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Crack nucleation and stage I propagation in high strain fatigue—I. Microscopic and interferometric observations
CRr-\CK NUCLE.4TIOX .4ND STAGE I PROPAGATION IN HIGH STRAIN FATIGUE-I. MICROSCOPIC ASD INTERFEROMETRIC OBSERVATIOXS W’.H.
KDI*
and 6. LAIRD
Department of Mctnllurgy and Marcrids Science. il’nivcrsity of Pennqfvania. P-t 19171. t’.S.A.
Phiiadriphia.
details of crsck nucleation phenomena in the high strain fatigue of OFHC copper have been studied by optical microscopy and two-beam interferometry. By observation of artificially rumpled specimen suri~es. the plastic instability mechanism of crack nucleation has been ruled o=t in polycrystalline metals in favor of one which takes into account the derailed crystallographic aspecrs of slip in adjoining grains. As a result of this cyclic slip, a step is gradually built up at a sensitive grain boundary until it is approximately 1.5 pm high. at which point the stress concentration of the step is sutticirnt IO propagate a crack both alon,1’ the boundall; at the surface and into the bulk of the specimen.
Abstract-The
a 6tudi6 par microscopic optique et interf&omitris i deux faisceaus le d&ail des phinom2nes de germination des fissures da,3 du cuivrs OFHC soumis B des essais de fatigue 6 grand? dCformution. En observant des 6chantilloss dont les surfaces ttaienr artificicllement friptes. on a pu iliminer le mecanismt de prrmination des i%sures par instabiliti plasrique dans les mdtaux polycrista!lins. XI profit d’un mCcanismc tenant compte avec precision de la cristallographie du giissement dans des grains adjacents. Par suite du elissemsnt cycliqur. il se produit progressivement une maruhc, sur un joint de grains sensibie: lorsqu‘elle atteint unr hauteur de 1.5 em environ, la concentration de contraintes SW Is marche tst sufIisants pour qu’unc fissure se propapc Ie long du joint. en surf3ce et d3ns It matiriau massif. RCsum&-On
Zusammenfassung-Xfittels optischer Sfikroskopiz und Zwris:rahIinterferometrir uurden die Einzrlh&en drr RiBbiidungserscheinungen bei der Hochlastermiidung van OFHC-Kupfer untersucht. Mit der Beobachtucg kiinstlich aufgerauhter ProbenoberA#chrn wurden die plastischen InstabiIit%smrchanismen der RiRbildung in polykristallinen hfetallen tugunsten einer ausgeschirden. welche die genauen kristallografschen verh;iltnisse dsr Gleitung in den angrenzenden KGrnern bcriicksichtigt. Xls Ergebnis der zyklischcn Gleitprozessr wird an einer empfindlichen Komgrenze eine Stufe aIlm%hiich aufgebaut, bis sie rine HGhe YOIIungefdhr 1,s pm erreicht. Bei dieser Hahe reicht die Spannungskonzen-
tration aus, einen RiI3 entiang der Komgrenze sowohl an der OberfEiche als such ins Innere der Probe zu treiben,
1XTRODUCTIOX Fatigue failure occurs by crack nucleation and propaIn general crack nucleation in pure metals takes place at persistent slip bands or at the intersections of grain boundaries with the free surface[l]. The mode of crack nucleation and the associated deformation phenomena depend on the fat conditions, such as stress amplitude, test temperature and slip character of the material being tested. For instance, when the applied stress is low (long life fatigue). most of the applied plastic strain is concentrated in a few persistent slip bands [Z] some of which develop into cracks with continued cycling. and the surface topography observed by taper sectioning or interferometry is of the notch-peak type [lJ. On the other hand. when the stress is high (high strain fatigue). grain boundaries become the preferred gation.
* ?;on--at Department of Materials Engineer+ Vniwrsitv.
Philadelphia
PA 19104, U.S.A.
Drexel
sites for crack nucleation, and high degrees OCplastic distortion and surface rumpling are commonly observed Cl]. Another interesting phenomenon reported in high strain fatigue is the plastic instability etEct caused by the strain gradient which results from differences in cross sectional area of a specimen being tested: Coffin [3] has demonstrated both formally and experimentally that any specimen of varying cross section (for instance, a. specimen with an haur glass shape of gage section) will undergo changes during strain cycling, i.e. under longitudinal strain control, the thinner section becomes thinner by redistribution of material to the thicker sections. This phenomenon will continue until interrupted by the nucleation and propagation of a crack. Since a high degree of surface rumpling occurs prior to crack nucleation in high strain fatigue, Laird and Krause [4J developed a model of crack nucleation based on plastic instability. They assumed
that piastic instability can occur on a micro-scale in such a way that the depth of a crease for rumple! on the surface of a specimen undergoing cyclic plastic strain deepens with increasing numbsr of cycles until the strain concentration of the crease becomes 55 large that the crease constitutes a micro-crack. Although experiments with plasticine [A] and grease coating on rubber [S] have shown that this type of plastic instability does cause cracking in those marerials, the applicability of this plastic instability model to the crack nucleation process in metals is yet to be proven. The roles of crystallographic shear and of grain boundaries have not previously been checked. The purpose of the present work is to examine the details of the surface phenomena associated with crack nucleation and Stage I growth in high strain fatigue and to understand the basic mecchanism of these processes. The results of the investigation are presented in two parts. the first of which here contains phenomenological observations made to test the applicability of the plastic instability model to metals as well as morphological observations on the grain boundary deformations which lead to crack nucleation. In Part Il. the experimental observations are used to develop the mechanism of crack nucleation and of Stage I propagation. EXPERIMEXTAL (a) Tar @!I’ the phtic instnbilify modd To test this model. \ve decided to form artificial rumpI& on the surface of a fatigue specimen and to
observe the morphoIo&xtl dtvslopment of the rumples when the specimen ~v.v;ts c&d. Since the proposed mechanism might be influenced by (I) shape changes associated with the operation of different slip planes in tension and compression such as is observed in b.c.c. metals E&8] and 12) stip mode [9]. polycryst&line OFHC copper was chosen as the test material. Specimens were machined from bar stock f10.3 mm) with hourglass shape sage sections !to permit high strains) having a minimum diameter of 9.1 mm and two flats were milled on opposite sides of the sage section to accommodate areas of artiticial rumples. All specimens were annealed in sacuum for I h at 9GWC before the artificial rumples of approximate sine form were produced on the two flats through the LW.Z of photo-resist etching and ~Ie~tropoIishing techniques. The wave length of the rumpfes was about 60,um and the depth of the grooves was varied in the range between 1 and 6 blrn. Typical rumples on the surface of an uncycled specimen are shown by interferometry in Fig. 1. where the approximate sine form of the surface is indicated by the interference fringes. Note that the wave length of the rumples is smaller than the grain size of the copper (0.3 mm). High strain fatigue tests were carried out by controlling the stroke displacement of the actuator of an ~lectroh~draul~~ testing machine up to i: 2.54 mm. Specimens were brought to zero load and zero strain after sufficient numbers of cycles had elapsed to develop cracks and removed from the testing machine for microscopic observations of the rumples in the gage section.
Fig. I. Interferogram of the artificial rumples produced on the surface of a specimen before cycling.
Kl>f A>= LAIRD:
OBSERvctTIONS OF HIGH
In order to check the rolr of grain structure in ths crack nuclzation process, plain. unrumpled OFHC coppsr specimens were also studied. The specimens wer2 machined into the shape sho\h-n in Fig. 3. The factors important in the design and preparation of this specimen were as follows. (1) In low c>cclrfatigue ttsts. the hourglass shape of gage section is frequrntly adopted in order to avoid buckling. However. th2 hourglass shape is inconvenient for the purpose of surface obxrva tion because of the varying cross-sectional area along the specimen axis and the short working distance and small depth of field of optical microscopes. Consequently. replicas have to be usrd to record the parface morphology. Furthermore if on2 usrd hourglass spscim2ns it is necessary to smploj- a diametral extensometer for measuring strain. Sincr th2 sxtsnsometer has to be locatrd at th2 minimum gage cross-section ars;t. it is difficult to take surfacs rsplicas from that arca. Thzrefors, a straight cylindrical gage section ws used instead of ths hourglass shape. The maximum applied plastic limited to amplitude u’as therefore strain about + OS”,,. (2) In order to facilitate microscopic observations of the spzcimen gags surface and to make good quality replicas the surfacz to be observed should be fiat. (3) It is nzcessary to attach an estrnsometer to the specimsn shoulders in order to provide a working area for replication and to prevent th2 knife edges oi the clip-on type extensometer from digging into the specimen and giving rise to premature crack nuclsation. (4) Since a large grain size is expected to enhance th2 topographical changes induced by plastic deformation at grain boundaries and also to facilitate observations of the early stages of cracking, a large grain size was preferred. To obtain a large grain size. the strain-anneal method was used; as-machined spzcimens were initially anneaisd under argon for 1 h at 9CO’C and then . glvsn a tenslIe stram 0: 3”; p rior to reann2aling for 9 h at 9WC. This msthod, howvsvsr. was expected to promote on subsequent cycling a miniature necking effect in the gage ssction due to the 3:: tension strain. probably associated with inhomogeneity in ths prsstrain. To circumvent th2 problem. a large amount of material had to be rsmoved from the surfacr to obtain fairly smooth flats free of incipient necking in the gage s2ction. Tiiersfore, as an alternative to tensile strain-anneal. some of the specimens wer2 strain cycled to the onset of the plateau of the harden12.7mm
STR.uN
FATIGUE
ing curse at f O.?‘, plastic amplitude before reannraling for 9 h at Y-WC. These sp2cimsns showsd general recrystaflization and grain coarsening with fairly uniform grain sizes of about 0.3 mm. After rcLrystaliimtion and grain growth. the specimens were carefully hand polished and then rlectropoiished bsforr fatigue testing. Most of the surface obxrvations wer2 made through single stage replicas. Acetylcdiulose replicating film ha$ing a thickness of 0.031 mm was used for th2 rrplication. Since the replicating film is so thin it does not require the application of pressure to conform to the surface topography and takes only about fiv2 mintuss to dp compIrte1): in a normal !aborator); atmosphere without th2 aid of a blo\ver. All spscimens a2r2 tested at room trmperature and subjected to a constant cyclic plastic strain amplituds with z2ro mean strain. Strain was measured using an Instron clip-on typs extsnsometer. the knife edges bring applied to the specimen shoulders. Frzqusntly tests were stopped at zero load and maximum plastic strain limits (both tension and compression) to take replicas from thz surf& of the flats cut in the gage section. At each stop the actuator was held in th2 ~irnc position until the rspiica was completely dry. so significant creep via Stress relief \vas observed during the holding periods. RESULTS
Typical surface deformation observed in the specimens with artificial rumples is shown in Fig. 3. which was taken after 1350 cycles at a stroke limit of 2.54 mm (approximately equal to a plastic strain amplitude of O.Sg;). As can be noted in the figure the crack nucleation process does not appear to be influenced by the rumples. All cracks are intrrganular as have besn observed by many previous investigators [I. 10, I I] in smooth specimens and the shapes of the rumples appear to be somewhat distorted due to inhomogeneous plastic deformation varying from one grain to anothsr as well as within a sir@2 grain. Therefore. it is clear that the sine-form rumples of various amplitudes produced on the surfacss of the specimens have too small an effect on the strain gradient to act importantly as crack nuclei. On the other hand. the inhomogeneity in plastic deformation in polycrystalline materials appears to be more responsible for the det-elopment of the highly irregular surface contour as well as the nucleation of cracks at grain boundaries, In the following section details of the nucleation process associated with the plastic deformation near or at grain boundaries are illustratsd. (b) Crack nz~~enrion in the specimens with smooth
I_
\
73-m
cz.%m,R
Fig. 1. Standard specimen
\
FLAT
used for surface
t observation.
779
j?afs
rsplicating technique employed in the pp:sent investigation was found to be very effective in detecting the details of the changes in surface morphoiogy The
30
KIM *SD LAIRD:
OBSERVATIOXS
OF HIGH STRAIN FATIGUE
Fig. 3. (a) Artifi cial rumples observed after 1350 cycles showing preferred nucleation at grain boundaries. (b) Detail of the intergranular cracks observed in the area of (a).
with cycling. An example of the progressive surface deformations near a particular grain boundary with increasing number of cycles is shown in Fig. 4. The specimen was strain cycled at a plastic strain amplitude of & 0.577& Until 52 cycles had been applied the trace of the boundary in the surface remained sharp and clear without showing signi&ant evidence of crack nucleation. After 81 cycles (Fig. 4c) some disturbances, an indication of a crack nucleus, appeared along the traces of the boundary and increased in intensity with further cycling (Fig. Id). Since the sequences of the developmenr of the morphologies shown in Fig. 4 were recorded by replicating tape, it is probable that the tape, liquified by drops of acetone, could flow into micro-crevices when it was applied to the specimen surface. Therefore, the disturbed boundary traces which appears as a ribbon
in Fig. 4(d), can represent the depth of the microcrevice formed at the grain boundan_ if the replica was well dried before being taken ofi the surface and was handled carefully after that. It is considered, therefore, that the intense dark line at the grain boundary (Fig. 4b) which may be catled a “crack embryo” grows simultaneously along the boundary and, proportionally, into the bulk of the specimen. The width of the ribbon in Fig. 4(d) is about 7pm. Vertical displacements of the grain.s adjacent to the grain boundary shown in Fig. 4 were observed by inierferometry (Fig. 5). It ought to be noted in these figures and all other interferograms that the surface geometry represented by the fringe contour is highly exaggerated because of the large differences between the horizontal magnification (of the optical microscope) and the vertical magnification {of the interfer-
Fig. 1. Development of a crack nucleus in specimen C34, cycled at E, = 2 0.57~0. The micrographs were taken in seriatim and at the tension plastic strain limit. (a) .After 21 cwtes. (21T1. (b) 52f, grain boundary darkening. an indication of a discontinuity at the boundary. (CJ >lT. (d) 191T---replication technique.
ometer). It can be clearly observed, however, that a small step started to form after 30 cycles (the slight off-set of the central dark fringe crossing the boundary in Fig. 5b) and kept growing at the boundary. After 52 cycies the step height increased to about 0.9 .nm.* The micrograph taken from the same replica (Fig. Jb) does not show a clear indication of cracking. In other words. cracking is preceded by the formation of a grain boundary step. which as a stress raiser could play an important role in crack nucleation. * Due to inherent problems with thin replicating film. such SLSa slightly wavy surface. plus the surface corrugation in the specimen itself, focal irregularities of the fringe contour were inevitable. Therefore, the step height measurements ax only approximate values.
After 80 cycles the step height increased to about 1.5 pm and the crack at this boundary became clearly noticeable (Fig. 4). The growth of a grain boundary step and its behavior during stress reversals were traced with increasing number of cycles in another specimen which was cycled at a plastic strain amplitude of & 0.76”;. A small step of approsimately 0.1 pm height formed at the grain boundary after only 10 cycles (Fig 6ai and upon reversing the load this step seems to disappear (Fig. 6b). After 30 cycles and stopped at tension the step height increased to 0.4 pm. which then decreased to 0.15 pm upon reversing the load. In this way the step height observed both in tension and compression continued to incrras; with increasing number of
752
KiM AXD LXiRD:
OBSERVATIOXS
OF .HIGH STRAIN FATIGUE
Fig. 5. Interferometric observation of the development of the crack nucleus shown in Fig. 4. Fringes shifted in the direction marked with the arrowhead indicate depressions as known from the operating nature of the instrument and verified against a scratch. (a) 6T. (.b) 301. the fringes are completely displaced at the boundary indicating development of 3 90- step, the step height is - 0.45 pm. (c) 41T, step height is -0.6itm. (d) 81T. step height is - 1.5 pm-replication technique.
cycles, although the step in tension always appeared to be higher than in compression. The boundary step observed after 60 cycles and at tension increased to 5 1.5 ilrn, and by this time a clear indication of a microcrack was observed by regular microscopy. Another interesting feature associated with crack nucleation was observed in a specimen the surface of which had been lightly scratched with a needle point before electropolishing and testing. The scratches were made in order to facilitate locating the same are-a in each replica taken at the various stages of the fatigue life. One of the scratches crossing a grain boundary is shown in Fig. 7. The specimen was cycled at a plastic strain amplitude of i 0.5% and the stress axis is perpendicular to the scratch. After 120 cycles a slight off-set of the scratch line. an indication of grain boundary sliding, was observed at the intersection of the scratch with the grain boundary lying approximately 45’ to the stress axis. The off-set became obvious after 100 more cycles (Fig. 7~). At the end of 600 strain cycles the boundary turned into a microcrack and the scratch was displaced as much as 10 pm.
(cj Stage 1 crack propagation
Stage I crack propagation has been defined as the stage where cracks propagate along the active slip planes (specific crystallographic planes) which are usually inclined at approximately 45’ to the applied stress axis. This definition, however. is not btictly applicable to high strain fatigue where crack nucleation and growth occur along sections which are not crystallographic planes at all. Therefore. the term “Stage I propagation” will be used somewhat loosely for the moment to describe the stage of crack propagation before that which occurs by the plastic bhmting process. Various stages of Stage I cracks were examined by using the xanning electron microscope for observing the gage surface and by longitudinally sectioning for observations of crack path and depth. A specimen was lightly electropolishcd after 100 cycles in saturation at a plastic strain amplitude of 0.7:,<. Optical microscopic observation of this specimen showed that most of the deformation marks were removed except a few short and intense deformation traces along
Fig. 6. Interferograms showing grain boundary step growth (specimen C23, cycled at ep = i 0.76”.,1. Fringes shifted in the direction of the arrowhead indicate depressions. (a) IOT, a small step of 0.1 pm has developed. (bt Upon load reversal (1OC) this step is cancelled, almost completely. (c) 3OT, the step height has increased to -0.4 !trn. (d) Upon load reversal (3oC). the step height is partially cancelled: 0.15~1m. (e) 60T. the step height has increased to - l.jpm. 10 At 60C. the step height is reduced to -0.9 !trn-replication technique.
grain boundaries. This observation is reminiscent of the “persistent grain boundaries” observed by Smith [lZ] on his aluminum specimens lightly electropolished after cycling in long Iife fatigue but at higher temperature where grain boundary nucleation was preferred[iZ]. When the surface was observed with an SEM at high magnitude. the intense deformation trace was revealed as a microcrack with a very shallow but clearly observable depth (Fig. S). The crack length on the surface was IlOpm before the electropolishing. but the length measured after the electropolishing was only 27ilm. This indicares that only this particular portion (27 .um in length) of the grain boundary crack on the surface had obtained an appreciable depth when the electropolishing was carried out after 100 cycles in saturation. whereas most of the surface crack had not. and this particular portion is in the same region as that where the crack
nucleus was initially observed Cl?]. Thus. it crtn be deduced from this observation that once a crack nucleus forms along a portion of a grain boundary observable on the surface, the crack grows along the boundary both on the surface and into the bulk simultaneously so that the Stage I crack front adopts a thumb-nail shape; the front ahva)s leads at the point where the crack first started. This is considered typical of Stage I propagation and was confirmed by a series of longitudinal sectioning experiments on specimens cycled a larger fraction of the expected life so that the cracks on the sectioned face were large enough to be observed by optical microscop!. The longitudinal sectioning was made by means of a spark cutter through a major cracked grain boundary close to the nucleation site. The particular boundar!, and the nucleation site could be identified easily from the series of replicas taken at various stages during the
7y-t
KIM and LAfRD:
OBSERVATIONS
OF HIGH STRALV FATIGUE
Fig. 7. Grain boundary sliding associated with intergranular cracking in high strain fatigue at room temperature: (a) 5iT. (bj SlC, the sliding effect is not clear at this stage. (c) 11YT. the scratch line (the vertical line in the middle of the figure) is clearly displaced at the boundary. (.d) 11YC. upon reversing load. the displacement is not canceiled. (e) 220T. the sliding has produced further-reptication technique. (f) After 600 cycles, unloaded to zero load and strain. The displacement of the scratch is about 20 pm (real surface). Specimen ClO. tested at ep = & 0.5’?&
KIM ASD LAIRD:
OIISERV.%TiOYS OF HIGH STRXIX FATIGUE
Fig. 8. la) Stage I crack observed after 100 cycles in satuiation at E,~= k 0.7”w lb) and (c) The same crack as that in (a) but after light slcctropoit~hiny.
Fi_e. 9. Differences in nucleation site (a), and cycled at E, = 2 0.5’, with
crack depths observed in longitudinal sections thraqh the first reco&zed further along the boundary from that nucleation site (51. Specimen CX. strain sectioned after 640 cycies. Also note that rhz crack path in ia) is aqmmetric respect to the boundary trace Iemphasized with dot& lines).
7%
KM ASD LXIRD:
OBSERVATIONS OF HIGH SfRMN FbfIGt’E
fatigue test. Then, the cut section was incrementally ground to check the crack depth variation till it met. and passe& the nucleation site. Whenever it was desired the sectioned face was polished and etched. and micrographs of the crack at that section on both the sectioned face and the free surface were taken. All specimens examined showed the Same result that the deepest crack coincided aith the crack nucleation sit<. An example is shown in Fig. 9. The crack depth corresponding to the nucleation site is 180pm while that away from the nucteation site is S1 jrm. It is also interesting to note that a major portion of the crack path belongs to one side of the grain boundary trace emphasized with a dotted line in Fig. 9(a). This observation has been especially useful in identifying the mechanism of Stage I crack propagation (Section 2). DISCUSSION The piesent results have confirmed that the intersections of grain boundaries with the surface are the most favorable sites for crack nucleation in high strain fatigue. They have demonstrated. however. that such a choice of site is not associated with a plastic instability process operating in conjunction with an “orange peel’ surface rumple introduced in the first few cycles. Instead. the nature of the gross deformation within the grains and the compatibility of slip at the grain boundaries appear to be the more important factors in defining the crack site. A plastic instability process requires that the deformation be homogeneous, that the hardening be in saturation, and that local variations in surface topography cause a redistribution in the volumes of the material. In spite of
the great homogeneity of the disIoc=tion structures in copper c?cted at high strainsE1-Q the slip processes continue to be importantly affected by the nystallographic aspects of slip. Thus the specific orientations oiadjoining grains and their effect on the slip dominate the crack nucleation process. Although a plastic instability process now is considered unlikely to cause crack nucleation in poIycr+alline material. it remains a possible mechanism in those situations where the plastic deformation is reasonably homogeneous. for example in monocrystalline material cycled at strains much higher than those in which persistent slip bands are formed[Z]. To our knowledge, there exists no observations by which such a suggestion can be tested. The present results have documented the details of crack nucleation in a ductile metal. and show that grain boundary steps must first be developed. These steps grow with increasing numbers of cycles, are larger in tension than in compression, and are partly cancelled when the applied strain is pulsed in the compression stroke. These broad features apply throughout the nucleation period. Although the interferograms clearly demonstrate the development of the steps at grain boundaries where cracks nucleate, they do not give precise information on the actual geometry, flank angle and root radius. of the step. It is evident, however, from the scanning micrograph shown in Fig. 10 that the grain boundary steps have flank angle of approximately 90’ and a sharp root radius. This step-like surface geometry formed at grain boundaries and associated with crack nucleation in high strain fatigue can be seen in the results of previous investigators (e.g. 15) al-
Fig. 10. Scanning electron micrograph showing the intersection of the fracture surface with the free surface. Note the 90’ flank an_gle surface step and the intergranular crack associated with it. The specimen was strain cycled at Ed = k 0.7”; and lasted for 915 cycles.
though the resolution and extent of such observations
were not sufficient to identify the role of the steps emphasized here. The role Of surface steps as VZi~ effective stress raisers ou a mart macro scale has been studied by Marsh [ 163 following the seminal work of Inglis [ 1.71. Marsh has shown that the stress concentration factor is proportional to I hx. h being the step height and r the radius at the step root. Although no attempt has been made here to measure the actual values of , h .;. Fig. 10 demonstrates qualitatively that the value of , i;; for the surface steps should be high; r. difficult to see precisely and probably varying along the length of the crack, appears to lie in the range h’fOQ5 < r < lr:lO. In particular a step with a 90’ flank angle. which is close the case observed in the present investigation. is reported nearly as severe a stress concentrator as a GrifiithP crack[l6]. This high degree of stress concentration at the root of a surface step is consistent with the observation that once a small grain boundary step formed an the snrface. a clearly distinguishable crack developed in relatively few more c)-cles (Figs. sd). It is apparent. however, that a step _ 0.1 /Lrn high does not constitute a crack. if we define a crack as a stress concentrator sufficient to localize strain sigiri$cnntl~ in its immediate neighborhood. The observations reported here show that the slip in the adjoining grains dominates the cyclical. vertical displacements at the active grain boundary until the step height is about 1.5 ilrn high. The localization of slip at the step then develops slo~vly into Stage I growth. The build-up of the crack nucleating step is retarded by the partial cancellation of the step when the specimen is cycled in compression. It would be interesting to investigate whether or not the mechanism observed here in copper is accelerated in those mattrials[&-YJ which show different slip planes in tension and compression. The techniques developed here would be ideal for this purpose.
this small step continued to row with increasing numbers of @es until a micro-crack developed. On the btiis of these observations, it is suggested that a c7ask nudeus can be defined s a grain boundary step with a height of I _ 2,~m. (3) Those Fain boundaries which are preferred for crack nucleation are also preferred for subsequent growth of the crack. Once a crack nucleus is formed in a grain boundary, it continues to grow both along the boundar>- at the surface and into the bulk and thus forms a “thumb-naif’ configuration. nis information should be helpful in identifying crack nucleation sites on fracture surfaces ot’ specimens broken in high strain Migiie. (3) Grain boundary sliding is found to occur during crack nucleation and Stage I propagation in high strain fatigue at room temperat~lre. (4) The plastic instability mechanism of crack nucleation is considered rather unlikely in polycrystalline materials. Instead. inhomogeneity of slip between adjoining grains causes vertical surface displacements which develop into crack-nucleating steps. .~cknort,le~~ij7mirnrs--Thzexcellent advice and support of Mr. R. de la Veauv in connection with the mechanical testing is deeply appreciated. This work was supported by the National Science Foundation tmdcr Grant No. DMR76-006X3 through the Laboratory for Research on the Structure of Matter. L’niversity of Pennsylvania.
REFERENCES 1. C. Laird and D. J. Duquette, Corrosion Futigue (edited 2. 3.
3. 5. 6. 7. 8. 9.
by A. J. McEvily and R. W. Staehlej. Nat. .&soc. Corrosion Enzr.. Houston, Texas f1973). J. M. Finley and C. Laird, Pkl. .\f’&. 31. 539 (1975). L. F. Coffin. Jr.. Trans. .-IS,LIE 82D. 671 (t960). C. Laird and A. R. Krause, 1ut. J. Fracrurr Mrch. 1. ‘19 (1965). L. Northcott and H. G. Baron. f. Iran Srecl fnsr. 181, 385 (19563. H. D. Nine, J. appl. Phys. 44, 4875 (1973). H. Slu_ehrabi. Proo. NATO Advanced Study Inst.; Z. Mr~tulik. 66. 719 t1975). R. Neumann. 2. Metailk. 66, 26 (1975). C. Laird and C. E. Felmer. Trans. AlME 239. f07-t 119761
CONcLI_sIONS
of
We draw the following conclusions from our study the high strain fatigue of OFHC copper using opti-
cal microscopy and interferometry. (1) The development of grain boundary cracks on highly polished specimen surfaces has been documented. In all cases crack nucleation was preceded by the formation of a small step at a sensitive grain boundary in very early stages of the fatigue life? and
10. D. S. Kemsley. Phil. Mng. 2. 131 (19571 11. C. Laird and G. C. Smith, PM. Mny. 7. 847 (1962). 12. G. C. Smith. Proc. R. Sot. AZ-ii. 159 (1957). i3. W. H. Kim and C. Laird Mater. Sci. Ertgq (to be published). 14. c. E. Feltner and C. Laird, dctu .Wer. 13. 1633 (1967). i5 R. C. Boettner, C. Laird and A. J. klicE\ily. Trans. t6. ..-ll.$fE 233. 379 (1965). D. M. Marsh, Frucrttre of Solids (edited by D. C. Drucker and J. J. Gilman). Interscience, New York t.1962). 17. C. E. Inglis. ?-inns. Nnrai drclts. London 55. 219 (1913).
KDI*
and 6. LAIRD
Department of Mctnllurgy and Marcrids Science. il’nivcrsity of Pennqfvania. P-t 19171. t’.S.A.
Phiiadriphia.
details of crsck nucleation phenomena in the high strain fatigue of OFHC copper have been studied by optical microscopy and two-beam interferometry. By observation of artificially rumpled specimen suri~es. the plastic instability mechanism of crack nucleation has been ruled o=t in polycrystalline metals in favor of one which takes into account the derailed crystallographic aspecrs of slip in adjoining grains. As a result of this cyclic slip, a step is gradually built up at a sensitive grain boundary until it is approximately 1.5 pm high. at which point the stress concentration of the step is sutticirnt IO propagate a crack both alon,1’ the boundall; at the surface and into the bulk of the specimen.
Abstract-The
a 6tudi6 par microscopic optique et interf&omitris i deux faisceaus le d&ail des phinom2nes de germination des fissures da,3 du cuivrs OFHC soumis B des essais de fatigue 6 grand? dCformution. En observant des 6chantilloss dont les surfaces ttaienr artificicllement friptes. on a pu iliminer le mecanismt de prrmination des i%sures par instabiliti plasrique dans les mdtaux polycrista!lins. XI profit d’un mCcanismc tenant compte avec precision de la cristallographie du giissement dans des grains adjacents. Par suite du elissemsnt cycliqur. il se produit progressivement une maruhc, sur un joint de grains sensibie: lorsqu‘elle atteint unr hauteur de 1.5 em environ, la concentration de contraintes SW Is marche tst sufIisants pour qu’unc fissure se propapc Ie long du joint. en surf3ce et d3ns It matiriau massif. RCsum&-On
Zusammenfassung-Xfittels optischer Sfikroskopiz und Zwris:rahIinterferometrir uurden die Einzrlh&en drr RiBbiidungserscheinungen bei der Hochlastermiidung van OFHC-Kupfer untersucht. Mit der Beobachtucg kiinstlich aufgerauhter ProbenoberA#chrn wurden die plastischen InstabiIit%smrchanismen der RiRbildung in polykristallinen hfetallen tugunsten einer ausgeschirden. welche die genauen kristallografschen verh;iltnisse dsr Gleitung in den angrenzenden KGrnern bcriicksichtigt. Xls Ergebnis der zyklischcn Gleitprozessr wird an einer empfindlichen Komgrenze eine Stufe aIlm%hiich aufgebaut, bis sie rine HGhe YOIIungefdhr 1,s pm erreicht. Bei dieser Hahe reicht die Spannungskonzen-
tration aus, einen RiI3 entiang der Komgrenze sowohl an der OberfEiche als such ins Innere der Probe zu treiben,
1XTRODUCTIOX Fatigue failure occurs by crack nucleation and propaIn general crack nucleation in pure metals takes place at persistent slip bands or at the intersections of grain boundaries with the free surface[l]. The mode of crack nucleation and the associated deformation phenomena depend on the fat conditions, such as stress amplitude, test temperature and slip character of the material being tested. For instance, when the applied stress is low (long life fatigue). most of the applied plastic strain is concentrated in a few persistent slip bands [Z] some of which develop into cracks with continued cycling. and the surface topography observed by taper sectioning or interferometry is of the notch-peak type [lJ. On the other hand. when the stress is high (high strain fatigue). grain boundaries become the preferred gation.
* ?;on--at Department of Materials Engineer+ Vniwrsitv.
Philadelphia
PA 19104, U.S.A.
Drexel
sites for crack nucleation, and high degrees OCplastic distortion and surface rumpling are commonly observed Cl]. Another interesting phenomenon reported in high strain fatigue is the plastic instability etEct caused by the strain gradient which results from differences in cross sectional area of a specimen being tested: Coffin [3] has demonstrated both formally and experimentally that any specimen of varying cross section (for instance, a. specimen with an haur glass shape of gage section) will undergo changes during strain cycling, i.e. under longitudinal strain control, the thinner section becomes thinner by redistribution of material to the thicker sections. This phenomenon will continue until interrupted by the nucleation and propagation of a crack. Since a high degree of surface rumpling occurs prior to crack nucleation in high strain fatigue, Laird and Krause [4J developed a model of crack nucleation based on plastic instability. They assumed
that piastic instability can occur on a micro-scale in such a way that the depth of a crease for rumple! on the surface of a specimen undergoing cyclic plastic strain deepens with increasing numbsr of cycles until the strain concentration of the crease becomes 55 large that the crease constitutes a micro-crack. Although experiments with plasticine [A] and grease coating on rubber [S] have shown that this type of plastic instability does cause cracking in those marerials, the applicability of this plastic instability model to the crack nucleation process in metals is yet to be proven. The roles of crystallographic shear and of grain boundaries have not previously been checked. The purpose of the present work is to examine the details of the surface phenomena associated with crack nucleation and Stage I growth in high strain fatigue and to understand the basic mecchanism of these processes. The results of the investigation are presented in two parts. the first of which here contains phenomenological observations made to test the applicability of the plastic instability model to metals as well as morphological observations on the grain boundary deformations which lead to crack nucleation. In Part Il. the experimental observations are used to develop the mechanism of crack nucleation and of Stage I propagation. EXPERIMEXTAL (a) Tar @!I’ the phtic instnbilify modd To test this model. \ve decided to form artificial rumpI& on the surface of a fatigue specimen and to
observe the morphoIo&xtl dtvslopment of the rumples when the specimen ~v.v;ts c&d. Since the proposed mechanism might be influenced by (I) shape changes associated with the operation of different slip planes in tension and compression such as is observed in b.c.c. metals E&8] and 12) stip mode [9]. polycryst&line OFHC copper was chosen as the test material. Specimens were machined from bar stock f10.3 mm) with hourglass shape sage sections !to permit high strains) having a minimum diameter of 9.1 mm and two flats were milled on opposite sides of the sage section to accommodate areas of artiticial rumples. All specimens were annealed in sacuum for I h at 9GWC before the artificial rumples of approximate sine form were produced on the two flats through the LW.Z of photo-resist etching and ~Ie~tropoIishing techniques. The wave length of the rumpfes was about 60,um and the depth of the grooves was varied in the range between 1 and 6 blrn. Typical rumples on the surface of an uncycled specimen are shown by interferometry in Fig. 1. where the approximate sine form of the surface is indicated by the interference fringes. Note that the wave length of the rumples is smaller than the grain size of the copper (0.3 mm). High strain fatigue tests were carried out by controlling the stroke displacement of the actuator of an ~lectroh~draul~~ testing machine up to i: 2.54 mm. Specimens were brought to zero load and zero strain after sufficient numbers of cycles had elapsed to develop cracks and removed from the testing machine for microscopic observations of the rumples in the gage section.
Fig. I. Interferogram of the artificial rumples produced on the surface of a specimen before cycling.
Kl>f A>= LAIRD:
OBSERvctTIONS OF HIGH
In order to check the rolr of grain structure in ths crack nuclzation process, plain. unrumpled OFHC coppsr specimens were also studied. The specimens wer2 machined into the shape sho\h-n in Fig. 3. The factors important in the design and preparation of this specimen were as follows. (1) In low c>cclrfatigue ttsts. the hourglass shape of gage section is frequrntly adopted in order to avoid buckling. However. th2 hourglass shape is inconvenient for the purpose of surface obxrva tion because of the varying cross-sectional area along the specimen axis and the short working distance and small depth of field of optical microscopes. Consequently. replicas have to be usrd to record the parface morphology. Furthermore if on2 usrd hourglass spscim2ns it is necessary to smploj- a diametral extensometer for measuring strain. Sincr th2 sxtsnsometer has to be locatrd at th2 minimum gage cross-section ars;t. it is difficult to take surfacs rsplicas from that arca. Thzrefors, a straight cylindrical gage section ws used instead of ths hourglass shape. The maximum applied plastic limited to amplitude u’as therefore strain about + OS”,,. (2) In order to facilitate microscopic observations of the spzcimen gags surface and to make good quality replicas the surfacz to be observed should be fiat. (3) It is nzcessary to attach an estrnsometer to the specimsn shoulders in order to provide a working area for replication and to prevent th2 knife edges oi the clip-on type extensometer from digging into the specimen and giving rise to premature crack nuclsation. (4) Since a large grain size is expected to enhance th2 topographical changes induced by plastic deformation at grain boundaries and also to facilitate observations of the early stages of cracking, a large grain size was preferred. To obtain a large grain size. the strain-anneal method was used; as-machined spzcimens were initially anneaisd under argon for 1 h at 9CO’C and then . glvsn a tenslIe stram 0: 3”; p rior to reann2aling for 9 h at 9WC. This msthod, howvsvsr. was expected to promote on subsequent cycling a miniature necking effect in the gage ssction due to the 3:: tension strain. probably associated with inhomogeneity in ths prsstrain. To circumvent th2 problem. a large amount of material had to be rsmoved from the surfacr to obtain fairly smooth flats free of incipient necking in the gage s2ction. Tiiersfore, as an alternative to tensile strain-anneal. some of the specimens wer2 strain cycled to the onset of the plateau of the harden12.7mm
STR.uN
FATIGUE
ing curse at f O.?‘, plastic amplitude before reannraling for 9 h at Y-WC. These sp2cimsns showsd general recrystaflization and grain coarsening with fairly uniform grain sizes of about 0.3 mm. After rcLrystaliimtion and grain growth. the specimens were carefully hand polished and then rlectropoiished bsforr fatigue testing. Most of the surface obxrvations wer2 made through single stage replicas. Acetylcdiulose replicating film ha$ing a thickness of 0.031 mm was used for th2 rrplication. Since the replicating film is so thin it does not require the application of pressure to conform to the surface topography and takes only about fiv2 mintuss to dp compIrte1): in a normal !aborator); atmosphere without th2 aid of a blo\ver. All spscimens a2r2 tested at room trmperature and subjected to a constant cyclic plastic strain amplituds with z2ro mean strain. Strain was measured using an Instron clip-on typs extsnsometer. the knife edges bring applied to the specimen shoulders. Frzqusntly tests were stopped at zero load and maximum plastic strain limits (both tension and compression) to take replicas from thz surf& of the flats cut in the gage section. At each stop the actuator was held in th2 ~irnc position until the rspiica was completely dry. so significant creep via Stress relief \vas observed during the holding periods. RESULTS
Typical surface deformation observed in the specimens with artificial rumples is shown in Fig. 3. which was taken after 1350 cycles at a stroke limit of 2.54 mm (approximately equal to a plastic strain amplitude of O.Sg;). As can be noted in the figure the crack nucleation process does not appear to be influenced by the rumples. All cracks are intrrganular as have besn observed by many previous investigators [I. 10, I I] in smooth specimens and the shapes of the rumples appear to be somewhat distorted due to inhomogeneous plastic deformation varying from one grain to anothsr as well as within a sir@2 grain. Therefore. it is clear that the sine-form rumples of various amplitudes produced on the surfacss of the specimens have too small an effect on the strain gradient to act importantly as crack nuclei. On the other hand. the inhomogeneity in plastic deformation in polycrystalline materials appears to be more responsible for the det-elopment of the highly irregular surface contour as well as the nucleation of cracks at grain boundaries, In the following section details of the nucleation process associated with the plastic deformation near or at grain boundaries are illustratsd. (b) Crack nz~~enrion in the specimens with smooth
I_
\
73-m
cz.%m,R
Fig. 1. Standard specimen
\
FLAT
used for surface
t observation.
779
j?afs
rsplicating technique employed in the pp:sent investigation was found to be very effective in detecting the details of the changes in surface morphoiogy The
30
KIM *SD LAIRD:
OBSERVATIOXS
OF HIGH STRAIN FATIGUE
Fig. 3. (a) Artifi cial rumples observed after 1350 cycles showing preferred nucleation at grain boundaries. (b) Detail of the intergranular cracks observed in the area of (a).
with cycling. An example of the progressive surface deformations near a particular grain boundary with increasing number of cycles is shown in Fig. 4. The specimen was strain cycled at a plastic strain amplitude of & 0.577& Until 52 cycles had been applied the trace of the boundary in the surface remained sharp and clear without showing signi&ant evidence of crack nucleation. After 81 cycles (Fig. 4c) some disturbances, an indication of a crack nucleus, appeared along the traces of the boundary and increased in intensity with further cycling (Fig. Id). Since the sequences of the developmenr of the morphologies shown in Fig. 4 were recorded by replicating tape, it is probable that the tape, liquified by drops of acetone, could flow into micro-crevices when it was applied to the specimen surface. Therefore, the disturbed boundary traces which appears as a ribbon
in Fig. 4(d), can represent the depth of the microcrevice formed at the grain boundan_ if the replica was well dried before being taken ofi the surface and was handled carefully after that. It is considered, therefore, that the intense dark line at the grain boundary (Fig. 4b) which may be catled a “crack embryo” grows simultaneously along the boundary and, proportionally, into the bulk of the specimen. The width of the ribbon in Fig. 4(d) is about 7pm. Vertical displacements of the grain.s adjacent to the grain boundary shown in Fig. 4 were observed by inierferometry (Fig. 5). It ought to be noted in these figures and all other interferograms that the surface geometry represented by the fringe contour is highly exaggerated because of the large differences between the horizontal magnification (of the optical microscope) and the vertical magnification {of the interfer-
Fig. 1. Development of a crack nucleus in specimen C34, cycled at E, = 2 0.57~0. The micrographs were taken in seriatim and at the tension plastic strain limit. (a) .After 21 cwtes. (21T1. (b) 52f, grain boundary darkening. an indication of a discontinuity at the boundary. (CJ >lT. (d) 191T---replication technique.
ometer). It can be clearly observed, however, that a small step started to form after 30 cycles (the slight off-set of the central dark fringe crossing the boundary in Fig. 5b) and kept growing at the boundary. After 52 cycies the step height increased to about 0.9 .nm.* The micrograph taken from the same replica (Fig. Jb) does not show a clear indication of cracking. In other words. cracking is preceded by the formation of a grain boundary step. which as a stress raiser could play an important role in crack nucleation. * Due to inherent problems with thin replicating film. such SLSa slightly wavy surface. plus the surface corrugation in the specimen itself, focal irregularities of the fringe contour were inevitable. Therefore, the step height measurements ax only approximate values.
After 80 cycles the step height increased to about 1.5 pm and the crack at this boundary became clearly noticeable (Fig. 4). The growth of a grain boundary step and its behavior during stress reversals were traced with increasing number of cycles in another specimen which was cycled at a plastic strain amplitude of & 0.76”;. A small step of approsimately 0.1 pm height formed at the grain boundary after only 10 cycles (Fig 6ai and upon reversing the load this step seems to disappear (Fig. 6b). After 30 cycles and stopped at tension the step height increased to 0.4 pm. which then decreased to 0.15 pm upon reversing the load. In this way the step height observed both in tension and compression continued to incrras; with increasing number of
752
KiM AXD LXiRD:
OBSERVATIOXS
OF .HIGH STRAIN FATIGUE
Fig. 5. Interferometric observation of the development of the crack nucleus shown in Fig. 4. Fringes shifted in the direction marked with the arrowhead indicate depressions as known from the operating nature of the instrument and verified against a scratch. (a) 6T. (.b) 301. the fringes are completely displaced at the boundary indicating development of 3 90- step, the step height is - 0.45 pm. (c) 41T, step height is -0.6itm. (d) 81T. step height is - 1.5 pm-replication technique.
cycles, although the step in tension always appeared to be higher than in compression. The boundary step observed after 60 cycles and at tension increased to 5 1.5 ilrn, and by this time a clear indication of a microcrack was observed by regular microscopy. Another interesting feature associated with crack nucleation was observed in a specimen the surface of which had been lightly scratched with a needle point before electropolishing and testing. The scratches were made in order to facilitate locating the same are-a in each replica taken at the various stages of the fatigue life. One of the scratches crossing a grain boundary is shown in Fig. 7. The specimen was cycled at a plastic strain amplitude of i 0.5% and the stress axis is perpendicular to the scratch. After 120 cycles a slight off-set of the scratch line. an indication of grain boundary sliding, was observed at the intersection of the scratch with the grain boundary lying approximately 45’ to the stress axis. The off-set became obvious after 100 more cycles (Fig. 7~). At the end of 600 strain cycles the boundary turned into a microcrack and the scratch was displaced as much as 10 pm.
(cj Stage 1 crack propagation
Stage I crack propagation has been defined as the stage where cracks propagate along the active slip planes (specific crystallographic planes) which are usually inclined at approximately 45’ to the applied stress axis. This definition, however. is not btictly applicable to high strain fatigue where crack nucleation and growth occur along sections which are not crystallographic planes at all. Therefore. the term “Stage I propagation” will be used somewhat loosely for the moment to describe the stage of crack propagation before that which occurs by the plastic bhmting process. Various stages of Stage I cracks were examined by using the xanning electron microscope for observing the gage surface and by longitudinally sectioning for observations of crack path and depth. A specimen was lightly electropolishcd after 100 cycles in saturation at a plastic strain amplitude of 0.7:,<. Optical microscopic observation of this specimen showed that most of the deformation marks were removed except a few short and intense deformation traces along
Fig. 6. Interferograms showing grain boundary step growth (specimen C23, cycled at ep = i 0.76”.,1. Fringes shifted in the direction of the arrowhead indicate depressions. (a) IOT, a small step of 0.1 pm has developed. (bt Upon load reversal (1OC) this step is cancelled, almost completely. (c) 3OT, the step height has increased to -0.4 !trn. (d) Upon load reversal (3oC). the step height is partially cancelled: 0.15~1m. (e) 60T. the step height has increased to - l.jpm. 10 At 60C. the step height is reduced to -0.9 !trn-replication technique.
grain boundaries. This observation is reminiscent of the “persistent grain boundaries” observed by Smith [lZ] on his aluminum specimens lightly electropolished after cycling in long Iife fatigue but at higher temperature where grain boundary nucleation was preferred[iZ]. When the surface was observed with an SEM at high magnitude. the intense deformation trace was revealed as a microcrack with a very shallow but clearly observable depth (Fig. S). The crack length on the surface was IlOpm before the electropolishing. but the length measured after the electropolishing was only 27ilm. This indicares that only this particular portion (27 .um in length) of the grain boundary crack on the surface had obtained an appreciable depth when the electropolishing was carried out after 100 cycles in saturation. whereas most of the surface crack had not. and this particular portion is in the same region as that where the crack
nucleus was initially observed Cl?]. Thus. it crtn be deduced from this observation that once a crack nucleus forms along a portion of a grain boundary observable on the surface, the crack grows along the boundary both on the surface and into the bulk simultaneously so that the Stage I crack front adopts a thumb-nail shape; the front ahva)s leads at the point where the crack first started. This is considered typical of Stage I propagation and was confirmed by a series of longitudinal sectioning experiments on specimens cycled a larger fraction of the expected life so that the cracks on the sectioned face were large enough to be observed by optical microscop!. The longitudinal sectioning was made by means of a spark cutter through a major cracked grain boundary close to the nucleation site. The particular boundar!, and the nucleation site could be identified easily from the series of replicas taken at various stages during the
7y-t
KIM and LAfRD:
OBSERVATIONS
OF HIGH STRALV FATIGUE
Fig. 7. Grain boundary sliding associated with intergranular cracking in high strain fatigue at room temperature: (a) 5iT. (bj SlC, the sliding effect is not clear at this stage. (c) 11YT. the scratch line (the vertical line in the middle of the figure) is clearly displaced at the boundary. (.d) 11YC. upon reversing load. the displacement is not canceiled. (e) 220T. the sliding has produced further-reptication technique. (f) After 600 cycles, unloaded to zero load and strain. The displacement of the scratch is about 20 pm (real surface). Specimen ClO. tested at ep = & 0.5’?&
KIM ASD LAIRD:
OIISERV.%TiOYS OF HIGH STRXIX FATIGUE
Fig. 8. la) Stage I crack observed after 100 cycles in satuiation at E,~= k 0.7”w lb) and (c) The same crack as that in (a) but after light slcctropoit~hiny.
Fi_e. 9. Differences in nucleation site (a), and cycled at E, = 2 0.5’, with
crack depths observed in longitudinal sections thraqh the first reco&zed further along the boundary from that nucleation site (51. Specimen CX. strain sectioned after 640 cycies. Also note that rhz crack path in ia) is aqmmetric respect to the boundary trace Iemphasized with dot& lines).
7%
KM ASD LXIRD:
OBSERVATIONS OF HIGH SfRMN FbfIGt’E
fatigue test. Then, the cut section was incrementally ground to check the crack depth variation till it met. and passe& the nucleation site. Whenever it was desired the sectioned face was polished and etched. and micrographs of the crack at that section on both the sectioned face and the free surface were taken. All specimens examined showed the Same result that the deepest crack coincided aith the crack nucleation sit<. An example is shown in Fig. 9. The crack depth corresponding to the nucleation site is 180pm while that away from the nucteation site is S1 jrm. It is also interesting to note that a major portion of the crack path belongs to one side of the grain boundary trace emphasized with a dotted line in Fig. 9(a). This observation has been especially useful in identifying the mechanism of Stage I crack propagation (Section 2). DISCUSSION The piesent results have confirmed that the intersections of grain boundaries with the surface are the most favorable sites for crack nucleation in high strain fatigue. They have demonstrated. however. that such a choice of site is not associated with a plastic instability process operating in conjunction with an “orange peel’ surface rumple introduced in the first few cycles. Instead. the nature of the gross deformation within the grains and the compatibility of slip at the grain boundaries appear to be the more important factors in defining the crack site. A plastic instability process requires that the deformation be homogeneous, that the hardening be in saturation, and that local variations in surface topography cause a redistribution in the volumes of the material. In spite of
the great homogeneity of the disIoc=tion structures in copper c?cted at high strainsE1-Q the slip processes continue to be importantly affected by the nystallographic aspects of slip. Thus the specific orientations oiadjoining grains and their effect on the slip dominate the crack nucleation process. Although a plastic instability process now is considered unlikely to cause crack nucleation in poIycr+alline material. it remains a possible mechanism in those situations where the plastic deformation is reasonably homogeneous. for example in monocrystalline material cycled at strains much higher than those in which persistent slip bands are formed[Z]. To our knowledge, there exists no observations by which such a suggestion can be tested. The present results have documented the details of crack nucleation in a ductile metal. and show that grain boundary steps must first be developed. These steps grow with increasing numbers of cycles, are larger in tension than in compression, and are partly cancelled when the applied strain is pulsed in the compression stroke. These broad features apply throughout the nucleation period. Although the interferograms clearly demonstrate the development of the steps at grain boundaries where cracks nucleate, they do not give precise information on the actual geometry, flank angle and root radius. of the step. It is evident, however, from the scanning micrograph shown in Fig. 10 that the grain boundary steps have flank angle of approximately 90’ and a sharp root radius. This step-like surface geometry formed at grain boundaries and associated with crack nucleation in high strain fatigue can be seen in the results of previous investigators (e.g. 15) al-
Fig. 10. Scanning electron micrograph showing the intersection of the fracture surface with the free surface. Note the 90’ flank an_gle surface step and the intergranular crack associated with it. The specimen was strain cycled at Ed = k 0.7”; and lasted for 915 cycles.
though the resolution and extent of such observations
were not sufficient to identify the role of the steps emphasized here. The role Of surface steps as VZi~ effective stress raisers ou a mart macro scale has been studied by Marsh [ 163 following the seminal work of Inglis [ 1.71. Marsh has shown that the stress concentration factor is proportional to I hx. h being the step height and r the radius at the step root. Although no attempt has been made here to measure the actual values of , h .;. Fig. 10 demonstrates qualitatively that the value of , i;; for the surface steps should be high; r. difficult to see precisely and probably varying along the length of the crack, appears to lie in the range h’fOQ5 < r < lr:lO. In particular a step with a 90’ flank angle. which is close the case observed in the present investigation. is reported nearly as severe a stress concentrator as a GrifiithP crack[l6]. This high degree of stress concentration at the root of a surface step is consistent with the observation that once a small grain boundary step formed an the snrface. a clearly distinguishable crack developed in relatively few more c)-cles (Figs. sd). It is apparent. however, that a step _ 0.1 /Lrn high does not constitute a crack. if we define a crack as a stress concentrator sufficient to localize strain sigiri$cnntl~ in its immediate neighborhood. The observations reported here show that the slip in the adjoining grains dominates the cyclical. vertical displacements at the active grain boundary until the step height is about 1.5 ilrn high. The localization of slip at the step then develops slo~vly into Stage I growth. The build-up of the crack nucleating step is retarded by the partial cancellation of the step when the specimen is cycled in compression. It would be interesting to investigate whether or not the mechanism observed here in copper is accelerated in those mattrials[&-YJ which show different slip planes in tension and compression. The techniques developed here would be ideal for this purpose.
this small step continued to row with increasing numbers of @es until a micro-crack developed. On the btiis of these observations, it is suggested that a c7ask nudeus can be defined s a grain boundary step with a height of I _ 2,~m. (3) Those Fain boundaries which are preferred for crack nucleation are also preferred for subsequent growth of the crack. Once a crack nucleus is formed in a grain boundary, it continues to grow both along the boundar>- at the surface and into the bulk and thus forms a “thumb-naif’ configuration. nis information should be helpful in identifying crack nucleation sites on fracture surfaces ot’ specimens broken in high strain Migiie. (3) Grain boundary sliding is found to occur during crack nucleation and Stage I propagation in high strain fatigue at room temperat~lre. (4) The plastic instability mechanism of crack nucleation is considered rather unlikely in polycrystalline materials. Instead. inhomogeneity of slip between adjoining grains causes vertical surface displacements which develop into crack-nucleating steps. .~cknort,le~~ij7mirnrs--Thzexcellent advice and support of Mr. R. de la Veauv in connection with the mechanical testing is deeply appreciated. This work was supported by the National Science Foundation tmdcr Grant No. DMR76-006X3 through the Laboratory for Research on the Structure of Matter. L’niversity of Pennsylvania.
REFERENCES 1. C. Laird and D. J. Duquette, Corrosion Futigue (edited 2. 3.
3. 5. 6. 7. 8. 9.
by A. J. McEvily and R. W. Staehlej. Nat. .&soc. Corrosion Enzr.. Houston, Texas f1973). J. M. Finley and C. Laird, Pkl. .\f’&. 31. 539 (1975). L. F. Coffin. Jr.. Trans. .-IS,LIE 82D. 671 (t960). C. Laird and A. R. Krause, 1ut. J. Fracrurr Mrch. 1. ‘19 (1965). L. Northcott and H. G. Baron. f. Iran Srecl fnsr. 181, 385 (19563. H. D. Nine, J. appl. Phys. 44, 4875 (1973). H. Slu_ehrabi. Proo. NATO Advanced Study Inst.; Z. Mr~tulik. 66. 719 t1975). R. Neumann. 2. Metailk. 66, 26 (1975). C. Laird and C. E. Felmer. Trans. AlME 239. f07-t 119761
CONcLI_sIONS
of
We draw the following conclusions from our study the high strain fatigue of OFHC copper using opti-
cal microscopy and interferometry. (1) The development of grain boundary cracks on highly polished specimen surfaces has been documented. In all cases crack nucleation was preceded by the formation of a small step at a sensitive grain boundary in very early stages of the fatigue life? and
10. D. S. Kemsley. Phil. Mng. 2. 131 (19571 11. C. Laird and G. C. Smith, PM. Mny. 7. 847 (1962). 12. G. C. Smith. Proc. R. Sot. AZ-ii. 159 (1957). i3. W. H. Kim and C. Laird Mater. Sci. Ertgq (to be published). 14. c. E. Feltner and C. Laird, dctu .Wer. 13. 1633 (1967). i5 R. C. Boettner, C. Laird and A. J. klicE\ily. Trans. t6. ..-ll.$fE 233. 379 (1965). D. M. Marsh, Frucrttre of Solids (edited by D. C. Drucker and J. J. Gilman). Interscience, New York t.1962). 17. C. E. Inglis. ?-inns. Nnrai drclts. London 55. 219 (1913).