A method for predicting tensile strength of fiber reinforced composites considering micro-crack propagation failure

Abstract

The application discloses a kind of fiber reinforced composite tensile strength prediction method considering micro crack propagation failure, comprising the following steps: step 1: according to matrix material tensile strength and fracture toughness, calculate micro crack average half length a;Step 2: according to fiber diameter, spacing and the average half length a of matrix micro crack obtained in step 1, shape correction factor F is calculated;Step 3: according to fiber diameter, spacing, elastic modulus and matrix material elastic modulus, calculate the shared load correction function f;Step 4: according to the shape correction factor obtained in step 2, the shared load correction function obtained in step 3 and matrix material tensile strength, calculate fiber reinforced composite tensile strength;The method solves the problem of accurate prediction of fiber reinforced composite tensile strength, and the method can be simultaneously applied to the tensile strength prediction of other wire reinforced composites, such as reinforcing steel.

Description

Technical Field

[0001] This invention relates to the technical field of tensile strength methods for fiber-reinforced composite materials, and more specifically to a method for predicting the tensile strength of fiber-reinforced composite materials that takes into account microcrack propagation failure. Background Technology

[0002] Carbon fiber and other materials, due to their excellent tensile strength, have been widely used in composite materials to significantly improve the load-bearing capacity of structural components. Accurate prediction of the tensile strength of the fiber-matrix composite material is a prerequisite for the design and evaluation of fiber-reinforced composite materials; therefore, accurate prediction of the tensile strength of fiber-reinforced materials is crucial. Currently, theoretical and simulation methods are commonly used to predict the tensile strength of fiber-reinforced composite materials. Simulation methods often use finite element method (FE) software to create three-dimensional cells (RVE) and perform cell stretching to obtain the material's tensile strength. However, simulation methods suffer from inefficiency and indirectness during iterative design processes; theoretical prediction methods, on the other hand, are efficient and convenient.

[0003] Currently, the relationship between the tensile strength of composite materials and the fiber ratio, fiber modulus, etc., is often derived simply through the load-sharing mechanism. Generally, the predicted results for fiber reinforcement show a stronger reinforcing effect than the matrix material. However, actual experimental evidence shows that the strength of fiber is degraded due to its heterogeneous inclusion, and it does not necessarily produce an absolute reinforcing effect. Therefore, the predicted values ​​are often higher than the experimental values ​​and have a large error. Thus, an accurate method for predicting the tensile strength of fiber-reinforced composite materials is still lacking. Summary of the Invention

[0004] The objective of this invention is to provide a method for predicting the tensile strength of fiber-reinforced composite materials that takes into account microscopic defects, fiber reinforcement, and the effect of defect inclusion reduction. This method is convenient to use and has a wide range of applications, and can be applied to materials such as press-fit / cast explosives and concrete.

[0005] The present invention achieves the above objectives through the following technical solutions:

[0006] A method for predicting the tensile strength of fiber-reinforced composites considering microcrack propagation failure includes the following steps:

[0007] Step 1: Calculate the average half-length 'a' of the microcracks based on the tensile strength and fracture toughness of the matrix material;

[0008]

[0009] Step 2: Calculate the shape correction factor F based on the fiber diameter, spacing, and the average half-length a of the matrix microcracks obtained in Step 1;

[0010] Step 3: Calculate the shared load correction function f(w,d,E) based on the fiber diameter, spacing, elastic modulus, and matrix material elastic modulus. 纤维 E 基体 (arrangement dimension), where d is the fiber diameter, w is the fiber spacing, and E 纤维 E represents the fiber modulus. 基体 The matrix modulus;

[0011] Step 4: Calculate the tensile strength of the fiber-reinforced composite material based on the shape correction factor obtained in Step 2, the shared load correction function obtained in Step 3, and the tensile strength of the matrix material.

[0012]

[0013] Where f is the fiber-shared load correction function, σ t0 σ represents the tensile strength of the composite material. t,基体 This represents the tensile strength of the matrix material.

[0014] In step 2,

[0015] The shape correction factor F can be divided into the following cases:

[0016] Unidirectional fiber: The shape correction factor parallel to the fiber arrangement direction is F = 1, and the shape correction factor perpendicular to the fiber arrangement direction is F = F1(s1)F2(s2);

[0017] Bidirectional fibers: The shape correction factor parallel to the fiber arrangement plane is F = F1(s1)F2(s2), and the shape correction factor perpendicular to the fiber arrangement plane is F = F1 2 (s1)F2 2 (s2);

[0018] Triaxial fiber: shape correction factor is F = F1 2 (s1)F2 2 (s2);

[0019] The calculation methods for F1(s1) and F2(s2) are as follows;

[0020]

[0021]

[0022] In step 2, F2(s2) can be calculated in another way:

[0023]

[0024] In step 3

[0025] Depending on the arrangement direction, f(w,d,E)纤维 E 基体 The arrangement dimension can be divided into three cases:

[0026] When fibers are arranged in one direction, the correction function for the shared load along the parallel and perpendicular fiber directions is:

[0027]

[0028] When the fibers are arranged in two directions, the correction functions for the shared load parallel to and perpendicular to the fiber arrangement plane are respectively,

[0029]

[0030] When three-dimensional fibers are arranged, the correction function for the shared load in all directions is the same.

[0031]

[0032] The beneficial effects of this invention compared to the prior art are:

[0033] 1) This invention provides a method for predicting the tensile strength of fiber-reinforced composite materials considering microcrack propagation failure;

[0034] 2) This prediction method considers both the fiber reinforcement effect and the fiber inclusion reduction effect, resulting in high prediction accuracy and wide applicability;

[0035] 3) This prediction method does not require simulation and the prediction process is convenient. Attached Figure Description

[0036] Figure 1 Schematic diagram of the double-edged sword effect in fiber-reinforced materials

[0037] Figure 2 Schematic diagram of fiber weakening effect calculation Detailed Implementation

[0038] The present invention will be further described below with reference to embodiments. These embodiments are merely some, not all, of the embodiments of the present invention. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention.

[0039] This invention proposes a method for predicting the tensile strength of fiber-reinforced composites considering microcrack propagation failure. This method solves the problem of accurate prediction of the tensile strength of fiber-reinforced composites and can also be applied to the prediction of the tensile strength of composites reinforced with other wires, such as steel bars.

[0040] Example 1

[0041] Fiber-reinforced composites such as Figure 1 As shown, when a load is applied in the vertical direction, the fibers parallel to the loading direction will share the load with the matrix, thus producing a reinforcing effect on the material; however, the fibers perpendicular to the loading direction will not only fail to share the load, but will also cause higher interfacial stress due to the large difference in modulus between the fiber and matrix materials, further leading to interfacial tensile failure and defects. Therefore, the fibers perpendicular to the loading direction will have a weakening effect on the material.

[0042] Regarding the reinforcing effect, based on the fiber-shared load, the equivalent tensile strength of the composite material without considering the weakening effect is:

[0043] σ t0 =f(w,d,E) 纤维 E 基体 (arrangement dimension)σ t,基体 (1)

[0044] Where, f(w,d,E) 纤维 E 基体 , where arrangement dimension) is the fiber-shared load correction function, σ t0 σ represents the tensile strength of the composite material. t,基体 d is the tensile strength of the matrix material, w is the fiber diameter, and E is the fiber spacing. 纤维 E represents the fiber modulus. 基体 The matrix modulus.

[0045] Depending on the arrangement direction, f(w,d,E) 纤维 E 基体 The arrangement dimension can be divided into three cases:

[0046] ① When the fibers are arranged in one direction, the correction function for the shared load along the parallel and perpendicular fiber directions is:

[0047]

[0048] ② When the fibers are arranged in two directions, the correction functions for the shared load parallel to and perpendicular to the fiber arrangement plane are respectively,

[0049]

[0050] ③ When the three-dimensional fiber arrangement is used, the load correction function for all directions is the same.

[0051]

[0052] Regarding the defect mitigation effect, since brittle matrix materials contain widely distributed microcracks / microdefects, failure during tensile testing is often dominated by microcrack propagation. For a microcrack length of 2a, the stress intensity factor is...

[0053]

[0054] In the formula: K I σ is the stress intensity factor, a is the tensile stress, a is the half-length of the microcrack in the matrix material, and F is the shape correction factor.

[0055] For the matrix material, the shape correction factor is 1, i.e.

[0056]

[0057] Among them, K IC For the fracture toughness of the matrix material, σ t,基体 This represents the strength of the matrix material without the introduction of fibers.

[0058] The introduction of fibers will further increase microcracks, such as Figure 2 As shown, the defects introduced by the fibers are equivalent to initial microcracks connecting the matrix near the fibers. Furthermore, due to the spatial distribution of the fibers, the interaction between these microdefects must also be considered. Therefore, for the matrix material in fiber-reinforced materials, the relationship between its fracture toughness and the maximum tensile stress it can withstand is as follows:

[0059]

[0060] In the formula: F is the shape correction factor.

[0061] Taking into account both equations (6) and (7), the introduction of fibers causes a degradation in the strength of the matrix material.

[0062]

[0063] σ t，基体0 σ represents the strength of the matrix material considering the effects of fiber defects after fiber introduction; that is, the strength of the matrix material after the strength degradation caused by the introduction of fibers. t,基体 This represents the strength of the matrix material without the introduction of fibers.

[0064] Consulting any fracture mechanics handbook, the shape correction factor for a circular inclusion-bonded edge crack is:

[0065]

[0066] In the formula: d is the fiber diameter.

[0067] The shape correction factor for multi-crack interactions is:

[0068]

[0069] or

[0070]

[0071] In the formula: w is the fiber spacing.

[0072] The overall shape correction factor can be categorized into the following cases:

[0073] ① Unidirectional fiber: The shape correction factor parallel to the fiber arrangement direction is F = 1, and the shape correction factor perpendicular to the fiber arrangement direction is F = F1(s1)F2(s2);

[0074] ② Bidirectional fiber: The shape correction factor parallel to the fiber arrangement plane is F = F1(s1)F2(s2), and the shape correction factor perpendicular to the fiber arrangement plane is F = F1 2 (s1)F2 2 (s2);

[0075] ③ Triaxial fibers: The shape correction factor is F = F1 2 (s1)F2 2 (s2).

[0076] Combining the reinforcing effect formula (1) and the weakening effect formula (8), the formula for predicting the tensile strength of fiber-reinforced composite materials can be obtained as follows:

[0077]

[0078] The following needs to be explained: This prediction method requires that the matrix material fails before the fiber material during tensile failure. Therefore, the limitation for applying this method is that the fiber failure strain, i.e., the failure stress, is higher than that of the matrix material.

[0079] Specific implementation plan:

[0080] 1) Calculate the average half length a of the microcrack based on the tensile strength and fracture toughness of the matrix material, or give the average half length a of the microcrack directly based on experiments or experience;

[0081]

[0082] 2) Calculate the shape correction factor F based on the fiber diameter, spacing, and half-length a of the matrix microcracks obtained in step 1).

[0083] The shape correction factor can be categorized into the following cases:

[0084] ① Unidirectional fiber: The shape correction factor parallel to the fiber arrangement direction is F = 1, and the shape correction factor perpendicular to the fiber arrangement direction is F = F1(s1)F2(s2);

[0085] ② Bidirectional fiber: The shape correction factor parallel to the fiber arrangement plane is F = F1(s1)F2(s2), and the shape correction factor perpendicular to the fiber arrangement plane is F = F1 2 (s1)F2 2(s2);

[0086] ③ Triaxial fibers: The shape correction factor is F = F1 2 (s1)F2 2 (s2).

[0087] The calculation methods for F1(s1) and F2(s2) are as follows;

[0088]

[0089]

[0090] or

[0091]

[0092] 3) Calculate the shared load correction function f(w,d,E) based on the fiber diameter, spacing, elastic modulus, and matrix material elastic modulus. 纤维 E 基体 (arrangement dimension);

[0093] Depending on the arrangement direction, f(w,d,E) 纤维 E 基体 The arrangement dimension can be divided into three cases:

[0094] ① When the fibers are arranged in one direction, the correction function for the shared load along the parallel and perpendicular fiber directions is:

[0095]

[0096] ② When the fibers are arranged in two directions, the correction functions for the shared load parallel to and perpendicular to the fiber arrangement plane are respectively,

[0097]

[0098] ③ When the three-dimensional fiber arrangement is used, the load correction function for all directions is the same.

[0099]

[0100] 4) Calculate the tensile strength of the fiber-reinforced composite material based on the shape correction factor obtained in step 2), the shared load correction function obtained in step 3), and the tensile strength of the matrix material;

[0101]

[0102] This invention has been successfully applied to explosive materials at the Institute of Chemical Materials, China Academy of Engineering Physics, enabling accurate testing of the tensile strength of fiber-reinforced explosive materials and achieving excellent application results.

[0103] The elastic modulus of the selected explosive material is E.基体 =6GPa, tensile strength is σ t,基体 =6MPa, fracture toughness is K IC =0.3MPa·m 0.5 The microcrack size is a = 0.8 mm, and the selected fiber elastic modulus is E. 纤维 =300GPa, fiber diameter d=0.218mm, fiber spacing w=3mm, fibers are arranged in one direction, and the loading direction is parallel to the fiber arrangement direction.

[0104] 1) The average half-length of the microcrack, a = 0.8 mm, was calculated based on the tensile strength and fracture toughness of the matrix material;

[0105]

[0106] 2) Calculate the shape correction factor F based on the fiber diameter, spacing, and half-length a of the matrix microcracks obtained in step 1). In this example, the fibers are unidirectional, so the shape correction factor parallel to the fiber arrangement direction is F = 1.

[0107] 3) Calculate the shared load correction function f(w,d,E) based on the fiber diameter, spacing, elastic modulus, and matrix material elastic modulus. 纤维 E 基体 (arrangement dimension); In this example, it is a unidirectional fiber, and the loading direction is parallel to the fiber direction, therefore;

[0108]

[0109] 4) Calculate the tensile strength of the fiber-reinforced composite material based on the shape correction factor obtained in step 2), the shared load correction function obtained in step 3), and the tensile strength of the matrix material;

[0110]

[0111] The tensile strength of the composite material in this case is 7.2 MPa.

[0112] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the tensile strength of fiber-reinforced composite materials considering microcrack propagation failure, characterized in that, Includes the following steps: Step 1: Calculate the average half-length 'a' of the microcracks based on the tensile strength and fracture toughness of the matrix material; ； Step 2: Calculate the shape correction factor F based on the fiber diameter, spacing, and the average half-length a of the matrix microcracks obtained in Step 1; Step 3: Calculate the shared load correction function based on fiber diameter, spacing, elastic modulus, and matrix material elastic modulus. Where d is the fiber diameter, w is the fiber spacing, and E 纤维 E represents the fiber modulus. 基体 The matrix modulus; Step 4: Calculate the tensile strength of the fiber-reinforced composite material based on the shape correction factor obtained in Step 2, the shared load correction function obtained in Step 3, and the tensile strength of the matrix material. ， Where f is the fiber-shared load correction function, σ t0 σ represents the tensile strength of the composite material. t,基体 The tensile strength of the matrix material; In step 3 Depending on the orientation of the arrangement There are three scenarios: When fibers are arranged in one direction, the correction function for the shared load along the parallel and perpendicular fiber directions is: When the fibers are arranged in two directions, the correction functions for the shared load parallel to and perpendicular to the fiber arrangement plane are respectively, When three-dimensional fibers are arranged, the correction function for the shared load in all directions is the same. 。 2. The method for predicting the tensile strength of fiber-reinforced composite materials considering microcrack propagation failure according to claim 1, characterized in that, In step 2, The shape correction factor F can be divided into the following cases: Unidirectional fibers: The shape correction factor parallel to the fiber arrangement direction is F=1, and the shape correction factor perpendicular to the fiber arrangement direction is... ; Bidirectional fibers: The shape correction factor parallel to the fiber arrangement plane is... The shape correction factor perpendicular to the fiber arrangement plane is ; Triaxial fiber: shape correction factor is ; in, and The calculation method is as follows; ， 。 3. The method for predicting the tensile strength of fiber-reinforced composite materials considering microcrack propagation failure according to claim 2, characterized in that, In step 2, There is another calculation method: .

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