YIELD POINT PHENOMENA IN METALS AND ALLOYS Yield Point Phenomena • In Metals and Alloys E. O. Hall Plenum Press NEW YORK © E. O. Hall 1970 Softcover reprint of the hardcover 1s t edition 1970 US Edition published by PLENUM PRESS a division of Plenum Publishing Corporation, 227 West 17th Street, New York, NY 10011 Library of Congress Catalog Card Number 75-120336 ISBN-13: 978-1-4684-1862-0 e-ISBN-13: 978-1-4684-1860-6 001: 10.1007/978-1-4684-1860-6 Preface Exceptions to the rule are always interesting, and the anomalies in the stress-strain curves of mild steel and in many other metals and alloys have excited the curiosity of engineers and scientists for well over a hundred years. Yet it is only during the last twenty years that significant theoretical advances have been made, and the aim of this book has been to examine these theories against the background of the considerable volume of experimental results published over the last few years, up to mid-1969. Hence this review volume has a two-fold aim; the first chapter attempts to review the general theories of yield point phenomena, using sufficient examples only to illustrate the theories. This chapter is intended to be complete in itself, and could be read by under graduates who wish to appraise rapidly the general background to the problem. The remaining chapters deal, in turn, with the various alloys exhibiting yield point phenomena. Thus, chapter 2 on mild steel, is a more extensive study of quench and strain ageing, while Chapter 3 is on the refractory metals and discusses theories of the low-temperature strength. The next concerns hydrogen in meta-Is. Chapters 5 and 6 discuss the face-centred cubic alloys, particularly the cases of the unloading yield point and intermetallic compounds. Chapter 7 covers hexagonal and ionic structures. A brief final chapter considers the areas where further research may be fruitful. Some knowledge of dislocation theory and stereographic projection must be assumed, but the aim is to make the book as self-contained as possible, and of interest to a wide range of solid-state physicists, metallurgists and engineers. Acknowledgments I started this book while on sabbatical leave at the University of Cambridge in 1966 and therefore wish to thank both the University of Newcastle, for granting the leave, and Professor R. W. K. Honey combe, of Cambridge University, for the use of facilities in his department. In addition, the help given by colleagues in supplying either unpublished data, or data prior to publication, is acknowledged in the text. Finally, I wish to thank Mrs. J. Saunders and Mrs. E. Burns for their careful typing of the draft and final copy respectively. Contents Preface v Acknowledgments VI List of Plates viii 1 YIELD POINT PHENOMENA AND THEIR THEOR- ETICAL BACKGROUND 1 Introduction - The effects of tensile machine and specimen stiffness - Types of yield point effects - The upper yield point-experimental-The upper yield point-theoretical - The lower yield point - Strain ageing - Pseudo yield points 2 IRON AND ITS ALLOYS 65 Introduction - Effects of carbon, nitrogen and other elements - Quench ageing - Yielding behaviour - Strain ageing kinetics - Effects of radiation damage-Single crystals - Steels 3 THE GROUP VA AND VIA METALS 127 Introduction - Vanadium - Chromium - Niobium - Molyb denum - Tantalum - Tungsten - Alloys of these metals Discussion 4 HYDROGEN IN METALS 157 Hydrogen embrittlement - Solubility of hydrogen in metals - Mild steel-Group Va and VIa metals - Nickel Palladium - Titanium and zirconium 5 ALUMINIUM AND ITS ALLOYS 171 Introduction - The unloading yield point effect - ' Com mercially pure' aluminium - Aluminium-copper alloys Aluminium-magnesium alloys - Other aluminium alloys Theories ofy ield points in aluminium alloys viii Contents 6 OTHER FACE-CENTRED CUBIC METALS AND ALLOYS 201 Introduction - Copper and its dilute alloys - Brass - Silver and its alloys - Nickel and its alloys - Thorium - Ordered alloys 7 MISCELLANEOUS MATERIALS 233 Introduction - Whiskers - Ionic crystals - Semiconducting materials - Hexagonal metals and alloys 8 DISCUSSION 256 APPENDIX 260 BIBLIOGRAPHY 262 INDEX 287 List of Plates opposite page 1.1 Luders bands in mild steel 24 1.2 Luders bands in pie dish 24 1.3 Shear at front of Luders band 25 1.4 Luders bands in mild steel 25 1.5 Luders bands 25 1.6 Dislocation loops 56 1.7 Dislocation cell structure 56 2.1 Dislocations in N-Fe alloy 57 2.2 Band markings in mild steel 57 2.3 Stacking faults in steel 57 3.1 Defects in chromium 152 3.2 Strain markings in tantalum 152 4.1 Luders bands in steel strip 153 4.2 Dislocation patterns in nickel 153 5.1 Band markings in AI-Cu alloy 184 5.2 Strains in AI-Mg alloy 184 7.1 Dislocations in Mg-Th alloy 185 1 Yield Point Phenomena and their Theoretical Background 1.1 Introduction When certain materials such as mild steel are deformed in tension, it is found that the stress-strain curve is not smooth, but shows marked irregularities, with negative slopes occurring at or near the initial yield on the curve. The actual shape of the stress-strain curve is de pendent, to some extent, on the type and characteristics of the tensile testing machine used; nevertheless one may include all cases where Sa/S€ is negative as examples of yield point effects deserving attention. Again using mild steel as an example, the progress of deformation may be divided into three stages, as shown in Fig. 1.1. The normal elastic extension AB is terminated at a stress level known as the upper yield stress au. Deformation then proceeds at a decreased stress level known as the lower yield stress aL, but the deformation at this stage is not homogeneous: the specimen is divided into regions, known as Luders bands (after Luders (1860)t), where the strain has the value shown in Fig. 1.1, and other regions which are not yet deformed €L with zero strain. These bands are also known as Hartmann lines, after Hartmann (1896) or as 'stretcher strains'. Since this Luders strain can in steel be as high as 5%, dependent on grain size, the deformed regions on a test specimen may be clearly shown under conditions of critical illumination. Plate 1.1(a) shows a Luders band in a steel strip specimen, and Plate l.1(b) in a stiffer, heavier specimen. Although the morphology differs in the two cases, in both specimens the upper yield stress may be regarded as a nucleation stress, and the lower yield stress as the growth stress, of the Luders bands themselves. t In fact, these bands were first noted by Piobert (1842) - French publica tions often refer to these bands as the Piobert-Luders phenomena. 1- 2 Yield Point Phenomena in Metal and Alloys Thus, at the lower yield stress, deformation proceeds by the growth of Luders bands, which spread along the specimen, until at the point D (Fig. 1.1) the entire surface of the test specimen is covered, and all areas of the test length have been strained by an amount Beyond €L. this point, from D to the ultimate tensile stress at E, deformation is essentially homogeneous and thereafter necking develops, leading to normal ductile fracture at F. As will be seen, there are numerous variants of this stress-strain curve, dependent on material, temperature, grain size and other metallurgical variables; nevertheless these general principles may apply. The technological importance of yield points is great; in pressed mild steel components for example, the Luders bands may Siress E , I F o I I I I ,I I J I ,I ,I I A I ~L $Iroin FIGURE 1.1. Diagrammatic stress-strain curve of mild steel lead to markings resulting from the inhomogeneous deformation these are commonly known as stretcher strains. Plate 1.2 shows a typical example in a pressed steel pie dish, where in most cases cus tomers are not concerned with irregularities on the underside of pies, but in other examples of large pressed components, such as motor car bodies, stretcher strains make it difficult to achieve the high degree of surface finish required prior to painting. Elaborate procedures are adopted, such as deforming the sheets by temper rolling, or roller levelling by a total amount somewhat less than so that on subse €L, quent pressing, deformation will occur virtually homogeneously from the numerous Luders band nuclei so produced (see, for example, Butler and Wilson (1963) and Verduzco and Polakowski (1966». Yield Point Phenomena and their Theoretical Background 3 Although in certain alloy systems the Luders strains may exceed several hundred per cent, in others the value of may be exceedingly €L small. The variations involved and their dependence on the metal lurgical variables is the core of this monograph. 1.2 The effects oft ensile machine and specimen stiffness Before studying yield point phenomena any further, it is necessary to dispose of two elementary, yet important, aspects of the measure ment of yield points; the effects of the tensile machine and specimen stiffness. Tensile machines are divided into two types, the so-called 'soft' and 'hard' machines. In the former, the load is considered con nected to the specimen by a soft spring, so that if the specimen yields suddenly the load is virtually unaffected. Deadweight loading, hy draulic machines and pivoted beam type tensile machines come in this category, although in the latter, some allowance can be made by not ing the drop in the beam as the yield point is reached. But for follow ing rapid changes in load, such as is found with mild steel at elevated temperatures, these are of limited value. For accurate measurements, and to follow rapid changes in load, hard machines are necessary. Here the load is measured and transmitted to the specimen by a load cell and stiff members, so that very small sudden elongations in the specimen result in a large drop in load, and accurate and rapid record ing of load is likewise essential. Tensile machines of the Instron type or, for lighter loads, the inverted Polanyi type described by Adams (l959), are convenient for this study. Load cells, with outputs recorded on fast (1 s F.S.D.) recorders, are also essential. The effects of machine rigidity may be simply illustrated by reference to Fig. 1.2(a). Here, the tensile specimen shown is imagined to have a Young's modulus E, while the machine and supporting members have an effective spring constant K. Thus, under a load L, the extension of the system is L/K + Ll/(AE) where 1 is the specimen length and A its cross section. If the specimen extends by an amount Sl the overall extension is constant; the load measured changes by SL so that SL(1/K + l/(AE)) + L Sl/(AE) = 0 SL/L = - Sl/(AE/K + /) For a given value of Sl, it can easily be seen that as K 0 for very ---,)0- o. soft machines, SL/L ---,)0- The spring constant K of the machine may be determined quite
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