Composite material interlayer fatigue layering extension experiment method based on crack length-flexibility relation

Abstract

The invention discloses a composite material interlayer fatigue layering extension experiment method based on a crack length-flexibility relation, and belongs to the field of composite material engineering technology application. Compared with a traditional method that the experiment needs to be paused for multiple times in the cyclic loading process and the fatigue crack length is observed through sampling in the fatigue stratification extension experiment, the invention provides the fatigue in-situ stratification extension experiment method of the composite material under the cyclic load based on the crack length-flexibility relation. According to the method, the whole fatigue experiment process can be continuous and uninterrupted, the crack propagation length and the fracture toughness are obtained through in-situ test calculation, the precision of a fatigue layering propagation experiment can be improved, and the experiment operation is simpler, more convenient and easier to implement. In addition, the experimental method has the advantages of being clear in physical significance, remarkably increasing the number of data samples and the like, and has important popularization and application values in the field of composite material engineering technology application.

Description

Technical Field

[0001] The present invention belongs to the field of application of composite material engineering technology, and is mainly applied to fields such as aerospace, new automobiles and ships, and new energy equipment. Specifically, it relates to an experimental method for interlaminar fatigue delamination propagation of plain woven composite materials based on the crack length-flexibility relationship. Background Technique

[0002] Fiber-reinforced polymer (FRP) composite materials have excellent properties such as high specific strength, high specific stiffness, fatigue resistance, and corrosion resistance, and are widely used in many fields such as aerospace, automobiles, ships, and buildings. For example, the wings of space shuttles, engine blades, and the shells of automobiles. One type of plain woven composite material is formed by weaving carbon fibers in two directions to form a single layer, and then multiple single layers are laid together in the same direction and cured at high temperature by adding epoxy resin. As Figure 1 shown, there are a large number of interfaces inside. In practical applications, composite materials usually receive various load conditions, such as static, fatigue, and impact. Since the load-bearing capacity of the matrix is much smaller than that of the fibers, matrix failure and delamination are two main failure modes.

[0003] In the experiments on various properties of composite materials (static, fatigue, impact, etc.), it is found that in fatigue experiments, delamination phenomena will first appear in the specimens, and then fracture will occur after a long time. The characteristics of such delamination are that it is not easy to be discovered and can expand at a low stress level; delamination phenomena can also be found near the impact point of the plate-like structure after impact experiments, and after the delamination appears, the stiffness of the structure is reduced to a certain extent. In real life, most delamination phenomena are hidden inside the structure and are not easy to be discovered during service. And this fatigue delamination propagation makes the stress-displacement transfer relationship of the material discontinuous, making it impossible to accurately evaluate the structural mechanical properties, and it is difficult to estimate the damage to the structure and its strength, resulting in major potential safety hazards in the use of the structure. Therefore, accurately measuring the interlaminar fatigue delamination propagation performance of composite materials is of great significance for predicting the failure strength of composite materials and structural design.

[0004] For the experimental method of the interlaminar fracture toughness of composite materials, the experimental standard ASTM D5528 is usually referred to. However, during the experimental process, the determination method of the important parameter "fatigue crack length" used to calculate the fracture toughness has always been the key influencing factor for the final experimental result. The method recommended in the standard is to paste a scale indicator strip for manual reading, but in actual tests, many materials or actual working conditions are not the same as those required in the experimental standard. If the experimental standard is continued to be copied, there will be a large deviation.

[0005] At present, the fatigue crack growth is mainly described based on the Paris formula in fracture mechanics, as shown in Equation (1):

[0006]

[0007] In the formula, a is the crack length, N is the number of stress cycles, both C and n are material constants, and G is the energy release rate. da / dN represents the crack growth rate, which is the change rate of the crack length a with the number of stress cycles N under the action of fatigue load, reflecting the speed of crack growth. For the fitting function f(G) of the energy release rate G, usually referring to the ASTM D6115 experimental standard, the modified beam theory is used for calculation, and the calculation method is as shown in Equation (2):

[0008]

[0009] In the formula, G is the energy release rate, P is the load magnitude, δ is the displacement of the loading point, b is the specimen width, a is the crack length, and |Δ| is the correction value of the crack length. The correction method is as Figure 2 shown. In the figure, λ is the flexibility, representing the displacement caused by a unit force, and the calculation method is as shown in Equation (3):

[0010]

[0011] In the formula, λ is the flexibility, δ is the displacement of the loading point, and P is the load magnitude. In the composite material fatigue crack growth experiment, usually the fatigue delamination growth initiation test method recommended in the standard ASTM D6115 is adopted. However, due to problems such as fiber bridging, uncertainty in the manufacturing process, and inaccurate crack length measurement, there are often large discreteness in the experimental results. In addition, with different experimental purposes and experimental materials, there are also large differences in the results.

[0012] To sum up, for the experimental method of testing the interlaminar fatigue delamination growth performance of composite materials, as the fatigue crack gradually grows, its crack growth rate da / dN continuously decreases, and it will bring certain difficulties to read the crack length a. The current common solution is to pause the experiment multiple times during the fatigue experiment, take out the specimen to observe and record the crack length a under the microscope. The testing process is time-consuming and laborious, and multiple interruptions of the fatigue experiment process will directly affect the accuracy of the experimental results. For the double-cantilever beam specimen for recording the crack length, see Figure 3 . In addition, for reading the crack length a at a relatively low level of the energy release rate G, there are still difficulties in the existing experimental methods, and the testing error is relatively large. Summary of the Invention

[0013] In view of the deficiencies of the existing experimental methods for evaluating the interlaminar fatigue delamination growth performance of composite materials, which are cumbersome to operate and have large errors, the present invention proposes an experimental method for interlaminar fatigue delamination growth of composite materials based on the crack length-flexibility relationship.

[0014] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0015] An experimental method for interlaminar fatigue delamination growth of composite materials based on the crack length-flexibility relationship, the method is:

[0016] Step 1: Perform a quasi-static experiment according to the ASTM D5528 experimental standard, and build an experimental test system. See Figure 4 , and obtain the crack length-flexibility relationship curve from the quasi-static experiment. See Figure 5 ;

[0017] Step 2: From the crack length-flexibility relationship curve obtained from the quasi-static experiment, it can be found that the relationship between the crack length and the cube root of the flexibility is highly linear, and the slopes are almost the same at the same temperature (as Figure 5 shown). Therefore, define the slope of the relationship curve between the crack length and the cube root of the flexibility as "k", that is

[0018]

[0019] In the formula, k is the slope of the crack length-flexibility relationship curve; λ is the flexibility, that is, the displacement generated by a unit force; a is the crack length; |Δ| is the correction value of the crack length;

[0020] Step 3: According to the theory of mechanics of materials, the flexibility λ of the cantilever beam specimen is:

[0021]

[0022] In the formula, a is the crack length; |Δ| is the correction value of the crack length; E is the elastic modulus of the material; I is the cross-sectional moment of inertia of the cantilever beam specimen;

[0023] Step 4: Substitute formula (5) into formula (4) to obtain the expression (6) of the physical quantity k, that is:

[0024]

[0025] It can be seen from expression (6) that the physical quantity k is only related to temperature. Therefore, as long as the elastic modulus E value of the material under different temperature environments is measured, the numerical value of the physical quantity k at different temperatures can be calculated from formula (6);

[0026] Step 5: After obtaining the k value under different temperature environments by this method, the slope of the relationship curve between crack length and flexibility at this temperature can be determined. Only one more data point needs to be added to completely determine the relationship curve between crack length and flexibility, and this data point is obtained using the pre-cracking process;

[0027] Step 6: After determining the slope k value of the crack length-flexibility relationship curve, the crack length correction value |Δ|, and the flexibility λ in the quasi-static experiment, the crack length a is calculated by formula (4), and its expression is shown in formula (7):

[0028]

[0029] Evaluate the interlaminar fatigue performance of the composite material according to the crack length a.

[0030] The beneficial effects of the present invention compared with the prior art are as follows: This method proposes a method for calculating the relationship between crack length and flexibility, which can realize continuous and uninterrupted fatigue experiment process, in-situ test and calculation to obtain the crack length a, improve the accuracy of fatigue delamination propagation experiment, and at the same time the experimental operation is more simple and easy. In addition, this experimental method also has advantages such as clear physical meaning and significantly increasing the number of data samples, and has important promotion and application value in the field of composite material engineering technology applications. Brief Description of the Drawings

[0031] Figure 1 It is a process diagram of the formation of plain woven composite materials;

[0032] Figure 2 It is a diagram of the correction method for the crack length correction value |Δ| of the modified beam theory;

[0033] Figure 3 It is an example diagram of the preparation before the experiment of a double-cantilever beam specimen, (a) pasting scale labels; (b) spraying speckles;

[0034] Figure 4 It is a diagram of the experimental test system built;

[0035] Figure 5 It is a diagram of the crack length-flexibility relationship of a plain woven composite material double-cantilever beam specimen;

[0036] Figure 6 It is a diagram of the energy release rate curve of the interlaminar fatigue delamination propagation experiment, (a) 20°C; (b) 20°C; (c) 100°C;

[0037] Figure 7 It is a Paris curve diagram of the fatigue delamination propagation rate. Detailed Embodiment

[0038] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0039] The present invention proposes a fatigue delamination propagation experimental method based on the crack length-flexibility relationship for plain woven composites. Compared with the traditional fatigue delamination propagation experiment method that requires multiple pauses during the cyclic loading process to sample and observe the fatigue crack length, the present invention proposes a fatigue in-situ delamination propagation experimental method for composites under cyclic loads based on the crack length-flexibility relationship. This method can achieve continuous and uninterrupted throughout the fatigue experiment process, in-situ test and calculate the crack propagation length and fracture toughness, which can improve the accuracy of the fatigue delamination propagation experiment, and the experimental operation is more simple and easy. In addition, this experimental method also has advantages such as clear physical meaning and significantly increasing the number of data samples, and has important promotion and application value in the field of composite material engineering technology applications. Specific Embodiment 1:

[0041] A composite material interlaminar fatigue delamination propagation experimental method based on the crack length-flexibility relationship, the method is:

[0042] Step 1: Conduct a quasi-static experiment according to the ASTM D5528 experimental standard, build an experimental test system, see Figure 4 , obtain the crack length-flexibility relationship curve from the quasi-static experiment, see Figure 5 ;

[0043] Step 2: From the crack length-flexibility relationship curve obtained from the quasi-static experiment, it can be found that the relationship between the crack length and the cube root of the flexibility is highly linear, and the slopes are almost the same at the same temperature (as Figure 5 shown), therefore, define the slope of the relationship curve between the crack length and the cube root of the flexibility as "k", that is

[0044]

[0045] In the formula, k is the slope of the crack length-flexibility relationship curve; λ is the flexibility, that is, the displacement generated by a unit force; a is the crack length; |Δ| is the correction value of the crack length;

[0046] Step 3: According to the theory of mechanics of materials, the flexibility λ of the cantilever beam specimen is:

[0047]

[0048] In the formula, a is the crack length; |Δ| is the correction value of the crack length; E is the elastic modulus of the material; I is the cross-sectional moment of inertia of the cantilever beam specimen;

[0049] Step 4: Substitute Equation (5) into Equation (4) to obtain the expression (6) of the physical quantity k, i.e.:

[0050]

[0051] It can be seen from the expression that the physical quantity k is only related to temperature. Therefore, as long as the elastic modulus E values of the material under different temperature environments are measured, the numerical values of the physical quantity k at different temperatures can be calculated from Equation (6);

[0052] Step 5: After obtaining the k values under different temperature environments by this method, the slope of the relationship curve between crack length and compliance at this temperature can be determined. Only one more data point is needed to completely determine the relationship curve between crack length and compliance, and this data point is obtained using the pre-cracking process.

[0053] During the pre-cracking process, record the initial crack length, load-displacement curve, and crack length after pre-cracking. Calculate the loading compliance λ using the load-displacement curve in the rising section, as shown in Equation (3), to form one data point with the initial crack length. Since then, the crack length-compliance relationship of this specimen has been completely determined, and at the same time, the crack length correction value |Δ| is also determined, that is, the abscissa value of the intersection point of the crack length-compliance relationship curve and the abscissa axis, as shown in Figure 2 .

[0054] Step 6: After determining the slope k value, crack length correction value |Δ|, and compliance λ of the crack length-compliance relationship curve in the quasi-static experiment, calculate the crack length a from Equation (4), and its expression is shown in Equation (7):

[0055]

[0056] Evaluate the interlaminar fatigue performance of the composite material according to the crack length a.

[0057] Calculate important parameters such as the energy release rate interval, fatigue delamination propagation rate, and fatigue delamination propagation threshold during the fatigue experiment based on the crack length calculated by this method. This experimental method can be used to evaluate the interlaminar fatigue performance of composite materials from multiple perspectives.

[0058] The described method is applicable to the interlaminar fracture toughness experiments of plain woven composites, fiber-reinforced composite laminates, etc. without bridging phenomena, as well as the evaluation of the interlaminar fatigue fracture performance of other three-dimensional fiber-reinforced composites that can avoid the participation of z-direction fibers.

[0059] Example 1: Comparison of the crack length calculated by this method with the crack length results observed by optical microscopy.

[0060] Based on the quasi-static experimental data, the compliance λ calculated by formula (3), the physical quantity k calculated by formula (6), and the crack length correction value |Δ| determined based on the crack length-compliance relationship curve are substituted into formula (7): The crack length a can be calculated.

[0061] To compare the calculation results of this method with the observation results of an optical microscope under different temperature environments, after the experiment, the test piece was placed under the optical microscope to observe the crack tip position and measure the crack length. Table 1 shows the comparison of the crack length calculated by this method and the crack length observed by the optical microscope. Among them, the calculated fatigue crack lengths at 20°C, 60°C, and 100°C are 62.7 mm, 66.3 mm, and 69.8 mm respectively; the crack lengths measured by the microscope are 61.07 mm, 66.7 mm, and 71.52 mm respectively. The results show that the errors between the calculated values and the experimental values of the crack lengths at 20°C, 60°C, and 100°C are 2.7%, 0.6%, and 2.4% respectively, and the two are in good agreement.

[0062] Calculating the crack length by this method means saving the steps of taking images and manually marking the crack length in the traditional experimental method, and at the same time greatly increasing the available data points, providing strong support for calculating other characterization parameters such as the crack growth rate.

[0063] Table 1 Comparison of the crack length calculated by this method and the crack length observed by the optical microscope

[0064] Temperature environment (°C) Calculated crack length (mm) Observed crack length (mm) Error between calculated value and experimental value (%) 20 62.7 61.07 2.7 60 66.3 66.7 0.6 100 69.8 71.52 2.4

[0065] Example 2: Determine the crack length a based on the crack length-compliance relationship and calculate the energy release rate interval.

[0066] When determining the maximum displacement of the fatigue experiment, 90% of the maximum energy release rate is used as the starting state. During the experiment, as the crack propagates, the compliance of the specimen gradually decreases, the energy release rate gradually decreases, and thus the delamination propagation rate decreases. For the traditional method, the appearance of this phenomenon means that in the middle and late stages of the experiment, it is relatively difficult to read the crack length a, and it is very easy to have a result where the manual measurement error is greater than the crack growth increment. In this case, it is difficult to determine the energy release rate interval throughout the experimental test.

[0067] Implementing this method, since there is no need to visually read the crack length a, the energy release rate interval throughout the experimental test can be evaluated, making full use of the experimental data. See Figure 6 . For the initial energy release rate G init_f and the shutdown energy release rate G stop_f are statistically analyzed and the ratio is calculated. The results are shown in Table 2. It can be found from the table that: G init_fThe proportion is large enough and relatively consistent with expectations; G stop_f The proportion is at a relatively low level, crack propagation is relatively slow, the significance of continuing the experiment is small, and the downtime is appropriate.

[0068] Table 2 Statistics of the starting and ending energy release rates for the interlayer fatigue delamination propagation experiment

[0069] Specimen number <![CDATA[G init_f (J / m 2 )]]> <![CDATA[G init_f Ratio (%)]]> <![CDATA[G stop_f (J / m 2 )]]> <![CDATA[G stop_f Ratio (%)]]> DCBPL-20 462.37 82.6 219.70 39.2 DCBPL-60 482.47 85.3 204.88 36.2 DCBPL-100 580.72 83.7 202.69 29.2

[0070] Example 3: Determine the crack length a based on the crack length-flexibility relationship and calculate the fatigue delamination propagation rate.

[0071] In this method, the Paris formula used for fitting adopts formula (1): In the formula, a is the crack length, N is the number of stress cycles, C and n are both material constants, and G is the energy release rate. da / dN represents the crack propagation rate, which is the rate of change of the crack length a with the number of stress cycles N under the action of fatigue load, reflecting the speed of crack propagation. For the fitting function f(G) of the energy release rate G, the fitting results are n = -0.006T2 + 0.0694T + 3.9933 and log10C = -0.0006T2 + 0.0936T - 4.2615.

[0072] Figure 7 For the Paris curve of the fatigue delamination propagation experiment, the abscissa used is the proportion of the energy release rate, and the ordinate is the fatigue delamination propagation rate. The data is logarithmically processed. In data selection, follow the photographing frequency in the traditional experimental method: take a point every 40 seconds within the first 1000 cycles, take a point every 300 cycles between 1000 and 10000 cycles, and take a point every 1000 cycles after 10000 cycles. It can be found from the experimental results that as the temperature gradually increases, the corresponding Paris curve moves upward, that is, at the same energy release rate level, the higher the temperature, the greater the fatigue delamination propagation rate.

Claims

1. An experimental method for fatigue delamination growth of composite laminates based on the crack length-compliance relationship, characterized in that: The method is as follows: Step 1: Conduct a quasi-static experiment according to the ASTM D5528 experimental standard, set up an experimental test system, and obtain a crack length-compliance relationship curve from the quasi-static experiment; Step 2: From the crack length-compliance relationship curve obtained in the quasi-static experiment, define the slope of the relationship curve of the one-third power of the crack length-compliance as "k", that is In the formula, k is the slope of the crack length-compliance relationship curve; λ is the compliance, that is, the displacement generated by a unit force; a is the crack length; |Δ| is the correction value of the crack length; Step 3: According to the theory of mechanics of materials, the compliance λ of the specimen is: In the formula, a is the crack length; |Δ| is the correction value of the crack length; E is the elastic modulus of the material; I is the cross-sectional moment of inertia of the cantilever beam specimen; Step 4: Substitute Equation (5) into Equation (4) to obtain the expression (6) of the physical quantity k, that is: It can be seen from the expression that the physical quantity k is only related to temperature; Step 5: After obtaining the k value under different temperature environments by this method, the slope of the relationship curve between the crack length and the compliance at this temperature can be determined. Only one more data point is needed to completely determine the relationship curve between the crack length and the compliance, and the pre-cracking process is used to obtain this data point; Step 6: After determining the slope k value, the crack length correction value |Δ|, and the compliance λ of the crack length-compliance relationship curve in the quasi-static experiment, the crack length a is calculated by formula (4), and its expression is shown in formula (7): Evaluate the interlaminar fatigue performance of the composite material according to the crack length a.

2. The experimental method for fatigue delamination propagation of composite material interlayers based on the crack length-flexibility relationship according to claim 1, characterized in that: The method is applicable to the interlaminar fracture toughness experiments of plain woven composites, fiber-reinforced composite laminates, etc. without bridging phenomenon, and the evaluation of the interlaminar fatigue fracture performance of other three-dimensional fiber-reinforced composites that can avoid the participation of z-direction fibers.

3. The experimental method for fatigue delamination growth of composite material interlayers based on the crack length-flexibility relationship according to claim 1, characterized in that: In Step 5, during the pre-cracking process, record the initial crack length, load-displacement curve, and the crack length after pre-cracking; calculate the loading compliance λ using the load-displacement curve in the rising section, see formula (3) for details Form one data point with the initial crack length; since then, the crack length-compliance relationship of this specimen is completely determined, and at the same time, the crack length correction value |Δ| is also determined, that is, the abscissa value of the intersection point of the crack length-compliance relationship curve and the abscissa.

4. The experimental method for fatigue delamination growth of composite material interfaces based on the crack length-flexibility relationship according to claim 1, characterized in that: In Step 6, based on the crack length calculated by this method, important parameters such as the energy release rate range, fatigue delamination propagation rate, and fatigue delamination propagation threshold during the fatigue experiment process are calculated. This experimental method can be used to evaluate the interlaminar fatigue performance of composite materials from multiple angles.

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