CN114139388A - Method for predicting non-closed hysteresis loop of fiber reinforced ceramic matrix composite - Google Patents
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Abstract
The invention provides a method for predicting a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite, and belongs to the technical field of prediction of the non-closed hysteresis loop of the composite. The method for predicting the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite comprises the steps of firstly determining the crack distance of a matrix according to a matrix random fracture model, determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length by adopting a fracture mechanics interface debonding rule, then analyzing the fiber axial stress distribution in the unloading and reloading processes on the basis, and further obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes so as to predict the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite. The method provided by the invention can accurately predict the non-closed hysteresis behavior of the fiber reinforced ceramic matrix composite.
Description
Technical Field
The invention relates to the technical field of composite material non-closed hysteresis loop prediction, in particular to a method for predicting a fiber reinforced ceramic matrix composite material non-closed hysteresis loop.
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 evolution of the fiber reinforced ceramic matrix composite structure needs to be analyzed, and a related theoretical prediction method is not established at present aiming at the non-closed hysteresis behavior of the fiber reinforced ceramic matrix composite.
Disclosure of Invention
The invention aims to provide a method for predicting a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite, which can accurately predict the non-closed hysteresis behavior of the fiber reinforced ceramic matrix composite.
In order to achieve the above object, the present invention provides the following technical solutions:
the invention provides a method for predicting a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite, which comprises the following steps:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length according to the fracture mechanics interface debonding criterion;
(3) according to an interface slippage mechanism in the unloading and reloading processes, obtaining a fiber axial stress distribution equation in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length, the unloading interface reverse slippage length and the reloading interface new slippage length obtained in the step (2);
(4) according to a load transfer mechanism between the fiber and the matrix, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length obtained in the step (2), the unloading interface reverse slip length, the reloading interface new slip length and the fiber axial stress distribution equation in the unloading and reloading processes obtained in the step (3), so as to predict the non-closed hysteresis loop 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 iscrackingIs 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 interfacial debonding length in step (2) is represented by formula 2:
wherein L isdebondingIs the interfacial debonding length, σmaxFor peak fatigue stress, VfIs the fiber volume content, V, in the composite materialmIs the volume content of matrix in the composite material, RfIs the fiber radius, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the modulus of elasticity, τ, of the composite materialiFriction shear stress, gamma, in the interfacial debonding regioniIs the interfacial debonding energy, and rho is the shear-lag model parameter.
Preferably, the unloading interface reverse slip length in the step (2) is as shown in formula 3:
wherein L iscounter_slipFor the length of the reverse slip of the unloading interface, σunloadingTo unload the stress.
Preferably, the reloading interface new slip length in the step (2) is as shown in formula 4:
wherein L isnew_slipFor reloading the interface with new slip length, σreloadingTo reload the stress.
Preferably, the fiber axial stress distribution equation during unloading in step (3) is as shown in formula 5:
in the formula, σf(x) Is the axial stress of the fiber, x is the axial value, sigmafoFor the fibre axial stress, σ, in the interfacial bonding zonemoAxial stress of the substrate in the interface bonding zone, LcrackingThe matrix crack spacing.
Preferably, the fiber axial stress distribution equation during the reloading in the step (3) is shown as formula 6:
preferably, the stress-strain relation equation of the fiber reinforced ceramic matrix composite material during unloading in the step (4) is shown as formula 7:
wherein epsilonunloadingTo relieve strain, αcIs the coefficient of thermal expansion of the composite material, alphafIs the fiber thermal expansion coefficient, delta T is the difference between the testing temperature and the preparation temperature, eta is the interfacial debonding ratio, and gamma is the interface reverse slipShifting ratio;
the η is determined by equation 8, and the γ is determined by equation 9:
preferably, the stress-strain relationship equation of the fiber reinforced ceramic matrix composite material during the reloading in step (4) is shown as formula 10:
wherein epsilonreloadingTo reload strain, σ is the stress,
the new slip ratio of the interface is obtained;
the above-mentioned
Determined by equation 11:
the invention provides a method for predicting a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite, which comprises the steps of firstly determining the crack distance of a matrix according to a matrix random fracture model, determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length by adopting a fracture mechanics interface debonding rule, then analyzing the fiber axial stress distribution in the unloading and reloading processes on the basis, and further obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes so as to predict the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite. The method provided by the invention can accurately predict the non-closed hysteresis behavior of the fiber reinforced ceramic matrix composite.
Drawings
FIG. 1 is a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite of the present invention;
FIG. 2 is a graph illustrating experimental and theoretical prediction of a non-closed hysteresis loop for a fiber reinforced ceramic matrix composite material according to the present invention.
Detailed Description
The symbols, meanings and obtaining methods related to the method for predicting the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite provided by the invention 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 description of parameters in the method for predicting non-closed hysteresis loop of fiber reinforced ceramic matrix composite
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 the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material provided by the present invention:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length according to the fracture mechanics interface debonding criterion;
(3) according to an interface slippage mechanism in the unloading and reloading processes, obtaining a fiber axial stress distribution equation in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length, the unloading interface reverse slippage length and the reloading interface new slippage length obtained in the step (2);
(4) according to a load transfer mechanism between the fiber and the matrix, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length obtained in the step (2), the unloading interface reverse slip length, the reloading interface new slip length and the fiber axial stress distribution equation in the unloading and reloading processes obtained in the step (3), so as to predict the non-closed hysteresis loop 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 a matrix random fracture model, wherein the crack spacing of the matrix is preferably as shown in a formula 1:
wherein L iscrackingIs 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.
The method determines the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length according to the fracture mechanics interface debonding rule.
In the present invention, the interfacial debonding length is preferably as shown in formula 2:
wherein L isdebondingIs the interfacial debonding length, σmaxFor peak fatigue stress, VfIs the fiber volume content, V, in the composite materialmIs the volume content of matrix in the composite material, RfIs the fiber radius, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the modulus of elasticity, τ, of the composite materialiFriction shear stress, gamma, in the interfacial debonding regioniIs the interfacial debonding energy, and rho is the shear-lag model parameter.
In the invention, the fracture mechanics interface debonding criterion can consider the influence of the interface debonding energy on the interface debonding; the invention preferably adopts a formula shown in formula 2, and can accurately predict the debonding length of the interface.
In the present invention, the unloading interface reverse slip length is preferably as shown in formula 3:
wherein L iscounter_slipFor the length of the reverse slip of the unloading interface, σunloadingTo unload the stress.
In the invention, the fracture mechanics interface debonding criterion can consider the influence of the interface debonding energy on the interface reverse slip length extension; the invention preferably adopts a formula shown in formula 3, and can accurately predict the reverse slip length of the interface.
In the present invention, the reloading interface new slip length is preferably as shown in formula 4:
wherein L isnew_slipFor reloading the interface with new slip length, σreloadingTo reload the stress.
In the invention, the fracture mechanics interface debonding criterion can consider the influence of the interface debonding energy on the expansion of the new slippage length of the interface; the invention preferably adopts a formula shown in formula 4, and can accurately predict the new slippage length of the interface.
According to the interface slippage mechanism in the unloading and reloading processes, the fiber axial stress distribution equation in the unloading and reloading processes is obtained by utilizing the matrix crack spacing, the interface debonding length, the unloading interface reverse slippage length and the reloading interface new slippage length.
In the present invention, the fiber axial stress distribution equation during the unloading process is preferably as shown in formula 5:
in the formula, σf(x) Is the axial stress of the fiber, x is the axial value, sigmafoFor the fibre axial stress, σ, in the interfacial bonding zonemoAxial stress of the substrate in the interface bonding zone, LcrackingThe matrix crack spacing.
As shown in formula 5, when the axial stress distribution of the fiber in the unloading process is researched, the area section from the crack of the matrix to 1/2 of the distance between the cracks of the adjacent matrix is preferably researched, and the area section is more preferably divided into interface reverse slip areas [ 0-L ]counter_slip]Interfacial slip zone [ L ]counter_slip～Ldebonding]And interfacial bonding region [ Ldebonding～Lcracking/2]And different calculation methods are provided for different areas so as to improve the accuracy of the fiber axial stress distribution prediction result in the unloading process. When x is equal to Lcounter_slipDuring the unloading process, the axial stress of the fiber in the unloading process can be substituted into any formula for calculation, and preferably substituted into a formula for an interface reverse slip region for calculation; when x is equal to LdebondingAxial stress of the fiber during unloadingThe calculation can be carried out by substituting into any formula, preferably into a formula for the interfacial slip zone.
The invention preferably adopts a formula shown in formula 5, and can obtain the distribution conditions of the axial stress of the fibers in different areas in the unloading process.
In the present invention, the fiber axial stress distribution equation during the reloading process is preferably as shown in formula 6:
as shown in formula 6, when the axial stress distribution of the fiber in the reloading process is researched, the area section from the crack of the matrix to 1/2 of the distance between the cracks of the adjacent matrix is preferably researched, and the area section is more preferably divided into new sliding areas (0-L) of the interfacenew_slip) Interfacial reverse slip region (L)new_slip～Lcounter_slip) Interfacial slip zone (L)counter_slip～Ldebonding) And an interface bonding region (L)debonding～LcrackingAnd/2) and aiming at different areas, different calculation methods are provided so as to improve the accuracy of the fiber axial stress distribution prediction result in the reloading process. When x is equal to Lnew_slipDuring the process, the axial stress of the fiber in the reloading process can be substituted into any formula for calculation, and preferably substituted into a formula for a new sliding zone of the interface for calculation; when x is equal to Lcounter_slipDuring the process, the axial stress of the fiber in the reloading process can be substituted into any formula for calculation, and preferably substituted into a formula for an interface reverse slip region for calculation; when x is equal to LdebondingIn the case of a fiber axial stress during the reloading process, the axial stress can be calculated by substituting the axial stress into any formula, preferably into a formula for the interfacial slippage zone.
The invention preferably adopts a formula shown in formula 6, and can obtain the distribution condition of the axial stress of the fiber in different areas in the reloading process.
According to the load transfer mechanism between the fiber and the matrix, the stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes is obtained by utilizing the matrix crack distance, the interface debonding length, the unloading interface reverse slip length, the reloading interface new slip length and the fiber axial stress distribution equation in the unloading and reloading processes, so that the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material is predicted.
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 7:
wherein epsilonunloadingTo relieve strain, αcIs the coefficient of thermal expansion of the composite material, alphafThe thermal expansion coefficient of the fiber is adopted, delta T is the difference value between the testing temperature and the preparation temperature, eta is the interface debonding ratio, and gamma is the interface reverse slip ratio;
the η is preferably determined by equation 8, and the γ is preferably determined by equation 9:
in the present invention, the stress-strain relationship equation of the fiber reinforced ceramic matrix composite during the reloading process is preferably as shown in formula 10:
wherein epsilonreloadingTo reload strain, σ is the stress,
the new slip ratio of the interface is obtained;
the above-mentioned
Preferably determined by equation 11:
according to the stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes, the change curve of the stress along with the strain under the unloading and reloading conditions is obtained, and therefore the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material is obtained.
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 non-closed hysteresis behavior of the fiber reinforced ceramic matrix composite, and the fiber reinforced ceramic matrix composite can be specifically a woven ceramic matrix composite; in the embodiment of the invention, the woven SiC/SiC ceramic matrix composite is used as a test sample, and the non-closed hysteresis loop of the test sample is predicted.
The method comprises the steps of firstly determining the crack distance of a matrix according to a matrix random fracture model, determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length by adopting a fracture mechanics interface debonding rule, and then analyzing the fiber axial stress distribution in the unloading and reloading processes on the basis, so as to obtain a stress-strain relation equation of the fiber reinforced ceramic matrix composite in the unloading and reloading processes, thereby predicting the non-closed hysteresis loop of the fiber reinforced ceramic matrix composite. Specifically, fig. 1 shows a non-closed hysteresis loop of the fiber-reinforced ceramic matrix composite according to the present invention, and as can be seen from fig. 1, the hysteresis loop is non-closed during the unloading and reloading processes, such that the non-closed hysteresis behavior of the fiber-reinforced ceramic matrix composite can be accurately predicted.
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
Establishing a required stress-strain relation equation according to the prediction method provided by the invention, taking the woven SiC/SiC ceramic matrix composite material as a test sample, and predicting a non-closed hysteresis loop of the test sample:
providing parameters: vf＝0.44，Rf＝6.5μm，Ef＝372GPa，Em＝550GPa，αf＝4.5×10-6/℃，αm＝4.6×10-6/℃，τi＝50MPa，Γi＝2.5J/m2；
The preparation temperature of the composite material is 1020 ℃, the test temperature is 20 ℃, and the delta T is-1000 ℃;
and then establishing a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes according to the formulas 1-11 so as to obtain a stress-strain relation, and further constructing a stress-strain relation curve shown in figure 2 so as to obtain a non-closed hysteresis loop of the fiber reinforced ceramic matrix composite material. The solid line in fig. 2 is a stress-strain relationship curve constructed by the method, and different points are actual test data, so that the shape and position of the non-closed hysteresis loop predicted by the method provided by the invention are consistent with the experimental data, which shows that the method provided by the invention can accurately predict the non-closed hysteresis loop 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 (9)
1. A method for predicting a non-closed hysteresis loop of a fiber reinforced ceramic matrix composite, comprising the steps of:
(1) determining the crack spacing of the matrix according to the matrix random fragmentation model;
(2) determining the interface debonding length, the unloading interface reverse slip length and the reloading interface new slip length according to the fracture mechanics interface debonding criterion;
(3) according to an interface slippage mechanism in the unloading and reloading processes, obtaining a fiber axial stress distribution equation in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length, the unloading interface reverse slippage length and the reloading interface new slippage length obtained in the step (2);
(4) according to a load transfer mechanism between the fiber and the matrix, obtaining a stress-strain relation equation of the fiber reinforced ceramic matrix composite material in the unloading and reloading processes by utilizing the matrix crack spacing obtained in the step (1), the interface debonding length obtained in the step (2), the unloading interface reverse slip length, the reloading interface new slip length and the fiber axial stress distribution equation in the unloading and reloading processes obtained in the step (3), so as to predict the non-closed hysteresis loop 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 iscrackingIs 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 interfacial debonding length in step (2) is represented by formula 2:
wherein L isdebondingIs the interfacial debonding length, σmaxFor peak fatigue stress, VfIs the fiber volume content, V, in the composite materialmIs the volume content of matrix in the composite material, RfIs the fiber radius, EfIs the modulus of elasticity of the fiber, EmAs a matrix elastic modulus, EcIs the modulus of elasticity, τ, of the composite materialiFriction shear stress, gamma, in the interfacial debonding regioniIs the interfacial debonding energy, and rho is the shear-lag model parameter.
4. The method of claim 3, wherein the unloading interface reverse slip length in step (2) is as shown in equation 3:
wherein L iscounter_slipFor the length of the reverse slip of the unloading interface, σunloadingTo unload the stress.
5. The method of claim 4, wherein the reloading interface new slip length in step (2) is as shown in equation 4:
wherein L isnew_slipFor reloading the interface with new slip length, σreloadingTo reload the stress.
6. The method of claim 5, wherein the fiber axial stress distribution during unloading in step (3) is represented by equation 5:
in the formula, σf(x) Is the axial stress of the fiber, x is the axial value, sigmafoFor the fibre axial stress, σ, in the interfacial bonding zonemoAxial stress of the substrate in the interface bonding zone, LcrackingThe matrix crack spacing.
7. The method of claim 6, wherein the fiber axial stress distribution during the reloading in step (3) is given by the equation of equation 6:
8. the method according to claim 7, wherein the stress-strain relationship equation for the fiber reinforced ceramic matrix composite material during unloading in step (4) is given by equation 7:
wherein epsilonunloadingTo relieve strain, αcIs the coefficient of thermal expansion of the composite material, alphafThe thermal expansion coefficient of the fiber is adopted, delta T is the difference value between the testing temperature and the preparation temperature, eta is the interface debonding ratio, and gamma is the interface reverse slip ratio;
the η is determined by equation 8, and the γ is determined by equation 9:
9. the method according to claim 8, wherein the stress-strain relationship equation for the fiber reinforced ceramic matrix composite material during the reloading in step (4) is as shown in equation 10:
wherein epsilonreloadingTo reload strain, σ is the stress,
the new slip ratio of the interface is obtained;
the above-mentioned
Determined by equation 11:
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| CN113032982A (en) * | 2021-03-10 | 2021-06-25 | 南京航空航天大学 | Prediction method of fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage |
| CN113051719A (en) * | 2021-03-10 | 2021-06-29 | 南京航空航天大学 | Prediction method of tensile-compression fatigue hysteresis loop of woven ceramic matrix composite |
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| CN113051719A (en) * | 2021-03-10 | 2021-06-29 | 南京航空航天大学 | Prediction method of tensile-compression fatigue hysteresis loop of woven ceramic matrix composite |
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