Mechanical Behavior of Materials under Dynamic Loads: Symposium Held in San Antonio, Texas, September 6-8, 1967

434 Pages·1968·13.55 MB·English

by  Markus Reiner (auth.)

Mechanical Behavior of Materials
under Dynamic Loads
Mechanical
Behavior of Materials under
Dynamic Loads
SYMPOSIUM
HELD IN SAN ANTONIO, TEXAS, SEPTEMBER 6-8, 1967
SPONSORED BY THE ARMY RESEARCH OFFICE, DURHAM
AND THE SOUTHWEST RESEARCH INSTITUTE
EDITOR
Ulric S. Lindholm
SOUTHWEST RESEARCH INSTITUTE
SAN ANTONIO, TEXAS
Springer-Verlag New York Inc .• 1968
ISBN-13: 978-3-642-87447-5 e-ISBN-13: 978-3-642-87445-1
DOl: 10.1007/978-3-642-87445-1
All rights reserved.
No part of this book may be translated
or reproduced in any form without
written permission from Springer-Verlag.
© 1968 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1968
Library of Congress Catalog Card Number 68-22687
Title Number 1501
PREFACE
An adequate physical and mathematical description of material be
havior is basic to all engineering applications. Fortunately, many prob
lems may be treated entirely within the framework of elastic material
response. While even these problems may become yuite complex be
cause of geometrical and loading conditions, the linearity, reversibility,
and rate independence generally applicable to elastic material descrip
tion certainly eases the task of the analyst. Today, however, we are in
creasingly confronted with practical problems which involve material
response which is inelastic, hysteretic and rate dependent combined
with loading which is transient in nature. These problems include, for
instance, structural response to moving or impulsive loads, all the areas
of ballistics (internal, external and terminal), contact stresses under
high speed bearings, high speed machining, rolling and other metal
working processes, explosive and impact forming, shock attenuation
structures, seismic wave propagation, and many others of equal im
portance. As these problems were encountered, it became increasingly
evident that we did not have at hand the physical or mathematical
description of the behavior of materials necessary to produce realistic
solutions. Thus, during the last ten years particularly, there has been
considerable effort expended toward the generation of both experi
mental data on the dynamic mechanical response of materials as well
as the formulation of realistic constitutive theories. It was the purpose
of the Symposium at which the articles in this book were presented to
discuss and review recent developments in this field.
Dynamic loading in the present context was taken to include de
formation rates above those achieved on the standard laboratory
testing machine (commonly designated as static or quasi-static). While
slow tests may encounter time-dependent effects, such as creep and
stress-relaxation, and therefore are in a sense dynamic, these topics
were not explicitly included in the Symposium. Rather, the emphasis
was on rates of loading encountered in impact problems where in
ertia forces as well as viscous type forces may playa dominant role. The
reader will find papers related to the interpretation of results from
high-speed testing machines, impact or impulsive loading of bars,
plates, cylinders and spheres, and the propagation of cracks; all with
the purpose of defining the intrinsic dynamic mechanical properties
v
vi Preface
of the materials under study. There are, in addition, papers dealing
with the fundamentals of the development of a basic constitutive
theory for solids. This theory is developed in different papers from
the standpoints of classical continuum mechanics, from the fundamen
tal laws of thermodynamics, and from the microscopic point of view
through consideration of dynamic dislocation mechanisms for crystal
line solids. It was the intention of the organizers of the Symposium to
bring together those applying these apparently divergent approaches
to the same basic end objective, since it was felt that future develop
ments in this area will depend upon a synthesis of the results from such
areas as mechanics, thermodynamics, the materials sciences, and cer
tain aspects of solid state physics.
While the majority of the papers are concerned with the plastic
flow of metals, other materials treated include those which exhibit
viscoelastic behavior, rocks, and a specific foam composition. This
distribution is not in proportion to importance, but rather reflects the
relative level of effort in the technical community on dynamic proper
ties of the several classes of materials. The future will undoubtedly see
an increased interest in the non-metallics as their applications expand.
The Symposium was held on September 6-8, 1967, in San Antonio,
Texas, and was attended by approximately 150 persons. There were
five technical sessions with invited technical papers being presented
by distinguished researchers from this country and abroad. At the
conclusion of the technical presentations, the five session chairmen
were given the unenviable task of summarizing in a few (10) minutes
the papers presented and the state-of-the-art in their areas of interest.
These closing comments are included at the end of this volume and
are well worth the readers' close attention.
The program was as follows:
WEDNESDAY, SEPTEMBER 6
Session Ia 9:00 am
CHAIRMAN: U. S. Lindholm, Southwest Research Institute
Martin Goland, President, Southwest Research Institute: Welcoming Re
marks
Sudhir Kumar, Army Research Office-Durham, Durham, N.C.: Me
chanics/Materials Aspects of Dynamic Loading
Session Ib 10:00 am
CHAIRMAN: W. Prager, University of California at San Diego
M. Reiner, Technion-Israel Institute of Technology, Haifa, Israel:
Dynamical Strength of an Ideal Solid With Definite Constitutive Equation
(Presented by Dr. Amnon Foux)
J. F. Bell, The Johns Hopkins University, Baltimore, Maryland: An Ex-
Preface vii
perimental Stud" of Illstability Phenomena III the Initiation of Plastic Waves
ill LOll.£!: Roell'
0, W, Dillon, Jr., Cniversity of Kentucky, Lexington, Kentucky: Plastic
De/ormation Waves and Heat (;enended Sear the Yield Point of Annealed
Aluminum
Session II 2 :00 pm
CIIAIRMAr-.;: D, C, Drucker, Brown Cniversity, Providence, R.I,
p, Perzvna, Polish .-\cademv of Sciences, V\' arsaw, Poland: On Thermo
dynamic Foundations of ViscojJlasticity
LT, S, Lindholm, Southwest Research I nstitute: Some EXjJerimellts ill
DYllamic Plasticity Cllder Combined Stress
,\1, F, Kanninen, \, K, '\lukherjee, A, R, Rosenfield, and G, T Hahn,
Battelle '\Iemorial Institute, Columbus, Ohio: The Speed of Dllctile
emf'k ProjJap,ation and the Dynamics oj Flow ill ;'vIetals
J :\1. Kraft't, :'\aval Research Laboratorv, \\'ashington, D,C: DYllamic
l'vIechanica/ Behlwior of i'vIetal at the Tij) o/a Plalle Strain Crack
T H l' R S DAY, S E PTE M B E R 7
Session III 9:00 am
CHAIRMAN: J. D. Campbell, Cniversitv of Oxford, Oxford, England
J. J. Gilman, Cniversitv of Illinois, Crbana, Illinois: Dynamical Behavior
of Dislo((Jtiolls
S. R. Bodner, Technion - Israel Institute of Technology, Haifa, Israel:
Constitutive Equations for Dynamic Material Behrn'ior
J. W. Edington, Battelle '\femorial Institute, Columbus, Ohio: Effect 0/
Strain Rate on the Dislocation Substructure in Dr/onned Siobium SinKlr
CI),stals
W. J. Gillich, C .S. Army Ballistic Research Laboratories, Aberdeen
Proving Ground, Marvland: Constitutive Relationships From Impact
Studies
Session IV
CHAIRMAN: C. D. Lundergan, Sandia Corporation, Albuquerque, N.M.
A. H. Jones, C J. Maiden, S . .J. Green, and H. Chin, General '\fotors
Technical Center, Warren, Michigan: Prediction oj Elastic-Plastic Wave
Profiles ill AlulIlinllm 1060-0 ('nder Cniaxial Strain LoadinK
C. H. Karnes, Sandia Corporation, Albuquerque, N.M.: The Plate Im
jJact COllfiKlImtioll lor Determillilll,i Mechani((ll ProjJuties of Alaterials at
HiKh Strain Rates
E. A. Ripperger. The Cniversitv of Texas, Austin, Texas, and H. Wat
son, Jr., Southern '\1ethodist University, Dallas, Texas: The Relationship
Belil'efll the COllstitutil'e Equation lind Ollf-Dimensiolllllliim'l' ProjJIll,iatioll
1. M. Fyfe, Cniversity of Washington, Seattle, Washington: Plane-Strain
Plastic WIlL'e ProjJlll,illtion in a Dynamical/y Loaded Hal/ow Cylinder
mii Preface
FRIDAY, SEPTEMBER 8
Session V 8:30 am
CHAIRMAN: D. M. Forney, Jr., AFML, Wright-Patterson Air Force Base,
Ohio
N. Cristescu, Mathematical Institute, Bucarest, Romania: Dynamic Plas
ticity Under Combined Stress
K. C. Valanis, Iowa State University, Ames, Iowa: Unified Theory ofTher
momechanical Behavior of Viscoelastic Materials
W. E. Jahsman, Lockheed Missiles and Space Company, Palo Alto,
California: Static and Dynamic Material Behavior of Syntactic Foam
J. B. Cheatham, Jr., Rice University, Houston, Texas: The Effect of Pres
sure, Temperature, and Loading Rate on the Mechanical Properties of Rocks
The Symposium was held under the joint sponsorship of the Army
Research Office - Durham and the Southwest Research Institute. The
committee responsible for the planning and arrangements for the
Symposium were:
Ulric S. Lindholm, Southwest Research Institute, San Antonio, Texas
(CHAIRMAN)
Sudhir Kumar, Army Research Office-Durham, Durham, North Carolina
(HONORARY CO-CHAIRMAN)
H. Norman Abramson, Southwest Research Institute, San Antonio, Texas
(HONORARY CO-CHAIRMAN)
Philip H. Francis, Southwest Research Institute, San Antonio, Texas (SEC
RETARY)
David L. Black, Southwest Research Institute, San Antonio, Texas (SYM
POSIUM COORDINATOR)
U. S. LINDHOLM, Editor
INTRODUCTION
MECHANICS/MATERIALS, ASPECTS
OF DYNAMIC LOADING
SUDHIR KUMAR
U.S. Army Research Office-Durham
Durham, N.C'.
The behavior of materials under dynamic loads is obviously of con
siderable interest ill most mechanical analyses of design problems
where dynamic loads are present. Unfortunately, much of the engi
neering design today is still based on the static loading properties of
the material rather than dynamic properties. Quite often this means
over-design at best apd incorrect design resulting in failure in the
worst cases. The problem, however, has continued to exist due to in
sufficient basic knowledge and understanding of the behavior of dif
ferent materials in spite of significant advances made in the recent
past. This conference, and several other conferences [1-7] sponsored
by ARO-D, AIME, ASTM, OSR, ASME and Battelle in the last eight
years, is essentially an attempt towards such advancement.
The complex nature of the dynamic behavior problem can be seen
from Fig. I -I, which depicts the whole range of interaction of dynamic
loads with various materials. Ideally, it will be desirable to know the
mechanical response to the full range of dynamic loads for each ma
terial. However, certain load-material interactions have more relative
importance for engineering design, and significant work on them
exists already. Uniquely, the metals under both static and dynamic
loads can be cited as the outstanding case. Botb the continuum mechan
ics engineers and the metallurgical engineers found these materials to
be most attractive to study. At the same time, it must be confessed that,
relatively speaking, these materials were easier to handle for analysis
and for scientifically planned and reproducible experiments. Even so,
there is a great deal that we don't understand about them, in spite of
voluminous scientific literature existing in this area. Each type of load
response, e.g., creep, vibratory or hypervelocity impact, is a big field
IX
x Introduction
Creep and Re Vibratory & Low Velocity High Velocity Hypervelocity
laxation type Transient Impact Impact Impac>t
loads, thermal Loads (millisecs. ) (microsecs. ) (vel. C)
I ads
Geologic Metallic Plastics Natural Or Composite
Rocks, Soil s, Metals and Polymeric, ganic, Inor FRP,
Ceramics, Alloys Organic & ganic & Sandwich,
Concrete, I norgan ic, Fibrous Sol id Pr opel
Plasters, etc. Synthetic Wood, Cotton, lant, etc.
Silk, Wool,
etc.
Fig. 1-1. Load Material Interaction.
in itself. Of course, the importance of plastics and composite materials
has been steadily growing as they become more and more competitive
with metals. Consequently, more work on them would be normally
expected in the future. For certain engineering problems and applica
tions, e.g" in foundations of buildings and other structures, the knowl
edge of behavior of soils and rock strata is of utmost importance.
Much of the investigations for such materials have been in the creep
type or slow strain rate studies. Engineering problems concerned with
higher rates of loading have to be solved by empirical and trial-and
error methods while using very high factors of safety. As more tools
for scientific investigation of dynamic behavior of materials become
available, the activity and results in this field are also bound to grow.
The subject of the symposium today is thus a most challenging one and
it offers a lot of open fields for exploration.
The mechanical response of various materials may be classified in
several types, as shown in Fig. 1-2. For each type of behavior there is a
primary load environment. Considerable work has been done in creep,
fatigue, fracture and hypervelocity impact in the past. During and
after the World War II period, extensive activity in plastic wave propa
gation, notably by von Karman [8] and Taylor [9], also took place. It is
perhaps noteworthy that about ten years back the knowledge of the
true mechanical behavior of materials in the low and high energy
Introduction xi
Types of Behavior of Primary
Materials Under Load -Environment
Dynamic Loads
]
Ablation
High and Moderate
Creep, Relaxation Temps.
-
Fatigue Elastic Range
Vibration or
Viscoelastic
Low Energy Impact
Elastic -
Elasto-Plastic Vibration or High
- Energy Impact
Fluid-like Flow and ] Very High Vel. or
State Transformation, Hypervel.
e. g., Solid to Gas Impact
Crack Propagation & ]
Environmental Fractu re
Embrittlement
Fracture - both
brittle & ductile
Fig. 1-2. Material Behavior-Load Environment Diagram.
impact range covering the elastic, elasto plastic and viscoelastic type
behavior, the strain rate and thermodynamic effects, and the associ
ated dislocation dynamics was quite elementary. Recognizing this,
about seven years back ARO-D initiated a small basic research program
to attempt to fill this gap. But before we get to that, it is proper to men
tion that load environment, which is primarily considered in this pro
gram, is only one of the four physical environments (Fig. 1-3) which in
fluence the behavior of materials. Of course, the problem being quite
complex, it was desirable to consider the environment parameters
separately in order of their importance to the engineering problems.
Moreover, limited funds required limitation of the scope of this pro
gram. At this point a brief mention of the ARO-D research programs is
in order. The various basic research projects supported by this agency
are in two major categories: one, Exploratory Basic Research, or basic
research in any area of choice of the investigator; and two, Oriented
Basic Research, or research in specific areas selected by ARO-D for
existing gaps and relative importance. The area of "Mechanical Be
havior of Materials under Dynamic Loads" was selected as one such
area for Oriented Basic Research. Including this conference today,
eight projects have been supported during the last six years. Five re-