AN ULTRASONIC STUDY OF THE BEHAVIOR OF DISLOCATIONS UNDER HIGH SPEED PLASTIC DEFORMATION IN ALUMINUM

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AN ULTRASONIC STUDY OF THE BEHAVIOR OF DISLOCATIONS UNDER HIGH SPEED PLASTIC

DEFORMATION IN ALUMINUM

J. Shioiri, K. Sakino, K. Satoh

To cite this version:

J. Shioiri, K. Sakino, K. Satoh. AN ULTRASONIC STUDY OF THE BEHAVIOR OF DISLOCA-

TIONS UNDER HIGH SPEED PLASTIC DEFORMATION IN ALUMINUM. Journal de Physique

Colloques, 1985, 46 (C10), pp.C10-333-C10-336. �10.1051/jphyscol:19851074�. �jpa-00225459�

AN ULTRASONIC STUDY OF THE BEHAVIOR OF DISLOCATIONS UNDER HIGH SPEED PLASTIC DEFORMATION IN ALUMINUM

J. SHIOIRI, K. SAKINO AND K. SATOH'

College of Engineering, Hosei University, ~ o g a n e i - s h i , Tokyo,

~ a p a n -

'Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan

Abstract - In order to detect the behavior of dislocations at high rates of strain, time-resolved measurement of the ultrasonic attenuation under dynamic plastic deformation was made. The experimental technique, the theoretical background of this method and the results of the measurements made for poly- crystalline aluminum are presented together with brief discussion.

I - INTRODUCTION

For the purpose of obtaining experimental information on the behavior of disloca- tions at high rates of strain, Shioiri and Satoh tried time-resolved measurements of the ultrasonic attenuation and velocity in specimens undergoing dynamic plastic de- formation /1,2,3/. Recently, by improving the ultrasonic apparatus and experimental technique, the measurement has become possible at strain rates and temperatures ranging respectively up to 8000 /sec and 500 K. In this paper, the experimental technique, the theoretical background of this method and the results of measurements made for polycrystalline high purity aluminum are presented together with a brief discussion.

I1 - EXPERIMENTAL METHOD

The ultrasonic apparatus used in this work is shown in Fig. 1. The resolution time of this apparatus is 3 usec for the repeated pulse method and 1 psec for the isolated pulse method /3/. Details of the apparatus and experimental technique were already reported in Refs. 1, 2 and 3. The set up around the specimen is shown in Fig. 2.

The ultrasonic pulses were sent at right angles to the dynamic compression imposed by the split Hopkinson pressure bar apparatus. In the measurements at elevated temperatures, lithium niobate transducers were used together with, as the coupler, a silicone adhesive.

I11 - THEORETICAL BACKGROUND FOR FCC METALS

In pure fcc metals, the intrinsic drag against dislocation motion given in a linear viscous form is very small, and, except at very high strain rates, the dislocation motion is controlled also by the thermally assisted cutting of the forest disloca-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851074

C10-334 JOURNAL DE PHYSIQUE

-

oc pulse generator

Specimen

Fig.1 - Ultrasonic apparatus.

digital memory

Fig. 2 - Set-up around specimen.

(1) Specimen (2) Transducers (3) Hopkinson bars

tions. As is shown in Fig. 3, the moving dislocation segments repeat the thermally assisted cutting and the jump motion controlled by the intrinsic drag. The shear strain rate under the resolved shear stress T can be.given by

where N is the number of the moving segments per unit volume, L is the mean distance between the forest dislocations, b is the Burgers vector, t is the waiting time in

t

the thermally assisted cutting, tv is the time required by one jump motion, U is the _L -

activation energy, cr is the activation volume -Lb , k is the Boltzmann constant, T is the absolute temperature and B is the damping constant.

Mobile segment

Forest dislocation

L: Mean distance between • • .

forest dislocations .

(a) (b)

Fig. 3 - Kinetic model for dislocation segment motion.

imposed upon the dynamic plastic deformation, (AX), and (AV/V)m, can be given by

respectively, where Q is an orientation factor depending upon the orientation of the slip system, G is the elastic modulus in shear, 7 is given by Eq. (1) and T O is the resolved shear stress due to the imposed dynamic loading / 3 / . It was shown in Ref.

3 that the (tt+tv)<<l/f holds under the condition of the present experiment. At relatively lower strain rate, where the motion of the dislocations is controlled mainly by the thermally assisted cutting of the forest dislocations, i.e. when tt>>t the following approximation holds /3/:

vy

As pointed out in the previous paper /2,3/, the attenuation shows a large drop when the deformation stops and, further, the amount of the drop can be directly related to the attenuation due to the dislocations moving under the deformation.

IV - EXPERIMENTAL RESULTS AND DISCUSSION

Measurements were made for polycrystalline high purity (99.999%) aluminum at strain rates ranging up to 8000 /sec and at temperatures of 288, 400 and 500 K. The ultra- sonic frequency was 10 MHz. The attenuation due to moving dislocations, (Ah),,

which was determined from the drop of the attenuation at the end of the deformation is shown in Fig. 4. Solid curves in this figure are theoretical curves calculated by using Eq. (2) with Eq. (1) under the assumption that the mean distance between the forest dislocations, L, and the density of the moving dislocations, NL, are in- dependent of the strain rate. The values of L and NL were so chosen that the best fit with the experimental data was obtained. For B, the values presented by Gorman et al. /4/ were used; that is, 2.50, 3.16 and 3 . 7 5 ~ 1 0 - ~ dyn sec/cm respectively for 2

0.3

f = 10 MHz E = 0.05

Fig. 4 - Attenuation due to moving dislocations vs strain rate: - fitted curves

calculated using Eq. (2) with Eq. (1); --- deviation from calculated curves.

C10-336 JOURNAL DE PHYSIQUE

288, 400 and 500 K (the value for 500 K was extrapolated). For the other physical quantities and constants known values and relationships given in Ref. 3 were used.

The values of L can be determined by Eq. (4) from the experimental data of (Ah),i ,.

the lower'strain rate range using the approximation a = ~ b ~ . Thus determined values was 4.75~10-' cm, and was independent of the temperature. If L is assumed to ke independent of the strain rate i too, it is possible to determined NL against &.

Actually, however, as is seen in Fig. 4, NL which is assumed to be independent of i

gives very good fit with the experimental data except at the high strain rate end.

On the other hand, NL depends strongly upon the temperature; the values of NL deter- 7 2

mined by the curve fitting in Fig. 4 are 2.4, 4.3 and 6.8x10 /cm for 288, 400 and 500 K, respectively.

Figure 5 shows the transition in the rate controlling mechanism of the dislocation motion, from the thermally assisted cutting of the fo~est dislocations to the in- trinsic viscous drag, in terms of tv/(t +t ) against E . The curves in this figure

t v

were calculated with Eq. (1) using the same numerical values and relationships as in the calculation of the curves in Fig. 4. Figure 5 indicates that the transition occurs gradually through the strain rate range from lo3 to 10 /sec. 4

Fig. 5 - Transition in the rate controlling mechanism of dislocation motion in terms of tv/(tt+tv).

ACKNOWLEDGEMENTS

This work is a part of the project "Research on Ultrasonic Spectroscopy and Its Applications to Materials Science" aided by Grant-in-Aid for Special Project Re- search of The Ministry of Education, Science and Culture of Japan. The authors are grateful to The Mitsubishi Foundation for their financial support.

REFERENCES

/I/ Shioiri, J. and Satoh, K., Inst. Phys. Conf. Ser. No.21 (1974) 154.

/2/ Shioiri, J. and Satoh, K., ibid. No.47 (1980) 121.

/3/ Shioiri, J. and Satoh, K., ibid. No.70 (1984) 89.

/ 4 / Gorman, J. A,, Wood, D. S. and Vreeland, T. Jr., J. Appl. Phys. 3 (1969) 833.