracture of the resin-rich zone at the initial crack tip.

[0079] After the rapid decrease of the load ends, the 0 / / 0 specimen decreases in a relatively slow and smooth trend; after the load-displacement curve of the 0 / / θ specimen enters the nonlinear stage, the load shows a slow growth trend and decreases slowly after reaching the peak value. Among them, the 0 / / 90 specimen is the most obvious, which is due to the fact that a large number of fiber bridges significantly improve the interfacial delamination resistance of 0 / / 90, proving that the fiber layup angle plays a key role in improving the delamination fracture resistance of composite materials.

[0080] Figure 3 (a), (b), (c), (d), (e) respectively show the R curve of the critical fracture toughness of the CFRP laminate with θ = 0°, 30°, 45°, 60° and 90°. It is found that the specimens with different fiber layup angles exhibit different structural fracture toughness characteristics. The initial fracture toughness and the steady-state interlaminar fracture toughness of the CFRP laminates with different interlaminar fiber layup angles are shown in Table 2.

[0081] Table 2 Interlaminar fracture toughness values of DCB specimens

[0082]

[0083] As can be seen from Table 2, the greater the interlaminar fiber layup angle θ, the greater the initial fracture toughness of the specimen. Among them, the G INI of the 0 / / 0 specimen is the smallest, about 30 J / m PROP , which indicates that the fiber bridging effect at the interface of the 0 / / 0 specimen is the least significant, and the R curve is flat. Unlike the 0 / / 0 specimen, the fracture toughness-crack propagation length curves of the 0 / / 30, 0 / / 45, 0 / / 60 and 0 / / 90 specimens all exhibit obvious R curve behavior. In the 0 / / 30 specimen, G 2 is about 190 J / m PROP higher than G INI . In the 0 / / 45 specimen, G 2 is about 310 J / m PROP higher than G INI . In the 0 / / 60 specimen, G 2 is about 300 J / m PROP higher than G INI .2 Approximately. In the 0 / / 90 sample, G PROP Average compared to G INI 380J / m 2 The phenomenon is due to the smooth propagation of cracks along the interface in the 0 / / 0 sample, resulting in a weak fiber bridging effect; while in the 0 / / θ sample, the increased θ leads to a more severe crack deflection, a more tortuous propagation path, and an increased energy dissipation path (such as matrix tearing and fiber breakage), thus increasing fiber bridging. This indicates that fiber bridging significantly improves interlaminar fracture toughness, and the fiber layup angle has a significant impact on the R-curve.

[0084] DCB specimens with different interlayer fiber layup angles exhibited different damage characteristics during static testing. The delamination propagation paths of the static test specimens are as follows: Figure 4 As shown. Experimental observations indicate that DCB specimens with different fiber layup angles exhibit varying delamination paths and bridging morphologies during crack propagation. For example... Figure 4 As shown in (a), for the 0 / / 0 specimen, the fiber orientation of adjacent layers is consistent, the stress concentration at the crack tip is low, and the propagation resistance mainly comes from matrix fracture. Its delamination propagation path extends along the interlaminar interface of the laminate, with a straight path and almost no deflection or bifurcation. In this case, the bridging fiber is aligned with the layup direction and crosses the open cantilever interface along the delamination propagation direction. For the 0 / / θ specimen, the bridging fiber connects the upper and lower cantilever in the width direction, and the fiber bridging area shows an increase in range with increasing interlaminar fiber angle.

[0085] like Figure 4 As shown in (b), the fiber angle at the delamination interface of the 0 / / 30 sample is small, and the crack tends to propagate along the interface, but may be slightly deflected or locally penetrate into adjacent layers; Figure 4 As shown in (c), the cracks in the 0 / / 45 sample tend to branch or extend along the fiber direction of adjacent layers (45° direction), forming a "serrated" or "wavy" path; Figure 4 As shown in (d) and (e), cracks in the 0 / / 60 and 0 / / 90 samples tend to deflect into adjacent layers, forming a tortuous propagation path (such as a "Z" shape). This requires overcoming more fiber breakage and matrix tearing, resulting in an irregular, tortuous morphology. Experimental phenomena indicate that fiber bridging has a significant impact on delamination propagation, and this impact is closely related to the fiber layup angle. Furthermore, the interlayer fiber layup angle also affects the path morphology of delamination propagation.

[0086] Figure 5 This demonstrates the influence of interlayer fiber angle on crack propagation path, where Figure 5DCB experiments of (a), (b), (c) in FIG. 1 are 0 / / 0, 0 / / 45 and 0 / / 90 interfaces, respectively. The fracture surfaces of the samples after failure were characterized by SEM and the crack propagation mechanism model was established according to the observation results. From the micro-morphology graph, it can be observed that the fracture surfaces of the samples after failure exist fractured matrix and exposed fibers formed after the separation of matrix / fiber, and compared with the 0 / / 0 sample, the 0 / / 45 and 0 / / 90 samples exist deep concave surfaces formed by crack propagation across the layers. As shown in the crack propagation mechanism model, with the change of the fiber layer angle, the 45° and 90° interlaminar fiber directions hinder the crack propagation path, causing the crack to expand tortuously in the thickness direction. Therefore, compared with the 0 / / 0 sample, the actual crack propagation area of the 0 / / 45 sample and the 0 / / 90 sample significantly increases under the unit crack propagation length.

[0087] Figure 5 It is illustrated that due to the angle between the fiber distribution direction of the 0 / / θ sample and the crack propagation direction, the crack front experiences continuous jumping under the fiber hindering, causing the crack propagation path to become more tortuous. This tortuous path means that the crack not only expands in the delamination expansion direction, but also produces back-and-forth displacement in the material thickness direction, forming a complex expansion trajectory, increasing the actual damage area of the sample when the crack propagation unit length Δa, and causing the initial fracture toughness to increase.

[0088] S4、Due to the heterogeneous structure and anisotropic characteristics of composite materials, the stress distribution around the crack tip in these materials is much more complex than in isotropic materials. The energy release rate (G) is defined as the rate of change of potential energy of the structure system with respect to the crack surface area. When G reaches its critical value G C , crack propagation will occur. The ASTM D5528 standard combines this concept with the characteristics of the DCB sample to analyze crack propagation, assuming that the crack in the DCB sample expands uniformly under constant displacement or load. When the delamination expands slightly (Δa), the strain energy release rate of the sample can be determined according to linear elastic fracture mechanics through the following expression:

[0089]

[0090] where b is the width of the DCB sample, and a is the effective delamination length of the DCB sample. The energy release rate of mode I delamination (G I ) is defined as the incremental rate of change of the total elastic energy (U) of the structure with respect to the crack propagation, which is usually expressed by the increment of crack length (da) in the case of DCB sample, because the width (b) of the sample is consistent. However, this method assumes that the crack expands along a linear path, ignoring the complexity caused by the change of interlaminar fiber orientation, which can cause the crack to deviate in the multidirectional laminate, causing changes in the crack propagation path.

[0091] To investigate the evolution mechanism of the path change and its effect on the initial fracture toughness G INI Based on the analysis and discussion of the calculation effect, a method to modify the calculation of the initial fracture toughness at the crack tip is proposed, which is based on the decoupling of the damage mechanism at the crack tip, G INI The fracture toughness is composed of three different toughening mechanisms:

[0092] G INI = G I-MC + G I-FD + G I-FB ;

[0093] In the formula, G INI represents the initial fracture toughness of crack propagation, G I-MC represents the fracture toughness of matrix cracking damage during crack propagation. G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, G I-FB represents the fracture toughness of alternating matrix / fiber separation-induced fiber bridging damage.

[0094] In the 0 / / 0 interface DCB specimen, the delamination path does not deviate. Therefore, according to the complex damage type of composite delamination, the initial fracture toughness G INI of the 0 / / 0 specimen is first set as:

[0095]

[0096] In the formula, G I-MC-0 / / 0 represents the matrix cracking fracture toughness of the 0 / / 0 layer, G I-FD-0 / / 0 represents the continuous fiber / matrix separation fracture toughness of the 0 / / 0 layer, G I-FB-0 / / 0 represents the alternating fiber / matrix separation fracture toughness of the 0 / / 0 layer. Because the crack propagation path mainly affects the damage path in front of the crack tip, it has little to do with fiber bridging, so G I-FB is not included in all subsequent formulas. Δa -FD is obtained by fitting experimental data, representing the fracture toughness released during the formation of fiber bridging. As a reference value, it is used to define the area of the expansion relative to the 0 / / 0 layer when the matrix / fiber separation releases fracture energy. The value does not affect the calculation result.

[0097] When the fiber layer direction is at a certain angle to the crack propagation direction, a multi-phase field of matrix and fiber mixed in the crack tip area will appear. Due to the huge difference in strength between the fiber and the matrix material, the high-strength fiber will guide the crack tip to change direction and develop in the form of matrix cracking or matrix / fiber separation that is easier to damage. Especially the matrix / fiber separation damage, because the fiber position is close to the crack tip, the delamination propagation path is greatly affected by the fiber orientation angle.

[0098] For example, with 0 / / 90 laminates, as shown in Figure 6 (a) and Figure 6 (b), the 90° oriented fibers appear as a right circular section of the fiber on the x-y section of the crack propagation. As the crack continues to propagate, it needs to cross this right circular section in both length and thickness directions. There are mainly two forms for the crack tip to cross the fiber: the first is the tangential crack propagation path as shown in Figure 6 (c), where the crack follows a tangent path to cross the fiber section. The second is the arc crack propagation path as shown in Figure 6 (d), where the crack follows an arc path to cross the fiber section.

[0099] For non-0° fiber orientation angles, when the crack propagates in the x direction by Da, it needs to propagate not only in the length x direction, but also in the thickness y direction. This indicates that the change of the fiber orientation angle will lead to the change of the actual fracture area needed for the crack to propagate in the x direction, and further lead to the change of the fracture toughness.

[0100] Taking 0 / / 0 and 0 / / 90 fiber orientation angles as examples, the tangential crack propagation path and the arc crack propagation path are calculated respectively, and the changes of these paths are quantified in the form of fracture area. If the 0 / / 90 matrix / fiber separation crack follows the tangential crack propagation path, the fracture toughness released by the delamination propagation is calculated as:

[0101]

[0102] If the 0 / / 90 matrix / fiber separation crack follows the arc crack propagation path, the fracture toughness released by the delamination propagation is calculated as:

[0103]

[0104] Then further consider the influence of three groups of different fiber orientation angles on the crack propagation path and orientation, and four typical fiber orientation angles of 30°, 45°, 60° and 90° intuitively show the different section shapes of the fibers with different orientation angles on the x-y plane of crack propagation. When the four typical fiber cracks with 30°, 45°, 60° and 90° orientation angles propagate in the x direction by a length, the corresponding distances need to be crossed in the thickness direction y, as shown in Figure 7 (a), (b), (c), (d).

[0105] From the figure, it can be observed that as the fiber orientation angle changes, the evolution trend of the crack propagation path also changes. Based on this mechanism, the initial fracture toughness prediction calculation formula for 0 / / 30, 0 / / 45 and 0 / / 60 samples is established:

[0106] The initial fracture toughness prediction calculation formula along the tangential crack propagation path is:

[0107]

[0108] where, is the angle between the tangent and the x direction, G INI-0 / / θ-TAN is the initial fracture toughness calculated along the tangential crack propagation path, is a function related to θ, G I-FB-0 / / θ is the 0 / / θ ply alternating fiber / matrix debonding fracture toughness.

[0109] The initial fracture toughness prediction formula along the arc crack propagation path is:

[0110]

[0111] where, INI-0 / / θ-ARC is the initial fracture toughness calculated along the arc crack propagation path.

[0112] S5, by changing only the interlaminar fiber ply angle of the DCB specimen, the initial fracture toughness of any other ply angle DCB specimen is derived from the initial fracture toughness of two sets of fiber ply angle specimens. Based on the proposed tangential and arc models, combined with the experimental results in the experiment, the reliability of this method is verified.

[0113] Tangential crack propagation path model:

[0114] For the tangential crack propagation path model, first, the curve fitting is performed according to the tangential path angle, and the point with the easiest tangential path is calculated, 0 / / 30, 0 / / 45, 0 / / 60 specimen tangential crack propagation path model confirmation function of tangential expansion angle respectively as Figure 8 (a), (b), (c) shown. Based on the tangential crack propagation path model and the initial fracture toughness data of 0 / / 0 230.3 J / m 2 and the initial fracture toughness data of 0 / / 90 ply angle specimen 265.7 J / m 2 , the initial fracture toughness of 0 / / 30, 0 / / 45 and 0 / / 60 ply specimens is predicted by using the tangential crack propagation path model, and the error analysis results compared with the experimental values are shown in Table 3.

[0115] Table 3 Correction of initial fracture toughness of I-type delamination

[0116] Lay-up sequence G INI (J / m 2 )experiment G INI (J / m 2 ) predicted Error (%) 0 / / 30 235.10 245.56 4.45％ 0 / / 45 247.10 255.24 3.29％ 0 / / 60 253.10 260.91 3.09％

[0117] Table 3 shows the comparison between the initial fracture toughness of 0 / / 30, 0 / / 45 and 0 / / 60 specimens obtained by theoretical prediction calculation and experimental measurement, which verifies the reliability and accuracy of this method in the evaluation of the initial fracture toughness of CFRP laminates.

[0118] Arc crack propagation path model:

[0119] Based on the tangential crack propagation path model, the initial fracture toughness of 0 / / 30, 0 / / 45 and 0 / / 60 specimens were predicted using the initial fracture toughness of 0 / / 0 specimen (230.3 J / m 2 ) and 0° / / 90° specimen (265.7 J / m 2 ). As shown in Table 4, the comparison results between the theoretical prediction and experimental measurement show that the prediction error is less than 10.0%, which verifies the reliability and accuracy of the method in the evaluation of the initial fracture toughness of CFRP laminates.

[0120] Table 4 Correction of initial fracture toughness of type I delamination

[0121]

[0122]

[0123] This method is not only applicable to the ply angle involved in the current study, but also can be extended to other interlaminar ply configurations. By introducing the concept of relative thickness of interlaminar multi-directional plies, the initial fracture toughness of DCB specimens with all interlaminar ply angles can also be calculated. The comparison with experimental data shows that the error is generally controlled within 10%. From the perspective of fracture mechanics, this further emphasizes the close relationship between crack propagation trend and fiber ply angle.

[0124] As shown by the above type I delamination propagation experiment, fiber bridging phenomenon exists in specimens with different ply configurations, and the greater the interlaminar ply angle θ, the more obvious the fiber bridging phenomenon. Compared with the smooth propagation of the crack along the interface of the 0 / / 0 specimen, the crack of the 0 / / θ specimen presents a cross-layer propagation characteristic, the tortuosity of the propagation path increases, and the energy dissipation path increases. The 0 / / θ specimen has a higher initial fracture toughness, which proves that the fiber ply angle has a significant impact on the initial fracture behavior of composites.

[0125] Microscopic section characterization shows that the crack propagation damage mode is mainly matrix cracking and matrix / fiber separation, and compared with the 0 / / 0 specimen, the 0 / / θ specimen has a deep concave interface formed by cross-layer crack propagation. The fibers of the 0 / / θ specimen are hindered by directional action, forcing the crack front to jump continuously in the thickness direction, forming an expansion trajectory with reciprocating displacement.

[0126] Combining experimental results and microscopic damage analysis, this method not only considers the diversity of crack propagation path and damage scale, but also effectively improves the prediction accuracy of the initial fracture performance of composite type I delamination.

[0127] Therefore, the application adopts the above-mentioned I-type initial fracture toughness analytical calculation method considering the fiber layer angle to provide a new, physical mechanism-based prediction tool for the fracture analysis of the composite material, so that the fracture behavior of the material under different layer configurations can be more accurately predicted at the design stage, thereby avoiding the influence of experimental errors.

[0128] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, but not to limit them. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for analytical calculation of mode I initial fracture toughness considering fiber ply angle, characterized by: The method comprises the following steps: S1, design and prepare a multi-directional layer angle DCB sample, and carry out a DCB experiment; S2, calculate the I-type interlaminar fracture toughness-crack length data of the DCB sample with different interlaminar layer angles according to the data obtained in the experiment in S1, and draw an R curve; S3, observe the crack propagation path of the sample in the experiment in S1, characterize the fracture surface of the sample after damage by SEM, and establish a crack propagation mechanism model according to the observation results; S4, establish an analytical calculation method of the I-type delamination initial fracture toughness considering the influence of the fiber layer angle according to the crack propagation mechanism model obtained in S3; In S4, the initial fracture toughness of I-type delamination is determined according to the crack propagation mechanism model of S3 The fracture toughness is composed of three different toughening mechanisms, namely: ； wherein, Gc,0represents the initial fracture toughness of crack propagation, Gc,1represents the fracture toughness of the matrix cracking damage during crack propagation, Gc,2represents the fracture toughness of the continuous matrix / fiber debonding damage, Gc,3represents the fracture toughness of the alternating matrix / fiber debonding- induced fiber bridging damage; In the 0 / / 0 interface DCB sample, the delamination path does not deviate, and according to the complex damage type of the composite material delamination, the initial fracture toughness of the 0 / / 0 sample is: ； wherein, represents the 0 / / 0 ply matrix cracking fracture toughness, represents the 0 / / 0 ply continuous fiber / matrix debonding fracture toughness, represents the 0 / / 0 ply alternating fiber / matrix debonding fracture toughness, as a reference value, used to define the area of the expansion relative to the 0 / / 0 ply when the matrix / fiber debonding release fracture energy is taken, the value does not affect the calculation result; Considering the influence of the fiber orientation angles of 30°, 45°, 60° and 90° on the crack propagation path, the initial fracture toughness prediction and calculation formula of the 0 / / 30, 0 / / 45, 0 / / 60 and 0 / / 90 samples along the tangential and arc crack propagation paths is established; In S4, the initial fracture toughness prediction and calculation formula along the tangential crack propagation path is: ； wherein is the angle of the tangent with the x-direction, is the initial fracture toughness calculated along the tangential crack propagation path, is the fracture toughness of the , related function, is 0 ply alternation fiber / matrix debonding fracture toughness; The initial fracture toughness prediction and calculation formula along the arc crack propagation path is: ； wherein, Kic is the initial fracture toughness calculated along the arcuate crack propagation path; S5, predict the initial fracture toughness of the samples with different fiber layer angles by the I-type delamination initial fracture toughness analytical method considering the influence of the fiber layer angle, and verify the accuracy of the I-type delamination initial fracture toughness analytical method considering the influence of the fiber layer angle.

2. The method for calculating mode I initial fracture toughness considering fiber ply angle according to claim 1, characterized in that: In S1, the DCB specimen layup was designed as: [0 12 / / / 0 13 ], wherein = 0°, 30°, 45°, 60° and 90°, the symbol / / indicates the position where a pre-made crack is introduced in the preparation, a 13 μm thick polytetrafluoroethylene film is laid artificially as a pre-crack in the middle of the 12th and 13th layers of the specimen, the laminated plate is cut into 180 mm long, 25 mm wide, 4.8 mm thick, and the pre-set effective crack length a0= 30 mm.

3. The method of claim 1, wherein the method is characterized by: In S1, when carrying out the DCB experiment, the I-type delamination experiment is carried out on a universal testing machine by using a double cantilever beam sample, the displacement-load data of the quasi-static delamination expansion are recorded in real time by the universal testing machine, and the corresponding crack propagation length is recorded by a digital camera system.

4. The method of claim 1, wherein the method is characterized by: In S2, the interlaminar fracture toughness is calculated by the modified beam theory method, and the formula is as follows: ； wherein, is the load, is the applied displacement, is the specimen width, is the delamination length, is the crack tip delamination length correction factor, whose eigenvalue is obtained by least square fitting the cubic root of the compliance to the delamination length , the compliance being the ratio of the loading point displacement and the applied load: .

5. The method of claim 1, wherein the method is characterized by: In S3, the crack propagation paths of the samples with different interlaminar fiber ply angles were observed during the static experiment, and 0 / / 0 and 0 / / 90 were compared The differences between the samples were observed by SEM, the microstructure of the fractured matrix and exposed fibers was analyzed, and a mechanism model was established to explain the influence of different fiber ply angles on the crack propagation path, including the tangential crack propagation path model and the arc crack propagation path model.

6. The method of claim 1, wherein the method is characterized by: In S5, in the case of only changing the interlaminar fiber layer angle of the DCB sample, the initial fracture toughness of the DCB sample with any other layer angle is derived by the initial fracture toughness of the two groups of fiber layer angle samples, the reliability of the method is verified based on the tangential crack propagation path model and the arc crack propagation path model and the experimental results.

7. The method for calculating the mode I initial fracture toughness considering the fiber ply angle according to claim 6, characterized in that: The specific operation of S5 is as follows: based on the tangential crack propagation path model and the arc crack propagation path model, the initial fracture toughness data are combined, the most easily expanded point of the tangential path is determined by fitting a curve, the initial fracture toughness of the samples with different fiber layer angles is predicted, and the prediction results are compared with the experimental data to verify the accuracy and reliability of the method in predicting the initial fracture toughness of the samples with different fiber layer angles.

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