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Research on Fatigue Curves for Pre-corroded Aircraft Structures
V ol. 17
No. 4
CH INES E JO U RN A L O F AER ON A U TICS
November 2004
Research on Fatigue Curves for Pre corroded Aircraft Structures WANG Zhong bo, L IU Wen t ing, HE Xiao fan ( School of A er onautic Science and T echnology , Beij i ng Univer si ty of A eronauti cs and A st ronaut ics , Beij i ng 100083 , China) Abstract:
T o quantitatively evaluate the effects of corrosion during g rounding on fatigue life of aircraft
structures, a new pow er equation is proposed using two variable linear reg ression method. T hat the slope is a constant and the lo garithmic intercept is a linear function of pre corr osion time makes t his equation advantageous: it has a simple form, its parameters hav e unambiguous technical and geometrical mean ings, and it facilitates engineering applications. T hr ee parameter equat ions after pr e corrosio n are ob tained from back calculation of fatigue limits, w hich have been successfully used to pr edict safe life o f air craft structures in corrosive environment. Key words:
fatigue life; pr e corrosio n; fatig ue curve; regr ession analysis; life prediction; cor rosion , 贺小帆. 中国航 空学报( 英文版) , 2004, 17( 4) :
飞机结构预腐蚀疲劳曲线研究. 王忠波, 刘文 220- 223. 摘
要: 为评估地面停放预腐蚀对飞 机结构 疲劳寿 命的影响, 采 用二元 线性回 归方法建 立了一 种
新的预腐蚀疲劳曲线幂函数表达式。该曲线的指数为常量而对数 截距是预 腐蚀时间的 线性函数。 这两个特 性使得曲线形式简单, 参数几何、工程含义明确, 并易于工程 应用。通过寿 命反推建 立了 参数修正的三参数预腐蚀疲劳曲线, 该曲线已成功用 于飞机结构腐蚀条件下的疲劳寿命估算。 关键词: 疲劳寿命; 预腐蚀; 疲劳曲线; 回归分析; 寿命估算; 腐蚀 文章编号: 1000 9361( 2004) 04 0220 04
中图分类号: V215 2; O346 2
文献标识码: A
Corrosion t hat occurs during grounding, re f erred to as pre corrosion, in fatigue crit ical loca
eff ect s of pre corrosion are considered. ( 1) T he life modified equat ions[ 5 7] are gener
t ions of an aircraf t st ruct ure causes a reduct ion in fat igue lif e[ 1 4] . M uch research has been conduct ed
ally w rit ten as N( 0) = CN ( t )
N ( t ) = CN ( t )
(C
- m
S
) ( 1)
to quant itatively evaluate the ef fects of pre corro sion and a number of equations have been proposed
N ( t ) = CN ( t )
for t he descript ion of fatigue curves ( also referred
where CN ( t ) denot es t he pre corrosion f act or,
to as S N curves) aft er pre corrosion, w hich are called t S N curves w here t is pre corrosion
first def ined by L iu[ 2] et al t o represent fatigue be
[ 5 11]
N( 0) = CN ( t )
cA 1 ( S - c) ( 2)
havior aft er pre corrosion, to prevent it being con
time . In this research, a new pow er equat ion is proposed based on t hese st udies and t he back cal
f used w ith paramet er C ; parameters m , C, A , and c are est im ated from f at ig ue data obt ained in
culat ion of f at ig ue lim it s of t hree param eter equa t ions aft er pre corrosion are presented f or saf e life
laborat ory air and at room t em perat ure ( hereaf ter
predict ion of aircraft st ruct ures suf fering from pre
in general environment) . ( 2) T he general f orm of t he paramet er modi
corrosion.
f ied equations[ 8-
1 1 1
New Pow er Equation
Existing equations T he equat ions ment ioned above can be divided
into tw o t ypes according t o the w ays in w hich t he R eceived dat e: 2004 02 18; R evision received dat e: 2004 04 22 Foundation it em: A eronautical Pre research Foun dation
S
11]
m( t)
is ( 3)
N ( t ) = C ( t)
A P( t ) S = cP ( t ) 1+ N P ( t ) ( t ) P whereparameters m ( t ) , C ( t ) , A P ( t ) ,
( 4) P(
t)
N ovember 2004
Research on Fat igue Curves f or Pre corroded A ircraft St ruct ures
221
and cP ( t ) are funct ions of pre corrosion time; and P is t he survival probability. Equat ions estimated by Wang [ 8, 9] et al are specif ic ones only corresponding t o several given pre corrosion t ime, and t he pow er equation pro posed by Yang [ 10] et al is not practical due to t he complex relat ion lg C ( t ) 1 2
t .
New equation
Fat igue t ests of un corroded and pre corroded specimens w ith a cent ral hole for w ing skin are per f ormed at tw o stress levels using a stress ratio of
Fig. 1
t S N cur ves and S N curve
slope m ( t ) degenerat es into a constant m t , and
0 06 in general environment[ 5] . Result s are list ed
that t he log arithmic int ercept is linearly related t o pre corrosion t im e, i e. , lg C ( t ) = a+ bt . T he
in T able 1.
former characterist ic can be called t he constant
Table 1
Fatigue test results af ter pre corrosion
Pre corrosion
S 1 = 140 0M Pa
slope, and the lat ter is named the log linear inter
S 2 = 100 0M Pa
cept here.
t ime/ d 0
N / cycle
n
s
N / cycle
n
s
47 898
4
0. 038 4
154 578
4
0. 026 8
5
60 014
4
0. 034 1
167 831
4
0. 042 1
respectively approximate to m 0 = 3 325 8 and C 0
10
51 410
4
0. 030 9
151 321
4
0. 049 3
20
31 486
4
0. 039 9
98 057
4
0. 048 2
= 1011
45
19 168
4
0. 052 2
51 631
6
0. 039 8
environment [ 5] indicates t he f easibilit y of t he new
According to t he characterist ics of fat igue be havior aft er
pre corrosion
for
aircraf t
struc
t ures[ 2 4, 6, 11] , t wo assumpt ions can be made: fa t igue lif e aft er pre corrosion of a given t ime f it s a log normal dist ribut ion, i e. , lg N ( t ) N ( ( t ) , 2
( t ) ) ; t he standard deviat ion is a constant inde
pendent on stress level and pre corrosion time, i e. , ( t ) = . Conduct ing
tw o variable
linear
regression
yields lg N ( t ) = 11 64492- 0 01121 t - 3 20298lg S ( 5)
T hat m t = 3 202 98 and C ( 0) = 1011 852 5
644 92
are
of t he S N curve obt ained in general
equation, w hich is show n in F ig 1. ( 2)
T he geometrical meaning of the constant
slope is clearly illust rat ed by the parallel straig ht lines in F ig. 1. In addit ion, if a preliminary life predict ion of an aircraft operat ing in w eak corrosive environment is demanded, m t may t ake m 0 value. Finally, this charact eristic facilit at es parameter es t imat e and helps reduce bot h corrosion and fatigue test s. ( 3) T he log linear int ercept shows that t he log lif e af ter pre corrosion is a linear funct ion of pre corrosion t ime at a specif ic st ress level as shown in Fig 2 . If fat igue life af ter pre corrosion of t is
Regression result s are list ed in T able 2 and f it ting curves are show n in F ig 1. Table 2 Regression results b0
b1
11. 64492 - 0. 01121- 3. 20298 t0 t1 t2 21. 49
R2
R2
F
0. 971
0. 963
118. 86
b2
9. 33
12. 27
s
n
0. 060
10
F rom Eq ( 5) a new pow er equation describ ing t S N curves is obt ained S mt 1. 3
N ( t ) = 10 a+ b t
( 6)
Advantages of new equation ( 1)
From Eq ( 6) , it can be seen that t he
F ig. 2 F itting curves at S 1 = 140 0M Pa and S 2= 100 0M P a
div ided by that of 0, t he single paramet er ex ponent
222
WAN G Zhong bo, L IU Wen t ing , HE Xiao fan
equation of C t curve can be obtained that is adopt ed by He
[ 12]
to demonstrate t he generalit y of C t
curves
CJA
vice is made of 30CrM nSiNi2A forging w ith I shaped sect ion. T he fat igue crit ical location is one of t he fastener holes of t he low er flange for t he
( a- m lgS )+ bt
C N ( t ) = N ( t ) = 10 ( aN ( 0) 10
= 10 bt ( 7)
beam w ith theoret ical stress concentrat ion f act or K t = 2 35. T he values for shape parameters of ma
( 4) According t o the second assumpt ion, t he
t erial P S N curve w it h the same K t at the st ress
t
m
t
lg S )
similar conclusions can be draw n for P S N curves aft er pre corrosion, also called t P S N curves.
2
T hree parameter Equat ion
Since est ablishing all t he t hree relat ions be t w een parameters cP ( t ) , A P ( t ) and
P(
t ) in Eq
( 4) to pre corrosion t ime t w ould be a prohibit ive task in engineering, Eq ( 4) is reduced to a simpler form AP S = cP ( t ) 1 + N P P w here A P and
P
( 8)
rat io R * = 0 18 are A P = 99 96,
P
= 0 4702.
Safe life of its similar aircraf t is determ ined by N P ( t ) = 1558 - 16 4525t 0 6678 . cP ( t ) for each year are back calculated, then life predict ion are carried out according to M iner! s law. T he predict ed saf e life corresponding to 100 flight hours per year in general env ironment is 2911 flight hours and in corrosion environment is 2731 flig ht hours neg lect ing the ef fects of corrosion during flig ht [ 2, 4, 6] . T he rat io of t he latt er t o the former, called fatigue lif e fact or, is 0 904. Fat igue curves
are shape param eters of the P S *
N curve estimated at a given st ress rat io R in g eneral environm ent [ 11] . Such a P S N curve,
aft er pre corrosion of 0, 10, 20, and 30 years are shown in Fig. 3.
however, is usually unavailable in design phrase be cause struct ural f at igue test s are ex pensive and t ime consuming . T o solve t he problem, A P and P are subst it uted by mat erial const ants or by the shape paramet ers f or the corresponding fatigue crit ical lo cat ion of its prot ot ype or of a similar aircraft be cause t hese t wo locat ions have a approximate t heo retical st ress concentrat ion fact or, have similar de sign detail f eature, are made of t he same material and experienced t he same process. T herefore, t he
F ig 3
Fatig ue curves for the main beam after pr e corrosion of 0, 10, 20 and 30 years
third parameter cP ( t ) can be back calculated as follows on t he assumption that they have t he same t P S N curves[ 13] . Safe lif e of t he protot ype or of t he similar air craft aft er pre corrosion of t t ime is calculat ed by N P ( t ) = N ( t ) / L f = [ N ( 0) - atb ] / L f ( 9) w here N ( 0) is the mean lif e in general environ
3
Conclusions
( 1) T he new pow er equat ion has tw o subst an t ial characterist ics: the const ant slope and t he log linear int ercept . T hese tw o charact eristics lead t o
ment ; a and b are const ants det ermined by fatigue
many advant ages t he new equation has a simple form; its parameters have unambiguous t echnical
test s[ 3] ; and L f is life scatt er f act or, usually 4- 6
and geometric meanings; and it facilit at es engi
for aircraft structures. L et N P ( t ) be t he object life, we can det ermine cP ( t ) by any suit able
neering applicat ions. ( 2) T hree parameter equat ions aft er pre cor
met hod such as the bisect ion met hod. An f ollowing
rosion obt ained from back calculat ion of fatigue
example shows t he feasibilit y of t his method. T he main beam of an aircraft current ly in ser
limits are pract ical for life predict ion of aircraft struct ures operating in corrosive environment .
N ovember 2004
Research on Fat igue Curves f or Pre corroded A ircraft St ruct ures
223
寿命分析[ J] . 中国工程科学, 2002, 4( 6) : 33- 35.
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Hu R W. Durability and reliabilit y of aircraf t st ruct ure un der
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[ D ] . 北京: 北京航空航天大学, 2003.
naut ics, 1996, 22( 3) : 259- 263. ( in Ch inese)
He X F. R esearch on aircraf t st ructural lif e reliabilit y k ey t echniques un der corrosion condit ion [ D ] . Beijing: Beijing
刘文
, 蒋冬滨. 飞机结构关键危险部位加速腐蚀试验环
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W ang Z B, Liu W T . An improved nominal stress approach and its applicat ion [ J] . Journal of Beijing U niversit y of A ero
Li Y H. A research on evaluating t echnique for lif e syst em of
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陈群志, 刘文
, 徐晓飞. 预腐蚀对飞机 结构寿命影响 研
Chen Q Z, Liu W T , Xu X F. Invest igat ion of t he pre corro sion ef fects on t he aircraft st ructures lif e [ J] . A ct a M echanica Solida Sinica, 1998, 19( S ) : 38- 43. ( in Chinese) 陈群志. 腐蚀环 境 下 飞 机结 构 日 历 寿 命技 术 体 系 研 究 [ D ] . 北京: 北京航空航天大学, 1999. Chen Q Z. Calendar lif e of aircraf t st ructure under corrosive environment s [ D ] . Beijing: Beijing U niversity of A eronaut ics and Ast ronautics, 1999. ( in Chinese) 王斌团. 结构疲劳日历寿命及 其概率研 究[ D ] . 西 安: 西 北工业大学, 2000. W ang B T. Struct ural fat igue calendar life an d its probabilit y [ D ] . Xi∀ an: N ort hw est ern Polyt echnical U niversit y, 2000. ( in Chinese) 王斌团, 范建华, 杨庆雄. 金属材料大气 环境静态腐蚀 老 化的疲劳 特 性 [ J] . 金 属 学 报, 1999, 35 ( 11) : 1163 1166. W ang B T, Fan J H, Y ang Q X. Fat igue property of m etals pre corroded in atmosphere environment [ J] . A ct a M etallur gica Sinica, 1999, 35( 11) : 1163- 1166. ( in Chinese) [ 9]
王斌团, 杨庆雄. LC4CS 铝合金和 30CrM nSiN i2A 钢在 大 气环境 预腐 蚀后 的 疲劳 曲 线. 机 械强 度, 2000, 22 ( 3 ) : 222- 223, 227. W ang B T . Y ang Q X . S - N curves for LC4CS aluminum and 30CrM nSiN i2A steel pre corroded in at mosphere envi ronment . Journal of M echanical S trengt h, 2000, 22( 3) : 222 - 223, 227. ( in Chinese)
[ 10]
. 改进名义 应力法 及其 应用 [ J ] . 北京 航
[ D ] . 北京: 北京航空航天大学, 2001.
究[ J] . 固体力学学报, 1998, 19( 增刊) : 38- 43.
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王忠波, 刘文
李玉海. 腐蚀条 件 下 飞 机结 构 寿 命 体 系评 定 技 术 研 究
( in Chinese)
[ 7]
nese) [ 13]
空航天大学学报, 2001, 27( 增刊) : 17- 20.
Beijing U niversit y of Aeronaut ics and A st ronautics, 2001.
[ 6]
U niversit y of A eronautics and Ast ronaut ics, 2003. ( in Ch i
A stronaut ica Sinica, 1998, 19( 4) : 434- 438. ( in Chinese)
aircraft st ructures under corrosive condit ion [ D ] . Beijing:
[ 5]
贺小帆. 腐蚀条件下飞机 结构寿 命可 靠性关 键技 术研 究
[ J] . Journal of Beijing U niversity of Aeronaut ics and Ast ro
境谱研究[ J] . 航空学报, 1998, 19( 4) : 434- 438. Liu W T, Jiang D B. St udy on accelerated corrosion t est en
[ 4]
胡仁伟. 腐蚀条件下飞机结构耐久性与可靠性[ D ] . 北京:
杨晓华, 姚卫星, 陈跃良. 基于动态曲线 的飞机结构日 历
nese)
Biographies: WANG Zhong bo Born in 1977, he re ceived the B. S. deg ree in flig ht v ehicle design and engineering at Beijing U niver sity of Aeronautics and Astronautics ( BUA A) in 2000. Now he is a Ph. D. candidate in eng ineering mechanics. His r esearch inter ests include fatigue analysis in cor rosive environment and fat igue properties of T itanium alloy w elding str uctures. T el: ( 010) 82315738, E mail: aerobo @ 163. com LIU Wen ting Bor n in 1940, Pro fessor of BU AA. He w as contributed to these areas: fatig ue and fr actur e mechanics; structural durability and reliability ; dam age tolerance design; probabilistic fr ac tur e mechanics. No w he is interested in life estimation of air craft structures in corrosive env ironment. T el: ( 010) 82315738, E mail: lw t_ jiang @ 163. com HE Xiao fan Born in 1976, he received t he B. S. deg ree at BU AA in 1998 and the Ph. D. degree in 2003. Now he is working as a Post doctor in Station o f Aeronaut ic & Astro nautic Science and T echnolog y. H is research interests include structural life reliability under corrosive condition and struc tural durability. T el: ( 010) 82315738, E mail: buaa_he @ cert. or g. cn
No. 4
CH INES E JO U RN A L O F AER ON A U TICS
November 2004
Research on Fatigue Curves for Pre corroded Aircraft Structures WANG Zhong bo, L IU Wen t ing, HE Xiao fan ( School of A er onautic Science and T echnology , Beij i ng Univer si ty of A eronauti cs and A st ronaut ics , Beij i ng 100083 , China) Abstract:
T o quantitatively evaluate the effects of corrosion during g rounding on fatigue life of aircraft
structures, a new pow er equation is proposed using two variable linear reg ression method. T hat the slope is a constant and the lo garithmic intercept is a linear function of pre corr osion time makes t his equation advantageous: it has a simple form, its parameters hav e unambiguous technical and geometrical mean ings, and it facilitates engineering applications. T hr ee parameter equat ions after pr e corrosio n are ob tained from back calculation of fatigue limits, w hich have been successfully used to pr edict safe life o f air craft structures in corrosive environment. Key words:
fatigue life; pr e corrosio n; fatig ue curve; regr ession analysis; life prediction; cor rosion , 贺小帆. 中国航 空学报( 英文版) , 2004, 17( 4) :
飞机结构预腐蚀疲劳曲线研究. 王忠波, 刘文 220- 223. 摘
要: 为评估地面停放预腐蚀对飞 机结构 疲劳寿 命的影响, 采 用二元 线性回 归方法建 立了一 种
新的预腐蚀疲劳曲线幂函数表达式。该曲线的指数为常量而对数 截距是预 腐蚀时间的 线性函数。 这两个特 性使得曲线形式简单, 参数几何、工程含义明确, 并易于工程 应用。通过寿 命反推建 立了 参数修正的三参数预腐蚀疲劳曲线, 该曲线已成功用 于飞机结构腐蚀条件下的疲劳寿命估算。 关键词: 疲劳寿命; 预腐蚀; 疲劳曲线; 回归分析; 寿命估算; 腐蚀 文章编号: 1000 9361( 2004) 04 0220 04
中图分类号: V215 2; O346 2
文献标识码: A
Corrosion t hat occurs during grounding, re f erred to as pre corrosion, in fatigue crit ical loca
eff ect s of pre corrosion are considered. ( 1) T he life modified equat ions[ 5 7] are gener
t ions of an aircraf t st ruct ure causes a reduct ion in fat igue lif e[ 1 4] . M uch research has been conduct ed
ally w rit ten as N( 0) = CN ( t )
N ( t ) = CN ( t )
(C
- m
S
) ( 1)
to quant itatively evaluate the ef fects of pre corro sion and a number of equations have been proposed
N ( t ) = CN ( t )
for t he descript ion of fatigue curves ( also referred
where CN ( t ) denot es t he pre corrosion f act or,
to as S N curves) aft er pre corrosion, w hich are called t S N curves w here t is pre corrosion
first def ined by L iu[ 2] et al t o represent fatigue be
[ 5 11]
N( 0) = CN ( t )
cA 1 ( S - c) ( 2)
havior aft er pre corrosion, to prevent it being con
time . In this research, a new pow er equat ion is proposed based on t hese st udies and t he back cal
f used w ith paramet er C ; parameters m , C, A , and c are est im ated from f at ig ue data obt ained in
culat ion of f at ig ue lim it s of t hree param eter equa t ions aft er pre corrosion are presented f or saf e life
laborat ory air and at room t em perat ure ( hereaf ter
predict ion of aircraft st ruct ures suf fering from pre
in general environment) . ( 2) T he general f orm of t he paramet er modi
corrosion.
f ied equations[ 8-
1 1 1
New Pow er Equation
Existing equations T he equat ions ment ioned above can be divided
into tw o t ypes according t o the w ays in w hich t he R eceived dat e: 2004 02 18; R evision received dat e: 2004 04 22 Foundation it em: A eronautical Pre research Foun dation
S
11]
m( t)
is ( 3)
N ( t ) = C ( t)
A P( t ) S = cP ( t ) 1+ N P ( t ) ( t ) P whereparameters m ( t ) , C ( t ) , A P ( t ) ,
( 4) P(
t)
N ovember 2004
Research on Fat igue Curves f or Pre corroded A ircraft St ruct ures
221
and cP ( t ) are funct ions of pre corrosion time; and P is t he survival probability. Equat ions estimated by Wang [ 8, 9] et al are specif ic ones only corresponding t o several given pre corrosion t ime, and t he pow er equation pro posed by Yang [ 10] et al is not practical due to t he complex relat ion lg C ( t ) 1 2
t .
New equation
Fat igue t ests of un corroded and pre corroded specimens w ith a cent ral hole for w ing skin are per f ormed at tw o stress levels using a stress ratio of
Fig. 1
t S N cur ves and S N curve
slope m ( t ) degenerat es into a constant m t , and
0 06 in general environment[ 5] . Result s are list ed
that t he log arithmic int ercept is linearly related t o pre corrosion t im e, i e. , lg C ( t ) = a+ bt . T he
in T able 1.
former characterist ic can be called t he constant
Table 1
Fatigue test results af ter pre corrosion
Pre corrosion
S 1 = 140 0M Pa
slope, and the lat ter is named the log linear inter
S 2 = 100 0M Pa
cept here.
t ime/ d 0
N / cycle
n
s
N / cycle
n
s
47 898
4
0. 038 4
154 578
4
0. 026 8
5
60 014
4
0. 034 1
167 831
4
0. 042 1
respectively approximate to m 0 = 3 325 8 and C 0
10
51 410
4
0. 030 9
151 321
4
0. 049 3
20
31 486
4
0. 039 9
98 057
4
0. 048 2
= 1011
45
19 168
4
0. 052 2
51 631
6
0. 039 8
environment [ 5] indicates t he f easibilit y of t he new
According to t he characterist ics of fat igue be havior aft er
pre corrosion
for
aircraf t
struc
t ures[ 2 4, 6, 11] , t wo assumpt ions can be made: fa t igue lif e aft er pre corrosion of a given t ime f it s a log normal dist ribut ion, i e. , lg N ( t ) N ( ( t ) , 2
( t ) ) ; t he standard deviat ion is a constant inde
pendent on stress level and pre corrosion time, i e. , ( t ) = . Conduct ing
tw o variable
linear
regression
yields lg N ( t ) = 11 64492- 0 01121 t - 3 20298lg S ( 5)
T hat m t = 3 202 98 and C ( 0) = 1011 852 5
644 92
are
of t he S N curve obt ained in general
equation, w hich is show n in F ig 1. ( 2)
T he geometrical meaning of the constant
slope is clearly illust rat ed by the parallel straig ht lines in F ig. 1. In addit ion, if a preliminary life predict ion of an aircraft operat ing in w eak corrosive environment is demanded, m t may t ake m 0 value. Finally, this charact eristic facilit at es parameter es t imat e and helps reduce bot h corrosion and fatigue test s. ( 3) T he log linear int ercept shows that t he log lif e af ter pre corrosion is a linear funct ion of pre corrosion t ime at a specif ic st ress level as shown in Fig 2 . If fat igue life af ter pre corrosion of t is
Regression result s are list ed in T able 2 and f it ting curves are show n in F ig 1. Table 2 Regression results b0
b1
11. 64492 - 0. 01121- 3. 20298 t0 t1 t2 21. 49
R2
R2
F
0. 971
0. 963
118. 86
b2
9. 33
12. 27
s
n
0. 060
10
F rom Eq ( 5) a new pow er equation describ ing t S N curves is obt ained S mt 1. 3
N ( t ) = 10 a+ b t
( 6)
Advantages of new equation ( 1)
From Eq ( 6) , it can be seen that t he
F ig. 2 F itting curves at S 1 = 140 0M Pa and S 2= 100 0M P a
div ided by that of 0, t he single paramet er ex ponent
222
WAN G Zhong bo, L IU Wen t ing , HE Xiao fan
equation of C t curve can be obtained that is adopt ed by He
[ 12]
to demonstrate t he generalit y of C t
curves
CJA
vice is made of 30CrM nSiNi2A forging w ith I shaped sect ion. T he fat igue crit ical location is one of t he fastener holes of t he low er flange for t he
( a- m lgS )+ bt
C N ( t ) = N ( t ) = 10 ( aN ( 0) 10
= 10 bt ( 7)
beam w ith theoret ical stress concentrat ion f act or K t = 2 35. T he values for shape parameters of ma
( 4) According t o the second assumpt ion, t he
t erial P S N curve w it h the same K t at the st ress
t
m
t
lg S )
similar conclusions can be draw n for P S N curves aft er pre corrosion, also called t P S N curves.
2
T hree parameter Equat ion
Since est ablishing all t he t hree relat ions be t w een parameters cP ( t ) , A P ( t ) and
P(
t ) in Eq
( 4) to pre corrosion t ime t w ould be a prohibit ive task in engineering, Eq ( 4) is reduced to a simpler form AP S = cP ( t ) 1 + N P P w here A P and
P
( 8)
rat io R * = 0 18 are A P = 99 96,
P
= 0 4702.
Safe life of its similar aircraf t is determ ined by N P ( t ) = 1558 - 16 4525t 0 6678 . cP ( t ) for each year are back calculated, then life predict ion are carried out according to M iner! s law. T he predict ed saf e life corresponding to 100 flight hours per year in general env ironment is 2911 flight hours and in corrosion environment is 2731 flig ht hours neg lect ing the ef fects of corrosion during flig ht [ 2, 4, 6] . T he rat io of t he latt er t o the former, called fatigue lif e fact or, is 0 904. Fat igue curves
are shape param eters of the P S *
N curve estimated at a given st ress rat io R in g eneral environm ent [ 11] . Such a P S N curve,
aft er pre corrosion of 0, 10, 20, and 30 years are shown in Fig. 3.
however, is usually unavailable in design phrase be cause struct ural f at igue test s are ex pensive and t ime consuming . T o solve t he problem, A P and P are subst it uted by mat erial const ants or by the shape paramet ers f or the corresponding fatigue crit ical lo cat ion of its prot ot ype or of a similar aircraft be cause t hese t wo locat ions have a approximate t heo retical st ress concentrat ion fact or, have similar de sign detail f eature, are made of t he same material and experienced t he same process. T herefore, t he
F ig 3
Fatig ue curves for the main beam after pr e corrosion of 0, 10, 20 and 30 years
third parameter cP ( t ) can be back calculated as follows on t he assumption that they have t he same t P S N curves[ 13] . Safe lif e of t he protot ype or of t he similar air craft aft er pre corrosion of t t ime is calculat ed by N P ( t ) = N ( t ) / L f = [ N ( 0) - atb ] / L f ( 9) w here N ( 0) is the mean lif e in general environ
3
Conclusions
( 1) T he new pow er equat ion has tw o subst an t ial characterist ics: the const ant slope and t he log linear int ercept . T hese tw o charact eristics lead t o
ment ; a and b are const ants det ermined by fatigue
many advant ages t he new equation has a simple form; its parameters have unambiguous t echnical
test s[ 3] ; and L f is life scatt er f act or, usually 4- 6
and geometric meanings; and it facilit at es engi
for aircraft structures. L et N P ( t ) be t he object life, we can det ermine cP ( t ) by any suit able
neering applicat ions. ( 2) T hree parameter equat ions aft er pre cor
met hod such as the bisect ion met hod. An f ollowing
rosion obt ained from back calculat ion of fatigue
example shows t he feasibilit y of t his method. T he main beam of an aircraft current ly in ser
limits are pract ical for life predict ion of aircraft struct ures operating in corrosive environment .
N ovember 2004
Research on Fat igue Curves f or Pre corroded A ircraft St ruct ures
223
寿命分析[ J] . 中国工程科学, 2002, 4( 6) : 33- 35.
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Biographies: WANG Zhong bo Born in 1977, he re ceived the B. S. deg ree in flig ht v ehicle design and engineering at Beijing U niver sity of Aeronautics and Astronautics ( BUA A) in 2000. Now he is a Ph. D. candidate in eng ineering mechanics. His r esearch inter ests include fatigue analysis in cor rosive environment and fat igue properties of T itanium alloy w elding str uctures. T el: ( 010) 82315738, E mail: aerobo @ 163. com LIU Wen ting Bor n in 1940, Pro fessor of BU AA. He w as contributed to these areas: fatig ue and fr actur e mechanics; structural durability and reliability ; dam age tolerance design; probabilistic fr ac tur e mechanics. No w he is interested in life estimation of air craft structures in corrosive env ironment. T el: ( 010) 82315738, E mail: lw t_ jiang @ 163. com HE Xiao fan Born in 1976, he received t he B. S. deg ree at BU AA in 1998 and the Ph. D. degree in 2003. Now he is working as a Post doctor in Station o f Aeronaut ic & Astro nautic Science and T echnolog y. H is research interests include structural life reliability under corrosive condition and struc tural durability. T el: ( 010) 82315738, E mail: buaa_he @ cert. or g. cn