CN113032982B - Prediction method for fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage - Google Patents
Prediction method for 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. Analyzing a matrix and a fiber breaking process of the woven ceramic matrix composite material, and determining a random cracking process of matrix cracks, fiber breaking probability and stress born by intact fibers; based on the unloading and reloading sliding mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the breakage of the matrix and the fiber 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 the matrix and the fiber breakage factors on the fatigue hysteresis loop, can accurately predict the damage problem of the matrix and the fiber breakage to the woven ceramic matrix composite material, and improves the accuracy of the prediction 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 braided 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, 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. LEAP (Leading Edge Aviation Propulsion) series engines developed by CFM corporation, the high pressure turbine uses a woven ceramic matrix composite component, the LEAP-1B engine powering both the air passenger a320 and the boeing 737MAX, and the LEAP-X1C engine powering 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 fatigue load, the woven ceramic matrix composite material has multiple damage mechanisms such as matrix multi-cracking, fiber/matrix interface debonding and slipping, so that obvious hysteresis phenomenon appears on a stress-strain curve in the unloading and reloading processes.
At present, the influence of matrix and fiber breakage on the hysteresis loop is not considered in the research of the fatigue hysteresis loop of the woven ceramic matrix composite material (Li Longbiao, research of the fatigue hysteresis loop model of the fiber reinforced ceramic matrix composite material [ J ], mechanics theory report, 2014, 5:710-729). How to consider the influence of matrix and fiber breakage on the fatigue hysteresis loop of the woven ceramic matrix composite material and monitor the damage of the matrix and fiber breakage on the composite material is a key technical problem to be solved in the practical engineering application of the woven ceramic matrix composite material structure.
Disclosure of Invention
The invention aims to provide a prediction method for 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 a fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage, which comprises the following steps:
(1) Analyzing the matrix breaking 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 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;
analyzing the fiber breaking process of the woven ceramic matrix composite material, and obtaining fiber breaking probability and intact fiber bearing stress based on the overall load bearing criterion;
(2) According to fracture mechanics interface debonding criteria, based on interface debonding and sliding mechanisms, respectively establishing an interface debonding length equation, an unloading interface reverse sliding length equation and a reloading interface new sliding length equation;
(3) According to the matrix fracture theory, based on the matrix crack random cracking process, the fiber fracture probability and the intact fiber bearing stress in the step (1) and the interface debonding length equation, the unloading interface reverse sliding length equation and the reloading interface new sliding length equation in the step (2), a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a medium crack unloading stress-strain relation equation, a medium crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation in the step (1), further a woven ceramic matrix composite material hysteresis loop stress-strain relation equation is established, and a woven ceramic matrix composite material fatigue hysteresis loop considering matrix and fiber fracture is predicted.
Preferably, in the step (1), the short crack, the medium crack and the long crack are respectively:
short crack, L cracking <L debonding ；
Middle crack, L debonding <L cracking <2L debonding ；
Long crack, 2L debonding <L cracking ；
Wherein L is cracking For matrix crack spacing, L debonding Is the interface debonding length;
the breaking process of the matrix of the woven ceramic matrix composite material is determined by the formulas shown in 1-5:
wherein L is the initial analog total length, L eff For effective simulation length, P (x) is the distribution function of matrix crack spacing greater than interfacial debonding length, P R (x) For the distribution function that the crack spacing of the matrix is smaller 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 a 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 is 0 For reference area, L R For reference length, sigma 0 For reference stress, m is the matrix weibull modulus.
Preferably, in the step (1), the fiber breaking process of the woven ceramic matrix composite material is determined by the formula shown in formulas 7 to 9:
wherein phi is the stress born by intact fiber, q is the fiber fracture probability, phi b Load bearing for breaking fiber, m f For the fiber Weibull modulus, sigma fc Is the characteristic strength of the fiber, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f Is the fiber volume content in the composite material.
Preferably, in the step (2), the fracture mechanics interface debonding criterion satisfies an equation shown in formula 10:
wherein Γ is d To release the bonding energy of the interface, w f (0) Axial displacement of the planar fiber for the crack of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, r f Is the fiber radius tau i And F is the load bearing of the matrix crack plane fiber.
Preferably, in the step (2), the interfacial debonding length equation is shown in formula 11:
wherein V is m Is the volume content of the matrix in the composite material, E m Modulus of elasticity of matrix, E c Is the elastic modulus of the composite material, ρ is shear model parameter, E f Is a fiberA dimensional elastic modulus;
the unloading interface reverse slip length equation is shown in fig. 12:
wherein L is cs Reverse slip length for unloading interface;
the reload interface new slip length equation is shown in fig. 13:
wherein L is ns The interface is reloaded with a new slip length.
Preferably, in the step (3), the hysteresis loop stress-strain relation equation of the woven ceramic matrix composite is shown in formula 14:
wherein ε c Is composite material hysteresis loop strain, P S (x) As a short crack distribution function, P M (x) As the distribution function of middle cracks, P L (x) Epsilon as a long crack distribution function th For thermal residual strain, σ f (z) is the fiber axial stress distribution.
Preferably, in the step (3), the long crack unloading stress-strain relation equation is shown in formula 15:
wherein ε UL For long crack unloading strain, r f Is the radius of the fiber, phi U To unload intact fibers to bear stress, L 0 And L 1 Is a long crack coefficient;
the long crack reload stress-strain relationship equation is shown in equation 16:
wherein ε RL Reloading strain for long cracks, phi R Bearing stress for reloading intact fibers;
the L is 0 Determined by a formula shown in 17-1, L 1 Determined by the formula shown in equation 17-2:
preferably, in the step (3), the intermediate crack unloading stress-strain relation equation is shown in formula 18:
wherein ε UM For unloading strain from the middle crack, M 0 、M 1 And M 2 Is the medium crack coefficient.
The mid-crack reload stress-strain relationship equation is shown in equation 19:
wherein ε RM Reloading the medium crack with strain;
the M is 0 Determined by a formula shown in the formula 20-1, M 1 Determined by a formula shown in 20-2, M 2 Determined by the formula shown in equation 20-3:
preferably, in the step (3), the stress-strain relation equation for unloading the short crack is shown in formula 21:
wherein ε US For short crack unloading strain, sigma tr_unloading To relieve the transition stress, S 0 、S 1 And S is 2 Is the fracture coefficient;
the short crack reload stress-strain relationship equation is shown in equation 22:
wherein ε RS Reloading strain, sigma, for short cracks tr_reloading Loading the transition stress again;
the S is 0 Is determined by a formula shown in a formula 23-1, S 1 Determined by the formula shown in the formula 23-2, S 2 Determined by the formula shown in equation 23-3:
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 24:
wherein V is f_loading Fiber volume content in the stress loading direction for composite materials
The invention provides a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material taking matrix and fiber breakage into consideration, which specifically comprises the steps of analyzing the matrix and fiber breakage process of the woven ceramic matrix composite material, and determining the random cracking process of matrix cracks, fiber breakage probability and intact fiber bearing stress; based on unloading and reloading sliding mechanisms, unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the breakage of the matrix and the fiber, namely, an axial stress-strain relation equation of the unloading fiber of short cracks, medium cracks and long cracks is obtained, so that a stress-strain hysteresis loop of the woven ceramic matrix composite material is predicted. The method provided by the invention considers the influence of the matrix and the fiber breakage factors on the fatigue hysteresis loop, can accurately predict the damage problem of the matrix and the fiber breakage to the woven ceramic matrix composite material, and improves the accuracy of the prediction of the hysteresis loop of the woven ceramic matrix composite material.
Drawings
FIG. 1 is a graph of the axial stress distribution of a fiber for unloading short, medium and long cracks and reloading the fiber in accordance with the present invention;
FIG. 2 is a graph showing the fatigue hysteresis loop of the woven ceramic matrix composite material according to the present invention as tested and theoretically predicted.
Detailed Description
The symbols, meanings and acquisition methods related in the prediction method of the fatigue hysteresis loop of the woven ceramic matrix composite material considering the matrix and the fiber 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 prediction method of fatigue hysteresis loop of woven ceramic matrix composite material considering matrix and fiber breakage
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 process of the prediction method of the fatigue hysteresis loop of the woven ceramic matrix composite material taking the matrix and the fiber breakage into consideration, provided by the invention:
(1) Analyzing the matrix breaking 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 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;
analyzing the fiber breaking process of the woven ceramic matrix composite material, and obtaining fiber breaking probability and intact fiber bearing stress based on the overall load bearing criterion;
(2) According to fracture mechanics interface debonding criteria, based on interface debonding and sliding mechanisms, respectively establishing an interface debonding length equation, an unloading interface reverse sliding length equation and a reloading interface new sliding length equation;
(3) According to the matrix fracture theory, based on the matrix crack random cracking process, the fiber fracture probability and the intact fiber bearing stress in the step (1) and the interface debonding length equation, the unloading interface reverse sliding length equation and the reloading interface new sliding length equation in the step (2), a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a medium crack unloading stress-strain relation equation, a medium crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation in the step (1), further a woven ceramic matrix composite material hysteresis loop stress-strain relation equation is established, and a woven ceramic matrix composite material fatigue hysteresis loop considering matrix and fiber fracture is predicted.
The invention provides a prediction method of a fatigue hysteresis loop of a woven ceramic matrix composite material taking matrix and fiber breakage into consideration, which specifically comprises the steps of analyzing the matrix and fiber breakage process of the woven ceramic matrix composite material, and determining the random cracking process of matrix cracks, fiber breakage probability and intact fiber bearing stress; based on unloading and reloading sliding mechanisms, unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the breakage of the matrix and the fiber, namely, an axial stress-strain relation equation of the unloading fiber of short cracks, medium cracks and long cracks is obtained, so that a stress-strain hysteresis loop of the woven ceramic matrix composite material is predicted.
According to the random cracking theory of the matrix, the matrix breaking process of the woven ceramic matrix composite material is analyzed, and based on the cracking characteristics and breaking length of the matrix, 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, 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 breaking 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 respectively:
short crack, L cracking <L debonding ；
Middle crack, L debonding <L cracking <2L debonding ；
Long crack, 2L debonding <L cracking ；
Wherein L is cracking For matrix crack spacing, L debonding Is the interfacial debonding length.
The invention preferably divides the short crack, the middle crack and the long crack according to the mode, can better describe the breaking condition of the matrix, and is beneficial to obtaining a real hysteresis relationship.
In the present invention, the matrix breaking process of the woven ceramic matrix composite material is preferably determined by the formula shown in formulas 1 to 5:
wherein L is the initial analog total length, L eff For effective simulation length, P (x) is the distribution function of matrix crack spacing greater than interfacial debonding length, P R (x) To a matrix crack spacing less thanThe distribution function of the interface debonding length, N is the breaking number of the matrix, x is the axial value, sigma is the stress, N is the breaking density of the matrix, delta D Is a 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 is 0 For reference area, L R For reference length, sigma 0 For reference stress, m is the matrix Weibull modulus
In the invention, the method preferably determines the matrix cracking process of the woven ceramic matrix composite material through the formulas shown in formulas 1-5, can characterize the matrix cracking condition, and is beneficial to better obtaining the matrix cracking condition.
In the present invention, the fiber breaking process of the woven ceramic matrix composite material is preferably determined by the formula shown in formulas 7 to 9:
wherein phi is the stress born by intact fiber, q is the fiber fracture probability, phi b Load bearing for breaking fiber, m f For the fiber Weibull modulus, sigma fc Is the characteristic strength of the fiber, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f Is the fiber volume content in the composite material.
The method preferably determines the fiber breaking process of the woven ceramic matrix composite material through the formulas shown in formulas 7-9, can better represent the fiber breaking condition, and is favorable for better analyzing the fiber breaking condition.
According to the fracture mechanics interface debonding criterion, an interface debonding length equation, an unloading interface reverse sliding length equation and a reloading interface new sliding length equation are respectively established based on an interface debonding and sliding mechanism. In the present invention, the fracture mechanics interface debonding criterion preferably satisfies the equation of formula 10:
wherein Γ is d To release the bonding energy of the interface, w f (0) Axial displacement of the planar fiber for the crack of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, r f Is the fiber radius tau i And F is the load bearing of the matrix crack plane fiber.
In the present invention, the interfacial debonding length equation is preferably as shown in formula 11:
wherein V is m Is the volume content of the matrix in the composite material, E m Modulus of elasticity of matrix, E c Is the elastic modulus of the composite material, ρ is shear model parameter, E f Is the elastic modulus of the fiber;
the unloading interface reverse slip length equation is preferably as shown in equation 12:
wherein L is cs Reverse slip length for unloading interface;
the reload interface new slip length equation is preferably as shown in equation 13:
wherein L is ns The interface is reloaded with a new slip length.
According to a matrix breaking theory, 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 are established based on the matrix crack random cracking process, the fiber breaking probability, the intact fiber bearing stress, the interface debonding length equation, the unloading interface reverse sliding length equation and the reloading interface new sliding length equation; and establishing a braided ceramic matrix composite material hysteresis loop stress-strain relation equation according to the short crack unloading stress-strain relation equation, the short crack reloading stress-strain relation equation, the middle crack unloading stress-strain relation equation, the middle crack reloading 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 and consider a matrix and a fiber broken braided ceramic matrix composite material fatigue hysteresis loop. In the present invention, the fiber fracture probability and the intact fiber bearing stress are boundary conditions that determine the axial stress distribution of the fiber and the matrix during unloading and reloading.
In the invention, the hysteresis loop stress-strain relation equation of the woven ceramic matrix composite material is preferably shown as formula 14:
wherein ε c Is composite material hysteresis loop strain, P S (x) As a short crack distribution function, P M (x) As the distribution function of middle cracks, P L (x) Epsilon as a long crack distribution function th For thermal residual strain, σ f (z) is the fiber axial stress distribution.
In the present invention, the equation of equation 14 takes into account the impact of different matrix fracture lengths on the hysteresis relationship.
In the present invention, the long crack unloading stress-strain relation equation is preferably as shown in formula 15:
wherein ε UL For long crack unloading strain, R f Is the radius of the fiber, phi U To unload intact fibers to bear stress, L 0 And L 1 Is a long crack coefficient; the method comprises the steps of carrying out a first treatment on the surface of the
The long crack reload stress-strain relationship equation is preferably as shown in equation 16:
wherein ε RL Reloading strain for long cracks, phi R Bearing stress for reloading intact fibers;
the L is 0 Preferably, L is determined by the formula shown in formula 17-1 1 Preferably determined by the formula shown in formula 17-2:
in the present invention, the mid-crack unloading stress-strain relationship equation is preferably as shown in formula 18:
wherein ε UM For unloading strain from the middle crack, M 0 、M 1 And M 2 Is the medium crack coefficient；
The mid-crack reload stress-strain relationship equation is preferably as shown in formula 19:
wherein ε RM Reloading the medium crack with strain;
the M is 0 Preferably, M is determined by the formula shown in formula 20-1 1 Preferably, M is determined by the formula shown in formula 20-2 2 Preferably consists of
The formula shown in formula 20-3 determines:
in the present invention, the short crack unloading stress-strain relation equation is preferably as shown in formula 21:
wherein ε US For short crack unloading strain, sigma tr_unloading To relieve the transition stress, S 0 、S 1 And S is 2 Is the fracture coefficient.
As shown in formula 21, the present invention preferably includes both cases of unloading interface partial slip and interface complete slip, wherein σ, when studying short crack unloading stress-strain relationship>σ tr_unloading The time represents the sliding of the unloading interface part, and sigma is less than or equal to sigma tr_unloading Representing complete sliding of the unloading interface, in this way, the device can be refinedAnd interface slippage condition is analyzed, so that the axial stress distribution of the fiber is reasonably determined.
In the present invention, the short crack reload stress-strain relation equation is preferably as shown in formula 22:
wherein ε RS Reloading strain, sigma, for short cracks tr_reloading Loading the transition stress again;
the S is 0 Preferably determined by the formula shown in formula 23-1, S 1 Preferably determined by the formula shown in formula 23-2, S 2 Preferably determined by the formula shown in formula 23-3:
as shown in formula 22, the invention preferably comprises reloading the interface with partial slip and complete interface slip, wherein sigma is less than or equal to sigma, when researching the stress-strain relationship of the reloading of the short crack tr_reloading Time represents reload interface partial slip, sigma>σ tr_reloading The time represents that the reloaded interface slides completely, and the interface sliding condition can be analyzed accurately by adopting the method, so that the axial stress distribution of the fiber can be determined reasonably.
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 24:
wherein V is 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.
The method analyzes the matrix and the fiber breaking process of the woven ceramic matrix composite material, and determines the random cracking process of matrix cracks, the fiber breaking probability and the stress born by intact fibers; based on the unloading and reloading sliding mechanism, the unloading and reloading constitutive relation of the woven ceramic matrix composite material considering the breakage of the matrix and the fiber 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, unloading and reloading of cracks with different lengths are illustrated, so that the influence of crack lengths on stress distribution can be seen to be great, and therefore, the method provided by the invention can be used for establishing corresponding unloading and reloading stress-strain relation equations for cracks with different lengths, considering the influence of the broken length of a matrix on a hysteresis loop, and being beneficial to better predicting the hysteresis loop, so that the damage of the matrix and the broken fibers on the woven ceramic matrix composite material can be monitored, and the safety of the woven ceramic matrix composite material structure in the practical engineering application process is improved.
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 an unloading stress-strain relation equation of cracks with different lengths, reload the stress-strain relation equation and weave a hysteresis loop stress-strain relation equation of a ceramic matrix composite material, and specifically, the woven ceramic matrix composite material (SiC/SiC) is taken as a test sample, the test sample is subjected to loading and unloading tests, and the fatigue hysteresis loop of the test sample is predicted:
providing parameters: v (V) f ＝0.46，R f ＝6.5μm，E f ＝319GPa，E m ＝450GPa，τ i ＝12MPa，Γ d ＝2J/m 2 ，m＝10，m f ＝5；χ＝0.5；
And then obtaining a stress-strain relation equation of the hysteresis loop of the woven ceramic matrix composite material shown in the formula 14, and unloading stress-strain relation equations and reloading stress-strain relation equations of cracks with different lengths shown in the formulas 15-16, 18-19 and 21-22 according to the formulas 1-5, 7-8 and 11-13, so as to obtain a stress-strain relation, and obtaining the hysteresis loop of the woven ceramic matrix composite material.
Fig. 2 shows a fatigue hysteresis loop of the woven ceramic matrix composite material predicted by the method according to the invention, the solid line in fig. 2 shows a stress-strain relation curve constructed by adopting the scheme, and the difference points are actual test data, so that the shape and the position of the hysteresis loop predicted by the method according to the invention are identical with those of experimental data, and the method provided by the invention can accurately predict the fatigue hysteresis loop of the woven ceramic matrix composite material considering the breakage of the matrix and the fiber.
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 (6)
1. A prediction method for a fatigue hysteresis loop of a woven ceramic matrix composite material considering matrix and fiber breakage comprises the following steps:
(1) Analyzing the matrix breaking 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 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;
analyzing the fiber breaking process of the woven ceramic matrix composite material, and obtaining fiber breaking probability and intact fiber bearing stress based on the overall load bearing criterion;
(2) According to fracture mechanics interface debonding criteria, based on interface debonding and sliding mechanisms, respectively establishing an interface debonding length equation, an unloading interface reverse sliding length equation and a reloading interface new sliding length equation;
(3) According to a matrix breaking theory, based on the matrix crack random cracking process, the fiber breaking probability and the intact fiber bearing stress in the step (1) and the interface debonding length equation, the unloading interface reverse sliding length equation and the reloading interface new sliding length equation in the step (2), a short crack unloading stress-strain relation equation, a short crack reloading stress-strain relation equation, a medium crack unloading stress-strain relation equation, a medium crack reloading stress-strain relation equation, a long crack unloading stress-strain relation equation and a long crack reloading stress-strain relation equation in the step (1), further establishing a woven ceramic matrix composite material hysteresis loop stress-strain relation equation, and predicting a woven ceramic matrix composite material fatigue hysteresis loop taking the matrix and the fiber breaking into consideration;
in the step (1), the short crack, the medium crack and the long crack are respectively:
short crack, L cracking <L debonding ；
Middle crack, L debonding <L cracking <2L debonding ；
Long crack, 2L debonding <L cracking ；
Wherein L is cracking For matrix crack spacing, L debonding Is the interface debonding length;
the breaking process of the matrix of the woven ceramic matrix composite material is determined by the formulas shown in 1-5:
wherein L is the initial analog total length, L eff For effective simulation length, P (x) is the distribution function of matrix crack spacing greater than interfacial debonding length, P R (x) The crack spacing of the matrix is smaller than the distribution function of the interface debonding length, N is the breaking number of the matrix, x is the axial value, sigma is the stress, and N is the breaking density of the matrixDegree, delta D Is a 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 is 0 For reference area, L R For reference length, sigma 0 As reference stress, m is the matrix weibull modulus;
in the step (3), the long crack unloading stress-strain relation equation is shown in formula 15:
wherein ε UL For long crack unloading strain, r f Is the radius of the fiber, phi U To unload intact fibers to bear stress, L 0 And L 1 Is a long crack coefficient; τ i Friction shear stress for interface debonding zone E f Is the elastic modulus of fiber, L cs Reverse slip length for unloading interface;
the long crack reload stress-strain relationship equation is shown in equation 16:
wherein ε RL Reloading strain for long cracks, phi R To reload intact fibres to take up stress, L ns New slip length for reloading the interface;
the L is 0 Determined by a formula shown in 17-1, L 1 Determined by the formula shown in equation 17-2:
in the step (3), the intermediate crack unloading stress-strain relation equation is shown in formula 18:
wherein ε UM For unloading strain from the middle crack, M 0 、M 1 And M 2 Is the medium crack coefficient;
the mid-crack reload stress-strain relationship equation is shown in equation 19:
wherein ε RM Reloading the medium crack with strain;
the M is 0 Determined by a formula shown in the formula 20-1, M 1 Determined by a formula shown in 20-2, M 2 Determined by the formula shown in equation 20-3:
in the step (3), the stress-strain relation equation for unloading the short crack is shown in formula 21:
wherein ε US For short crack unloading strain, sigma tr_unloading To relieve the transition stress, S 0 、S 1 And S is 2 Is the fracture coefficient;
the short crack reload stress-strain relationship equation is shown in equation 22:
wherein ε RS Reloading strain, sigma, for short cracks tr_reloading Loading the transition stress again;
the S is 0 Is determined by a formula shown in a formula 23-1, S 1 Determined by the formula shown in the formula 23-2, S 2 Determined by the formula shown in equation 23-3:
2. the method according to claim 1, wherein in the step (1), the fiber breaking process of the woven ceramic matrix composite material is determined by the formulas shown in formulas 7 to 9:
wherein phi is the stress born by intact fiber, q is the fiber fracture probability, phi b Load bearing for breaking fiber, m f For the fiber Weibull modulus, sigma fc Is the characteristic strength of the fiber, χ is the effective volume content coefficient of the fiber of the composite material along the stress loading direction, V f Is the fiber volume content in the composite material.
3. The method according to claim 2, wherein in the step (2), the fracture mechanics interface debonding criterion satisfies an equation shown in equation 10:
wherein Γ is d To release the bonding energy of the interface, w f (0) Axial displacement of the planar fiber for the crack of the matrix; v (x) is the axial displacement of the fiber relative to the matrix, r f And F is the radius of the fiber, and F is the crack plane fiber of the matrix to bear load.
4. A prediction method according to claim 3, wherein in the step (2), the interfacial debonding length equation is as shown in formula 11:
wherein V is m Is the volume content of the matrix in the composite material, E m Modulus of elasticity of matrix, E c Is the elastic modulus, ρ of the composite materialIs a shear model parameter;
the unloading interface reverse slip length equation is shown in fig. 12:
the reload interface new slip length equation is shown in fig. 13:
5. the method according to claim 4, wherein in the step (3), the equation of the hysteresis loop stress-strain relationship of the woven ceramic matrix composite is shown in formula 14:
wherein ε c Is composite material hysteresis loop strain, P S (x) As a short crack distribution function, P M (x) As the distribution function of middle cracks, P L (x) Epsilon as a long crack distribution function th For thermal residual strain, σ f (z) is the fiber axial stress distribution.
6. The method according to any one of claims 2 to 5, 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 V is f_loading Is the fiber volume content of the composite material along the stress loading direction.
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