CN109598098A - A kind of prediction technique for weaving ceramic matric composite stable state MATRIX CRACKING stress for considering environment and influencing - Google Patents
A kind of prediction technique for weaving ceramic matric composite stable state MATRIX CRACKING stress for considering environment and influencing Download PDFInfo
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Abstract
The invention belongs to ceramic matric composite stable state MATRIX CRACKING stress prediction technical fields, and in particular to a kind of prediction technique for weaving ceramic matric composite stable state MATRIX CRACKING stress for considering environment and influencing.Stable state MATRIX CRACKING stress distribution equation provided by the invention, fiber/matrix interfacial detachment area Friction Shearing Stress using fiber/matrix interface oxidation area's Friction Shearing Stress under the conditions of fiber/matrix interface oxidation section length, temperature and under the conditions of temperature constructs to obtain, it is incorporated into temperature and oxidative factors in stable state MATRIX CRACKING stress equation, the crack stress for weaving ceramic matric composite stable state matrix for Accurate Prediction provides foundation.Embodiment the result shows that, prediction technique provided by the invention can predict braiding ceramic matric composite in different crack stress at use temperature.
Description
Technical field
The invention belongs to ceramic matric composite stable state MATRIX CRACKING stress prediction technical fields, and in particular to a kind of consideration
The prediction technique for the braiding ceramic matric composite stable state MATRIX CRACKING stress that environment influences.
Background technique
Braiding ceramic matric composite has many advantages, such as high temperature resistant, corrosion-resistant, low-density, Gao Biqiang, Gao Bimo, compared to height
Temperature alloy is able to bear higher temperature, reduces cooling air-flow, and then improves turbine efficiency and therefore have become aeroplane engine
A variety of devices such as machine combustion chamber, turborotor, turbine shroud ring, jet pipe prepare material.The LEAP developed by CFM company
The high-pressure turbine of (Leading EdgeAviation Propulsion, LEAP) Engine Series just uses braiding ceramic base
Composite material, for example, LEAP-1B engine provides power for Air Passenger A320 and Boeing-737 MAX, and LEAP-X1C engine is
The sole power device that C919 is selected.
In order to guarantee to weave ceramic matric composite reliability and safety used in aircraft and aero-engine structure
Property, domestic and foreign scholars make the exploitation for weaving ceramic matric composite Performance Evaluation, damage development, intensity and life prediction tool
For a main direction of studying.Such as Li Longbiao provides a kind of the pre- of unidirectional ceramic matric composite stable state MATRIX CRACKING stress
Survey method is (referring to Modeling first matrix cracking stress of fiber-reinforced ceramic-
matrix composites considering fiber fracture.Theoretical andAppliedFracture
Mechanics 2017；92:24-32.), but the accuracy of prediction result is unsatisfactory.
Summary of the invention
The purpose of the present invention is to provide a kind of braiding ceramic matric composite stable state MATRIX CRACKINGs that consideration environment influences
Temperature and oxidative factors are included in forecast system by the prediction technique of stress, prediction technique provided by the invention, improve prediction knot
The accuracy of fruit.
To achieve the goals above, the invention provides the following technical scheme:
The present invention provides a kind of the pre- of braiding ceramic matric composite stable state MATRIX CRACKING stress that consideration environment influences
Survey method, includes the following steps:
(1) it is based on shear-lag model, constructs stable state MATRIX CRACKING stress distribution equation；
The stable state MATRIX CRACKING stress distribution equation includes stable state MATRIX CRACKING catchment stress distribution equation and stable state
MATRIX CRACKING upstream stress distribution equation；
Stable state MATRIX CRACKING catchment stress distribution equation utilizes fiber/matrix interface oxidation section length, temperature strip
Fiber/matrix interface oxidation area's Friction Shearing Stress under part and the fiber/matrix interfacial detachment area friction under the conditions of temperature are cut and are answered
Power constructs to obtain；
(2) it is based on fracture mechanics interfacial detachment criterion, is cut using the fiber/matrix interfacial detachment area friction under the conditions of temperature
Fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of stress and temperature constructs fiber/matrix interfacial detachment section length side
Journey；
(3) energy balance relations, the stable state MATRIX CRACKING stress distribution equation obtained using the step (1), institute are based on
The fiber/matrix interfacial detachment section length equation that step (2) obtains is stated, binding fiber/basal body interface aoxidizes section length, and building is steady
State MATRIX CRACKING equilibrium relation equation, prediction braiding ceramic matric composite stable state MATRIX CRACKING stress.
Preferably, in the step (1),
Catchment fiber axial direction stress distribution equation is as shown in Equation 1:
Catchment matrix axial direction stress distribution equation is as shown in Equation 2:
Upstream fiber axial direction stress distribution equation is as shown in Equation 3:
Upstream matrix axial direction stress distribution equation is as shown in Equation 4:
1~4 formula of formula,
F indicates fiber,
M indicates matrix,
D indicates catchment,
U indicates upstream,
Z indicates axial value,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
VfIndicate braiding ceramic base fiber volume fraction,
σ indicates stress,
σf D(z) catchment fiber axial stress is indicated,
σm D(z) catchment matrix axial stress is indicated,
σf U(z) upstream fiber axial stress is indicated,
σm U(z) upstream matrix axial stress is indicated,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus.
Preferably, the fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of the temperature is as shown in Equation 5:
Fiber/matrix interfacial detachment area Friction Shearing Stress under the conditions of the temperature is as shown in Equation 6:
In formula 5 and 6,
τ0_fIndicate fiber/matrix interface oxidation area Friction Shearing Stress,
τ0_iIndicate fiber/matrix interfacial detachment area Friction Shearing Stress,
αrfIndicate fiber radial direction thermal expansion coefficient,
αrmIndicate matrix radial thermal expansion coefficient,
T0Indicate composite material preparation temperature,
T indicates that composite material uses temperature,
μ indicates braiding ceramic matric composite fiber/matrix interfacial friction factor,
A indicates braiding ceramic matric composite elastic constant.
Preferably, the braiding ceramic matric composite fiber/matrix interfacial friction factor passes through sluggish Dissipated energy prediction
Method obtains.
Preferably, fracture mechanical interface unsticking criterion is as shown in Equation 7 in the step (2):
In formula 7, ξdIndicate fiber/matrix interfacial detachment energy,
F indicates that matrix cracking plane fibers undertake load,
When indicating z=0, fiber axial displacement to unsticking section length derivation,
When indicating z=0, fiber with respect to matrix axial displacement to interfacial detachment section length derivation,
Dz indicates axial differential.
Preferably, the fiber axial displacement is as shown in Equation 8:
In formula 8, wf(z) fiber axial displacement is indicated.
Preferably, the fiber is the absolute of fiber axial displacement and matrix axial direction displacement difference with respect to the axial displacement of matrix
Value；
Described matrix axial displacement is as shown in Equation 9:
The fiber is as shown in Equation 10 with respect to the axial displacement of matrix:
In formula 9 and formula 10,
wm(z) matrix axial displacement is indicated,
V (z) indicates fiber with respect to matrix axial displacement.
Preferably, fiber/matrix interfacial detachment section length equation is as shown in Equation 11 in the step (2):
In formula 11,
ξdIndicate fiber/matrix interfacial detachment energy；
ldIndicate fiber/matrix interfacial detachment section length.
Preferably, energy balance relations are as shown in Equation 12 in the step (3):
In formula 12,
R indicates matrix radius,
GmIndicate matrix modulus of shearing,
R indicates radial coordinate,
Dr indicates radial differential；
ξmIndicate base fracture energy.
Preferably, stable state MATRIX CRACKING equilibrium relation equation is as shown in Equation 13 in the step (3):
In formula 13,WithEquation parameter is respectively indicated, respectively as shown in formula 14~16；
In formula 13~16,
σmcIndicate MATRIX CRACKING stress,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
ξmIndicate base fracture energy,
VfIndicate braiding ceramic base fiber volume fraction,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius.
The present invention is first based on shear-lag model building stable state MATRIX CRACKING stress distribution equation, is based on fracture mechanics interfacial detachment
Criteria construction fiber/matrix interfacial detachment section length equation, is then based on energy balance relations, utilizes stable state MATRIX CRACKING stress
Equation and fiber/matrix interfacial detachment section length equation construct stable state MATRIX CRACKING equilibrium relation equation.It is provided by the invention steady
State MATRIX CRACKING stress distribution equation, utilizes the fiber/matrix interface under the conditions of fiber/matrix interface oxidation section length, temperature
Fiber/matrix interfacial detachment area Friction Shearing Stress under the conditions of zoneofoxidation Friction Shearing Stress and temperature constructs to obtain, make temperature and
Oxidative factors are incorporated into stable state MATRIX CRACKING equilibrium relation equation, weave ceramic matric composite stable state matrix for Accurate Prediction
Crack stress provide foundation.Embodiment the result shows that, prediction technique provided by the invention can predict braiding ceramic base it is compound
Material is in different crack stress at use temperature.
Detailed description of the invention
Fig. 1 is the structural schematic diagram that cracking-unsticking weaves ceramic matric composite；
Fig. 2 is the shear lag single cell model that cracking-unsticking weaves ceramic matric composite；
Fig. 3 is the comparison diagram of 1 prediction result and experimental result of the embodiment of the present invention；
In Fig. 1 and 2,1 it is unsticking area, 2 is zoneofoxidation, 3 is catchment, 4 be expansion area, 4-1 and 4-2 is expansion area side
Boundary, 5 be upstream, 6 be matrix cracking plane, 7 be fiber, 8 be matrix, 9 be matrix cracking tip, z indicate axial direction, σ
Indicate stress.
Specific embodiment
The present invention relates to physical parameter and symbol are more, summarize in table 1.
The relevant physical parameter statistical form of the present invention of table 1
The prediction technique that ceramic matric composite stable state MATRIX CRACKING stress is woven for clear statement, present invention preferably provides
Cracking-debonding braiding ceramic matric composite structural schematic diagram (shown in Fig. 1) and cracking-unsticking braiding ceramic base are compound
The shear lag single cell model of material (shown in Fig. 2).
As shown in Fig. 1~2, in the present invention, cracking-debonding braiding ceramic matric composite structure includes: de-
Viscous area 1, zoneofoxidation 2, catchment 3, expansion area 4, stress boundary 4-1, stress boundary 4-2, upstream 5, matrix cracking plane 6,
Fiber 7, matrix 8 and matrix cracking tip 9.
In the present invention, the braiding ceramic matric composite is under conditions of by stress (σ), it may appear that matrix is split
The phenomenon that line-fiber cracking unsticking, unsticking area 1 is consequently formed；It is line of demarcation with matrix cracking 6, it is fine along fiber axially direction
The length that dimension 7 is detached from matrix is fiber/matrix interfacial detachment section length (ld)；After matrix is cracked, oxygen in air into
Enter the crackle gap of matrix, and then forms zoneofoxidation 2；It is line of demarcation with matrix cracking plane 6, along fiber axially direction,
The length that fiber 7 is contacted with air is fiber/matrix interface oxidation section length (ζ).
In the present invention, braiding ceramic matric composite it is cracked-debonding after, formed 6 He of matrix cracking plane
Matrix cracking tip 9, the region where described matrix crack tip 9 are expansion area 4, and the expansion area 4 passes through stress boundary 4-1
It is separated with catchment 3, the expansion area 4 is separated by stress boundary 4-2 and upstream 5.
Based on table 1, Fig. 1 and 2, the braiding ceramic matric composite stable state matrix that the present invention influences the consideration environment is opened
The specific embodiment for splitting the prediction technique of stress carries out as described below:
The present invention provides a kind of the pre- of braiding ceramic matric composite stable state MATRIX CRACKING stress that consideration environment influences
Survey method, includes the following steps:
(1) it is based on shear-lag model, constructs stable state MATRIX CRACKING stress distribution equation；
The stable state MATRIX CRACKING stress distribution equation includes stable state MATRIX CRACKING catchment stress distribution equation and stable state
MATRIX CRACKING upstream stress distribution equation；
Stable state MATRIX CRACKING catchment stress distribution equation utilizes fiber/matrix interface oxidation section length, temperature strip
Fiber/matrix interface oxidation area's Friction Shearing Stress under part and the fiber/matrix interfacial detachment area friction under the conditions of temperature are cut and are answered
Power constructs to obtain；
(2) it is based on fracture mechanics interfacial detachment criterion, is cut using the fiber/matrix interfacial detachment area friction under the conditions of temperature
Fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of stress and temperature constructs fiber/matrix interfacial detachment section length side
Journey；
(3) energy balance relations, the stable state MATRIX CRACKING stress distribution equation obtained using the step (1), institute are based on
The fiber/matrix interfacial detachment section length equation that step (2) obtains is stated, binding fiber/basal body interface aoxidizes section length, and building is steady
State MATRIX CRACKING equilibrium relation equation, prediction braiding ceramic matric composite stable state MATRIX CRACKING stress.
The present invention is based on shear-lag models, construct stable state MATRIX CRACKING stress distribution equation；
The stable state MATRIX CRACKING stress distribution equation includes stable state MATRIX CRACKING catchment stress distribution equation and stable state
MATRIX CRACKING upstream stress distribution equation；
Stable state MATRIX CRACKING catchment stress distribution equation utilizes fiber/matrix interface oxidation section length, temperature strip
Fiber/matrix interface oxidation area's Friction Shearing Stress under part and the fiber/matrix interfacial detachment area friction under the conditions of temperature are cut and are answered
Power constructs to obtain.
In the present invention, stable state MATRIX CRACKING catchment stress distribution equation preferably includes catchment fiber and axially answers
Power distribution equation and catchment matrix axial direction stress distribution equation；The stable state MATRIX CRACKING upstream stress distribution equation is preferred
Including upstream fiber axial direction stress distribution equation and upstream matrix axial direction stress distribution equation.
In the present invention, the catchment fiber axial direction stress distribution equation is preferably as shown in Equation 1:
The catchment matrix axial direction stress distribution equation is preferably as shown in Equation 2:
When the present invention constructs catchment stress distribution equation (as shown in formula 1 and formula 2), preferably by fiber/matrix interface point
For zoneofoxidation (0~ζ) and unsticking area (ζ~ld), and calculated for the stress of different zones, to improve the essence of stress distribution
Accuracy weaves ceramic matric composite stable state MATRIX CRACKING stress to subsequent prediction.When axial direction (z) value is zoneofoxidation endpoint value
When (i.e. ζ), can choose and calculated in any one stress distribution equation, preferably substitute into for oxidation region equation into
Row calculates.
In the present invention, the upstream fiber axial direction stress distribution equation is preferably as shown in Equation 3:
The upstream matrix axial direction stress distribution equation is preferably as shown in Equation 4:
1~4 formula of formula,
F indicates fiber,
M indicates matrix,
D indicates catchment,
U indicates upstream,
Z indicates axial value,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
VfIndicate braiding ceramic base fiber volume fraction,
σ indicates stress,
σf D(z) catchment fiber axial stress is indicated,
σm D(z) catchment matrix axial stress is indicated,
σf U(z) upstream fiber axial stress is indicated,
σm U(z) upstream matrix axial stress is indicated,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus.
In the present invention, described compound containing coefficient of discharge (χ) and braiding ceramic base along stress loading direction fiber effective volume
The braiding dimension of fiber is related in material:
When the braiding dimension of the braiding ceramic matric composite is 2, χ 0.5；
When the braiding dimension of the braiding ceramic matric composite is 2.5, χ 0.75；
When the braiding dimension of the braiding ceramic matric composite is 3, χ 0.93.
In the present invention, the fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of the temperature is preferably such as 5 institute of formula
Show:
Fiber/matrix interfacial detachment area Friction Shearing Stress under the conditions of the temperature is preferably as shown in Equation 6:
In formula 5 and 6,
τ0_fIndicate fiber/matrix interface oxidation area Friction Shearing Stress,
τ0_iIndicate fiber/matrix interfacial detachment area Friction Shearing Stress,
αrfIndicate fiber radial direction thermal expansion coefficient,
αrmIndicate matrix radial thermal expansion coefficient,
T0Indicate composite material preparation temperature,
T indicates that composite material uses temperature,
μ indicates braiding ceramic matric composite fiber/matrix interfacial friction factor,
A indicates braiding ceramic matric composite elastic constant.
In the present invention, the braiding ceramic matric composite fiber/matrix interfacial friction factor preferably passes through sluggish consumption
Energy prediction technique is dissipated to obtain.The present invention is specifically obtained to the braiding ceramic matric composite fiber/matrix interfacial friction factor
The method of obtaining does not have particular/special requirement, using mode well known to those skilled in the art.
The present invention is based on fracture mechanics interfacial detachment criterion, are rubbed using the fiber/matrix interfacial detachment area under the conditions of temperature
The fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of shear stress and temperature is wiped, the fiber/matrix interfacial detachment head of district is constructed
Spend equation.
In the present invention, the fracture mechanics interfacial detachment criterion is preferably as shown in Equation 7:
In formula 7, ξdIndicate fiber/matrix interfacial detachment energy,
F indicates that matrix cracking plane fibers undertake load,
When indicating z=0, fiber axial displacement to unsticking section length derivation,
When indicating z=0, fiber with respect to matrix axial displacement to interfacial detachment section length derivation,
Dz indicates axial differential.
In the present invention, the fiber axial displacement is as shown in Equation 8:
In formula 8, wf(z) fiber axial displacement is indicated.
In the present invention, the fiber is fiber axial displacement and matrix axial direction displacement difference with respect to the axial displacement of matrix
Absolute value；
Described matrix axial displacement is as shown in Equation 9:
The fiber is as shown in Equation 10 with respect to the axial displacement of matrix:
In formula 9 and formula 10,
wm(z) matrix axial displacement is indicated,
V (z) indicates fiber with respect to matrix axial displacement.
The present invention utilizes formula 7~10, and fiber/matrix interfacial detachment section length equation, the fiber/matrix interface can be obtained
Unsticking section length equation is as shown in Equation 11:
In formula 11,
ξdIndicate fiber/matrix interfacial detachment energy；
ldIndicate fiber/matrix interfacial detachment section length.
After obtaining stable state MATRIX CRACKING stress equation and fiber/matrix interfacial detachment section length equation, the present invention is based on energy
Equilibrium relation is measured, the stable state MATRIX CRACKING stress distribution equation and fiber/matrix interfacial detachment section length equation, knot are utilized
Condensating fiber/basal body interface aoxidizes section length, constructs stable state MATRIX CRACKING equilibrium relation equation, prediction braiding ceramic matric composite
Stable state MATRIX CRACKING stress.
In the present invention, the energy balance relations are preferably as shown in Equation 12:
In formula 12,
R indicates matrix radius,
GmIndicate matrix modulus of shearing,
R indicates radial coordinate,
Dr indicates radial differential；
ξmIndicate base fracture energy.
In the present invention, the stable state MATRIX CRACKING equilibrium relation equation is preferably as shown in Equation 13:
In formula 13,WithEquation parameter is respectively indicated, respectively as shown in formula 14~16；
In formula 13~16,
σmcIndicate MATRIX CRACKING stress,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
ξmIndicate base fracture energy,
VfIndicate braiding ceramic base fiber volume fraction,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius.
In the present invention, the braiding ceramic matric composite stable state MATRIX CRACKING equilibrium relation equation is to open about matrix
Split stress (σmc) quadratic equation with one unknown, solution obtains two values, wherein positive value is pre- for required MATRIX CRACKING stress of the invention
Measured value.The present invention can get the braiding ceramics for considering environmental factor, especially temperature and oxidative factors preferably by formula 13~16
The predicted value of based composites stable state MATRIX CRACKING stress, predicted value reliability are higher.
In order to further illustrate the present invention, below with reference to embodiment on a kind of volume for considering environment and influencing provided by the invention
The prediction technique for knitting ceramic matric composite stable state MATRIX CRACKING stress is described in detail, but cannot be interpreted as them pair
The restriction of the scope of the present invention.
Embodiment 1
With control of two-dimensional braided ceramic matric composite (2D C/SiC) for test sample, under 700 DEG C of air environments of high temperature, point
Stable state MATRIX CRACKING stress Yang Hua not be predicted after 4h and 6h.
Sample parameters are as follows: Vf(%)=40, χ=0.5, Ef=200GPa, Em=350GPa, Gm=145GPa, rf=3.5
μm、ξd=1.2J/m2、τ0_i=6MPa, τ0_f=1MPa, αrf=-0.38 × 10-6/℃、αrm=4.6 × 10-6/ DEG C, μ=0.1,
ζ=25 μm, T0=1000 DEG C.
By above-mentioned parameter substitute into stable state MATRIX CRACKING stress distribution equation, fiber/matrix interfacial detachment section length equation and
In stable state MATRIX CRACKING equilibrium relation equation, the stable state MATRIX CRACKING stress for obtaining test sample, as predicted value are solved.Prediction
As a result as shown in figure 3, specific test result is shown in Table 2.
Comparative example 1
By 1 test sample of embodiment, the MATRIX CRACKING stress of test sample tests knot as a comparison at room temperature
Fruit sees Fig. 3 and table 2.
2 embodiment 1 of table and 1 test result of comparative example
| Test condition | 700℃-4h | 700℃-6h |
| The present invention | 28.0MPa | 24.0MPa |
| Comparative example | 31.0MPa | 20.5MPa |
By the test result of table 2 and Fig. 3 it is found that scheme provided by the invention can be under hot conditions, when difference oxidation
Between the crack stress of braiding ceramic matric composite stable state matrix predicted, relative to comparative example room temperature test result
Speech, there are significant differences for the test result of scheme test result and comparative example provided by the invention, it was demonstrated that composite material uses temperature
Degree and oxidative factors produce influence to the crack stress of composite material stable state matrix, further relate to scheme tool provided by the invention
There is higher reliability.
As seen from the above embodiment, the braiding ceramic matric composite stable state matrix provided by the invention for considering environmental factor
Crack stress prediction technique, it is contemplated that temperature and oxidation are to the friction of braiding ceramic matric composite fiber/matrix interfacial detachment area
The influence of shear stress obtains the fiber/matrix interfacial detachment section length for considering that environment influences using Method of Fracture Mechanics, in conjunction with
Energy budget method predicts braiding ceramic matric composite stable state initial substrate crack stress, and prediction result high reliablity can push away
It is wide to use.
Although above-described embodiment is made that detailed description to the present invention, it is only a part of the embodiment of the present invention,
Rather than whole embodiments, people can also obtain other embodiments under the premise of without creativeness according to the present embodiment, these
Embodiment belongs to the scope of the present invention.
Claims (10)
1. a kind of prediction technique for weaving ceramic matric composite stable state MATRIX CRACKING stress for considering environment and influencing, including it is as follows
Step:
(1) it is based on shear-lag model, constructs stable state MATRIX CRACKING stress distribution equation；
The stable state MATRIX CRACKING stress distribution equation includes stable state MATRIX CRACKING catchment stress distribution equation and stable state matrix
Crack upstream stress distribution equation；
Under the conditions of stable state MATRIX CRACKING catchment stress distribution equation is using fiber/matrix interface oxidation section length, temperature
Fiber/matrix interface oxidation area's Friction Shearing Stress and temperature under the conditions of fiber/matrix interfacial detachment area Friction Shearing Stress structure
It builds to obtain；
(2) it is based on fracture mechanics interfacial detachment criterion, utilizes the fiber/matrix interfacial detachment area Friction Shearing Stress under the conditions of temperature
With the fiber/matrix interface oxidation area Friction Shearing Stress under the conditions of temperature, fiber/matrix interfacial detachment section length equation is constructed；
(3) energy balance relations, the stable state MATRIX CRACKING stress distribution equation obtained using the step (1), the step are based on
Suddenly the fiber/matrix interfacial detachment section length equation that (2) obtain, binding fiber/basal body interface aoxidize section length, construct stable state base
Body cracking equilibrium relation equation, prediction braiding ceramic matric composite stable state MATRIX CRACKING stress.
2. prediction technique as described in claim 1, which is characterized in that in the step (1),
Catchment fiber axial direction stress distribution equation is as shown in Equation 1:
Catchment matrix axial direction stress distribution equation is as shown in Equation 2:
Upstream fiber axial direction stress distribution equation is as shown in Equation 3:
Upstream matrix axial direction stress distribution equation is as shown in Equation 4:
1~4 formula of formula,
F indicates fiber,
M indicates matrix,
D indicates catchment,
U indicates upstream,
Z indicates axial value,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
VfIndicate braiding ceramic base fiber volume fraction,
σ indicates stress,
σf D(z) catchment fiber axial stress is indicated,
σm D(z) catchment matrix axial stress is indicated,
σf U(z) upstream fiber axial stress is indicated,
σm U(z) upstream matrix axial stress is indicated,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus.
3. prediction technique as claimed in claim 1 or 2, which is characterized in that the fiber/matrix interface oxygen under the conditions of the temperature
It is as shown in Equation 5 to change area's Friction Shearing Stress:
Fiber/matrix interfacial detachment area Friction Shearing Stress under the conditions of the temperature is as shown in Equation 6:
In formula 5 and 6,
τ0_fIndicate fiber/matrix interface oxidation area Friction Shearing Stress,
τ0_iIndicate fiber/matrix interfacial detachment area Friction Shearing Stress,
αrfIndicate fiber radial direction thermal expansion coefficient,
αrmIndicate matrix radial thermal expansion coefficient,
T0Indicate composite material preparation temperature,
T indicates that composite material uses temperature,
μ indicates braiding ceramic matric composite fiber/matrix interfacial friction factor,
A indicates braiding ceramic matric composite elastic constant.
4. prediction technique as claimed in claim 3, which is characterized in that braiding ceramic matric composite fiber/matrix circle
Face coefficient of friction passes through sluggish Dissipated energy prediction technique and obtains.
5. prediction technique as described in claim 1, which is characterized in that be broken mechanical interface unsticking criterion in the step (2)
It is as shown in Equation 7:
In formula 7, ξdIndicate fiber/matrix interfacial detachment energy,
F indicates that matrix cracking plane fibers undertake load,
When indicating z=0, fiber axial displacement to unsticking section length derivation,
When indicating z=0, fiber with respect to matrix axial displacement to interfacial detachment section length derivation,
Dz indicates axial differential.
6. prediction technique as claimed in claim 5, which is characterized in that the fiber axial displacement is as shown in Equation 8:
In formula 8, wf(z) fiber axial displacement is indicated.
7. prediction technique as claimed in claim 5, which is characterized in that the fiber is fiber axis with respect to the axial displacement of matrix
To the absolute value of displacement and matrix axial direction displacement difference；
Described matrix axial displacement is as shown in Equation 9:
The fiber is as shown in Equation 10 with respect to the axial displacement of matrix:
In formula 9 and formula 10,
wm(z) matrix axial displacement is indicated,
V (z) indicates fiber with respect to matrix axial displacement.
8. such as the described in any item prediction techniques of claim 1,2,4~7, which is characterized in that fiber/base in the step (2)
Body interface unsticking section length equation is as shown in Equation 11:
In formula 11,
ξdIndicate fiber/matrix interfacial detachment energy；
ldIndicate fiber/matrix interfacial detachment section length.
9. prediction technique as claimed in claim 1 or 2, which is characterized in that energy balance relations such as formula 12 in the step (3)
It is shown:
In formula 12,
R indicates matrix radius,
GmIndicate matrix modulus of shearing,
R indicates radial coordinate,
Dr indicates radial differential；
ξmIndicate base fracture energy.
10. prediction technique as described in claim 1, which is characterized in that stable state MATRIX CRACKING equilibrium relation in the step (3)
Equation is as shown in Equation 13:
In formula 13,WithEquation parameter is respectively indicated, respectively as shown in formula 14~16；
In formula 13~16,
σmcIndicate MATRIX CRACKING stress,
χ expression contains coefficient of discharge along stress loading direction fiber effective volume,
ξmIndicate base fracture energy,
VfIndicate braiding ceramic base fiber volume fraction,
ζ indicates fiber/matrix interface oxidation section length,
ldIndicate fiber/matrix interfacial detachment section length；
EfIndicate fiber isotropic modulus,
EmIndicate matrix elastic modulus,
EcIndicate braiding ceramic matric composite elasticity modulus,
τf(T) the fiber/matrix interface oxidation area friction shear stress under the conditions of temperature is indicated,
τi(T) the fiber/matrix interfacial adhesion area friction shear stress under the conditions of temperature is indicated,
rfFor fiber radius.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110864976A (en) * | 2019-12-02 | 2020-03-06 | 南京航空航天大学 | Method for observing consumption length of stress oxidation interface of ceramic matrix composite |
| CN111400922A (en) * | 2020-03-23 | 2020-07-10 | 南京航空航天大学 | Method for calculating stress-strain behavior of unidirectional ceramic matrix composite material by adding and removing random strain |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104866690A (en) * | 2015-06-16 | 2015-08-26 | 南京航空航天大学 | Method for predicating stress-strain behavior under arbitrary loading and unloading of one-way ceramic matrix composite |
| CN105701312A (en) * | 2015-12-17 | 2016-06-22 | 南京航空航天大学 | Complex braided structure ceramic matrix composite fatigue retardation behavior prediction method |
| CN105760605A (en) * | 2015-12-17 | 2016-07-13 | 南京航空航天大学 | Prediction method for fatigue life of complex braided structure ceramic-based composite material |
| US20180150618A1 (en) * | 2016-11-29 | 2018-05-31 | The Boeing Company | Porosity simulation for oxide ceramic matrix composites |
-
2019
- 2019-01-23 CN CN201910061936.8A patent/CN109598098A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104866690A (en) * | 2015-06-16 | 2015-08-26 | 南京航空航天大学 | Method for predicating stress-strain behavior under arbitrary loading and unloading of one-way ceramic matrix composite |
| CN105701312A (en) * | 2015-12-17 | 2016-06-22 | 南京航空航天大学 | Complex braided structure ceramic matrix composite fatigue retardation behavior prediction method |
| CN105760605A (en) * | 2015-12-17 | 2016-07-13 | 南京航空航天大学 | Prediction method for fatigue life of complex braided structure ceramic-based composite material |
| US20180150618A1 (en) * | 2016-11-29 | 2018-05-31 | The Boeing Company | Porosity simulation for oxide ceramic matrix composites |
Non-Patent Citations (5)
| Title |
|---|
| LI LONGBIAO: "Modeling first matrix cracking stress of fiber-reinforced ceramic-matrix composites considering fiber fracture", 《THEORETICAL AND APPLIED FRACTURE MECHANICS》 * |
| LI LONGBIAO: "Time-dependent damage and fracture of fiber-reinforced ceramic-matrix composites at elevated temperatures", 《COMPOSITE INTERFACES 》 * |
| LONGBIAO LI: "Modeling matrix cracking of fiber-reinforced ceramic-matrix composites under oxidation environment at elevated temperature", 《THEORETICAL AND APPLIED FRACTURE MECHANICS》 * |
| LONGBIAO LIZ ET AL.: "Estimate interface frictional coefficient of ceramic matrix composites from hysteresis loops", 《JOURNAL OF COMPOSITE MATERIALS》 * |
| P.REYNAUD: "Cyclic fatigue of ceramic-matrix composites at ambient and elevated temperatures", 《COMPOSITES SCIENCE AND TECHNOLOGY》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110864976A (en) * | 2019-12-02 | 2020-03-06 | 南京航空航天大学 | Method for observing consumption length of stress oxidation interface of ceramic matrix composite |
| CN111400922A (en) * | 2020-03-23 | 2020-07-10 | 南京航空航天大学 | Method for calculating stress-strain behavior of unidirectional ceramic matrix composite material by adding and removing random strain |
| CN111400922B (en) * | 2020-03-23 | 2021-09-07 | 南京航空航天大学 | Method for calculating stress-strain behavior of unidirectional ceramic matrix composite material by adding and removing random strain |
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