A method for calculating an oxidation constitutive model of a fiber bundle ceramic matrix composite material

Abstract

The application discloses a kind of fibre bundle ceramic matrix composite oxidation constitutive model calculation method, comprising: constructing ceramic matrix composite oxidation kinetics model, the oxygen concentration distribution in crack depth direction is calculated;Determine carbon-oxygen reaction rate, deduce the change relation of tensile strength of C fibre bundle and oxidation temperature, oxygen concentration;According to the tensile strength of C fibre bundle at different temperatures, the strength distribution of C fibre in-situ monofilament at room temperature is equivalently offset;Based on shear lag model, the fibre stress distribution of interface slip zone, positive slip zone and reverse slip zone between fibre and matrix is calculated;The distribution of matrix crack propagation and crack spacing is calculated, and the mechanical response of matrix is obtained;According to the mechanical damage model of fibre and matrix, the stress-strain response curve of fibre bundle ceramic matrix composite in high-temperature oxidation environment is calculated.The application can accurately describe the damage evolution of fibre, interface and matrix in the oxidation process, and greatly reduce the amount of calculation.

Description

Technical Field

[0001] This invention relates to the field of materials mechanics, specifically to a method for calculating the oxidative constitutive model of fiber bundle ceramic matrix composites. Background Technology

[0002] Fiber bundle ceramic matrix composites (CMCs) are widely used in high-temperature structural components such as aerospace engines due to their high strength, good high-temperature resistance, and low density. When these materials operate in extreme environments, they are often subjected to alternating complex operating conditions. Simultaneously, the high-temperature oxidizing environment causes irreversible chemical reactions within the material, resulting in various damage modes such as interfacial debonding, fiber oxidation, and matrix cracking, thus significantly affecting the mechanical properties of CMCs.

[0003] The mechanical behavior of ceramic matrix composites exhibits significant nonlinear characteristics, and their complex microstructure and damage evolution make accurate prediction of material properties difficult. Especially under high-temperature oxidizing conditions, oxygen diffuses into the material interior through matrix cracks and pores, inducing interfacial oxidation and fiber degradation, leading to a continuous decrease in material strength and stiffness. This cumulative effect of micro-damage makes the macroscopic mechanical response of the material even more challenging. Summary of the Invention

[0004] The purpose of this invention is to disclose a method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites. By studying oxygen diffusion, oxidation reaction rate, and the microscopic damage evolution mechanism of the material, a mechanical response model suitable for the multi-component coupling effect of fibers, interfaces, and matrix under high-temperature oxidation conditions is established. This invention fully considers the strength decay, crack propagation, and nonlinear deformation characteristics of ceramic matrix composites under high-temperature oxidation conditions, and can accurately describe the oxidation constitutive relationship of the material at different temperatures.

[0005] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites, the method comprising the following steps:

[0007] S1: Based on the mixing and diffusion mechanism of oxygen in the crack channel, an oxidation kinetic model of ceramic matrix composites is constructed to calculate the oxygen concentration distribution in the crack depth direction;

[0008] S2: Determine the carbon-oxygen reaction rate and deduce the relationship between the tensile strength of C fiber bundles and the changes in oxidation temperature and oxygen concentration;

[0009] S3: Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted;

[0010] S4: Based on the shear lag model, calculate the stress distribution in the fiber and matrix respectively;

[0011] S5: The critical strain energy method is used to calculate the distribution of crack propagation and crack spacing in the matrix, and to obtain the mechanical response of the matrix;

[0012] S6: Based on the mechanical damage model of the fiber and the matrix, calculate the stress-strain response curve of the fiber bundle ceramic matrix composite material under high temperature oxidation environment.

[0013] As a preferred example, in step S1, based on the steady-state diffusion assumption, the oxygen concentration distribution along the crack depth direction satisfies the following differential equation:

[0014]

[0015] In the formula, The diffusion flux within the crack channel, This represents the oxygen concentration at an oxidation time t at a crack depth y in the coating. To control the rate at which oxygen is consumed by chemical reactions within the body.

[0016] As a preferred example, in step S1, the diffusion behavior of oxygen inside the crack is described by a mixed diffusion model, and the diffusion flux expression is:

[0017]

[0018] In the formula, D eff is the equivalent diffusion coefficient of oxygen.

[0019] As one preferred example, in step S1, the chemical reaction consumption rate of oxygen is... The calculation formula is:

[0020]

[0021] In the formula, k(T) is the reaction rate constant at temperature T, which follows the Arrhenius equation:

[0022]

[0023] In the formula, k0 is the pre-exponential factor of the reaction rate constant; E a R is the activation energy of the reaction. g is the gas constant.

[0024] Step S2 further includes:

[0025] Assuming that the fiber strength during oxidation is directly proportional to its bearing area, then the fiber strength at time t is:

[0026]

[0027] In the formula, It is the strength of intact fibers, R f (t) represents the fiber radius at time t, R f0 The initial fiber radius;

[0028] Step S3 further includes:

[0029] Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted, and the shift amount Δσ(T,t) is expressed as:

[0030]

[0031] In the formula, σ0 is the fiber breaking strength at room temperature, and R f (T,t) represents the fiber radius after oxidation at temperature T for time t.

[0032] 6. The method for calculating the constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that step S4 further includes:

[0033] According to the shear lag model, the stress distribution on the fiber is as follows:

[0034]

[0035] In the formula, σ is the external load acting on both ends of the fiber bundle composite material, and v f It is the volume percentage of the fiber, τ i It is the interfacial shear stress between the fiber and the matrix in the slip zone, where x is the size of the slip zone and d is the shear stress at the interface. f σ is the sliding distance. f0 The normal stress in the bonded zone is numerically equal to the fiber stress when the matrix cracks and when no interfacial debonding occurs, where L is the matrix crack spacing and r is the fiber stress. f The initial fiber radius;

[0036] The stress distribution on the matrix is ​​as follows:

[0037]

[0038] In the formula, σ m0 For the normal stress of the matrix in the bonding zone, v m It is the volume percentage of the matrix.

[0039] Step S5 further includes:

[0040] According to the critical strain energy criterion, crack propagation occurs when the strain energy of the matrix reaches a critical value. The formula for calculating the critical strain energy is as follows:

[0041]

[0042] Among them, U m A is the critical strain energy of the matrix. m d is the cross-sectional area of ​​the matrix. f This represents the sliding distance.

[0043] As a preferred example, in step S6, the average stress and strain of the fiber bundle ceramic matrix composite material are calculated using the mixing law:

[0044]

[0045] In the formula, σ c For material stress, ε c For material strain.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] This invention provides a method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites, which can efficiently predict the mechanical properties of such composites in high-temperature oxidizing environments. The proposed oxidation constitutive model of fiber bundle ceramic matrix composites combines oxygen diffusion and oxidation damage mechanisms. Based on the material composition parameters of fiber bundle ceramic matrix composites at different temperatures, the tensile stress-strain response curves of the composites are calculated, thus accurately describing the damage evolution of fibers, interfaces, and the matrix during oxidation. Furthermore, the simplified calculation method significantly reduces the computational load, demonstrating strong engineering application value. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of an oxygen diffusion model;

[0049] Figure 2 This is a schematic diagram showing the variation of oxygen concentration with crack depth under different temperature conditions.

[0050] Figure 3 This is a simulation graph showing the relationship between fiber strength and oxidation time and temperature.

[0051] Figure 4 Figure 1 shows the strength distribution of carbon fibers at different oxidation temperatures.

[0052] Figure 5 Schematic diagram of constitutive prediction results for oxidation at different temperatures;

[0053] Figure 6 The flowchart shows the calculation method for the oxidative constitutive model of fiber bundle ceramic matrix composites. Detailed Implementation

[0054] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0055] This invention discloses a method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites, the method comprising the following steps:

[0056] S1: Based on the mixing and diffusion mechanism of oxygen in the crack channel, an oxidation kinetic model of ceramic matrix composites is constructed to calculate the oxygen concentration distribution in the crack depth direction;

[0057] S2: Determine the carbon-oxygen reaction rate and deduce the relationship between the tensile strength of C fiber bundles and the changes in oxidation temperature and oxygen concentration;

[0058] S3: Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted;

[0059] S4: Based on the shear lag model, calculate the stress distribution in the fiber and matrix respectively;

[0060] S5: The critical strain energy method is used to calculate the distribution of crack propagation and crack spacing in the matrix, and to obtain the mechanical response of the matrix;

[0061] S6: Based on the mechanical damage model of the fiber and the matrix, calculate the stress-strain response curve of the fiber bundle ceramic matrix composite material under high temperature oxidation environment.

[0062] See Figure 6 The method specifically includes the following steps:

[0063] Step S1, the gas diffusion mechanism of oxygen in the crack channel is as follows: Figure 1 As shown, an oxidation kinetic model for ceramic matrix composites is constructed.

[0064] The boundary conditions are set such that at the crack inlet (y=0), the oxygen concentration is the same as the external gas concentration, and at the crack bottom (y=L), the oxygen concentration is affected by the oxidation reaction, satisfying the condition of oxygen consumption and diffusion flux balance.

[0065]

[0066] The oxidation kinetic equation at any time t is rewritten as a first-order ordinary differential equation with respect to the crack depth y over time dt, thus transforming the boundary value problem into an initial value problem to obtain its numerical solution. By setting the diffusion time and the number of steps for crack depth, the variation of oxygen concentration with temperature and crack depth is obtained.

[0067] The oxidation kinetics satisfy the above equations at any time t, and therefore can be written as a first-order ordinary differential equation of y over time dt. The boundary value problem is then transformed into an initial value problem to obtain its numerical solution. In this example, the diffusion time is set to 1000 s, and the crack depth steps are 50 steps.

[0068] Based on the steady-state diffusion assumption, the oxygen concentration distribution along the crack depth direction satisfies the following differential equation:

[0069]

[0070] In the formula, The diffusion flux within the crack channel, This represents the oxygen concentration at an oxidation time t at a crack depth y in the coating. To control the rate at which oxygen is consumed by chemical reactions within the body.

[0071] Inside the crack, the diffusion behavior of oxygen is described by a mixed diffusion model, and the diffusion flux is expressed as:

[0072]

[0073] In the formula, D eff Let be the equivalent diffusion coefficient of oxygen. According to the mixing-diffusion mechanism, the equivalent diffusion coefficient D... eff Represented as:

[0074]

[0075] Where D F D is the Fick diffusion coefficient. k Knudsen diffusion coefficient

[0076]

[0077] In the formula, T is the absolute temperature, P is the system pressure, and Σ V The diffusion volume of the molecule is 18.9 cm³ for CO. 3 / mol), CO2 was 26.9 (cm³). 3 / mol), O2 was 16.6 (cm). 2 / mol), where M is the molar mass of the mixed gas;

[0078]

[0079] In the formula, S is the crack cross-section, and Pe is the perimeter of the pore cross-section. R represents the average speed of molecules. g The value is 8.314 J / mol·K.

[0080] Oxygen consumption rate in chemical reactions The calculation formula is:

[0081]

[0082] In the formula, k(T) is the reaction rate constant at temperature T, which follows the Arrhenius equation:

[0083]

[0084] In the formula, k0 is the pre-exponential factor of the reaction rate constant; E a R is the activation energy of the reaction. g Here is the gas constant. The oxygen diffusion calculation results are as follows: Figure 2 As shown.

[0085] Step S2: Based on the concentration calculation results in step S1, and using the oxidation kinetic model, determine the carbon-oxygen reaction rate and derive the relationship between the tensile strength of the C fiber bundle and the changes in oxidation temperature and oxygen concentration.

[0086] Based on the oxidation kinetics model, the expression for the carbon-oxygen reaction rate is determined as follows:

[0087]

[0088] In the formula, E r The activation energy for the reaction is set to 200 kJ / mol.

[0089] fiber radius consumption r over time f (t) can be described as:

[0090]

[0091] The relationship between the fiber radius at the crack tip and time as oxidation proceeds is expressed as follows:

[0092] R f (t)=R f0 +h I -r f (t);

[0093] In the formula, the initial fiber radius R f0 The value is 6.5um, h I This indicates that the PyC interface thickness is 0.5 × 10⁻⁶. -6 .

[0094] Assuming that the fiber strength during oxidation is directly proportional to its bearing area, then the fiber strength at time t is:

[0095]

[0096] In the formula, The strength of intact fibers is taken as 5.12 GPa, R f (t) represents the fiber radius at time t; the fiber strength calculation results are as follows: Figure 3 As shown

[0097] Step S3: Calculate the fiber strength results and, based on the breaking force value of the carbon fiber bundle, perform an equivalent offset on the carbon fiber strength distribution under different oxidation temperature environments.

[0098] Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted, with the shift amount being:

[0099]

[0100] In the formula, R f (T,t) represents the fiber radius after oxidation at temperature T for time t. The offset results are as follows: Figure 4 As shown.

[0101] Step S4: Based on the interface slip model, calculate the fiber and matrix stress distribution in the forward slip zone, reverse slip zone, and undebonded zone, respectively.

[0102] According to the shear lag model, the stress distribution on the fiber is as follows:

[0103]

[0104] In the formula, σ is the external load acting on both ends of the fiber bundle composite material, and v f It is the volume percentage of the fiber, τ i It is the interfacial shear stress between the fiber and the matrix in the slip zone, where x is the size of the slip zone and d is the shear stress at the interface. f σ is the sliding distance. f0 The normal stress in the bonded zone is numerically equal to the fiber stress when the matrix cracks and when no interfacial debonding occurs, where L is the matrix crack spacing and r is the fiber stress. f The initial fiber radius;

[0105] The stress distribution on the matrix is ​​as follows:

[0106]

[0107] In the formula, σ m0 For the normal stress of the matrix in the bonding zone, v m It is the volume percentage of the matrix.

[0108] σ f0 , σ m0 The calculation can be expressed as:

[0109]

[0110] E c =v f E f +v m E m

[0111]

[0112] In the formula, E c E refers to the elastic modulus of composite materials. f It is the elastic modulus of the fiber, E m It is the elastic modulus of the matrix, α c α f These are the coefficients of thermal expansion of the composite material and the fiber, respectively, and ΔT is the difference between the composite material preparation temperature and room temperature.

[0113] Step S5: According to the critical strain energy criterion, crack propagation occurs when the strain energy of the matrix reaches a critical value. The formula for calculating the critical strain energy is as follows:

[0114]

[0115] Among them, U m A is the critical strain energy of the matrix. m This represents the cross-sectional area of ​​the matrix.

[0116] Step S6: Calculate the average stress and strain of the fiber bundle ceramic matrix composite material using the mixing law.

[0117]

[0118] In the formula, σ c For material stress, ε c For material strain. Constitutive calculation results are as follows: Figure 5 As shown.

[0119] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0120] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, produce instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, causing a series of operational steps to be executed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that run on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0123] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0124] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating the constitutive model of an oxidation system for fiber bundle ceramic matrix composites, characterized in that, The method includes the following steps: S1: Based on the mixing and diffusion mechanism of oxygen in the crack channel, an oxidation kinetic model of ceramic matrix composites is constructed to calculate the oxygen concentration distribution in the crack depth direction; S2: Determine the carbon-oxygen reaction rate and deduce the relationship between the tensile strength of C fiber bundles and the changes in oxidation temperature and oxygen concentration; S3: Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted; S4: Based on the shear lag model, calculate the stress distribution in the fiber and matrix respectively; S5: The critical strain energy method is used to calculate the distribution of crack propagation and crack spacing in the matrix, and to obtain the mechanical response of the matrix; S6: Based on the mechanical damage model of the fiber and the matrix, calculate the stress-strain response curve of the fiber bundle ceramic matrix composite material under high temperature oxidation environment.

2. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, In step S1, based on the steady-state diffusion assumption, the oxygen concentration distribution along the crack depth direction satisfies the following differential equation: In the formula, The diffusion flux within the crack channel, This represents the oxygen concentration at an oxidation time t at a crack depth y in the coating. To control the rate at which oxygen is consumed by chemical reactions within the body.

3. The method for calculating the constitutive model of fiber bundle ceramic matrix composites according to claim 2, characterized in that, In step S1, within the crack, the diffusion behavior of oxygen is described by a mixed diffusion model, and the diffusion flux expression is: In the formula, D eff is the equivalent diffusion coefficient of oxygen.

4. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 2, characterized in that, In step S1, the chemical reaction consumption rate of oxygen The calculation formula is: In the formula, k(T) is the reaction rate constant at temperature T, which follows the Arrhenius equation: In the formula, k0 is the pre-exponential factor of the reaction rate constant; E a R is the activation energy of the reaction. g is the gas constant.

5. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, Step S2 further includes: Assuming that the fiber strength during oxidation is directly proportional to its bearing area, then the fiber strength at time t is: In the formula, It is the strength of intact fibers, R f (t) represents the fiber radius at time t, R f0 The initial fiber radius is given.

6. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, Step S3 further includes: Based on the tensile strength of C fiber bundles at different oxidation temperatures, the strength distribution of in-situ C fiber monofilaments at room temperature is equivalently shifted, and the shift amount Δσ(T,t) is expressed as: In the formula, σ0 is the fiber breaking strength at room temperature, and R f (T,t) represents the fiber radius after oxidation at temperature T for time t.

7. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, Step S4 further includes: According to the shear lag model, the stress distribution on the fiber is as follows: In the formula, σ is the external load acting on both ends of the fiber bundle composite material, and v f It is the volume percentage of the fiber, τ i It is the interfacial shear stress between the fiber and the matrix in the slip zone, where x is the size of the slip zone and d is the shear stress at the interface. f σ is the sliding distance. f0 The normal stress in the bonded zone is numerically equal to the fiber stress when the matrix cracks and when no interfacial debonding occurs, where L is the matrix crack spacing and r is the fiber stress. f The initial fiber radius; The stress distribution on the matrix is ​​as follows: In the formula, σ m0 For the normal stress of the matrix in the bonding zone, v m It is the volume percentage of the matrix.

8. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, Step S5 further includes: According to the critical strain energy criterion, crack propagation occurs when the strain energy of the matrix reaches a critical value. The formula for calculating the critical strain energy is as follows: Among them, U m A is the critical strain energy of the matrix. m d is the cross-sectional area of ​​the matrix. f This represents the sliding distance.

9. The method for calculating the oxidation constitutive model of fiber bundle ceramic matrix composites according to claim 1, characterized in that, In step S6, the average stress and strain of the fiber bundle ceramic matrix composite are calculated using the mixing law: In the formula, σ c For material stress, ε c For material strain.

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