FRACTURE OF A SUPERPLASTIC TERNARY BRASS

S. SAGAT and D. ivl. R. TAPLIN* Fuel and IMaterials Division. CRNL. Chalk River. Ontario, Canada

Abstract-A study has been made of flow and fracture in a strain-rate sensitive ternary brass at ~8~C over the strain-rate range 10 -‘-IO-3 min- ‘. The material is superplastic with an optimum ductility at 6OO’C. Plastic flow is accompanied by the continuous development of intergranular and interphase cavities. Under these conditions failure occurs without measurable external necking. The instability of plastic Row is analyzed in terms of the development of internal bifurcations (analogous to diffuse, multiple, external necks for non-cavitating superplastic alloys) and the linking of cavities by internal necking (analogous to rapid preferential growth of one external neck). It is concluded that for precise analysis of void-linkage a dynamic model is required as opposed to the current quasi-sta- tic models. An experimental basis for this work is provided.

R&urn&On a ttudiC la diformation et la rupture d’un laiton ternaire sensible B Ia vitesse de diforma- tion entre 400 et 8OO’C pour des vitesses de deformation comprises entre 10-I et 10e3 min-‘. Le matiriau est superplastique et sa ductilitC est optimale B 6OO’C. La diformation plastique est accom- pagnee par le dCveloppement continu de cavitts intergranulaires et interphases. Dans ces conditions, la rupture se produit sans striction externs mesurable. On analyse l’instabilit0 de la d&formation en terme du d&veloppement de bifurcations inrerncs (analogues aux strictions diffuses. multiples ou externes pour les dliages superplastiques r&istants B la cavitations et de la liaison des cavites par des strictions internes (analogue B la croissance rapide pr~f~rentielle d’une striction extsrne). On con&t que l’analyse p&se de la liaison des cavitCs necessite un mod&Ie dynamique. par opposition aux mod*Ies quasi-stati- ques habituels. On fournit une base expirimcntale pour cc travail.

Zusammenfassung-FIieBen und Bruch einer dehngeschwindigkeits-empfindlichen tern&en Messingle- gierung wurde untersucht bei 400 bis 8OO’C iiber einen Bereich der Dehngeschwindigkeit von IO-’ bis IO-’ min- ‘. Das Material ist superplastisch mit optimaler Duktilitlt bei 6OO’C. Plastisches FlieDen ist begleitet von einer kontinuierlichen Ausbildung von Hohlrlumen zwischen Kiirnern und Phasen. Unter diesen Bedingungen tritt Bruch ohne meI3bare luDere Einschniirung auf. Die Instabilitlt des plastischen FlieDens wird nit der Entwicklung interner Zweiergabelungen (analog zu diffusen, mehr- fachen externen EinschnIirungen bei nicht-hohlraumbildenden superplastischen Legierungen) und dem ZusammenschIuB von Hohlrlumen durch innere Einschntirungen (analog dem bevorzugten Wachsen einer iiuBeren EinschtGirung) erkllirt. Es u-ird gefolgert, daB fiir eine genaue Analyse des Zusammen- wachsens von Hohlrlumen ein dvnamisches >fodell erforderlich ist, im Gegensatz zu den bisher angew- endeten statischen Modellen. *

INTRODUCTION

Fracture is the Cinderella and Flow the ugly sister. Flow has received much attention from metal scien- tists, to little avail, compared to the real appeal of fracture. Thus it has also been in research on super- plasticity. Mechanisms of deformation have been studied ad nauseum whilst the problem of fracture has

been neglected-only remembered by those with an eye for a pretty face amongst the cinders. Hot fracture is indeed a major problem and the study of fracture in superplastic alloys is relevant both for its own sake and because it provides insight into the general prob- lem of fracture at high temperatures. It is not the first stage of fracture which seems to be the most important here but the last. Accordingly the present work-which is part of an overall project in Waterloo and Havana concerned largely with the final stage of fracture in brittle superplastic alloys of Cu [l-3] and Al [4, S].

* Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada.

Superplastic alloys which do not cavitate fail by intrinsic plastic failure, preceding which can be dis- tinguished two geometrical instabilities of flow [6,7]. The first instability involves the formation of many diffuse necks at a strain somewhat higher than the point of maximum pulling force. It seems that a qua- si-static model may be adequate to explain this be- haviour. The second instability occurs much later on and involves the rapid and preferential growth of one neck accompanied by a marked increase in the flow stress. This behaviour can onIy be explained in terms of a dynamic model-and none thus far exist for the problem of bifurcation in materials, generally, let alone for strain-rate sensitive metals.

In alloys which cavitate during superplastic flow

the problem of failure seems to be even more com- plex. However. the particular aim of the present work was to try to isolate the problem of cavitation and fracture in a superplastic alloy by studying a material which cavitates extensively during superplastic flow

yet exhibits no external necking prior to failure. This avoids the problem of the interaction of external in- stabilities (necks) with internal instabilities (cavities).

308 SAGAT ASD TAPLIN: FRACTURE OF SUPERPLASTIC BRASS

I I , I 0 5 IO 15 20

TIME (hours)

Fig. 1. Mean interphase spacing vs time at 7OO’C. Linear coarsening rate 2.5 pm/ hr.

The research thus aims to provide a basis for further analytical work on the final stages of failure in strain- rate sensitive materials.

EXPERIMENTAL

The material chosen was a 60/40 brass to which had been added 3% Fe. The alloy (58.5% Cu: 38.5% Zn: 3% Fe) was prepared by extrusion to give an q’j phase diameter of about 10 pm throughout which was a distribution of Fe-rich particles of varying size up to 20 pm diameter but mostly 0.5 q dia. Material of three principal grain sizes (12, 31 and 54 pm) was used for the main body of the work. These were obtained by annealing at 7Oo’C for varying periods (Fig. 1). This plot shows that after coarsening to about 30pm grain size in 1 h the alloy exhibits a linear coarsening rate of the order of 2.5 lrn!hr over the range l-20 hr at 700°C.

Mechanical testing was carried out on solid cylin- drical bars of 16 mm2 cross sectional area and 16 mm gauge length at a constant true strain-rate at tempera- tures up to 800°C. A floor model Instron was modi- fied by incorporating a variable speed motor and a linear potentiometer to give a constant true strain-rate accurate to 1.40/, [8]. High temperature tests were per- formed in a three-zone furnace where each zone was individually controlled by a Eurotherm proportional controller giving a hot zone which could be held to

500 600 700 600

TEMPERATURE (“Cl

Fig. 2. Total elongation vs temperature at a constant strain-rate of C = lo-’ min-‘.

4

uJ= 2 I

WC

0 I I I

500 600 700 6

TEMPERATURE (‘Cl)

IO

Fig. 3. Neck-growth parameter measured on fractured samples vs test temperature.

a constant temperature with a tolerance of + 3°C over 150 mm.

RESULTS

Mechanical behaviour

To determine the optimum temperature for super- plastic deformation material with a grain size of 12 pm was tested at various temperatures (500--SOO’C) at a constant true strain-rate of 1- = lo-’ min- I. The results are recorded in Fig. 2 where it is seen that a maximum linear tensile strain is obtained at about 675% However, this plot records the percentage total elongation and this may not give the optimum tem- perature for maximum uniform deformation. Thus a neck growth parameter (difference between transverse true strain in the neck, E, and true uniform strain, cY) has been plotted against temperature in Fig. 3. It is seen that at intermediate temperatures deforma- tion is uniform especially at 600°C where no necking was detectable at all. At 650°C deformation is some- what non-uniform and at 800°C the material separ- ates by intrinsic plastic failure. It is apparent that 6OO’C is the optimum temperature for neck resistant deformation of this alloy at a strain-rate of lo-* min-’ and this temperature was thus chosen for most of the work.

100

0co1 0.010 O.lbO I

STRAIN RATE (min-‘1 Fig. 4. Total elongation vs strain rate at 6OO’C.

00

SAGAT AND TAPLIN: FRACTURE OF SUPERPLASTIC BRASS 309

, 0.001 0.010 0400 I.000

STRAIN RATE (min-‘1

Fig. 5. Neck growth parameter of the fractured samples vs true strain-rate.

The optimum strain-rate was determined for this temperature by a series of tests at various strain-rates. Figures 4 and 5 represent plots of elongation against strain-rate and neck-growth parameter against strain rate, respectively. The deformation is uniform below a strain-rate of i = 2 x lo-’ mine1 and at this point also, the maximum ductility occurs. The true stress- true strain curves obtained at different strain-rates are shown in Fig. 6. The flow stress was computed from the instantaneous force, monitored by the machine and the corresponding cross-section computed assum- ing uniform deformation and constant volume of the sample. The effect of temperature on the true stress/ true strain relationship is shown in Fig. 7. Deforma- tion at room temperature is characterized by a high rate of work hardening and high level of the flow stress. (The maximum tensile strength was 478 MN/m’.) Instability of flow occurred at a true strain of E = 0.29 (approximately at the point of maximum force) which is in good agreement with the limit strain E, determined graphically by the Considkre construc- tion. Deformation at 300°C is close to a steady-state flow condition and up to 6%X, deformation remained uniform so that the u+ curves were computed assum- ing constant volume and uniform flow of the speci- men. At temperatures above 65o”C, deformation

STRESS CbLCULATED FROU FRACTURED WPLE FOR CURVE 8

01 { 02 014

I

Ok

t i

0.0 0.6 I.0 I.2 I.4

TRUE STRAIN

Fig. 6. True stress-true strain curves tested at 600°C. 1-4=2x lo-‘tnin-‘, 2 -C = 10-‘min. 3-i= 5 x IO-*min. 4-L=2 x IO-‘min-‘. j-i= 10-2min, 6-~=5~1O-‘~n-~,7-~=2x 10-3min-L,8-6=

5 x lo-‘min.

/

o-o 0.2 04 0.6 08 [ , :I j TRUE STRAIN

m 6 I-

0, , I I I

00 0.2 o-4 0.6 0.8 I.0 i.2 14

TRUE STRAIN

Fig. 7. True stress-true strain curves tested at a constant true strain-rate of i = lo-* min-’ and different tempera- tures: (a) I-2O’C. 2--3OO’C. (b) l-500°C. 1--600°C.

3-700°C. 4-8OO’C.

becomes increasingly non-uniform and at SOO” the material fails by intrinsic plastic failure. Since these curves were computed also assuming uniform exten- sion, they deviate from real values--particularly in the final stages of deformation.

The effect of grain size (average interphase spacing) over the range 12-54pm is recorded in Fig. 8 for tests at 600°C and lo-’ min- 1 strain-rate. Table 1 records the pertinent data from these plots. All grain sizes deformed uniformly without measurable neck formation.Theinitialflowstressincreasedmarkedlywith increasing grain size confirming the fact that deforma- tion is controlled largely by grain/phase boundary sliding and boundary diffusion. The relationship observed is 0 = cLP where c = 0.43 and a = 0.7. Both parameters c and a depend on strain. The ductility decreased with increasing grain size suggesting that the mean size of cavities is important in controlling ductility and fracture. Strain-softening was apparent during a large part of deformation for the coarser grain-sizes compared with a strain hardening in the finest grain size. It seems evident that the strain har- dening arises mainly from structural coarsening. In the final stages of deformation the flow stress abruptly increases, regardless of the magnitude of the inter- phase spacing. This final increase of the flow stress is also associated with an increase of load carrying

310 SAGAT AND TAPLIN: FRACTURE OF SUPERPLASTIC BRASS

ot 1 I , f I t

50 0.2 0.4 0.6 0.8 I,0 1.2 1.4

TRUE STRAiN

Fig. 8. Effect of grain size on u-s relation, tested at 600°C and a constant true strain-rate of i = 10-2min-‘:

ability during the last period of deformation (Fig. 9) establishing that it must arise from a dynamic effect involving the internal discontinuities since no external necking is observedat this strain-rate. The variation of the neck growth parameter in various conditions is recorded in Table 2.

Strain-rate ~rdening of the alloy at various temperatures is illustrated in Fig. IO. The data were obtained by a change-rate method [7]. The slope of the logarithmic plot of true stress vs true strain, represents the magnitude of the strain-rate sensitivity index tn. It should be noted that the apparently ano- molous effect at 800°C is due to the fact that at 800°C the material is 100% fl phase and coarse grained. The variation of m with temperature, at a strain-rate of &= 2 x 10-2min-‘, is shown in Fig. 11. It is appar- ent that the strain-rate sensitivity index-temperature curve is similar to the elongation-tem~~ture curve shown in Fig. 2 except that the maximum strain-rate sensitivity occurs at 6CWC in accordance with the ductility as measured by uniform elongation rather than at 675°C where the maximum elongation is observed.

The effect of grain-size on variation of m is shown in Fig. 12. Two distinct features of these curves are worthy of comment. Firstly, at intermediate strain- rates when a maximum uniform extension was achieved, the m-value decreases as the grain size is increased. Secondly, the maximum in the m - t rela- tion is advanced to a lower level of strain-rate with increase of grain-size.

The effect of strain on the m - 2 relation at 600°C is shown in Fig. 13. A striking similarity between the effect of grain-size and the effect of strain indirectly suggests that coarsening of the structure takes place

Table 1

31 0.6 250

38 6.9 176

j

0 I I ,

0.0 0.3 d6 0.9 I.2

TRUE STRAIN

5

Fig. 9. Load-elongation curves tested at 600°C and differ- ent strain-rates: li = 10m3 min-‘, 2-G = 12” min,

3i = 1W ’ min.

during deformation of the alloy. In addition it is observed that in the material tested at the optimum strain-rate interval of 2 = tom2 to 2 x 10e2 min-t, the value of m progressively decreases with strain due to the coarsening of the structure.

Some compression tests were also carried out mainly for metallographic purposes because they allowed rapid quenching of the sample following deformation. In order to decrease the friction between the sample and the compression bars powdered graphite was used (powdered glass was unsuccessful). Despite lubrication slight barrelling occurred at reductions over 50%. The true stress/true strain curves in compression were found to be identical with those in tension up to a true strain of about 1.2. Beyond this strain in tension the flow stress increased markedly whereas in compression no marked increase was observed up to a strain of 2.4 (90% reduction). No cavitation was observed in compression whilst other structural changes were identical. Thus the marked increase in tension must be associated with the final stage of cavitation.

041 t , /

oco1 0010 O-100 I

STRAIN RATE (min”) 00

Fig. IO. Logarithmic plot of true stress vs true strain-rate at different temperatures: 1-KWC, 2--SO@‘C, Z-6OO*C,

4-700°C. 5-800°C.

SAGAT AXD TAPLIN: FRACTURE OF SCPERPLASTIC BRASS

Table 2

Structural ch7yrs

Optical metaIlography of material deformed at &WC and a strain-rate of 2 x 10- ’ min- ’ to various strains established three distinct changes:

(1) The initially elongated and banded structure gradually changes to a fully equiaxed homogeneous structure which is maintained throughout the remain- ing deformation. Banding is virtually eliminated by E = 0.4.

(2) There is strain-induced coarsening of the struc- ture. In the head section of the specimen the grain size remains constant whereas in the gauge length the grain size increases from 12 to 45pm at a true strain of 1.5. The rate of coarsening during deformation is 30jrm/hr whereas during simpIe annealing it is 2 ,i~m/hr at &WC.

(3) Deformation is accompanied by interphase and intergranular cavitation throughout the gauge length. Cavities can be detected at a strain of 0.03 and are abundant at a strain of 0.4 (Figs. 14 and 15).

Studies of the surface deformation of material with an average grain size of 54pm deformed in’ argon at 600°C and a strain-rate of 2 x lo-’ rnin-’ using fine fiducial lines revealed the following features:

(1) absence of slip lines; (2) offsets at grain and phase boundaries indicating

both grain and phase boundary sliding; (3) grain rotation: (4) intergranular cavitation.

An extensive study of the dislocation substructures was also made by transmission electron microscopy.

fn I / 0.2; ! I

400 m 600 700 8GO

TEMPERATURE PC f

Fig. 11. Dependence of m on temperature at true strain- rate of P = 2 x lo-’ min-‘.

001 O~OIG 04GG f

STRAIN RATE (min“l

311

10

Fig. I?. Effect of gain size on m-2 relation 3t 6WC. 1-f: = 51 Jml. 3-x = 31 Jim, 3-z = 13 jrm.

This involved rapid quenching of specimens com- pressed varying amounts at 6WC at varying strain- rates in the range 10-‘-10-3 min-‘. Polishing of the multiphase structure presented some difficulties [SJ. A major feature of this work was the virtual absence of dislocations in the material deformed in the opti- mum superplastic range. This does not preclude dislo- cation activity. It was established that results were realistic and that dislocations had not been lost dur- ing quenching or preparation. At higher strain-rates (5 x lo- ’ min- ‘) some dislocation substructures were apparent involving the formation of subgrains.

Quantitative metallography established that the preferential sites for cavity nucleation were the inter- faces of the coarse Fe particles (Table 3). These par- ticles were virtually pure b.c.c, iron thus the mechani- cal properties of the particles themselves cannot be responsible for this as b.c.c. iron is quite soft at 6OO’C compared to the r-fi brass. Thus the weak interface must be responsible.

Table 3 shows that at low strains most of the cavi- ties are associated with coarse Fe particles whereas at higher strains cavity nucleation at z fr hundaries becomes almost equally dominant. The change in number of cavities per unit area is shown in Fig. 16.

Fig. 13. Effect of strain on m-2 retation 3t 6oO’C. t---e = 0.05w.3, 2-G = 0.7-0.8. 3-6 = i.l-1.3.

SAGAT .&?;D T,APLIS: FRACTURE OF SIIPERPL.ASTIC BRASS

@O 05 I.0 I.5 TRUE STRAIN

Fig. 14. Area ?a of cavities vs true strain at &WC and c = 2 x IO-‘min-‘.

This relationship is approximately linear Gth strain. However the area1 fraction of cavities increases more rapidly with strain (Fig. 14) due to their rapid growth. At higher and lower strain-rates the extent of cavi- tation is reduced at 600°C (Table 4).

This seems to resuft from a balance between stress and sliding-both of which are necessary for cavity

Tahte 3. Rcl~tivc number oiczvities at d&rent nwkttion sites

, iitrzb. ’ 1

3.si i lil 1 x/3 /

/ !I.‘)3 ;

boundrri*s j bounifarirs i bmndacits 1 ::;l:“,:Lf: j

s’: i i 28X i 5: 57:: )

0.10 I 2: 9’. : 32:: F 351

o.io i 3’ 2 j ?.5Z i 52; 1

nucleation f3]. .At low strain-rates the stress is low and at high strain-rates the contribution due to sfid- ing is reduced. These results are in accord with a recent model presented [3]. Similarly the extent of cavitation is reduced with increasing temperature (Table 5).

Observations of the progress of cavitation to final fracture can be described in terms of strain-rate and temperature. Since growth of the cavities occurs con- comitantly with large plastic how it is reasonable to assume that most of the growth occurs by plastic deformation rather than vacancy condensation and grain’phase boundary sliding. This procss of growth is generally negiected in creep but it is certainly im- portant there also. The present observations also

(bl Cd) Fig. 15. Optical micrographs showing microsfructures of material deformed. at 60WC and h = 1 x ;S- 1 min-L to various levels of true strain. Tensile axis vertical (75 x 1: la) .s ‘u 0.4. (b) E ii 0.7. (cJ E _ Z-2,

(d) E v 1.4.

SAGAT AZD TAPLW: FRACTURE

TRUE STRAIN

Fig. 16. The number of cavities per unit area as a function of true strain at 600°C and 2 x 10ez min-‘.

demonstrated the dominant influence of the strain- rate sensitivity index in determining the rate of cavity interlinkage and final rupture-hence at 600°C strain- rate has a dominant influence on the rate of interlin- kage largely irrespective of the total cavity volume present. At room temperature the material fails by normal ductile rupture, at 8OO’C the material fails by intrinsic plastic rupture whilst, as noted at %O-650°C an essentially brittle, neck-free fracture mode is observed along with a high tensile ductility.

DISCUSSION

It has been shown elsewhere [73 that the 0-e curves provide necessary information regarding the stability of plastic how in strain-rate sensitive materials. In alloys which do not cavitate the flow has been charac- terized by two instabilities. One or more diffused necks develop on the specimen gauge length and the material separates at a point. In alloys which do cavi- tate during high tem~rature deformation, the forma- tion of intergranular cavities hampers the flow and causes premature failure.

The true stress-true strain relations of the alloy deformed at 6OO@C will be discussed in connection with the geometrical instabilities of plastic Row. A set of b-e curves obtained at different strain-rates is shown in Fig. 6. At lower strains (e c 0.7), the curves generally exhibit strain hardening at low strain-rates and slight strain softening at high strain-rates. Similar results in a microduplex r/b brass were reported by Suery and Baudelet [9]. These authors described CH curves in terms of two processes, i.e. structural coar- ~ning/re~ning and continuous transfo~ation of in- itial fibrous structure (due to extrusion) into an

Table 4. Effect of strain-rate on the extent of cavitation at a strain E = 0.4 after testing at

6OOC

Id’ 360

2 x LO -2

1200

10-L 820

OF SUPERPLASTIC BRASS 313

Table 5. Effect of temperature on the extent of cavitation at a strain-rate of 2 x LO-’ at a strain

E = 0.4

500°C 1350 600% 1200

700% 200

MO% 150

equiaxed structure. Both factors concurrentIy act dur- ing deformation, accordingly inhuence the tevel of the flow stress. The strain hardening observed at low strain rates was described [9] in terms of a prevatence of structural coarsening over the breakdown of the fibrous structure. The strain softening occurring at high strain-rates was explained on the basis of struc- tural refinement (the grain-size was reported to de- crease) and breakdown of the fibrous structure. At intermediate strain-rates both factors may cancel each other out and the stress remains approximately con- stant. This concept seems to be acceptable also for our alloy except for the fact that no structural refine- ment at high strain rates has been observed. Strain induced coarsening occurs in the whole range of strain-rates employed, however its rate decreases with increasing strain-rate due to shorter times of testing,

The 0-c curves obtained in the present alloy and in binary z/p brass [l] exhibit, in the final stages of deformation, an increase of load carrying ability (Fig. 9) accompanied by a rapid increase of the flow stress (Fig. 6). This feature is interesting from a point of view that despite the fact material at this stage of deformation is quite heaviiy cavitated, the Ioad carry- ing ability increases. When interpreting these observa- tions it is necessary to recaII that the ~-6 curves were computed by assuming that the volume of specimen remains constant during extension. Formation of cavities, however, increases the volume of the sample and the calculated true stress is accordingly less. The corrected CM curve cr, for the alloy deformed at 6OO’C

C

I - y=l-ill

I

0.8 I.2 6

TRUE STRAIN

Fig 17. u-FI curve deformed at 6OO’C and g = Z x IO-’ min-’ together with the parameter y showing the onset

of instability f.

311 SAGAT AND TAPLIN: FRACTURE OF SUPERPLASTIC BRASS

and e = 2 x IO-’ min- ’ is shown in Fig. 17 together with the parameter 7.

According to the Hart criterion [6] the onset of plastic instability occurs when

‘J=l-m*

(where 7 = l/cr(d+ie), m* = Ua(du/&) and G, E and 1 are true stress, true strain and true strain-rate re- spectively), i.e. at true strain of en = 0.38 in Fig. 1.5, while the Considire strain l c is equal to approxi- mately 0.03. Experimentally, however, no formation of neck has been observed at eu and moreover, defor- mation remains uniform until failure. On the other hand it is seen that the predicted onset of instability coincides approximately with the measurable onset of cavitation. It is therefore suggested that the onset of plastic instability in the alloy is associated more with formation of “internal” non-uniformities (cavi- ties) rather than with “external” necks. To achieve a picture of the cavitation behaviour during deforma- tion a metallographic examination of deformed material has been carried out. A series of micrographs (Fig. 15) shows the formation, growth and interlin- kage of cavities in the final stages of deformation. As the deformation proceeds the number of cavities increases and they continuously grow. The high value of the strain-rate sensitivity index minimizes the rate of growth of internal necks between individual cavi- ties in a manner analogous to the way the rate of external necks is reduced [7]. At this stage of defor- mation no preferential growth of the internal necks is apparent and deformation is quasi-uniform. When some of the necks are strained to such a degree that no more superplastic deformation in the neck region is possible, the deformation in such a region may be retarded, since a higher flow stress is needed for non- superplastic flow. This process could be repeated suc- cessively a number of times accompanied by an in- crease of the flow stress. Finally the deformation can- not be transferred to another region and instability II occurs in such a way that one set of necks begin to grow preferentially followed by successive separ- ation of individual necks allowing cavity interlinkage in a direction normal to the applied stress. During this process deformation is localized and the local strain-rate increases significantly increasing the level of the flow stress and load until fracture occurs. This final process is clearly demonstrated in Figure 1% and d and is controlled by dynamic or “over- shoot” effects as in neck growth of non-cavitating superplastic alloys [7]. Figure 15(c) records condi- tions at a true strain of l = 1.2, where the void in the central region of the micrograph was formed as a consequence of the separation of several necks (some of them still being visible). This seems to occur simultaneously in several places of the cross-section (in .Fig. 15(c) another void is formed on the left of the central void). The deformation proceeds by separ- ation of additional necks allowing interlinkage of these large voids (Fig. 15d), until the sample is separ-

ated completely. When interpreting the plastic flow of the alloy in terms of parameter y. it is seen that after instability I, 7 continuously decreases below the critical value and eventually reaches a negative value. In the final stages of deformation behaviour, 7 abruptly increases and remains above the critical value until failure. Since y is computed from the slope of CM curve, the increase of ?-value is caused by the increase of the flow stress due to the dynamicallycon- trolled, localized flow in the final stage of deforma- tion. To obtain a true y-value the 0-e curve needs to be corrected for the increase of local strain-rate which in the case where internal non-uniformities are formed, would be extremely complicated.

The point at which instability II occurs is deter- mined by the distribution and size of the cavities. Since no necking occurs, cavity growth is uniform throughout the gauge length and few large cavities form, as observed. The instability criterion adopted for rupture is that of Brown and Embury [lo] who suggest that a critical condition is achieved when the cavity length is equal to the spacing. In view of the high density of cavitation and uniformity of size, void linkage would then be very rapid once initiated. A simpler model involves a criterion for failure whereby the cavity length equals a small multiple of the grain size, say 1OOpm. This would also fit the experimental observations.

CONCLUSIONS

1. The plastic flow of the ternary brass at 600°C is characterized by strain-induced coarsening of the structure and formation of intergranular cavities. Deformation is controlled by grain/phase boundary sliding together with boundary diffusion.

2. The process of fracture may be analyzed in an analogous way to flow instability in non-cavitating superplastic alloys. Thus the onset of cavitation (an internal, diffuse bifurcation) is analogous to the onset of external, diffuse necks (instability I). The onset of cavity linkage of rapid internal necking between cavi- ties is analogous to the preferential rapid growth of a single external neck (instability II).

3. The onset of plastic instability I (marked cavi- tation) occurs when y = 1 - m* with nucleation at the Considere strain l , = 0.03. Nucleation sites are the Fe particles and a//? boundaries.

4. Instability II is associated with the separation of internal necks followed by rapid interlinkage of cavities in a direction normal to the applied stress. This instability is not reflected in y-values since no correction for localized increase of strain-rate has been made in this work. It can be approximately explained in terms of a Brown-Embury type mode1 modified for strain-rate sensitive materials. An accu- rate analysis would require a dynamic model for in- ternal necking.

5. A characteristic feature of the fracture of the alloy is the increase of load-carrying ability in the

SAGAT AND TAPLIN: FRACTURE OF SUPERPLASTIC BRASS 316

final stage of deformation despite the fact that the material is very heavily cavitated at this stage of deformation. The final rupture is macroscopically planar without necking. Clearly final rupture must thus be controlIed by dynamic effects. This is also the case for necking in non-cavitating strain-rate sen- sitive materials. An experimental basis for such an analysis is provided.

Ac~~w~edge~~ts-This work has been supported by the National Research Council of Canada.

REFERENCES

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3. R. G. Fleck, C. J. Beevers and D. M. R. Taplin, .tfet. Sci. 9, 49 (1975): J. .Mat. Sci. 9, 241 (1974).

4. M. W. A. Bright. D. M. R. Taplin and H. W. Kerr, JAS‘ME, J. Eng. Xfur. 12, 1 (1974).

5. Tomas Delgado. Maria-Christina Mellian and D. M. R. Taplin, Unpublished Research. Universidad de la Habana, Cuba, 1975. Superplasticity and cavitation in an industrial aluminium alloy.

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