CN104978490A - Novel method for forecasting calendar life of metal structure of aging aircraft - Google Patents

Abstract

A novel method for forecasting a calendar life of a metal structure of an aging aircraft. The method comprises five steps of: S1, establishing a prior-corroded metal material fatigue property S-N-t curve surface representation model; S2, according to a relative coefficient optimization method, establishing a prior-corroded metal material fatigue property S-N-t curve surface parameter fitness method; S3, establishing a prior-corroded metal material fatigue S-N-t curve surface model in a random stress ratio; S4, establishing a calendar life calculating formula for the metal structure of the aging aircraft under a spectrum load; and S5, substituting material fatigue properties with different prior-corrosion life limits, which are measured by testing, and a fatigue load spectrum counting processing result into the calendar life calculating formula to determine the calendar life of the metal structure of the aging aircraft. The novel method is simple and practical; a small number of model parameters need to be measured by testing; and the calendar life of the metal structure of the aging aircraft can be determined only by substituting the material corrosion fatigue properties with different prior-corrosion life limits and fatigue load spectrum data into the calendar life calculating formula.

Description

A kind of new method predicting Aircraft metal structure calendar life

Technical field

The invention provides a kind of new method predicting Aircraft metal structure calendar life, belong to Structural Metallic Fatigue and determine longevity technical field.

Background technology

Along with the continuous increase of Years Of Service, the problem that Aircraft structure is subject to environmental corrosion becomes increasingly conspicuous, and therefore, its metal structure calendar life evaluation problem becomes very important.For a long time, large quantity research is carried out to Aircraft corrosion of metal structure fatigue problem both at home and abroad, be intended to research corrosion environment to the impact of Structural Metallic Fatigue characteristic and failure damage mechanism, set up accurate Aircraft metal structure calendar life appraisal procedure.At present, the appraisal procedure of Aircraft corrosion of metal structure environment lower fatigue lifetime is mainly from the angle of metal erosion damage development, adopt the method for fracturing mechanics, predicting and evaluating is carried out to the fatigue lifetime of materials and structures under corrosion environment, but the method comes with some shortcomings: (1) needs the material parameter of measurement more, not only need the number of the microcosmic etch pit measuring material or body structure surface, the degree of depth, shape etc., and need the crack expansion characteristic measuring material (to comprise pit, short crack and long crack spreading rate), (2) corrosion of metal structure predicted often only considers the rupture failure process of certain crucial pit fatigue lifetime, and the interaction ignored between pit, be not inconsistent with actual conditions.In fact, a considerable amount of aircraft (as requiring assistance and Special Aircraft etc.) flight rate is lower, most of the time parks on ground during one's term of military service, the erosion of corrosion-vulnerable environment, and aloft high altitude environment often hazardous medium content and relative humidity lower, more weak to the Influence of Fatigue Properties of structure, the damage mode of its metal construction is the alternation procedure of the fatigue damage of the corrosion damage parked of ground and airflight, therefore, be necessary, for its corrosion and the tired feature alternately damaged, to set up the appraisal procedure of simple and practical calendar life.For this reason, establish a kind of new appraisal procedure of Aircraft metal structure calendar life herein, there is simple and practical, that precision is high advantage, only need to measure the Fatigue Characteristics of Materials under different pre-etching calendar limit year, just can calculate spectrum and carry lower Aircraft metal structure calendar life, the present invention has Important Academic meaning and engineer applied is worth.

Summary of the invention

1, object: the object of the invention is to provide a kind of new method predicting Aircraft metal structure calendar life, the method desired parameters is few, it is easy to calculate, and computational accuracy advantages of higher, for the evaluation of Aircraft metal structure calendar life, there is important value.

2, technical scheme: a kind of new method predicting Aircraft metal structure calendar life, the method concrete steps are as follows:

Step one, pre-etching Metal Material Fatigue performance S-N-t surface representing model

Material or structural fatigue performance adopt three parameter Power Functions expression formulas under appointment stress ratio to characterize usually, therefore, specify stress ratio R ₀under, the material that the different calendar corrosion time limit is corresponding or structural fatigue performance (i.e. S-N curve) can be written as

${\[S_{max,R_0}-S_0\left(t\right)\]}^{m}N=C---\left(1\right)$

In formula, represent and specify stress ratio R ₀the maximum stress that when the lower life-span will be N, material can bear; S ₀t () is the matching fatigue limit under different calendar limit year; M and C represents curve of fatigue form parameter; N represents fatigue lifetime.

Obviously, stress ratio R is specified ₀under, the fatigue limit of the pre-etching metal material of the different calendar corrosion time limit can reduce along with the increase of the pre-etching time limit, therefore, needs to introduce influence coefficient k and revises material corrosion fatigue strength, namely

S ₀(t)＝S ₀·k(t) (2)

The influence coefficient that in formula, k (t) is corrosion fatigue strength, S ₀for fatigue limit when material does not corrode.

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, and therefore, under specifying stress ratio, the calendar corrosion time limit and Fatigue Strength Effect Relationship of Coefficients formula can be expressed as

k(t)＝1-α·t ^β(3)

In formula, α, β are fitting coefficient, and t is calendar limit year.Parameter alpha and β reflection be the material constant of Fatigue Strength Effect coefficient and calendar limit year relation.

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R ₀under the S-N-t characterization model of material prior-corroded fatigue characteristic:

${\[S_{max,R_0}-S_0(1-\mathrm{\α}\·t^{\mathrm{\β}})\]}^{m}N=C---\left(4\right)$

Formula (4) reflect fatigue stress S, fatigue lifetime N and calendar corrosion time limit t triangular relation, become S-N-t surface model.Model (4) is containing undetermined parameter m, C and S ₀, estimate by following method.

Step 2, the matching of pre-etching Metal Material Fatigue performance S-N-t Surface Parameters

Make X=lg N, Y=lg [S _max-(1-α t ^β) S ₀], a=lg C, b=-m, then can be obtained by transform (4)

X＝a+bY (5)

Can find out that from formula (5) X and Y is in line relation, according to correlation coefficient method, then

$a=\stackrel{\‾}{x}-b\stackrel{\‾}{y}---\left(6\right)$

$b=\frac{L_{YX}}{L_{YY}}---\left(7\right)$

$r=\frac{L_{YX}}{\sqrt{L_{YY}\·L_{XY}}}---\left(8\right)$

In formula:

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i---\left(9\right)$

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i---\left(10\right)$

$L_{xx}=\underset{i=1}{\overset{n}{\Σ}}{x}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)}^2---\left(11\right)$

$L_{yy}=\underset{i=1}{\overset{n}{\Σ}}{y}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)}^2---\left(12\right)$

$L_{xy}=\underset{i=1}{\overset{n}{\Σ}}{x}_i{y}_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)---\left(13\right)$

Above in all formulas l _yYand L _yXall with α, β and S ₀relevant, be α, β and S ₀function.Therefore a, b and r are also α, β and S ₀function.Due to required α, β and S ₀related coefficient absolute value must be made | r (α, β, S ₀) | get maximum, therefore can obtain solving S ₀, the equation of α and β:

$\left\{\begin{array}{c}\frac{L_{x0}}{L_{yx}}-\frac{L_{y0}}{L_{yy}}=0\\ \frac{L_{x1}}{L_{yx}}-\frac{L_{y1}}{L_{yy}}=0\\ \frac{L_{x2}}{L_{yx}}-\frac{L_{y2}}{L_{yy}}=0\end{array}\right.---\left(14\right)$

In formula:

$L_{x0}=\ln 10\frac{\∂L_{yx}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(15\right)$

$L_{y0}=\ln 10\frac{\∂L_{yy}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(16\right)$

$L_{x1}=\ln 10\frac{\∂L_{yx}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(17\right)$

$L_{y1}=\ln 10\frac{\∂L_{yy}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(18\right)$

$L_{x2}=\ln 10\frac{\∂L_{yx}}{\∂S_0}=\underset{i=1}{\overset{n}{\Σ}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)x_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(19\right)$

$L_{y2}=\ln 10\frac{\∂L_{yy}}{\∂S_0}=\underset{i=1}{\overset{n}{\Σ}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)y_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(20\right)$

By numerical solution system of equations (14), α, β and S can be tried to achieve ₀.Can m and C be obtained finally by following formula:

m＝-L _yx/L _yy(21)

Pre-etching Metal Material Fatigue performance S-N-t curved surface under step 3, arbitrarily stress ratio

Owing to often containing the load (S under different stress ratio in actual fatigue load spectrum _a, S _m), and generally only carry out appointment stress ratio R in actual tests process ₀under torture test, therefore need the load correction under stress ratio different in loading spectrum to the stress ratio R specified ₀under.The graceful equation in linear Gourde(G) of load correction is

$\frac{S_a}{S_{-1}}+\frac{S_m}{{\mathrm{\σ}}_b}=1---\left(23\right)$

According to stress ratio definition, can obtain

$R=\frac{S_{\min }}{S_{\max }}=\frac{S_m-S_a}{S_m+S_a}---\left(24\right)$

Formula (24) also can be written as

$S_m=\frac{(1+R)S_a}{(1-R)}---\left(25\right)$

$S_{max}=\frac{2S_a}{(1-R)}---\left(26\right)$

Formula (25) is substituted into formula (23), the stress ratio R specified can be obtained ₀under the graceful equation in linear Gourde(G):

$\frac{S_{a,R_0}}{S_{-1}}+\frac{(1+R_0)\·S_{a,R_0}}{{\mathrm{\σ}}_b\·(1-R_0)}=1---\left(27\right)$

In formula represent and specify stress ratio R ₀under stress amplitude.

Simultaneous equations (23) and (27), obtain

$S_{a,R_0}=\frac{S_a\·(1-R_0)\·{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(28\right)$

Formula (26) is substituted into formula (28), can obtain specifying stress ratio R ₀lower maximum stress formula:

$S_{\max ,R_0}=\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(29\right)$

Formula (29) is substituted into the S-N-t characterization model that formula (4) just can obtain the material prior-corroded fatigue characteristic under any stress ratio:

${\[\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}-(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\]}^{m}N=C---\left(30\right)$

Step 4, spectrum carry lower Aircraft metal structure calendar life computing formula

Under normal circumstances, as shown in Figure 1, its damage mode is that corrosion damage that pre-etching causes is parked on ground and the mechanical fatigue that airflight fatigue load causes damages the process hocketed to load/environment-time history that Aircraft metal construction is born; Because of the reason of user demand, the flight rate difference (in namely annual load-time history, fatigue load cycle index is different) that aircraft is annual, therefore, need the accumulated damage carrying out year by year to the aged process that Aircraft Metal Structure is annual, determine the calendar corrosion fatigue life of its metal construction.

According to Miner cumulative damage theory, the calendar life of Aircraft metal construction can be obtained:

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{N_{ij}}=1---\left(32\right)$

In formula, n _ijfor the cycle index of i-th grade of load in jth year loading spectrum, N _ijfor the cycle index of fatigure failure occurred under i-th grade of test load independent role when jth year material, M is load cycle sum in jth year loading spectrum, and T is the calendar life that structure occurs when losing efficacy.

By the formula that formula (31) substitution formula (32) can obtain computation structure calendar life be

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{C}{\[\frac{2S_{a,ij}{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_{m,ij})\·(1-R_0)+S_{a,ij}\·(1+R_0)}-(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\]}^m=1---\left(33\right)$

In formula, S _{a, ij}and S _{m, ij}be respectively stress amplitude and the average of i-th grade of load cycle in jth year loading spectrum.

Step 5, spectrum are carried lower Aircraft metal structure calendar life and are calculated

Actual measurement fatigue load spectrum is carried rain-flow counting result n _tj, (S _a) _tj, (S _m) _tjwith the S-N-t curved surface that corrosion fatigue test measures, substitute into equation (33), by numerical solution, can in the hope of calendar life T.

3, advantage and effect: the invention provides a kind of new method predicting Aircraft metal structure calendar life, be characterized in simple and practical, model desired parameters is less, only need the fatigue behaviour of different pre-etching time limit material to substitute in computation model, just can obtain the calendar life of Aircraft metal construction.

Accompanying drawing explanation

Fig. 1 is the Load-environment course schematic diagram of Aircraft Metal Structure.

Fig. 2 is the FB(flow block) of the method for the invention.

In figure, symbol description is as follows:

In Fig. 2, S is fatigue stress, and N is the life-span, and t is the calendar corrosion time limit

Embodiment

Fig. 2 is the FB(flow block) of the method for the invention, and the present invention divides five steps to realize, and is specially:

Step one, pre-etching Metal Material Fatigue performance S-N-t surface representing model

Material or structural fatigue performance adopt three parameter Power Functions expression formulas under appointment stress ratio to characterize usually, therefore, specify stress ratio R ₀under, the material that the different calendar corrosion time limit is corresponding or structural fatigue performance (i.e. S-N curve) can be written as

${\[S_{max,R_0}-S_0\left(t\right)\]}^{m}N=C---\left(1\right)$

In formula, represent and specify stress ratio R ₀the maximum stress that when the lower life-span will be N, material can bear; S ₀t () is the matching fatigue limit under different calendar limit year; M and C represents curve of fatigue form parameter; N represents fatigue lifetime.

Obviously, stress ratio R is specified ₀under, the fatigue limit of the pre-etching metal material of the different calendar corrosion time limit can reduce along with the increase of the pre-etching time limit, therefore, needs to introduce influence coefficient k and revises material corrosion fatigue strength, namely

S ₀(t)＝S ₀·k(t) (2)

The influence coefficient that in formula, k (t) is corrosion fatigue strength, S ₀for fatigue limit when material does not corrode.

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, and therefore, under specifying stress ratio, the calendar corrosion time limit and Fatigue Strength Effect Relationship of Coefficients formula can be expressed as

k(t)＝1-α·t ^β(3)

In formula, α, β are fitting coefficient, and t is calendar limit year.Parameter alpha and β reflection be the material constant of Fatigue Strength Effect coefficient and calendar limit year relation.

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R ₀under the S-N-t characterization model of material prior-corroded fatigue characteristic:

Formula (4) reflect fatigue stress S, fatigue lifetime N and calendar corrosion time limit t triangular relation, become S-N-t surface model.Model (4) is containing undetermined parameter m, C and S ₀, estimate by following method.

Step 2, the matching of pre-etching Metal Material Fatigue performance S-N-t Surface Parameters

Make X=lg N, Y=lg [S _max-(1-α t ^β) S ₀], a=lg C, b=-m, then can be obtained by transform (4)

X＝a+bY (5)

Can find out that from formula (5) X and Y is in line relation, according to correlation coefficient method, then

$a=\stackrel{\‾}{x}-b\stackrel{\‾}{y}---\left(6\right)$

$b=\frac{L_{YX}}{L_{YY}}---\left(7\right)$

$r=\frac{L_{YX}}{\sqrt{L_{YY}\·L_{XX}}}---\left(8\right)$

In formula:

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i---\left(9\right)$

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i---\left(10\right)$

$L_{xx}=\underset{i=1}{\overset{n}{\Σ}}{x}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)}^2---\left(11\right)$

$L_{yy}=\underset{i=1}{\overset{n}{\Σ}}{y}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)}^2---\left(12\right)$

$L_{xy}=\underset{i=1}{\overset{n}{\Σ}}{x}_i{y}_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)---\left(13\right)$

Above in all formulas l _yYand L _yXall with α, β and S ₀relevant, be α, β and S ₀function.Therefore a, b and r are also α, β and S ₀function.Due to required α, β and S ₀related coefficient absolute value must be made | r (α, β, S ₀) | get maximum, therefore can obtain solving S ₀, the equation of α and β:

$\left\{\begin{array}{c}\frac{L_{x0}}{L_{yx}}-\frac{L_{y0}}{L_{yy}}=0\\ \frac{L_{x1}}{L_{yx}}-\frac{L_{y1}}{L_{yy}}=0\\ \frac{L_{x2}}{L_{yx}}-\frac{L_{y2}}{L_{yy}}=0\end{array}\right.---\left(14\right)$

where

$L_{x0}=\ln 10\frac{\∂L_{yx}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(15\right)$

$L_{y0}=\ln 10\frac{\∂L_{yy}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(16\right)$

$L_{x1}=\ln 10\frac{\∂L_{yx}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(17\right)$

$L_{y1}=\ln 10\frac{\∂L_{yy}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(18\right)$

$L_{x2}=\ln 10\frac{\∂L_{yx}}{\∂S_0}=\underset{i=1}{\overset{n}{\Σ}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)x_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(19\right)$

$L_{y2}=\ln 10\frac{\∂L_{yy}}{\∂S_0}=\underset{i=1}{\overset{n}{\Σ}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)y_i}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0\left(1-{\mathrm{\αt}}^{\mathrm{\β}}\right)}---\left(20\right)$

By numerical solution system of equations (14), α, β and S can be tried to achieve ₀.Can m and C be obtained finally by following formula:

m＝-L _yx/L _yy(21)

$C={10}^{(\stackrel{\‾}{x}-\stackrel{\‾}{y}\·L_{yx}/L_{yy})}---\left(22\right)$

Pre-etching Metal Material Fatigue performance S-N-t curved surface under step 3, arbitrarily stress ratio

Owing to often containing the load (S under different stress ratio in actual fatigue load spectrum _a, S _m), and generally only carry out appointment stress ratio R in actual tests process ₀under torture test, therefore need the load correction under stress ratio different in loading spectrum to the stress ratio R specified ₀under.The graceful equation in linear Gourde(G) of load correction is

$\frac{S_a}{S_{-1}}+\frac{S_m}{{\mathrm{\σ}}_b}=1---\left(23\right)$

According to stress ratio definition, can obtain

$R=\frac{S_{min}}{S_{\max }}=\frac{S_m-S_a}{S_m+S_a}---\left(24\right)$

Formula (24) also can be written as

$S_m=\frac{(1+R)S_a}{(1-R)}---\left(25\right)$

$S_{max}=\frac{2S_a}{(1-R)}---\left(26\right)$

Formula (25) is substituted into formula (23), the stress ratio R specified can be obtained ₀under the graceful equation in linear Gourde(G):

$\frac{S_{a,R_0}}{S_{-1}}+\frac{(1+R_0)\·S_{a,R_0}}{{\mathrm{\σ}}_b\·(1-R_0)}=1---\left(27\right)$

In formula represent and specify stress ratio R ₀under stress amplitude.

Simultaneous equations (23) and (27), obtain

$S_{a,R_0}=\frac{S_a\·(1-R_0)\·{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(28\right)$

Formula (26) is substituted into formula (28), can obtain specifying stress ratio R ₀lower maximum stress formula:

$S_{\max ,R_0}=\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(29\right)$

Formula (29) is substituted into the S-N-t characterization model that formula (4) just can obtain the material prior-corroded fatigue characteristic under any stress ratio:

${\[\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}-(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\]}^{m}N=C---\left(30\right)$

Step 4, spectrum carry lower Aircraft metal structure calendar life computing formula

Under normal circumstances, as shown in Figure 1, its damage mode is that corrosion damage that pre-etching causes is parked on ground and the mechanical fatigue that airflight fatigue load causes damages the process hocketed to load/environment-time history that Aircraft metal construction is born; Because of the reason of user demand, the flight rate difference (in namely annual load-time history, fatigue load cycle index is different) that aircraft is annual, therefore, need the accumulated damage carrying out year by year to the aged process that Aircraft Metal Structure is annual, determine the calendar corrosion fatigue life of its metal construction.

According to Miner cumulative damage theory, the calendar life of Aircraft metal construction can be obtained:

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{N_{ij}}=1---\left(32\right)$

In formula, n _ijfor the cycle index of i-th grade of load in jth year loading spectrum, N _ijfor the cycle index of fatigure failure occurred under i-th grade of test load independent role when jth year material, M is load cycle sum in jth year loading spectrum, and T is the calendar life that structure occurs when losing efficacy.

Formula (31) is substituted into formula (32), the formula of computation structure calendar life can be obtained:

${\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{C}\[\frac{2S_{a,ij}{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_{m,ij})\·(1-R_0)+S_{a,ij}\·(1+R_0)}-(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\]}^m=1---\left(33\right)$

In formula, S _{a, ij}and S _{m, ij}be respectively stress amplitude and the average of i-th grade of load cycle in jth year loading spectrum.

Step 5, spectrum are carried lower Aircraft metal structure calendar life and are calculated

Actual measurement fatigue load spectrum is carried rain-flow counting result n _tj, (S _a) _tj, (S _m) _tjwith the S-N-t curved surface that corrosion fatigue test measures, substitute into equation (33), by numerical solution, can in the hope of calendar life T.

Claims (2)

1. predict a new method for Aircraft metal structure calendar life, it is characterized in that: the method concrete steps are as follows:

Step one, pre-etching Metal Material Fatigue performance S-N-t surface representing model

Material or structural fatigue performance adopt three parameter Power Functions expression formulas under appointment stress ratio to characterize usually, therefore, specify stress ratio R ₀under, the material that the different calendar corrosion time limit is corresponding or structural fatigue performance (i.e. S-N curve) can be written as

${\[S_{max,R_0}-S_0\left(t\right)\]}^{m}N=C---\left(1\right)$

In formula, represent and specify stress ratio R ₀the maximum stress that when the lower life-span will be N, material can bear; S ₀t () is the matching fatigue limit under different calendar limit year; M and C represents curve of fatigue form parameter; N represents fatigue lifetime.

Obviously, stress ratio R is specified ₀under, the fatigue limit of the pre-etching metal material of the different calendar corrosion time limit can reduce along with the increase of the pre-etching time limit, therefore, needs to introduce influence coefficient k and revises material corrosion fatigue strength, namely

S ₀(t)＝S ₀·k(t) (2)

The influence coefficient that in formula, k (t) is corrosion fatigue strength, S ₀for fatigue limit when material does not corrode.

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, and therefore, under specifying stress ratio, the calendar corrosion time limit and Fatigue Strength Effect Relationship of Coefficients formula can be expressed as

k(t)＝1-α·t ^β(3)

In formula, α, β are fitting coefficient, and t is calendar limit year.Parameter alpha and β reflection be the material constant of Fatigue Strength Effect coefficient and calendar limit year relation.

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R ₀under the S-N-t characterization model of material prior-corroded fatigue characteristic:

${\[S_{max,R_0}-S_0(1-\mathrm{\α}\·t^{\mathrm{\β}})\]}^{m}N=C---\left(4\right)$

Formula (4) reflect fatigue stress S, fatigue lifetime N and calendar corrosion time limit t triangular relation, become S-N-t surface model.Model (4) is containing undetermined parameter m, C and S ₀, estimate by following method.

Step 2, the matching of pre-etching Metal Material Fatigue performance S-N-t Surface Parameters

Make X=lgN, Y=lg [S _max-(1-α t ^β) S ₀], a=lgC, b=-m, then can be obtained by transform (4)

X＝a+bY (5)

Can find out that from formula (5) X and Y is in line relation, according to correlation coefficient method, then

$a=\stackrel{\‾}{x}-b\stackrel{\‾}{y}---\left(6\right)$

$b=\frac{L_{YX}}{L_{YY}}---\left(7\right)$

$r=\frac{L_{YX}}{\sqrt{L_{YY}\·L_{XX}}}---\left(8\right)$

In formula:

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i---\left(9\right)$

$\stackrel{\‾}{y}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i---\left(10\right)$

$L_{xx}=\underset{i=1}{\overset{n}{\Σ}}{x}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)}^2---\left(11\right)$

$L_{yy}=\underset{i=1}{\overset{n}{\Σ}}{y}_i^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)}^2---\left(12\right)$

$L_{xy}=\underset{i=1}{\overset{n}{\Σ}}{x}_i{y}_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\Σ}}{x}_i\right)\left(\underset{i=1}{\overset{n}{\Σ}}{y}_i\right)---\left(13\right)$

Above in all formulas l _yYand L _yXall with α, β and S ₀relevant, be α, β and S ₀function.Therefore a, b and r are also α, β and S ₀function.Due to required α, β and S ₀related coefficient absolute value must be made | r (α, β, S ₀) | get maximum, therefore can obtain solving S ₀, the equation of α and β:

$\left\{\begin{array}{c}\frac{L_{x0}}{L_{yx}}-\frac{L_{y0}}{L_{yy}}=0\\ \frac{L_{x1}}{L_{yx}}-\frac{L_{y1}}{L_{yy}}=0\\ \frac{L_{x2}}{L_{yx}}-\frac{L_{y2}}{L_{yy}}=0\end{array}\right.---\left(14\right)$

In formula:

$L_{x0}=ln10\frac{\∂L_{yx}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{S_0{t}^{\mathrm{\β}}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(15\right)$

$L_{y0}=ln10\frac{\∂L_{yy}}{\∂\mathrm{\α}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{S_0{t}^{\mathrm{\β}}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{S_0{t}^{\mathrm{\β}}}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(16\right)$

$L_{x1}=\ln 10\frac{\∂L_{yx}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{x}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{x}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(17\right)$

$L_{y1}=\ln 10\frac{\∂L_{yy}}{\∂\mathrm{\β}}=\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}{y}_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{y}_i\underset{i=1}{\overset{n}{\Σ}}\frac{{\mathrm{\α\βS}}_0{t}^{\mathrm{\β}-1}}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(18\right)$

$L_{x2}=\ln 10\frac{\∂L_{yx}}{\∂S_0}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)x_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(19\right)$

$L_{y2}=ln10\frac{\∂L_{yy}}{\∂S_0}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{({\mathrm{\αt}}^{\mathrm{\β}}-1)y_i}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}-\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_i\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\mathrm{\αt}}^{\mathrm{\β}}-1}{{\left(S_{\max ,R_0}\right)}_i-S_0(1-{\mathrm{\αt}}^{\mathrm{\β}})}---\left(20\right)$

By numerical solution system of equations (14), α, β and S can be tried to achieve ₀.Can m and C be obtained finally by following formula:

m＝-L _yx/L _yy(21)

$C={10}^{(\stackrel{\‾}{x}-\stackrel{\‾}{y}\·L_{yx}/L_{yy})}---\left(22\right)$

Pre-etching Metal Material Fatigue performance S-N-t curved surface under step 3, arbitrarily stress ratio

Owing to often containing the load (S under different stress ratio in actual fatigue load spectrum _a, S _m), and generally only carry out appointment stress ratio R in actual tests process ₀under torture test, therefore need the load correction under stress ratio different in loading spectrum to the stress ratio R specified ₀under.The graceful equation in linear Gourde(G) of load correction is

$\frac{S_a}{S_{-1}}+\frac{S_m}{{\mathrm{\σ}}_b}=1---\left(23\right)$

According to stress ratio definition, can obtain

$R=\frac{S_{min}}{S_{\max }}=\frac{S_m-S_a}{S_m+S_a}---\left(24\right)$

Formula (24) also can be written as

$S_m=\frac{(1+R)S_a}{(1-R)}---\left(25\right)$

$S_{max}=\frac{2S_a}{(1-R)}---\left(26\right)$

Formula (25) is substituted into formula (23), the stress ratio R specified can be obtained ₀under the graceful equation in linear Gourde(G):

$\frac{S_{a,R_0}}{S_{-1}}+\frac{(1+R_0)\·S_{a,R_0}}{{\mathrm{\σ}}_b\·(1-R_0)}=1---\left(27\right)$

In formula represent and specify stress ratio R ₀under stress amplitude.

Simultaneous equations (23) and (27), obtain

$S_{a,R_0}=\frac{S_a\·(1-R_0)\·{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(28\right)$

Formula (26) is substituted into formula (28), can obtain specifying stress ratio R ₀lower maximum stress formula:

$S_{\max ,R_0}=\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}---\left(29\right)$

Formula (29) is substituted into the S-N-t characterization model that formula (4) just can obtain the material prior-corroded fatigue characteristic under any stress ratio:

${\[\frac{2S_a{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_m)\·(1-R_0)+S_a\·(1+R_0)}-(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\]}^{m}N=C---\left(30\right)$

Step 4, spectrum carry lower Aircraft metal structure calendar life computing formula

Under normal circumstances, as shown in Figure 1, its damage mode is that corrosion damage that pre-etching causes is parked on ground and the mechanical fatigue that airflight fatigue load causes damages the process hocketed to load/environment-time history that Aircraft metal construction is born; Because of the reason of user demand, the flight rate difference (in namely annual load-time history, fatigue load cycle index is different) that aircraft is annual, therefore, need the accumulated damage carrying out year by year to the aged process that Aircraft Metal Structure is annual, determine the calendar corrosion fatigue life of its metal construction.

According to Miner cumulative damage theory, the calendar life of Aircraft metal construction can be obtained:

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{N_{ij}}=1---\left(32\right)$

In formula, n _ijfor the cycle index of i-th grade of load in jth year loading spectrum, N _ijfor the cycle index of fatigure failure occurred under i-th grade of test load independent role when jth year material, M is load cycle sum in jth year loading spectrum, and T is the calendar life that structure occurs when losing efficacy.

By the formula that formula (31) substitution formula (32) can obtain computation structure calendar life be

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{C}{\text{\[}\frac{2S_{a,ij}{\mathrm{\σ}}_b}{({\mathrm{\σ}}_b-S_{m,ij})\·(1-R_0)+S_{a,ij}\·(1+R_0)}\text{-}(1-\mathrm{\α}\·t^{\mathrm{\β}})\·S_0\text{\]}}^m=1---\left(33\right)$

In formula, S _{a, ij}and S _{m, ij}be respectively stress amplitude and the average of i-th grade of load cycle in jth year loading spectrum.

Step 5, spectrum are carried lower Aircraft metal structure calendar life and are calculated

Actual measurement fatigue load spectrum is carried rain-flow counting result n _tj, (S _a) _tj, (S _m) _tjwith the S-N-t curved surface that corrosion fatigue test measures, substitute into equation (33), by numerical solution, can in the hope of calendar life T.

2. advantage and effect: the invention provides a kind of new method predicting Aircraft metal structure calendar life, the method desired parameters is few, it is easy to calculate, computational accuracy is high, only need the fatigue behaviour of different pre-etching time limit material and fatigue load modal data to substitute in model herein, just can determine the calendar life of Aircraft metal construction.