CN110147618A - Aero engine turbine blades reliability estimation method based on fracture mechanics - Google Patents
Aero engine turbine blades reliability estimation method based on fracture mechanics Download PDFInfo
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- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/006—Crack, flaws, fracture or rupture
- G01N2203/0067—Fracture or rupture
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/026—Specifications of the specimen
- G01N2203/0262—Shape of the specimen
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- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
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- G01N2203/067—Parameter measured for estimating the property
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
Abstract
The invention discloses a kind of aero engine turbine blades reliability estimation method based on fracture mechanics, the following steps are included: S1, establishing using turbo blade as research object the simplified model of blade profile, using the stress intensity factor containing initial I type crackle turbo blade at Finite element arithmetic blade root, and bring into form factor calculation formula, determine form factor parameter；S2, it is based on generalized stress Strength Interference Model, establishes turbo blade reliability model；S3, the probability density function for establishing load and fracture toughness establish life expectance model and reliability model to blade in conjunction with Paris formula, and are solved to obtain the reliability of turbo blade with the situation of change in service life to model.The present invention considers initial imperfection present in blade, as basic assumption, establishes crack propagation life of the blade surface I type crackle under cyclic loading, the life prediction of blade and reliability assessment can be made more accurate.
Description
Technical field
The invention belongs to Probabilistic Life Prediction field, in particular to a kind of aero-turbine leaf based on fracture mechanics
Piece reliability estimation method.
Background technique
The common failure mode of aero engine turbine blades is fatigue fracture.At present to the conventional method of its life prediction
It is load to be divided into height Zhou Zaihe by load number and stress intensity, and calculate separately the theoretical service life under each load, uses
Fatigue Summation Damage Theory mathematic(al) expectation based on Miner rule.The working environment very severe of aero-engine, is running
Period can be involved in some travel fatigue gravels, these travel fatigue gravels being under fast state can hit turbine blade surface, make to it
At serious damage, its surface is made easily to germinate initial crack.In addition processing, transport, corrosion etc. also sprout blade initial crack
Life has a certain impact.Basic assumption of the invention be to recognize that in structure there is undiscovered initial imperfection, crackle or its
He damages.Assuming that blade surface existing defects, the extension service life of crackle is blade entire life, calculates it and splits under certain loads
Extension service life of line and quantified to some uncertain influence factors being capable of bimetry and assessment reliability.
The estimation of crack propagation life belongs to the scope of fracture mechanics.It is infinitely great in stress theory due to splitting at point, therefore
Stress strength factor K is introduced in fracture mechanics to assess " stress " that splits at point, fracture toughness KICIndicate " intensity " of material.K
Size can reflect the degree of strength of crack tip stress field.KICIt is the build-in attribute of material, is generally measured by test.
According to the angular relationship of load and crack surface, crackle form can be divided into three types: I type crackle, II type crackle,
Type III crackle respectively corresponds opening mode, sliding mode, tearing mode crack.Wherein I type crackle is most commonly seen in engineering, and value can
It is calculated by formula (1):
Wherein, σ is additional nominal stress, and a is crack size, to the half that crackle is crack length is buried, is split to surface
Line is crack depth.F is form factor, and value depends on shape, the size of component, and crack position and loading method etc., it can
To be constant, it is also possible to the function of crack size a.
When primary structure member is Infinite Plate, form factor f is 1.Primary structure member can not be unlimited in actual conditions
Greatly, crack length is sometimes or even the part of only plate.Still need the value to form factor f to study.For
Some standard components can be obtained by consulting reference books.For non-standard component, can be obtained by finite element simulation technology
?.
By the calculating formula of stress intensity factor it is found that the main reason for causing material stress intensity factor to disperse is load width
The uncertainty of degree.Therefore stress intensity factor is represented by the function of load amplitude.
It, can be by integrating acquisition to formula (2) for bearing the crack propagation life estimation of cyclic loading component:
Reliability model of the blade under specified life can be established by the model of stress-strength interference of broad sense.It can basis
Formula (3) establishes the reliability model of blade:
R=P (K < KIC) (3)
Wherein, K is stress intensity factor, KICFor the fracture toughness of blade.When the stress strength factor K of crack tip region
Greater than fracture toughness KICWhen, structural break.
It is above-described on condition that known members stress intensity factor, value can be inquired by Materials Handbook.But for
This non-standard structural element of aero engine turbine blades, any Materials Handbook can not all find its exact stress intensity because
Subvalue.It here is mainly that form factor f is difficult to obtain.
The crack propagation life that the above calculates is deterministic, and its service life is not known by many in a practical situation
How these uncertain factors are just included in life prediction and reliability assessment, carry out corresponding research by the influence of factor
Work, is of great significance.
Summary of the invention
It considers it is an object of the invention to overcome the deficiencies of the prior art and provide one kind and is initially lacked present in blade
It falls into, as basic assumption, establishes crack propagation life of the blade surface I type crackle under cyclic loading, leaf can be made
The more accurate aero engine turbine blades reliability assessment based on fracture mechanics of the life prediction of piece and reliability assessment
Method.
The purpose of the present invention is achieved through the following technical solutions: the aero-turbine leaf based on fracture mechanics
Piece reliability estimation method, comprising the following steps:
S1, the simplified model that blade profile is established using turbo blade as research object, obtain at blade root using FInite Element
Stress intensity factor containing initial I type crackle turbo blade, and stress intensity factor is brought into form factor calculation formula, really
The value for the shape factor parameter that shapes；
S2, it is based on generalized stress Strength Interference Model, by stress strength factor K obtained in S1 and fracture toughness KICInto
Row compares, and establishes turbo blade reliability model；
S3, the probability density function for establishing load and fracture toughness establish life expectance mould to blade in conjunction with Paris formula
Type and reliability model, and solved to obtain the reliability of turbo blade with the situation of change in service life to model.
Further, the step S1 includes following sub-step:
S11, hypothesis crackle are I type through wall flaw, and through-thickness carries out subdivision to leaf three-dimensional model, it is established that two
The blade profile simplified model of dimension；Subdivision is carried out to crack tip region: crack tip being constrained in circle, circle constrains in
In quadrangle；
S12, the material properties for defining model built；
S13, blade simplified model is divided with structuring quadrilateral mesh, and crack tip grid is encrypted
Processing；
S14, stress strength factor K will be exported as the course output parameter of ABAQUS；
S15, apply load and constraint and solving model to blade simplified model, obtain the nominal stress σ at blade root；
S16, the stress intensity factor value K and nominal stress σ obtained using Finite-Element Solution, acquire form factor according to the following formula
Value:
Wherein, f is form factor, and a is crack length, and K is stress intensity factor.
Further, the step S2 concrete methods of realizing are as follows: using the model of stress-strength interference of broad sense, by stress sheet
It is shown as stress intensity factor, strain is expressed as the fracture toughness of material, constructs a fracture Interference Model；Leaf destruction probability is used
Following formula indicates:
Wherein, P (K > KIC) indicate that stress strength factor K is greater than fracture toughness KICProbability, when stress intensity factor is big
Material is broken when fracture toughness；f(KIC) indicate fracture toughness KICProbability density function；F (K) indicates stress strength factor K
Probability density function；
The reliability of blade subtracts its fracture probability for 1, thus establishes the reliability model of blade are as follows:
P=1-F (6).
Further, the step S3 includes following sub-step:
S31, the extension service life for calculating crackle:
The spreading rate of crackle is calculated using Paris formula:
Wherein, a is crack length, and N is stress-number of cycles, and Δ K is stress-intensity factor range, and C, m are material parameter；
Take Initial crack length a0With critical crack length acFor range of integration, above formula both ends are integrated, are obtained:
Wherein, NcFor crack propagation life；
It enablesIt is obtained as m ≠ 2:
It is obtained as m=2:
Wherein, NcFor crack propagation life, Δ σ is nominal stress amplitude,
S32, critical crack size a is calculatedcValue:
S33, by critical crack size acValue substitute into formula (9) or formula (10), by KICWith Δ σ as variable, then the service life by
Formula (12) indicates:
N=φ (KIC,Δσ) (12)；
S34, failure rate and reliability are indicated by formula (13) and formula (14) respectively:
F '=P (N < N0) (13)
R=1-F '=P (N > N0) (14)
S35, stress amplitude and fracture toughness are substituted into formula (13) and formula (14), acquires failure rate of the blade under a certain service life
And reliability.
The beneficial effects of the present invention are: the present invention is compared with Traditional measurements life expectance reliability method, it is contemplated that blade
Present in initial imperfection as basic assumption establish crack propagation longevity of the blade surface I type crackle under cyclic loading
Life, can make the life prediction of blade and reliability assessment more accurate.
The present invention is using FInite Element come the method for identified sign intensity factor.Stress intensity factor calculation formula is analyzed
It is found that its value is difficult to the acquisition that determining key point is form factor f.The present invention establishes the simplified model of blade profile,
By carrying out Finite Element Simulation Analysis to the I type static state crackle under tensional state, its stress intensity factor, then anti-release shape are obtained
The size of the shape factor.
The present invention has comprehensively considered the uncertain influence to life prediction of load and material, and analyzing influences the service life not
Uncertainty is quantified as obeying the variable of a certain distribution by deterministic key parameter, to establish life expectance model
And reliability model, quantitatively analyze the life expectance and reliability of aero engine turbine blades.
Detailed description of the invention
The flow chart of Fig. 1 present invention calculating aero-turbine axis reliability；
Fig. 2 crack growth rate and stress intensity factor range relational graph；
Blade profile simplified model figure after Fig. 3 subdivision；
The grid dividing figure of Fig. 4 blade profile of the present invention；
Generalized stress Strength Interference Model figure used in Fig. 5 present invention；
Fig. 6 present invention considers the probability distribution graph in the service life under the influence of load material uncertainty；
Fig. 7 is variation diagram of the blade reliability of the present invention with the service life.
Specific embodiment
Technical solution of the present invention is further illustrated with reference to the accompanying drawing.
As shown in Figure 1, the purpose of the present invention is achieved through the following technical solutions: the aviation hair based on fracture mechanics
Motivation turbo blade reliability estimation method, which comprises the following steps:
S1, the simplified model that blade profile is established using turbo blade as research object, obtain at blade root using FInite Element
Stress intensity factor containing initial I type crackle turbo blade, and stress intensity factor is brought into form factor calculation formula, really
The value for the shape factor parameter that shapes；
Specifically include following sub-step:
S11, hypothesis crackle are I type through wall flaw, and through-thickness carries out subdivision to leaf three-dimensional model, it is established that two
The blade profile simplified model of dimension；Subdivision is carried out to crack tip region: crack tip being constrained in circle, circle constrains in
In quadrangle；The simplified model of blade profile as shown in Figure 2 is established, parameter is measured by UG software.Bottom side length 3.8mm, crackle
Locate side length 2.6mm, the long 1mm of top margin.Crackle is defined as blackening a length of 0.3mm of straight line in figure, carries out subdivision to crack tip, splits point
Border circular areas radius is 0.15mm, and square area side length is 0.6mm.
S12, the material properties for defining model built；Definition material is TC4 titanium alloy, elasticity modulus 110GPa, Poisson
Than being 0.35, cell type is homogeneity solid element.
S13, blade simplified model is divided with structuring quadrilateral mesh, global grid is having a size of 0.5；Meanwhile
The border circular areas of crack tip is divided with grid is scanned, and is divided into 36 parts, and encrypt to crack tip grid
Processing；Grid dividing and the result split at point after mesh refinement are as shown in Figure 3；And crack tip grid is encrypted；
S14, stress strength factor K will be exported as the course output parameter of ABAQUS；It is general that type definition, which will be solved,
Static linear analysis, setting output item are K；10 incremental steps are set, thus can intuitively find out K value as load increases
Situation of change.
S15, apply load and constraint and solving model to blade simplified model, obtain the nominal stress σ at blade root；With
ANSYS applies the load working condition of 1844.8rad/s revolving speed to the leaf model of the present embodiment, and obtaining the stress at blade root is
380MPa。
S16, the stress intensity factor value K and nominal stress σ obtained using Finite-Element Solution, acquire form factor according to the following formula
Value:
Wherein, f is form factor, and a is crack length, and K is stress intensity factor.The load that ANSYS is analyzed is applied
It is added to built simplified model.Bottom edge is fixed edge, applies corresponding constraint, and top margin applies the tensile stress of 380MPa, solving model.
The value of stress intensity factor is obtained as shown in figure 4, K is when load is 380MPaσ is nominal stress, cracks
Side length is 2.6mm, therefore nominal stress σ is 146MPa；A is crack length, is 0.3mm in the present embodiment；K be stress intensity because
Son is in the present embodimentObtaining form factor f is 1.206.
S2, it is based on generalized stress Strength Interference Model, by stress strength factor K obtained in S1 and fracture toughness KICInto
Row compares, and establishes turbo blade reliability model；Concrete methods of realizing are as follows: using the model of stress-strength interference (broad sense of broad sense
Model of stress-strength interference it is as shown in Figure 5), stress is expressed as stress intensity factor, the fracture that strain is expressed as material is tough
Property, construct an Interference Model；Leaf destruction probability is indicated with following formula:
Wherein, P (K > KIC) indicate that stress strength factor K is greater than fracture toughness KICProbability, when stress intensity factor is big
Material is broken when fracture toughness；f(KIC) indicate fracture toughness KICProbability density function；F (K) indicates stress strength factor K
Probability density function；
The reliability of blade subtracts its fracture probability for 1, thus establishes the reliability model of blade are as follows:
P=1-F (17).
S3, the probability density function for establishing load and fracture toughness establish life expectance mould to blade in conjunction with Paris formula
Type and reliability model, and solved to obtain the reliability of turbo blade with the situation of change in service life to model；
Life expectance fail-safe analysis of the present embodiment with aero engine turbine blades under 0-1844 (rad/s) operating condition
For, establish the specific steps of its life expectance reliability model are as follows:
S31, the fatigue life that can be approximated to be blade by Such analysis crack propagation life；Calculate the extension longevity of crackle
Life:
The spreading rate of crackle is calculated using Paris formula:
Wherein, a is crack length, and N is stress-number of cycles, and Δ K is stress-intensity factor range, and C, m are material parameter；
Take Initial crack length a0With critical crack length acFor range of integration, above formula both ends are integrated, are obtained:
Wherein, NcFor crack propagation life；
It enablesIt is obtained as m ≠ 2:
It is obtained as m=2:
Wherein, NcFor crack propagation life, Δ σ is nominal stress amplitude；
S32, pass through access associated materials handbook and document, fracture toughness KICForFollowing formula is brought into calculate
Critical crack size acValue:
S33, it is observed by the section to some broken blades, the initial crack size length before crack propagation is general
No more than 0.03mm, therefore initial crack size a is defined in this example0For 0.03mm.Acquiring critical crack size by formula (22) is
0.076mm；Parameter is checked according to Materials Handbook in formula: C 6.9E-12, m 3；By critical crack size acValue substitute into formula
(20) or formula (21), the fatigue life of blade is thus obtained.
In fact, awing due to space shuttle, maximum (top) speed is not a definite value, with certain dispersion
Property, service life and unreliable for being calculated with deterministic revolving speed.And the fracture toughness of material and the manufacture of material, transport work
Environment etc. has relationship, therefore it is also not a determining value.Regarding stress amplitude and fracture toughness as obedience just in this example
State distribution, the coefficient of variation are 0.1 variable, then ask its life expectance and reliability.By KICWith Δ σ as variable, then the service life by
Formula (23) indicates:
N=φ (KIC,Δσ) (23)；
S45, in KICUnder the influence of Δ σ variable, N obeys certain distribution；Failure rate and reliability respectively by formula (24) and
Formula (25) indicates:
F '=P (N < N0) (24)
R=1-F '=P (N > N0) (25)
S35, the stress amplitude for obeying a certain distribution and fracture toughness are substituted into formula (24) and formula (25), blade can be acquired and existed
Failure rate and reliability under a certain service life.It is a probability by what is obtained after the data substitution Life Prediction Model of the present embodiment
Model, and the model is solved using the method for Monte-Carlo step, obtain the density function in service life as shown in fig. 6, reliability with
The situation of change in service life is as shown in Figure 7.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.This field
Those of ordinary skill disclosed the technical disclosures can make according to the present invention and various not depart from the other each of essence of the invention
The specific variations and combinations of kind, these variations and combinations are still within the scope of the present invention.
Claims (4)
1. the aero engine turbine blades reliability estimation method based on fracture mechanics, which comprises the following steps:
S1, the simplified model that blade profile is established using turbo blade as research object are obtained at blade root using FInite Element containing just
The stress intensity factor of beginning I type crackle turbo blade, and stress intensity factor is brought into form factor calculation formula, determine shape
The value of shape factor parameter；
S2, it is based on generalized stress Strength Interference Model, by stress strength factor K obtained in S1 and fracture toughness KICCompared
Compared with establishing turbo blade reliability model；
S3, the probability density function for establishing load and fracture toughness, in conjunction with Paris formula to blade establish life expectance model and
Reliability model, and model is solved, the reliability of turbo blade is obtained with the situation of change in service life.
2. the aero engine turbine blades reliability estimation method according to claim 1 based on fracture mechanics, special
Sign is that the step S1 includes following sub-step:
S11, hypothesis crackle are I type through wall flaw, and through-thickness carries out subdivision to leaf three-dimensional model, it is established that two-dimensional
Blade profile simplified model；Subdivision is carried out to crack tip region: crack tip being constrained in circle, circle constrains in four sides
In shape；
S12, the material properties for defining model built；
S13, blade simplified model is divided with structuring quadrilateral mesh, and crack tip grid is carried out at encryption
Reason；
S14, stress strength factor K will be exported as the course output parameter of ABAQUS；
S15, apply load and constraint and solving model to blade simplified model, obtain the nominal stress σ at blade root；
S16, the stress intensity factor value K and nominal stress σ obtained using Finite-Element Solution, acquire the value of form factor according to the following formula:
Wherein, f is form factor, and a is crack length, and K is stress intensity factor.
3. according to claim 1 establish reliability model to turbo blade, the variation of its reliability is analyzed, feature exists
In the step S2 concrete methods of realizing are as follows: using the model of stress-strength interference of broad sense, by stress be expressed as stress intensity because
Son, strain are expressed as the fracture toughness of material, construct a fracture Interference Model；Leaf destruction probability is indicated with following formula:
Wherein, P (K > KIC) indicate that stress strength factor K is greater than fracture toughness KICProbability, when stress intensity factor be greater than fracture
Material is broken when toughness；f(KIC) indicate fracture toughness KICProbability density function；F (K) indicates that the probability of stress strength factor K is close
Spend function.
The reliability of blade subtracts its fracture probability for 1, thus establishes the reliability model of blade are as follows:
P=1-F (3).
4. according to claim 1 establish reliability model to turbo blade, the variation of its reliability is analyzed, feature exists
In the step S3 includes following sub-step:
S31, the extension service life for calculating crackle:
The spreading rate of crackle is calculated using Paris formula:
Wherein, a is crack length, and N is stress-number of cycles, and Δ K is stress-intensity factor range, and C, m are material parameter；
Take Initial crack length a0With critical crack length acFor range of integration, above formula both ends are integrated, are obtained:
Wherein, NcFor crack propagation life；
It enablesIt is obtained as m ≠ 2:
It is obtained as m=2:
Wherein, NcFor crack propagation life, Δ σ is nominal stress amplitude,
S32, critical crack size a is calculatedcValue:
S33, by critical crack size acValue substitute into formula (6) or formula (7), by KICWith Δ σ as variable, then the service life is by formula (9)
It indicates:
N=φ (KIC,Δσ) (9)；
S34, failure rate and reliability are indicated by formula (10) and formula (11) respectively:
F '=P (N < N0) (10)
R=1-F '=P (N > N0) (11)
S35, stress amplitude and fracture toughness are substituted into formula (10) and formula (11), acquire failure rate of the blade under a certain service life with can
By property.
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