DUCTILE FRACTURE INITIATION IN PURE ALPHA-FE.CU)

AUG 8O R N GARDNER. H G WILSDORF N00014-75C-0A91

UNCLASSIFIED UVA/52535V/MSGO/10OUNEEi IIIIEI-EI

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1 1 RESEARCH LABORATORIES FOR THE ENGINEERING SCIENCES

SCHOOL OF ENGINEERING AND

APPLIED SCIENCE*i

UNIVERSITY OF VIRGINIA

Charlottesville, Virginia 22901

A Report

DUCTILE FRACTURE INITIATION IN PURE a-Fe

Submitted to:

Office of Naval Research800 N. Quincy Street

Arlington, Virginia 22217A Y, :Submitted by:

R. N. Gardner /H. G. F. Wilsdorf " •

Professor

Contract NOOOJ4-75-C-06 91

IC.) Report No. UVA/525354/MS80/IO1

LAJ Aukust 1980

80 8 28 075............

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RESEARCH LABORATORIES FOR THE ENGINEERING SCIENCES

Members of the faculty who teach at the undergraduate and graduate levels and a number ofprofessional engineers and scientists whose primary activity is research generate and conduct theinvestigations that make up the school's research program. The School of Engineering and Applied Scienceof the University of Virginia believes that research goes hand in hand with teaching. Early in thedevelopment of its graduate training program, the School recognized that men and women engaged inresearch should be as free as possible of the administrative duties involved in sponsored research. In 1959,therefore, the Research Laboratories for the Engineering Sciences (RLES) was established and assigned theadministrative responsibility for such research within the School.

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A Report

DUCTILE-FRACTURE INITIATION IN.PURE cz-Fe 2

Submitted to:

Office of Naval Research800 N. Quincy Street

Arlington, Virginia 22217

Submitted by:

R. N./Gardner'I

H. G. F., Wilsdorf

Department of Materials Science

RESEARCH LABORATORIES FOR THE ENGINEERING SCIENCES

SCHOOL OF ENGINEERING AND APPLIED SCIENCE

UNIVERSITY OF VIRGINIA

CHARLOTTESVILLE, VIRGINIA

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R/p ," R fp .UVA/S25354/MS80/lf)I Copy' No .Jl

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ABSTRACT

Single crystal a-Fe whiskers, grown by the reduction of ferrouschloride by hydrogen have been strained to fracture in an Instron ten-sile testing machine and in a bench straining device at various elonga-tion rates at room temperature. Whiskers were found to exhibit macro-scopic slip behavior strongly dependent upon elongation rate while thegeometric reduction in area and the fracture mode remained in all casesidentical. Ductile rupture of iron whiskers produces a characteristicallyshaped chisel-edge fracture whose geometry is sensitive to crystal orien-tation, due to the geometry of active slip systems, but which is not afunction of strain rate. The micromechanisms of ductile rupture of thesesingle crystals are strongly affected by dislocation dynamics. The de-velopment of dislocations necessary to accommodate an extensive reductionin area appears to be independent of the nature of surface slip observed.Dislocation structures form small volume elements which are separatedfrom one another by dislocation cell walls. The accommodation of largestrains as well as the reduction in area is determined by the movementof dislocations on the order of a distance equal to that of the disloca-tion cell size. The boundaries of the cell and/or the cell volume couldthen be expected to be specifically related to the site where the initi-ation of fracture occurs.

a-Fe single crystals of high purity were strained to fracture by in-situ high voltage electron microscopy. This method permitted recordingof events leading to the failure of the crystal at high magnifications.Specifically, observations were made regarding the first step in the frac-ture mechanism, namely the initiation of voids, which occurred after adislocation pattern of cells had developed. The cell size was found to bea few tens of nanometers in diameter and, because of the small scale ofthe dislocation patterns, a direct observation of void initiation was notpossible. However, the misorientation between cells could be determinedhv electron diffraction techniques leading to the conclusion that voidinitiarion took place at cell walls and at the boundaries of deformationmicrotwins. The high energy of these interfaces is another factor sup-porting the tbove conclusion.

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Ductile Fracture Initiation inPure ex-Fe:

4 Part I. MacroscopicObservations of theDeformation History andFailure of Crystals

4R. N. GARDNER AND H. G. F. WILSDORF

J

~' 4Reprinted from

A< - METALLURGICAL Physical Metallurgy

TRANSACTIONS A Materials ScienceVOLME I I A. NUMBER 4 APRIl. 19MI

Ductile Fracture Initiation in Pure c -Fe:Part I. Macroscopic Observations of theDeformation History and Failure of Crystals

R. N. GARDNER AND H. G. F. WILSDORF

Single crystal a-Fe whiskers, grown by the reduction of ferrous chloride by hydrogen havebeen strained to fracture in an Instron tensile testing machine and in a bench straining de-vice at various elongation rates at room temperature. Whiskers were found to exhibitmacroscopic slip behavior strongly dependent upon elongation rate while the geometric re-duction in area and the fracture mode remained in all cases identical. Ductile rupture ofiron whiskers produces a characteristically shaped chisel-edge fracture whose geometryis sensitive to crystal orientation, due to the geometry of active slip systems, but whichis not a function of strain rate. The micromechanisms of ductile rupture of these singlecrystals are strongly affected by dislocation dynamics. The development of dislocationsnecessary to accomodate an extensive reduction in area appears to be independent of thenature of surface slip observed. Dislocation structures form small volume elements whichare separated from one another by dislocation cell walls. The accommodation of large strainsas well as the reduction in area is determined by the movement of dislocations on the orderof a distance equal to that of the dislocation cell size. The boundaries of the cell and/orthe cell volume could then be expected to be specifically related to the site where the in-itiation of fracture occurs.

THE mode of ductile fracture in metals and alloys is EXPERIMENTALdependent upon the dislocation structures that evolve Crystals were grown by the reduction of ferrousduring the deformation history of a crystal. The failure chloride by hydrogen. The exact nature of crystal

of a single crystal as a result of simple shear on a growth and geometries of crystals obtained from theprimary glide plane is well understood whereas rupture gof a similar crystal necessitates a more complex ar-.rangement of dislocations and requires a detailed de- Crystals whose initial gage length approximated in allcases 0.5 cm, were strained to fracture in an Instronscription of phenom ena occurring during necking. From t n i et si g m c i e a e l a e c t a n nthis description we may then identify those sites where tensile testing machine as well as a bench strainingthe initiation of fracture will occur. device, at elongation rates varying from 10-' cm s to

The basic concepts involved in fracture initiation in 83 0c/.Cytl eecaatrzdbtbleanmeas conce rived infrmatur on e before and after deformation in the scanning electronclen mtal hae benderived from a number of

macroscopic observations of the strain rate depend- microscope (SEM) and through the use of the X-ray

ence of the appearance of glide on the surface of metal precession method."

crystals, the observed geometry of reduction in area All crystals in this study were taken from the same

aof -Fe single crystals, as well as a complete descrip- batch (growth boat) in order to minimize effects of un-

tion of the deformation history of single crystal iron controlled variation in quality and composition.

whiskers strained to fracture., Verification of theimplied micromechanisms of fracture has been in- RESULTS

sured by their direct observation during in silu strain- High purity single crystal a-Fe whiskers with theiring in the High Voltage Electron microscope." - ' The stress axes parallel to 1IlO, 111), 211), or (100) were

dependence of slip trace depth on elongation rate in strained to fracture. The strengths of these crystalsIt conjunction with the observation that the geometric re- varied systematically with orientation and were found

duction in area is elongation rate independent demands to be in the range of 0.6 to 9 W pascals (Pa).an accounting of dislocation movements on the order Three-stage hardening was uniformly exhibited by

" of a small volume rather than the large distances giv- the majority of crystals studied, as was almost 100 pcting rise to slip steps. This is of fundamental import- reduction in area, i.e., chisel edge fracture. The chiselance to a description of the micromechanisms of frac- edge fracture appeared "crystallographic" in nature.ture. The information gained as a result of this study That is, edges of certain orientations were consistently

j has helped to elucidate several critical features of along identical directions, these directions being re-ductile fracture of metals in general. lated to the initial geometry, and reductions in area

R. N. (ARI)NItR i Semt R r i N , t. 3%| o ( ,11 P11 .M repeatedly demonstrated the same geometric behavior('enter. ( trdl Rcc h I a t , St P .MN 510. .l II (, as will be summarized later.

WI " WItSIX1RI: i Will J l Ir,, Pofcor eIUtMerikr,, k S I lhool oI The subsequent geometries of crystals strained at

I 'liinctrilngJi d ,pphcd Science. t nmvermlI'y oi Virvitim.i, ( lirltml ',- two different elongation rates i0 7 - 10- cm, s, and it)i11t% VA "101. 8.33 Y 10' cm s, are compared in tie micrographs

,tlwripi iihmitlted ()tlolw'r It,, S)N. shown in Fig. l(a) and (h) and demonstrate tie depend-

I4SN 0 1Q1 11 -llf$8lM.'t I1MI1 ,\ I I R(,I(%',t IR%%*,.( l1ONV ' 19\O %Ni l KIt AN SO)(ll l I I .IIN.) SISll "I I 1\ PKII I' 1. .t "

I" III1l I At II:R(if(_A_ _ II I_ 0I \M -

ence of surface slip trace depth on elongation rate. electron beam in the HVEM at an elongation rate ofHowever, the formation of either planar or wavy slip about 7 x 10 cm/s. Glide packets were observed todepends upon the number of active slip systems. The have formed by abrupt slip, i.e., the formation of amore numerous the active slip systems, the wavier is large slipped area in an abrupt or jerky motion. Thethe appearance of slip. The formation of coarse wavy large slip packets seen may be due to some type ofslip (Fig. 2(a)) was observed in crystals that were channel formation" or slip instability. 0

elongated at the slowest rate, 10- ' cm> s, used in this Crystals strained in an Instron tensile testing ma-study. What is consistent throughout the slow elonga- chine at an elongation rate of 8.33 x 10-4 cm/s still ex-tion rate experiments is the coarseness of the slip hibited coarse slip, yet little packet formation was ob-traces, and, where few slip systems are active, slip served. Where small slip packets formed, small yieldpacket formation, points occurred along the length of the three-stage

The crystal shown in Fig. l(a) has been observed hardening curves.by "shadow" contrast, i.e., the contrast obtained from Finally, at the higher elongation rates tested, it be-the outline of a nontransmissionable crystal under the came increasingly difficult to image discrete traces

in the SEM due to inadequate resolution (200A). At thehighest elongation rates at which specimens werestrained, that is at 8.33 x 10-, cm/s, the appearance ofglide on the surface of crystals was in the form of veryfine traces. These results vary only slightly with crys-tal orientation and such differences, again, depend onlyupon the number of slip systems activated.

Each crystal of a particular crystallographic orien-tation demonstrated the same geometry of the reducedarea of the fractured end regardless of the rate atwhich it was strained to failure. Figure 3 shows thisgeometry in three crystals strained at three eloniga-tion rates, while the overall geometry is that shown in

(a)

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I, , 11141 111, fill, , .1" l '. ,I )),I , I.' t SI%I llcrogfli Il crN- j i'r..okntL'd Ili tenion along tire

ilfk-r O.Ai i d1e-l,'ii l~i l in Ion Ii- i 1 rIl' I ' .iil il pti i\O Ien lp'arns-'' o n h rfa' a1isls i, 5") ' 1115 t'll .I l ! '. lolil Is rd'.,1111W be'n liound Io \%lr% %tih lonigation rate. S- ki reseohltoll estilmated at

str imu t., i ., t 1 ' llli t c 111 t r si n. v d ilon trlhe 200 \ %% a, iot ible ito resolve shp title 'lruoture on crystals strained at,hh ~ ~ ~ \ 1 1- ,I l~l.' I*c II1.11 ) '1 .'1 .ll-t l~ s, ll~ l' in .111 v'loiivt limi tale's highe¢r tlianr 10 ' crii!/%. "I'11¢e . crysuils have bee .n Suh-

Is- ci l sti il tt.111 IIt I li II " 'Id ,l 0. 1 le, I 1 .1 1,is Int ll g tllon rats ol r le ' X 1() 7 cints and (t1) 1 K 3 XIl 0it) Ili I li" sr\ tak' I'. lrac lure ips ,irs viewed |roii tire side.

I.. 1 i , I I i ,so I-I MI TALl UR6I(AI TRANSACTIONS A

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Figs. 5(a), 3, and 4 (representing crystals whose ten-sile axes are oriented along the (110) and (100) respec-

- tively) demonstrate that the mode of fracture in thesej Ip p -whiskers is independent of elongation rate.

(a)

(a)

(b)Fig. 4 SI-M micrograph of crystals having a <100> tensile axis, dis-play similar failure geometries. but exhibit slightly differing slip be-havior. The elongation rates were (a) 5 X 10- cm/s. and (Of 8.33 X

(b) 10-

cm/s. The fracture tips of crystals are viewed from the sides ofthe ends.

311)(oo)

( -0

:ig. 3 SEM micrograph of three crystals having tensile axes oriented (a)"long the <1 I1> direclion that have been strained at elongation ratesof ((I) , X 10 co/s. () 8.33 X I10 cm/s. and Ic) 8.33 X 102 cr/s. Fig. 5 Summary of the reduction in area and cross-sectional changesThe resultant crystallography of reduction in area is independent of ol(ia-Fe whiskers. In all cases, the uniform development of a chiselelongation rate. rhe fracture tips of crystals are viewed "end-on", edge is seen.

MI.TAI tt'RGI'A[ TRANSACTIONS A VOLM[I IIA. APRIL 1980 655

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A summary of cross-sectional changes of the whis- tioned invariant direction and the longitudinal axis ofkers preceding chisel edge fracture is given in Fig. 5. the crystal exhibits a 100 pct reduction in length.'The development of the chisel edge is quite uniform The findings of the precession method indicate thatspecifically, there is invariably an invariant direction i) large lattice rotations are continuous and are at aalong which there is no reduction in length, while that maximum about the invariant axis, and ii) rotationsdirection which is perpendicular to both the aforemen- of volume elements are discovered to be both clock-

wise and counterclockwise about the invariant axis."These results are consistent with the determinationof the dependence of slip trace depth on elongationI

010o) While the slip trace depth was dependent upon both/ elongation rate and the movement of dislocations over

JioOJlarge distances, the same fracture behavior was ob-

~E~~l~o1 /served in crystals subjected to higher elongation rates I1110)and all samples of similar orientation exhibited com-

parable amounts of volume rotation.The geometry of reduction in area is dependent upon W

volume rotations about an invariant axis. This axis isth) a (110) crystallographic direction. As seen in Fig. 6,

(100 {Ii00 this would be expected from the activation of (111) slip

0 11111ii) directions. Crystals only experience reduction in length0(111{1la) along crystallographic directions or axes which are per-

C>. ----- pendicular to those axes about which maximum volume

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I i Ii~tiuih. Iticrii( iniiiiov cric i o h per, ve iii thicc crxn ~he. [ekn poethat give rI it) *1 I~le imexiil obeve Leniiie. ofR.IA rA\SA(1 ion.

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due lo - .iiglni e et. hfw e h ereo

It is assumed, then, that dislocation dynamics dic-Table I. Summary of Active Glide Systems Leading to Fracture tate a consistent determining mechanism for disloca-

. .. .. .tion motion over the range of elongation rates fromprimary Aictive Slip System in the 1 -6t 1 -2 M/ . ,3Vxte'al(;eo'etiy llenp leSfsai 10 to 10- cm/s. 2 ' 3 However, the rate of uniform cell

development is expected to vary with strain as well asA1 .. ... (211) Ii I ,l.(-i ) 1i iil with strain rate. During increasing strain, cell develop-

glide oIT 10111 (11o1 11l11 ment will become complete and cells will shrink insize

B lIll ilO) I IlIlOll 11111 by the process of similitude."," Deformed crystals in

C Iil (11211 il)ltI1111i which dislocations have some degree of three-dimen-glide, ol 11111 1 -11) 111 sional mobility and where there are several mutually

1) 1 I)[l 1. il lll.ll It I ).l12l)IIil1 independent noncoplanar slip systems contain disloca-glide loo 10(11l (23) 11111 tion configurations which approach that of ideal mini-

(((2 lIl mum energy storage. When a crystal experiences an''3)111111 increasing strain rate, cell size shrinks rapidly and the

T 100i i-) II].(lii2)11111it lowest energy configuration is unattainable as a result.(I- I' I III 11. 1l Ii211 The relative magnitudes of stored energy of theseI 2il 111) Ilil1l2) [111].l12 111-11] networks can be expected to vary with loop size."C As

*11 simple glide ofl were t' 0:1c1. tile active Slip systeul which would he evion- one would expect, the larger the loops, the smaller the'ibie 1, give,,. energy per unit area. Hence, it is observed that crys-

tals experiencing slow strain rates will have larger

three-dimensional cell networks than those crystalsexperiencing high strain rates.

Table II. Some Initial Schmid Factors of Pertinent Slip Systems" Microscopically, only those segments of disloca-tions which shear cells are visible, although it is, of

rIen'ile )iicction Slip System Initial Schmid Factor course, recognized that dislocation continuity is required

101iI 0.47 The passage of dislocations through large networks,

131-111i11 0.4o then, will give rise to discretely spaced slip steps. The

(loll TIll 0.41 passage of large numbers of dislocations over the con-

11111 ('11111 0.31 siderable distance represented by the crystal may

(312)111 0.30 cause the appearance of slip packets as well as the ap-l 11111)1i 0.27 pearance of 'slip channels'. Hence, it is probable that

2 i 11iti 0.i5 with decreasing cell size, the appearance of glide on

IlX11i) I F)Iill 0.4 the surface of the crystal becomes finer and finer.(Il3I 1111 0.46 Of particular importance is the observation that the1(11 l iTII 0.41 geometry of tie reduction in area which results from

f1 m 10 [ITIl 0.41 straining these whiskers is independent of the strain(1 -n'!l1 o. (.) rate. The precession method indicates that large lat-12I1i 11lit 0.31 tice rotations of small volume elements have taken

11 1 11 0-30 place. Glide packet formation in crystals strained at

*,\ c'liplel Iiilig ot Sdmild Ia hrs has heen onipiled prcviously.' slow elongation rates results in diffraction maxima inX-ray patterns which are discrete points, and thesediscrete points indicate a few degrees of rotation foreach packet. As the size of rotating volume elements

rotation does tke place. While over 100 crystals were decreases, the diffraction maxima become convoluted.strained to fracture, this was consistently found to be In the necked region, the diffraction maxima arethe case. Table I summarizes the active glide systems smoothly and continuously streaked as a result of thisand designates those systems which may give rise to uniform rotation of small volume elements throughoutsimple glide off and Table It gives the relevant Schmid the length of the necked region. The fact that diffrac-factors. The active slip systems were determined by tion maxima are streaked demands that the size of ro-slip trace analysis. Shear fracture was only observed tating volumes must be smaller than the resolving limit

t to occur twice. of the technique used, estimated at about 1 gim. There-fore, the observed reduction in area must depend upon

DISCUSSION the rotation of existing volume elements and not uponDtile movement of dislocations over long distances that

The correlation between the macroscopically ob- give rise to slip packets. This, however, would not be

served slip lines and the dislocation arrangements the case with respect to simple shear fracture which

causing these surface steps is complex. For extremely requires the activation of only one slip system and en-7 slow elongation rates of 10-7 cm,'s where atypical tails only simple macroscopic rotation.

structures are observed, one expects in bec metals that Thus, the incorporation into the boundaries of thethe mode of deformation itself differs from that mode ends of a dislocation, which have sheared a volume ele-controlling the deformation processes at higher elonga- ment. results in the rigid relative rotation of the vol-tion rates." That is, one may assume that the mocha- ume element with respect to the original matrix ofnism overcoming the Peierls friction for dislocation cells. This fundamental process is only dependentmotion is not rate-controlling and that the mobility of upon the rate of dislocation motion and upon the move-screw dislocations at extremely slow rates of strain ment of dislocations over short distances as opposedis governed by the non-conservative motion of jogs." to the appreciable distances moved in the formation of

MI I % I I I Rl A[ IR \ANS( II1ONS ,A VOI IMI IIA. APRIl [I9,0 (i ,

pon - 11110L?. & ;,- -7-.

slip steps. The above is essential to the description of necking process is independent of elongation rate andthe deformation history of single crystals prior to frac- remains uniform throughout the necked region of theture. crystal. The description of the fracture processes in

The volume element rotations, which describe the these whiskers must find its basis in the rotating vol-phenomenology of stage III hardening, are particularly ume elements or their surrounding boundaries. Thesignificant in the description of the geometrical changes initiation of a crack during the process of rupture can-in the necked region of a-Fe single crystals. In order not be understood in terms of motion of many disloca-to establish the relationship between macroscopically tions over large distances, rather, it is due to theobserved rupture (100 pct reduction in area) and the small rotated volume element and its subsequent bound- idislocation microstructure, one must first consider the aries. This, then, must be the site where a detailed

nature of the dislocation structures arising just prior description of fracture begins.to crack initiation and the disposition of dislocationswhich may in itself give rise to fracture initiation. i

To date, various dislocation pile-up models have been ACKNOWLEDGMENTSthe popular explanation for fracture initiation in clean The support of this research by the Metallurgymetals. Zener17 suggested that a pileup of dislocations Branch, Office of Naval Research is gratefully acknow-

tiBrnch ofic af crack. Cottrerch prpoe thatfl incabccwrysagainst a "strong obstacle" could lead to the forma- edged.tion of a crack. Cottrell"' proposed that in a bcc crys-

tal, the following dislocation reaction could occur:REFERENCES

[I + [ 111 : a [001 I [ 1 . R. N. Gardner. MS lhesis. [Universv ,I Virginia. ('hirloe ville. VA. 1)75.2. R. N. Gardne, and II. (;. 1. Wilsdoil: hroc. 41h Int. (l.l l ractur T. NI. R.

where a is the lattice parameter giving rise to a sessile laplin, ed.. vol. If. pp. 34Q-5. Uniersity Wateloo |hess. Waterloo. Canada.

dislocation. This leads to the assumption that the micro- I177.crack due to the pile-up of dislocations at this sessile 3. R. N. Gardnei, T. C. Pollxk. and If. G. F. Wilsdorf: Water. Sc. Fng. 197'.dislocation forms in the (001) plane. Stroh19 elaborated vol. 29. pp. 14,)-74.4. . N. Gardner: I)11. Dissetation. Unive, sits of Virginia. C'harhot tesvill. VA.

upon an idea postulated by Orowan,2 namely that a sub- 4.

boundary may act as a stress raiser in the solid, by 5. R. W. Bauer. R. N. Gardnei. R. L. [yes. Ji.. 1'. C. Pollock. and I. G. F.

considering that if a part of a dislocation wall inter- Wilsdml: I S. S Japian I/:31 .Senfinar. pp. 102-05. IHoolul. III.

acts with a strong obstacle while the other part is be- 197,.

6. U . Pollock: P10,). Ilisse, taioti. Uniiversili; ol'Vireita ht~tevle Aing pulled by the applied stress, a crack ensues. 1977. irnia Charhtesvile. VA.

The credibility of such explanations is questionable. 7. R. N. Gardner: J. Ch t. Growt, 107s. vol. 43, pp. 42'5-32.

The majority of pile-up mechanisms would necessitate S. R. N. (Giler and R. II. Ilauscoi: .alr Sci ]'i. 7. 197(,. -22 pp. 1,--70

a one-to-one correspondence between obstacles and 9. A. [I.tIf. J. Richter. K. Schaubit,. CI. Loos, and ('. NfullaiUs. Matlr. SI.

voids which is not seen, and further experimental evi- hig.. 0175. vi. 20. pp. 113-22.

dence concerning their importance in metals has been 10. w. L. Piotrosskii: I'h.l). I)tsseratou. tn,,srsy el Virginia. Chatlrt,,vrlle.SV.A. l't65.lacking. 11. V, CGinn. 'h.K Status.s ;ii. I ,I,,. vl. 5. pp. hQ6-202.

Rather, it is our contention that some other micro- 12. II. L PickelA. Lassle. and I. Conrad: Acta ket.. 196h. %ol. 16. pp. 33"-45.

structural feature, which is in itself a direct conse- 13. K. R. 1lvans and I. B. Schwenk: .cta.1c'., 1970. vol. 18. pp. I-8

quence of the observed reduction in area, may give rise 14. 1). Kuhliiann-Wilsdor: Work Ilardening. J. P. Ilirh and J. Weinan. cd,..to ductile fracture initiation in pure metals.' ~

p. 07- 139. C(tin and Breach. NY. 1908.Is. 1). KIhiman-Wilsdorf: Trans. 1IS-A41,1 . I162. vol. 224. pp. 104 "-,1.

It, S. P. Agraswal. G. A. Sargent. and It. Conrad: l /. Tram.. 1974 . l 5. pp.CONCLUSION 2415- 22.

C .I C. Zener: Iratt. Metals.1 p. 3, ASNI. Clewland. OIl. 1948.

The deform ation behavior of a-Fe crystals strained Is. A. I1. (o trell: Tran,, T.S-,III. , 1 ( ,; v8,l. 21', pp. 1)'-2'0 .

in tension describes a complex rotation of coherent dif- 1,). A. N. Stoh: Phil. lag.. 1]Q. vol. 3, pp. 5o7-(ot),.20. [. Oro, an: Dvloations III .Metals. p. ot). AIN11. NY. 154.

fracting volume elements exhibiting a consistent be- 21. R. N. Gardner and 11, (. F. \Wilvrfmv: fe't. Trans. A, 19N}, o I IA. pp. v59-

havior as required by the reduction geometry. The W)

V,,' t I1 II I A. .I\RllI 10)0 \I I IAt I RICAl I RANSACTIONS A

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III

Ductile Fracture Initiation inPure ot-Fe:

I Part II. MicroscopicObservations of an InitiationMechanism

R. N. GARDNER AND H. G. F. WILSDORF

METALLURGICAL Physical Metallurgy'] TR NSAC IONSand:TRANSACTIONS A Materials Science%().I'ME 1IA, N MBHER 4 APRIL 1980

11in

I

Ductile Fracture Initiation in Pure ao-Fe:Part II. Microscopic Observations ofan Initiation Mechanism

R. N. GARDNER AND H. G. F. WILSDORF

aY-Fe single crystals of high purity were strained to fracture by in-silu high voltage elec-tron microscopy. This method permitted recording of events leading to the failure of thecrystal at high magnifications. Specifically, observations were made regarding the firststep in the fracture mechanism, namely the initiation of voids, which occurred after a dislo-cation pattern of cells had developed. The cell size was found to be a few tens of nanome-ters in diameter and, because of the small scale of the dislocation patterns, a direct ob-servation of void initiation was not possible. However, the misorientation between cellscould be determined by electron diffraction techniques leading to the conclusion that voidinitiation took place at cell walls and at the boundaries of deformation microtwins. Thehigh energy of these interfaces is another factor supporting the above conclusion.

PROGRESS has been made in the past decade with re- ditions in the necked region." ': Hence, a triaxial statespect to the elucidation of the fundamental aspects of of stress exists in those regions of samples where voidductile fracture. The fibrous mode of ductile fracture, initiation takes place and in fact one expects that theseoften termed microvoid coalescence, is known to pro- stress conditions may well be essential to the forma-ceed through the sequence of initiation, growth, and tion of the final dislocation structure found at the initia-coalescence of voids, tion of fracture.

The initiation of voids in the fibrous mode of frac- Another point of apparent confusion is the distinctionture has in the past been solely associated with the between the failure modes of simple shear fracture andpresence of inclusions or particles in a multiphase al- rupture. The former failure mode does not require theloy system. Mechanisms have been proposed whereby participation of precipitate particles, and true void in-initiation sites are thought to be due to dislocation in- itiation does not occur in a sample failing due to sim-teractions at the particle-matrix interface, or, slip- ple shear. On the other hand, ductile rupture is a moreinduced fracture of a second phase particle.' 2 Numer- complex phenomenon and this paper deals with the com-ous reviews concerning particle fracture have been plex dislocation arrangements responsible for thiscompleted and are available in the literature. - This mode of failure as interpreted from the in-situ investi-communication reports experimental findings with re- gation conducted.spect to essential aspects of the initiation process in A further comment concerning the nature of thesepure a-Fe, and offers alternative mechanisms for duc- iii-sihu fracture studies is appropriate to this lasttile fracture initiation. point. Generally, most investigators studying micro-

The first direct evidence for crack initiation in pre- structural effects on fracture initially strain a crystalcipitate-free crystals was obtained as a result of in- to fracture, then section the sample prior to recording,it studies in the high voltage electron microscope the dislocation arrangements present. Consequently,(tVEM).' Although additional studies have been con- information regarding the dislocation patterns presentpleted in support of this conclusion, - in general, within the narrow region of the shear band is not ob-the imlplicatiois of the results of these investigations tainable when using Fuch a technique. Hence the ad-with respect to their importance to ductile fracture vantage of the il-s i/u study of fracture is that one ismay not have been fully comprehended or apprecia~ed. not limited merely to information from outside the re-

One issue which has long been controversial con- gion of greatest dislocation activity, i.e., from outsidecerns the state ot stress at the point of failure initia- the shear band.tion in ductile "thin sheet specimens.- The differencein fracture mode between bulk crystals and thin foils EXPERIMENTALhave been comprehensively investigated IA and it hasbeen demonstrated that void formation is taking place Techniques employed in the growth and characteriza-regardless of specimen thickness. Further, in the case tion of crystals have been described elsewhere.'of rupture (which is invariably preceded by severe The preparation of samples for the ill-siu investi-necking in ductile metals) or indeed in the case of any gations involved mounting the filaments on copper sup-test specimen under the conditions of a uniaxial stress, ports. These copper supports, prepared by a photo-

.j I a reduction in area will give rise to triaxial stress con- fabrication process similar to the one outlined byLyles," not only serve as a means of holding the small

'-R crystals, but also provide a way in which to transmitR. N. (,ARI)N[ R isSenior Rcw1'archl Sclentl~t. 3M (Copany. 3M('cltLcr. (cni~l R¢t';rclh [.., lrC'. St. Hilt[. M1N 55 10;llt J lId t . l". a uniaxial stress to the whisker. Single crystals were

W, I S[))RI i Wilh .Ioion Prolesor ot Mlaterials ScicC'e. Sciool of glued to the copper supporting grid: specifically, aI-n tgietri a Applied Sc'lll' te , Univcrtty of Virginia. ('ll;rlottc'- polymer resin manufactured by Bakelite Company and

fiec. VA "_21101. soluble in cyclohexanone (C,;HjO) was used.Manuscrpl ublittet Ottober 1(. I-18. Tensile supl)orts were placed in a hydraulically

'M I AlI.I R(,](At I R.\VACI IONS/A 1940 .AM RItAN SOCI- I |-OR MI AI S ANI) V(IM| I I A.APRII Pli) 65'9,' ,. l~tIM %IFIAI1.11R(I('AI SOC'IFIIY( AINII

'i. I

-ilb,'

loaded tensile apparatus designed and built for use in of "prepared" crystals, 4 to 5 gim in thickness (hencea RCA 500 kV HVEM. This tensile stage is similar in they were not initially transmissionable) in order todesign to that constructed by Wilsdorf. 8 The hydraulic be able to draw analogies from a complete microstruc-system was fully enclosed to alleviate an earlier prob- tural analysis of bulk, 3-D crystals after deformationlem caused by the presence of air bubbles admitted into as applied to "real" materials.the system, which in turn had resulted in variations inthe elongation rates of tensile specimens. RESULTS

Dynamic studies involving direct observation of in-situ fracture were recorded on videotape at a view- More than sixty crystals were examined during in-ing speed of thirty images per second. The recorder situ straining in the HVEM. These samples were in-was coupled with a low light level image intensifier. itially examined by shadow contrast. As the crystalsThe elements of this monitoring system have been re- became transmissionable during straining, it was notedviewed elsewhere. 3" 17 that the dislocation density was extremely high. How-

All transmission microscopy was performed using ever, at higher magnifications, networks of dislocationsan accelerating voltage of 500 kV, and 250 Am con- could be imaged and existing layers of networks whichdenser aperture. All micrographs were taken during were present even to the very ends of the crack flanksdynamic, iii-siti fracture. Objective apertures used were observed.ranged in size, the smallest being a 5 gim aperture Figure 1 is typical of the network structures seenwhich was utilized in order to compensate for the ob- and displays cells of about 15 nm in size. In this micro-served losses in image contrast due to the high accele- graph it is noticeable that the networks of cells are in-rating voltage of the electrons. deed continuous to the edge of the crack flank. The

Micrographs have been shown in an earlier publica- point designated by the black arrow is the thinnest re-tion which are representative of trans missionable crys- gion of this crystal. Proceeding from the edge of the

tals that were obtained from some of the "controlled" crystal into the thicker region of the specimen, layer

growth runs performed."' Due to variations of nucleat- upon layer of cells still satisfy the conditions for dif-ing surfaces, the external geometries of crystals were fraction contrast and hence imaging of descrete cell

regulated with precision by the controlled addition of boundaries becomes difficult. High dislocation densi-

small amounts of oxygen during growth. The result- ties and small cells such as these are the reason that

ing whiskers are trans missionable and of a ribbon- it is difficult to determine the nature of the braided or

like geometry which has been shown to be ideal for Jii- lacey contours at high deformations. 2 ° The layers of

situ HVEM fracture experiments, in particular be- cells mentioned above can cause periodicities in in-

cause transmissionable crystals do not require pre- tensities that are observed in the form of fringes (Fig.

paration techniques such as electrolytic thinning and 2). Selected area diffraction (SAD) patterns were taken

ion milling which can damage samples. 9 In contrast, of the areas noted in Fig. 3.

the micrographs depicted in this communication are At this point, it might be mentioned that in a generalfield of extinction contours, a periodic extinction of thetransmitted wave, in this case due to foil bending, ap-

pears as in Fig. 4(a). The extinction distances for low

A A5P A order reflections are about a few tens of nanometersand increase with increasing order of reflection. Arotation of a volume element about the long axis of thecontour leads to the displacement of part of the con-tour. Numerous displacements of this type result inthe appearance of 'braided contours.'

do Selected area diffraction patterns were taken to as-certain the character of the microstructure under ex-amination. Analytical methods for calculating diffrac-tion patterns containing twin reflections are availablein the literature. 2 3 However, when patterns do notcontain simple twin relationships, these methods canbecome cumbersome. The method employed by theauthors is that as outlined by Kelly" and reviewed byEdingtonY involving the use of twin stereograms. Theprocess entailed the indexing of all major types of zoneaxis patterns appearing on a diffraction pattern. It thenbecame necessary to locate these on a twin stereo-gram: to calculate the correct orientation relationshipsbetween patterns, and finally to identify any double dif-fraction spots if present.

Figure 5 is representative of the SAD patterns takenof the crack flanks shown in Fig. 3. The area encom-

q, J passed by the SAD aperture is approximately 500 nmaverage angles of rotation are about 20 deg, and the

Iic. I Reprcscnative HVIM micrograph (500 kV) displaying ccll at presence of deformation twins is apparent. A largethe crjck cdc (dark arrow) which hccamc diflicilt to discern i the number of crystals were observed to have such defor-thicker rcpons ol the cryt2 sihbl 6arrow). mation twins. The determination of Fig. 5(a) required

6W)ii VOI(rUM I I1A. APRH IQ MITALLUR(;ICAL TRANSACTIONS A

•-

0 , :ig. 2 ie .Irro%% denolc, pjrallelfringe,. m lidcalivc of ovcrlying rTpcll ive

iicro lrUctures IdcliltfiCd ill 1:ig. IJ., 41 Small cells+ Other Interesting lpatth+rnS

,klis'playing Somc periodicit of con Irlare ohscetd ill tile h oonl otr, of iili,

At;. lmicrogr~ih (lV I>Ni . 50f V).

II

the overlay of various separate patterns to form the The (002) spot would then be oriented 110 deg from thecomposite patterns ultimately achieved in Fig. 6. In perpendicular of the [1101 direction in the original [1131this particular pattern, overlavint! (311 and parallel zone axis patterns. Hence, the appearance of a parallel

, (511) patterns, as well as radial asterism of diffrac- [3311 zone axis pattern which is parallel to the [1101* i ion maxima, indicate the degree of cell rotations. The zone axis pattern results from rotation that is attribu-

(01) spot of the [3111 zone axis pattern may be trans- table to deformation. Slip, then, has preceded the for-formed by twinning about the (112) to form the (1 3 mation of deformation twins and continues after twin--4 3 1 '3) spots of a twinned matrix. The relationship ning has taken place. This is in agreement with thebetween the matrix pattern and the new zone axis pat- findings of a study by Mahajan :

on deformation twin-1s tern of tile twin can be found by taking the dot pr(xuct ning in a Mo-35 at. pct Re alloy.of the two unit vectors. That is, for (A B) (AB) cos,', Figure 5(b) displays spots resulting from discreteo ,ne obtains 'l, 33.29 dleg. maxima. Most streaking recorded by electron dif-

A few degrees off the reflectinlg zone axis is the fraction is spotty. This pattern is indexed in Fig. 7.,114, zone axis. Deformation twinning (If this zone Zone axis patterns again have twin relationships. Theaxis llav appear oil the pattern. Tile reflections of tie pattern taken of area C in Fig. 3 is displayed in Fig. 8.(114) zole axis form a parallel pattern with Ile origin.al The *h, spacings are all indexed: much streaking is

(113) and ,115) zone axes reflections. hlence. perpeln- observed.Sdicular to tile 11101 direction. among tie s ots of the All additional relpresentative example of the crackpattern would appear the (442) sx lt. Twinning of this flank of these crystals is given in Fig. 9. Fig. 10 dis-si )0 would give rise t, the 1002) pt and t111ile sulbse- plays eontours conosed of a network of cells. SADJ (ILIent overlaying zone axis pattern would hi the 11101. patterns were taken at different positions: these are

Ni I t II Ri.[l N1 I R\N" , Il1)%Nx % \ l %lt I IIN. ,I\ RI It) l I

U -

s'.

shown in Fig. ll(at) through (c). Because of the small of the diffraction maxima. Figure l1(a) shows a SADsize of filaments, it was not possible to place them in pattern which was taken when the foil orientation wasa tilt stage after fracture and so only slight tilting was close to the (111) zone axis, and the figure displaysdone and the rotations are limited. However, a great overlaying patterns, some possibly due to volume ro-deal of information may still be gained by examination tations. In the case of a volume element oriented with

its IlIi axis parallel to the electron beam, the twinnedregion would be oriented either along the [1151 or along

L M O l1its [1111 direction, depending upon the specific com-A posite plane of the twin, (112) or (112) respectively.

In either case, twin spots would overlap the matrixspots and one could not differentiate between the two.However, the formation of the (031) twin spot and anoverlaying [3311 foil axis pattern was observed. if (031)is attributed to a twinned volume, then the twinned ma-terial is oriented along its [1151 axis. This results

* -d ij

ig.3 I)iitfraction patterns were taken front thc regions marked.

2h 2k 21hkl

2h2k 21 a(al

(d -- .h k I

* -yhkl hki(h k"I

I-ic.~~~~~~~~~ k I i iii i~rpcc~~ikIitIoi racdrlc\ roir.I, \cnci ic!il -licii hkiii~i~ la rcu.

~(d) 0 --

'" I" h k I (

tl .4 hc Inc i ra\is i g represents ii I fou tir l io hraidtc" or

'iiL'cn " uol ,. (,I ,\ ctri.i . iii held .xin c tionl Il ti y r(/1tllrolIn 'lctdim lite foli. ~ l mlidl is tic to j pe.rliodtic c.\tiriction ()I (lie'

; 'l ; ~~ph: .1loul lIll" c ;l ',d o ile 'olotlr Fe',Hii inl 11e unliformn di,pla.ce-

rolilic ,ohui ic CIL cli. s ariV 111,111 III i/ . it May h diffiullt to distill FSg. Rc lrc.'iilIa ivc o1 scl'ccd area dIl'fractlio pallcrn, takcrn ol" ~~~giln,lil ) ' ,et.'k'll indl,loh al ontoir(II, M il'h re.,Olt, 111, ,C.l'fe t e" ',.llt~aliy the .'l'a,:k flanlks. (,fI) f]it, patternl is, .omnplete.ly de.',erlnirme, fitl th,,. fl

rcsills ili s c i i nc apparli,, n of cihitieiilr,. as ilhlisra tld ti liiiir scric%, i " igtir s. 0) Noi that lit dilfraction iia\1im1a arc ai) I in ill,. la ' cr, il rotald clk " ill giio rise to tic 'lraidcd appear- discrctc array of spots. All spots haw (/hh l Spacing, attributable to bcc111Cot n .'1ili" r. I fi, clic. ot..lrs whln small tilocation c lls Ii. irol.

w,, V0 I M) IIA. A'RIl I 9S0 MITAIIUR(;I(AI IRANSA('IlONS A

11

_ ! -

3111

11

12 II3.f.

1 110 1:331)0

[I M tIt i 11 1 m ' I Ill j1 1 ,1 1 ill I . I I 1 , J .1 , 1 1

di tl ~i I tll,

from the tact that the 10311 pole falls about 7 deg from after the twin volume has formed. As one might ex-the (115) basic circle on the back side ol the reference pect, the appearance of (110) spots 90 deg to (011) spotssphere. Spots indexed 4 3 (011) and 1 3 (415) in Fig. 12 suggest that (011) is the axis of rotation of the (115)may arise from the diffraction of the (031) twin spot zone axis pattern.fromi the (01!) and (121) points of the matrix. In Fig. 11(b) and (c), large continuous volume rota-

Other anomalous spots may also be ex)lained in a tions appear in the 110) zone axis pattern, while in thesimilar manner. Therefore. what has been formed is (100, zone axis pattern a tendency towards an over-.tn apparent 1331 1 beam axis pattern over the 11111 ma- laying pattern is seen. These series of patterns aretrix pattern (Fig. 13). (110) spots near those which indicative of the same type of patterns obtained fromform iiart of the 1331 pattern may belong to a 100 the precession method. h The X-ray precession methodxttern. Spots indexed as 4 3 (011) and 1 3 (4151 may is a nondestructive and easy-to-interpret record of the

compose the rest oit the 100 pattern. The 100 pat- deformation process as it is a direct enlargement oftern nust tit- due to the rotations of the 115 zone axis the reciprocal lattice. As opposed to representing onlyabout the 110 as shown in Fig. 14. This can oIly a "selected area", rather it represents an averagingcui t II plastic deformation has taken place affect over a large volume. Specifically, then, as the

preceding presentation of diffraction analyses indica-ted, large volume rotations, overlaying zone axis pat-terns, and twinning as observed in this study are con-

1 PM sistent with the results obtained from both the X-rayprecession method and the electron diffraction pat-terns.During in-silu straining experiments, pinholes were

A observed to form at various points along the width ofthe ribbons, within the narrow region along the lengthof the sample that is the shear band. Pinholes and thinspots were on the order of a small cell in size, and

were noticed to occur at cell boundaries. However,this phenomenon was, in general, photographed andobserved by mass thickness contrast (Fig. 15).

If one now considers the resulting fractured end of acrystal, that during straining displayed voids and holeformation as observed by mass thickness contrast, the)resence of holes in front of the cracked edge and arather jagged foil crack flank becomes apparent bydiffraction contrast (Fig. 16). Diffraction patterns ofthe area where holes are seen indicate little distortion.Along the region of the jagged foil, twin relationshipsare once again observed. Thus, both dislocation sub-boundaries as well as deformation twins were ob-served to be the initiation sites for microcrack for-

1ma iron.

I,,'w 10 tA rea Bi A Io inet wr

4 (i eIM IA I .ICApIlr ti-o i alo IJ n IO 11

i . ... . .. ... IX I II ~ IIRt Ii ~ I 1 t i (,( t IIA'5I II

U

*

pdi• 0 0•

003 A )31 A

"b 0 A0.®

- AA(

4 •4' ° 49db 03 -, o "4 2

0~ ~ 0 011Fig -2 1"l )011Tlo is, 11doo0. Il ii ofpssbe * r

110 /e iji i& r sa euto ou ertto leeNtl

' *

.44

shear bn pi t o of e s d lction ctiityIn l ig pt rna r Ao i d ) 'n o n t k d in P ig . 14 . th i p p e r n c e o f cp

•I 1)J)1 /0th ix h pit Irn i i', .1 rsiilt I1 wf hnii ro IaI Ofl whcr'j the

1331 p ittaLcrnt I w r u't ol t'kintmttg

t] shear band is the site of greatest dislocation activity

'f and hence the largest angle sub-boundaries are formedin the narrow region of the shear band. This concept

(h) requires the presence of relatively high angle bound-

I .. I I SAl) patrn of ara A. H. and C it ig, ). Iarge. co'itituous aries only within the narrow region defined by the%olhmmm roilatiom giw rise to streaked ill'tration r njmmo nll B an1id c. shear band and not over the entire necked portion of

lStreikimig a , .a result of dtulc d1 itraction appears in both pattern%. the sample. Observation of the crack flanks in the

HVEM has provided information as to the state of sub-DISCUSSION boundaries in the shear band at fracture.

Early in the deformation history of these crystals,The blueprint for ductile fracture may be considered dislocations move in such a manner that the stress

to begin at the initiation of Stage II hardening and is re- field of each dislocation is "screened" from that of* lated to subsequent sub-boundary formation.' 3 The every other dislocation. Consequently, three-dimen-

MI 1AI II R ,I( A IR ,A%%A( IION S VOI IMI IIA.APRIL 14K8m ,(5

, ........--------------------------.. ..

sional networks of cells form in accordance with the formity in the strength of low angle boundaries ob-meshlength theory of workhardening."' t ' This initial served in meas 0 3 ~might be ascribed to a meredislocation pattern will shrink in size as a result of statistical effect. In either case, the meshlength theorythe principle of similitude.' 1 ' However, complete describes a cell pattern where cell components con-

similitude in single crystals is not necessary for the tinue to shrink in size while at the same time they aremeshlength theory of workhardening to be applicable, increasing in continuity, thereby occupying a greater

It is probable that this lack of homogeneity in cell volume of metal. This process continues throughoutshrinkage in single crystals and polycrystalline foils Stage 11 hardening until a minimum cell size is achieved

is responsible for the nonuniformity of boundaries that at the beginning of Stage I. At this point in the defor-exists at sites of fracture initiation. Or, the nonuni- mation process agenerally continuous three dimnional

network of cells exist.Stage Ill hardening may thus be described as result-

ing from the motion of dislocations through networksof cells. The i-corporation of the dislocation into acell wall causes rigid relative rotation of (lhe cell's in-terior with respect to its surroundings. This is a ge-

2to ometric p~henomenon of great consequence of fracture.in At this point, let us consider the apparent causes ot

fracture initiation at sub-boundaries. Fracture initia-

formed part of a tensile sample and is thus determinedto be- due to the dislocation structures which areformed late in Stage Ill hardening. The degree of de-

210- formation preceding Stage Ill depends upon several351 variables and differs from orientation to orientation.

331 331imlplving once again that large rotations or misorien-

Ii_ 13 Indcl d pilmi I" t i l t I iIha V i 10 p'Ilrl i ~sirno' icre. Ihit wivxlrr Ii I -- I lit, and firs I ntii rfrriltect ti I rrL

0(1>115

1 v 4 llid i I ii ilm p-it~mOLll)'llj-

tw l. 1k -N fO 1di 111 A I . IO 1, 1 . i

%Ii tr,~ w ii~ , ~ i l M ,'113,1" )1,1111 1 11l o Il ' ,o " la il% -, " ~ c t t111(1"'11( 1111 OwHO ' I M IdVN Vrl 0t' ioit fIi-O a md Iitn I,-v1i m d~ o.1. 1Ldl,1,1

M t t o,"

* 4 0115)

tions of (110) Ni grains, 900 (mN/m) is the energy atabout 20 deg of misorientation.40

The existence of dislocation cells, as well as the oc-currence of cell rotations in samples subjected to

~ stresses as great as their ultimate tensile stress are

A,0.P phenomena which correspond well with the findings ofAO5"'A other wtuih .heailgdformead Coe 1in their experi-

ments wthevldeomdiron wire, discovered thatcells had formed and were present in samples whichunderwent as much as a 99.9 pet reduction in theiroriginal cross-sectional areas. They found miisorien-tations between cells of about 15 to 20 deg. In a micro-structural analysis of severely drawn irun wires, Lang-ford and Cohen found that there were varying valuesand distributions for angles of misorientation. whichwere related to the degree of work-hardening. A statis-tical variation in the strength of boundaries was oh-serv'ed. Thus, there are sub-boundaries whose anglesof mnisorientat ion, or st rengths, are approximately thesamie as those of typical grain boundaries. Their workwas also evidence for an increase in width of the dis-tribut ion of angles of misorientat ions with increasingwire, drawing strain. At it true strain of 7 the authorsfound that cells and grains were indistinguishable.

Thet physical limitations of this i-si/u IIVEM studyWerE' (Ililt t0 the smahll cell Sizes. It has not been pos-sible to detert mine the( exact dist ibution in angular mis-orientation. Langford and Cohien have stated that their

IlL U.,11.It I t h. m t'eotjlimd1 11,1111tt 11"n aIpproach imay III applied to cell sizes of 50 nni if the1 .11, 1whi Cld 'hit, accelerating voltage was about 1100 kV.2' The mini-

I ''II- rIIn Cell si/es they stUdied were 0.1 1-in. at an ac-

celerating voltage of 800 WV. The 20 ni cell size seenill this effort did not allow lor- such an eloquent study.

t.l111, III hlit I' It'S do Doi o I 1.11111 latt II Ilc(- Consider. t hen the case of one boundary separatingiilltt~i ttI Ut t itt two v'olunt meement s that arIe rotated about a common

_tt0 -it ItI RC tiltt-55 IVIIOl lol s IIoItI ISt'riLot Vt't i - axis. The incorporation of dislocations, which haveall11ill %ki. found i'ti hlu l oil a t 24 disloctiorn illtin sheared the( adjacent volume element, into the bound-

I llti ' .'Ititill .Iilv hl.I2 w t'o'hit ( ary continues to increase thie relative misorientationItlodIf" loll hs. M0IIS MUCt unll it SIighiA. SI'IrVS of the boundary.

1-11i i1-1.Ili' VIIttt 111101l.1-t Is. O llit'ld.E 5111111 .SU)L 113 F"t' i-: s d~etint'd as thet energy of fracture necessary for11( LII 1111it lol..l'i'I~'I~t' O~tIt ilt~~iit it decohiesion airoiss this or' any interface. For a metal

vow t.i -i vc mt'~llIid We11iichl~' havot)I ditaktilit' In l of single, phase'. this is mierel eqialent to the energy

of1. -alic , I 1.11 V occu fi t 1 1 Illr 1111 slt v IIIii ito l l' li'orli'llt7, 2

l~ 'iI . (%,x. .lttmid I tic', a t osil itId Ii(tiil'i III Itlherei' , is thet( sui'tace ener'gy and ') p is the energy of

II1110 Ic.t 11.il tttttll.tili. Thv, ttlivi sho~wnl, 1111, intt'itace orl tttundai'v under discussion. For per-* I ltit-i :ite ttttlicaion 1.11'I Ailtil' (ilt'~s it sailitlv' tict regListr *v oit ilolact ilg surfaces, )1, 0. represent-

I1.1liiit Ill IitJi \-.1tl'til. Ih iit -I' i'ii'ii.t loll ilt Il)- llt tilt' triivial cast' wherte tilt work necessary to cause

Intl1 iiv" at1 tiin I bmtinllt.iruid'' t nllt

11 I.Ikt ltaci, nor- tract uri' is equal to te surfact' energy (of tIlt' new sur-* 'I I"- ltcle t'51'Iili Im oliii sI'itll pll.s' pill It'll's. im-ets treated. it is .lpparet that the( incrtease in 'i h

I li ol '' 11 AI 'Aiill hinditl.ti'','~l An1 (10 I' tl(''ili. tHaMt-LsilIS durling Cell rotation lowers the( amotunt of

, r o , i t t i i t t i l ' I t iL i tf I I i I t ' . 5 o f S ~ I i4 ' t ' l a l ) o % % A o ri k n e t ' s s a i 'v l o r t i a c t u i e , o r d e c o hi e s i o n o f t h eit lIt-,-% ttoullt.l IllS kitill as roiliien'lct' boultl1'is sndal', Invo'ilve'd. it)o ccur'. Tliervtore, at high stress

I" c i i t114 1%ill - r'i'li'dtt r 1'l'',st I 'tr 1 ,pc (i' t 11' 1111- Itv Is h Ii' bounda rv hivi jg l it la rgest valIue of ) , is ab., A .11 )1'4111 A cllr~n~'lllI i 'ii'lit-1t slit's. Wivti'tiii ill' liri 'l'it'( sit' liii inicl'icrack nucleation. Thus, it is

tiiiilltthr% I, .1 'po''clal comcilId.ii'it''-iiilld.1 r. lIligI anleIt sien that1 Inlit ial t'rack fornmatio1n at sub-boundaries

tttllflI''. of .1 1-tllilti"l it(II'tluill sithttilldtiry. it ill- \%ill it' inirget icatly favored ovter anly inlpurity-free,

(I-Itt I .e'i, tof Ikk0 crI' stll.llit1.11' ti 5(11 11 tht ll'l.i' s tilt Crack Initiat ion should take place at cell walls in

Y tili ttil'i',~iliti' It' N'two'll .ii(,lllt S i .1 l I N'ltit' su lrs tilt' v ri'iltsjsndilg dettiesiun energy fort fi'ac-

.ILot1 III . lill',iiiliaitloll I,; 51111 Itt I'.tllti' Iloill 11 t) 600h iundfarv-tti-solii vapo(r tret' vnrv' Values range

oiN .I:t in Cti t tilt tilnill'.Fill' nllsiriilai-~ titil .thtut 0.25 to 0.45. and were taken at relatively

IH II, I% l % t I \ 1K I 19 o I,,

high temperature. This suggests that the energy for whiskers examined in this study exhibited ultimate ten- Lfracture may be reduced by as much as 25 pct. sile stresses as high as 109 Pa at room temperature.

To the above simple considerations, it may be added Similar values of fracture stress have been reportedthat the degree or relative misorientation which the by Allen, et al for iron single crystals of 99.96 petcrystal is able to accommodate before failure occurs, purity, which failed by cleavage at low temperatures .

3

is somewhat dependent upon the strain rate imposed on Allen further observed the same range of nucleatingthe sample." However, these variations will probably stress for twins at low temperatures as has been ob-only be of importance to dynamic shock loading, which served in this effort. This is important because twin-is not being considered here. n:g in bcc metals at room temperature has previously

Having studied the relative energetics of crack in- been reported only in substitutional solid solution al-itiation at sub-boundaries, the expected position of loys where a low stacking fault energy exists and hasthese boundaries with respect to the test sample may generally been associated with the nucleation of defor-be examined. It is as a consequence of the dynamics mation twins by some investigators .

4 It appears thenof dislocations describing this event that the largest that twinning in these crystals may obey a critical re-dislocation motion causing an increase in the energy of solved shear stress law.the boundary will occur along the predicted shear band. The crystallographic character of fracture planesThis is necessarily due to the fact that dislocation mo- displayed by the single crystals upon failure inherentlytion during plastic deformation is largely dependent depends upon dislocation processes leading to fractureupon shear stresses. Thus, once nucleated, a crack and hence arises from substructures which have evolvedpropagating along the shear band is actually preceded during deformation. These fracture modes remain atby other microcracks which are at the same time nu- all times microscopically crystallographic often givingcleating at sub-boundaries just ahead of the crack rise to fracture geometries which appear even macro-front. This phenomenon has been substantiated by the scopically crystallographic. Clearly, these crystalsfindings of other investigators, who report cracks are not failing due to a simple shear process."opening along the shear band at the same time and Characterization of the deformation history preced-ahead of the primary crack. ' ", 2 ing fracture of these crystals has revealed that the

One can identify the nature of the stresses that are geometry of reduction in area, as well as the work-present at fracture by close inspection of the edges of hardening rates of these crystals are dependent upunthe crystal in Fig. 1 where one sees the --triangular" the number of active slip systems.2 ' On the other hand,appearance of cells. Irregularly shaped cells indicate the whiskers' geometry of reduction in area, a pre-that relaxation has not yet occurred in these areas. dictable property of crystal orientation, is independepil

Models that have been used to explain crack forma- of elongation rate, unlike slip trace depth.2 The rota-tion due to twins are based on stress concentrations tional behavior observed is reminiscent of that founddue to dislocation pile-ups at obstacles such as a in the formation of bcc textures."' Specifically, it isgrain boundary, -'2 , 3 twin boundary:" or, due to the in- observed that as a consequence of the activation oftersection of two twins," ' -

' due to the combination of slip systems having (111) Burgers vectors, the oncethe slip dislocations producing ao (001) dislocations"' highly oriented sample displays much streaking of dif-or finally, due to a reaction between emissary slip fraction maxima about a (111) texture axis.dislocations.' 9 Additional models describe cleavage The evolution of dislocation structures necessary toas the result of the fracture of a deformation twin' 5

1 accommodate the geometric reduction in area is suchor explain that failure occurs as a result of a shock that small volume elements form. These volume ele-wave which is radiated when a twin strikes an obsta- ments, although too small to be resolved by simplecle .

2 X-ray diffraction techniques, are directly observed inHere again one suspects that the decohesion of the the HVEM to be dislocation cell structures that exist L

twin boundary initiates a crack. This occurrence may throughout the late deformation stages and fracture it-be described as a pseudocleavage crack in that it may self. Since the geometric reduction in area is uniformoccur in an abrupt fashion. Decohesion of the energeti- despite any possible variations in strain rate, then thecally favored boundary can occur at a speed limited accommodation of large strains as well as the reduc-only by the rate of propagation of the last dislocations tion in area must be determined by the movements ofwhich are incorporated into the boundary, providing dislocations on the order of distances equal to those

* the minimum energy for decohesion at the boundary in- of the dislocation cell size. In addition, since sharpterface. straight chisel edges are not observed in the fractured

An initial crack has now been formed, and the link- ends of the crystal, but rather very ragged edges, thising of microcracks formed at sub-boundaries may be implies that microstructures present in the neck of thedescribed either by the movement of a large number crystal, specifically boundaries and microtwins, pro- Pof vacancies from nearby boundaries (as a reaction to vide initiation sites for fracture. Detailed diffraction

large stress fields) or by dislocation activity. Previ- analysis has demonstrated that considerable misorien-ous studies have implied that dimple density or crack tation between dislocation cells exists as a result ofspacing is dependent upon strain rate.3 This may sug- deformation. Thus, voids initiating late in the stagesgest a vacancy mechanism, but it is most probably due of ductile fracture initiate due to decohesion at highto a strain rate dependency of the cell size. angle, high energy sub-boundaries and twin boundaries

as has been observed in the HVEM.3 °,0 7 The presenceSUMMARY of precipitate particles therefore is a sufficient but not

a necessary condition for ductile fracture initiation.

The presence of twins in these crystals is directly Since the completion of this investigation, microcrackrelated to their ultimate tensile strength. The iron formation at cell walls has also been observed directly

WK VOI M I IIA. %PR IL I )SO MITALLURGICAL TRANSACTIONS A

in the HVEM, in single crystal Be, ° , "' giving further 21, F. S. Meievran and M. II. Richman: Trais. TMS-AIM.., 1963, vol. 227. pp.

support to the conclusions of this study. In Be (hcp), 1044-4h.22. 0. Johari and G. Thomas: Trans. TMS-AIMI-, 1964, Vol. 230, pp. 597-91).

the stacking fault energy is lower than that found in 2.1. C. M. Wayiran and R. Bullough: Trans. TMS-AIMI', 1966, vol. 236, pp. 1711-a-Fe (bcc) and one would expect larger cell sizes.These larger cell sizes are clearly advantageous in 24. P. M. Kelly: Trans. TMS.AIM'. 1965, vol. 233, pp. 264-65.

the HVEM in that they allow for better imaging of ii- 25. J. W. Edington: Practical Electron Microscopy in Materials Science. MacMillan

situ crack initiation at the lower magnifications neces- Phillips Technical Lbrary. Eindhoven. Netherlands 1"77.for na io T m26. S. Mahajan: Phil. Mag., 1972, vol. 26. pp. 161-71.

sary f - experiments.' n27. S. Mahajan: Phil. Mag.. 1969. vol. 19, pp. 99-204.has shown microcrack initiation at cell walls in a 28. R. N. Gardner and R. II. flanscoin: Mater Sci. Eng., 1976. vol. 22, pp. 167-70.

movie on i,-situ plastic deformation of iron (Ref. 58) 2'. R. N. Gardner and 11. G. F. Wilsdorf: Met. Trans. A, 1980. vol. I IA. pp. 653-

and H. Fujita has communicated the occurence of simi- 59.lar phenomena in aluminum. 5 ' It is apparent, then, that 30. R. N. Gardner. T. C. Pollock. and It. G. F. Wilsdorf: Mater. Sci. Lng.. 1977.

the process of decohesion at sub-boundaries is funda- vol. 29. pp. 169-74.31. D. Kuhlhann-Wilsdorf: Trans. TMS-AIME. 1962. vol. 224. pp. 1047-61.

mental to the mechanism of mechanical failure of 32. D. Kuhllann-Wilsdorf: Workhardening, J. P. Hirth and T. Weertmnan. eds.. pp.heavily workhardened pure metals. 97-13), Gordon & Breach, NY, 1968.

33. D. Kuhlmann-Wilsdorf: Met. Trans.. 1970, Vol. 1, pp. 3173-79.34. D. Kuhlhnann.Wilsdorf: Prot. Sirp. Work Ilardening Tens Fatigue, 1975.

ACKNOWLEDGMENTS A. W. Thorpso.r ed., pp, 1-44, AIME. NY, '177.35 G. Lurgford and M. Cohen: Traits. ASM, 1969. vol. 62, p. 623.

The support of this research by the Metallurgy 36. J. I). Boyd. J. D. i-tbury, and U. M. Sargent: 5cr. Met.. 1976. vol. 10. no. I0,

Branch, Office of Naval Research, is gratefully ac- pp. 401-03.knowledged. 37. W. J. Witconth: PO's. StarrsSolidi 1974. vol. 22, pp. 299-304.

38. I. L. French and P. F. Weinrich: Met. Trans. A. 1976, vol. 7A, pp. 1841-45.3'. S. S. flecker L. E. Cox. and 1). F. Stein: J. Metals, 1476. vol. 28. no. 12. p.

REFERENCES A52.40. L. 1. Mul: Interfacial Phernrmnena in Metals and .4tlls, p. 143. Addison-

I J urland Irans F'lS-.IlIMI. 1 43. Vol. 22_7, pp 114,-50. Wesley, Reading. MA. 1975.2. J. I. Botbt ..lta .llct.. 117. ol. 25. pp, 903-t. 41. 1. Kovacs: Met. Trans.,. I'71. vol. 2. pp. 96 1-66.I.R %, Bailer Ph.I)lts,eltation. Unvt.esit, of Virginta. Charlottesville. VA, 42. C. Zettet . Fracture o Metals. p. 3. ASM. Cleveland. Oil, 1948.

1"5 43. A. N. Strolt: Phil. Mag. 195S, vol. 3. pp. 597-600.4 1) Block PhI) )ts itwtaon. Tech. Iloges'kool Dellt, Netherlands. 197 1. 44. W. I). Biggs and P. .. Pratt: Ata AMer.. 1460, vol. 6. pp. 6'4-703.5. J. R Loss . Frat. .I'cth.. I4to . ,,l. 1. p 47 45 D. lctl: A ta .ht., 1960, vol. 8, pp. 1 1- 18.t, A. . Rosenfield Alet. Rer., 146S, vol. 12 I. pp. 20-40. 4(6. R. londa: J. phls. Soc. Jpn. 19h,1. vol. Il. pp. 1309-21.

1), . (rtrran. LNm Scassan. tttd 1). A. Shockei : Plits . 7*,lav. 1177. -l1 30. 47. R. W. ('ahn J hist. Metals. 1t55, vol. 83, pp. 493-1..no I. pp. 46-55. 4s. A. I. (ottiell frais. TM -AIM.. 195,. vol. 212. pp. 192-202,

. R. W Bauer, R. II. Rcr , . . L% les. Jr.. and II. G. I. Wilsdodl Jernkrort. 4'4. A. W. Sees yk: .4tta Met. l1t42. vol. 10. pp. 2(3-812.

lint. 19' 1. ol. I i5. p 403 50. K. Kitalita Proc. lit lii, ( 'Cf. lractre. 1. Yokohort and M. Ichikawa, eds..R %% Bar. R II Get,. R. L Lle,, J.s and II. G. F Wtlsdor. Pr,-v. 29th vol. 2. p. 659, Soc. Strength and Fractrte o Materials. Tokyo. Japan. 1400.•trllt titne 11, I t)r,. Sri. .1Amt 1'. 130. la.tot's Publishing Division. 5I, T. Sakaki and T. Nakanra: J. Iron Steclinst. Jpitl 173. Vol. 5). p. 455.

Hat, n r oge, L.A. I)')" . 52 .I. oinhogeni Traim 1iffS-/lIM". 1941, Vol. 22 1. pp. 71 1-15.

It. K. W 11 Barter .ttn II. .. F. Wtlsdort Str. % ., 1473. vol . .i p. 12131-20. 53. N. P Allen, B. F. Hopkins. and J. McL.-nnan Prrv. Roy. Sor. 1950. vol A234.I J. A Al\1 and K. R . Asnio ,s I ng ract. the It 7'. vol. 4. pp. t 1.2 S pp. 22 1-4t.

12. R I. 1 sr arid II. (, F Wilsdo t i ta let.. 175. vol 23. pp, 'tr.17. 54. G. F. Boiling and R. 1I, Rtchman. Cat. J. Phys.. 1967, vol. 45. pp. 541-57.13 R W Barter ia IIa 1 F Wli do It 1r,,. hit ( mu on Ii) taittt ('rack Propa. 55. R. N. Gardner and II. G. F. Wildort: Prot. 41h /it. (Ctl . it Fra(ture. T, M. R

cgat crc. ; C. Sit, ed . pp. 14- 'I . No ordhl it Pn rlt u lrt g, Leyde. Il 73. raplhi. ed.. vol. II, pp. 341c-i(. Unwersit% it Waterlho Press. Waterloo. Canada.14. (, Iltiltet Ihechatriral Ietalltrgr p 344. Mcraw 11l. Nevw Y rrk. NY. I '77.

'O1, %i. II. '. Klug and L I. Ales ande X-ra Difyicttwnt Metiod.. p. 709,. John Wiley15 I) A. Rvdet. I. 1. ).tvnie. I Btough. and 1: R. Ilutchings Mhetals llandhrck, & Sons. New York. 1474

It I- Bo.rci. ed, soI. I0. pn. 1t)

,,SM, Ohit. I975. 57. R. W. Barter. R. N. (;adter. R. L Lyles. Jr.. T. C. Pollock. and i. . F.tI, R. N Galdnet . ( (;row ti. It47S. vol. 43. pp. 425-32. Wilsdort: r cc. U. .-Japran 111/I Sewinar. pp 102-O5. Ihonlulu, Ill Nagoya

I7

R.I t 1,ies Jr. MS Ihemis.p 14li I nversty of Virginia. (harlottesv ille, VA, University, Nagora. Japan. l 47r.1071. 58. T. Inra. I)islocation Movie Sholtrun at tire LT.S.-Japan UIVEM Settinal, lionolulu.

1,. iti G F Wclsd,tt Rr. SciI.inrrum , 1tii. 'ol 2'). pp. 323-24. December (,-Il. Departtent ol Metallury, Uiversit ol Nagoya. Japan 117(,1i

1 r N. NO)r PI) I)cssertat in. nivcrt o Virginia. {'haltesville. VA. 5t). li Fujita: Personal Ccommurrrtinication to I. (. F Wilsdor, 1)epatttent o Ma-I o?7 tet ials Scietre and Ingieering. Osaka University. Yarradakairt. Suitsa 565.

20 G Lan ghlrd ai t L ('then Mtr . itrats...I. 197i . Vol. (A pp. 401- 10 I )7(..

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