ULTRASONIC ATTENUATION MEASUREMENTS DURING ROOM TEMPERATURE CREEP WITH TRESS DECREMENTS IN 5N ALUMINIUM

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ULTRASONIC ATTENUATION MEASUREMENTS DURING ROOM TEMPERATURE CREEP WITH

TRESS DECREMENTS IN 5N ALUMINIUM

A. Vincent, S. Djeroud, R. Fougeres

To cite this version:

A. Vincent, S. Djeroud, R. Fougeres. ULTRASONIC ATTENUATION MEASUREMENTS DURING

ROOM TEMPERATURE CREEP WITH TRESS DECREMENTS IN 5N ALUMINIUM. Journal de

Physique Colloques, 1987, 48 (C8), pp.C8-203-C8-208. �10.1051/jphyscol:1987828�. �jpa-00227132�

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ULTRASONIC ATTENUATION MEASUREMENTS DURING ROOM TEMPERATURE CREEP WITH .TRESS DECREMENTS IN 5N ALUMINIUM

A. VINCENT" * *

"

, S

.

^DJEROUD*and R. FOUGERES"

" ~ r o u p e s dlEtudes de MBtallurgie Physique et de Physique des Mat6riaux (UA-341), INSA de Lyon, BAt. 502,

F-69621 Villeurbanne Cedex, France

" " ~ a b o r a t o i r e de rraitement du Signal et d'vltrasons, INSA de Lyon, Bat. 502, F-69621 Villeurbanne Cedex, France

R6sum6

-

Nous pr6sentons dans cet article les resultats originaux de mesures d1att6nuation ultrasonore rhaliskes pendant des essais de fluage interrompus par des reductions successives (66) de la contrainte de fluage. Chaque saut

( A 6

f staccompagne g&n&ralement dsune augmentation de lsatt8nuation ; nhanmoins, dans le cas du fluage en loi tm, an observe une diminution de llatt&nuation lors du premier sautA6. Ncus presentons un modkle qui permet dlexpliquer ces r6sultats et dsen deduire des informations qualitatives et quantitatives sur le r81e des contraintes internes et celui de llannihilation des dislocations par glissement d&i&

,

lors du fluage de llAluminium 5N B tempkrature ambiante

.

Abstract

-

This paper deals with new results ccncerning ultrasonic attenuation measurements performed during creep tests interrupted by successive stress reductions 06

.

During each stress decrement

A 6 ,

an attenuation increase

hots

is generally observed ; nevertheless, in the case of power-time law creep an anomalous attenuation decrease is induced by the first stress decrement. These results are discussed in terms of dislocation mechanisms in order to provide quantitative and qualitative informations about the role of internal stresses and dislocation annihilations by cross-slip in room temperature creep of 5N Aluminium.

INTRODUCTION

In the past, the creep characteristics of pure metals have been studied extensively by mechanical macroscopic stress-strain measurements /I-4/. These characteristics have been discussed in terms of microscopic mechanisms, sometimes with reference to T.E.M. observations /5/. Nevertheless, the dislocation mechanisms governing the deformation laws are not yet well established / 6 / .

In another route, ultrasonic measurements have been widely applied to the study of anelastic /7-8/, plastic /9/ and fatigue /lo/ deformation processes, providing useful informations about dislocation mobility during these processes. To our knowledge, up to now, such a kind of measurements had not been applied successfully to the study of creep processes in pure metals.

So, in a recent study / T I / , it was attempted, through ultrasonic measurements, to provide experimental data about the role of anelasticity phenomena in the internal stress evaluation by the well known dip-test method /3/. The aim of this paper is to discuss the most recent attenuation measurements carried out in this field and to show how they lead us tc quantitative and qualitative informations about the role of internal stresses and dislocation annihilations in room temperature creep of Aluminium.

EXPERIMENTAL RESULTS

This study was carried out on pure pclycrystalline aluminium (99.998%) obtained by extrusion followed by machining and then recrystallization at 450°C for one hour ; the grain size thus obtained is of the order of 1 mm. The diameter of the useful part of a specimen is 9 mm ; the useful length, 40 mm long, is terminated at both

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987828

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JOURNAL DE PHYSIQUE

A AD((~O-A~/PS) o

8

-

⁰ ⁵ ¹⁰ ¹⁵^tMPa1

7

-

6

-

5

-

4

-

3

-

2

-

1

-

0 ^t

*

0 5 10 15 20 (mnl

Fig. 1 : A : Schematic procedure and definitions used in a step by step unloading.

B : Example of recording attenuation change versus time during the whole experiment ; plastic deformation induced by loading

Ep

= 0.2 %

C : Magnitude of attenuation increase versus Stress 6p at T = 300 K ; a)

Ep

= 0.3 5, ⁰ ⁶ ² 0.47 MPa, r,,, = 5.9 MPa ;

-

^1.6^%, ACTS ^0.65^MPa,

rmax

= 17.3 ma.

b)ep

-

Fig. 2 : Detailed recording o f A N versus time Fig. 3 : Magnitude of attenuation during the first decrement in the case ep=3.7% ; d,ecrease versus creep rate domain I creep time 6=6m, ; I1 stress 8 creep-

decrement ; 111 again constant stress.

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temperature tests of pure materials. Strain is measured by means of an extensometer (M.T.S. Type 632.26C) leading, via an appropriate commercial amplifier, to a resolution of Simultaneously with the oreep test, an ultrasonic longitudinal pulsed wave, whose frequency

Y

is about 16.5 MHz, is sent periodically through the specimen with a propagation direction parallel to the tensile axis ; the emission and the reception of the waves are obtained by means of two quartz transducers glued to the free, flat, parallel sides of each head of the specimen. .Changes in the amplitude of the first transmitted echo are followed by a system developed in our laboratory and stored in a computer memory. Then, the corresponding attenuation variations Ad are computed frcm these data with reference to the attenuationd at the beginning of the recording ; an overall resolution of about 0.001 db/ p s is obtained.

Following the application of the initial load, the stress a is alternatively kept constant and decreased (fig. 1 A) ; the interval of time (t,) elapsing between two unloading9

,

as the stress decrement itself (

A61 ,

are fixed for a given overall test. The typical behaviour of the attenuation variation

Ao(

during such a test is shown in Fig. 1'B : a large increase in attenuation is observed during the plastic deformation induced by the initial loading ; then, the attenuation decreases at constant stress and generally it increases during each unloading. The magnitude of this increase arising at each stress reduction will be hereafter labelled

Aocs.

The evolution of this quantity ( Ad,) is reported in Fig. 1 C (for two initial plastic strains) as a function of the stress c frcm which a stress reduction

A 6

is applied(see Fig.1 A).When 6 is decreased Piom the initial creep stress Qimaxr

AcA

rises steeply, goes threug! a maximum value situated at

6p

= 0.85 C,,, and then Ads decreases smoothly. This kind of behaviour, which has been reported in Fig. 1 C for two plastic prestrains ( 6p t 0.3% and 1.6%)

,

has been observed in the whole range of preplastic strain 0. l$<

ep

(4% that has been investigated.

Nevertheless, an anomalous behaviour of Ao( has been discovered for the first stress decrement when Cp exceeds about 0.4 % ; it is reported in Fig. 2 in the case where

Ep

⁼^3.7 % : on the contrary to what is observed in Fig. 1 B, a marked decrease in the attenuation is induced by the first stress decrement (domain 11) ; at the end of this decrement the attenuation is rather constant ; then the attenuation behaviour is again that of the normal kind : a decrease in attenuation is observed during the constant stress time (domain 1111, followed by an increase

(AM,)

during the next stress jump. The magnitude of the anomalous decrease in attenuation, hereaft~r called A d d has been found to be tightly correlated with the creep strain rate &creep measured just before the stress decrement was applied.

This correlation is reported in Fig. 3 where the different strain rates have been obtained by changing either the oreep time (to) preceding the stress decrement, or the stress 6,, or the temperature (between 280 K and 310 K).

DISCUSSION

On the attenuation increases

(AdS)

The mechanism responsible for this phenomenon has been discussed in details elsewhere /11/ ; this discussion is summarized in what follows.

In the temperature range investigated in this work, the oreep phenomenon is generally ascribed to dislocation movements /6/ ; then, from the work of GRANATO and LUCKE /12/, in the low megahertz range, the attenuation o<can be expressed as :

oCu Kd A L~ (1) with K d = factor depending upon temperature and ultrasonic frequency, A = density of mobile dislocations

,

L = average free loop length.

Thus, the first attenuation increase which is observed at the beginning of the experiment (Fig. 1 B) is mainly due to the increase in induced by the initial plastic deformation.

In other respects, let us recall that the dislocation movements during creep must be of a jerky nature because they are controlled by the thermally assisted jumping of dislocations over obstacles.90, during the constant stress time, those dislocations that are immobilized before overcoming these obstacles can be reached by point

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JOURNAL DE PHYSIQUE

defects which are mobile in aluminium at room temperature /13/ ; this mechanism is schematized in Fig. 4 (A+B); so, the time dependent attenuation decrease observed during each constant stress pericd (Fig. 1 B) is well explained by such a pinning of dislocation loops. Then, during a stress decrement the line tension tends to move the dislocation loop backwards so that three events may occur for a dislocation loop pinned in the above way by weakly interactive point defects :

i) for a small stress decrement and at low temperature the dislocation loop remains pinned by the immobile point defects.

ii) for a suitable stress decrement and an intermediate temperature, the breakaway of the loop from pinning defects occurs (Fig. 4 B+C).

iii) at higher temperature, the pinning defects are mobile enough to be dragged transversaly by the dislocation during its movement induced by the stress decrement.

Fig. 4 Dislocation pinning and depinning A : a free dislccation loop at the end of plastic loading ; B : pinned state at the end of constant stress time ; C : depinning induced by the stress decrement.

In the case of aluminium at room temperature, it has been established in previous studies /7/ that, among these mechanisms, the breakaway is the only one that leads to an increase in the ultrasonic attenuation ; then, it must be concluded that attenuation increases are due to dislocation-point defect breakawaysoccurringduring the successive unlcadings of the specimen ; therefore

Ads

can be expressed as :

Ad

N K , h (LN4

-

¹⁴⁾ ^{(2) where} A is the dislocation line density

concerned with the breakaway (one has to distinguish

hy

from h because of dislccations that are not reached by point defects and because of those concerned with the above situations (i) and (iii)), LN is the lcop length between hard obstacles (nodes or jogs) and 1 is the free loop length between weak pinning points (point defects).

As soon as a dislocation major loop has been pinned by a first pcint defect; the relation LN4

>>

l4 is satisfied. Then, from this model (relation (2)) it follows that is dependent mainly on h y. Fcr a given initial plastic deformation (

Ep)

this dislocation density concerned with the breakaway depends itself upon :

i) the probability that a motionless dislccation lcop will be reached by a mobile point defect (Fig. 4 B) : cn one hand this probability should be decreased by an increase in the delay time (tm) necessary for a point defect to reach the loop by a diffusion process ; on the other hand this probability should be increased by an increase in the waiting time (tw) of a dislocation line in front of a discrete hard obstacle.

ii) the probability that the stress decrement induces the breakaway of these dislocations : in the temperature range investigated in this study (i.e. around room temperature) a competition arises between the breakaway and dragging mechanisms /7/ ; thus, the breakaway probability appears to be a complicated function of T and magnitude of stress variation /14/.

In spite of this complexity, as a first approach, the evolution of A(XS ( 6 )

reported in Fig. l C can be easily understood on the following basis : as tte experiment was carried cut at constant temperature with identical successive stress decrements and intervals of time tp between these, the migration time tm and the breakaway probability of a pinned loop should not change noticeably between successive stress reductions. Moreover, around room temperature, the dislocation density induced by the initial plastic deformation is not expected to evolve noticeably, except at 6 = or% aTmX (this situation will be discussed in details in the next Section). Then, these arguments lead us to the conclusion that the behaviour of

Ac<

during unloading can be explained only in terms of a waiting

(6)

where

y o

is the attempt frequency, k is the Boltzmann constant

, ^AG

is the GIBBS free energy of activation to overcome the barrier which is often written as :

A G = (Fo -(6f

-

^Zi).b.AA) ⁽⁴⁾ ^{with Fo}⁼ total free energy to overcome the barrier, f = Schmid factor, t i = long-range internal stress opposite to the effect of the applied tensile stress (C), h A = activation area

.

From relations (3) and (41, it can be easily seen that tw will go through a maximal value as a function of 6 when the condition 6.f = t i is fulfilled. In this particular situation,Ay should also be maximal because the point defects have the longest time to reach and pin the dislocations. In fact, as all the microscopic parameters f, F o , A ~ and

Zi

are distributed, the preceding conditions must be considered as only roughly satisfied on averaged parameters.

Thus from all these arguments it can be concluded that the maximum of

AgS

plotted as a function o f c p (Fig. 1 C) arises from this process : that is to say the stress

CTp, from which the unloading jump l e g s to* maximum value of

A &

,,is roughly equal to the average internal stress 6 i = Zi/f acting backwards on the dislocation movement. This conclusion is in good accordance with previous experiments carried out by a classical dip-test method on the same aluminium at room temperature /16/ :

the occurrence of a backward strain was established as the creep stress is reduced below acritical value (equal approximatively to the internal stress). Finally, the result Ciz 0,856max can be obtained from Fig. 1 C.

Moreover, considering the other characteristics of Fig. 1 C on the basis of this model leads us to the following comments : the evolutions of are not symmetrical around Cip

=. ^pi ,

in the same way that the forward and reverse creep strains were not symmetrical in a dip-test /16/.Theseresults could indicate that the long-range internal stresses felt by the dislocaticns are strongly reduced when these dislocations move backwards in their glide plane : actually this should be consistent with internal stresses ascribed to the cell walls /17/ of the cell structure that have also beenobserved in the present experimental conditions by T.E.M.. Moreover, as it will be seen in the next Section, dislocation annihilations should influence internal stresses only at the beginning of the first stress decrement because they occur mainly in this domain.

On the anomalous attenuation decrease (hid)

Let us recall that this anomalous attenuaticn decrease reported in Fig. 2 arises only during the first stress decrement and if the amount of plastic prestrain exceeds about 0.4%. Then,, on the basis of the string model (relation (l)), an attenuation decrease could be ascribed either to a free loop length shortening or a dislocation density lowering. A free loop length shortening could be considered only in terms of a pinning of dislocations by point defects during the load decrement itself. Such a dynamic pinning by mobile point defects of the waiting dislocations, which number is increasing as the stress is decreasing, is not consistent with the model developed in the previous section : indeed, the same unloading stress rate is not expected, during the first stress decrement, to allow a pinning of the dislocations by the point defects and, then, during the subsequent stress decrement, to induce the breakaway from these pinning points (Fig. 4 B+C).

Therefore, a dislocation density lowering must be considered in order to explain the anomalous attenuation decrease. At first let us notice that such an assumption is in good accordance with the fact that this phenomenon is observed only if

Ep

exceeds about 0.4 $. Indeed, as it was pointed out in a previous paper /11/, below this value the creep strain follows a logarithmic-time law, whereas a power-time law is obtained beyond

Cp=

^0.4^$. Thus, this correlation suggests that the anomalous behaviour of d could be associated to the occurrence of new mechanisms for dislccation motions during power-law creep.

Finally, the attenuation phenomenon could be explained by following the approach proposed by ESTRIN and KUBIN /18/ of the mobile dislocation density evolution in deforped crystals :

A

= ( C ~ / ( A Y ~ b)

- c2]icreep -

^{C3 exp[-} ^(IcS

-

^{( 6 f}

-z~)~AB)NT]

(5) where C1,

*c2

and C3 are which ace assumed to remain constant during an unloading decrement.

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JOURNAL DE PHYSIQUE

The first term in the right-hand side of equation (5) is a production term controlled by the back stress from previously emitted dislocations that must have travelled a distanceyc before a new dislocation can be generated by the source. The second term relates immobilization of mobile dislocations on a spatially organized forest structure (Franck network, Cell wall). The third term takes account of the mobile density decrease by annihilation of screw dislocations occurring bycross-slip as suggested by POIRIER /19/ or NIX et a1 /20/ (Fcs is the total free energy to activate the cross-slip at zero stress and A B is the activation area).

It is rather difficult to estimate the relative magnitude of the different terms in equation (5) ; nevertheless, from the fact that

Ao(

(t) is almost constant after few minutes elapsed at constant stress (domain I, Fig.21, in comparison yith what occurs during the stress jump (domain 11, Fig.2), it can be ded~ced~that h r o in these conditions just preceding the stress jump ; i.e., the whole &,dependent term and the term associated to the cross-slip process are then of the same order of magnitude.

Therefore, the evolution of

J\.

depends only on the stress sensitivity of

&,

^compared

to that of the cross-slip annihilation process ; this sensitivity is directly related to activation areas : for cross~slip, from /21,/ A B would be small, of the order of few b2 in Aluminium ; on the contrary,

Ecreep

which is, at least partially, controlled by overcoming of obstacles lying in the glide plane (as it was considered in the previous Section), is characterized by an activation area two orders of magnitude larger in our experimental conditions /22/.

Finally, considering the expression (5) and the above mentioned arguments leads to a negative rate

A

at the beginning of unloading, which is in good acccrdance with the experimental attenuation decrease (beginning domain 11, Fig.2) ; then, the end of domain I1 where the attenuation is again almost constant could be associated to a stress domain where neither of both mechanisms (creation and annihilation).would be noticeably activated : this hypothesis is well supported by the fact that &=is very small in this stress range.

Moreover, by integrating equation (5) over the stress decrement domain, it-can be shown easily /22/ that the total density decrease varies mainly as

ECreep

( 6 = 6max) : this result is in satisfactory agreement with the evolution of A d d shown in Fig. 3.

REFERENCES

/I/ SHERBY O.D., LITTON J.L., DORN J.E., Acta Met. 5 (1957) 219 /2/ GROH P. and CONTE R., Acta Met. 19 (1971) 895

/3/ AHLQUIST C.N. and NIX W.D., Acta Met. 19 (1971) 373 /4/ GIBELING J.C. and NIX W.D., Acta Met. 29 (1981) 1769 /5/ CAILLARD D. and MARTIN J.L., Acta Met. 31 (1983) 813

/6/ OIKAWA H. AND LANGDON G., in "Creep Behaviour of crystalline solidsn, B.

WILSHIRE and R.W. EVANS ed., Pineridge' Press, ( 1985) 33 /7/ VINCENT A. and PEREZ J., Phil. Mag. A, 40,3 (1979) 377

/8/ GREMAUD G. and BUJARD M., J. de Physique C 10, 12, 46 (1985) 315 /9/ HIKATA A., CHICK B., ELBAUM C and TRUELL R. Acta Met. 10 (1962) 423

/lo/ CHICOIS J., FOUGERES R., GUICHON G., HAMEL A. et VINCENT A., Acta Met. 34,11 (1986) 2157

/11/ VINCENT A., DJEROUD S., FOUGERES R., to appear in Proceedings of the 2nd Intern. Symposium on Nondestructive Characterization of Materials, MONTREAL /12/ GRANATO A. and LUCKE K., J. Appl. Phys. 27,6 (1956) 583

/13/ VINCENT A,, SEYED REIHANI S.M., PEREZ J., Phys. Stat. Sol. (a), 39 (1977) 651 /14/ GREMAUD G., J. de Physique C 9, 12, 44 (1983) 607

/15/ GIBBS G.B., Phys. Stat. Sol. 10 (1965) 507

/16/ CHICOIS J., HAMEL As, FOUGERES R., ESNOUF C., FANTOZZI G., J. de PhyS. C 5, 10, 42 (1981) 169

/17/ CHICOIS J. These de Doctorat d8Etat, I.N.S.A. LYON, (1987) /18/ ESTRIN Y., KUBIN L.P., Acta Met. 34,12 (1986) 2455

/19/ POIRIER J.P. Rev. Phys. appl., 12 (1976) 148

/20/ NIX W.D., GIBELING J.C., HUGHES D.A., Metall. Trans., 16 A (1985) 2215 /21/ BONNEVILLE J. and ESCAIG B. Acta Met. 27 (1979) 1477