CN104978490B - A kind of method for predicting Aircraft metal structure calendar life - Google Patents

Abstract

A kind of new method for predicting Aircraft metal structure calendar life, this method has five big steps：Step 1: setting up pre-etching Metal Material Fatigue performance S N t surface representing models；Step 2: according to correlation coefficient method, setting up pre-etching Metal Material Fatigue performance S N t Surface Parameters approximating methods；Step 3: the tired S N t surface models for the pre-etching metal material set up under any stress ratio；Step 4: setting up spectrum carries lower Aircraft metal structure calendar life calculation formula；Step 5: the fatigue of materials performance and fatigue load spectrum that test the different pre-etching time limits determined are counted into result, substitute into calendar life calculation formula, determine the calendar life of Aircraft metal structure.The present invention is simple and practical, and the model parameter that required experiment is determined is few, it is thus only necessary to by the material corrosion fatigue behaviour and fatigue load modal data of the different pre-etching time limits, substitutes into calendar life computation model, so that it may determine the calendar life of Aircraft metal structure.

Description

A kind of method for predicting Aircraft metal structure calendar life

Technical field

The present invention provides a kind of new method for predicting Aircraft metal structure calendar life, belongs to Structural Metallic Fatigue and determines Longevity technical field.

Background technology

With being continuously increased for Years Of Service, the problem of Aircraft structure is by environmental corrosion becomes increasingly conspicuous, therefore, its Metal structure calendar life evaluation problem becomes particularly significant.For a long time, it is tired to Aircraft corrosion of metal structure both at home and abroad Labor problem has carried out numerous studies, it is intended to study influence and failure damage mechanism of the corrosive environment to Structural Metallic Fatigue characteristic, Set up accurate Aircraft metal structure calendar life appraisal procedure.At present, it is tired under Aircraft corrosion of metal structure environment The appraisal procedure in labor life-span is mainly the angle from metal erosion damage development, using the method for fracture mechanics, to corrosion The fatigue life of material and structure is predicted and assessed under environment, but this method comes with some shortcomings：(1) material measured is needed Expect that parameter is more, not only need to measure number, depth, shape of microcosmic etch pit of material or body structure surface etc., and need Determine the crack expansion characteristic (including pit, short crack and long crack spreading rate) of material, the corrosion of metal structure of (2) prediction Fatigue life often only considers the rupture failure process of some crucial pit, and ignores the interaction between pit, with reality Situation is not inconsistent.In fact, a considerable amount of aircrafts (are such as required assistance and Special Aircraft), flight rate is relatively low, most of during one's term of military service Time parks on ground, the erosion of corrosion-vulnerable environment, and high altitude environment in-flight often hazardous medium content and relatively wet Degree is relatively low, weaker to the Influence of Fatigue Properties of structure, and the damage mode of its metal structure is corrosion damage and sky that ground is parked The alternation procedure of the fatigue damage of middle flight, therefore, it is necessary to which the characteristics of replacing damage with fatigue for its corrosion, sets up simple The appraisal procedure of practical calendar life.Therefore, establishing a kind of new assessment of Aircraft metal structure calendar life herein Method, has the advantages that simple and practical, precision is high, it is thus only necessary to which the fatigue of materials determined under different pre-etching calendar limit years is special Property, it just can calculate spectrum and carry lower Aircraft metal structure calendar life, the present invention has Important Academic meaning and engineer applied Value.

The content of the invention

1st, purpose：It is an object of the present invention to provide a kind of new method for predicting Aircraft metal structure calendar life, the party Parameter needed for method is few, it is easy to calculate, and computational accuracy it is high the advantages of, have for the evaluation of Aircraft metal structure calendar life Important value.

2nd, technical scheme：A kind of new method for predicting Aircraft metal structure calendar life, this method specific steps are such as Under：

Step 1: pre-etching Metal Material Fatigue performance S-N-t surface representing models

Material or structural fatigue performance are generally characterized using the three parameter Power Functions expression formulas specified under stress ratio, therefore, Specify stress ratio R₀Under, different calendars, which corrode the corresponding material of the time limit or structural fatigue performance (i.e. S-N curves), to be written as

In formula,Represent to specify stress ratio R₀The maximum stress that material can be born when the lower life-span will be N；S₀(t) it is difference Fitting fatigue limit under calendar limit year；M and C represent curve of fatigue form parameter；N represents fatigue life.

Obviously, stress ratio R is specified₀Under, the fatigue limit of the pre-etching metal material of the different calendars corrosion time limits can be with The increase of the pre-etching time limit and reduce, accordingly, it would be desirable to introduce influence coefficient k material corrosion fatigue strength is modified, i.e.,

S₀(t)=S₀·k(t) (2)

K (t) is the influence coefficient of corrosion fatigue strength, S in formula₀Fatigue limit when not corroding for material.

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, it is therefore intended that under stress ratio, day The corrosion time limit is gone through to be represented by with Fatigue Strength Effect Relationship of Coefficients formula

K (t)=1- α t^β (3)

α, β are fitting coefficient in formula, and t is calendar limit year.What parameter alpha and β reflected is Fatigue Strength Effect coefficient and calendar The material constant of time limit relation.

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R₀Under material prior-corroded fatigue characteristic S-N-t characterization models：

Formula (4) reflects fatigue stress S, fatigue life N and the calendar corrosion triangular relations of time limit t, bent as S-N-t Surface model.Model (4) contains undetermined parameter m, C and S₀, can estimate by the following method.

Step 2: pre-etching Metal Material Fatigue performance S-N-t Surface Parameters are fitted

Make X=lgN, Y=lg [S_max-(1-αt^β)S₀], a=lgC, b=-m can then be obtained by transform (4)

X=a+bY (5)

From formula (5) it can be seen that X and Y are in line relation, according to correlation coefficient method, then

In formula：

Above in all formulasL_YYAnd L_YXWith α, β and S₀It is relevant, it is α, β and S₀Function.Therefore a, b and r are also α, β and S₀ Function.Due to required α, β and S₀Coefficient correlation absolute value must be made | r (α, β, S₀) | maximum is taken, therefore can obtain solving S₀, α and β equation：

In formula：

By numerical solution equation group (14), α, β and S can be tried to achieve₀.M and C can be obtained finally by following formula：

M=-L_yx/L_yy (21)

Step 3: pre-etching Metal Material Fatigue performance S-N-t curved surfaces under any stress ratio

Due to having usually contained the load (S under different stress ratios in actual fatigue load spectrum_a, S_m), and actual tests process In general only carry out specifying stress ratio R₀Under fatigue test, it is therefore desirable to the load correction under different stress ratio in loading spectrum To the stress ratio R specified₀Under.The graceful equation in linear Gourde(G) of load correction is

Defined, can obtained according to stress ratio

Formula (24) can be also written as

Formula (25) is substituted into formula (23), the stress ratio R that can be specified₀Under the graceful equation in linear Gourde(G)：

In formulaRepresent to specify stress ratio R₀Under stress amplitude.

Simultaneous equations (23) and (27), are obtained

Formula (26) is substituted into formula (28), you can obtain specifying stress ratio R₀Lower maximum stress formula：

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

Step 4: spectrum carries lower Aircraft metal structure calendar life calculation formula

Under normal circumstances, load/environment-time history that Aircraft metal structure is born is as shown in figure 1, it damages mould Formula is that mechanical fatigue damage that the corrosion damage that pre-etching causes and airflight fatigue load cause is parked alternately in ground Process；The reason for because of use demand, the annual flight rate of aircraft is different, and (fatigue is carried in i.e. annual load-time history Lotus cycle-index is different), accordingly, it would be desirable to the aged process annual to Aircraft Metal Structure carries out accumulated damage year by year, it is determined that The calendar corrosion fatigue life of its metal structure.

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

In formula, n_ijFor the cycle-index of i-stage load in jth year loading spectrum, N_ijFor material, in jth year, i-stage is tested The cycle-index of fatigue rupture occurs under load independent role, M is load cycle sum in jth year loading spectrum, and T is structure Calendar life during failure.

By formula (30) substitute into formula (31) can obtain calculate the structure calendar life-span formula be

In formula, S_a,ijAnd S_m,ijThe stress amplitude and average of i-stage load cycle respectively in jth year loading spectrum.

Calculated Step 5: spectrum carries lower Aircraft metal structure calendar life

Actual measurement fatigue load spectrum is carried into rain-flow counting result n_tj、(S_a)_tj、(S_m)_tjDetermined with corrosion fatigue test S-N-t curved surfaces, substitute into equation (32), can be in the hope of calendar life T by numerical solution.

3rd, advantage and effect：The invention provides it is a kind of predict Aircraft metal structure calendar life new method, its Feature is simple and practical, and parameter is less needed for model, it is thus only necessary to substitutes into the fatigue behaviour of different pre-etching time limit materials and counts Calculate in model, it is possible to obtain the calendar life of Aircraft metal structure.

Brief description of the drawings

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.

Symbol description is as follows in figure：

S is fatigue stress in Fig. 2, and N is the life-span, and t is that calendar corrodes the time limit

Embodiment

Fig. 2 is the FB(flow block) of the method for the invention, and five steps of the present invention point are realized, are specially：

Step 1: pre-etching Metal Material Fatigue performance S-N-t surface representing models

Material or structural fatigue performance are generally characterized using the three parameter Power Functions expression formulas specified under stress ratio, therefore, Specify stress ratio R₀Under, different calendars, which corrode the corresponding material of the time limit or structural fatigue performance (i.e. S-N curves), to be written as

In formula,Represent to specify stress ratio R₀The maximum stress that material can be born when the lower life-span will be N；S₀(t) it is difference Fitting fatigue limit under calendar limit year；M and C represent curve of fatigue form parameter；N represents fatigue life.

Obviously, stress ratio R is specified₀Under, the fatigue limit of the pre-etching metal material of the different calendars corrosion time limits can be with The increase of the pre-etching time limit and reduce, accordingly, it would be desirable to introduce influence coefficient k material corrosion fatigue strength is modified, i.e.,

S₀(t)=S₀·k(t) (2)

K (t) is the influence coefficient of corrosion fatigue strength, S in formula₀Fatigue limit when not corroding for material.

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, it is therefore intended that under stress ratio, day The corrosion time limit is gone through to be represented by with Fatigue Strength Effect Relationship of Coefficients formula

K (t)=1- α t^β (3)

α, β are fitting coefficient in formula, and t is calendar limit year.What parameter alpha and β reflected is Fatigue Strength Effect coefficient and calendar The material constant of time limit relation.

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R₀Under material prior-corroded fatigue characteristic S-N-t characterization models：

Formula (4) reflects fatigue stress S, fatigue life N and the calendar corrosion triangular relations of time limit t, bent as S-N-t Surface model.Model (4) contains undetermined parameter m, C and S₀, can estimate by the following method.

Step 2: pre-etching Metal Material Fatigue performance S-N-t Surface Parameters are fitted

Make X=lgN, Y=lg [S_max-(1-αt^β)S₀], a=lgC, b=-m can then be obtained by transform (4)

X=a+bY (5)

From formula (5) it can be seen that X and Y are in line relation, according to correlation coefficient method, then

In formula：

Above in all formulasL_YYAnd L_YXWith α, β and S₀It is relevant, it is α, β and S₀Function.Therefore a, b and r are also α, β and S₀ Function.Due to required α, β and S₀Coefficient correlation absolute value must be made | r (α, β, S₀) | maximum is taken, therefore can obtain solving S₀, α and β equation：

where

By numerical solution equation group (14), α, β and S can be tried to achieve₀.M and C can be obtained finally by following formula：

M=-L_yx/L_yy (21)

Step 3: pre-etching Metal Material Fatigue performance S-N-t curved surfaces under any stress ratio

Due to having usually contained the load (S under different stress ratios in actual fatigue load spectrum_a, S_m), and actual tests process In general only carry out specifying stress ratio R₀Under fatigue test, it is therefore desirable to the load correction under different stress ratio in loading spectrum To the stress ratio R specified₀Under.The graceful equation in linear Gourde(G) of load correction is

Defined, can obtained according to stress ratio

Formula (24) can be also written as

Formula (25) is substituted into formula (23), the stress ratio R that can be specified₀Under the graceful equation in linear Gourde(G)：

In formulaRepresent to specify stress ratio R₀Under stress amplitude.

Simultaneous equations (23) and (27), are obtained

Formula (26) is substituted into formula (28), you can obtain specifying stress ratio R₀Lower maximum stress formula：

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

Step 4: spectrum carries lower Aircraft metal structure calendar life calculation formula

Under normal circumstances, load/environment-time history that Aircraft metal structure is born is as shown in figure 1, it damages mould Formula is that mechanical fatigue damage that the corrosion damage that pre-etching causes and airflight fatigue load cause is parked alternately in ground Process；The reason for because of use demand, the annual flight rate of aircraft is different, and (fatigue is carried in i.e. annual load-time history Lotus cycle-index is different), accordingly, it would be desirable to the aged process annual to Aircraft Metal Structure carries out accumulated damage year by year, it is determined that The calendar corrosion fatigue life of its metal structure.

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

In formula, n_ijFor the cycle-index of i-stage load in jth year loading spectrum, N_ijFor material, in jth year, i-stage is tested The cycle-index of fatigue rupture occurs under load independent role, M is load cycle sum in jth year loading spectrum, and T sends out for structure Calendar life during raw failure.

Formula (30) is substituted into formula (31), can obtain calculating the formula in structure calendar life-span：

In formula, S_a,ijAnd S_m,ijThe stress amplitude and average of i-stage load cycle respectively in jth year loading spectrum.

Calculated Step 5: spectrum carries lower Aircraft metal structure calendar life

Actual measurement fatigue load spectrum is carried into rain-flow counting result n_tj、(S_a)_tj、(S_m)_tjDetermined with corrosion fatigue test S-N-t curved surfaces, substitute into equation (32), can be in the hope of calendar life T by numerical solution.

Claims (1)

1. a kind of method for predicting Aircraft metal structure calendar life, it is characterised in that：This method is comprised the following steps that：

Step 1: characterizing pre-etching Metal Material Fatigue performance S-N-t surface models

Material or structural fatigue performance are generally characterized using the three parameter Power Functions expression formulas specified under stress ratio, it is therefore intended that Stress ratio R₀Under, different calendars, which corrode the corresponding material of the time limit or structural fatigue performance S-N curves, to be written as

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

In formula,Represent to specify stress ratio R₀The maximum stress that material can be born when the lower life-span will be N, S₀(t) it is different calendars Fitting fatigue limit under the time limit, m and C represent curve of fatigue form parameter；N represents fatigue life；

Obviously, stress ratio R is specified₀Under, the fatigue limit of the pre-etching metal material of the different calendar corrosion time limits can be with pre-etching The increase of the time limit and reduce, accordingly, it would be desirable to introduce influence coefficient k material corrosion fatigue strength is modified, i.e.,

S₀(t)=S₀·k(t) (2)

K (t) is the influence coefficient of corrosion fatigue strength, S in formula₀Fatigue limit when not corroding for material；

In fact, corrosion fatigue influence coefficient and calendar limit year are monotone decreasing relation, it is therefore intended that under stress ratio, calendar is rotten The erosion time limit is represented by with Fatigue Strength Effect Relationship of Coefficients formula

K (t)=1- α t^β (3)

α, β are fitting coefficient in formula, and t is calendar limit year, and what parameter alpha and β reflected is Fatigue Strength Effect coefficient and calendar limit year The material constant of relation；

Formula (2) and formula (3) are substituted into formula (1), can obtain specifying stress ratio R₀Under material prior-corroded fatigue characteristic S-N-t Characterization model：

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

Formula (4) reflects fatigue stress S, fatigue life N and the calendar corrosion triangular relations of time limit t, as S-N-t curved dies Type, model (4) contains undetermined parameter m, C and S₀, can be estimated by step 2；

Step 2: fitting pre-etching Metal Material Fatigue performance S-N-t Surface Parameters

Make X=lgN,A=lgC, b=-m, then can be obtained by transform (4)

X=a+bY (5)

From formula (5) it can be seen that X and Y are 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：

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

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

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

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

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

Formula (6) is into formula (13)L_yyAnd L_yxWith α, β and S₀It is relevant, it is α, β and S₀Function, therefore a, b and r also for α, β and S₀Function；Due to required α, β and S₀Coefficient correlation absolute value must be made | r (α, β, S₀) | maximum is taken, therefore can obtain solving S₀,α With β equation：

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

In formula：

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

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

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

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

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

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

By numerical solution equation group (14), α, β and S can be tried to achieve₀, m and C can be obtained finally by following formula：

M=-L_yx/L_yy (21)

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

Step 3: characterizing pre-etching Metal Material Fatigue performance S-N-t surface models under any stress ratio

Due to having usually contained the load under different stress ratios in actual fatigue load spectrum, and typically only enter during actual tests The specified stress ratio R of row₀Under fatigue test, it is therefore desirable to the load correction under different stress ratio in loading spectrum is arrived answering of specifying Power compares R₀Under, the graceful equation in linear Gourde(G) of load correction is

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

Defined, can obtained according to stress ratio

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

Formula (24) can be also 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 that can be specified₀Under the graceful equation in linear Gourde(G)：

$\frac{S_{a,R_0}}{S_{-1}}+\frac{(1+R_0)\·S_{a,K_0}}{{\mathrm{\σ}}_b\·(1-R_0)}=1---\left(27\right)$

In formulaRepresent to specify stress ratio R₀Under stress amplitude；

Simultaneous equations (23) and (27), are obtained

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

Formula (26) is substituted into formula (28), you can obtain specifying stress ratio R₀Lower 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 signs that formula (4) just can obtain the material prior-corroded fatigue characteristic under any stress ratio Model：

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

Step 4: calculating spectrum carries lower Aircraft metal structure calendar life formula

Under normal circumstances, load/environment-time history that Aircraft metal structure is born is that what pre-etching was caused parked in ground The process of the mechanical fatigue damage that corrosion damage and airflight fatigue load are caused alternately；The reason for because of use demand, The annual flight rate of aircraft is different, i.e., fatigue load cycle-index is different in annual load-time history, accordingly, it would be desirable to The aged process annual to Aircraft Metal Structure carries out accumulated damage year by year, determines the calendar corrosion fatigue longevity of its metal structure Life；

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

$\underset{j=1}{\overset{T}{\Σ}}\underset{i=1}{\overset{M}{\Σ}}\frac{n_{ij}}{N_{ij}}=1---\left(31\right)$

In formula, n_ijFor the cycle-index of i-stage load in jth year loading spectrum, N_ijFor material in jth year i-stage test load The cycle-index of fatigue rupture occurs under independent role, M is load cycle sum in jth year loading spectrum, and T is that structure fails When calendar life；

By formula (30) substitute into formula (31) can obtain calculate the structure calendar life-span formula 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(32\right)$

In formula, S_a,ijAnd S_m,ijThe stress amplitude and average of i-stage load cycle respectively in jth year loading spectrum；

Step 5: prediction spectrum carries lower Aircraft metal structure calendar life

Actual measurement fatigue load spectrum is carried into rain-flow counting result n_ij、S_a,ij、S_m,ijThe S-N-t determined with corrosion fatigue test is bent Face, substitutes into equation (32), can be in the hope of calendar life T by numerical solution.