The concept of internal stress in the creep of metals and single-phase alloys

Scripta METALLURGICA et M A T E R I A L I A

V o l . 25, pp. 5 1 1 - 5 1 6 , 1991 Printed in t h e U . S . A .

Pergamon Press plc All rights reserved

THE CONCEPT OF INTERNAL STRESS IN THE CREEP OF METALS AND SINGLE-PHASE

ALLOYS

O. Ajaja Department of Physics Obafemi Awolowo University Ile-lfe, Nigeria (Received

October

I. In the power law creep regime,

23,

1990)

Introduction

the steady-state

creep rate ( e )

is usually related to the applied

S

stress

(~) by an expression

of the form e

~ n,

where

n is about

5 for pure metals

and Class

S

II-type alloys and 3 for Class I solid solutions (i). Dislocation glide is believed to be jerky in Class II materials, i.e. a dislocation spends a relatively long time waiting at an obstacle and, upon overcoming it, glides rapidly to the next obstacle. Dislocations glide viscously in Class I alloys, for instance by dragging along a s61ute atmosphere. In an attempt to explain certain aspects of creep behaviour such as creep transients and unusually high stress sensitivities associated with constant structure tests, it has been suggested that dislocation glide during creep occurs not under the full influence of the applied stress, but rather under an effective stress ~-~i' where ~i is the internal stress. This internal stress is believed by many investigators

to exist in the form of a long range resistance

The strain transient dip technique

to dislocation

(2) has been widely employed

glide

(2,3).

in the measurement

of ~..

In this

1

technique, a creeping sample is subjected to an instantaneous stress reduction (A¢). It is believed that the initial creep rate immediately following the stress drop is positive if the new stress ~-A~ is greater than mi' zero if ~-A~ = ~i and negative if ~-A~ < ¢i" The measurements have shown,

among other things,

that ~.

increases

during

the normal

transient

creep of Class

II

1

materials but decreases during the inverse transient creep which is characteristic of Class I alloys (2). There is no consensus among the various researchers on the origin of this internal stPess. It has been associated with subgrain boundaries (4-6), and, more recently, with the "heterogeneous nature" of plastic deformation (7).

The interpretation Of the results of the strain transient dip test raises important questions, some of which have been pointed out by other workers (8). The decrease in internal stress during transient creep in Class I alloys (e.g. AI-SMg (2)), for instance, is difficult to explain considering that the dislocation structure prevailing in such materials immediately after loading is not much different from that of the annealed state, since little or no plastic loading strain is generated (9). One is thus faced with the dilemma of explaining how the internal stress of a crept sample can be lower than that of an annealed sample of the same material. Also, the notion of subgrain strengthening in Class II materials is by no means firmly established (7,10,II), nor is it. clear how a heterogeneous dislocation structure could possible arise, for instance, in Class I materials in which the dislocation distributions are known to be fairly uniform (9,12). The possible source of internal stress thus remains obsecure. In this investigation a modified version of the stress drop test has been performed with a view to providing a further understanding of the kinetics of transient creep. The concept of internal stress is re-examined in the light of the new data generated.

0036-9748/91 Copyright (c) 1 9 9 1

511 $ 3 . 0 0 + .00 Pergamon Press

plc

512

INTERNAL

2.

STRESS

Vol.

25,

No.

3

Experimental Procedures

Constant stress creep tests were performed on aluminium of 99.9% purity using an Andrade-type cam lever. The cylindrical test specimens of 35 mm gauge length and 6 mm diameter were annealed in. air at 773 K for 3600 s prior to creep. The furnace temperature was maintained at 623 (±I) K during each creep test, which was carried out in air under a base stress of 17.33 MPa. The extension of the test specimen during creep was measured with a Schaevitz LVDT giving a strain resolution of better than 2x10 -6. At steady-state, the stress was instantaneously increased by h~+ and immediately (within one second) reduced by Aq_ • The initial stress increase was done with the aim of introducing an instantaneous plastic strain in the deforming sample prior to stress reduction. Various combinations of ~ + (ranging from 1.73 MPa to 11.25 MPa) and ~ _ (from 1.73 MPa to 23.40 MPa) were used and the transient creep behaviour following each stress change cycle was displayed on a strip chart recorder. Some direct stress reduction tests were also carried out during primary and steady-state creep.

3.

Results

Under a base stress of 17.33 MPa at 623 K, the steady-state creep rate of the aluminium samples is 1.40xi0 -5 s "I. Preliminary strain transient dip tests performed at steady-state show that the initial strain rate immediately after the stress reduction is positive for Av < 6.92 MPa and distinctly negative for A~ > 8.67 MPa. A period of stagnation (i.e. zero apparent creep rate) is observed for 6.92 MPa < A~ < 8.67 MPa, followed by a positive creep rate. By conventional interpretation, this would imply that the internal stress for this material lies between 8.67 and 10.41MPa, or 0.50 < ~i/~ < 0.60, which is in agreement with values which have been reported for aluminium (2,7). The stress change experiments in this study can be classified into three groups: Ca) A~+ = Av_ , i.e. no net reduction in stress, (b) A~ - A~+ < 6.92 MPa, corresponding to a net stress reduction such that the final stress is higher than the "internal stress," and (c) Av A~+ > 8.67 MPa, giving a final stress which is lower than the "internal stress."

4.0

(A) (O) (C]

3.~ v

Ao'(MPa)

A~p{%)

(~ixl0Ss "~

1.73 5.55 11.25

0.005 0.128 0.703

ZOO 2.88 3.61,

w

2.0

~" ~'~--IJ,Ox lO'Ssl 1.0

1

2

3 't x l0 ~ Is)

~,

Fig. I Creep stress by a stress MPa at

rate (~) versus time it) after a increase (Av), immediately followed stress reduction (A~). The creep before the stress change is 17.33 623 K.

Vol.

25,

For ~ +

No.

3

INTERNAL

= ~¢_ (= h~), the original

stress

STRESS

513

is restored after the alteration

in stress during which

an instantaneous

plastic strain ~c is generated. The values of ~¢ used are 1.73 MPa, 5.55 MPa, P and 11.25 MPa. For each of the stress changes, the initial creep rate (e.) immediately after the 1 stress change is higher than the (original) steady-state creep rate and it decreases gradually (normal transient) to the steady-state value (Fig. I). The values of ~¢, be and e. which are p z listed in Fig. i show that both Ae and e. are highest for the largest stress change and decrease p z with decreasing ~ . For ~¢ = 1.73 MPa, steady-state is re-established within 400 s while it takes an increasingly longer period as ~ increases.

When the stress on a sample creeping at steady-state is reduced directly by 1.73 MPa, a brief inverse transient creep (~ > O) results which is followed by a period of perceptibly constant creep rate. If, however, the stress is first increased by ~ + C= 7.87 MPa) and then immediately reduced by A~_ (= 9.60 MPa),

corresponding

to a net stress reduction

of 1.73 bIPa, a new t~rpe of

transient creep behaviour emerges (Fig. 2). This is normal transient creep (~ < O) which is, however, preceded by a brief period (less than I0 s) of low creep rate. A similar behaviour is observed for a stress reduction of 3.46 MPa accomplished directly (Fig. 3A), and through a stress increase of 7.87 MPa immediately followed by a stress reduction of 11.33 MPa (Fig. 3B).

20 15

1(]

(A) &o'.=1.73 HPo (6) ,",o'÷ = 7.~,7 MPo, A o" = 9.60 MPo.

6

(A) ~o'.---3.&6MPo (B) Ao';..~7.E7MPo,~ o ' . = 1 ~

6

5 2 O

1

2

3

O

1

t x 10~ (s)

Fig. 2

Creep transients

2

3

t x 10 z Is)

following a direct

Fig. 3

As in Fig. 2 for (A) A~_ = 3.46 MPa

stress reduction of 1.73 MPa (A),

and (B) ~ +

and after a stress increase of 7.87 MPa followed by a stress reduction of 9.60 blPa (B).

~_

= 7.87 MPa followed by

= 11.33 MPa.

Figs. 4A and 5A show the transient creep curves following direct stress reductions of 10.38 MPa and 12.11MPa, respectively. The anelastic creep observed under these conditions is, according to the internal stress concept, a consequence of the new stress being lower than the internal stress which was developed at the original stress. New types of creep transients are observed when the net reduction in stress is accomplished through the stress increase/stress reduction cycle. In FiE. 4B a fast anelastic creep (which lasts for about 5 s) is followed by a normal transient creep behaviour in which e (which is positive) gradually decreases. A similar observation is recorded in Fig. 5B except that a stagnation period (e = O) appears between the fast anelastic and the normal transient creep stages. For very large (net) stress reduction (z 13.84 MPa), the shape of the anelastic creep 'curve is not appreciably altered by the new stress charge technique, although the anelastic creep strain at any given instant of time is somewhat reduced.

514

INTERNAL

STRESS

Vol.

25,

No.

3

0.5 0.5 0 ~-0.5

(k} AO".=10.36NPo (9) Acr.,:8.55 HPQ.Ao'_:19.03MPo

(A) A~:12.11HPo (B] A~:1125MPa, A~:23,35MPo

0

J~

f,

-11.5

~ -,o -1.0 -1.5

I

I

I

I

1

I x10"l(s)

I

2

3

x 10"~ (s)

Fig. 4

As in Fig. 2 for (A) A~_ = 10.38 MPa

Fig. 5

As i n F i g .

2 for

(A) A =

= 1 2 . 1 1 HPa

and (B) A~+ = 8.65 MPa followed by

and (B) A~+ = 11.25 MPa followed by

A~_ = 19.03 MPa.

A~

= 23.36 MPa.

At various stages of creep under a base stress of ~I = 17.33 MPa, the stress was reduced by 1.73 MPa

to ~2 =

15.60 MPa and

the

subsequent

transient

creep was

investigated.

The

parameters

extracted from the stress drop tests are the creep rate prior to stress reduction (cI), the creep rate immediately following the stress reduction

(~2) and the constant structure stress exponent

(N) obtained from the relationship ci/c2 = (~I/~2)N. These parameters are all listed in Table 1 along with the type of transient creep behaviour following stress reduction. The transient behaviour is normal at true creep strains (e) of 1.57Z and 5.61Z, corresponding to early stages of primary creep. At c = 11.11%, a brief inverse "transient (lasting less than 30 s) is followed by normal transient and at steady-state (c = 28.41~), the brief inverse transient is followed by a stage of constant creep rate.

TABLE I Parameters Obtained from Stress Drop Tests Performed at Various Stages of Creep under a Base Stress of 17.33 MPa at 623 K ( ~ = 1.73 MPa)

True Creep Strain

cI x 10s

c2 x 10s

(s-I)

(s-i)

1.57

6.33

2.16

10.4

Normal

5.61

3.65

1.22

10.6

Normal

11.11

2.66

0.86"

10.9

Brief Inverse/Normal

28.41 (Steady-State)

1.40

0.49"

10.1

Brief Inverse/Linear

c (%)

N

Type of Creep Transient at

°Creep rate immediately after the brief inverse transient.

2

Vol.

25,

No.

3

INTERNAL

4.

Normal transient creep, according internal stress (2,7). For A~+ =

STRESS

515

Discussion

to the internal stress concept, reflects an increasing A~_ (Fig. i), the internal stress after steady-state is

re-established should be the same as that before the stress change (the creep rate is the same). An increasing internal stress (associated with the normal transient creep) following the stress change is thus possible only if the internal stress had been lowered (instantaneously) during the stress change. This does not seem plausible since the stress change is accompanied by a net instantaneous plastic strain which means that fresh dislocations must have been generated. The internal stress, accordin E to classical work-hardening, can only increase as a result of dislocation multiplication. The low initial creep rate which normally follows a direct stress reduction (Figs. 2A and 3A) is believed to be due to the development of a high internal stress at the original creep stress (7). By this reasoning, the high initial creep rate which appears following the stress increase/reduction cycle (Figs. 2B and 3B) again implies that the internal stress had been lowered during the stress change. This, as earlier noted, cannot be reconciled with classical work-hardening behaviour.

The observations of Figs. 4 and 5 indicate that forward creep occurs well below the level of the apparent internal stress if an instantaneous plastic strain is introduced prior to stress reduction, which is clearly not consistent with the concept of internal stress. Table 1 shows that for stress drops performed during primary creep, normal transient creep is always observed at the lower stress. It is also observed that the constant structure stress exponent remains essentially constant during creep, regardless of the creep stage. At c = 1.57Z for instance, which corresponds to just 120 s of creep at 17.33 MPa, the value of N is about the same as at steady-state. Since subgrains are not yet formed at such an early stage of primary creep, it is clear that the high stress exponent cannot, in this case, be ascribed to subgrain strengthening. The foregoing observations underscore the need to re-examine the concept of internal stress. The introduction of the instantaneous plastic strain (through a stress increase) immediately before a stress reduction results, at least for moderate stress reductions, in a creep rate which is higher than would be observed following a direct stress reduction. If we ignore the concept of a long range internal stress, then dislocation glide can be considered to occur under the full influence of the applied stress. The dislocation velocity is thus a function only of e (at a given temperature) and remains insensitive to changes in the dislocation structure. The creep rate (under a given stress) is then determined by the density of dislocations which are in glide motion at any instant, or the mobile dislocation density (Taylor-Orowan equation). The unusually low creep rate which follows direct stress reduction during creep must be ascribed to a low mobile dislocation density at the lower stress. It has indeed been demonstrated recently with the aid of dislocation distributions developed during steady-state creep that this behaviour can be explained on the basis of an abrupt reduction in the mobile dislocation density (13). The new observation that the initial creep rate increases if the stress reduction is preceded by an instantaneous plastic strain suggests that the mobile dislocation density is boosted by freshly generated dislocations. It is important to note that the high creep rate is not simply a consequence of the high dislocation density which is established at the higher stress. If that were to be the case, direct stress drop tests performed during steady-state creep should yield higher than usual initial rates of creep (rather than the unusually low rates observed) following the stress reduction, since a higher dislocation density (p) is associated with the original stress (~ ~ ~ ) . It is thus logical to conclude that freshly generated dislocations are potentially more mobile than network dislocations, or those dislocations which, through recovery, have been able to re-arrange themselves into low energy (stable) configurations. This is in agreement with Alden's view (14) on the evolution of mobile dislocation density during plastic deformation.

516

INTERNAL

STRESS

Vol.

25,

No.

3

The occurrence of creep at stresses lower than the apparent internal stress can be rationalized if the creep transient following a stress change is considered to be made up of two super-lmposlng components: positive creep due to continued forward glide of the mobile dislocations and anelastic creep due to the ~ run-back of immobile dislocations, as has been suggested by Lloyd and McElroy (8). By introducing freshly generated dislocations before the stress drop, forward creep is boosted through an increased mobile dislocation density, resulting in a depression of the stress level at which negative creep appears after stress reduction. A similar observation has been reported for partlcle-strengthened Cu-AI crystals in which prior creep at a high stress induces creep at low stresses under which creep is ordinarily not observed in the annealed material (15). The brief periods of low (inverse) creep rate preceding the normal transient creep in the Figs. 2B and 3B as well as the brief anelastic creep in Figs. 4B and 5B would naturally result from the super-imposltion of the two strain components immediately after stress reduction. In closlng, it Is noted that the high moblllty of freshly generated dislocations (relative to network dislocations} readily explains the normal primary creep behavlour In Class II materials, which usually follows an appreciable loading strain. Class I alloys which show little or no (plastic} loading strain and partlcle-strengthened alloys which are crept at stresses lower than the yield stress often display inverse primary creep behavlour. Thls is expected in vlew of the very low initial (mobile) dislocation density and its subsequent increase during primary creep. It Is instructive that the shape of the primary creep curve in both types of materials (16-18) has been changed from inverse to normal simply by prestralnlng prior to creep. On the other hand, inverse transient creep behavlour has been observed in single crystals of ~-Fe tested under a low stress such that little or no plastic strain is generated upon loading (19). Acknowledgement

The experlments reported herein were performed while the author was on sabbatical leave at the National Unlverslty of Singapore. The financial support provided by the NUS Is gratefully acknowledged.

References I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19.

O.D. Sherby and P.M. Burke, Prog. Mater. Sci. 13, 325 (1968). C.N. Ahlquist and W.D. Nix, Acta Metall. 19, 373 (1971). J. Cadek, Mater. Sci. and Engr. 94, 79 (1987). O.D. Sherhy, R.H. Klundt and A.K. Miller, Metall. Trans. 8A, 843 (1977). J.C. Gibeling and W.D. Nix, Acta Metall. 28, 1743 (1980). A.S. Argon and S. Takeuchi, Acta Metall. 29, 1877 (1981}. R.W. Evans, W.J.F. Roach and B. Wilshire, Scripta Metall. 19, 999 (1985). G.J. Lloyd and R.J. McElroy, ActaMetall. 22, 339 (1974). F.A. Mohamed and T.G. Langdon, Acta Metall. 22, 779 (1974). O. AJaJa and A.J. Ardell, Phil. Mag. A. 39, 65 (1979). M.C. Tsenn and N.L. Carter, Scripta Metall. 24, 1115 (1990). R. Horiuchi and M. Otsuka, Trans. Jpn. Inst. Met. 13, 284 (1972). O. AJaJa, Scripta Metall. 24, 1435 (1990). T.H. Alden, Metall. Trans. 18A, 51 (1987). G.J. Llyod, R.J. McElroy and J.W. Martin, Proc. 3rd Intl. Conf. on Strength of Metals and Alloys, p. 185, Inst. of Metals, London (1973). J.B. Fagbulu and O. Ajaja, J. Mater. Sci. Lett. 6, 894 (1987). R.W. Evans and B. Wilshire, Creep of Metals and Alloys, p. 102, Inst. of Metals, London (1985). ' G.R. L e v e r a n t and B.H. K e a r , M e t a l l . T r a n s . 1, 491 ( 1 9 7 0 ) . T. I t k u b o , H. Otkawa and S. K a r a s h i m a , S c r t p t a M e t a l l . 5, 837 ( 1 9 7 1 ) .