CN113051720B - Prediction method for crack opening displacement of woven ceramic matrix composite material considering matrix breakage - Google Patents
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- 239000011159 matrix material Substances 0.000 title claims abstract description 132
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- 239000011153 ceramic matrix composite Substances 0.000 title claims abstract description 67
- 238000000034 method Methods 0.000 title claims abstract description 58
- 239000000463 material Substances 0.000 title claims abstract description 52
- 238000005336 cracking Methods 0.000 claims abstract description 55
- 239000000835 fiber Substances 0.000 claims abstract description 43
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- 239000002131 composite material Substances 0.000 claims abstract description 21
- 230000007246 mechanism Effects 0.000 claims abstract description 7
- 238000005315 distribution function Methods 0.000 claims description 19
- 238000004088 simulation Methods 0.000 claims description 6
- 238000009940 knitting Methods 0.000 description 5
- 238000012360 testing method Methods 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 2
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- 239000000956 alloy Substances 0.000 description 1
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- 239000000919 ceramic Substances 0.000 description 1
- 238000002485 combustion reaction Methods 0.000 description 1
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Abstract
The invention provides a prediction method of crack opening displacement of a woven ceramic matrix composite material considering matrix breakage, and belongs to the technical field of prediction of crack opening displacement of composite materials. The method analyzes the cracking process of the matrix of the woven ceramic matrix composite material and divides the cracks of the matrix of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks; obtaining a matrix crack random cracking process according to a matrix random cracking theory; establishing an interface debonding length equation according to a fracture mechanical interface debonding criterion; and finally, according to the sliding mechanism of the fiber relative to the matrix at the interface, based on the random cracking process of the matrix crack and the interface debonding length equation, respectively establishing a short crack expansion displacement equation, a medium crack expansion displacement equation and a long crack expansion displacement equation, so that the crack expansion displacement of the woven ceramic matrix composite material considering the matrix breakage can be accurately predicted.
Description
Technical Field
The invention relates to the technical field of composite material crack opening displacement prediction, in particular to a prediction method of a woven ceramic matrix composite material crack opening displacement considering matrix 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, reduce cooling air flow and improve turbine efficiency compared with high-temperature alloy, and is currently applied to an aeroengine combustion chamber, a turbine guide vane, a turbine shell ring, a tail nozzle and the like. A LEAP (Leading EdgeAviation Propulsion) series of engines developed by CFM company, the high pressure turbine uses a woven ceramic matrix composite component, the LEAP-1B engine powers both the air passenger A320 and the Boeing 737MAX, and the LEAP-X1C engine powers the large aircraft C919.
In order to ensure the reliability and safety of the braided ceramic matrix composite in the structures of aircraft and aeroengines, researchers at home and abroad use the development of ceramic matrix composite performance evaluation, damage evolution, strength and life prediction tools as the key of the seaworthiness evidence collection of ceramic matrix composite structural components. Under the action of external load, the crack of the matrix opens to cause oxidation damage in the composite material, and the strength and the service life of the composite material are affected.
At present, the research on the crack opening displacement of the matrix of the woven ceramic matrix composite material does not consider the influence of matrix breakage on the crack opening displacement. How to consider the influence of matrix fracture factors on the crack opening displacement of the woven ceramic matrix composite material is a key technical problem to be solved in practical engineering application of the woven ceramic matrix composite material structure.
Disclosure of Invention
The invention aims to provide a prediction method for crack opening displacement of a woven ceramic matrix composite material by considering matrix breakage, and the prediction method provided by the invention considers the influence of matrix breakage factors on the crack opening displacement of the woven ceramic matrix composite material and can accurately predict the crack opening displacement of the woven ceramic matrix composite material, namely short cracks, medium cracks and long cracks.
In order to achieve the above object, the present invention provides the following technical solutions:
the invention provides a prediction method of crack opening displacement of a woven ceramic matrix composite material considering matrix breakage, which comprises the following steps:
(1) Analyzing the matrix cracking process of the woven ceramic matrix composite material according to the matrix random cracking theory, and dividing the matrix cracks of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks based on the matrix cracking characteristics and the breaking lengths; 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;
(2) Establishing an interface debonding length equation according to a fracture mechanical interface debonding criterion;
(3) And (3) respectively establishing a short crack opening displacement equation, a medium crack opening displacement equation and a long crack opening displacement equation based on the random cracking process of the matrix cracks in the step (1) and the interface debonding length equation obtained in the step (2) according to the sliding mechanism of the fiber relative to the matrix at the interface, so as to predict and consider the crack opening displacement of the woven ceramic matrix composite material with broken matrix.
Preferably, in the step (1), the short crack, the medium crack and the long crack are respectively:
Short crack, L cracking<Ldebonding;
Medium crack, L debonding<Lcracking<2Ldebonding;
long cracks, 2L debonding<Lcracking;
Wherein L cracking is the matrix crack spacing, and L debonding is the interfacial debonding length.
Preferably, in the step (1), the cracking process of the matrix of the woven ceramic matrix composite material is determined by a formula shown in formulas 1 to 5:
Wherein L is the initial simulation total length, L eff is the effective simulation length, P (x) is the distribution function of the matrix crack spacing being greater than the interface debonding length, P R (x) is the distribution function of the matrix crack spacing being less than the interface debonding length, N is the matrix breaking number, x is the axial value, sigma is the stress, N is the matrix breaking density, delta D is the Dirac function, phi (sigma, L eff) is the matrix Weibull function;
the phi (sigma, L eff) is determined by the formula shown in equation 6:
wherein A 0 is the reference area, L R is the reference length, sigma 0 is the reference stress, and m is the matrix Weibull modulus.
Preferably, in the step (2), the fracture mechanics interface debonding criterion satisfies an equation shown in formula 7:
wherein Γ d is interface debonding energy, w f (0) is axial displacement of the matrix crack plane fiber, v (x) is axial displacement of the fiber relative to the matrix, r f is fiber radius, τ i is interface shear stress, and F is matrix crack plane fiber bearing load.
Preferably, in the step (2), the interfacial debonding length equation is shown in formula 8:
Wherein V m is the volume content of the matrix in the composite material, E m is the elastic modulus of the matrix, E c is the elastic modulus of the composite material, ρ is the shear model parameter, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f is the volume content of the fiber in the composite material, and E f is the elastic modulus of the fiber.
Preferably, in the step (3), the long crack opening displacement equation is shown in formula 9:
Wherein COD is the expansion displacement, sigma fo is the axial stress of the fiber in the interface bonding area, sigma mo is the axial stress of the matrix in the interface bonding area, and eta is the interface debonding ratio;
the eta is determined by a formula shown in a formula 10;
The middle crack opening displacement equation and the short crack opening displacement equation are shown in formula 11:
Preferably, the effective volume content coefficient of the fiber of the woven ceramic matrix composite material along the stress loading direction satisfies the formula shown in formula 12:
Wherein V f_loading is the fiber volume content of the composite material along the stress loading direction.
The invention provides a prediction method of crack opening displacement of a woven ceramic matrix composite material in consideration of matrix breakage, which specifically comprises the steps of analyzing the matrix cracking process of the woven ceramic matrix composite material, and dividing the matrix cracks of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks; obtaining a matrix crack random cracking process according to a matrix random cracking theory; establishing an interface debonding length equation according to a fracture mechanical interface debonding criterion; and finally, according to the sliding mechanism of the fiber relative to the matrix at the interface, based on the random cracking process of the matrix crack and the interface debonding length equation, respectively establishing a short crack expansion displacement equation, a medium crack expansion displacement equation and a long crack expansion displacement equation, so as to predict the crack expansion displacement of the woven ceramic matrix composite material taking the matrix breakage into consideration. The method provided by the invention considers the influence of the matrix breaking factor on the crack opening displacement of the woven ceramic matrix composite material, and can accurately predict the crack opening displacement of the woven ceramic matrix composite material, namely the short crack, the middle crack and the long crack.
Drawings
FIG. 1 is a schematic drawing of the long crack opening displacement of a woven ceramic matrix composite matrix crack according to the present invention;
FIG. 2 is a schematic representation of the mid-crack opening displacement of a crack in a woven ceramic matrix composite matrix in accordance with the present invention;
FIG. 3 is a schematic representation of short crack opening displacement of a woven ceramic matrix composite matrix crack according to the present invention;
FIG. 4 is a graph showing the comparison of predicted values and test values of crack opening displacement of different lengths of the woven ceramic matrix composite material according to the invention.
Detailed Description
The symbols, meanings and acquisition methods related in the prediction method of the crack opening displacement of the woven ceramic matrix composite material considering matrix breakage are summarized in the table 1, and in the following specific embodiments, except for special description, the symbol meanings and acquisition methods in each equation or relation are all based on the content of the table 1, and are not repeated.
TABLE 1 parameter description in the method for predicting crack opening displacement of woven ceramic matrix composites considering matrix fracture
Note that: in table 1, the composite material represents a woven ceramic matrix composite material, the fibers represent fibers in the woven ceramic matrix composite material, the matrix represents a matrix in the woven ceramic composite material, the axial direction refers to the stress loading direction, and the interface refers to the matrix/fiber interface.
Based on the description of table 1, the following description is given to the specific implementation procedure of the prediction method of the crack opening displacement of the woven ceramic matrix composite material, which is provided by the invention and considers the breakage of the matrix:
the invention provides a prediction method of crack opening displacement of a woven ceramic matrix composite material considering matrix breakage, which comprises the following steps:
(1) Analyzing the matrix cracking process of the woven ceramic matrix composite material according to the matrix random cracking theory, and dividing the matrix cracks of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks based on the matrix cracking characteristics and the breaking lengths; 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;
(2) Establishing an interface debonding length equation according to a fracture mechanical interface debonding criterion;
(3) And (3) respectively establishing a short crack opening displacement equation, a medium crack opening displacement equation and a long crack opening displacement equation based on the random cracking process of the matrix cracks in the step (1) and the interface debonding length equation obtained in the step (2) according to the sliding mechanism of the fiber relative to the matrix at the interface, so as to predict and consider the crack opening displacement of the woven ceramic matrix composite material with broken matrix.
According to the method, the influence of the matrix breaking factor is considered, the matrix cracking process of the woven ceramic matrix composite material is analyzed, and the matrix cracks of the woven ceramic matrix composite material are divided into short cracks, medium cracks and long cracks; obtaining a matrix crack random cracking process according to a matrix random cracking theory; determining the interface debonding length by a fracture mechanics method; and finally, according to the sliding mechanism of the fiber relative to the matrix at the interface, establishing crack opening displacement equations with different lengths based on the random cracking process of the matrix crack and the interface debonding length equation, so as to predict the crack opening displacement of the woven ceramic matrix composite material taking the matrix breakage into consideration.
The method analyzes the cracking process of the matrix of the woven ceramic matrix composite material and divides the cracks of the matrix of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks; and 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.
In the present invention, the short crack, the medium crack and the long crack are preferably respectively:
Short crack, L cracking<Ldebonding;
Medium crack, L debonding<Lcracking<2Ldebonding;
long cracks, 2L debonding<Lcracking;
Wherein L cracking is the matrix crack spacing, and L debonding is the interfacial debonding length.
The invention divides the short crack, the middle crack and the long crack according to the mode, can more reasonably determine the influence of the breaking length of the matrix on the opening displacement, and is beneficial to determining the opening displacement of the crack.
In the invention, the cracking process of the matrix of the woven ceramic matrix composite material is preferably determined by the formula shown in the formulas 1-5:
Wherein L is the initial simulation total length, L eff is the effective simulation length, P (x) is the distribution function of the matrix crack spacing being greater than the interface debonding length, P R (x) is the distribution function of the matrix crack spacing being less than the interface debonding length, N is the matrix breaking number, x is the axial value, sigma is the stress, N is the matrix breaking density, delta D is the Dirac function, phi (sigma, L eff) is the matrix Weibull function;
The phi (sigma, L eff) is preferably determined by the formula shown in equation 6:
wherein A 0 is the reference area, L R is the reference length, sigma 0 is the reference stress, and m is the matrix Weibull modulus.
In the invention, the cracking process of the matrix of the woven ceramic matrix composite material is preferably determined by the formulas shown in the formulas 1-5, so that the matrix breaking process can be reasonably represented, and the distribution function of different matrix breaking lengths can be obtained.
According to the fracture mechanics interface debonding criterion, an interface debonding length equation is established. In the present invention, the fiber/matrix interface debonding criterion preferably satisfies the equation of formula 7:
wherein Γ d is interface debonding energy, w f (0) is axial displacement of the matrix crack plane fiber, v (x) is axial displacement of the fiber relative to the matrix, r f is fiber radius, τ i is interface shear stress, and F is matrix crack plane fiber bearing load.
In the present invention, the interfacial debonding length equation is preferably as shown in formula 8:
Wherein V m is the volume content of the matrix in the composite material, E m is the elastic modulus of the matrix, E c is the elastic modulus of the composite material, ρ is the shear model parameter, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f is the volume content of the fiber in the composite material, and E f is the elastic modulus of the fiber.
According to the sliding mechanism of the fiber relative to the matrix at the interface, based on the random cracking process of the matrix crack and the interface debonding length equation, a short crack expansion displacement equation, a medium crack expansion displacement equation and a long crack expansion displacement equation are respectively established, so that the crack expansion displacement of the woven ceramic matrix composite material which considers the matrix breakage is predicted.
In the present invention, the long crack opening displacement equation is preferably as shown in formula 9:
Wherein COD is the expansion displacement, sigma fo is the axial stress of the fiber in the interface bonding area, sigma mo is the axial stress of the matrix in the interface bonding area, and eta is the interface debonding ratio;
The η is preferably determined by the formula shown in formula 10;
in the present invention, the middle crack opening displacement equation and the short crack opening displacement equation are preferably both shown in formula 11:
In the present invention, the crack spacing L cracking between the middle and short cracks is different, and the opening displacement of the middle and short cracks can be determined by equation 11.
In the formula related by the technical scheme, the effective volume content coefficient χ of the fiber of the woven ceramic matrix composite material along the loading direction preferably meets the formula shown in the formula 12:
Wherein V f_loading is the fiber volume content of the composite material along the stress loading direction.
In the present invention, the effective volume content coefficient (χ) of the fiber in the stress-loading direction is related to the knitting dimension of the fiber in the knitted ceramic matrix composite:
When the knitting dimension of the knitted ceramic matrix composite is 2, χ is 0.5;
When the knitting dimension of the knitted ceramic matrix composite is 2.5, χ is 0.75;
when the knitting dimension of the knitted ceramic matrix composite is 3, χ is 0.93.
In a specific embodiment of the present invention, the knitting dimension of the knitted ceramic matrix composite is preferably 2.
In the formula related to the above technical solution, the shear model parameter (ρ) is preferably calculated by a shear model, and the shear model is preferably a BHE shear model. The present invention has no special requirements for the calculation mode, and the calculation mode is adopted by a mode well known to a person skilled in the art.
According to the method, the base cracks of the woven ceramic matrix composite material are divided into short cracks, medium cracks and long cracks, corresponding crack opening displacement equations are established according to the lengths of the base cracks, as shown in figures 1-3, the opening displacement of the cracks with different lengths can be shown, and therefore the obvious influence of the crack lengths on the opening displacement can be seen.
The technical solutions of the present invention will be clearly and completely described in the following in connection with the embodiments of the present invention. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
The method provided by the invention is adopted to establish crack opening displacement equations with different lengths, specifically, a woven ceramic matrix composite (SiC/SiC) is used as a test sample, a tensile test is carried out on the test sample, and the crack opening displacement is predicted:
providing parameters ：Vf＝66％,rf＝6.5μm,Ef＝350GPa,Em＝404GPa,τi＝12MPa,Γd＝1J/m2,χ＝0.5;
And then obtaining crack opening displacement equations shown in formulas 9-10 according to formulas 1-5 and formulas 7-8, so as to predict the crack opening displacement of the woven ceramic matrix composite material taking the matrix breakage into consideration.
FIG. 4 is a graph showing the comparison of predicted values and test values of Crack opening displacements of different lengths of the woven ceramic matrix composite material according to the invention, wherein the differences represented by Cracks 1-4 in FIG. 4 are Crack opening displacements of different positions observed in the test process, and the solid line is Crack opening displacement predicted by the method provided by the invention.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (4)
1. A prediction method for crack opening displacement of a woven ceramic matrix composite material considering matrix breakage comprises the following steps:
(1) Analyzing the matrix cracking process of the woven ceramic matrix composite material according to the matrix random cracking theory, and dividing the matrix cracks of the woven ceramic matrix composite material into short cracks, medium cracks and long cracks based on the matrix cracking characteristics and the breaking lengths; 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;
(2) Establishing an interface debonding length equation according to a fracture mechanical interface debonding criterion;
(3) According to the sliding mechanism of the fiber relative to the matrix at the interface, based on the random cracking process of the matrix crack in the step (1) and the interface debonding length equation obtained in the step (2), respectively establishing a short crack opening displacement equation, a medium crack opening displacement equation and a long crack opening displacement equation, so as to predict and consider the crack opening displacement of the woven ceramic matrix composite material with broken matrix;
in the step (1), the short crack, the medium crack and the long crack are respectively:
Short crack, L cracking<Ldebonding;
Medium crack, L debonding<Lcracking<2Ldebonding;
long cracks, 2L debonding<Lcracking;
Wherein, L cracking is the matrix crack spacing, L debonding is the interface debonding length;
in the step (1), the cracking process of the matrix of the woven ceramic matrix composite material is determined by a formula shown in formulas 1-5:
Wherein L is the initial simulation total length, L eff is the effective simulation length, P (x) is the distribution function of the matrix crack spacing being greater than the interface debonding length, P R (x) is the distribution function of the matrix crack spacing being less than the interface debonding length, N is the matrix breaking number, x is the axial value, sigma is the stress, N is the matrix breaking density, delta D is the Dirac function, phi (sigma, L eff) is the matrix Weibull function;
the phi (sigma, L eff) is determined by the formula shown in equation 6:
wherein A 0 is a reference area, L R is a reference length, sigma 0 is a reference stress, and m is a matrix Weibull modulus;
in the step (2), the fracture mechanics interface debonding criterion satisfies the equation shown in formula 7:
wherein Γ d is interface debonding energy, w f (0) is axial displacement of the matrix crack plane fiber, v (x) is axial displacement of the fiber relative to the matrix, r f is fiber radius, τ i is interface shear stress, and F is matrix crack plane fiber bearing load.
2. The prediction method according to claim 1, wherein in the step (2), the interfacial debonding length equation is as shown in formula 8:
Wherein V m is the volume content of the matrix in the composite material, E m is the elastic modulus of the matrix, E c is the elastic modulus of the composite material, ρ is the shear model parameter, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f is the volume content of the fiber in the composite material, and E f is the elastic modulus of the fiber.
3. The prediction method according to claim 2, wherein in the step (3), the long crack opening displacement equation is as shown in formula 9:
Wherein COD is the expansion displacement, sigma fo is the axial stress of the fiber in the interface bonding area, sigma mo is the axial stress of the matrix in the interface bonding area, and eta is the interface debonding ratio;
the eta is determined by a formula shown in a formula 10;
The middle crack opening displacement equation and the short crack opening displacement equation are shown in formula 11:
4. A method according to claim 2 or 3, wherein the effective volume content coefficient of the fibers of the woven ceramic matrix composite material in the stress loading direction satisfies the formula shown in formula 12:
Wherein V f_loading is the fiber volume content of the composite material along the stress loading direction.
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| CN111523232A (en) * | 2020-04-23 | 2020-08-11 | 南京航空航天大学 | Method for predicting tensile behavior of woven ceramic matrix composite material with consideration of thermal fatigue damage |
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| CN111523232A (en) * | 2020-04-23 | 2020-08-11 | 南京航空航天大学 | Method for predicting tensile behavior of woven ceramic matrix composite material with consideration of thermal fatigue damage |
| CN111523237A (en) * | 2020-04-24 | 2020-08-11 | 南京航空航天大学 | Prediction method of creep rupture behavior of woven ceramic matrix composite material considering random load influence |
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| Title |
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| 杨福树 ; 孙志刚 ; 李龙彪 ; 高希光 ; 宋迎东 ; .界面脱粘对正交铺设SiC/CAS复合材料基体开裂的影响.复合材料学报.2012,(04),全文. * |
| 界面脱粘对正交铺设SiC/CAS复合材料基体开裂的影响;杨福树;孙志刚;李龙彪;高希光;宋迎东;;复合材料学报;20120209(04);全文 * |
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