Table Of ContentO F F I C E O F NAVAL R E S E A R C H
S T R U C T U R A L M E C H A N I C S S E R I E S
HIGH TEMPERATURE
STRUCTURES AND MATERIALS
PROCEEDINGS OF THE THIRD SYMPOSIUM
ON NAVAL STRUCTURAL MECHANICS
Held a t C o l u m b i a Univers i ty , N e w York, N Y .
J a n u a r y 2 3 - 2 5 , 1963
Sponsored by the Office of Naval Research
and Columbia University
Edited by
A. M. FREUDENTHAL
B. A. BOLEY
H. LIEBOWITZ
S Y M P O S I U M P U B L I C A T I O N S D I V I S I O N
PERGAMON PRESS
O X F O R D • L O N D O N • N E W Y O R K • PARIS
1964
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PREFACE
THE Third Symposium on Naval Structural Mechanics was held from January 23
to January 25, 1963, at Columbia University. It was sponsored jointly by the
Structural Mechanics Branch of the Office of Naval Research of the U.S. Navy
and the Department of Civil Engineering and Engineering Mechanics of
Columbia University.
The symposium was devoted to structural mechanics under conditions of
elevated temperatures. It was intended to cover the various aspects of structural
design for elevated temperature service. For this purpose papers were invited
covering the following areas:
Material aspects of elevated temperature design.
Effects of high speed environment.
Thermal stress analysis.
Design criteria and reliability.
The sessions were planned so that each of them would be devoted to one specific
aspect of the field. By requesting the speakers to present reviews of the present
status of the field with particular emphasis on their own contributions to it, it
was hoped to provide an integrated picture of the various aspects of elevated
temperature design. It was also hoped that the collaboration in one conference
of material physicists, mechanicians, and structural designers concerned with the
problem of elevated temperature effects on the performance and safety of
modern structures would at least in part bridge the gaps existing between the
three groups.
The first day of the conference was devoted entirely to material aspects, the
second day to the effects of high speed environment and thermal stress analysis
and the third day to design criteria and reliability. The present volume contains
the full text of all papers presented at the conference, including written con-
tributions to the discussion, as well as the panel discussion following the session
on design criteria and reliability in edited form.
The complete program of the conference follows:
Wednesday, January 23, 1963
Session I : 9.15 a.m.
Chairman: Harold Liebowitz, Head, Structural Mechanics Branch, and
Engineering Advisor, Office of Naval Research.
Opening of the Symposium by Dr. Grayson Kirk, President, Columbia
University, and Rear Admiral L. D. Coates, Chief of Naval Research,
Department of the Navy.
v
vi P R E F A C E
Chairman: Clarence Zener (Westinghouse Central Laboratory)
Material Aspects of Elevated Temperature Design
Warren P. Mason (Bell Telephone Laboratories): Temperature Depend-
ence of Elastic and Anelastic Properties in Solids.
Joseph A. Pask (University of California): Thermo-Mechanical Be-
havior of Ceramics.
Session I I : 2 p.m.
Chairman: S. Stanford Manson (Lewis Research Center, NASA, Cleveland,
Ohio)
Material Aspects of Elevated Temperature Design
John E. Dorn and Jim D . Mote (University of California): Physical
Aspects of Creep.
Nicholas J. Grant and Arthur W. Mullendore (Massachusetts Institute
of Technology): Creep Fracture and the Third Stage of Creep.
Shuji Taira (Kyoto University): Thermal Fatigue and Its Relation to
Creep Rupture and Mechanical Fatigue.
Thursday, January 24, 1963
Session I I I : 9 a.m.
Chairman: Maurice A. Biot (New York, New York)
Effects of High Speed Environment
F. Philip Bowden and John H. Brunton (Cavendish Laboratory, Cam-
bridge, England): The Behavior of Materials at Supersonic Speeds.
E. Scala (Cornell University): Material Aspects of the Re-entry Problem.
Bruno A. Boley (Columbia University): Analysis of Problems of Heat
Conduction and Melting.
Session IV. 2 p.m.
Chairman: Raymond D. Mindlin (Columbia University)
Thermal Stress Analysis
Heinz Parkus (Technische Hochschule, Vienna, Austria): Solution of
Thermoelastic Boundary Value Problems.
Eli Sternberg (Brown University): Analysis of Thermal Stresses in
Viscoelastic Solids.
L. M. Kachanov (Leningrad State University, U.S.S.R.): Analytical
Methods of Creep Design, Especially within the Nonlinear Range,
(presented by title)
Banquet: 7 p.m.
P R E F A C E vii
Friday, January 25, 1963
Session V: 9 a.m.
Chairman: Walter J. Trapp (Materials Laboratory, ASD, Dayton, Ohio)
Design Criteria and Reliability
Alfred M. Freudenthal (Columbia University): Reliability under Ele-
vated Temperature Conditions.
M. O. W. Wolfe (Royal Aircraft Establishment, Farnborough, England):
Elevated Temperature Design and Design Criteria
Panel Discussion on Design Criteria
W. Boccius (Lockheed Missiles and Space Company, Sunnyvale, Cali-
fornia).
A. M. Freudenthal (Columbia University, New York, New York).
J. M. Hedgepeth (Martin Company, Baltimore, Maryland).
H. Lowndes (ASD, Wright-Patterson Air Force Base, Dayton, Ohio).
M. O. W. Wolfe (Royal Aircraft Establishment, Farnborough, Hants,
England).
The editors would like to express their appreciation of the cooperation
received from authors, sessions chairmen, discussors, and panel members.
Columbia University gratefully acknowledges the support of the Structural
Mechanics Branch of the Office of Naval Research of the U.S. Navy in the
organization of the Conference and the valuable assistance given by Mr. J. M.
Crowley of that Office and Mr. Irving S. Rudin of the Naval Research Labor-
tory, and also expresses thanks to those members of the staff of the Department
of Civil Engineering and Engineering Mechanics of Columbia University who
contributed to the success of the Conference; in particular to Professor J. M.
Garrelts, Executive Officer of the Department, to Professor R. A. Heller of the
Committee on Arrangements, and to Miss Joan Breslin for her assistance in the
organization and editorial work.
WELCOMING REMARKS
GRAYSON K I R K
President, Columbia University
MORE than a dozen years ago I recall being with President Eisenhower, then
here at Columbia, when, thanks to the cooperation which had been given to
us by the Navy, we dedicated our new cyclotron. At that time it was one of the
largest, I believe, anywhere. Now, after only a dozen years, it is small in com-
parison with similar research tools elsewhere.
But it was then a most impressive facility and the crowd that had gathered
for the dedication was greatly interested in it. Quite clearly, General Eisenhower
had to say something about a machine whose actual workings he did not
understand in any detail. So he said, " I wish I had the time to tell you all about
this new cyclotron and how it works; but I have time only to push the button
and let some of the other people talk to you about what will go on here."
Everyone laughed because he had said what was felt by most of the non-
scientists in the audience.
I must confess that I have a similar feeling this morning when I attempt to
say a few words of greeting to the members of a Conference assembled to study
high temperature structures and materials.
As a political scientist and as an administrator of the University for a decade
or more, I am somewhat more familiar with the high temperatures of faculty
members than of structures and materials. But this is not your topic, and I
lose, therefore, my only possible opportunity to make a substantial contri-
bution to your work.
It is one of the very pleasant duties of a university to arrange meetings like
this one; to bring together from all parts of this country and from other coun-
tries experts with a major interest in a special subject of great importance. Thus,
the university serves as a medium by which the latest ideas can be pooled and
examined in that spirit of give-and-take which is characteristic of modern science
and which has brought about such rapid development.
The university, as handmaiden and host, of course is a beneficiary because of
its opportunity to participate and the opportunity for its colleagues to listen.
I trust that during today, tomorrow, and Friday there will be a series of extremely
interesting discussions. I know the program has been planned carefully over a
long period of time, and so, not to waste any more of your time, I will now end
my remarks and permit you to begin the work which you have come together
to undertake. I wish you a good and fruitful meeting and I hope the University
may have the pleasure of welcoming you all again, at some future time, to
Morningside.
x i
OPENING OF THE SYMPOSIUM
REAR ADMIRAL L. D. COATES, U.S.N.
Chief of Naval Research
I T is indeed a pleasure to join with President Kirk in welcoming you to the
Third Symposium on Naval Structural Mechanics. Every other year since
1958 the Office of Naval Research has sponsored a symposium in this field,
and we are especially pleased to have Columbia University serve as the host
for this year's meeting.
ONR's association with Columbia in the field of structural mechanics, parti-
cularly in the field of thermal stress, extends back for nearly 15 years. Begin-
ning first with low temperature work and then moving on to elevated tempera-
tures, Columbia's Department of Civil Engineering with O N R support has
consistently pioneered in laying a foundation of fundamental theory needed
to solve the problems of structural and material stress.
In this connection I am happy to announce that the Navy in a joint program
with the Air Force is completing plans for setting up at Columbia this country's,
if not the world's, first educational research institute specifically designed for
the study of fatigue. As all of you well know, the increasing severity of operating
conditions for both military and civilian vehicles and equipment has created
a demand for longer operational life and increasing use of both high temperature
and high strength structural materials. At the same time, although there has
been a great deal of experimentation and testing in exploring the fatigue pheno-
menon in metals, what has really been needed is emphasis on the interdiscip-
linary study of fatigue. Only through a broad, coordinated program that cor-
relates and evaluates all the numerous and various factors that contribute to
fatigue failures can we design structures efficiently where fatigue is a known
rather than an unknown quantity and thereby greatly increase reliability. We
at O N R feel that the Fatigue Institute at Columbia, which is an expansion of
the work at the Fatigue Laboratory here, will be a major step toward filling the
gap.
In another unusual program here, O N R is encouraging advanced study and
research in the aero-structural sciences by providing funds to permit Columbia
each year to give three promising structural mechanics researchers an oppor-
tunity to perform studies and research here on a post-doctoral level. N o t only
will this encourage urgently needed structural engineers to engage in theoretical
work but the Navy will benefit by establishing contact with some of the most
brilliant of the coming generation of engineers and scientists.
This type of program will also help in correcting a serious deficiency that
has resulted from obsolescence in engineering training in this country. Too many
xiii
xiv O P E N I N G O F T H E S Y M P O S I U M
engineering schools and engineering students have been inclined to accept
handbook knowledge as sufficient for advanced engineering design. The fact is
that there is a lack of sound theoretical understanding of engineering principles
now essential to accomplish significant technological advances. As a result
of this lack, the Navy and other consumers of engineering technology are
finding themselves shortchanged in acquiring the talent and information they
need to solve their problems. More than ever, academic institutions must foster
educational and research programs aimed at attaining this critical objective.
A distinctive feature of this symposium series is that we have been able to
attract the leading experts in the field from abroad who have accepted our
invitation to submit papers. This year we have an excellent representation on
the program, including two papers by investigators from Great Britain, as well
as papers by prominent scientists from Japan, Austria and Russia. I relish the
international flavor of this symposium since it clearly demonstrates that science
cannot be contained within national boundaries. It also underlines that there are
distinct advantages to be gained from cooperative efforts, a philosophy in
which O N R ardently believes and which it practices. By exchanging information
from all parts of the world in a symposium such as this one, we can all move
more rapidly and effectively toward the goals that we all desire to reach.
These O N R symposia are somewhat different from the annual technical
society meetings in that our purpose is to survey and evaluate particular fields
rather than to report solely on new research. The organizers of this symposium
stated their intention of selecting speakers for their eminence in significant
phases of the several disciplines involved in elevated temperature mechanics,
and I am sure that a perusal of the program will convince you that they have
admirably succeeded.
The high temperature field has been of major interest to the Navy for some
time. The unusual and extreme environments in which our equipment has to
function explains that interest. For more than a decade, for example, we have
been working with nuclear reactors and the unique high temperature problems
they create. We are constructing aircraft and missiles that are steadily pro-
gressing in speeds from the supersonic to the hypersonic range. These structures
are being increasingly exposed to the mechanical, physical, and chemical effects
of hypersonic airflow. The ablation of missiles during the re-entry phase is of
particular concern. If we had not been able to achieve some solution to this
problem, the Navy's Polaris missile, which is now one of this nation's major
deterrents against threatened aggression, would not be able to function as
effectively as it does.
Just after the war, our objective was to design materials and structures which
could withstand temperatures of a few hundred degrees; today we are con-
quering temperatures of several thousand degrees. Although we have come a
long way, the challenges ahead are still as great and even greater than those
we have faced in the past. For example, we certainly need to know much more
about the ablation phenomenon. This could permit us to increase the angle of
re-entry and thereby significantly increase a missile's striking ability. We are
O P E N I N G O F T H E S Y M P O S I U M XV
now concerned with velocities so great that thermal effects in certain cases
actually can cause catastrophic deterioration of the surface. This phenomenon
has yet to be thoroughly investigated either by experimental or by theoretical
methods, and our research is aiming toward that end.
There is no question that theoretical analyses are of major importance in
determining the stresses in the behavior of structures. A fundamental under-
standing of the mechanics not only of ablation but also of such phenomena as
creep and stability is needed to help us solve the problems in continuum mech-
anics.
The gathering of such data requires the intensive, coordinated efforts of
applied mechanics people, chemical engineers, solid state physicists, and applied
mathematicians as well as metallurgists. In addition to original basic research,
there is also a constant demand for improved instrumentation to measure high
temperature phenomena.
Although the U.S. Navy has its own special interests in gathering and applying
this information, it should be obvious that application of this knowledge goes
well beyond the military area. Human progress over the past centuries has been
largely geared to the pace at which man learned how to escape from the re-
strictions of his natural environment. One of his chief weapons in this step-by-
step mastery of his environment has been his increasing ability to create more
and more sophisticated materials and structures both for his comfort and his
protection against natural and human hostile forces. This will continue to be
the key to our progress, especially now as we raise our eyes more boldly to the
challenge of outer space.
All of the work covered in the papers of this symposium is an important
part of this critical effort. I congratulate you on your past achievements, and I
look forward to the many triumphs that are ahead of you.
TEMPERATURE DEPENDENCE OF ELASTIC
AND ANELASTIC PROPERTIES IN SOLIDS
WARREN P . MASON
Bell Telephone Laboratories Incorporated, Murray Hill, N e w Jersey
1 . I N T R O D U C T I O N
T H E temperature and frequency dependence of the elastic and anelastic proper-
ties of solids has been used to investigate a large number of solid state pheno-
mena. The list of processes so investigated is now very long and includes such
phenomena as thermal relaxation, phonon-phonon scattering, phonon-electron-
magnetic field effects, point and line imperfections, magnetic and electrostatic
domain motion, phonon-magnon interactions, interaction of acoustic waves
with electron and nuclear spins, phonon masers and ultrasonic amplification in
piezoelectric semiconductors. Obviously, all of these cannot be discussed. The
present paper selects from these subjects those which appear to be more closely
related to the subject matter of this conference, namely thermal and phonon-
phonon interactions, effect of imperfections on thermal conductivity, the stress
induced motion of electrons and holes in semiconductors and the internal
friction due to point and line imperfections (i.e. dislocations). The motion of
dislocations at high stress values is probably related to creep and fatigue
occurring in metals.
1.1. Thermoelastic Efects
The type of data obtained by acoustic means can be illustrated by two well-
known examples which date back to 1940. In the first example, many metals
1
vibrating in flexure were shown by Bennewitz and Roetger to have internal
friction peaks of the type shown by Fig. 1, at low frequencies. This curve is for
2
Geiman silver. This effect was explained by Zener to be due to the fact that
there is a temperature difference between the expanded and the compressed
parts of the bar which diffuses across the width w with a time constant equal
to
(1)
where D is the thermal diffusion constant K/pCp, K is the thermal conductivity
and pCp the specific heat per unit volume and w the width of the vibrating bar.
The height of the peak is determined by the relaxation strength A which in this
2 1
