Procedia Engineering 55 ( 2013 ) 636 – 644
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. doi: 10.1016/j.proeng.2013.03.307
International Conference on Cree
Damage Mechanisms and
HDepartment of Materials Science & Engineering, Un
The primary cause of fatigue damage is usually intim material and details of the loading conditions, variou of fatigue damage evolution in low and high cycl discussed. Various forms of fatigue damage and life-will be illustrated. In particular, the fatigue propert microstructural mechanisms and the question of the e © 2013 The Authors. Published by Elsevier Ltd. Sele Centre for Atomic Research
Keywords: Fatigue crack initiation; LCF; HCF; UHCF; fatig
The history of fatigue research dates back to became an increasingly important problem. This behaviour of steel specimens subjected to cycl kinds of metals and other materials have been has remained a topic of prime interest, academ materials and their use in more and more deman
Only after Ewing and Humfrey had shown th developed at the surface during cyclic loadin microstructural processes that lead to fatigue deformation generally leads to microstructural After initial cyclic hardening or softening, some of fatigue damage become apparent which ultim and the responsible life-controlling microstructu
E-mail address: email@example.com
ep, Fatigue and Creep-Fatigue Interaction [CF-6
Fatigue Lives: From the Low to th
igh Cycle Regime
niversity of Erlangen-Nürnberg,Martensstr. 5, 91058 Erlangen, German
mately related to some form of cyclic slip irreversibilities. Depen s types of fatigue crack initiation are observed. Here, typical ex le fatigue (LCF, HCF) and ultrahigh cycle fatigue (UHCF) -controlling microstructural mechanisms in different metals and ties of ultrafine-grained (UFG ) materials will be discussed, a existence of a fatigue limit in the UHCF regime will be considere ection and/or peer-review under responsibility of the Indira Gand
gue lives; fatigue limit
o the middle of the 19th century, when failures of railway s was the motivation for Wöhler’s first systematic studies lic loading . Since then, fatigue damage and failures studied extensively. Until today, research on fatigue heh mically and with regard to the development of new imp nding fields of application.
hat, in fatigued steels, microcracks initiated in slip bands ng , were the mechanisms of cyclic deformation a
failures studied in more detail. Today, it is clear that changes by the accumulation of repeated cyclic micros etimes followed by a steady state of cyclic saturation, firs mately lead to fatigue failure. The evolution of fatigue d ural mechanisms vary from material to material and depe
heny ding on xamples will be d alloys and the ed. dhi y axles s of the s of all haviour proved which nd the cyclic strains. st signs damage end on © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
the conditions of cyclic loading. In ductile metals, some sort of cyclic strain localization (e.g. in persistent slip bands: PSBs) frequently occurs and leads to the initiation of cracks at the surface, compare . Other forms of fatigue damage are also quite common, e.g. at grain boundaries. On the other hand, in heterogeneous materials containing inclusions or pores, the latter can be sites of beginning subsurface fatigue damage and can even control fatigue life ín the regime of very low loading amplitudes and correspondingly very high fatigue lives, when fatigue damage at the surface develops only very slowly. Materials such as high-strength steels containing inclusions show this behaviour in the regime of ultrahigh cycle fatigue (UHCF) or very high cycle fatigue (VHCF).
The present work focuses on just a few of the characteristics of fatigue behaviour. The different types of fatigue life diagrams for low and high cycle fatigue (LCF, HCF) will first be described, followed by a discussion of the significance of fatigue crack initiation relative to fatigue crack propagation. Then, the microstructural mechanisms of cyclic strain localization in PSBs will be discussed. The final two sections are devoted to two topics of quite recent interest, namely the fatigue of ultrafine-grained (UFG) materials and fatigue in the UHCF regime of very low loading and exceptionally high fatigue lives.
2. Fatigue life representations – Wöhler (S-N), Coffin-Manson and Basquin Plots
Since the pioneering experiments of Wöhler, it has become customary to plot fatigue life data in so-called Wöhler or S-N diagrams (S: stress, N: number of cycles). It is interesting to note that, to the best knowledge of the author, Wöhler never presented his data in graphical form bu usually only in lengthy tables . Figure 1 shows schematically a Wöhler (S-N) plot in which the stress amplitude Δσ/2 (Δσ: stress range) is plotted against the number of cycles to failure, Nf. In this particular case, a plateau (stress level Rw) is indicated in the
low-stress (long life) HCF regime, implying that a fatigue limit exists in the sense that at stress levels below the plateau, fatigue life should become infinite. For decades, the general opinion was that, in particular in the case of ferritic steels, a true fatigue limit existed in the HCF range.
Fig. 1. Schematic Wöhler (S-N) fatigue life curve (with a fatigue limit), hysteresis loops are indicated. After .
Only in recent years has it been questioned whether such a fatigue limit extends beyond the HCF into the UHCF range, compare Section 6. While it had become clear after the work of Ewing and Humfrey that there must be some microplastic deformation occurring during fatigue, the plastic strain amplitude had not been used in the description of fatigue life until Coffin  and Manson  formulated the fatigue life law named after them in the fifties of the last century. The role played by the plastic strain amplitude Δεpl/2 (Δεpl: plastic strain
range) is indicated in Fig. 1, showing typical open hysteresis loops (stress σ vs. strain ε ), for different levels of the stress amplitude. The widths of these loops at zero stress (identical to Δεpl) decreases as the stress level
decreases but vanishes only below the fatigue limit at which it is still finite (some 10-5 to 10-4), indicating that such low plastic strain amplitudes are non-damaging, probably because they are almost reversible in a microstructural sense and do not cause irreversible damaging changes at the surface.
Following the work of Morrow , very useful fatigue life laws based on cyclic-stress-strain relationships can be formulated. In addition to the Wöhler or S-N plot of stress amplitude Δσ/2 vs. Nf , it is common to make
also use of the Basquin relation for the HCF range:
b f f el
and the Coffin-Manson law for the LCF regime:
c f f pl
Here, Δεel/2 is the elastic strain amplitude, E is Young’s modulus; σf’ and εf’ are the fatigue strength and
fatigue ductility coefficients, respectively, and b and c are the fatigue strength and the fatigue ductility exponents, respectively. Since the total strain is εt = εpl + εel, these two laws add up to the total strain fatigue life
relationship, compare : c f f b f f pl el t
which corresponds in the asymptotic limit of large strain amplitudes to the Coffin-Manson relation, whereas, at very low amplitudes, it approaches the relation between stress amplitude and number of cycles to failure as in the Wöhler-type S-N plot. For this reason, the use of this total strain fatigue life relation is sometimes favoured and very useful, see Section 5.
3. Early fatigue damage: the french curve – initiation of critical cracks
As early as in 1933, French proposed the so-called “critical damage curve” for materials of known S-N curve exhibiting a fatigue limit . This approach assumes that the material is initially defect-free. The French curve which is obtained in a two-stage fatigue experiment, compare , represents “cum grano salis” the number of cycles necessary for the initiation of a crack of a critical length which is roughly equal to the critical size of non-propagating cracks. Depending on the details, the lengths of these initially formed microcracks in a fatigued steel have been found by Klesnil  to lie in the range between just a few and some ten microns. The number of cycles separating the French curve from the S-N curve at a particular stress level can be considered to represent the period of crack propagation after microcracks of critical size have been initiated.
Figure 2 shows, as an example from Klesnil’s work, a French curve obtained on the Czechoslovak low-carbon steel ýSN 12 010 . In this case, microcracks of a few microns in length were noted at stress levels below the French curve, and longer microcracks of ca. 100 μm length, lying in persistent slip bands (PSBs), were observed at higher stress levels. In the present context, it is important to note, compare Fig. 2, that the period of crack propagation occupies a large fraction of fatigue life at high stress levels in the LCF range and decreases continuously with decreasing stress level until it becomes almost negligible at the HCF level of the fatigue limit. Thus, in HCF, fatigue crack initiation occupies a major fraction of fatigue life, as found in some standard text-books  and in more detail in . Moreover, this should be even more true important in UHCF at very high Nf, see Section 6.
Fig. 2. Example of French curve for steel ýSN 12010, compared with fatigue life curve. Failures or no failure are indicated by upward/downward. arrows, respectively. From , after M. Klesnil 
4. Cyclic strain localization in persistent slip bands
Cyclic strain localization in PSBs and the initiation of fatigue cracks in fcc metals have received much attention since the pioneering work of Thompson et al. . In PSBs, the local plastic strain amplitude is enhanced by two orders of magnitude or more, compared to the surrounding matrix. Fatigue crack initiation occurs at the surface at the sites of emerging PSBs, where complex extrusions develop. While it is true that the importance of PSBs is more or less confined to fatigued simple ductile materials and is of much less relevance with respect to the fatigue resistance of structural materials of practical importance, the work on PSBs has fascinated many researchers and has led to a generally improved understanding of dislocation behaviour in fatigued metals, as discussed, for example, in [3,12,13,14].
With the aid of TEM it became possible to characterize in detail the dislocation distributions and to identify the governing dislocation mechanisms of cyclic strain localization in PSBs of fcc single crystals with the so-called “ladder structure” or “wall structure”. Based thereupon, Essmann et al.  developed a semi-quantitative model (called EGM model subsequently) of the evolution of the surface relief of PSBs at the sites of emerging PSBs, in fair agreement with observations. In the model, the steady-state equilibrium of the defect content in cyclic saturation is analyzed semi-quantitatively, taking into account the production and annihilation of dislocations and point defects. For details, the reader is referred to [3,12,13]. The underlying assumptions are so general that the predictions, perhaps with slight modifications, will also apply to other materials in which PSBs do not necessarily have the ladder structure. In passing, it should be noted that Brown had developed a detailed model of the dislocation processes in PSBs, paying special attention to the stress singularity at the surface site of an emerging PSB . In a later extension of the model, Brown and Nabarro  arrived at a model of extrusion formation that, in its net result, is very similar to the EGM model.
Fig.3. Schematic illustration of evolution of surface relief at emerging PSB in the absence of diffusional effects. a) Interfacial dislocations accumulate at PSB-matrix interfaces. b) Rapid formation of “static” extrusions by emergence of interfacial PSB-matrix dislocations.
c) Gradual roughening of surface of extrusion by random slip in PSB. After [3,12,13].
initiation growth Failure French Curve initiation growth Failure French Curve c) c)
Figure 3 shows in a strongly simplified view the subsequent stages of the dislocation pattern in a PSB, as envisaged in the EGM model. In this picture, the dislocation dipoles which prevail in a high density are omitted. Then, in cyclic saturation, essentially only so-called PSB-matrix interface dislocation layers are left, as shown in Fig. 3a. During subsequent cyclic deformation, these interface dislocations glide out step by step, leaving slip steps at the surface behind which constitute extrusions, as shown in Fig. 3b. The EGM model predicts the initial rapid growth of these so-called static extrusions of height e. The extruded volume matches precisely the volume of vacancy-type defects that accumulate in cyclic saturation. The local vacancy defect concentration
C in the dislocation walls (volume fraction fw ≈ 0.1) of the ladder structure is established as
the result of a balance between annihilations of very close (vacancy) edge dipoles and formation of edge dipoles.
C is estimated as 6×10-3. Slipping out of so-called PSB-matrix interface dislocations leads to a
one-dimensional elongation of the PSB lamella in the direction of the Burgers vector b, creating one static extrusion of height e on each side of the crystal:
e ≈ 0.5 sat v
C fw ≈ 3×10-4 D, (4)
where D is the specimen diameter measured in the direction of the Burgers vector. Thus, it is predicted that the extrusion heights will be the larger, the thicker the fatigued single crystal is. In the case of a polycrystal, D would represent the grain size, and the predicted height of an extrusion in a surface grain would be twice as large as according to eq. (4), because only one extrusion would form. Nonetheless, extrusions in polycrystals should be much smaller than in single crystals because the grain size is generally much smaller than the specimen diameter. The described purely mechanical material extrusion process can operate in particular at low temperatures, as had been observed, compare [3,13,14]. Continued cyclic deformation will lead to a gradual surface roughening of extruded PSB material, see Fig. 3c, which can be estimated semi-quantitatively [3,12,13] and which should be similar in polycrystals and in single crystals. Stage I shear cracks are initiated at the PSB-matrix interfaces and/or in locations of stress enhancement in the roughened extrusion surface.
Since the EGM model deals almost exclusively with the formation of extrusions and not of intrusions, some clarifying comments on the role of intrusions are in place. Before the advent of TEM and before high-resolution SEM techniques had become available, the very early models of the surface profiles of PSBs were constructed to predict so-called “extrusion-intrusion pairs”, as summarized in . Today, it is clear these views are no longer tenable. Thus, the EGM model essentially predicts only extrusions. Intrusion-like deepenings which can be regarded as microcracks are considered to arise as a consequence of the extrusions that develop first. Polák, in an attempt to extend the EGM-model , considered also the migration of point defects from the PSB band to the surrounding matrix. A more detailed discussion of the model and its consequences is found in the recent review by Man et al. [18,19]. Essentially, the Polák model then predicts, in addition to the extrusions forming at the surface in the centre of the PSB, intrusions at both PSB-matrix interfaces. Man et al. have studied the PSB surface profiles, mainly on fatigued polycrystalline stainless steel, in great detail, using in particular atomic force microscopy (AFM), as summarized in . While it cannot be denied that the authors succeeded to reveal many previously unknown details, it is noted, in passing, that their observations would have been even more informative had the studies been performed on monocrystalline material, in which the effects would have been significantly larger. Nonetheless, the author maintains that, most “intrusions” revealed by Man et al. were in fact embryonic cracks. The reasons are that the bulk of the experimental observations indicate clearly that the dominant effects observed are as follows. 1) At the very beginning, bulgy extrusions form. 2) Only later, “intrusion-like” deepenings, described as “very fine and thin in comparison with extrusions”  are observed to develop. 3) They are not formed on both sides of the extrusion but “at the side of the extrusion where the emerging active slip plane is inclined to the surface at an acute angle” . This corresponds to the PSB-matrix interface at which crack initiation is expected to occur preferentially [12,15,16].
These experimental facts suggest strongly that the “intrusions” are much less dominant than the extrusions and that they do not develop by a mechanism comparable to that of extrusion formation, as proposed by Polák.
Rather, much of the experimental evidence suggests that “intrusions” develop as a consequence of the previously formed extrusions and are in fact embryonic stage I shear cracks.
5. UFG Materials
In recent years, bulk UFG (ultrafine grain size: below one micron) materials have attracted considerable attention. These materials have attractive mechanical properties, in particular extraordinary high strength and appreciable ductility. They are produced by severe plastic deformation techniques such as ECAP (equal channel angular pressing), compare . The fatigue properties of these materials are interesting ín several respects, compare [21-23]. In UFG copper, fatigue damage occurs in the form of macroscopic shear banding, and cyclic softening accompanied by “bimodal” grain coarsening is observed, compare Fig. 4.
Fig. 4. Cyclic strain localization and shear banding in UFG copper fatigued at RT. Stress axis horizontal. Surface observations. a) Shear bands in “patches”. b) Extended shear bands. c) TEM observation of locally coarsened grain/subgrain microstructure. From [22,23].
It is interesting that the fatigue lives of UFG materials, when plotted in HCF and UHCF Wöhler (S-N) diagrams, are always larger than those of the conventional grain (CG) size counterparts, whereas the opposite is true, when the fatigue life data are plotted in LCF Coffin-Manson fatigue life diagrams. The latter is believed to be a consequence of the reduced ductility of the ECAP-processed material. This behaviour can be understood in a total strain fatigue life diagram [22,23]. Considering UFG materials as “strong” and CG materials as “ductile” materials, as shown in Fig. 5, it follows that the fatigue life curves of both classes of materials are expected to intersect. Thus, the fatigue lives of UFG materials should be larger than those of CG materials in the HCF regime (corresponding to the Wöhler-type S-N plot), but smaller in the LCF range (corresponding to the Coffin-Manson plot). This prediction has been verified for UFG specimens of α-brass (see Fig. 6), aluminium and UFG copper .
Fig. 6. Crossing of fatigue life curves of UFG a
The ductility of UFG materials can be enh strength. Then a bimodal grain size distributio (compare Fig. 4c), develops which, in the case LCF range. Figure 7 shows fatigue life da microstructures and, in addition, with a bimodal different microstructures) are shown in a Wöhle 7b). In the first case, ECAP-processed UFG c copper and CG copper. In the second case, one by CG copper and, finally, UFG copper. The fatigue-resistant than the CG copper in both cas bimodally coarsened UFG copper exhibits hig amplitudes investigated . Such improveme structures have so far not been reported for oth bimodal UFG copper was more fatigue-resistant strain fatigue life diagram, the bimodally coar copper in the whole range of amplitudes inve introduction of bimodal grain structures have so
Fig.7. Fatigue life data of commercial purity ECAP-proc copper. a) Wöhler (S-N) plot, stress amplitude Δσ/2 vs. nu
Δεpl/2 vs. Nf .From . 103 10 10-3 10-2 Δσ/2 = co Δσ/2 = co
/2r 103 10 10-3 10-2 Δσ/2 = co Δσ/2 = co
and CG α-brass in total strain strain fatigue life diagram. After . hanced by a mild annealing treatment at the expense of
on, similar to the one that evolves during cyclic deform of copper, leads to a significant fatigue life enhancement ata of commercial purity copper with CG and UFG l grain distribution . The data (lumped together for th er-type S-N plot (Fig. 7a) and also in a Coffin-Manson plo copper exhibits the longest fatigue lives, followed by bi finds the longest fatigue lives for the bimodal copper, fo e important result is that the bimodal UFG copper was
ses. As a consequence, in a total strain fatigue life diagra gher fatigue lives than the CG copper in the whole ra
ens of the fatigue strength by introduction of bimodal her UFG materials than copper. The important result is th
t than the CG copper in both cases. As a consequence, in rsened UFG copper exhibits higher fatigue lives than th
estigated . Such improvemens of the fatigue stren far not been reported for other UFG materials than coppe
essed UFG copper, compared with bimodally coarsened UFG copper an umber of cycles to failure, Nf. b) Coffin-Manson plot, plastic strain amp
See text and original publication for details. 4
105 106 107
nst., Δεpl/2 = const., CG-α-brass, d ≈ 40 μm nst., Δεpl/2 = const., UFG-α-brass, d ≈ 750 nm
reversals to failure, 2 Nf α αα αEUDVV 8)*VWURQJ &*GXFWLOH 4 105 106 107 nst., Δεpl/2 = const., CG-α-brass, d ≈ 40 μm nst., Δεpl/2 = const., UFG-α-brass, d ≈ 750 nm
reversals to failure, 2 Nf α αα αEUDVV 8)*VWURQJ &*GXFWLOH f some mation t in the G grain e three ot (Fig. imodal llowed s more am, the nge of l grain hat the a total he CG gth by er. nd CG plitude
6. Ultrahigh Cycle Fatigue (UHCF)
Laboratory fatigue tests are usually confined to some 107 cycles. However, in practice, there are many examples of failures after much larger numbers of cycles, with Nf in the range of 109 cycles or more, e.g. in vibrating or rotating machine components. Research in the UHCF regime has become an important topic, referred to as UHCF or VHCF, since the International Conference “Fatigue Life in Gigacycle Regime“ (later called VHCF-1) in the year 1998. The problem at the heart of UHCF is whether a “traditional” fatigue limit in HCF extrapolates into the UHCF range and poses the question whether a fatigue limit exists in the UHCF regime.
Early research focused primarily on high-strength steels which did not show a fatigue limit beyond the HCF regime, but failed by subsurface so-called “fish-eye” fractures in UHCF. The cracks initiated at internal heterogeneities, in particular, non-metallic inclusions of ca. 10 μm diameter [25,26]. Bathias  has explained in a schematic diagram how the crack initiation frequency and sites vary from LCF to HCF and then UHCF, compare Fig. 8. In the LCF range, many crack initiation sites develop at the surface. In the HCF regime, surface damage still occurs but in a less severe manner. Thus the crack initiation sites are similar but less severe and fewer. Finally, in the UHCF range, at even smaller stress amplitudes, surface damage becomes more or less negligibly small. Then, cracks that initiate at internal heterogeneities can slowly grow to the surface and become life-controlling.
Fig. 8. Schematic of shift of fatigue crack initiation sites from surface to interior .
Fig. 9. Schematic fatigue life diagram for LCF, HCF and UHCF ranges. After [26,27].
Nishijima and Kanazawa  have interpreted the HCF/UHCF fatigue life data in terms of a dual-stage fatigue life diagram, based on the superposition of two separate fatigue life plots describing fatigue life for surface and subsurface failure, respectively. Summarizing, the fatigue lives can then be represented schematically over the whole range, from LCF to UHCF, as shown in Fig. 9 , with approximate boundaries separating the regimes of HCF and UHCF, on the one hand, and surface and subsurface internal failures on the other hand.
More recently, attention was also focused on UHCF of simple single-phase materials without internal heterogeneities. In the case of copper fatigued ultrasonically for more than 1010 cycles well below the traditional PSB threshold, fatigue-induced surface roughening, cyclic strain localization in PSB-like bands and
stage I shear cracks were observed , as proposed in an earlier model of UHCF of ductile fcc metals , compare Fig. 10. The question whether these cracks were non-propagating or whether they could ultimately lead to failure is still under discussion. In Fig.10a, in a FIB section parallel to the stress axis, the fatigue-induced surface roughness is clearly recognizable and can be evaluated quantitatively to yield a very low cyclic slip irreversibility of just some 10-4 . However, the cumulative irreversible cyclic shear strain is nonetheless very large (>30!!) because of the very high number of cycles. Fig.10b shows clearly that cyclic strain localization has occurred as a consequence of the very high number of loading cycles in spite of the fact that the loading amplitude was below the traditional PSB threshold.
Fig.10. Copper polycrystal fatigued at RT below the traditional ultrasonic PSB threshold to N = 1.59×1010 cycles, σ: stress axis. a) Surface
roughness profile and stage I crack initiation (FIB). b) Lamellae of slip localization (SEM). The stress axis is horizontal. From .
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