A semi-analytical method for determining the fracture toughness and bridging stress of composite laminates in end-loaded splitting mode

Abstract

The present invention relates to a semi-analytical method for determining the fracture toughness and bridging stress of an end-load splitting mode of a composite material laminate, comprising the following steps: (1) designing and manufacturing a composite material specimen for an end-load splitting test; (2) carrying out a delamination test using a test device; (3) recording the test load and displacement to obtain the specimen flexibility; (4) measuring the initial delamination length of the specimen and the delamination length at unloading and the corresponding specimen flexibility to obtain expressions for the bending modulus and shear modulus; (5) deriving an expression for the fracture toughness; (6) deriving an expression for the shear displacement of the prefabricated crack tip; (7) fitting a relationship curve between the fracture toughness and the shear displacement of the prefabricated crack tip; (8) differentiating the relationship curve with respect to the shear displacement of the prefabricated crack tip to obtain the bridging stress; the semi-analytical method proposed in the present invention can be used to determine the fracture toughness and bridging stress in the end-load test of composite materials without the need to monitor the crack length in real time or design additional tests, thereby simplifying the test process, shortening the test cycle, and improving the accuracy of the measurement results.

Description

Technical Field

[0001] The present invention relates to the technical field of measuring mode II delamination fracture toughness and bridging stress of composite materials, and in particular to a semi-analytical method for measuring fracture toughness and bridging stress of composite laminates in an end-load splitting test. Background Art

[0002] Composite materials are widely used in aerospace, vehicles, machinery and other fields due to their advantages such as high specific strength and specific stiffness and good designability. As one of the important basic structural forms, composite laminates are prone to delamination damage due to the lack of fibers reinforcing in the thickness direction. Delamination often occurs inside the structure and cannot be directly detected on the surface. Moreover, once delamination damage occurs in the structure, the local stiffness will decrease, so that the structure will further delaminate and be damaged, which makes delamination a major hidden danger in the actual use of composite materials. Therefore, studying the mechanism and impact of delamination damage and then improving the performance of composite materials in resisting delamination damage has important theoretical significance and application value.

[0003] Type II delamination propagation in composite materials has a significant impact on the integrity and safety of laminates, yet relatively little research has been conducted on this issue compared to Type I. End-load splitting tests not only produce stable crack propagation but are also unaffected by specimen size, making them commonly used to determine the fracture toughness of type II delamination propagation in composite materials. Fiber bridging is a unique phenomenon that occurs during the delamination propagation process in composite laminates. Bridging fibers can bear a portion of the load, and the emergence of this toughening mechanism causes the fracture toughness of delamination propagation to vary with crack propagation. To fully leverage the advantages of composite materials, it is essential to accurately measure the fracture toughness and bridging stress of composite materials in end-load splitting tests.

[0004] Existing methods for determining the fracture toughness and bridging stress in end-load splitting tests of composite materials require real-time measurement of crack propagation length or the design of additional tests to determine the required engineering parameters. In reality, monitoring the propagation length of a Type II delamination crack is difficult and easily affected by operator influence. Furthermore, designing additional tests not only increases experimental costs and prolongs the test cycle, but also inevitably introduces other errors. Therefore, it is necessary to provide a semi-analytical method for determining the fracture toughness and bridging stress in end-load splitting tests of composite materials to address the shortcomings of existing measurement methods. Summary of the Invention

[0005] The technical problem addressed by this invention is to provide a novel method for determining the fracture toughness and bridging stress in end-load splitting tests of composite materials. This proposed semi-analytical method only requires measuring the specimen's initial delamination length and the delamination length at unloading, along with the corresponding compliance, thus avoiding the need for real-time monitoring of crack propagation length and designing additional experiments to obtain engineering parameters. Therefore, this method not only significantly simplifies the testing process, shortens the testing cycle, and reduces testing costs, but also improves the accuracy of the measurement results.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a semi-analytical method for determining the fracture toughness and bridging stress of the end-load splitting mode of a composite laminate, comprising the following steps:

[0007] Step 1: Design and manufacture composite laminate specimens required for end-load splitting test;

[0008] Step 2: Performing a composite material type II delamination extension test on the sample prepared in the above step using an end-load splitting test apparatus;

[0009] Step 3, record the load and displacement obtained in the test, and calculate the compliance of the specimen based on the recorded data;

[0010] Step 4: Measure the initial delamination length and delamination length of the sample during unloading and their corresponding flexibility to obtain the bending modulus E f and shear modulus G 13 and the expression of the layer length a;

[0011] Step 5, calculate and obtain the expression of mode II fracture toughness;

[0012] Step 6, calculate and obtain the expression of the shear displacement of the prefabricated crack tip;

[0013] Step 7, drawing and fitting a relationship curve between fracture toughness and shear displacement at the prefabricated crack tip;

[0014] Step 8, G obtained from step 7 II (δ t * ) expression for the shear displacement δ of the prefabricated crack tip t * Taking the derivative, we get the bridging stress.

[0015] Furthermore, the composite laminate specimens used in the test were prepared using T800 carbon fiber reinforced epoxy resin-based composite materials;

[0016] Furthermore, the composite laminate specimen involved in step 1 is made of (45° / -45° / 0°6) S / / (-45° / 45° / 0°6) S Designed and manufactured with ply angles of

[0017] Furthermore, the compliance C in step 3 is defined as the ratio of the displacement of the loading point to the applied load, that is:

[0018]

[0019] Where d and P are the displacement of the loading point and the applied load, respectively;

[0020] Furthermore, the relationship between flexibility and layer length in step 4 is as follows:

[0021]

[0022] Where b and L are the width and length of the free end of the specimen, respectively, and h is half of the total thickness of the specimen;

[0023] Substituting the measured initial delamination length and delamination length of the specimen at unloading and their corresponding compliance, i.e. (a0, C0) and (a1, C1), into the above formula, we can obtain:

[0024]

[0025]

[0026]

[0027] Furthermore, the formula for determining the mode II fracture toughness using the flexibility method in step 5 is:

[0028]

[0029] Among them, G Ⅱ is the type II fracture toughness, N2 is the loading block and large displacement correction coefficient, and F2 is the large displacement correction factor; the expressions of N2 and F2 are:

[0030]

[0031]

[0032] Where l1 and l2 are the sizes of the loading blocks; the values of θ2, θ3, and θ4 are 0, and the expressions of θ1 and θ5 are:

[0033]

[0034]

[0035] Substituting the relationship between flexibility and delamination length in step 4 into the above equation, the expression for fracture toughness can be obtained as follows:

[0036]

[0037] Among them, the bending modulus E f and shear modulus G 13 The expression of the layer length a is obtained through step 4;

[0038] Furthermore, in step 6, a pair of unit loads in opposite directions are applied to the prefabricated crack tip, and the shear displacement of the prefabricated crack tip can be obtained by the unit load method, which is expressed as:

[0039]

[0040] Among them, δ t * and a0 are the shear displacement and initial delamination length of the pre-crack tip, respectively;

[0041] Furthermore, the fitting formulas used in step 7 to describe the nonlinear and linear relationships between the fracture toughness and the shear displacement at the prefabricated crack tip are:

[0042]

[0043] G II (δ t * )=k1δ t * +k2

[0044] Among them, G tip is the starting value of mode II delamination fracture toughness, K a ,K b ,K c ,K d ,k1 and k2 are fitting parameters;

[0045] Furthermore, the bridging stress in step 8 can be calculated by the fracture toughness G II (δ t * ) expression is derived with respect to the prefabricated crack tip:

[0046]

[0047]

[0048] where τ is the bridging stress.

[0049] The advantages of the present invention compared with the prior art are:

[0050] (1) Compared with existing research, the present invention does not need to monitor the delamination extension length in real time during the test, thus avoiding the problem of difficult crack monitoring of type II delamination and reducing the test cost;

[0051] (2) The present invention can obtain the bending modulus and shear modulus through theoretical analysis, without the need to design additional experiments, thus simplifying the test process, shortening the test cycle, and avoiding errors that may be introduced by the operator, thereby improving the accuracy of the measurement results;

[0052] (3) The determination results of the present invention have been verified by combining experimental verification with simulation. The determination values obtained by the semi-analytical method are in good agreement with the method given in the ISO 15114 standard, indicating that the determination method of the present invention has good applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is an implementation flow chart of the present invention;

[0054] Figure 2 is the configuration and geometric dimensions of the end-load splitting test specimen (unit: mm);

[0055] Figure 3 is a schematic diagram of the end-load splitting test apparatus;

[0056] Figure 4 is the relationship between the fracture toughness and delamination length of carbon fiber / epoxy composite laminates;

[0057] Figure 5 is the relationship between the fracture toughness and delamination length of glass fiber / polyester composite laminates;

[0058] Figure 6 is the fitting curve of the fracture toughness of carbon fiber / epoxy composite laminate and the shear displacement of the prefabricated crack tip;

[0059] Figure 7 is the fitting curve of the fracture toughness of glass fiber / polyester composite laminate and the shear displacement of the prefabricated crack tip;

[0060] Figure 8 is the bridging stress distribution of glass fiber / polyester composite laminate;

[0061] Figure 9 It is a schematic diagram of the trilinear constitutive cohesion model;

[0062] Figure 10 It is a finite element model for simulation of type II delamination expansion of carbon fiber / epoxy composite laminates;

[0063] Figure 11 This is a comparison chart of the predicted load-displacement response of type II delamination expansion of carbon fiber / epoxy composite laminates and the experimental results. DETAILED DESCRIPTION

[0064] The present invention will be further described in detail below with reference to the embodiments.

[0065] The present invention provides a semi-analytical method for determining the fracture toughness and bridging stress of a composite material laminate in an end-load splitting mode, and the specific implementation steps are as follows:

[0066] Step 1: Design and manufacture the specimens required for the end-load splitting test according to ISO 15114. The layup order of the specimens is (45° / -45° / 0°6) S / / (-45° / 45° / 0°6) S The specimen configuration and geometric dimensions required for the end-load splitting test are as follows: Figure 2 As shown. The composite laminate is made of T800 carbon fiber material;

[0067] Step 2: Conduct end-load splitting test on composite laminates according to ISO 15114 standard. Figure 3 Schematic diagram of the test setup. L is the length of the free end. The loading mode is displacement-controlled. To ensure stable delamination expansion, a low loading rate of 0.1 mm / min was selected to obtain sufficient data points.

[0068] Step 3: Record the load and displacement applied during the end-load splitting test of the composite laminate, and obtain the specimen compliance according to the definition of compliance;

[0069]

[0070] Step 4: Measure the initial delamination length and delamination length of the specimen during unloading, as well as their corresponding compliance, and substitute them into the relationship between compliance and delamination length:

[0071]

[0072] Solve the above relationship to obtain the bending modulus E f and shear modulus G 13 and the expression of the layer length a;

[0073]

[0074]

[0075]

[0076] Steps 5 and 6: Calculate and obtain the fracture toughness and shear displacement at the pre-crack tip in the end-load splitting test. The expressions are:

[0077]

[0078]

[0079] Among them, the bending modulus E involved in the above formula f and shear modulus G13 The expression of the delamination length a has been given in step 4. The relationship between fracture toughness and delamination length is as follows: Figure 4 As shown; In order to verify the effectiveness of the semi-analytical method for laminates of other materials, Figure 5 The calculation results of glass fiber / polyester unidirectional laminate are given;

[0080] Step 7: Draw and fit the relationship curve between fracture toughness and prefabricated crack tip shear displacement. The results are as follows: Figure 6 The fitting formula is shown below. For comparison, the results of the three calculation methods in the ISO 15114 standard, the values of the fitting parameters and the fitting degree R are also given. 2 As shown in Table 1;

[0081] G II (δ t * )=k1δ t * +k2

[0082] The fitting results show that the semi-analytical method proposed in this invention is in good agreement with the results obtained by the three calculation methods given in the ISO 15114 standard, and the fitting degree R 2 is greater than 0.96, proving the accuracy of the fitting formula used in step 7;

[0083] For the glass fiber / polyester unidirectional laminate, the relationship curve between fracture toughness and prefabricated crack tip shear displacement is also drawn and fitted. The results are as follows: Figure 7 The fitting formula is shown below. For the convenience of comparison, the results obtained by the experimental flexibility method and the beam model are also given, as well as the values of the fitting parameters and the fitting degree R. 2 As shown in Table 2;

[0084]

[0085] Table 1 Parameter values and R of carbon fiber / epoxy composite laminate data fitting using three calculation methods 2 value

[0086]

[0087] Table 2 Parameter values and R of glass fiber / polyester composite laminate data fitting using two calculation methods 2 value

[0088]

[0089] Step 8: Fracture toughness G obtained from step 7 II (δ t *) expression for the shear displacement δ of the prefabricated crack tip t * Taking the derivative, we get the bridging stress as follows:

[0090]

[0091]

[0092] For carbon fiber / epoxy composite laminates, the bridge stress is a constant, the same as k1, and the value of k1 is listed in Table 1. For glass fiber / polyester composite laminates, the bridge stress distribution is as follows Figure 8 shown.

[0093] Finally, taking the carbon fiber / epoxy composite laminate as an example, the obtained bridging stress is introduced into Figure 9 The trilinear constitutive cohesive force model shown in FIG is used to perform numerical simulation on the type II delamination expansion behavior of the laminate to further verify the semi-analytical method proposed in the present invention; the established finite element model is shown in FIG. Figure 10 As shown in the figure, the comparison between the experimental load-displacement response and the predicted results is as follows: Figure 11 As shown in the figure, it can be seen that the predicted results are in good agreement with the experimental results, which further verifies the applicability of the semi-analytical method proposed in the present invention for determining the fracture toughness and bridging stress of composite laminates in end-load splitting mode.

[0094] Some parts not described in detail in the present invention belong to the common knowledge of those skilled in the art;

[0095] The above description is only part of the specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person familiar with the art within the technical scope disclosed in the present invention should be covered by the protection scope of the present invention.

Claims

1. A semi-analytical method for determining the fracture toughness and bridging stress of composite laminates in end-loaded splitting mode, characterized by The following steps are involved: Step 1: Design and manufacture composite laminate specimens required for end-load splitting test; Step 2: Performing a composite material type II delamination extension test on the sample in step 1 using an end-load splitting test apparatus; Step 3, record the load and displacement obtained in the test, and calculate the compliance of the specimen based on the recorded data; The compliance C in step 3 is defined as the ratio of the displacement of the loading point to the applied load, that is: Where d and P are the displacement of the loading point and the applied load, respectively; Step 4: Measure the initial delamination length and delamination length of the sample during unloading and their corresponding sample flexibility to obtain the bending modulus E f and shear modulus G 13 and the expression of the layer length a; In step 4, the flexibility and the layer length have the following relationship: Where b and L are the width and length of the free end of the specimen, respectively, and h is half of the total thickness of the specimen; Substituting the measured initial delamination length and delamination length at unloading and their corresponding specimen compliance, i.e. (a0, C0) and (a1, C1), into the above formula, we can obtain: Step 5, calculate and obtain the expression of mode II fracture toughness; The formula for determining the mode II fracture toughness using the flexibility method in the steps is: Among them, G Ⅱ is the type II fracture toughness, N2 is the loading block and large displacement correction coefficient, and F2 is the large displacement correction factor; the expressions of N2 and F2 are: Where l1 and l2 are the sizes of the loading blocks; the values of θ2, θ3, and θ4 are 0, and the expressions of θ1 and θ5 are: Substituting the relationship between flexibility and delamination length in step 4 into the above equation, the expression for fracture toughness can be obtained as follows: Among them, the bending modulus E f and shear modulus G 13 The expression of the layer length a has been obtained through step 4; Step 6, calculate and obtain the expression of the shear displacement of the prefabricated crack tip; In step 6, a pair of unit loads in opposite directions are applied to the prefabricated crack tip. The shear displacement of the prefabricated crack tip can be obtained according to the unit load method, and the expression is: Among them, δ t * and a0 are the shear displacement and initial delamination length of the pre-crack tip, respectively; Step 7, drawing and fitting a relationship curve between fracture toughness and shear displacement at the prefabricated crack tip; The fitting formulas used in step 7 to describe the nonlinear and linear relationships between fracture toughness and prefabricated crack tip shear displacement are: G II (d t * )=k1δ t * +k2 Among them, G tip is the starting value of mode II delamination fracture toughness, K a ,K b ,K c ,K d ,k1 and k2 are fitting parameters; Step 8, G obtained from step 7 II (δ t * ) expression for the shear displacement δ of the prefabricated crack tip t * Take the derivative and get the bridging stress; The bridging stress in step 8 can be calculated by G II (δ t * ) expression is derived with respect to the prefabricated crack tip: where τ is the bridging stress.

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