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The effects of prestrain on the creep and fracture behavior of polycrystalline copper
Materials Science and Engineering, 43 (1980) 271 - 280 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
271
The Effects of Prestrain on the Creep and Fracture Behaviour of Polycrystalline Copper
J. D. PARKER* and B. WILSHIRE Department of Metallurgy and Materials Technology, University College, Singleton Park, Swansea (Gt. Britain) (Received August 29, 1979,in revised form November 16, 1979)
SUMMARY Constant-stress creep tests were carried out using polycrystalline copper samples which had been prestrained by different amounts either at room temperature or at the creep temperature o f 686 K. A comparison o f the behaviour o f oxygen-free copper with that o f samples containing oxygen showed that prestraining invariably resulted in a reduction in creep ductility whereas the creep rate and rupture life could be increased or decreased depending on the e x t e n t to which the incidence of grain boundary cavities was affected. The changes in creep and fracture properties associated with different prestrain treatments are interpreted in terms o f the varying contributions o f the grain interiors and the grain boundary zones to the overall creep strain.
1. INTRODUCTION A number of investigations have been undertaken to examine the influence of preexisting dislocation substructures on the creep and fracture properties of metals and alloys. These studies have been concerned with the effects that the degree of room temperature prestraining [ 1 - 3 ] , the prestraining temperature [4] and the prestraining m e t h o d [5, 6] have on these properties. However, rationalization of the results obtained has been complicated by the variations in the prestraining procedures used. For example, when a sample is deformed in tension at room temperature *Present address: Marchwood Engineering Laboratories, Central Electricity Generating Board, Matchwood, Southampton, Hampshire, Gt. Britain.
and recovery is allowed to occur during heating to the creep temperature, the subsequent creep and fracture behaviour differs appreciably from that reported when the creep properties are determined immediately after a tensile prestrain at the creep temperature [4]. In the present programme the data recorded using these two methods of prestraining are shown to be interpretable in terms of the deformation characteristics observed after stress reductions during creep. In addition the prestraining techniques employed demonstrate the relevance of strain localization in the grain boundary regions during high temperature creep and fracture of polycrystalline copper.
2. THE EFFECTS OF PRESTRAIN ON PRIMARY AND SECONDARY CREEP The present programme was carried out using oxygen-free high conductivity copper. Test pieces with a gauge length of 25.4 m m and a diameter of 4.46 mm were annealed in vacuo at 1073 K for 10.8 ks to give a uniform grain size of 0.2 mm. High precision creep tests were performed in tension at 686(. +1) K using constant-stress equipment [ 7]. Changes in specimen length could be monitored to 10 nm using a pair of differential capacitance transducers linked to a digital print-out system which allowed strain versus time readings to be obtained at preset time intervals of 1 s or more. Over the entire stress range studied at 686 K the annealed polycrystalline copper exhibited normal primary and secondary creep behaviour, i.e. after the instantaneous specimen extension on loading, the creep rate decayed t h r o u g h o u t the primary stage until a
272
2 5 z
~
/ o/•
7-5
7 no
05
12-5 2
4
6
8 TIME
10
[2
14
16
~
,C
Ao2~ ~
/o/ °/ o/
5 °~
e~
°/°"
/
,/
8
i
iI
3
0.6
3
s4
ks
Fig. 1. Creep curves o b t a i n e d at 55 M N m - 2 a n d 6 8 6 K for o x y g e n - f r e e c o p p e r samples w h i c h h a d b e e n p r e s t r a i n e d b y various a m o u n t s at r o o m t e m perature.
1
_
~
m~"
l_._ |_o~._R-,~L~e--F__A~A 3
6 Timeks
9
F i g . 2. C r e e p c u r v e s o b t a i n e d
constant rate was attained during the secondary stage. The present work established that not only the form of the primary creep curve but also the secondary creep rates eventually obtained could be changed considerably by varying the prestrain treatment. The principal features of the prestraining methods used and the behaviour observed can be summarized as follows. (1) At room temperature the samples were prestrained 5, 7.5, 10 and 12.5% at 10 -3 s-1 using an Instron tensile machine. In all cases the prestrained specimens were heated to the test temperature of 686 K in 1.8 ks and were stabilized under zero load at this temperature for a further 7.2 ks. Creep testing was then carried out in the normal way using applied stresses in the range 20 - 70 MN m -2. Figure 1 illustrates the primary and secondary creep curves obtained at 55 MN m -2 for a series of room temperature prestrains. The general shapes of the primary creep curves recorded with this m e t h o d of prestraining were similar to those for the annealed material. The behaviour observed is directly in agreement with the conclusion (1) that, with prestrain levels sufficient to eliminate the initial specimen extension on loading under the creep conditions studied, the primary creep strains and the secondary creep rates decrease with increasing amounts of room temperature prestrain. (2) Prestraining at the creep temperature of 686 K was carried out using the constantstress creep equipment. Samples were subjected to predetermined stresses which gave instantaneous strains on loading of 5, 7.5, 10 and 15%. As soon as this rapid strain had been completed, the load was reduced to continue the test to failure at a new steady stress value.
C
12 at 55 MN
m -2
and
6 8 6 K for a n n e a l e d c o p p e r (curve A), for a sample p r e s t r a i n e d b y 7.5% at t h e creep t e m p e r a t u r e (curve B) a n d for a s p e c i m e n p r e s t r a i n e d b y 7.5% at r o o m t e m p e r a t u r e (curve C). A detailed version o f t h e early stages for curves B a n d C are s h o w n in t h e inset.
The normal primary stages obtained for annealed copper and for samples prestrained at room temperature were eliminated by the high temperature prestraining m e t h o d used (Fig. 2). When the level of prestrain introduced at the creep temperature exceeded the initial specimen extension expected for the annealed material at the creep stress under study, an incubation period of zero creep rate was observed before creep began. After the incubation period the creep rate gradually accelerated until a new secondary rate was attained (Fig. 2, curve B). The duration of the incubation period and the time to reach the secondary creep stage increased and the value of the secondary creep rate decreased as larger prestrains were introduced at the creep temperature.
3. R A T E - C O N T R O L L I N G CREEP
PROCESSES DURING
Although the form of the creep curves and the magnitude of the creep rates recorded could be varied considerably, the processes controlling the deformation rates did n o t appear to be altered by the range of prestraining conditions studied. Thus for example an activation energy of about 115 kJ mol-1 for creep was obtained from temperature cycling experiments undertaken during the secondary creep stage both for annealed copper and for the prestrained samples. These
273
INITIAL APPLIE D STRESS,o',:73 B MN/m 2
K
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STEADY-STATE CREEP R A T E ' E s = 2 ( : ~ I ( ~ S s ' I / ' v / STAGE I!
Z
j=" if STRESS REDUCTION, A 0.=18.45 MN/m2
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~" ...-,~
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i~INCU~I,T ION .~'" • / PERIOD -" STAGE ! .
I
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~ - 2oo s-4
Fig. 3. T h e strain v s . time b e h a v i o u r o b s e r v e d a f t e r a stress r e d u c t i o n o f 18.45 MN m - 2 during s e c o n d a r y c r e e p o f a n n e a l e d c o p p e r at 73.8 MN m - 2 s h o w i n g t h e a c c e l e r a t i o n in creep rate o b t a i n e d a f t e r t h e i n c u b a t i o n period.
values are consistent with the observation that the activation energy for creep becomes equal to t h a t (about 200 kJ mo1-1) for selfdiffusion only at temperatures in excess of about 850 K; this suggests that, for both the annealed and the prestrained conditions, creep is controlled by dislocation-enhanced diffusion [8]. The effects of different prestrain treatments on creep behaviour can be readily interpreted by comparing the shapes of the creep curves obtained for the prestrained samples (Fig. 2) with the strain v e r s u s time readings recorded after small stress reductions during secondary creep of annealed copper. Figure 3 illustrates the behaviour found when the applied stress o was decreased by a small a m o u n t Ao = 0.030 - 0.3a and the test was continued under the reduced stress OR = o -- Ao. Immediately after a small stress reduction an incubation period of zero creep rate was always observed before creep recommenced at the lower stress level. After the incubation period the creep rate gradually accelerated (during the period designated stage I) until an apparently steady rate was achieved (designated stage II). However, the stage II creep rate gH was invariably found to be lower than the secondary creep rate f o u n d for an uninterrupted test performed entirely at the reduced stress level; e . g . gi~ = 2.2 × 10 -6 s-1 after the stress reduction from 73.8 to 53.35 MN m -2 compared with a secondary creep rate of 5 × 10 -6 s-1 for a conventional creep test at 53.35 MN m -2
with the annealed copper (Fig. 3). The occurrence of incubation periods of zero creep rate after even very small stress reductions (5o ~ 0.030) suggests that the dislocation substructure developed during secondary creep must change by recovery before creep can recommence at the reduced stress level, i.e. for both the annealed and the prestrained materials creep is recovery con~olled. During secondary creep of both the annealed and the prestrained copper a poorly developed subgrain boundary structure exists with a three-dimensional network of dislocations evident within the subcells. Dislocation substructures of this type have been interpreted in terms of a recovery model for creep [9] in which diffusion-controlled growth and rearrangement of the network occurs until link lengths between nodes are generated which are sufficiently long to act as dislocation sources, allowing slip to occur. With this model for creep, incubation periods of zero creep rate are expected since even the longest link lengths present immediately after the stress reductions are too short to act as sources. Recovery and rearrangement processes occurring during the incubation period eventually develop link lengths capable of acting as sources which allow creep to recommence. Continued recovery then causes the gradual increase in creep rate during stage I. However, even when a true creep strain of 0.05 had occurred after a stress reduction from 73.8 to 53.35 MN m -2, the dislocation substructure was indistinguishable from that observed prior to the stress decrease. The low stage II creep rates then result from the fact t h a t the sources generated have to operate in the presence of a dislocation density well above the equilibrium v ~ u e for the reduced stress level. The creep behaviour of samples prestrained either at room temperature or at the creep temperature (Fig. 2) can be interpreted in terms of the source generation model [9]. (1) The creep curves obtained when tests were carried out immediately after rapid prestraining at the creep temperature (Fig. 2, curve B) were very similar to the strain v e r s u s time characteristics recorded after small stress reductions during secondary creep (Fig. 3). When high dislocation densities are introduced by a rapid prestrain at the creep temperature, a period of zero creep rate is there-
274 fore observed until recovery enables creep t o commence. Under the conditions examined, the recovery processes failed to develop the equilibrium substructure for the creep stress studied so that the secondary creep rate eventually established decreased with increasing prestrain levels. (2) When prestraining was under t a ke n at r o o m temperature, recovery occurred during heating to the creep temperature. With this form of prestrain, incubation periods of zero creep rate are n o t expected since sources have already been developed at the start of the creep test. Even so, the high dislocation densities arising from the r o o m temperature prestraining were n o t fully recovered so that the creep rates observed are again lower than those f o r annealed material (Fig. 2, curve C).
4. INHOMOGENEITY OF CREEP STRAIN Studies o f the mechanisms of creep which utilize stress reduction techniques m a y lead to the impression that d e f o r m a t i o n occurs in an essentially h o mo ge ne ous m a nne r in polycrystalline solids. However, the relevance of strain inhomogeneity during creep was illustrated by examining the distortions evident after a known creep strain of an initially regular surface grid consisting of an array o f squares with edge lengths of a b o u t 8 pm (Fig. 4). The grid was pr oduc e d on a flat surface ( ab out 2 mm wide along the entire length o f the specimens) by vacuum deposition of carbon through a fine nickel mesh [ 1 0 ] . The d ef o r mati on pattern near one of the grain boundaries evident after creep of annealed co p p er under argon at 686 K is shown in Fig. 4. Clearly the sliding displacem e n t is n o t uniform, even along an individual facet, and the m a x i m u m displacements were generally recorded well away f r om the triplep o i n t junctions [ 1 0 ] . T o determine the effects o f prestraining on the sliding behaviour, the surface d e f o r m a t i o n patterns were studied for annealed samples and for specimens which had been prestrained 7.5% at the creep temperature. In all cases the test pieces were cooled u n d er load when the creep rate during the tertiary stage had accelerated to a value o f three times the secondary rate. The average sliding offsets were then measured
Fig. 4. An optical micrograph illustrating the grid appearance after creep of annealed copper at 55 MN m-2 and 686 K. The stress axis is vertical. The sliding displacements are clearly not uniform along the grain boundary facet denoted AB. (Magnification, 280x .) TABLE 1 Grain boundary displacement measurements obtained when the creep rate during the tertiary stage had accelerated to three times the secondary creep rate Material condition
S tress
(MN m-2)
Average 95% longitudinal confidence displacement limit
(Urn} Annealed
69 55 41.4
0.84 1.26 0.84
-+0.13 -+0.32 ± 0.14
Prestrained 7.5% at creep ternperature
69 55 41.4
0.90 1.32 0.81
+-0.16 -+0.18 -+0.18
from the grain b o u n d a r y displacements occurring for selected grid lines (1 in 10) chosen to be parallel to and perpendicular to the tensile axis. The average longitudinal displacement values w are presented in Table 1. The fact that displacements are blocked at triple points suggests that sliding c a n n o t provide an i n d e p e n d e n t c o m p o n e n t of the macroscopic strain since sliding c a n n o t be considered as the relative m o v e m e n t of rigid grains [10, 11]. Determinations of the average sliding offsets c a n n o t therefore be used to derive a meaningful estimate of the c o n t r i b u t i o n of sliding to the overall creep strain.
275 Studies of the grid patterns and the sliding displacements led to two main conclusions. (1) At a given creep stress the sliding displacements were similar (Table 1}, even though the creep rates and the total creep strains for the annealed material were markedly greater than for the prestrained samples (Fig. 2). It can therefore be concluded that, under the present conditions, prestraining reduces the extent to which the grains deform w i t h o u t significantly affecting the sliding behaviour. (2) Consideration of the detailed appearance of the grid lines after creep confirms that grains do n o t move relative to each other as rigid units. Bends were frequently f o u n d near the boundaries, giving a sliding offset w i t h o u t a discernible displacement of the overall line [10]. Under the present conditions, sliding appears to be related to the deformation of a zone adjacent to the grain boundary so that creep deformation can be considered to be made up of (a) grain boundary sliding and associated deformation in regions adjacent to the boundaries and (b) overall grain deformation [1]. With annealed materials, both the grain and the grain boundary zones contribute to the total creep strain. In contrast, the introduction of high dislocation densities by prestraining reduces the contribution made by the grains whereas the zone deformation is relatively unaffected because of rapid recovery in regions adjacent to the boundaries.
5. TERTIARY CREEP PROCESSES The creep curves presented in Fig. 2 show that, after the secondary creep stage for both the annealed and the prestrained samples, the creep rate gradually accelerates during the tertiary stage, leading to fracture. Under the present testing conditions, failure of the annealed material occurred by the nucleation, growth and eventual coalescence of grain boundary cavities to form intergranular cracks. The appearance of the fracture surface for a test carried out at 55 MN m -2 and 686 K is shown in Fig. 5. This type of cavity development was f o u n d n o t only over the entire stress range studied for the annealed material but also for all levels and types of prestrain examined. The fracture mode
Fig. 5. A scanning electron micrograph showing grain boundary cavities observed for annealed copper tested to fracture at 55 MN m-2 and 686 K. (Magnification, 1800x .) therefore appears to be unaffected by the prestraining conditions investigated. In order to study the development of cavities during creep, samples of annealed copper were cooled under load after varying fractions of the creep life at 55 MN m -2. Metallographic examination of polished longitudinal sections showed that isolated cavities were discernible early during the secondary creep stage. The number and size of cavities increased with increasing creep strain until fracture occurred. An estimate of the fractional void volume A V / V at any instant during a creep test was then produced by determining the fractional area A A / A of cavities and cracks using a Cambridge quantitative television microscope. The results obtained (Fig. 6) can be described by AA/A
= ~V/V
~ e - - e*
where e* represents the creep strain at which the void area v e r s u s strain relationship becomes linear. This behaviour is similar to that previously f o u n d to represent the fractional change in density as a function of the creep strain for copper [12] and for nickel [13], i.e. the void volume increases linearly with creep strain t h r o u g h o u t secondary and tertiary creep. In the absence of microstructural instabilities such as recrystallization or extensive grain growth, tertiary creep begins when the
276 i
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0
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2 3 4 5 CREEP SI"RAIN ( ° / o )
6
Fig. 6. T h e s t r a i n d e p e n d e n c e o f t h e f r a c t i o n a l a r e a o f cavities and cracks observed on polished longitudinal sections of annealed copper tested at 55 MN m -2 a n d 6 8 6 K.
number and size of voids are sufficient to affect the creep rate. There is, however, no generally accepted mechanism whereby the voids cause an acceleration in deformation rate during the tertiary stage. In order to understand the processes causing tertiary creep, it can be assumed that the secondary creep rate represents the deformation rate unaffected by cavitation. The acceleration in creep rate then reflects the enhancement of the deformation processes due to the presence of the increasing number and size of voids and may be quantified in terms of the strain above that expected from an extrapolation of the secondary stage. The tertiary creep strain etert Can be calculated from the total creep strain: etert = e - - ( e 0 + e p +
gst)
where e 0 and ep are the initial strain on loading and the total primary creep strain respectively. Then, since the duration of tertiary creep depends on the material and the testing conditions, the time dependence of etert was considered by reference to the "fractional t i m e " ftert spent in the tertiary stage which is defined as t -- t T ftert - - t F -- t T
is the time to the onset of tertiary creep and t F is the time to fracture. The variation of etert with fte~t is illustrated in Fig. 7 for annealed copper and for the sample prestrained 7.5% at the creep temperature. These results demonstrate that, at the same where tw
ftcrt Fig. 7. T h e v a r i a t i o n in the t e r t i a r y creep strain ete~ as a f u n c t i o n o f t h e f r a c t i o n a l t i m e ftert s p e n t in t h e t e r t i a r y s t a g e f o r t e s t s c a r r i e d o u t a t 55 M N m - 2 f o r annealed copper and for samples which had been prestrained by 7.5% at the creep temperature of 686 K.
applied stress level, the shape of the tertiary creep curve for polycrystalline copper was unaffected by the prestrain treatments studied. The present observations lead to a new interpretation for the occurrence of tertiary creep. (1) The cavity distribution at fracture for the sample deformed 7.5% at the creep temperature prior to loading appeared to be identical with that observed for the annealed copper tested at the same creep stress (Fig. 5). However, the prestrain markedly reduces the overall creep strain (Fig. 2) by restricting grain deformation without a corresponding effect on the grain boundary zone behaviour. The observation that the tertiary behaviour is comparable for the annealed and for the prestrained samples (Fig. 7) therefore suggests that the acceleration in creep rate is a consequence of cavitation which enhances the deformation rate in the grain boundary zones. (2) The linear dependence of the cavity volume on the creep strain (Fig. 6) indicates that the cavity growth processes are dependent on the deformation processes occurring during creep [13]. It may then be concluded that, as the number and size of cavities increase during the tertiary stage, the creep rate accelerates as a result of stress concentrations developed locally around the voids. In turn, since the deformation processes control the rate of void growth, the enhanced deformation rates in the grain boundary zones lead to a corresponding increase in void growth rates. In this way a linear dependence
277
of the void volume on the creep strain is expected t h r o u g h o u t the tertiary stage.
6. C A V I T A T I O N P R O C E S S E S D U R I N G C R E E P
When failure occurs by cavitation, the creep life may be determined either by the rate of cavity development or by the rate of growth of intergranular cracks [14]. The observation that well-formed cavities were evident over the entire fracture surface suggests that rupture is controlled by cavity formation rather than by the propagation of a crack under the direct action of the maxim u m principal stress. Furthermore, density measurements have established that cavities are present early in the creep life of polycrystalline copper [ 1 2 ] , suggesting that cavity nucleation is relatively easy. The creep rupture life therefore appears to be determined primarily by the rate of cavity growth. The conclusion that void growth is controlled by the deformation behaviour is supported by the relationship found between the rupture life and the creep rate which is illustrated in Fig. 8 for the samples prestrained at room temperature. As observed for a wide range of metals and alloys, when polycrystalline copper is tested in the annealed condition t~ = E/~s
with E ~ 0.04. When the prestrain level is
L
2
IO TIME
IOO TO FRACTURE
ks
Fig. 8. The relationship between the secondary creep rate and the rupture life for annealed copper and for samples prestrained for various a m o u n t s at r o o m temperature: o, annealed; v, 5% prestrain; A, 7.5% prestrain; m, 10% prestrain; 4, 12.5% prestrain.
sufficient to cause a reduction in creep rate, the results obtained for the prestrained samples do n o t lie on the same straight line as that found for the non-prestrained material, i.e. the value of E decreases with increasing prestrain until a limiting value is reached. Even so, for any specified type and a m o u n t of prestrain the rupture life is inversely proportional to the secondary creep rate. Since the time to fracture appears to be governed primarily by the rate of void growth, the present observations suggest that the rate of cavity development is proportional to the creep rate, i.e. for both the annealed and the prestrained materials the cavity growth is controlled by the deformation processes occurring during creep. A decrease in the magnitude of E (= gs X tF) with larger prestrain levels is expected since the creep rate can be decreased by over an order of magnitude whereas the rupture life was increased by less than a factor of 3 under the same conditions (Fig. 2). Prestrain reduces the creep rate within the grains without an equivalent effect on the grain boundary zone behaviour. Since cavity growth is dependent on the deformation rate, the fact that the rupture life is relatively unaffected by the prestrain indicates that deformation p~'ocesses occurring in the grain boundary zones determine the rate of cavity development. The present work offers a means of distinguishing between two models for cavity development, both of which lead to void growth rates directly controlled by the deformation processes. (1) It is generally agreed that grain boundary sliding is a necessary prerequisite for cavity nucleation. The relationship between the rupture life and the creep rate has therefore been interpreted on the basis that, if grain boundary sliding can cause nucleation of cavities, then continued sliding should result in void growth [13]. This model is consistent with the fact that, since grain deformation rates are reduced without a corresponding effect on the overall sliding behaviour, prestrain exerts a greater effect on the creep rate than on fracture. However, with the sliding growth of cavities an irregular cavity shape was expected rather than the regular lenticular shape observed (Fig. 5). Furthermore, the sliding displacements are
278
non-uniform (Fig. 4) whereas the cavities were found to be relatively uniform in size over entire grain boundary facets. Void growth controlled exclusively by the rate of grain boundary sliding therefore appears to be improbable. (2) An alternative model for cavity growth [15] involves the concept that dislocations arriving at the boundary from the grain interior can move along the boundary by a combination of glide and climb. On reaching the boundary, a dislocation of Burgers vector b can be regarded as being resolved into two components, b, normal to the boundary and bp parallel to the boundary. The c o m p o n e n t b, is made to climb along the boundary by the direct stress resolved normal to the boundary and the c o m p o n e n t bp glides along the boundary under the action of the shear stress resolved parallel to the boundary. In this way the cavities nucleated by grain boundary sliding may grow both by absorption of vacancies generated by the non-conservative movement of the lattice dislocation along the boundary and by continued sliding which results from movement of the screw component. With this model the cavity development depends on a combination of slip within the lattice, grain boundary sliding and absorption of vacancies generated by movement of the dislocation in the boundary plane. All these processes are related to the rate of arrival of dislocations from the lattice so that a relationship between the creep rate and the rupture life is expected. However, for this model to account for the present results, the dislocations moving along the boundaries causing cavity growth must have originated in the grain boundary zones rather than in the grain interior. In this way, since the zone deformation is relatively unaffected compared with that of the grains, the prestrain can exert a greater effect on the creep rate than on the time to fracture.
rupture life and a considerable reduction in the total creep strain to failure. However, prestraining can result in entirely different behaviour, e.g. with Nimonic 80A (trademark of Henry Wiggin and Co. Ltd.), although the creep ductility is again reduced, the creep rate is increased and the rupture life is decreased with increasing amounts of room temperature prestrain. These effects were attributed to the major increase in the incidence of grain boundary cavities found on prestraining this multiphase alloy [2]. All the prestrain effects described in Sections 2 - 6 were obtained using oxygenfree copper which had been annealed initially at 1073 K under a vacuum of 0.01 N m -2. In a further series of experiments the samples were tested after being annealed under a vacuum of 1 kN m-2. This difference in initial heat treatment procedure did not significantly reduce the time to fracture of the specimens tested in the non-prestrained state. However, for samples prestrained 7.5% at room temperature, the creep life of the material annealed under a poor vacuum was markedly shorter than that for specimens heat treated using high vacuum procedures (Fig. 9). Moreover, metallographic examination of these prestrained samples confirmed that the use of the poorer vacuum led to a considerable increase in the incidence of grain boundary cavities. In order to identify the causes of this difference in cavitation behaviour, a detailed microstructural study was undertaken for samples annealed using these two different r
3 B cr
n w W rr t.)
7. P R E S T R A I N E F F E C T S ON F R A C T U R E BEHAVIOUR
The results obtained with oxygen-free copper are directly in agreement with those reported for polycrystalline nickel [1, 4], i.e. prestrain levels giving an increase in creep resistance also lead to a slight improvement in
i
2
4
5 TIME ks
i
8
i
I0
Fig. 9. Creep curves r e c o r d e d at 55 MN m - 2 for samples p r e s t r a i n e d by 7.5% at r o o m t e m p e r a t u r e : curve A, b e h a v i o u r o f a sample p r e s t r a i n e d a f t e r an initial h e a t t r e a t m e n t u n d e r a v a c u u m o f 0.01 N m - 2 ; curve B, results o b t a i n e d for a s p e c i m e n a n n e a l e d u n d e r a v a c u u m o f 1 kN m -2.
279
Fig. 10. G r a i n b o u n d a r y voids o b s e r v e d a f t e r h o l d i n g a s a m p l e , w h i c h h a d b e e n p r e s t r a i n e d b y 7.5% at r o o m t e m p e r a t u r e , for 7.2 ks u n d e r zero load a t t h e c r e e p t e m p e r a t u r e o f 6 8 6 K. T h e s p e c i m e n h a d b e e n initially h e a t t r e a t e d u n d e r a v a c u u m o f 1 kN m - 2 p r i o r to prestraining. T h e foil was e x a m i n e d using a n A E I EM7 high voltage e l e c t r o n m i c r o s c o p e (1 MV).
vacuum levels. Each group of specimens was prestrained 7.5% at r o o m temperature, heated to'the creep temperature of 686 K and held for 7.2 ks under zero load before cooling, i.e. the samples were subjected to the standard procedures used at the c o m m e n c e m e n t of the creep tests b u t were n o t loaded at the creep temperature. The samples were subsequently thinned and the resulting foils were examined using an AEI EM7 high voltage electron microscope (1 MV). With the specimens annealed under a poor vacuum, extensive void formation was observed at grain boundaries (Fig. 10) whereas no voids were discernible with test pieces annealed under the high vacuum. (It should be noted that samples annealed using these high and low vacuum procedures were also heated to the creep temperature and held for 7.2 ks b u t without being prestrained. In this case neither sample exhibited the extensive void formation shown in Fig. 10.) Clearly with samples that contain oxygen a high incidence of voids was introduced by the prestraining procedures whereas this effect was n o t f o u n d with the oxygen-free copper. This observation is directly in agreement with that of Lagarde and Biscondi [16] who showed that, with copper bicrystals, lenticular shaped cavities were formed during creep only when some oxygen was present in the material.
By considering the influence of prestrain on cavity nucleation, a consistent interpretation can be provided for the fact that the creep ductility is invariably reduced whereas prestraining can lead to increases or decreases in both the creep rate and the rupture life. (1) It is generally agreed that cavities are nucleated as a consequence of plastic strain and all models for nucleation require a concentrated normal traction at a local region by means of shear relaxation against a suitable obstacle, with the plastic strain arising as a result of transgranular slip and/or grain boundary sliding [14]. Thus for example grain boundary sliding may result in stress concentrations sufficient to nucleate cavities at ledges formed where slip bands intersect the boundaries, at cusps produced where subgrain boundaries meet the grain boundaries or at particles and inclusions. The observation that the cavity incidence is increased markedly by prestraining only with copper annealed under a poor vacuum indicates that cavities form preferentially at grain boundary particles such as inclusions, carbides etc. [17]. In this way an increased cavity incidence accompanying prestrain treatments is expected for Nimonic 80A [ 2] and for copper that contains oxygen b~t n o t for pure nickel [1] and oxygen-free copper. (2) With oxygen-free copper, prestraining reduces the grain deformation rates w i t h o u t a corresponding effect on the zone behaviour and hence on the void growth rates. Since the cavity incidence is also unaffected, substantially lower creep rates and ductilities can be obtained with no significant change in the creep life. However, with copper that contains oxygen the rupture life is impaired as a result of the extensive cavitation caused by prestraining. In this case the creep rate may be increased or decreased depending on whether the reduced contribution of the grain interiors can be offset by the enhanced deformation rates expected in the grain boundary zones when a high incidence of cavities is developed at the start of the test. The ductility is therefore invariably reduced, whereas the creep rate and rupture life may be increased depending on the extent to which the cavity incidence is affected by the prestrain treatment.
280 8. CONCLUSIONS
(1) The rate-controlling process during the creep of polycrystalline copper was unaffected by prestraining either at room temperature or at the test temperature of 686 K. The behaviour was consistent with a recovery model for creep based on diffusion-controlled growth of the three-dimensional dislocation network to produce link lengths between nodes which were long enough to act as dislocation sources, allowing slip to occur. (2) Studies of the surface deformation patterns for prestrained and non-prestrained samples illustrate the need to distinguish between the deformation occurring within the grains and within the grain boundary zones during creep. This zone deformation comprises grain boundary sliding and associated deformation in regions of the grains adjacent to the boundaries. (3) In the absence of recrystallization or grain growth, tertiary creep commences when cavities developing on grain boundaries reach a size sufficient to affect the creep rate. The acceleration in creep rate during the tertiary stage is shown to be a result of the cavities enhancing the deformation rates in the grain boundary zones. (4) Cavities, nucleated primarily at inclusions present at grain boundaries, grow at rates determined by the rate of deformation in the grain boundary zones. Lattice dislocations originating within the zones arrive at the grain boundaries and cause void growth by moving along the boundary plane by a combination of glide and climb. (5) With oxygen-free copper the high dislocation density introduced by prestraining reduces the creep rate of the grain interiors whereas the zone deformation is relatively unaffected because of the rapid rates of recovery near grain boundaries. Since the cavity incidence is not changed significantly by the prestrain treatments, this leads to reductions in the creep rate and the ductility but only a slight improvement in rupture life. (6) With copper that contains oxygen, prestraining leads to a higher cavity incidence as
a result of void formation at the inclusions present. The enhanced deformation rates of the boundary zones due to this cavity development can offset the reduction in the creep rate of the grain interiors. In this way, although the ductility is again reduced, prestraining can result in increased creep rates and markedly reduced rupture lives.
ACKNOWLEDGMENT
One of the authors (J.D.P.) is indebted to the Science Research Council for the provision of a research studentship.
REFERENCES 1 P. W. Davies, J. D. Richards and B. Wilshire, J. Inst. Met., 90 (1961 - 1962) 431. 2 B. F. Dyson and M. J. Rogers, Met. Sci., 8 (1974} 261. 3 B. J. Cane and G. W. Greenwood, Met. Sci., 9 (1975) 55. 4 P. W. Davies, J. D. Richards and B. Wilshire, Metallurgia, 68 (1963) 259. 5 O. D. Sherby, A. Goldberg and J. E. Dorn, Trans. A m . Soc. Met., 46 (1954) 681. 6 W. C. Harrigan, C. R. Barrett and W. D. Nix, MetalL Trans., 4 (1973) 1615. 7 J. D. Parker and B. Wilshire, Met. Sci., 12 (1978) 453. 8 C. R. Barrett and O. D. Sherby, Trans. Metall. Soc. AIME, 230 (1964) 1322. 9 P. W. Davies and B. Wilshire, Scr. Metall., 5 (1971) 475. 10 J. D. Parker and B. Wilshire, Mater. Sc£ Eng., 29 (1977) 219. 11 U. F. Kocks, Metall. Trans., 1 (1970) 1121. 12 R. C. Boettner and W. D. Robertson, Trans. Metall. Soc. AIME, 221 (1961) 613. 13 P. Bowring, P. W. Davies and B. Wilshire, Met. Sc£ J., 2 (1968) 168. 14 D. McLean, B. F. Dyson and D. M. R. Taplin, Proc. 4th Int. Conf. on Fracture, University o f Waterloo, Ontario, 1977, Vol. 1, Pergamon, Oxford, 1978, p. 325. 15 Y. Ishida and D. McLean, Met. Sci. J., 1 (1967) 171. 16 P. Lagarde and M. Biscondi, J. Phys. Radium, 36 (1975) 297. 17 B. F. Dyson, M. S. Loveday and M. J. Rogers, Proc. R. Soc. London, Set. A, 349 (1976) 245.
271
The Effects of Prestrain on the Creep and Fracture Behaviour of Polycrystalline Copper
J. D. PARKER* and B. WILSHIRE Department of Metallurgy and Materials Technology, University College, Singleton Park, Swansea (Gt. Britain) (Received August 29, 1979,in revised form November 16, 1979)
SUMMARY Constant-stress creep tests were carried out using polycrystalline copper samples which had been prestrained by different amounts either at room temperature or at the creep temperature o f 686 K. A comparison o f the behaviour o f oxygen-free copper with that o f samples containing oxygen showed that prestraining invariably resulted in a reduction in creep ductility whereas the creep rate and rupture life could be increased or decreased depending on the e x t e n t to which the incidence of grain boundary cavities was affected. The changes in creep and fracture properties associated with different prestrain treatments are interpreted in terms o f the varying contributions o f the grain interiors and the grain boundary zones to the overall creep strain.
1. INTRODUCTION A number of investigations have been undertaken to examine the influence of preexisting dislocation substructures on the creep and fracture properties of metals and alloys. These studies have been concerned with the effects that the degree of room temperature prestraining [ 1 - 3 ] , the prestraining temperature [4] and the prestraining m e t h o d [5, 6] have on these properties. However, rationalization of the results obtained has been complicated by the variations in the prestraining procedures used. For example, when a sample is deformed in tension at room temperature *Present address: Marchwood Engineering Laboratories, Central Electricity Generating Board, Matchwood, Southampton, Hampshire, Gt. Britain.
and recovery is allowed to occur during heating to the creep temperature, the subsequent creep and fracture behaviour differs appreciably from that reported when the creep properties are determined immediately after a tensile prestrain at the creep temperature [4]. In the present programme the data recorded using these two methods of prestraining are shown to be interpretable in terms of the deformation characteristics observed after stress reductions during creep. In addition the prestraining techniques employed demonstrate the relevance of strain localization in the grain boundary regions during high temperature creep and fracture of polycrystalline copper.
2. THE EFFECTS OF PRESTRAIN ON PRIMARY AND SECONDARY CREEP The present programme was carried out using oxygen-free high conductivity copper. Test pieces with a gauge length of 25.4 m m and a diameter of 4.46 mm were annealed in vacuo at 1073 K for 10.8 ks to give a uniform grain size of 0.2 mm. High precision creep tests were performed in tension at 686(. +1) K using constant-stress equipment [ 7]. Changes in specimen length could be monitored to 10 nm using a pair of differential capacitance transducers linked to a digital print-out system which allowed strain versus time readings to be obtained at preset time intervals of 1 s or more. Over the entire stress range studied at 686 K the annealed polycrystalline copper exhibited normal primary and secondary creep behaviour, i.e. after the instantaneous specimen extension on loading, the creep rate decayed t h r o u g h o u t the primary stage until a
272
2 5 z
~
/ o/•
7-5
7 no
05
12-5 2
4
6
8 TIME
10
[2
14
16
~
,C
Ao2~ ~
/o/ °/ o/
5 °~
e~
°/°"
/
,/
8
i
iI
3
0.6
3
s4
ks
Fig. 1. Creep curves o b t a i n e d at 55 M N m - 2 a n d 6 8 6 K for o x y g e n - f r e e c o p p e r samples w h i c h h a d b e e n p r e s t r a i n e d b y various a m o u n t s at r o o m t e m perature.
1
_
~
m~"
l_._ |_o~._R-,~L~e--F__A~A 3
6 Timeks
9
F i g . 2. C r e e p c u r v e s o b t a i n e d
constant rate was attained during the secondary stage. The present work established that not only the form of the primary creep curve but also the secondary creep rates eventually obtained could be changed considerably by varying the prestrain treatment. The principal features of the prestraining methods used and the behaviour observed can be summarized as follows. (1) At room temperature the samples were prestrained 5, 7.5, 10 and 12.5% at 10 -3 s-1 using an Instron tensile machine. In all cases the prestrained specimens were heated to the test temperature of 686 K in 1.8 ks and were stabilized under zero load at this temperature for a further 7.2 ks. Creep testing was then carried out in the normal way using applied stresses in the range 20 - 70 MN m -2. Figure 1 illustrates the primary and secondary creep curves obtained at 55 MN m -2 for a series of room temperature prestrains. The general shapes of the primary creep curves recorded with this m e t h o d of prestraining were similar to those for the annealed material. The behaviour observed is directly in agreement with the conclusion (1) that, with prestrain levels sufficient to eliminate the initial specimen extension on loading under the creep conditions studied, the primary creep strains and the secondary creep rates decrease with increasing amounts of room temperature prestrain. (2) Prestraining at the creep temperature of 686 K was carried out using the constantstress creep equipment. Samples were subjected to predetermined stresses which gave instantaneous strains on loading of 5, 7.5, 10 and 15%. As soon as this rapid strain had been completed, the load was reduced to continue the test to failure at a new steady stress value.
C
12 at 55 MN
m -2
and
6 8 6 K for a n n e a l e d c o p p e r (curve A), for a sample p r e s t r a i n e d b y 7.5% at t h e creep t e m p e r a t u r e (curve B) a n d for a s p e c i m e n p r e s t r a i n e d b y 7.5% at r o o m t e m p e r a t u r e (curve C). A detailed version o f t h e early stages for curves B a n d C are s h o w n in t h e inset.
The normal primary stages obtained for annealed copper and for samples prestrained at room temperature were eliminated by the high temperature prestraining m e t h o d used (Fig. 2). When the level of prestrain introduced at the creep temperature exceeded the initial specimen extension expected for the annealed material at the creep stress under study, an incubation period of zero creep rate was observed before creep began. After the incubation period the creep rate gradually accelerated until a new secondary rate was attained (Fig. 2, curve B). The duration of the incubation period and the time to reach the secondary creep stage increased and the value of the secondary creep rate decreased as larger prestrains were introduced at the creep temperature.
3. R A T E - C O N T R O L L I N G CREEP
PROCESSES DURING
Although the form of the creep curves and the magnitude of the creep rates recorded could be varied considerably, the processes controlling the deformation rates did n o t appear to be altered by the range of prestraining conditions studied. Thus for example an activation energy of about 115 kJ mol-1 for creep was obtained from temperature cycling experiments undertaken during the secondary creep stage both for annealed copper and for the prestrained samples. These
273
INITIAL APPLIE D STRESS,o',:73 B MN/m 2
K
"
STEADY-STATE CREEP R A T E ' E s = 2 ( : ~ I ( ~ S s ' I / ' v / STAGE I!
Z
j=" if STRESS REDUCTION, A 0.=18.45 MN/m2
~I! : 2 2 xlO'b S-I
~" ...-,~
ILl)
i~INCU~I,T ION .~'" • / PERIOD -" STAGE ! .
I
~_~_~ .." "'~kVERAGE~l : IxIO~S" TIME
~ - 2oo s-4
Fig. 3. T h e strain v s . time b e h a v i o u r o b s e r v e d a f t e r a stress r e d u c t i o n o f 18.45 MN m - 2 during s e c o n d a r y c r e e p o f a n n e a l e d c o p p e r at 73.8 MN m - 2 s h o w i n g t h e a c c e l e r a t i o n in creep rate o b t a i n e d a f t e r t h e i n c u b a t i o n period.
values are consistent with the observation that the activation energy for creep becomes equal to t h a t (about 200 kJ mo1-1) for selfdiffusion only at temperatures in excess of about 850 K; this suggests that, for both the annealed and the prestrained conditions, creep is controlled by dislocation-enhanced diffusion [8]. The effects of different prestrain treatments on creep behaviour can be readily interpreted by comparing the shapes of the creep curves obtained for the prestrained samples (Fig. 2) with the strain v e r s u s time readings recorded after small stress reductions during secondary creep of annealed copper. Figure 3 illustrates the behaviour found when the applied stress o was decreased by a small a m o u n t Ao = 0.030 - 0.3a and the test was continued under the reduced stress OR = o -- Ao. Immediately after a small stress reduction an incubation period of zero creep rate was always observed before creep recommenced at the lower stress level. After the incubation period the creep rate gradually accelerated (during the period designated stage I) until an apparently steady rate was achieved (designated stage II). However, the stage II creep rate gH was invariably found to be lower than the secondary creep rate f o u n d for an uninterrupted test performed entirely at the reduced stress level; e . g . gi~ = 2.2 × 10 -6 s-1 after the stress reduction from 73.8 to 53.35 MN m -2 compared with a secondary creep rate of 5 × 10 -6 s-1 for a conventional creep test at 53.35 MN m -2
with the annealed copper (Fig. 3). The occurrence of incubation periods of zero creep rate after even very small stress reductions (5o ~ 0.030) suggests that the dislocation substructure developed during secondary creep must change by recovery before creep can recommence at the reduced stress level, i.e. for both the annealed and the prestrained materials creep is recovery con~olled. During secondary creep of both the annealed and the prestrained copper a poorly developed subgrain boundary structure exists with a three-dimensional network of dislocations evident within the subcells. Dislocation substructures of this type have been interpreted in terms of a recovery model for creep [9] in which diffusion-controlled growth and rearrangement of the network occurs until link lengths between nodes are generated which are sufficiently long to act as dislocation sources, allowing slip to occur. With this model for creep, incubation periods of zero creep rate are expected since even the longest link lengths present immediately after the stress reductions are too short to act as sources. Recovery and rearrangement processes occurring during the incubation period eventually develop link lengths capable of acting as sources which allow creep to recommence. Continued recovery then causes the gradual increase in creep rate during stage I. However, even when a true creep strain of 0.05 had occurred after a stress reduction from 73.8 to 53.35 MN m -2, the dislocation substructure was indistinguishable from that observed prior to the stress decrease. The low stage II creep rates then result from the fact t h a t the sources generated have to operate in the presence of a dislocation density well above the equilibrium v ~ u e for the reduced stress level. The creep behaviour of samples prestrained either at room temperature or at the creep temperature (Fig. 2) can be interpreted in terms of the source generation model [9]. (1) The creep curves obtained when tests were carried out immediately after rapid prestraining at the creep temperature (Fig. 2, curve B) were very similar to the strain v e r s u s time characteristics recorded after small stress reductions during secondary creep (Fig. 3). When high dislocation densities are introduced by a rapid prestrain at the creep temperature, a period of zero creep rate is there-
274 fore observed until recovery enables creep t o commence. Under the conditions examined, the recovery processes failed to develop the equilibrium substructure for the creep stress studied so that the secondary creep rate eventually established decreased with increasing prestrain levels. (2) When prestraining was under t a ke n at r o o m temperature, recovery occurred during heating to the creep temperature. With this form of prestrain, incubation periods of zero creep rate are n o t expected since sources have already been developed at the start of the creep test. Even so, the high dislocation densities arising from the r o o m temperature prestraining were n o t fully recovered so that the creep rates observed are again lower than those f o r annealed material (Fig. 2, curve C).
4. INHOMOGENEITY OF CREEP STRAIN Studies o f the mechanisms of creep which utilize stress reduction techniques m a y lead to the impression that d e f o r m a t i o n occurs in an essentially h o mo ge ne ous m a nne r in polycrystalline solids. However, the relevance of strain inhomogeneity during creep was illustrated by examining the distortions evident after a known creep strain of an initially regular surface grid consisting of an array o f squares with edge lengths of a b o u t 8 pm (Fig. 4). The grid was pr oduc e d on a flat surface ( ab out 2 mm wide along the entire length o f the specimens) by vacuum deposition of carbon through a fine nickel mesh [ 1 0 ] . The d ef o r mati on pattern near one of the grain boundaries evident after creep of annealed co p p er under argon at 686 K is shown in Fig. 4. Clearly the sliding displacem e n t is n o t uniform, even along an individual facet, and the m a x i m u m displacements were generally recorded well away f r om the triplep o i n t junctions [ 1 0 ] . T o determine the effects o f prestraining on the sliding behaviour, the surface d e f o r m a t i o n patterns were studied for annealed samples and for specimens which had been prestrained 7.5% at the creep temperature. In all cases the test pieces were cooled u n d er load when the creep rate during the tertiary stage had accelerated to a value o f three times the secondary rate. The average sliding offsets were then measured
Fig. 4. An optical micrograph illustrating the grid appearance after creep of annealed copper at 55 MN m-2 and 686 K. The stress axis is vertical. The sliding displacements are clearly not uniform along the grain boundary facet denoted AB. (Magnification, 280x .) TABLE 1 Grain boundary displacement measurements obtained when the creep rate during the tertiary stage had accelerated to three times the secondary creep rate Material condition
S tress
(MN m-2)
Average 95% longitudinal confidence displacement limit
(Urn} Annealed
69 55 41.4
0.84 1.26 0.84
-+0.13 -+0.32 ± 0.14
Prestrained 7.5% at creep ternperature
69 55 41.4
0.90 1.32 0.81
+-0.16 -+0.18 -+0.18
from the grain b o u n d a r y displacements occurring for selected grid lines (1 in 10) chosen to be parallel to and perpendicular to the tensile axis. The average longitudinal displacement values w are presented in Table 1. The fact that displacements are blocked at triple points suggests that sliding c a n n o t provide an i n d e p e n d e n t c o m p o n e n t of the macroscopic strain since sliding c a n n o t be considered as the relative m o v e m e n t of rigid grains [10, 11]. Determinations of the average sliding offsets c a n n o t therefore be used to derive a meaningful estimate of the c o n t r i b u t i o n of sliding to the overall creep strain.
275 Studies of the grid patterns and the sliding displacements led to two main conclusions. (1) At a given creep stress the sliding displacements were similar (Table 1}, even though the creep rates and the total creep strains for the annealed material were markedly greater than for the prestrained samples (Fig. 2). It can therefore be concluded that, under the present conditions, prestraining reduces the extent to which the grains deform w i t h o u t significantly affecting the sliding behaviour. (2) Consideration of the detailed appearance of the grid lines after creep confirms that grains do n o t move relative to each other as rigid units. Bends were frequently f o u n d near the boundaries, giving a sliding offset w i t h o u t a discernible displacement of the overall line [10]. Under the present conditions, sliding appears to be related to the deformation of a zone adjacent to the grain boundary so that creep deformation can be considered to be made up of (a) grain boundary sliding and associated deformation in regions adjacent to the boundaries and (b) overall grain deformation [1]. With annealed materials, both the grain and the grain boundary zones contribute to the total creep strain. In contrast, the introduction of high dislocation densities by prestraining reduces the contribution made by the grains whereas the zone deformation is relatively unaffected because of rapid recovery in regions adjacent to the boundaries.
5. TERTIARY CREEP PROCESSES The creep curves presented in Fig. 2 show that, after the secondary creep stage for both the annealed and the prestrained samples, the creep rate gradually accelerates during the tertiary stage, leading to fracture. Under the present testing conditions, failure of the annealed material occurred by the nucleation, growth and eventual coalescence of grain boundary cavities to form intergranular cracks. The appearance of the fracture surface for a test carried out at 55 MN m -2 and 686 K is shown in Fig. 5. This type of cavity development was f o u n d n o t only over the entire stress range studied for the annealed material but also for all levels and types of prestrain examined. The fracture mode
Fig. 5. A scanning electron micrograph showing grain boundary cavities observed for annealed copper tested to fracture at 55 MN m-2 and 686 K. (Magnification, 1800x .) therefore appears to be unaffected by the prestraining conditions investigated. In order to study the development of cavities during creep, samples of annealed copper were cooled under load after varying fractions of the creep life at 55 MN m -2. Metallographic examination of polished longitudinal sections showed that isolated cavities were discernible early during the secondary creep stage. The number and size of cavities increased with increasing creep strain until fracture occurred. An estimate of the fractional void volume A V / V at any instant during a creep test was then produced by determining the fractional area A A / A of cavities and cracks using a Cambridge quantitative television microscope. The results obtained (Fig. 6) can be described by AA/A
= ~V/V
~ e - - e*
where e* represents the creep strain at which the void area v e r s u s strain relationship becomes linear. This behaviour is similar to that previously f o u n d to represent the fractional change in density as a function of the creep strain for copper [12] and for nickel [13], i.e. the void volume increases linearly with creep strain t h r o u g h o u t secondary and tertiary creep. In the absence of microstructural instabilities such as recrystallization or extensive grain growth, tertiary creep begins when the
276 i
i
f
i
i
12 I'O 7 0 -- 0 8
O004
x
0002
0'4 0.2 0
i
0
0"2
04
(30
08
L
f
0
0
I
2 3 4 5 CREEP SI"RAIN ( ° / o )
6
Fig. 6. T h e s t r a i n d e p e n d e n c e o f t h e f r a c t i o n a l a r e a o f cavities and cracks observed on polished longitudinal sections of annealed copper tested at 55 MN m -2 a n d 6 8 6 K.
number and size of voids are sufficient to affect the creep rate. There is, however, no generally accepted mechanism whereby the voids cause an acceleration in deformation rate during the tertiary stage. In order to understand the processes causing tertiary creep, it can be assumed that the secondary creep rate represents the deformation rate unaffected by cavitation. The acceleration in creep rate then reflects the enhancement of the deformation processes due to the presence of the increasing number and size of voids and may be quantified in terms of the strain above that expected from an extrapolation of the secondary stage. The tertiary creep strain etert Can be calculated from the total creep strain: etert = e - - ( e 0 + e p +
gst)
where e 0 and ep are the initial strain on loading and the total primary creep strain respectively. Then, since the duration of tertiary creep depends on the material and the testing conditions, the time dependence of etert was considered by reference to the "fractional t i m e " ftert spent in the tertiary stage which is defined as t -- t T ftert - - t F -- t T
is the time to the onset of tertiary creep and t F is the time to fracture. The variation of etert with fte~t is illustrated in Fig. 7 for annealed copper and for the sample prestrained 7.5% at the creep temperature. These results demonstrate that, at the same where tw
ftcrt Fig. 7. T h e v a r i a t i o n in the t e r t i a r y creep strain ete~ as a f u n c t i o n o f t h e f r a c t i o n a l t i m e ftert s p e n t in t h e t e r t i a r y s t a g e f o r t e s t s c a r r i e d o u t a t 55 M N m - 2 f o r annealed copper and for samples which had been prestrained by 7.5% at the creep temperature of 686 K.
applied stress level, the shape of the tertiary creep curve for polycrystalline copper was unaffected by the prestrain treatments studied. The present observations lead to a new interpretation for the occurrence of tertiary creep. (1) The cavity distribution at fracture for the sample deformed 7.5% at the creep temperature prior to loading appeared to be identical with that observed for the annealed copper tested at the same creep stress (Fig. 5). However, the prestrain markedly reduces the overall creep strain (Fig. 2) by restricting grain deformation without a corresponding effect on the grain boundary zone behaviour. The observation that the tertiary behaviour is comparable for the annealed and for the prestrained samples (Fig. 7) therefore suggests that the acceleration in creep rate is a consequence of cavitation which enhances the deformation rate in the grain boundary zones. (2) The linear dependence of the cavity volume on the creep strain (Fig. 6) indicates that the cavity growth processes are dependent on the deformation processes occurring during creep [13]. It may then be concluded that, as the number and size of cavities increase during the tertiary stage, the creep rate accelerates as a result of stress concentrations developed locally around the voids. In turn, since the deformation processes control the rate of void growth, the enhanced deformation rates in the grain boundary zones lead to a corresponding increase in void growth rates. In this way a linear dependence
277
of the void volume on the creep strain is expected t h r o u g h o u t the tertiary stage.
6. C A V I T A T I O N P R O C E S S E S D U R I N G C R E E P
When failure occurs by cavitation, the creep life may be determined either by the rate of cavity development or by the rate of growth of intergranular cracks [14]. The observation that well-formed cavities were evident over the entire fracture surface suggests that rupture is controlled by cavity formation rather than by the propagation of a crack under the direct action of the maxim u m principal stress. Furthermore, density measurements have established that cavities are present early in the creep life of polycrystalline copper [ 1 2 ] , suggesting that cavity nucleation is relatively easy. The creep rupture life therefore appears to be determined primarily by the rate of cavity growth. The conclusion that void growth is controlled by the deformation behaviour is supported by the relationship found between the rupture life and the creep rate which is illustrated in Fig. 8 for the samples prestrained at room temperature. As observed for a wide range of metals and alloys, when polycrystalline copper is tested in the annealed condition t~ = E/~s
with E ~ 0.04. When the prestrain level is
L
2
IO TIME
IOO TO FRACTURE
ks
Fig. 8. The relationship between the secondary creep rate and the rupture life for annealed copper and for samples prestrained for various a m o u n t s at r o o m temperature: o, annealed; v, 5% prestrain; A, 7.5% prestrain; m, 10% prestrain; 4, 12.5% prestrain.
sufficient to cause a reduction in creep rate, the results obtained for the prestrained samples do n o t lie on the same straight line as that found for the non-prestrained material, i.e. the value of E decreases with increasing prestrain until a limiting value is reached. Even so, for any specified type and a m o u n t of prestrain the rupture life is inversely proportional to the secondary creep rate. Since the time to fracture appears to be governed primarily by the rate of void growth, the present observations suggest that the rate of cavity development is proportional to the creep rate, i.e. for both the annealed and the prestrained materials the cavity growth is controlled by the deformation processes occurring during creep. A decrease in the magnitude of E (= gs X tF) with larger prestrain levels is expected since the creep rate can be decreased by over an order of magnitude whereas the rupture life was increased by less than a factor of 3 under the same conditions (Fig. 2). Prestrain reduces the creep rate within the grains without an equivalent effect on the grain boundary zone behaviour. Since cavity growth is dependent on the deformation rate, the fact that the rupture life is relatively unaffected by the prestrain indicates that deformation p~'ocesses occurring in the grain boundary zones determine the rate of cavity development. The present work offers a means of distinguishing between two models for cavity development, both of which lead to void growth rates directly controlled by the deformation processes. (1) It is generally agreed that grain boundary sliding is a necessary prerequisite for cavity nucleation. The relationship between the rupture life and the creep rate has therefore been interpreted on the basis that, if grain boundary sliding can cause nucleation of cavities, then continued sliding should result in void growth [13]. This model is consistent with the fact that, since grain deformation rates are reduced without a corresponding effect on the overall sliding behaviour, prestrain exerts a greater effect on the creep rate than on fracture. However, with the sliding growth of cavities an irregular cavity shape was expected rather than the regular lenticular shape observed (Fig. 5). Furthermore, the sliding displacements are
278
non-uniform (Fig. 4) whereas the cavities were found to be relatively uniform in size over entire grain boundary facets. Void growth controlled exclusively by the rate of grain boundary sliding therefore appears to be improbable. (2) An alternative model for cavity growth [15] involves the concept that dislocations arriving at the boundary from the grain interior can move along the boundary by a combination of glide and climb. On reaching the boundary, a dislocation of Burgers vector b can be regarded as being resolved into two components, b, normal to the boundary and bp parallel to the boundary. The c o m p o n e n t b, is made to climb along the boundary by the direct stress resolved normal to the boundary and the c o m p o n e n t bp glides along the boundary under the action of the shear stress resolved parallel to the boundary. In this way the cavities nucleated by grain boundary sliding may grow both by absorption of vacancies generated by the non-conservative movement of the lattice dislocation along the boundary and by continued sliding which results from movement of the screw component. With this model the cavity development depends on a combination of slip within the lattice, grain boundary sliding and absorption of vacancies generated by movement of the dislocation in the boundary plane. All these processes are related to the rate of arrival of dislocations from the lattice so that a relationship between the creep rate and the rupture life is expected. However, for this model to account for the present results, the dislocations moving along the boundaries causing cavity growth must have originated in the grain boundary zones rather than in the grain interior. In this way, since the zone deformation is relatively unaffected compared with that of the grains, the prestrain can exert a greater effect on the creep rate than on the time to fracture.
rupture life and a considerable reduction in the total creep strain to failure. However, prestraining can result in entirely different behaviour, e.g. with Nimonic 80A (trademark of Henry Wiggin and Co. Ltd.), although the creep ductility is again reduced, the creep rate is increased and the rupture life is decreased with increasing amounts of room temperature prestrain. These effects were attributed to the major increase in the incidence of grain boundary cavities found on prestraining this multiphase alloy [2]. All the prestrain effects described in Sections 2 - 6 were obtained using oxygenfree copper which had been annealed initially at 1073 K under a vacuum of 0.01 N m -2. In a further series of experiments the samples were tested after being annealed under a vacuum of 1 kN m-2. This difference in initial heat treatment procedure did not significantly reduce the time to fracture of the specimens tested in the non-prestrained state. However, for samples prestrained 7.5% at room temperature, the creep life of the material annealed under a poor vacuum was markedly shorter than that for specimens heat treated using high vacuum procedures (Fig. 9). Moreover, metallographic examination of these prestrained samples confirmed that the use of the poorer vacuum led to a considerable increase in the incidence of grain boundary cavities. In order to identify the causes of this difference in cavitation behaviour, a detailed microstructural study was undertaken for samples annealed using these two different r
3 B cr
n w W rr t.)
7. P R E S T R A I N E F F E C T S ON F R A C T U R E BEHAVIOUR
The results obtained with oxygen-free copper are directly in agreement with those reported for polycrystalline nickel [1, 4], i.e. prestrain levels giving an increase in creep resistance also lead to a slight improvement in
i
2
4
5 TIME ks
i
8
i
I0
Fig. 9. Creep curves r e c o r d e d at 55 MN m - 2 for samples p r e s t r a i n e d by 7.5% at r o o m t e m p e r a t u r e : curve A, b e h a v i o u r o f a sample p r e s t r a i n e d a f t e r an initial h e a t t r e a t m e n t u n d e r a v a c u u m o f 0.01 N m - 2 ; curve B, results o b t a i n e d for a s p e c i m e n a n n e a l e d u n d e r a v a c u u m o f 1 kN m -2.
279
Fig. 10. G r a i n b o u n d a r y voids o b s e r v e d a f t e r h o l d i n g a s a m p l e , w h i c h h a d b e e n p r e s t r a i n e d b y 7.5% at r o o m t e m p e r a t u r e , for 7.2 ks u n d e r zero load a t t h e c r e e p t e m p e r a t u r e o f 6 8 6 K. T h e s p e c i m e n h a d b e e n initially h e a t t r e a t e d u n d e r a v a c u u m o f 1 kN m - 2 p r i o r to prestraining. T h e foil was e x a m i n e d using a n A E I EM7 high voltage e l e c t r o n m i c r o s c o p e (1 MV).
vacuum levels. Each group of specimens was prestrained 7.5% at r o o m temperature, heated to'the creep temperature of 686 K and held for 7.2 ks under zero load before cooling, i.e. the samples were subjected to the standard procedures used at the c o m m e n c e m e n t of the creep tests b u t were n o t loaded at the creep temperature. The samples were subsequently thinned and the resulting foils were examined using an AEI EM7 high voltage electron microscope (1 MV). With the specimens annealed under a poor vacuum, extensive void formation was observed at grain boundaries (Fig. 10) whereas no voids were discernible with test pieces annealed under the high vacuum. (It should be noted that samples annealed using these high and low vacuum procedures were also heated to the creep temperature and held for 7.2 ks b u t without being prestrained. In this case neither sample exhibited the extensive void formation shown in Fig. 10.) Clearly with samples that contain oxygen a high incidence of voids was introduced by the prestraining procedures whereas this effect was n o t f o u n d with the oxygen-free copper. This observation is directly in agreement with that of Lagarde and Biscondi [16] who showed that, with copper bicrystals, lenticular shaped cavities were formed during creep only when some oxygen was present in the material.
By considering the influence of prestrain on cavity nucleation, a consistent interpretation can be provided for the fact that the creep ductility is invariably reduced whereas prestraining can lead to increases or decreases in both the creep rate and the rupture life. (1) It is generally agreed that cavities are nucleated as a consequence of plastic strain and all models for nucleation require a concentrated normal traction at a local region by means of shear relaxation against a suitable obstacle, with the plastic strain arising as a result of transgranular slip and/or grain boundary sliding [14]. Thus for example grain boundary sliding may result in stress concentrations sufficient to nucleate cavities at ledges formed where slip bands intersect the boundaries, at cusps produced where subgrain boundaries meet the grain boundaries or at particles and inclusions. The observation that the cavity incidence is increased markedly by prestraining only with copper annealed under a poor vacuum indicates that cavities form preferentially at grain boundary particles such as inclusions, carbides etc. [17]. In this way an increased cavity incidence accompanying prestrain treatments is expected for Nimonic 80A [ 2] and for copper that contains oxygen b~t n o t for pure nickel [1] and oxygen-free copper. (2) With oxygen-free copper, prestraining reduces the grain deformation rates w i t h o u t a corresponding effect on the zone behaviour and hence on the void growth rates. Since the cavity incidence is also unaffected, substantially lower creep rates and ductilities can be obtained with no significant change in the creep life. However, with copper that contains oxygen the rupture life is impaired as a result of the extensive cavitation caused by prestraining. In this case the creep rate may be increased or decreased depending on whether the reduced contribution of the grain interiors can be offset by the enhanced deformation rates expected in the grain boundary zones when a high incidence of cavities is developed at the start of the test. The ductility is therefore invariably reduced, whereas the creep rate and rupture life may be increased depending on the extent to which the cavity incidence is affected by the prestrain treatment.
280 8. CONCLUSIONS
(1) The rate-controlling process during the creep of polycrystalline copper was unaffected by prestraining either at room temperature or at the test temperature of 686 K. The behaviour was consistent with a recovery model for creep based on diffusion-controlled growth of the three-dimensional dislocation network to produce link lengths between nodes which were long enough to act as dislocation sources, allowing slip to occur. (2) Studies of the surface deformation patterns for prestrained and non-prestrained samples illustrate the need to distinguish between the deformation occurring within the grains and within the grain boundary zones during creep. This zone deformation comprises grain boundary sliding and associated deformation in regions of the grains adjacent to the boundaries. (3) In the absence of recrystallization or grain growth, tertiary creep commences when cavities developing on grain boundaries reach a size sufficient to affect the creep rate. The acceleration in creep rate during the tertiary stage is shown to be a result of the cavities enhancing the deformation rates in the grain boundary zones. (4) Cavities, nucleated primarily at inclusions present at grain boundaries, grow at rates determined by the rate of deformation in the grain boundary zones. Lattice dislocations originating within the zones arrive at the grain boundaries and cause void growth by moving along the boundary plane by a combination of glide and climb. (5) With oxygen-free copper the high dislocation density introduced by prestraining reduces the creep rate of the grain interiors whereas the zone deformation is relatively unaffected because of the rapid rates of recovery near grain boundaries. Since the cavity incidence is not changed significantly by the prestrain treatments, this leads to reductions in the creep rate and the ductility but only a slight improvement in rupture life. (6) With copper that contains oxygen, prestraining leads to a higher cavity incidence as
a result of void formation at the inclusions present. The enhanced deformation rates of the boundary zones due to this cavity development can offset the reduction in the creep rate of the grain interiors. In this way, although the ductility is again reduced, prestraining can result in increased creep rates and markedly reduced rupture lives.
ACKNOWLEDGMENT
One of the authors (J.D.P.) is indebted to the Science Research Council for the provision of a research studentship.
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