CN109264023A - Initial fatigue quality appraisal procedure based on analysis of uncertainty - Google Patents
Initial fatigue quality appraisal procedure based on analysis of uncertainty Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
- B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
- B64F5/60—Testing or inspecting aircraft components or systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01N2203/0058—Kind of property studied
- G01N2203/006—Crack, flaws, fracture or rupture
- G01N2203/0062—Crack or flaws
- G01N2203/0066—Propagation of crack
Abstract
The initial fatigue quality appraisal procedure based on analysis of uncertainty that the invention proposes a kind of, the height of the Equivalent Initial Flaw Size no longer component of stress for all fractures that durability test is obtained, but data set carries out initial fatigue quality assessment as a whole, improve data sample capacity, it ensure that the authenticity of analysis result, and simplify flow chart of data processing；By EIFS-TTCI data conversion formula, obtained EIFS data set is converted to the TTCI data set for obeying three-parameter weibull distribution, is facilitated and is carried out parameter determination and examine；Fuzzy theory is introduced, more unascertained informations can be excavated from data, improve the calculating accuracy of cumulative failure probability；Using the parameter of gray system theory estimation TTCI distribution, it is more suitable for the less situation of increment.Sample size can be improved in the present invention, abundant mining data includes unascertained information, and Simplified analysis process reduces amount of calculation, is more suitable for the less situation of sample size, guarantees that assessment result is truer, accurate.
Description
Technical field
It is the invention belongs to Airplane Structure Durability design field, in particular to a kind of original tired based on analysis of uncertainty
Labor method for evaluating quality and device.
Background technique
Durability Design is one of the Important Thought for instructing the structures such as aircraft, automobile, ship to design, common analysis method
One of be exactly probabilistic fracture mechanics analysis (PFMA, Probabilistic Fracture Mechanics Analysis) method.
When carrying out durability analysis, need to obtain initial fatigue quality (IFQ, the Initial Fatigue of material and structure
Quality).And Equivalent Initial Flaw Size (EIFS, Equivalent Initial Flaw Size) distribution is as original tired
The important component of labor quality model, for describing the initial fatigue quality and probabilistic fracture mechanics analysis of material structure
Key input data in method, directly affect durability analysis result.
When carrying out durability analysis, the result of durability analysis is more accurate, is more conducive to aeroplane structure design, therefore mention
Key input data, that is, initial fatigue quality assessment accuracy in high probability fracture mechanics analysis method is highly desirable.Often
It is quasi- frequently with crackle sprouting time (TTCI, Time To Crack Initiation) in probabilistic fracture mechanics analysis method
Durability test fracture data are divided into difference in TTCI fitting process by the legal initial fatigue quality data for obtaining material and structure
Stress level, and generality condition hypothesis is combined to optimize processing, obtain the general initial fatigue quality data of material structure.
However since TTCI fitting process thinks that the spreading rate of the crackle under same stress level is identical, the random of crack propagation is had ignored
Property, so that initial fatigue quality assessment result is untrue；Simultaneously as TTCI fitting process need for fracture data to be divided into it is different
Stress level is handled, so that the fracture data under each stress level are less, the rand estination that TTCI fitting process uses is acquired
The cumulative failure probability of TTCI, is not suitable for the less situation of this sample size, and the accuracy of calculating is to be improved；In addition,
The parameter that TTCI distribution is determined using fitting process, is also not suitable for the less situation of sample size；Finally, fracture data need using
Generality condition easily brings accumulated error it is assumed that cause data handling procedure many and diverse.
Thus, it is desirable to have a kind of technical solution overcomes or at least mitigates at least one drawbacks described above of the prior art.
Summary of the invention
The initial fatigue quality appraisal procedure based on analysis of uncertainty that the object of the present invention is to provide a kind of, to solve
The above problem.
The technical scheme is that a kind of initial fatigue quality appraisal procedure based on analysis of uncertainty, including
Step 1: obtaining the data of crack length a and crack propagation time t of multiple fractures to (a, t)；
Multiple fractures are obtained by durability test, multiple fracture analysis are obtained with the data of crack length and time
To (a, t)；
Step 2: being fitted the crack growth rate parameter Q of each fracture；
The crack length of acquisition and the data of crack propagation time are fitted (a, t) by crack propagation model, obtained
Obtain the crack growth rate parameter Q of crackle on fracture；
Step 3: the Equivalent Initial Flaw Size a (0) by being back-calculated to obtain each fracture constructs EIFS data set；
The crack growth rate parameter Q for obtaining fracture, calculates each fracture according to the crack growth rate model of use
Equivalent Initial Flaw Size a (0), and the Equivalent Initial Flaw Size a (0) under all stress levels is constituted into an EIFS data
EIFS data set is converted to the TTCI for obeying three parameter weibull distribution using EIFS-TTCI data conversion formula by collection
Data set；
Step 4: calculating TTCI data cumulative failure probability；
The cumulative failure probability in TTCI data set at each element is acquired using fuzzy theory；
Step 5: determining the parameter in TTCI distribution；
The parameter of TTCI distribution is estimated using gray system theory；
Step 6: determining whole general Equivalent Initial Flaw Size EIFS distribution；
According to EIFS distribution and the transformational relation of TTCI distribution and the data conversion formula of the two, the ginseng of EIFS distribution is found out
Number completes initial fatigue quality assessment.
Further, the crack growth rate parameter Q computation model are as follows:
Lna (t)=lna (0)+Qt
In formula: the crack length that a (t) is the crack propagation time when being t；A (0) is the Equivalent Initial Flaw Size of fracture；Q
For crack growth rate parameter.
Further, the fitting formula of crack growth rate parameter Q is
In formula: m is group number of the fracture crack length with crack propagation time data to (a, t) on fracture；akFor fracture
The crack length value of upper k-th of (a, t) data centering；tkFor the crack propagation time of k-th of (a, t) data centering on fracture
Value.
Further, Equivalent Initial Flaw Size a (0) calculation method are as follows:
In formula, Q-is according to current fracture (a, t) data to the crack growth rate parameter acquired.
Further, the EIFS-TTCI data conversion formula are as follows:
T=-ln A
In formula: T is TTCI data set；A is EIFS data set.
Further, using fuzzy theory, cumulative failure probability is asked using the integral of normal information diffusion estimation, is calculated public
Formula are as follows:
In formula: ti(i=1,2,3 ..., n) it is sample；N is sample size；H is experience window width.
Further, the calculation method of the experience window width h are as follows:
In formula, the value of y and the element number n of matrix T are related.
Further, the estimated value of the parameter alpha in TTCI distribution and ε are as follows:
In formula:For common shape parameter,For general distribution lower limit,Intermediate quantity and.
Further, the general Equivalent Initial Flaw Size EIFS is distributed as
In formula:For general constant,For the general distribution upper limit.
Further, the present invention is suitable for the compatible estimation of distribution parameters of three parameter weibull, or is suitable for three parameters
Weibull estimation of distribution parameters.
The present invention is less in order to solve sample data volume in TTCI fitting process under stress level at different levels, and need to take into account structure
The versatility problem of the initial fatigue quality of material, using the Equivalent Initial Flaw Size under all stress levels as a data
Collection is handled, and sample size is both increased, and in turn simplifies analysis process, more meet the objective law of crack propagation, as a result more
It is true and reliable；It proposes EIFS-TTCI conversion formula, the EIFS data set for obeying the compatible distribution of three parameter Weibull is converted to
It is true to solve the compatible distribution of three parameter Weibull for the TTCI data set for determining the mature obedience three-parameter weibull distribution of method
Determine the problem that method is single, precision is low；And new fuzzy theory analyzing and processing data is used, more letters are obtained from sample
Breath, is more suitable for the less situation of sample.
Detailed description of the invention
In order to illustrate more clearly of technical solution provided by the present application, attached drawing will be briefly described below.It is aobvious and easy
Insight, drawings discussed below are only some embodiments of the present application.
Fig. 1 is the initial fatigue quality appraisal procedure flow chart of the invention based on analysis of uncertainty.
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class
As label indicate same or similar element or element with the same or similar functions.Described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to use
It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiments of the present invention, ordinary skill people
Member's every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.Under
Face is described in detail the embodiment of the present invention in conjunction with attached drawing 1.
Probabilistic fracture mechanics analysis PFMA is a kind of common Airplane Structure Durability analysis method, and key theory is former
Beginning fatigue quality IFQ model, to describe the fatigue properties of material, structure.Equivalent Initial Flaw Size EIFS is a kind of with one
The Virtual Fatigue defect of measured length, the size of this defect and influence are determined that after material and structural generation come out, it
It is a stochastic variable, obeys the compatible distribution of three parameter Weibull.For the initial fatigue quality IFQ for characterizing material structure, commonly use
The distribution of Equivalent Initial Flaw Size EIFS describes, and Equivalent Initial Flaw Size EIFS distributed model is referring to expression formula 1, assessment
Initial fatigue quality IFQ is parameter a, x determined in formula 1uAnd B.Crack initiation time TTCI is initial fatigue quality IFQ model
In another physical quantity, it indicates that fatigue crack from equivalent original dimension expands to the crack propagation with reference to needed for crack length
Time, generally obedience three-parameter weibull distribution, mathematical model is referring to expression formula 2.
The sum of distribution function of both Equivalent Initial Flaw Size EIFS and crack initiation time TTCI is 1.
In formula: α is form parameter；xuTo be distributed the upper limit；B is constant.
In formula: α is form parameter, identical as the value of α in formula (1)；ε is distribution lower limit；β is scale parameter.
Initial fatigue quality appraisal procedure based on analysis of uncertainty of the invention, specifically includes:
Step 1: the crack length and crack propagation time data for obtaining all fractures are to (a, t)；
After completing durability test, fracture fatigue striation/striation is analyzed, the crack length of each fracture is obtained
With crack propagation time data to (a, t).
Step 2: calculating the crack growth rate parameter Q of each fracture；
The computation model for the crack growth rate Q that the present invention uses is referring to expression formula 3:
Lna (t)=lna (0)+Qt (3)
In formula: crack length when a (the t)-crack propagation time is t；A (0) is the Equivalent Initial Flaw Size of fracture；
Q-crack growth rate parameter.
Due to crack growth rate parameter Q be it is unknown, using least square method fitting acquire, expression formula be formula (4):
In formula: the fracture crack length on m-fracture is with crack propagation time data to the group number of (a, t)；ak- fracture
The crack length value of upper k-th of (a, t) data centering；tkThe crack propagation time of k-th of (a, t) data centering on-fracture
Value.
Step 3: calculating the Equivalent Initial Flaw Size a (0) of each fracture, and by the equivalent initial imperfection ruler of all fractures
Very little a (0) is as a set.
Using least square method when calculating (0) a, expression formula such as formula (5):
In formula: Q-, to the crack growth rate parameter acquired, is determined according to current fracture (a, t) data by formula (4).
After the Equivalent Initial Flaw Size a (0) for acquiring all fractures, it is initial to obtain an one-dimensional equivalent for descending arrangement
Flaw size EIFS data matrix A=[a1(0),a2(0),a3(0),...,an(0)], then data conversion is carried out, is converted to one
Crack initiation time TTCI data matrix T=[t1(0),t2(0),t3(0),...,tn(0)].TTCI data matrix obeys three ginsengs
Number Weibull distribution, conversion formula are formula (6)
T=-lnA (6)
Step 4: calculating TTCI data cumulative failure probability；
Since TTCI data may be less, the calculation expression of the cumulative failure probability at each sample point is formula (7)
In formula: h-experience window width, calculation formula are formula (8).
The value of y and the element number n of matrix T are related in formula (8), see the table below.
The value of 1 y of table
Step 5: determining parameter alpha, β and the ε in TTCI distribution；
The consecutive value formation sequence of each element in matrix T is acquired first, matrix X is formed, referring to formula (9)
Then it calculates consecutive value and generates corresponding derivative clear figure, and form matrix Y, referring to formula (10)
Intermediate quantity is acquired by formula (11) againWith
The estimated value for finally acquiring the parameter alpha and ε in TTCI distribution, such as formula (12).
Step 6: whole general Equivalent Initial Flaw Size EIFS distribution is determined, such as formula (13).
So far, parameter alpha, B and the x in EIFS distributionuIt all determines, i.e. the assessment of completion initial fatigue quality.
The height of the Equivalent Initial Flaw Size no longer component of stress for all fractures that the present invention obtains durability test, and
It is that data set carries out initial fatigue quality assessment as a whole, improves data sample capacity, ensure that analysis result
Authenticity, and simplify flow chart of data processing；Secondly, proposing EIFS-TTCI data conversion formula, the EIFS data set that will be obtained
The TTCI data set for obeying three-parameter weibull distribution is converted to, is more convenient to determine using mature theoretical method progress parameter
And inspection；Fuzzy theory is introduced, more unascertained informations can be excavated from data, improve the meter of cumulative failure probability
Calculate accuracy；Using the parameter of gray system theory estimation TTCI distribution, it is more suitable for the less situation of increment.The present invention is from more
From the aspect of a, raising sample size, abundant mining data include unascertained information, and Simplified analysis process reduces calculating
Workload is more suitable for the less situation of sample size, guarantees that assessment result is truer, accurate.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by those familiar with the art, all answers
It is included within the scope of the present invention.Therefore, protection scope of the present invention should be with the scope of protection of the claims
It is quasi-.
Claims (10)
1. a kind of initial fatigue quality appraisal procedure based on analysis of uncertainty, which is characterized in that including
Step 1: obtaining the data of crack length a and crack propagation time t of multiple fractures to (a, t)；
Multiple fractures are obtained by durability test, multiple fracture analysis are obtained with the data pair of crack length and time
(a,t)；
Step 2: being fitted the crack growth rate parameter Q of each fracture；
The crack length of acquisition and the data of crack propagation time are fitted (a, t) by crack propagation model, broken
The crack growth rate parameter Q of crackle on mouth；
Step 3: the Equivalent Initial Flaw Size a (0) by being back-calculated to obtain each fracture constructs EIFS data set；
The crack growth rate parameter Q for obtaining fracture, the equivalent of each fracture is calculated according to the crack growth rate model of use
Initial Flaw Size a (0), and the Equivalent Initial Flaw Size a (0) under all stress levels is constituted into an EIFS data set,
EIFS data set is converted to by the TTCI number for obeying three parameter weibull distribution using EIFS-TTCI data conversion formula
According to collection；
Step 4: calculating TTCI data cumulative failure probability；
The cumulative failure probability in TTCI data set at each element is acquired using fuzzy theory；
Step 5: determining the parameter in TTCI distribution；
The parameter of TTCI distribution is estimated using gray system theory；
Step 6: determining whole general Equivalent Initial Flaw Size EIFS distribution；
According to EIFS distribution and the transformational relation of TTCI distribution and the data conversion formula of the two, the parameter of EIFS distribution is found out,
Complete initial fatigue quality assessment.
2. the initial fatigue quality appraisal procedure according to claim 1 based on analysis of uncertainty, which is characterized in that institute
State crack growth rate parameter Q computation model are as follows:
Lna (t)=lna (0)+Qt
In formula: the crack length that a (t) is the crack propagation time when being t；A (0) is the Equivalent Initial Flaw Size of fracture；Q is to split
Line spreading rate parameter.
3. the initial fatigue quality appraisal procedure according to claim 2 based on analysis of uncertainty, which is characterized in that split
The fitting formula of line spreading rate parameter Q is
In formula: m is group number of the fracture crack length with crack propagation time data to (a, t) on fracture；akFor kth on fracture
The crack length value of a (a, t) data centering；tkFor the crack propagation time value of k-th of (a, t) data centering on fracture.
4. the initial fatigue quality appraisal procedure according to claim 3 based on analysis of uncertainty, which is characterized in that institute
State Equivalent Initial Flaw Size a (0) calculation method are as follows:
In formula, Q-is according to current fracture (a, t) data to the crack growth rate parameter acquired.
5. the initial fatigue quality appraisal procedure according to claim 4 based on analysis of uncertainty, which is characterized in that institute
State EIFS-TTCI data conversion formula are as follows:
T=-ln A
In formula: T is TTCI data set；A is EIFS data set.
6. the initial fatigue quality appraisal procedure according to claim 5 based on analysis of uncertainty, which is characterized in that answer
With fuzzy theory, cumulative failure probability, calculation formula are asked using the integral of normal information diffusion estimation are as follows:
In formula: ti(i=1,2,3 ..., n) it is sample；N is sample size；H is experience window width.
7. the initial fatigue quality appraisal procedure according to claim 6 based on analysis of uncertainty, which is characterized in that institute
State the calculation method of experience window width h are as follows:
In formula, the value of y and the element number n of matrix T are related.
8. the initial fatigue quality appraisal procedure according to claim 7 based on analysis of uncertainty, which is characterized in that
The estimated value of parameter alpha and ε in TTCI distribution are as follows:
In formula:For common shape parameter,For general distribution lower limit,Intermediate quantity and.
9. the initial fatigue quality appraisal procedure according to claim 8 based on analysis of uncertainty, which is characterized in that institute
General Equivalent Initial Flaw Size EIFS is stated to be distributed as
In formula:For general constant,For the general distribution upper limit.
10. -9 any initial fatigue quality appraisal procedure based on analysis of uncertainty according to claim 1, feature
It is, is suitable for the compatible estimation of distribution parameters of three parameter weibull, or be suitable for three parameter weibull estimation of distribution parameters.
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| CN110032786A (en) * | 2019-04-03 | 2019-07-19 | 西北工业大学 | The appraisal procedure of nickel-based monocrystal film hole structure part initial fatigue quality |
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| CN112881208A (en) * | 2021-01-14 | 2021-06-01 | 北京航空航天大学 | Equivalent initial defect size determination and evaluation method |
| CN114056599A (en) * | 2021-12-23 | 2022-02-18 | 中国飞机强度研究所 | Airplane climate environment adaptive capacity evaluation method based on grey correlation degree |
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| CN114056599A (en) * | 2021-12-23 | 2022-02-18 | 中国飞机强度研究所 | Airplane climate environment adaptive capacity evaluation method based on grey correlation degree |
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