A method for predicting the non-closed hysteresis loop of fiber reinforced ceramic matrix composites

Abstract

The present invention provides a method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic-based composite material, and belongs to the technical field of predicting a non-closed hysteresis loop of a composite material. The method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic-based composite material provided by the present invention first determines the matrix crack spacing according to a matrix random fracture model, and uses a fracture mechanics interface debonding criterion to determine the interface debonding length, the unloading interface reverse slip length, and the reloading interface new slip length, and then analyzes the fiber axial stress distribution during unloading and reloading on this basis, and then obtains the stress-strain relationship equation of the fiber-reinforced ceramic-based composite material during unloading and reloading, thereby predicting the non-closed hysteresis loop of the fiber-reinforced ceramic-based composite material. The method provided by the present invention can accurately predict the non-closed hysteresis behavior of fiber-reinforced ceramic-based composite materials.

Description

Technical Field

[0001] The invention relates to the technical field of composite material non-closed hysteresis loop prediction, in particular to a method for predicting a fiber-reinforced ceramic-based composite material non-closed hysteresis loop. Background Art

[0002] Fiber-reinforced ceramic-based composites have the advantages of high temperature resistance, corrosion resistance, low density, high specific strength and high specific modulus. Compared with high-temperature alloys, fiber-reinforced ceramic-based composites can withstand higher temperatures, reduce cooling airflow, and improve turbine efficiency. They have been used in aircraft engine combustion chambers, turbine guide blades, turbine casing rings, and tail nozzles.

[0003] In order to ensure the reliability and safety of fiber-reinforced ceramic matrix composites used in aircraft and aero-engine structures, researchers at home and abroad regard the development of fiber-reinforced ceramic matrix composite performance evaluation, damage evolution, strength and life prediction tools as the key to the airworthiness certification of fiber-reinforced ceramic matrix composite structural components. In order to ensure the reliability and safety of fiber-reinforced ceramic matrix composite structures during use, it is necessary to analyze the fatigue damage evolution of fiber-reinforced ceramic matrix composite structures. For the non-closed hysteresis behavior of fiber-reinforced ceramic matrix composites, no relevant theoretical prediction methods have been established. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic-based composite material. The method provided by the present invention can accurately predict the non-closed hysteresis behavior of a fiber-reinforced ceramic-based composite material.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0006] The present invention provides a method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic matrix composite material, comprising the following steps:

[0007] (1) Determine the matrix crack spacing based on the matrix random fracture model;

[0008] (2) Determine the interface debonding length, the reverse slip length of the unloading interface, and the new slip length of the reloading interface according to the interface debonding criterion of fracture mechanics;

[0009] (3) according to the interface slip mechanism during the unloading and reloading process, the fiber axial stress distribution equation during the unloading and reloading process is obtained by using the matrix crack spacing obtained in step (1) and the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2);

[0010] (4) according to the load transfer mechanism between the fiber and the matrix, the matrix crack spacing obtained in step (1), the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2), and the fiber axial stress distribution equation during the unloading and reloading process obtained in step (3) are used to obtain the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading and reloading process, thereby predicting the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material;

[0011] There is no time sequence limitation for step (1) and step (2).

[0012] Preferably, the matrix crack spacing in step (1) is as shown in Formula 1:

[0013]

[0014] Among them, L cracking is the matrix crack spacing, L sat is the crack spacing of the saturated matrix, σ m is the matrix axial stress, σ R is the matrix cracking characteristic stress, and m is the matrix Weibull modulus.

[0015] Preferably, the interface debonding length in step (2) is as shown in Formula 2:

[0016]

[0017] Among them, L debonding is the interface debonding length, σ max is the fatigue peak stress, V f is the volume content of fiber in the composite material, V m is the volume content of the matrix in the composite material, R f is the fiber radius, E f is the fiber elastic modulus, E m is the matrix elastic modulus, E c is the elastic modulus of the composite material, τ i is the friction shear stress in the interface debonding zone, Γ i is the interface debonding energy, and ρ is the shear lag model parameter.

[0018] Preferably, the reverse slip length of the unloading interface in step (2) is as shown in Formula 3:

[0019]

[0020] Among them, L counter_slip is the reverse slip length of the unloading interface, σ unloading To unload stress.

[0021] Preferably, the new slip length of the reloaded interface in step (2) is as shown in Formula 4:

[0022]

[0023] Among them, L new_slip is the new sliding length of the reloading interface, σ reloading To reload stress.

[0024] Preferably, the fiber axial stress distribution equation during the unloading process in step (3) is as shown in Formula 5:

[0025]

[0026] In the formula, σ f (x) is the fiber axial stress, x is the axial value, σ fo is the fiber axial stress in the interface bonding zone, σ mo is the axial stress of the matrix in the interface bonding area, L cracking is the matrix crack spacing.

[0027] Preferably, the fiber axial stress distribution equation during the reloading process in step (3) is as shown in Formula 6:

[0028] Preferably, the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading process in step (4) is as shown in Formula 7:

[0029]

[0030] Among them, ε unloading is the unloading strain, α c is the thermal expansion coefficient of the composite material, α f is the thermal expansion coefficient of the fiber, ΔT is the difference between the test temperature and the preparation temperature, η is the interface debonding ratio, and γ is the interface reverse slip ratio;

[0031] The η is determined by equation 8, and the γ is determined by equation 9:

[0032]

[0033]

[0034] Preferably, the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the reloading process in step (4) is as shown in Formula 10:

[0035]

[0036] Among them, ε reloading is the reloading strain, σ is the stress, is the new slip ratio of the interface;

[0037] Said Determined by formula 11:

[0038]

[0039] The present invention provides a method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic matrix composite material. First, the matrix crack spacing is determined according to a matrix random fracture model, and the interface debonding length, the unloading interface reverse slip length, and the reloading interface new slip length are determined using the fracture mechanics interface debonding criterion. Then, on this basis, the fiber axial stress distribution during the unloading and reloading process is analyzed, and then the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading and reloading process is obtained, so as to predict the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material. The method provided by the present invention can accurately predict the non-closed hysteresis behavior of the fiber-reinforced ceramic matrix composite material. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material in the present invention;

[0041] Figure 2 It is the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material experimentally and theoretically predicted in the present invention. DETAILED DESCRIPTION

[0042] The symbols, meanings and acquisition methods involved in the method for predicting the non-closed hysteresis loop of fiber-reinforced ceramic matrix composite materials provided by the present invention are summarized in Table 1. In the following specific implementation methods, unless otherwise specified, the meanings and acquisition methods of the symbols in each equation or relationship are based on the contents of Table 1 and will not be repeated one by one.

[0043] Table 1 Parameters in the method for predicting the non-closed hysteresis loop of fiber-reinforced ceramic matrix composites

[0044]

[0045]

[0046]

[0047] Note: In Table 1, composite material refers to fiber reinforced ceramic matrix composite material, fiber refers to the fiber in fiber reinforced ceramic matrix composite material, matrix refers to the matrix in fiber reinforced ceramic matrix composite material, axial direction refers to the stress loading direction, and interface refers to matrix / fiber interface.

[0048] Based on the description in Table 1, the specific implementation process of the method for predicting the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material provided by the present invention is described as follows:

[0049] (1) Determine the matrix crack spacing based on the matrix random fracture model;

[0050] (2) Determine the interface debonding length, the reverse slip length of the unloading interface, and the new slip length of the reloading interface according to the interface debonding criterion of fracture mechanics;

[0051] (3) according to the interface slip mechanism during the unloading and reloading process, the fiber axial stress distribution equation during the unloading and reloading process is obtained by using the matrix crack spacing obtained in step (1) and the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2);

[0052] (4) according to the load transfer mechanism between the fiber and the matrix, the matrix crack spacing obtained in step (1), the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2), and the fiber axial stress distribution equation during the unloading and reloading process obtained in step (3) are used to obtain the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading and reloading process, thereby predicting the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material;

[0053] There is no time sequence limitation for step (1) and step (2).

[0054] The present invention determines the matrix crack spacing according to the matrix random fracture model, and the matrix crack spacing is preferably as shown in Formula 1:

[0055]

[0056] Among them, L cracking is the matrix crack spacing, L sat is the crack spacing of the saturated matrix, σ m is the matrix axial stress, σ R is the matrix cracking characteristic stress, and m is the matrix Weibull modulus.

[0057] In the present invention, the saturated matrix crack spacing is a stable value of the matrix crack spacing; the present invention preferably adopts the formula shown in Formula 1, which can obtain the matrix crack spacing under different stresses.

[0058] The invention determines the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length according to the fracture mechanics interface debonding criterion.

[0059] In the present invention, the interface debonding length is preferably as shown in Formula 2:

[0060]

[0061] Among them, L debonding is the interface debonding length, σ max is the fatigue peak stress, V f is the volume content of fiber in the composite material, V m is the volume content of the matrix in the composite material, R f is the fiber radius, E f is the fiber elastic modulus, E m is the matrix elastic modulus, E c is the elastic modulus of the composite material, τ i is the friction shear stress in the interface debonding zone, Γ i is the interface debonding energy, and ρ is the shear lag model parameter.

[0062] In the present invention, the fracture mechanics interface debonding criterion can take into account the influence of interface debonding energy on interface debonding; the present invention preferably adopts the formula shown in Formula 2, which can accurately predict the interface debonding length.

[0063] In the present invention, the reverse slip length of the unloading interface is preferably as shown in Formula 3:

[0064]

[0065] Among them, L counter_slip is the reverse slip length of the unloading interface, σ unloading To unload stress.

[0066] In the present invention, the fracture mechanics interface debonding criterion can take into account the influence of the interface debonding energy on the extension of the interface reverse slip length; the present invention preferably adopts the formula shown in Formula 3, which can accurately predict the interface reverse slip length.

[0067] In the present invention, the new slip length of the reloading interface is preferably as shown in Formula 4:

[0068]

[0069] Among them, L new_slip is the new sliding length of the reloading interface, σ reloading To reload stress.

[0070] In the present invention, the fracture mechanics interface debonding criterion can take into account the influence of interface debonding energy on the extension of the new interface slip length; the present invention preferably adopts the formula shown in Formula 4, which can accurately predict the new interface slip length.

[0071] According to the interface slip mechanism during unloading and reloading, the present invention utilizes the matrix crack spacing, interface debonding length, unloading interface reverse slip length and reloading interface new slip length to obtain the fiber axial stress distribution equation during unloading and reloading.

[0072] In the present invention, the fiber axial stress distribution equation during the unloading process is preferably as shown in Formula 5:

[0073]

[0074] In the formula, σ f (x) is the fiber axial stress, x is the axial value, σ fo is the fiber axial stress in the interface bonding zone, σ mo is the axial stress of the matrix in the interface bonding area, L cracking is the matrix crack spacing.

[0075] As shown in Formula 5, when studying the axial stress distribution of the fiber during unloading, the present invention preferably studies the region from the matrix crack to the 1 / 2 distance between the adjacent matrix cracks, and more preferably divides this region into the interface reverse slip region [0~L counter_slip ]、interface slip zone [L counter_slip ~L debonding ] and the interface bonding area [L debonding ~L cracking / 2], and different calculation methods are proposed for different regions to improve the accuracy of the prediction results of the fiber axial stress distribution during unloading. counter_slip When x=L debonding When , the fiber axial stress during unloading can be substituted into any formula for calculation, preferably substituted into the formula for the interface slip zone for calculation.

[0076] The present invention preferably adopts the formula shown in Formula 5, which can obtain the fiber axial stress distribution in different areas during the unloading process.

[0077] In the present invention, the fiber axial stress distribution equation during the reloading process is preferably as shown in Formula 6:

[0078] As shown in Formula 6, when studying the axial stress distribution of the fiber during the reloading process, the present invention preferably studies the region from the matrix crack to the 1 / 2 distance between the adjacent matrix cracks, and more preferably divides this region into the interface new slip zone (0~L new_slip ), interface reverse slip zone (L new_slip ~L counter_slip), interface slip zone (L counter_slip ~L debonding ) and the interfacial bonding area (L debonding ~L cracking / 2), and different calculation methods are proposed for different regions to improve the accuracy of the prediction results of the fiber axial stress distribution during the reloading process. new_slip When x=L, the fiber axial stress during the reloading process can be substituted into any formula for calculation, preferably into the formula for the new slip zone of the interface for calculation; counter_slip When x=L, the fiber axial stress during the reloading process can be substituted into any formula for calculation, preferably into the formula for the interface reverse slip zone for calculation; debonding When , the fiber axial stress during the reloading process can be substituted into any formula for calculation, preferably substituted into the formula for the interface slip zone for calculation.

[0079] The present invention preferably adopts the formula shown in Formula 6, which can obtain the fiber axial stress distribution in different areas during the reloading process.

[0080] According to the load transfer mechanism between the fiber and the matrix, the present invention utilizes the matrix crack spacing, interface debonding length, unloading interface reverse slip length and reloading interface new slip length as well as the fiber axial stress distribution equation during the unloading and reloading process to obtain the stress-strain relationship equation of the fiber reinforced ceramic matrix composite material during the unloading and reloading process, thereby predicting the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material.

[0081] In the present invention, the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading process is preferably as shown in Formula 7:

[0082]

[0083] Among them, ε unloading is the unloading strain, α c is the thermal expansion coefficient of the composite material, α f is the thermal expansion coefficient of the fiber, ΔT is the difference between the test temperature and the preparation temperature, η is the interface debonding ratio, and γ is the interface reverse slip ratio;

[0084] The η is preferably determined by Formula 8, and the γ is preferably determined by Formula 9:

[0085]

[0086]

[0087] In the present invention, the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the reloading process is preferably as shown in Formula 10:

[0088]

[0089] Among them, ε reloading is the reloading strain, σ is the stress, is the new slip ratio of the interface;

[0090] Said It is preferably determined by formula 11:

[0091]

[0092] The present invention obtains stress-strain variation curves under unloading and reloading conditions according to the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during unloading and reloading, thereby obtaining a non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material.

[0093] In the present invention, in the formula involved in the above technical solution, the shear lag model parameter (ρ) is preferably calculated by a shear lag model, and the shear lag model is preferably a BHE shear lag model. The present invention has no special requirements for the calculation method, and a method familiar to those skilled in the art can be used.

[0094] The technical solution provided by the present invention is suitable for predicting the non-closed hysteresis behavior of fiber-reinforced ceramic-based composite materials, and the fiber-reinforced ceramic-based composite materials can specifically be a woven ceramic-based composite material; in an embodiment of the present invention, a woven SiC / SiC ceramic-based composite material is specifically used as a test sample, and its non-closed hysteresis loop is predicted.

[0095] The present invention first determines the matrix crack spacing based on the matrix random fracture model, and uses the fracture mechanics interface debonding criterion to determine the interface debonding length, the unloading interface reverse slip length, and the reloading interface new slip length. Then, on this basis, the fiber axial stress distribution during the unloading and reloading process is analyzed, and the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading and reloading process is obtained, so as to predict the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material. Specifically, Figure 1 is the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material of the present invention, Figure 1 It can be seen that during the unloading and reloading process, the hysteresis loop shows a non-closing phenomenon, which can achieve an accurate prediction of the non-closing hysteresis behavior of fiber-reinforced ceramic matrix composites.

[0096] The technical solutions in the present invention will be described clearly and completely below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0097] Example 1

[0098] According to the prediction method provided by the present invention, the required stress-strain relationship equation is established, the woven SiC / SiC ceramic matrix composite material is used as a test sample, and its non-closed hysteresis loop is predicted:

[0099] Provide parameters: V f =0.44, R f =6.5μm, E f =372GPa, E m =550GPa, α f =4.5×10 -6 / ℃,α m =4.6×10 -6 / ℃,τ i =50MPa,Γ i =2.5J / m 2 ;

[0100] The preparation temperature of the composite material is 1020°C, and the test temperature is 20°C, so ΔT = -1000°C;

[0101] Then, according to equations 1 to 11, the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during unloading and reloading is established to obtain the stress-strain relationship, and then the following is constructed: Figure 2 The stress-strain relationship curve shown in the figure obtains a non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material. Figure 2 The solid line in the middle is the stress-strain relationship curve constructed by the present scheme, and the different points are the actual test data. It can be seen that the shape and position of the non-closed hysteresis loop predicted by the method provided by the present invention are consistent with the experimental data, indicating that the method provided by the present invention can accurately predict the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material.

[0102] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting a non-closed hysteresis loop of a fiber-reinforced ceramic matrix composite material, characterized in that: Follow these steps: (1) Determine the matrix crack spacing based on the matrix random fracture model; (2) Determine the interface debonding length, the reverse slip length of the unloading interface, and the new slip length of the reloading interface according to the fracture mechanics interface debonding criterion; (3) according to the interface slip mechanism during the unloading and reloading process, the fiber axial stress distribution equation during the unloading and reloading process is obtained by using the matrix crack spacing obtained in step (1) and the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2); (4) according to the load transfer mechanism between the fiber and the matrix, the matrix crack spacing obtained in step (1), the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length obtained in step (2), and the fiber axial stress distribution equation during the unloading and reloading process obtained in step (3) are used to obtain the stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading and reloading process, thereby predicting the non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite material; There is no time sequence limit for step (1) and step (2); The interfacial debonding length in step (2) is as shown in Formula 2: Among them, L debonding is the interface debonding length, σ max is the fatigue peak stress, V f is the volume content of fiber in the composite material, V m is the volume content of the matrix in the composite material, R f is the fiber radius, E f is the fiber elastic modulus, E m is the matrix elastic modulus, E c is the elastic modulus of the composite material, τ i is the friction shear stress in the interface debonding zone, Γ i is the interface debonding energy, ρ is the shear lag model parameter; The reverse slip length of the unloading interface in step (2) is shown in Formula 3: Among them, L counter_slip is the reverse slip length of the unloading interface, σ unloading is the unloading stress; The new slip length of the reloaded interface in step (2) is shown in Formula 4: Among them, L new_slip is the new sliding length of the reloading interface, σ reloading To reload stress; The fiber axial stress distribution equation during the unloading process in step (3) is shown in Formula 5: In the formula, σ f (x) is the fiber axial stress, x is the axial value, σ fo is the fiber axial stress in the interface bonding zone, σ mo is the axial stress of the matrix in the interface bonding area, L cracking is the matrix crack spacing; The fiber axial stress distribution equation during the reloading process in step (3) is shown in Formula 6: The stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the unloading process in step (4) is shown in Formula 7: Among them, ε unloading is the unloading strain, α c is the thermal expansion coefficient of the composite material, α f is the thermal expansion coefficient of the fiber, ΔT is the difference between the test temperature and the preparation temperature, η is the interface debonding ratio, and γ is the interface reverse slip ratio; The η is determined by equation 8, and the γ is determined by equation 9: The stress-strain relationship equation of the fiber-reinforced ceramic matrix composite material during the reloading process in step (4) is shown in Formula 10: Among them, ε reloading is the reloading strain, σ is the stress, is the new slip ratio of the interface; Said Determined by formula 11:

2. The method according to claim 1, characterized in that The matrix crack spacing in step (1) is as shown in Formula 1: Among them, L sat is the crack spacing of the saturated matrix, σ m is the matrix axial stress, σ R is the matrix cracking characteristic stress, and m is the matrix Weibull modulus.

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