SOL~ICATlOr~ PROCESSING TN 630 ,f-53 McGRAW-HILL SERIES IN MATERIALS SCIENCE AND ENGINEERING Editorial Board MICHAEL B BEVER M E SHANK CHARLES A WERT ROBERT F MEHL, Honorary Senior Advisory Editor A VITZUR: Metal Forming: Processes and Analysis AZAROFF: Introduction to Solids BARRETTAND MASSALSKI:Structure of Metals BLATT: Physics of Electronic Conduction in Solids BRICK, GORDON, AND PHILLIPS: Structure and Properties of Alloys BUERGER: Contemporary Crystallography BUERGER: Introduction to Crystal Geometry DE HOFF AND RHINES: Quantitative Microscopy DRAUGLIS, GRETZ, AND JAFFEE: Molecular Processes on Solid Surfaces ELLIOTT: Constitution of Binary Alloys, First Supplement FLEMINGS: Solidification Processing GILMAN: Micromechanics of Flow in Solids GORDON: Principles of Phase Diagrams in Materials Systems GUY: Introduction to Materials Science HIRTH AND LOTHE: Theory of Dislocations KANNINEN, ADLER, ROSENFIELD,AND JAFFEE: Inelastic Behavior of Solids MILLS, ASCHER, AND JAFFEE: Critical Phenomena in Alloys, Magnets, and Super-conductors MURR: Electron Optical Applications in Materials Science PAUL AND WARSCHAUER:Solids under Pressure ROSENFIELD,HAHN, BEMENT,AND JAFFEE: Dislocation Dynamics ROSENQVIST:Principles of Extractive Metallurgy RUDMAN, STRINGER, AND JAFFEE: Phase Stability in Metals and Alloys SHEWMON: Diffusion in Solids SHEWMON: Transformations in Metals SHUNK: Constitution of Binary Alloys, Second Supplement WERT AND THOMSON: Physics of Solids McGRAW-HILL BOOK COMPANY New York St Louis San Francisco Dusseldorf Johannesburg Kuala Lumpur London Mexico Montreal New Delhi Panama Rio de Janeiro Singapore Sydney Toronto MERTON C FLEMINGS Abex Professor of Metallurgy Massachusetts Institute of Technology Solidification Processing This book was set in Times Roman The editors were B J Clark and Michael Gardner; the production supervisor was Joan M Oppenheimer The drawings were done by John Cordes, J & R Technical Services, Inc The printer and binder was The Maple Press Company Library of Congress Cataloging in Publication Data Flemings, Merton C 1929Solidification processing (McGraw-Hill series in materials science and engineering) Includes bibliographical references I Title Solidification Alloys 73-4261 TN690.F59 669'.9 ISBN 0-07-021283-x SOLIDIFICA PROCESSING nON Copyright © 1974 by McGraw-HilI, Inc All rights reserved Printed in the United States of America No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher 567 89-MAMM-76 54321 CONTENTS ~~ T ~:J.>fJ~~:\"",1 - , '''' ~-, ~OTr clr.:.H.:J~~1;;;.f " V· ···· ~ Preface (JH) IX Heat Flow in Solidification r;( !:J.J~~ l.r Growth of Single Crystals Solidification of Castings and Ingots' Casting Processes Employing Insulating Molds Casting Processes in which Interface Resistance is Dominant 12 Analytic Solutions for Ingot Casting Solidification of Alloys Problems in Multidimensional Heat Flow 17 21 24 Plane Front Solidification of Single-phase Alloys 31 Introduction 31 Equilibrium Solidification No Solid Diffusion 33 Limited Liquid Diffusion, No Convection Effect of Convection Czochralski Growth (Crystal Pulling) 34 36 41 44 vi Cellular Solidification Plane Front Solidification of Polyphase Alloys Solidification of Castings and Ingots CONTENTS Zone Melting 115 107 167 172 134 154 146 104 127 120 114 135 112 105 93 66 87 141 157 117 160 94 77 58 75 73 85 83 64 46 49 53 51 Nucleation Kinetics Fluid Flow andof Interface Thermodynamics Solidification Polyphase of Solidification Alloys: Castings and Ingots CONTENTS 290 246 244 234 214 252 279 275 286 284 239 229 264 263 274 295 200 215 267 208 224 219 273 272 177 188 183 207 203 193 191 187 180 vii viii Tabulation ofand Error Functions Tables of Approximate Thermal Data Processing Properties CONTENTS Growth 349 335 328 344 347 309 308 341 338 331 305 301 319 318 312 356 359 357 PREFACE This book has grown largely out of a lecture course given to senior-level and graduate students at Massachusetts Institute of Technology It is intended for use in courses of this type, and also for the practicing engineer and research worker The essential aim of the book is to treat the fundamentals of solidification processing and to relate these fundamentals to practice Processes considered include crystal growing, shape casting, ingot casting, growth of composites, and splat-cooling The book builds on the fundamentals of heat flow, mass transport, and interface kinetics Starting from these fundamentals, the basic similarities of the widely different solidification processes become evident Problems at the end of each chapter relate principles to practice, illustrating important differences, as well as similarities between processes Two years of college-level mathematics provides ample background for solving the problems given and for adequate comprehension of the text In addition, it is desirable, though not necessary, that the student have a previous course in structure of materials Emphasis of the book is on metallic alloys, but other materials are also considered An essential element of all solidification processes is heat flow This subject is treated in the first chapter, primarily to lend cohesiveness to the material to follow It provides an excellent basis for description and comparison of solidification processes, and it can be treated with rather simple assumptions regarding the solidification mechanism Chapter deals with mass transport ("solute redistribution") in single-crystal growth A quantitative description of transport in this type of solidification is"greatly simplified by the fact that the liquid-solid interface is single phase and planar Equations derived in this chapter are also useful in describing dendritic solidification, except that they must be applied to tiny regions on the order of the dendrite arm spacmg Chapter deals with the important question of how to maintain a plane front in crystal growth, and of how solute redistribution occurs when the plane front breaks down to form "cells." Plane-front solidification is considered again in Chap 4, this time for polyphase alloys, such as eutectics and off-eutectic "composites" solidified with an essentially planar liquid-solid interface This chapter is the first to utilize the 350 PROCESSING / - AND PROPERTIES • • • ••••• • •••II ••I• • (0) I (b) • •••• ••• •• • • • • • • • • • ["• , :: ":''':: ' .: , •• ' • '.',,' •••••• ' ' • " (c) 00 ••••• 0' : •••••• I FIGURE 10-19 Schematic illustration of effect of working on second-phase particles (a) Particles and particle spacing are not changed by working; (b) particles deform plastically; and (c) particles fracture break during working Now working alters diffusion distance, as shown in Fig 1O-19b and c, and so can be expected to alter the rate of solutionizing The way the included second phase deforms (or fractures) during working depends sensitively on temperature and rolling conditions, and so it is no wonder that conflicting results are sometimes obtained as to the effect of working on homogenization even for the same alloy Figure 10-20 Shows the effect of one working practice on rate of solutionizing of a high-strength AI-Zn-Mg-Cu alloy Here the second phase deformed and fractured during working, and so the rate of solutionizing depended sensitively on the amount of reduction A similar working practice on a different alloy (AI-4.5% Cu) had little effect on the rate of solutionizing because the second phase particles were not significantly deformed by the working 2.24 Nonmetallic inclusions in steel behave during working as the nonequilibrium second phases observed above Softer inclusions deform plastically, whereas harder ones either break up or remain intact during working Sometimes hard inclusions, such as A1203, separate from a softer phase such as an alumino-silicate phase during working How an inclusion behaves during working depends on its deformability with respect to the surrounding matrix, and so it is dependent both on deformation rate and temperature as well as inclusion composition Optimum working practice (with regard to inclusions) would appear to be those practices that break down large inclusions into less harmful dispersions by promoting their fracture 24-26 Much can be found in the literature on the effects of ingot structure on the properties of wrought material Second-phase particles, whether retained nonequilibrium alloy second phases or nonmetallic inclusions, are particularly injurious EFFECTS OF WORKING .•.• • 1\ .J 0BEFORE 0.9 REDUCTION >0 0; 1/2" FROM CHILL SOLUTION TREATED H 01 lCl J.J J