FATIGUE LIFE PREDICTION OF 3-D PROBLEMS BY DAMAGE MECHANICS WITH SPECTRUM LOADING

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1 ICAS 00 CONGRESS FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH SPECTRUM LOAING Iqbal Raool Mon, Xing Zhang* and yu Cui* partnt of Aropac, Collg of Aronautical Enginring, National Univrity of Scinc and Tchnology, Pakitan *partnt of Flight Vhicl ign and Applid Mchanic, Bijing Univrity of Aronautic and Atronautic, Bijing-0008, PR China Kyword: daag chanic, pctru loading, fatigu lif prdiction, loading qunc Abtract Th iportanc of applid load on th tructur br cannot b dnid in fatigu lif prdiction. A baic probl in fatigu rarch i th prdiction of lifti of a tructural part whn th aplitud of cyclic load vari in prcribd fahion with th nubr of cycl. Thi papr prnt th prdiction of fatigu liv for - probl in lato-platic rang with variabl load aplitud. Th ffct of loading qunc on th fatigu lif of a tructur br and th validity of Minr rul ar tudid. Th coputational thod i drivd according to daag chanic, thory of platicity and finit lnt analyi (FEA. A two-block cyclic loading i conidrd with highlow and low-high load qunc. To conidr th ffct of th high tr lvl byond th yilding point of atrial in on load block, dforation thory and itration thod ar applid to th tr analyi of th firt load cycl. Th daag volution undr givn tr and daag fild for ach block loading i dtrind by daag volution quation. Furthror, an additional loading thod i introducd to prfor th tr analyi with givn daag fild to avoid th rabling of th tiffn atrix of tructur br. aag incrnt at critical lnt i conidrd a tp lngth intad of load cycl incrnt. Coprhniv coputr progra ar dvlopd to conidr both latic and lato-platic ca. INTROUCTION Structur ar rarly trd rpatdly at a ingl load lvl, and th failur of a tructur i, thrfor, th rult of fatigu daag accuulation caud by a ultiplicity of loading cycl having diffrnt aplitud and frqunci. A it i known, th prdiction of fatigu lif undr pctru loading ha bn th ubjct of xtniv rarch. A iplt and wll-known odl of fatigu daag accuulation i propod by Palgrn [] and Minr [] known a Minr Rul. According to th rul, th failur in a ulti-tag loading i dfind by ni i Ni whr, n i i th nubr of load cycl at load lvl i, and N i th total fatigu lif at th a load lvl in contant aplitud.. According to Minr rul, th daag producd by i for n i cycl i dfind a n i /N i and th individual daag ar additiv and indpndnt of loading qunc. Thi iplt approach do not, in gnral, coply with rality. It i hown fro xprintal rarch that th qunc of loading can ignificantly affct th lifti of a pcin. In ulti-tag contant aplitud loading, th lft id of abov quation, which i oti trd Minr indx, i uually diffrnt fro unity and i dpndnt on loading qunc.

2 Iqbal Raool Mon, Zhang Xing &Cui yu A ipl ca of two block cyclic loading i conidrd with th tr lvl in high-low and low-high qunc, a hown in Fig- and. Th aplitud of loading in ach rpctiv block i kpt contant but diffrnt fro ach othr. Both latic and lato-platic ca caud by load block ar invtigatd to th ffct of th cobination and qunc of diffrnt load aplitud. Fatigu lif proprti of th tructur br undr contant aplitud loading ar ndd a a balin data [5]. Th ffct of high-load cycl on fatigu lif at ubqunt low-load cycl ar dtrind by coparing th coputational rult fro th variablaplitud analyi with th balin data. aag chanic-finit lntadditional load thod for th prdiction of crack initiation lif with daag incrnt a tp lngth i introducd [4]. Rabling of tiffn atrix during atrial dgradation i liinatd by u of thi approach, hnc th CPU ti i dratically rducd. Coprhniv coputr progra ar dvlopd to catr for both latic and lato-platic ca. INITIAL ELASTO-PLASTIC ANALYSIS uring th firt cycl of rpatd loading, if th tr lvl at th critical point( of tructur br i byond th yilding point, th critical zon bco platic.. Govrning Equation Th gnral govrning quation fro olid chanic ar givn a follow: i j ( u i, j + u j, i ( ji, j + B i 0 ( i j l j pi on S p, u i ui on S u (. Contitutiv Rlation and Platic Corrction Th dviatoric train and tr coponnt can b givn a ij ij δ ij kk, ij ij δ ij kk (4 whr, kk and kk ar th hydrotatic tr and volu train, rpctivly, δ ij i th kronckr dlta, ij and ij ar th dviatoric tr and train coponnt, rpctivly. Th rlationhip btwn dviatoric tr and train coponnt can b givn by th dforation thory of Hncky a follow: ij ij (5 whr, and ar th quivalnt tr and train, rpctivly. Th rlationhip btwn hydrotatic tr and volu train can b drivd fro Hook Law a follow: kk K kk (6 whr, K i th bulk odulu in tr of La contant. Eqn-4 can b r-writtn aftr ubtitution of qn-5 and 6 a follow: ij ij + δ ij K kk (7 whr, E( w ( or E ( w (8 E ( In which w can b dcribd a th rlativ rduction of young udulu du to platic ffct and i th initial daag bfor th firt cycl of loading, if any. It i aud that th rlationhip btwn and i th a a that in uni-axial tr ca. Eqn-7 can finally b writtn in th following for ( ( P, (9 ij ij ( In abov quation, ij i th linar tr coponnt and ( P, ij i th tr rduction coponnt caud by platicity and daag, givn a follow: ij

3 FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH TWO-BLOCK LOAING ij, ij ij kk ij ( ( P E + δ K, E ( w + w (0 For th ca of linar hardning, w can b xprd a p w ( ξ ( whr, ξ can b dtrind by th latoplatic curv hown in Fig-, a follow: u ξ ( E( u In which, u, and u, ar th ultiat and yilding tr and train, rpctivly.. Elato-Platic Finit Elnt Analyi According to abov lato-platic contitutiv rlation, th tr coponnt of an lnt can b xprd a: {} {} ( {} ( P, [ ] [ ]{} {} ( P, E B δ ( in which, [E] i th atrix of lnt atrial tiffn,[b] th atrix of train-diplacnt tranforation and {δ} th vctor of lnt nodal point diplacnt. By applying th principl of virtual work at lnt lvl, w will gt [ ] {} { } {} ( P, K δ F + F (4 T K B E B dv - th lnt whr, [ ] [ ] [ ] [ ] V tiffn atrix F T T N P dv N P - th convntional {} [ ] { } [ ] { }d + v V S lnt nodal forc vctor {} ( P, T [ ] {} ( P, F B dv - th additional nodal V forc vctor to conidr th rlativ rduction of tiffn du to platic ffct and initial daag, if any. Expanding ach atrix and vctor in qn- 4 at tructur lvl, th govrning yt of non-linar quation i abld a follow: ij [ ]{} {}{} ( P, K δ F + F (5 whr, [K] i th atrix of global tiffn of - ound body, {δ} th vctor of global nodal point diplacnt, {F} th ovrall nodal forc vctor caud by original loading and {F} (P, th additional nodal forc vctor at tructur lvl to conidr th ffct of platicity and initial daag tat. To olv qn-5, an additional loaditration thod i introducd..4 Itration Mthod Solution In th firt tp of itration it i aud that th atrial i linarly latic, that i w ( P, 0, ij Eij 0 (6 whr, 0 rprnt th initial daag tat bfor itration proc. In th cond tp, if th tr lvl i abov th yild liit thn w p ( (, P ξ, E ( w + w ij Siilarly, for th n th tp p ( w n ξ and n ( P, ij n E ij ( ij n ( n wn + ( n wn ( 0 (7 (8 Th yt of quation at tructur lvl for th n th tp ha th for [ ]{} {}{} ( P, K δ n F + F n (9 Th itration proc will b paud whn th rlativ rror in th n and n- at critical lnt i l thn %. Th olution of itration thod i hown in Fig-4. A Coputr progra i dvlopd for th lato-platic finit lnt analyi by an of th itration thod to dtrin th initial lato-platic quivalnt tr and th odifid tr ratio, which will b ud in th daag analyi latr.

4 Iqbal Raool Mon, Zhang Xing &Cui yu.5 Additional Load for Str Analyi uring aag Evolution Sinc th tiffn of tructur br rduc with vry incrnt of daag, th concpt of daag-inducd additional load i introducd in ordr to avoid rcurrnt calculation of th tiffn atrix during daag volution. It i known that aftr th initial loading, th tr and train coponnt will vary in latic rang undr ubqunt loading, with th conidration of th daag coupling ffct. Thn, w hav ij C ijkl ( kl (0 whr, ij and ij ar th rang of variation of train and tr coponnt, rpctivly. According to qn-0, w hav E + ( i j i j E whr, ij can b dfind a th rang of variation of latic tr coponnt, i.., i C ( E j i j k l and ij th rang of variation of daaginducd additional tr coponnt, i.., i j C i j k l k l ( By ubtituting th quation into th quilibriu quation and boundary condition, w gt: E ji + + 0, j Bi Bi in v (4 E i j l j p i + pi on S p (5 whr, B i ji, j i th rang of variation of daag-inducd additional body forc coponnt and pi i j l j i th rang of variation of daag-inducd additional urfac traction coponnt FINITE ELEMENT ANALYSIS FOR GIVEN AMAGE FIEL Additional load-finit lnt thod [] i introducd in th analyi of - tr fild for givn daag fild. By an of daag coupld contitutiv rlation, w hav E E B δ (6 i j {} ( [ ] {} ( [ ] [ ] {} k l ar th vctor for th rang of variation of tr, train and diplacnt coponnt of an lnt, rpctivly, i th daag of th lnt. By applying th principl of virtual work at lnt lvl, w can obtain whr {}, {} and {} δ [ K] {} {} {} δ F + F (7 whr, {} F i th vctor for th rang of variation of convntional nodal forc and {} F th vctor for th rang of variation of additional nodal forc givn by {} F [ K ] {} δ (8 Expanding ach atrix and vctor in qn- 7 to th ordr of global lvl, th govrning yt of quation i abld a follow [ K]{} {} F + {} F δ (9 whr, {} F and {} F ar th vctor for th rang of variation of convntional nodal forc and additional nodal forc at th tructur lvl, rpctivly. Obviouly, with th application of additional load thod, th analyi of diplacnt and tr fild for a daagd body can b carrid out a that for ound body. - h arrangnt i alo optiizd by convrgnc tt. In th finit lnt analyi th nodal point diplacnt ar obtaind by uing 8-nod brick lnt. Thn ach brick lnt i dividd into 5 four-nod ttrahdral lnt for furthr daag analyi. Aftr obtaining th nodal point diplacnt for ach brick lnt, th tr fild and additional load vctor can b calculatd by uing qn-6 and 8 fro ttrahdral lnt. 4 EQUATIONS OF AMAGE EVOLUTION Laitr and Chaboch ar aongt tho rarchr who introducd quation of daag volution during 970. Th quation of daag volution can b xprd a follow: 4

5 FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH TWO-BLOCK LOAING d dn q γ ( R (0 whr, N an th nubr of load cycl, γ, and q rprnt th atrial bhavior which can b dtrind by an of convntional fatigu tting, and i th rang of variation of quivalnt tr givn by ( R ( with R bing th tr ratio in on load cycl. Eqn 0 can alo b writtn in th for of quivalnt tr a follow: d dn q α ( whr, α can b xprd a follow, α β( R n ( hr, β, n, and q ar atrial dpndnt contant which can b tiatd with th hlp of S-N curv of atrial for at lat two tr ratio ca. 5 AMAGE FIEL ANALYSIS AN LIFE PREICTION For th phyically nonlinar probl caud by tr-daag coupling, th incrnt of daag in a critical lnt i takn a th tp lngth to analyz th crack initiation and crack propagation for th tructur br undr rpatd loading. In vry tag of crack initiation and crack propagation, th currnt critical lnt i lctd through th ant of daag volution rat d/dn for all lnt. For a givn incrnt of daag * of currnt critical lnt, th rlvant incrnt in load cycl and th daag incrnt of othr lnt ar givn by N β ( + q + q (, (4 whr, * rprnt th fild quantiti for currnt critical lnt. Thn, th currnt daag fild will b xprd by * + * and + for th currnt critical lnt and othr on, rpctivly. Th corrponding fild quantiti ui, ij and ij (i, j,, can b obtaind by th finit lntadditional loading thod. Th abov two proc will b procdd altrnativly and paud whn th daag in th currnt critical lnt rach.0. Th nubr of load cycl for th coplt failur of th firt critical lnt rprnt th crack initiation lif. Th total nubr of load cycl during crack initiation i, thn, givn by th following xprion, N M N r r (5 whr, M i th nubr of tp during crack initiation, and N r th nubr of load cycl of th r th tp of crack initiation. 6 FATIGUE ANALYSIS UNER SPECTRUM LOAING For iplicity, th load pctru conit of only on priod with two block of cyclic loading at diffrnt tr lvl. Th load aplitud rain contant within ach block but diffrnt fro on block to anothr. To invtigat th validity of Minr Rul and th ffct of load qunc, all poibl load ca hav bn conidrd, including Elato-Elatic, Elato-Platic, Plato-Elatic and Plato-Platic load ca. 6. Elato-Elatic Load Ca In thi ca th tr lvl in ach of th block i blow th yild liit. Th load pctru i hown in Fig-. Th tr-train rlation for thi ca i hown in Fig-5. Th nubr of load cycl N for th firt block i a givn quantity a follow: N kn f (6 whr, N f i th crack initiation lif undr contant aplitud loading and k (< a known quantity to dfin th nubr of load cycl of block-. 5

6 Iqbal Raool Mon, Zhang Xing &Cui yu 6.. Fatigu aag Analyi for t Block Th daag analyi for block- i th a a that of contant aplitud fatigu analyi. Th additional load-finit lnt forulation for block- can b givn in th for of th rang of variation a follow [ K]{ δ } { F } { F } + (7 whr, { F } and { F } ar th rang of variation of convntional and additional load for block-, rpctivly. Th daag volution quation for block- ha th for d dn, β (8 Th n th incrnt of load cycl * corrponding to th daag incrnt in block- can b givn a N * n, β * q ( ( * (, n q + (9 Suation of th incrnt of load cycl, finally, will rach th givn nubr of load cycl, N, a follow: Nn, N with * * (40 n whr, * i th daag of critical lnt at th nd of block-. It ut b ntiond that in ach tp of daag incrnt th corrponding fild quantiti u i, ij, ij and can b obtaind by th finit lnt thod with additional load. 6.. Fatigu aag Analyi for nd Block Whn th nubr of load cycl i qual to N th load aplitud i changd fro to (Fig-5. In ordr to calculat th ridual lif du to th loading of block-, th additional loadfinit lnt forulation for block- ha th for, δ F + F (4 [ ]{ } { } { } K whr, { F } i th rang of variation of additional load caud by th daag of all lnt. Th daag volution quation for block- ha th for d dn, β (4 Th n th incrnt of load cycl corrponding * to in block- can b givn a N * n, β * q ( ( * (, n q + (4 Th abov proc will b accoplihd, whn *. Thn, th uation of th incrnt of load cycl will giv th ridual fatigu lif a follow: N n, N with * (44 n 6.. Total Fatigu Lif Aftr dtrining th nubr of load cycl for ach block, th fatigu lif of tructur br will b N cr N + N (45 Th Minr Rul indx can b dfind at thi tag a follow: n N N i + (46 i N i, cr N, cr N, cr whr, N,cr and N,cr ar th fatigu liv fro contant load aplitud fatigu analyi for rpctiv load. If th uation in Eqn-46 clo to unity, thn it i hown that Minr Rul i availabl. Siilar analyi can b carrid out whn th qunc of applid load i rvrd, to how th availability of Minr Rul and th ffct of load qunc on total fatigu lif. Th load pctru for rvr qunc i hown in Fig-. 6

7 FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH TWO-BLOCK LOAING 6. Elato-Platic Ca In thi ca pur latic dforation occur in block- and platic dforation tak plac only at critical zon in block-. It i aud that th for of th load pctru i iilar to Fig-. Fatigu daag analyi for block- in thi ca i a a that in lato-latic ca. 6.. Fatigu aag Analyi for Block- At firt, an additional load-itration thod i introducd to giv th platic corrction for block- in ordr to dtrin th initial lato-platic axiu quivalnt tr and odifid tr ratio. According to qn-9, th forulation in finit lnt analyi ha th for [ K]{ } { F } { F } ( P, δ + (47 whr, { F } i th vctor for th variation of convntional loading corrponding to P P,ax P,in (Fig-, and { F } ( P, i th vctor for th variation of additional load to conidr th atrial dgradation aftr th firt block and th ffct of platicity. Aftr th copltion of abov itration proc, th variation of tr, (,, corrponding to P i obtaind. Thn, th rang of variation of quivalnt tr,,, corrponding to P P,ax P, in can b dtrind by an of th finit lnt analyi with additional load in ordr to conidr th daag caud by block-. Thrfor, th odifid tr ratio will b obtaind a follow: (,,ax,in + (48,in,ax, (49,in and R (50,ax Abov rang of variation of quivalnt tr,,, and odifid tr ratio, R, obtaind will b applid in qn-4 to dtrin th initial daag volution ratio, (d/dn, for block-. According to qn-4 to qn-4, th incrnt of load cycl and th corrponding diplacnt, tr and daag fild will b calculatd for ach tp of daag incrnt. Evntually, whn *, th ridual fatigu lif will b obtaind by u of qn-44. Th trtrain rlation for th lato-platic ca i hown in Fig Plato-Elatic Ca In thi ca, block- will cau platic dforation and block-, th latic on in a tructur br. Th load pctru i hown in Fig-. Additional load-itration thod i introducd to giv th platic corrction for block-. Th forulation in finit lnt analyi ha th following for δ F + F (5 whr, { F } P [ ]{ } { } { } P K i th vctor for th rang of variation of additional load to conidr th ffct of platicity. Aftr th copltion of itration proc, th axiu quivalnt tr,, and th odifid tr ratio, R, obtaind will b applid in qn-8 to 40 a an initial data to dtrin th fatigu lif, N, for block-. Whn th nubr of load cycl arriv at N, th load aplitud i changd. Th forulation in finit lnt analyi will hav th for of qn-4, in which, { } F i thn, th vctor for th variation of convntional loading corrponding to P P,ax P,in (Fig-. Th axiu quivalnt tr, and odifid tr ratio obtaind will b applid to dtrin th ridual fatigu lif N du to block-, according to qn- 4 to 44, until *. Th tr-train rlation for th plato-latic ca i hown in Fig Plato-Platic Ca In thi ca platic dforation will tak plac in both th block. Aftr th application of load in block-, thr i going to b a platic dforation and atrial will undrgo a prannt t. Th forulation in finit lnt, 7

8 Iqbal Raool Mon, Zhang Xing &Cui yu analyi will b diffrnt dpnding upon th load qunc. If th load in block- i lowr than in block-, thn nw yild and ultiat liit ar rquird to b calculatd for th itration approach applid to block-. Whra, thr will b no chang in th liit if block- loading i highr than Low-High Squnc Additional load-itration thod i applid to block- for platic corrction. Th load pctru i hown in Fig-. Th finit lnt analyi will b prford according to qn-5, thn qn-7 to 40. Aftr th application of block-, furthr platic dforation will tak plac du to th highr load lvl of block-. Thn, to prfor th analyi of platicity, nw yild and ultiat liit for tr and train ar calculatd by tranforation of co-ordinat yt to co-ordinat yt (Fig-8 a follow: u whr,,ax u,,in,in,, u u, E + (5 i th nw yilding train of th atrial daag caud by block-. Additional load-itration thod, with abov yild and ultiat liit, i applid to giv platic corrction to block- in ordr to dtrin th nxt initial axiu tr and odifid tr ratio. Th forulation in finit lnt analyi ha th for of qn-5. Th ridual fatigu lif N will thn b calculatd in a iilar proc a that for block- in latoplatic ca. Th tr-train rlation for lowhigh qunc i hown in Fig High-Low Squnc In thi ca, additional load-itration thod i applid for platic corrction to block- only. Th load pctru i hown in Fig-. Th forulation in finit lnt analyi ha th for of qn-5, thn qn-7 to 40. Aftr th application of load cycl N for block-, th load aplitud i changd and th atrial will follow linarly latic bhavior. Th forulation in finit lnt analyi for block- will thn b govrnd by qn-4 and ridual fatigu lif N will b thn dtrind by qn-4 and 44. Th tr-train rlation for high-low qunc i hown in Fig-9. 7 NUMERICAL RESULTS AN ANALYSIS Coprhniv coputr progra ar dvlopd bad on th abov-ntiond thory to prfor th additional load-itration thod, linarly latic FEA, lato-platic FEA, daag chanic-linarly FEA with additional load, and daag chanic-lato-platic FEA with additional load. With th hlp of th progra th fatigu liv for abov diffrnt ca ar prdictd. Bfor th application of abov approach for th invtigation of pctru loading, thy ar applid to prdict th fatigu liv undr contant load aplitud for vrification. Th nurical rult ar in good agrnt with th xprintal data a hown in Tabl-. Variabl load aplitud in two tp ar applid to pcin ad of LC4CS aluinu alloy and 0CrMnSiNiA tl alloy with tr concntration factor (K t of.0 and.0, and tr ratio R0.5. Th coputational rult ar hown in Fig-0 to how th availability of Minr Rul for diffrnt ca and th analyi for ach ca i givn blow: 7. Elato-Elatic Ca Fatigu lif prdiction analyi for pcin ad of LC4CS aluinu alloy, with K t.0 and R 0.5 i carrid out at contant load aplitud and two tp variabl load aplitud. Th load lvl in both block ar conidrd to b latic. It i found that th Minr Rul i availabl for thi typ of loading. Th rvral of loading qunc do not affct th total fatigu lif of th pcin. 8

9 FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH TWO-BLOCK LOAING 7. Elato-Platic Ca Fatigu lif prdiction for th a pcin a ntiond abov i prford whn block- undrgo latic dforation and block-, platic dforation. Fro coputational rult it i found that Minr Rul can b atifid approxiatly only in tho ca whn th diffrnc in th load aplitud of both block- and i all. If th diffrnc i largr, thn Minr Rul i not availabl. It i hown that load qunc ha a ignificant ffct on th total fatigu lif of tructur br whn th diffrnc in load aplitud of block i gratr. Th fatigu lif of th pcin i xtndd ignificantly whn a low on follow th high lvl load. Thi phnonon uggt that xpour to diu cycl fatigu (MCF prior to high cycl fatigu (HCF ay ffct HCF lif. Thi nurical rult ha alo bn vrifid by o xprintal work prford in [6]. 7. Plato-Elatic Ca Fatigu lif prdiction for th a pcin i prford whn platic dforation tak plac in block- and latic on in block-. Th xpour of MCF prior to HCF xtnd th HCF lif by approxiatly two ti. With th incra in th diffrnc of load aplitud th xtnion factor will incra and vic vra. 7.. Plato-Platic Ca Fatigu lif prdiction undr variabl load aplitud for th pcin ad fro 0CrMnSiNiA tl alloy with K t.0,.0 and R0.5 and pcin ad fro LC4CS aluinu alloy with K t.0 and R0.5, i takn a nurical xapl. Platic dforation tak plac in both th block. It i obrvd that whn th diffrnc btwn two load lvl i largr, th availability of Minr rul bco rot and th chang of load qunc affct th total fatigu lif ignificantly. Morovr, MCF prtraining prior to HCF ay alo xtnd th fatigu lif of pcin in plato-platic ca. 8 CONCLUSIONS. Linar aag Accuulation Rul (Minr rul i availabl in th lato-latic ca of two-block loading, whn th loading in both block i blow th yild liit. It ay b availabl in o of lato-platic, platolatic and plato-platic ca whn th diffrnc btwn load aplitud of pctru loading i all or th loading ar clo to th yild liit of th atrial.. Thr i a dirct ffct of loading qunc on fatigu lif if th diffrnc btwn th variabl load lvl i largr in th ca of lato-platic, plato-latic and plato-platic variabl aplitud load.. Expour of MCF prior to HCF loading ay xtnd HCF lif ignificantly. Which how that fatigu lif of a tructur br can b xtndd by a uitabl choic of MCF prtraining. 4. U of additional loading thod intad of th daag chanic-finit lnt thod of variabl tiffn and daag incrnt at critical lnt a tp lngth intad of th incrnt of loading cycl i or flxibl and rduc th coputational ti ignificantly. 9 REFERENCES [] Palgrn, A., Enduranc of ball baring, Z. Vr. t. Ing., 94 68, 9. [] Minr, M. A., Cuulativ daag in fatigu, J. Appl. Mch., Tran. A. Soc. Mch. Engr., , A-49 [] Iqbal Raool, Zhang Xing, Cui yu, Fatigu lif prdiction of - probl by daag chanicfinit lnt additional load thod, 7 th Intr Fatigu Congr, 999, Bijing, pp 87-8 [4] Zhang Xing, Zhao Jun and Zhng Xu-ong, Mthod of daag chanic for prdiction of tructur br fatigu liv, Handbook of Fatigu Crack Propagation in Mtallic Structur, 994, pp 47-5 [5] Iqbal Raool Mon, Cui yu, Zhang Xing, Fatigu lif prdiction of - probl by daag coupld 9

10 Iqbal Raool Mon, Zhang Xing &Cui yu lato-platic chanic, rd Aian-Pacific Confrnc on Aropac Tchnology and Scinc, 000, Kuning, China, pp 07- [6] G.Whatly,. Bowan, Y. Etri, X.Z.Hu, Intraction btwn LCF and HCF in coon tallic atrial, 7 th Intr Fatigu Congr, 999,Bijing, pp [7] Jan Laitr, A cour on aag Mchanic, Springr-Vrlag, 987 [8] Handbook of Mchanical Proprti of Aircraft Structural Mtal, Intitut of Aronautical Matrial, 98, Bijing Spcin K t LC4CS.0 0CrMnS inia 0CrMnS inia.0.0 Str (Mpa Coputd Fatigu Lif (log 0 Exprintal Fatigu Lif (log Tabl-, Coparion of coputational and xprintal fatigu liv for contant load aplitud P,ax P,in N Block- N Block- P,in P,ax Fig-, Load pctru (low-high ca t Fig-, Str-Strain curv for linarly hardning atrial,ax ( ( p ax ax ( in ( p in Fig-4, Itration thod,ax,in,in Fig-5, Str-Strain curv for latolatic ca u E we u,ax P,ax P,in N Block- N Block- P,in P,ax Fig-, Load pctru (high-low ca t,ax,in,in (, Fig-6, Str-Strain curv for latoplatic ca 0

11 FATIGUE LIFE PREICTION OF - PROBLEMS BY AMAGE MECHANICS WITH TWO-BLOCK LOAING,ax,ax,in,in (, Fig-7, Str-Strain curv for platolatic ca,ax,ax,in,in (, Fig-8, Str-Strain curv for Platoplatic (low-high ca,ax,ax (,,in,in Fig-9, Str-Strain curv for platoplatic (high-low ca Noral Load Squnc Noral Squnc Rvr Squnc Palgrn-Minr Minr Indx Minr Indx 4 5 Rvr Load Squnc L-H L-H H-L E-E E-P P-E P-P P-P P-P Fig-0, Availability of Minr' Rul for all th ca in noral and rvr qunc loading