CN114139385A - Method for predicting fatigue damage of fiber reinforced ceramic matrix composite through tangent modulus - Google Patents
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Abstract
The invention provides a method for predicting fatigue damage of a fiber reinforced ceramic matrix composite through a tangent modulus, and belongs to the technical field of composite fatigue damage prediction. The method specifically comprises the steps of obtaining a complete fiber bearing load at a peak stress position in the unloading and reloading processes according to a total load bearing criterion, obtaining an interface debonding length and a sliding length (including an unloading interface reverse sliding length and a reloading new interface sliding length) based on the complete fiber bearing load according to a fracture mechanics interface debonding criterion, determining a matrix crack interval according to a matrix random fracture model, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes on the basis, further obtaining a tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes, and predicting the fatigue damage of the fiber reinforced ceramic matrix composite material. The method provided by the invention can accurately predict the fatigue damage of the fiber reinforced ceramic matrix composite material through the tangent modulus.
Description
Technical Field
The invention relates to the technical field of composite material fatigue damage prediction, in particular to a method for predicting fatigue damage of a fiber reinforced ceramic matrix composite material through a tangent modulus.
Background
The fiber reinforced ceramic matrix composite has the advantages of high temperature resistance, corrosion resistance, low density, high specific strength, high specific modulus and the like, and compared with high-temperature alloy, the fiber reinforced ceramic matrix composite can bear higher temperature, reduce cooling airflow and improve turbine efficiency, and is applied to aeroengine combustors, turbine guide vanes, turbine shell rings, tail nozzles and the like at present.
In order to ensure the reliability and safety of the fiber reinforced ceramic matrix composite material used in the structures of airplanes and aeroengines, researchers at home and abroad use the development of tools for performance evaluation, damage evolution, strength and service life prediction of the fiber reinforced ceramic matrix composite material as the key for airworthiness evidence obtaining of structural parts of the fiber reinforced ceramic matrix composite material. In order to ensure the reliability and safety of the fiber reinforced ceramic matrix composite structure in the using process, the fatigue damage and the durability of the fiber reinforced ceramic matrix composite structure need to be deeply researched, and a method for predicting the fatigue damage of the fiber reinforced ceramic matrix composite through the tangent modulus is not established at present.
Disclosure of Invention
The invention aims to provide a method for predicting fatigue damage of a fiber reinforced ceramic matrix composite through a tangent modulus.
In order to achieve the above object, the present invention provides the following technical solutions:
the invention provides a method for predicting fatigue damage of a fiber reinforced ceramic matrix composite through a tangent modulus, which comprises the following steps:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) obtaining the intact fiber bearing load at the peak stress position in the unloading and reloading processes according to the overall load bearing criterion;
according to the fracture mechanics interface debonding rule, using intact fibers at the peak stress position in the unloading and reloading processes to bear load to obtain an interface debonding length, an unloading interface reverse slip length and a reloading new interface slip length;
(3) according to a fiber slip mechanism in the unloading and reloading processes, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes by utilizing the matrix crack spacing in the step (1) and the intact fiber bearing load, the interface debonding length, the unloading interface reverse slip length and the reloading new interface slip length at the peak stress position in the unloading and reloading processes in the step (2);
(4) obtaining the tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes according to the stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes in the step (3), so as to predict the fatigue damage of the fiber reinforced ceramic matrix composite material;
the step (1) and the step (2) are not limited in time sequence.
Preferably, the crack spacing of the substrate in the step (1) is as shown in formula 1:
wherein L iscIs the crack spacing of the matrix, LsatTo saturate the matrix crack spacing, σmIs the axial stress of the matrix, σRM is the matrix cracking characteristic stress and the matrix Weibull modulus.
Preferably, the intact fiber load at peak stress during unloading and reloading in step (2) is obtained according to equation 2:
wherein σmaxFor peak fatigue stress, VfFor the fibre volume content, phi is the load carried by the intact fibre, sigmafcIs the characteristic strength of the fiber, mfIs the fiber weibull modulus.
Preferably, the interfacial debonding length in step (2) is represented by formula 3:
wherein L isdIs the interfacial debonding length, rfIs the radius of the fiber, VmAs a volume content of the matrix, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, tauiIs interfacial shear stress, gammaiIs the interfacial debonding energy, and σ is the nominal stress.
Preferably, the unloading interface reverse slip length in the step (2) is as shown in formula 4:
wherein L isyFor the length of reverse slip of the unloading interface, phiuStress-bearing for unloading intact fibres, σuTo unload the stress.
Preferably, the reloading of the new interface slip length in step (2) is as shown in formula 5:
wherein L iszTo reload the slip length of the new interface, phirStress-bearing for reloading intact fibres,. sigmarTo reload the stress.
Preferably, the stress-strain relation equation of the fiber reinforced ceramic matrix composite material during unloading in step (3) is shown as formula 6:
wherein epsilonunloadingTo relieve strain, LcIs the crack spacing of the matrix, alphacIs the coefficient of thermal expansion of the composite material, alphafFor fiber thermal expansion coefficient, Δ T is the difference between the test temperature and the preparation temperature.
Preferably, the stress-strain relationship equation of the fiber reinforced ceramic matrix composite material during the reloading in step (3) is shown in formula 7:
wherein epsilonreloadingTo reload strain.
Preferably, the tangential modulus of the fiber reinforced ceramic matrix composite during unloading in step (4) is as shown in formula 8:
wherein, said ∑ isuTo unload the tangent modulus, Δ εuTo unload strain differential;
the delta epsilonuDetermined by equation 9:
preferably, the tangential modulus of the fiber reinforced ceramic matrix composite during the reloading in step (4) is as shown in formula 10:
wherein, said ∑ isrTo reload tangent modulus, Δ εrTo reload strain differentials;
the delta epsilonrDetermined by equation 11:
wherein σminIs fatigue valley stress.
The invention provides a method for predicting fatigue damage of a fiber reinforced ceramic matrix composite material through a tangent modulus, which specifically comprises the steps of obtaining a complete fiber bearing load at a peak stress position in the unloading and reloading processes according to a total load bearing criterion, obtaining an interface debonding length and a sliding length (including an unloading interface reverse sliding length and a reloading new interface sliding length) based on the complete fiber bearing load according to a fracture mechanics interface debonding criterion, determining a matrix crack interval according to a matrix random fracture model, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes on the basis, further obtaining the tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes, and predicting the fatigue damage of the fiber reinforced ceramic matrix composite material. The method provided by the invention can accurately predict the fatigue damage of the fiber reinforced ceramic matrix composite material through the tangent modulus.
Drawings
FIG. 1 is a graph comparing the hysteresis loops of fiber reinforced ceramic matrix composites predicted experimentally and theoretically in accordance with the present invention;
FIG. 2 is a graph comparing the tangent modulus of fiber reinforced ceramic matrix composites predicted experimentally and theoretically according to the present invention.
Detailed Description
The symbols, meanings and obtaining methods related to the method for predicting fatigue damage of the fiber reinforced ceramic matrix composite material through the tangent modulus are summarized in table 1, and in the following specific embodiment, except for special description, the symbol meanings and obtaining methods in each equation or relational expression are based on the contents in table 1 and are not repeated one by one.
TABLE 1 parameter description of method for predicting fatigue damage of fiber reinforced ceramic matrix composite by tangential modulus
Note: the composite material in Table 1 represents a fiber reinforced ceramic matrix composite material, the fibers represent fibers in the fiber reinforced ceramic matrix composite material, the matrix represents the matrix in the fiber reinforced ceramic matrix composite material, the axial direction refers to the stress loading direction, and the interface refers to the matrix/fiber interface.
Based on the description in table 1, the following description is provided for the specific implementation process of the method for predicting fatigue damage of fiber reinforced ceramic matrix composite material by using tangent modulus according to the present invention:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) obtaining the intact fiber bearing load at the peak stress position in the unloading and reloading processes according to the overall load bearing criterion;
according to the fracture mechanics interface debonding rule, using intact fibers at the peak stress position in the unloading and reloading processes to bear load to obtain an interface debonding length, an unloading interface reverse slip length and a reloading new interface slip length;
(3) according to a fiber slip mechanism in the unloading and reloading processes, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes by utilizing the matrix crack spacing in the step (1) and the intact fiber bearing load, the interface debonding length, the unloading interface reverse slip length and the reloading new interface slip length at the peak stress position in the unloading and reloading processes in the step (2);
(4) obtaining the tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes according to the stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes in the step (3), so as to predict the fatigue damage of the fiber reinforced ceramic matrix composite material;
the step (1) and the step (2) are not limited in time sequence.
The method determines the crack spacing of the matrix according to the matrix random fracture model. In the present invention, the matrix crack spacing is preferably as shown in formula 1:
wherein L iscIs the crack spacing of the matrix, LsatTo saturate the matrix crack spacing, σmIs the axial stress of the matrix, σRM is the matrix cracking characteristic stress and the matrix Weibull modulus.
In the present invention, the saturated matrix crack spacing is a stable value of the matrix crack spacing; the invention preferably adopts a formula shown in formula 1, and can obtain the crack spacing of the matrix under different stresses.
According to the overall load bearing criterion, obtaining the intact fiber bearing load at the peak stress position in the unloading and reloading processes; and according to the fracture mechanics interface debonding rule, using the intact fibers at the peak stress position in the unloading and reloading processes to bear the load to obtain the interface debonding length, the unloading interface reverse slip length and the reloading new interface slip length.
In the present invention, the intact fiber load at peak stress during the unloading and reloading is preferably obtained according to equation 2:
wherein σmaxFor peak fatigue stress, VfFor the fibre volume content, phi is the load carried by the intact fibre, sigmafcIs the characteristic strength of the fiber, mfIs the fiber weibull modulus.
The invention preferably adopts the mode to obtain the intact fiber bearing load at the peak stress position in the unloading and reloading processes, and considers the random fiber fracture process, so that the intact fiber bearing stress predicted at the peak stress position is more accurate.
In the present invention, the interfacial debonding length is preferably as shown in formula 3:
wherein L isdIs the interfacial debonding length, rfIs the radius of the fiber, VmAs a volume content of the matrix, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, tauiIs interfacial shear stress, gammaiIs the interfacial debonding energy, and σ is the nominal stress.
The method preferably adopts the mode to obtain the interface debonding length, the influence of fiber breakage on the interface debonding is considered, and the predicted interface debonding length is more accurate.
In the present invention, the unloading interface reverse slip length is preferably as shown in formula 4:
wherein L isyFor the length of reverse slip of the unloading interface, phiuStress-bearing for unloading intact fibres, σuTo unload the stress.
The unloading interface reverse slip length is preferably obtained by adopting the method, the influence of fiber breakage on the interface reverse slip length is considered, and the predicted unloading interface reverse slip length is more accurate.
In the present invention, the reloading new interface slip length is preferably as shown in equation 5:
wherein L iszTo reload the slip length of the new interface, phirStress-bearing for reloading intact fibres,. sigmarTo reload the stress.
The reloading new interface sliding length is preferably obtained by adopting the mode, the influence of fiber breakage on the reloading new interface sliding length is considered, and the predicted reloading new interface sliding length is more accurate.
According to the fiber slip mechanism in the unloading and reloading processes, the stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes is obtained by utilizing the crack spacing of the matrix and the load born by the intact fibers at the peak stress position, the debonding length of the interface, the reverse slip length of the unloading interface and the slip length of the reloading new interface in the unloading and reloading processes.
In the present invention, the stress-strain relation equation of the fiber reinforced ceramic matrix composite during the unloading process is preferably as shown in formula 6:
wherein epsilonunloadingTo relieve strain, LcIs the crack spacing of the matrix, alphacIs the coefficient of thermal expansion of the composite material, alphafFor fiber thermal expansion coefficient, Δ T is the difference between the test temperature and the preparation temperature.
The method preferably adopts the mode to obtain the strain of the fiber reinforced ceramic matrix composite material in the unloading process, considers the influence of fiber fracture on the unloading strain of the composite material, and predicts more accurate strain of the fiber reinforced ceramic matrix composite material in the unloading process.
In the present invention, the stress-strain relation equation of the fiber reinforced ceramic matrix composite during the reloading process is preferably as shown in formula 7:
wherein epsilonreloadingTo reload strain.
The invention preferably adopts the mode to obtain the strain of the fiber reinforced ceramic matrix composite material in the reloading process, considers the influence of fiber fracture on the reloading strain of the composite material, and predicts more accurate strain of the fiber reinforced ceramic matrix composite material in the reloading process.
In the present invention, the tangential modulus of the fiber reinforced ceramic matrix composite during the unloading process is preferably as shown in formula 8:
wherein, said ∑ isuTo unload the tangent modulus, Δ εuTo unload strain differential;
the delta epsilonuDetermined by equation 9:
wherein σmaxThe fatigue peak stress.
The invention preferably adopts the mode to obtain the tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading process, and the obtained tangent modulus can more accurately reflect the damage in the composite material by considering various damage mechanisms, such as matrix cracking, interface debonding and fiber fracture.
In the present invention, the tangential modulus of the fiber reinforced ceramic matrix composite during the reloading is shown as formula 10:
wherein, said ∑ isrTo reload tangent modulus, Δ εrTo reload strain differentials;
the delta epsilonrDetermined by equation 11:
wherein σminIs fatigue valley stress.
The tangential modulus of the fiber reinforced ceramic matrix composite in the reloading process is preferably obtained by adopting the mode, and the obtained tangential modulus can more accurately reflect the damage in the composite by considering various damage mechanisms, such as matrix cracking, interface debonding and fiber fracture.
In the formula related to the technical scheme, the shear model parameter (rho) is preferably obtained by calculating a shear model, and the shear model is preferably a BHE shear model. The present invention does not require any special calculation means, and may be implemented in a manner known to those skilled in the art.
The technical scheme provided by the invention is suitable for predicting the crack opening displacement of the fiber reinforced ceramic matrix composite, and the fiber reinforced ceramic matrix composite can be a woven ceramic matrix composite specifically; in the embodiment of the invention, the woven SiC/SiC ceramic matrix composite is taken as a test sample.
The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
In the embodiment, the woven SiC/SiC ceramic matrix composite is used as a test sample, and the fatigue damage of the fiber reinforced ceramic matrix composite is predicted through the tangent modulus:
providing parameters: vf＝0.35，rf＝7.5μm，Ef＝200GPa，Em＝300GPa，αf＝3×10-6/℃，αm＝4×10-6/℃，τi＝40MPa，Γi＝5J/m2，mf＝5，σfc＝2.0GPa；
The preparation temperature of the composite material is 1020 ℃, the test temperature is 20 ℃, and the delta T is-1000 ℃;
and then obtaining the tangent modulus of the fiber reinforced ceramic matrix composite according to the formulas 1-11, and further realizing the prediction of the fatigue damage of the fiber reinforced ceramic matrix composite.
FIG. 1 is a comparison graph of the hysteresis loops of the fiber reinforced ceramic matrix composite according to the present invention, wherein the solid line in FIG. 1 is the actual test data, and the dotted line is the predicted result according to the present invention; as can be seen from fig. 1, the hysteresis loop predicted by the method of the present invention matches the experimental data. FIG. 2 is a graph showing the tangent modulus of the fiber reinforced ceramic matrix composite according to the present invention, as predicted by the experiment and theory, and the solid line in FIG. 2 is the actual test data and the dotted line is the predicted result according to the present embodiment; as can be seen from FIG. 2, the tangential moduli at different peak stresses predicted by the method provided by the present invention are consistent with the test data. In conclusion, the method can accurately predict the fatigue damage of the fiber reinforced ceramic matrix composite.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (10)
1. A method for predicting fatigue damage of a fiber reinforced ceramic matrix composite through a tangent modulus comprises the following steps:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) obtaining the intact fiber bearing load at the peak stress position in the unloading and reloading processes according to the overall load bearing criterion;
according to the fracture mechanics interface debonding rule, using intact fibers at the peak stress position in the unloading and reloading processes to bear load to obtain an interface debonding length, an unloading interface reverse slip length and a reloading new interface slip length;
(3) according to a fiber slip mechanism in the unloading and reloading processes, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes by utilizing the matrix crack spacing in the step (1) and the intact fiber bearing load, the interface debonding length, the unloading interface reverse slip length and the reloading new interface slip length at the peak stress position in the unloading and reloading processes in the step (2);
(4) obtaining the tangent modulus of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes according to the stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes in the step (3), so as to predict the fatigue damage of the fiber reinforced ceramic matrix composite material;
the step (1) and the step (2) are not limited in time sequence.
2. The method of claim 1, wherein the substrate crack spacing in step (1) is as shown in equation 1:
wherein L iscIs the crack spacing of the matrix, LsatTo saturate the matrix crack spacing, σmIs the axial stress of the matrix, σRM is the matrix cracking characteristic stress and the matrix Weibull modulus.
3. The method of claim 1, wherein the intact fiber loading at peak stress during unloading and reloading in step (2) is obtained according to equation 2:
wherein σmaxFor peak fatigue stress, VfFor the fibre volume content, phi is the load carried by the intact fibre, sigmafcIs the characteristic strength of the fiber, mfIs the fiber weibull modulus.
4. The method of claim 3, wherein the interfacial debonding length in step (2) is shown by formula 3:
wherein L isdIs the interfacial debonding length, rfIs the radius of the fiber, VmAs a volume content of the matrix, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, tauiIs interfacial shear stress, gammaiIs the interfacial debonding energy, and σ is the nominal stress.
5. The method of claim 4, wherein the unloading interface reverse slip length in step (2) is as shown in equation 4:
wherein L isyFor the length of reverse slip of the unloading interface, phiuStress-bearing for unloading intact fibres, σuTo unload the stress.
6. The method of claim 5, wherein the step (2) reloading a new interface slip length is as shown in equation 5:
wherein L iszTo reload the slip length of the new interface, phirStress-bearing for reloading intact fibres,. sigmarTo reload the stress.
7. The method according to claim 6, wherein the stress-strain relationship equation for the fiber reinforced ceramic matrix composite material during unloading in step (3) is as shown in equation 6:
wherein epsilonunloadingTo relieve strain, LcIs the crack spacing of the matrix, alphacIs the coefficient of thermal expansion of the composite material, alphafFor fiber thermal expansion coefficient, Δ T is the difference between the test temperature and the preparation temperature.
8. The method according to claim 7, wherein the stress-strain relationship equation for the fiber reinforced ceramic matrix composite material during the reloading in step (3) is as shown in equation 7:
wherein epsilonreloadingTo reload strain.
9. The method according to claim 8, wherein the tangential modulus of the fiber reinforced ceramic matrix composite material during unloading in step (4) is as shown in equation 8:
wherein, said ∑ isuTo unload the tangent modulus, Δ εuTo unload strain differential;
the delta epsilonuDetermined by equation 9:
10. the method according to claim 9, wherein the tangential modulus of the fiber reinforced ceramic matrix composite during the reloading in step (4) is as shown in equation 10:
wherein, said ∑ isrTo reload tangent modulus, Δ εrTo reload strain differentials;
the delta epsilonrDetermined by equation 11:
wherein σminIs fatigue valley stress.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114936474A (en) * | 2022-06-24 | 2022-08-23 | 南京航空航天大学 | Method for predicting interface shear stress of fiber reinforced ceramic matrix composite material through hysteresis loop width |
| CN114943148A (en) * | 2022-05-20 | 2022-08-26 | 南京航空航天大学 | Method for predicting interface property of fiber reinforced ceramic matrix composite material through tangent modulus |
| CN117571507A (en) * | 2024-01-16 | 2024-02-20 | 中国航空工业集团公司金城南京机电液压工程研究中心 | Calculation method of interface shear stress value of unidirectional composite material |
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2021
- 2021-12-03 CN CN202111465610.5A patent/CN114139385A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114943148A (en) * | 2022-05-20 | 2022-08-26 | 南京航空航天大学 | Method for predicting interface property of fiber reinforced ceramic matrix composite material through tangent modulus |
| CN114936474A (en) * | 2022-06-24 | 2022-08-23 | 南京航空航天大学 | Method for predicting interface shear stress of fiber reinforced ceramic matrix composite material through hysteresis loop width |
| CN117571507A (en) * | 2024-01-16 | 2024-02-20 | 中国航空工业集团公司金城南京机电液压工程研究中心 | Calculation method of interface shear stress value of unidirectional composite material |
| CN117571507B (en) * | 2024-01-16 | 2024-04-09 | 中国航空工业集团公司金城南京机电液压工程研究中心 | Calculation method of interface shear stress value of unidirectional composite material |
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