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On the stability of the creep substructure in NaCl single crystals
Materials Science and Engineering, A 113 (1989) 161 - 175
161
On the Stability of the Creep Substructure in NaCI Single Crystals* S. V. RAJ
Lewis Research Center, National Aeronautics and Space Administration, MS 49-1, 21000 Brookpark Road, Cleveland, OH 44135 (U.S.A.)
G. M. PHARR
Department of Materials Science, Rice University, P.O. Box 1892, Houston, TX 77251 (U.S.A.)
J. D. WH1TTENBERGER
Lewis Research ('enter, National Aeronautics and Space Administration, 21000 Brookpark Road, Cleveland, OH 44135 (U.S.A.) (Received November 25, 19881
Abstract
Microstructural observations were conducted on NaCl single crystals after creep. The microstructure after a stress increase followed by a stress decrease consisted primarily of cells; no significant number of subgrains were observed although they were present in the microstructures produced during uninterrupted tests. Prestraining in the exponential creep regime produced an uniform distribution oJ dislocations and a few subboundaries which transformed to equiaxed subgrains when tested in the power law creep region. This substructure was similar to that observed in an as-received specimen deformed to an equivalent strain. Prior creep in the power law creep region produced equiaxed subgrains whose boundaries were found to be mechanically stable when the specimen was retested in the exponential creep region. The role of subboundary migration in the formation of new subgrains is discussed. 1. Introduction
At intermediate values of normalized stress o/G, the steady state creep rate g is usually given by [1]
g = A D ° G b ( ° ] " exp Qc) -kT kG/ -RT
(11
mann's constant, T is the absolute temperature, o is the applied stress, Qc is the activation energy for creep, R is the universal gas constant, and A and n are constants. Typically, n -- 4-5 for a large number of materials [2, 3] exhibiting metal-type or class M behavior. At high stresses, the power law relation given by eqn. (11 breaks down, and the creep rate exhibits an exponential dependence on normalized stress over a large range of stresses and temperatures as
where A~ and B are constants. Alternatively, if creep data are represented by a power law relation, then n increases monotonically with a~ T [2] to values of n "> 4. It is now generally accepted that power law creep is controlled by the rate of climb of edge dislocations with Qc "~ Q1, where QI is the activation energy for lattice diffusion [1, 4-6]. Dislocation climb in this deformation regime results in the formation of subgrains, where the subgrain size d~ is related to the applied stress through [1, 5, 7-9]
=K
(s/
where D 0 is a frequency factor, G is the shear
modulus, b is the Burgers vector, k is Boltz*Paper presented at the 2nd International Conference on Low-Energy Dislocation Structures, Charlottesville, VA, August 13-17, 1989. 0921-5093/89/$3.50
where m and K are constants. It was shown in an earlier publication [9] that, although several combinations of m and K can be found in the literature, the values m = 1 and K = 23 generally lead © Elsevier Sequoia/Printed in The Netherlands
162
to a good representation of experimental data. )X similar relation has been suggested for the stress dependence of the cell size with m = 2 [7, 8]. A question of fundamental importance that has been the subject of some discussion in recent years is related to the applicability of eqn. (3) to situations involving stress reductions, where it is not clear whether the subgrain size corresponding to the new reduced stress is smaller [10-13] or equal [14-24] to that predicted by the equation. This topic has an important bearing on the role of subboundary migration during creep [19, 21-28]. Microstructural observations after a stress reduction essentially deal with the instability of the original subgrains produced during creep at the higher stress; hence, the stress and temperature conditions chosen generally correspond to the power law creep regime where welldeveloped subgrains form during deformation. While these stress reduction experiments deal with the specific question of subgrain coarsening after a stress decrease, they do not address the problem of the stability of other types of substructure (e.g. cells or forest dislocations), initially formed under one combination of stress and temperature, under a new set of creep conditions. Essentially, these experiments can be conducted by producing the initial microstructure in the exponential creep region and then examining its stability under power law creep conditions. Conversely, the stability of a subgrain microstructure, initially produced under power law creep conditions, can be investigated under stress and temperature conditions corresponding to the exponential creep region. Both these experiments on prestrained microstructures can provide useful information on their strengthening effects and their stability, while examining the universality of eqn. (3) under a variety of conditions. A question related to the latter point can be asked: how do new subgrains form during creep when the undeformed material contains large subgrains? New results are presented in this paper which address these points. The present paper is divided into several parts. First, the qualitative and quantitative characteristics of substructures formed in the power law and the exponential creep regions are examined. Second, the results of special experiments, which address the question of microstructural stability, are discussed. Third, the role of subboundary migration in the formation of new subgrains is examined. Single-crystal sodium chloride (NaC1)
was chosen as the model material for study in this investigation for several reasons: (1) to eliminate the complicating effects of grain boundaries and alloying elements, which are generally associated with polycrystalline materials and solid solution alloys respectively; (2) the creep behavior of this material is well documented [4, 10, 14, 19, 29-35]; (3) substructural observations can be made on this material using relatively simple etch pit techniques for microstructural characterization.
2. Experimental details Creep specimens with approximate dimensions of 7 mm x 5 mm x 5 mm were cleaved from 1 in cubes of NaC1 single crystals oriented in the (100) direction. These crystals, which were procured from Harshaw-Filtrol, Inc., had impurity contents of 19 ppm Ca, 15 ppm Fe and 4 ppm Mg. Constant-stress compression creep tests were conducted in a nitrogen atmosphere using a computer-controlled lever arm machine, which enabled the simultaneous monitoring of strain, temperature and load during the course of the test. The accuracy of load control was better than 1 N, while the strain and temperature measurements were accurate to 10 -5 and 1 K respectively. Prior to testing, the specimen was maintained at the test temperature for at least 2 h. The stress axis was parallel to the (001) orientation of the crystal and, typically, the specimens were deformed in the temperature range 373-1023 K to the desired value of strain. After deformation, the specimens were cooled under load in a blast of compressed air to preserve the creep microstructure. Specimens were prepared for microstructural examination by initially lapping them on a damp cloth clamped to a static polishing wheel using a 90% ethanol-10% water polishing solution. The lapping was continued until sufficient material had been removed to ensure that the observed microstructure was representative of the bulk. Next, the damaged layers produced by the lapping technique were removed by a two-stage chemical polishing procedure consisting of an initial 5-15 s rinse in the ethanol-water solution followed by an additional rinse (less than 5 s) in deionized water. The polished specimens were etched by immersion in a solution of 23 ml of ethanol, 2 ml of deionized water and 25 mg of CdCI 2 [36] for times varying between 5 and 35 s.
163 The etching times were found to be extremely sensitive to the deformation histories of the specimens with shorter times required for those tested at low temperatures and high stresses. After etching, the specimens were rinsed in propyl alcohol and dried in a jet of Freon gas. Almost all microstructural observations were made on sections perpendicular to the stress axis and represent the {001} planes except where indicated. The dislocation density and the subgrain size of the asreceived material were about 10 H~m 2 and 1500 /xm respectively.
3. Substructural characterization in the power law and exponential creep regimes Figures l(a) and l(b) show the variation in the creep rate with strain e at 973 K and 473 K respectively, for several stresses between 0.60 and 18.0 MPa. As shown in Fig. l(a), genuine steady state is observed when e >/0.2 under creep conditions of T = 9 7 3 K and (7=0.60 MPa (o/G=7.5x10 5). True steady state creep behavior was usually observed for T> 873 K and o/G 0.5 (Fig. l(b)). A double-logarithmic plot of gkT/Dc] Gb against o/G is shown in Fig. 2, where g represents
the creep rate at e = 0.2 and Dc~- is the intrinsic diffusion coefficient of chlorine ions in NaCI. The temperature dependence of Dc]- was determined by replotting diffusion data obtained from several sources [37-40] against the inverse of the absolute temperature; a linear regression line through these data gave the following relation:
I
I
G = 1.81 × 1 0 4 - 10.23T
NaCl
10-3
108
<001>
I I lilqi I I NaCl _
0.60 MPa (a)
10-6 10-1
'S
.w
I
I
I
I
I
I
[
100
.Icl
-
10-3
X
~"
~
18.0 MPa
- -
T JOOqJ>3K - -
[7
473
A
573 673
0
773
? 0
873 973
I
i
1 1
10-12
10-6
" ~
8.0
l
MPa
lO-16
10-7 10-8
ii
5 . 0 ~
10-4 10-5
I ' l ll'l I
x I m I
-- o 11023 __ 1.0
10-8
Ilqili l
%
( $98-
• w 10-q
10-2
(5)
I
E-0.2 T (K) 373
104
10-5
(4)
)
(MPa)
i lillllI I ililill I
<001>
_
T = 973 K
10-4
I
where eqn. (5) represents a reformatted expression originally used by Frost and Ashby [41]. As shown in Fig. 2, the high temperature and low stress data can be represented by a power law relation with a stress exponent of about 5, while at low temperatures and high stresses the normalized creep rate increases exponentially with normalized stress. The transition from the power law to the exponential region first occurs at a critical value of normalized stress (o/G)pL. B of a b o u t 3 x l 0 ~.
I
I
2s
(where the activation energy is expressed in kJ mol- 1). The temperature dependence of the shear modulus for NaCI was calculated from
1012
10-2
230 / -~/(m
Dc, = 8 . 0 x l 0 - 2 e x p
10-6 0
(~>
I
0,1
I
0.2
I
0.3 E
I
O.q
I
0,5
l ilihhl 10-5
i ilihhl
l ilihhl
lO-q
10-3
l ilihhl 10-2
l ilihh 10-1
O/O 0.6
Fig. 1. Plot of strain rate g against creep strain e for NaCI single crystals deformed at (a) 973 K and (b) 473 K.
Fig. 2. D o u b l e - l o g a r i t h m i c p l o t o f gkTtDci-Gb vs. (JiG f o r NaCI single crystals deformed to a true strain of about 0.20. The deviation from a power law relation with a slope of about fivefirst occurs at (o/G)pLB= 3 × 10 4.
164
Fig. 3. Creep microstructures in NaCI single crystals at normalized stresses o/G of (a) 7.5 x 10 5, (b) 2.2 × 10 -4, (c) 4.0 × 10 4 and (d) 1.4 × 10- 3: C, cell; P, primary subboundary; S, secondary subboundary.
Details of the effect of stress, temperature and strain on the creep microstructure will be published elsewhere, and only a brief description is provided here. Figure 3 shows examples of typical microstructures formed at different values of normalized stress. Large equiaxed primary subgrains P, subdivided by a network of secondary subboundaries S and cells C, were observed under steady state conditions (Fig. 3(a)). The primary subboundaries, which were narrow and well defined, could not be resolved into indi-
vidual etch pits at any magnification when viewed under an optical microscope. In contrast, the cell boundaries were broader and more diffuse than the subboundaries and could be resolved into individual etch pits at sufficiently high magnifications, and the cell boundary misorientation angle was estimated to be less than 0.1 °. The morphology of the secondary subboundaries lay somewhere between those two extremes as they consisted of distinct and overlapping etch pits which could not be individually resolved.
165
In comparison with those which formed during steady state creep, the cell boundaries were wider and the number of secondary subboundaries fewer under non-steady state conditions. This was true even for stress and temperature conditions corresponding to the power law creep region in Fig. 2. An example of this is shown in Fig. 3(b) for a specimen deformed at a value of o/G = 2.2 x 10 4, where it is seen that, while the primary subgrains are still equiaxed, the cell boundaries within many of them (e.g. A in Fig. 3(b)) are extremely coarse in contrast with those shown in Fig. 3(a); however, narrow cell boundaries and secondary subboundaries are evident within some of the primary subgrains (e.g. B in Fig. 3(b)). It was also observed that the number of secondary subboundaries were large in those primary subgrains which contained a larger proportion of narrow walled cells (e.g. compare regions A and B in Fig. 3(b)). It is clear from these observations (Figs. 3(a) and 3(b)) that the steady state microstructure involves a refinement of the cell boundaries and the formation of secondary subboundaries. It is important to note that the descriptions of the steady state and the nonsteady state microstructures outlined here were found to be valid in most, but not all, instances. There was an increase in the aspect ratios of many of the primary subgrains at or just above (a/G)PLB (Fig. 3(C)). Typically, the long boundaries of these subgrains were oriented along-the (110) direction so that the subgrains collectively presented a ladder-like morphology. Similar creep microstructures of elongated and equiaxed subgrains, often distributed in alternate bands of narrow and wide subgrains, have been observed in other materials [5, 42-50]. Significantly, there was a great difference in the internal microstructures of the elongated and the equiaxed subgrains as is evident through a comparison of regions A and B in Fig. 3(c). The elongated subgrains had a higher dislocation density, larger number of cells with coarse boundaries and fewer secondary subboundaries than their equiaxed neighbors. At very high values of normalized stress, corresponding to exponential creep (Fig. 2), the microstructure consisted primarily of an uniform distribution of etch pits and a few slip traces (Fig. 3(d)); however, subgrains were observed in the exponential creep region above 473 K when e>0.2. Figure 4 shows the variation in the subgrain and the cell size dc normalized by the Burgers
106
- I I111'IW I I 'I~
I
Illqlj
I
'1'111-
1.0
~
cms7
105
~ SUBGRAINS--
0"45~ ~.0 ~ ~
%
~
\
NaCl
(001) dc/b
ds/b
104 -- 473 -- 573
[] Z~
0 A
673
<~
@
873
'~
0 V
973 598- i
@
Q
--
T (K)
_-
773
{1
x
iI
0
823 } 103 i0-6
%
I
i lJlild
10-5
, l,l,hI
10-4
I tllHd I i IJlih 10-3
10-2
OIG
Fig. 4. Variations in single crystals.
d,./b and d,/b against o/G for NaCl
vector (b = 3.99 x 10 u~ m [41]), with the normalized stress, where the data have been obtained at different temperatures and at various values of strain. The normalized value of the power law breakdown stress (o/G)PLB is also indicated in the figure. It is evident that dJb decreases with an increase in the normalized stress in accordance with eqn. (3) with m-~ 1.1 and K = 15. These values of m and K fall within the range of values reported earlier for other ionic crystals [9]. Similarly, dc/b decreases with increasing values of a/G with the magnitudes of m and K being about 0.45 and 930 respectively. These results suggest that the cell size exhibits a weaker dependence on the applied stress than the subgrain size and, while these observations are in agreement with those reported by Goel et al. [22] on an A1-Zn alloy, they do not agree with other results on iron-base alloys [7, 8, 51], where it was found that the stress dependence of the cell size was better represented by m = 2 and K = 0.2. 4. Microstructural stability Although the microstructural observations reported in Section 2 provide important information on the qualitative and quantitative aspects of
166 10-2
10
i
I
I
i
I NaCI <001> = 673 K
3 ~
10-td
/ ~ 3 . 5 f~a '= .w
10-5
10-6
10 - 7
,0-8!
0 - 3 0
I
0.1
-
I 0.2
-
3 5
I
0.3 E
-
-
I
O.q
3 0 MPa
I 0.5
0.6
Fig. 5. Comparison of g-e plots for NaCI single crystals obtained at 673 K for uninterrupted and stress change tests: o~ = 3.5 MPa; 02 = 3.0 MPa.
the creep substructure, they do not address the problem of microstructural stability when the testing conditions are changed. Investigations on microstructural stability generally involve producing an initial microstructure under one set of experimental conditions which is then subjected to a different set of deformation conditions to understand how it transforms to the final substructure. The results of these experiments performed on NaC1 are discussed below.
4.1. Effect of stress reduction Figure 5 compares the creep curves obtained in two uninterrupted tests conducted at 673 K, and under stresses of 3.0 MPa and 3.5 MPa (o/G =2.7 x ] 0 - 4 and 3.1 x 1 0 - 4 respectively), with that obtained in a stress change experiment, where the stress was first increased from 3.0 to 3.5 MPa and later reduced back to the original value of stress. The creep curves obtained in the uninterrupted tests exhibit a prolonged primary region which tends towards steady state behavior. The increase in stress from 3.0 to 3.5 MPa results in an initial increase in the creep rate by about an order of magnitude above that at the new value of stress. However, the creep rate after the stress increase falls rapidly from this maximum value to values which are slightly below those for the uninterrupted test. On reducing the stress from 3.5 to 3.0 MPa, the initial creep rate after the stress reduction is lower than that at 3.0 MPa but rises rapidly to values which are close to those obtained in the single test. The final microstructures formed in the uninterrupted tests consisted of equiaxed and elongated subgrains subdivided by cells (Fig. 6). The average values of the cell and subgrain size
Fig. 6. Substructures produced in NaCI single crystals deformed to e = 0 . 4 7 at 673 K in an uninterrupted test: (a) o 1 = 3.5 MPa ( o J G = 3.1 x 10-4); (b) 02 = 3.0 MPa (a2/G =2.7×10-4).
formed under these conditions are tabulated in Table l. The effect of the stress change experiment described above resulted in a microstructure (Fig. 7) which is vastly different from those obtained under single-stress conditions (Fig. 6). In essence, the two stress changes resulted in a microstructure which was essentially devoid of any subgrains, except at the edges of the specimen* but consisted of an almost uniform distribution of cells some of which were oriented along *Table 1 also shows the average size of the subgrains formed at the edges of the specimen after the stress reduction, but no special significance can be attributed to the fact that this value is smaller than that obtained at a single stress of 3.0 MPa since only a few measurements could be made.
167
TABLE 1 Comparison of the average sizes of cells and subgrains formed at 673 K after a stress reduction with those produced during creep under a single stress Material condition
Test parameters
As received
7=673 K 13.9_+ 1.5 o = 3.0 M P a e = 0.46
70.0_+6.5
As received
10.9_+1.0 7'= 6 7 3 K o = 3.5 Mpa
36.7_+4.5
,," =
Stress change from 3.(t to 3.5 to 3.0 M P a
dc (pm)
d, (/~m)
0.46
T=673 K o = 3.0 M P a e = 0.08 ~
8.3_+0.9
55.8_+10.5 ~
T h e error limits were determined at the 95°/,, confidence level.
"Strain after the stress reduction. bThese values represent the average sizes of subgrains present near the edges of the specimen.
the (110) direction (Figs. 7(a) and 7(b)). Evidence that these microstructural features are cells, and not subgrains, is clearly demonstrated in Fig. 7(c), where the individual etch pits in the cell boundaries are visible at a higher magnification. The cellular microstructure shown in Fig. 7 is somewhat similar to that present within the subgrains in Fig. 6(b), and the average cell size formed after the stress reduction is in agreement with those produced in the uninterrupted test to within a factor of 2 (Table 1 ), which is within the range of experimental scatter usually associated with such measurements. As the creep rates after the stress reduction are similar to those observed in the uninterrupted test at 3.0 MPa (Fig. 5), it can be concluded that the cellular, and not the subgrain, microstructure
ol (010)
Fig. 7. Microstructures of an NaCI specimen deformed to e = 0 . 4 8 at 6 7 3 K in stress change experiment: (a) a uniform distribution of cells; (b) a magnified view of region A in (a); (c) cell boundaries present in region B in (b).
168
determines the creep rate at 673 K. The similarities in the cell sizes formed in the uninterrupted and the stress change tests (Table 1), however, suggest that the processes occurring in the cell boundaries are important in determining creep behavior. This suggestion is consistent with the fact that steady state creep behavior was generally observed in the g-e plots when the cell boundaries had become relatively narrow (Fig. 3(a)). There has been a considerable amount of discussion in the literature [10-24] regarding the stability of subgrains after a stress reduction. It was concluded from experiments of NaCI [10], AgCI [11], copper [12] and A1-5wt.%Zn [13] that the subgrains formed at the higher stress are relatively stable after a stress reduction and do not increase to a size consistent with the reduced stress in accordance with eqn. (3). However, Miller et al. [16] criticized some of these observations [11, 12] and pointed out that the creep strain after the stress reduction was insufficient to allow any substantial subgrain coarsening to occur for steady state values to be attained. Although Langdon et al. [13] addressed this criticism by measuring the subgrain size after steady state creep was re-established (i.e. after a shear strain 7 of about 0.09 following the stress reduction), their observations do not agree with other results on aluminum [18, 20, 21, 23, 24], AI-5wt.%Zn [22] and NaCI [19]. Soliman and coworkers [21-23] attempted to account for this discrepancy by suggesting that Langdon et al. [13] may have erroneously measured the cell size rather than the subgrain size, since the evidence on aluminum [18, 20, 21, 23, 24], AI-5wt.%Zn [22] and NaC1 [19] clearly demonstrated that substantial subgrain coarsening occurs after a stress reduction with a corresponding increase in the creep rate. It was observed that this subgrain coarsening involved the dissolution of some subboundaries and the migration of others [19, 21-24]. The results pesented in Figs. 5-7 clearly indicate that the cellular microstructure is essentially stable even after a strain e of about 0.08 after the stress reduction. The criticisms applied to previous investigations [11-13] cannot be applied to the present observations since sufficient strain was allowed after the stress reduction and the microstructural observations reported here are unambiguous. However, there is an important difference between the present results and those reported in the other investigations [10-24]. The
microstructure formed after the stress change is essentially devoid of subgrains and therefore does not resemble those formed in the uninterrupted tests (Fig. 6) despite the fact that the creep rates after the stress increase and the stress decrease are comparable with those observed in the uninterrupted test (Fig. 5). The general absence of subgrains in the microstructure formed after the stress change experiment (Fig. 7), except at the edges of the specimen, is especially puzzling since they are present in those formed during the uninterrupted tests conducted at 3.5 MPa (Fig. 6(a)) and 3.0 MPa (Fig. 6(b)). Table 2 compares the experimental conditions used in the present study with those employed in other investigations on subgrain stability [13, 18-24], where the creep strain e R after the stress reduction was sufficiently large to permit the new creep rate to be comparable with that at the reduced stress. The information tabulated in Table 2 includes material composition, the test procedure, where al and a2 are the stresses before and after stress reduction respectively, the test temperature and its fraction eR of the absolute melting point Tm and general information on the stability of the initial substructure. It is noted that the values of T, T/Tm, a l / O 2 and e R shown in Table 2 represent the range of experimental conditions, and e R was derived from values of shear strain reported in some of the original investigations [13, 21-24] by using the relation ~eR = 7/3. An examination of Table 2 shows that the final substructure was attained in all cases when eR> 0.03. This condition was easily fulfilled in the present investigation so that the final microstructure after the stress reduction is expected to contain well-developed subgrains of an average size consistent with either that at al = 3.5 MPa or as = 3.0 MPa. Yet, as shown in Fig. 7, this was not the case, and instead few subgrains were observed after the stress reduction. In recent experiments on aluminum [23, 24], it was observed that the cellular microstructure was fairly stable below 0.65 Tm and for Ol/O2 < 1.2. As shown in Table 2, the magnitudes of T/Tm = 0.63 and a~/o 2 ~-1.2 used in the present investigation are in reasonable agreement with the testing conditions on aluminum [23, 24] for which cell stability has been reported. Ginter et al. [23] suggested that the presence of cells within a subgrain may interfere with subboundary migration and dissolution but it is unlikely that this reasoning
169 TABLE 2 Tabulation of the range of experimental conditions used in several investigations on subgrain coarsening after a stress reduction
Material
lmpurio' content
Test T procedure a (K)
T/Tm
Ol/O" 2
AI
99.999 (wt.%)
o~ to o:
573
0.61
1.80-4.35 0.08-0.12 Subgrain coarsening
AI
99.99 (wt.%)
o~ to a 2
610-923
0.65-0.99 1.40-6.80 0.04-0.06 Subgrain coarsening
Soliman etal. {21]
99.99(wt.%)Al
a t to 02
573-593
0.61-0.64 1.20-2.00 0.07-0.10 Stable cells; subgrain coarsening
Ginter etal.[23]
99.98(wt.%)Al
a~ to 02
573-923
0.61-0.99 1.05-4.00 0.07-0.13 Cells stable atlow Mohamed etal. values of Tand [24] all 02; subgrain coarsening
AI-5(wt.%)Zn
a t to 02
573
0.63
A1-5(wt.%)Zn
o mto o 2
650-893
0.70-0.99 1.30-4.00 0.05-0.07 Subgrain coarsening
8R b
4.25
0.03
Remarks
No subgrain coarsening
ReJbrence Ferreira and Stang [18, 20]
Langdon et al. [13] Goel etal.[22]
NaC1 (100)
3 ppm Ca'-+
a~ to a 2
923-1033 0.86-0.96 2.40
0.065
Subgrain coarsening
Eggeler and Blum [ 19]
NaCI (001}
19 ppm Ca 2+ 4 ppm Mg2 + 15 ppm
o, to a~ to a,
673
0.08
Cells; subgrains absent
Present invesligation
0.63
1.15
F e 3+ a o I > 0 2.
beRwas determined from the shear strain values reported in some of the original investigations [13, 21-24] by using a conversion factor of 3. a p p l i e s to t h e p r e s e n t stress c h a n g e results since n o s u b g r a i n s w e r e o b s e r v e d . P e r h a p s , t h e stress i n c r e a s e p r i o r to t h e stress d e c r e a s e m a y h a v e i n f l u e n c e d the final m i c r o s t r u c t u r e b u t f u r t h e r e x p e r i m e n t a t i o n m u s t b e c o n d u c t e d to c o n f i r m this.
4.2. Effect o f prior deformation on creep substructure Two types of experiments were conducted on NaC1 single crystals in o r d e r to s t u d y t h e effect o f prior deformation on the creep behavior and the final m i c r o s t r u c t u r e . In t h e first series of e x p e r i m e n t s , w h i c h was d e s i g n e d to test t h e u n i v e r s a l i t y o f eqn. (3), a s p e c i m e n was d e f o r m e d to a true s t r a i n ~ o f a b o u t 0.20 at 4 7 3 K a n d 10.0 M P a ( a / G = 7 . 5 x 10-4), w h i c h c o r r e s p o n d s to n o r m a l i z e d values o f c r e e p rate a n d stress well within the e x p o n e n t i a l c r e e p r e g i o n (Fig. 2). T h e specim e n was c l e a v e d p a r a l l e l to t h e stress axis, a n d both halves were polished and etched. As shown in Fig. 8, t h e s u b s t r u c t u r e after c r e e p u n d e r t h e s e c o n d i t i o n s c o n s i s t e d o f an u n i f o r m d i s t r i b u t i o n o f e t c h pits a n d a few i l l - f o r m e d s u b b o u n d a r i e s . O n e half o f t h e c l e a v e d s p e c i m e n was t h e n d e f o r m e d
a
-
'ltm lalm
Fig. 8. Microstructure of an NaC1 specimen deformed to e=0.12 at 473K under a stress of 10.0 MPa (o/G= 7.5 x 10 4). f u r t h e r to a s t r a i n e of a b o u t 0.43 at 8 7 3 K u n d e r a stress o f 1.0 M P a (i.e. o / G = 1.0 x 10 -4) c o r r e s p o n d i n g to t h e p o w e r law c r e e p r e g i o n in Fig. 2, and the creep curve obtained under these conditions is s h o w n in Fig. 9 a l o n g with that for an asr e c e i v e d s p e c i m e n . In o r d e r to a s c e r t a i n t h e effect of static r e c o v e r y o n t h e initial p r e s t r a i n e d m i c r o -
170
1°-3 ~\
I
I
I
I
I
Io41-- ~
I
~
~-AS-RECEIVED
I ~.-_~./ "~
~
10-6 ~
io71
0
INa_~J I --
II
1"010]
T = 873 K o = 1.0 MPa
ORE-STRAINED-"
'
-
I
0.1
-
I
0.2
l
0.3
I
0.4 E
I
0.5
I
0.6
I
0.7
0,8
Fig. 9. Comparison of the g-e plots for as-received and prestrained NaCI specimens at 873 K under a stress of 1.0 MPa. The prestrained specimen was initially crept to e = 0,2 at 473 K under a stress of 10.0 MPa.
structure, the other half of the cleaved specimen was also placed in the creep machine close to the test specimen in such a manner that there was no applied stress on it. The initial creep rate of the prestrained specimen was less than 10- 8 s- l (i. e. below the detection limit of the strain-measuring equipment), and measurable creep was detectable only after a period of 1 h. A linear extrapolation of the data lying in the exponential creep region in Fig. 2 to o / G = 1.0x 10 - 4 suggests that the creep rate corresponding to the microstructure shown in Fig. 8 should be of the order of 10-13 s-1, which would account for the fact that the initial creep rates were immeasurably small in the predeformed specimen. Following this initial period of immeasurable creep, the creep rate rises by several orders of magnitudes to about 2 x 10 -5 s-1 during the first few per cent strain and then gradually decreases to values close to that observed for the as-received specimen when e > 0.3 (Fig. 9). The microstructure of the prestrained specimen after subsequent creep to a true strain of about 0.43 is shown in Fig. 10, where it is seen that well-developed primary subgrains containing cells and a few secondary subboundaries have formed from the initial substructure shown in Fig. 8. This microstructure is similar to that observed on an as-received specimen deformed to an almost identical value of strain (Fig. 11 ). The cell and subgrain sizes of the prestrained and the asreceived materials are also in agreement to within a factor of 2 (Table 3), which is the normal level of experimental scatter associated with these measurements [9]. These results clearly demonstrate the uniqueness of eqn. (3) in determining
Fig. 10. Microstructure of the prestrained NaCI specimen shown in Fig. 8 after a creep strain of about 0.43 at 873 K under a stress of 1.0 MPa (o/G = 1.l × 10-4).
Fig. 11. Microstructure of an as-received NaC1 specimen deformed to a true strain of about 0.4 at 873 K under a stress of 1.0 MPa (o/G = 1.1 x 10-4).
both the cell and the subgrain sizes under these conditions. Figure 12 shows the effect of static recovery on the initial predeformed microstructure (Fig.
171 TABLE 3 Comparison of the average sizes of cells and subgrains formed at 873 K under a stress of 1.0 MPa in prestrained and as-received specimens
Material condition
Test parameters
dc (/am)
d~ (/am)
As received
7"= 873 K 19.5 +_ 1.8 o = 1.0 MPa e=0.40
193.5 _+30.5
Prior creep to e = 0.2 at T= 473 K and o = 10.0 MPa
19.1_+2.1 T=873 K o = 1.0 Mpa e = 0.43
126.3+_35.3
The error limits were determined at the 95% confidence level.
Fig. 13. Microstructure of an NaCI specimen deformed to e = 0.2 at 923 K under a stress of 0.65 MPa.
Imhl ~q~ Fig. 12. Effect of static annealing at 873 K on the prestrained microstructure (o = 0 MPa).
8). Although the extent of recovery due to this annealing treatment is not as extensive as that during deformation, it is not negligible and, as shown in Fig. 12, a few large subgrains, subdivided by cells, have formed. A comparison of Figs. 10 and 12 clearly demonstrates that stressassisted recovery is much faster than static recovery. The sigmoidal primary creep behavior (Fig. 9) observed in the prestrained material is analogous to similar behavior reported for Cu-16at.% AI [52], where it was concluded that the initial rise in the creep rate was associated with an increase in the density of mobile dislocations while the subsequent fall in the creep rate resulted from an increase in the long-range internal stress due to newly formed subboundaries as well as a decrease in the mobile dislocation density. Therefore, it follows that the microstructure produced after prior creep at T = 473 K and o = 10.0 MPa (Fig. 8) results in a low mobile dislocation density, so that the initial creep rates are immeasurably
small when the specimen is retested at 7`= 873 K and o = 1.0 MPa (Fig. 9). The initial increase in t h . creep rate observed for e ~<0.05 (Fig. 9) can be attributed to the increasing effect of recovery which results in a relative increase in the density of mobile dislocations. However, continued recovery would lead to an annihilation of excess dislocations and the formation of cell and subgrain boundaries, so that the long-range stresses acting on the mobile dislocations due to these boundaries increases and the creep rate begins to decrease. The second set of experiments was designed to test the possibility that the original subboundaries may break up during a stress increase. In order to address this point regarding the mechanical stability of subboundaries, a specimen was crept to a true strain of about e -~ 0.20 at 923 K under a stress of 0.65 MPa (¢y/G=7.5 × 10 5) corresponding to the power law creep regime in Fig. 2. This deformation resulted in a microstructure consisting of large equiaxed primary subgI:ains containing a network of cells (Fig. 13). The specimen was then retested at 473 K under a stress of 10.0 MPa ( a / G = 7 . 5 × 10-4), where the stress and temperature conditions correspond to the
172
'-~
'~ •w
1°-2/
I
I
10-4 L_
~. ~
I
I
INaCl I °=
l°'°~a
~ ~ E C E I V E D
10-5_
10_6_PRE-SR I AN I E~D / ~ I o.o,
I o.08
I o.12
I
tr
0.1
I
I
0.20
0.24
0.28
Fig. 14. Comparison of g-e plots for as-received a n d prestrained NaCl specimens at 473 K under a stress of 10.0 MPa. The prestrained specimen was initially crept to e = 0.2 at 923 K under a stress of 0.65 MPa.
exponential creep region in Fig. 2. The creep curves for the prestrained and as-received specimens are shown in Fig. 14, where it is seen that the creep rates for the predeformed specimen are smaller than those for the as-received material. After deformation to an instantaneous strain of about 0.034, an examination of one of the surfaces perpendicular to the stress axis showed evidence of slip bands traversing the original subboundaries (Sb)(Fig. 15(a)). On repolishing and re-etching the surface, it was found that the original subboundaries were still intact (Fig. 15(b)) and localized migration of the subboundaries appeared to have occurred in some areas (e.g. A in Fig. 15(b)). However, there was no evidence of any catastrophic rupture of these boundaries. Instead, the cellular microstructure, initially present within the primary subgrains (Fig. 13), was more or less replaced by an uniform distribution of etch pits, but it was not clear whether the increase in the dislocation density resulted from a dissolution of the original cell boundaries shown i n Fig. 13 into individual dislocations or by the generation of fresh dislocations from newly activated sources. Continued deformation to a strain of about 0.18 (Fig. 14) resulted in the localized migration of the original subgrain boundaries as indicated by the arrows in Fig. 16(a) and in the formation of new subgrains. It was observed that the migration of the old subboundaries was partly responsible for the nucleation of new subgrains. Other evidence in support of the role of subboundary migration in the creation of new subgrains during creep is provided in Section 3.3. In many areas of
El
Fig. 15. Creep microstructures of the prestrained NaC1 specimen shown in Fig. 13 after deformation to an instantaneous true strain of about 0.034 at 473 K under a stress of 10.0 MPa: (a) unpolished surface showing slip lines crossing a subboundary (Sb) originally formed during prior creep to e ~ 0 . 2 at 923 K under a stress of 0.65 MPa; (b) polished surface demonstrating that the original subboundaries are still mechanically intact but show evidence of localized migration in some regions (e.g. at A).
173
Fig. 17. Microstructure of an as-received NaCI specimen deformed to a strain of about 0.2 at 473 K under a stress of 10.0 MPa and with o/G = 7.5 × 10 4.
the specimen, the r a n d o m dislocation microstructure shown in Fig. 15(b) was found to have been completely replaced by new subgrains (Fig. 16(b)). T h e s e microstructures are quite different from that for an as-received specimen deformed to e-~0.2 (Fig. 17), where it is seen that the substructure consists of a mixture of long subboundaries and regions of high and low dislocation densities. However, well-formed subgrains similar to those shown in Fig. 16(b) were observed in the as-received material when e = 0.5. Therefore, the lower creep rates observed in the prestrained material (Fig. 14) can be attributed to the longrange internal stresses associated with the original and the newly f o r m e d subboundaries which effectively results in a lateral shift of the g-e plot to lower values of strain. T h r e e conclusions may be drawn f r o m the a b o v e observations. First, the presence of subboundaries in the initial microstructure can lead to significant strengthening effects. Second, the original subboundaries are mechanically stable even when the normalized stress is increased by an order of magnitude. Third, the original subboundaries play an important role in the development of the final microstructure by aiding the nucleation of new subgrains.
Fig. 16. Microstructures of the prestrained NaCI specimen shown in Fig. 13 after creep to e-~0.18 at 473 K under a stress of 10.0 MPa: (a) the original subboundaries show evidence of localized migration as indicated by the arrows; (b) new subgrains within the original subgrains.
4.3. Role of subboundary migration in the formation of new subgrains New subgrains can f o r m by several different mechanisms such as dislocation climb, cell rotation, or the bowing of a s u b b o u n d a r y during
174
migration. The latter mechanism appears to be especially important in transforming large subgrains, typically found in annealed ionic crystals, to smaller ones of an equilibrium size given by eqn. (3). An example of this is shown in Fig. 18. In this case, an annealed NaCI single crystal having an average subgrain size of about 1500 ~m was deformed to a true strain of about 0.35 at 573 K under a stress of 12.0 MPa ( o / G = 9.8 × 10 -4) in less than 10 s. Despite the short time for which the specimen was stressed, it is evident from Fig. 18(a) that the transformation to the final microstructure is essentially complete in large areas of the specimen. This transformation occurs by the migration (e.g. A in Fig. 18(a)) and bowing of the original subboundaries (e.g. B in Figs. 18(a) and 18(b)), and the subsequent pinching-off and separation of the bowed segments (e.g. C in Fig. 18(a)). For this to happen, the segment must bow beyond a critical radius R = flGb/o, where fl is a constant so that, when ds = 2 R, this process leads to a stress dependence of the subgrain size similar to that given by eqn. (3). Figure 18 once again confirms that the original subboundaries exhibit a high degree of mechanical stability as demonstrated earlier (Figs. 15 and 16) and aid in the formation of new subgrains.
5. Summary and conclusions
Fig. 18. Formation of new subgrains from a large subgrain originally present in an as-received NaCI specimen. The specimen was crept to e--0.34 in about 10 s at 573 K under a stress of 12.0 MPa: (a) localized migration at A, subboundary bowing at B, and pinching-off and separation of segments of the bowed boundary at C; (b) magnified view of region B shown in (a).
The results of experiments conducted to test the stability of creep substructures produced in the power law and exponential creep regions under different conditions are summarized below. (1) A stress increase from 3.0 to 3.5 MPa followed by a stress decrease from 3.5 to 3.0 MPa at 673 K resulted in the formation of cells and, in contrast with the substructures formed during the uninterrupted tests, few subgrains were observed in the stress change experiment. (2) Microstructures corresponding to the exponential creep region, and essentially consisting of an uniform distribution of dislocations and a few subboundaries, transformed to equiaxed subgrains and cells when creep was continued in the power law creep region. (3) Prior creep in the power law creep region followed by subsequent deformation in the exponential creep regime resulted in a stronger material, and the subboundaries present in the prestrained material were found to be mechanically stable at the higher stress and lower temperature.
175
(4) Subboundary migration plays an important role in the formation of new subgrains. Acknowledgments This investigation was partially supported by a faculty development grant from IBM Corporation and partly by the Lewis Research Center. References I J. E. Bird, A. K. Mukherjee and J. E. Dorn, in D. G. Brandon and A. Rosen (eds.), Quantitative Relation Between Properties and Microstructure, Israel Universities Press, Jerusalem, 1969, p. 255. 2 W. Blum and B. Reppich, Acts Metall., 17119691 959. 3 S.V. Raj, Scr. Metall.. 20(1986) 1333. 4 0 . D. Sherby and P. M. Burke, Prog. Mater. Sci., 13 (1967) 325. 5 S. Takeuchi and A. S. Argon, J. Mater. Sci., II (19761 1542. 6 W. D. Nix and B. Ilschner, in R Haasen, V. Gerold and G. Kostorz (eds.), l'roc. 5th Int. Conj. on the Strength of. Metals and Alloys, Vol. 3, Pergamon, Oxford, 19811, p. 1503. 7 C. M. Young and O. D. Sherby, J. Iron Steel Inst., London, 211 (1973) 641/. 8 A. W. Thompson, Metall. Trans. A, 8 (1977) 833. 9 S. V. Raj and G. M. Pharr, Mater. Sei. Eng., 81 119861 217. 1(1 J. E Poirier, Philos. Mag., 26 (1972) 713. 11 V. Pontikis and J. E Poirier, Philos. Mag., 32 (1975) 577. 12 J.D. Parker and B. Wilshire, Philos. Mag., 34 (1976) 485. 13 T. G. Langdon, R. B. Vastava and E Yavari, in P. Haasen, V. Gerold and G. Kostorz (eds.), Proc. 5th Int. Conf. on the Strength of Metals and Alloys, Vol. 1, Pergamon, Oxford, 1979, p. 271. 14 S. L. Robinson, P. M. Burke and O. D. Sherby, Philos. Mag., 2911974)423. 15 O. D. Sherby, R. H. Klundt and A. K. Miller, Metall. Trans. A, 8 (1977) 843. 16 A. K. Miller, S. L. Robinson and O. D. Sherby, Philos. Mag., 36 ( 197711757. 17 W. Blum, A. Absenger and R. Feilhauer, in R Haasen, V. Gerold and G. Kostorz (eds.), Proc. 5th Int. Conf. on the Strength of Metals and Alloys', Vol. 1, Pergamon, Oxford, 1979, p. 265. 18 I. Ferreira and R. G. Stang, Mater. Sci. Eng., 38 119791 169. 19 G. Eggeler and W. Blum, Philos. Mag. A, 44 ( 1981 ) 1065. 20 I. Ferreira and R. G. Stang, Acts MetalL, 31 (1983) 585. 21 M. S. Soliman, T. J. Ginter and F. A. Mohamed, Philos. Mag. A, 48(1983) 63. 22 A. Goel, T. J. Ginter and F. A. Mohamed, MetalL Trans. A, 141198312309. 23 T. J. Ginter, M. S. Soliman and F. A. Mohamed, Philos. Mag. A, 5011984) 9.
24 F. A. Mohamed, M. S. Soliman and M. S. Mostafa, l'hilos. Mag. A, 51 (1985) 559. 25 S. F. Exell and D. H. Warrington, I'hilos. Mag., 26 (1972) 1121. 26 F. Vollertsen, R. Hofbeck and W. Blum. Mater. Sci. Eng., ¢'~7(1984) Lg. 27 I). Caillard and J. L. Martin, Rev. I'hvs. Appl., 22 119871 169. 28 M. Biberger and W. Blum. in E O. Kettunen, T. K. Lepist6 and M. E. Lehtonen (eds.), Proc. 8th Int. Conf. on the Strength of Metals and Alloys, Vol. 2, Pergamon, Oxford, 1988, p. 875. 29 B. llschner and B. Reppich, l'h~:~. Status Solidi, 3 (1963) 2093. 311 R.J. Stokes, l'roc. Br. Ceram. Sot., 6 (1966) 189. 31 W. Blum and B. Ilschner, Phys. Status Solidi, 20 119671 629. 32 F. Schuh, W. Blum and B. llschner, Proc. Br. Ceram. Sot., 15(19701143. 33 J. P. Poirier, Philos. Mag., 26119721 7/11. 34 E. Fries, J. Deschamps and J. Castaing, Radiat. EJ]I, 74 (1983) 329. 35 E. M. Nadgornyi and H. P. Strunk, Phys. Status Solidi A, 104119871 193. 36 V. H. Babu and K. G. Bansigir, J. Appl. Phys., 38 11967) 908. 37 L. G. Harrison, J. A. Morrison and R. Rudham, Trans. Faraday Soc., 5411958111/6. 38 L. W. Barr, I. M. Hoodless, J. A. Morrison and R. Rudham, Trans. Faraday Soe., 56 (1960) 697. 39 L. W. Barr, J. A. Morrison and E A. Schroeder, J. AppL Phys., 30 (1965) 624. 40 M. Beniere, F. Beniere, C. R. A. Catlow, A. K. Shukla and C. N. R. Rao, J. Phys. ('hem. Solids, 38 ( 1977~ 521 41 H. J. Frost and M. F. Ashby, DeJorrnation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, Pergamon, Oxford, 1982, p. 76. 42 V. P. Gupta and R R. Strutt. Can. J. l'hys., 45 11967) 1213. 43. A. H. Clauer, B. A. Wilcox and J. R Hirth, Acta MemlL, 18119701 381. 44. T. Hasegawa, R. Hasegawa and S. Karashima, Trans. Jpn. Inst. Met.. 111197111101. 45 T. Hasegawa, S. Karashima and R. Hasegawa, MetalL Trans., 2(197111449. 46 A. Orlowi, M. Pahutov~i and J. 0adek, Philos. Mag., 25 (1972) 865. 47 W. Hi,ither and B. Reppich, Philos. Mag., 28 (1973) 363. 48 K. Ichihashi, H. Oikawa and S. Karashima, Trans. JIm. Inst. Met., 17 (1976) 408. 49 H. J. Kestenbach, T. L. da Silveira and S. N. Monteiro, Metall. Trans. A, 7119761155. 511 H. J. Kestenbach, W. Krause and T. L. da Silveira, Acta Metall., 26 (1978) 661. 51 V. K. Sikka, H. Nahm and J. Moteff, Mater. Sci. Eng., 20 11975155. 52 T. Hasegawa, Y. Ikeuchi and S. Karashima, Met. Sci. J., 6 (I 972) 78.
161
On the Stability of the Creep Substructure in NaCI Single Crystals* S. V. RAJ
Lewis Research Center, National Aeronautics and Space Administration, MS 49-1, 21000 Brookpark Road, Cleveland, OH 44135 (U.S.A.)
G. M. PHARR
Department of Materials Science, Rice University, P.O. Box 1892, Houston, TX 77251 (U.S.A.)
J. D. WH1TTENBERGER
Lewis Research ('enter, National Aeronautics and Space Administration, 21000 Brookpark Road, Cleveland, OH 44135 (U.S.A.) (Received November 25, 19881
Abstract
Microstructural observations were conducted on NaCl single crystals after creep. The microstructure after a stress increase followed by a stress decrease consisted primarily of cells; no significant number of subgrains were observed although they were present in the microstructures produced during uninterrupted tests. Prestraining in the exponential creep regime produced an uniform distribution oJ dislocations and a few subboundaries which transformed to equiaxed subgrains when tested in the power law creep region. This substructure was similar to that observed in an as-received specimen deformed to an equivalent strain. Prior creep in the power law creep region produced equiaxed subgrains whose boundaries were found to be mechanically stable when the specimen was retested in the exponential creep region. The role of subboundary migration in the formation of new subgrains is discussed. 1. Introduction
At intermediate values of normalized stress o/G, the steady state creep rate g is usually given by [1]
g = A D ° G b ( ° ] " exp Qc) -kT kG/ -RT
(11
mann's constant, T is the absolute temperature, o is the applied stress, Qc is the activation energy for creep, R is the universal gas constant, and A and n are constants. Typically, n -- 4-5 for a large number of materials [2, 3] exhibiting metal-type or class M behavior. At high stresses, the power law relation given by eqn. (11 breaks down, and the creep rate exhibits an exponential dependence on normalized stress over a large range of stresses and temperatures as
where A~ and B are constants. Alternatively, if creep data are represented by a power law relation, then n increases monotonically with a~ T [2] to values of n "> 4. It is now generally accepted that power law creep is controlled by the rate of climb of edge dislocations with Qc "~ Q1, where QI is the activation energy for lattice diffusion [1, 4-6]. Dislocation climb in this deformation regime results in the formation of subgrains, where the subgrain size d~ is related to the applied stress through [1, 5, 7-9]
=K
(s/
where D 0 is a frequency factor, G is the shear
modulus, b is the Burgers vector, k is Boltz*Paper presented at the 2nd International Conference on Low-Energy Dislocation Structures, Charlottesville, VA, August 13-17, 1989. 0921-5093/89/$3.50
where m and K are constants. It was shown in an earlier publication [9] that, although several combinations of m and K can be found in the literature, the values m = 1 and K = 23 generally lead © Elsevier Sequoia/Printed in The Netherlands
162
to a good representation of experimental data. )X similar relation has been suggested for the stress dependence of the cell size with m = 2 [7, 8]. A question of fundamental importance that has been the subject of some discussion in recent years is related to the applicability of eqn. (3) to situations involving stress reductions, where it is not clear whether the subgrain size corresponding to the new reduced stress is smaller [10-13] or equal [14-24] to that predicted by the equation. This topic has an important bearing on the role of subboundary migration during creep [19, 21-28]. Microstructural observations after a stress reduction essentially deal with the instability of the original subgrains produced during creep at the higher stress; hence, the stress and temperature conditions chosen generally correspond to the power law creep regime where welldeveloped subgrains form during deformation. While these stress reduction experiments deal with the specific question of subgrain coarsening after a stress decrease, they do not address the problem of the stability of other types of substructure (e.g. cells or forest dislocations), initially formed under one combination of stress and temperature, under a new set of creep conditions. Essentially, these experiments can be conducted by producing the initial microstructure in the exponential creep region and then examining its stability under power law creep conditions. Conversely, the stability of a subgrain microstructure, initially produced under power law creep conditions, can be investigated under stress and temperature conditions corresponding to the exponential creep region. Both these experiments on prestrained microstructures can provide useful information on their strengthening effects and their stability, while examining the universality of eqn. (3) under a variety of conditions. A question related to the latter point can be asked: how do new subgrains form during creep when the undeformed material contains large subgrains? New results are presented in this paper which address these points. The present paper is divided into several parts. First, the qualitative and quantitative characteristics of substructures formed in the power law and the exponential creep regions are examined. Second, the results of special experiments, which address the question of microstructural stability, are discussed. Third, the role of subboundary migration in the formation of new subgrains is examined. Single-crystal sodium chloride (NaC1)
was chosen as the model material for study in this investigation for several reasons: (1) to eliminate the complicating effects of grain boundaries and alloying elements, which are generally associated with polycrystalline materials and solid solution alloys respectively; (2) the creep behavior of this material is well documented [4, 10, 14, 19, 29-35]; (3) substructural observations can be made on this material using relatively simple etch pit techniques for microstructural characterization.
2. Experimental details Creep specimens with approximate dimensions of 7 mm x 5 mm x 5 mm were cleaved from 1 in cubes of NaC1 single crystals oriented in the (100) direction. These crystals, which were procured from Harshaw-Filtrol, Inc., had impurity contents of 19 ppm Ca, 15 ppm Fe and 4 ppm Mg. Constant-stress compression creep tests were conducted in a nitrogen atmosphere using a computer-controlled lever arm machine, which enabled the simultaneous monitoring of strain, temperature and load during the course of the test. The accuracy of load control was better than 1 N, while the strain and temperature measurements were accurate to 10 -5 and 1 K respectively. Prior to testing, the specimen was maintained at the test temperature for at least 2 h. The stress axis was parallel to the (001) orientation of the crystal and, typically, the specimens were deformed in the temperature range 373-1023 K to the desired value of strain. After deformation, the specimens were cooled under load in a blast of compressed air to preserve the creep microstructure. Specimens were prepared for microstructural examination by initially lapping them on a damp cloth clamped to a static polishing wheel using a 90% ethanol-10% water polishing solution. The lapping was continued until sufficient material had been removed to ensure that the observed microstructure was representative of the bulk. Next, the damaged layers produced by the lapping technique were removed by a two-stage chemical polishing procedure consisting of an initial 5-15 s rinse in the ethanol-water solution followed by an additional rinse (less than 5 s) in deionized water. The polished specimens were etched by immersion in a solution of 23 ml of ethanol, 2 ml of deionized water and 25 mg of CdCI 2 [36] for times varying between 5 and 35 s.
163 The etching times were found to be extremely sensitive to the deformation histories of the specimens with shorter times required for those tested at low temperatures and high stresses. After etching, the specimens were rinsed in propyl alcohol and dried in a jet of Freon gas. Almost all microstructural observations were made on sections perpendicular to the stress axis and represent the {001} planes except where indicated. The dislocation density and the subgrain size of the asreceived material were about 10 H~m 2 and 1500 /xm respectively.
3. Substructural characterization in the power law and exponential creep regimes Figures l(a) and l(b) show the variation in the creep rate with strain e at 973 K and 473 K respectively, for several stresses between 0.60 and 18.0 MPa. As shown in Fig. l(a), genuine steady state is observed when e >/0.2 under creep conditions of T = 9 7 3 K and (7=0.60 MPa (o/G=7.5x10 5). True steady state creep behavior was usually observed for T> 873 K and o/G
the creep rate at e = 0.2 and Dc~- is the intrinsic diffusion coefficient of chlorine ions in NaCI. The temperature dependence of Dc]- was determined by replotting diffusion data obtained from several sources [37-40] against the inverse of the absolute temperature; a linear regression line through these data gave the following relation:
I
I
G = 1.81 × 1 0 4 - 10.23T
NaCl
10-3
108
<001>
I I lilqi I I NaCl _
0.60 MPa (a)
10-6 10-1
'S
.w
I
I
I
I
I
I
[
100
.Icl
-
10-3
X
~"
~
18.0 MPa
- -
T JOOqJ>3K - -
[7
473
A
573 673
0
773
? 0
873 973
I
i
1 1
10-12
10-6
" ~
8.0
l
MPa
lO-16
10-7 10-8
ii
5 . 0 ~
10-4 10-5
I ' l ll'l I
x I m I
-- o 11023 __ 1.0
10-8
Ilqili l
%
( $98-
• w 10-q
10-2
(5)
I
E-0.2 T (K) 373
104
10-5
(4)
)
(MPa)
i lillllI I ililill I
<001>
_
T = 973 K
10-4
I
where eqn. (5) represents a reformatted expression originally used by Frost and Ashby [41]. As shown in Fig. 2, the high temperature and low stress data can be represented by a power law relation with a stress exponent of about 5, while at low temperatures and high stresses the normalized creep rate increases exponentially with normalized stress. The transition from the power law to the exponential region first occurs at a critical value of normalized stress (o/G)pL. B of a b o u t 3 x l 0 ~.
I
I
2s
(where the activation energy is expressed in kJ mol- 1). The temperature dependence of the shear modulus for NaCI was calculated from
1012
10-2
230 / -~/(m
Dc, = 8 . 0 x l 0 - 2 e x p
10-6 0
(~>
I
0,1
I
0.2
I
0.3 E
I
O.q
I
0,5
l ilihhl 10-5
i ilihhl
l ilihhl
lO-q
10-3
l ilihhl 10-2
l ilihh 10-1
O/O 0.6
Fig. 1. Plot of strain rate g against creep strain e for NaCI single crystals deformed at (a) 973 K and (b) 473 K.
Fig. 2. D o u b l e - l o g a r i t h m i c p l o t o f gkTtDci-Gb vs. (JiG f o r NaCI single crystals deformed to a true strain of about 0.20. The deviation from a power law relation with a slope of about fivefirst occurs at (o/G)pLB= 3 × 10 4.
164
Fig. 3. Creep microstructures in NaCI single crystals at normalized stresses o/G of (a) 7.5 x 10 5, (b) 2.2 × 10 -4, (c) 4.0 × 10 4 and (d) 1.4 × 10- 3: C, cell; P, primary subboundary; S, secondary subboundary.
Details of the effect of stress, temperature and strain on the creep microstructure will be published elsewhere, and only a brief description is provided here. Figure 3 shows examples of typical microstructures formed at different values of normalized stress. Large equiaxed primary subgrains P, subdivided by a network of secondary subboundaries S and cells C, were observed under steady state conditions (Fig. 3(a)). The primary subboundaries, which were narrow and well defined, could not be resolved into indi-
vidual etch pits at any magnification when viewed under an optical microscope. In contrast, the cell boundaries were broader and more diffuse than the subboundaries and could be resolved into individual etch pits at sufficiently high magnifications, and the cell boundary misorientation angle was estimated to be less than 0.1 °. The morphology of the secondary subboundaries lay somewhere between those two extremes as they consisted of distinct and overlapping etch pits which could not be individually resolved.
165
In comparison with those which formed during steady state creep, the cell boundaries were wider and the number of secondary subboundaries fewer under non-steady state conditions. This was true even for stress and temperature conditions corresponding to the power law creep region in Fig. 2. An example of this is shown in Fig. 3(b) for a specimen deformed at a value of o/G = 2.2 x 10 4, where it is seen that, while the primary subgrains are still equiaxed, the cell boundaries within many of them (e.g. A in Fig. 3(b)) are extremely coarse in contrast with those shown in Fig. 3(a); however, narrow cell boundaries and secondary subboundaries are evident within some of the primary subgrains (e.g. B in Fig. 3(b)). It was also observed that the number of secondary subboundaries were large in those primary subgrains which contained a larger proportion of narrow walled cells (e.g. compare regions A and B in Fig. 3(b)). It is clear from these observations (Figs. 3(a) and 3(b)) that the steady state microstructure involves a refinement of the cell boundaries and the formation of secondary subboundaries. It is important to note that the descriptions of the steady state and the nonsteady state microstructures outlined here were found to be valid in most, but not all, instances. There was an increase in the aspect ratios of many of the primary subgrains at or just above (a/G)PLB (Fig. 3(C)). Typically, the long boundaries of these subgrains were oriented along-the (110) direction so that the subgrains collectively presented a ladder-like morphology. Similar creep microstructures of elongated and equiaxed subgrains, often distributed in alternate bands of narrow and wide subgrains, have been observed in other materials [5, 42-50]. Significantly, there was a great difference in the internal microstructures of the elongated and the equiaxed subgrains as is evident through a comparison of regions A and B in Fig. 3(c). The elongated subgrains had a higher dislocation density, larger number of cells with coarse boundaries and fewer secondary subboundaries than their equiaxed neighbors. At very high values of normalized stress, corresponding to exponential creep (Fig. 2), the microstructure consisted primarily of an uniform distribution of etch pits and a few slip traces (Fig. 3(d)); however, subgrains were observed in the exponential creep region above 473 K when e>0.2. Figure 4 shows the variation in the subgrain and the cell size dc normalized by the Burgers
106
- I I111'IW I I 'I~
I
Illqlj
I
'1'111-
1.0
~
cms7
105
~ SUBGRAINS--
0"45~ ~.0 ~ ~
%
~
\
NaCl
(001) dc/b
ds/b
104 -- 473 -- 573
[] Z~
0 A
673
<~
@
873
'~
0 V
973 598- i
@
Q
--
T (K)
_-
773
{1
x
iI
0
823 } 103 i0-6
%
I
i lJlild
10-5
, l,l,hI
10-4
I tllHd I i IJlih 10-3
10-2
OIG
Fig. 4. Variations in single crystals.
d,./b and d,/b against o/G for NaCl
vector (b = 3.99 x 10 u~ m [41]), with the normalized stress, where the data have been obtained at different temperatures and at various values of strain. The normalized value of the power law breakdown stress (o/G)PLB is also indicated in the figure. It is evident that dJb decreases with an increase in the normalized stress in accordance with eqn. (3) with m-~ 1.1 and K = 15. These values of m and K fall within the range of values reported earlier for other ionic crystals [9]. Similarly, dc/b decreases with increasing values of a/G with the magnitudes of m and K being about 0.45 and 930 respectively. These results suggest that the cell size exhibits a weaker dependence on the applied stress than the subgrain size and, while these observations are in agreement with those reported by Goel et al. [22] on an A1-Zn alloy, they do not agree with other results on iron-base alloys [7, 8, 51], where it was found that the stress dependence of the cell size was better represented by m = 2 and K = 0.2. 4. Microstructural stability Although the microstructural observations reported in Section 2 provide important information on the qualitative and quantitative aspects of
166 10-2
10
i
I
I
i
I NaCI <001> = 673 K
3 ~
10-td
/ ~ 3 . 5 f~a '= .w
10-5
10-6
10 - 7
,0-8!
0 - 3 0
I
0.1
-
I 0.2
-
3 5
I
0.3 E
-
-
I
O.q
3 0 MPa
I 0.5
0.6
Fig. 5. Comparison of g-e plots for NaCI single crystals obtained at 673 K for uninterrupted and stress change tests: o~ = 3.5 MPa; 02 = 3.0 MPa.
the creep substructure, they do not address the problem of microstructural stability when the testing conditions are changed. Investigations on microstructural stability generally involve producing an initial microstructure under one set of experimental conditions which is then subjected to a different set of deformation conditions to understand how it transforms to the final substructure. The results of these experiments performed on NaC1 are discussed below.
4.1. Effect of stress reduction Figure 5 compares the creep curves obtained in two uninterrupted tests conducted at 673 K, and under stresses of 3.0 MPa and 3.5 MPa (o/G =2.7 x ] 0 - 4 and 3.1 x 1 0 - 4 respectively), with that obtained in a stress change experiment, where the stress was first increased from 3.0 to 3.5 MPa and later reduced back to the original value of stress. The creep curves obtained in the uninterrupted tests exhibit a prolonged primary region which tends towards steady state behavior. The increase in stress from 3.0 to 3.5 MPa results in an initial increase in the creep rate by about an order of magnitude above that at the new value of stress. However, the creep rate after the stress increase falls rapidly from this maximum value to values which are slightly below those for the uninterrupted test. On reducing the stress from 3.5 to 3.0 MPa, the initial creep rate after the stress reduction is lower than that at 3.0 MPa but rises rapidly to values which are close to those obtained in the single test. The final microstructures formed in the uninterrupted tests consisted of equiaxed and elongated subgrains subdivided by cells (Fig. 6). The average values of the cell and subgrain size
Fig. 6. Substructures produced in NaCI single crystals deformed to e = 0 . 4 7 at 673 K in an uninterrupted test: (a) o 1 = 3.5 MPa ( o J G = 3.1 x 10-4); (b) 02 = 3.0 MPa (a2/G =2.7×10-4).
formed under these conditions are tabulated in Table l. The effect of the stress change experiment described above resulted in a microstructure (Fig. 7) which is vastly different from those obtained under single-stress conditions (Fig. 6). In essence, the two stress changes resulted in a microstructure which was essentially devoid of any subgrains, except at the edges of the specimen* but consisted of an almost uniform distribution of cells some of which were oriented along *Table 1 also shows the average size of the subgrains formed at the edges of the specimen after the stress reduction, but no special significance can be attributed to the fact that this value is smaller than that obtained at a single stress of 3.0 MPa since only a few measurements could be made.
167
TABLE 1 Comparison of the average sizes of cells and subgrains formed at 673 K after a stress reduction with those produced during creep under a single stress Material condition
Test parameters
As received
7=673 K 13.9_+ 1.5 o = 3.0 M P a e = 0.46
70.0_+6.5
As received
10.9_+1.0 7'= 6 7 3 K o = 3.5 Mpa
36.7_+4.5
,," =
Stress change from 3.(t to 3.5 to 3.0 M P a
dc (pm)
d, (/~m)
0.46
T=673 K o = 3.0 M P a e = 0.08 ~
8.3_+0.9
55.8_+10.5 ~
T h e error limits were determined at the 95°/,, confidence level.
"Strain after the stress reduction. bThese values represent the average sizes of subgrains present near the edges of the specimen.
the (110) direction (Figs. 7(a) and 7(b)). Evidence that these microstructural features are cells, and not subgrains, is clearly demonstrated in Fig. 7(c), where the individual etch pits in the cell boundaries are visible at a higher magnification. The cellular microstructure shown in Fig. 7 is somewhat similar to that present within the subgrains in Fig. 6(b), and the average cell size formed after the stress reduction is in agreement with those produced in the uninterrupted test to within a factor of 2 (Table 1 ), which is within the range of experimental scatter usually associated with such measurements. As the creep rates after the stress reduction are similar to those observed in the uninterrupted test at 3.0 MPa (Fig. 5), it can be concluded that the cellular, and not the subgrain, microstructure
ol (010)
Fig. 7. Microstructures of an NaCI specimen deformed to e = 0 . 4 8 at 6 7 3 K in stress change experiment: (a) a uniform distribution of cells; (b) a magnified view of region A in (a); (c) cell boundaries present in region B in (b).
168
determines the creep rate at 673 K. The similarities in the cell sizes formed in the uninterrupted and the stress change tests (Table 1), however, suggest that the processes occurring in the cell boundaries are important in determining creep behavior. This suggestion is consistent with the fact that steady state creep behavior was generally observed in the g-e plots when the cell boundaries had become relatively narrow (Fig. 3(a)). There has been a considerable amount of discussion in the literature [10-24] regarding the stability of subgrains after a stress reduction. It was concluded from experiments of NaCI [10], AgCI [11], copper [12] and A1-5wt.%Zn [13] that the subgrains formed at the higher stress are relatively stable after a stress reduction and do not increase to a size consistent with the reduced stress in accordance with eqn. (3). However, Miller et al. [16] criticized some of these observations [11, 12] and pointed out that the creep strain after the stress reduction was insufficient to allow any substantial subgrain coarsening to occur for steady state values to be attained. Although Langdon et al. [13] addressed this criticism by measuring the subgrain size after steady state creep was re-established (i.e. after a shear strain 7 of about 0.09 following the stress reduction), their observations do not agree with other results on aluminum [18, 20, 21, 23, 24], AI-5wt.%Zn [22] and NaCI [19]. Soliman and coworkers [21-23] attempted to account for this discrepancy by suggesting that Langdon et al. [13] may have erroneously measured the cell size rather than the subgrain size, since the evidence on aluminum [18, 20, 21, 23, 24], AI-5wt.%Zn [22] and NaC1 [19] clearly demonstrated that substantial subgrain coarsening occurs after a stress reduction with a corresponding increase in the creep rate. It was observed that this subgrain coarsening involved the dissolution of some subboundaries and the migration of others [19, 21-24]. The results pesented in Figs. 5-7 clearly indicate that the cellular microstructure is essentially stable even after a strain e of about 0.08 after the stress reduction. The criticisms applied to previous investigations [11-13] cannot be applied to the present observations since sufficient strain was allowed after the stress reduction and the microstructural observations reported here are unambiguous. However, there is an important difference between the present results and those reported in the other investigations [10-24]. The
microstructure formed after the stress change is essentially devoid of subgrains and therefore does not resemble those formed in the uninterrupted tests (Fig. 6) despite the fact that the creep rates after the stress increase and the stress decrease are comparable with those observed in the uninterrupted test (Fig. 5). The general absence of subgrains in the microstructure formed after the stress change experiment (Fig. 7), except at the edges of the specimen, is especially puzzling since they are present in those formed during the uninterrupted tests conducted at 3.5 MPa (Fig. 6(a)) and 3.0 MPa (Fig. 6(b)). Table 2 compares the experimental conditions used in the present study with those employed in other investigations on subgrain stability [13, 18-24], where the creep strain e R after the stress reduction was sufficiently large to permit the new creep rate to be comparable with that at the reduced stress. The information tabulated in Table 2 includes material composition, the test procedure, where al and a2 are the stresses before and after stress reduction respectively, the test temperature and its fraction eR of the absolute melting point Tm and general information on the stability of the initial substructure. It is noted that the values of T, T/Tm, a l / O 2 and e R shown in Table 2 represent the range of experimental conditions, and e R was derived from values of shear strain reported in some of the original investigations [13, 21-24] by using the relation ~eR = 7/3. An examination of Table 2 shows that the final substructure was attained in all cases when eR> 0.03. This condition was easily fulfilled in the present investigation so that the final microstructure after the stress reduction is expected to contain well-developed subgrains of an average size consistent with either that at al = 3.5 MPa or as = 3.0 MPa. Yet, as shown in Fig. 7, this was not the case, and instead few subgrains were observed after the stress reduction. In recent experiments on aluminum [23, 24], it was observed that the cellular microstructure was fairly stable below 0.65 Tm and for Ol/O2 < 1.2. As shown in Table 2, the magnitudes of T/Tm = 0.63 and a~/o 2 ~-1.2 used in the present investigation are in reasonable agreement with the testing conditions on aluminum [23, 24] for which cell stability has been reported. Ginter et al. [23] suggested that the presence of cells within a subgrain may interfere with subboundary migration and dissolution but it is unlikely that this reasoning
169 TABLE 2 Tabulation of the range of experimental conditions used in several investigations on subgrain coarsening after a stress reduction
Material
lmpurio' content
Test T procedure a (K)
T/Tm
Ol/O" 2
AI
99.999 (wt.%)
o~ to o:
573
0.61
1.80-4.35 0.08-0.12 Subgrain coarsening
AI
99.99 (wt.%)
o~ to a 2
610-923
0.65-0.99 1.40-6.80 0.04-0.06 Subgrain coarsening
Soliman etal. {21]
99.99(wt.%)Al
a t to 02
573-593
0.61-0.64 1.20-2.00 0.07-0.10 Stable cells; subgrain coarsening
Ginter etal.[23]
99.98(wt.%)Al
a~ to 02
573-923
0.61-0.99 1.05-4.00 0.07-0.13 Cells stable atlow Mohamed etal. values of Tand [24] all 02; subgrain coarsening
AI-5(wt.%)Zn
a t to 02
573
0.63
A1-5(wt.%)Zn
o mto o 2
650-893
0.70-0.99 1.30-4.00 0.05-0.07 Subgrain coarsening
8R b
4.25
0.03
Remarks
No subgrain coarsening
ReJbrence Ferreira and Stang [18, 20]
Langdon et al. [13] Goel etal.[22]
NaC1 (100)
3 ppm Ca'-+
a~ to a 2
923-1033 0.86-0.96 2.40
0.065
Subgrain coarsening
Eggeler and Blum [ 19]
NaCI (001}
19 ppm Ca 2+ 4 ppm Mg2 + 15 ppm
o, to a~ to a,
673
0.08
Cells; subgrains absent
Present invesligation
0.63
1.15
F e 3+ a o I > 0 2.
beRwas determined from the shear strain values reported in some of the original investigations [13, 21-24] by using a conversion factor of 3. a p p l i e s to t h e p r e s e n t stress c h a n g e results since n o s u b g r a i n s w e r e o b s e r v e d . P e r h a p s , t h e stress i n c r e a s e p r i o r to t h e stress d e c r e a s e m a y h a v e i n f l u e n c e d the final m i c r o s t r u c t u r e b u t f u r t h e r e x p e r i m e n t a t i o n m u s t b e c o n d u c t e d to c o n f i r m this.
4.2. Effect o f prior deformation on creep substructure Two types of experiments were conducted on NaC1 single crystals in o r d e r to s t u d y t h e effect o f prior deformation on the creep behavior and the final m i c r o s t r u c t u r e . In t h e first series of e x p e r i m e n t s , w h i c h was d e s i g n e d to test t h e u n i v e r s a l i t y o f eqn. (3), a s p e c i m e n was d e f o r m e d to a true s t r a i n ~ o f a b o u t 0.20 at 4 7 3 K a n d 10.0 M P a ( a / G = 7 . 5 x 10-4), w h i c h c o r r e s p o n d s to n o r m a l i z e d values o f c r e e p rate a n d stress well within the e x p o n e n t i a l c r e e p r e g i o n (Fig. 2). T h e specim e n was c l e a v e d p a r a l l e l to t h e stress axis, a n d both halves were polished and etched. As shown in Fig. 8, t h e s u b s t r u c t u r e after c r e e p u n d e r t h e s e c o n d i t i o n s c o n s i s t e d o f an u n i f o r m d i s t r i b u t i o n o f e t c h pits a n d a few i l l - f o r m e d s u b b o u n d a r i e s . O n e half o f t h e c l e a v e d s p e c i m e n was t h e n d e f o r m e d
a
-
'ltm lalm
Fig. 8. Microstructure of an NaC1 specimen deformed to e=0.12 at 473K under a stress of 10.0 MPa (o/G= 7.5 x 10 4). f u r t h e r to a s t r a i n e of a b o u t 0.43 at 8 7 3 K u n d e r a stress o f 1.0 M P a (i.e. o / G = 1.0 x 10 -4) c o r r e s p o n d i n g to t h e p o w e r law c r e e p r e g i o n in Fig. 2, and the creep curve obtained under these conditions is s h o w n in Fig. 9 a l o n g with that for an asr e c e i v e d s p e c i m e n . In o r d e r to a s c e r t a i n t h e effect of static r e c o v e r y o n t h e initial p r e s t r a i n e d m i c r o -
170
1°-3 ~\
I
I
I
I
I
Io41-- ~
I
~
~-AS-RECEIVED
I ~.-_~./ "~
~
10-6 ~
io71
0
INa_~J I --
II
1"010]
T = 873 K o = 1.0 MPa
ORE-STRAINED-"
'
-
I
0.1
-
I
0.2
l
0.3
I
0.4 E
I
0.5
I
0.6
I
0.7
0,8
Fig. 9. Comparison of the g-e plots for as-received and prestrained NaCI specimens at 873 K under a stress of 1.0 MPa. The prestrained specimen was initially crept to e = 0,2 at 473 K under a stress of 10.0 MPa.
structure, the other half of the cleaved specimen was also placed in the creep machine close to the test specimen in such a manner that there was no applied stress on it. The initial creep rate of the prestrained specimen was less than 10- 8 s- l (i. e. below the detection limit of the strain-measuring equipment), and measurable creep was detectable only after a period of 1 h. A linear extrapolation of the data lying in the exponential creep region in Fig. 2 to o / G = 1.0x 10 - 4 suggests that the creep rate corresponding to the microstructure shown in Fig. 8 should be of the order of 10-13 s-1, which would account for the fact that the initial creep rates were immeasurably small in the predeformed specimen. Following this initial period of immeasurable creep, the creep rate rises by several orders of magnitudes to about 2 x 10 -5 s-1 during the first few per cent strain and then gradually decreases to values close to that observed for the as-received specimen when e > 0.3 (Fig. 9). The microstructure of the prestrained specimen after subsequent creep to a true strain of about 0.43 is shown in Fig. 10, where it is seen that well-developed primary subgrains containing cells and a few secondary subboundaries have formed from the initial substructure shown in Fig. 8. This microstructure is similar to that observed on an as-received specimen deformed to an almost identical value of strain (Fig. 11 ). The cell and subgrain sizes of the prestrained and the asreceived materials are also in agreement to within a factor of 2 (Table 3), which is the normal level of experimental scatter associated with these measurements [9]. These results clearly demonstrate the uniqueness of eqn. (3) in determining
Fig. 10. Microstructure of the prestrained NaCI specimen shown in Fig. 8 after a creep strain of about 0.43 at 873 K under a stress of 1.0 MPa (o/G = 1.l × 10-4).
Fig. 11. Microstructure of an as-received NaC1 specimen deformed to a true strain of about 0.4 at 873 K under a stress of 1.0 MPa (o/G = 1.1 x 10-4).
both the cell and the subgrain sizes under these conditions. Figure 12 shows the effect of static recovery on the initial predeformed microstructure (Fig.
171 TABLE 3 Comparison of the average sizes of cells and subgrains formed at 873 K under a stress of 1.0 MPa in prestrained and as-received specimens
Material condition
Test parameters
dc (/am)
d~ (/am)
As received
7"= 873 K 19.5 +_ 1.8 o = 1.0 MPa e=0.40
193.5 _+30.5
Prior creep to e = 0.2 at T= 473 K and o = 10.0 MPa
19.1_+2.1 T=873 K o = 1.0 Mpa e = 0.43
126.3+_35.3
The error limits were determined at the 95% confidence level.
Fig. 13. Microstructure of an NaCI specimen deformed to e = 0.2 at 923 K under a stress of 0.65 MPa.
Imhl ~q~ Fig. 12. Effect of static annealing at 873 K on the prestrained microstructure (o = 0 MPa).
8). Although the extent of recovery due to this annealing treatment is not as extensive as that during deformation, it is not negligible and, as shown in Fig. 12, a few large subgrains, subdivided by cells, have formed. A comparison of Figs. 10 and 12 clearly demonstrates that stressassisted recovery is much faster than static recovery. The sigmoidal primary creep behavior (Fig. 9) observed in the prestrained material is analogous to similar behavior reported for Cu-16at.% AI [52], where it was concluded that the initial rise in the creep rate was associated with an increase in the density of mobile dislocations while the subsequent fall in the creep rate resulted from an increase in the long-range internal stress due to newly formed subboundaries as well as a decrease in the mobile dislocation density. Therefore, it follows that the microstructure produced after prior creep at T = 473 K and o = 10.0 MPa (Fig. 8) results in a low mobile dislocation density, so that the initial creep rates are immeasurably
small when the specimen is retested at 7`= 873 K and o = 1.0 MPa (Fig. 9). The initial increase in t h . creep rate observed for e ~<0.05 (Fig. 9) can be attributed to the increasing effect of recovery which results in a relative increase in the density of mobile dislocations. However, continued recovery would lead to an annihilation of excess dislocations and the formation of cell and subgrain boundaries, so that the long-range stresses acting on the mobile dislocations due to these boundaries increases and the creep rate begins to decrease. The second set of experiments was designed to test the possibility that the original subboundaries may break up during a stress increase. In order to address this point regarding the mechanical stability of subboundaries, a specimen was crept to a true strain of about e -~ 0.20 at 923 K under a stress of 0.65 MPa (¢y/G=7.5 × 10 5) corresponding to the power law creep regime in Fig. 2. This deformation resulted in a microstructure consisting of large equiaxed primary subgI:ains containing a network of cells (Fig. 13). The specimen was then retested at 473 K under a stress of 10.0 MPa ( a / G = 7 . 5 × 10-4), where the stress and temperature conditions correspond to the
172
'-~
'~ •w
1°-2/
I
I
10-4 L_
~. ~
I
I
INaCl I °=
l°'°~a
~ ~ E C E I V E D
10-5_
10_6_PRE-SR I AN I E~D / ~ I o.o,
I o.08
I o.12
I
tr
0.1
I
I
0.20
0.24
0.28
Fig. 14. Comparison of g-e plots for as-received a n d prestrained NaCl specimens at 473 K under a stress of 10.0 MPa. The prestrained specimen was initially crept to e = 0.2 at 923 K under a stress of 0.65 MPa.
exponential creep region in Fig. 2. The creep curves for the prestrained and as-received specimens are shown in Fig. 14, where it is seen that the creep rates for the predeformed specimen are smaller than those for the as-received material. After deformation to an instantaneous strain of about 0.034, an examination of one of the surfaces perpendicular to the stress axis showed evidence of slip bands traversing the original subboundaries (Sb)(Fig. 15(a)). On repolishing and re-etching the surface, it was found that the original subboundaries were still intact (Fig. 15(b)) and localized migration of the subboundaries appeared to have occurred in some areas (e.g. A in Fig. 15(b)). However, there was no evidence of any catastrophic rupture of these boundaries. Instead, the cellular microstructure, initially present within the primary subgrains (Fig. 13), was more or less replaced by an uniform distribution of etch pits, but it was not clear whether the increase in the dislocation density resulted from a dissolution of the original cell boundaries shown i n Fig. 13 into individual dislocations or by the generation of fresh dislocations from newly activated sources. Continued deformation to a strain of about 0.18 (Fig. 14) resulted in the localized migration of the original subgrain boundaries as indicated by the arrows in Fig. 16(a) and in the formation of new subgrains. It was observed that the migration of the old subboundaries was partly responsible for the nucleation of new subgrains. Other evidence in support of the role of subboundary migration in the creation of new subgrains during creep is provided in Section 3.3. In many areas of
El
Fig. 15. Creep microstructures of the prestrained NaC1 specimen shown in Fig. 13 after deformation to an instantaneous true strain of about 0.034 at 473 K under a stress of 10.0 MPa: (a) unpolished surface showing slip lines crossing a subboundary (Sb) originally formed during prior creep to e ~ 0 . 2 at 923 K under a stress of 0.65 MPa; (b) polished surface demonstrating that the original subboundaries are still mechanically intact but show evidence of localized migration in some regions (e.g. at A).
173
Fig. 17. Microstructure of an as-received NaCI specimen deformed to a strain of about 0.2 at 473 K under a stress of 10.0 MPa and with o/G = 7.5 × 10 4.
the specimen, the r a n d o m dislocation microstructure shown in Fig. 15(b) was found to have been completely replaced by new subgrains (Fig. 16(b)). T h e s e microstructures are quite different from that for an as-received specimen deformed to e-~0.2 (Fig. 17), where it is seen that the substructure consists of a mixture of long subboundaries and regions of high and low dislocation densities. However, well-formed subgrains similar to those shown in Fig. 16(b) were observed in the as-received material when e = 0.5. Therefore, the lower creep rates observed in the prestrained material (Fig. 14) can be attributed to the longrange internal stresses associated with the original and the newly f o r m e d subboundaries which effectively results in a lateral shift of the g-e plot to lower values of strain. T h r e e conclusions may be drawn f r o m the a b o v e observations. First, the presence of subboundaries in the initial microstructure can lead to significant strengthening effects. Second, the original subboundaries are mechanically stable even when the normalized stress is increased by an order of magnitude. Third, the original subboundaries play an important role in the development of the final microstructure by aiding the nucleation of new subgrains.
Fig. 16. Microstructures of the prestrained NaCI specimen shown in Fig. 13 after creep to e-~0.18 at 473 K under a stress of 10.0 MPa: (a) the original subboundaries show evidence of localized migration as indicated by the arrows; (b) new subgrains within the original subgrains.
4.3. Role of subboundary migration in the formation of new subgrains New subgrains can f o r m by several different mechanisms such as dislocation climb, cell rotation, or the bowing of a s u b b o u n d a r y during
174
migration. The latter mechanism appears to be especially important in transforming large subgrains, typically found in annealed ionic crystals, to smaller ones of an equilibrium size given by eqn. (3). An example of this is shown in Fig. 18. In this case, an annealed NaCI single crystal having an average subgrain size of about 1500 ~m was deformed to a true strain of about 0.35 at 573 K under a stress of 12.0 MPa ( o / G = 9.8 × 10 -4) in less than 10 s. Despite the short time for which the specimen was stressed, it is evident from Fig. 18(a) that the transformation to the final microstructure is essentially complete in large areas of the specimen. This transformation occurs by the migration (e.g. A in Fig. 18(a)) and bowing of the original subboundaries (e.g. B in Figs. 18(a) and 18(b)), and the subsequent pinching-off and separation of the bowed segments (e.g. C in Fig. 18(a)). For this to happen, the segment must bow beyond a critical radius R = flGb/o, where fl is a constant so that, when ds = 2 R, this process leads to a stress dependence of the subgrain size similar to that given by eqn. (3). Figure 18 once again confirms that the original subboundaries exhibit a high degree of mechanical stability as demonstrated earlier (Figs. 15 and 16) and aid in the formation of new subgrains.
5. Summary and conclusions
Fig. 18. Formation of new subgrains from a large subgrain originally present in an as-received NaCI specimen. The specimen was crept to e--0.34 in about 10 s at 573 K under a stress of 12.0 MPa: (a) localized migration at A, subboundary bowing at B, and pinching-off and separation of segments of the bowed boundary at C; (b) magnified view of region B shown in (a).
The results of experiments conducted to test the stability of creep substructures produced in the power law and exponential creep regions under different conditions are summarized below. (1) A stress increase from 3.0 to 3.5 MPa followed by a stress decrease from 3.5 to 3.0 MPa at 673 K resulted in the formation of cells and, in contrast with the substructures formed during the uninterrupted tests, few subgrains were observed in the stress change experiment. (2) Microstructures corresponding to the exponential creep region, and essentially consisting of an uniform distribution of dislocations and a few subboundaries, transformed to equiaxed subgrains and cells when creep was continued in the power law creep region. (3) Prior creep in the power law creep region followed by subsequent deformation in the exponential creep regime resulted in a stronger material, and the subboundaries present in the prestrained material were found to be mechanically stable at the higher stress and lower temperature.
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(4) Subboundary migration plays an important role in the formation of new subgrains. Acknowledgments This investigation was partially supported by a faculty development grant from IBM Corporation and partly by the Lewis Research Center. References I J. E. Bird, A. K. Mukherjee and J. E. Dorn, in D. G. Brandon and A. Rosen (eds.), Quantitative Relation Between Properties and Microstructure, Israel Universities Press, Jerusalem, 1969, p. 255. 2 W. Blum and B. Reppich, Acts Metall., 17119691 959. 3 S.V. Raj, Scr. Metall.. 20(1986) 1333. 4 0 . D. Sherby and P. M. Burke, Prog. Mater. Sci., 13 (1967) 325. 5 S. Takeuchi and A. S. Argon, J. Mater. Sci., II (19761 1542. 6 W. D. Nix and B. Ilschner, in R Haasen, V. Gerold and G. Kostorz (eds.), l'roc. 5th Int. Conj. on the Strength of. Metals and Alloys, Vol. 3, Pergamon, Oxford, 19811, p. 1503. 7 C. M. Young and O. D. Sherby, J. Iron Steel Inst., London, 211 (1973) 641/. 8 A. W. Thompson, Metall. Trans. A, 8 (1977) 833. 9 S. V. Raj and G. M. Pharr, Mater. Sei. Eng., 81 119861 217. 1(1 J. E Poirier, Philos. Mag., 26 (1972) 713. 11 V. Pontikis and J. E Poirier, Philos. Mag., 32 (1975) 577. 12 J.D. Parker and B. Wilshire, Philos. Mag., 34 (1976) 485. 13 T. G. Langdon, R. B. Vastava and E Yavari, in P. Haasen, V. Gerold and G. Kostorz (eds.), Proc. 5th Int. Conf. on the Strength of Metals and Alloys, Vol. 1, Pergamon, Oxford, 1979, p. 271. 14 S. L. Robinson, P. M. Burke and O. D. Sherby, Philos. Mag., 2911974)423. 15 O. D. Sherby, R. H. Klundt and A. K. Miller, Metall. Trans. A, 8 (1977) 843. 16 A. K. Miller, S. L. Robinson and O. D. Sherby, Philos. Mag., 36 ( 197711757. 17 W. Blum, A. Absenger and R. Feilhauer, in R Haasen, V. Gerold and G. Kostorz (eds.), Proc. 5th Int. Conf. on the Strength of Metals and Alloys', Vol. 1, Pergamon, Oxford, 1979, p. 265. 18 I. Ferreira and R. G. Stang, Mater. Sci. Eng., 38 119791 169. 19 G. Eggeler and W. Blum, Philos. Mag. A, 44 ( 1981 ) 1065. 20 I. Ferreira and R. G. Stang, Acts MetalL, 31 (1983) 585. 21 M. S. Soliman, T. J. Ginter and F. A. Mohamed, Philos. Mag. A, 48(1983) 63. 22 A. Goel, T. J. Ginter and F. A. Mohamed, MetalL Trans. A, 141198312309. 23 T. J. Ginter, M. S. Soliman and F. A. Mohamed, Philos. Mag. A, 5011984) 9.
24 F. A. Mohamed, M. S. Soliman and M. S. Mostafa, l'hilos. Mag. A, 51 (1985) 559. 25 S. F. Exell and D. H. Warrington, I'hilos. Mag., 26 (1972) 1121. 26 F. Vollertsen, R. Hofbeck and W. Blum. Mater. Sci. Eng., ¢'~7(1984) Lg. 27 I). Caillard and J. L. Martin, Rev. I'hvs. Appl., 22 119871 169. 28 M. Biberger and W. Blum. in E O. Kettunen, T. K. Lepist6 and M. E. Lehtonen (eds.), Proc. 8th Int. Conf. on the Strength of Metals and Alloys, Vol. 2, Pergamon, Oxford, 1988, p. 875. 29 B. llschner and B. Reppich, l'h~:~. Status Solidi, 3 (1963) 2093. 311 R.J. Stokes, l'roc. Br. Ceram. Sot., 6 (1966) 189. 31 W. Blum and B. Ilschner, Phys. Status Solidi, 20 119671 629. 32 F. Schuh, W. Blum and B. llschner, Proc. Br. Ceram. Sot., 15(19701143. 33 J. P. Poirier, Philos. Mag., 26119721 7/11. 34 E. Fries, J. Deschamps and J. Castaing, Radiat. EJ]I, 74 (1983) 329. 35 E. M. Nadgornyi and H. P. Strunk, Phys. Status Solidi A, 104119871 193. 36 V. H. Babu and K. G. Bansigir, J. Appl. Phys., 38 11967) 908. 37 L. G. Harrison, J. A. Morrison and R. Rudham, Trans. Faraday Soc., 5411958111/6. 38 L. W. Barr, I. M. Hoodless, J. A. Morrison and R. Rudham, Trans. Faraday Soe., 56 (1960) 697. 39 L. W. Barr, J. A. Morrison and E A. Schroeder, J. AppL Phys., 30 (1965) 624. 40 M. Beniere, F. Beniere, C. R. A. Catlow, A. K. Shukla and C. N. R. Rao, J. Phys. ('hem. Solids, 38 ( 1977~ 521 41 H. J. Frost and M. F. Ashby, DeJorrnation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, Pergamon, Oxford, 1982, p. 76. 42 V. P. Gupta and R R. Strutt. Can. J. l'hys., 45 11967) 1213. 43. A. H. Clauer, B. A. Wilcox and J. R Hirth, Acta MemlL, 18119701 381. 44. T. Hasegawa, R. Hasegawa and S. Karashima, Trans. Jpn. Inst. Met.. 111197111101. 45 T. Hasegawa, S. Karashima and R. Hasegawa, MetalL Trans., 2(197111449. 46 A. Orlowi, M. Pahutov~i and J. 0adek, Philos. Mag., 25 (1972) 865. 47 W. Hi,ither and B. Reppich, Philos. Mag., 28 (1973) 363. 48 K. Ichihashi, H. Oikawa and S. Karashima, Trans. JIm. Inst. Met., 17 (1976) 408. 49 H. J. Kestenbach, T. L. da Silveira and S. N. Monteiro, Metall. Trans. A, 7119761155. 511 H. J. Kestenbach, W. Krause and T. L. da Silveira, Acta Metall., 26 (1978) 661. 51 V. K. Sikka, H. Nahm and J. Moteff, Mater. Sci. Eng., 20 11975155. 52 T. Hasegawa, Y. Ikeuchi and S. Karashima, Met. Sci. J., 6 (I 972) 78.