The creep fracture of copper and magnesium

THE N.

CREEP G.

FRACTURE

NE~DHA~,t

OF

COPPER

J. E. WHEATLEYT

and

AND G.

W.

MAGNESIUM* GREE~OOD~

The creep life of copper and magnesium has been measured over a range of stress levels and the cavity population and resultant density changes determined at intervals during creep with the aim of assessing the build up of damage that eventually leads to fracture. For both metals, it is shown that the density change is initally approximately proportional to &to3 where E is the oreep strain after time t under a stress u. This relationship holds throughout the most of the areep life for copper but, for magnesium in the later stages of creep, the density change tends to become proportional to (st~~)‘.~. For both metals the number of cavities is roughly proportional to the creep strain and the creep life varies as (I- &. Crack propagation between cavities appears difficult and the observations show that a high fraction of the grain boundary area transverse to the applied stress is cavitated before fracture takes place. The similarity in behaviour of copper and magnesium implies that detailed crystal structure is relatively unimportant in cavitation failure, although the cavities are frequently of a crystallographic form. LA RUPTURE AU FLUAGE DU CUIVRE ET DU ~A~~SIUM On a mesure la dur6e de vie en fluage du ouivre et du magnesium pour diverse8 valeurs de la. contrainte, et on & determine le nombre de cavites et les ehangements correspondants de densite pendant le fluage, dans le but de preciser Bventuellement la formation du dommage qui conduit 8, la rupture. On a montre pour les deux m&aux que la variation initial0 de densite eat approximativement proport#ionnelleh sto3, oh F est la deformation au fluage apres un temps t sons une contrainte (r. Cette relation rest%valable pendant presque toute la d&e de vie du cuivre, mais, dans le c&sdu magnesium, le changement de densite tend h devenir proportionnel it (&to3)l.5 dans les derniers stades du fluage. Pour les deux metaux, le nombre de cavites est grossierement proportionnel it la. deformation de fluege et la duree de vie varie comme o+. Ls propagation des fissures entre les cavil& semble difficile et on observe des cavites sur une grande pertie de la surface des joints de grains perpendiculaires B la contrainte appliquee avant que lrt rupture ne se produise. La similitude des comportements du cuivre et du magnesium implique clue la, structure cristalline preoise est relativement peu importante dans le phenomee de rupture par cavitation, bien que les eavites aient suvent une forme cristsllogmphique KRIECHBRUCH VON KUPFER UND MAGNESIA Die Lebansd&uer von Kupfer und Magnesium im Kriechve~uch wurde in einem Sp~nn~gs~reich gemessen. Au~erdem wurden die Hohl~~diehte und die resultierenden Dieh~~nderungen w&rend des Kriechversuchs in bestimmten Intervallen mit dem Ziel bestimmt, den Aufbau der sum Brueh fiibrenden Gitterst&ungen zu rmtarsuchen. Fur beide Metalle ist die Diohte&nderung anfangs etwa proportional zu .sta3, wobei E die Kriechab. gleitung nach der Zeit t und bai der Spannung (r ist Diese Besiehnng gilt fur Kupfer fast fiir das ganze Kriechleben; fur Magnesium wird in spilteren Kriechstadien die Diohtellnderung proportional zu (.st~~)‘*~. In beiden Metallen ist die Zahl der Hohlriiume etwa proportional zur Kriechdehnung und die Lebensdauer der Kriechproben variiert mit u-4. RiDausbreitung zwischen Hohlriiumen ist nur schwer moglich und die Beobachtungen zeigen, da9 ein grol3erAnteil der senkreoht zur anliegenden Spannung existierenden Korngrenzenbereiche Hohlriiume enthiilt bevor der Bruoh erfolgt. Die Ahnlichkeit des Verheltens von Kupfer und Magnesium zeigt, da3 drts Hohlraumbruchverhalten von der Kristallstruktur relativ wenig abhiingt, obwohl die Hohlriiume h&fig kristallographische Form besitzen. INTRODUCTION

extensively(rWg) but the aim of the present study was to make a quantitative &~es~ent of creep damage before the stage when sudden fracture occurred. &vita-tion in copper is also well known(l**lr) and a comparison is made between the failure modes of copper and magnesium in creep.

The sudden failure of many metals and alloys during creep is well known and has been much studied.fl-*) At low stresses, fracture oocurs by the linking of cavities or cracks along grain boundaries that are approximately perpendicular to the applied stress. It is now established that cavities are nucleated early in the creep life and that nucleation of new cavities generahy continues during creep,(5) particularly at temperatures and stresses where substantial grsin boundary sliding occurs but where recrystallization does not take place.(s) Fine grain size material is generally more resistant to c&vitation failure.(s) Cavitation in magnesium has been investigated

EXPERIMENTAL

* Received July 19, 1974. t Department of Metallurgy, University of Sheffield, St. George’s Square, Sheffield Sl 3JD, U.K. ACTA METALLURGICA,

VOL.

23, JANUARY

1975

METHODS

The composition of the magnesium and copper used in the present work are shown in Tables 1 and 2. The magnesium was supplied in the form of rod 19 mm dia. To obtain a constant and uniform grain size that was stable during subsequent creep testing, the specimens were iirst strained 2.8 per cent at room temperature and annealed for 20 mm, at 620°C in argon. The meen grain size, as determined by linear intercept, was 340 pm. The gauge length of the creep specimens was 63.5 mm and their dia 12.7 mm. 23

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TABLE 1. Chemical analysis of the magnesium used showed that the following elements were present in ppm by weight Al 40

Ca 20

Mn 200

Fe 100

Cu 100

Ni 10

Pb 300

Si 30

Sn 30

Zn 300

TABLE 2. The following elements were present in ppm by weight in OFHC Copper Bi 11

Cd 1

Pb 10

P 3

Hg 1

S 18

Zn 1

To obtain a constant and uniform size in the copper specimens, the bar as received was 19 mm dia and was swaged at room temperature down to 10.2 mm, prior to annealing at 800% in vacuum for 30 min. The mean grain size was then 230 pm. The creep specimens had a gauge length of 26.4 mm and a dia of 6.35 mm. All creep tests were made in argon with the temperature along the specimen gauge lengths constant to within 2°C. Density changes at intervals during creep were determined by a hydrostatic displacement method. Longitudinal sections were taken from specimens after specific creep strains. Both metals were first polished on emery papers down to “600” grade. After this stage the polishing sequence for magnesium involved “Silvo” metal polish, *pm diamond paste on a selvet cloth, fast and slow cutting grade alumina and finally, polishing on a y-alumina imp~~ated cloth. Subsequently, a light etch in 2 per cent nital was given. For copper the polishing sequence was 1 pm followed by *pm diamond paste on a selvet cloth and finally a “skid” polisho3) was carried

------I I I

I” _ P i”

Id_-

0,s-i

‘9

0

0

lo-‘-

:i

!I

0

d

I w,MNm‘2

Fra. 1. The variation of minimum oreep rate d with stress rr for magnesium of grain size 340 ,mn at 300” (cixdes) and for copper of grain size 230 pm at 600°C (squares).

t,*s

tL

w , MNm‘*

FIG. 2. The variation of creep life t, with stress d for magnesium at 300°C (circles) and for copper at 500°C (squitres).

out on a selvet cloth using a paste of calcined magnesium and a solution of 9 g/l of ammonium persulphate in distilled water. This provided %Islight etching yet still retained the true shape of the cavity section. EXPERIMENTAL RESULTS THEIR INTERPRETATION

AND

The form of the creep curves for both metals were of the usual type, displaying primary, secondary and tertiary stages. (I41 The variation of minimum creep rate d with stress a is shown in Fig. 1 where the relationship is of the form B cc ~5, In the specimens where creep was continued up to the point of sudden fracture, it was found that the creep life t, cc CT-~,as illustrated in Fig. 2. This implies that the elongation to fracture is not strongly sensitive to the applied stress but that creep ductility for both met,ats under these conditions decreases with a decrease in stress level. This aspect is in marked contrast to fracture in many metals at low temperatures(i5) where brittleness increases with stress and with strain rate. The behaviour at high temperatures strongly suggests that time dependent processes partly govern fracture such that creep damage builds up with time and the influence of strain is of lesser importance. From the measurement of density change -Ap/p at intervals during the creep life, it is shown in Fig. 3 that, for copper t,hroughout its creep life and for magnesilim in the early stages of creep, approximately, - Af~p cc et$ where E is the creep strain after time t. In the later stages of creep,

NEEDHAM

el al.:

CREEP

FRACTURE

OF

COPPER

AND

MAGNESIUM

25

are consistent with the equation -Ap/p cc &F2, as in Fig. 4. Measurements of density changes simply provide an assessment of the total volume of all the cavities present without discrimination of their size, shape or number. Metallographic studies both by optical and by scanning electron microscopy, however, reveal that, in the present conditions, cavities in magnesium and in copper are of a predominantly faceted form, as in Fig. 5, and it is found, approximately, that the number of cavities increases linearly with strain. Such observations suggest that cavities have characteristics quite different from those of cracks where a crack length and effective tip root radius can be defined. It remains unclear, however, Fro. 3. The variation of the fractional density change -Ap/p with the parameter &r3 for magnesium at 300°C and copper at 500°C at the following stress levels. Magnesium Copper 0 20.7 MN/m* 0 4.83 MN/m* A 5.84 MN/ma 2 ;;:; :q:: n 6.90 MN/m* + 7.59 MN/m* V 8.25 MN/m*

the relationship for magnesium tends to the form -Aplp cc (~ta~)l*~. Equations of this general form but with some variation in the stress dependence of the density change, now appear to apply for a number of metals.(la) It seems likely that dependence on stress may be partly related to the stress dependence of creep rate and may be strongly sensitive to composition. Although nickel shows a relationship of the form -ApIp cc Eta’, when results on X-O.1 wt. % Pd alloys are considered, the data(l*) Fig. 5. A facetted cavity in copper observed by scanning electron microscopy ( X 5000).

c

trr*.*. s(Nni*

I*‘*

Pm. 4. The relation between the fractional densit{ change and the parameter staa.* for a nickel -0.1 wt. /0 palladium alloy plotted from the dataof Bowring, Davies and Wilshire’* at the following stress levels. 0 100 MN/m2 a 154 MN&a [? 178 MN/ma 0 215 MN/m2

to what extent deformation processes, other than vacancy diffusion may contribute to their growth. When there is a high stress dependence of creep rate it appears reasonable to suppose that there will be the greatest opportunity for deformation by dislocations to aid cavity growth. In the present work, although B CCc5 for magnesium and copper in the ranges investigated, the complete suppression of cavity formation by the superimposition of hydrostatic pressure,@‘*ll) indicates that vacancy diffusion and condensation have a predominating influence on cavity growth. Thus, it seems that such vacancy processes may govern the growth of cavities whilst the overall creep process is determined principally by dislocation glide and climb. This situation may be reconciled by the consideration that distances between cavities are much smaller

26

ACTA

METALLURGICA,

FIG. 6. Cavities nearly linked together on a grain boundary in copper approximately perpendicular to the tensile stress ( x 500).

than between grain bounda~es and cavity growth only makes a small cont~bution to creep strain. A striking feature is the retention of cavity shape almost up to the point when fracture occurs (Fig. 7). This implies that cracking of the gram boundary area between cavities is a difficult process and that separation at grain boundaries must depend on cavities growing sufficiently large that they coalesce. It was further noted that cavities in copper rarely had their largest dimension greater than about 20 pm and that the linear growth rate was most rapid when cavities were small and slowed considerably when cavities increased in size. This form of growth is generally in accord with growth by vacancy condensation where the rate of increase of cavity volume dvldt is given@O) approximately by the relation dvldt N rrD,woSl/kT, where _D, is the grain boundary self diffusion coefficient, w the effective grain boundary width, 52 the atomic volume, ?c Boltzmann’s constant, cr the creep stress and T the absolute ~mperature. Under the present con~tions~ for copper at 5OO*C, the product Dsw - 3 x IO-21 ms/sec, &T = 1.06 x lo-20 J St.- 1O-29m3 and when G = 2 x IO7N/m2, we ’ calculate dvldt - 1.8 X 1O-22m3/sec or about 16(pm)3 per day. This rate is about adequate to account for the growth rates observed. If it is accepted that the cavity volume is described by an equation of the above form, then we may write v cc ot, and referring to the density change during creep -APIP cc .zta3, it follows that the number of cavities of n must take the form n oc &e. By consideration of the ~lationship between creep life tf and stress, of the form tf CC11~4,and making the appro~mation that the parameters influencing n

VOL.

23,

1975

and v hold to the point of fracture, then an assessment can be made of the variation of the amount of cavitated grain boundary when fracture takes place at different stress levels. When there are n, cavities per unit area at the instant of fracture and the average volume of each cavity is v~, the fraction of the grain boundary area occupied by cavities is nf#3. Using the relationships v, oc otf and n, oc o2~f where tf and ef are respectively the creep life time and strain, then r&‘” cx ((r’$)(df)2/3 cc 08f%ft~‘3. Now the creep strain is given by E cc dt and the time to fracture obeyed the relation tf cc 110~. Substituting for ef and tf, we obtain the relation ?&3 CCo. This suggests that the fraction of grain boundary area occupied by cavities at fracture tends to be greater at the higher stress levels. It implies that a higher stress does not have the effect of causing cracking between the oavities and this is further supported by the greater creep ductility at higher stresses within the range studied in the present work. By substituting instead for tf and (T, we obtain alternatively that n#’ cc cf, supporting the experimental observations that Edwas approximately proportional to (T. Since et changes only by a factor of about two over the range studied in the present experiments, it follows that the area fraction of gram boundaries occupied by cavities at fracture similarly varies over only a smaI1 range. The development of cavitation was found to be similar throughout the entire cross sections of the specimens studied, unlike some other observations that have been made. Thus, it was considered that the free surfaces of the specimens had a negligible effect on behaviour. CONCLUSIONS

The experiments showed a strikingly similar behaviour of ma,gnesium and copper in their cavitation behaviour, indicating that the crystallography of the metal has negli~ble influence on the phenomena although cavities tended to be faceted and preserved their form almost up to the point when fracture occurred. Cavities grew rapidly in the early stages but their growth rate in terms of linear dimensions progressively decreased in a way compatible with an approximately constant rate of volume increase. Cracking between cavities appeared difficult and cracks were rarely found even when cavities had almost coalesced. The creep ductility increased approximately as the applied stress over the range studied and the fractional area of grain boundaries occupied by cavities at fracture tended to increase in a similar manner.

NEEDHAM

CREEP

et al.:

FRACTURE

The creep life t, was found to vary as o-4 and this relationship nucleation

may

be interpreted

and growth consistent

variation

of the density

by -Ap/p a &to3. The experimental suggest

methods

in terms

with the determined

change

results

of cavity

during

creep given

and their interpretation

of quantifying

the

build

up

creep damage that are similar for both magnesium copper

and

about

creep

thus

make

life from

possible

some

observations

at

of and

predictions an

earlier

stage. ACKNOWLEDGEMENTS

We

are

grateful

much

useful

JEW)

also

to many

discussion wish

to

and

thank

colleagues

for

two

of our

of us (NGN

and

the

Science

Council for the receipt of Research

Research

Studentships.

REFERENCES 1. J. N. GREENWOOD, D. R. MILLER and J. W. SUITER, Acta Met. 2, 250 (1954). 2. N. J. GRANT, Fracture, Proc. Conf. on Atomic Mechanisms

OF

COPPER

AND

MAGNESIUM

27

of Fracture, p. 562. Wiley, New York (1959). 3. R. V. DAY, J. Iron Steel Inst. 208, 279 (1965). 4. G. W. GREENWOOD,Proc. International Conf. on Interfaces, Melbourne, p. 223, Butterworths, London (1969). 5. A. GITTINS, Met. Sci. J. 1, 214 (1967). 6. D. M. R. TAPLIN and V. N. WHITTAKER, J. Illat. Metals 92, 426 (1963, 1964). 7. P. E. BROOKES, N. KIRBY and W. T. BURKE, J. Inst. Metals 88, 500 (1959, 1960). 8. A. E. B. PRESLAND and R. I. HUTCHINSON, J. Inaf. Metals 92, 264 (1963). 9. R. T. RATCLIFFE and G. W. GREENWOOD, Phil. Mug. 12, 59 (1965). 10. R. C. BOETTNER and W. D. ROBERTSON, Trans. Met. Sot. A.I.M.E. 221, 613 (1961). 11. D. HULL and D. E. RIMMER, Phil. Mag. 4, 673 (1959). 12. R. T. RATCLIFFE, Brit. J. Appl. Phya. 10, 1193 (1965). 13. D. M. R. TAPLIN and L. J. BARKER, Acta Met. 14, 1527 (1966). 14. 0. D. SHERBY and P. M. BURKE, Prog. Mat. Sci. 13, 326 (1967). of Fracture Mechanics. 15. J. F. KNOTT, Fundamentals Butterworths, London (1973). 16. D. A. WOODFORD, Met. Sci. J. 3, 50 (1969). 17. D. A. WOODFORD, Met. Sci. J. 3,234 (1969). 18. P. BOWRING, P. W. DAVIES andB. WILSHIRE, Met. Sci. J. 2, 168 (1968). N. G. NEEDHAM and G. W. GREENWOOD (to be published). M. V. SPEIGHT and J. E. HARRIS, Met. Sci. J. 1, 83 (1967).