CN113032982A - Prediction method of fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage - Google Patents
Prediction method of fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage Download PDFInfo
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Abstract
The invention provides a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage, and belongs to the technical field of composite material fatigue hysteresis loop prediction. The method provided by the invention specifically comprises the steps of analyzing the matrix of the woven ceramic matrix composite and the fiber breaking process, and determining the random cracking process of matrix cracks, the fiber breaking probability and the intact fiber bearing stress; based on the unloading and reloading slippage mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the matrix and the fiber breakage is obtained, so that the stress-strain hysteresis loop of the woven ceramic matrix composite material is predicted. The method provided by the invention considers the influence of matrix and fiber breakage factors on the fatigue hysteresis loop, can accurately predict the damage problem of matrix and fiber breakage on the woven ceramic matrix composite material, and improves the prediction accuracy of the hysteresis loop of the woven ceramic matrix composite material.
Description
Technical Field
The invention relates to the technical field of composite material fatigue hysteresis loop prediction, in particular to a prediction method of a woven ceramic matrix composite material fatigue hysteresis loop considering matrix and fiber breakage.
Background
The woven ceramic matrix composite has the advantages of high temperature resistance, corrosion resistance, low density, high specific strength, high specific modulus and the like, can bear higher temperature compared with high-temperature alloy, reduces cooling airflow and improves turbine efficiency, and is applied to aeroengine combustors, turbine guide blades, turbine shell rings, tail nozzles and the like at present. The LEAP (leading Edge Aviation Propulsion) series engine developed by CFM company, the high-pressure turbine adopts a woven ceramic matrix composite material component, the LEAP-1B engine provides power for an air passenger A320 and a Boeing 737MAX, and the LEAP-X1C engine provides power for a large aircraft C919.
In order to ensure the reliability and safety of the woven ceramic matrix composite material used in the structures of airplanes and aero-engines, researchers at home and abroad use the development of tools for performance evaluation, damage evolution, strength and service life prediction of the ceramic matrix composite material as the key for obtaining evidence of airworthiness of the structural parts of the ceramic matrix composite material. Under the action of fatigue load, multiple damage mechanisms such as matrix multi-cracking, fiber/matrix interface debonding and slipping occur in the woven ceramic matrix composite, so that the stress-strain curve has an obvious hysteresis phenomenon in the unloading and reloading processes.
At present, the fatigue hysteresis loop of the woven ceramic matrix composite is researched, and the influence of matrix and fiber breakage on the hysteresis loop is not considered (Lilong Biao, research on a fatigue hysteresis loop model of the fiber reinforced ceramic matrix composite [ J ], mechanical science report 2014, 5: 710-. How to consider the influence of matrix and fiber breakage on the fatigue hysteresis loop of the woven ceramic matrix composite and monitor the damage of the matrix and the fiber breakage on the composite is a key technical problem to be solved in the practical engineering application of the woven ceramic matrix composite structure.
Disclosure of Invention
The invention aims to provide a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material by considering matrix and fiber breakage.
In order to achieve the above object, the present invention provides the following technical solutions:
the invention provides a prediction method of fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage, which comprises the following steps:
(1) analyzing the matrix fracture process of the woven ceramic matrix composite according to the matrix random fracture theory, and dividing the matrix cracks of the woven ceramic matrix composite into short cracks, medium cracks and long cracks based on the matrix fracture characteristics and the fracture length; obtaining a matrix crack random cracking process according to a matrix random cracking theory, wherein the matrix crack random cracking process is represented by a short crack distribution function, a medium crack distribution function and a long crack distribution function;
analyzing the fiber breaking process of the woven ceramic matrix composite, and obtaining the fiber breakage probability and the intact fiber bearing stress based on the overall load bearing criterion;
(2) respectively establishing an interface debonding length equation, an unloading interface reverse slip length equation and a reloading interface new slip length equation according to a fracture mechanics interface debonding rule and based on an interface debonding mechanism and a slip mechanism;
(3) according to a matrix fracture theory, establishing a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a middle crack unloading stress-strain relation equation, a middle crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation based on the matrix crack random cracking process, the fiber fracture probability and the intact fiber borne stress in the step (1) and the interface debonding length equation, the unloading interface reverse slip length equation and the reloading interface new slip length equation in the step (2), and further establishing a stress-strain relation equation of the woven ceramic matrix composite material hysteresis loop so as to predict the fatigue hysteresis loop of the woven ceramic matrix composite material considering matrix and fiber breakage.
Preferably, in the step (1), the short crack, the medium crack and the long crack are respectively:
short crack, Lcracking<Ldebonding；
Middle crack, Ldebonding<Lcracking<2Ldebonding；
Long crack, 2Ldebonding<Lcracking；
Wherein L iscrackingIs the crack spacing of the matrix, LdebondingIs the interfacial debonding length;
the breaking process of the matrix of the woven ceramic matrix composite is determined by a formula shown in formulas 1-5:
wherein L is the initial simulated total length, LeffFor effective simulated length, P (x) is a distribution function of the crack spacing of the matrix greater than the debond length of the interface, PR(x) Is a distribution function of matrix crack spacing smaller than interface debonding length, N is matrix fracture number, x is axial value, sigma is stress, N is matrix fracture density, and deltaDIs the dirac function, phi (sigma, L)eff) Is a matrix Weibull function;
the phi (sigma, L)eff) ByThe formula shown in equation 6 determines:
wherein A is0Is a reference area, LRTo reference length, σ0For reference stress, m is the matrix Weibull modulus.
Preferably, in the step (1), the fiber breaking process of the woven ceramic matrix composite is determined by a formula shown in formulas 7 to 9:
wherein phi is the stress borne by the intact fiber, q is the fiber fracture probability, phibFor breaking the fibres to bear the load, mfIs the Weibull modulus, σ, of the fiberfcThe characteristic strength of the fiber is X is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, VfIs the fiber volume content in the composite material.
Preferably, in the step (2), the criterion of fracture-mechanical interface debonding satisfies the equation shown in formula 10:
wherein, gamma isdIs interfacial debonding energy, wf(0) The axial displacement of the crack plane fiber of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, rfIs the radius of the fiber, τiIs the friction shear stress of the debonding area of the interface, and F is the crack planar fiber of the matrixThe dimension bears the load.
Preferably, in the step (2), the interfacial debonding length equation is shown in formula 11:
wherein, VmIs the matrix volume content in the composite material, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, EfIs the fiber modulus of elasticity;
the unloading interface reverse slip length equation is shown in equation 12:
wherein L iscsIs the unloading interface reverse slip length;
the reloading interface new slip length equation is shown in equation 13:
wherein L isnsThe new slip length for the reload interface.
Preferably, in the step (3), the stress-strain relation equation of the hysteresis loop of the woven ceramic matrix composite material is shown in formula 14:
wherein epsiloncStrain of hysteresis loop of composite material, PS(x) As a function of short crack distribution, PM(x) As a function of the median crack distribution, PL(x) As a function of the long crack distribution,. epsilonthIs the thermal residual strain, σf(z) is the fiber axial stress distribution.
Preferably, in the step (3), the long crack unloading stress-strain relation equation is as shown in formula 15:
wherein epsilonULStress relief for long cracks, rfIs the radius of the fiber, [ phi ]UStress-bearing for unloading intact fibres, L0And L1The long crack coefficient;
the long crack reload stress-strain relation equation is shown as formula 16:
wherein epsilonRLFor reloading long cracks with strain, [ phi ]RBearing stress for reloading intact fibers;
said L0Determined by the formula shown in formula 17-1, L1Determined by the formula shown in equation 17-2:
preferably, in the step (3), the equation of the stress-strain relation of the medium fracture unloading is shown as formula 18:
wherein epsilonUMRelief of strain for median cracks, M0、M1And M2The median crack coefficient.
The mid-crack reload stress-strain relation equation is shown as formula 19:
wherein epsilonRMReloading the median crack with strain;
the M is0Determined by the formula shown in equation 20-1, M1Determined by the formula shown in equation 20-2, M2Determined by the formula shown in equation 20-3:
preferably, in the step (3), the short crack unloading stress-strain relation equation is as shown in formula 21:
wherein epsilonUSStress relief for short crackstr_unloadingTo relieve the transition stress, S0、S1And S2Is the fracture coefficient;
the short crack reloading stress-strain relationship equation is shown in equation 22:
in the formula, epsilonRSRe-stressing the short cracks with strain, σtr_reloadingTo reload the transformation stress;
said S0Determined by the formula shown in formula 23-1, S1Determined by the formula shown in formula 23-2, S2By the formula 23-The formula shown in fig. 3 determines:
preferably, the fiber effective volume content coefficient of the woven ceramic matrix composite material along the stress loading direction satisfies the formula shown in the formula 24:
wherein, Vf_loadingFiber volume content of composite material along stress loading direction
The invention provides a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage, which specifically comprises the steps of analyzing the matrix of the woven ceramic matrix composite material and the fiber breakage process, and determining the random cracking process of matrix cracks, the fiber breakage probability and the stress born by intact fibers; based on the unloading and reloading slippage mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the matrix and the fiber breakage, namely the short crack, the middle crack and the long crack loading and unloading fiber axial stress-strain relation equation is obtained, so that the stress-strain hysteresis loop of the woven ceramic matrix composite material is predicted. The method provided by the invention considers the influence of matrix and fiber breakage factors on the fatigue hysteresis loop, can accurately predict the damage problem of matrix and fiber breakage on the woven ceramic matrix composite material, and improves the prediction accuracy of the hysteresis loop of the woven ceramic matrix composite material.
Drawings
FIG. 1 is a graph of short, medium and long crack unload and reload fiber axial stress profiles in accordance with the present invention;
FIG. 2 is a fatigue hysteresis loop of the woven ceramic matrix composite material according to the experimental and theoretical predictions of the present invention.
Detailed Description
The symbols, meanings and obtaining methods related to the prediction method of the fatigue hysteresis loop of the woven ceramic matrix composite material considering the matrix and the fiber breakage provided by the invention are summarized in table 1, and in the following specific implementation mode, 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 in prediction method of fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage
Note: the composite material in Table 1 represents a woven ceramic matrix composite, the fibers represent fibers in the woven ceramic matrix composite, the matrix represents the matrix in the woven ceramic matrix composite, the axial direction refers to the direction of stress loading, and the interface refers to the matrix/fiber interface.
Based on the description in table 1, the following description is made on the specific implementation process of the prediction method of fatigue hysteresis loop of the woven ceramic matrix composite material considering matrix and fiber breakage provided by the present invention:
(1) analyzing the matrix fracture process of the woven ceramic matrix composite according to the matrix random fracture theory, and dividing the matrix cracks of the woven ceramic matrix composite into short cracks, medium cracks and long cracks based on the matrix fracture characteristics and the fracture length; obtaining a matrix crack random cracking process according to a matrix random cracking theory, wherein the matrix crack random cracking process is represented by a short crack distribution function, a medium crack distribution function and a long crack distribution function;
analyzing the fiber breaking process of the woven ceramic matrix composite, and obtaining the fiber breakage probability and the intact fiber bearing stress based on the overall load bearing criterion;
(2) respectively establishing an interface debonding length equation, an unloading interface reverse slip length equation and a reloading interface new slip length equation according to a fracture mechanics interface debonding rule and based on an interface debonding mechanism and a slip mechanism;
(3) according to a matrix fracture theory, establishing a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a middle crack unloading stress-strain relation equation, a middle crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation based on the matrix crack random cracking process, the fiber fracture probability and the intact fiber borne stress in the step (1) and the interface debonding length equation, the unloading interface reverse slip length equation and the reloading interface new slip length equation in the step (2), and further establishing a stress-strain relation equation of the woven ceramic matrix composite material hysteresis loop so as to predict the fatigue hysteresis loop of the woven ceramic matrix composite material considering matrix and fiber breakage.
The invention provides a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage, which specifically comprises the steps of analyzing the matrix of the woven ceramic matrix composite material and the fiber breakage process, and determining the random cracking process of matrix cracks, the fiber breakage probability and the stress born by intact fibers; based on the unloading and reloading slippage mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the matrix and the fiber breakage, namely the short crack, the middle crack and the long crack loading and unloading fiber axial stress-strain relation equation is obtained, so that the stress-strain hysteresis loop of the woven ceramic matrix composite material is predicted.
According to the matrix random cracking theory, the matrix breaking process of the woven ceramic matrix composite is analyzed, and cracks of the matrix of the woven ceramic matrix composite are divided into short cracks, medium cracks and long cracks based on the matrix cracking characteristics and the breaking length; obtaining a matrix crack random cracking process, wherein the matrix crack random cracking process is represented by a short crack distribution function, a medium crack distribution function and a long crack distribution function; and analyzing the fiber breaking process of the woven ceramic matrix composite material, and obtaining the fiber breakage probability and the intact fiber bearing stress based on the overall load bearing criterion.
In the present invention, the short crack, the medium crack and the long crack are preferably:
short crack, Lcracking<Ldebonding；
Middle crack, Ldebonding<Lcracking<2Ldebonding；
Long crack, 2Ldebonding<Lcracking；
Wherein L iscrackingIs the crack spacing of the matrix, LdebondingThe interfacial debonding length.
According to the invention, the short cracks, the medium cracks and the long cracks are preferably divided according to the mode, so that the breaking condition of the matrix can be better described, and the real hysteresis relationship can be obtained.
In the invention, the breaking process of the matrix of the woven ceramic matrix composite is preferably determined by a formula shown in formulas 1-5:
wherein L is the initial simulated total length, LeffFor effective simulated length, P (x) is a distribution function of the crack spacing of the matrix greater than the debond length of the interface, PR(x) Is a distribution function of matrix crack spacing smaller than interface debonding length, N is matrix fracture number, x is axial value, sigma is stress, N is matrix fracture density, and deltaDIs the dirac function, phi (sigma, L)eff) Is a matrix Weibull function;
the phi (sigma, L)eff) Determined by the formula shown in equation 6:
wherein A is0Is a reference area, LRTo reference length, σ0For reference stress, m is the matrix Weibull modulus
In the invention, the cracking process of the matrix of the woven ceramic matrix composite is preferably determined by the formula shown in the formula 1-5, the matrix fracture condition can be represented, and the matrix fracture condition can be better obtained.
In the invention, the fiber breaking process of the woven ceramic matrix composite is preferably determined by a formula shown in formulas 7-9:
wherein phi is the stress borne by the intact fiber, q is the fiber fracture probability, phibFor breaking the fibres to bear the load, mfIs the Weibull modulus, σ, of the fiberfcThe characteristic strength of the fiber is X is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, VfIs the fiber volume content in the composite material.
The method preferably determines the fiber breaking process of the woven ceramic matrix composite material through a formula shown in the formula 7-9, can better represent the fiber breaking condition, and is favorable for better analyzing the fiber breaking condition.
According to the invention, an interface debonding length equation, an unloading interface reverse slip length equation and a reloading interface new slip length equation are respectively established based on an interface debonding mechanism and a slip mechanism according to a fracture mechanics interface debonding criterion. In the present invention, the criterion of fracture-mechanics interface debonding preferably satisfies the equation shown in equation 10:
wherein, gamma isdIs interfacial debonding energy, wf(0) The axial displacement of the crack plane fiber of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, rfIs the radius of the fiber, τiThe frictional shear stress of the interface debonding area is shown, and F is the load borne by the crack plane fiber of the matrix.
In the present invention, the interfacial debonding length equation is preferably as shown in formula 11:
wherein, VmIs the matrix volume content in the composite material, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, EfIs the fiber modulus of elasticity;
the unloading interface reverse slip length equation is preferably as shown in equation 12:
wherein L iscsIs the unloading interface reverse slip length;
the reloading interface new slip length equation is preferably as shown in equation 13:
wherein L isnsThe new slip length for the reload interface.
According to a matrix fracture theory, establishing a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a middle crack unloading stress-strain relation equation, a middle crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation based on the matrix crack random cracking process, the fiber fracture probability, the intact fiber borne stress, the interface debonding length equation, the unloading interface reverse slip length equation and the reloading interface new slip length equation; and establishing a stress-strain relation equation of the hysteresis loop of the woven ceramic matrix composite according to the short crack unloading stress-strain relation equation, the short crack reloading stress-strain relation equation, the medium crack unloading stress-strain relation equation, the long crack unloading stress-strain relation equation and the long crack reloading stress-strain relation equation, so as to predict the fatigue hysteresis loop of the woven ceramic matrix composite in consideration of matrix and fiber breakage. In the invention, the fiber fracture probability and the intact fiber bearing stress are boundary conditions for determining the distribution of axial stress of the fiber and the matrix in the unloading and reloading processes.
In the present invention, the stress-strain relation equation of the hysteresis loop of the woven ceramic matrix composite material is preferably as shown in formula 14:
wherein epsiloncStrain of hysteresis loop of composite material, PS(x) As a function of short crack distribution, PM(x) As a function of the median crack distribution, PL(x) As a function of the long crack distribution,. epsilonthIs the thermal residual strain, σf(z) is the fiber axial stress distribution.
In the present invention, the formula shown in equation 14 considers the influence of different matrix fracture lengths on the hysteresis relationship.
In the present invention, the long crack unload stress-strain relation is preferably as shown in equation 15:
wherein epsilonULStress relief for long cracks, RfIs the radius of the fiber, [ phi ]UStress-bearing for unloading intact fibres, L0And L1The long crack coefficient; (ii) a
The long crack reload stress-strain relation equation is preferably as shown in equation 16:
wherein epsilonRLFor reloading long cracks with strain, [ phi ]RBearing stress for reloading intact fibers;
said L0Preferably determined by the formula shown in formula 17-1, L1Preferably determined by the formula shown in equation 17-2:
in the present invention, the equation of the stress-strain relation for medium crack unloading is preferably as shown in formula 18:
wherein epsilonUMRelief of strain for median cracks, M0、M1And M2Is the median crack coefficient;
the mid-crack reload stress-strain relationship equation is preferably as shown in equation 19:
wherein epsilonRMReloading the median crack with strain;
the M is0Preferably determined by the formula shown in formula 20-1, M1Preferably determined by the formula shown in formula 20-2, M2Preferably made of
The formula shown in equation 20-3 determines:
in the present invention, the short crack unload stress-strain relation equation is preferably as shown in formula 21:
wherein epsilonUSStress relief for short crackstr_unloadingTo relieve the transition stress, S0、S1And S2The fracture coefficient is shown.
As shown in formula 21, when the stress-strain relationship of short crack unloading is studied, the stress-strain relationship preferably comprises two conditions of partial slippage and complete slippage of an unloading interface, wherein sigma is>σtr_unloadingRepresenting partial slippage of the unloading interface, sigma ≦ sigmatr_unloadingThe unloading interface is completely slipped, and the interface slipping condition can be accurately analyzed by adopting the method, so that the fiber axial stress distribution can be reasonably determined.
In the present invention, the short crack reloading stress-strain relation equation is preferably as shown in formula 22:
in the formula, epsilonRSRe-stressing the short cracks with strain, σtr_reloadingTo reload the transformation stress;
said S0Preferably determined by the formula shown in formula 23-1, S1Preferably determined by the formula shown in formula 23-2, S2Preferably determined by the formula shown in equation 23-3:
as shown in formula 22, when studying the relationship between the short crack reloading stress and the strain, the invention preferably comprises two conditions of reloading interface partial slip and interface complete slip, wherein sigma is less than or equal to sigmatr_reloadingTime represents the partial slip of the reloading interface, σ>σtr_reloadingThe reloading interface completely slides, and the interface sliding condition can be accurately analyzed by adopting the method, so that the fiber axial stress distribution can be reasonably determined.
In the present invention, in the formula related to the above technical solution, the fiber effective volume content coefficient χ of the woven ceramic matrix composite material in the loading direction preferably satisfies the formula shown in formula 24:
wherein, Vf_loadingThe fiber volume content of the composite material along the stress loading direction is shown.
In the present invention, the fiber effective volume fraction (χ) in the stress loading direction is related to the weave dimension of the fibers in the woven ceramic matrix composite:
when the braiding dimensionality of the braided ceramic matrix composite material is 2, the x is 0.5;
when the braiding dimensionality of the braided ceramic matrix composite material is 2.5, the x is 0.75;
and when the weaving dimension of the woven ceramic matrix composite material is 3, the x is 0.93.
In a specific embodiment of the present invention, the woven ceramic matrix composite preferably has a weave dimension of 2.
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 method analyzes the matrix of the woven ceramic matrix composite and the fiber breaking process, and determines the random cracking process of matrix cracks, the fiber breaking probability and the intact fiber bearing stress; based on the unloading and reloading slippage mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the matrix and the fiber breakage is obtained, so that the stress-strain hysteresis loop of the woven ceramic matrix composite material can be accurately predicted. As shown in FIG. 1, the unloading of the cracks with different lengths and the reloading of the axial stress distribution of the fibers are illustrated, so that the stress distribution is greatly influenced by the lengths of the cracks, and therefore, the method provided by the invention can be used for establishing corresponding unloading and reloading stress-strain relation equations aiming at the cracks with different lengths, the influence of the fracture length of the matrix on the hysteresis loop can be considered, the hysteresis loop can be better predicted, the damage of the matrix and the fracture of the fibers to the woven ceramic matrix composite material can be monitored, and the safety of the woven ceramic matrix composite material in the actual engineering application process is improved.
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
The method provided by the invention is adopted to establish an unloading stress-strain relation equation, a reloading stress-strain relation equation and a stress-strain relation equation of the woven ceramic matrix composite material hysteresis loop of the cracks with different lengths, and particularly, the woven ceramic matrix composite material (SiC/SiC) is used as a test sample, the loading and unloading test is carried out on the test sample, and the fatigue hysteresis loop is predicted:
providing parameters: vf＝0.46，Rf＝6.5μm，Ef＝319GPa，Em＝450GPa，τi＝12MPa，Γd＝2J/m2，m＝10，mf＝5；χ＝0.5；
And then obtaining a stress-strain relation equation of the woven ceramic matrix composite material hysteresis loop shown in the formula 14, an unloading stress-strain relation equation and a reloading stress-strain relation equation of the cracks with different lengths shown in the formulas 15 to 16, 18 to 19 and 21 to 22 according to the formulas 1 to 5, 7 to 8 and 11 to 13, so as to obtain a stress-strain relation and obtain the woven ceramic matrix composite material hysteresis loop.
Fig. 2 is a fatigue hysteresis loop of the woven ceramic matrix composite material predicted by experiments and theories in the invention, a solid line in fig. 2 is a stress-strain relation curve constructed by adopting the scheme, and different points are actual test data.
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 prediction method of fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage comprises the following steps:
(1) analyzing the matrix fracture process of the woven ceramic matrix composite according to the matrix random fracture theory, and dividing the matrix cracks of the woven ceramic matrix composite into short cracks, medium cracks and long cracks based on the matrix fracture characteristics and the fracture length; obtaining a matrix crack random cracking process according to a matrix random cracking theory, wherein the matrix crack random cracking process is represented by a short crack distribution function, a medium crack distribution function and a long crack distribution function;
analyzing the fiber breaking process of the woven ceramic matrix composite, and obtaining the fiber breakage probability and the intact fiber bearing stress based on the overall load bearing criterion;
(2) respectively establishing an interface debonding length equation, an unloading interface reverse slip length equation and a reloading interface new slip length equation according to a fracture mechanics interface debonding rule and based on an interface debonding mechanism and a slip mechanism;
(3) according to a matrix fracture theory, establishing a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a middle crack unloading stress-strain relation equation, a middle crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation based on the matrix crack random cracking process, the fiber fracture probability and the intact fiber borne stress in the step (1) and the interface debonding length equation, the unloading interface reverse slip length equation and the reloading interface new slip length equation in the step (2), and further establishing a stress-strain relation equation of the woven ceramic matrix composite material hysteresis loop so as to predict the fatigue hysteresis loop of the woven ceramic matrix composite material considering matrix and fiber breakage.
2. The prediction method according to claim 1, wherein in the step (1), the short crack, the medium crack and the long crack are respectively:
short crack, Lcracking<Ldebonding；
Middle crack, Ldebonding<Lcracking<2Ldebonding；
Long crack, 2Ldebonding<Lcracking；
Wherein L iscrackingIs the crack spacing of the matrix, LdebondingIs the interfacial debonding length;
the breaking process of the matrix of the woven ceramic matrix composite is determined by a formula shown in formulas 1-5:
wherein L is the initial simulated total length, LeffFor effective simulated length, P (x) is a distribution function of the crack spacing of the matrix greater than the debond length of the interface, PR(x) Is a distribution function of matrix crack spacing smaller than interface debonding length, N is matrix fracture number, x is axial value, sigma is stress, N is matrix fracture density, and deltaDIs the dirac function, phi (sigma, L)eff) Is a matrix Weibull function;
the phi (sigma, L)eff) Determined by the formula shown in equation 6:
wherein A is0Is a reference area, LRTo reference length, σ0For reference stress, m is the matrix Weibull modulus.
3. The prediction method according to claim 2, wherein in the step (1), the fiber breaking process of the woven ceramic matrix composite material is determined by the formula shown in the formulas 7-9:
wherein phi is the stress borne by the intact fiber, q is the fiber fracture probability, phibFor breaking the fibres to bear the load, mfIs the Weibull modulus, σ, of the fiberfcThe characteristic strength of the fiber is X is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, VfIs the fiber volume content in the composite material.
4. The prediction method according to claim 3, wherein in the step (2), the fracture-mechanics interface debonding criterion satisfies an equation shown in formula 10:
wherein, gamma isdIs interfacial debonding energy, wf(0) The axial displacement of the crack plane fiber of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, rfIs the radius of the fiber, τiThe frictional shear stress of the interface debonding area is shown, and F is the load borne by the crack plane fiber of the matrix.
5. The prediction method according to claim 4, wherein in the step (2), the interfacial debonding length equation is shown in formula 11:
wherein, VmIs the matrix volume content in the composite material, EmAs a matrix elastic modulus, EcIs the elastic modulus of the composite material, rho is the shear model parameter, EfIs the fiber modulus of elasticity;
the unloading interface reverse slip length equation is shown in equation 12:
wherein L iscsIs the unloading interface reverse slip length;
the reloading interface new slip length equation is shown in equation 13:
wherein L isnsThe new slip length for the reload interface.
6. The prediction method according to claim 5, wherein in the step (3), the stress-strain relation equation of the hysteresis loop of the woven ceramic matrix composite material is shown as formula 14:
wherein epsiloncStrain of hysteresis loop of composite material, PS(x) As a function of short crack distribution, PM(x) As a function of the median crack distribution, PL(x) As a function of the long crack distribution,. epsilonthIs the thermal residual strain, σf(z) is the fiber axial stress distribution.
7. The prediction method according to claim 6, wherein in the step (3), the long crack unload stress-strain relation equation is shown as equation 15:
wherein epsilonULStress relief for long cracks, rfIs the radius of the fiber, [ phi ]UStress-bearing for unloading intact fibres, L0And L1The long crack coefficient;
the long crack reload stress-strain relation equation is shown as formula 16:
wherein epsilonRLFor reloading long cracks with strain, [ phi ]RBearing stress for reloading intact fibers;
said L0Determined by the formula shown in formula 17-1, L1Determined by the formula shown in equation 17-2:
8. the prediction method of claim 7, wherein in the step (3), the equation of the stress-strain relation of the medium fracture unloading is shown as formula 18:
wherein epsilonUMRelief of strain for median cracks, M0、M1And M2The median crack coefficient.
The mid-crack reload stress-strain relation equation is shown as formula 19:
wherein epsilonRMReloading the median crack with strain;
the M is0Determined by the formula shown in equation 20-1, M1Determined by the formula shown in equation 20-2, M2Determined by the formula shown in equation 20-3:
9. the prediction method according to claim 8, wherein in the step (3), the short crack unload stress-strain relation equation is expressed by equation 21:
wherein epsilonUSStress relief for short crackstr_unloadingTo relieve the transition stress, S0、S1And S2Is the fracture coefficient;
the short crack reloading stress-strain relationship equation is shown in equation 22:
in the formula, epsilonRSRe-stressing the short cracks with strain, σtr_reloadingTo reload the transformation stress;
said S0Determined by the formula shown in formula 23-1, S1Determined by the formula shown in formula 23-2, S2Determined by the formula shown in equation 23-3:
10. the prediction method according to any one of claims 3 to 9, wherein the fiber effective volume content coefficient of the woven ceramic matrix composite material in the stress loading direction satisfies the formula shown in formula 24:
wherein, Vf_loadingThe fiber volume content of the composite material along the stress loading direction is shown.
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