Effect of stress reductions on the stress exponent and subgrain size in an Al-Zn alloy

Effect of Stress Reductions on the Stress Exponent and Subgrain Size in an Al-Zn Alloy

ANURAG GOEL, TIMOTHY J. GINTER, and FARGHALLI A. MOHAMED

Stress change and uninterrupted tests were performed on an AI-5 wt pct Zn alloy over the high temperature range (0.7 to 0.99 T~,, where T,, is the melting point) and at a normalized stress range extending from 10 -s to 2 • 10 -4. Two techniques, etch-pit (EP) and transmission electron microscopy (TEM), were used to examine dislocation substructure developed during creep. The results of stress reduction tests, when compared with those of uninterrupted tests, lead to two findings: (a) there is no difference between the stress exponents determined from stress reduction tests and uninterrupted tests, and (b) after a stress reduction the subgrain size, measured by both EP and TEM, coarsens, reaching the steady-state value determined in an uninterrupted test at the reduced stress. TEM micrographs show that subgrain coarsening during the transient period after a stress reduction involves substructural activities such as subgrain boundary dissolution. Also, TEM examination of the interiors of subgrains occasionally reveals the presence of a cellular substructure which resembles very small subgrains. The characteristics of this cellular substructure are discussed with reference to recent conflicting evidence concerning the ability of the subgrain size to coarsen after a stress reduction.

I. INTRODUCTION

A s a result of many investigations on the high-temperature creep of pure metals and solid-solution alloys,~-5 two re- lations are well established. The first relation describes the dependence of the steady-state creep rate, 5', on the applied stress, r, at large grain sizes and intermediate stresses (10 -5 G < ~- < 10 -3 G, where G is the shear modulus) and can be expressed as h2'3

= B O - / C ) o I f ]

where B is a function of temperature and n is the stress exponent; for pure metals and alloys of the metal class,* n is close to 5 whereas for alloys of the alloy class,* n is about

*"Alloy" class and "metal" class correspond to Sherby and Burke's 4 "class I" and "class II", respectively.

3. The second relation describes the dependence of the average subgrain size, 6, measured during the steady-state creep of metals and alloys of the metal class on the applied stress and is represented b y ~'z

~/b = 10(~-/C)-' [2]

where b is the Burgers vector. Equation [2] was originally suggested by Bird et a l . ~ and was based on an analysis of the data of a number of materials, with the exception of AI whose polarized light optical data gave subgrain sizes larger than those predicted from the equation. However, a very recent investigation on A1, 6 using both TEM and EP, demonstrates that optical techniques tend to overestimate subgrain size and that the data, when taken from representative TEM measurements, are consistent with Eq. [2].

Equations [1] and [2] imply that under steady-state creep conditions both 3; and 6 are not dependent on the loading

ANURAG GOEL, formerly Graduate Student, University of California, Irvine, CA 92717, is now with Amada Engineering, La Mirada, CA 90638. TIMOTHY ]. GINTER, Graduate Research Assistant, and FARGHALLI A. MOHAMED, Associate Professor, are with the Department of Mechani- cal Engineering, University of California, Irvine, CA 92717.

Manuscript submitted April 12, 1983.

METALLURGICAL TRANSACTIONS A

history of the specimen being tested but are uniquely determined by the value of the applied stress. On the basis of this implication, it is expected that if the applied stress is rapidly changed either by an increase or by a decrease, both 3) and 6, following a period of transient creep, will reach new values that are appropriate to the new stress level.

A recent investigation on an AI-5 wt pct Zn alloy 7 veri- fied the above expectation in the case of stress increase tests but not in the case of stress reduction tests. Accord- ing to the results of that investigation, 7 the final creep rate after a stress reduction is slower than the steady- state rate that would be determined from an uninterrupted test at the reduced s t ress- -a finding which leads to a higher stress exponent--and the subgrain size does not coarsen even after creep strains of more than 15 pct were allowed at the reduced stress.

The results of the investigation on A1-5 pct Zn 7 are in conflict with those of most recent creep investigations on NaC18 and AI 9.t~ which show clearly that there is no difference between the subgrain size measured in stress reduction tests and that obtained from uninterrupted tests. Addi- tionally, the conflict between the results on A1-5 pct Zn 7 and those of A1 m is not limited to the ability of subgrains to coarsen after stress reductions but extends to the value of the subgrain size as measured in uninterrupted tests by TEM. For AI-5 pct Zn, the reported values of subgrain sizes 7 at normalized stresses of 3.4 z 10 -4 and 8.1 x 10 -5 are 1.5 and 4.6/xm, respectively. In contrast, based on the TEM subgrain size data of AI, 6'1~ which were reported elsewhere 6'") and which obey Eq. ]2}, the subgrain sizes obtained in uninterrupted tests at these two normalized stresses are 9 and 35/xm, respectively. The apparent difference in subgrain size between AI and A1-5 pct Zn is baffling in view of the observation that the subgrain-stress relation represented by Eq. [2] is found ~'2'6 to be obeyed by many materials despite differences in stacking fault energy and solute content.

It is the purpose of the present paper to describe the results of a detailed investigation on AI-5 pct Zn which was undertaken in an attempt to resolve the conflict in behavior between AI and the alloy.

VOLUME 14A, NOVEMBER 1983--2309

II. EXPERIMENTAL PROCEDURES

AI-5 pct Zn was supplied by Kaiser Aluminum and Chemical Corporation. The as-cast ingots were homoge- nized at 773 K for 48 hours and air cooled. After scalping 0.5 cm from each surface, they were flash heated to 589 K and stabilized at this temperature for one hour, and then hot rolled to a final thickness of 2.5 cm. The final prod- uct contained the following elements in wt pct: Zn-5.12 (equivalent to 2.2 at. pct), Si-0.001, Fe- < 0.005, and Mg-0.001. The remainder is A1.

Double-shear specimens of shape described elsewhere 11 were machined from the material. The double-shear configuration was selected for two reasons: to simplify the testing procedure--for this configuration constant load implies constant stress-- and to avoid the problem of necking which may limit the amount of uniform strain available in the course of the stress reduction experiments.

Before creep testing, all specimens were annealed in situ for 15 hours at 893 K, resulting in an average grain size of approximately 6 mm. Creep tests were conducted in air in three-zone furnace. The test temperature was monitored with chromel-alumel thermocouples held in contact with the specimen, and maintained to within --_ 1 K of the reported temperature. Stress change tests were performed by rapidly removing or adding loads.

The strain during creep was measured with a linear vari- able differential transformer (LVDT), accurate to --- 1.27 x 10 -3 mm, and amplifier, and monitored directly on a strip- chart recorder. After straining, specimens were cooled rapidly under load to preserve the substructure developed during creep.

For the purpose of substructure examination, two techniques were used: etch-pit (EP) and transmission electron microscopy (TEM). EP samples were individually mounted, mechanically polished, electro-polished in a mixture of 15 pct perchloric acid in methanol, and finally etched at 233 K in a modified Lacombe and Beaujard etchant. ~z The chemical composition of the etchant was as follows: methyl alcohol 50 cc, hydrochloric acid 32 cc, nitric acid 50 cc, and hydrofioric acid 4 cc. Although the above etch-pit technique does not always directly reveal isolated dislocations, it gives excellent subboundary definition. In estimating the average subgrain size, care was exercised to test more than one specimen under the same experimental conditions and to use numerous representative photographs. Samples for TEM were first mechanically polished to a thickness of 0.010 cm. Thin foils were then prepared using the window technique, at an applied voltage of 8 V, and a polishing solution of 15 pct perchloric acid in methanol which was surrounded by a dry ice-acetone bath to keep the electrolyte temperature at 193 K; the window technique was adopted because it results in large thin areas when carefully applied. Thin foils were examined in a JEOL-100C electron micro- scope operating at 100 KV. TEM measurements, as mentioned elsewhere, 6'm were conducted by preparing a large number of thin foils from several specimens deformed at each stress and by using numerous transmission micrographs ( -30) of representative areas of foils.

III. EXPERIMENTAL RESULTS

The results are given in two sections: in the first section, the results on the mechanical behavior of A1-5 pct Zn are described, and in the second section the substructural data obtained from the etch-pit procedure and TEM technique are presented and correlated with the mechanical behavior.

A. Mechanical Behavior

Creep tests were performed in the temperature range of 650 to 893 K. This range, which is equivalent to a normalized temperature range of 0.7 to 0.99 T,~, where T,~ is the melting point of the alloy (= 903 K), includes the two test temperatures of 823 K and 673 K used by Langdon et al. 7 in their investigation on A1-5 pct Zn.

1. Uninterrupted tests

Figure 1, in which shear strain is plotted against time, shows a typical creep curve obtained in the normalized temperature range of 0.7 to 0.99 T~. As seen in the figure, the creep curve exhibits a decelerating primary creep stage up to ---30 pct, and thereafter the creep behavior is steady- state. The shape of the creep curve is therefore similar to those reported in well-annealed A1, ]'~~ with the exception that no extensive instantaneous strain was observed upon loading. An important feature which was noted in many uninterrupted creep tests and which is demonstrated by the creep curve of Figure 1 is that the steady-state creep rate remains essentially the same even at strains as large as 125 pct. This finding not only indicates that the technique of double-shear can provide constant steady-state rates up to creep strains much larger than those previously reported "'u (3' -- 85 pct), but also establishes double-shear testing as an appropriate procedure for conducting stress-change experiments which involve more than one stress change; the formation of necks and the development of surface irregu- larities during tensile creep testing may lead to uncertainties in measuring steady-state creep rate after stress changes even if only one stress change is attempted. 9

1.3

1.2

I,I

1.0

0 9

O8

~. o7 O 6

0.5

0.4

O3

0 2

0.1

0.0

l I I I I I I 1 7

A I - 5 % Z n / T,K T,MPo

I I I I I I 2 4 6 8 10 12

t, min Fig. 1 - -Example of creep curve forAI-5 pct Zn.

I I 14 16 18

2310--VOLUME 14A, NOVEMBER 1983 METALLURGICAL TRANSACTIONS A

The dependence of the steady-state creep rate on the applied stress was investigated by conducting a series of uninterrupted tests at three different temperatures: 893 K, 823 K, and 650 K. The results are shown in Figure 2, where steady-state creep rate, ~/, is plotted against the applied shear stress, T, on a logarithmic scale. The stress exponent for AI-5 pct Zn, as estimated from the data of Figure 2, is independent of temperature and is close to a value of 4.6. This value is in excellent agreement with that reported for A1 by several investigators. U~

Two methods were used to determine the activation energy for creep. In the first method, the data of Figure 2 were used to plot logarithmic ~,G"-~T against I /T at ~- = 1 MPa, and the activation energy was then determined from the slope of the resultant straight line which, according to well- documented analyses, TM is equal to Q,/2.3R (where Q, is the true activation energy and R is the gas constant). In the second method, 15 the temperature was changed rapidly by a small amount AT (=15 K) and Q was calculated from the expression TM

;y2G'~- ~T2/ ~GT- ITI Q, = R In [3]

TI - T2/T, T2

where ~, and 72 are the instantaneous creep rates immedi- ately preceding and following the change in temperature from T~ to T2, and n = 4.6 (Figure 2). Figure 3, where ~ is plotted against 7, shows an example of the temperature change method; the specimen was subjected to a rapid change of 15 K while under a constant shear stress of 0.3 MPa. In estimating Q from the two methods, informa- tion concerning the shear modulus, G, was taken from the data available on the AI-Zn system.*6 The two values of Q obtained from the analysis of the data of the two methods are essentially the same; the first method yields 141 + 10 kJ/ mole and the second method yields 139 +4 kJ/mole, The average value of Q = 140 kJ/mole for A1-5 pct Zn is almost equal to that reported for Al ~v (Q = 142 U/mole) under similar creep conditions (T > 0.65 T,,), showing that

t0-2

t0-3

T . ~ 10-4

10-5

10-6

0.1 LO

T , M P o

Fig. 2 - - L o g ~, v s log r for A1-5 pct Zn for 3 test temperatures.

{ | | ] I 1 t 1 |

/ AI- 5o/. Zn

~7 893 / J / / / 0 6 5 0

46

I0.0

the addition of about 2 at. pct zinc to AI has no significant effect on the activation energy for creep in AI.

2. Stress change tests

Stress change tests were performed using the same procedure described by Soliman et ai.l~ According to the procedure, a single specimen is crept at ~'~ to within steady- state creep, ~ , and then the initial stress, 7~, is rapidly reduced. After the stress reduction, sufficient strain was allowed to ascertain the presence of the new steady-state creep rate, 3'2. Finally, the reduced stress, z2, is rapidly increased to its original value of T~ and the test is continued until steady-state creep is reached. Because both the stress reduction and the stress increase are performed on the same specimen, the procedure has the advantage of providing a direct comparison between the stress exponent estimated from the stress reduction and that estimated from the stress increase.

Three typical examples for the application of the above procedure at 893 K, 823 K, and 650 K are shown in Fig- ures 4(a), 4(b), and 4(c), respectively, where the creep rate, ~/, is plotted as a function of creep strain, 7. Despite differences in the values of temperature and the initial stress, the results of the three stress change tests, as plotted in Fig- ures 4(a), 4(b), and 4(c), exhibit several common features. Firstly, following the stress reduction from ~'l to ~'2, the creep rate increases and reaches the new steady-state value that would be obtained in an uninterrupted test at the reduced stress level, ~z. Secondly, the creep rate, ~/, following the stress increase from ~'2 to r~, reaches a stead.c-state value which agrees with the steady-state rate established before the stress reduction from rl and ~'2; this feature demonstrates the validity of the experimental procedure at large strains. Thirdly, the stress exponent estimated from the stress change [n = (In ~/1/%)/(ln zl/~2)], whether a decrease or an increase, agrees with that obtained from uninterrupted tests (n = 4.6 +-- 0.1).

Many tests similar to those presented in Figures 4(a), (b), and (c) were conducted and the results, which are documented in Table I, demonstrate clearly that there is no difference between the stress exponent obtained from stress reduction tests and that obtained from uninterrupted tests.

B. Substructural Results

A recent investigation 6 on subgrain size in A1 demonstrated that TEM is not a practical technique to examine

10-3 I I I I I I

A I - 5 % Z n d=6mm

T=O.3MPa

- 10_ 4 Q=136 143KJ mole -t

- ~

10_5 __ AT=I5K 15K __

l l I I I l 01 0 2 0 5 0 4 0 5 0 6 0.7 0 8

Y Fig. 3--Log ~/ vs 7 for AI-5 pct Zn showing activation energy measurement by abrupt change in temperature.

METALLURGICAL TRANSACTIONS A VOLUME 14A~ NOVEMBER I983 - - 23 ~ i

I m .>.

I m

l__ I I I I 10-2 AI-5%Zn

T=895K

T=0 6MPo

. . . . . . . . . . . . . T . . . .

io-3 - I

n= n :46

I I

10-4 ~s i I

. . . . I . . . . . . . . . . . .

' ~ r : o 3MPa

io-5 I I I I o.o 0.2 0.4 0.6 0.8

(a)

10-2

10-3 _--

10-4

10-5 0.0

I I I I A1-5%Zn T=823K

T=I.0MPo

n:4G n:4.6

.... _2__ I I I I

02 0.4 0.6 08

T

(b)

10-2

10-3

10-4

I AI- 5%Zn T=650K

I I I

T=2 48MPo

__5__ ~ . . . . . ; ....

( ~ ' : I 98MPo

io -5 I I I I oo 02 04 o6 o8

)"

(c) Fig. 4--Examples of stress change experiments for A1-5 pct Zn; "), represents the steady-state creep rate of an uninterrupted test conducted at the reduced stress. The 2 solid arrows indicate strain rates used to calculate n.

subgrain size at low stresses and high temperatures due to the coarse nature of the substructure and that the EP procedure is not appropriate at high stresses and low temperatures because of the difficulty in identifying very small subgrains. On the basis of this finding in AI and in view of the simi-

Table I. R e s u l t s o f S t r e s s R e d u c t i o n E x p e r i m e n t s P e r f o r m e d on AI-5 Pc t Z n

T, K ~'1, MPa ~'z, MPa 4/1, s- ' ~/2, s-~ n

893 0.60 0.39 9.0 x [0 -4 1.2 x 10 -4 4.7 0.60 0.30 1.3 X 10 -3 5.4 X 10 5 4.6 0.60 0.15 1.1 X 10 -3 1.6 X 10 -6 4.7

823 1.0 0.75 1.1 x 10 -~ 2.9 x 10 -4 4.4 1.0 0.50 [.0 X 10 -3 4.2 • 10 -5 4.6 1.0 0.25 t.2 X 10 -3 1.8 X 10 -6 4.7

650 3.96 1.98 2 • 10 -3 8.5 X 10 -5 4.6 2.97 1.98 5.4 X 10 -4 8.4 X 10 5 4.6 2.48 1.98 1.7 X 10 -4 6.0 X 10 -5 4.7 1.98 1.50 8.7 X 10 .-5 2.5 X 10 -5 4.4

n from uninterrupted tests = 4.6 +-0.1

larities in mechanical behavior between A1 and A1-5 pct Zn, as illustrated in Section A, it was decided to use TEM in examining the subgrain size of the alloy at T = 650 K and to adopt the EP procedure in measuring the subgrain size at T > 650 K.

1. Etch-pit data

To examine the ability of subgrain size to coarsen as a result of a stress reduction, the average steady-state subgrain size in specimens subjected to a stress reduction from ~'l to r2 was compared to the average steady-state subgrain sizes in specimens subjected to ~'l and I"2 in uninterrupted tests. The average subgrain size was estimated by: (a) using a linear intercept method, (b) considering subgrains in the central part of the section of the sample since it was found that the subgrain size, 6, near the surface is smaller than that in the center, and (c) constructing histograms which give the relative frequency of the subgrain size as a function of the size; these histograms were plotted by using numerous representative photographs of several specimens tested under the same experimental conditions.

A typical example of the above procedure at 823 K is shown by Figures 5(a), 5(b), and 5(c). Figures 5(a) and 5(b) show etch-pit photographs for specimens tested in uninterrupted experiments at 1.0 MPa and 0.25 MPa, respectively, whereas Figure 5(c) shows a photograph for a specimen which was subjected to a stress reduction from 1.0 MPa to 0.25 MPa. Inspection of the three photographs along with others for the same stresses shows that the subgrain size is inhomogeneous and that as a result of the stress reduction, from 1.0 MPa to 0.25 MPa, the subgrain size not only coarsens but also reaches the size appropriate to the reduced stress (~- = 0.25 MPa). These two characteristics, the inhomogeneity of subgrains and their ability to coarsen after the stress reduction, are manifested by the histograms of Figures 6(a) and 6(b) which give the relative frequency of subgrain size as a function of size for the uninterrrupted tests at T2 = 0.25 MPa and the stress reduction tests (from ~'l = 1.0 to z2 = 0.25 MPa), respectively.

A comparison between the results of Figure 6(a) and that of Figure 6(b) shows that the two plotted histograms are nearly identical: there is no difference in the average subgrain size between the two types of tests, and the maximum relative frequency appears in each case to be very close to the average subgrain size. By using standard statistical


(a)

Z

0 uJ n- u_

uJ >

k-

.J uJ mr

I

2 0

15

5

5 0 1 5 0 2 5 0

I 1

-1 I I I I I |

A I - 5 % Z n

T = S Z S K

UNINTERRUPTED TEST, T =0 ~SMPo

~ = 3 4 5 ~ m

I i

550 4 5 0 5 5 0 6 5 0 7 5 0

8,/a.m

(a)

8 5 0 9 5 0

I I I I I I I

~ A I - 5 % Z n

T= 8 2 5 K

Z INITIAL STRESS, ~ =I.OMPo I~1 / REDUCED STRESS, 2-z= 0 2 5 M P O

o I ~ =542~,m I.IJ

> t.-- _J w 0~.

3 5 0 4 5 0 5 5 0 6 5 0 7 5 0 8 5 0 9 5 0

8,Fro

(b) Fig. 6 - - Relative frequency of subgrain size vs subgrain size, 8, at 823 K (EP): (a) uninterrupted test, r2 = 0.25 MPa; (b) stress reduction test, r~ = 1.0 MPa and ~'2 = 0.25 MPa.

I I

2O

15

5

5 0 150 2 5 0

(b)

(c) Fig. 5 - - E P photographs for A1-5 pct Zn crept to within steady-state at 823 K: (a) uninterrupted test, r~ = 1.0 MPa; (b) uninterrupted test, ~'2 = 0.25 MPa; and (c) stress reduction test, ~'~ = 1.0 MPa and "r2 = 0.25 MPa.

e~

107 - -

Io ~ =--

I0 5

1 0 4 - -

I 0 3 ,,

I I A I - 5' / . Zn

EP TEM OUNINTERRUPTED TESTS OOUNINTERRUPTED TESTS

REDUCTION TESTS REDUCTION TESTS iNITIAL STRESS INITIAL STRESS

# 0 . 6 M P O �9 �9 3 . 9 6 M P a .0 MPo

0 0 - - GINTER AND MOHAMED

I

[ I I I I I I I I ] iO-S iO -4

T/G

- - t 0 3

io z

Io

io-3

E

ao

Fig. 7 - - L o g (8/b) vs log (r/G) for AI-5 pct Zn; horizontal diamonds represent mesh size of cellular substructure.

procedures reported elsewhereJ 8 the error (using 95 pct confidence limit) in calculating the average subgrain size was estimated to be about +-10 pct of the reported mean value; for example, the error in the average subgrain size of Figure 6(a) is ---35/zm.

METALLURGICAL TRANSACTIONS A VOLUME 14A, NOVEMBER 1983--2313

r r A I - 5 % Z n

3 5 0 =

"t" = O . 3 M P o

3 0 0

E ::L

250

200 I

T = O . B M P o

150 0.0 0 .05 0.10 0.15 0 .20 0 .25 0 .30

zxu Fig. 8 - - Subgrain size, 3, vs amount of strain increment, ~ 7, after a stress reduction from 0.6 MPa to 0.3 MPa. Open circles represent subgrain size obtained from uninterrrupted tests at initial and final stresses.

The subgrain size data based on stress reduction tests together with those obtained from uninterrupted tests are plotted as ~/b vs 7/G on a logarithmic scale in Figure 7. It is evident that no difference in position exists between the two sets of data and that both fall very close to the line determined previously from subgrain size data of A1. 6

In addition to measuring steady-state subgrain sizes in the alloy at the reduced stresses, efforts were made to examine the change in subgrain size following a stress reduction as a function of strain increment during the transient period. Figure 8, where 8 is plotted against strain increment, AT, provides an example of such an examination and shows two interesting features: (a) the subgrain size has attained the new steady-state value at about A3, = 16 pct, a value which is comparable to the amount of strain increment (A 7 --~ 14 pct) necessary for the creep rate after the stress reduction to reach the new steady-state rate, and (b) the subgrain size coarsens appreciably during the initial part of the transient period,* reaching almost 90 pct of its final value after

*For strain increments less than 0.5 pct, changes in subgrain size are not noted or, if noted, are within the range of experimental error.

A7 -~ 7 pct.

2. TEM results

TEM was used for substructural examination of specimens tested at 650 K in a normalized stress range extending from ziG = 1 • 10 -4 tO 2 • 10 -4. The choice of this stress range was dictated by two findings: the breakdown of the creep power law at normalized stresses greater than 3 x 10 -4, and the inability of the TEM technique to provide representative measurements of subgrain size at normalized stresses less than 1 x 10 -4. As in the etch-pit procedure, the average subgrain size was estimated by considering numerous representative micrographs of several specimens crept under the same conditions and by constructing histograms as exemplified by Figure 9.

27

>- u Z 14.1 ::3 0 tl.l

h

tl.l

l--

,J l.IJ n,*

24

21

18

15

12

9

6

3

0 0 3 6 9

A I - 5 % Zn

UNINTERRUPTED TEST, " t '=3,96 MPo g = 12/~..m

24 27 30 I

12 15 18 21 3:3 36

8 , F m

Fig. 9--Relat ive frequency of subgrain size v s subgrain size, 3, for AI- 5 pct Zn tested at 650 K (TEM).

The results of TEM measurements are in harmony with those of the etch-pit procedure: following a stress reduction, subgrain size coarsens, reaching the size appropriate to the reduced stress level. For example, the average steady-state subgrain sizes in AI-5 pct Zn specimens that were crept in uninterrupted tests at 650 K and 12/zm and 26/zm for stress levels of 3.96 and 1.98 MPa, respectively. When the applied stress was reduced from 3.96 to 1.98 MPa in a stress change test, the average steady-state subgrain size was measured to be 29 ~m, a value which is nearly the same as that obtained from the uninterrupted test at 1.98 MPa. The TEM subgrain size data of A1-5 pct Zn, when plotted in Figure 7, as 8/b vs r/G, fall slightly below the solid line representing recent TEM data on subgrain size in A1. 6

Unlike the etch-pit procedure, TEM can reveal the details of the dislocation substructure. This advantage was utilized to examine the substructural activities associated with the coarsening process. Micrographs of Figure 10 show examples of some substructural activities noted in a specimen crept at 650 K for 3 pct strain increment after a stress reduction from 3.96 MPa to 1.98 MPa; Figure 10(a) shows a subboundary in the process of dissolution and Figure 10(b) shows a wavy subboundary. Features like those seen in Figures 10(a) and 10(b) were noted frequently in thin foils prepared from specimens which were quenched under load during the transient period following stress reductions.

In addition to revealing some of the substructural activities during the transient period, TEM micrographs show the details of dislocation configurations and arrangements in the interiors of subgrains. In this context, three configurations were seen: (a) sets of loosely knitted tangles of dislocations, (b) cellular substructure which occupies the interiors of few subgrains at 650 K and which is similar to that previously reported in A1, l~ and (c) incomplete long subboundaries. Configuration (a) is shown in Figure 11 (a) and configuration (b) is shown in Figure ll(b).

Of the three above configurations, the cellular substructure appears to be the most interesting feature, largely because under normal magnifications (20,000x) this substructure seems to resemble small subgrains, as shown in Figure ll(c), and, in the absence of careful examination of thin foils, may be easily confused with real subgrains. More


(a) (a)

(b)

Fig. 10--TEM micrographs of AI-5 pct Zn tested at 650 K: (a) subboundary dissolution observed at 3 pct strain after a stress reduction from r~ = 3.96 MPa to r2 = 1.98 MPa; (b) wavy subboundary observed under the same conditions as (a).

significant is the finding that the mesh size of the cellular substructures increases only weakly with stress and exhibits very little change after a stress reduction (Figure 7). It is worth mentioning that due to the small size of the cellular substructure, the average mesh size was determined very easily using few thin foils; in contrast, representative measurements of real subgrains required the use of numerous foils having large thin areas.

IV. DISCUSSION

The present investigation shows that the creep behavior of AI-5 pct Zn, as determined from uninterrupted creep tests, agrees with that reported for pure Ah ~,10,17 This agreement is manifested by close correspondence in the value of the stress exponent, the activation energy for creep, and the average subgrain size.

(b)

(c)

Fig. 11 - - T E M micrographs of AI-5 pct Zn tested at 650 K: (a) loosely knitted dislocation tangles; (b), (c) cellular substructure occasionally observed inside subgrains.

METALLURGICAL TRANSACTIONS A VOLUME 14A, NOVEMBER 1983--2315

The similarity in creep behavior between A1-5 pct Zn and AI is not confined to the results of uninterrupted tests but extends to the results of stress reduction tests. As described in Section III, stress reduction experiments on A1-5 pct Zn lead to the following findings: (a) the stress exponent inferred from stress reduction is essentially equal to that determined from uninterrupted tests (Table I), (b) the increase in the creep rate during the transient period, following the stress reduction, is paralleled by a corresponding increase in the subgrain size, (c) the subgrain size after a stress reduction coarsens, reaching the size that is determined from an uninterrupted test performed at the reduced stress level, and (d) subgrain coarsening during the transient period at the reduced stress involves substructural activities such as subboundary dissolution. These findings are in complete harmony with those most recently reported for AI. t0

The similarities between the creep characteristics of A1- 5 pct Zn and those of A1 show that under the present experimental conditions A1-5 pct Zn behaves as a metal class alloy ~-5 and that the creep behavior of the alloy is therefore controlled by some form of dislocation climb process. L~9-2~

Recently, a deformation criterion was developed 5 to pre- dict the class of behavior of a particular solid-solution alloy, whether metal class (climb-controlled creep) or alloy class (viscous-glide controlled creep). The deformation criterion may be expressed in the following normalized form:

kT ~2 B(F.._F]3(D~](G)2 ,4] ectl2Gb3,] \Gb/ \DJ

where k is Boltzmann's constant, e is the atom misfit ratio, c is the solute concentration, B is a constant, F is the stacking fault energy of the alloy, D~ is the diffusion coeffi-

IO 3

r

I ' - (,9 102

I I I I I~ '" l I 7 .4

893K ~ fil -5%Zn / [

L~- ~ 823K

_ ,~ 650K

CLIMB ~ VISCOUS GLIDE IO - - {METAL CLASS)

I I I 1 ~ , , , I I I 10 -15 i 0 -14 10.13 IC) 12 iO "11

( - ~ b ) 3 Dc

Fig. 12--The deformation criterion for solid-solution alloys represented by logarithmically plotting

v s \Gb/ \D,]

Experimental results obtained on A1-5 pct Zn at 3 different temperatures are shown.

cient for the climb process, D u is the diffusion coefficient for the glide process, and o- is the tensile applied stress (tr = 27). The value of B was estimated as 10 t3 by using the data of an A1-3 pct Mg alloy" which reveals a transi- tion from viscous glide behavior to dislocation climb behavior at o'/G = 1.2 • 10 -4. In Figure 12, the criterion is depicted graphically by plotting [kT/(ect/ZGb3)] 2 vs [(F/Gb)3(Dc/Dg) (tr/G) 2] on a logarithmic scale; the solid line at 45 deg represents Eq. [4] and defines the boundary between the two classes of behavior. In order to examine the correlation between the prediction of the deformation criterion, as represented by Eq. [4], and experimental data of At-5 pct Zn, it is necessary to estimate D~, Dg, and F for the alloy.

Most recent considerations 22'23 of the role of diffusion in the creep of binary solid-solution alloys suggest that the following diffusion coefficients are more appropriate for describing climb-controlled behavior and viscous glide- controlled behavior:

Dc = f (XAD~( + xBD~) [5a]

0 In FA) + [5bl

0 In xA

respectively, wherefis a correlation factor, XA and xn are the respective atomic fractions, D* and D/~ are the tracer diffusivities of A and B in the alloy, and Fa is the activity coefficient for A species. For calculating Dc and Dg for A1-5 pct Zn, AI tracer diffusion coefficients were taken from the data of Stoebe et al. z4 while Zn tracer diffusion coefficients were taken from the data of Hilliard et al. 25 Table II gives the values of D~,, D]I, De, Dg, and Dc/Dg.

The value of F for A1-5 pct Zn is not available, but it is possible to make an estimate by using the normalized creep data. 5'26 In Figure 13, the data obtained at various stresses and different temperatures were normalized in terms of the Dorn equation Lt7 by plotting (~,kT)/(DcGb) against ,'riG on a logarithmic scale. For the purpose of comparison, A1 data obtained in previous investigations 27'28 under a similar normalized temperature range were also included in Figure 13; they are represented by a solid line. As seen in the figure, the normalized creep data of AI-5 pct Zn cluster about the line representing A1, suggesting that the stacking fault energy of the alloy, F, may be nearly equal to that for A1; FA~ = 200 erg/cm 2. This inference is based on the results 5 of a recent analysis of the creep data of various fcc metals and alloys of metal class which show that the normalized creep rate, (:ykT)/(DGb), at constant normalized stress is related t to (F/Gb) 3.

tMost recently, Argon et al. 29'3~ attributed this cubic dependence of the normalized rate on F/Gb to: (a) a second power dependence of the climb velocity on F/Gb and (b) a linear power dependence of the mobile dislocation on F/Gb.

Table II. Values of Diffusion Coefficients for AI-5 Pct Zn

T, K D~, cm 2 s -~ D~n, cm 2 s ~ De, cm z s -~ D 8, cm 2 s -1 Dc/Dg 650 7.70 • 10 -12 4.94 X 10 -II 1.1 • 10 -ll 4.19 • 10 -11 0.26 823 1.02 • l0 -9 6.26 • l0 9 1.46 X 10 -9 5.34 • l0 -9 0.27 893 4.30 • l0 9 2.61 X 10 8 6.13 X 10 -9 2.23 X 10 -8 0.27

*Thermodynamic factor, 2S F = 0.95


~ C9

10 -8 - -

10-9 _ _

i0-10 =----

jO - Ig - -

10-12 - -

10-13 - -

10-14 _ _

10-15

I I I I I I I I I

v 8 9 3 K A I - 5 % Z n z~ 8 2 3 K

o 650K

AI

J I I I I I 1 1 0 - 5 1 0 - 4

T/G Fig. 13--Normalized creep rate vs normalized stress (logarithmic scale) for AI-5 pct Zn; solid line represents the creep data of A1. 27'2g

Having estimated the values of Dc/Dg and F / G b for A1-5 pct Zn, the data of the alloy obtained at 893 K, 823 K, and 650 K were then superimposed on Figure 12; e (= 0.02) was taken from Reference 31. As shown by the figure, the three horizontal lines representing the three temperatures fall on the left side of the boundary, where climb controls, in agreement with the prediction of the deformation criterion.

The present results on A1-5 pet Zn disagree with those reported by Langdon et al. 7 for the same alloy. The major points of the disagreement are related to:

1. The stress exponent obtained f rom stress reduction tests

Langdon et al. 7 reported that stress reduction tests performed on A1-5 pct Zn lead to an overestimation of the stress exponent. In contrast, the present stress reduction tests, including those performed at the same temperature (T = 823 K) used by Langdon et al. , revealed no difference between the stress exponent inferred from stress reduction tests and that obtained from uninterrupted tests; the present results on stress reductions are obtained from creep experiments which, unlike those of Langdon et al. , involve two stress changes* and which are performed over wide ranges

*As suggested by Eggeler and Blum, s stress change experiments which involve more than one stress change are necessary for a reliable determina- tion of the stress exponent.

of experimental conditions.

METALLURGICAL TRANSACTIONS A

2. Subgrain coarsening fol lowing stress reductions

Langdon et al. 7 reported no subgrain coarsening in A1- 5 pct Zn as a result of stress reductions even though: (a) creep rates measured in their experiments following stress reductions increased to values which are only slightly lower than steady-state rates appropriate to the reduced stress levels, and (b) creep strains of more than 15 pet were allowed at the reduced stresses.** This contrasts with the

**In this case, the stability of subgrains cannot be attributed to the absence of sufficient creep strain at the reduced stress. 32

present evidence which shows that an increase in the creep rate following the stress reduction is paralleled by a corresponding increase in the subgrain size (Figure 8), and that the subgrain size coarsens significantly after small strain increments of the order 4 pct to 6 pet at the reduced stresses.

3. The subgrain size

The TEM subgrain sizes reported by Langdon et al. 7 in A1-5 pet Zn are given in Figure 14 which also includes the TEM and EP data on subgrain size obtained in three investigations: the present investigation on AI-5 pet Zn, the investigation by Blum et al. 33 on AI-ll pet Zn, and the investigation by Soliman et al.~~ on A1. It is clear from Figure 14 that the present subgrain size data on A1-5 pet Zn are in good agreement with those on AI-11 pet Zn 33 and A1,1~ and that the data of the three investigations fall within a very narrow band whose position is approximately one order of magnitude above the data points of Langdon et al.

While the reason for the higher stress exponent obtained in the stress reduction experiments of Langdon et al. 7 is not clear, the results of the present investigation do offer a possible explanation for the discrepancy connected with the subgrain size and its ability to coarsen after stress reductions. As mentioned in Section III-B, examination of thin foils prepared from specimens crept in both uninterrupted and stress reduction tests occasionally show, as illustrated by the TEM micrographs of Figures 10(b) and ll(b), the presence of a cellular substructure which resembles small subgrains and which occupies the interiors of few large subgrains at 650 K. The average mesh size of this cellular substructure, as shown in Figure 14, is weakly sensitive to

..Q

GO

,o,J IO s

J J 0 e e o A1-5% Zn (Present) o e �9

AI ( M o h a m e d et . al,) o&oAi i --VEP

AI - I I% Zn (Blum et. al.) - -~ ' tOM

AI- 5% Zn (Longdon et.al ) �9 -- iO 3

_ _ ~ U l l < > o Cellular Substcucture

io z E

" ' ~ . ~ v ~

" i f o 6' o

[

10 5

10 4 - -

10 3 J I I I I I I I I I i0-~ 10-4 10-3

T / G Fig. 14--Log (6/b) vs log ('r/G) for AI-Zn alloys and AI.

VOLUME 14A, NOVEMBER 1983--2317

stress. In the absence of careful examination of thin foils, it is quite possible that under normal magnifications (-20,000 x) the cellular substructure may be confused with the real subgrains, leading not only to a significant under- estimation of the subgrain size but also to an erroneous finding that the subgrain size does not coarsen after a stress reduction. This possibility seems to be supported by the observation that the subgrain sizes reported by Langdon et al. ,7 as plotted in Figure 14, fall very close to the present data and AI data 1~ on the cellular substructure.

V. CONCLUSIONS

1. The creep characteristics of A1-5 pct Zn, including the stress exponent, the activation energy for creep, and the stress dependence of the subgrain size, agree with those of pure A1.

2. Under the present experimental conditions (10 -5 < r/G < 2 • 10 -4 and 0.7 <- T/Tm <- 0.99), A1-5 pct Zn behaves as a metal class alloy, a finding which is in agreement with the prediction of the deformation criterion for solid-solution alloys.

3. After a stress reduction, both the creep rate and the subgrain size, as measured by EP and TEM, increase, reaching the steady-state values which would be obtained in an interrupted test at the reduced stress.

4. There is no difference between the stress exponent obtained from stress reduction tests and that obtained from uninterrupted tests.

5. The average steady-state subgrain sizes of A1-5 pct Zn, whether measured in stress reduction or in uninterrupted tests, agree with those reported in A11~ and Al- l1 pct Zn.33

6. The subgrain sizes measured in an earlier investigation 7 on A1-5 pct Zn are almost one order of magnitude smaller than those obtained in the present investigation but are comparable with the mesh sizes of a cellular substructure observed occasionally in the interiors of large subgrains.

ACKNOWLEDGMENTS

This work was supported by the National Science Foun- dation under Grant No. DMR 80-25280. Thanks are ex- tended to M. Soliman for his assistance in the experimental work and to Verna Bruce for typing the manuscript.

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Effect of stress reductions on the stress exponent and subgrain size in an Al-Zn alloy

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Transcript of Effect of stress reductions on the stress exponent and subgrain size in an Al-Zn alloy