CN112307605B - Unidirectional ceramic matrix composite thermal expansion coefficient prediction method considering damage evolution - Google Patents
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- 239000011153 ceramic matrix composite Substances 0.000 title claims abstract description 53
- 238000000034 method Methods 0.000 title claims abstract description 49
- 230000008646 thermal stress Effects 0.000 claims abstract description 45
- 239000011159 matrix material Substances 0.000 claims abstract description 31
- 239000000463 material Substances 0.000 claims abstract description 21
- 230000035882 stress Effects 0.000 claims abstract description 10
- 239000000835 fiber Substances 0.000 claims description 56
- 238000002360 preparation method Methods 0.000 claims description 4
- 230000000630 rising effect Effects 0.000 claims description 2
- 239000000758 substrate Substances 0.000 claims description 2
- 238000005336 cracking Methods 0.000 abstract description 3
- 238000010438 heat treatment Methods 0.000 abstract description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 239000002131 composite material Substances 0.000 description 2
- 229920000049 Carbon (fiber) Polymers 0.000 description 1
- 230000006978 adaptation Effects 0.000 description 1
- 239000004917 carbon fiber Substances 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000000265 homogenisation Methods 0.000 description 1
- 150000001247 metal acetylides Chemical class 0.000 description 1
- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite by considering damage evolution, wherein in the process of deformation of the ceramic matrix composite by heating, thermal stress is generated in components to generate damage, and the stress distribution of the components is further changed by the damage evolution, so that the macroscopic deformation of the material is changed, and the thermal expansion coefficient is influenced. According to the method, the damage such as matrix cracking and interface sliding is considered, the forward and reverse sliding length of the interface caused by temperature change is calculated, the influence of the damage evolution on component stress distribution is considered when the macroscopic deformation of the material is calculated, and the macroscopic thermal strain and the thermal expansion coefficient of the material are finally calculated, so that the accuracy of a prediction result can be greatly improved.
Description
Technical Field
The invention belongs to the field of composite mechanical property prediction, and particularly relates to a unidirectional ceramic matrix composite thermal expansion coefficient prediction method considering damage evolution.
Background
The ceramic matrix composite is an ideal material for hot end components of aerospace vehicles due to the advantages of high temperature resistance and low density. As a hot end component, the ceramic matrix composite structure has a large temperature variation range during operation, thereby causing thermal deformation. Therefore, the structural design of the ceramic matrix composite requires that designers accurately predict the thermal expansion coefficient of the material. At present, a linear elastic method is often adopted for predicting the thermal expansion coefficient of the unidirectional ceramic matrix composite material, and the general flow of the method is as follows: 1) Obtaining performance parameters such as thermal expansion coefficient and elastic modulus of the component phase through test or theoretical calculation; 2) Establishing an RVE model capable of reflecting the mesoscopic structural characteristics; 3) Substituting the component phase performance parameters into an RVE model, and obtaining the thermal expansion coefficient of the unidirectional ceramic matrix composite through homogenization calculation. For example, document [ Shen Shidian ] prediction of thermal expansion coefficient of ceramic matrix composite based on XCT technology: the prediction methods of university of aerospace in south Beijing, 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 ofthe European Ceramic Society,2007,27(12)：3551-3560.]. do not consider the evolution of damage during thermal expansion of ceramic matrix composites, and it is believed that the coefficient of thermal expansion of the composites depends only on the coefficient of thermal expansion and the elastic parameters of the components. In fact, in the thermal deformation process of the ceramic matrix composite, thermal stress is generated in components to generate damage, and the macroscopic deformation of the material is further changed by the evolution of the damage to influence the thermal expansion coefficient, so that the thermal expansion coefficient of the unidirectional ceramic matrix composite cannot be accurately predicted only by adopting the existing linear elastic method.
How to accurately predict the thermal expansion coefficient of the unidirectional ceramic matrix composite is an important and difficult technical problem in the field.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material by considering damage evolution.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
The method for predicting the thermal expansion coefficient of the unidirectional ceramic matrix composite material by considering damage evolution is characterized by comprising the following steps of:
Step 1: respectively calculating the thermal stress of the fiber and the thermal stress of the matrix at the room temperature T 1;
Step 2: calculating the matrix crack spacing at room temperature by matrix thermal stress at room temperature T 1;
Step 3: calculating the interfacial forward slip length at room temperature by using the fiber thermal stress at room temperature T 1;
Step 4: calculating the thermal stress of the fiber after the temperature is increased to T 2;
Step 5: calculating the interface reverse slip length caused by the temperature rise to T 2 from the interface forward slip length at the room temperature T 1 and the fiber thermal stress at the temperature T 2;
Step 6: calculating the unidirectional ceramic matrix composite thermal strain of which the temperature is increased from T 1 to T 2 according to the fiber thermal stress and the interface forward sliding length at the room temperature T 1 and the fiber thermal stress and the interface reverse sliding length at the temperature T 2;
Step 7: the thermal expansion coefficient of the unidirectional ceramic matrix composite between the temperatures T 1 and T 2 is calculated according to the thermal strain of the unidirectional ceramic matrix composite with the temperature rising from T 1 to T 2.
In order to optimize the technical scheme, the specific measures adopted further comprise:
Further, in step 1, the method for calculating the thermal stress of the fiber is as follows:
the method for calculating the thermal stress of the substrate comprises the following steps:
Wherein σ f,1 and σ m,1 are respectively the thermal stress of the fiber and the matrix at room temperature T 1, E f and E m are respectively the elastic modulus of the fiber and the matrix, v f and v m are respectively the volume fraction of the fiber and the matrix, α f and α m are respectively the thermal expansion coefficients of the fiber and the matrix, and T 0 is the preparation temperature of the ceramic matrix composite.
Further, in step 3, the method for calculating the forward sliding length of the interface is as follows:
Where d + is the interfacial forward slip length at room temperature T 1, r f is the fiber filament radius, τ is the interfacial shear stress, and σ f,1 is the fiber thermal stress at room temperature T 1.
Further, in step 4, the method for calculating the thermal stress of the fiber is as follows:
Wherein σ f,2 is the fiber thermal stress at the temperature T 2, E f and E m are the elastic moduli of the fiber and the matrix respectively, v f and v m are the volume fractions of the fiber and the matrix respectively, α f and α m are the thermal expansion coefficients of the fiber and the matrix respectively, and T 0 is the preparation temperature of the ceramic matrix composite.
Further, in step 5, the method for calculating the interface reverse slip length includes:
Where d - is the interfacial reverse slip length at temperature T 2, r f is the fiber filament radius, τ is the interfacial shear stress, σ f,2 is the fiber thermal stress at temperature T 2, and d + is the interfacial forward slip length at room temperature T 1.
Further, in step 6, the method for calculating the thermal strain of the unidirectional ceramic matrix composite material comprises the following steps:
In the method, in the process of the invention, The ceramic matrix composite is subjected to thermal strain when the temperature is increased 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 fiber filament radius, alpha f is the thermal expansion coefficient of the fiber, tau is the interfacial shear stress, d + is the interfacial forward sliding length at room temperature T 1, d - is the interfacial reverse sliding length at temperature T 2, sigma f,1 is the fiber thermal stress at room temperature T 1, and sigma f,2 is the fiber thermal stress at temperature T 2.
Further, in step 7, the method for calculating the thermal expansion coefficient of the unidirectional ceramic matrix composite material is as follows:
wherein alpha c is the thermal expansion coefficient of the unidirectional ceramic matrix composite between the room temperature T 1 and the temperature T 2, Is the thermal strain of the ceramic matrix composite as the temperature rises from T 1 to T 2.
The beneficial effects of the invention are as follows: the invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite by considering damage evolution, wherein in the process of deformation of the ceramic matrix composite by heating, thermal stress is generated in components to generate damage, and the stress distribution of the components is further changed by the damage evolution, so that the macroscopic deformation of the material is changed, and the thermal expansion coefficient is influenced. According to the method, the damage such as matrix cracking and interface sliding is considered, the forward and reverse sliding length of the interface caused by temperature change is calculated, the influence of the damage evolution on component stress distribution is considered when the macroscopic deformation of the material is calculated, and the macroscopic thermal strain and the thermal expansion coefficient of the material are finally calculated, so that the accuracy of a prediction result can be greatly improved.
Drawings
FIG. 1 is a flow chart of the present invention for predicting the coefficient of thermal expansion of a unidirectional ceramic matrix composite.
FIG. 2 is a schematic illustration of matrix cracking and interfacial forward slip at room temperature.
FIG. 3 is a schematic diagram of interface reverse slip as temperature increases.
FIG. 4 is a graph comparing the predicted result of the present invention with the predicted result of the current linear elastic method.
The reference numerals are as follows: 1-fiber, 2-matrix, 3-forward slip zone, 4-reverse slip zone, 5-no slip zone.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings.
The invention provides a method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite material in consideration of damage evolution, which is shown in figure 1 and comprises the following steps:
Step 1: the fiber thermal stress σ f,1 and the matrix thermal stress σ m,1 at room temperature T 1 were calculated separately:
step 2: as shown in fig. 2, 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 fig. 2, the interfacial forward slip length at room temperature is calculated from the fiber thermal stress at room temperature T 1
Step 4: the fiber thermal stress σ f,2 after the temperature is raised to T 2 is calculated:
Step 5: as shown in fig. 3, the interfacial reverse slip length resulting from the temperature rise to T 2 is calculated
Step 6: calculation of ceramic matrix composite thermal Strain at temperature from T 1 to T 2
Step 7: calculating the thermal expansion coefficient of the ceramic matrix composite between the temperatures T 1 and T 2
In order to enable the person skilled in the art to better understand the technical scheme and the beneficial effects in the application, the application predicts the thermal expansion coefficients of unidirectional SiC/SiC ceramic matrix composite materials at different temperatures (T 2 =100 and 200 … … ℃ 1500 ℃). The basic parameters of the material are as follows ：Ef＝140GPa,Em＝350GPa,αf＝3.1×10-6/℃,αm＝4.6×10-6/℃,vf＝0.325,vm＝0.675,rf＝6.5μm,T0＝1000℃,τ＝17MPa.
The fiber thermal stress σ f,1 and the matrix thermal stress σ m,1 at room temperature T 1 =25 ℃ were calculated:
The matrix crack spacing L at room temperature was calculated, which in this example was calculated using the common Weibull model:
wherein, the model parameter L sat＝0.2mm,σ0 = 60mpa and m = 3.
Calculating the interfacial forward slip length at room temperature as
The fiber thermal stress σ f,2 after the temperature rise to T 2 =100 ℃ was calculated:
Calculating the interfacial reverse slip length after the temperature rises to T 2 =100℃
Calculating the unidirectional SiC/SiC ceramic matrix composite thermal strain of which the temperature is increased from T 1 =25 ℃ to T 2 =100 DEG C
Calculating the thermal expansion coefficient of the unidirectional SiC/SiC ceramic matrix composite at the temperature T 2 = 100 DEG C
The thermal expansion coefficients of the unidirectional SiC/SiC ceramic matrix composite materials at the temperature of T2=200 and 300 … … ℃ are calculated by the same method, and are shown in figure 4.
The present example also predicts the thermal expansion coefficients of unidirectional SiC/SiC ceramic matrix composites at different temperatures using existing linear elastic methods, as shown in fig. 4. It can be seen that the linear elastic method is significantly larger in predicted thermal expansion coefficient because the influence of the evolution of the damage is not considered.
It should be noted that the terms like "upper", "lower", "left", "right", "front", "rear", and the like are also used for descriptive purposes only and are not intended to limit the scope of the invention in which the invention may be practiced, but rather the relative relationship of the terms may be altered or modified without materially altering the teachings of the invention.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the invention without departing from the principles thereof are intended to be within the scope of the invention as set forth in the following claims.
Claims (6)
1. The method for predicting the thermal expansion coefficient of the unidirectional ceramic matrix composite material by considering damage evolution is characterized by comprising the following steps of:
Step 1: respectively calculating the thermal stress of the fiber and the thermal stress of the matrix at the room temperature T 1;
Step 2: calculating the matrix crack spacing at room temperature by matrix thermal stress at room temperature T 1;
Step 3: calculating the interfacial forward slip length at room temperature by using the fiber thermal stress at room temperature T 1;
Step 4: calculating the thermal stress of the fiber after the temperature is increased to T 2;
Step 5: calculating the interface reverse slip length caused by the temperature rise to T 2 from the interface forward slip length at the room temperature T 1 and the fiber thermal stress at the temperature T 2;
step 6: the unidirectional ceramic matrix composite thermal strain at a temperature from T 1 to T 2 is calculated from the fiber thermal stress and the interface forward slip length at room temperature T 1, the fiber thermal stress and the interface reverse slip length at temperature T 2:
In the method, in the process of the invention, The ceramic matrix composite material is subjected to thermal strain when the temperature is increased 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 fiber filament radius, alpha f is the thermal expansion coefficient of the fiber, tau is the interfacial shear stress, d + is the interfacial forward sliding length at room temperature T 1, d - is the interfacial reverse sliding length at temperature T 2, sigma f,1 is the fiber thermal stress at room temperature T 1, and sigma f,2 is the fiber thermal stress at temperature T 2;
Step 7: the thermal expansion coefficient of the unidirectional ceramic matrix composite between the temperatures T 1 and T 2 is calculated according to the thermal strain of the unidirectional ceramic matrix composite with the temperature rising from T 1 to T 2.
2. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite in consideration of damage evolution as claimed in claim 1, wherein the method comprises the following steps: in step 1, the method for calculating the thermal stress of the fiber comprises the following steps:
the method for calculating the thermal stress of the substrate comprises the following steps:
Wherein σ f,1 and σ m,1 are respectively the thermal stress of the fiber and the matrix at room temperature T 1, E f and E m are respectively the elastic modulus of the fiber and the matrix, v f and v m are respectively the volume fraction of the fiber and the matrix, α f and α m are respectively the thermal expansion coefficients of the fiber and the matrix, and T 0 is the preparation temperature of the ceramic matrix composite.
3. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite in consideration of damage evolution as claimed in claim 1, wherein the method comprises the following steps: in the step 3, the method for calculating the forward sliding length of the interface comprises the following steps:
Where d + is the interfacial forward slip length at room temperature T 1, r f is the fiber filament radius, τ is the interfacial shear stress, and σ f,1 is the fiber thermal stress at room temperature T 1.
4. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite in consideration of damage evolution as claimed in claim 1, wherein the method comprises the following steps: in step 4, the method for calculating the thermal stress of the fiber comprises the following steps:
Wherein σ f,2 is the fiber thermal stress at the temperature T 2, E f and E m are the elastic moduli of the fiber and the matrix respectively, v f and v m are the volume fractions of the fiber and the matrix respectively, α f and α m are the thermal expansion coefficients of the fiber and the matrix respectively, and T 0 is the preparation temperature of the ceramic matrix composite.
5. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite in consideration of damage evolution as claimed in claim 1, wherein the method comprises the following steps: in step 5, the method for calculating the interface reverse slip length comprises the following steps:
Where d - is the interfacial reverse slip length at temperature T 2, r f is the fiber filament radius, τ is the interfacial shear stress, σ f,2 is the fiber thermal stress at temperature T 2, and d + is the interfacial forward slip length at room temperature T 1.
6. The method for predicting the thermal expansion coefficient of a unidirectional ceramic matrix composite in consideration of damage evolution as claimed in claim 1, wherein the method comprises the following steps: in the step 7, the method for calculating the thermal expansion coefficient of the unidirectional ceramic matrix composite material comprises the following steps:
wherein alpha c is the thermal expansion coefficient of the unidirectional ceramic matrix composite between the room temperature T 1 and the temperature T 2, Is the thermal strain of the ceramic matrix composite as the temperature rises from T 1 to T 2.
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| 陶瓷基复合材料基体随机开裂的损伤模拟;孙志刚;宋迎东;苗艳;李龙彪;;复合材料学报;20090815(04);全文 * |
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