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Significance of initiation, propagation and closure of microcracks in high cycle fatigue of ductile metals
Engineering Fracture Mechanics Vol. 15. No. 3-4. pp. 445-456. 1981
0013-794418 11070445-1802.0010 @ 1981 Pergamon Press Ltd.
Printed in Great Britain.
SIGNIFICANCE OF INITIATION, PROPAGATION AND CLOSURE OF MICROCRACKS IN HIGH CYCLE FATIGUE OF DUCTILE METALS HIRONOBU NISITANI Faculty of Engineering, Kyushu University, Fukuoka 812, Japan
and KEN-ICHI TAKAO Faculty of Science and Engineering, Saga University, Saga 840, Japan Abstract-The initiation, propagation and closure behavior of microcracks were investigated through successive observations of fatigue process on the plain specimen surface in rotating bending tests of a mild steel, an n-brass and Al-alloys. The essential difference of crack initiation process and the behavior of microcracks was recognized between an age-hardened Al-alloy and the other annealed metals. Based on the results, the characteristics in fatigue under various loading conditions, such as (i) fatigue behavior under two-steps loading, (ii) coaxing effect of a low carbon steel and (iii) size effect of a notched specimen and fatigue notch sensitivity, were consistently explained with special reference to the behavior of fatigue microcracks.
1. INTRODUCTION well known that fatigue cracks are usually initiated at free stirface in high cycle fatigue of ductile metals under various loading conditions. Therefore, it is one of the effective means to observe in detail the crack initiation and propagation processes on the specimen surface, in making fatigue mechanisms clear. In the present study, the characteristics of initiation process of fatigue cracks were made clear in the first place through the detailed observation on the surface of plain specimens of several metals. That is, rotating bending fatigue tests were carried out on the plain specimens of electropolished Al-alloy, a-brass and low carbon steels, and observations of fatigue process were made successively on the plastic replicas of the specimen surface, with special attention being given to the starting point of fatigue fracture, in order to investigate the difference in the mechanisms of crack initiation among the metals used [ 1,2]. In the second place, the reason why a low carbon steel has a distinct fatigue limit was explained from the behavior of fatigue microcracks. That is, when the stress equal to the fatigue limit was repeated on a plain specimen of low carbon steel more than 10’ cycles, non-propagating microcracks were formed on the specimen surfaceD]. The mechanism of non-propagation of fatigue microcracks were discussed through successive observations of crack initiation process and the opening and closing behavior of the microcrack[4]. Based on the observations made on the surface of plain specimens under constant stress amplitudes, characteristic fatigue behaviors under various conditions, such as (i) fatigue behavior under two-steps loading, (ii) coaxing effect of a low carbon steel and (iii) fatigue behavior of notched specimens, were explained.
IT IS
2. MATERIALS, SPECIMENS AND TESTING PROCEDURES Materials used are an annealed and an age-hardened Al-alloy (0.2% offset yield strengths of 34 MPa and 250 MPa, respectively; UTS’s of 127MPa and 309 MPa, respectively), an annealed a-brass (0.2% offset yield strength of 100 MPa, UTS of 211 MPa) and annealed low carbon steels [steel A(0.13% C): LYS of 203 MPa, UTS of 327 MPa; steel B(0.17% C): LYS of 211 MPa, UTS of 379 MPa]. Dimensions of the specimen are shown in Fig. 1. Since the fatigue notch factor K, of the low carbon steel specimen having the form shown in Fig. 1 is about 1.06, this type of specimen can be used as a plain specimen. The fine shallow notch has been introduced in order to localize the severely damaged region and to follow the starting point of final fracture easily. 445
446
H. NISITANI and K. TAKAO
Fig. 1. Dimensions of a specimen (p = 5, p, = 0, pz = 100 for an Al-alloy; p = 5, p, = 20, pz = x for a low carbon steel and an cr-brass; all dimensions in mm).
Before testing, the specimens, except the ones used in the measurement of COD, were electropolished to remove more than 20 pm of the work hardened surface layer. The testing machine used was the Ono type rotating bending fatigue machine operated at the speed of about 3000 rpm. The notched surfaces of specimens were replicated at pertinent intervals during stress repetitions to observe fatigue process successively by using optical- and electron-microscopes (TEW. The specimens, made of prestrained steel B and having fine parallel lines drawn at 45” to the specimen axis on the surface, were also prepared to measure the crack opening displacement COD of the microcrack at the maximum and minimum stresses during one stress cycle. The COD was obtained by measuring the displacement of parallel lines on the electron micrographs (~10,000) of the microcrack, as shown in Fig. 10(a). 3. ~ULTSANDDISCUSSION 3.1Behavior of fatigue microcracks under constant stress amplitudes 3.1.1 Successive observations of initial fatigue processes. Figure 2 shows the change in the surface state of an agehardened Al-alloy, due to the repetitions of the stress (about 36% higher than the fatigue strength at 10’ cycles) at which fatigue life Ni is about 4 x 10’ cycles. Figure 3 shows the electron micrographs of mid portions in Fig. 2. These figures indicate that a slip band of an Al-alloy initiates in a fairly small region (less than 3 pm at N = 2.6 x 104)compared to the grain size (about 100 pm), and it gradually grows as the number of cycles N increases. A microcrack initiates within the slip band. The matrix around the slip band does not change at all from the original surface state as shown in Fig. 3. These phenomena may be due to the local work softening and associated rapid growth of the slip band during stress repetitions [S]. Figure 4 shows the change in the surface state of steel A, due to the repetitions of the stress (about 15% higher than the fatigue limit) at which fatigue life N, is about 1.5 X lo6 cycles. Figure 5 shows the electron micrographs of mid portions in Fig. 4. The depth or contrast of shade in the same region (mostly along or near the grain boundary) which is to become a crack increases with increasing N, with almost no increase in size of the region on the optical micrographs (see Fig. 4). In a low carbon steel, slip lines of nearly the same size as a grain are formed during the tirst few ten thousand cycles of stress, unlike those of an age-hardened Al-alloy. Successive cycles produce additional slip bands and also concentrate heavy slips at and near the same region which is to become a crack (see Fig. 5). Thus, the initiation process of fatigue crack in a low carbon steel is such that the region is being disrupted heavily and as a whole and then turns into a crack the size of a grain. After the initiation, the crack begins to propagate into neighboring grains due to the repetitions of stress and strain at the regions near the crack tip [ 1,2]. The same initiation processes as in a low carbon steel are also recognized in the other annealed carbon steels 161.
441
Cycle fatigue of ductile metals
6x10'
N=O
8x10L
a, -147 MPa,
10 x10'
Nf"4.0x105,
12x10'
Axial -_.__direction ___+
14x10*
, 50um,
Fig. 2. The change in surface state of an age-hardened Al-alloy.
Fig. 3. Electron micrographs of mid portions in Fig. 2.
N=D
5X10‘ a,=196 MPa,
1CXlU'
Nt = 1.5 x IS",
20 x 10% Ax-ialdirection < _
40X10‘
‘
iC u 111
Fig. 4. The change in surface state of an annealed low carbon steel (steel A).
H. NISITANI and K. TAKAO
N = 5 x 10’
al x lo*
10 x lo*
40x109 / 5um
)
Fig. 5. Electron micrographs of mid portions in Fig. 4.
N=O
10'
4x10"
10‘
"a -167 MPa (q,,=172 MPa
),
Fig.& Thechangein surfacestateof anannealed low car~nsteel(steei its fatigue limit.
N=O
10" oa=i37 MPa,
2nllY Mf=l.lxla",
107
Axial direction * ----*
6 x10"
2x107 ,;o?!~,
A)at~estressampiitude siightly~low
10x10'
Axial direction <
Fig. 7. The change in surface state of an annealed o-brass.
20x1GU SOFirn
449
Cycle fatigue of ductile metals
lo*
N-O oa=
78 MPa,
5x10"
40x10'
20 x10*
10 x10'
AGal direction -.-. *
Nf"1.0~10~.
L_W.J
Fig 8. The change in surface state of an annealed Al-alloy.
N ‘0
loxlO*
12x10*
~a=196 #Pa--235 MPa(changed at *
),
16x10" Axi+aldirectp
1 5Oum
Fig. 12. The change in surface state under two-steps loading of a steel A. The stress amplitude was increased before initiation of a crack the size of a grain.
N=O
2x10'(*)
10x10'
~~~a=235MPa-t196 MPa (changed at *)
,
70 x10* Axzdl_r%on
,
5Oum
Fig. 13. The change in surface state under two-steps loading of a steel A. The stress amplitude was decreased before initiation of a crack the size of a grain.
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H. NISITANI and K. TAKAO
Fig. 14. Electron micrographs of mid portions in Fig. 13.
N=O oa -235
lo4 MPa-+196
6 x10+(*)
MPa (changed
16x10'
dt *), Axial direction % __-____.~
,_J~__J~I J
Fig. 15. The change in surface state under two-steps loading of a steel A. The stress amplitude was decreased after the initiation of a crack the size of a grain.
oaa: 176 MPa(p) N=lO'
oB =181 'N=lO'
MPatQ)
aa ~186
MPafR)
N =lO' Axigl
aa=
N=5x105 direc&ion
MPa(Sf N=lO"
N =2x106
, SOtim,
Fig. 17. Behavior of a microcrack at stepwise increasing stress amplitudes of a steel A (Stress amplitudes P - S correspond to those in Fig. 16, respectively).
451
Cyclefatigueof ductilemetals
Figure 6 shows the change in the surface state of steel A, due to the repetitions of the stress slightly below the fatigue limit. The same initiation process of a crack as the one due to cycling of the stress higher than the fatigue limit, is recognized to occur during the first lo6 cycles. This figure indicates that the fatigue limit of a low carbon steel is not the limiting reversed stress under which the fatigue crack is not formed, but is the one under which a crack the size of a grain initiates, propagates a little and then stops progagating. The formation mechanism of a non-propagating microcrack will be discussed in Section 3.1.3. Figures 7 and 8 show the change in the surface of an a-brass and an annealed Al-alloy, respectively, due to the repetitions of stresses higher than respective fatigue strengths at 10’ cycles. Although the regions, which are to become cracks in the case of these metals, are different from that of steel A and are the regions along twin boundaries or along slip bands within grains, initiation processes of cracks are almost the same as the one in steel A as described above. Unlike an age-hardened Al-alloy, slip bands are produced not only along the region to become a crack but also along the other portion within grains. 3.1.2 Difference in crack initiation processes between an age-hardened Al-alloy and annealed metals. Figure 9 shows schematic illustrations of the crack initiation processes of an agehardened Al-alloy and annealed metals (a low carbon steel, an a-brass and an Al-alloy). As described in the above section, the starting region of fatigue cracking of an age-hardened Al-alloy is much smaller than a grain and extends gradually toward the grain boundary. When the static extension is applied to the specimen having a slip band (less than 20 pm on the surface) than a grain (about 100 pm), the opening of the slip band is recognized clearly even if the static strain is comparatively small (less than 0.3%)[7]. This result indicates that it is difficult to distinguish the small slip band from a microcrack, or the initiation process from the propagation process. As seen from Fig. 9(a), a slip band (or a crack) propagates toward a grain boundary to become a crack the size of a grain. Thus, the fatigue process of an age-hardened Al-alloy can be subdivided into Forsyth’s well known stage I and stage II crack propagation processes [II]. As illustrated in Fig. 9(b), the crack initiation process of annealed metals is entirely different from the crack propagation process which follows later. Until the initiation of a crack, fatigue damage is accumulated gradually at the same region (shaded area in Fig. 9(b)) whose dimensions are closely related to the grain size and then the region (a grain boundary for a low carbon steel, slip bands within the grain for an a-brass and an annealed Al-alloy) turns into a crack as a whole. The characteristics of crack propagation may not be included in this process unlike the process of an age-hardened Al-alloy. When the static extension is applied to the specimen of steel B after stress cycling of 30% of the mean crack initiation life, the region which is to become a crack the size of a grain does not open up even under the total strain of 4%[7]. Thus, at a very early stage of stress cycling, the fatigue damage in annealed metals begins to be
=-I
=I
(a) Age-hardened
%qo
‘,
(b) Annealed
Fig. 9. Schematic
Fraturc
surface
Al-alloy
,l
=1
low carbon
illustrations
Fracture surface steel
of fatigue
,
a-brass,
Al-alloy
crack initiation
processes.
H. NISITANI and K. TAKAO
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accumulated at the definite region (a grain boundary or a slip band) having a finite size. After sufficient accumulation of fatigue damage, the region tends to be opened up easily even under a comparatively low stress and a crack the size of a grain initiates. After the initiation of cracks in the two types of metals, the cracks propagate by the concentration of stress and strain at the regions near crack tips. It has been made clear from the above discussion that the crack initiation process of an age-hardened Al-alloy is essentially different from those of annealed metals. From the difference, it is suggested that the thickness of the surface layer affecting the crack initiation is largely different between the two types of metals, i.e. the surface layer of an age-hardened Al-alloy is much thinner than those of annealed metals. This is closely related further that an age-hardened Al-alloy is more notch-sensitive in fatigue than annealed metals as will be discussed later. 3.1.3 Fatigue limit of a low carbon steel and non-propagating microcracks. As discussed in Section 3.1.1, the fatigue limit of a low carbon steel is the limiting reversed stress under which a crack the size of a grain propagates a little and then stops propagating[4]. In this section, the relation between the presence of a fatigue limit of a low carbon steel and the formation mechanism of non-propagating microcrack is discussed on the basis of the observation of opening and closing behaviors near the tips of non-propagating and propagating cracks. Figure 10 shows a measuring method of COD at various distances x from the crack tip and the relation between COD and x, for propagating and non-propagating microcracks having almost the same size (about 0.1 mm on the surface). Figure 11 shows the relation between COD and x, for a so-called non-propagating fatigue crack and a propagating one which have emanated from the rim of a small blind hole (diameter; 0.5 mm, depth; 0.3 mm) drilled on the surface of a round bar specimen (diameter; 5 mm) of an annealed 0.19% carbon steel[lO]. Figure 10 indicates that the opening-and-closing behavior of a non-propagating microcrack is different very much from that of a propagating one. That is, the shape of the rim near the tip of the former on the surface of a specimen shows the “cusp” type, while that of the latter shows
(b)
ia)
Fig. 10. Crack opening displacement (COD) of propagating and non-propagating microcracks of a steel E, (a) COD measuring method, (b) COD at various distances x from the crack tip.
I
(pm)
Fig. Il. Crack opening displacement (COD) of propagating and non-propagating cracks emanating from a small blind hole, at various distances x from the crack tip.
Cycle fatigue of ductile metals
453
the “blunt” type at the maximum stress in a cycle of the respective reversed stresses. The COD near the tip of the former is much smaller than that of the latter (e.g. at x = 3 pm, 0.03 pm for the former while 0.2 pm for the latter), and the non-propagating microcrack is almost closed at or near the tip even under the maximum stress during stress cycling. These behaviors are also recognized in the case of the so-called non-propagating crack emanating from the rim of a hole (Fig. 11)[9, lo]. If the crack hardly opens near the tip even at the maximum stress (i.e. the opening ratio U = AK,e/AK = 0),, the concentration of stress and strain will not occur in the region near the crack tip and the crack will not propagate further. Such a non-propagating microcrack as described above is not observed on the surface of metals other than mild steels, which have no definite fatigue limits. Propagation or nonpropagation of a microcrack produced by the reversed stress of interest is mainly due to the difference in the work hardening at the crack tip and in the associated strain aging between the two kinds of metals[3]. 3.2 Behavior of microcracks under various loading conditions 3.2.1 Fatigue behavior under two-steps loading. Figures 12 and 13 show the change in the surface state when the stress amplitude is increased (Fig. 12) or reduced (Fig. 13) at the asterisked number of cycles before the initiation of a crack the size of a grain of steel A. Figure 14 shows the TEM micrographs of mid portions of Fig. 13. Figure 15 shows the change in the surface state when the stress amplitude is reduced after the initiation of a crack[l]. The crack initiation process of steel A has already been described in Section 3.1 (see Figs. 4-6). These figures indicate that if the stress amplitude is changed before the initiation of a crack the fatigue damage under the second stress amplitude is accumulated at the same region that was damaged by the first stress amplitude. On the other hand, if the stress amplitude is changed after the initiation of a crack the fatigue damage is mainly concentrated at the region ahead of the crack tip by the second stress amplitude and the crack propagates. It has been reported in regard to the fatigue behavior of a low carbon steel under varying load conditions that (i) a linear summation of cycle ratio Z(n/N) calculated on the basis of the formation life of a fatigue microcrack is nearly equal to unity (Miner’s rule nearly holds)[ll] and (ii) when the number of cycles of overstress is much smaller than that of the stress equal to or slightly below the fatigue limit, I;(n/N) calculated on the basis of the life to fatigue fracture is much smaller than unity[l2]. The former may be due to the fact that the fatigue damage is accumulated at the same region which is to become a crack when the stress amplitude is changed during the crack initiation process. The latter may be explained mainly on the basis of the change in the opening ratio U due to the variation of stress amplitude, that is, as described in Section 3.1.3, a non-propagating microcrack is formed under the repetitions of the stress equal to or slightly below the fatigue limit and the opening ratio U of the crack is nearly equal to zero during stress cycling. If the overstress is applied a few times to the specimen having a non-propagating microcrack, the crack starts to open clearly (II > 0) [lo] and begins to propagate even under the subsequent cycles of the former stress level. Accordingly, the extremely small value of Z(n/N) results. 3.2.2 Coaxing effects of a low carbon steel. Figure 16 shows the S-N curve and the increase in fatigue limit due to the coaxing effect of steel A. In this figure, P means the initial fatigue limit, Q and R mean subsequent increased fatigue limits, and at the stress level S the specimen failed. Figure 17 shows the behavior of microcracks observed on the above specimen during cycling of stress amplitudes increased stepwisely. P, Q, R and S correspond to the stress levels in Fig. 16, respectively [ 131. As shown in Fig. 17, the non-propagating microcrack, which is produced after 10’ cycles of the stress of the initial fatigue limit (stress level P; 176MPa), does not almost propagate or propagates a little by the stepwise increase in the stress level before the last stress level (stress level S) is reached. Moreover, the starting point of the final fracture is the non-propagating microcrack which is produced by the initial stress level at 10’ cycles. This phenomenon is ascribed to the fact that the region ahead of the tip of the non-propagating microcrack is strengthened by the work hardening and the associated strain aging due to cycling of each fatigue limit [3].
454
H. NISITANI and K. TAKAO
.
o-
0
Broken
--P-
Not broken
Fig. 16. S-N curve of a steel A and the increase in the fatigue limit due to the coaxing effect.
The non-propagating microcrack opens hardly near the crack tip even under the maximum stress under which the crack is formed, but opens up after increasing the stress level and the crack begins to propagate. In the case of a small increase in stress level (e.g. about 5.6% of the fatigue limit from P to Q and from Q to R), the crack propagates a little and then stops propagating within the strengthened region as described above. In this case, the crack hardly opens near the crack tip during one stress cycle[4]. At the stress level S, the crack grows gradually and the specimen is broken finally. 3.2.3 Fatiguebehaviorof notchedsimilarspecimensof steel B. Figure 18shows S-N curves and initiationlines of onegrain size crackof notched similar specimens (ratio of similarity; 1:Zanda large specimen has a notch root radius p of 1 mm in Fig. 1) of steel B[14]. The process of crack initiation for the notched specimen is the same one as described in Sections 3.1.1 and 3.1.2. When the same nominal stress is reversed on two similar specimens, the maximum stresses at notch roots are equal to each other because of the same stress concentration factor. However, the stress gradient at the notch root of a small specimen is twice as that of a large one. Therefore, the mean reversed stress within the definite thickness of the thin surface layer at the notch root is conversely higher for a large one. In other words, a fatigue crack initiates more easily in the large specimen than in the small specimen under the same stress amplitude. The effect of the stress gradient on the initiation of a fatigue crack is recognized usually at the stress level higher than the fatigue limit and more remarkably under the stress level near the fatigue limit. The distinct difference in the crack initiation life between a small specimen and a large one is ascribed to the fact that the crack of this material initiates as a unit at the definite region about the size of a grain. If this definite region (the definite thickness of the thin surface layer) is related to crack initiation, the crack initiation should be affected not only by the maximum reversed stress but also by the stress gradient there. This is the cause for the size effect in fatigue. 3.2.4 Notch sensitivity in fatigue of an age-hardened Al-alloy and a low carbon steel. Figure 19 shows the relation between the stress gradient ,& = (l/a,,,)(d~/dz),=,,; z is the distance from the surface of a notch root] and the maximum reversed stress KU,,,, at the crack initiation limit, in an age-hardened Al-alloy and steel B[14]. In this figure, (T,, means the maximum nominal reversed stress that causes nearly the same damage at the notch root as the one at the surface of an plain specimen after 10’ cycles of the stress of the fatigue limit. Therefore, a horizontal line (K,~,,,,,/c,,,,= 1) means that the maximum stress at the notch root is equal to the fatigue limit of a plain specimen. Figure 20 shows the relation between the fatigue notch factors of the specimens having the same form and size in the two metals. These figures indicate that an Al-alloy is more notch sensitive than a low carbon steel with regard to the initiation of fatigue cracks. This seems to be mainly due to the fact that the thickness of the surface layer affecting the crack initiation is much smaller for an Al-alloy than for steel B, reflecting the difference in the appearance of crack initiation between the two metals (Figs. 2 and 4).
455
Cycle fatigue of ductile metals
4.CONCLUSIONS The following conclusions were reached with regard to fatigue behaviors of a plain specimen under constant stress ampIitudes. (1) The crack initiation process in an age-hardened Al-alloy may correspond to Forsyth’s stage I crack propagation. However, the initiation process in annealed metals such as a low carbon steel, a-brass and an annealed Al-alloy is the one in which the definite regions whose
h
b.
Notbroken. witbut NotbWcn,with a
a
“on-prop.
crack
non-prop. crack
Positions of replication
Fig.
18. S-N curves of notched similar specimens of a steel B.
Fig. 19. Relation between the stress gradient .y and the maxims stress amplitude at the notch mot under repetitions of stress equal to fatigue limit.
Fig. 20. Comparison of fatigue notch factors between an Al-alloy and a low carbon steel. Wt.4 Vol. IS. No. U-M
456
H. NISITANI and K. TAKAO
sizes are closely related to the grain size, turn gradually into free surfaces as a whole by the repetitions of slip with increasing number of stress cycles. The initiation processes of annealed metals are essentially different from the later propagation processes. (2) The fatigue limit of a low carbon steel is the maximum stress at which the fatigue crack the size of a grain propagates into neighboring grains and then becomes a non-propagating microcrack. Such a crack is almost closed at or near its tip even under the maximum tensile stress in one cycle of the reversed stress under which the crack is formed. The followings are also obtained under various loading conditions. (3) Under two-steps loading on a low carbon steel, when the stress amplitude is changed before the initiation of a crack the size of a grain, the fatigue damage by repetitions of the second stress amplitude is accumulated at the region which is to become a crack, the same as the one damaged by the first stress amplitude. This gives one of the reasons why a linear summation of cycle ratio ~(~~~} calcuIated on the basis of the formation life of a fatigue microcrack is nearly equal to unity. (4) The coaxing effect of a low carbon steel is closely related to the behavior of a fatigue microcrack produced by the first stress level which is equat to or slightly below its fatigue limit, i.e. mainly due to the non-propagation of the crack under successive stress levels which are slightly higher than the fatigue limit of the virgin specimen. (5) From the results of the fatigue test on notched similar specimens of a low carbon steel, the initiation process of a crack the size of a grain in a notched specimen is the same one as in the plain specimen. AIthough the maximum stresses at the notch roots are equal to each other in the similar specimens, the stress gradient of a small specimen is higher than that of a large one and the crack initiation life for the former is larger than that for the latter. The fatigue limit of the former is also higher than that of the latter (the size effect). (6) An age-hardened Al-alloy is more notch-sensitive in fatigue than a low carbon steel. This is due to the difference in the initiation processes of fatigue microcracks of the two metals.
REFERENCES [t] H. Nisitani and K. Takao, Successive observations of fatigue process in low carbon steel by electron microscope.
Pm. Int. Conf. Mech. Behavior of Materials 2, 153(1972). [2] H. Nisitani and K. Takao, Successive observations of fatigue process in carbon steel, 7:3 brass and Al-alloy by electron microscope. Trans. Japan Sot. Mech. Engrs. 40.3254 (1974)(in Japanese). [3] H. Nisitani and S. Nisida, Correlation between the existence of fatigue limit and non-propagating microcrack. Buif. Japan Sm. Mech. Engrs. 17, I (1974). [4] K. Takao and H. Nisitani, Opening-and-closing-behavior of non-propagating microcracks in rotating bending and torsional fatigue tests of carbon steels. L Sot. Mnt. Sci., J~pun 28,873 (1979)(in Japanese). [S] C. A. Stubbington and P. J. E. Forsyth, Some observations on micro-structural damage produced by fatigue of an aluminium-7.5%zinc-2.5% magnesium alloy at temperatures between room temperature and 250°C. Acta Met.14, 5 (1966). [6] H. Ninitani and I. Chishiro, Non-propagating microcracks of plain specimens and fatigue notch sensitivity in annealed or heat-treated O.S%Csteel. Trans. Japon Sm. Mech. Engrs. 40,41 (1973)(in Japanese). [7] K. Takao and H. Nisitani, Investigation of fatigue crack inditiation by successive observations of surface. Trans. Jupan Sot. Mech. Engrs 46-A. 123(1980)(in Japanese). [S] P. 3. E. Forsyth, A two stage process of fatigue crack growth. Proc. Crack Prop. Symp., Crun~e~~1,76 (1962). [9] H. Nisitani and K. Takao, Behavior of a tip of non-propagating fatigue crack during one stress cycle. EngrrgFract. Mech. 6,253 (1974). [IO] H. Nisitani and M. Kage, Observation of crack closure phenomena at the tip of a fatigue crack by electron microscopy. Proc. ICF iV 2-B. 1099(1977). [I I] H. Nisitani and Y. Yoshikawa, Fatigue damage of electropolished carbon steel specimens with a shallow groove under two stress levels. Bull. Japan Sot. Mech. Engrs. 12, 172(1969). II?] E. Gassner, Effect of variable load and cumulative damage on fatigue in vehicle and air plane structures. Proc. fnf. Conf. Fatigue of Metals 304 (19.56). (131 H. Nisitani and T. Ikenaga, Relation between coaxing effect and micro-cracks of carbon steel. Science of Machine 27, 995 (1975)(in Japanese). (141 K. Takao, H. Nisitani and H. Sakaguchi, Relation between crack initiation process and notch sensitivity in rotating bending fatigue .f. Sot. Mat. Sci. Japan 29,982 (1980)(in Japanese). (Received 23 January 1981;receioed for publication 3 March 19811
0013-794418 11070445-1802.0010 @ 1981 Pergamon Press Ltd.
Printed in Great Britain.
SIGNIFICANCE OF INITIATION, PROPAGATION AND CLOSURE OF MICROCRACKS IN HIGH CYCLE FATIGUE OF DUCTILE METALS HIRONOBU NISITANI Faculty of Engineering, Kyushu University, Fukuoka 812, Japan
and KEN-ICHI TAKAO Faculty of Science and Engineering, Saga University, Saga 840, Japan Abstract-The initiation, propagation and closure behavior of microcracks were investigated through successive observations of fatigue process on the plain specimen surface in rotating bending tests of a mild steel, an n-brass and Al-alloys. The essential difference of crack initiation process and the behavior of microcracks was recognized between an age-hardened Al-alloy and the other annealed metals. Based on the results, the characteristics in fatigue under various loading conditions, such as (i) fatigue behavior under two-steps loading, (ii) coaxing effect of a low carbon steel and (iii) size effect of a notched specimen and fatigue notch sensitivity, were consistently explained with special reference to the behavior of fatigue microcracks.
1. INTRODUCTION well known that fatigue cracks are usually initiated at free stirface in high cycle fatigue of ductile metals under various loading conditions. Therefore, it is one of the effective means to observe in detail the crack initiation and propagation processes on the specimen surface, in making fatigue mechanisms clear. In the present study, the characteristics of initiation process of fatigue cracks were made clear in the first place through the detailed observation on the surface of plain specimens of several metals. That is, rotating bending fatigue tests were carried out on the plain specimens of electropolished Al-alloy, a-brass and low carbon steels, and observations of fatigue process were made successively on the plastic replicas of the specimen surface, with special attention being given to the starting point of fatigue fracture, in order to investigate the difference in the mechanisms of crack initiation among the metals used [ 1,2]. In the second place, the reason why a low carbon steel has a distinct fatigue limit was explained from the behavior of fatigue microcracks. That is, when the stress equal to the fatigue limit was repeated on a plain specimen of low carbon steel more than 10’ cycles, non-propagating microcracks were formed on the specimen surfaceD]. The mechanism of non-propagation of fatigue microcracks were discussed through successive observations of crack initiation process and the opening and closing behavior of the microcrack[4]. Based on the observations made on the surface of plain specimens under constant stress amplitudes, characteristic fatigue behaviors under various conditions, such as (i) fatigue behavior under two-steps loading, (ii) coaxing effect of a low carbon steel and (iii) fatigue behavior of notched specimens, were explained.
IT IS
2. MATERIALS, SPECIMENS AND TESTING PROCEDURES Materials used are an annealed and an age-hardened Al-alloy (0.2% offset yield strengths of 34 MPa and 250 MPa, respectively; UTS’s of 127MPa and 309 MPa, respectively), an annealed a-brass (0.2% offset yield strength of 100 MPa, UTS of 211 MPa) and annealed low carbon steels [steel A(0.13% C): LYS of 203 MPa, UTS of 327 MPa; steel B(0.17% C): LYS of 211 MPa, UTS of 379 MPa]. Dimensions of the specimen are shown in Fig. 1. Since the fatigue notch factor K, of the low carbon steel specimen having the form shown in Fig. 1 is about 1.06, this type of specimen can be used as a plain specimen. The fine shallow notch has been introduced in order to localize the severely damaged region and to follow the starting point of final fracture easily. 445
446
H. NISITANI and K. TAKAO
Fig. 1. Dimensions of a specimen (p = 5, p, = 0, pz = 100 for an Al-alloy; p = 5, p, = 20, pz = x for a low carbon steel and an cr-brass; all dimensions in mm).
Before testing, the specimens, except the ones used in the measurement of COD, were electropolished to remove more than 20 pm of the work hardened surface layer. The testing machine used was the Ono type rotating bending fatigue machine operated at the speed of about 3000 rpm. The notched surfaces of specimens were replicated at pertinent intervals during stress repetitions to observe fatigue process successively by using optical- and electron-microscopes (TEW. The specimens, made of prestrained steel B and having fine parallel lines drawn at 45” to the specimen axis on the surface, were also prepared to measure the crack opening displacement COD of the microcrack at the maximum and minimum stresses during one stress cycle. The COD was obtained by measuring the displacement of parallel lines on the electron micrographs (~10,000) of the microcrack, as shown in Fig. 10(a). 3. ~ULTSANDDISCUSSION 3.1Behavior of fatigue microcracks under constant stress amplitudes 3.1.1 Successive observations of initial fatigue processes. Figure 2 shows the change in the surface state of an agehardened Al-alloy, due to the repetitions of the stress (about 36% higher than the fatigue strength at 10’ cycles) at which fatigue life Ni is about 4 x 10’ cycles. Figure 3 shows the electron micrographs of mid portions in Fig. 2. These figures indicate that a slip band of an Al-alloy initiates in a fairly small region (less than 3 pm at N = 2.6 x 104)compared to the grain size (about 100 pm), and it gradually grows as the number of cycles N increases. A microcrack initiates within the slip band. The matrix around the slip band does not change at all from the original surface state as shown in Fig. 3. These phenomena may be due to the local work softening and associated rapid growth of the slip band during stress repetitions [S]. Figure 4 shows the change in the surface state of steel A, due to the repetitions of the stress (about 15% higher than the fatigue limit) at which fatigue life N, is about 1.5 X lo6 cycles. Figure 5 shows the electron micrographs of mid portions in Fig. 4. The depth or contrast of shade in the same region (mostly along or near the grain boundary) which is to become a crack increases with increasing N, with almost no increase in size of the region on the optical micrographs (see Fig. 4). In a low carbon steel, slip lines of nearly the same size as a grain are formed during the tirst few ten thousand cycles of stress, unlike those of an age-hardened Al-alloy. Successive cycles produce additional slip bands and also concentrate heavy slips at and near the same region which is to become a crack (see Fig. 5). Thus, the initiation process of fatigue crack in a low carbon steel is such that the region is being disrupted heavily and as a whole and then turns into a crack the size of a grain. After the initiation, the crack begins to propagate into neighboring grains due to the repetitions of stress and strain at the regions near the crack tip [ 1,2]. The same initiation processes as in a low carbon steel are also recognized in the other annealed carbon steels 161.
441
Cycle fatigue of ductile metals
6x10'
N=O
8x10L
a, -147 MPa,
10 x10'
Nf"4.0x105,
12x10'
Axial -_.__direction ___+
14x10*
, 50um,
Fig. 2. The change in surface state of an age-hardened Al-alloy.
Fig. 3. Electron micrographs of mid portions in Fig. 2.
N=D
5X10‘ a,=196 MPa,
1CXlU'
Nt = 1.5 x IS",
20 x 10% Ax-ialdirection < _
40X10‘
‘
iC u 111
Fig. 4. The change in surface state of an annealed low carbon steel (steel A).
H. NISITANI and K. TAKAO
N = 5 x 10’
al x lo*
10 x lo*
40x109 / 5um
)
Fig. 5. Electron micrographs of mid portions in Fig. 4.
N=O
10'
4x10"
10‘
"a -167 MPa (q,,=172 MPa
),
Fig.& Thechangein surfacestateof anannealed low car~nsteel(steei its fatigue limit.
N=O
10" oa=i37 MPa,
2nllY Mf=l.lxla",
107
Axial direction * ----*
6 x10"
2x107 ,;o?!~,
A)at~estressampiitude siightly~low
10x10'
Axial direction <
Fig. 7. The change in surface state of an annealed o-brass.
20x1GU SOFirn
449
Cycle fatigue of ductile metals
lo*
N-O oa=
78 MPa,
5x10"
40x10'
20 x10*
10 x10'
AGal direction -.-. *
Nf"1.0~10~.
L_W.J
Fig 8. The change in surface state of an annealed Al-alloy.
N ‘0
loxlO*
12x10*
~a=196 #Pa--235 MPa(changed at *
),
16x10" Axi+aldirectp
1 5Oum
Fig. 12. The change in surface state under two-steps loading of a steel A. The stress amplitude was increased before initiation of a crack the size of a grain.
N=O
2x10'(*)
10x10'
~~~a=235MPa-t196 MPa (changed at *)
,
70 x10* Axzdl_r%on
,
5Oum
Fig. 13. The change in surface state under two-steps loading of a steel A. The stress amplitude was decreased before initiation of a crack the size of a grain.
450
H. NISITANI and K. TAKAO
Fig. 14. Electron micrographs of mid portions in Fig. 13.
N=O oa -235
lo4 MPa-+196
6 x10+(*)
MPa (changed
16x10'
dt *), Axial direction % __-____.~
,_J~__J~I J
Fig. 15. The change in surface state under two-steps loading of a steel A. The stress amplitude was decreased after the initiation of a crack the size of a grain.
oaa: 176 MPa(p) N=lO'
oB =181 'N=lO'
MPatQ)
aa ~186
MPafR)
N =lO' Axigl
aa=
N=5x105 direc&ion
MPa(Sf N=lO"
N =2x106
, SOtim,
Fig. 17. Behavior of a microcrack at stepwise increasing stress amplitudes of a steel A (Stress amplitudes P - S correspond to those in Fig. 16, respectively).
451
Cyclefatigueof ductilemetals
Figure 6 shows the change in the surface state of steel A, due to the repetitions of the stress slightly below the fatigue limit. The same initiation process of a crack as the one due to cycling of the stress higher than the fatigue limit, is recognized to occur during the first lo6 cycles. This figure indicates that the fatigue limit of a low carbon steel is not the limiting reversed stress under which the fatigue crack is not formed, but is the one under which a crack the size of a grain initiates, propagates a little and then stops progagating. The formation mechanism of a non-propagating microcrack will be discussed in Section 3.1.3. Figures 7 and 8 show the change in the surface of an a-brass and an annealed Al-alloy, respectively, due to the repetitions of stresses higher than respective fatigue strengths at 10’ cycles. Although the regions, which are to become cracks in the case of these metals, are different from that of steel A and are the regions along twin boundaries or along slip bands within grains, initiation processes of cracks are almost the same as the one in steel A as described above. Unlike an age-hardened Al-alloy, slip bands are produced not only along the region to become a crack but also along the other portion within grains. 3.1.2 Difference in crack initiation processes between an age-hardened Al-alloy and annealed metals. Figure 9 shows schematic illustrations of the crack initiation processes of an agehardened Al-alloy and annealed metals (a low carbon steel, an a-brass and an Al-alloy). As described in the above section, the starting region of fatigue cracking of an age-hardened Al-alloy is much smaller than a grain and extends gradually toward the grain boundary. When the static extension is applied to the specimen having a slip band (less than 20 pm on the surface) than a grain (about 100 pm), the opening of the slip band is recognized clearly even if the static strain is comparatively small (less than 0.3%)[7]. This result indicates that it is difficult to distinguish the small slip band from a microcrack, or the initiation process from the propagation process. As seen from Fig. 9(a), a slip band (or a crack) propagates toward a grain boundary to become a crack the size of a grain. Thus, the fatigue process of an age-hardened Al-alloy can be subdivided into Forsyth’s well known stage I and stage II crack propagation processes [II]. As illustrated in Fig. 9(b), the crack initiation process of annealed metals is entirely different from the crack propagation process which follows later. Until the initiation of a crack, fatigue damage is accumulated gradually at the same region (shaded area in Fig. 9(b)) whose dimensions are closely related to the grain size and then the region (a grain boundary for a low carbon steel, slip bands within the grain for an a-brass and an annealed Al-alloy) turns into a crack as a whole. The characteristics of crack propagation may not be included in this process unlike the process of an age-hardened Al-alloy. When the static extension is applied to the specimen of steel B after stress cycling of 30% of the mean crack initiation life, the region which is to become a crack the size of a grain does not open up even under the total strain of 4%[7]. Thus, at a very early stage of stress cycling, the fatigue damage in annealed metals begins to be
=-I
=I
(a) Age-hardened
%qo
‘,
(b) Annealed
Fig. 9. Schematic
Fraturc
surface
Al-alloy
,l
=1
low carbon
illustrations
Fracture surface steel
of fatigue
,
a-brass,
Al-alloy
crack initiation
processes.
H. NISITANI and K. TAKAO
452
accumulated at the definite region (a grain boundary or a slip band) having a finite size. After sufficient accumulation of fatigue damage, the region tends to be opened up easily even under a comparatively low stress and a crack the size of a grain initiates. After the initiation of cracks in the two types of metals, the cracks propagate by the concentration of stress and strain at the regions near crack tips. It has been made clear from the above discussion that the crack initiation process of an age-hardened Al-alloy is essentially different from those of annealed metals. From the difference, it is suggested that the thickness of the surface layer affecting the crack initiation is largely different between the two types of metals, i.e. the surface layer of an age-hardened Al-alloy is much thinner than those of annealed metals. This is closely related further that an age-hardened Al-alloy is more notch-sensitive in fatigue than annealed metals as will be discussed later. 3.1.3 Fatigue limit of a low carbon steel and non-propagating microcracks. As discussed in Section 3.1.1, the fatigue limit of a low carbon steel is the limiting reversed stress under which a crack the size of a grain propagates a little and then stops propagating[4]. In this section, the relation between the presence of a fatigue limit of a low carbon steel and the formation mechanism of non-propagating microcrack is discussed on the basis of the observation of opening and closing behaviors near the tips of non-propagating and propagating cracks. Figure 10 shows a measuring method of COD at various distances x from the crack tip and the relation between COD and x, for propagating and non-propagating microcracks having almost the same size (about 0.1 mm on the surface). Figure 11 shows the relation between COD and x, for a so-called non-propagating fatigue crack and a propagating one which have emanated from the rim of a small blind hole (diameter; 0.5 mm, depth; 0.3 mm) drilled on the surface of a round bar specimen (diameter; 5 mm) of an annealed 0.19% carbon steel[lO]. Figure 10 indicates that the opening-and-closing behavior of a non-propagating microcrack is different very much from that of a propagating one. That is, the shape of the rim near the tip of the former on the surface of a specimen shows the “cusp” type, while that of the latter shows
(b)
ia)
Fig. 10. Crack opening displacement (COD) of propagating and non-propagating microcracks of a steel E, (a) COD measuring method, (b) COD at various distances x from the crack tip.
I
(pm)
Fig. Il. Crack opening displacement (COD) of propagating and non-propagating cracks emanating from a small blind hole, at various distances x from the crack tip.
Cycle fatigue of ductile metals
453
the “blunt” type at the maximum stress in a cycle of the respective reversed stresses. The COD near the tip of the former is much smaller than that of the latter (e.g. at x = 3 pm, 0.03 pm for the former while 0.2 pm for the latter), and the non-propagating microcrack is almost closed at or near the tip even under the maximum stress during stress cycling. These behaviors are also recognized in the case of the so-called non-propagating crack emanating from the rim of a hole (Fig. 11)[9, lo]. If the crack hardly opens near the tip even at the maximum stress (i.e. the opening ratio U = AK,e/AK = 0),, the concentration of stress and strain will not occur in the region near the crack tip and the crack will not propagate further. Such a non-propagating microcrack as described above is not observed on the surface of metals other than mild steels, which have no definite fatigue limits. Propagation or nonpropagation of a microcrack produced by the reversed stress of interest is mainly due to the difference in the work hardening at the crack tip and in the associated strain aging between the two kinds of metals[3]. 3.2 Behavior of microcracks under various loading conditions 3.2.1 Fatigue behavior under two-steps loading. Figures 12 and 13 show the change in the surface state when the stress amplitude is increased (Fig. 12) or reduced (Fig. 13) at the asterisked number of cycles before the initiation of a crack the size of a grain of steel A. Figure 14 shows the TEM micrographs of mid portions of Fig. 13. Figure 15 shows the change in the surface state when the stress amplitude is reduced after the initiation of a crack[l]. The crack initiation process of steel A has already been described in Section 3.1 (see Figs. 4-6). These figures indicate that if the stress amplitude is changed before the initiation of a crack the fatigue damage under the second stress amplitude is accumulated at the same region that was damaged by the first stress amplitude. On the other hand, if the stress amplitude is changed after the initiation of a crack the fatigue damage is mainly concentrated at the region ahead of the crack tip by the second stress amplitude and the crack propagates. It has been reported in regard to the fatigue behavior of a low carbon steel under varying load conditions that (i) a linear summation of cycle ratio Z(n/N) calculated on the basis of the formation life of a fatigue microcrack is nearly equal to unity (Miner’s rule nearly holds)[ll] and (ii) when the number of cycles of overstress is much smaller than that of the stress equal to or slightly below the fatigue limit, I;(n/N) calculated on the basis of the life to fatigue fracture is much smaller than unity[l2]. The former may be due to the fact that the fatigue damage is accumulated at the same region which is to become a crack when the stress amplitude is changed during the crack initiation process. The latter may be explained mainly on the basis of the change in the opening ratio U due to the variation of stress amplitude, that is, as described in Section 3.1.3, a non-propagating microcrack is formed under the repetitions of the stress equal to or slightly below the fatigue limit and the opening ratio U of the crack is nearly equal to zero during stress cycling. If the overstress is applied a few times to the specimen having a non-propagating microcrack, the crack starts to open clearly (II > 0) [lo] and begins to propagate even under the subsequent cycles of the former stress level. Accordingly, the extremely small value of Z(n/N) results. 3.2.2 Coaxing effects of a low carbon steel. Figure 16 shows the S-N curve and the increase in fatigue limit due to the coaxing effect of steel A. In this figure, P means the initial fatigue limit, Q and R mean subsequent increased fatigue limits, and at the stress level S the specimen failed. Figure 17 shows the behavior of microcracks observed on the above specimen during cycling of stress amplitudes increased stepwisely. P, Q, R and S correspond to the stress levels in Fig. 16, respectively [ 131. As shown in Fig. 17, the non-propagating microcrack, which is produced after 10’ cycles of the stress of the initial fatigue limit (stress level P; 176MPa), does not almost propagate or propagates a little by the stepwise increase in the stress level before the last stress level (stress level S) is reached. Moreover, the starting point of the final fracture is the non-propagating microcrack which is produced by the initial stress level at 10’ cycles. This phenomenon is ascribed to the fact that the region ahead of the tip of the non-propagating microcrack is strengthened by the work hardening and the associated strain aging due to cycling of each fatigue limit [3].
454
H. NISITANI and K. TAKAO
.
o-
0
Broken
--P-
Not broken
Fig. 16. S-N curve of a steel A and the increase in the fatigue limit due to the coaxing effect.
The non-propagating microcrack opens hardly near the crack tip even under the maximum stress under which the crack is formed, but opens up after increasing the stress level and the crack begins to propagate. In the case of a small increase in stress level (e.g. about 5.6% of the fatigue limit from P to Q and from Q to R), the crack propagates a little and then stops propagating within the strengthened region as described above. In this case, the crack hardly opens near the crack tip during one stress cycle[4]. At the stress level S, the crack grows gradually and the specimen is broken finally. 3.2.3 Fatiguebehaviorof notchedsimilarspecimensof steel B. Figure 18shows S-N curves and initiationlines of onegrain size crackof notched similar specimens (ratio of similarity; 1:Zanda large specimen has a notch root radius p of 1 mm in Fig. 1) of steel B[14]. The process of crack initiation for the notched specimen is the same one as described in Sections 3.1.1 and 3.1.2. When the same nominal stress is reversed on two similar specimens, the maximum stresses at notch roots are equal to each other because of the same stress concentration factor. However, the stress gradient at the notch root of a small specimen is twice as that of a large one. Therefore, the mean reversed stress within the definite thickness of the thin surface layer at the notch root is conversely higher for a large one. In other words, a fatigue crack initiates more easily in the large specimen than in the small specimen under the same stress amplitude. The effect of the stress gradient on the initiation of a fatigue crack is recognized usually at the stress level higher than the fatigue limit and more remarkably under the stress level near the fatigue limit. The distinct difference in the crack initiation life between a small specimen and a large one is ascribed to the fact that the crack of this material initiates as a unit at the definite region about the size of a grain. If this definite region (the definite thickness of the thin surface layer) is related to crack initiation, the crack initiation should be affected not only by the maximum reversed stress but also by the stress gradient there. This is the cause for the size effect in fatigue. 3.2.4 Notch sensitivity in fatigue of an age-hardened Al-alloy and a low carbon steel. Figure 19 shows the relation between the stress gradient ,& = (l/a,,,)(d~/dz),=,,; z is the distance from the surface of a notch root] and the maximum reversed stress KU,,,, at the crack initiation limit, in an age-hardened Al-alloy and steel B[14]. In this figure, (T,, means the maximum nominal reversed stress that causes nearly the same damage at the notch root as the one at the surface of an plain specimen after 10’ cycles of the stress of the fatigue limit. Therefore, a horizontal line (K,~,,,,,/c,,,,= 1) means that the maximum stress at the notch root is equal to the fatigue limit of a plain specimen. Figure 20 shows the relation between the fatigue notch factors of the specimens having the same form and size in the two metals. These figures indicate that an Al-alloy is more notch sensitive than a low carbon steel with regard to the initiation of fatigue cracks. This seems to be mainly due to the fact that the thickness of the surface layer affecting the crack initiation is much smaller for an Al-alloy than for steel B, reflecting the difference in the appearance of crack initiation between the two metals (Figs. 2 and 4).
455
Cycle fatigue of ductile metals
4.CONCLUSIONS The following conclusions were reached with regard to fatigue behaviors of a plain specimen under constant stress ampIitudes. (1) The crack initiation process in an age-hardened Al-alloy may correspond to Forsyth’s stage I crack propagation. However, the initiation process in annealed metals such as a low carbon steel, a-brass and an annealed Al-alloy is the one in which the definite regions whose
h
b.
Notbroken. witbut NotbWcn,with a
a
“on-prop.
crack
non-prop. crack
Positions of replication
Fig.
18. S-N curves of notched similar specimens of a steel B.
Fig. 19. Relation between the stress gradient .y and the maxims stress amplitude at the notch mot under repetitions of stress equal to fatigue limit.
Fig. 20. Comparison of fatigue notch factors between an Al-alloy and a low carbon steel. Wt.4 Vol. IS. No. U-M
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H. NISITANI and K. TAKAO
sizes are closely related to the grain size, turn gradually into free surfaces as a whole by the repetitions of slip with increasing number of stress cycles. The initiation processes of annealed metals are essentially different from the later propagation processes. (2) The fatigue limit of a low carbon steel is the maximum stress at which the fatigue crack the size of a grain propagates into neighboring grains and then becomes a non-propagating microcrack. Such a crack is almost closed at or near its tip even under the maximum tensile stress in one cycle of the reversed stress under which the crack is formed. The followings are also obtained under various loading conditions. (3) Under two-steps loading on a low carbon steel, when the stress amplitude is changed before the initiation of a crack the size of a grain, the fatigue damage by repetitions of the second stress amplitude is accumulated at the region which is to become a crack, the same as the one damaged by the first stress amplitude. This gives one of the reasons why a linear summation of cycle ratio ~(~~~} calcuIated on the basis of the formation life of a fatigue microcrack is nearly equal to unity. (4) The coaxing effect of a low carbon steel is closely related to the behavior of a fatigue microcrack produced by the first stress level which is equat to or slightly below its fatigue limit, i.e. mainly due to the non-propagation of the crack under successive stress levels which are slightly higher than the fatigue limit of the virgin specimen. (5) From the results of the fatigue test on notched similar specimens of a low carbon steel, the initiation process of a crack the size of a grain in a notched specimen is the same one as in the plain specimen. AIthough the maximum stresses at the notch roots are equal to each other in the similar specimens, the stress gradient of a small specimen is higher than that of a large one and the crack initiation life for the former is larger than that for the latter. The fatigue limit of the former is also higher than that of the latter (the size effect). (6) An age-hardened Al-alloy is more notch-sensitive in fatigue than a low carbon steel. This is due to the difference in the initiation processes of fatigue microcracks of the two metals.
REFERENCES [t] H. Nisitani and K. Takao, Successive observations of fatigue process in low carbon steel by electron microscope.
Pm. Int. Conf. Mech. Behavior of Materials 2, 153(1972). [2] H. Nisitani and K. Takao, Successive observations of fatigue process in carbon steel, 7:3 brass and Al-alloy by electron microscope. Trans. Japan Sot. Mech. Engrs. 40.3254 (1974)(in Japanese). [3] H. Nisitani and S. Nisida, Correlation between the existence of fatigue limit and non-propagating microcrack. Buif. Japan Sm. Mech. Engrs. 17, I (1974). [4] K. Takao and H. Nisitani, Opening-and-closing-behavior of non-propagating microcracks in rotating bending and torsional fatigue tests of carbon steels. L Sot. Mnt. Sci., J~pun 28,873 (1979)(in Japanese). [S] C. A. Stubbington and P. J. E. Forsyth, Some observations on micro-structural damage produced by fatigue of an aluminium-7.5%zinc-2.5% magnesium alloy at temperatures between room temperature and 250°C. Acta Met.14, 5 (1966). [6] H. Ninitani and I. Chishiro, Non-propagating microcracks of plain specimens and fatigue notch sensitivity in annealed or heat-treated O.S%Csteel. Trans. Japon Sm. Mech. Engrs. 40,41 (1973)(in Japanese). [7] K. Takao and H. Nisitani, Investigation of fatigue crack inditiation by successive observations of surface. Trans. Jupan Sot. Mech. Engrs 46-A. 123(1980)(in Japanese). [S] P. 3. E. Forsyth, A two stage process of fatigue crack growth. Proc. Crack Prop. Symp., Crun~e~~1,76 (1962). [9] H. Nisitani and K. Takao, Behavior of a tip of non-propagating fatigue crack during one stress cycle. EngrrgFract. Mech. 6,253 (1974). [IO] H. Nisitani and M. Kage, Observation of crack closure phenomena at the tip of a fatigue crack by electron microscopy. Proc. ICF iV 2-B. 1099(1977). [I I] H. Nisitani and Y. Yoshikawa, Fatigue damage of electropolished carbon steel specimens with a shallow groove under two stress levels. Bull. Japan Sot. Mech. Engrs. 12, 172(1969). II?] E. Gassner, Effect of variable load and cumulative damage on fatigue in vehicle and air plane structures. Proc. fnf. Conf. Fatigue of Metals 304 (19.56). (131 H. Nisitani and T. Ikenaga, Relation between coaxing effect and micro-cracks of carbon steel. Science of Machine 27, 995 (1975)(in Japanese). (141 K. Takao, H. Nisitani and H. Sakaguchi, Relation between crack initiation process and notch sensitivity in rotating bending fatigue .f. Sot. Mat. Sci. Japan 29,982 (1980)(in Japanese). (Received 23 January 1981;receioed for publication 3 March 19811