Type I initial fracture toughness analytical calculation method considering fiber laying layer angle

Abstract

The invention discloses an I-type initial fracture toughness analytical calculation method considering a fiber layering angle, and belongs to the technical field of composite material fracture mechanics, and the I-type initial fracture toughness analytical calculation method comprises the following steps: carrying out a DCB experiment; calculating I-type interlayer fracture toughness-crack length data according to data obtained by the experiment, and drawing an R curve; observing a crack propagation path of the sample in the experiment, and establishing a crack propagation mechanism model according to an observation result; according to the obtained crack propagation mechanism model, establishing an I-type layering initial fracture toughness analytical calculation method considering the fiber layering angle influence; and predicting the initial fracture toughness of the samples with different fiber laying layer angles. According to the I-type initial fracture toughness analytical calculation method considering the fiber laying layer angle, a new prediction tool based on a physical mechanism is provided for fracture analysis of a composite material, so that fracture behaviors of the material under different laying layer configurations can be predicted more accurately in a design stage, and the analysis accuracy of the I-type initial fracture toughness is improved. Therefore, the influence of experimental errors is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of composite material fracture mechanics, and more particularly to an analytical calculation method for the mode I initial fracture toughness considering fiber ply angles. Background Art

[0002] Carbon fiber reinforced resin matrix composites are widely used in the fields of aerospace and shipbuilding due to their advantages such as high specific strength, high specific modulus, high temperature resistance, corrosion resistance, and high design freedom. However, due to the significant weakness of the interlaminar properties of the laminated structure compared to the in-plane properties, delamination damage has become one of the most common and dangerous failure modes. Among them, mode I delamination seriously threatens the structural integrity and service safety due to the easy initiation of stiffness and strength losses, which has attracted much attention to the research on the initiation and propagation mechanisms of delamination under complex working conditions. The ASTM D5528 international standard formulated by the American Society for Testing and Materials (ASTM) as the mode I static delamination test specification, although initially designed for unidirectional laminates with 0° interlaminar interfaces, this method has been extended to the characterization of mode I delamination behavior and the determination of fracture toughness for composite laminates with interface angles of [0 n-1 / θ / / 0 n . In view of the universality of the application of multi-angle ply designs of composite materials and the significant influence of the interlaminar fiber angle on the delamination behavior, the static delamination experimental research on multi-directional laminates is of crucial significance for ensuring the structural safety and reliability.

[0003] Current research shows that the crack tip damage in mode I delamination of composite laminates stems from 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 including continuous and alternating fiber / matrix debonding, and the fiber / matrix interface strength is significantly weaker than the matrix self-cracking strength. It should be noted that the delamination front jump phenomenon caused by alternating fiber / matrix interface debonding can form fiber bridging. The failure mechanism of composite multi-directional laminates is very complex and 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 adjacent fiber plies on the delamination plane. In the past few decades, a large number of researchers have carried out a large number of experimental studies on the delamination behavior of multi-directional laminates, and the research focus has mainly been on the influence of the fiber ply angle at the delamination interface on the delamination path and the R-curve. Among them, the initial fracture toughness, steady-state fracture toughness, and the evolution mechanism of crack propagation behavior are all affected by the fiber ply angle. At present, the influence of the fiber ply angle on the delamination path morphology and energy dissipation mechanism has been widely recognized by researchers, but there is no consensus on its influence on the calculation of the initial fracture toughness G INI at the crack tip. Summary of the Invention

[0004] The object of the present invention is to provide an analytical calculation method for the mode I initial fracture toughness considering the fiber ply angle, which provides a new prediction tool based on physical mechanisms for the fracture analysis of composite materials, enabling more accurate prediction of the fracture behavior of materials under different ply configurations at the design stage, thereby avoiding the influence of experimental errors.

[0005] To achieve the above object, the present invention provides an analytical calculation method for the mode I initial fracture toughness considering the fiber ply angle, comprising the following steps:

[0006] S1. Design and prepare a multi-directional ply angle DCB specimen and conduct a DCB experiment;

[0007] S2. Calculate the data obtained from the experiment in S1 to obtain the mode I interlaminar fracture toughness - crack length data of the DCB specimens with different interlaminar ply angles and plot an R curve;

[0008] S3. Observe the crack propagation path of the specimen in the S1 experiment, use SEM to characterize the cross-section of the specimen after failure and establish a crack propagation mechanism model based on the observation results;

[0009] S4. Establish an analytical calculation method for the mode I delamination initial fracture toughness considering the influence of the fiber ply angle based on the crack propagation mechanism model obtained in S3;

[0010] S5. Predict the initial fracture toughness of specimens with different fiber ply angles through the analytical method for the mode I delamination initial fracture toughness considering the influence of the fiber ply angle, and verify the accuracy of the analytical method for the mode I delamination initial fracture toughness considering the influence of the fiber ply angle.

[0011] Preferably, in S1, the ply design of the DCB specimen is: [0 12 / / θ / 0 13 , where θ = 0°, 30°, 45°, 60° and 90°, the symbol / / represents the position where a pre-crack is introduced during preparation, a 13-μm-thick polytetrafluoroethylene film is artificially laid between the 12th and 13th layers of the specimen as a pre-crack, the laminate is cut into a length of 180 mm, a width of 25 mm, and a thickness of 4.8 mm, and the effective pre-crack length a0 = 30 mm.

[0012] Preferably, in S1, when conducting the DCB experiment, a double-cantilever beam specimen is used for the mode I delamination experiment on a universal testing machine, and the universal testing machine records the displacement-load data of the quasi-static delamination propagation in real time and records the corresponding crack propagation length through 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] Among them, P is the load, δ is the applied displacement, b is the width of the specimen, a is the delamination length, and △ is the correction coefficient of the delamination length at the crack tip. Its characteristic value is obtained by performing a least-squares graph of the delamination length a with the cube root of the compliance C. The compliance C is the ratio of the displacement at the loading point to the applied load: δ / P.

[0016] Preferably, in S3, observe the crack propagation paths of specimens with different interlayer fiber lay-up angles during the static experiment, compare the differences between 0 / / 0 and 0 / / θ specimens, observe the cross-section of the specimens after failure using SEM, analyze the microscopic characteristics of the fractured matrix and exposed fibers, and establish a mechanism model based on the results to explain the influence of different fiber lay-up angles on the crack propagation path, including a tangential crack propagation path model and an arc crack propagation path model.

[0017] Preferably, in S4, based on the crack propagation mechanism model in S3, determine the mode I delamination initiation fracture toughness G INI Composed of the fracture toughnesses of three different toughening mechanisms, namely:

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

[0019] Among them, G INI represents the crack propagation initiation fracture toughness, G I-MC represents the fracture toughness of matrix cracking damage during the crack propagation formation process, G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, G I-FB Obtained by fitting according to the experimental data, representing the fracture toughness caused by alternating matrix / fiber separation - induced fiber bridging damage;

[0020] In the 0 / / 0 interface DCB specimen, the delamination path does not shift. According to the complex damage types of composite material delamination, assume the initial fracture toughness of the 0 / / 0 specimen is:

[0021]

[0022] Among them, G I-MC-0 / / 0 represents the matrix cracking fracture toughness of the 0 / / 0 lay-up, G I-FD-0 / / 0 represents the continuous fiber / matrix separation fracture toughness of the 0 / / 0 lay-up, G I-FB-0 / / 0 represents the alternating fiber / matrix separation fracture toughness of the 0 / / 0 lay-up, Δa -FD As a reference value, it is used to define the area expanded relative to the 0 / / 0 lay-up when the matrix / fiber separation releases fracture energy, and the value does not affect the calculation result;

[0023] Consider the influence of fiber orientation angles of 30°, 45°, 60° and 90° on the crack propagation path, and establish the prediction calculation formulas for the initial fracture toughness of 0 / / 30, 0 / / 45, 0 / / 60 and 0 / / 90 specimens along the tangential and arc crack propagation paths.

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

[0025]

[0026] Wherein, 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 alternating fiber / matrix separation fracture toughness of the 0 / / θ ply;

[0027] The prediction calculation formula for the initial fracture toughness 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, under the condition of only changing the interlayer fiber ply angle of the DCB specimen, the initial fracture toughness of the DCB specimen with any other ply angle is deduced through the initial fracture toughness of two groups of specimens with known fiber ply angles, and based on the proposed tangential crack propagation path model and the arc crack propagation path model, combined with the experimental results for calculation to verify the reliability of this method.

[0031] Preferably, the specific operation of S5 is: based on the tangential crack propagation path model and the arc crack propagation path model, combined with the initial fracture toughness data, determine the most easily expandable point of the tangential path by fitting a curve, predict the initial fracture toughness of specimens with different fiber ply angles, and compare the prediction results with the experimental data for verification. Similarly, the same operation is performed on the arc crack propagation path model to verify the accuracy and reliability of this method in predicting the initial fracture toughness of specimens with different fiber ply angles.

[0032] Therefore, the present invention adopts the above-mentioned type I initial fracture toughness analytical calculation method considering the fiber ply angle, and has the following beneficial effects:

[0033] (1) It provides a new physical - mechanism - based prediction tool for the fracture analysis of composite materials, enabling more accurate prediction of the fracture behavior of materials under different ply configurations at the design stage, thus avoiding the influence of experimental errors.

[0034] (2) It deepens the understanding of the damage and fracture mechanisms of composite materials and also provides an effective calculation tool for the design and manufacture of composite materials, helping to improve the structural performance and reliability of materials. In addition, the introduced normalization process provides a flexible and general theoretical framework for the fracture analysis of composite materials, supporting researchers to adjust the material ply design according to specific application requirements.

[0035] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0036] Figure 1 is a schematic diagram of the DCB specimen and DCB experiment of the present invention;

[0037] Figure 2 is the load - displacement curve of the DCB specimens with different inter - layer fiber ply angles of the present invention;

[0038] Figure 3 is the R - curve of the DCB specimens with different inter - layer fiber ply angles of the present invention;

[0039] Figure 4 is the delamination propagation path of the static test specimens of the DCB specimens with different inter - layer fiber ply angles of the present invention;

[0040] Figure 5 is the cross - sectional morphology diagram and crack propagation mechanism model of the specimens with different inter - layer fiber plies of the present invention;

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

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

[0043] Figure 8 is the confirmation function diagram of the tangential crack propagation path model for the tangential propagation angle of the present invention. Detailed Embodiments

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention pertains.

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

[0047] S1. Design and prepare a multi-directional ply angle DCB specimen. The ply design of the DCB specimen is: [0 12 / / θ / 0 13 , where θ = 0°, 30°, 45°, 60° and 90°. The symbol / / indicates the position where a prefabricated crack is introduced during preparation. A 13-μm-thick polytetrafluoroethylene film is manually laid between the 12th and 13th layers of the specimen as the pre-set crack. The laminate is cut into a length of 180 mm, a width of 25 mm, and a thickness of 4.8 mm, and the pre-set effective crack length a0 = 30 mm. Conduct a DCB experiment. When conducting the DCB experiment, a mode I delamination experiment is carried out on a universal testing machine using a double-cantilever beam specimen. The universal testing machine records the displacement-load data of the quasi-static delamination propagation in real time and records the corresponding crack propagation length through a digital camera system.

[0048] S2. Calculate the mode I interlaminar fracture toughness - crack length data of the DCB specimens with different interlaminar ply angles from the data obtained in the experiment in S1, and plot them into an R curve. Calculate the interlaminar fracture toughness by the modified beam theory method. The formula is as follows:

[0049]

[0050] where P is the load, δ is the applied displacement, b is the width of the specimen, a is the delamination length, △ is the correction coefficient of the delamination length at the crack tip, and its characteristic value is obtained by making a least-squares graph of the cube root of the compliance C against the delamination length a. The compliance C is the ratio of the displacement at the loading point to the applied load: δ / P.

[0051] S3. Observe the crack propagation path of the specimen in the experiment in S1. Characterize the cross-section of the specimen after failure by SEM and establish a crack propagation mechanism model according to the observation results. The specific operation is as follows: Observe the crack propagation path of the specimens with different interlaminar fiber ply angles during the static experiment, compare the differences between the 0 / / 0 and 0 / / θ specimens, observe the cross-section of the failed specimen by SEM, analyze the microscopic characteristics of the fractured matrix and the exposed fibers, and establish a mechanism model based on the results to explain the influence of different fiber ply angles on the crack propagation path, including a tangential crack propagation path model and an arc crack propagation path model.

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

[0053] Based on the crack propagation mechanism model in S3, determine the mode I delamination initial fracture toughness G INI Composed of the fracture toughness of three different toughening mechanisms, namely:

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

[0055] Among them, G INI represents the initial fracture toughness of crack propagation, G I-MC represents the fracture toughness of matrix cracking damage during the formation of crack propagation, G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, G I-FB is obtained by fitting experimental data and represents the fracture toughness of alternating matrix / fiber separation-induced fiber bridging damage;

[0056] In the 0 / / 0 interface DCB specimen, the delamination path does not shift. According to the complex damage types of composite material delamination, the initial fracture toughness of the 0 / / 0 specimen is set as:

[0057]

[0058] Among them, 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, Δa -FD As a reference value, it is used to define the area expanded relative to the 0 / / 0 ply when the matrix / fiber separation releases fracture energy, and the value taken does not affect the calculation result.

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

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

[0061]

[0062] Among them, 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 alternating fiber / matrix separation fracture toughness of the 0 / / θ ply.

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

[0064]

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

[0066] S5. Predict the initial fracture toughness of specimens with different fiber ply angles by using the analytical method for the initial fracture toughness of mode I delamination considering the influence of fiber ply angles, and verify the accuracy of the analytical method for the initial fracture toughness of mode I delamination considering the influence of fiber ply angles.

[0067] When only changing the interlayer fiber ply angle of the DCB specimen, based on the initial fracture toughness of two groups of specimens with known fiber ply angles, deduce the initial fracture toughness of DCB specimens with any other ply angle. Based on the proposed tangential crack propagation path model and arc crack propagation path model, combine with the experimental results for calculation to verify the reliability of this method. The specific operation is as follows: Based on the tangential crack propagation path model and arc crack propagation path model, combine with the initial fracture toughness data, determine the most easily expandable point of the tangential path by fitting the curve, predict the initial fracture toughness of specimens with different fiber ply angles, and compare the prediction results with the experimental data for verification. Similarly, perform the same operation on the arc crack propagation path model to verify the accuracy and reliability of this method in predicting the initial fracture toughness of specimens with different fiber ply angles.

[0068] Example 1

[0069] The present invention provides an analytical calculation method for the mode I initial fracture toughness considering the fiber ply angle, including the following steps:

[0070] S1. Design and prepare DCB specimens with multi-directional ply angles and conduct DCB experiments. Prepare DCB specimens of CFRP laminates made of 24 layers of T700 grade unidirectional carbon fiber / epoxy resin prepreg (EV201 - 35% - 12KHF30F - U - 200gsm - 1000, Hengshen) by manual layup and then using autoclave curing process. Its basic mechanical properties are shown in Table 1. In order to deeply explore the propagation behavior of mode I delamination of composites, design five groups of DCB specimens with different interlayer ply directions. The ply design of the DCB specimens is: [0 12 / / θ / 0 13 , where θ = 0°, 30°, 45°, 60° and 90°. The symbol / / indicates the position where a prefabricated crack is introduced during preparation. The specific ply method is as Figure 1 (c) shown. Manually lay a 13 - μm - thick polytetrafluoroethylene film between the 12th and 13th layers of the specimen as a pre - set crack. Cut the laminate into a length of 180 mm, a width of 25 mm, and a thickness of 4.8 mm. The effective pre - set crack length a0 = 30 mm. The geometric dimensions are as Figure 1 (d) shown.

[0071] Table 1 Mechanical property parameters of composite laminates

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

[0073] Note: E - Elastic modulus; G - Shear modulus; ν - Poisson's ratio; 1 - Fiber direction; 2 - Matrix direction; 3 - Thickness direction of the layer.

[0074] Based on the ASTM D5528 standard, the mode I delamination test was carried out on a WANCE TSE254C universal testing machine using a double - cantilever beam specimen. The test equipment is as Figure 1 (a) shown. The pre - cracked and specimen defects were inspected by non - destructive ultrasonic C - scanning. Specimens without any obvious defects were selected. A 20 - mm hinge was bonded to the front end of the specimen, and thin white paint was sprayed on both sides to improve the visibility of the delamination surface, and a scale paper tape was pasted to help monitor the crack propagation length as Figure 1 (b) shown. The specimen was fixed in the machine fixture through a pair of separable hinges. One end of the metal plate of the hinge 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 testing machine for displacement - load data 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 - controlled, and the quasi - static loading rate was set at 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 calculated using the Modified Beam Theory (MBT) provided by the DCB test standard ASTM D5528. The formula is as follows:

[0076]

[0077] In the formula, P is the load, δ is the applied displacement, b is the specimen width, a is the delamination length, Δ is the correction coefficient of the delamination length at the crack tip, and its characteristic value is obtained by making a least - squares plot of the compliance C against the effective delamination length a. The compliance C is the ratio of the displacement at the loading point to the applied load: δ / P.

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

[0079] The 0 / / 0 specimen decreases at a relatively slow and smooth trend after the rapid decrease of the load ends; for the 0 / / θ specimen, after the load-displacement curve enters the non-linear stage, the load shows a slow growth trend and then slowly decreases after reaching the peak. Among them, the phenomenon of the 0 / / 90 specimen is the most obvious. This is because a large number of fiber bridges significantly improve the interface delamination resistance of 0 / / 90, proving that the fiber ply angle plays a key role in improving the delamination fracture resistance of composites.

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

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

[0082]

[0083] As can be seen from Table 2, the larger the interlayer fiber ply angle θ of the specimen, the greater the initial fracture toughness. Among them, the difference between G INI and G PROP is relatively small, about 30 J / m 2 . This indicates that in the same material system, the fiber bridging effect at the interface of the 0 / / 0 specimen is the least significant, and the R-curve is flat. Different from the 0 / / 0 specimen, the fracture toughness - crack propagation length curves of the 0 / / 30, 0 / / 45, 0 / / 60, and 0 / / 90 specimens all show obvious R-curve behavior. In the 0 / / 30 specimen, both G PROP are about 190 J / m INI higher than G 2 . In the 0 / / 45 specimen, both G PROP are about 310 J / m INI higher than G 2 . In the 0 / / 60 specimen, both G PROP are about 300 J / m INI higher than G2 or so. In the 0 / / 90 specimen, G PROP is higher than G INI by about 380 J / m 2 or so. This phenomenon is because the crack in the 0 / / 0 specimen propagates smoothly along the interface, and the fiber bridging effect is weak; in the 0 / / θ specimen, as θ increases, the crack deflection intensifies, the tortuosity of the propagation path rises, and the energy dissipation path increases (such as matrix tearing and fiber fracture), and the fiber bridging phenomenon increases, indicating that the fiber bridging phenomenon significantly improves the interlaminar fracture toughness, and the fiber ply angle has an obvious influence on the R curve.

[0084] DCB specimens with different interlaminar fiber ply angles showed different damage characteristics during the static experiment. The delamination propagation paths of the static test specimens are as Figure 4 shown. Experimental observations show that DCB specimens with different fiber ply angles exhibit diverse delamination paths and bridging morphologies during crack propagation. As Figure 4 (a) shows, for the 0 / / 0 specimen, the fiber directions of adjacent layers are the same, 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 ply interface of the laminate, with a straight path and almost no deflection or bifurcation. In this case, the bridging fibers are in the same direction as the ply direction and span the open cantilever interface along the delamination propagation direction. For the 0 / / θ specimen, the bridging fibers connect the upper and lower cantilevers in the width direction, and the range of the fiber bridging region shows an increase with the increase of the interlaminar fiber angle.

[0085] As Figure 4 (b) shows, for the 0 / / 30 specimen, the fiber angle at the delamination interface is small, and the crack tends to propagate along the interface but may undergo slight deflection or locally enter the adjacent layer; as Figure 4 (c) shows, for the 0 / / 45 specimen, the crack tends to bifurcate or propagate along the fiber direction of the adjacent layer (in the 45° direction), forming a "zigzag" or "wavy" path; as Figure 4 (d), (e) show, for the 0 / / 60 specimen and the 0 / / 90 specimen, the crack tends to deflect into the adjacent layer, forming a tortuous propagation path (such as a "Z" shape), which needs to overcome more fiber fractures and matrix tears, presenting an irregular tortuous morphology. The experimental phenomena show that the influence of fiber bridging on delamination propagation is very significant, and this influence is closely related to the fiber ply angle. In addition, the interlaminar fiber ply angle also affects the path morphology of delamination propagation.

[0086] Figure 5 shows the influence of the interlaminar fiber angle on the crack propagation path, where Figure 5Among them, (a), (b), and (c) are DCB experiments on 0 / / 0, 0 / / 45, and 0 / / 90 interfaces respectively. The crack propagation mechanism model was established by characterizing the cross-section of the specimen after failure through SEM and based on the observation results. From the microtopography images, it was observed that the cross-section of the specimen after failure had fractured matrix and exposed fibers formed after the separation of the matrix / fiber. Moreover, compared with the 0 / / 0 specimen, the 0 / / 45 and 0 / / 90 specimens had deep concave surfaces formed due to the cross-layer propagation of cracks. As shown in the crack propagation mechanism model, with the change of the fiber ply angle, the fiber directions between the 45° and 90° layers hindered the crack propagation path, resulting in the tortuous propagation of the crack in the thickness direction. Therefore, compared with the 0 / / 0 specimen, at the unit crack propagation length, the actual crack propagation area of the 0 / / 45 specimen and the 0 / / 90 specimen increased significantly.

[0087] Figure 5 It was shown that due to the angle between the fiber distribution direction and the crack propagation direction in the 0 / / θ specimen, the crack front experienced continuous jumps under the hindrance of the fibers, resulting in a more tortuous crack propagation path. This tortuous path means that the crack not only propagates in the delamination direction but also generates reciprocating displacements in the thickness direction of the material, forming a complex propagation trajectory and increasing the actual damage area when the specimen crack propagates by a unit length Δa, leading to an increase in the initial fracture toughness.

[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 the potential energy of the structural system with respect to the crack surface area. When G reaches its critical value G C c, crack propagation will occur. ASTM D5528 standard combines this concept with the characteristics of DCB specimens to analyze crack propagation, assuming that the crack propagates uniformly in the DCB specimen under constant displacement or load. When a small delamination occurs (Δa), according to linear elastic fracture mechanics, the strain energy release rate of the specimen can be determined by the following expression:

[0089]

[0090] where b is the width of the DCB specimen and a is the effective delamination length of the DCB specimen. The mode I delamination energy release rate (G I ) is defined as the incremental rate of change of the total elastic energy (U) of the structure with respect to crack propagation. In the case of a DCB specimen, it is usually expressed by the increment of the crack length (da) because the width (b) of the specimen is constant. However, this method assumes that the crack propagates along a linear path, ignoring the complexity caused by the change of the interlayer fiber orientation, which may cause the crack to deviate in a multi-directional laminate, resulting in a change in the crack propagation path.

[0091] To explore the evolution mechanism of path changes and its influence on the initial fracture toughness G at the crack tip, a method for modifying the calculation of the initial fracture toughness at the crack tip is proposed based on analysis and discussion. According to the decoupling of the damage mechanism at the crack tip, G INI is composed of the fracture toughness of three different toughening mechanisms: INI

[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 the formation of crack propagation. G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, and 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 shift. Therefore, according to the complex damage types of composite delamination, first set the initial fracture toughness G INI of the 0 / / 0 specimen as:

[0095]

[0096] Among them, 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, and G I-FB-0 / / 0 represents the alternating fiber / matrix separation fracture toughness of the 0 / / 0 ply. Because the crack propagation path mainly affects the damage path at the leading edge of the crack tip and has little correlation with fiber bridging, therefore, G I-FB in all subsequent formulas is obtained by fitting experimental data and represents the fracture toughness released during the formation of fiber bridging. Δa -FD is used as a reference value to define the area expanded relative to the 0 / / 0 ply when the matrix / fiber separation releases fracture energy, and its value does not affect the calculation result.

[0097] When the fiber ply direction makes a certain angle with the crack propagation direction, a multi-phase field of matrix and fiber mixture will appear in the crack tip region. Due to the huge difference in strength between the fiber and matrix materials, the high-strength fiber will guide the crack tip to change direction and develop towards the form of easier-to-damage matrix cracking or matrix / fiber separation. Especially for matrix / fiber separation damage, since the fiber position is close to the crack tip, the delamination propagation path is greatly affected by the fiber orientation angle.

[0098] ​Taking the 0 / / 90 laminate as an example, as Figure 6 (a) and Figure 6 (b) show, the fibers with a 90° orientation angle appear as circular cross-sections of the fibers on the x-y cross-section of crack propagation. When the crack continues to propagate, it needs to cross this circular cross-section in the length and thickness directions. There are mainly two forms for the crack tip to cross the fibers: The first is the tangential crack propagation path as shown in Figure 6 (c), where the crack crosses the fiber cross-section along the tangential path of the circle. The second is the arc crack propagation path as shown in Figure 6 (d), where the crack crosses the fiber cross-section along the arc path.

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

[0100] Taking the 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 these path changes are quantified in the form of fracture area. If the 0 / / 90 matrix / fiber separation crack propagates along the tangential crack propagation path, the calculation formula for the fracture toughness released by delamination propagation is expressed as:

[0101]

[0102] When the 0 / / 90 matrix / fiber separation crack propagates along the arc crack propagation path, the fracture toughness released by delamination propagation is expressed as:

[0103]

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

[0105] It can be observed from the figure that with the change of the fiber orientation angle, the evolution trend of the crack propagation path also changes. Based on this mechanism, the prediction calculation formulas for the initial fracture toughness of the 0 / / 30, 0 / / 45, and 0 / / 60 specimens are established:

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

[0107]

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

[0109] Prediction calculation formula for the initial fracture toughness along the arc crack propagation path:

[0110]

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

[0112] S5. When only changing the interlayer fiber ply angle of the DCB specimen, the initial fracture toughness of the DCB specimen with any other ply angle is deduced through the initial fracture toughness of two known groups of specimens with different fiber ply angles. 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, according to the tangential path angle fitting curve, the tangential path point that is most likely to propagate is calculated. The confirmation functions of the tangential crack propagation path models of the 0 / / 30, 0 / / 45, and 0 / / 60 specimens for the tangential propagation angle are shown in Figure 8 (a), (b), and (c) respectively. Based on the tangential crack propagation path model and the initial fracture toughness data of 230.3 J / m 2 for 0 / / 0 and the initial fracture toughness data of 265.7 J / m 2 for the 0 / / 90 ply angle specimen, the tangential crack propagation path model is used to predict the initial fracture toughness of the 0 / / 30, 0 / / 45, and 0 / / 60 ply specimens. The error analysis results compared with the experimental values are shown in Table 3.

[0115] Table 3 Correction of the mode I delamination initial fracture toughness

[0116] Ply sequence <![CDATA[G INI (J / m 2 ) experiment]]> <![CDATA[G INI (J / m 2 ) Prediction]]> 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 the 0 / / 30, 0 / / 45, and 0 / / 60 specimens calculated by theoretical prediction and the experimental measurement values, verifying 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 specimens with ply angles of 0 / / 0 (230.3 J / m 2 ) and 0° / / 90° (265.7 J / m 2 ) was used to predict the initial fracture toughness of 0 / / 30, 0 / / 45, and 0 / / 60 specimens. As shown in Table 4, the comparison results between the theoretical prediction values and the experimental measurement values indicate that the prediction errors are all lower than 10.0%, verifying the reliability and accuracy of this method in the evaluation of the initial fracture toughness of CFRP laminates.

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

[0121]

[0122]

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

[0124] The above Mode I delamination propagation experiments show that fiber bridging phenomena exist in specimens with different ply configurations, and the fiber bridging phenomenon is more obvious with the increase of the interlayer ply angle θ. Compared with the smooth crack propagation along the interface in 0 / / 0 specimens, the cracks in 0 / / θ specimens show the characteristics of interlayer propagation, with an increase in the tortuosity of the propagation path and an increase in the energy dissipation path. The 0 / / θ specimens have higher initial fracture toughness, demonstrating that the fiber ply angle has a significant impact on the initial fracture behavior of composites.

[0125] Microscopic cross-section characterization shows that the crack propagation damage modes are mainly matrix cracking and matrix / fiber separation. Compared with 0 / / 0 specimens, 0 / / θ specimens have deep concave interfaces formed by crack interlayer propagation. In 0 / / θ specimens, the fibers force the crack front to produce continuous jumps in the thickness direction through directional hindrance, forming an extended trajectory with reciprocating displacement.

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

[0127] Therefore, the present invention adopts the above-mentioned analytical calculation method for the I-type initial fracture toughness considering the fiber ply angle, providing a new prediction tool based on physical mechanisms for the fracture analysis of composite materials, enabling more accurate prediction of the fracture behavior of materials under different ply configurations at the design stage, thereby avoiding the influence of experimental errors.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An analytical calculation method for the initial fracture toughness of Mode I considering the fiber lay-up angle, characterized in that: It includes the following steps: S1. Design and prepare a multi-directional ply angle DCB specimen and conduct a DCB experiment; S2. Calculate the data obtained from the experiment in S1 to obtain the mode I interlaminar fracture toughness - crack length data of DCB specimens with different interlaminar ply angles and plot them into an R curve; S3. Observe the crack propagation path of the specimen in the S1 experiment, use SEM to characterize the cross-section of the specimen after failure, and establish a crack propagation mechanism model based on the observation results; S4. Establish an analytical calculation method for the mode I delamination initiation fracture toughness considering the influence of fiber ply angle based on the crack propagation mechanism model obtained in S3; S5. Predict the initiation fracture toughness of specimens with different fiber ply angles through the analytical method of mode I delamination initiation fracture toughness considering the influence of fiber ply angle, and verify the accuracy of the analytical method of mode I delamination initiation fracture toughness considering the influence of fiber ply angle.

2. The analytical calculation method for the I-type initial fracture toughness considering the fiber lay-up angle according to claim 1, wherein: In S1, the layup design of the DCB specimen is: [0 12 / / θ / 0 13 , where θ = 0°, 30°, 45°, 60° and 90°. The symbol / / indicates the position where a pre-crack is introduced during preparation. A 13-μm-thick polytetrafluoroethylene film is manually laid between the 12th and 13th layers of the specimen as the pre-crack. The laminate is cut into a length of 180 mm, a width of 25 mm, and a thickness of 4.8 mm. The effective pre-crack length a0 = 30 mm.

3. The analytical calculation method for the I-type initial fracture toughness considering the fiber ply angle according to claim 1, wherein: In S1, when conducting the DCB experiment, a double-cantilever beam specimen is used for the mode I delamination experiment on a universal testing machine. The universal testing machine records the displacement-load data of quasi-static delamination propagation in real time and records the corresponding crack propagation length through a digital camera system.

4. The analytical calculation method for the initial fracture toughness of Mode I considering the fiber lay-up angle according to claim 1, characterized in that: In S2, the interlaminar fracture toughness is calculated by the modified beam theory method, and the formula is as follows: where P is the load, δ is the applied displacement, b is the specimen width, a is the delamination length, △ is the correction coefficient of the delamination length at the crack tip, and its characteristic value is obtained by making a least-squares graph of the cube root of the compliance C against the delamination length a. The compliance C is the ratio of the displacement at the loading point to the applied load: δ / P.

5. The analytical calculation method for the I - type initial fracture toughness considering the fiber ply angle according to claim 1, characterized in that: In S3, observe the crack propagation path of specimens with different interlaminar fiber ply angles during the static experiment, compare the differences between 0 / / 0 and 0 / / θ specimens, observe the cross-section of the specimen after failure with SEM, analyze the microscopic characteristics of the fractured matrix and exposed fibers, and establish a mechanism model based on the results 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 analytical calculation method for the I - type initial fracture toughness considering the fiber ply angle according to claim 1, characterized in that: In S4, based on the crack propagation mechanism model of S3, the initial fracture toughness G of mode I delamination is determined INI It consists of the fracture toughnesses of three different toughening mechanisms, namely: G INI = G I-MC + G I-FD + G I-FB ; Among them, G INI represents the initial fracture toughness of crack propagation, G I-MC represents the fracture toughness of matrix cracking damage during the formation of crack propagation, G I-FD represents the fracture toughness of continuous matrix / fiber separation damage, G I-FB Obtained by fitting experimental data, it represents the fracture toughness of alternating matrix / fiber separation-induced fiber bridging damage; In the 0 / / 0 interface DCB specimen, the delamination path does not shift. According to the complex damage type of composite material delamination, assume the initiation fracture toughness of the 0 / / 0 specimen is: Among them, G I-MC-0 / / 0 represents the cracking fracture toughness of the 0 / / 0 ply matrix, 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, Δa -FD As a reference value, it is used to define the area expanded relative to the 0 / / 0 ply when the matrix / fiber separation release fracture energy is released, and its value does not affect the calculation results; Considering the influence of fiber orientation angles of 30°, 45°, 60°, and 90° on the crack propagation path, establish the prediction calculation formulas for the initiation fracture toughness of 0 / / 30, 0 / / 45, 0 / / 60, and 0 / / 90 specimens along the tangential and arc crack propagation paths.

7. An analytical calculation method for the initial fracture toughness of mode I considering the fiber ply angle according to claim 1, characterized in that: In S4, the prediction calculation formula for the initiation fracture toughness along the tangential crack propagation path is: Among them, is the angle between the tangent and the x direction, and G INI-0 / / θ-TAN is the initial fracture toughness calculated along the tangential crack propagation path, is a function related to θ and , and G I-FB-0 / / θ is the alternating fiber / matrix separation fracture toughness of the 0 / / θ ply; The prediction calculation formula for the initiation fracture toughness along the arc crack propagation path is: Among them, G INI-0 / / θ-ARC is the initial fracture toughness calculated along the arc crack propagation path.

8. The analytical calculation method for the initial fracture toughness of Mode I considering the fiber lay-up angle according to claim 1, characterized in that: In S5, when only changing the interlaminar fiber ply angle of the DCB specimen, deduce the initiation fracture toughness of any other ply angle DCB specimen through the known initiation fracture toughness of two groups of specimens with different fiber ply angles. Based on the proposed tangential crack propagation path model and arc crack propagation path model, calculate in combination with the experimental results to verify the reliability of this method.

9. An analytical calculation method for the initial fracture toughness of Mode I considering the fiber ply angle according to claim 8, 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, combined with the initial fracture toughness data, the most easily expandable point of the tangential path is determined by fitting the curve, the initial fracture toughness of specimens with different fiber ply angles is predicted, and the predicted results are compared and verified with the experimental data. Similarly, the same operation is carried out on the arc crack propagation path model to verify the accuracy and reliability of this method in predicting the initial fracture toughness of specimens with different fiber ply angles.

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