Elasticity and Strength in Glasses

287 Pages·1980·8.514 MB·English

by  D.R. UHLMANN and N.J. KREIDL (Eds.)

Contributors
A. S. ARGON
ROGER F. BARTHOLOMEW
F. M. ERNSBERGER
S. W. FREIMAN
ROBERT GARDON
HARMON M. GARFINKEL
GLASS:
SCIENCE AND TECHNOLOGY
Edited by D. R. UHLMANN
DEPARTMENT OF MATERIALS SCIENCE
AND ENGINEERING
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS
N. J. KREIDL
DEPARTMENT OF CHEMICAL
AND NUCLEAR ENGINEERING
UNIVERSITY OF NEW MEXICO
ALBUQUERQUE, NEW MEXICO
VOLUME 5
Elasticity and Strength in Glasses
(yjP) 1980
ACADEMIC PRESS
A Subsidiary of Harcourt Brace Jovanovich, Publishers
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COPYRIGHT © 1980, BY ACADEMIC PRESS, INC.
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United Kingdom Edition published by
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Library of Congress Cataloging in Publication Data
Main entry under title:
Elasticity and strength in glasses.
(Glass ; v. 5)
Includes index.
1. Glass. 2. Elasticity. I. Uhlmann, Donald
Robert. II. Kreidl, N. J. III. Series.
TP848.G56 vol.5 [TA450] 666Ms [620.Γ4432] 80-38
ISBN 0-12-706705-1 (v. 5)
PRINTED IN THE UNITED STATES OF AMERICA
80 81 82 83 9 8 7 6 5 4 3 2 1
List of Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
A. S. ARGON (79), Department of Mechanical Engineering, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139
ROGER F. BARTHOLOMEW (217), Corning Glass Works, Sullivan Park,
Corning, New York 14830
F. M. ERNSBERGER(l,133),PPG/rcrfwsines, Inc., Pittsburgh, Pennsylvania
15238
S. W. FREIMAN (21), Fracture and Deformation Division, National Bureau
of Standards, Washington, D.C. 20234
ROBERT GARDON (145), Engineering and Research Staff, Ford Motor
Company, Dearborn, Michigan 48121
HARMON M. GARFINKEL (217), Corning Glass Works, Sullivan Park,
Corning, New York 14830
Vll
Preface
Recent years have seen a notable series of developments that have
emphasized the importance of amorphous solids (glasses). These include
activity in the areas of fiber optics, optical waveguides, amorphous semi­
conductors, glass lasers, glass-ceramic materials, and photochromic
glasses, to name only a few. In addition to advances related to these areas
of technological application, there have also been notable improvements in
our understanding of the structure, processing, and properties of glass-
forming materials. Regrettably, most of the information developed in these
areas is contained in a myriad of individual research papers and in-house
knowledge, rather than in any convenient central reference source. The
time seemed appropriate, therefore, to bring together the available knowl­
edge about this important class of materials.
"Glass: Science and Technology," of which this volume is the first to
appear, will be broad in its scope. The topics covered will range from fun­
damental understanding of the structure and properties of glasses—based
on applying the disciplines of physics, chemistry, and materials science to
amorphous materials—to highly applied areas such as the melting of glass,
its forming in various shapes, and the use of glass in various important
technological applications. Wherever possible, the common features and
notable differences between glasses and other types of materials will be
highlighted.
At this time 12 volumes are planned. The tentative program is
1 Structure of Glass
2 Submicrostructure of Glass
3 Glass Forming Systems and Glass Ceramic Materials
4 Diffusion, Viscous Flow, and Relaxation Phenomena
5 Elasticity and Strength in Glasses
6 Electrical Properties of Glasses
7 Optical Properties of Glasses
8 Processing of Oxide Glasses
9 Processing of Polymers
10 Thermal and Magnetic Properties of Glasses
11 Glass Surfaces
12 Tabulation of Data
IX
X PREFACE
In view of the rapid progress in understanding and controlling mechani­
cal properties during the past years it seemed appropriate to come out with
Volume 5 first. It appears that much of the confusion about competitive
views of glass as brittle or deformable can now be resolved by relatively
simple concepts.
Engineers have developed and successfully used ideas that clearly distin­
guish the mechanical properties of the glass from the influence of the num­
ber, distribution, size, and shape of flaws, particularly in the surface. Frac­
ture mechanics has been mobilized to predict strength and lifetime under
defined service conditons. The classic art of increasing surface strength by
compression in the flawed surface layer, using controlled quenching, has
been subjected to careful analysis leading to improved products. At the
same time numerous new methods of introducing compression layers by
manipulating composition and structure have become available and are
understood in considerable detail. The editors are confident that in this
treatise the dissemination of the most recent knowledge and its use in this
field has been entrusted to highly competent workers.
GLASS: SCIENCE AND TECHNOLOGY, VOL. 5
CHAPTER 1
Elastic Properties of Glasses
F. M. Ernsberger
PPG INDUSTRIES, INC.
PITTSBURGH, PENNSYLVANIA
I. Introduction 1
II. The Nature of Elasticity in Glasses 2
III. Measurement of Elastic Constants 3
IV. Prediction of Elastic Constants 4
V. Empirical Correlations 5
VI. The Acoustoelastic Effect 7
VII. Phase Separation 8
VIII. Anomalous Elastic Properties of Glasses 9
A. Compressibility 9
B. Non-Hookean Behavior 10
C. Strain Dependence of Poisson's Ratio 11
D. Temperature Dependence of Elasticity 11
IX. Hardness 12
X. Microplasticity 14
References 17
I. Introduction
This review is limited to vitreous silica and the silicate glasses, including
those that contain moderate amounts of other network formers such as
B 0 , A1 0 , and P 0 . Chalcogenide, metallic, and organic glasses are spe­
2 3 2 3 2 5
cifically excluded, although certain concepts may be applicable to these
glasses as well.
It is assumed that the reader is familiar with the definitions and interre­
lationships of the three constants used in small-deformation stress-strain
analysis of isotropic materials. With minor exceptions, glasses are fully
isotropic, even in the form of drawn fibers.
No attempt has been made to assemble data as such; the treatment is
meant instead to identify concepts that have general validity and to empha­
size recent developments. The older literature, including much systematic
Copyright © 1980 by Academic Press, Inc.
All rights of reproduction in any form reserved.
ISBN 0-12-706705-1
2 F. M. ERNSBERGER
property data, is reviewed in a treatise by Morey (1954). The subject is also
briefly reviewed in a recent treatise by Babcock (1977).
In the final two sections, the discussion will depart from the domain of
true elasticity to provide an introduction to the interesting and controversial
behavior of glass at very high levels of stress, such as those applied in an
indentation hardness test. Under these conditions, brittle glasses behave in
what looks very much like a plastic manner.
II. The Nature of Elasticity in Glasses
There is a widespread opinion that glasses are supercooled liquids and
therefore have a finite viscosity at ordinary ambient temperatures. Stories
are told of glasses flowing under their own weight: of ancient windowpanes
that are thicker at the bottom; of glass that has sagged in storage. These
observations must find other explanations, because glasses of commercially
useful compositions are in fact rigid solids at ordinary temperatures. Vit­
reous silica in particular is a nearly ideal elastic material; that is, it does not
creep under load, and it recovers instantly after a prolonged deformation.
On the other hand, glasses that contain substantial amounts of network-
modifying oxides (NagO, CaO, etc.) often exhibit both creep and delayed
recovery. It is probably this behavior that is responsible for many of the
observations that have been erroneously ascribed to cold viscous flow.
These delayed-elastic effects have such long relaxation times that they are
sometimes difficult to distinguish from true viscous flow. Douglas (1966)
stated that "any experiment which purports to measure a viscosity greater
than 1016 poises needs to be examined extremely carefully."
The atomic mechanisms responsible for these ambient-temperature vis-
coelastic effects have not been fully explicated, but there is little doubt that
monovalent cations are involved. The mobility of these ions is severely
restricted by steric and electrostatic considerations, but nevertheless inter­
nal-friction and conductivity measurements show that cation mobility is
detectable down to temperatures approaching that of liquid nitrogen.
The time-dependent nature of the stress-strain behavior of glasses natu­
rally becomes more pronounced as the temperature is raised. These effects
constitute a specialized technical study that will be discussed under the
general topic "Relaxation Phenomena" in this volume. For present pur­
poses it is enough to state that the time dependence of mechanical behavior
of the glasses under consideration is seldom large enough to influence the
measurement of elastic constants, particularly at the high measurement fre­
quencies normally employed.
A more-significant consideration, and one peculiar to glasses, is the state
of anneal, sometimes termed "stabilization." The elastic constants, along
1. ELASTIC PROPERTIES OF GLASSES 3
with density, refractive index, and other intensive properties, change sig­
nificantly with the rate of cooling of a glass through its "transformation
range." The transformation range of a glass may be defined as that temper­
ature range within which its properties spontaneously change at an experi­
mentally observable rate. The property changes arise from changes in the
density of packing. Obviously the limits of this range have no fundamental
definition, but are determined by the time allotted to the experiment and by
the sensitivity of the measurement. In practical terms, the existence of this
stabilization effect means that property data of extraordinary precision
have no particular absolute significance unless the thermal history of the
sample is carefully specified.
III. Measurement of Elastic Constants
Ultrasonic techniques continue to be favored for measurement of the
elastic constants of glasses. Manghnani and his co-workers specialize in
this field. They have elevated the pulse-echo technique to new levels of
precision and accuracy by the superposition of pulses and echoes in the
manner of interferometry. Even the elusive Poisson ratio is being reported
to four significant figures.
With such precision at hand, it becomes profitable to study the effects of
pressure and temperature on the elastic constants. Manghnani et al. (1969)
measured the constants for Vycor high-silica glass to 8 kbar. Skolowski and
Manghnani (1969) measured calcium aluminate glasses to 3.5 kbar. Subse­
quently, Manghnani (1972) measured six glasses in the Na20-Ti0 -Si0
2 2
system to 7 kbar and 300°. Manghnani (1974) has also studied the new low-
expansion glasses in the Si0 -Ti0 system as a function of temperature,
2 2
pressure, and composition. Data on a commercially produced soda-lime
glass to 400° are awaiting publication.
An elegant new measurement technique appeared recently with the pub­
lication of a paper by Huang et al. (1973) on a determination of elastic
constants by Brillouin scattering. A few words about the principles under­
lying this unusual technique are appropriate.
At any temperature above absolute zero, all elastic solids contain ther­
mally activated density fluctuations that propagate within the solid in all
directions at sonic velocities with many superimposed frequencies. If a
transparent elastic solid is probed with a laser, Brillouin scattering occurs
from those trains of density waves whose frequency and direction of prop­
agation happen to satisfy the Bragg condition for the laser beam; Rayleigh
scattering occurs as well, of course. Thus the spectrum of the scattered
light consists of five lines: a central Rayleigh peak at the laser frequency
flanked symmetrically by pairs of sum-and-difference peaks. One pair
4 F. M. ERNSBERGER
reveals the frequency of the longitudinal acoustic mode; the other, that of
the transverse mode. Thus it is possible to calculate both Young's modulus
and the shear modulus and, from these, Poisson's ratio.
The acoustic frequencies involved are in the hypersonic range; that is, in
gigahertz. Nevertheless the elastic constants are not distinguishably differ­
ent from those measured at low frequencies.
An unusual ultrasonic technique was described by Fräser and LeCraw
(1964). The elastic constants were deduced from observations of reso­
nances excited in a small spherical specimen. Soga and others (1967, 1968)
subsequently applied this technique in several interesting studies of glasses
and ceramics. The main advantage seems to be in the small size (300 /xm-
5 mm) and simple geometry of the samples that are used.
A novel method for the measurement of elastic constants was demon­
strated by Sinha (1977). A strip of elastic material whose thickness is not
too small relative to its width will exhibit a saddle-shaped (anticlastic) cur­
vature when bent. The elastic constants can be deduced from appropriate
measurements of this complex curvature. The results are not highly precise
(only two significant figures were obtained), but the method has the advan­
tage that it is applicable at elevated sample temperatures when noncontact-
ing optical methods are used to obtain the curvatures.
Elastic constants can sometimes be estimated from information that
might seem to be totally unrelated. For example, Szigeti (1950) proposed
an equation relating the bulk modulus of crystals to the maximum fre­
quency of infrared reflection. Anderson (1965) subsequently demonstrated
the applicability of this equation to glass.
The existence of this relationship illustrates the great fundamental signif­
icance of elastic constants, related as they are to interatomic forces and
vibrational frequencies. Sanditov and Bartenev (1973) have proposed rela­
tionships between bulk modulus and still other solid-state properties such
as thermal expansion coefficient, glass transition temperature, and micro-
hardness. It does not appear that these have yet been independently
verified.
IV. Prediction of Elastic Constants
One of the ultimate goals of scientific endeavor is to make empirical mea­
surements unnecessary. This goal has been attained when our understand­
ing of a phenomenon becomes so profound that the desired quantities can
be calculated from a few fundamental constants. A paper by Makishima
and Mackenzie (1973) embodies a significant degree of progress in this
direction.
The derivation is adapted from an existing theoretical treatment of