CN110096732A - A kind of ceramic matric composite remaining Stiffness Prediction method under stress oxidation environment - Google Patents
A kind of ceramic matric composite remaining Stiffness Prediction method under stress oxidation environment Download PDFInfo
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Abstract
A kind of remaining Stiffness Prediction method that the invention discloses ceramic matric composites under stress oxidation environment, comprising the following steps: determine unidirectional SiC/SiC matrices of composite material crackle number；Determine crack width changing rule；Determine oxide thickness on carbon interface consumption length and silicon carbide fibre；Fiber stretch modulus after identified sign oxidation；The stress distribution of fiber in identified sign oxidation process；Determine fiber characteristics intensity distribution；Determine fibrous fracture score；It determines and reloads rear fibre stress distribution；Determine unidirectional SiC/SiC composite material Residual Stiffness；The present invention can accurately provide unidirectional SiC/SiC composite material in stress oxidation Residual Stiffness after a certain period of time, it can predict that the safe handling for unidirectional SiC/SiC composite material provides theories integration to the Residual Stiffness performance under unidirectional SiC/SiC composite material stress oxidation environment.
Description
Technical field
The invention belongs to material stiffness electric powder prediction, in particular to a kind of ceramic matric composite is in stress oxidation ring
Remaining Stiffness Prediction method under border.
Background technique
Silicon carbide fibre ceramics of silicon carbide toughened based composites (Continuous silicon carbide fiber
Reinforced silicon carbide composites, hereinafter referred to as SiC/SiC) there is high temperature resistant, low-density, high ratio
By force, the excellent properties such as Gao Bimo have become the important candidate material of aero-engine hot-end component at present.
Since pyrolytic carbon and the compatibility of silicon carbide fibre, matrix are preferable, mutually it is widely used in SiC/SiC as interface
Material.SiC/C/SiC material is mainly used in high temperature (> 900 DEG C) stress oxidation environment at present.In the present context, due to stress
There are matrixes will appear cracking, the oxidizing gas in environment can enter material internal and the interface C, SiC by matrix cracking
Oxidation reaction occurs for the component materials such as fiber, matrix, so that the rigidity of material is degenerated.
Residual Stiffness of the unidirectional SiC/SiC material under stress oxidation environment is quickly and effectively calculated, can be material
Intensity, life appraisal during military service provide important theoretical foundation, and provide indispensable technology for reliability of material design
Support.Currently, the technology of Residual Stiffness of the SiC/SiC material unidirectional for determination under stress oxidation environment mainly has following two
Kind:
" Yang Chengpeng rectifys osmanthus fine jade, Wang Bo, the oxidative damage and rigidity model [J] of Du Long .2D-C/SiC composite material to document
Composite material journal, 2009,26 (03): scanning electron microscope analysis knot of the 175-181. " based on the unstressed oxidation experiment of 2D-C/SiC
Fruit establishes the meso mechanical model of analysis of material stiffness injury, obtains material vertical and horizontal elasticity according to fiber mean strain
Modulus considers that fiber oxidation causes material effective bearing area to reduce, can predict 900 DEG C or less using the method for bulk modulus
2D-C/SiC material initial tensile modulus.But this method does not consider that stress is to matrix cracking width and crack density in oxidation process
Influence, and study C/SiC material fiber and interface oxidation mechanism and 900 DEG C or more SiC/SiC material fibers, interface and
Matrix aoxidizes that degradation mechanism is different, therefore unidirectional SiC/SiC material remains under the unpredictable high temperature stress oxidation environment of this method
Remaining rigidity.
Patent CN105631148A " unidirectional ceramic matric composite mechanic performance analyzing method under stress oxidation environment " base
In the oxidation mechanism of unidirectional ceramic matric composite, composite material volume fraction changing rule is considered, it is multiple to obtain unidirectional ceramic base
Condensation material matrix cracking number and crack width can be used to predict that 400-900 DEG C of unidirectional ceramic base is compound with the situation of change of stress
Situation of change of the material Residual Stiffness under stress oxidation environment, but material involved in this method is also C/SiC, and is considered
Temperature range it is lower, therefore the oxidation mechanism under stress oxidation environment is different from unidirectional SiC/SiC material, leads to mechanical property
Deterioration law is also different, thus under unpredictable high temperature stress oxidation environment unidirectional SiC/SiC material Residual Stiffness.
Therefore, it is necessary to provide it is a kind of it is simple and effective, can be under the unidirectional SiC/SiC material stress oxidation environment of Accurate Prediction
The method of Residual Stiffness.
Summary of the invention
The present invention in view of the above shortcomings of the prior art, provides a kind of ceramic matric composite and is left in stress oxidation environment
Remaining Stiffness Prediction method, with solve it is existing in the prior art can not Accurate Prediction go out unidirectional SiC/SiC material in stress oxygen
The problem of changing the Residual Stiffness variation under environment.
To achieve the above object, the technical solution adopted by the present invention are as follows:
A kind of ceramic matric composite remaining Stiffness Prediction method under stress oxidation environment, comprising the following steps:
Step (1), the matrix cracking number for determining unidirectional SiC/SiC material: consider thermal residual strain, made according to tensile stress
The stress undertaken with lower substrate determines that crackle number is with the variation of stress in matrix；
Step (2) determines crack width changing rule: considering that the matrix of residual stress and unidirectional SiC/SiC material is held
The stress of load determines crack width with the variation tendency of stress according to matrix original crack width；
Step (3) determines oxide thickness on carbon interface consumption length and silicon carbide fibre: establishing unidirectional SiC/SiC material
Expect stress oxidation model, is based on mass transfer theory, establishes the oxygen in two stages in unidirectional SiC/SiC material stress-oxidation process
Change kinetics equation and acquire oxygen concentration field in conjunction with boundary condition, and then obtains considering the carbon interface consumption length of stress
With silicon carbide fibre in cracks oxide thickness；
Fiber stretch modulus after step (4), identified sign oxidation: the MATRIX CRACKING feature of unidirectional SiC/SiC material is established
Volume elements, in conjunction with step (3) as a result, obtaining fiber oxidation defect distribution rule, the relatively entire oxygen of residual fiber after determining oxidation
The volume content of chemical fibre dimension, thus fiber stretch modulus after being aoxidized；
The stress distribution of fiber in step (5), identified sign oxidation process: considering that interface caused by fiber oxidation consumes,
Obtain the stress distribution on fiber；
Step (6) determines fiber characteristics intensity distribution: considering defect caused by fiber oxidation, is obtained based on step (3)
Cracks oxide thickness obtains the regularity of distribution of fiber characteristics intensity after fiber oxidation diameter reduces；
Step (7) determines fibrous fracture score: stress distribution and step (6) institute in the fiber in conjunction with obtained by step (5)
Fiber characteristics intensity distribution is obtained, fibrous fracture score after stress oxidation is calculated；
Step (8), determining fibre stress distribution after reloading stress: the fibrous fracture score in conjunction with obtained by (7) considers to unload
Residual stress in fiber is carried after external carbuncle, obtains reloading the fibre stress regularity of distribution after stress based on interface friction model；
Step (9) determines unidirectional SiC/SiC material Residual Stiffness: the fiber stretch modulus in conjunction with obtained by step (4) and step
(8) fibre stress is distributed after gained reloads stress, the mean strain of fiber under external force after being aoxidized, and is calculated single
Residual Stiffness to after the oxidation of SiC/SiC material stress.
Further, the step (1) the following steps are included:
Assuming that Poisson is obeyed in the matrix failure of unidirectional SiC/SiC material under tensile stress effect of unidirectional SiC/SiC material
Distribution, then matrix generates at least one crackle and the probability that fails are as follows:
P (ξ=σ, η=Ls)=1-exp {-M (A) }, N (A) >=1
Wherein:
In formula, P (ξ, η) indicates that characteristic length is Ls, stress be σ when matrix failure probability, M (A) be dimensionless Poisson
Parameter, N (A) are to crack item number, σ under stressmcFor the initial cracking stress of matrix, σRIt is characterized stress, σthIt is residual
Waste heat stress, m are Weibull modulus；
It can be simulated under stress in unidirectional SiC/SiC material matrix by computer programming using Monte Carlo method
Crackle number.
For the influence for eliminating matrix total length, crack density ρ is selectedcFunction as axial stress splits matrix surface
Line is characterized:
In formula, ρcFor matrix cracking density, n is crackle number.
Further, in the step (2), matrix cracking width can be indicated are as follows:
In formula, e indicates crack width when temperature is T, stress is σ, e0Indicate initial crack width, T0For preparation temperature,
△ T is the difference of preparation temperature and Current Temperatures, αf、αmRespectively indicate fiber and matrix thermal expansion coefficient, EfIndicate the initial bullet of fiber
Property modulus, VmIndicate matrix initial volume score.
Further, in the step (3), two oxidation kinetics equations are established are as follows:
Micro-crack diffusion phase:
Interface diffusion phase:
In formula, y indicates the coordinate value of matrix cracking depth direction, rtIndicate distance of the matrix surface to the fiber center of circle, hm
(y, t) is SiO at a time t, a certain matrix cracking depth y2For layer relative to wall surface thickness outstanding, d is crack width
Half, D1、D2Respectively indicate the effective diffusion cofficient that oxygen is spread in micro-crack and interface is spread, C0Indicate extraneous gas
Bulk concentration, CO2Indicate oxygen concentration in diffusion admittance, α indicates the ratio between CO and oxygen mole flux in diffusion admittance, gm、gfRespectively
1mol SiO is generated for matrix and fiber2The amount of the substance of required oxygen, ρsFor SiO2Density, Bf、BmRespectively fiber and base
The parabola constant that body is reacted with oxygen, pf、pmRespectively fiber and matrix are the same as oxygen index of Response, C*For 1 standard atmospheric pressure
The oxygen concentration of lower pure oxygen, MsFor SiO2Molal weight, z indicate fiber axial direction coordinate value, yf(t)、ym(t) respectively
The SiO generated on fiber and matrix when for a certain moment t2Thickness, rm、rfFibrillar center is respectively indicated to matrix surface oxide layer
The distance of outer surface is at a distance from fibrillar center to fiber surface oxide layer outer surface；
Wherein: C0、C*It can be acquired by The Ideal-Gas Equation:
In formula, P is a standard atmospheric pressure, i.e. 0.1MPa, R are ideal gas constant (R=8.314J/ (molK)),
T is temperature.
Boundary condition in the step (3) is divided into 3 parts:
First part: crack tip (y=0) has:
Second part: (z=l at interface oxidationr), have:
Part III: crackle bottom (y=L, z=0) has:
In formula, k indicates reaction between carbon and oxygen rate constant, pcFor reaction between carbon and oxygen order, π indicates pi, lrIndicate that carbon interface disappears
Length is consumed, L is crack depth, hm(t) SiO at a certain moment t lower substrate crackle bottom end (y=L) is indicated2Layer is prominent relative to wall surface
Thickness out；
Above-mentioned second order differential equation is asked based on classical four step Runge-Kutta according to upper boundary conditions
Solution, obtains any time oxygen concentration field, and then acquires unidirectional SiC/SiC material carbon interface consumption length lr, fiber is in crackle
The SiO that place's oxidation generates2Thickness yfint(t)。
Further, the step (4) the following steps are included:
Fiber oxidation post-tensioning elasticity modulus is calculated using composite rate:
Ef' (z)=EfV′f(z)+Eo(1-V′f(z))
In formula, Ef' (z) is fiber stretch modulus after aoxidizing at z, EfAnd E0Respectively intact SiC fiber and SiO2Oxide layer
Elasticity modulus, V 'f(z) it is volume content of the residue SiC fiber relative to oxidized fibre at z, is acquired by following formula:
In formula: rf0It indicates that initial fiber radius, δ (z, t) are t moment, fiber oxidation flaw size at a certain coordinate z, is
Convenient for calculating, it is assumed that defect caused by fiber oxidation consumes section linear decrease along interface, then it is indicated with following formula:
In formula: vfFor fiber oxidation volume expansion ratio, lr(t) for t moment carbon interface consume length, other parameters with for the first time
Meaning is identical when appearance.
Further, fibre stress is divided into four-stage in the step (5):
Stage one: unidirectional SiC/SiC material is not oxidized, and fibre stress distribution meets:
In formula,For the stress that fiber during stress oxidation carries, σcIndicate the stress applied when oxidation, VfTable
Show that fiber initial volume score, τ are shear stress on interface, ldIndicate crackle side unsticking section length, lcIndicate feature unit length,
EcIndicate Modulus of Composites, σf0Indicate interfacial adhesion area fibre stress, other parameters are identical as meaning when first appearing；
Stage two: unidirectional SiC/SiC is materials from oxidizing, but interfacial detachment area is not overlapped, and fibre stress distribution is full
Foot:
In formula: H (t) indicates t moment cracks fiber maximum stress, σ 'f0Indicate this stage interfacial adhesion area fibre stress,
U(z)、U(z-lrIt (t)) is unit-step function, other parameters are identical as meaning when first appearing.Unit-step function U
(z-z0) is defined as:
Stage three: unidirectional SiC/SiC is materials from oxidizing, and interfacial detachment area is overlapped, and fibre stress distribution meets:
Parameter is identical as meaning when first appearing in formula；
Stage four: unidirectional SiC/SiC material carbon interface is totally consumed, and fibre stress distribution meets:
Parameter is identical as meaning when first appearing in formula.
Further, fiber characteristics intensity after being aoxidized in the step (6) are as follows:
In formula: σf(z, t) is at a time t, the fiber characteristics intensity at a certain coordinate position z,For intact fibre
The intensity of dimension, δd(t) a certain moment t is indicated, in matrix cracking bottom end (y=L, z ∈ (0, d)) fiber oxidation flaw size, σd
(t) t moment cracks fibre strength is indicated, ζ indicates the position that oxidation defect size is equal at fibrous fracture critical defect size
Length away from Crack Center, a indicate fibrous fracture critical defect size；It is expressed from the next:
Wherein, KICFor the fracture toughness of fiber, Y is material parameter relevant with shape.
Further, the step (7) the following steps are included:
Assuming that the intensity distribution of initial fiber meets Two-parameter Weibull Distribution, then fibrous fracture probability Φ are as follows:
In formula, LgTo integrate segment length, m is Weibull modulus, l0For reference length.By fiber axial direction stress distribution and fibre
Dimensional feature intensity distribution substitutes into fibrous fracture probability expression, obtains the fibrous fracture probability Φ in entire feature volume elementsL:
In formula, l is the length of model, I1~I5Respectively interface is respectively as follows: along the integral of each segmentation
In formula, H is fiber bridging traction, and ζ (t) is that fiber oxidation flaw size δ (t) is equal to fiber critical defect size a
Length of the position at place away from matrix cracking center, other parameters are identical as meaning when first appearing.
Further, the step (8) the following steps are included:
After the consumption of unidirectional SiC/SiC material stress oxygenation level, after external force unloading, there are still remnants to slide in fiber
Stress；The stress when the stress applied again is less than stress oxidation, the fibre stress in unsticking area is acquired using interface friction model
Distribution:
In formula: σ 'f(z) it indicates to reload the stress distribution after stress in fiber, boundary after stress is reloaded in H ' expression
Face consumes section stress, and z ' expression reloads after stress that stress increases segment length, σ " in fiberf0Boundary after stress is reloaded in expression
The stress that face bond regions fiber is born, σtIndicate the stress reloaded, EmIndicate matrix elastic modulus, other parameters with for the first time
Meaning is identical when appearance.
Further, the step (9) the following steps are included:
After unloading, in new outer load σtUnder effect, in conjunction with reload obtained by step (8) rear fiber residue stress distribution and
Rigidity after the oxidation of fibre stress obtained by step (4), the mean strain ε that fiber generatesfIt indicates are as follows:
In formula, lsCharacterize the parameter of critical glide length；
Not considering creep effect, the mean strain of unidirectional SiC/SiC material is consistent with the mean strain of unbroken fiber,
Obtain the Residual Stiffness E of unidirectional SiC/SiC materialcAre as follows:
In formula, lsFor critical glide length, indicate are as follows:
ls=rf0H/2τ
Remaining parameter meaning is identical as when first appearing.
Compared with prior art, the invention has the following advantages:
The present invention considers in unidirectional SiC/SiC material that stress is close to matrix cracking width and crackle in oxidation process
The influence of degree, at the same consider oxygen to the oxidation of composite inner crackle wall, oxygen enter behind crackle bottom to fiber,
The oxidation at interface and matrix, can accurately provide material in stress oxidation Residual Stiffness after a certain period of time, can be to unidirectional SiC/
Residual Stiffness performance under SiC material stress oxidation environment is predicted that the safe handling for unidirectional SiC/SiC material provides reason
By support.
Detailed description of the invention
Fig. 1 is matrix cracking density with plus load change curve；
Fig. 2 is matrix cracking width with temperature and stress changing curve；
Fig. 3 is unidirectional SiC/SiC material model；
Fig. 4 is unidirectional SiC/SiC material model side view；
Fig. 5 is geometrical morphology at unidirectional SiC/SiC material crack；
Fig. 6 is geometrical morphology at unidirectional SiC/SiC material interface diffusion admittance；
Fig. 7 is that interface consumes length change curve under 80MPa loading environment；
Fig. 8 is that interface consumes length change curve under 200MPa loading environment；
Fig. 9 is fiber oxidation layer thickness variation curve under 80MPa loading environment；
Figure 10 is fiber oxidation layer thickness variation curve under 200MPa loading environment；
Figure 11 is the unidirectional uniform cracking model of SiC/SiC material matrix；
Figure 12 is unidirectional SiC/SiC material matrix cracking feature volume elements；
Figure 13 is fibre stress distribution before aoxidizing；
Figure 14 is fibre stress distribution after oxidation (unsticking area is underlapped)；
Figure 15 is fibre stress distribution (unsticking area overlapping) after oxidation；
Figure 16 is to reload oxidized fibre stress distribution when stress distribution and unsticking area are underlapped in rear fiber to compare；
Figure 17 is remaining stiffness variation curve under 80MPa loading environment；
Figure 18 is remaining stiffness variation curve under 200MPa loading environment；
Figure 19 is unidirectional SiC/SiC material Residual Stiffness change curve in 900 DEG C of environment；
Figure 20 is the Residual Stiffness analogue value and test value comparison diagram after 120MPa, 1200 DEG C of stress oxidations.
Specific embodiment
Below with reference to embodiment, the present invention will be further explained.
Embodiment
In the present embodiment, by unidirectional SiC/SiC material at 900-1200 DEG C, residual intensity under stress oxidation environment is carried out
Prediction technique, specifically includes the following steps:
Step (1) determines unidirectional SiC/SiC material matrix crackle number: considering thermal residual strain, is acted on according to tensile stress
The stress that lower substrate undertakes determines that crackle number is with the variation of stress in matrix；
Step (1) specifically includes the following steps:
The intensity of unidirectional SiC/SiC material matrix everywhere has certain dispersibility, and cracking of the matrix under stress is
One random process.According to Monte Carlo Method, it is assumed that matrix failure probability obey Poisson distribution, stress lower substrate generate to
The probability for lacking a Crack and failing are as follows:
P (ξ=σ, η=Ls)=1-exp {-M (A) }, N (A) >=1 (1)
In formula, it is L that P (ξ, η), which is characterized length,s, stress be σ when matrix failure probability, M (A) be dimensionless Poisson join
Number, N (A) are to crack item number, σ under stressmcFor the initial cracking stress of matrix, σRIt is characterized stress, σthFor remnants
Thermal stress, m are Weibull modulus.
It can be simulated under stress in unidirectional SiC/SiC material matrix by computer programming using Monte Carlo method
Crackle number.
For the influence for eliminating matrix total length, crack density ρ is selectedcFunction as axial stress splits matrix surface
Line is characterized:
In formula, ρcFor matrix cracking density, n is crackle number.
Fig. 1 is to simulate to obtain crack density with tensile stress change curve according to the method that step (1) provides.It can see
Out, with the increase of stress, crack density constantly increases, and crackle is pushed the speed and increased as stress increases.
Step (2) determines crack width changing rule: considering that the matrix of residual stress and unidirectional SiC/SiC material is held
The stress of load determines crack width with the variation tendency of stress according to matrix original crack width；
In step (2), crack width expression formula under stress are as follows:
In formula, e indicates crack width when temperature is T, stress is σ, e0Indicate initial crack width, T0For preparation temperature,
△ T is the difference of preparation temperature and Current Temperatures, and composite material preparation temperature takes 1200 DEG C；αf、αmRespectively indicate fiber and matrix heat
The coefficient of expansion, EfIndicate fiber initial elastic modulus, VmIndicate matrix initial volume score.Table 1 gives for determining matrix
The parameter value of crack width variation.
Table 1 determines the parameter of matrix cracking change width
Fig. 2 is to calculate crack width with applied stress, oxidizing temperature situation of change according to above-mentioned crack width expression formula.
It can be seen from the figure that the width of crackle increases with the increase of applied stress and applied stress size is positively correlated；Identical
Under the conditions of outer load, temperature is lower, and crack width is bigger.
Step (3) establishes oxidation kinetics equation, determines oxide thickness on carbon interface consumption length and silicon carbide fibre
Degree: establishing unidirectional SiC/SiC material stress model of oxidation, is based on mass transfer theory, establishes unidirectional SiC/SiC material stress-oxygen
The oxidation kinetics equation in two stages acquires oxygen concentration field in conjunction with boundary condition during change, and then obtains considering stress
The carbon interface consumption length and silicon carbide fibre of effect are in cracks oxide thickness；
Composite material stress oxidation model is initially set up, as shown in figure 3, the model side view is as shown in Figure 4.Stress oxidation
R involved in modelf0、rm0-rf0、rt-rm0In generation, refers to initial fiber radius, interfacial thickness, matrix ligament thickness in model respectively.Wherein
rm0Indicate initial substrate inside radius, rtDistance of the expression matrix surface to the fiber center of circle.Taking for this Model Parameter is provided by table 2
Value.
2 composite material stress oxidation kinetic parameters of table
| Parameter | Value |
| Initial fiber radius rf0/μm | 7 |
| Initial substrate inside radius rm0/μm | 7.1 |
| Interfacial thickness rm0-rf0/μm | 0.1 |
| Matrix ligament thickness rt-rm0/μm | 2.9 |
| Distance r of the matrix surface to the fiber center of circlet/μm | 10 |
Two stages of stress oxidation are respectively that diffusion phase and oxygen are in interface diffusion phase in micro-crack for oxygen, respectively
As shown in Figure 5,6.During oxygen is spread to material internal, first have to take by the micro-crack in SiC matrix along crackle
Depth direction is the direction y, and when oxygen reaches at micro-crack bottom interface, meeting is rapidly and the interface C reacts to form annular shape
Gas diffusion paths, and continue to aoxidize the interface C by the diffusion admittance of interface, taking fiber axially is the direction z.
The oxidation kinetics equation established accordingly is as follows:
Micro-crack diffusion phase:
Interface diffusion phase:
In formula, d is the half of crack width e, hm(y, t) is SiO at a time t, a certain matrix cracking depth y2Layer
Relative to wall surface thickness outstanding, D1、D2Respectively indicate effective diffusion system that oxygen is spread in micro-crack and interface is spread
Number, C0Indicate ambient atmos concentration,Indicate oxygen concentration in diffusion admittance, α indicates rubbing for CO and oxygen in diffusion admittance
The ratio between your flux, value isgm、gfRespectively matrix and fiber generate 1mol SiO2The amount of the substance of required oxygen, takes
Value isρsFor SiO2Density, value 2.2g/cm3, Bf、BmIt is normal to be divided into the parabola that fiber and matrix are reacted with oxygen
Number, pf、pmRespectively with oxygen index of Response, value is as shown in table 3 for fiber and matrix, C*Pure oxygen is depressed for 1 normal atmosphere
Oxygen concentration, MsFor SiO2Molal weight, value 60g/mol, yf(t)、ym(t) fiber when being respectively a certain moment t
With the SiO generated on matrix2Thickness, rm、rfFibrillar center is respectively indicated in oxidation process to matrix surface oxide layer outer surface
Distance is at a distance from fibrillar center to fiber surface oxide layer outer surface；
Wherein C0、C*It can be acquired by The Ideal-Gas Equation:
In formula, P is a standard atmospheric pressure, i.e. 0.1MPa, R are ideal gas constant (R=8.314J/ (molK)),
T is temperature.
3 fiber of table, matrix parabola constant and index
The boundary condition of the above-mentioned differential equation is divided into 3 parts:
First part: crack tip (y=0) has:
Second part: (z=l at interface oxidationr), have:
Part III: crackle bottom (y=L, z=0) has:
In formula, pcFor reaction between carbon and oxygen index, value 0.3, L is crack depth, and value is 2.9 μm, and k indicates reaction between carbon and oxygen
Rate constant, π indicate pi, lrIndicate that carbon interface consumes length, hm(t) a certain moment t lower substrate crackle bottom end (y=is indicated
L SiO at)2For layer relative to wall surface thickness outstanding, other parameters are identical with meaning is first appeared.K is indicated are as follows:
K=0.486exp (- 104433/RT) (12)
Wherein meaning of parameters and value are identical as when first appearing.
Above-mentioned second order differential equation is asked based on classical four step Runge-Kutta according to upper boundary conditions
Solution can be obtained concentration variation of the oxygen in diffusion admittance, and then carbon interface oxidation length l under any moment be calculatedr, it is fine
Tie up the SiO generated in cracks oxidation2Thickness yfint(t)。
Fig. 7-10 is to be disappeared according to carbon interface under the conditions of above-mentioned equation 80MPa, 200MPa stress oxidation obtained from of solution
Consumption length changes with time relational graph and fiber oxidation layer thickness chart.
Fiber stretch modulus after step (4), identified sign oxidation: the MATRIX CRACKING feature of unidirectional SiC/SiC material is established
Volume elements, in conjunction with step (3) as a result, obtaining fiber oxidation defect distribution rule, the relatively entire oxygen of residual fiber after determining oxidation
The volume content of chemical fibre dimension, thus fiber stretch modulus after being aoxidized；
As shown in figure 11, it is assumed that crackle is evenly distributed in matrix, wherein lcFor crack spacing, l is model total length.Accordingly
Feature unit such as Figure 12, the d being directed to comprising single fiber and surrounding matrix between the neighboring cracks of foundation are crack width
Half, lrLength is consumed for interface, crackle side unsticking section length is ld, feature unit entire length is crack spacing lc, σc
For the stress applied when oxidation.
For step (4) the following steps are included: after fibre stress oxidation, the formation of oxide on surface can change the stretching bullet of fiber
Property modulus, table can be carried out with stretch modulus of the composite rate formula to the oxidized fibre that residual fiber after oxidation and oxide layer form
Show:
Ef' (z)=EfV′f(z)+Eo(1-V′f(z)) (13)
Wherein, Ef' (z) is fiber stretch modulus after oxidation, EfAnd E0Respectively intact SiC fiber and SiO2Oxide layer
Elasticity modulus, E in the present embodiment0Take 70GPa, V 'fIt (z) is volume content of the residue SiC fiber relative to oxidized fibre at z, it can
It is acquired by following formula:
In formula: rf0It indicates that initial fiber radius, δ (z, t) are t moment, fiber oxidation flaw size at a certain coordinate z, is
Convenient for calculating, it is assumed that defect caused by fiber oxidation consumes section linear decrease along interface, then it is indicated with following formula:
In formula: vfFor fiber oxidation volume expansion ratio, value 1.39, lr(t) length is consumed for t moment carbon interface, other
Parameter is identical as meaning when first appearing.
The stress distribution of unsticking area fiber in step (5), identified sign oxidation process: consider interface caused by fiber oxidation
Consumption, obtains the stress distribution on fiber；
The unidirectional state of oxidation of the SiC/SiC material internal fiber in oxidation process median surface can be divided into four-stage, fiber
Middle stress distribution is also classified into four-stage；
Stage one: unidirectional SiC/SiC material is not oxidized, and fibre stress distribution meets:
In formula,For the stress that fiber during stress oxidation carries, σcIndicate the stress applied when oxidation, VfTable
Show that fiber initial volume score, τ are shear stress on interface, value 4MPa, EcIndicate Modulus of Composites, σf0Indicate boundary
Face bond regions fibre stress, other parameters are identical as meaning when first appearing.
Stage two: unidirectional SiC/SiC is materials from oxidizing, but interfacial detachment area is not overlapped, and fibre stress distribution is full
Foot:
In formula: H (t) indicates t moment cracks fiber maximum stress, σ 'f0Indicate this stage interfacial adhesion area fibre stress,
U(z)、U(z-lrIt (t)) is unit-step function, other parameters are identical as meaning when first appearing.Function U (z-z0) it is unit
Jump function, is defined as:
Stage three: unidirectional SiC/SiC is materials from oxidizing, and interfacial detachment area is overlapped, and fibre stress distribution meets:
Parameter is identical as meaning when first appearing in formula.
Stage four: unidirectional SiC/SiC material carbon interface is totally consumed, and fibre stress distribution meets:
Parameter is identical as meaning when first appearing in formula.
Figure 13-15 is respectively stress distribution situation in one, two, three fiber of stage.As can be seen from Figure, fine in crackle section
It is constant and maximum to tie up the stress born.With interfacial detachment, due to the presence of shear stress on interface, the stress in fiber linearly subtracts
Small, when interfacial detachment area is not overlapped, stress is remained unchanged in interfacial adhesion area fiber.
Step (6) determines fiber characteristics intensity distribution after oxidation: considering defect caused by fiber oxidation, is based on step (3)
Obtained cracks oxide thickness obtains the regularity of distribution of fiber characteristics intensity after fiber oxidation diameter reduces；
In formula: σf(z, t) is at a time t, the fiber characteristics intensity at a certain coordinate position z, δd(t) certain is indicated
One moment t, in matrix cracking bottom end (y=L, z ∈ (0, d)) fiber oxidation flaw size, σd(t) cracks fiber is indicated
Intensity, ζ indicate length of the position away from Crack Center that oxidation defect size is equal at fibrous fracture critical defect size,It is complete
The intensity of good fiber, a indicate fibrous fracture critical defect size, are expressed from the next:
Wherein, KICFor the fracture toughness of fiber, Y is material parameter relevant with shape,Value is 0.5MPam-0.5。
Step (7) determines fibrous fracture score: stress distribution and step (6) institute in the fiber in conjunction with obtained by step (5)
Fiber characteristics intensity distribution is obtained, fibrous fracture score after stress oxidation is calculated；
During stress oxidation, fiber will appear fracture failure behavior, and fracture fiber cannot carry.Assuming that initial fiber
Intensity distribution meet Two-parameter Weibull Distribution, then fibrous fracture probability Φ are as follows:
In formula, LgTo integrate segment length, m is Weibull modulus, value 4, l0For reference length, value 25mm will
Fiber axial direction stress distribution and fiber characteristics intensity distribution substitute into fibrous fracture probability expression, obtain in entire feature volume elements
Interior fibrous fracture probability ΦL:
In formula, l is the length of model, I1~I5Respectively interface is respectively as follows: along the integral of each segmentation
In formula, H is fiber bridging traction, and ζ (t) is that fiber oxidation flaw size δ (t) is equal to fiber critical defect size a
Length of the position at place away from matrix cracking center, other parameters are identical as meaning when first appearing.
Step (8) determines and reloads rear fibre stress distribution: the fibrous fracture score in conjunction with obtained by (7) considers that unloading is outer
Residual stress in fiber after stress obtains reloading the fibre stress regularity of distribution after stress based on interface friction model；
After the consumption of composite material stress oxidation interface, after external force unloading, there are still certain remnants slidings in fiber
Stress.The stress when the stress applied again is less than stress oxidation, can be in the hope of the fiber in unsticking area using interface friction model
Stress distribution:
In formula: σ 'f(z) it indicates to reload the stress distribution in rear fiber, rear interface consumption section is reloaded in H ' expression
Stress, z ' expression reload stress in rear fiber and increase segment length, σ "f0Rear interfacial adhesion area fiber receiving is reloaded in expression
Stress, EmIndicate matrix elastic modulus, value 400GPa, σtIndicate the stress that reloads, other parameters and when first appearing
Meaning is identical.
Figure 16 shows residual stress distribution in required fiber, and is compared with stress distribution in preceding fiber is not unloaded
Compared with, it can be seen that bearing stress when reloading in interfacial detachment section fibre declines again after having slightly rising, this is because
The presence of remaining slippage stress after stress oxidation.
Step (9) determines material Residual Stiffness: obtained by the fiber stretch modulus in conjunction with obtained by step (4) and step (8) again
Fibre stress is distributed after loading stress, and the mean strain of fiber under external force after being aoxidized calculates unidirectional SiC/SiC
Residual Stiffness after material stress oxidation
σ is carried outsidetUnder effect, in conjunction with step (8) Chinese style (26) and step (4) Chinese style (13), what fiber generated is averagely answered
Become εfIt can indicate are as follows:
In formula, lsCharacterize the parameter of critical glide length；
Do not consider creep effect, the mean strain of composite material is consistent with the mean strain of unbroken fiber, can obtain list
To the Residual Stiffness of SiC/SiC composite material are as follows:
In formula, lsFor critical glide length, may be expressed as:
ls=rf0H/2τ (31)
Remaining parameter is identical as meaning when first appearing.
Figure 17-19 is calculated according to the formula (13) of the formula (30) of step (9), the formula (26) of step (8) and step (4)
The unidirectional SiC/SiC material Residual Stiffness versus time curve arrived.Figure 17 is unidirectional SiC/ under 80MPa difference oxidizing temperature
SiC material Residual Stiffness changes with time, and Figure 18 is that unidirectional SiC/SiC material is remaining just under 200MPa difference oxidizing temperature
Degree changes with time, and Figure 19 is that unidirectional SiC/SiC material Residual Stiffness changes with time under 900 DEG C of different stress.It can be with
Find out, the Residual Stiffness of unidirectional SiC/SiC material is reduced with the increase of oxidization time；As the temperature increases, unidirectional SiC/SiC
The Residual Stiffness deterioration velocity of material is faster.In addition, in identical temperature and oxidization time, with the increase of applied stress,
The Residual Stiffness degeneration of unidirectional SiC/SiC material is faster, and more early to enter the stage steadily reduced, this shows that the interface C has consumed
Completely.
Table 4 and Figure 20 are that unidirectional SiC/SiC material is simulated using the method for the present invention after 120MPa, 1200 DEG C of stress oxidations
Residual Stiffness and test value obtain comparing result.It can be seen in figure 20 that in the initial stage of oxidation, the residue of model prediction
Rigidity is higher；With the progress of oxidation, the prediction result and test value of model are gradually coincide.As shown in Table 4, the mould of Residual Stiffness
The error maximum of analog values and test value is no more than 10%, this shows this calculation method reasonability with higher, can be effective
Predict Residual Stiffness of the unidirectional SiC/SiC material under stress oxidation environment.
4 initial stage of table Residual Stiffness predicted value and test value errors table
| Time (s) | Test value | The analogue value | Error (%) |
| 2 | 0.96033 | 0.9995 | 4 |
| 6 | 0.93524 | 0.99379 | 6.26 |
| 50 | 0.8665 | 0.93979 | 8.46 |
| 70 | 0.83853 | 0.91919 | 9.62 |
| 120 | 0.81422 | 0.87489 | 7.45 |
The above is only a preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (10)
1. a kind of ceramic matric composite remaining Stiffness Prediction method under stress oxidation environment, which is characterized in that including following
Step:
Step (1), the matrix cracking number for determining unidirectional SiC/SiC material: consider thermal residual strain, acted on down according to tensile stress
The stress that matrix undertakes determines that crackle number is with the variation of stress in matrix；
Step (2) determines crack width changing rule: considering what the matrix of residual stress and unidirectional SiC/SiC material was undertaken
Stress determines crack width with the variation tendency of stress according to matrix original crack width；
Step (3) determines oxide thickness on carbon interface consumption length and silicon carbide fibre: establishing unidirectional SiC/SiC material and answers
Power model of oxidation is based on mass transfer theory, and the oxidation for establishing two stages in unidirectional SiC/SiC material stress-oxidation process is dynamic
Mechanical equation acquires oxygen concentration field in conjunction with boundary condition, and then obtains considering the carbon interface consumption length and carbon of stress
SiClx fiber is in cracks oxide thickness；
Fiber stretch modulus after step (4), identified sign oxidation: establishing the MATRIX CRACKING feature volume elements of unidirectional SiC/SiC material,
In conjunction with step (3) as a result, obtaining fiber oxidation defect distribution rule, the relatively entire oxidized fibre of residual fiber after determining oxidation
Volume content, thus fiber stretch modulus after being aoxidized；
The stress distribution of fiber in step (5), identified sign oxidation process: consider that interface caused by fiber oxidation consumes, obtain
Stress distribution on fiber；
Step (6) determines fiber characteristics intensity distribution: considering defect caused by fiber oxidation, the crackle obtained based on step (3)
Locate oxide thickness, obtains the regularity of distribution of fiber characteristics intensity after fiber oxidation diameter reduces；
Step (7) determines fibrous fracture score: fiber obtained by the stress distribution and step (6) in the fiber in conjunction with obtained by step (5)
Characteristic strength distribution, calculates fibrous fracture score after stress oxidation；
Step (8), determining fibre stress distribution after reloading stress: the fibrous fracture score in conjunction with obtained by (7) considers outside unloading
Residual stress in fiber after stress obtains reloading the fibre stress regularity of distribution after stress based on interface friction model；
Step (9) determines unidirectional SiC/SiC material Residual Stiffness: the fiber stretch modulus in conjunction with obtained by step (4) and step (8)
Fibre stress is distributed after gained reloads stress, the mean strain of fiber under external force after being aoxidized, and is calculated unidirectional
Residual Stiffness after the oxidation of SiC/SiC material stress.
2. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, the step (1) the following steps are included:
Assuming that Poisson distribution is obeyed in the matrix failure of unidirectional SiC/SiC material under tensile stress effect of unidirectional SiC/SiC material,
Then matrix generates at least one crackle and the probability that fails are as follows:
P (ξ=σ, η=Ls)=1-exp {-M (A) }, N (A) >=1
Wherein:
In formula, P (ξ, η) indicates that characteristic length is Ls, stress be σ when matrix failure probability, M (A) be dimensionless Poisson parameter, N
It (A) is to crack item number, σ under stressmcFor the initial cracking stress of matrix, σRIt is characterized stress, σthIt is answered for residual heat
Power, m are Weibull modulus；
Crackle under stress in unidirectional SiC/SiC material matrix can be simulated by computer programming using Monte Carlo method
Number,
For the influence for eliminating matrix total length, crack density ρ is selectedcAs axial stress function to the crackle of matrix surface into
Row characterization:
In formula, ρcFor matrix cracking density, n is crackle number.
3. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is: in the step (2), matrix cracking width can be indicated are as follows:
In formula, e indicates crack width when temperature is T, stress is σ, e0Indicate initial crack width, T0For preparation temperature, Δ T
For the difference of preparation temperature and Current Temperatures, αf、αmRespectively indicate fiber and matrix thermal expansion coefficient, EfIndicate fiber initial elasticity
Modulus, VmIndicate matrix initial volume score.
4. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, in the step (3), establishes two oxidation kinetics equations are as follows:
Micro-crack diffusion phase:
Interface diffusion phase:
In formula, y indicates the coordinate value of matrix cracking depth direction, rtIndicate distance of the matrix surface to the fiber center of circle, hm(y,t)
For SiO at a time t, a certain matrix cracking depth y2For layer relative to wall surface thickness outstanding, d is the one of crack width
Half, D1、D2Respectively indicate the effective diffusion cofficient that oxygen is spread in micro-crack and interface is spread, C0Indicate that ambient atmos are dense
Degree, CO2Indicate oxygen concentration in diffusion admittance, α indicates the ratio between CO and oxygen mole flux in diffusion admittance, gm、gfRespectively base
Body and fiber generate 1mol SiO2The amount of the substance of required oxygen, ρsFor SiO2Density, Bf、BmRespectively fiber and matrix with
The parabola constant of oxygen reaction, pf、pmRespectively fiber and matrix are the same as oxygen index of Response, C*It is pure for 1 normal atmosphere pressure
The oxygen concentration of oxygen, MsFor SiO2Molal weight, z indicate fiber axial direction coordinate value, yf(t)、ymIt (t) is respectively certain
The SiO generated on fiber and matrix when one moment t2Thickness, rm、rfFibrillar center is respectively indicated to matrix surface oxide layer appearance
The distance in face is at a distance from fibrillar center to fiber surface oxide layer outer surface；
Wherein: C0、C*It can be acquired by The Ideal-Gas Equation:
In formula, P is a standard atmospheric pressure, i.e. 0.1MPa, R are ideal gas constant (R=8.314J/ (molK)), and T is temperature
Degree.
Boundary condition in the step (3) is divided into 3 parts:
First part: crack tip (y=0) has:
Second part: (z=l at interface oxidationr), have:
Part III: crackle bottom (y=L, z=0) has:
In formula, k indicates reaction between carbon and oxygen rate constant, pcFor reaction between carbon and oxygen order, π indicates pi, lrIndicate carbon interface consumption length
Degree, L is crack depth, hm(t) SiO at a certain moment t lower substrate crackle bottom end (y=L) is indicated2Layer is outstanding relative to wall surface
Thickness；
Above-mentioned second order differential equation is solved based on classical four step Runge-Kutta according to upper boundary conditions,
Any time oxygen concentration field is obtained, and then acquires unidirectional SiC/SiC material carbon interface consumption length lr, fiber is in cracks oxygen
Metaplasia at SiO2Thickness yfint(t)。
5. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, the step (4) the following steps are included:
Fiber oxidation post-tensioning elasticity modulus is calculated using composite rate:
Ef' (z)=EfV'f(z)+Eo(1-V'f(z))
In formula, Ef' (z) is fiber stretch modulus after aoxidizing at z, EfAnd E0Respectively intact SiC fiber and SiO2The bullet of oxide layer
Property modulus, V'f(z) it is volume content of the residue SiC fiber relative to oxidized fibre at z, is acquired by following formula:
In formula: rf0Indicate initial fiber radius, δ (z, t) is t moment, fiber oxidation flaw size at a certain coordinate z, for convenient for
It calculates, it is assumed that defect caused by fiber oxidation consumes section linear decrease along interface, then it is indicated with following formula:
In formula: νfFor fiber oxidation volume expansion ratio, lr(t) length is consumed for t moment carbon interface.
6. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is that fibre stress is divided into four-stage in the step (5):
Stage one: unidirectional SiC/SiC material is not oxidized, and fibre stress distribution meets:
In formula,For the stress that fiber during stress oxidation carries, σcIndicate the stress applied when oxidation, VfIndicate fiber
Initial volume score, τ are shear stress on interface, ldIndicate crackle side unsticking section length, lcIndicate feature unit length, EcIt indicates
Modulus of Composites, σf0Indicate interfacial adhesion area fibre stress, other parameters are identical as meaning when first appearing；
Stage two: unidirectional SiC/SiC is materials from oxidizing, but interfacial detachment area is not overlapped, and fibre stress distribution meets:
In formula: H (t) indicates t moment cracks fiber maximum stress, σ 'f0Indicate this stage interfacial adhesion area fibre stress, U
(z)、U(z-lrIt (t)) is unit-step function；Unit-step function U (z-z0) is defined as:
Stage three: unidirectional SiC/SiC is materials from oxidizing, and interfacial detachment area is overlapped, and fibre stress distribution meets:
Stage four: unidirectional SiC/SiC material carbon interface is totally consumed, and fibre stress distribution meets:
In formula: H (t) indicates t moment cracks fiber maximum stress.
7. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, fiber characteristics intensity after oxidation in the step (6) are as follows:
In formula: σf(z, t) is at a time t, the fiber characteristics intensity at a certain coordinate position z,For the strong of intact fiber
Degree, δd(t) a certain moment t is indicated, in matrix cracking bottom end (y=L, z ∈ (0, d)) fiber oxidation flaw size, σd(t) table
Show t moment cracks fibre strength, ζ indicates oxidation defect size equal to the position at fibrous fracture critical defect size away from crackle
The length at center, a indicate fibrous fracture critical defect size；It is expressed from the next:
Wherein, KICFor the fracture toughness of fiber, Y is material parameter relevant with shape.
8. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, the step (7) the following steps are included:
Assuming that the intensity distribution of initial fiber meets Two-parameter Weibull Distribution, then fibrous fracture probability Φ are as follows:
In formula, LgTo integrate segment length, m is Weibull modulus, l0For reference length；Fiber axial direction stress distribution and fiber is special
It levies intensity distribution to substitute into fibrous fracture probability expression, obtains the fibrous fracture probability Φ in entire feature volume elementsL:
In formula, l is the length of model, I1~I5Respectively interface is respectively as follows: along the integral of each segmentation
In formula, H is fiber bridging traction, and ζ (t) is that fiber oxidation flaw size δ (t) is equal at fiber critical defect size a
Length of the position away from matrix cracking center.
9. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, the step (8) the following steps are included:
After the consumption of unidirectional SiC/SiC material stress oxygenation level, there are still remnants slidings to answer after external force unloading, in fiber
Power；The stress when the stress applied again is less than stress oxidation acquires the fibre stress point in unsticking area using interface friction model
Cloth:
In formula: σ 'f(z) it indicates to reload the stress distribution after stress in fiber, interface consumes after stress is reloaded in H' expression
Duan Yingli, z' expression reload after stress that stress increases segment length, σ " in fiberf0Interfacial adhesion after stress is reloaded in expression
The stress that area's fiber is born, σtIndicate the stress reloaded, EmIndicate matrix elastic modulus.
10. ceramic matric composite according to claim 1 remaining Stiffness Prediction method under stress oxidation environment, special
Sign is, the step (9) the following steps are included:
After unloading, in new outer load σtUnder effect, rear fiber residue stress distribution and step are reloaded in conjunction with obtained by step (8)
(4) rigidity after the oxidation of gained fibre stress, the mean strain ε that fiber generatesfIt indicates are as follows:
In formula, lsCharacterize the parameter of critical glide length；
Do not consider creep effect, the mean strain of unidirectional SiC/SiC material is consistent with the mean strain of unbroken fiber, obtains
The Residual Stiffness E of unidirectional SiC/SiC materialcAre as follows:
In formula, lsFor critical glide length, indicate are as follows:
ls=rf0H/2τ。
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| JP2021092894A (en) * | 2019-12-09 | 2021-06-17 | Ｔｏｙｏ Ｔｉｒｅ株式会社 | Calculation method of weibull coefficient for cross-linkage polymer model, system, and program |
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