Cyclic deformation and fatigue behaviour of ?-iron mono-and polycrystals

International Journal of Fracture, Vol. 17, No. 2, April 1981 © 1981 Sijthoff & Noordhoff International Publishers Alphen aan den Rijn, The Netherlands

193

Cyclic deformation and fatigue behaviour of a-iron mono- and polycrystais

H. M U G H R A B I , K. HERZ* and X. STARK**

Max-Planck-Institut fiir Metallforschung, Institut fiir Physik, Heisenbergstrasse l, 7000 Stuttgart 80, W-Germany

(Received February 8, 1980; in revised form June 13, 1980)

A B S T R A C T The reported studies are based on a series of cyclic deformation tests that were conducted at room temperature on decarburized high-purity a-iron specimens in mono- and polycrystalline form. The experimental data cover plastic strain ranges Aepl in the regime 10 4 ~< Aep~ ~< 10 2 and variations in cyclic plastic strain rates ~pt between - 10 -5 and - 10 2 s ~. In the case of single crystals, the effect of solute carbon ( -30 wt.ppm) was investigated as well. The mechanical data were supplemented by detailed studies of the dislocation arrangements by transmission electron microscopy and of the surface patterns by scanning electron and optical microscopy.

Detailed accounts are given of the following topics: cyclic hardening and saturation, dislocation mechanisms, shape changes due to asymmetric slip of screw dislocations, cyclic stress-strain response and fatigue crack initiation.

Under conventional conditions of "high" k.t (~>10 4s ~) the fatigue behaviour of a-iron at room temperature reflects the low mobility of the screw dislocations which is characteristic of the low- temperature mode of deformation of body-centred cubic (b.c.c.) metals. As a consequence the behaviour exhibits significant differences with respect to that of fatigued face-centred cubic (f.c.c.) metals such as: strongly impeded dislocation multiplication below Aept - 5 × 10 -4, appreciable secondary slip at higher Aepl leading to a cell structure (persistent slip bands do not form), shape changes due to asymmetric slip of screw dislocations and a relatively high effective stress level.

The reduction of ~p~ and the presence of solute carbon atoms modify this behaviour significantly, making it more similar to that of f.c.c, metals. In all cases it was found that only the athermal component of the peak (saturation) stress but not the latter itself represents a suitable measure of the properties of the dislocation substructure.

On the basis of the cyclic deformation behaviour and of observations of trans- and intergranular fatigue crack initiation it was concluded that the fatigue limit of a-iron is an intrinsic property of the b.c.c. structure whose characteristics, however, are affected sensitively by interstitial impurity content and by the strain rate of the fatigue test.

I. Introduction

The basic mechanisms of metal fatigue have been studied in most detail on face- centred cubic (f.c.c.) metals and to a much smaller extent on metals of other crystal structures (for a review, cf. Grosskreutz and Mughrabi [1]). In the case of body- centred cubic (b.c.c.) metals the glide properties of dislocations are rather complex and depend sensitively on temperature, strain rate, small amounts of (interstitial) impurities and on the sense of deformation. Thus it is not surprising that a compre- hensive understanding of the behaviour of b.c.c, metals under cyclic stressing is still

* Present address: Staatliche Materialpriifungsanstalt, Universit/it Stuttgart, 7000 Stuttgart 80, F.R. Germany **Present address: Siemens AG, WIS MB TE 112, Balanstr. 73, 8000 Miinchen 80, F.R. Germany.

0376-9429/81/020193-28 $00.20/0 Int. Journ. of Fracture, 17 (1981) 193-220

194 H. Mughrabi et al.

lacking. On the other hand, it must be considered unfortunate that little use has so far been made of the fact that the unidirectional deformation properties (in tension and compression) of b.c.c, metals have been investigated rather extensively during the last two decades and that interesting differences and similarities with respect to the mechanical behaviour of f.c.c, metals have been established (cf. the reviews by Hirsch [2], Christian [3] and ~estak and Seeger [4]).

During the last 6 years the room-temperature cyclic deformation and fatigue behaviour of a-iron, which is perhaps, traditionally, the most important b.c.c, metal, have been investigated in a series of investigations in our laboratory. In most cases single crystals were used in order to facilitate the study of the complex crystallographic aspects of the glide behaviour of b.c.c, metals. The following presentation will be based on the central results of these investigations which will be contrasted against the background of related studies and discussed in the light of our current knowledge of dislocation glide properties in b.c.c, metals. The major topics will be cyclic hardening and saturation, the cyclic stress-strain response, the evolution of the dislocation substructure, asymmetric slip behaviour, the development of the surface pattern and the initiation of fatigue cracks.

2. Basic aspects of the dislocation glide behaviour in b.c.c, metals

Detailed accounts of the glide properties of dislocations in b.c.c, metals can be found in the cited reviews [2-4]. Here, a simplified description will be given of the central facts. A major difference of the mechanical behaviour of b.c.c, metals with respect to that of f.c.c, metals is the strong dependence of the flow stress on temperature and strain rate at low temperatures. This can be accounted for in terms of a proposal by Hirsch, cf. [2], who first recognized the distinguished r61e of the screw dislocations. Since the Burgers vector of the dislocations in the b.c.c, lattice is a /2( l l l ) (a: elementary cube edge), screw dislocations possess an extended core structure with a three-fold symmetry in their low-energy form and are sessile at low stresses. The transition of the extended sessile core to a glissile (planar) core is, intrinsically, a thermally activated process which requires high stresses at low temperatures. This explains the strong increase of the flow stress tr (or resolved shear stress ~-) of b.c.c. metals with decreasing temperature T (cf. Fig. la) in terms of a growing lattice friction stress and the fact that the screw dislocations can cross slip readily once they begin to glide.

In analogy to Seeger's theory of the dependence of the flow stress of f.c.c, metals on temperature T and strain rate ~ [5], it is convenient to describe -r (or tr) in terms of an athermal component ZG (or O'G) and an effective stress ~*( or tr*) which depends on

and T but only weakly on the density p and arrangement of the dislocations:

~" = ZG + ~*(~, T). (1)

In the b.c.c, lattice the dominant contribution to z* is the lattice friction stress (comparable to the Peierls-Nabarro stress) experienced by the screw dislocations. This is in contrast to the situation in the case of f.c.c, metals where ~-* is due largely to dislocation intersections [5] and not to a lattice friction stress. The athermal component ~G arises from the elastic interaction of the dislocations during glide and is usually related to the dislocation density p through

ZG = a G b X / p . (2)

Here G is shear modulus, b the modulus of the Burgers vector and a a geometrical constant (a -0 .1 -0.4) which depends on the arrangement of the dislocations.

Int. Journ. of Fracture, 17 (1981) 193-220

Cyclic deformation and fatigue behaviour o[ a-iron mono- and polycrystals 195

0" =IO'G + O'*(~,T)

<To T>To

,,

I I

To=To (~) (a)

I

T<To I T>To P

ve << v~ I Vo- v~ i

t

i 4 I

(b)

Figure I. Temperature dependence of the deformation behaviour of b.c.c, metals (schematically) (a) Temperature dependence of the flow stress ~. (b) Glide mode of dislocation segment (anchored at two pinning points) at low and intermediate temperatures.

At low temperatures ~* is rather high and considerably larger than ~ , as opposed to the case of f.c.c, metals where or* is always much smaller than crc. At intermediate temperatures above the transition temperature To (cf. Fig. la), o'* becomes negligibly small and the overall behaviour exhibits remarkable similarities to that of f.c.c, metals [2-4, 6]. The transition temperature To is, typically, -0.1 -0 .2 Tm in degree Kelvin (Tin: melting temperature) and lies considerably below the regime of self-diffusion. It is important to note that To is shifted to higher temperatures with increasing ~ [5]. In the case of a-Iron, To lies around room temperature at "low" strain rates ( ~ l0 -5 s-') but is significantly higher at "high" strain rates ( ~ l0 -+ s-l). Here, it should be emphasized that conventional cyclic strain rates in fatigue tests are "high" in the above classification. Hence, cyclic deformation of a-iron (and niobium) at room temperature will in most cases be controlled by the low-temperature deformation mode. (In the case of the refractory b.c.c, transition metals, e.g. tantalum, tungsten and molybdenum, To lies so high that the low-temperature mode will operate at any commonly employed strain rate at room temperature.)

Figure lb shows schematically the modes of dislocation propagation below and above To. In the low-temperature regime, the impeded glide of the screw dislocations makes dislocation multiplication by irreversible bowing a difficult process, whereas, for T ~ To, the mobilities of screw and non-screw dislocations become more comparable, permitting Frank-Read type dislocation sources to operate more easily, as is generally the case in f.c.c, metals.

The more complex glide elements of b.c.c, metals are conveniently described in the [001] pole figure shown in Fig. 2. For orientations of the stress axis of single crystals, characterized by the angles X and ~, glide occurs predominantly along the most highly stressed slip direction [l 11]. The macroscopically observed slip planes however, are frequently ill-defined and do not correspond to the lowest-index plane (101) (which we shall call the "nominal" primary glide plane) but to other planes of the [l l l]-zone which are described by the angle ~ . The observed waviness of the

Int. Journ. o[ Fracture, 17 (1981) 193-220


110

~o, l ~ / ~ m rs~

'1111 _%

Figure 2. Characterization of glide elements, mrss denotes the plane of maximum resolved shear stress and bp the primary Burgers vector. The angles X, ~ and qr are described in the text. After ~estfik and Seeger [4].

slip lines at the top face of crystals, i.e. where the primary Burgers vector bp = a/2 [111] emerges, in particular around and above T0, reflects the fact that the glide of the screw dislocations is inherently accompanied by frequent cross slip.

Differences between the glide properties in tension and compression represent additional features which are unknown from f.c.c, metals. These asymmetry effects depend on the orientation of the crystal axis and manifest themselves in the operation of different glide planes and in different flow stresses in tension and compression. They are also a consequence of the core structure of the screw dislocations and are therefore of particular significance in the low-temperature regime.

For our subsequent discussion of cyclic deformation the following features are noteworthy. 1)The screw dislocations experience a lattice friction stress which depends strongly on temperature and strain rate and gives rise to or*. 2) The glide of the screw dislocations is accompanied by easy cross slip. 3) Screw dislocations can exhibit asymmetric slip during forward and reverse motion. In addition, it should be noted that these properties depend sensitively on the purity of the specimens and can be modified appreciably by small amounts of impurities, in particular by solute interstitial atoms.

3. Experimental details

The observations were performed on cylindrical specimens of a-iron (purchased from Vacuumschmelze, Hanau) with a nominal purity of 99.98%. The single crystal specimens were prepared from single crystal rods of 4 mm diameter and about 15 cm in length that had been grown by the strain-anneal technique. These specimens had "nominal" single-slip orientations of 5 ° < X < 15° and 45 ° < ~ < 55 ° (cf. Fig. 2) with Schmid factors of -0 .5 (referred to the nominal primary slip system (701) [111]). They were 3 mm in diameter and had gauge lengths of -12 mm. The polycrystalline specimens were prepared from the same material and had a gauge length of 4 mm and a diameter of 2 mm. After decarburization by annealing in dry hydrogen at 760°C up to 250 h the solute interstitial content was generally (considerably) less than 5 wt.ppm. In some of the monocrystailine specimens carbon contents of -15 or -30 wt.ppm were intentionally retained or introduced by a carburizing treatment.

All cyclic deformation tests were performed in symmetric push-pull at room temperature using closed-loop control of the plastic strain range Aep~ and a constant


Cyclic deformation and fatigue behaviour of a-iron mono- and polycrystals 197

plastic strain rate ~pt (~pl = 2Aept" u, u: frequency). The fatigued specimens were subsequently investigated by standard metallographic techniques. For further details reference will be made to the original publications.

4. Cyclic hardening

4.1 Mechanical measurements

Here, we shall confine ourselves to cyclic hardening under conditions of "high" ~pl which are typical of conventional fatigue tests. The corresponding development of the deformation-induced dislocation arrangements will be discussed in Section 4.2. Examples of the effects of unconventionally "low" ~p¿ and of the solute carbon content will be considered later (Sections 6 and 7).

A set of cyclic hardening curves obtained at ~p~ = 4.5 x l0 -4 s-' on decarburized single crystals is shown in Fig. 3 in the form of a plot of the axial peak stress against the cumulative plastic strain e,l.cun~ = 2 N " Aepl (N: number of cycles) for different values of Aep~. Here and subsequently the peak stress is denoted by tr and is taken as the mean value of the axial peak stresses in tension and compression;* since the peak stresses in compression generally exceeded those in tension by up to 5%. In Fig. 3, two features are of interest: l) For Aep~ -values of some 10 -4, cyclic hardening is almost totally absent, no cyclic hardening could be detected at Aep~ = 10 -4. By contrast, f.c.c, metals, e.g. copper, nickel and silver, show significant cyclic hardening even in the range Aept <~ 10 -5 [8, 9]. Studies of amplitude-dependent internal friction at high or ultrasonic frequencies corresponding to "high" ~pt also show that irreversible changes in microstructure do not occur in a-iron below plastic strains of - 10 -4 [10-12], whereas, in the case of copper, irreversible changes are observed already at plastic strains of ~> 10 -6 [12-14].** 2) At higher Aep~, cyclic hardening is rapid initially, followed by a tendency of the peak stress to saturate. A saturation peak stress trs can usually be defined, although some times cumulative plastic strains up to -100 may be required in order to attain saturation.

MPo] I00

50

(7

kg

8

6

2

gpl : 4.5 ~ I0 -~ s- ~ dEpl O. 009 O. 006

0.0015 00005

71 I I L I I . ~ _

2 3 ~ 5 5 ep/c~,rn

Figure 3. Cyclic hardening curves of decarburized a-iron single crystals at room temperature. [7].

* The use of ~r (instead of ~-) is motivated by the difficulty in defining an appropriate resolved shear stress in view of the complex glide geometry discussed in Section 2.

**The plastic strains cited follow from the total strains measured in internal friction by subtraction of the elastic strains as estimated for stresses typical of the fatigue limits under the given conditions.



Figure 4. Dislocation arrangements in (101)-sections of a-iron single crystals after cyclic deformation at Aepl = 5 × 10 -3 and ~pl = 10 _3 s -I [21], cf. also [1]. (a) 8 cycles, primary edge dislocation multipoles. (b) 42 cycles, dislocation networks containing primary and secondary dislocations. Note curved free primary dislocations having predominantly screw character. (c)42 cycles, note attractive junction (left) and repulsive junction (right) in encircled region formed by interaction between primary (screw) dislocations and secondary forest dislocations. (d) 2000 cycles, dislocation cell structure. Note changing background contrast indicative of misorientations across cell walls.

Strain rate changes during the cyclic deformation test permit the determination of the components or~ and or* [8, 9, 15-17] in a similar fashion as in unidirectional deformation [181. The increase of tr during hardening is found to be largely due to an increase of or~, i.e. to an increase of the dislocation density, as in tensile deformation [4, 181.

4.2 Transmission electron microscopy (TEM) observations

The evolution of the dislocation substructure during fatigue at very low Aept(-10 -4) was studied by TEM on decarburized a-iron single crystals which were irradiated with fast neutrons before thinning in order to pin the dislocations [8, 9, 19, 20]. It was found that at "high" ~p~ even excessive cyclic deformation (ep~.cum- 100) led only to a minor increase in dislocation density mainly in the form of screw dislocation segments corresponding to a density of only l07 c m -2. These observations suggest that dislocation glide occurs by the low-temperature mode indicated in Fig. lb in a quasi-



reversible fashion, whereby the plastic strain is carried largely by the mobile non- screw dislocation segments with only little lateral displacement of the screw segments. Thus the negligible cyclic hardening at low Aepl (cf. Fig. 3) is simply a consequence of strongly impeded dislocation multiplication.

In the following we shall discuss the evolution of the dislocation pattern during cycling at intermediate to high Ae,t. Figures 4a-d show a series of TEM micrographs of sections parallel to the (701) planes of crystals deformed cyclically at "high" ~pl (10 -3 s -j) at Aep~ = 5 x 10 3. These specimens contained 15 wt.ppm carbon in solid solution and were aged after the test for 2 h at 80°C in order to pin the dislocations [16, 21]. At the "high" strain rate of - f0 -3 s -~ the overall behaviour and the observed dislocation arrangements (at high Aep~) were similar to decarburized specimens [9, 16]. Pronounced effects of the solute carbon atoms are, however, observed at "low" kp~ of

10 ~ s -~ (cf. Sections 6 and 7). After a few cycles (Fig. 4a) the dislocation pattern is reminiscent of the early

stage of fatigue of copper single crystals at similar amplitudes [1, 22]. Dense multipole clusters consisting predominantly of primary edge dislocations prevail, suggesting that slip is largely confined to the primary slip system and that screw dislocations annihilate mutually by stress-induced cross slip. In addition, some coplanar dislocations could be identified at this stage [21]. Somewhat later in the rapid hardening stage the dense arrays of primary edge dislocations disappear* and, instead, rather complicated dislocation networks consisting of primary and secondary dislocations (Fig. 4b) develop out of attractive junctions formed by the elastic interaction between primary glide dislocations and secondary forest dislocations of predominant screw character (Fig. 4c). The free dislocations between the networks, as observed in the unloaded state, exhibit curvatures which do not vary significantly from place to place. This suggests that the curvatures reflect equilibrium configurations mainly due to the counteracting line tension and lattice friction stresses and that there are no significant long-range internal stresses, as are observed in similarly deformed copper crystals [1]. During further cyclic deformation the networks link up and, in cyclic saturation, a closed three-dimensional cell structure is observed (Fig. 4d). The cell boundaries do not exhibit any preferential (crystallographic) alignment. They correspond to rather regular low-angle (twist-) boundaries that continue to become sharper during further cycling in saturation [17]. At the same time the misorientations across the cell boundaries increase and attain the order of degrees, giving rise to a severe X-ray Laue asterism which eventually makes the recognition of X-ray diffraction spots on Laue patterns impossible [17, 21]. These observations indicate that secondary slip is enforced at a rather early stage as a consequence of the impeded generation of mobile primary (non-screw) dislocations, similar to the case of the low-temperature unidirectional deformation of b.c.c, metals [2-4]. The fact that the (long) glide dislocations observed during rapid hardening (Figs. 4b, c) and (in the interior of the cells) in saturation [8, 19, 21, 23, 24] have predominantly screw character provides further evidence of the low mobility of the screw dislocations and of the impeded dislocation multiplication. In summary, the formation of a dislocation cell structure must be seen as a consequence of slip activity on more than one slip system which in turn stems from the relatively low mobility of the screw dislocations. Nonetheless, it must be assumed that the screw dislocations

* At lower amplitude (Aept = 1.8 × 10 3) and strain rate (ep~ = 3.5 x 10 4 s ~) dense multipoles of primary edge dislocations formed and persisted into early cyclic saturation in similar spec imens [I, 21]. Since this was not observed under comparable condit ions in decarburized spec imens which exhibited a cell s tructure [8, 9, 19, 20], it mus t be concluded that the behaviour at lower Aepj was affected by the carbon content under the stated conditions.

Int. Journ. of Fracture, 17 (1981) t93-220


are mobile enough to allow interactions between screw dislocations of the active slip systems. These stringent conditions are presumably fulfilled best in a range of temperatures not too far below the transition temperature To at the strain rate of the test (cf. Fig. la).

Evaluations of the dislocation densities accumulated during cyclic hardening showed that the density of primary dislocations exceeded that of the secondary dislocations by 30-50% [21]. This finding and the analysis of asymmetric slip [7] (cf. Section 5) provide the only evidence that, in spite of appreciable secondary slip, the primary slip system plays a distinguished role. The overall dislocation densities are almost one order of magnitude lower than in copper single crystals deformed cyclically in a comparable manner [1]. A plausible interpretation of this behaviour is that, except during the first few cycles, dense edge dislocation multipole clusters such as the "veins" in copper do not form because the low-temperature deformation mode promotes the preferential formation of screw dislocations which can annihilate to a large extent except for those retained in the cell boundaries. The relative frequency of dislocation annihilation suggests that, in spite of certain differences in the dislocation mechanisms with regard to copper crystals at similar amplitudes (for a discussion, cf. [1]), cyclic saturation is essentially also brought about by a dynamic equilibrium between the multiplication and annihilation of dislocations and not by quasi-reversible dislocation glide as at lower Aept.

In the experiments discussed ~-*, the effective and ~c, the athermal component of the peak resolved shear stress r were of comparable magnitude, the total dislocation density was found to be related toTo (but not to ~!) by Eqn. (2) with a -0 .1 [16]. The rather low value of a is consistent with the absence of appreciable long-range internal stresses and the presence of low-energy dislocation arrangements such as networks and subcell boundaries.

The described features of cyclic hardening and of the evolution of the dislocation substructure are also reflected in a number of investigations by other authors. Thus the rapid decrease of the rate of cyclic hardening below Aept ~ 10 -3 is evident in the studies of Yoshikawa and Okamoto [25] and of Ikeda [23, 26] on a-iron single crystals of other orientations at and also below room temperature.

Dislocation distributions similar to those discussed above have been observed by other authors on fatigued mono-crystalline [23, 24, 26, 27] and polycrystalline [28-35] specimens of a-iron. These studies have been reviewed in [l]. In particular, it has been noted that, at low amplitudes (of stress or strain), the dislocation microstructure is only weakly developed and contains (jogged) screw dislocations [27, 29, 31], whereas a three-dimensional cell structure prevails at higher amplitudes [23, 24, 28, 30, 31, 33, 34]. In addition, the observation of dense bands of dislocations and dislocation loops, sometimes arranged in rows, has been reported after cycling at low amplitudes [29, 32, 35]. According to Wei and Baker [35], the latter features are more pronounced in the near-surface regions. Still, similar observations have been reported for bulk material by McGrath and Bratina [31] and Bergstr6m et al. [32]. Existing differences between the results of different authors are presumably related to dissimilar experimental conditions with respect to testing procedure, effectively imposed cyclic strain rate and most importantly, specimen purity (cf. Sections 6 and 7).

5. Asymmetric slip and shape changes

In a study on a-iron single crystals fatigued in torsion, Nine [36] concluded that the observed slip planes were different for forward and reverse shear deformations. Similar effects of slip plane asymmetry have been observed on a-iron [7] and also on



niobium [37-39] single crystals in push-pull fatigue experiments at constant Ae~t. In these latter cases asymmetric slip manifested itself mainly in shape changes of the originally round cross sections which were found to become increasingly elliptical during cyclic hardening and, to a smaller extent, in saturation.

The development of these shape changes in terms of the ratio dm,x/drnin of the major to the minor axis [7] is shown in Fig. 5 for decarburized a-iron single crystals which were cycled at different Aepl (Fig. 1). The following features are noteworthy. For similar values of e , ..... the shape changes are small at low Aepl (no shape changes could be detected for Aeot = 10 4) and increase considerably with increasing Ae~t up to Aept- 5 × 10 -3, Beyond this amplitude the dependence on Aept becomes negligible. Since the asymmetric slip which is responsible for the shape changes [7, 36-38] stems from the non-equivalence of forward and reverse glide of the screw dislocations, it can be concluded from Fig. 5 that the screw dislocations perform only small displacements in the range of cyclic microstrains of some 10 -4 but glide more extensively as Ae~ approaches values characteristic of cyclic macrostrains ( - 5 × 10 3).

There is a close similarity between this description of the transition from cyclic micro- to macrostrains in terms of increasing glide of screw dislocations and the unidirectional yielding behaviour of a-iron at low temperatures as investigated by Solomon and McMahon [40], cf. also [41]. This analogy, in combination with the prevailing slip-plane asymmetry and the fact that the shape changes were found to be considerably smaller at "low" ~p~ [7], substantiates our earlier conclusion that, at room-temperature and "high" kpt, the overall behaviour is controlled largely by the low-temperature deformation mode.

A quantitative understanding of the shape changes at room temperature at small ep~ .... has been obtained for specimens orientated for single slip. In this case, only dislocations of the primary slip system need to be considered [7, 37, 38]. More complicated shape changes whose origin still needs clarification have been observed by Ikeda [23, 26] on a-iron single crystals of multiple slip orientations at, above and below room-tempteraure. In the case of polycrystals, individual grains at the surface suffer shape changes similar to those described giving rise to a striking roughening of the surface. The latter can lead to crack initiation at grain boundaries [7, 15], cf. Section 8.2.

dmax dram

4 1 3 t dcp~ 0009

i ' /

12 depl : 0006

] d e p , = O O O 6 y ~ 0 1 5 /

~i~ / / / o c2/7 ] _ / / i o c2/2 I // ~ • c2/3 i / / A ~ ~ o c2/,

5 tO ?5 cpt, cure

Figure 5. Development of cross-sectional shape changes of decarburized a-iron single crystals during cyclic deformation at different Ae0~ [7]. For details see text.


Cyclic deformation and [atigue behaviour of a-iron mono- and polycrystals 203

6. Cyclic stress-strain curves

The cyclic stress-strain (c.s.s.) curves, i.e. plots of cyclic saturation stress os versus plastic strain amplitude Aepl, of a-iron mono- and polycrystals depend characteristically on cyclic strain rate ~o~ [8, 9, 15, 19, 20] and carbon content [9, 20]. In this section we shall discuss typical examples in terms of the dislocation mechanisms responsible and shall present corresponding microstructural observations in Section 7.

Figure 6a shows the c.s.s, curve of decarburized a-iron single crystals deformed cyclically at the largest conventional, i.e. "high" strain rate (10 2 s-') investigated. The dependence of the athermal and effective stress components in saturation, o-s.o and o-*, respectively, on Aept are plotted as well. The c.s.s, curve at "high" ~,~ exhibits the following interesting features*: 1) In the range of very low Aepl (~<2x 10-4), o',

~,[MP4 W .//'I

o •

120

100

8£

60'

/ / : /

/ 20~- . /

I J

k

[MPa]

200.

~r

6,,

a)

lO0.

a~'pt [ 10-']

as,as.G t ~ /m,.,-h

20

7o

/

I

I

O = O.15 Hz

. O~s "

~pl =3.5 ~70-%

-o's,G ~,~ 0 =0.75Hz

b)

0 4 8 12 A EoI "10 3

* The considerable scatter of the data points in Fig. 6a at very low AEp~ ( < 6 x 10 4) s tems f rom experimental difficulties at the rather high frequencies required (up to 50 Hz) and f rom the fact that, because of the unusually slim and pointed shape of the hysteresis loops [20, 42], small errors in Aept cause appreciable uncertainties in t~. In this context, it is worthwhile pointing out that the basic features recognizable in Fig. 6a are also apparent in a qualitatively similar though slightly less marked fashion at strain rates of - l0 -3 s -1 at which the mentioned experimental limitations do not arise [7, 16, 19, 20].

Int. Journ. o[Fracture, 17 (1981) 193-220


120

I00

#0

60

6s,a

o ~ O G,

,° I 20'

L

/ x

....* t , , - • GS

1 2 3 4 5 # 7 ~ 9 Z~¢p I L J~lO*3~

c)

6~ Np4

100' 6'~

/ ' 60*

I /

// 1

.,.L 2

~ ~ 6s

t, 6 8 10 12 14 16 18 20

a ~pl {10 -~ ] d)

Figure 6. Cyclic stress-strain curves of a-iron mono- and polycrystals (a) Decarburized a-iron single crystals, k = 10 2 s-1 [8, 19, 20]. (b) Decarburized a-iron single crystals, ~pt = 2.5 x 10 -5 s t. [8, 19, 20]. (c ) Single crystals of a-iron+30wt.ppm carbon, ~p~ = 2.5 × 10 -5 s ~. [9, 20]. (d) Decarburized a-iron polycrystals. Measurements at constant cyclic plastic strain rate ~pt = 3.5 x 10 4 s I (full curves) Measurements at constant frequency v = 0.15 H z (dashed curves) I15].

increases sharply [19, 20, 42]. This increase is not associated with cyclic hardening (which is not observed) and is hence not due to an increase of p and o-~.G but to the growing effective stress ~r* as the screw dislocations begin to move [42]. 2) Up to Aept ~ 10 -3 a small plateau is observed. In contrast to the much more extended plateau exhibited by f.c.c, single crystals [1, 8, 9, 42, 43], this plateau is not related to persistent slip bands (PSBs) but is a result of the impeded cyclic hardening (cf. Section 4, Fig. 2) due to the still limited glide of the screw dislocations [7-9, 15, 16, 20, 42]. 3) Above Aep~ - 5 x 10 -4 cyclic hardening is enhanced by increasing glide of screw dislocations and enforced secondary slip which lead to a cell structure [8, 9, 19]. 4) At all values of A%I >, 2 × 10 -4, the effective saturation stress component tr* is consider-

Int. Journ. of Fracture, 17 (1981) 193 -220


ably larger than tr,.o [8, 19, 20]. It is important to note that this behaviour is fully consistent with the conclusions deduced from the asymmetric slip (cf. Section 5).

The behaviour is qualitatively similar at a somewhat lower strain rate ~p~ = 4.5 × 10 -4 S -1 [7, 16, 19, 20], the main difference being that, since a* is only about half as large as at ~pt = 10 -2 s -1, o-s.G exceeds ~r* beyond Aept- 3 × 10 -3. Recent studies of Ackermann [39, cf. 9, 43] and Anglada and Guiu [38] on niobium single crystals at room temperature indicate that the described c.s.s, behaviour is general to b.c.c, metal crystals at deformation temperatures which lie somewhat below the transition temperature To at the strain rate of the test (cf. Fig. la). As in the case of unidirectional deformation [2-4], modifications of this behaviour are expected at lower temperatures at which the screw dislocations are even less mobile.

The c.s.s, curve of decarburized a-iron polycrystals with a mean grain size o f - 1 0 0 / ~ m at ~pl =3 .5× 10-4S -1, is shown in Fig. 6b. Because of the overall similarity to that of single crystals at "high" ~p,, the behaviour is suggested to be governed by the glide properties of screw dislocations in a similar manner [15, 42], The important role of the cyclic strain rate ~pt is underlined by a comparison with tests at constant frequency v. Figure 6b shows that in the latter case the plateau at small Aept is only reflected in the trs.~ vs. Aept but not in the ors vs. Aep~ plot, since ~p~ and hence or* decrease with decreasing Aept. For the same reason o-* and try, measured at constant frequency, become increasingly larger (than at constant kpt), with increasing Aept in the range of higher Aept. Nonetheless, the reverse is true for the corresponding trs.o-values, the reason being that the cyclic hardenability is enhanced at lower strain rates [8, 9, 15, 16], cf. also Section 7.3.

The dislocation model presented in Fig. lb affords a simple explanation for this behaviour. Reducing the strain rate affects a transition from the low- towards the intermediate-temperature mechanism of dislocation g~ide and a tendency to form more of the dense multipolar arrays of non-screw dislocations, somewhat similar to those formed in f.c.c, metals [1, 9, 15, 16]. At "high" strain rates, on the other hand, the low-temperature deformation mode produces mainly screw dislocations (on more than one glide system) many of which can annihilate while the others are retained in the form of the low-angle subcell boundaries. Hence a higher dislocation density giving rise to a higher trs.c can accumulate at lower than at higher ~p~. These observations demonstrate that it is essential to obtain c.s.s, data of b.c.c, metals at constant ~pt rather than at constant v [15, 16, 42].

In their work on polycrystalline a-iron, Abdel Raouf and co-workers [44, 45-] emphasize correctly that the total saturation stress tr, increases with increasing ~pt but do not point out that their cyclic hardening data show clearly, as in our work, that cyclic hardening is largest at the lowest ~pt investigated. The c.s.s, data (tr~ vs. Aepl) obtained by these authors and by Wachob and Johnson [46] on a-iron polycrystals are very similar to our results [15] but do not extend to the range of low Aep~ where the plateau appears. Particular merits of these investigations are that they cover ranges of temperature up to 540°C [45] and down to 173 K [46].

Before turning our attention to the c.s.s, curves at unconventionally "low" kpt we wish to point out that the c.s.s, behaviour of pure a-iron at conventional ("high") strain rates is remarkable in at least two aspects with respect to that of f.c.c, metals: 1) The cyclic hardenability in the range of low to intermediate Aept (some l0 -3) is considerably lower [1]. 2) In agreement with the earlier contention of Wood and and co-workers [20], PSBs which are a common feature in f.c.c, metals were not observed [9]. In f.c.c, metal single crystals, PSBs can traverse the entire specimen cross-section and govern the c.s.s, behaviour over a wide range of Aep~ [1, 9, 42, 43, 47-49].

The c.s.s, curve of decarburized a-iron single crystals at "low" ~p~ (2.5 x 10 5 s-t),



shown in Fig. 6c, differs appreciably from that at "high" ~p~: 1) Cyclic hardening is non-negligible down to the lowest values of Aspt investigated. 2) tr* is only a small fraction of the value at "high" ~pt (cf. Fig. 6a). 3) o-s,s represents the dominant contribution to ~rs over the entire range of Aepl. All these features indicate characteristically that the thermally activated glide of the screw dislocations is enhanced considerably at low ~pt, thereby facilitating dislocation multiplication by a glide mode more similar to that in f.c.c, metals (as indicated in Fig. lb for b.c.c, metals at intermediate temperatures) than to that operating in the low-temperature regime [8, 9, 19, 20]. These conclusions are further substantiated by Berg-Barrett X-ray topography [20] and by the TEM observations [8, 19, 20], cf. also Section 7.2.

The effect of the "low" strain rate is even more pronounced in carburized a-iron single crystals. This is shown in Fig. 6d for specimens containing 30 wt.ppm carbon in solid solution [9, 20]. As mentioned earlier, the carbon content does not modify the behaviour at "high" ~pt (and high Aep~) appreciably. However, at "low" ~p~ the enhanced mobility of the screw relative to the non-screw dislocations, in combination with the preferential obstruction of the non-screw dislocations by the carbon atoms, leads to comparable mobilities of screw and non-screw dislocations and a very similar glide behaviour as in f.c.c, metals [9,20]. Thus, dislocation multiplication and cyclic hardening are very pronounced even at very low Aep~ and ~rs increases sharply with increasing Aep~. The c.s.s, curve exhibits a sharp break at Aept ~< 4 × l0 4. Beyond that amplitude PSBs form in increasing number with further increase in Asp~ and spread across the whole cross-section of the crystals (cf. Section 7). This process is accompanied by distinct cyclic softening before final saturation, as the plastic strain becomes more and more localized in the PSBs and is strongly reminiscent of PSB-formation in f.c.c, metal crystals [9, 43, 49]. Also we note that, in the Aep~-regime of PSB-formation, ~r~ is controlled largely by the plastic flow in the PSBs and increases only weakly, giving rise to a "plateau-like" c.s.s, behaviour (cf. Fig. 6d) similar to that in f.c.c, crystals [9, 42, 47-49].

7. Microstructural features in cyclic saturation

7.1 Surface observations

In this section we shall confine ourselves to observations on fatigued single crystals representative of the conditions corresponding to Figs. 6a, 6c and 6d. In the range of Aept <~ 2 - 3 × 10 -4 it was difficult in all cases to detect any features by optical or scanning electron (SEM) microscopy on specimens fatigued well into cyclic saturation. In particular, there was no evidence of PSBs which are easily recognizable in f.c.c, single crystals fatigued in the range of much smaller Ae,~(--5 × 10 -5- 10 -4) and above [8, 9, 49].

Under conditions of "high" ~pl, the decarburized a-iron single crystals exhibit slip lines which are rather diffuse and wavy except at the side face (121) (which contains the primary Burgers vector bp) (cf. Fig. 2), where they appear straight as in monotonic deformation [2-4, 6]. These slip lines become observable at Aepl- 3 × 10 -4 and intensify at higher Aept, accompanied by the increasing formation of "kink-band-like" surface markings which follow the trace of the ( i l l ) plane perpendicular to (/01) and are most pronounced on the side face (121) [9, 20]. These observations are similar to those of Doner and co-workers [50] and Ackermann [39, cf. 9] on niobium single crystals. Figure 7 shows SEM-micrographs typical of Aepwvalues of some 10 3. At the top face, where b o emerges (Fig. 7a), rather ill-defined and inexpressive bands of slip can be seen whose mean direction deviates consider-



Figure 7. Surface pattern (SEM) of decarburized a- i ron single crystals fatigued well into cyclic saturation, ~pt = 10 2s ~, Aepj = 6 × 10 -3, stress axis vertical. (a) Top face, trace of (/01) approximately horizontal. (b) Between top and side faces, nearer to grips.

ably from the trace of the nominal primary slip plane (701) and which correspond roughly to (211). In addition, faint traces belonging to (701) can sometimes be seen as well. In the study of Hempei and co-workers [51] on a-iron single crystals of similar orientation the observed slip traces belonged to the (701) glide plane. This difference with respect to our observations could be due to the fact that the specimens of Hempel and co-workers contained 0.006% carbon. Figure 7b shows a picture taken from the same specimen as Fig. 7a but from an area nearer to the grips where the surface pattern generally was more developed and where failure frequently occurred. In this case the specimen was rotated by 45 ° around its axis and the photographed area corresponds to a position between top and side face. Again the rough but more or less homogeneously distributed slip bands correspond approximately to (?.11). At the bottom right a microcrack following the direction of the slip traces has developed.

Figure 8 is representative of decarburized a-iron single crystals deformed cyclically into early saturation at "low" ~p~. At low magnification the dominant features on the top face (Fig. 8a) are "kink-band-like" markings along the trace of (111). In addition, however, fainter slip traces belonging to the nominal primary slip plane can be seen. They are most easily recognized in the "kink bands" and in broad ( - 100/~m) unidentified bands traversing the latter under an angle and, to a smaller degree,

Figure 8. Surface pat tern (SEM) of decarburized a- i ron single crystals fatigued into early cyclic saturation, ~pl = 2.5 × 10 -~ s ~, Aep~ = 8.5 × 10 3. Stress axis vertical. Top face. Trace of (/01) approximately horizontal (at vertex). See text for details. (a) Low magnification. "Kink bands" parallel to ( I 11) and slip traces parallel to (701). (b) Higher magnification. Slip traces parallel to (/01).



Figure 9. Surface pattern of single crystals of ca-iron + 30 wt.ppm carbon fatigued into saturation, ept = 2.5 × 10 s s ~, {~,l = 6 × 10 3. Stress axis vertical. Top face, trace of (101) approximately horizontal at vertex [9, 20]. (a) Low magnification (optical micrograph). "Pers i s ten t" slip bands (PSBs) parallel to trace of (]01). (b) Higher magnification (SEM). Wavy PSBs approximately parallel to trace of (]01).

between the "kink bands". At higher magnification, these slip traces had the appearance of clustered rough slip bands separated by rather featureless bands (Fig. 8b).

The appearance of the nominal primary slip plane (]01) is further enhanced at "low" kpl in the crystals containing 30wt.ppm carbon in solid solution (Fig. 9). Beyond Aep~ - 4 x 10 -4 slip traces along (/01) which increases in number with increasing Aept [9, 20] are clearly visible (Fig. 9a). Some broad "kink bands" can still be seen in some areas but they are no longer dominant. At higher magnification, it becomes obvious that the slip traces correspond to localized wavy slip bands which are reminiscent of PSBs and out of which material has been extruded (Fig. 9b).

7.2 Dislocation arrangement in the bulk

As discussed in Section 4, the low-temperature mode of deformation which prevails at "high" kpl produces little microstructurai changes at low Aepl and leads to a cell structure above Aepl--5 × 10 -4 (Fig. 4d). The cell structures observed in sections parallel to (101) and in other sections, e.g. (121), are similar and do not exhibit any preferential crystallographic direction or relation to the "nominal" primary slip system (101) [111]. This may be one reason for the inexpressive surface pattern (Fig. 7a). Still, it is unclear how the kink bands discussed in Section 7.1 and in [9] originate, since no corresponding dislocation arrangement was observed in the bulk. Possibly they correspond to a long-range correlation of the mutual misorientations between dislocation cells (cf. Section 4).

At "low" kpt dislocations of the primary slip system become much more dominant. In decarburized single crystals dense multipole clusters of primary edge- dislocation dipoles similar to those in fatigued f.c.c, metals [1] were observed at amplitudes as low as ~ept = 10 4 [8, 9, 19, 20]. At higher Aepl, dense muitipole bundles and walls perpendicular to bp consisting predominantly of primary edge dislocations were observed in some areas, while cell structures prevailed in other areas, as shown in Fig. 10a in a section parallel to (]01). TEM-micrographs of the (121) section show, in addition to the walls perpendicular to bp, wavy dislocation layers roughly parallel to (101) (Figs. 10b and c) and irregular dislocation cell structures (Fig, 10c) corresponding to those visible in the (101)-section (Fig. 10a). The overall impression is that, under the described experimental conditions, single slip manifesting itself in the dislocation bundles and walls perpendicular to bp in some areas, is in competition with a still

Ira. Journ. of Fracture, 17 (1981) 193-220

Cyclic deformation and fatigue behaviour o[ a-iron mono- and polycrystals 209

Figure 10. Dislocation arrangement in decarburized a-iron single crystal fatigued into cyclic saturation at ~pl = 2.5 × 10 s s ~ and Aeut = 5 × 10 3 [19, 20]. (a) Section parallel to nominal primary glide plane (i01) showing co-existence of dense (primary) edge-dislocation walls perpendicular to bp and of dislocation cell structure. (b) (12 D-section (perpendicular to (70 I)) with dislocation walls perpendicular to bp, dislocation ceils and dislocation layers approximately parallel to trace of (]01). (c) (121)-section. Note dislocation walls perpendicular to bp and dislocation layers roughly parallel to trace of (701).

existing tendency towards strong secondary slip activity which leads to cell structures in other areas, similar to Fig. 4d. A comparison of these observations with the surface pattern (Fig. 8) suggests strongly that the "kink-band-like" surface markings within which (101) slip traces are well developed (Fig. 8b) belong to slabs of material in which single slip dominates and which are roughly parallel to (111). These slabs are separated by other parallel slabs in which appreciable secondary slip gives rise to a



dislocation cell structure and only poorly developed features on the surface. The secondary slip activity is even less pronounced in the single crystals

containing 30 wt.ppm carbon in solid solution when fatigued at "low" kp~. In these specimens dense multipole bundles and walls perpendicular to bp, consisting predominantly of primary edge dislocations (and elongated pinched-off dipole loops), prevail at all Aept investigated. Figure 1 la shows an example from a section parallel to (701). (121)-sections perpendicular to (101) reveal that, in addition to the dense dislocation arrays perpendicular to bp, dislocation layers parallel to (701) extend through the former structures at an early stage in cyclic saturation (Fig. 1 lb). Figure I lc shows that, at a later stage in saturation, dislocation-poor channels running parallel to the trace of (101) traverse the dense dislocation arrays. The spacings between these channels, measured perpendicular to (]0 I), relate well with the spacings between the PSBs visible on the surface (Fig. 9).

Dislocation-poor channels are sometimes also observed in the (i01)-section (Fig. 1 la) along [111] and, less frequently, [121]. In the former case this would be consistent with the idea that these channels belong to PSBs that have traversed the primary glide plane by cross slip. The waviness of the PSBs, as seen on the top face (Fig. 9b), does indeed suggest that the PSBs meander around (701) by frequent cross slip. We conclude that the dislocation-poor channels correspond to the PSBs apparent at the surface and that they extend roughly parallel to (101) throughout the crystal. The fact that their formation is accompanied by cyclic softening (cf. Section 6) suggests that they are softer than the surrounding "matrix" which forms initially during cyclic hardening and out of which they evolve and that

Figure 11. Dis loca t ion a r r a n g e m e n t s in a - i r o n + 3 0 w t . p p m ca rbon single c rys t a l s f a t igued at ~ = 2.5 × 10 5 s ~. See tex t for deta i ls [9, 20]. (a) Aep~ = 6 × 10 3, sa tu ra t ion , (101)-sect ion. (b) Ae,~ - 5 × 10 a, ear ly sa tura t ion , (121)-section. (c) ~ep~ = 6 × 10 -3, sa tu ra t ion , (121)-sect ion.



the cyclic strain becomes highly localized in them after extensive dislocation annihilation has reduced the density of obstacles considerably.

A close similarity exists between these findings and PSBs observed by Wilson and Tromans [52] in surface-grains of a low-carbon steel that was fatigued in the as-quenched state at temperatures of 60 ° and 130°C. As pointed out in [9], the concept of dynamic strain aging [52] provides a satisfactory interpretation in the sense that the presence of carbon atoms at a moderately elevated temperature [52] at "high" ~pt or at room temperature but at a "low" strain rate (as in our case) renders screw and edge dislocation mobilities roughly equal and leads to dense edge-dislocation multipole arrays and subsequent instabilities in the form of PSBs just like in f.c.c, metals [1, 8, 9, 47-49]. A difference exists with regard to the structure of the PSBs. In f.c.c. metals the PSBs exhibit the so-called ladder structure [1, 48], whereas the PSBs in the case discussed appear to be almost dislocation-free channels. This is presumably due to the fact that the local strain rate in the PSBs is enhanced as a consequence of the approximately 100-fold strain localization [43] which suggests that in these PSBs the low-temperature deformation mode operates in spite of the nominally "low" ~,~. Isolated cell walls in the PSBs (cf. Fig. 1 la) lend some support to this interpretation.

7.3 Uniqueness of cyclic saturation state

Feltner and Laird [53] have classified a-iron as a wavy-slip material with a history- independent c.s.s.-curve. Other authors have subsequently investigated the influence of prior mechanical work [33, 54[ and of changes in Ae W [33, 34, 46] or epl [44, 46] on the final saturation stress value and on the dislocation microstructure of a-iron polycrystals. With one exception [34], these authors conclude that the saturation stress is a unique function of Aept, ~pt and T. Abdel Raouf and co-workers [33, 44] reported in addition that changes in ~p~ or Ae# changed the cell size to that value that would have been obtained in a test on a virgin specimen at the final value of ~pl and/or Ae,~. Chopra and Gowda [34], however, noted that, following a change from high to low Aep~, the peak stress and, in particular, the cell size may or may not convert to the cell size characteristic of a virgin specimen cycled at the lower Ae#.

In our own experiments on a-iron single crystals the changes in saturation peak stress following a change in ~,1 seemed to be reversible, as shown schematically in Fig. 12a [8]. In spite of this behaviour, the dislocation substructure did not fully convert to that characteristic of the final cycling mode. Thus, an a-iron single crystal that was first cycled into saturation at Aept = 5 × l0 3 and ~p~ = 2.5 x l0 -~ s -l, where- upon ~,~ was changed to l 0 -2 S -1 and cycling continued till a new saturation stress had

O( - F e 6

Epl 1

~pl,2 > ~pl,1

Cu

• [ ~1.2 1 ~p, 1

~'pl.2 " gpI, 1

a) N b) N

Figure 12. Schematic representation of response of peak stress ~ in cyclic saturation to change in cyclic plastic strain rate ~pl, characteristic of Aep~-values of some l0 3 [8], (a) a-Iron single crystals. (b) Copper single crystals.



been attained, exhibited a dislocation cell structure characteristic of the "high" strain rate which was, however, interspersed with dislocation walls perpendicular to bp similar to those in Figs. 9b and c. These walls had obviously been inherited and retained from the first deformation at "low" ~p~. (The reverse case, i.e. changing from "high" to "low" ~p~, was not investigated). These studies suggest, as first demonstrated by Lukfis and Klesnil [55] on copper for changes from high to low Ae,l, that even if the mechanical c.s.s.-response may indicate a fully reversible behaviour, this need not be true for the microstructure.

Finally, it is worthwhile pointing out that the c.s.s.-response of a-iron, following a change in ~p~, differs characteristically from that of a f.c.c, metal such as copper (cf. Fig. 12b). Following a change to a higher ~pt, an instantaneous increase in stress is observed in both cases which corresponds primarily to the difference between the effective stress levels at the two strain rates. Subsequently, the peak stress exhibits transient softening in the case of iron and transient hardening in the case of copper till the new saturation value is attained. (The opposite behaviour is observed when ~pl is reduced). Similar observations have been made by Abdel Raouf and Plumtree [44] and Wachob and Johnson [46] on a-iron polycrystals. The transient behaviour in the case of copper conforms with expectation in the sense that, upon increasing ~p~, ~r~,s is raised because of reduced dynamic recovery. The same would be true in a-iron, if the change in k,j did not at the same time affect the dislocation glide mode in a fundamental way. However, as discussed earlier in Section 6, cyclic hardening and hence ~r~,6 are larger at "low" kp~ (intermediate-temperature mode) than at "high" kp~ (low-temperature mode). Hence the net increase in trs following an increase in R,t is the result of the instantaneous increase in tr* and the superimposed gradual transient decrease in ~r~,s. These experiments substantiate, as could be expected from Eqns. (1) and (2), that o's,s (and not ~r~ !) is in good approximation a unique function of A~p~ and kpt in tests at constant (room) temperature. While the distinction between tr, and tr~,6 i~ not crucial in the case of f.c.c, metals, it is essential for b.c.c, metals, since tr* can exceed ~r~,G considerably at high ~pl (cf. Fig. 6a) or low T.*

7.4 Quantitative characterization of dislocation arrangements

Figures 13a and b show total dislocation densities p and mean cell sizes d in saturation, respectively, plotted versus tr~,6 and, for comparison, also versus cry. The data correspond to decarburized single crystals that were fatigued at widely differing Aepl and kpt [19, 20]. The values d were determined from mean linear intercepts on TEM-micrographs such as Fig. 4d, assuming a spherical shape of the cells [56]. Generally speaking, big differences between tr~ and ty~.s for a given p or d correspond to "high" kp~. It is evident, as in the case of the dislocation density during cyclic hardening [16] which was discussed in Section 4, that both p and d relate uniquely only with cr~,s but not with o-~. The fact that the quadratic relationship between tr,.s and p (cf. Eqn. 2) is only approximately obeyed in Fig. 13a is presumably due to an underestimation of p in the range of high dislocation densities, where individual dislocations in the cell walls are very difficult to resolve. The relationship between d and o'~,s lies between an inverse and a HalI-Petch type relationship (Fig. 13b). This suggests, according to an investigation on sub-boundary strengthening by Abson and Jonas [57], that the cell walls observed in fatigued a-iron represent boundaries of a strength intermediate between that of grain boundaries and of subcell boundaries

* Preliminary tests on niobium single crystals [39] indicate that, in this respect, the behaviour at room temperature is more similar to that of copper.



i ~ [cm-2] / " ( , .1.7 lo 1 ? o',~}

a / o x o

, .// o ./ °

109" x /

20 40 60 80 100

o',.~ [MPoJ 0,} o 0"° [MPo]

d from]

3O

20- • *

o o

o

k_

40 60 80 100

• ~,,o [,pol b) o o, [MPol

Figure 13. Dependence of parameters characterist ic of dislocation a r rangements in cyclically deformed decarburized a- i ron single crystals on saturat ion s tress [19,20l. (a) Total dislocation densi ty p as a funct ion of trs and tr,.6. (b) Mean cell diameter d as a funct ion of tr, and ~r~,G.

formed in high-temperature creep. Previously, Abdel Raouf and co-workers had reported an inverse relationship between d and trs for a-iron polycrystals fatigued at different Aepl [33] and different ~p~ [44]. However, our studies on single crystals (in which the structure is more homogeneous than in polycrystals) cover a range of d at least three times larger and indicate strongly that d decreases with increasing trs.G, regardless of whether tr~ increases or decreases. In particular, for a given Aepl, specimens cycled at "high" kpl can exhibit a larger tr, but a smaller tr~.G and hence a larger cell size than specimens cycled at "low" ~pt. This conclusion is complementary to the interpretation given in Section 7.4 for the c.s.s.-response following a change in kpt (Fig. 12a).

8. Fatigue crack initiation

8.l Single crystals

In our work on decarburized a-iron single crystals fatigued at "high" ~pt PSBs were strikingly absent in observations of the surface appearance and of the microstructure in the bulk [8, 9]. Crack initiation was frequently observed to occur (near the grips) in illdefined slip bands (Fig. 7b) which bear no obvious crystallographic relationship to the dislocation cell structure in the bulk. Slip-band cracking has indeed been observed before by other authors [24, 51, 58] on a-iron crystals cycled under conditions of "high" ~pt. The work by Hempel et al. [51, 58] is particularly noteworthy, since these authors reported examples of crack initiation in coarse slip bands that strongly resembled PSBs. Still, since their specimens contained 0.006% carbon, their results

lnt. Journ. of Fracture, 17 (1981) 193-220


do not necessarily contradict our conclusion that PSBs are absent in pure iron [8, 9] and also in pure niobium [9, 39] crystals at room temperature. Also, according to Hempel et al. [51, 58] specimens orientated for single slip should exhibit slip bands which follow the (101) plane, whereas in our case the slip bands corresponded approximately to (211). The latter finding suggests the possible importance of the slip plane asymmetry discussed in Section 5 as a controlling factor, since (211) corresponds approximately to the slip plane operating in compression, whereas the active slip plane in tension is (101) [7].

There can be little doubt that the preferred occurrence of slip-band cracking near the grips is associated with shape changes which develop (in addition to cross- sectional shape changes) as a result of asymmetric slip because of the constraints of the grips [7]. The work of Nine [36, 59] on a-iron and niobium single crystals fatigued in torsion and studies by Ikeda [23] and ourselves [7] on a-iron single crystals fatigued in push-pull suggest that fatigue is accelerated by the development (near the grips) of regions of localized deformation (by asymmetric slip). Thus Nine has shown that specimens of orientations for which asymmetric slip is not observed have longer fatigue lifetimes than those which exhibit asymmetric slip [59]. Attention must, however, be drawn to the fact that a discrepancy exists between these observations and the repeatedly reported insensitivity of the fatigue life of a-iron single crystals to specimen orientation [24, 60, 61], although perhaps not as many orientations as would have been desirable were investigated in these studies. Two other modes of fatigue crack initiation that have not been investigated so far but which appear possible in the light of the present studies [9] are l) cracking in kink bands at sites of marked surface rumpling in a fashion related to that demonstrated recently on copper crystals [62] and 2) slip-band cracking by near-surface glide processes which may differ substantially from those in the bulk [35], as suggested by studies on fatigued a-iron [63] and molybdenum [64] polycrystals which revealed a higher dislocation density near the surface than in the bulk.

In the case of a-iron single crystals which were fatigued at "low" ~pt, tests to failure were not performed, since this would have been too time-consuming at frequencies of - l 0 -3 Hz. Nevertheless, the rough slip bands parallel to (101) in the decarburized specimens (Fig. 8) and the PSBs along (101) in the specimens containing 30wt.ppm carbon (Fig. 9) must be considered as preferential sites for "crystallographic" slip-band cracking.

8.2 Polycrystais

A striking feature of published observations of crack initiation in polycrystalline a-iron or low-carbon steel fatigued at conventional, i.e. "high" ~p~ is that, in addition to reports on crack initiation in slip bands [29, 30, 35, 51, 58, 65, 66], the frequency of intergranular crack initiation has repeatedly been emphasized [10, 28, 51, 58, 60, 66-71]. Most of these studies refer (also) to conditions of high-cycle fatigue [10, 51, 58, 60, 66-71] under which fatigue crack initiation in f.c.c, metals like copper occurs predominantly in PSBs cf. Laird and Duquette [72]. Hence, the previously discussed rather different features of slip bands in a-iron as compared to copper*, cf. [28, 67],

* An unresolved discrepancy exists about the effect of ultrasonic fatigue frequencies as compared to conventional frequencies on the appearance of slip bands in high-cycle fatigue of a-iron and copper. While Wood and Mason [10, 12] found an enhanced concentration of slip into isolated slip lines in both metals, Awatani and co-workers [67] observed no appreciable effect in copper but noted a striking, almost complete absence of slip lines at ultrasonic frequencies in a-iron. Clearly, in our picture, ultrasonic frequencies should enhance the effect of "high" ~pt and promote a less damaging slip mode in a-iron at low amplitudes.



which make the former less susceptible to crack initiation [28] could be a possible reason for preferential intercrystalline crack initiation in polycrystalline a-iron. On the other hand, Golland and James [68, 69] suggested grain boundary embrittlement by even the smallest amount of oxygen to be the major cause. However, in many of the cited studies, intercrystalline cracking did not appear to be a result of enbrittlement but rather of localized cyclic deformation at the grain boundaries [15, 51, 58, 66, 67, 70, 71]. Moreover, since studies on fatigued polycrystalline molybdenum by Beard- more and Thornton [73] revealed a similar type of preferential crack initiation at grain boundaries, the possibility is suggested that the effect is general to fatigued b.c.c. polycrystals when the low-temperature mode of deformation prevails.

It was suggested by one of the authors and Wiithrich [7, 15] that incompatible shape changes induced by asymmetric slip in neighbouring grains at the surface can provoke crack initiation at grain boundaries. This possibility was tested by fatigue tests on decarburized a-iron polycrystals. The development of fatigue damage under conditions, where asymmetric slip was expected to be most severe, i.e. high Aep~ and "high" ~pt (cf. Section 5), was compared with observations at the same Aepl but at "low" ~pl, where slip plane asymmetry effects should be less pronounced [7, 15, 74]. Figures 14a and b show examples of crack initiation under the two conditions. At "high" ~pt, slip bands developed at a much slower rate than at "low" ~p~, just as in the case of single crystals (cf. Figs. 7a, 8a), whereas a surface rumpling due to shape changes of the grains built up much more rapidly and eventually led to crack initiation at grain boundaries which were approximately perpendicular to the stress axis (Fig. 14a). At "low" ~pl, crack initiation occurred much earlier in the more severe slip bands (Fig. 14b). The conclusion that, at conventional ("high") kpt, intergranular cracking provoked by asymmetric slip, should be the dominant mode of crack initiation has received considerable support through a recent study by Magnin and Driver [75] on two b.c.c, iron-based alloys (Fe-3%Si , F e - 26%Cr- 1% Mo) at room temperature. These authors demonstrated, as in the studies on a-iron [7, 10, 74], that the low- temperature mode (characterized by "high" dp~, high ~r* and strong asymmetric slip) promotes intergranular crack initiation. Furthermore they showed that critical strain rates exist, above and below which crack initiation occurs in the inter- and transgranular modes, respectively, cf. also [15].

Figure 14. Fatigue crack initiation in a- i ron polycrystals at different cyclic plastic strain rates ~p~. Aepl = 1.5 × 10 2. Stress axis vertical [15,74]. (a) "High" ~p~ (3.5 x 10 3 s-~). 1360 cycles. Intergranular fatigue crack initiation. (b) " L o w " ~pt (3.75 x 10 5 s ~). 375 cycles. Transgranular fatigue crack initiation.



9. The fatigue limit

In the past the discussion of the fatigue limit of a-iron (and low-carbon steels) was based mainly on data of the type first obtained by W6hler, cf. [76], i.e. on so-called S-N curves [32, 60, 61, 77-84]. The reported work suggests that one shortcoming of this approach arises from the fact that S-N curves are not usually obtained at constant cyclic plastic strain rate ~pl, as would be desirable for strain-rate- sensitive materials, but rather at constant frequency under conditions of prescribed constant load amplitude. The question whether, in the case of a-iron, the fatigue limit is intrinsically related to the b.c.c, structure [28, 32, 82-84] or due to initial dislocation locking [78,79] or to strain aging during fatigue [77,80,811 by solute interstitial atoms (carbon, nitrogen, oxygen), cf. the overview by Adair and Lipsitt [84], has frequently been considered in the light of the existence or non-existence of a fatigue limit in combination with a sharp knee in the S-N curve [77-84].

While the present work does not encompass a study of fatigue lifes, it clarifies in reasonable detail the dislocation glide processes up to the point of fatigue crack initiation under conditions of constant plastic strain amplitude. Moreover, the micro- scopic processes investigated were found to relate to a remarkable degree to peculiarities in the shape of the c.s.s, curves. From this point of view, it appears possible to characterize essential features of the stress and strain fatigue limits (see the work by Luk~i~ and co-workers [85], Laird [86] and ourselves I7-9, 15, 42, 49]) for the following cases: a) Decarburized a-iron fatigued at "high" ~pl, b) Decarburized a-iron fatigued at "low" kp~ and c) a-Iron containing solute carbon fatigued at "low" kpt.*

The experiments on decarburized a-iron mono- and polycrystals at "high" ~,~ (case a) indicate clearly that a narrow range of Aep~ and cr~ exists, corresponding to the plateau of the c.s.s, curve (cf. Figs. 6a and 6b), in which a transition occurs from quasi-reversible to irreversible dislocation glide. This transition is characterized by increasing glide activity of the relatively immobile screw dislocations accompanied by microstructural changes (cell formation), development of (ill-defined) slip bands and evolution of shape changes. The latter two effects have been identified as the dominant causes of fatigue crack initiation in mono- and polycrystals. Since both effects are intrinsically related to the glide of screw dislocations, they exhibit similar dependences on Ae,~ and kpl. These features justify the expectation that, in conventional fatigue tests at "high" ~,p~, decarburized a-iron possesses a fatigue limit as an intrinsic property [28, 32, 82-84] related to the peculiarities of the glide behaviour of screw dislocations in a b.c.c, lattice. The precise threshold value of mept is not easy to determine in the type of experiments described (for a recent discussion, see [42]) and is estimated to lie in the range 10 4<~mept ~<4× 10 -4. The threshold stress amplitude, on the other hand, should correspond rather well to the stress level of the plateau of the c.s.s, curve and should lie slightly below the macroscopic yield stress of the virgin material measured at the strain rate of the fatigue test [42], cf. also the earlier discussions [1, 7-9, 15, 16]. For the cases investigated, the stress fatigue limits, as deduced from c.s.s, data, are as follows: - 4 0 MPa for decarburized a-iron single crystals fatigued at kvl = 4.5 × 10-4 S I, -90 MPa for decarburized a-iron single crystals fatigued at ~pt = 10 2s ~ and - 8 5 M P a for decarburized a-iron polycrystals fatigued at kpl = 3.5 × 10-4 s ~.

For a-iron single crystals containing - 3 0 wt.ppm carbon in solid solution and fatigued at "low" ko~ (case c) the threshold amplitudes (Aep~ <~ 4× 10 4 and ~r~

* It should be clear that this discussion does not encompass the effects of surface quality and environment but refers to the given experimental conditions, i.e. specimens with chemically polished surfaces fatigued in air.



100 MPa) beyond which PSBs are observed (cf. Fig. 6d) should correspond to strain and stress fatigue limits, respectively, as in the similar case of fatigued f.c.c, metal single crystals [8, 9, 42, 49, 86], It should be noted that here, as opposed to case a, the stress fatigue limit lies well above the yield stress of the virgin material because considerable cyclic hardening associated with dynamic strain aging precedes the formation of the PSBs. The case of decarburized a-iron single crystals fatigued at "low" ~pt (case b) lies somewhere between the two extreme situations just discussed. The experimental data available do not permit deciding whether a well-defined threshold exists, especially since the c.s.s, curve (cf. Fig. 6c) does not exhibit any easily recognizable characteristic feature in the regime of low Ae,t.

In summary, we conclude that pure a-iron fatigued under conventional conditions ("high" ~,~) at room temperature should exhibit an intrinsic fatigue limit. The related finite plastic deformation threshold, cf. [8, 9, 42, 85, 86], can be viewed in the vein of earlier considerations by Gough [87], Dehlinger [88] and Hempel and co-workers [58, 60]. The evidence suggests strongly that the physical origin of the fatigue limit of a-iron is related to the b.c.c, structure, as suggested previously by Ferro and co-workers [82, 83], Wood and co-workers [28], Adair and Lipsitt [84], BergstrSm and co-workers [32] and by ourselves [7-9, 15, 42]. However, the "characteristics" of the fatigue limit, cf. Adair and Lipsitt [84], such as the magnitude of the stress fatigue limit, the existence or non-existence of a sharp knee in the S-N curve, etc., are modified appreciably by the interaction of dislocations with solute interstitials and, in addition, by the strain rate of the tests.

I0. Conclusions and final remarks

The main results of this investigation on the fatigue of a-iron at room temperature can be summarized as follows:

1. The cyclic deformation behaviour of pure a-iron in conventional tests at "high" ~pl is controlled by the low-temperature mode of deformation of b.c.c, metals and differs fundamentally from that of f.c.c, metals.

2. Characteristic features such as impeded cyclic hardenability at low Aept, considerable secondary glide activity, asymmetric slip of screw dislocations and a high effective stress level are general consequences of the low-temperature glide properties of the screw dislocations in the b.c.c, a-iron lattice.

3. The absence of persistent slip bands comparable to those in f.c.c, metals and the dominance of intergranular fatigue crack initiation in pure a-iron polycrystals represent further characteristics.

4. Both the reduction of ~p~ and the addition of solute interstitial (carbon) atoms modify the c.s.s, response and the evolution of the dislocation substructure appreciably and promote a behaviour that is more similar to that of f.c.c, metals.

5. In all cases the pertinent stress parameter that characterizes the properties of the dislocation arrangements formed is found to be the athermal component of the (saturation) peak stress but not the latter itself.

6. A physical basis for the fatigue limit of a-iron can be deduced from the fundamental cyclic deformation properties in conjunction with surface and microstructural observations. The fatigue limit is concluded to be intrinsically related to the b.c.c, structure. Its characteristics depend sensitively on t~p~ and solute carbon content.

The mechanical data and the microstructural observations underline the need for careful control and characterization of specimen purity and alloying content and the



importance of maintaining the cyclic strain rate constant in future fatigue studies on b.c.c, metals. Rewarding areas for further research are considered to be studies of the orientation-dependence of the fatigue properties of a-iron single crystals, combined studies on a-iron mono- and polycrystals below and above room temperature and complementary work on other b.c.c, metals and alloys.

Acknowledgments

It is a pleasure to thank Prof. A. Seeger and Dr. M. Wilkens for their interest and support of this work over the years.

R E F E R E N C E S

[1] J.C. Grosskreutz and H. Mughrabi, in Constitutive Equations in Plasticity, edited by A.S. Argon, MIT Press, Cambridge, Mass. (1975) 251-326.

[2] P.B. Hirsch, in Proceedings of International Conference on the Strength of Metals and Alloys, Supplement to the Transactions of the Japan Institute of Metals 9 (1968) XXX-XXXIX.

[3] J.W. Christian, in Proceedings of Second International Conference on the Strength of Metals and Alloys, Asilomar, American Society for Metals, Metals Park, Ohio (1970) 31-70.

[4] B. Sestfik and A. Seeger, Zeitschrift fiir Metallkunde 69 (1978) 195-202, 355-363, 425-432. [5] A. Seeger, The Philosophical Magazine, Series 7, 45 (1954) 771-773. [61 B. ~est~k and A. Seeger, physica status solidi (b) 43 (1971) 433 444. [7] H. Mughrabi and Ch. WOthrich. The Philosophical Magazine 33 (1976) 963-984. [8] H. Mughrabi, K. Herz and F. Ackermann, in Proceedings of Fourth International Conference on the

Strength of Metals and Alloys, Nancy, Vol. 3 (1976) 1244-1248. [9] H. Mughrabi, F. Ackermann and K. Herz, in Fatigue Mechanisms, Proceedings of an ASTM-NBS-

NSF Symposium, edited by J.T. Fong, American Society for Testing and Materials, Philadelphia ASTM-STP 675 (1979) 69-105.

[10] W.A. Wood and W.P. Mason, Journal of Applied Physics 39 (1968) 4514-4516. [11] C.F. Burdett, The Philosophical Magazine 24 (1971) 1459-1464. [12] W.P. Mason, Engineering Fracture Mechanics 8 (1976) 89-101. [13] T. Nakamura and K. Ishii, Proceedings of Fifth International Conference on Internal Friction and

Ultrasonic Attenuation in Solids, Aachen, edited by D. Lenz and K. LOcke, Springer Verlag, Berlin-Heidelberg-New York, Volume II, (1975) 478--485.

[14] H. Miillner, P. Bajons, H. Kousek and B. Weiss, Proceedings of Fifth International Conference on Internal Friction and Ultrasonic Attenuation in Solids, Aachen, edited by D. Lenz and K. LOcke, Springer Verlag, Berlin-Heidelberg-New York, Volume II, (1975) 76-383.

[15] H. Mughrabi, Zeitschrift fiir Metallkunde 66 (1975) 719-724. [16] H. Mughrabi, K. Herz and X. Stark, Acta Metallurgica 24 0976) 659-668. [17] H. Mughrabi, R. KOtterer, K. Lubitz and H. Kronm~iller, physica status solidi (a) 38 (1976) 261-270. [18] J.T. Michalak, Acta Metallurgica 13 (1965) 213-222. [19] K. Herz, H. Mughrabi and M. Wilkens, Arbeitsbericht MPI 77/P3 (in English) des Max-Planck-

Instituts for Metallforschung, Institut for Physik, Stuttgart, Federal Republic of Germany (1977). [20] K. Herz, Doctorate Thesis, Stuttgart University (1976). [21] X. Stark, Diplom Thesis, Stuttgart University (1973). [22] J.R. Hancock and J.C. Grosskreutz, Acta Metallurgica 17 (1969) 77-97. [23] S. Ikeda, Transactions of the Japan Institute of Metals 20 (1979) 235-243. [24] F.V. Lawrence, Jr. and R.C. Jones, Metallurgical Transactions 1 (1970) 367-376. [25] A. Yoshikawa and M. Okamoto, Supplement to Transactions of the Japan Institute of Metals 9 (1968)

471-475. [26] S. Ikeda, in Proceedings of 5th International Conference on the Strength of Metals and Alloys, Aachen

Vol. 2 (1979) 1157-1162. [27] J. Krej~i and P. Lukfi~, physica status solidi (a) 5 (1971) 315-325. [28] W.A. Wood, W.H. Reimann and K.R. Sargant, Transactions of the Metallurgical Society of AIME 230

0964) 511-518. [29] P. Luk~i~ and M. Klesnil, Czechoslovak Journal of Physics B 14 (1964) 600-607. [30] P. Luk~i~, M. Klesnil and P. Ryg, Zeitschrift far Metallkunde 56 (1965) 109-113. [31] J.T. McGrath and W.J. Bratina, The Philosophical Magazine 12 (1965) 1293-1305.


Cycl ic de fo rma t ion and fa t igue behav iour o f a - i ron m o n o - and po lycrys ta l s 219

[32] Y. Bergstr6m, O. Vingsbo and G. Lagerberg, Materials Science and Engineering 5 (1969/70) 153-162. [33] H. Abdel Raouf, P.P. Benham and A. Plumtree, Canadian Metallurgy Quarterly 10 (1971) 87-95. [34] O.K. Chopra and C.V.B. Gowda, The Philosophical Magazine 30 (1974) 583-591. [35] R.P. Wei and A.J. Baker, The Philosophical Magazine 12 (1965) 1005-1020. [36] H.D. Nine, The Philosophical Magazine 26 (1972) 1409-1418. [37] R. Neumann, Zeitschrift fiir Metallkunde 66 (1975) 25-32. [38] M. Anglada and F. Guiu, in Proceedings of 5th International Conference on the Strength of Metals and

Alloys, Aachen Vol. 2 (1979) 1237-1241. [39] F. Ackermann, Max-Planck-Institut ffir Metallforschung (1978/79), unpublished work. [40] H.D. Solomon and C.J. McMahon, Jr. in Work-Hardening, edited by J.P. Hirth and J. Weertmann,

Gordon and Breach, New York (1968) 311-332. [41] A. Seeger and B. ~estfik, Scripta Metallurgica 5 (1971) 875-882. [42] H. Mughrabi, Scripta Metallurgica 13 (1979) 479--484. [43] H. Mughrabi, in Proceedings of Fifth International Conference on the Strength of Metals and Alloys,

Aachen (1979) edited by P. Haasen, V. Gerold and G. Kostorz, Pergamon Press, Oxford and New York Vol. 3 (1980) 1615-1638.

[44] H. Abdel Raouf and A. Plumtree, Metallurgical Transactions 2 (1971) 1863-1867. [45] H. Abdel Raouf, A. Plumtree and T.H. Topper, in Cyclic Stress-Strain Behaviour-Analysis, Experi-

mentation and Failure Prediction, ASTM STP 519, American Society for Testing and Materials (1973) 28-57.

[46] H.F. Wachob and H.H. Johnson, Metallurgical Transactions 10A (1979) 305-310. [47] A.T. Winter, The Philosophical Magazine 30 (1974) 719-738. [48] P.J. Woods, The Philosophical Magazine 28 (1973) 155-191. [49] H. Mughrabi, Materials Science and Engineering 33 (1978) 207-223. [50] M. Doner, J.C. Diprimio and E.I. Salkovitz, Acta Metallurgica 21 (1973) 1547-1559. [51] M. Hempel, A. Kochend6rfer and E. Hillnhagen, Archly fiir das Eisenhiittenwesen 28 (1957) 433 4A.4. [52] D.V. Wilson and J.K. Tromans, Acta Metallurgica 18 (1970) 1197-1208. [53] C.E. Feltner and C. Laird, Transactions of the Metallurgical Society of AIME 245 (1969) 1372-1373. [54] H. Abdel Raouf and A. Plumtree, Metallurgical Transactions 2 (1970) 1251-1254. [55] P. Lukfi~ and M. Klesnil, Materials Science and Engineering 11 (1973) 345-356. [56] C.S. Smith and L. Guttman, Transactions AIME 197 (1953) 81-87, Journal of Metals (January 1953). [57] D.J. Abson and J.J. Jonas, Metal Science Journal 4 (1970) 24-28. [58] M. Hempel, in Fracture, edited by B.L. Averbach, D.K. Felbeck, G.T. Hahn and D.A. Thomas,

Technology Press MIT and John Wiley & Sons, Inc., New York (1959) 376-411. [59] H.D. Nine, Journal of Applied Physics 44 (1973) 4875-4881. [60] M. Hempel, A. Kochend6rfer and E, Hillnhagen, Archio fiir das Eisenhiittenwesen 28 (1957) 417-422. [61] H.A. Lipsitt and G.T. Horne, Proceedings of the International Conference on Fatigue of Metals, The

Institution of Mechanical Engineers and The American Society of Mechanical Engineers (1956) 513-519.

[62] M. Saletore and R. Taggart, Materials Science and Engineering 36 (1978) 259-270. [63] V.S. Ivanova, V.M. Goritskiy, L.G. Orlov and V.F. Terent'yev, Fizika metallov i metaUovedenia 34

(1972) 456--463. [64] V.F. Terent'yev, I.S. Kogan and L.G. Orlov, Fizika metallov i metaUovedenia 40 (1975) 199-202. [65] R.C. Boettner and A.J. McEvily, Jr., Acta Metallurgica 13 (1965) 937-946. [66] D.J. Lloyd and A.P. Greenough, Metal Science Journal 4 (1970) 180-183. [67] J. Awatani, K. Katagiri and A. Koreeda, Bulletin of the Japan Society of Mechanical Engineers 12

(1969) 1320-1328. [68] D.I. Golland and P.L. James, Acta Metallurgica 15 (1967) 1889-1894. [69] D.I. Golland and P,L. James, Metal Science Journal 4 (1970) 113-118. [70] H. Nisitani and K. Takao, in Proceedings of the 1971 International Conference on Mechanical

Behaviour of Materials, The Society of Materials Science, Japan, Vol. II (1972) 153-164. [71] K. Katagiri, J. Awatani, A. Omnra, K. Koyanagi and T. Shiraishi, in Fatigue Mechanisms, Proceedings

of an ASTM-NBS-NSF symposium, edited by J.T. Fong, American Society for Testing and Materials, Philadelphia (1979) 106-128.

[72] C. Laird and D.J. Duquette, in Corrosion Fatigue, NACE-2, edited by A.J. McEvily and R.W. Staehle, National Association of Corrosion Engineers, Houston (1971) 88-117.

[73] P. Beardmore and P.H. Thornton, Acta Metallurgica 18 (1970) 109-115. [74] H. Mughrabi, Proceedings of NATO Advanced Study Institute on Surface Effects in Crystal Plasticity,

edited by R.M. Latanision and J.T. Fourie, Noordhoff, Leyden (1977) 479-485. [75] T. Magnin and J.H. Driver, Materials Science and Engineering 39 (1979) 175-185.



[76} A. W6hler, cf. abstracted account in Engineering (London) 11 (1871) 199-200, 221,244, 261, 299-300. 327, 349-350, 397, 439-441.

[77] H.A. Lipsitt and G.T. Horne, American Society for Testing Materials, Proceedings 57 (1957) 587-599. [78] G. Oates and D.V. Wilson, Acta Metallurgica 12 (1964) 21-33. [79] P.O. Kettunen, Journal of the Iron and Steel Institute 202 (1964) 209-215. [80] M. Klesnil, Metal Treatment and Drop Forging 32 (1965) 55-63. [81] J.T. McGrath, W.J. Bratina and A. Plumtree, in Quantitative Relation Between Properties and

Microstructure, edited by D.G. Brandon and A. Rosen, Israel University Press, Jerusalem (1969) 391-397. [82] A. Ferro and G. Montalenti, The Philosophical Magazine 10 (1964) 1043-1052. [83] A. Ferro, P. Mazzetti and G. Montalenti, The Philosophical Magazine 12 (1965) 867-875. [84] A.M. Adair and H.A. Lipsitt, Transactions of the Metallurgical Society of AIME 236 (1966) 1235-1237. [85] P. Luk~i~, M. Klesnil and J. Pol~k, Materials Science and Engineering 15 (1974) 239-245. [86] C. Laird, Materials Science and Engineering 22 (1976) 231-236. [87] H.J. Gough, 8th Edgar Marburg Lecture, Proceedings of the Thirty-Sixth Annual Meeting, American

Society for Testing Materials 33 (1933) 3-114. [88] U. Dehlinger, Zeitschrift fiir Metallkunde 44 (1953) 240-242.

RI~SUME

Les r6sultats rapport6s dans le m6moire sont bas6s sur une s6rie d'essais de d6formation cyclique qui ont 6t6 conduits h temp6rature ambiante sur des 6chantillons de fer a d6carbur6s ~t haute puret6 sous une forme mono- et polycristalline. Les donn6es exp6rimentales couvrent les amplitudes de d6formation plastique Aep~ correspondant /i l0 4 <~ Aep~ ~< l0 2 ainsi que des variations dans la vitesse de d6formation plastique comprises entre 10 _5 et 10 2 s t. Dans le cas de cristaux simples, on a 6galement 6tudi6 les effects du C en solution (~v30 ppm). Les donn6es m6caniques ont 6t6 compl6t6es par des 6tudes d6taill6es des arrangements des dislocations, en utilisant la microscopie 61ectronique ~ transmission, ainsi que les aspects des surfaces en utilisant la microscopie optique et la microscopie 61ectronique 5. balayage.

On a trait~ dans le d6tail les sujets suivants: accroissement cyclique et saturation, m6canisme de dislocation, modification de forme associ6e h des glissements assym6triques de dislocation vis, r6ponse cyclique contrainte/dilatation et amorgage de la fissure de fatigue.

Sous les conditions conventionnelles de haute vitesse de d6formation plastique (sup6rieure fi l0 4 s ~) le comportement en fatigue du fer a ~ la temp~.rature ambiante rend compte de la faible mobilit6 des dislocations vis, ce qui est caract6ristique d'un mode de d6formation h basse temp6rature des m6taux cubiques centr6s. En cons6quence, le comportement fait 6tat de diff6rences significatives par rapport aux m6taux cubiques faces centr6s soumis ~ fatigue tels que: une intense multiplication des dislocations en-dessous Ae,~ r~ 5 × l0 ~, un glissement secondaire appr6ciable pour des valeurs de Aept sup6rieures qui conduit fi une structure en cellules (c.h.d que des bandes de glissement persistantes ne se forment point), des modifications de forme dues /t des glissements assym6triques de dislocation vis, ainsi qu'un niveau de contrainte effective relativement 61ev6.

La r6duction de la vitesse de d6formation plastique et la presence d'atomes de C en solution modifient ce comportement de mani6re significative, et le rapprochent davantage de celui des m6taux cubiques centr6s. Dans tousles cas, on a prouv6 que seule la composante athermique de la contrainte de saturation, d6faut de cette derni~re, repr6sente une mesure appropri6e des propri6t6s des substructures de dislocation.

Sur base du comportement h la d6formation cyclique et des observations d'amorqage de fissure de fatigue trans- et intergranulaire, on a conclu que la limite de fatigue du fer a est une propri6t6 intrins~que d'une structure cubique centr6e dont les caract6ristiques toutefois, se trouvent 6tre sensiblement affect6es par la teneur en impuret6s intersticielles et par la vitesse de d6formation de l'essai de fatigue.


Cyclic deformation and fatigue behaviour of ?-iron mono-and polycrystals

Documents

Transcript of Cyclic deformation and fatigue behaviour of ?-iron mono-and polycrystals