shaniavsky_practical_view_gcf_aircraft_parts.pdf

International

International Journal of Fatigue 28 (2006) 1647–1657

JournalofFatigue

www.elsevier.com/locate/ijfatigue

Technical paper

Fatigue limit – Material property as an opened or closed system?Practical view on the aircraft components failures in GCF area

A.A. Shanyavskiy *

State Center for Safety of Civil Aviation Flights, Airport Sheremetievo, Moscow 124340, Russia

Received 17 November 2004; received in revised form 9 November 2005; accepted 15 December 2005Available online 6 May 2006

Abstract

In the presented paper the macroscopically seen phenomenon of the fatigue crack originating inside of specimens in area of very-high-cycle fatigue (VHCF) for lifetime to failure more than 109 cycles is explained on the basis of synergetic approaches when the knowledgeabout bifurcation’s points used to show self-organized change in material sensitiveness to cyclic loads in different media areas whereexceeds maximum stress-state. The discussed bifurcation diagram was constructed, using knowledge about scale levels for plastic defor-mation processes. This synergetic view on the cause of the fatigue crack origin displacement from the materials surface in area of highcycle fatigue (HCF) to the inside of specimens is illustrated by fatigue tests results for hardened materials of Ti- and Al-based alloys inareas of low cycle fatigue (LCF) and HCF.

The cracks distribution in time for in-service fatigued aircraft components has three pikes of their maximum failure intensity. Thissituation is general for all components operated in areas of LCF–HCF–VHCF. Aircraft components failures features in area of VHCFare discussed for blades of Ti-, Al-, and Ni-based alloys, gears of helicopters reducers, and shafts of aircraft engines.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Gigacycle fatigue; Synergetic; Bifurcation; Aircraft components; Quantitative fractography; Failure analyses; Lifetime to failure; Crack growthperiod

1. Introduction

Lifetimes (durability) to failure for aircraft componentscan be estimated by the various criteria because of widerange of in-service loading conditions. The fatigue limit,rw1, or the lifetime to fatigue failure of metallic materialsis criterion, which used for estimating structural reliabilityof majority aircraft components [1]. The number of cyclesfor an aircraft component which can be realized beforein-service fatigue failure, is determined by the WohlerS–N curve in dependence on the cyclic loads conditions.Three areas of cyclic loads condition, named low-(LCF),high-(HCF), and very-high-cycle fatigue (VHCF) can beseen for different aircraft components. The fatigue limit,rw1, usually determined in area of HCF as a material prop-

0142-1123/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2005.12.008

* Tel.: +7 095 578 4704; fax: +7 095 737 6094.E-mail address: [email protected].

erty to prevent fatigue failure, is used to estimate a smallerstress level under which in-service aircraft components can-not be fatigued on the basis of 107 cycles.

The shape of the load cycle on aircraft components andstress amplitude depended on the cyclic loads frequency.An increase in the frequency of cyclic load is followed bya load amplitude decrease. The cyclic load acceleration ineach cycle tends to be closer and closer to the accelerationfrom the dynamic load for increases beyond 103 Hz. Withan increase in frequency, the relaxation processes in mate-rials, which occur in each cycle of loading, are less and lessin evidence.

The lifetime to failure of structural components, Nf,have to be estimated under low amplitudes of multiaxialcyclic loads [1]. For example, blades of aircraft engines[2], gears of helicopter reducers [3] and shafts of aircraftstructures [4] are subjected to biaxial cyclic loads under,for instance, simultaneous rotation or torsion and bending.For multiparametric cyclic loads the lifetime to failure, Nf,

mailto:[email protected]

Nomenclature

Fi(X1, X2 . . .Xi) functional correction to the materialparameters (Nf, Np; and etc.)

ND designed durability (lifetime) for aircraft compo-nents

Nf lifetime to failure for in-service fatigued compo-nents

Np fatigue crack growth periodPin probability of fatigue crack initiation inside of

the specimenPs probability of the single crack origination on the

specimen surface or in the internal volumepHB hydrogen factor of environment influence on the

fatigue crack initiationR stress ratio (rmin/rmax)mst material stress-state ahead of the stress raiser

srs stress raiser shape and their sizes in the threedimensions

amin angle of the Woeler-curve for the stress raisermaximum influence of fatigue crack initiation

amax angle of the Woeler-curve for the fatigue crackinitiation under the surface in LCF–HCF–VHCF areas

k biaxial stress ratio between principal stresses(r1/r2)

rw1 fatigue limit in high-cycle-fatigue (HCF)rw2 fatigue limit in very-high-cycle-fatigue (VHCF)ri/ru ratio between maximum cyclic stress level and

ultimate tensile stressXi parameters of the loading cycle (temperature,

frequency, R, and etc.)

Fig. 1. The lifetime (a) to failure, Nf, and (b) the ratio, Np/Nf, for centralcracks fatigued cruciform specimens of the D16T aluminum alloy(analogue 2024T3) subjected to various R and k ratios.

1648 A.A. Shanyavskiy / International Journal of Fatigue 28 (2006) 1647–1657

the crack growth period, Np, their ratio Np/Nf, and the fati-gue limit rw1 can be calculated from the next relations:

N f ¼ ðN fÞ0F 1ðX 1;X 2 . . . X iÞ ð1ÞNp=N f ¼ ðN p=N fÞ0F 2ðX 1;X 2 . . . X iÞ ð2Þrw1 ¼ ðrw1Þ0F 3ðX 1;X 2 . . . X iÞ ð3ÞðN fÞ0; ðN p=N fÞ0; ðrw1Þ0; for the F 1 ¼ F 2 ¼ F 3 ¼ 1 ð4Þ

In the case of biaxial cyclic loads, experimental datashow increasing, Nf, for increasing stress ratio, R, and biax-ial stress ratio, kr, in the range �1.0 < kr < + 1.5 [5]. Therecan be seen drastic change of the durability, Nf, and theratio Np/Nf for the fatigue crack growth period Np independence of the simultaneous influence R and kr ratioson the fatigue crack growth process, as shown in Fig. 1.The frequency of the multiaxial cyclic loads can be up to104 Hz and at the moment of the in-service limit state therealized durability can be of 1010–1011 cycles.

At the same time, in-service fatigue failures of aircraftcomponents can be seen for the shortest lifetime becauseof wide range of materials damage [1]. Most of all, speci-mens tested in area of VHCF have shown that fatigue fail-ures under a smaller uniaxial stress level than the fatiguelimit, rw1, can be seen for lifetime to failure in the rangeof 108–1010 cycles [6,7].

That is why the question about fatigue limit existencefor metallic materials has to be discussed.

2. Bifurcation points for the S–N curve at the LCF–HCF–

GCF transitions

In-service cyclic loading of a construction element mayinduce evolution of its structure on the microscopic-scalelevel, associated with the achievement of the critical dislo-cation density. Damage is accumulated in the materialdepending on stress state, applied-loading frequency spec-trum or R magnitudes, etc. Storage and dissipation ofenergy are the two concurrent competing processes experi-

enced by the material under the loading. The material con-dition is evolving parallel to continued energy exchangewith the environment until the crack nucleated and grownto a critical size.

Numerous investigations of the dislocation structure of ametal indicate that the accumulating process of damageduring its cyclic loading appears ordered and self-organized

Fig. 2. Probabilities of the fatigue crack appearance, Pin, inside of thespecimen volume and, Pos, the single origin formation in dependence onthe stress ratio ri/ru.

A.A. Shanyavskiy / International Journal of Fatigue 28 (2006) 1647–1657 1649

around the specimen surface [8,9]. The critical condition ofa material, which corresponds to the initiation of the crackon the specimen surface and its growth during a loadingcycle, may be associated with the level of damage or defectdensity that will be the same whatever different are the waysor conditions of the cyclic loading. Based on this idea, onecan use a single synergetical approach to the analysis ofcrack-initiation and crack-growth stages [1,10].

A metal under the cyclic loads represents an opendynamic system, which is far from equilibrium; the systemis exercising a series of sequential transitions from one toanother stability state and the continued energy exchangewith the environment. Once the system has come to a cer-tain critical condition, the homogeneous equilibrium is notstable any more; therefore, inhomogeneities appear in thesystem, to be defined as dissipative structure [11,12]. Withthe dissipative structures thus formed, the inhomogeneousstate of the open system acquires stability against small dis-turbances. In an open system, they recognize the stabilitystate of two kinds, homogeneous or inhomogeneous. It ispredominantly in the homogeneous stability state thatone dissipative structure is replaced by another, whichresults in continuous evolution of the open system. There-fore, an open system must keep stable as long as a certaindominating mechanism of damage accumulation persistswithin a certain period of time, the mechanism being char-acteristic of a dominating type of dissipative structure.

As cyclic loading of a construction element is contin-uing, mechanisms of damage accumulation replace oneanother sequentially. Then, the contribution of a newmechanism may alternatively grow or cease. An open sys-tem evolves by passing through the critical states, referredto as the bifurcation points, to, alternatively, a stability orinstability condition [11]. As long as the system experiencesfluctuations, it cannot avoid instability immediately beforea bifurcation point. The newly activated processes of dam-age accumulation develop or, alternatively, die out,depending on whether the system is able to be the self-orga-nized absorption of energy in the ways that shift the con-struction element toward a greater stability, i.e., longerlife times. The general principle of self-organization is thataltering the parameters of the extrinsic (applied) influence(the kind or way of cyclic loading) results not in the occur-rence of the structures hierarchy but rather in switching onthe fracture mechanisms operative in the system. Depend-ing on the conditions of cyclic loading, the mechanismsmay be complicated to a greater or smaller extent, andthe system stress-state changes from the lower to higherlevel of self-organization.

In a material capable of resistance to cyclic loading, thereason for the self-organized transitions through the bifur-cation points is to only make operative the least-fracture

mechanism (the deformation mechanism that helps reduc-ing the fracture scale to the possible lowest level); hence,the least energy fraction is given, per loading cycle, to theformation of free surface. Such a behavior requires involve-ment of increasingly complicated concurrent processes.

Materials during damage accumulation under the cyclicloads have minimum two points of bifurcation which char-acterized changes of their state: the first change correlatesto the crack initiation, and the second change correlatesto the material failure. The lifetime to failure for metalsincluded itself both periods for damage accumulationbefore and after the fatigue crack initiation. The momentof the crack initiation and disposition of the crack originon or inside of the specimen surface depended on a metalstate, the environment influence on the specimen surface,the state of the surface (gardened or not) and external con-ditions for cyclic loads [13–20]. This point of bifurcation ischaracterized by the fatigue crack origin, which has evolu-tion for its disposition in material volume in dependence onthe cyclic loads level [6,7,15].

The evolution of an open system is commonly discussed[1,9,10] in the terms of microscopic, mesoscopic, or macro-scopic scale levels. The first is relevant to the effects on thescale of atomic spacing, the second, to the behavior ofatomic ensembles, and the third, to the creation of bulkyspace structures.

Metallic materials have to be considered as an open sys-tem under cyclic loads in the case of fatigue crack origina-tion on the specimen surface. The crack origination insideof material has to be considered as the case of partly closedsystem. The crack origination inside of the specimen in theLCF–HCF areas is well known phenomenon which can beseen for surfacely peened specimens or hardened specimensthrough all section [20].

On the basis of the well-known experimental results[6,7,15–19], summarizing above presented knowledgeabout evolution of an open system, there can be introducedthe bifurcation diagram for description of the evolution of

the fatigue origin disposition from the material external (sur-

face) to the internal volume for LCF–HCF–VHCF areas, asshown in Fig. 2. Several drastic transitions in metal behav-ior under the cyclic loads for the fatigue crack originationcan be seen during stress level decreasing.

The first (1) bifurcation point characterized by the tran-sition from the damaged material behavior under the cyclic

Fig. 3. Wohler diagrams (1–4) for various situations of the fatigue crackinitiation in metals (comments are presented in the paper).


loads without fatigue crack initiation to the material frac-ture when the fatigue crack initiation takes place underthe material surface (internal crack) in the VHCF area.There is the second (2) transition in the material state fromthe partly closed to the opened system for a metal stateunder the cyclic loads when the fatigue crack originationplace has a self-organized change of its disposition fromthe internal material volume to the specimen surface. Thethird (3) bifurcation point reflects the transition in the fati-gue fracture origination from the single to the multi-originson the specimen surface. The last (4) bifurcation point bor-dered two areas of the material state when the fatigue crackhas origination on (before the point) and under (after thepoint) the specimen surface.

Fig. 4. Schema of the fatigue cracks distribution in dependence on in-service lifetime, overview of the two engines fracture (a, b) D30 and (c) D30KUbecause of titanium compressors disks fatigue failure (pointed by arrows), and the fatigue crack distribution for these engines (d), (e), respectively.

Fig. 5. Schema (a) of the blade loading in service, (b) overview of the fatigue fracture surface for one of the fatigued ventilator blade, (c), (d) fatiguefracture area (2) performed because of the static crack, which was introduced in material during manufacturing procedure.

Fig. 6. Cracks distribution (a) by the lifetime to failure for titanium bladesof aircraft engines and (b) by the number of flights for fatigue crackpropagation.


At last, the generalized Wohler S–N curve can be seenfor material damage as an opened or partly closed system(see Fig. 3). The first curve (1) reflects material damage inthe case of corrosion fatigue, when the fatigue crack origi-nates on the specimen surface [15–17,19]. This is the case ofthe absolutely open system. The system is exercising a ser-ies of sequential transitions from one to another stabilitystate and the continued energy exchange with the environ-ment. The environment influence on the material state isdominant for fatigue crack initiation on the specimen sur-face. The second curve (2) reflects the well known WohlerS–N curve for a metal as an opened system for the moder-ate environment influence of the fatigue crack originationon the specimen surface in areas of the HCF–LCF, butthe crack origination take place under the surface for thelifetime to failure less than 103 cycles [13]. The third (3)curve characterizes a metal as the partly closed system,when the fatigue crack originates under the specimen sur-face. There can be seen for the third (3) curve the reallymaterial property to prevent the fatigue crack initiationunder the cyclic loads for all stress levels. The environmentinfluence on the specimen surface is not enough to damagematerial as an open system for fatigue crack initiation onthe surface. The stress level of the transition from the crackinitiation on the surface (an open system) to the crack ini-tiation under the surface (partly closed system) dependedon the environment composition, material sensitiveness tothe environment [1,19], or material sensitiveness to thestress concentration. At last, the curve (4) characterizes amaterial state as a partly closed system when materialshave hardened surfaces and compressive internal residualstresses through all the section. The fatigue crack originatesunder the specimen surface in all areas of the HCF–LCF–


VHCF, and there can be exceeded maximum materialsdurability under the cyclic load in the areas for any stresslevel ri. The next relation can summarize the discussed sit-uations (see Fig. 3):

Fig. 7. Overview (a) for in-service damages and fatigue failures of two titanium1010 because of its damage on the base surface.

For the open system

ai ¼ amax½1� F ðpH BÞ � F ðsrsÞ � F ðmstÞ� F ðX 1;X 2 . . . X iÞ� ð5Þ

blades, and (b) view of the local origin of the steel blade fatigued near to


For the partly closed system

ai ¼ amax; at

F ðpH BÞ ¼ F ðsrsÞ ¼ F ðmstÞ ¼ F ðX 1;X 2 . . . X iÞ ¼ 0 ð6Þ

Fig. 8. Overview (a) of the fatigued turbine blade (A – area of the fatigue fract(c) the blade fracture area with (1) intergranular fracture because of creep princrement in flight in the crack growth length, a, up to critical distance ac, an

Table 1Fatigue-life data and the ratio Np/Nf for several types of in-service damaged

Number Reducer Life-time (h) Torque (rev/min)

1 R-7 5850–3662 23702 VR-8A 9313–4486 25103 R-26 654 26704 Tail-reducer 4800 3860

3. Lifetime to failure for fatigued aircraft components

Statistical analyses of in-service lifetime for varioustypes of aircraft components that were fatigued in LCF–

ure), (b) fatigue cracks distribution in dependence on the ratio Nf/ND, andocedure, (2) fatigue fracture zone, and dependences of the crack growthd the number of flights for two fatigued blades.

aircraft gears for helicopters Mi-8, Mi-6 and Ka-26

Life-time, cycles Np/Nf Damage

(8.3–5.2) · 108 4–7% Spline fatigue failure(1.4–0.68) · 109 0.5–1.0% Static crack108 1.5% Corner damage1.1 · 109 0.9% Material fault


HCF–VHCF areas have shown two peaks for maximumfrequency of their failures [1] (see Fig. 4). The first peakreflects the in-service shortest lifetime due to materialfaults, which influenced the period of fatigue crack initia-tion. The next peak refers to a bad of material state that,for instance, in LCF is sensitive to service cycle waveformsfor titanium alloys [11]. The last peak characterizes a prac-tical lifetime to failure, i.e., a good material state.

For example, in-service fatigue failures of the titaniumcompressor disks in area of the first and the second peaksusually occur due to a material sensitivity to the trapezoi-dal cyclic load waveform (see Fig. 4). Fatigue cracks havea possibility to take the facetted pattern of a fracture sur-face under this cyclic load waveform because of materialspreference to a quasi-cleavage fracture process during ahold (dwell) time period. This mechanism occurs in materi-als during a specific stress-state involving residual stressesat metallurgical interface boundaries or because of low-level interfacial (or inter-granular) strength under dwell-time conditions. The crack initiation can be seen on thediscs surface for the discussed above cases of componentsfailures around first and the second peaks of the crack dis-tribution, but for the hardened surface, fatigue crack initi-ation takes place under specimens surface for the facettedpattern fracture surface formation [15].

Fig. 9. Overview of the fracture surface, schema this surface and fracture surfacof the crack increment in flight and the number of flights on the crack growth

3.1. Blades

Ventilator blades manufactured from D1T Al-basedalloy (Al–Cu–Mg) had flown 1600 h before fatigue failures.They are subjected to biaxial cyclic loads and can have nearto 108 cycles of the lifetime to failure (see Fig. 5). The fati-gue crack initiation was only seen because of material dam-ages. For example, one of them was performed because ofthe local fast fracture from the surface during manufactur-ing procedure. The fatigue crack has been initiated underthe blade surface from the area of the static fracture. Inother cases, fatigue cracks initiation took place on theblade surface from different mechanical damages.

Earlier fatigue failures of aircraft engines having tita-nium or steel blades took place because of in-service mate-rial damages from foreign bodies in flight or during repair[2]. The lifetime to failure after the material damage fortitanium blades depended on the damage shape and sizesin depth and by the blade surface (see Fig. 6). At themoment of blades damage, their in-service lifetime can bein the wide range for cyclic loads number. For instant, atthe frequency 1 KHz for blades of the last low-pressurecompressor stages for in-service operating time 18,000 h,the lifetime to failure in a number of cycles will be nearto 1000 · 18,000 · 3600 = 6.5 · 1010. There can be seen

e in the origin one of the in-service failed helicopter gear with dependencieslength, a.


fatigue failure for a damaged blade in area of VHCF (seeFig. 7). The crack growth period for in-service damagedblades can have part of 30–60% from the lifetime to failureafter the damage influence of the fatigue crack initiation.The crack growth period has not big variation for bladesof different compressor stages and type of engines. Themost cases of the blade failures took place during the crackgrowth period not more than 50 flights.

The first peak for maximum frequency of the turbineblades in-service failures can be seen because of bad mate-rial state [21], which has the sensitiveness to earlier per-forming creep process (see Fig. 8). Then, this process alsowill be performed in material for in-service fatigued bladesaround the second peaks. But the second peak will be alsorealized because of two processes for the material in a goodstate. The origin area performs because of creep processand, then, the fatigue crack growth will be realized up toa critical length under the operated conditions.

3.2. Gears

The helicopter gears were produced from 12Cr–2N–4Vsteel with recommended mechanical properties: ultimate

Fig. 10. Overview of the aircraft AN-24 engine place (a) after the shaft ventilashown by arrow), and (c) the fatigue cracks distribution in dependence on the

stress and yield stress were no less than 1000 and800 MPa, respectively, and the reduction of area was inthe range 50–55%. The fatigue crack development in heli-copter gears takes place under regularly repeated blocksof cyclic loads from flight-to-flight throughout the regimeof VHCF [3]. Gears that have a cyclic life of more than5000 h are subjected to 109 cycles or more if each toothof one gear goes into contact with the teeth of the matinggear once per revolution (see Table 1).

Estimations of the fatigue crack growth period in helicop-ter gears have shown that cyclic loading is in the very-high-cycle regime. At the moment of fatigue failure the crackgrowth period occurs during 27 or 300 h and depends onthe position of the fatigue crack origin in the gear and, also,on the path of crack growth (see Fig. 9). The ratio of fatiguecrack growth life to lifetime (durability) was in the range of0.1% and 0.5–1% for the durability of investigated gears,which lay in the range of 5.76 · 108 and 4.66 · 109 cycles,respectively. The ratio will be less for non-damaged gearsbecause the durability decreases more than the crack growthlife as the stress concentration decreases. Variations in thecrack growth period in gears are a result of crack origin loca-tional variations in the investigated gears.

tor was gone out, (b) fatigued shaft with and without blades (fatigue crackin-service lifetime.


3.3. Shafts

The shafts usually manufactured from Cr–Ni–Mo steel,having yield stress and ultimate stress near to 1500 and1800 MPa, respectively. In-service failures of shafts sub-jected to rotation or torsion and bending are the resultsof various causes [4,22]. For example, the fracture processof the shaft of oil pump was developed in the next conse-quence. The static fracture zones were created first and abig stress concentration was introduced. The highest stressexisted around of the shaft face from the bending-torsionloading. The crack growth rate along the face under thisloading was higher than for any place in the depth direc-

Fig. 11. Overview of the shaft fracture surface (a) with two origins introduccascade of cracks origination because of the fretting procedure, (c) overviewcorner, and (d) the fatigue fracture origin area near to the hole corner.

tion from the face. It was not only the torsion that pro-duced fatigue fracture. The bending cannot be only oneto produce the fatigue fracture too. Therefore the fatiguefracture could be initiated only after the static fracturewas developed during repair.

The ventilator shafts of the aircraft AN-24 had in flightfailures (see Fig. 10), because of two causes [22]. In the onecase, there was fretting process by splines under the bend-ing-torsion because of the bad joining state (see Fig. 11). Inanother case of the shaft fatigue failures, there was thematerial damage during manufacturing procedure in thecorner of the hole (see Fig. 11). It was VHCF area forthe in-service failed shafts because of both causes. The first

ed because of fretting procedure and corner hardening of the hole 9, (b)of the shaft fracture surface because of the crack initiation from the hole


maximum of shafts fatigue failures took place because offretting process and material damage simultaneously. Itwas near to 3 · 107 cycles for shafts in-service lifetime.Then the crack number drastically decreases for lifetimeincreasing, as shown in Fig. 10. The new cracks generationin shafts was seen after their in-service lifetime near to2.5 · 108 cycles. It was a new fatigue cracks originationfrom the fretting pitting. This situation was the criticalfor the realized type of splines joining.

4. Conclusion

The fatigue limit for metallic materials is necessary andimportant characteristic to compare their resistance to cyc-lic loads in the standard case. But the critical situation forthe in-service fatigue crack initiation in metals can be seenfor a stress level more less than fatigue limit because ofmany causes: material damage during manufacture proce-dure, corrosion, fretting process, different ways for cracksorigination and etc. That is why the knowledge aboutmaterial fracture in VHCF area must be taken in accountto estimate in-service lifetime for structural materials.

Materials in VHCF area should be considered as apartly closed system. In this case the system has evolutionof the stress-state independently of the environment influ-ence, but a stress-state inside of the surface lay or defectsat the material surface can influence the crack originationfrom the surface. This situation in VHCF area has to beconsidered as the evolution of the open synergetical system.

References

[1] Shanyavskiy AA. The damage tolerance concept of fatigue crackingin aviation structures. Synergetics in engineering applications.Monograph, Ufa (Russian), 2003.

[2] Shanyavskiy AA. Fatigue in-service cracks growth in rotor blades ofaircraft engines. In: Wu XR, Wang ZG, editors. Fatigue’99,proceedings of the seventh international fatigue congress, vol. 1/4.Beijing, PR China: Higher Education Press, Emas; 1999. p. 1989–94.

[3] Shanyavskiy AA, Skvortsov GV. Crack growth in the gigacyclefatigue regime for helicopter gears. Fatigue Fract Eng Mater Struct1999;22:609–19.

[4] Shaniavski AA, Tushentsov AL. In-service cracks growth in shafts ofaircraft structures under simultaneous rotation or torsion andbending. In: Brown MW, de los Rios ER, Miller KJ, editors.Proceedings of the ECF12 fracture from defects, vol. 1. UK: EMASPublishing; 1998. p. 199–204.

[5] Shaniavski AA, Orlov EF, Koronov MZ. Fractographic analyses offatigue crack growth in D16T alloy subjected to biaxial cyclic loads atvarious R-ratios. Fatigue Fract Eng Mater Struct 1995;18:1263–76.

[6] Kanazawa K, Nishijima S. Fatigue fracture of low alloy steel at ultra-high-cycle region under elevated temperature condition. In: Brown

MW, de los Rios ER, Miller KJ, editors. Proceedings of the ECF12fracture from defects, vol. 1. UK: EMAS Publishing; 1998. p. 369–74.

[7] Sakai T, Takeda M, Shiozawa K, Ochi Y, Nakajiama M, NakamuraT, et al. Experimental evidence of duplex S–N characteristics in widelife region for high strength steels. In: Wu Xue-Ren, Wang Zhong-Guang, editors. Proceedings of the seventh international fatiguecongress, vol. I. Beijiing, PR China: Higher Education Press; 1999. p.573–8. Fatigue’99, 8-12 June, 1999.

[8] Hertzberg RW. Deformation and fracture mechanisms of engineeringmaterials. New York: Wiley; 1983.

[9] Panin VE. (Ed.) Physical mesomechanics of heterogeneous media andcomputer-aided design of materials, Cambridge, 1988.

[10] Shanyavskiy AA. Synergetical models of fatigue-surface appearancein metals: the scale levels of self-organization, the rotation effects, anddensity of fracture energy. In: Franzisconys K, editor. PROBAMAT– 21st century: probabilities and materials. Netherlands: KluwerAcademic Publisher; 1998. p. 11–44.

[11] Haken G. Synergetics. The hierarchy of instabilities in self-organisedsystems and devices (Russian translation), Mir, Moscow (Russia)1985.

[12] Ebeling V. Structures formed by irreversible processes. Introductionto the theory of dissipative structures (Russian translation), Mir,Moscow (Russia) 1979.

[13] Miller KJ. Creep process and fracture. In: Mechanical and thermalbehaviour of metallic materials. Proceedings of the internationalschool Phisics ‘‘Enrico Fermi’’. Amsterdam, NY, Oxford: Nofth-Holland Publishing Company; 1982. p. 65–147.

[14] Komotori J, Shimizu M. Microstructural effects on fatigue mecha-nisms and fatigue life in extremely low cycle fatigue. In: Beynon JH,Brown MW, Lindley TC, Smith RA, Tomkins B, editors. Engineeringagainst fatigue. Rotterdam/Brookfield: A.A. Balkema; 1999. p.133–40.

[15] Shanyavskiy AA, Losev AI. The effect of loading waveform andmicrostructure on the fatigue response of titanium aero-enginecompressor disk alloys. Fatigue Fract Eng Mater Struct 2003;26:329–42.

[16] Ragab A, Alawi H, Sorein K. Corrosion fatigue of steel in variousaqueous environments. Fatigue Fract Eng Mater Struct 1989;12(6):469–80.

[17] Fuchs HO, Stephens RI. Metal fatigue in engineering. New York:Wiley; 1980.

[18] Corrosion fatigue: mechanics, metallurgy, electrochemistry, andengineering. ASTM STP 801, ASTM, Philadelphia, 1983.

[19] Ko HN, Itoga H, Tokaji K, Nakajima M. In: Bloom AF, editor.Proceedings of the fatigue 2002. Stockholm, Sweden: EMAS; 2002. p.2533–40.

[20] Shanyavskiy AA. The effects of loading waveform and microstructureon the fatigue response of Ti–6AL–2Sn–4Zn–2Mo alloy. FatigueFract Eng Mater Struct 2005;28:195–204.

[21] Shanyavskiy AA. Durability and fatigue cracks growth life forturbine blades of aircraft engine NK-8-2U. In: Fatigue and durabilityassessment of materials, components and structures (Fatigue 2003),Proceedings of the fifth international conference EIS, Cambridge,UK, 7–9 April, 2003. p. 73–80.

[22] Shanyavskiy AA, Tushentsov AL. Regularities of fatigue cracksinitiation and propagation in the shaft spline joins for the engineAI-24 propeller. Sciences works of Society of IndependentInvestigators for Aircraft Accidents, vol. 15, Moscow, Russia,2003. p. 64–81.

shaniavsky_practical_view_gcf_aircraft_parts.pdf

Documents