Method for predicting cracking stress of fiber reinforced ceramic matrix composite matrix

Abstract

The invention discloses a method for predicting the cracking stress of a fiber-reinforced ceramic matrix composite matrix. The method is characterized by comprising the following steps of: obtaining interface parameters of a CMC (Carboxy Methylated Cellulose) material system through a nanoindentation fiber push-in experiment and an interface parameter solving model; according to the interface parameter solving model, interface elastoplasticity and different interface response combinations caused by different materials are considered in a nanoindented fiber push-in experiment; establishing three corresponding steady-state matrix cracking energy balance equations by considering the elastoplasticity of the interface and different response combinations caused by different materials of the interface in the fiber pulling-out process when the matrix is cracked, and substituting the upstream interface shear stress, the downstream interface shear stress and the downstream interface shear stress into the three established matrix cracking stress prediction models; according to the method, the plastic response of the interface in the matrix cracking process and the critical conditions of different mechanical responses of different materials in the fiber pulling-out process are considered, so that the established matrix cracking stress prediction model is more reliable, and the accuracy is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of ceramic-based composite materials, and in particular relates to a method for predicting matrix cracking stress of a fiber-reinforced ceramic-based composite material. Background Art

[0002] For CMC (Ceramic matrix composites), matrix cracking will reduce the modulus of CMC, allowing oxidants to enter the composite material and weaken the overall performance of the material. Since matrix cracking is the starting point for significant damage to CMC, accurate prediction and analysis of it is very important for optimizing the design of CMC.

[0003] At present, there are many methods for predicting matrix cracking stress. Most of them are to establish a model for the CMC matrix cracking process and perform stress analysis, and combine the CMC geometric material parameters with the fiber / matrix interface parameters to form a calculation prediction model for matrix cracking stress. However, some of the currently established matrix cracking stress prediction methods have the following disadvantages:

[0004] ① The possible plastic response of the interface during matrix cracking is not considered, which may lead to deviations in the prediction results of matrix cracking stress;

[0005] ② The combination of mechanical responses of different materials that may exist at the interface during the matrix cracking process when the fiber is pulled out is not considered. For example, only the combination of two mechanical responses of interface debonding and interface sliding of a single material is considered. For different CMC material systems, there may be other types of mechanical response combinations other than interface debonding and interface sliding at the interface during the matrix cracking process. Ignoring this point may affect the prediction results.

[0006] ③ There is no complete model and method for different materials, which affects the prediction results of cracking stress when the matrix cracks in different CMC material systems. Summary of the invention

[0007] The present invention aims at solving the problems existing in the prior art and proposes a method for predicting matrix cracking stress of a fiber reinforced ceramic matrix composite material. The first purpose is to solve the problem that the prior art does not consider the plastic response that may exist at the interface during the matrix cracking process, thus causing deviation in the matrix cracking stress prediction result; the second purpose is to solve the problem that the prior art does not consider the mechanical response combination of different materials at the interface when the fiber is pulled out during the matrix cracking process, thus causing deviation in the matrix cracking stress prediction result; the third purpose is to solve the problem that the prior art does not form a set of perfect cracking stress prediction models and methods for different materials, thus causing deviation in the cracking stress analysis prediction result when the matrix cracks.

[0008] The present invention proposes the following technical solutions to solve the problems existing in the prior art:

[0009] A method for predicting matrix cracking stress of fiber-reinforced ceramic matrix composite materials is characterized by comprising the following steps:

[0010] Step 1: Obtain the interface parameter τ of the CMC material system through nanoindentation fiber push-in experiment and interface parameter solution model s , τ y , d ; This interface parameter solution model takes into account the interface elastic-plasticity and the different interface response combinations caused by different materials in the nanoindentation fiber push-in experiment;

[0011] Among them, τ s is the interfacial sliding stress, that is, the sliding resistance that needs to be overcome for the relative sliding of the fiber / matrix after the interface between the fiber / matrix is ​​debonded; τ y is the interface yield stress, that is, the yield resistance that needs to be overcome when the interface between the fiber and the matrix undergoes yield deformation; d is the interfacial debonding toughness, i.e., the energy condition required for debonding to occur at the interface between fiber and matrix;

[0012] Step 2: Considering the elastic-plasticity of the interface during fiber pull-out when the matrix cracks, as well as the different response combinations of the interface due to different materials, three corresponding steady-state matrix cracking energy balance equations are established, and the upstream stress and Downstream stress and Substituting into the established energy balance equation, three matrix cracking stress prediction models are obtained; the upstream stress is the stress distribution of the non-cracked part of the material, and the downstream stress is the stress distribution of the cracked part of the material; wherein, and That is, they are the axial stresses of the fiber and matrix at the upstream when the interface is in the elastic stage; and τ i D (z) are the downstream fiber axial stress, downstream matrix axial stress, and downstream interface shear stress, respectively;

[0013] The upstream stress of step 2 and The details are as follows:

[0014] 1) Ignoring the influence of Poisson's ratio, initial residual stress and interface axial stress, the total axial stress σ applied satisfies the following formula:

[0015] σ=c f σf (z)+c m σ m (z) (1)

[0016] where c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; σ f and σ m are the fiber and matrix axial stresses respectively, and are unknown variables related to σ.

[0017] 2) When z→∞ at the upstream and downstream ends, the strain of the fiber and matrix is ​​equal to the CMC strain:

[0018]

[0019] Among them, ε f and ε m are the axial strains of the fiber and matrix, respectively, and ε is the CMC strain, both of which are unknowns related to σ; E = c f E f +c m E m is the CMC Young's modulus, is the known material parameter, E f and E m are the Young’s modulus of the fiber and matrix, respectively, which are known material parameters.

[0020] So when z=∞, the fiber and matrix stresses are:

[0021]

[0022] here and That is, the axial stress of the fiber and the upstream stress of the matrix when the interface is in the elastic stage and the material is not cracked, which is an unknown number related to σ. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of the CMC. All three are known material parameters. σ is the applied matrix cracking stress, which is an unknown number.

[0023] The downstream stress of step 2 and The details are as follows:

[0024] 1) According to the displacement continuity, when the fiber is pulled out when the matrix cracks, the displacement relationship between the fiber, interface and matrix when the interface is still in an elastic state is:

[0025]

[0026] where u f and um are the axial displacements of the fiber and matrix, respectively, are unknown variables related to σ, and the depth z can be defined by oneself; here R f is the fiber radius, It is defined as the effective radius of the substrate subjected to concentrated axial load, which is a known material parameter; v i (z) and v m (z) are the shear displacements of the interface and the matrix, respectively;

[0027] 2) The fiber and matrix satisfy the following physical geometric relationship:

[0028]

[0029] 3) According to the shear lag analysis, the axial stress relationship at the fiber / interface can be expressed as:

[0030]

[0031] 4) According to the physical and geometric relationship between the fiber and the matrix, the downstream stress distribution that satisfies the boundary conditions when the interface is in the elastic stage during the matrix cracking process can be derived:

[0032]

[0033] in, and They are the downstream fiber axial stress, the downstream matrix axial stress, and the downstream interface shear stress, which are all unknowns related to σ. The depth z can be defined by oneself;

[0034] c f and c m are the fiber and matrix volume fractions, respectively, which are known material parameters;

[0035] E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of the CMC, all three are known material parameters; ρ is the CMC material parameter, which is a known number; R f is the fiber radius, which is a known material parameter; at this time, the interface is still in an elastic state.

[0036] The step 2 obtains three matrix cracking stress prediction models, which are as follows:

[0037] (1) The three critical stresses σ are obtained d , σ y , σ s Three corresponding relations σ y >σ d >σ s ; σ y >σ s >σd ; σ d >σ y >σ s , as the basis for the subsequent matrix cracking prediction model; the three corresponding relationships are when the matrix cracking fiber is pulled out, with the increase of the matrix cracking stress σ, the downstream interface shear force τ in the elastic stage i (z) is also set when it gradually increases;

[0038] σ d is the critical load size when the interface debonds when the matrix cracks; σ y is the critical load size when the interface yields when the matrix cracks; σ s It is the critical load size when relative sliding occurs between fiber / matrix after interface debonding when the matrix cracks.

[0039] (2) Based on the first critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the first debonding-controlled matrix cracking stress prediction model is established: 2 +λ2σ+λ3=0; where σ is the matrix cracking stress to be determined, and λ1, λ2 and λ3 are all unknown parameters containing the matrix cracking stress σ;

[0040] (3) Based on the second critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the first sliding-controlled matrix cracking stress prediction model is established: β1σ 2 +β2σ+β3=0; where σ is the matrix cracking stress to be determined, and β1, β2 and β3 are all unknown parameters containing the matrix cracking stress σ;

[0041] (4) Based on the third critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the third post-yield debonding controlled matrix cracking stress prediction model is established: γ1σ 2 +γ2σ+γ3=0; where σ is the matrix cracking stress to be determined, and γ1, γ2 and γ3 are all unknown parameters containing the matrix cracking stress σ.

[0042] Furthermore, the first relationship σ y >σ d >σ s : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes interface debonding d >The critical stress σ that causes relative sliding of fiber / matrix s This situation is due to: the critical stress σ that causes relative sliding of the fiber / matrix s<Critical stress σ for interface debonding d , so when debonding occurs, relative sliding between the fiber / matrix occurs immediately; since the critical stress for the interface to yield is σ y The critical stress that causes debonding at the interface is σ d , so debonding has occurred before the interface has yielded and relative sliding has occurred between the matrix / fiber;

[0043] Furthermore, the second relationship σ y >σ s >σ d : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s >The critical stress σ that causes interface debonding d This situation is due to: the critical stress σ that causes debonding at the interface d <The critical stress σ that causes relative sliding between fiber and matrix s , so relative sliding does not occur immediately when debonding occurs; due to the critical yield stress σ y The critical stress that causes debonding at the interface is σ d , so debonding occurs before the interface yields;

[0044] Furthermore, the third relationship σ d >σ y >σ s : Critical stress σ for interface debonding d >The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s , this situation is due to the critical stress σ that causes the interface to yield y <Critical stress σ for interface debonding d , and the critical stress σ that causes relative sliding between fiber and matrix s <Critical stress σ for interface debonding d , so the material will yield before debonding occurs, and relative sliding will occur between the fiber / matrix immediately after debonding occurs.

[0045] Furthermore, the first debonding controlled matrix cracking stress prediction model λ1σ is established. 2 +λ2σ+λ3=0, that is: when σ y >σ d >σ s When the matrix cracking stress prediction model is defined as debonding controlled type, the process is as follows:

[0046] 1) According to the shear lag analysis, the downstream debonding area (0<z≤l d )’s stress distribution:

[0047]

[0048] Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0049] 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l d )’s stress distribution:

[0050]

[0051] Among them l d is the debonding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter.

[0052] 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0053]

[0054] The left side of formula (11) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (11) is the sum of the energy released by the new surface formed by the cracking of the matrix and the new surface formed by the debonding of the interface.

[0055] 4) The first debonding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (9) and formula (10) into formula (11) yields the debonding-controlled matrix crack prediction model:

[0056]

[0057] Furthermore, the first debonding controlled matrix cracking stress prediction model λ1σ2 The specific λ1, λ2 and λ3 in +λ2σ+λ3=0 are as follows:

[0058] 1) Expressions of λ1, λ2 and λ3:

[0059]

[0060] In formula (13), only l d is an unknown parameter related to σ, and the rest are known parameters; l d is the debonding length, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the interfacial sliding stress, ξ d is the interface debonding toughness, and both are known parameters obtained through interface testing;

[0061] 2) Debonding length l d The solution:

[0062] σ d It can be determined by the following formula:

[0063]

[0064] is the equivalent shear modulus, is a known material parameter; σ d is a known number. When the interface remains intact during matrix cracking, the matrix cracking stress is:

[0065]

[0066] c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter;

[0067] When σ is satisfied d >σ0, it can be seen that debonding will not occur during the matrix cracking process; when σ d When <σ0, the matrix cracking process is accompanied by debonding sliding. dThe size of is given by:

[0068]

[0069] 3) Substitute formula (16) into formula (13) to obtain the expressions of λ1, λ2 and λ3β3 with respect to σ as the unknown variable. Finally, substitute λ1, λ2 and λ3 into formula (12) to solve the cubic equation with respect to σ and obtain the prediction result of the first cracking model.

[0070] Furthermore, the second sliding-controlled matrix cracking stress prediction model β1σ is established. 2 +β2σ+β3=0, that is: when σ y >σ s >σ d When the matrix cracking stress prediction model is defined as sliding controlled type, the process is as follows:

[0071] 1) According to the shear lag analysis, the downstream sliding area (0<z≤l s )’s stress distribution:

[0072]

[0073] Among them l s is the sliding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0074] 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l s )’s stress distribution:

[0075]

[0076] Among them, l s is the sliding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter.

[0077] 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0078]

[0079] The left side of formula (19) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (19) is the sum of the energy released by the new surface formed by matrix cracking and the new surface formed by interface debonding.

[0080] 4) The second sliding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Formula (17) and formula (18) are substituted into formula (19) to obtain the sliding-controlled matrix crack stress prediction model.

[0081] β1σ 2 +β2σ+β3=0 (19)

[0082] Furthermore, the second sliding-controlled matrix cracking stress prediction model β1σ 2 The specific details of β1, β2 and β3 in +β2σ+β3=0 are as follows:

[0083] 1) Expression of β1, β2 and β3:

[0084]

[0085] Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, is the interface sliding toughness, and both are known parameters obtained through interface testing. s is the sliding length and is an unknown parameter related to σ.

[0086] 2) Sliding length l s The solution:

[0087] σ s It can be determined by the following formula:

[0088]

[0089] σ s is a known parameter. When σ d >σ0, it can be seen that no sliding will occur during the matrix cracking process. d When <σ0, the matrix cracking process is accompanied by sliding. sThe size of is given by:

[0090]

[0091] 3) Substitute formula (23) into formula (21) to obtain the expressions of β1, β2 and β3 with respect to σ as the unknown variable. Finally, substitute β1, β2 and β3 into formula (28) to solve the cubic equation with respect to σ and obtain the prediction results of the second cracking model.

[0092] Furthermore, the third post-yield debonding controlled matrix cracking stress prediction model γ1σ is established. 2 +γ2σ+γ3=0, that is: when σ d >σ y >σ s When the matrix cracking stress prediction model is defined as post-yield debonding control type, the process is as follows:

[0093] 1) According to the shear lag analysis, it is found that in the downstream debonding area (0<z≤l d )’s stress distribution:

[0094]

[0095] Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0096] 2) According to the shear lag analysis, the downstream yield region (l d <z≤l d +l p )’s stress distribution:

[0097]

[0098] Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress, τ y is the yield stress, and are all known interface parameters.

[0099] 3) Under the condition of ensuring stress continuity, the unyielded and undebonded area (z>l) in the downstream is obtained.s +l p )’s stress distribution:

[0100]

[0101] Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress, τ y is the yield stress, and are all known interface parameters.

[0102] 4) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0103]

[0104] The left side of formula (27) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (27) is the sum of the energy released by the new surface formed by matrix cracking and the new surface formed by interface debonding.

[0105] 5) The third post-yield debonding controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (24), formula (25) and formula (26) into formula (27) yields the post-yield debonding controlled matrix crack stress prediction model:

[0106] γ1σ 2 +γ2σ+γ3=0 (27)

[0107] Furthermore, the third post-yield debonding controlled matrix cracking stress prediction model γ1σ 2 In the equation +γ2σ+γ3=0, γ1, γ2 and γ3 are as follows:

[0108] 1) Expressions of γ1, γ2 and γ3:

[0109]

[0110] Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, τ y is the yield stress, and both are known parameters obtained through interface testing. d is the debonding length, l p is the yield length, and are unknown parameters related to σ.

[0111] 2) Yield length l p and debonding length l d The solution:

[0112] σ y It can be determined by the following formula:

[0113]

[0114] in is the interface yield toughness, a known parameter obtained through interface testing, so σ y is a known parameter. When σ y >σ0, it can be seen that no yield phenomenon will occur during the matrix cracking process. y <σ0<σ d When the matrix cracking process is accompanied by yielding, p The size of is given by:

[0115]

[0116] When σ is satisfied d When <σ0, the matrix cracking process is accompanied by debonding sliding. d The size of is given by:

[0117]

[0118] 3) Substitute formula (31) and formula (32) into formula (29) to obtain the expressions of γ1, γ2 and γ3 with respect to σ as the unknown variable. Finally, substitute γ1, γ2 and γ3 into formula (28) to solve the cubic equation with respect to σ to obtain the prediction results of the third cracking model.

[0119] Advantages and effects of the present invention

[0120] 1. In the technical solution of this patent, since the plastic response of the interface during the matrix cracking process is taken into account, the established matrix cracking stress prediction model is more reliable, so the prediction accuracy is improved;

[0121] 2. In the technical solution of this patent, the critical conditions of different mechanical responses of different materials during fiber pullout when the interface is cracked in the matrix are taken into account, and then a matrix cracking stress prediction model considering the sequence of mechanical responses of the interface and the combination of responses is established. Therefore, by using this patented technology, by performing a simple nanoindentation fiber test on the CMC material and obtaining the interface parameters, the mechanical response combination and degree of the interface during the matrix cracking process can be obtained through the interface parameters, and then the CMC matrix cracking stress can be predicted, which has the effect of low cost and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 This is a flow chart of the method for predicting matrix cracking stress of fiber-reinforced ceramic-based composite materials of the present invention;

[0123] Figure 2 Schematic diagram of matrix cracking;

[0124] Figure 3 yes Figure 2 A partial enlarged view of area A. DETAILED DESCRIPTION

[0125] Design principle of the present invention

[0126] 1. Innovation of the present invention

[0127] One of the innovations is that the possible plastic response of the interface during the matrix cracking process is considered. When the three critical stresses exist σ d >σ y >σ s When the relationship is obtained, according to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation formula (27) of the post-yield debonding controlled type and the prediction model formula (28) of the post-yield debonding controlled type matrix cracking stress σ are obtained.

[0128] , and then according to formula (29)-(32), substitute formula (31) and formula (32) into formula (29) to obtain γ1, γ 2 Finally, replace γ1, γ2 and γ 3 Substituting into formula (28) and solving the cubic equation about σ, we can obtain the prediction results of the third cracking model.

[0129] The existing technology only considers the interface response when the fiber is pulled out during the matrix cracking process, without considering that the interface response of different materials is different when the matrix cracks. It only considers that there is no yield stage or plastic response in the interface response during the fiber pull-out process when the matrix cracks, and the fiber / matrix directly slides relative to each other after direct debonding. Downstream substrate axial stress The interface parameter yield stress τ is not considered. y Axial stress on downstream fibers Downstream substrate axial stress The influence of the interface parameter yield stress τ is not included in the energy balance equation. y , and its matrix cracking stress σ prediction model based on the energy balance equation is not accurate enough.

[0130] The post-yield debonding controlled energy balance equation (27) of the present invention is derived from equation (26), where: the downstream fiber axial stress is calculated as: Downstream substrate axial stress and the downstream interfacial shear stress When the interface yield stress parameter τ y The calculation is integrated; in the expression formula (29) of the present invention regarding γ1, γ2 and γ3, the interface yield stress parameter τ is also included. y Incorporated into computing;

[0131] The second innovation is to build three matrix cracking stress prediction models that can reflect the material's personalization:

[0132] ① The model roughly divides materials into three types, thereby realizing three matrix cracking stress prediction models that can reflect the individuality of the materials. The first of the three materials is that the interface debonds and slides at the same time during the matrix cracking process, and its three critical stresses satisfy the relationship σ y >σ d >σ s , due to the critical stress σ of relative sliding between fiber and matrix s <Interface debonding critical stressσ d , or the critical stress for interfacial debonding σ d > Critical stress σ for relative sliding of fiber / matrix s Therefore, when the interface debonds, sliding must also occur at the same time; the second is that when the matrix cracks, the interface does not debond, and the critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s >The critical stress σ that causes interface debonding d This situation is due to: the critical stress σ that causes debonding at the interface d<The critical stress σ that causes relative sliding between fiber and matrix s , when debonding occurs, the critical stress σ d Not enough to overcome the critical stress σ for slip s , so relative sliding does not occur immediately when debonding occurs; the third type is that yielding occurs before debonding, rather than debonding right away, and there is a yielding process before debonding. This material satisfies the relationship σ d >σ y >σ s , because the critical stress σ that causes the interface to yield y <Critical stress σ for interface debonding d , and the critical stress σ that causes relative sliding between fiber and matrix s <Critical stress σ for interface debonding d Therefore, the interface material will yield before debonding occurs, and relative sliding occurs between the fiber / matrix at the same time as cracking occurs.

[0133] ② For three different stress cracking models, this model calculates the upstream stress of each and Downstream stress and In the example, the interface parameter τ is introduced s , τ y , d Different types and quantities enable the realization of three matrix cracking stress prediction models that can reflect the material's individuality.

[0134] For the energy balance equation (11) of the first debonding-controlled matrix crack stress prediction model, it is only necessary to substitute the interface parameter τ s , d , no need to bring in τ y ;

[0135] For the energy balance equation (19) of the second sliding-controlled matrix crack stress prediction model, it is only necessary to substitute the interface parameter τ s , there is no need to include the yield stress τ in the interface parameters y and debonding toughnessξ d

[0136] For the energy balance equation (26) of the third post-yield debonding controlled matrix crack stress prediction model, the interface parameter τ needs to be substituted s , τ y , d .

[0137] 2. The “different materials” described in this embodiment refer to different material systems under the general category of ceramic-based composite materials that differ due to different preparation processes and components.

[0138] Based on the above invention principle, the present invention designs a method for predicting matrix cracking stress of fiber-reinforced ceramic matrix composite materials, such as Figure 1-3 As shown, its characteristics are: comprising the following steps:

[0139] Step 1: Obtain the interface parameter τ of the CMC material system through nanoindentation fiber push-in experiment and interface parameter solution model s , τ y , d ; This interface parameter solution model takes into account the interface elastic-plasticity and the different interface response combinations caused by different materials in the nanoindentation fiber push-in experiment;

[0140] Among them, τ s is the interfacial sliding stress, that is, the sliding resistance that needs to be overcome for the relative sliding of the fiber / matrix after the interface between the fiber / matrix is ​​debonded; τ y is the interface yield stress, that is, the yield resistance that needs to be overcome when the interface between the fiber and the matrix undergoes yield deformation; d is the interfacial debonding toughness, i.e., the energy condition required for debonding to occur at the interface between fiber and matrix;

[0141] Step 2: Considering the elastic-plasticity of the interface during fiber pull-out when the matrix cracks, as well as the different response combinations of the interface due to different materials, three corresponding steady-state matrix cracking energy balance equations are established, and the upstream stress and Downstream stress and Substituting into the established energy balance equation, three matrix cracking stress prediction models are obtained; the upstream stress is the stress distribution of the non-cracked part of the material, and the downstream stress is the stress distribution of the cracked part of the material; wherein, and That is, they are the axial stresses of the fiber and matrix at the upstream when the interface is in the elastic stage; and They are the downstream fiber axial stress, the downstream matrix axial stress, and the downstream interface shear stress;

[0142] The upstream stress of step 2 and The details are as follows:

[0143] 1) Ignoring the influence of Poisson's ratio, initial residual stress and interface axial stress, the total axial stress σ applied satisfies the following formula:

[0144] σ=c f σ f (z)+c m σ m (z) (32)

[0145] where c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; σ f and σ m are the fiber and matrix axial stresses respectively, and are unknown variables related to σ.

[0146] 2) When z→∞ at the upstream and downstream ends, the strain of the fiber and matrix is ​​equal to the CMC strain:

[0147]

[0148] Among them, ε f and ε m are the axial strains of the fiber and matrix, respectively, and ε is the CMC strain, both of which are unknowns related to σ; E = c f E f +c m E m is the CMC Young's modulus, is the known material parameter, E f and E m are the Young’s modulus of the fiber and matrix, respectively, which are known material parameters.

[0149] So when z=∞, the fiber and matrix stresses are:

[0150]

[0151] Here σ f U and σ m U That is, the axial stress of the fiber and the upstream stress of the matrix when the interface is in the elastic stage and the material is not cracked, which is an unknown number related to σ. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of the CMC. All three are known material parameters. σ is the applied matrix cracking stress, which is an unknown number.

[0152] The downstream stress of step 2 and The details are as follows:

[0153] 1) According to the displacement continuity, when the fiber is pulled out when the matrix cracks, the displacement relationship between the fiber, interface and matrix when the interface is still in an elastic state is:

[0154]

[0155] where u f and u m are the axial displacements of the fiber and matrix, respectively, are unknown variables related to σ, and the depth z can be defined by oneself; here R f is the fiber radius, It is defined as the effective radius of the substrate subjected to concentrated axial load, which is a known material parameter; v i (z) and v m (z) are the shear displacements of the interface and the matrix, respectively;

[0156] 2) The fiber and matrix satisfy the following physical geometric relationship:

[0157]

[0158] 3) According to the shear lag analysis, the axial stress relationship at the fiber / interface can be expressed as:

[0159]

[0160] 4) According to the physical and geometric relationship between the fiber and the matrix, the downstream stress distribution that satisfies the boundary conditions when the interface is in the elastic stage during the matrix cracking process can be derived:

[0161]

[0162] in, and They are the downstream fiber axial stress, the downstream matrix axial stress, and the downstream interface shear stress, which are all unknowns related to σ. The depth z can be defined by oneself;

[0163] c f and c m are the fiber and matrix volume fractions, respectively, which are known material parameters;

[0164] E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of the CMC, all three are known material parameters; ρ is the CMC material parameter, which is a known number; R f is the fiber radius, which is a known material parameter; at this time, the interface is still in an elastic state.

[0165] The step 2 obtains three matrix cracking stress prediction models, which are as follows:

[0166] (1) The three critical stresses σ are obtained d , σ y , σ s Three corresponding relations σ y >σd >σ s ; σ y >σ s >σ d ; σ d >σ y >σ s , as the basis for the subsequent matrix cracking prediction model; the three corresponding relationships are when the matrix cracking fiber is pulled out, with the increase of the matrix cracking stress σ, the downstream interface shear force τ in the elastic stage i (z) is also set when it gradually increases;

[0167] σ d is the critical load size when the interface debonds when the matrix cracks; σ y is the critical load size when the interface yields when the matrix cracks; σ s It is the critical load size when relative sliding occurs between fiber / matrix after interface debonding when the matrix cracks.

[0168] (2) Based on the first critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the first debonding-controlled matrix cracking stress prediction model is established: 2 +λ2σ+λ3=0; where σ is the matrix cracking stress to be determined, and λ1, λ2 and λ3 are all unknown parameters containing the matrix cracking stress σ;

[0169] (3) Based on the second critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the first sliding-controlled matrix cracking stress prediction model is established: β1σ 2 +β2σ+β3=0; where σ is the matrix cracking stress to be determined, and β1, β2 and β3 are all unknown parameters containing the matrix cracking stress σ;

[0170] (4) Based on the third critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the third post-yield debonding controlled matrix cracking stress prediction model is established: γ1σ 2 +γ2σ+γ3=0; where σ is the matrix cracking stress to be determined, and γ1, γ2 and γ3 are all unknown parameters containing the matrix cracking stress σ.

[0171] Furthermore, the first relationship σ y >σ d >σ s : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes interface debonding d >The critical stress σ that causes relative sliding of fiber / matrixs This situation is due to: the critical stress σ that causes relative sliding of the fiber / matrix s <Critical stress σ for interface debonding d , so when debonding occurs, relative sliding between the fiber / matrix occurs immediately; since the critical stress for the interface to yield is σ y The critical stress that causes debonding at the interface is σ d , so debonding has occurred before the interface has yielded and relative sliding has occurred between the matrix / fiber;

[0172] Furthermore, the second relationship σ y >σ s >σ d : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s >The critical stress σ that causes interface debonding d This situation is due to: the critical stress σ that causes debonding at the interface d <The critical stress σ that causes relative sliding between fiber and matrix s , so relative sliding does not occur immediately when debonding occurs; due to the critical yield stress σ y The critical stress that causes debonding at the interface is σ d , so debonding occurs before the interface yields;

[0173] Furthermore, the third relationship σ d >σ y >σ s : Critical stress σ for interface debonding d >The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s , this situation is due to the critical stress σ that causes the interface to yield y <Critical stress σ for interface debonding d , and the critical stress σ that causes relative sliding between fiber and matrix s <Critical stress σ for interface debonding d , so the material will yield before debonding occurs, and relative sliding will occur between the fiber / matrix immediately after debonding occurs.

[0174] Furthermore, the first debonding controlled matrix cracking stress prediction model λ1σ is established. 2 +λ2σ+λ3=0, that is: when σ y >σ d >σ sWhen the matrix cracking stress prediction model is defined as debonding controlled type, the process is as follows:

[0175] 1) According to the shear lag analysis, the downstream debonding area (0<z≤l d )’s stress distribution:

[0176]

[0177] Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0178] 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l d )’s stress distribution:

[0179]

[0180] Among them l d is the debonding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter.

[0181] 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0182]

[0183] The left side of formula (11) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (11) is the sum of the energy released by the new surface formed by the cracking of the matrix and the new surface formed by the debonding of the interface.

[0184] 4) The first debonding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (9) and formula (10) into formula (11) yields the debonding-controlled matrix crack prediction model:

[0185] λ1σ 2+λ2σ+λ3=0 (42).

[0186] Furthermore, the first debonding controlled matrix cracking stress prediction model λ1σ 2 The specific λ1, λ2 and λ3 in +λ2σ+λ3=0 are as follows:

[0187] 1) Expressions of λ1, λ2 and λ3:

[0188]

[0189] In formula (13), only l d is an unknown parameter related to σ, and the rest are known parameters; l d is the debonding length, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the interfacial sliding stress, ξ d is the interface debonding toughness, and both are known parameters obtained through interface testing;

[0190] 2) Debonding length l d The solution:

[0191] σ d It can be determined by the following formula:

[0192]

[0193] is the equivalent shear modulus, is a known material parameter; σ d is a known number. When the interface remains intact during matrix cracking, the matrix cracking stress is:

[0194]

[0195] c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter;

[0196] When σ is satisfied d>σ0, it can be seen that debonding will not occur during the matrix cracking process; when σ d When <σ0, the matrix cracking process is accompanied by debonding sliding. d The size of is given by:

[0197]

[0198] 3) Substitute formula (16) into formula (13) to obtain the expressions of λ1, λ2 and λ3β3 with respect to σ as the unknown variable. Finally, substitute λ1, λ2 and λ3 into formula (12) to solve the cubic equation with respect to σ and obtain the prediction result of the first cracking model.

[0199] Furthermore, the second sliding-controlled matrix cracking stress prediction model β1σ is established. 2 +β2σ+β3=0, that is: when σ y >σ s >σ d When the matrix cracking stress prediction model is defined as sliding controlled type, the process is as follows:

[0200] 1) According to the shear lag analysis, the downstream sliding area (0<z≤l s )’s stress distribution:

[0201]

[0202] Among them l s is the sliding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0203] 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l s )’s stress distribution:

[0204]

[0205] Among them, l s is the sliding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter.

[0206] 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0207]

[0208] The left side of formula (19) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (19) is the sum of the energy released by the new surface formed by matrix cracking and the new surface formed by interface debonding.

[0209] 4) The second sliding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Formula (17) and formula (18) are substituted into formula (19) to obtain the sliding-controlled matrix crack stress prediction model.

[0210] β1σ 2 +β2σ+β3=0 (50)

[0211] Furthermore, the second sliding-controlled matrix cracking stress prediction model β1σ 2 The specific details of β1, β2 and β3 in +β2σ+β3=0 are as follows:

[0212] 1) Expression of β1, β2 and β3:

[0213]

[0214] Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, is the interface sliding toughness, and both are known parameters obtained through interface testing. s is the sliding length and is an unknown parameter related to σ.

[0215] 2) Sliding length l s The solution:

[0216] σ s It can be determined by the following formula:

[0217]

[0218] σs is a known parameter. When σ d >σ0, it can be seen that no sliding will occur during the matrix cracking process. d When <σ0, the matrix cracking process is accompanied by sliding. s The size of is given by:

[0219]

[0220] 3) Substitute formula (23) into formula (21) to obtain the expressions of β1, β2 and β3 with respect to σ as the unknown variable. Finally, substitute β1, β2 and β3 into formula (28) to solve the cubic equation with respect to σ and obtain the prediction results of the second cracking model.

[0221] Furthermore, the third post-yield debonding controlled matrix cracking stress prediction model γ1σ is established. 2 +γ2σ+γ3=0, that is: when σ d >σ y >σ s When the matrix cracking stress prediction model is defined as post-yield debonding control type, the process is as follows:

[0222] 1) According to the shear lag analysis, it is found that in the downstream debonding area (0<z≤l d )’s stress distribution:

[0223]

[0224] Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter.

[0225] 2) According to the shear lag analysis, the downstream yield region (l d <z≤l d +l p )’s stress distribution:

[0226]

[0227] Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τs is the sliding stress, τ y is the yield stress, and are all known interface parameters.

[0228] 3) Under the condition of ensuring stress continuity, the unyielded and undebonded area (z>l) in the downstream is obtained. s +l p )’s stress distribution:

[0229]

[0230] Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress, τ y is the yield stress, and are all known interface parameters.

[0231] 4) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows:

[0232]

[0233] The left side of formula (27) is the elastic energy difference between the upstream uncracked part and the downstream cracked part, and the right side of formula (27) is the sum of the energy released by the new surface formed by matrix cracking and the new surface formed by interface debonding.

[0234] 5) The third post-yield debonding controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (24), formula (25) and formula (26) into formula (27) yields the post-yield debonding controlled matrix crack stress prediction model:

[0235] γ1σ 2 +γ2σ+γ3=0 (58)

[0236] Furthermore, the third post-yield debonding controlled matrix cracking stress prediction model γ1σ 2In the equation +γ2σ+γ3=0, γ1, γ2 and γ3 are as follows:

[0237] 1) Expressions of γ1, γ2 and γ3:

[0238]

[0239] Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, τ y is the yield stress, and both are known parameters obtained through interface testing. d is the debonding length, l p is the yield length, and are unknown parameters related to σ.

[0240] 2) Yield length l p and debonding length l d The solution:

[0241] σ y It can be determined by the following formula:

[0242]

[0243] in is the interface yield toughness, a known parameter obtained through interface testing, so σ y is a known parameter. When σ y >σ0, it can be seen that no yield phenomenon will occur during the matrix cracking process. y <σ0<σ d When the matrix cracking process is accompanied by yielding, p The size of is given by:

[0244]

[0245] When σ is satisfied d When <σ0, the matrix cracking process is accompanied by debonding sliding. d The size of is given by:

[0246]

[0247] 3) Substitute formula (31) and formula (32) into formula (29) to obtain the expressions of γ1, γ2 and γ3 with respect to σ as the unknown variable. Finally, substitute γ1, γ2 and γ3 into formula (28) to solve the cubic equation with respect to σ to obtain the prediction results of the third cracking model.

Claims

1. A method for predicting matrix cracking stress of fiber-reinforced ceramic matrix composite materials, characterized by: The following steps are involved: Step 1: Obtain the interface parameter τ of the CMC material system through nanoindentation fiber push-in experiment and interface parameter solution model s , τ y , d ; This interface parameter solution model takes into account the interface elastic-plasticity and the different interface response combinations caused by different materials in the nanoindentation fiber push-in experiment; Among them, τ s is the interfacial sliding stress, that is, the sliding resistance that needs to be overcome for the relative sliding of the fiber / matrix after the interface between the fiber / matrix is ​​debonded; τ y is the interface yield stress, that is, the yield resistance that needs to be overcome when the interface between the fiber and the matrix undergoes yield deformation; d is the interfacial debonding toughness, i.e., the energy condition required for debonding to occur at the interface between fiber and matrix; Step 2: Considering the elastic-plasticity of the interface during fiber pullout when the matrix cracks, as well as the different response combinations of the interface due to different materials, three corresponding steady-state matrix cracking energy balance equations are established, and the upstream stress and Downstream stress and downstream interfacial shear stress Substituting into the established energy balance equation, three matrix cracking stress prediction models are obtained; the upstream stress is the stress distribution of the non-cracked part of the material, and the downstream stress is the stress distribution of the cracked part of the material; wherein, and That is, they are the axial stresses of the fiber and matrix at the upstream when the interface is in the elastic stage; and They are the downstream fiber axial stress, the downstream matrix axial stress and the downstream interface shear stress respectively.

2. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 1, characterized in that: The upstream stress of step 2 and The details are as follows: 1) Ignoring the influence of Poisson's ratio, initial residual stress and interface axial stress, the total axial stress σ applied satisfies the following formula: σ=c f s f (z)+c m s m (z) (1) where c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; σ f and σ m are the fiber and matrix axial stresses respectively, and are unknown variables related to σ. 2) When z→∞ at the upstream and downstream ends, the strain of the fiber and matrix is ​​equal to the CMC strain: Among them, ε f and ε m are the axial strains of the fiber and matrix, respectively, and ε is the CMC strain, both of which are unknowns related to σ; E = c f E f +c m E m is the CMC Young's modulus, is the known material parameter, E f and E m are the Young’s modulus of the fiber and matrix, respectively, which are known material parameters. So when z=∞, the fiber and matrix stresses are: here and That is, the axial stress of the fiber and the upstream stress of the matrix when the interface is in the elastic stage and the material is not cracked, which is an unknown number related to σ. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of the CMC. All three are known material parameters. σ is the applied matrix cracking stress, which is an unknown number. The downstream stress of step 2 and The details are as follows: 1) According to the displacement continuity, when the fiber is pulled out when the matrix cracks, the displacement relationship between the fiber, interface and matrix when the interface is still in an elastic state is: where u f and u m are the axial displacements of the fiber and matrix, respectively, are unknown variables related to σ, and the depth z can be defined by oneself; here R f is the fiber radius, It is defined as the effective radius of the substrate subjected to concentrated axial load, which is a known material parameter; v i (z) and v m (z) are the shear displacements of the interface and the matrix, respectively; 2) The fiber and matrix satisfy the following physical geometric relationship: 3) According to the shear lag analysis, the axial stress relationship at the fiber / interface can be expressed as: 4) According to the physical and geometric relationship between the fiber and the matrix, the downstream stress distribution that satisfies the boundary conditions when the interface is in the elastic stage during the matrix cracking process can be derived: in, and They are the downstream fiber axial stress, the downstream matrix axial stress, and the downstream interface shear stress, which are all unknowns related to σ. The depth z can be defined by oneself; c f and c m are the fiber and matrix volume fractions, respectively, which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of the CMC, all three are known material parameters; ρ is the CMC material parameter, which is a known number; R f is the fiber radius, which is a known material parameter; at this time, the interface is still in an elastic state.

3. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 1, characterized in that: The step 2 obtains three matrix cracking stress prediction models, which are as follows: (1) The three critical stresses σ are obtained d , σ y , σ s Three corresponding relations σ y >σ d >σ s ; σ y >σ s >σ d ; σ d >σ y >σ s , as the basis for the subsequent matrix cracking prediction model; the three corresponding relationships are when the matrix cracking fiber is pulled out, with the increase of the matrix cracking stress σ, the downstream interface shear force τ in the elastic stage i (z) is also set when it gradually increases; σ d is the critical load size when the interface debonds when the matrix cracks; σ y is the critical load size when the interface yields when the matrix cracks; σ s It is the critical load size when relative sliding occurs between fiber / matrix after interface debonding when the matrix cracks. (2) Based on the first critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the first debonding-controlled matrix cracking stress prediction model is established: 2 +λ2σ+λ3=0; where σ is the matrix cracking stress to be determined, and λ1, λ2 and λ3 are all unknown parameters containing the matrix cracking stress σ; (3) Based on the second critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the second sliding-controlled matrix cracking stress prediction model is established: β1σ 2 +β2σ+β3=0; where σ is the matrix cracking stress to be determined, and β1, β2 and β3 are all unknown parameters containing the matrix cracking stress σ; (4) Based on the third critical stress relationship and the possible mechanical response combination of the interface under shear force when the fiber is pulled out during the matrix cracking process, the third post-yield debonding controlled matrix cracking stress prediction model is established: γ1σ 2 +γ2σ+γ3=0; where σ is the matrix cracking stress to be determined, and γ1, γ2 and γ3 are all unknown parameters containing the matrix cracking stress σ.

4. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 3, characterized in that: The first relationship σ y >σ d >σ s : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes interface debonding d >The critical stress σ that causes relative sliding of fiber / matrix s This situation is due to: the critical stress σ that causes relative sliding of the fiber / matrix s <Critical stress σ for interface debonding d , so when debonding occurs, relative sliding between the fiber / matrix occurs immediately; since the critical stress for the interface to yield is σ y The critical stress that causes debonding at the interface is σ d , so debonding has occurred before the interface has yielded and relative sliding has occurred between the matrix / fiber; The second relationship σ y >σ s >σ d : The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s >The critical stress σ that causes interface debonding d This situation is due to: the critical stress σ that causes debonding at the interface d <The critical stress σ that causes relative sliding between fiber and matrix s , so relative sliding does not occur immediately when debonding occurs; due to the critical yield stress σ y The critical stress that causes debonding at the interface is σ d , so debonding occurs before the interface yields; The third relationship σ d >σ y >σ s : Critical stress σ for interface debonding d >The critical stress σ that causes the interface to yield when the matrix cracks y >The critical stress σ that causes relative sliding of fiber / matrix s , this situation is due to the critical stress σ that causes the interface to yield y <Critical stress σ for interface debonding d , and the critical stress σ that causes relative sliding between fiber and matrix s <Critical stress σ for interface debonding d , so the material will yield before debonding occurs, and relative sliding will occur between the fiber / matrix immediately after debonding occurs.

5. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 3, characterized in that: The first debonding controlled matrix cracking stress prediction model λ1σ is established 2 +λ2σ+λ3=0, that is: when σ y >σ d >σ s When the matrix cracking stress prediction model is defined as debonding controlled type, the process is as follows: 1) According to the shear lag analysis, the downstream debonding area (0<z≤l d )’s stress distribution: Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter. 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l d )’s stress distribution: Among them l d is the debonding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter. 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows: Formula (11) The first term on the left side of the equal sign is (), the second term on the left side is (), and the right side of the equal sign is 4) The first debonding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (9) and formula (10) into formula (11) yields the debonding-controlled matrix crack prediction model: λ1σ 2 +λ2σ+λ3=0 (11).

6. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 5, characterized in that: The first debonding controlled matrix cracking stress prediction model λ1σ 2 The specific λ1, λ2 and λ3 in +λ2σ+λ3=0 are as follows: 1) Expressions of λ1, λ2 and λ3: In formula (13), only l d is an unknown parameter related to σ, and the rest are known parameters; l d is the debonding length, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the interfacial sliding stress, ξ d is the interface debonding toughness, and both are known parameters obtained through interface testing; 2) Debonding length l d The solution: σ d It can be determined by the following formula: G is the equivalent shear modulus, which is a known material parameter; σ d is a known number. When the interface remains intact during matrix cracking, the matrix cracking stress is: c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters; E f and E m are the Young's modulus of the fiber and matrix respectively, E is the Young's modulus of CMC, and all three are known material parameters; m is the matrix cracking toughness, which is a known material parameter; ρ is the material parameter, which is a known parameter; When σ is satisfied d >σ0, it can be seen that debonding will not occur during the matrix cracking process; when σ d When <σ0, the matrix cracking process is accompanied by debonding sliding. d The size of is given by: 3) Substitute formula (16) into formula (13) to obtain the expressions of λ1, λ2 and λ3β3 with respect to σ as the unknown variable. Finally, substitute λ1, λ2 and λ3 into formula (12) to solve the cubic equation with respect to σ and obtain the prediction result of the first cracking model.

7. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 3, characterized in that: The second sliding-controlled matrix crack stress prediction model β1σ is established. 2 +β2σ+β3=0, that is: when σ y >σ s >σ d When the matrix cracking stress prediction model is defined as sliding controlled type, the process is as follows: 1) According to the shear lag analysis, the downstream sliding area (0<z≤l s )’s stress distribution: Among them l s is the sliding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter. 2) Under the condition of ensuring stress continuity, the non-debonding area downstream (z>l s )’s stress distribution: Among them, l s is the sliding length, is an unknown number related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress and is a known interface parameter. 3) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows: 4) The second sliding-controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Formula (17) and formula (18) are substituted into formula (19) to obtain the sliding-controlled matrix crack stress prediction model. b1s 2 +β2σ+β3=0 (19).

8. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 7, characterized in that: The second sliding-controlled matrix crack stress prediction model β1σ 2 The specific details of β1, β2 and β3 in +β2σ+β3=0 are as follows: 1) Expression of β1, β2 and β3: Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, is the interface sliding toughness, and both are known parameters obtained through interface testing. s is the sliding length and is an unknown parameter related to σ. 2) Sliding length l s The solution: σ s It can be determined by the following formula: σ s is a known parameter. When σ d >σ0, it can be seen that no sliding will occur during the matrix cracking process. d When <σ0, the matrix cracking process is accompanied by sliding. s The size of is given by: 3) Substitute formula (23) into formula (21) to obtain the expressions of β1, β2 and β3 with respect to σ as the unknown variable. Finally, substitute β1, β2 and β3 into formula (28) to solve the cubic equation with respect to σ and obtain the prediction results of the second cracking model.

9. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 3, characterized in that: The third post-yield debonding controlled matrix crack stress prediction model γ1σ is established 2 +γ2σ+γ3=0, that is: when σ d >σ y >σ s When the matrix cracking stress prediction model is defined as post-yield debonding control type, the process is as follows: 1) According to the shear lag analysis, it is found that in the downstream debonding area (0<z≤l d )’s stress distribution: Among them l d is the debonding length, is an unknown number related to σ; τ s is the sliding stress and is a known interface parameter. 2) According to the shear lag analysis, the downstream yield region (l d <z≤l d +l p )’s stress distribution: Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress, τ y is the yield stress, and are all known interface parameters. 3) Under the condition of ensuring stress continuity, the unyielded and undebonded area (z>l) in the downstream is obtained. s +l p )’s stress distribution: Among them l d is the debonding length, l p is the yield length, which are all unknown variables related to σ; c f and c m are the volume fractions of fiber and matrix, respectively, and are known material parameters; E is the Young's modulus of CMC, and is a known material parameter, E f and E m are the Young's modulus of the fiber and matrix, respectively, which are known material parameters; R f is the fiber radius, which is a known material parameter; ρ is the material parameter, which is a known parameter; τ s is the sliding stress, τ y is the yield stress, and are all known interface parameters. 4) Obtaining the energy balance equation: According to the energy relationship between the upstream uncracked area and the downstream cracked area when the matrix cracks, the energy balance equation is obtained as follows: 5) The third post-yield debonding controlled matrix cracking stress prediction model is obtained: the upstream stress and Formula (3), downstream stress and Substituting formula (24), formula (25) and formula (26) into formula (27) yields the post-yield debonding controlled matrix crack stress prediction model: c1s 2 +γ2σ+γ3=0 (27).

10. The method for predicting matrix cracking stress of a fiber-reinforced ceramic matrix composite material according to claim 9, characterized in that: The third post-yield debonding controlled matrix cracking stress prediction model γ1σ 2 In the equation +γ2σ+γ3=0, γ1, γ2 and γ3 are as follows: 1) Expressions of γ1, γ2 and γ3: Among them, c f and c m are the volume fractions of fiber and matrix, respectively, both of which are known material parameters. f and E m are the Young's modulus of the fiber and matrix respectively, and E is the Young's modulus of CMC. All three are known material parameters. m is the matrix cracking toughness, which is a known material parameter. τ s is the interfacial sliding stress, τ y is the yield stress, and both are known parameters obtained through interface testing. d is the debonding length, l p is the yield length, and are unknown parameters related to σ. 2) Yield length l p and debonding length l d The solution: σ y It can be determined by the following formula: in is the interface yield toughness, a known parameter obtained through interface testing, so σ y is a known parameter. When σ y >σ0, it can be seen that no yield phenomenon will occur during the matrix cracking process. y <σ0<σ d When the matrix cracking process is accompanied by yielding, p The size of is given by: When σ is satisfied d When <σ0, the matrix cracking process is accompanied by debonding sliding. d The size of is given by: 3) Substitute formula (31) and formula (32) into formula (29) to obtain the expressions of γ1, γ2 and γ3 with respect to σ as the unknown variable. Finally, substitute γ1, γ2 and γ3 into formula (28) to solve the cubic equation with respect to σ to obtain the prediction results of the third cracking model.

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