Polygonization in strongly deformed metals

7 POLYGONIZATION

IN

DEFORMED

STRONGLY

METALS

C. Crussard, F. Aubertm, B..Tao~d and G. Wy ~ THE zxls-rElscz of polygonization has been established on single crs~tals or coarse-grained metals annealed after slight or moderate cold work, these observations having been carried out by means of micrography or x-ra~. It will be our aim here to present the experimental evidence for polygonization in fine-grained metals heavily cold worked before annealing, this ex'idence being based on micrography and x-ray studies, and also indirectly on observation of other physical properties (plasticity, thermoelectric power) which are influenced by polygonization, as will be shown later.

POLYGONIZATION

IN

COLD

ROLLED

COPPER

If,afterthe clcctropolishingofcoppcr in thcJacquct bath I the electrodes are short circuited, a selective deposit of copper is produced on the metal, which reveals very fine details. This fact was utilized in the study of stripsof copper annealed at 850°G and cold rolled from 7.7 to I ram. The obscrx'cd me.rkings axe related to the structure of the metal itself,and not to irregularconditions of the deposit, as is proved by the fact that, after re-polishingand re-etching,the same markings appear in theiroriginal places. The pattern of markings formed on cold rolled copper is shown in Figure ,,: bright patches on the surfacecorrespond to parts of the metal where a (100) plane is ncaxly paraUcl to the surface. Lines appear at these places that are fairlycontinuous and somewhat bent or forked, suggesting some "kindof bending in the lattice,which is certainly due to flcxural glide. After 100 hr annealing at 125°C different pattcrns are sometimes displayed (centre of Figure .v):the etchings consist of short segments, broken at rather large angles; the breaking points ofaU the linesdraw contours dividing the initial grain into sub-grains, and are very similar to LACOMSES intracrystalline contours, t This only occurs

PROGRESS

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PHYI~IC|

where the initial curvature was marked and suggests an incipient' PolFgonization. After annealing for 2 hr at 190°C, some new grains appear (centrrof Figure3); thus actual rcc~'stallizationhas begun. But where rccry..stallization has not taken place and where the surface is bright the appearance has changed: instead of being continuous the lines are fragmented into small segments or curves, having well defined ends, which form contours having roughly the same orientation~thin each grafm (Figure4)- Thus the bending ofthc latticeisno longer distributed over a11 the grains, but concentrated along some sub-boundaries. This again ~ggcsts genexalized polygonization. INFLUENCE

OF

POLYGONIZATION

ON

MECHANICAL

PROPERTIES

Ifany polygonization occurs in hca~dJy cold worked meta]s by annealing at temperatures just below the rccr'vstallizationpoint, it m a y bc possible to detect it by a change in the mechanical propcrtic~ RccrystaUization /a s/ra was first observed on aluminium by such a change. ~ For this purpose the exact shape of the strms-straincurve was studied as a function of tempexature. The metal used in this investigation was aluminium (99-99 per cent purity,) containing 0-004 per cent iron (after hot extrusion). Samples were machined out of these rods, annealed at various temperatures for 5 hours, and tested in Chevenard's tensile micromachinc. The photo.. graphic registering of the tensile curve facilitates very accurate analysis ofthe shape ofthe curve. Figure5 represents the elastic limits (measured limit of proportionality) and the stress for an elongation of 1 per cent as a function of the annealing temperature. The sharp decrease of the curve at 300°C indicates that recrystalLization is taking place, as is proved by x-ray analysis: at 300°C the samples arc wholly recrystallizcd; at 265°C there is no recrystallization; at 290"C there is a mixture o f new grains and distorted matrix (asterism). One of the Debye rings consisu of very small spots. This ring is a /fa doublet; the pattern of the spots is about the same on each component of the doublet and one can be approximately deduced from the other b~ translation. This corresponds to a Polygonized state. It is Possible that some of the spots indicate the formation of a few new grains; but on the transmitted part the halo due to the continuous 194

POLYQONIZATION

IN

STRONGLY

DF.FOR.MF..D

METAL$

spectrum of x-rays still shows a pronounced asterlsm, proving that the sample is not really recrystallized at 2650C. Great care must be taken in the interpretation of these x-ray diagrams because the outer layerJ of the samples, heavily cold worked by the cutting tool, r e c A ' y s t a l l h , ~ at lower temperature than the remainder of the material. Mistakes are best avoided by the removal of these layers, through electropolishing or etching, prior to annealing. It can be seen quite clearly from Figure5 that between temperatures of 250 ° and 280°C the elastic limit shows an initial drop, while the

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FigureS. I'atiatmR o f d a s ~ limit ( l ) and : per ctnt proof

Fifant 6.

healing ~ a t u r t , ah~~ w ~ 99"99prr a ~ a~td~ a ~

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tuft, d

Vadatzan of das~

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~ - ~ per ~

s~wd

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stress for 1 per cent elongation does not decrease much. This premature drop is one of the anomalies of this zone of annealing temperature. The shape o f the initial part of the stress-strain curve in thi~ region is also quite peculiar: it is known that a stress-strain curve has a roughly parabolic shape, that is, the stress ~ is related to the elongation • by a formula* of the type o == o o +

at"

The elastic strain is deduced from the measured strain to give c. Careful investigation shows that the value of m is not univenal for the whole range of the curve. For a small region of the curve m can best be computed by a differential method which was proposed by DE LAcouw, for the analysis of creep curves, s by which any clmnge of shape along the curve is clearly revealed. 195

PkOGP.~'SS

ZN MZTAr.

PEYS:C8

Let us now study the shape o f the first 2 per cent of"the curve, which m changes. For r e c ~ - ~ t ~ z e d samples a and : are positive, the lauer being of the order of 0"5 to 0"8 (we have detected values as high as l-0); then a0, as computed by the above method, approaches the observed ,d~tic lJxnit, which is genera].ly higher, direct observation being less accurate than calculation. For cold worked samples m has a negative value of the order o f - 0-9 to - - 1-1; here a 0 is not related to the elastic limit.

~ r h e n the material is annealed at 265 ° and 280°C

m equals zero, that is, the curve i~ logarithmic. The change is abrupt, m still being equal to -- 0-95 for samples annealed at 250°C. Thus, immediately below the temperature of genuine recrystaUization there is a narrow zone o f temperature where annealing produces a stress-strain curve of a special d ~ p e . It is interesting to compare these observatiom with materials where polygonization occurs, that is on coarse-grained slighdy cold worked cr~als. Samples of the same metal were recr~tallized to a grain =ire of 0-1 nun diameter, stretched 3"5 per cent and annealed at various temperatures for 0.5 hr. Recrystallization as seen by x-ray occurs between 400 ° and 450°C. Fight 6 shows the variation of the elastic limit with temperature or" annealing up to 450°C. As in Figure5, the drop from the cold worked state to the recr3~taJlized one occurs in two stages. It was thought that the metal is polygonizcd at the intermediate stage at about 350°C,. X-ray ana].vsis confirmed th• supposition: each grain produces a duster of sharp spots, thus the metal is recr~mallized /~ situ, that is heavily polygonized. Also, as was remarked in the cold worked or the recrystag lized state, the value of m changes at this intermediate stage. Thus, in heavily as in slightly cold worked metal~ recrystallization is preceded by an intermediate stage; as this corresponds to polygonization in the latter, it is reasonable to assume the same thing for the former. Other experiments were performed on wires of impure aluminium contaimng 0.41 per cent iron and 0"28 per cent silicon (no other impurities). Special grips had to be made to enable pieces of wire to be tested in C,hcvcnard's micromachine. Figure 7 s h o ~ the variation o f elastic limit as a function of the temperature of annealing. The shape of the curve is the same as for pure a]uminium: the drop occurs in two stages, separated by a zone of temperature where x-ray= show the metal to be polygonizcd. 196

POLYGONIZATION

IN

STRONGLY

THERMAL

DF-FORMED

METAL|

ANALYSIS

The energy stored in a cold worked metal is evolved as heat during annealing. A differential thermal anal~is between a cold worked sample and an annealed one of the same metal enables us to determine at which temperature this heat evolution occurs. The method was used in a sensitive device with the pure alurninium mentioned. Although the experiments have only recently been initiated, it a p p e a n that the heat evolution is very small during recovery and begins

Figure 7. gradati°n of elastic limit (!') and thenm~karte povxr (11) m a fuw,twn of anntaling to,qmatwr, alumisi~m 99"3 ~ r ~ cold &'awn. X-rays

..../

sharply between 280* to 285"C. Thus the stored energy is d i ~ p a t e d mainly at recrTstallizadon, which occurs at the temperature indicated by other experiments. X-RAY

STUDY

Some observations made on x-ray diagrams lead to a better understanding of the facts. In polygomzed p o l y ~ each block or crystallite of the structure gives a sharp spot. If the metal is coarsegrained these ~-pots are clustered along arcs of the Debye rings, extending over a few degrees; each arc corresponds to a whole grain. These spots are quite distant for high Bs~gg angles. I f the grain is finer, the different arcs merge together; thus it is difficult to distinguish between a polygonized metal and a recrystallized one with very fine grains. But the distinction can be effected by observing Ka doublet on back reflection, as mentioned earlier: in the polygonized state the pattern of spots from one component of the doublet to the other correspond due to asterism. It is also characteristic that, by transmission, the continuous spectrum of x-rays produces a pattern which, for polygonized metab, still shows a great asterism. By these m e a m we were able to

197

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PHYSICS

prove that the cold drawn aluminium crystals were polygonized after annealing at about 270°C. It is important to note that, even in the cold v'orked state, the I ~ b ~ rings are often not continuous but consist of spots (back reflection). These spots are perhaps not as sharp as in the polygonized state, but have about the same density. It is well kno~zl that in the cold worked state the deformation is heterogeneous. In other words, cold working generally leads to fragmentation, e except for single crystals deformed in a homogeneous way. A study of this fragmentation has been m a d e ~ (see p a r t i o , h r l y Figures 8 and .9 of this referunce) and it was concluded that high purity aluminium is alwa),s fragmented. T h e average size of the fragments o r cr).,~taUites could sometimes be deduced from the n u m b e r of spots produced by a grain of "imown value a n d it v'as found to be o f t h e o r d e r of 5 microns. A picture (Figure 8) obtained by means of ~ s x-ray microscopic method s shows the shape of the fragments o f a grain in a sheet of slightly bent alumlnium; the size is somewhat larger than mentioned above, but cold v ~ r k is sli,trht, so that it is probable that the type of fragmentation is the same in both samples. With impure aluminium fragmentation cannot be detected in single crystals, where it is probably too fine, but it appears quite distinctly in polycrystals. The phenomena cannot generally be observed in metals other than aluminium, excepting those having a low melting point. I f deformation is carried out at high temperatures or at low rates the fragmentation is much more pr~..ounced and distinct, indicating a relationship with densi~' of slip lines and size of the mosaic block after deform.ition. But it is not yet clear whether the observed fragments or crystallites form the mosaic blocks themseh'es or ff the)- are larger. T h e y may rather be related to deformation bands. This fragmentation greatly hinders the detection of the start o f polygonization by means of x-rays. It is, in fact, questionable whether a fragmented cold worked metal is not already polygonized. This involves a question of terminology which v'ill be discussed later. THERMOE|.ECTP.IC UEASU~ES As polygonization implies a movement of dislocations, in an impure metal it must also lead to a displacement of the foreign atoms by the Gourell mechanism. As thermoelectric measurements have been shown 198

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,li

Fillre 8. C-,oarse.grnlnldsii~t of a I ~

benl, J~rreU's nlthod (.~fah,nllv,allo~ aoo ×)

POLYGON[ZATION

IN

STRONGLY

DEFORMED

M£TAL|

to provide a v e ~ s~-~idve method of observing the changes m r~parfi° tion of foreign ator~,* the study of the v~u'hdon of ~ m o d e c u ' i c power during annealing at increasing temperatures is implied. Dislocations alone have been shown to have a very small effect on thermoelectric powcr of aluminJum l° (variation smaller than l0 4 v o h M e g r ~ ) . Thus any appreciable variation of the thcrmoclcctric power must be due to some kind of precipitation or dissoluuon of impurities, or possibly the formation of large CottreU a t m o s p h c n ~ The method for measuring the thermoelectric power directly at a given tcmperamrc has been described clscwhcrcA l The metal tested was the same wire of impure alumlnium as above. It was annealed at 500°C in order to dissoh'c about 0-006 per cent iron and all the silicon prcsent, air-quenched and cold drawn from 4 to 1 man diameter. (Silicon and iron both decrease the thcrmoclccudc power of aluminium. Thus an increase of this quantity corresponds to a precipitation.) Figure7 represents the thermoelectric power o f the as a function of temperature; the graph displa.~-s a sharp increase from 11300C and tends towards the value of pure atuminJum: some kind of precipitation is occurring. The variation occurs in three stages at temperatures o f a b o u t I70 °, 260 ° and 320°C respectively. These stages seem to correspond rather well to the procce~ses of recovery, polygoni-~ation and recr).~stallization, although the temperature of 320°C is too high for the latter and it is still not kno~.-a how recrystaUization can lead to a precipitation of impurities. A similar study has been carried out on an aluminium wire of similar composition, which consists of a few Q-lindrical grains and can therefore be considered to behave like a single crystal T h e wire was annealed at 600°C and stretched 18 per cent: its thermoelectric power shows no variation before 430°C, at which temperature genuine recrystallization occurs as shown by x-ray analysis, which reveals no fragmentation below 430°C. Here the precipitation is very pronounced but accompanies recrystallization. In an intermediate sample o f a coarse-grained wire stretched 20 per cent precipitation begins at 270°C, while true recrystallization is observed only at 310°C. Thus thermoelectric studies on an impure aluminium crystal show that, as it is increasingly fi'agmented by cold work, more precipitation precedes recrystalli'zation. The relation o f this precipitation with polygonization has been suggested by GALl'. 1. It will be discussed later.

199

PROGRZSS

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MZTAL

DISCUSSION

PHYSIC|

OF I~.RSULT|

A metal is said to bc polygnnized when, within each grain, lattice rows arc not continuously bent but broken into small segments, each of them making small angles with its ncighbours. T w o problems arise from this definition: x A question of scale: by the atomic scale, all bent crystals are polygonized. It is not intendcd to account for this 'polygonization'. Therefore a lower tin'fit must be assigned to the length o f the segments involved in the definition. Since x-rays show that, even in heavily cold worked metals, coherent domains of reflection have a length of about 10 -~ cm, it is appropriate to ~.lcct this limit. Thus the lower limit of polygonization is the mosaic structure., zs F ~ r 9. Ana~mml of aa ~ a i c

~

ia a me~al

P aaddaaic~.sF.$

2 The question also presents itselfwhether these segments must bc straight, or whether they can bc slightlybent when two kinds of impc:rfcctionsoccur along the atomic rows: local breakings, and bending over longer parts (Figure9)- The assumption .*hat the word polygonization expresses only a trend to lo,-~llzcthe curvature with angular discontinuities, 15ut does not exclude elastic curvaturc..~'.-:ems to be the most suitable solution here. Thus, whcrc x-rays show fragmentation, a cold worked metal exhibits polygonization and internal stresses together. T h e x - m y study mentioned in this chapter indicates that in aluminium this polygonization is on a rather large scale (order of 10 -s cm). It is more pronounced on polycrystals, due to heterogeneity in the stress distribution. Impurities decrease the scale of polygonization, so that it hardly can be detected by x-rays: single crystals of impure aluminium reveal no fragmentation or polygonization when deformed. Nevertheless one must remcmbcr that Guinier has observed polygonization on single crystals of impure alaminiumafter anncaling at a very high temperature (600°C). For other cubic metals the scale of polygonization seems smaller and must descend to the mosaic structure; also internal stresses are higher. Thus, there is a more or less continuous passage from the 200

P O L Y O O N I Z A T | O N IN STRONGLY D]~FORMZD MVTAL|

small and continuous curvature of bent single crystals to the mosaic su'ucmre of heavily deformed metals, going through an intermediate state of polygonLzation at the scale of the deformation bands. When such structures are annealed, the paRern of dislocations and the related stresses will tend to reach a more stable state (more localized rearrangement, which may have an effect on magnetic or electric properties, are not considered here). This can a F / o r / h a p p e n in two ways: i Annihilation of + and --, as suggested by BuRcr_~ This process can be called 'local recovery' and does not change the curvature at the mosaic scale. fi" Movements of dislocations, with a trend to group along subboundaries Ls. polygonization. This process is hindered by inadequate size of curvatures or by a predominance of impurities. Thus, polygonization occurs much more easily in a metal already fragmented by cold work and progresses during annealing by an increase of the distance between the sub-boundaries. Our thermal ~-~!)-~is experiments have shown that most of the dislocations present in the cold worked state disappear only during recrystallizadon; ~hus, if 'loc.al recover).' occurs in aluminium, it annihilates o n l y a few dislocations.

O n l y the t h e r m o d e c u ' i c c,dr~,e o f

Figure 7 can suggest a first stage recovery, as distinct from polygonlza. tion; but the bend in thi~ curve at 215°C may be due to experimental error.

Other experiments on aluminium (variation of elastic limit, or ~ a p e of the stress-strain curve ofx.ray diagrams and of thermoelectric power) all show that, where a metal is already fragmented or partly polygonized by cold work, polygonization progresses further during annealing, and just before recrystaUization reaches a relatively stable state of coarse polygonization (or recrystallization in situ). This state is not essential for recrystallization, as it is absent in the case of single crystals of impure aluminium which are not fragmented, or at least where it may occur on a much smaller scale. The precipitation of foreign elements accompanying polygonization can either be actual precipitation or formation of large CottreU atmospheres. The fact that the variation in thermoelectric power continues during recrystallization can be best explained by the second 201

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PHYSICS

hypothesis: a genuine precipitation occurring at the places where the atmospheres had united m a n y atoms. Micrography also shows a trend to polygonization in a fine scale for copper, so that the phenomenon appears to be quite general, at least for cubic meralt, SUMMARY

A special micrographic technique shows that in cold rolled copper amaealing develops sub-boundaries within the grains before actual recr,'stallization occurs. In heavily cold worked aluminium the crystals are fragmented as shown by x-rays, so that a partial polygonization is already present. This is not true for slightly cold worked, impure aluminium. During annealing of fragmented aluminium the drop of the e ! ~ c limit occurs in two stages. The first one co/responds to a progress of the polygortization, the second one to recrystallization. The state of coarse polygonization thus reached corTesponds to a special shape of the stress-~raJn curve. Thermoelectric study proves that this progression of the polygonization is accompanied by a partial precipitation of impurities. Recr3.~stallization can occur in single crTstals without prex-ious polygonization (at least on an observable scale).

IRIrFtKENCEI

I jAcQt;'rr, "P. Rt'c..M~ta/L 37 (194.o) 214 JxP.OSZEwmz-BorThowsv,J, M.. and SCHOOl, ,J. R~v. ~ . ~rm. ,.5 (|949) 9 ' LAcouR~, P. and Br.AWAR.o, L , 7 . Inn. M a . 74 (t947) I * Cm,s.~J~, C. tk'~. M ~ t a l l . 4t (t.cHI4) t t z 4 ~bld 41 ['9'44'1 45 ' oi" L~cou.~, J. ~,d 36 (7939) t78 • Horn:s, G. Bull. Acad. Belg. C¢. S~.. 23 (1936) 655 T CRu~,ru~, C Commamtcatwn au Con~r/s de l..tige 1947 Rt'v. univ. Min. p 47 , 7949 " BAxgr'rr, C S. Atom. ln~t. ?,Ira. E.ngr.~, Jttet. Technol. Tech. Publ..A'o. 7865, 1945 • (.;Rt'SSARD, C. and At,nF.~'nN, F. Put,. Mitall. 45 (1948) 470 '* lJrutol Con/create Pep. a947 p t19: Publ. Phys. Sac. J94B t, and ALaSERTL%F. /~.'..Meta./L 46 (1949) 661 a t GAL'r, J. K. Phd. J~fag. 7, 4 ° (1q49) ~o9 a s C~ur.~ucD, C. and Gt'IND;R, A..R,tv. Mtt~ll. 46 (7949) 6t

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