CN112307605B - Unidirectional ceramic matrix composite thermal expansion coefficient prediction method considering damage evolution - Google Patents

Abstract

The present invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material taking into account the evolution of damage. During the deformation process of the ceramic matrix composite material due to heat, thermal stress will be generated in the component, thereby causing damage. The evolution of the damage will further change the stress distribution of the component, thereby changing the macroscopic deformation of the material, thereby affecting the thermal expansion coefficient. The present invention takes into account damage such as matrix cracking and interface slip, calculates the forward and reverse slip lengths of the interface caused by temperature changes, takes into account the influence of these damage evolutions on the stress distribution of the component when calculating the macroscopic deformation of the material, and finally calculates the macroscopic thermal strain and thermal expansion coefficient of the material, which can greatly improve the accuracy of the prediction results.

Description

Prediction method of thermal expansion coefficient of unidirectional ceramic matrix composites considering damage evolution

Technical Field

The invention belongs to the field of prediction of mechanical properties of composite materials, and in particular relates to a method for predicting thermal expansion coefficient of unidirectional ceramic-based composite materials taking damage evolution into consideration.

Background technique

Ceramic matrix composites are ideal materials for hot-end components of aerospace vehicles due to their high temperature resistance and low density. As hot-end components, ceramic matrix composite structures have a large temperature variation range during operation, which causes thermal deformation. Therefore, the design of ceramic matrix composite structures requires designers to accurately predict the thermal expansion coefficient of the material. At present, the prediction of the thermal expansion coefficient of unidirectional ceramic matrix composites often uses the linear elastic method. The general process of this method is: 1) Obtain the performance parameters such as the thermal expansion coefficient and elastic modulus of the component phase through experiments or theoretical calculations; 2) Establish an RVE model that can reflect the microstructural characteristics; 3) Substitute the performance parameters of the component phase into the RVE model, and obtain the thermal expansion coefficient of the unidirectional ceramic matrix composite through homogenization calculation. For example, the literature [Shen Shidian. Prediction of thermal expansion coefficient of ceramic matrix composites based on XCT technology. Nanjing: Nanjing University of Aeronautics and Astronautics, 2017.] and [Michaux A, Sauder C, Camus G, et al. Young's modulus, thermal expansion coefficient and fracture behavior of selected Si-B-C based carbides in the 20-1200℃ temperature range as derived from the behavior of carbon fiber reinforced microcomposites [J]. Journal of the European Ceramic Society, 2007, 27 (12): 3551-3560.]. This prediction method does not take into account the damage evolution during the thermal expansion of ceramic matrix composites, and believes that the thermal expansion coefficient of the composite material depends only on the thermal expansion coefficient and elastic parameters of the components. In fact, during the thermal deformation of ceramic matrix composites, thermal stress will be generated in the components, resulting in damage. The evolution of damage will further change the macroscopic deformation of the material, thereby affecting the thermal expansion coefficient. Therefore, it is impossible to accurately predict the thermal expansion coefficient of unidirectional ceramic matrix composites using only the existing linear elastic method.

Currently, how to accurately predict the thermal expansion coefficient of unidirectional ceramic matrix composites is an important and difficult to solve technical problem in this field.

Summary of the invention

In view of the deficiencies in the prior art, the present invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material taking damage evolution into consideration.

To achieve the above object, the present invention adopts the following technical solutions:

A method for predicting thermal expansion coefficient of unidirectional ceramic matrix composite materials considering damage evolution is characterized by comprising the following steps:

Step 1: Calculate the fiber thermal stress and matrix thermal stress at room temperature _T1 respectively;

Step 2: Calculate the matrix crack spacing at room temperature from the matrix thermal stress at room temperature _T1 ;

Step 3: Calculate the interface forward slip length at room temperature based on the fiber thermal stress at room temperature _T1 ;

Step 4: Calculate the thermal stress of the fiber after the temperature rises to T ₂ ;

Step 5: Calculate the interface reverse slip length caused by the temperature rising to T ₂ based on the interface forward slip length at room temperature T ₁ and the fiber thermal stress at temperature T ₂ ;

Step 6: Calculate the thermal strain of the unidirectional ceramic matrix composite when the temperature rises from T ₁ to T ₂ based on the fiber thermal stress and interface forward slip length at room temperature T ₁ and the fiber thermal stress and interface reverse slip length at temperature T ₂ ;

Step 7: Calculate the thermal expansion coefficient of the unidirectional ceramic matrix composite material between temperatures T ₁ and T ₂ based on the thermal strain of the unidirectional ceramic matrix composite material when the temperature increases from T ₁ to T ₂ .

To optimize the above technical solutions, the specific measures taken also include:

Furthermore, in step 1, the method for calculating the fiber thermal stress is:

The method for calculating the thermal stress of the matrix is:

Wherein, σf _,1 and σm _,1 are the thermal stresses of the fiber and the matrix at room temperature _T1 , _Ef and _Em are the elastic moduli of the fiber and the matrix, _vf and _vm are the volume fractions of the fiber and the matrix, _αf and _αm are the thermal expansion coefficients of the fiber and the matrix, and _T0 is the preparation temperature of the ceramic matrix composite material.

Furthermore, in step 3, the method for calculating the interface forward slip length is:

Where d ₊ is the interface forward slip length at room temperature _T1 , _rf is the fiber single filament radius, τ is the interface shear stress, and σf _,1 is the fiber thermal stress at room temperature _T1 .

Furthermore, in step 4, the method for calculating the fiber thermal stress is:

Wherein, σf _,2 is the thermal stress of the fiber at temperature _T2 , _Ef and _Em are the elastic moduli of the fiber and the matrix, respectively, _vf and _vm are the volume fractions of the fiber and the matrix, respectively, _αf and _αm are the thermal expansion coefficients of the fiber and the matrix, respectively, and _T0 is the preparation temperature of the ceramic matrix composite material.

Furthermore, in step 5, the method for calculating the interface reverse slip length is:

Wherein, _d- is the reverse slip length of the interface at temperature _T2 , _rf is the radius of the fiber single filament, τ is the interface shear stress, σf _,2 is the fiber thermal stress at temperature _T2 , and d ₊ is the forward slip length of the interface at room temperature _T1 .

Further, in step 6, the method for calculating the thermal strain of the unidirectional ceramic matrix composite material is:

In the formula, is the thermal strain of the ceramic matrix composite material when the temperature rises from _T1 to _T2 , L is the matrix crack spacing at room temperature _T1 , _Ef is the elastic modulus of the fiber, _rf is the radius of the fiber single filament, _αf is the thermal expansion coefficient of the fiber, τ is the interface shear stress, d ₊ is the interface forward slip length at room temperature _T1 , d- _is the interface reverse slip length at temperature _T2 , σf _,1 is the fiber thermal stress at room temperature _T1 , and σf _,2 is the fiber thermal stress at temperature _T2 .

Further, in step 7, the method for calculating the thermal expansion coefficient of the unidirectional ceramic matrix composite material is:

Where _αc is the thermal expansion coefficient of the unidirectional ceramic matrix composite material between room temperature _T1 and temperature _T2 , is the thermal strain of the ceramic matrix composite material when the temperature rises from _T1 to _T2 .

The beneficial effects of the present invention are as follows: the present invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material taking into account the evolution of damage. In the process of deformation of the ceramic matrix composite material caused by heat, thermal stress will be generated in the component, thereby causing damage. The evolution of the damage will further change the stress distribution of the component, thereby changing the macroscopic deformation of the material, thereby affecting the thermal expansion coefficient. The present invention takes into account damage such as matrix cracking and interface slip, calculates the forward and reverse slip lengths of the interface caused by temperature changes, takes into account the influence of these damage evolutions on the stress distribution of the component when calculating the macroscopic deformation of the material, and finally calculates the macroscopic thermal strain and thermal expansion coefficient of the material, which can greatly improve the accuracy of the prediction results.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the present invention for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material.

Figure 2 is a schematic diagram of matrix cracking and interface positive slip at room temperature.

FIG3 is a schematic diagram of interface reverse slip when the temperature rises.

FIG. 4 is a comparison diagram of the prediction results of the present invention and the prediction results of the current linear elastic method.

The reference numerals are as follows: 1 - fiber, 2 - matrix, 3 - positive slip region, 4 - reverse slip region, 5 - non-slip region.

Detailed ways

The present invention will now be described in further detail with reference to the accompanying drawings.

The present invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material taking into account damage evolution, as shown in FIG1 , the method comprising the following steps:

Step 1: Calculate the fiber thermal stress σ _f,1 and matrix thermal stress σ _m,1 at room temperature T ₁ respectively:

Step 2: As shown in FIG2 , the matrix crack spacing L at room temperature is calculated from the matrix thermal stress σ _m,1 at room temperature T _1.

Step 3: As shown in Figure 2, the interface forward slip length at room temperature is calculated from the fiber thermal stress at room temperature _T1

Step 4: Calculate the fiber thermal stress σ _f,2 after the temperature rises to T ₂ :

Step 5: As shown in Figure 3, calculate the interface reverse slip length caused by increasing the temperature to _T2

Step 6: Calculate the thermal strain of the ceramic matrix composite when the temperature rises from _T1 to _T2

Step 7: Calculate the thermal expansion coefficient of the ceramic matrix composite between temperatures T ₁ and T ₂

In order to enable those skilled in the art to better understand the technical solutions and beneficial effects of the present application, the present application predicts the thermal expansion coefficient of unidirectional SiC/SiC ceramic matrix composite materials at different temperatures (T ₂ =100, 200...1500°C) in the embodiments. The basic parameters of the material are as follows: E _f =140 GPa, _Em =350 GPa, α _f =3.1×10 ^-6 /°C, α _m =4.6×10 ^-6 /°C, v _f =0.325, v _m =0.675, r _f =6.5 μm, T ₀ =1000°C, τ =17 MPa.

Calculate the fiber thermal stress σ _f,1 and matrix thermal stress σ _m,1 at room temperature T ₁ = 25°C:

The matrix crack spacing L at room temperature is calculated. In this embodiment, the common Weibull model is used to calculate the matrix crack spacing:

Wherein, the model parameters are L _sat =0.2 mm, σ ₀ =60 MPa, and m=3.

The interface forward slip length at room temperature is calculated as

Calculate the fiber thermal stress σ _f,2 after the temperature rises to T ₂ = 100°C:

Calculate the reverse slip length of the interface after the temperature rises to T ₂ = 100°C

Calculation of thermal strain of unidirectional SiC/SiC ceramic matrix composites when the temperature rises from T ₁ = 25°C to T ₂ = 100°C

Calculation of thermal expansion coefficient of unidirectional SiC/SiC ceramic matrix composites at temperature T ₂ = 100°C

Similarly, the thermal expansion coefficient of the unidirectional SiC/SiC ceramic matrix composite material at T2=200, 300...1500°C is calculated, as shown in FIG4 .

This embodiment also uses the existing linear elastic method to predict the thermal expansion coefficient of the unidirectional SiC/SiC ceramic matrix composite material at different temperatures, as shown in Figure 4. It can be seen that the linear elastic method predicts a significantly larger thermal expansion coefficient because it does not consider the influence of damage evolution.

It should be noted that the terms such as "upper", "lower", "left", "right", "front", "back", etc. cited in the invention are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (6)

1. A method for predicting thermal expansion coefficient of unidirectional ceramic matrix composite materials considering damage evolution, characterized in that it comprises the following steps: Step 1: Calculate the fiber thermal stress and matrix thermal stress at room temperature _T1 respectively; Step 2: Calculate the matrix crack spacing at room temperature from the matrix thermal stress at room temperature _T1 ; Step 3: Calculate the interface forward slip length at room temperature based on the fiber thermal stress at room temperature _T1 ; Step 4: Calculate the thermal stress of the fiber after the temperature rises to T ₂ ; Step 5: Calculate the interface reverse slip length caused by the temperature rising to T ₂ based on the interface forward slip length at room temperature T ₁ and the fiber thermal stress at temperature T ₂ ; Step 6: Based on the fiber thermal stress and interface forward slip length at room temperature _T1 , and the fiber thermal stress and interface reverse slip length at temperature _T2 , calculate the thermal strain of the unidirectional ceramic matrix composite material when the temperature rises from _T1 to _T2 : In the formula, is the thermal strain of the ceramic matrix composite material when the temperature rises from T ₁ to T ₂ , L is the matrix crack spacing at room temperature T ₁ , E _f is the elastic modulus of the fiber, r _f is the radius of the fiber single filament, α _f is the thermal expansion coefficient of the fiber, τ is the interface shear stress, d ₊ is the interface forward slip length at room temperature T ₁ , d _- is the interface reverse slip length at temperature T ₂ , σ _f,1 is the fiber thermal stress at room temperature T ₁ , and σ _f,2 is the fiber thermal stress at temperature T ₂ ; Step 7: Calculate the thermal expansion coefficient of the unidirectional ceramic matrix composite material between temperatures T ₁ and T ₂ based on the thermal strain of the unidirectional ceramic matrix composite material when the temperature increases from T ₁ to T ₂ . 2. The method for predicting thermal expansion coefficient of unidirectional ceramic matrix composite materials considering damage evolution according to claim 1, characterized in that: in step 1, the method for calculating fiber thermal stress is: The method for calculating the thermal stress of the matrix is: Wherein, σ _f,1 and σ _m,1 are the thermal stresses of the fiber and the matrix at room temperature T ₁ , E _f and _Em are the elastic moduli of the fiber and the matrix, v _f and v _m are the volume fractions of the fiber and the matrix, α _f and α _m are the thermal expansion coefficients of the fiber and the matrix, and T ₀ is the preparation temperature of the ceramic matrix composite material. 3. The method for predicting the thermal expansion coefficient of unidirectional ceramic matrix composite materials considering damage evolution according to claim 1, characterized in that: in step 3, the method for calculating the interface forward slip length is: Where d ₊ is the interface forward slip length at room temperature T ₁ , r _f is the fiber single filament radius, τ is the interface shear stress, and σ _f,1 is the fiber thermal stress at room temperature T ₁ . 4. The method for predicting thermal expansion coefficient of unidirectional ceramic matrix composite materials considering damage evolution according to claim 1, characterized in that: in step 4, the method for calculating fiber thermal stress is: Wherein, σf _,2 is the thermal stress of the fiber at temperature _T2 , _Ef and _Em are the elastic moduli of the fiber and the matrix, respectively, _vf and _vm are the volume fractions of the fiber and the matrix, respectively, _αf and _αm are the thermal expansion coefficients of the fiber and the matrix, respectively, and _T0 is the preparation temperature of the ceramic matrix composite material. 5. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material considering damage evolution according to claim 1, characterized in that: in step 5, the method for calculating the interface reverse slip length is: Wherein, d _- is the reverse slip length of the interface at temperature T ₂ , r _f is the radius of the fiber single filament, τ is the interface shear stress, σ _f,2 is the fiber thermal stress at temperature T ₂ , and d ₊ is the forward slip length of the interface at room temperature T ₁ . 6. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material considering damage evolution according to claim 1, characterized in that: in step 7, the method for calculating the thermal expansion coefficient of the unidirectional ceramic matrix composite material is: Where _αc is the thermal expansion coefficient of the unidirectional ceramic matrix composite material between room temperature _T1 and temperature _T2 , is the thermal strain of the ceramic matrix composite material when the temperature rises from _T1 to _T2 .