Method for calculating oxidation constitutive model of fiber bundle ceramic matrix composite

Abstract

The invention discloses a calculation method for an oxidation constitutive model of a fiber bundle ceramic-based composite material, which comprises the following steps: constructing an oxidation kinetic model of the ceramic-based composite material, and calculating oxygen concentration distribution in a crack depth direction; determining a carbon-oxygen reaction rate, and deducing a change relationship among the tensile strength of the C fiber bundle, the oxidation temperature and the oxygen concentration; according to the tensile strength of the C fiber bundle at different temperatures, performing equivalent offset on the strength distribution of the normal-temperature C fiber in-situ monofilament; calculating fiber stress distribution of an interface slip area, a forward slip area and a reverse slip area between the fiber and the matrix based on the shear hysteresis model; calculating matrix crack propagation and crack spacing distribution to obtain mechanical response of the matrix; and calculating a stress-strain response curve of the fiber bundle ceramic matrix composite material in a high-temperature oxidation environment according to a mechanical damage model of the fiber and the matrix. According to the method, the damage evolution of the fiber, the interface and the matrix in the oxidation process can be accurately described, and the calculation amount is greatly reduced.

Description

Technical Field

[0001] The invention relates to the technical field of material mechanics, and in particular to a calculation method for an oxidation constitutive model of a fiber bundle ceramic matrix composite material. Background Art

[0002] Fiber bundle ceramic matrix composites are widely used in high-temperature structural parts such as aerospace engines due to their high strength, good high-temperature resistance and low density. When these materials are used in extreme environments, they are often subjected to alternating complex working conditions. At the same time, the high-temperature oxidation environment causes irreversible chemical reactions inside the material, resulting in multiple damage modes such as interface debonding, fiber oxidation and matrix cracks, which significantly affect the mechanical properties of CMC materials.

[0003] The mechanical behavior of ceramic matrix composites exhibits obvious nonlinear characteristics. Its complex microstructure and damage evolution make it difficult to accurately predict the material properties. Especially in high-temperature oxidation environments, oxygen diffuses into the material through matrix cracks and pores, inducing interface oxidation and fiber degradation, which in turn causes continuous attenuation of material strength and stiffness. The cumulative effect of this microscopic damage makes the macroscopic mechanical response of the material more challenging. Summary of the invention

[0004] The purpose of the present invention is to disclose a calculation method for the oxidation constitutive model of fiber bundle ceramic matrix composite materials, and to establish a mechanical response model suitable for the multi-component coupling of fiber, interface and matrix under high-temperature oxidation environment by studying oxygen diffusion, oxidation reaction rate and material microscopic damage evolution mechanism. The present invention fully considers the strength attenuation, crack propagation and nonlinear deformation characteristics of ceramic matrix composite materials under high-temperature oxidation conditions, and can accurately describe the oxidation constitutive relationship of materials at different temperatures.

[0005] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

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

[0007] S1: Based on the mixed diffusion mechanism of oxygen in the crack channel, the 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 the C fiber bundle and the oxidation temperature and oxygen concentration;

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

[0010] S4: Based on the shear lag model, the stress distribution of the fiber and matrix is ​​calculated separately;

[0011] S5: Using the critical strain energy method, the distribution of matrix crack extension and crack spacing is calculated to obtain the mechanical response of the matrix;

[0012] S6: Based on the mechanical damage model of fiber and matrix, the stress-strain response curve of fiber bundle ceramic matrix composites in high temperature oxidation environment is calculated.

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

[0014]

[0015] In the formula, is the diffusion flux in the crack channel, represents the oxygen concentration at the coating crack depth y at oxidation time t, To control the rate at which oxygen is consumed by chemical reactions in 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] Where D eff is the equivalent diffusion coefficient of oxygen.

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

[0020]

[0021] Where k(T) is the reaction rate constant at temperature T, following the Arrhenius formula:

[0022]

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

[0024] Step S2 further comprises:

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

[0026]

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

[0028] Step S3 further comprises:

[0029] According to the tensile strength of the C fiber bundle at different oxidation temperatures, the strength distribution of the in-situ C fiber single filament at room temperature is equivalently offset, and the offset Δσ(T,t) is expressed as:

[0030]

[0031] Where σ0 is the fiber breaking strength at room temperature, R f (T,t) is the fiber radius oxidized at temperature T for t time.

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

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

[0034]

[0035] Where σ is the external load acting on both ends of the fiber bundle composite material, v f is the volume percentage of fiber, τ i is the interfacial shear stress between the fiber and the matrix in the slip zone, x is the size of the slip zone, d f is the slip distance, σ f0 is the fiber normal stress in the bonding area, which is numerically equal to the fiber stress when the matrix cracks and no interfacial debonding occurs, L is the matrix crack spacing, r f is the initial fiber radius;

[0036] The stress distribution on the substrate is:

[0037]

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

[0039] Step S5 further comprises:

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

[0041]

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

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

[0044]

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

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The present invention discloses a method for calculating an oxidation constitutive model of a fiber bundle ceramic matrix composite material, which can efficiently predict the mechanical properties of such composite materials in a high-temperature oxidation environment. The oxidation constitutive model of a fiber bundle ceramic matrix composite material proposed by the present invention combines oxygen diffusion and oxidation damage mechanisms, and calculates the tensile stress-strain response curve of the fiber bundle ceramic matrix composite material based on the material component parameters of the fiber bundle ceramic matrix composite material at different temperatures, thereby being able to accurately describe the damage evolution of the fiber, interface and matrix during the oxidation process, and greatly reduce the amount of calculation by simplifying the calculation method, which has strong engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of oxygen diffusion model;

[0049] Figure 2 Schematic diagram of the change of oxygen concentration with crack depth under different temperature environments;

[0050] Figure 3 This is a simulation diagram of the relationship between fiber strength, oxidation time and temperature;

[0051] Figure 4 This is the strength distribution diagram of carbon fiber at different oxidation temperatures;

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

[0053] Figure 6 This is a flow chart of the calculation method for the oxidation constitutive model of fiber bundle ceramic matrix composites. DETAILED DESCRIPTION

[0054] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0055] The present invention discloses a method for calculating an oxidation constitutive model of a fiber bundle ceramic matrix composite material, the method comprising the following steps:

[0056] S1: Based on the mixed diffusion mechanism of oxygen in the crack channel, the 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 the C fiber bundle and the oxidation temperature and oxygen concentration;

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

[0059] S4: Based on the shear lag model, the stress distribution of the fiber and matrix is ​​calculated separately;

[0060] S5: Using the critical strain energy method, the distribution of matrix crack extension and crack spacing is calculated to obtain the mechanical response of the matrix;

[0061] S6: Based on the mechanical damage model of fiber and matrix, the stress-strain response curve of fiber bundle ceramic matrix composites in high temperature oxidation environment is calculated.

[0062] See also Figure 6 , the method specifically comprises 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 of ceramic matrix composites is constructed.

[0064] The boundary conditions are set such that at the crack entrance (y = 0), the oxygen concentration is consistent with 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 for the crack depth y within time dt, so that the boundary value problem is transformed into an initial value problem to obtain its numerical solution. The diffusion time and crack depth steps are set to obtain the change of oxygen concentration with temperature and crack depth.

[0067] The oxidation kinetics at any time t satisfies the above equation, so it can be written as a first-order ordinary differential equation for y in time dt. The boundary value problem is transformed into an initial value problem to obtain its numerical solution. In this example, the diffusion time is set to 1000s and the crack depth step number is 50.

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

[0069]

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

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

[0072]

[0073] Where D eff is the equivalent diffusion coefficient of oxygen. According to the mixed diffusion mechanism, the equivalent diffusion coefficient D eff It is expressed as:

[0074]

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

[0076]

[0077] Where T is the absolute temperature, P is the system pressure, Σ V is the diffusion volume of the molecule, the value of CO is 18.9 (cm 3 / mol), CO2 is 26.9 (cm 3 / mol), O2 takes 16.6 (cm 2 / mol), M is the molar mass of the mixed gas;

[0078]

[0079] Where S is the crack section, Pe is the circumference of the hole section, represents the average rate of the molecules, R g The value is 8.314 J / mol·K.

[0080] Oxygen consumption rate by chemical reaction The calculation formula is:

[0081]

[0082] Where k(T) is the reaction rate constant at temperature T, following the Arrhenius formula:

[0083]

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

[0085] Step S2, according to the concentration calculation result in step S1, based on the oxidation kinetic model, determine the carbon-oxygen reaction rate, and deduce the relationship between the tensile strength of the C fiber bundle and the oxidation temperature and oxygen concentration.

[0086] Based on the oxidation kinetic model, the expression for determining the carbon-oxygen reaction rate is:

[0087]

[0088] In the formula, E r The activation energy of the reaction is taken as 200KJ / mol.

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

[0090]

[0091] As oxidation proceeds, the relationship between the fiber radius at the crack bottom and time is expressed as:

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

[0093] Where, the initial fiber radius R f0 The value is 6.5um, h I The thickness of the PyC interface is 0.5×10 -6 .

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

[0095]

[0096] In the formula, The intact fiber strength is 5.12 GPa, R f (t) is the fiber radius at time t; the fiber strength calculation results are as follows Figure 3 Shown

[0097] Step S3, the calculation result of the fiber strength is used to perform an equivalent shift on the carbon fiber strength distribution under different oxidation temperature environments according to the breaking force value of the carbon fiber bundle.

[0098] According to the tensile strength of the C fiber bundle at different oxidation temperatures, the strength distribution of the in-situ C fiber single filament at room temperature is equivalently offset, and the offset is:

[0099]

[0100] In the formula, R f (T, t) is the fiber radius at temperature T and oxidized for time t. The offset result is as follows Figure 4 shown.

[0101] Step S4, based on the interface slip model, respectively calculating the fiber and matrix stress distribution in the forward slip zone, the reverse slip zone and the non-debonding zone.

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

[0103]

[0104] Where σ is the external load acting on both ends of the fiber bundle composite material, v f is the volume percentage of fiber, τ i is the interfacial shear stress between the fiber and the matrix in the slip zone, x is the size of the slip zone, d f is the slip distance, σ f0 is the fiber normal stress in the bonding area, which is numerically equal to the fiber stress when the matrix cracks and no interfacial debonding occurs, L is the matrix crack spacing, r f is the initial fiber radius;

[0105] The stress distribution on the substrate is:

[0106]

[0107] In the formula, σ m0 is the matrix normal stress in the bonding area, v m 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 Refers to the elastic modulus of the composite material, E f is the elastic modulus of the fiber, E m is the elastic modulus of the matrix, α c , α f are the thermal expansion coefficients of the composite material and the fiber, respectively, and ΔT is the difference between the preparation temperature of the composite material and the room temperature.

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

[0114]

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

[0116] Step S6, calculating the average stress and strain of the fiber bundle ceramic matrix composite material by the mixed law:

[0117]

[0118] In the formula, σ c is the material stress, ε c is the material strain. The constitutive calculation results are as follows Figure 5 shown.

[0119] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt 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.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0120] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0121] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0122] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0123] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0124] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for calculating the oxidation constitutive model of a fiber bundle ceramic matrix composite material, characterized in that: The method comprises the following steps: S1: Based on the mixed diffusion mechanism of oxygen in the crack channel, the 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 the C fiber bundle and the oxidation temperature and oxygen concentration; S3: Based on the tensile strength of the C fiber bundle at different oxidation temperatures, the strength distribution of the in-situ C fiber single filament at room temperature is equivalently shifted; S4: Based on the shear lag model, the stress distribution of the fiber and matrix is ​​calculated separately; S5: Using the critical strain energy method, the distribution of matrix crack extension and crack spacing is calculated to obtain the mechanical response of the matrix; S6: Based on the mechanical damage model of fiber and matrix, the stress-strain response curve of fiber bundle ceramic matrix composites in high temperature oxidation environment is calculated.

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

3. The calculation method of the oxidation constitutive model of the fiber bundle ceramic matrix composite material according to claim 2 is characterized in that: In step S1, inside the crack, the diffusion behavior of oxygen is described by the mixed diffusion model, and the diffusion flux expression is: Where D eff is the equivalent diffusion coefficient of oxygen.

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

5. The calculation method of the oxidation constitutive model of the fiber bundle ceramic matrix composite material according to claim 1, characterized in that: Step S2 further comprises: Assuming that the fiber strength during oxidation is proportional to its bearing area, the fiber strength at time t is: In the formula, is the intact fiber strength, R f (t) is the fiber radius at time t, R f0 is the initial fiber radius.

6. The calculation method of the oxidation constitutive model of the fiber bundle ceramic matrix composite material according to claim 1, characterized in that: Step S3 further comprises: According to the tensile strength of the C fiber bundle at different oxidation temperatures, the strength distribution of the in-situ C fiber single filament at room temperature is equivalently offset, and the offset Δσ(T,t) is expressed as: Where σ0 is the fiber breaking strength at room temperature, R f (T,t) is the fiber radius oxidized at temperature T for t time.

7. The calculation method of the oxidation constitutive model of the fiber bundle ceramic matrix composite material according to claim 1 is characterized in that: Step S4 further comprises: According to the shear lag model, the stress distribution on the fiber is: Where σ is the external load acting on both ends of the fiber bundle composite material, v f is the volume percentage of fiber, τ i is the interfacial shear stress between the fiber and the matrix in the slip zone, x is the size of the slip zone, d f is the slip distance, σ f0 is the fiber normal stress in the bonding area, which is numerically equal to the fiber stress when the matrix cracks and no interfacial debonding occurs, L is the matrix crack spacing, r f is the initial fiber radius; The stress distribution on the substrate is: In the formula, σ m0 is the matrix normal stress in the bonding area, v m is the volume percentage of the matrix.

8. The calculation method of the oxidation constitutive model of the fiber bundle ceramic matrix composite material according to claim 1, characterized in that: Step S5 further comprises: According to the critical strain energy criterion, when the strain energy of the matrix reaches the critical value, crack propagation occurs. The calculation formula of the critical strain energy is: Among them, U m is the critical strain energy of the matrix, A m is the cross-sectional area of ​​the matrix, d f is the slip distance.

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

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