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

434 Pages·1968·13.55 MB·English
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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-

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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 an
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