Composite high temperature fatigue life prediction method considering thickness effect

Abstract

The application discloses a composite high-temperature fatigue life prediction method considering thickness influence, which firstly considers the influence of composite fatigue life dispersion, considers the strength contribution of the thickness of fiber layers with different orientations, secondly, assumes that the tensile strength σ ft and the compressive strength σ ξc have the same trend to accurately describe the fatigue behavior at different temperatures, and finally, a life prediction model of compressive dominant fatigue damage is provided to accurately describe the fatigue behavior at different temperatures. The method is not only simple, but also has high accuracy and great practical significance.

Description

Technical Field

[0001] This invention can be used in the field of fatigue life prediction of composite laminates under tensile-compressive cyclic loading in high-temperature environments. It is a fatigue life prediction method proposed to address the problem of large dispersion of fatigue life in carbon fiber laminates under constant high temperature. Background Technology

[0002] Composite materials have become a research hotspot in aerospace and other fields. Carbon fiber, glass fiber, and boron fiber have proven to be excellent composite reinforcement materials, especially carbon fiber. Since approximately half of the aerospace composite materials produced worldwide are carbon fiber reinforced composites, carbon fiber and its composites have significant development and application opportunities. Carbon fiber reinforced composites are used in aerospace applications due to their designability, corrosion resistance, structural dimensional stability, and good fatigue fracture resistance, and are primarily manufactured through compression molding. Although the application areas of carbon fiber reinforced concrete are constantly expanding, certain aspects of its properties and damage mechanisms still lack sufficient understanding. High-temperature resistance, durability, humidity sensitivity, and the variability of mechanical properties under fatigue loads are important issues that require attention, especially given the large dispersion of fatigue data for carbon fiber reinforced composites, which severely limits their application prospects in fatigue-critical components in aerospace applications. Therefore, studying the fatigue life of carbon fiber reinforced composites at high temperatures is of great significance. Summary of the Invention

[0003] The purpose of this invention is to propose an accurate fatigue life prediction model for carbon fiber reinforced composites under uniaxial cyclic loading at constant high temperature.

[0004] The present invention proposes a method for predicting the high-temperature fatigue life of composite materials considering the influence of thickness, the steps of which are as follows:

[0005] Step (1): To characterize the effect of the percentage of fiber layers with different orientations in the thickness direction on the strength of the composite laminate, the thickness of fiber layers with different orientations in the sample is considered, and is defined as follows:

[0006] L θ =L θ1 +L θ2 +…+L θn

[0007] Where n is the number of fiber layers with the same orientation, and θ is the fiber orientation angle, which are 0°, 45°, and 90° respectively. θ1 L is the thickness of the first fiber layer in the θ direction. θ2 It is the thickness of the second fiber layer in the θ direction, L θn L is the thickness of the fiber layer in the θ direction of the nth layer. θThis indicates the total thickness of fiber layers with the same orientation.

[0008] Step (2): In reality, the strength of multidirectional laminates with the same fiber layers is not exactly the same. In order to consider the contribution of fiber layer thicknesses with different orientations to the strength, the strength contribution coefficient ξ is as follows:

[0009]

[0010] F = L0 × σ 0c +L 45 ×σ 45c +L 90 ×σ 90c

[0011] In the formula, F i and F e These represent the strength contributions of the fully oriented fiber laminates in the ideal and experimental samples, respectively. σ 0c σ 45c σ 90c The static compressive strengths L0 and L1, corresponding to fiber orientation angles of 0°, 45°, and 90°, respectively. 45 L 90 These are the total thicknesses of the 0°, 45°, and 90° layers, respectively.

[0012] Step (3): The static strength and fatigue load level, considering the influence of fiber layer thickness, can be determined as follows:

[0013] S ξ =ξS f

[0014] σ ζ =ζσ

[0015] In the formula, S ξ and σ ξ S represents the actual static strength and fatigue strength, respectively, taking into account the influence of fiber layer thickness. f ξ and σ represent the static strength and fatigue strength during the test, respectively. If ξ > 1, it indicates that the load-bearing capacity of the multi-directional laminate specimen is overestimated, and the actual load on the specimen during the fatigue test is greater than the applied load. ξ f If ξ < 1, it indicates that the bearing capacity of the multi-directional laminate specimen is underestimated, the actual load on the specimen during the fatigue test is less than the applied load, and S ξ f The same applies to static strength.

[0016] Step (4): Considering the influence of fiber layer thickness, calculate the actual ultimate tensile strength and compressive strength using the equation from step (3). Furthermore, the high-temperature environment only affects the properties of the resin matrix; considering T... m ​​The temperature-dependent factors affecting matrix properties, characterizing the effect of temperature on compressive strength, are shown below:

[0017]

[0018]

[0019] Where T u σ is the maximum compression temperature of the multi-directional laminated plate sample, T0 is the reference temperature (room temperature), and T is the experimental temperature. ct It is the residual compressive strength of the multi-directional laminate specimen; σ ξc σ represents the upper limit of the actual compressive strength of the multi-directional laminate specimen; λ is a constant related to the matrix material. As temperature increases, the residual compressive strength σ... ct The degradation is gradual, until the temperature T approaches T0. m Then degradation accelerates. Ultimately, the multi-directional laminate specimen cannot withstand compressive loads, σ ct Approaching zero.

[0020] Step (5): When describing the actual stress-life (SN) curve considering the effect of fiber layer thickness, use the power-law regression equation at different temperatures:

[0021]

[0022] In the formula, S ξ For the maximum actual fatigue load, N f σ' represents the number of failure cycles. f and m are the fatigue strength coefficient and fatigue strength index, respectively.

[0023] Step (6): Compression-driven fatigue testing of composite materials cannot satisfy the degradation of resin matrix properties and cannot accurately predict fatigue life. Therefore, it is assumed that σ' ft and compressive strength σ ξc Following the same trend, this paper proposes a life prediction model for compression-dominated fatigue damage to accurately describe fatigue behavior at different temperatures. This model considers compressive strength and S... ξ The slope trend of the -N curve with temperature is expressed as follows:

[0024]

[0025]

[0026] In the formula, σ' ft S is the residual fatigue strength coefficient of the multi-directional laminate specimen. t γ is the applied fatigue load, and γ is a material-related parameter.

[0027] The advantage of this invention is that the prediction results considering the influence of fiber layer thickness are significantly better than the original data. Comparing the two results, it was found that the prediction results considering the influence of fiber layer thickness are within a three-fold range at different temperatures, which also proves that fiber orientation and layer thickness have a significant impact on the strength dispersion of multidirectional laminate specimens. Therefore, considering the large dispersion of composite materials, the life prediction results of this model agree well with the experimental data and have certain practical engineering significance. Attached Figure Description

[0028] Figure 1 Schematic diagram of multi-directional laminated sample stack

[0029] Figure 2 (a) Fiber orientation distribution in an ideal laminate sample

[0030] (b) Distribution of different fiber orientations in actual laminated plate samples

[0031] Figure 3 Actual ultimate tensile and compressive strength considering the effect of fiber layer thickness

[0032] Figure 4 Multi-directional laminate S at different temperatures: (a) RT, (b) 100℃, (c) 200℃ ξ -N relation

[0033] Figure 5 The calculation flowchart of the method of the present invention.

[0034] Figure 6 Tests and predictions of fatigue life of laminates at different temperatures Detailed Implementation

[0035] The specific implementation steps of this invention are described in conjunction with the accompanying drawings:

[0036] Step (1): We know that the in-plane load-bearing capacity of fiber layers with different orientations is completely different, with the 0° layer having the strongest load-bearing capacity. Therefore, the percentage of laminates with smaller orientation angles in the total thickness of the composite laminate (especially the 0° laminate in this experiment) may significantly affect the strength of the composite laminate. To characterize the effect of the percentage of fiber layers with different orientations in the thickness direction on the strength of the composite laminate, we consider the thickness of fiber layers with different orientations in the sample, which is defined as follows:

[0037] L θ =L θ1 +L θ2 +…+L θn

[0038] Where n is the number of fiber layers with the same orientation, and θ is the fiber orientation angle, which are 0°, 45°, and 90° respectively. θ1L is the thickness of the first fiber layer in the θ direction. θ2 It is the thickness of the second fiber layer in the θ direction, L θn L is the thickness of the fiber layer in the θ direction of the nth layer. θ This indicates the total thickness of fiber layers with the same orientation.

[0039] Step (2): As Figure 2 As shown, the strength of multidirectional laminates with the same fiber layers is not exactly the same. To account for the contribution of fiber layer thicknesses with different orientations to the strength, the strength contribution coefficient ξ is as follows:

[0040]

[0041] F = L0 × σ 0c +L 45 ×σ 45c +L 90 ×σ 90c

[0042] In the formula, F i and F e These represent the strength contributions of the fully oriented fiber laminates in the ideal and experimental samples, respectively. σ 0c σ 45c σ 90c The static compressive strengths L0 and L1, corresponding to fiber orientation angles of 0°, 45°, and 90°, respectively. 45 L 90 These are the total thicknesses of the 0°, 45°, and 90° layers, respectively.

[0043] Step (3): The static strength and fatigue load level, considering the influence of fiber layer thickness, can be determined as follows:

[0044] S ζ =ξS f

[0045] σ ξ =ξσ

[0046] In the formula, S ξ and σ ξ S represents the actual static strength and fatigue strength, respectively, taking into account the influence of fiber layer thickness. f ξ and σ represent the static strength and fatigue strength during the test, respectively. If ξ > 1, it indicates that the load-bearing capacity of the multi-directional laminate specimen is overestimated, and the actual load on the specimen during the fatigue test is greater than the applied load. ξ f If ξ < 1, it indicates that the bearing capacity of the multi-directional laminate specimen is underestimated, the actual load on the specimen during the fatigue test is less than the applied load, and S ξ f The same applies to static strength.​​

[0047] Step (4): Considering the influence of fiber layer thickness and the actual ultimate tensile strength and compressive strength calculated by the equation in step (3), respectively... Figure 3 The values ​​are plotted relative to the test temperature. Table 1 also lists all these experimental data and calculation results obtained at different temperatures. It can be seen that the actual tensile strength and compressive strength are uniformly distributed at different temperatures. Furthermore, the high-temperature environment only affects the properties of the resin matrix, considering T... m The temperature-dependent factors affecting matrix properties, characterizing the effect of temperature on compressive strength, are shown below:

[0048]

[0049]

[0050] Where T u σ is the maximum compression temperature of the multi-directional laminated plate sample, T0 is the reference temperature (room temperature), and T is the experimental temperature. ct It is the residual compressive strength of the multi-directional laminate specimen; σ ξc σ represents the upper limit of the actual compressive strength of the multi-directional laminate specimen; λ is a constant related to the matrix material. As temperature increases, the residual compressive strength σ... ct The degradation is gradual, until the temperature T approaches T0. m Then degradation accelerates. Ultimately, the multi-directional laminate specimen cannot withstand compressive loads, σ ct Approaching zero.

[0051] Step (5): The fatigue strength of the multi-directional laminate specimens also exhibits significant dispersion. Table 2 presents the fatigue parameters and actual fatigue strength based on Step 3 for all multi-directional laminate specimens tested under constant amplitude loading. It can be observed that the distribution of the fiber layers has a significant impact on both the static strength and fatigue strength of the multi-directional laminate specimens. The actual static and fatigue strengths calculated in Step (3) indicate that considering the influence of fiber layer thickness can be considered an effective method to reduce life dispersion under fatigue loading. Therefore, for the multi-directional laminate samples used in this study, considering the inherent physical differences within the samples is necessary and meaningful.

[0052] like Figure 4 As shown, after plotting the actual stress-life (SN) diagram considering the effect of fiber layer thickness, the power-law regression equations at different temperatures were determined:

[0053]

[0054] In the formula, S ξ For the maximum actual fatigue load, N f σ' represents the number of failure cycles. fand m are the fatigue strength coefficient and fatigue strength index, respectively.

[0055] Step (6): Assume σ' under high temperature conditions ft and compressive strength σ ξc Following the same trend, this paper proposes a life prediction model for compression-dominated fatigue damage to accurately describe fatigue behavior at different temperatures. This model considers compressive strength and S... ξ The slope trend of the -N curve with temperature is expressed as follows:

[0056]

[0057]

[0058] In the formula, σ' ft S is the residual fatigue strength coefficient of the multi-directional laminate specimen. t γ is the applied fatigue load, and γ is a material-related parameter.

[0059] like Figure 6 As shown, the model's prediction results considering the influence of fiber layer thickness are within three times, and the prediction effect is good. This also proves that fiber orientation and layer thickness have a great influence on the strength dispersion of multidirectional laminate specimens.

[0060] This invention provides a method for predicting the fatigue life of carbon fiber reinforced composites based on the influence of material thickness and constant high temperature. The method comprises the following steps: Step (1) characterizing the influence of the percentage of fiber layers with different orientations in the thickness direction on the strength of the composite laminate and defining it by formula; Step (2) considering the contribution of fiber layer thickness with different orientations to the strength, and the strength contribution coefficient ξ; Step (3) determining the static strength and fatigue load level affected by fiber layer thickness; Step (4) introducing T m The matrix properties are represented based on the effect of temperature; step (5) power-law regression equations at different temperatures; step (6) a life prediction model for compression-dominated fatigue damage is proposed to accurately describe fatigue behavior at different temperatures.

[0061] Table 1 Compressive strength and strength contribution coefficient ξ of the compressed specimen

[0062]

[0063]

[0064] Table 2 Fatigue load and strength contribution coefficient ξ of fatigue specimens

[0065]

[0066]

Claims

1. A method for predicting the high-temperature fatigue life of composite materials considering the influence of thickness, comprising the following steps: Step (1): To characterize the effect of the percentage of fiber layers with different orientations in the thickness direction on the strength of the composite laminate, the thickness of fiber layers with different orientations in the sample is considered, and is defined as follows: ； Where n is the number of fiber layers with the same orientation, and θ is the fiber orientation angle, which are 0°, 45° and 90° respectively; It is the thickness of the first fiber layer in the θ direction. It is the thickness of the second fiber layer in the θ direction, and so on. It is the thickness of the fiber layer in the θ direction of the nth layer. This indicates the total thickness of fiber layers with the same orientation angle; Step (2): In reality, the strength of multidirectional laminates with the same fiber layers is not exactly the same. In order to consider the contribution of fiber layer thicknesses with different orientations to the strength, the strength contribution coefficient ξ is as follows: ； ； In the formula, F i and F e These are the contribution strengths of the all-oriented fiber laminates in the ideal and experimental specimens, respectively; σ 0c、 σ 45c、 σ 90c These are the static compressive strengths of the fiber layer corresponding to fiber orientation angles of 0°, 45°, and 90°, L0 and L1. 45 L 90 These are the total thicknesses of the 0°, 45°, and 90° layers, respectively. Step (3): The static strength and fatigue load levels, considering the influence of fiber layer thickness, are determined as follows: ； ； In the formula, S ξ and σ ξ S represents the actual static strength and fatigue strength, respectively, taking into account the influence of fiber layer thickness. ƒ σ and σ' represent the static strength and fatigue strength during the test, respectively. Step (4): Considering the influence of fiber layer thickness, calculate the actual ultimate tensile strength and compressive strength using the equation in step (3); furthermore, the high-temperature environment only affects the properties of the resin matrix, considering T m The temperature-dependent factors affecting matrix properties, characterizing the effect of temperature on compressive strength, are shown below: ； ； Where T u σ is the maximum compression temperature of the multi-directional laminated plate sample, T0 is the reference temperature, and T is the experimental temperature; ct It is the residual compressive strength of the multi-directional laminate specimen; σ ξc σ represents the actual ultimate compressive strength of the multidirectional laminate specimen; λ is a constant related to the matrix material; as temperature increases, the residual compressive strength σ... ct The degradation is gradual, until the temperature T approaches T0. u Then degradation accelerates; ultimately, the multi-directional laminate specimen cannot withstand compressive loads, σ ct Approaching zero; Step (5): When describing the actual stress-life SN curve considering the effect of fiber layer thickness, use the power-law regression equation at different temperatures: ； In the formula, For the maximum actual fatigue load, N ƒ This represents the number of failure cycles. and m are the fatigue strength coefficient and fatigue strength index, respectively; Step (6): and compressive strength σ ξc A life prediction model for compression-dominated fatigue damage exhibiting the same trend, to accurately describe fatigue behavior at different temperatures, considering compressive strength and S... ξ -N curve slope trend with temperature; ； ； In the formula, It is the residual fatigue strength coefficient of the multi-directional laminate specimen. γ is the applied fatigue load, and γ is a material-related parameter.

2. The method for predicting the high-temperature fatigue life of composite materials considering the influence of thickness according to claim 1, characterized in that: In step (3), if ξ>1, it indicates that the bearing capacity of the multi-directional laminate specimen is overestimated, and the actual load on the specimen during the fatigue test is greater than the applied load, S ξ >S ƒ If ξ < 1, it indicates that the bearing capacity of the multi-directional laminate specimen is underestimated, the actual load on the specimen during the fatigue test is less than the applied load, and S ξ ƒ The same applies to static strength.​

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