Internal Friction and Ultrasonic Attenuation in Solids. Proceedings of The Third European Conference University of Manchester, England, 18–20 July 1980

386 Pages·1980·12.888 MB·English

by  C. C. Smith (Eds.)

Other Titles of Interest
BISWAS & DAVENPORT Extractive Metallurgy of Copper, Second Edition
CARTER et al. Metallic Shifts in NMR: A Review of the Theory
and Comprehensive Critical Data Compilation of
Metallic Materials
COUDURIERefa/. Fundamentals of Metallurgical Processes
EASTERLING Mechanisms of Deformation and Fracture
EVANS & LANGDON Structural Ceramics
HAASEN, GEROLD & Strength of Metals and Alloys (ICSMA 5)
KOSTORZ (in 3 volumes)
JAMES & ASHBEE Plasticity of Hot Glass-Ceramics
KUBACHEWSKI & Metallurgical Thermochemistry, Fifth Edition
ALCOCK
MOORE The Friction and Lubrication of Elastomers
PIGGOTT Load Bearing Fibre Composites
SMITH Fracture Mechanics—Current Status,
Future Prospects
TAPLIN Advances in Research on the Strength and
Fracture of Materials (ICF4) (in 6 volumes)
Related Pergamon Journals
Acta Metallurgica
Canadian Metallurgical Quarterly
Corrosion Science
Engineering Fracture Mechanics
Fatigue of Engineering Materials and Structures
Materials Research Bulletin
Metals Forum
Journal of Physics and Chemistry of Solids
Physics of Metals and Metallography
Scripta Metallurgica
Solid State Communications
INTERNAL FRICTION
AND
ULTRASONIC ATTENUATION
IN SOLIDS
Proceedings of the Third European Conference
University of Manchester, England, 18-20 July 1980
Edited by
C. C. SMITH
UMIST, England
Sponsored by
The Institute of Physics
Materials and Testing Group
PERGAMON PRESS
OXFORD · NEW YORK ■ TORONTO · SYDNEY ■ PARIS ■ FRANKFURT
U.K. Pergamon Press Ltd., Headington Hill Hall,
Oxford 0X3 OBW, England
U.S.A. Pergamon Press Inc., Maxwell House, Fairview Park,
Elmsford, New York 10523, U.S.A.
CANADA Pergamon of Canada, Suite 104, 150 Consumers Road,
Willowdale, Ontario M2J 1P9, Canada
AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., P.O. Box 544,
Potts Point, N.S.W. 2011, Australia
FRANCE Pergamon Press SARL, 24 rue des Ecoles,
75240 Paris, Cedex 05, France
FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg-Taunus,
OF GERMANY Hammerweg 6, Federal Republic of Germany
Copyright © 1980 Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system or transmitted
in any form or by any means: electronic, electrostatic,
magnetic tape, mechanical, photocopying, recording or
otherwise, without permission in writing from the
publishers.
First edition 1980
British Library Cataloguing in Publication Data
Internal friction and ultrasonic attenuation
in solids.
1. Internal friction - Measurement - Congresses
2. Ultrasonic waves - Congresses
I. Smith, C C
530.4Ί QC197 80-40935
ISBN 0-08-024771-7
In order to make this volume available as economically
and as rapidly as possible the authors' typescripts have
been reproduced in their original forms. This method
has its typographical limitations but it is hoped that they
in no way distract the reader.
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
Third European Conference on Internal Friction and
Ultrasonic Attenuation in Solids
University of Manchester
July 18-20, 1979
Sponsorship
Institute of Physics, Materials and Testing Group.
Conference Committee
Prof. W. Benoit, Lausanne,
Prof. J. De Fouguet, Poitiers,
Prof. P. Feltham, Uxbridge,
Prof. P.F. Gobin, Lyon,
Dr. M.J. Lea, London,
Dr. G.M. Leak, Manchester,
Dr. D. Lenz, Aachen,
Prof. K. Lucke, Aachen,
Dr. F.M. Mazzolai, Rome,
Prof. Ing. M. Nuovo, Rome,
Dr. R.A. Petlrick, Glasgow,
Prof. V.S. Postnikov, Voronezh,
Prof. A. Seeger, Stuttgart,
Dr. C.C. Smith, Manchester, (Conference Secretary).
Preface
Internal friction measurements provide a very sensitive technique for studying
structural features such as point defects, dislocations, interfaces and second
phases in solids and the processes by which these features contribute to
energy dissipation. Topics studied range from point defect interactions to
the establishment of high damping capacity materials for absorption of noise
and vibration. Materials investigated include pure metals and their alloys,
ceramics, glasses and polymers.
These proceedings contain the contributions to the third European Conference
held at Manchester University in July 1979. The European Conferences alternate
every two years with a series of International Conferences. This year an
effort has been made to increase the number of contributions on non-metallic
materials.
The editor would like to express his thanks to all who contributed to the success
of the Conference, particularly Dr. G.M. Leak and the staff of the Institute
of Physics. Thanks are also due to the Vice-Chancellor of Manchester University,
to Professor J. Colhoun and to the staffs of the Schuster Building, Owens Park
and the University Refectory. Finally thanks are also due to Mrs. Joan
Colclough and Mrs. Lilian Ratcliffe for their invaluable secretarial assistance.
Manchester C.C. Smith
Xlll
Dislocation Relaxation Peaks
D. H. Niblett
Physics Laboratory, The University, Canterbury, Kent, UK
ABSTRACT
A brief review is given of the internal friction peaks observed in face-centred
cubic, body-centred cubic and hexagonal metals which have been attributed to
dislocation relaxation processes.
KEYWORDS
Internal friction; metals; dislocation damping; relaxation processes.
INTRODUCTION
I have been asked by the organisers of this Conference to begin this first session
with a general introduction to the papers to be presented in the session. The
session is entitled "Dislocation Damping", but a closer inspection of the titles
of the papers shows that they are dealing essentially with dislocation relaxation
peaks in metals. Thus it would appear that a brief introduction to this subject
would be appropriate, particularly for the benefit of those participants whose
main interest is in other aspects of internal friction and ultrasonic attenuation.
THE BORDONI PEAK
Historically, the study of dislocation relaxation peaks began about thirty years
ago, when Bordoni (1954) first observed a peak in the internal friction of a
number of face-centred cubic metals at a temperature in the region 50 - 100K.
This initial discovery was followed by a period, between about 1955 and 1960, in
which many detailed investigations of the Bordoni peak were carried out, mainly
on copper, at Cornell, Oxford, Rome and elsewhere, and the results have been
reviewed by several authors (e.g. Niblett, 1966; De Batist, 1972). In particular,
the dependence on plastic deformation and the insensitivity of the temperature of
the peak to point defect concentration suggested that the Bordoni peak results
from an intrinsic property of dislocations. The variation of the temperature of
the Bordoni peak witfc frequency showed that it cpuld be attributed to a thermally-
activated relaxation process, with an activation energy in the case of copper of
about 0.12 eV.
Seeger(1956) proposed that the mechanism responsible for the Bordoni peak is the
3
4 D. H. Niblett
thermally-activated generation of pairs of kinks on dislocations. A dislocation
lying along a crystallographic direction in the lattice may form a pair of kinks
due to the combined action of thermal fluctuations and the stress field, the
segment between the kinks being transferred into the adjacent valley of the
Peierls potential. A relaxation peak occurs when the frequency of the applied
stress is comparable to the frequency of generation of double kinks. This
double-kink generation model was able to explain satisfactorily all the principal
features of the experimental results, and is now generally accepted. Modifications
have been introduced recently by Schlipf and Schindlmayr (1976) and Esnouf and
Fantozzi (1978) to try to account for the fact that the peak is broader than that
for a simple relaxation process.
Theoretical and experimental work on the Bordoni peak is still in progress, and
three of the papers at this session will be concerned with this topic, but
interest during recent years has shifted towards other dislocation relaxation
peaks.
OTHER PEAKS IN FCC METALS
It was soon discovered that the Bordoni peak was not the only internal friction
peak which occurred below room temperature in plastically-deformed face-centred
cubic metals. For example, in measurements by Niblett and Wilks (1957) on
copper at about 1 kHz there appeared, in addition to the Bordoni peak at about
75K, two smaller peaks at about 32K and 200K. The lower-temperature peak
generally behaves similarly to the Bordoni peak, and is believed to be due to a
similar mechanism in a different type of dislocation. The peak around 200K has
been investigated in detail, particularly by Hasiguti and co-workers in Japan.
They showed that in this temperature region three separate peaks could be
distinguished. These Hasiguti peaks, normally labelled P , P~ and P in order of
increasing temperature, were reviewed by Benoit (1977) at the Tokyo conference.
It is generally accepted that they result from an interaction between dislocations
and point defects. Possible models include the thermally-activated breakaway of
dislocations from point defects and the dragging of point defects by dislocations.
The Hasiguti peaks in copper will be the subject of a paper by the Aachen group
this afternoon.
PEAKS IN BCC AND HEXAGONAL METALS
So far we have been considering face-centred cubic metals. Somewhat similar
effects have also been observed in body-centred cubic metals, and these have been
studied in some detail. The early work was reviewed by Chambers (1966), who
designated the principal relaxation peaks in body-centred cubic metals as a, 3
and γ in ascending order of temperature. For example, in niobium at torsion
pendulum frequencies the α-peak occurs at about 120K and behaves rather like the
Bordoni peak in face-centred cubic metals. The 3-relaxation is really a number of
separate peaks occurring between 200K and 400K, and appears to be due to inter-
action between dislocations and point defects, like the Hasiguti peaks in face-
centred cubic metals. The γ-peak occurs at around 500K for niobium at about 1 Hz.
Seeger and Wuthrich (1976) have attributed the γ-peak to double-kink formation on
screw dislocations, with the α-peak ascribed tentatively to double-kink formation
on non-screw dislocations. Several of the papers in this session are concerned
with these relaxation peaks in body-centred cubic metals, so it will be interest-
ing to see whether they provide confirmation for this interpretation.
Very few measurements have been made on hexagonal close-packed metals, but a
broad peak has been observed in the region of 150 - 200K in zinc and magnesium.
Dislocation Relaxation Peaks 5
More experiments are needed on this group of metals: the paper by Fantozzi and
co-workers on magnesium at this conference should help to rectify this situation.
REFERENCES
Benoit, W. (1977). Hasiguti peaks and interaction between dislocations and point
defects. Proc. 6th ICIFUAS, Tokyo, 109-116.
Bordoni, P.G. (1954). Elastic and anelastic behaviour of some metals at very low
temperatures. J. Acoust. Soc. Am., 26, 49 5-502.
Chambers, R.H. (1966). Dislocation relaxations in body-centred cubic transition
metals. In W.P. Mason (Ed.), Physical Acoustics, Vol. IIIA.
Academic Press, New York. pp. 123-197.
De Batist, R. (1972). Internal Friction of Structural Defects in Crystalline
Solids. North-Holland, Amsterdam.
Esnouf, C. and G. Fantozzi (1978). Theoretical aspects of the Bordoni relaxation.
phys. stat. sol, (a), 47, 201-211.
Niblett, D.H. (1966). Bordoni peak in face-centred cubic metals. In W.P. Mason
(Ed.), Physical Acoustics, Vol. IIIA. Academic Press, New York. pp. 77-121.
Niblett, D.H. and J. Wilks (1957). The internal friction of cold-worked copper at
low temperatures. Phil. Mag ., _2 1427-1444.
9
Schlipf, J. and R. Schindlmayr (1976). The kinetics of double-kink rplaxation.
Nuovo Cim., 33Β, 22-28.
Seeger, A. (1956). On the theory of the low-temperature internal friction peak
observed in metals. Phil. Mag., _1, 651-662.
Seeger, A. and C. Wuthrich (1976). Dislocation relaxation processes in body-centred
cubic metals. Nuovo Cim., 33B, 38-75.
The Bordoni Peak in Copper Single
Crystals at Kilohertz Frequencies
H. Farman* and D. H. Niblett**
*lran University of Science and Technology, Narmak, Tehran, Iran
**Physics Laboratory, The University, Canterbury, Kent, UK
ABSTRACT
The internal friction of cold-worked single crystals of high-purity copper has been
measured in the temperature range from 60 to 200K at frequencies between 12 and
22 kHz. The temperature, height and shape of the Bordoni peak were studied as a
function of the magnitude of the resolved shear stress used to deform crystals of
<100>, <920> and <110> orientations. The peak was found to be much larger for
<110> crystals than for the other orientations; this difference is attributed to
the different dislocation structure observed by electron microscopy. Most of the
measurements were made without removing the ends of the crystal which had been
gripped in the tensometer; removal of these ends had an unexpectedly large effect
for the crystals of <110> orientation.
KEYWORDS
Internal friction; Bordoni peak; copper; dislocation damping; plastic deformation»
INTRODUCTION
Niblett and Wilks (1957) investigated the effect of different amounts of prior
deformation on the temperature, height and shape of the Bordoni peak in poly-
crystalline copper at „kilohertz frequencies. More recently, Brown and Niblett
(.1973) measured the internal friction of copper single crystals of <111>, <100>
and <110> orientations at kilohertz frequencies after prior extensions of 5%. The
first two behaved very similarly to polycrystalline copper after a similar de-
formation, but the Bordoni peak for the crystal of <110> orientation was much
larger than for the other crystals, it occurred at a slightly higher temperature
and it was relatively broad and asymmetric. This suggested the need for a more
systematic investigation of the effects of prior deformation on the Bordoni peak
in copper single crystals.
EXPERIMENTAL
The specimens used were high-purity (99.999%) copper single crystals, supplied by
Metals Research Ltd. in the form of cylindrical rods 10 cm long and 6 mm in diameter.
7
8 H. Farman and D. H. Niblett
The crystals were deformed by longitudinal extension at room temperature in a
Hounsfield tensometer. It is customary, when using this method of deformation, to
remove the ends of the crystal which have been gripped in the jaws of the tenso-
meter before measuring the internal friction. However, this procedure shortens
the crystal and is clearly not suitable for making a series of measurements on the
same crystal after gradually increasing prior strains. Therefore we decided to
make the internal friction measurements on the crystals without removing the
gripped ends; the effect of the gripped ends was examined after the final de-
formation.
The crystals were orientated with their axes close to the <100>, <9 20> and <110>
directions respectively. After each deformation the orientation was checked by
the Laue back-reflection X-ray method and the crystal was left at room temperature
for at least two days before its internal friction was measured. The internal
friction was measured in the temperature range from 60 to 200K for longitudinal
vibrations at frequencies between 12 and 22 kHz, using the technique described by
Brown and Niblett (1973).
RESULTS
The internal friction of the copper single crystal of <100> orientation was
measured at about 13 kHz after each of thirteen amounts of deformation, ranging up
to a resolved shear stress of 68.5 N mm"2, which produced an extension of 24%.
X^\
*° Xo (b)
£ x°
* \
x°
15 .Xo
• χ°0
X °
o o
o
X
o
a X°
o
10
X°
uo
X
O
X O
5
Xo
Xo
X °X 9
* * x ^
i 1 i 1 i
100 HO 180 60 100 HO 180
Temperature (K) Temperature (K)
Fig. 1. The internal friction of a copper single crystal of <100> orientation.
(a) 0 - 10 N mm"2; X - 20 N mm"2; · - 37 N mm"2; Δ - 58 N mm"2.
(b) 68.5 N mm"2. X - with gripped ends; 0 - without gripped ends.