F. V. L E N E L
0 . S. ANSELL
METALS, CERAMICS, POLYMERS
Interdisciplinary Aspects of Sintering and Plastic Deformation One of the most challenging problems facing technologists today i s that o f finding methods for predicting behavior o f materials under different environments and stress conditions. Several technologies are involved, and much can be gained through cross-fertilization among these areas; that is, through applying understanding achieved for one class of materials t o another class. However, little has been done in this direction, and the possibilities are just beginning to be explored. In this interdisciplinary aspect of materials, the llikon Corp. of Natick, Moss., is active. Its operations are diversified among several materials areas and, in accordance with this spread of interests, it i s sponsoring a series o f symposia, the first of which was held in Boston, Moss., earlier this year. In this symposium, research scientists, engaged in metals, ceramics, and polymers, met and discussed sintering ond plastic deformation for each o f these three important classes o f materials. Specifically, they discussed the driving forces which cause changes in geometry, and material transport mechanisms b y which these changes occur. Co-chairmen of the symposium were Professors F. V. Lenel and G. S. Ansell o f Rensselaer Polytechnic Institute. During the morning session, devoted t o sintering, Lenel discussed metals; Professor Robert Coble o f MIT, ceramics; and Dr. J. F. Lontz o f Du Pont, polymers. During the afternoon session, devoted to plastic deformation, Professor G. S. Ansell of Rensselaer discussed metals; Professor J. J. Gilmon o f Brown University, ceramics; and Professor S. S. Sternstein o f Rensselaer, polymers. After each session the speaker plus several invited scientists, including Dr. H. H. Hausner and Dr. 1. J. Bonis, president of Ilikon, conducted a panel discussion. 46
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As the basic phenomena of material sciences become more clearly understood, scientists interested in the structure and properties
of materials are
increasingly concerned with application of these basic phenomena to other classes of materials is the most important step in converting S’mtmng particulate . material such as metallic, ceramic, and polymeric powders into solid products. Several methcds are used. In one, the powder is pressed in a steel mold into the desired shape called a compact by metallurgists and ceramists, and a preform by polymer scientists. Then, to increase density, strength, and improve other physical properties, the compact or preform is sintered (also called liriig in ceramics) by heating to elevated temperatures. In another method, applicable to ceramics mainly, but also to metals, the powder is consolidated by slipcasting-i.e., by suspending the powder in a slurry and then casting the slurry into a mold, usually of plaster of Paris, which absorbs the liquid vehicle. Also, metal powders can be sintered as loose powder aggregates after being vibrated into a mold or they may be bot pressed-Le., pressed and heated at the same time. Polymers are often hot pressed or even extruded, but comparison of the mechanisms active with those active during sintering of metals and ceramics is dficult. Therefore the discussion of polymer sintering is confined to polytetrafluoroethylene (Teflon) which is commonly cold pressed and then sintered.
RlGlNAL 'HERE
When mixtures of powders are used, several variations are introduced into these procedures. One of the least understood effects is obtained when small additions are made to powders-for example, in metals the nickelactivated sintering of tungsten, and in ceramics the calcium oxideactivated sintering of beryllium. I n both cases, extremely small amounts of nickel or calcium oxide increases densification rate and lowers temperature at which the sintering occurs. After comparing the two phenomena, Coble postulates that this effect may result from rapid diffusion in a monolayer of the additive 3n the surface of the principal constituent. Changes in geometry during sintering are caused by changes in contact or neck area between the particles, decreases in total pore volume, and in the average distance between the centers of the particles. These changes have been studied in model experiments and in actual compacts and aggregates. The model experiments used are similar for all three types of materials. For example, sintering a small metal sphere in contact with a metal plate or two spheres of aluminum oxide in :ontact with each other; sintering three metal wires twisted together, or seven sections of polymer resin heading after they have been twisted; or sintering a metal wire or even a wound metal wire spool on a metal rod. Also, experiments on actual compacts or aggregates 2f the three materials closely resemble each other. Changes in pore shape, pore size, and size distribution can he observed. I n addition to pore characteristics, Coble emphasized that for crystalline materials, particularly metals and ceramic materials of ionic character, grain structure and grain size must he closely observed because of their influence on shrinkage characteristics. (Continued on next pagc) VOL 5 5
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In metal powder and ceramic powder compacts, surface tension forces are the most important driving forces causing increase in neck area, rounding and spheroidization of the pores, shrinkage of the pores, and densification. However, they are not the only forces acting on compacts. Recent careful studies by Lenel and others of shrinkage in copper powder aggregates and compacts have shown that gravity plays a role in sintering and that even residual streses from the pressing operation may cause dimensional changes. In sintering of polytetrafluoroethylene, Lontz showed that strain recovery which corresponds to the relief of residual stresses in metal powder compacts, is the dominant reason for dimensional changes in polytetrafluorethylene, but that surface free energy undoubtedly also provides part of the driving force for the process, since compacts with smaller voids coalesce more rapidly than those with larger voids. The first and by now classical model experiments on the mechanism of material transport in sintering powders are those of Kuczynski, first publiihed in 1949. Kuczynski observed the increase in neck area between spherical powder particles resting on flat plates with increasing time. From the relation between the radius of the neck area and the time of sintering, he deduced that in metals the mechanism of material transport should be vacancy diffusion, but in glasses it should be viscous creep. The model originally postulated by Kuuynski has since been considuably refined; particularly, the importance of grain boundaries as sinks for the vacancies which diffuse from the pores during shrinkaer of compacts has been brought out. It is
interesting to note that powder metallurgists as well as ceramists and polymer scientists go back to the Kuczynski concept, in either its original or m d i e d form, in order to analyze the material transport mechanism. For Fe& Coble showed that by using the diffusivities of iron and oxygen ions the s h r i i g e of compacts can be calculated quantitatively on the basis of the vacancy diffusion concept. O n the other hand, the sintering of aluminum oxide spheres, particularly under the influence of an externally applied load, cannot be so analyzed. Either modifications in the vacancy diffusion mechanism or an entirely different mechanism must be developed. Coble called attention to the fact that in ceramic materials with covalent bonding, such as silicon carbide or the diborides, complete densification during sintering without the application of external forces is not possible. This may result from the slow rate of vacancy dffision in these materials. Lontz's attempt to analyze the increase in the neck area between his polytetrafluoroethylene beads on the basis of Kuczynski's model for viscous creep in glasses was not successful when a steady state viscosity was introduced. He concludes that for polytetrafluoroethylene the simple viscosity component must be modified by an appropriate retardation constant or constants in order to take into account the viscoelastic behavior of his material. For metals, however, the mechanism postulated by Kuczynski is successful in explaining his original experiments, later experiments of Alexander and Balluffi on &e sintering of spools of copper wire, and Kuczynski's more recent experiments on three wires twisted
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A
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/
POWDER Q.4Rr'cLEs
GRAIN CBOUNDARIES
A Figure 3. The uaconry dffusionconcrpf. Vacancies dfue from neck o m rapidly olong groin barndories IO oun Mfoccr of pow& pwlules, nroducing nd mdniol rronspmr Io ntc& OW(I. This c o u m growlh in ptd mro. WilhmJ nuh boundwy paths f m dfw'm, r l o w bulk or uolwns d$@ion u d d @oc much s l o w neckgrawlh or rinlm'ng roles 46
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R
A
Figure 6.
B Trammission electron micrographs of AI-Mg alloys
C
A. A slip band containing many dislocations mouing diagonally across the figure. B. TWOdislocations nucleated at a hole in
the thin foil and moving into the material leaving slip traces behind. C. Dislocations moving toward a grain boundary
together. Nevertheless, it appears doubtful that all sintering phenomena in metal powders can be attributed to this mechanism. Recent experiments by Lenel and others led to the conclusion that in metal powder aggregates sintered at low temperatures, below one half of the melting point of the metal, as well as in metal powder compacts sintered at temperatures near the melting point, plastic flow must be an important material transport mechanism.
scribed two methods : l-rheological descriptions which historically have been emphasized. Here, mathematical expressions have been formulated which describe the deformation behavior of materials as a function of stress, strain, strain rate, and temperature. Although useful, these descriptions are tedious to obtain because extensive testing programs are needed where the material is deformed over the same range of test variables for which the description is to be applicable. After this long and expensive procedure, the resultant rheological expression is formulated and can be applied only to particular type of material tested. 2. During recent years, such rheological descriptions have been supplemented, and in some cases supplanted
Plastic Deformation
When stress is applied to materials, the total amount of deformation is composed of three parts-elastic, anelastic, and plastic. The instantaneous elastic and timedependent anelastic portions are both recoverable-i.e., disappear when the stress is removed. The plastic deformation occurs over a period of time and remains even after the stress is removed. For plastic deformation, participants of the symposium centered their discussion on the problem of predicting deformation behavior. The speakers de-
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s -r
B Figure 5. I n crystals, slip, twining, and dgusion are the only mechanisms which can provide for plastic deformation. Slip (left) and twining (right) are illustratedf o r sodium chloride crystals
Figure 7. A. Conformation of a single, flexible polymer macromolecule as it may exist in a bulk amorphous molecule. B. Statistical nature of the conformation, as embodied in the relative probability of occurrence W(r) of the chain end-to-end length, r. Deformation is resisted by an entropic restoring force caused by a disturbance of W(r> VOL. 5 5
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by studies of the fundamental nature of plastic deformation as related to the aggregate atomic structure of materials. Here, the emphasis was placed first upon how plastic deformation occurs within a general structural type-e.g., glasses, metals, and cross-linked polymers. Then, the effect of structural variations within each general structural type-e.g., precipitate phases in crystal lattices, and degree of cross-linking in polymerscan be understood and then quantitatively evaluated. This technique, therefore, can provide, not only the descriptive expressions obtained by rheological techniques for existing materials, but also the structural requirements necessary to tailor-make materials for particular applications. The speakers concentrated on this more fundamental approach towards plasticity in their respective fields. I n metals, Ansell showed that during the deformation of metals the over-all crystalline lattice must be maintained. This structural restriction is reflected in the nature of material transport during the deformation process. Slip, twining, and diffusion are the only material transport processes which can provide for plastic deformation with crystals. Of these, slip, or the consecutive shear displacement of atoms along crystallographic planes in crystallographic directions, is the most important. Since slip is a consecutive process, which starts at some point in a crystallographic plane (slip plane) and then spreads out, there must be a boundary in the slip plane separating the slipped region from the unslipped region of the slip plane. This boundary is called a dislocation. The shear displacement, the amount and direction of slip, coincides with the atomic spacing. Thus, when slip occurs, a n atom shifts from one lattice position to a neighboring lattice position, maintaining the crystalline structure. At the dislocation, or boundary of the slipped regions, however, the atoms are in transitional positions between lattice sites. The dislocation therefore is a defect with significant strain energy. As the dislocation moves, the crystal deforms. Thus, if one can evaluate the interaction of this high energy defect both with stresses applied to the crystal and the structure of the material, the deformation response can be predicted. When considering such evaluations, the behavior of metals is the most straight forward of all the crystalline solids. As a result of the metallic bond, the atomic shear process is relatively simple ; and metals form crystals of high symmetry and therefore contain a multiplicity of possible slip planes and directions. Ansell then demonstrated how, on the basis of dislocation theory, the mechanical behavior of metals can be predicted. T o illustrate, he calculated the yield strength of dispersion-strengthened alloys. I n combination with this calculation, transmission electron micrographs were shown, illustrating the movement of dislocations in metals. Gilman then continued this concept of dislocation theory to ceramic crystals. H e pointed out that in ceramic lattices, slip does not occur as simply as in metals. Brcause of the directional high energy ionic, 50
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covalent, or mixed bonding present in ceramics, the atomic shear process is more difficult. In an ionic lattice, for example, a simple shear of a n anion from one lattice site to a neighboring site could place the anion next to another anion on the adjacent lattice plane. T o maintain the correct ionic neighborhood after slip, the shear translations in ceramics often are complex and extensive. GilmanLdemonstrated, how, by considering the crystal structure and the nature of the bonding involved, the slip made in several types of ceramic materials can be predicted. H e showed the use of etch pit techniques to follow the slip process in crystals and to verify these predictions. Gilman then illustrated how this technique could be extended to measure the relationship between the applied stress and dislocation velocity in ceramics. These data can then be utilized to predict the stress-strain behavior of these materials. The concepts of dislocation and slip have recently been applied to highly crystalline polymers such as nylon and polyethylene. The results are very promising. HOUever, because the previous speakers concentrated on crystalline mechanisms of plastic deformation, Sternstein chose to discuss the material transport mechanisms responsible for plastic deformation in amorphous high polymers such as polystyrene, polymethylmethacrylate, and polycarbonates. The rudiments of phenomenological viscoelasticity were reviewed, and it was demonstrated how the immediate elastic deformation, retarded elasticity, and plastic deformation of a typical polymer could be incorporated into a suitable mathematical model. Also, the molecular responses responsible for retarded elasticity and plastic flow were discussed. The concepts of retardation time spectra and timetemperature superposition were discussed in terms of segmental diffusion and the theory of conformation entropy. These concepts were then used to elucidate the effects of cross-linking on plastic deformation and the phenomenon of the glass transition. A single conformation of a polymer molecule as it may exist in a bulk, amorphous polymer is indicated in Figure 7 4 and the statistical nature of these conformations, as embodied in the relative probability of occurrence, W(r),of a given value of chain end-to-end length, r , is shown in Figure 7B. Deformation of a bulk polymer results in a perturbation of the probability function W(r) which gives rise to an entropic restoring force which resists the deformation. The response of a polymer molecule to a force tending to cause redistribution of its component segments-Le., a change in its state of conformation, is time-dependent because of the intermolecular, dissipatk e force fields which hinder the diffusion of the segments. These dissipative force fields are active regardless of whether or not the polymer is cross-linked. Thus, segmental diffusion processes not only account for retarded elastic effects of each molecule, which are time-dependent but embody a thermodynamic restoring force, but also for plastic flow, which embodies a true translation of molecules past each other and is complete!!, irreversible.
