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By J. Brett, S. Friedman

A study of the diffusion of nickel into both fibrous and recrystallized 0.065-in.-diam silica-alumina doped tungsten wire at 1200°C has been conducted. The diffusion profiles were determined by chemical dissolulion of successive circumferential layers and spectro-photometric determination of nickel in the etchant. It was shown that the diffusion of nickel into tungsten is markedly structure-sensitive. No significant amount of nickel could be introduced at 1200°C into tungsten which had first been recrystallized at temperatures of 2300°C, leading to an upper limit estimate for the bulk diffusivity of nickel in tungsten of 10-11 sq cm per sec at 1200°C. However, nickel did diffuse into initially fibrous wires, caused re crystallization, and was alsays present at the advancing recrystallization front. The accumulation of nickel in an initially fibrous region ceases when the recrystallization front arrives. The characteristics of the resulting diffusion profiles are explained in terms of the relation between diffusion processes and micro structural changes. WHILE it is well-known that the presence of nickel and certain other metals causes low-temperature recrystallization of the cold-worked fibrous structure of doped tungsten,''' the character of the phenomenon is not well understood. Recently it was shown that the recrystallization reaction can be induced at low temperatures by the presence of solid nickel on the surface of doped wire, but not by exposure to nickel vapors.3 Once recrystallization was initiated, a continued source of nickel was required for propagation of the recrystallization front. The phenomenon appeared to be a complicated solid-state reaction since, in addition to the change in structure of the tungsten from fibrous to equiaxed grains, diffusion of nickel from the surface into the recrystallized and fibrous structures was occurring with possible chemical reaction between nickel and tungsten at the surface and interaction of nickel with the dopants which ordinarily stabilize the fibrous structure within the wire. The objective of the present work was to study the diffusion of nickel into fibrous and recrystallized tungsten structures in order to clarify the relationship of the diffusion process to nickel-induced recrystallization. Studies of interdiffusion in the Ni-W system4"7 have been principally concerned with the mobility of tungsten in nickel. Information on diffusion of nickel in tungsten is meager, and there seem to be no studies of the mobility of nickel in tungsten which elucidate the structural aspects of the phenomenon. The present experiments were designed to determine the diffusivity of nickel at 1200°C in fibrous tungsten, in large-grained tungsten prerecrystallized at high tem- perature, and in tungsten recrystallized at 1200°C due to the presence of nickel. Although the concentration profiles were determined in these experiments, unexpected changes in boundary conditions or complex diffusion paths complicated the analysis of these profiles so that the interpretation could not be readily expressed in terms of simple diffusivities. EXPERIMENTAL PROCEDURE The experiments were conducted on Sylvania 0.065-in.-diam silica-alumina doped commercial tungsten wire, hereafter designated as ordinary doped wire. A special lot of 0.065-in.-diam silica-alumina doped low-nickel wire was also used. Impurity analyses of the wire are given in Table I. The experimental design is shown in Fig. 1. All heat treatments were conducted in vacuum. Two groups of ordinary doped wire were prepared for diffusion with nickel. One group in the as-received (fibrous) condition was elec-tropolished, nickel-plated, and annealed at 1200°C for 20 and 40 hr, or was exposed to nickel vapor at 1200°C for 20 and 40 hr. The second group was recrystallized to an equiaxed grain structure at 2300°C for 3 hr, electropolished, nickel-plated, or exposed to nickel vapor for anneals at 1200°C for 20 and 40 hr.

Jan 1, 1969

By Robert J. De Angelis, James H. Barker

An improved method for solving dynawzical dislocation problems using a digital computer is described in this paper. Interactions between two distinct types of dislocations were studied: attractive screw dislocations; and Lomer lock forming dislocations. One dislocation is positioned in the lattice and is initially at rest, while the other dislocation is moved through the lattice on an intersecting slip plane at a constant velocity in the range 0.5 to 0.999C. (C is the transverse velocity of sound.) The results obtained from these computations indicate that screw dislocations account for a small fraction of the total strain over a wide portion of the range of velocities studied. They further indicate that mixed dislocations mainly repel other dislocations in the neighborhood of the active glide plane. From this a possible explanation for cell formation is put forth. The density of Lomer locks expected to exist after a strain of 0.2 was found to be 1.4 x 106 cm-2 which is in good agreement with indirect experimental estimates. IN the past, predictions of favorable or nonfavorable dislocation reactions were based on the associated changes in elastic strain energy. Such considerations take no account of the probability of the two dislocations coming into contact to react. Venables1 was the first to approach these probabilities by considering the interactions between two moving screw dislocations on perpendicular glide planes. Because of the restrictive types of dislocations and glide plane geometry employed, his results have limited application to metallic crystals. The work to be presented here develops a general approach to solving dynamical dislocation problems; either dislocation-dislocation interactions, presented here in detail, or dislocation interactions with any other suitably defined stress field. Two types of dislocation-dislocation interactions common to face centered cubic (fee) materials are considered: those between pure screw dislocations of opposite sign on intersecting slip planes and those between mixed dislocations on intersecting slip planes, that can react to form a perfect dislocation. This latter reaction, referred to as the Lomer reaction, produces a locked product dislocation that finds it energitical favorable to disassociate into two Shockley partials and a stair-rod dislocation. This partial configuration known as a Lomer-Cottrell (L-C) lock plays a major role in work hardening of fee crystals. seeger2 names the L-C lock as the prime contributor to Stage II hardening while Kuhlmann-wilsdorf3 and Meakin and Wils- dorf4 also state that it is a significant contributor to work hardening. However, with a few notable exceptions,5-7 direct observations of the Lomer lock and the L-C lock by electron transmission microscopy are scanty, and even these are subject to other interpretations.5,6 In a study of partial dislocations present in austenitic stainless steel, whelan8 did not observe any L-C locks at the head of pile-up groups. This result contradicted existing work hardening theories and led him to postulate an alternate theory based on the stress required to break away dislocations intersecting a pile-up group, from their stacking fault nodes. Due to the importance of the Lomer reaction in producing L-C locks which are an essential feature in current work hardening theories and because there exist no data giving direct quantitative values for the density of locks, and because there has even been some doubt expressed as to whether this important reaction occurs at all, a study of the dynamic behavior of the mixed dislocations which form the Lomer lock was undertaken. Due to their ability to cross-slip with relative ease, screw dislocations play an important role in the deformation of fee crystals. For this reason, the second type of reaction considered here is between screw dislocations of opposite sign. In addition, computations in volving screw dislocation interactions are relatively simple, thus providing a convenient check on the cornputational scheme employed. DEFINITION OF PROBLEM The force exerted on a dislocation due to a generalized stress field is given by the Peach and Koehler9 equation: Here t2 and b2 are respectively the tangent and Burgers vectors of the dislocation, and T1 is the stress dyadic defining the local stress field. The stress field may be externally applied or generated internally by the presence of a lattice defect, such as a second dislocation, as is the case in this work. Frank10 has shown that an equivalent momentum, P, of a screw dislocation can be defined by: Here, EST is the total energy of a screw dislocation and ESo is its rest energy. The left side of Eq. [2] is the time derivative of momentum and the right side is the position derivative of the energy due to the dynamical nature of the dislocation. The total energy of a dislocation is the sum of the potential and kinetic energies. Weertman11 has developed the expressions which were used here; these give the potential and kinetic energies of uniformly moving edge and screw dislocations in an isotropic medium.

Jan 1, 1969

By S. F. Frederick, G. F. Pittinato

The deformation mechanisms operating in Ti-5Al-2.5Sn at 20°K under uniaxial and biaxial stress fields were determined by using both optical and electron microscopy. In the uniaxially stressed specimens, de-fu~rnation twins were found only in the immediate vicinity of the fracture. Twinning was, however, established as a deformation mechanism under biaxial stress conditions. The same slip systems were opera-tiz,e under both uniaxial and biaxial stress. Prismatic slip was identified as the major slip syslem; however, basal and first-order pyramidal slip also occurred, but to a lesser degree. The interaction of moving dis-locations on intersecting slip planes resulted in the formation of jogs and dipoles. Hexagonal dislocation networks were formed only under biaxial stress conditions. A discussion is given on the formation of hexagonal dislocation networks. IT has been shown that titanium alloys can exhibit unusually high strengths when tested in a biaxial stress field.'-" The high biaxial strengths are a consequence of a strong basal plane sheet texture which results in distinctly anisotropic flow properties. This texture strengthening appears to decrease with decreasing temperature2 and would seem to indicate a change in deformation modes. For example, in a uniaxial tensile test, Ti-5A1-2.5Sn yields isotropically at 20°K but is strongly anisotropic at room temperature. The increase in biaxial ultimate over uniaxial strength at 20°K is also much less than at room temperature. It is known that titanium car] form deformation twins more readily at cryogenic temperatures than at room temperature.4 Since the formation of deformation twins will reduce the degree of basal texture in sheet material,' an accompanying decrease in texture strengthening would be expected. To investigate more fully the nature of texture strengthening at cryogenic temperatures, the deformation modes of Ti-5A1-2.5Sn tested in uniaxial and 1:1 biaxial tension at 20°K were studied by optical and electron transmission microscopy. EXPERIMENTAL PROCEDURE The uniaxial and biaxial stress test specimens were prepared from 0.020-in. thick sheets of Ti-5A1-2.5Sn ELI having the composition shown in Table I. Uniaxial stress conditions were obtained by using flat tensile specimens machined from the sheet material. The longitudinal axis of the tensile specimens was aligned perpendicular to the rolling direction of the sheet. Tile biaxial test specimens were prepared by rolling precut, 19-in.-lengths of sheet into 4-in.-diam cyl- inders. Following longitudinal butt welding, the cylinders were stress relieved at 1000°F for 4 hr. A 9-in. sq "window" was then chemically milled into each cylinder's surface reducing the wall thickness in the milled area to approximately 0.006 in. The testing procedure consisted of pressurizing the cylinders while simultaneously applying a tensile load. Using this technique, a 1:l axial to hoop stress was obtained. Complete details of the specimen and testing procedures are given in Refs. 1 and 2. The biaxial and uniaxial stress specimens were all tested in liquid hydrogen. Specimens for electron transmission microscopy were prepared by first chemically milling to a thickness of about 0.001 in. followed by electrolytic polishing to electron transmission thickness. The chemical milling solution, consisting of 800 ml of water,

Jan 1, 1970

By A. Moskowitz, L. S. Redmerski

The corrosion resistance of stainless steels can be strongly affected by surface treatments. Changes in corrosion resistance can relate to surface composition, integrity and stability of the passive film, and to surface profile (roughness). Operations producing oxidation at the surface, such as annealing, heat treating, and welding, can result in a chromium-rich scale and a chromium-depleted metal surface. In order to restore full corrosion resistance, chemical or mechanical clean-up techniques must remove not only the oxide, but also a very thin layer of metal. Laboratory and field test studies show that these factors are particularly significant in less highly alloyed steels. Annealing stainless in a reducing atmosphere (bright annealing) avoids chromium depletion, but as-bright-annealed material does not display optimum corrosion resistance in certain environments. Electro passiva-tion can be applied to improve pitting resistance without significantly changing bright surface appearance. Potentiometric studies show that electropassivated material also displays significantly greater resistance to breakdown of passivity in acid solutions. The application of special surface finishes for appearance purposes can affect corrosion resistance. Roughness is a key factor. Samples of related appearance but with different surface profiles can show significant differences in corrosion resistance. Thus nonreflec-tive stainless with a relatively smooth surface produced by a special rolling process is much superior to material chemically etched to a similar low reflectivity. THE corrosion resistance of a stainless steel is affected by other factors in addition to its bulk composition and metallurgical structure. These other factors include those relating to the specific chemical and physical condition of the steel's surface. This paper will consider certain aspects of surface condition in relation to corrosion resistance. In particular, studies will be described on the effects of oxidation encountered in heat treating or welding operations, of passivation after bright annealing, and of different surface finishes. EFFECTS DUE TO OXIDATION When stainless steels are exposed to high temperature in an oxidizing environment, as in annealing or welding, the oxides formed are relatively rich in chromium. As a consequence of oxidation, the metallic layer directly beneath the scale may be low in chromium to some very thin but finite depth.1"8 Such a change in chromium content could lower the corrosion resistance at the surface, whether or not the oxide layer is removed. Studies were performed relating to the effect of oxidation and chromium depletion produced during annealing and welding on the corrosion resistance of stainless steels. The nominal compositions of steels used in this study and others are given in Table I. A) Annealing Studies on 17 pet Cr Steels. 1) Effects of Pickling Treatments. Studies were performed to investigate the corrosion resistance of air annealed type 430 stainless as a function of the amount of electrolytic pickling after annealing. The material used in this study had been air annealed and electrolytically pickled in the mill. All scale had been removed, and yet the material showed unusually poor corrosion resistance. Laboratory electrolytic pickling studies were performed to determine whether additional metal removal from the surface would improve corrosion resistance. Electrolytic pickling was performed in a sulfuric acid bath using various conditions of bath acidity, temperature, time, and current density. The samples were then rated for corrosion resistance in a ferric chloride spot test. For this spot test, a solution was prepared by dissolving 10 g of FeCl3 . 6H2O, 5 g of NaCl, and 2.5 ml of concentrated HC1 in 200 ml of water. An area on a specimen was cleaned and a drop of test solution was placed on the prepared area. After 5 min, the drop was rinsed off and the area wiped dry. The spot was then rated between 1 and 5 by visual comparison with standard spots. The numerical rating of the standard spots can be described as follows: 1—No clouding of surface; 2—very slight clouding of surface; 3—slight clouding of surface; 4—moderate clouding of surface; 5—strong clouding of surface. A rating of 1 or 2 was considered to have passed the test, a rating of 4 or 5 represented failure, and a rating of 3 was considered borderline. The severity of etching in this test has been related to the actual chromium content at the surface.4 Etching (clouding) occurs on type 430 stainless (rating of 4 to 5) when the surface chromium content is 14 pct or less. The effects of current density and retention time when electrolytically repickling this material in 6 pct sulfuric acid are shown in Fig. 1. Increasing the cur-rent density or retention time improved corrosion resistance as measured by the spot test. Similarly, increasing acid concentration of the bath or bath tem-perature was found to improve corrosion resistance. The conditions making for improved spot ratings resulted in increased metal removal, regardless of specific pickling conditions used, Fig. 2.

Jan 1, 1970

By R. R. Vandervoort

The creep behavior of Nb(Cb), Ta, Mo, and W was determined under conditions of constant atomic dif-fzisivity, constant stress to elastic modulus ratio, and nearly equivalent grain size, and the steady-state creep rates obtained from these tests were correlated with calculated stacking fault energies for the metals. These results, in conjunction with similar data for several fccMetals,13 suggest that stacking fault energy may influence the creep strength ofbcc metals. The interrelationship between steady-state creep rate, subgrain size, and stacking fault energy was examined. It was found that the subgrain size for a given creep stress, increased as stacking fault energy increased, but that this relationship did not cormpletely account for the effect of stacking fault energy on creep rate. The crystallography and energetics of stacking fault formation in bcc metals has been discussed by a num-ber of authors,1-5 and impurity stabilized stacking faults on (112) planes have been observed in Nb,6,7 w,8,9 Fe,] and V" by transmission electron microscopy. However, a crucial question is whether or not stack-ing faults influence the mechanical strength of bcc metals. Potentially, stacking faults could increase strength by reducing the mobility of the partial dis-locations bounding the fault, by acting as barriers to slip dislocations, and by retarding the climb of dislo-cations during high-temperature deformation. The objective of this study was to seek a correlation be-tween creep strength and stacking fault energy for several bcc metals; namely, Nb, Ta, Mo, and W. The creep behavior of most polycrystalline metals and alloys at high temperatures and moderate stresses can be described by the following relation:11,12 im=Af(s) where i, = minimum creep rate, A = constant, j(s) = a function involving metallurgical structure, a = applied stress, E = average elastic modulus at the test tempera-ture, w = constant (equal to 5 for most pure metals), D = diffusion coefficient. One factor in the structure function F(s) which sig- R. R. VANDERVOORT, Member AlME is Research Metallurgist, Process and Materials Development Division, Chemistry Department, Lawrence Radiation Laboratory, University of California, Livermore, Calif. Manuscript submitted February 28, 1969. IMD nificantly affects the creep resistance of fcc metals is stacking fault energy, and creep rate has been shown to vary directly with stacking fault energy to the 3.5 power." In the latter investigation, four fcc metals of widely different stacking fault energies (Ag, Cu, Ni, and Al) were creep tested at a constant stress to modulus ratio of 1.21 x 10-4, at a constant diffusivity of 2.7 x 10-12 sq cm per sec, and at nearly equivalent grain sizes of about 0.7 mm. The creep data were then correlated with stacking fault energies. In the present study, a similar procedure was followed. All materials used in this work were consolidated by powder metallurgy techniques. Impurity contents in the as-received materials are listed in Table I. Chemical analyses showed that no measurable contamination of the test specimens occurred during pretest annealing treatments or creep testing. Specimens with a gage section 0.75 by 0.125 by 0.050 in. were creep tested in tension in a vacuum of less than 10-9 torr. Deformation at temperature was measured by tracking fiducial marks on the gage section of the specimen with an optical comparator. Optical deformation measurements also permitted observation of the macroscopic characteristics of the deformation Table I. Typical Specimen Impurity Content, ppm Nb Ta Mo W C 45 10 155 6 O 185 30 4 10 N 30 6 3 2 H 5 I 1 <1 als 3 10 2 15 Ca <5 I3 5 Cr 5 <3 10 <5 Cu 10 50 2 15 Fc 10 10 150 35 Ni 2 150 20 <5 Si <I0 1 3 <10 Ta 100 Ti 10 8 1 Zi 15 50 1 3 Table II. Test Conditions for Constant Stress-Modulus Ratio of 6 X 10.&apos; and Constant Diffusivity of 2.7 X 10-12 sq cm per see, and Grain Size Values for the Given Pretest Annealing Treatments Literature references Pretest Annealing for E and D Treatment Stress, Temperature, ___"&apos;Values__ Grain Tempera-Metal psi "C E D Size, mm ture, .C Time hr Nb 745 1525 14 15 to 17 0.83 1650 I Ta 1220 1770 18 19.20 O.91 1800 I Mo 1975 1630 18 21 0.77 2200 I W 2140 2265 18 22 040 2400 5

Jan 1, 1970

By C. F. Jenkins, G. V. Smith

Serrated plastic flow in stable austenitic alloys based on Fe/Ni has been shown to be related to the presence of carbon and/or chromium in the systems. Strength peaks and plateaus in the serrated-flow temperature region for a commercial alloy correlate with an increased dislocation content, arising, presumably, from enhanced multiplication as a result of a strong interaction between dislocations and solute atoms. The data generally support a mechanism controlled by migration of vacancies, with the energy for vacancy motion being modified by the presence of chromium. Chromium atom -dislocation interaction is responsible for effects above 500°C, whereas the defect interacting with dislocations between 200" and 500°C is suggested to be a carbon-vacancy Pair. ThE phenomenon of jerky flow, serrated flow, or the Portevin-le Chatelier (P-C) effect in austenitic stainless steels is usually attributed to substitutional at1,2 mospheres1,2 or to precipitates&apos;-4 which form at dislocations during plastic deformation. On the other hand, evidence exists which supports a direct inter-stitial-dislocation interaction mechanism for serrated flow in fcc Ni-C,5,6 Ni-H7-9 and in nickel-austenites containing carbon." The present work consists in a study of serrated plastic flow in stable austenitic al-loys. The effects of carbon and of chromium were investigated separately, and a commercial stainless steel with different levels of interstitial impurity concentration was studied in an attempt to delineate the combined effects of the alloying elements. EXPERIMENTAL TECHNIQUES a) Materials and Fabrication. A commercial AISI 330 stainless steel and several specially prepared aus-tenitic alloys have been studied. The experimental alloys were prepared by arc melting the constituents under purified argon. Analyses of the materials are given in Table I. The commercial alloy was obtained as 5/8 in. bar stock and rolled to 0.092 in. sq, with several intermediate anneals. At this stage some of the material was annealed in Pd-purified hydrogen at 1100°C to establish different levels of interstitial content. All other heat treatments were in vacuum (10-5 torr). The "pure" alloy ingots were swaged to 0.120-in. rod and annealed in Pd-purified hydrogen at 1100°C. The analyses for these conditions are also contained in Table I. Following the above treatment, the final wire sizes Table I. Chemical Analyses of Test Materials Hrin Hydrogen at Cr, Ni, Alloy 1lOO°C wt pct wt pct C, ppm* N, ppm* Type 330 As-received 14.78 33.25 430 300 Type 330 64 14.78 33.25 40 50 Type 330 200 14.78 33.25 27 21 Fe/35 Ni 72 - 35.10 <10 62 Fe/35 Ni 200 35.10 <I0 44 Fe/35 Nil15 Cr 72 14.95 34.94 <I0 61 Fe/35 Ni/15Cr 200 14.95 34.94 <10 45 Fe/35 Ni/C $ 35.OM 380 *Sensitivity: N t 5 ppm Ct10ppm. f Nominal Ni content. % A master NiC alloy was used in preparation of this material; courtesy of D.E. Sonon. were obtained by either swaging or cold drawing. The test results did not vary with these techniques. b) Specimen Preparation. Two sizes of specimen and two gripping systems were used. i) 0.070-in. wire with a chemically milled gage section: 0.75 in. long, 0.060 in. in diam. These were fastened into grips containing tapped grooves. ii) 0.050 in. wire, gage length 1.5 in. Ball bearings were welded to the ends of the wires and the gage length was taken to include all material between the welds. Socket-type grips were used with these specimens. With specimens of type ii), joining was performed in a specially constructed brass jig, under argon, and automatic timing was utilized in the procedure. No adverse effects of welding were noted. Specimens were encapsulated and solution treated for 1 hr at temperatures selected to produce the same average grain size, -50 µ. Annealing twin boundaries as well as normal crystal boundaries were counted. The temperatures used are listed in Table 11. Table 11. Specimen Size. Temperature of Heat Treatment and Resulting Grain Diameters for Test Materials Recrystallization Resulting Material Condition Temperature Grain Sue AISI 330 Not H purified 0.070 120O°C 45 to 55µ in, wire AlSl 330 H , pure, 0.070 in. 1150°C 45to55µ wire Fc/35Nil15Cr Pure, 0.070 in. wire 1000°C 45tossp Fe/Ni Pure. 0.070 in. wire 775°C 45 to 55µ Fe/Ni/C Pure, 0.050 in. wire 850°C 10 to 20p AlSl 330 Not purified, 0.050 1150CC 45to55p in. wire AlSl 330 ti, pure, 0.050 in. 1150°C 45to55p wire

Jan 1, 1970

By F. George, W. Tice, M. Salkind

It was found that Al-A13Ni could be readily cold rolled perpendicular to but not parallel to the whiskers. Reductions of more than 98 pct were achieved without cracking by rolling perpendicular to the whiskers, whereas extensive edge cracking was noted after only 15 pct reduction when rolling parallel to the whiskers. The longitudinal and transverse tensile strengths were nearly doubled, and the longitudinal yield strength more than tripled by cold rolling 50 pct in a direction perpendicular to the whiskers. The whiskers exhibited some waviness (elastic bending) as a result of cold rolling, but at very high reductions (greater than 75 pct) whisker fracture and misalignment became significant. A fine dislocation substructure in the matrix consisting of cells attached to the whiskers was pro -duced by cold rolling. Most of- the substructure was readily removed by a 1-hr anneal at 500°C. Cold rolling was found to substantially reduce the thermal stability of the microstructure at 610°C but did not affect the stability at 500°C. FIBER and whisker reinforced composite materials promise significant improvements in properties over conventional materials. Before they find wide use, however, it will be necessary to understand the response of these highly anisotropic materials to common metalworking processes. Most of the nonmetal-lic fiber reinforced materials have very low elongations (a few pct or less) in the direction of fiber alignment. Thus, metalworking techniques such as rolling and forging would not be as broadly applicable to these materials. This investigation was initiated to determine how a composite system consisting of Al3Ni whisker reinforced aluminum responded to rolling, what changes in the microstructure occurred, and the effect of deformation on the mechanical properties. The composite material studied was produced by unidirectional solidification of the A1-Al3Ni eutectic alloy&apos;-7 and consisted of 10 pct by volume of aligned whiskers of Alai in a matrix of aluminum. It should be pointed out that this system is not representative of all composite materials, and the results will therefore not be universally applicable. The A1-Al3Ni system is characterized by: 1) A strong fiber-matrix interfacial bond 2) A ductile matrix 3) A sufficiently low fiber content to allow significant plastic flow between fibers 4) Strong, completely elastic whiskers (tensile strength 400,000 psi, elastic modulus = 20 X 106 psi.1 These factors allow the material to be readily rolled perpendicular to the fibers. If the fiber-matrix bond were not strong, such a weak interface could fail during rolling. A measure of the ability of a composite to be rolled in the transverse direction can be obtained from noting the transverse tensile behavior. In the case of Al-Al3Ni,2 there is considerable ductility (15 to 30 pct). In the case of boron filament reinforced aluminum, for example, the transverse elongation is less than 1 pct,8 and the material could probably not be cold rolled as readily in that direction. EXPERIMENTAL PROCEDURE 3-in. diam ingots of A1-A13Ni eutectic were unidi-rectionally solidified in graphite crucibles. The starting materials consisted of 99.99+ pct pure nickel and aluminum, and the pure eutectic ingots were made with 6.2 wt pct Ni. The unidirectional solidification process (described in detail elsewhere1-3) consists of preparing a master heat of eutectic composition, remelting, and withdrawing the ingot vertically downward through the heat source at a controlled rate so that plane front solidification proceeds upward at a constant velocity. The resulting microstructure consists of 10 pct by volume of whiskers of very high aspect (length to diameter) ratio. The fiber lengths have not been measured because of the difficulty of detecting fiber ends9 but exceeds 104. There is some possibility that the fibers may be continuous within one grain. Flat sheet specimens 2¾ in. sq and approximately 0.2 in. thick containing whiskers parallel to the plane of the sheet and to one edge were used for this study. A1-A13Ni exhibits either a rod-like (high solidification rates) or a blade-like (low solidification rates) whisker morphology,1,3 and both types were studied. Rolling was accomplished using a two-high rolling mill at a speed of approximately 10 fpm. The rolling direction was either parallel to or perpendicular to the direction of growth (direction of whisker alignment). Reductions of from 0.002 to 0.03 in. per pass were used with the most common value being 0.005 in. per pass. Cold rolling of Al-Al3Ni to more than 98 pct reduction in thickness was accomplished with no intermediate anneals. In addition. a series of speci-mens was cold rolled 97 pct with a 1-hr, 500°C anneal in air after each 50 pet reduction. Tensile testing was accomplished using a Tinius-lsen four screw testing machine. Flat sheet specimens + in. wide and between 2 and 2; in. long with the thickness dependent upon rolling reduction, were used. The gage section was in. wide and 1 in. long. Strain was measured using a clip-on LVDT extensome-

Jan 1, 1970

By A. H. Larson, T. P. McNulty

RECENTLY, an investigation of the absorption of sulfur dioxide gas in molten binary copper alloys was conducted. A Sieverts-type apparatus, consisting of a mercury-filled gas dispensing buret and a mercury manometer, was used initially for determining the volume of gas absorbed as a function of pressure. The equilibration behavior of the alloys studied indicated that the mercury in the gas measuring system was absorbing sulfur dioxide. Owing to the widespread use of mercury as a displacement medium in absorption studies, an investigation was made to determine the nature and magnitude of the mercury - sulfur dioxide absorption effect. The gas measuring system was modified by substituting a Worden Quartz Products Type PDHV fused-quartz-spiral pressure gage for the mercury-filled dispenser and manometer. The dispensed gas volume at known temperature and atmospheric pressure was measured by evacuating a Pyrex vessel of known volume and by admitting sulfur dioxide into the vessel until the attached quartz pressure gage registered atmospheric pressure. Atmospheric pressure was measured concurrently with a separate mercury barometer. The volume of the empty sample chamber and its attendant apparatus was determined by measuring the equilibrium pressure accompanying the addition of a measured volume of sulfur dioxide into the initially evacuated system. The volume of the mercury sample was calculated from the density of mercury at the temperature of the study (25°C). Measured volumes of sulfur dioxide were then dispensed into the system and the equilibrium pressure accompanying each gas addition was determined. From the difference between the system volume and the mercury volume, the number of moles of gaseous sulfur dioxide remaining in the system at each pressure was calculated. The difference between the number of moles of gas dispensed into the system, denoted Enso2: and the number of moles of gas remaining in the system after absorption equilibrium had been attained, denoted nso2(g), was equal to the number of moles of absorbed gas, denoted nSO2. The number of moles of absorbed gas was then converted to absorbed volume, denoted VSo2, in cu cm at stp conditions of (PC and 760 mm Hg. Table I contains calculated values of Snso2, nSo2(g), and VSo2 for different sulfur dioxide pressures. In the original system, denoted Run I, volume limitations of the gas dispensing system prevented absorption studies at equilibrium pressures near atmospheric pressure, so a different gas dispensing system, denoted Run 11, was used for determining the last pressure reading in Table I. The data in Table I are expressed in terms of the absorption of sulfur dioxide in 49.68 cu cm of mercury. In Fig. 1, these data are expressed in terms of the absorption of sulfur dioxide in 100 cu cm of mercury. Since the absorption data plotted in Fig. 1 show a linear relationship, the volume of sulfur dioxide absorbed in mercury is a function of the first power of pressure. The absorption reaction is So2(gas) = SO2 (in Hg) The first-power pressure dependence, coupled with the fact that the sulfur dioxide could be removed from the mercury by applying vacuum, indicated reversible

Jan 1, 1967

By E. D. Levine

A study was made to delineate the dislocation mechanistns controlling prismatic and basal slip at low temperatu.ves in titanium containing approximately 100 ppm interstitial impurities. Mechanical tests were performed on single crystals prepared from electron-beam zone-refined crystal bar by a thermal cycling technique. Measurements were made of critical shear stress and activation volume as functions of temperature. The study revealed that, for prismatic slip, two overlapping thermally activated processes aye rate-controlling below 300°K. From absolute zero to 220°K, reasonable agreement is obtained between experiment and the mechanism which involves overcoming 01. the Peierl&apos;s stress by the formation of double kinks in dislocation lines lying in close-packed directions. Between 220°and 300°K prismatic slip is controlled by a difierent thermally activated process which is characterized by a stronger temperature dependence of critical shear stress. Above 300OK, prismatic slip is controlled by an athermal process. Basal slip is controlled by a thermally activated process between 195&apos; and 400°K. An approximate analysis suggests that it is the Peierl&apos;s mechanism that is rate-controlling in this range. Below 195°K, the occurrence of mechanical twinning obscures the features of basal slip. Above &apos;400 X, basal slip is controlled by an athermal process. TITANIUM, an hcp metal with a less-than-ideal axial ratio of 1.587, deforms primarily by {1010}( 1210) slip at low temperatures.&apos;-3 The critical shear stress is strongly affected by the presence of interstitial impurities. For example, churchman3 reported that a decrease in the combined nitrogen plus oxygen content from 0.1 to 0.01 pct decreased the critical shear stress for prismatic slip from 9.19 to 1.4 kg per sq mm at room temperature. Basal slip, however, is less strongly affected by interstitials; Churchman&apos;s data for {0001}( 1210) slip show a smaller decrease in critical shear stress from 10.90 to 6.3 kg per sq mm at room temperature, for the same decrease in interstitial content. In the present study, an attempt has been made to delineate the dislocation mechanisms controlling prismatic and basal slip in titanium. In view of the strong effects that impurities may have on at least some of these mechanisms, experiments were performed on material of reasonably high purity, so that comparisons could be made with investigations on material of both lower and higher impurity contents. EXPERIMENTAL PROCEDURE Single crystals were prepared from 1/4-in.-diam electron-beam zone-refined crystal bar, furnished by Materials Research Corp. The analysis of the zone-refined material is given in Table I, indicating that the interstitial content is of the same order as the purer of the two materials investigated by Churchman. The Vickers diamond pyramid hardness number of this material was 85.6. This value agrees quite well with the correlation between hardness and interstitial content proposed by Ogden and Jaffee.4 On the basis of hardness, the material investigated in this study is, therefore, intermediate in purity between that studied by Churchman (Vpn = 97) and that studied by Spangler and Herman (Vpn = 62.4).5 Single crystals were grown by thermal cycling through the a-ß transformation. Two-in.-long by 1/2-in.-diam bars were heat-treated in vacuum for 4 hr at 1160°C. The temperature of the furnace was then lowered to 865°C, and the specimens were maintained at this temperature for 7 days. This procedure was repeated several times, resulting in the growth of individual crystals up to 14 in. in length. Specimens for testing in direct shear along either {l010}(1210) or {0001}(1210) were obtained by electrical-discharge machining. The specimens were in the form of cylinders 1/4 in. in diam by approximately 1/2 in. in length, with a reduced section 1/8 in. in diam and a in. in length. All specimens were electropol-ished subsequent to electrical-discharge machining. The ends of the test specimens were cemented in stainless-steel collars. Shear tests were conducted in an Instron Tensile Tester at various temperatures from 4.2° to 508°K. Measurements were made of critical shear stress and activation volume. The latter measurements were performed by measuring the change in flow stress upon cycling the strain rate between ?1 = 2.62 x 10-3 per sec and ?2 = 2.62 x 10-4 per sec. Activation volume, I)*, is defined as u* =ßkT [11

Jan 1, 1967

By Emmanuel P. Papadakis

Ultrasonic velocity measurements have been made to study the preferred orientation in cube-textured copper. Methods applicable to thin specimens were employed since the specimens were necessarily of sheet material. The measured velocities in various directions in the sheet differed from the corresponding values in single-crystal copper by 1 to 6 pet. The distribution of the deviations indicated that the align-ment of the (001) planes with the rolling plane was better than the alignment of the [100]and [010] directions with the rolling and transverse directions. Ultrasonic pole figures (velocity us orientation) are shown to be useful in the study of preferred orientation. THIS paper describes one set of experiments in a continuing study of preferred orientation in worked metals. This study has been undertaken to investigate the fundamental properties of metals when used as propagation media for ultrasonic waves. Many such materials are of current or potential use in ultrasonic delay lines. Fundamental studies on ultrasonic propagation parameters such as velocity, attenuation, and diffraction (beam spreading) are of importance in the design of delay lines, in the development of nondestructive testing methods, and in the study of materials themselves. Preferred orientation in worked poly-crystalline metals influences all three above-mentioned parameters, and hence is of particular importance. When polycrystalline metals are subjected to mechanical working, they develop textures dependent upon their crystal structure and the symmetry of the working operation.&apos; The texture consists in the alignment of the crystallographic axes of the grains in preferred directions with respect to the symmetry axes of the working operation. Since the grains are elastically anisotropic, the elastic moduli of worked metals are anisotropic. Hence the velocities of elastic waves in worked metals depend on the directions of propagation and polarization. The worked metal may be thought of as taking on the elastic symmetry of a single crystal: so it possesses the same number of independent elastic moduli as the crystal class it simulates. In general, a worked metal does not adopt the crystalline symmetry of its own grains. For instance, most rolled sheet becomes effectively orthorhombic while all bar stock and wire develop hexagonal symmetry. However, certain metals with cubic crystal structure develop a cube texture upon rolling and annealing.= Nearly perfect alignment of [100]-type directions with the rolling direction, transverse direction, and rolling-plane norma1 can be achieved in certain fcc metals and alloys. These cube-textured rolled metals provide an excellent opportunity to test preferred orientation by means of elastic waves, since a worked metal with 100 pct cube texture would have elastic moduli identical to the moduli of its constituent metal. It is the purpose of this paper to present the results of an investigation upon cube-textured copper. Ultrasonic waves were used. The methods of measurement and the experimental results on the effective moduli will be given. The ultrasonic measurements will be shown to complement X-ray pole figures for the determination of preferred orientation in worked metals. EXPERIMENT To study cube - textured material, it was necessary to use thin-sheet material since a severe reduction in gage (95 to 99 pct) is necessary to produce cube texture. Special ultrasonic methods were needed to investigate the thin material at megacycle frequencies. A) Materials. The cube-textured material tested was a copper alloy containing 1 pct Zn. Specimens already measured for Young&apos;s modulus4 by Alers were kindly supplied by him. The specimens were slabs 3.00 by 0.25 in. cut from sheet 0.047 in. thick. The orientations of the long axes of the specimens with respect to the rolling direction were taken in 15-deg steps from 0 to 90 deg. B) Measurements. Two distinct experiments were performed to measure the phase velocity in these specimens. One measured the shear wave velocity for propagation in the 0.25-in. direction and polarization in the 3.00-in. direction. The other measured the velocity of both shear and longitudinal waves propagating in the thickness direction in the sheet. 1) Plate-Mode Measurements. The velocity of the zeroth-order shear mode5 was measured in the 0.25-in. direction in each strip. The specimens were ground thinner over half their length to assure that the first-order shear mode would be cut off below 6 Mc per sec, leaving the zeroth-order nondispersive shear mode as the only propagating mode. Piezoelectric ceramic transducers of 5 Mc per sec resonant frequency poled in their long direction were solder-bonded to the edges of the thin part of the slabs as in Fig. 1 after these edges had been made flat and parallel by fine grinding. These transducers produced waves polarized in the 3.00-in. direction and propa-

Jan 1, 1967

By M. J. Mullikin, J. B. Conway

Equations capable of representing combined first -and second-stage creep behavior include the Andrade, Cottrell-Aytekin, Garofalo, and de Lacombe equations along with a third-degree polynomial in t1/3. Employing some recent high- temperature creep data for arc-cast tungsten the effectiveness of these expressions was evaluated. It was found that, in this instance, the most accurate representations were afforded by the third-degree polynomial in t1/3 and the de Lacombe equation. Also noted was the fact that the Andrade equation gave results just slightly inferior to those obtained with the third-degree polynomial, definitely better than those due to the Cottrell-Aytekin equation, and slightly superior to those furnished by the Garofalo equation. EXPRESSIONS designed to describe combined first -and second-stage creep behavior must possess certain specific characteristics. At time zero the equation must reduce to a strain value corresponding to the instantaneous deformation on loading. Then in the early moments following load application transient-creep behavior must be described to reflect a creep rate which constantly decreases with time. And finally at larger time values linear (or at least nearly linear) strain-time behavior must be accounted for to yield the steady state or minimum creep rate. Some equations, such as the one based on the parabolic creep law, yield fairly satisfactory results in transient analyses but are not effective at all when combined first- and second-stage data are to be analyzed. Other equations give equally accurate results in both instances although in general the complexity of the equation is slightly increased. For example the Andrade1 equation: has found fairly general application in expressing first-stage creep behavior. Furthermore the contribution of the exponential term becomes more and more prominent as the time increases and causes this equation to exhibit a point of inflection at large values of time. With a proper selection of equation constants the curve can be made fairly flat in the region of the inflection point indicating a desirable equation form for combined first- and second-stage creep analysis. Another equation form with the proper characteristic is that of Cottrell and Aytekin:2 e =a +bt1/3 +ct [2] Obviously as time increases the first derivative of this expression approaches a constant value to suggest application to combined first- and second-stage creep analysis. Similarly a third-degree polynomial in t1/3: e -a + bt1/3 + ct2/3 +dt [3] has the same characteristics. Expressions of this type have been shown3 to be very effective in the analysis of transient-creep behavior and the fact that the first derivative has the same characteristic as Eq. [2] suggests use in the combined analysis.

Jan 1, 1967

Jan 1, 1967

By T. R. Cass

THE renewed interest in titanium, resulting from its increasing application as a structural material, has stimulated basic deformation studies on this metal. In the course of our work, we have developed a dislocation etchant and applied it to a perfection study of melt-grown single crystals as well as to a preliminary investigation of plastic deformation in titanium. The etchant, Keller&apos;s etch (21 cu cm HF, 64 cu cm HC1, 106 cu cm HNO3, and 160 cu cm H20), reveals the emergence of both grown-in and fresh dislocations on pure titanium and a-phase Ti-Al single crystals. Pits are produced only on surfaces within a few degrees of the basal plane; the more exactly parallel to a basal plane the surface is, the more distinct are the pits. The observed pit density, however, does not appear to depend on the surface orientation; the pits simul- taneously become less distinct as the misorientation from a basal plane increases. Etch times are short, a few seconds, for pure titanium; longer times are necessary for alloy crystals.

Jan 1, 1968

By C. A. Stickels

In a recent paper, Held1 showed that rolling conditions can have a marked effect on the volume fraction of surface texture produced in low-carbon steel. This variation in rolling texture is reflected in the recrys-tallization texture and affects the plastic properties of the annealed sheet. The fact that roll friction can influence the surface deformation texture in iron and steel has been known for some time;&apos;= but the magnitude of the effect has never been shown quite so clearly before. The analogous effect during wire drawing has been recognized for many year.4 Dillamore and Roberts5 examined surface textures in warm- and cold-rolled aluminum and copper. They found that when a surface texture was present it could be described as the interior texture rotated about the transverse sheet direction. The angle of rotation was a function of the type of lubrication, the amount of reduction per pass, and the temperature of rolling. The purpose of the present note is to show that surface textures in cold-rolled iron can also be described as interior textures rotated about the transverse sheet direction. Vacuum-melted electrolytic iron* was straight- rolled 90 pct at room temperature in a two-high rolling mill with 5-in.-diam rolls. Two rolling procedures were used: a) no lubrication with reductions of about 0.035 in. per pass, and b) heavy lubrication with lano-line and reductions of about 0.002 in. per pass. The final sheet thickness was 0.030 in. (110) pole figures were determined by transmission through specimens taken from the sheet surface and sheet midplane. The surface texture of the sheet cold-rolled according to procedure a is shown in Fig. l.* The shapes of the low-intensity contour lines indicate that the texture can be described as a partial fiber texture with a (110) fiber axis normal to the sheet. The approximate range of orientstions present is (011)[211] — (0ll)[100] — (011)[211]. This range of orientations is what one would obtain by rotating the interior texture 90 deg about the transverse sheet direction. The intensity of (110) and (222) reflections from planes parallel to the surface was measured after removing metal from the surface by chemical polishing. The surface texture here was confined to the outer

Jan 1, 1968

By G. Y. Chin, M. T. Dolan, W. L. Mammel

We have obtained by computer methods the solutions of the Taylor analysis1 for axisymmetric flow in bcc metals. Four modes of slip have been treated in detail:2-4 (111), {112}(111), {123}( 111), and a mixture of all three. In addition to obtaining anisotropy of strength data for randomly oriented or textured polycrystalline material,4 we have also obtained the lattice rotation resulting from slip on the predicted systems. The patterns of lattice rotation are essential to an improved understanding of texture development during deformation. The present note shows the results of lattice rotation for 5 pct axisymmetric compression, for fifty-two axial orientations distributed at 5-deg intervals throughout the standard stereographic triangle. The data are presented in Figs. 1 to 4 for the four modes of slip. The lattice rotation is indicated by a vector, the ends of which correspond to the positions before and after the deformation. The different vectors emanated from a given orientation represent different combinations of five slip systems that satisfy Taylor&apos;s minimum shear criterion.&apos; Fig. 1 shows the results for {110}< 111> slip. They are similar to those obtained by Bishop5 for the case of (111 )(110) slip in axisymrnetric tension, since in axisymmetric flow the sense of lattice rotation for {111)( 110) in tension is the same as that for (110) (111) in compression. The pattern of lattice rotation may be divided into three regions: region A in which the rotation is toward [100]; region B, toward [lll]; and region C, toward either [ loo] or L lll]. Although some slip combinations in region C lead to [1101, the latter is not stable as continued activity of the same combinations will eventually move the axis toward [loo] or Llll]. It may also be noted that [loo] is itself not stable. However, close inspection of the vectors in region A shows that it is impossible for an axial orientation within A to rotate outside its boundary. Hence after heavy compression, all orientations from A and some from C are expected to form a diffuse band in the [100] vicinity. By far the largest region is B. Here all orientations rotate to [lll], which is a truly stable position. Thus the [111] texture component is expected to be rather sharp. For the case of (112 }( 111) slip, Fig. 2, region C is enlarged at the expense of A, with B about the same as for {110}( 111) slip. A significant difference, however, is that [loo], as well as [Ill], is now truly stable. Fig. 3 shows the results of slip on {123}( 111) systems. Region B is substantially enlarged at the expense of C, with A being intermediate in size between the {110}(111) and {112}(111) cases. Like the case of {110)( 111) slip, [100] is itself unstable. However, the lattice rotations here are confined to less than 5 deg; hence it may be considered "stable" for practical purposes. Finally, Fig. 4 shows the results of mixed slip. Here region B is the largest, and C the smallest, of all the cases considered. Both [loo] and [ill] are stable. The behavior of the three corner positions is, in fact, identical to the case of {112)( 111) slip, Fig. 2; it turns out that in these positions for the mixed slip case, all the active slip systems (based on Taylor&apos;s criterion) belong to pure {112}( 111) .4 In summing up the results for the four modes of

Jan 1, 1968

By G. S. Cole, G. F. Bolling

ThIS note accompanies a study of grain structure changes in metal ingots produced by the alteration of fluid motion.1 Although the Prandtl Number of aqueous solutions is much higher than that for metals, it is quite instructive to see the simulation of freezing, as pointed out by Jackson and coworkers.2-4 Accordingly we have observed the effects of natural thermal convection, the changes induced by a steady-state rotation in one direction, and the changes under oscillation.&apos; Temperature measurements were made under duplicate conditions whenever the visual observations appeared interesting. A solution of 15 pct NH4C1 in water was chosen. In each case the solution was preheated to 90°C in a 4-in.-diam Pyrex beaker filled to a level of about 5-in. depth and covered to prevent convective air cooling. The beaker was then placed in a container of iced brine, suitably arranged on a rotating table for movement about its cylindrical axis. Upon immersion in the brine under static conditions, fluid flow was observed near the wall of the beaker before the onset of crystallization, which generally commenced only after the temperature fell to 51.5"C. The region of flow extended about 1 mm from the wall and could not be observed elsewhere. The measured radial temperature increased sharply within 1 cm from the wall and thus over a distance considerably greater than that observed for the flow. However, we note that this difference of approximately one order of magnitude between hydrodynamic and thermal boundary layers should be expected for aqueous solutions, in contrast to metallic liquids. Beyond this layer the temperature was isothermal at a given height and in general nearly 10°C warmer than at the wall. The overall visual observation was therefore supported quite well by temperature measurement. There was also a vertical temperature gradient of nearly 2°C per cm throughout the liquid increasing from the colder bottom; this of course could not be observed visually. Eventually crystals precipitated from solution. (It

Jan 1, 1968

By W. A. Tiller, W. C. Johnston

A high-temperature electromagnetic stirrer is described in which heating and stirring are accomplished by independently controlled power sources. The appavatus is suitable lor use at temperatures up to 1700°C in a variety of ambient atmospheres. Some typical examples of the homogenizatimz capabilities of the system are given. THERE are few processes in solidification that are not markedly affected by motion in the melt during freezing. In many instances, the mechanisms are diffusion-controlled, and the transport in the melt may be greatly accelerated by deliberately stirring the melt. In zone-refining, stirring1 assists the removal of rejected impurities from the interface, so the process proceeds at a faster rate. The transition from a planar to a cellular interface is caused by constitutional undercooling in the melt ahead of the interface: and stirring delays its onset. Stirring is valuable for homogenization of melts: and chemical reaction with sluggish kinetics may be accelerated. Finally, it has been observed that grain refinement is related to motion in the melt. Fine grain castings are usually produced by the addition of catalysts to the -melt,&apos; catalysts which are thought to act simply as hetereogeneous nucleation centers. Even here motion is important. Richards and Rostoker 5 applied ultrasonic vibration to a solidifying A1-Cu alloy which had been innoculated with a catalyst and found that the grain diameter fell linearly with the amplitude, the peak acceleration and the power input to the melt from the transducer. Finally, mechanical and electrical stirring alone have been used to generate a fine-grained structure.6,7 Johnston ef a1.&apos; have carried out a series of systematic investigations of grain refinement by electromagnetic stirring in a number of low melting point alloys. They found, for example, that the number of grains per unit volume in Pb-Sn alloys could be increased several orders of magnitude by stirring an undercooled melt at the moment of recalescence. In general, a relation AT .H = constant prevailed for a given grain size, where AT was the undercooling of the melt and H the field strength. In more recent work, deliberate homogeneous nucleation of slightly undercooled melts established that the mechanism of refinement must be one involving crystal fragmentation and subsequent multiplication, rather than a "shower" of nuclei effect.9 It is the purpose of this note to describe a stirring device suitable for use up to 1700°C. At low temperatures mechanical stirring and direct-current methods are feasible, but at high temperatures the problem of a protective atmosphere and of electrode corrosion rules out such procedures. The most convenient method for high temperatures is to use externally generated ac fields for both stirring and heating. With rf induction heating alone, considerable stirring and agitation can be achieved, but in general the penetration of field into the melt is small, and the stirring cannot be controlled independently of the heating. In the present experiments, separate power sources of different frequencies for heating and for stirring were used. A susceptor design was chosen so that the 450 kc rf heating field was completely absorbed in the susceptor. The stirring frequency, 400 cps, hereafter called the af field, was chosen so that a high penetration of the melt proper was achieved. EXPERIMENTAL APPARATUS The apparatus, Fig. 1, consists of a quartz tube and end plates, surrounded by an rf induction coil and six equally spaced af stirring coils, four of which are shown in full and a fifth in section. Each af stirring coil is a transformer of which the secondary is a single-turn water-cooled copper loop and the primary is composed of two 10 amp-117 v Variac cores as shown. These cores are cooled by forced air, as each of the six pairs will carry maximum currents of 15 amp for short periods. Each set of Variac windings are connected in series, but opposite sets are connected in parallel with a three-phase 400 cps 400-v source. By properly phasing the coils in this way, a rotating field is produced. Capacitors C1, C2, and C3 in Fig. 2 are used to match this inductive load to the generator. Fig. 3 shows a cutaway view of the quartz tube. The sample (1 in. diam by 1 in. high) is placed in a tapered alumina crucible. An axial W-26 pct Re thermocouple, enclosed by a protection tube, is provided. The cruci-

Jan 1, 1968

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,&apos; there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.&apos; The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:&apos;" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

By M. Metzger, L. E. Hendrickson

Grain boundary attack in 16 pct HCl was found to be substantially the same at low penetrations in zone-refined aluminum (individual impurities 0.1 at. ppm), superior electrolytically refined aluminum (51 at. ppm), and aluminum with various impurities at much higher levels. It was concluded that impurity atom segregation affecting corrosion would have been detected and that the corrosion susceptibility did not originate in this segregation but in the structure of the boundary. It was pointed out that the significance of most previous studies in this system had been obscured by an unrecognized autocatalytic copper reaction. Although general corrosion rate was also impurity-insensitive , there was shallow pitting attributed to iron seg-regation and a hillocked surface texture associated with copper; these were interpreted as due to cathodic damage affecting- cathode distribution. THE grain boundary corrosion suffered by high-purity aluminum in hydrochloric acid has been the object of some interest (the earlier work is summarized in Ref. 1). The central metallurgical question here is whether the corrosion susceptibility of a boundary originates in its structure or in impurity atom segregation. An attempt to study this question revealed large catalytic effects associated with small quantities of the copper impurity in the aluminum, 220 ppm, or in the corrodent, and these magnified the preferential boundary attack and obscured the intrinsic susceptibility question.&apos; After the catalytic effects had been examined,"&apos; test conditions could be designed to avoid them and methods developed for studying the shallow boundary penetrations prevailing when they were absent.= It then became possible to determine whether intrinsic boundary corrosion in aluminum involves impurity segregation. The older work provided no firm information on grain boundary segregation of specific solutes influencing corrosion although several studies suggested iron segregates.4,5 perryman4 found in 10 pct HC1 that the slowly developing (microns per month) grain boundary grooves were deeper in material of higher iron content (range 10 to 550 ppm, with 5 to 80 pprn Cu) but he did not measure the depths of general corrosion, which were probably several times greater, and his reference surfaces may have varied more than did the groove depths. Metzger and Intrater&apos;s results for 20 pct HC~,&apos; which yielded higher time-average rates (mm per month) and deeper penetrations, suggested that boundary segregation of iron (range 4 to 230 ppm, with 22 pprn Cu) decreased the penetration rate. However. in the stronger acid the autocatalytic l.E. HENDRICKSON, Student Member AIME ,and M. METZGER, Member AIME, are Research Assistant and Professor of Physical Metallurgy, respectively, Department of Mining, Metallurgy and Petroleum Engineering, University of Illinois, Urbana, Ill. Manuscript submitted March 11, 1968. IMD effect of the copper impurity is greater1,2 and it is now evident that their corrosion rates had been much magnified by this effect and did not provide a proper basis for the analysis of segregation. In exploratory studies of other solutes (made under the same conditions), 1000 ppm additions of Mg, Mn, or Si or 100 ppm Ca were without effect.1 Montariol6 noted that boundary attack in 22 pct HC1 persisted after zone refining although with fewer deep fissures (ranges 0.06 to 4 ppm Cu, 4 to 23 ppm Fe). Autocatalytic effects may have influenced these results also and those of Perryman.4 The present objective was, as a first step, to see whether quantitative tests designed to exclude autocatalytic influences would indicate the existence of low-level impurity effects on intrinsic boundary corrosion. Comparison of electrolytically refined with zone-refined aluminum of lower copper and iron contents revealed no differences in boundary corrosion, but certain impurity-sensitive differences in general corrosion morphology were noted and investigated further at higher impurity levels. I) EXPERIMENTAL PROCEDURE A) Material. A selection from commercially available material was made with the cooperation of several producers. An electrolytically refined lot (III-A, 1 ppm Cu, 2.4 ppm Fe) studied previously3 provided a starting point. Since material of substantially higher copper content could not be used if the autocatalytic corrosion reaction were to be avoided,2,3 a lot (III-B) of about the same purity was added as a check, two zone-refined lots (I-A and I-B) with copper and iron an order of magnitude lower were selected for comparison, and an intermediate lot (11) was included. Analytical data are given in Table I. For copper in I-B and iron in I-A and I-B, the actual concentration is thought to be near the limit given, i.e., about 0.1 ppm. For titanium, vanadium, and chromium in III-B, the actual amounts are thought to be, like those in III-A, substantially lower than in the zone-refined lots (these elements concentrate in the solid on freezing). Data are given later for some additional lots surveved. B) Specimen Preparation and Procedure. one by 3 cm blanks with a notched stem were cut from 1-mm cold-rolled sheet, annealed 24 hr in air at 650°C, and quenched in an air stream (42°C per sec initial cooling rate, 100 sec to cool to 100°C). The high annealing temperature maximized diffusivities and approach to equilibrium impurity distributions. A water quench, in principle more efficient in preserving the distribution established, was undesirable because the boundaries were almost plane and they tended to shear and migrate during the quench and thus to be separated from any existing impurity atmosphere. Test procedures, previously described,3 involved electropolish-ing, etching 2 min in 10 pct HF at 24.0°C, and expos-

Jan 1, 1969