Search Documents

By H. D. Colson, Robert A. Rapp

When a binary alloy is oxidized to form simultaneously an internal oxidation zone and an external scale which grows at a constant rate, the oxidation should reach a condition of steady shale, in which the internal oxidation zone is maintained at a time-independent thickness. Assuming an ideal model for the steady-state oxidation, the diffusion equation is solved for the steudy-state concentration profiles for oxygen and alloying- element in the metal. A theoretical prediction of' the steady-state thickness of the internal oxidation zone is made in terms of the experimental parameters. FOR the oxidation of binary alloys, Rhines, Johnson, and Anderson,1 as well as Mask: have derived equations describing the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which was assumed to mow according to a parabolic rate law. Experimental determinations of internal oxidation zone thicknesses beneath a Cu2O scale for Cu-Be and Cu-A1 alloys3,4 have shown some deviation from Maak's theoretical expressions, because the ideal model assumed for the calculation is not met experimentally. Some pure metals, such as columbium and tantalum oxidize at elevated temperatures and high oxygen pressures to form nonprotec-tive external scales which thicken at a constant rate. If such a base metal is alloyed with a solute element which may form a more stable oxide than the solvent oxide, then internal oxidation of solute may occur beneath the growing external scale. A review of the internal oxidation of alloys has been published recently.5 The purpose of this paper is to analyze theoretically for a binary alloy the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which grows at a constant rate. Consider an alloy A-B in which A is the more-noble solvent and B is the less-noble solute. The solute oxide is assumed to precipitate in internal oxidation as stoichiometric particles of BO, which are assumed to have a negligible solubility product in the A matrix. It is further assumed that the diffusion of oxygen through the zone of internal oxidation is not impeded by previously precipitated BO, particles. The specimen is assumed to be sufficiently thick so that the solute content in the center of the specimen does not change. For consistency: the following notation of Maak2 has been used:

Jan 1, 1967

By H. C. Chao, W. F. Hosford, L. H. Van Vlack

The negative "plastic Poisson's ratio" suggested in earlier studies of Mus deformation is analyzed, and the results are verified experimentally with NaCl crystals. In the early stages of deformation where the primary {110}(110) slip predominates, compression along. the [001] direction produces contraction along the lateral [011] direction plus a compensating expansion along. the [100] direction. With additional strain, the primary slip is supplemented by secondary {111}(110) slip so that the above contraction diminishes and a more typical deformation appears. THE shape change of bee and fee crystals deformed by compression or tension along [011] has been analyzed in some detail and shown to be responsible for the development of peculiar microstructures in [011] fiber textured polycrystals of these metals.1'3 This paper concerns the unusual shape change accompanying [011] compression of NaCl crystals. It is the direct outgrowth of an earlier investigation of the deformation of manganese sulfide inclusions in steel.3,4 In that investigation, cylindrical specimens of steel containing small oriented crystals of MnS were prepared by powder metallurgy and plastically compressed. The flow of the inclusions was determined relative to that of the steel by sectioning the composite and measuring the length-to-width ratio L/W of the inclusion and diameter-to-height D/H ratio of the steel cylinder on the plane of section. These L/W ratios, normalized by dividing by the initial LO/WO ratio of the inclusion, were compared with the normalized D/H ratio of the steel cylinder. Of particular interest here are the deformation characteristics of an inclusion oriented with [Oil] parallel to the compression axis. When measurements were made on sections parallel to the (100) plane of the inclusion, the L/IV ratios were only slightly in excess of unity, indicating a high apparent hardness of the [011] criented inclusion. However, measurements on a (011) plane of section resulted in L/W ratios which were much larger, Fig. 1. These observations prompted an analysis of the strains resulting from slip in an MnS crystal compressed along [011.]. CRYSTALLOGRAPHIC ANALYSIS Manganese sulfide has the NaCl crystal structure, and the predominant slip system is {110}(110). A secondary system, {111}(110), has also been reported.= {110}(110) Slip. When a crystal is subject to a uni-axial compressive stress 011 along [011], four slip systems, (101)[101.], (101)[101.], (110)[i10], and (110) [ 110], will be equally stressed with a shear stress t = 0.2 011 while the other two {110}( 110) systems will be unstressed. The normal strain En along any reference axis n resulting from slip is given by Schmid's law: en = S COS ?in COS in ?i 111 where ?in and +in are the angles between n and the i slip direction and n and the i slip plane normal, respectively, and where ?i is the shear strain on the i slip system, For the four active slip systems above, the cos ?in cos +in terms are all equal when the reference axes are the [011] compressive axis, [011] and [ 100]. Eq. [I.] therefore reduces to en - cos ?n cos +ny [2] where y =S?i for all slip systems. Substituting the appropriate angles, Eon = 0.25? 110 eon - 0.25y110 [3] €100 = -0.50y 110 The interesting feature of Eqs. [3] is that they predict that the strains in the [011] and [011] directions, resulting from {110}(110) slip, are equal and of the same sign. Thus when a crystal is compressed along [011], it will contract along the lateral [oil] direction

Jan 1, 1967

By V. O. Struebing, K. A. Johnson, F. H. Ellinger, C. C. Land

The system Pu-Ce-(Pu,Ce)Co2 has been investigated by thermal, micrographic, and X-ray diffraction methods. The principal characteristics of this system were found to be: 1) a "eutectic" valley extending across the phase diagram from the 6 Pu/Pu3 Co eutectic at 408°C to the 7 Ce/Ce24Co11 eutectic at 42Z°C, the maximum temperature in the valley being 443°C; 2) three ternary inter mediate phases, each having an appreciable mutual solid solubility for plutonium and cerium; 3) eleven four-phase equilibria comprising one eutectic, four peritectics, and six Class II reactions; 4) a pseudobinary section between the ternary phase A and the y Ce solid solution, and another such section between the 6 Pu solid solution and the 77 phase (Pu3 CO) containing cerium in solid solution. ALLOYS of plutonium that are completely molten at temperatures in the vicinity of 500°C are of interest for use in the liquid state as fast reactor fuels. Since exploratory work1,2 on Pu-Ce-Co alloys had indicated that a "eutectic" valley extended across the ternary system between the Pu-co[6 Pu/n (Pu3co)] and the Ce-CO[? Ce/? (ce24co11)] binary eutectics, thus allowing alloys of any plutonium concentration to be selected within the temperature limitation, the present investigation was begun for the purpose of accurately defining the "eutectic" valley. However, when the existence of three ternary intermediate phases and the consequent complexity of the liquid-solid equilibria were discovered, the investigation was expanded to cover the complete system, except for the corner between the isomorphous series PuCo2-CeCo2 and pure cobalt. 1) EXPERIMENTAL The purities of the alloy components are given in Table I. Alloy buttons, each weighing about 5 g, were prepared by arc melting the accurately weighed components (±0.1 mg) under a purified He-Ar atmosphere. Weight loss as a result of melting was usually less than 1 part in 1000; therefore, the buttons were not chemically analyzed. One half of each button was re-melted by induction heating in vacuo in a magnesia crucible and furnace-cooled, so as to produce a somewhat coarser microstructure than that of the rapidly cooled arc-melted button. About 20 g of each alloy to be examined by thermal analysis were remelted in vacuo in a tantalum crucible of the inverted thermocouple well type. The thermal, X-ray diffraction, heat treating, and micrographic methods used in this investigation were essentially the same as have been described in earlier reports.3,4 Two etchants for these alloys were found to be satisfactory: A) 8 (parts by volume) orthophosphoric acid, 5 ethanol, and 5 glycol; B) 7 tetraphosphoric acid, 36 water, and 57 2-ethoxyethanol. Etchant A was used at 5 to 6 v for 15 to 20 sec, and etchant B was used at 10 v for 10 sec. 2) THE LIMITING BINARY SYSTEMS 2.1) Plutonium-Cerium. The phase relationships of this system have been investigated by Ellinger, Land, and Cramer,5 and by Selle and Etter.6 The over-all agreement of their phase diagrams is good, but there are some discrepancies in the positions of some phase

Jan 1, 1967

By T. P. Floridis, J. H. Young

The need for close control of the phosphorus content of steels has led to numerous investigations on the equilibria of the dephosphorization reactions. Winkler and chipman1 have established the general conditions for effective dephosphorization of steel. They are high slag basicity, high oxygen potential, and low temperature. Other investigators have made additional contributions to the understanding of the dephosphorization process. The current status of the understanding of the dephosphorization of steel is concisely presented by Bodsworth2 and by Ward. The investigation reported in this communication was undertaken with the purpose of establishing the effect of additions of barium oxide and calcium fluoride on the dephosphorizing capacity of slags. Esin and Gel'd4 proposed that barium oxide, being more basic than calcium oxide, should cause an increase in dephosphorizing capacity when added to steelmaking slags, or when used as a substitute for calcium oxide. Derge5 has also proposed that in the future conventional slags might be replaced by BaO-Al2O3 slags. There is, however, no experimental evidence confirming the effect of barium oxide on the dephosphorizing capacity of slags. The effect of calcium fluoride on the dephosphorization of steel is not clearly understood. It is generally recognized that additions of calcium fluoride are beneficial. It is not clear, however, whether calcium fluoride affects the equilibrium of the dephosphorization reaction, or whether it simply causes an increase in the fluidity of the slag and, consequently, faster approach to equilibrium. The experimental procedure consisted in equilibrating synthetic molten slags with liquid copper at 1550°C under a gas stream containing argon, hydrogen, and water vapor. In all experiments the argon to hydrogen ratio was approximately 4:1, and the hydrogen to water ratio was 5.42:l. Molybdenum crucibles were used as containers for the slag and metal. Under the above-described conditions of temperature and composition of atmosphere, there was no observable attack of the crucibles by the metal, slag, or atmosphere. Copper was used instead of iron, because iron attacks molybdenum. The equilibration was made in a tubular furnace consisting of a recrystallized alumina tube. The alumina tube was heated by electrical resistance. A Pt-40 pct Rh wire winding was used for most runs. A silicon carbide tubular resistor was also used for some runs. Temperatures were measured with a Pt-Pt-Rh (10 pct Rh) thermocouple and kept constant within ±5°C. Equilibrium was approached from both sides, i.e., by adding the phosphorus either as oxide in the slag or as a phosphorus-rich alloy of phosphorus and copper. The holding time at the equilibrium temperature was 6 hr. At the end of each run the crucibles were rapidly cooled and removed from the furnace. The slag and metal were separated and analyzed. The experimental results are shown in Table I. The phosphorus content of the slag is expressed both as percent phosphorus pentoxide and as percent phosphorus. The basicity ratio is computed by dividing the number of moles of basic oxides-oxides of barium, calcium, magnesium, and sodium—by the number of moles of acidic oxides- oxides of aluminum, phosphorus, and silicon. Calcium fluoride is not included in the computation of the basicity ratio; i.e., calcium fluoride is assumed to be neither basic nor acidic. The distribution ratio of phosphorus—percentage of phosphorus in the slag divided by the percentage of phosphorus in the metal- is plotted in Fig. 1 against the basicity ratio. The results indicate that slags containing barium oxide have greater dephosphorizing capacity than slags containing calcium oxide. The high dephosphorizing capacity of slags containing sodium oxide and the low dephosphorizing capacity of magnesia-containing slags which already have been reported in the literature2 are confirmed by the results of this investigation. It appears that calcium fluoride has a beneficial effect on the distribution of phosphorus between slag and metal in acid slags only. Although the obtained distribution ratios between the phosphorus contents of slag and copper are not directly applicable to the dephosphorization of steel, they are sufficient for evaluating the effect of slag additions on the dephosphorizing capacity of slags in general. An increase in the ratio of distribution of phosphorus between slag and metal indicates lowering

Jan 1, 1968

By Steve H. Carpenter, Henry E. Otto

The explosive welding of metals is dependent upon the production of a jetting action caused by the collapsing of one metal plate against another. Successful welds are generally accomplished if the yield strength of the metals is in the range of 10,000 to 90,000 psi and the sonic velocity of the metal is greater than the detonation velocity of the explosive if direct contact explosive is being used.' Should the detonation velocity exceed the velocity of sound in the metal it may still be possible to obtain the jetting action and a good weld. However, in most cases where a high detonation velocity is used complications arise because of reflected shock waves which tear the bond apart as fast as it is put together.' Explosive welding of lead presents several problems since its yield strength and sound velocity are very low. Various values have been published3-5 for the velocity of sound in lead ranging from 2000~ to 23004 m per sec. Most of the high-order explosives have detonation velocities on the order of 6000 to 8000 m per sec, which precludes their use. The dynamites have a lower detonation velocity of around 2800 m per sec which is still somewhat too high. Lower-order explosives such as ammonium nitrate (1070 m per sec) must be used to weld lead in the as-received condition if the explosives are used in direct contact. Rather than use low-order explo'sives it was decided to alter the sonic velocity of the lead. The sonic velocity is directly related to the modulus of the material according to the following expression: Fig 1—Interface of explosive weld of lead to steel. Lead is on top As-polished Magnification 75 times as well as the yield strength. Bolling et al. 6 show that the shear modulus of lead single crystals increases from about 0.72 X1011 dynes per sq cm at 300°K to about 0.98 X1011 dynes per sq cm at 0°K, an increase of approximately 3 5 pct. This gives an increase in the sonic velocity of around 700 m per sec. Hence, the sonic velocity of lead at cryogenic temperatures is approximately equivalent to the detonation velocity of the low-order dynamites. We have obtained high-quality lead to steel explosive welds using a 40 pct dynamite in direct contact with the lead. Prior to detonation the lead was chilled with liquid nitrogen (78°K) to increase the strength and sonic velocity. Welds were made while the lead was cold. Specimen sizes were 3 by 6 in. A preset angle of 5 deg with a 0.10-in. standoff at the base was the geometrical setup used. The amount of explosive used for optimum welding of an 1/8 -in. -thick lead sheet to a steel plate was found to be 7 g per sq in. A PETN sheet explosive line wave generator was used to insure a linear detonation front through the dynamite. A photomicrograph of a lead-steel weld is shown in Fig. 1. The typical wave effect that constitutes a good explosive weld is present. When tested in shear, the weld failed in the lead, indicating that the bond is stronger than the lead base metal. Higher-order explosives were also tried without success. We believe this indicates the importance of matching the detonation velocity and the sonic velocity for successful explosive welding. Note Added in Proof. High quality explosive welds of lead to steel have recently been obtained at ambient temperature using a low velocity (1000 M per sec) free running dynamite. The weld interface obtained is comparable to Fig. 1. 'S. H. Carpenter, R. H. Wittman, and R. J. Carlson: Proceedings of the First International Conference of the Center for High Energy Forming, Syracuse University Press, syracu.se, N. Y., in press. 'A. HI Holtzman and G. R. Cowan: Welding Risearch. Council Bull., No. 104, April, 1965. 'Metals Handbook, 8 ed., p. 1062, Metals Park, Ohlo. 'J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger: Phys. Rev., 1957, vol. 108, pp. 196-216; 'L. V. Al'tshuler, K. K. Krupnikov, B. N. Ledener, V. I. Zuchikhin,

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;'= 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 W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.' This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2'3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.''' ~ohatgi' has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Dendritic aggregate of ice formed on freezing of aqueous soluitions has been studied. Chlorides of sodium, potassiutn, lithiunz , and hydroget1 were used as solutes. The spacing between ice platelets or den-drites was experimenlally found proportzonal to the square root of freezing time when the freezing rate was constant from beginrting to end of solidification; the constant freezing rates were obtained during freezing of small droplets of aqueous soliitions surrounded by relatively large heat sinks. The transverse growth velocity of the ice platelets is proportional to the square root of the freezing rate. During unidirectional freezing from a constant temperuture chill, the solution at each location is subjected to a spectrum of freezirtg rates. The freezing rate is ini- FREEZING of solutions has been a subject of investigation in many disciplines. Aqueous solutions offer the advantage of transparenty; their study is of special significance due to the increasing interest in freezing processes for desalination. In addition dendritic solidification of aqueous solutions is in many ways analogous to freezing of metallic solutions. Aqueous solutions of most ionic salts freeze with tially low, passes through a maximum, and then decreases until solidificatimz is complete. The den-drite spacing increases linearly with the distance from the chill surface; it is inversely profiortional to the square root of the maximum freezing rate. The dendrite spacings in the two systems (the constanl freezing rate and the varying freezing rate) are equal, when the maximum freezing rate of the varying freezing rate system equals the average freezing vale of the constant freezing rate system. Mass transport in interdendritic liquid duriug solidificatiotz is analyzed; the experimental observations indicate that maximum concentration difference (AC) and supercooling (AT) in the interdendritic liquid are indepexdent of freezing rate. the separation of practically pure ice crystals from the liquid phase; with very few exceptions there is no solid solubility of ionic salts in ice. As an ice crystal grows there is rejection of solute from the moving interface into the liquid. Since the rejected solute moves primarily by diffusion, concentration gradients are established in the liquid. The highest solute concentrations are found in liquid immediately adjacent to liquid-solid interfaces and lowest concentrations farthest from the interface. Two-phase equilibrium obtains only at the solid-liquid interface; at other locations the liquid becomes supercooled because temperature gradients are negligible compared to concentration gradients. This is an immediate consequence of the fact that thermal diffusivities are considerably higher than mass diffusivities.

Jan 1, 1968

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

Fluid flow strongly influences ingl structure and the columnar -to-equaaxed transition. Artificial flow patterns siwzilar to the nuturul ones act to induce this transition, while dampening forces act to suppress this transition. It is shown here how simple mechanical forces can be applied to a systerrz in order to induce or slipPvess relative fluid flow and the change both the structure transition and the exact structures obtained. The example used is the effect of slow rotations and oscillations 012 a cooling- ingot (of laboratory scale). The details of rotution and oscillation for various cooling rates, lenlperal~ire gradients, and sizes of ingot are related to other solidzfication variables. THE grain structure of a casting can be changed by altering the fluid motion during solidification. Just how important these changes are depends directly upon the degree to which the fluid motion can be controlled. An early step in understanding the nature and influences of fluid motion was taken by studying natural thermal convection; when a static mechanical device was used to suppress natural flow the result was opposite to that obtained when an electromagnetic device was used to augnlent flow in a pattern similar to the natural one. ''2 Suppression allowed more columnar growth to occur, but "augmented natural convection" brought about an earlier columnar-to-equiaxed transition (CET). Since the solidification of a free ingot must have characteristics somewhere between those displayed during suppression and augmentation, we know that natural convection must influence the CET. Further, since heat transfer in the liquid is always some time-dependent combination of convection and conduction, it can easily be guessed that the temperature gradient in the liquid is the vital factor affecting the CET.1,2 It is obvious that the structure arising from the unadulterated solidification of an ingot, without external influence, is rarely if ever the best possible one. Although the pattern of the natural fluid flow may be considered efficient, the magnitude of the flow and the heat transfer decrease freely from the outset. For a

Jan 1, 1968

By R. A. Flinn, R. D. Pehlke, D. R. Glass, P. O. Hays

Knowledge of the depth of penetralion of an oxygen jet into the bath of the oxygen converter and of the correlation of penetration with driuing pressuve, lance heighl, and nozzle throat area is vital to the understanding of converter operation. If the penetration is too shallow, then severe and hazardous slopping takes place. On the other hand, if the jel penetrates entirely Lhvough lhe bath for an apprcciublc period of time, bottom damage occurs. In addilion to measurement of the penetralion of the jel, knou~ledge of the circulatory movement in the bath is also of interest in order to evaluale various theories oj-concerter operating behavior which have been published. In this investigation, experimental converters were buill of IOU- , 300-, and 4000-lb capacity. Four independent methods were used to determine penelralion: the onset of bottom marking, a nitrogen bubbler probe, observation througlt an optical syslew built into the oxygen lance, and direcl viewing of the jet issuing from the bottom of the vessel. Good correlation zuas obtained, and empirical relalions for pvedicling perletration were found. These relations were conjzrmed by bottom marking tests in 55- and 110-ton vessels. Within the operaling conditions employed in these tests, the depth to which a single oxygen jet penetrated zuas found lo vary according to the relatiorl ThE technical literature is replete with data concerning the successful use of the basic oxygen furnace or converter in steelmaking. Experimental data are lacking, however, on the vital factors of the depth of penetration of the jet into the bath and the induced circulation. Commercial operating conditions usually have been the result of cut and try experiments in lance manipulation until satisfactory results were obtained. There have been, however, two hotly argued opposing theories concerning desirable depth of penetration and these are exemplified by the Schwarz and Miles patents1,2 on one hand and the Suess patent3 on the other. The Schwarz patent teaches that the jet, issuing from the nozzle at supersonic speed, penetrates deeply "so that the reactions between the iron and the oxygen and between the oxygen and the rest of the smelting components take place in the center of the bath". Specific operating suggestions are given by Miles.2 By contrast, the Suess patent calls for surface Circulalion was investigated by lour methods: by direct observation in 200-lb open baths, by the use of graphite rudders in the 300- and 4000-lb converlers, by direct observalion through an oplical system in the lance, and by various models al room temperature. All were in excellent agreement and indicated that the motion of the bath ulas up at the center, radially outluavd at the surface, and down at the sides. Experi-ments in small and in commercial vessels indicate that it is essential to operate with a jet penetration of approximately 50 pct of the bath depth. Surface blowing results in low oxygen eficienty and in hazardous conditions which may render the process inopeuable. RejYactory dartzage al the bottom of the vessel is only encountered when the jet penetrates to the bottom, and this can be avoided by properly applying the penetration formula. The application of this en/pirical formula in commercial peraations is best when limited to combinations of lance size, pressure, and height which are typically encounteved in the use of a single-hole lance. blowing so that "...the oxygen jet does not penetrate deeply into the molten metal bath and is confined to an impingement area at the central portion of the bath surface". These references are given merely to illustrate the basic differences between the two schools of thought and to point out the need for measurement of penetration for the sake of the operator. For example, it is shown later that inefficient and even dangerous conditions can arise if improper blowing conditions are used. Differences are also evident between the two schools of thought as to the mixing, circulation, and agitation which is to be accomplished by the jet. The Schwarz patent states that "surface contact is not sufficient in most cases to bring about quick reaction, the same as the blowing of the gas over the bath surface or the mere blowing of the gas onto the bath surface". The patent goes on to call for active mixing. In contrast the claims of the Suess patent call for "discharging a stream of oxygen ... to an extent to avoid material agitation of the bath by the oxygen stream". In this patent the circulation is said to be downward in the center and up at the sides of the vessel. A number of investigators4-12 have explored penetration and circulation in transparent models. In general, it is agreed in these tests that the circulation is upward at the center (along the sides of the jet cavity),

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,' 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 Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.' Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:' where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

By Y. Baskin

Solid-solubility relationships in the Pseudobinary systems UAS-UP, UAs-US. UAS-UC, aid UAs-UN were investigated. The first two systems exhibit complete mutual solubility, whereas the component compounds in the other two systenzs are immiscible. The above information, together with solid-solubility data joy six additional pseudobinary systems , were analyzed for compliance wilh the Hurrze-Rothery rules for rnetallic systems. The relative size difference of the component nonmetal atoms was found to be the dopainant jactor determining the extent of solid solubility between the NaC1-type uranium compounds. The anionic and covalent radii of the nonmetal atoms appear to be inadequate for these systems, but compuled radii based on rare earth compounds yield consistent results for the uranium compounds. THE actinide elements, like metallic elements of the transition and rare earth series, readily form binary compounds with nonmetallic elements of groups IV, V, and VI of the periodic table. Of particular importance are the NaC1-type equiatomic compounds with carbon, nitrogen, sulfur, phosphorus, and arsenic. The uranium members of this family of compounds have high melting points, are essentially stoichiometric, and exhibit various amounts of mutual solubility. Thus, they are of interest for investigating the factors governing the extent of solid solubility. Previous investigators have determined the solid-solubility limits in the pseudobinary systems between the compounds UC, UN, US, and UP. Anselin et a1 .' reported complete miscibility in the system UC-UN. Baskin and shalek 2 and Allbutt et a1.3 reported that UP and US exhibit complete mutual solubility. Shalek and white4 reported partial miscibility in the system US-UC. At 1800°C the maximum solubility of UC in US is 40 mol pct, but that of US in UC is 4 rnol pct. shalek5 found limited solubility in the system US-UN; the maximum solubility of UN in US is 11 rnol pct at 1800°C, while that of US in UN is only 0.3 mol pct. White and askin 6 found very limited miscibility in the system UP-UC at 1800°C. Approximately 7 mol pct UC is soluble in UP, but there is no solubility of UP in the monocarbide. Phase relations in the pseudo-binary system UN-UP were investigated by askin.' Approximately 0.7 mol pct UN is soluble in UP at 1800°C, while UP is immiscible in UN. The present study was carried out to explore the extent of terminal solubility in the systems UAs-UC, UAs-UN, UAs-US, and UAs-UP. This information, combined with existing data, provided a sufficient basis on which to determine the factors governing solid solubility in pseudobinary systems containing NaC1-type uranium conpounds. I) EXPERIMENTAL 1) Materials. The compounds UC and UN were obtained from the Kerr-McGee Corp. and United Nuclear Co., respectively. The US, UP, and UAs were synthesized by reacting finely divided uranium with H2 S, pH3, or AsH3 gas at low temperature (300° to 500°C), followed by homogenization in a vacuum at moderately high temperatures (1400° to 1700°c).8-10 The materials were essentially stoichiometric, with the exception of UC, which exhibited a C/U ratio of 1.05. Oxygen was the major contaminant in these compounds, ranging from 0.05 wt pct in US to 0.30 wt pct in UC, and it was generally combined with uranium to form UO2. The UO2 content in these materials was usually of the order of 1 wt pct, and did not exceed 2 wt pct. Furthermore, no evidence was found for a high-temperature reaction between uranium dioxide and any of the compounds. Chemical analyses of equilibrated compositions in the systems UAs-UP and UAs-US showed that the non-metal atom to uranium ratios averaged about 1.01, and that the oxygen contents ranged from 0.06 to 0.22 pct. However, the small deviations from stoichiome-try or the presence of minor oxygen impurities do not invalidate the conclusions to be drawn from this study. 2) Experimental Procedures. The component compounds in powdered from were blended in the desired proportions for 5 hr in the ball mill that consisted of stainless-steel balls in a plastic container. Chemical analyses indicated very little metallic pickup from the blending operation and virtually no increase in oxygen content. The pellets were pressed in a 0.270-in.-diam steel die under 40,000 psi pressure. One wt pct of stearic acid dissolved in CCl 4 served both as a binder and as a die lubricant. Chemical analyses revealed that the stearic acid left no carbon residue in the sintered samples. The pellets were sintered in vacuum in an unsealed tantalum crucible. The temperature, measured with a calibrated optical pyrometer, was maintained at 1800" + 30°C for 3 hr. This was sufficient time for attaining equilibrium as no change occurred in either the lattice parameters or the sharpness of the X-ray patterns when samples were annealed for longer periods of time. The pellets were cooled with the furnace. Debye-Scherrer powder patterns were taken at room temperature with a 114.59-mm-diam Norelco powder camera and CuKor radiation (CuGI = 1.5405A). Unit cell dimensions were determined from a Nelson-Riley extrapolation to the high-angle reflections. The values for were precise to k 0.001A. 11) RESULTS X-ray and met allographic investigation revealed that complete mutual solid solubility exists in the pseudobinary systems UAs-UP and UAs-US. The lattice parameter vs composition plots, Fig. 1, show a

Jan 1, 1968

By I. R. Kramer

The effect of the specimen diameter, d, on the flow stress, cra of polycrystalline aluminunz (99.997) was studied. The increase in the flow stress could be accountedfor by the increase in the surface layer stress, with decreasing specimen diameter. Both , and a, were found to be proportional to For the smaller-dianzeter specimen (< 0.033 in.) at strains less than aboul 0.1, the work hardening of the surface layer was greater than that associated with the bulk of the specimen. At higher strains the work hardening due to the bulk appears to be independent of the specimen diameter. THE increase in the strength of metals with decreasing diameter is well-known; however, an adequate explanation for the cause of the size effect is still lacking. The earliest systematic investigation of size effect appears to be that of Onol who reported that for aluminum monocrystals the resistance to slip at low strains increased as the specimen diameter decreased. A change in the stress-strain curve beyond 0.001 strain was not found. However, Suzuki et a1 .&apos; reported for monocrystals of a brass and copper having diameters in the range of 2 to 0.12 mm that the entire stress-strain curve was raised as the specimen diameter was decreased. The effect of size was most apparent when the diameter of the specimen was less than 0.5 mm. In the discussion of this paper Honey-combe reported a size effect in copper crystals as large as % in. diam. These results are in agreement with those of paterson3 and Garstone et al.4 While the majority of the investigations on size effects was conducted in terms of the variation in the diameter of the specimen, several investigators studied the influence of the specimen geometry. For example, Wu and smoluchowski 5 reported that in aluminum monocrystals the slip system was a function of the specimen dimension in the slip direction. King-man and Green 6 studied the influence of size on the compressive stress-strain relationship of aluminum monocrystals when the ratio of length to diameter was constant. Their specimen diameters ranged from to & in. For specimens oriented for single slip the critical resolved shear stress for the smaller-size specimens increased with decreasing diameter. No effect was observed in the large-size specimens. Specimens having an orientation near the corners of the stereographic triangle did not exhibit a size effect. Apparently, the increase in strength with decrease in the diameter of the specimen is a general phenomenon and has been observed in a brass |T and cadmium as well as in aluminum and copper.&apos; In a series of investigations (for example Ref. lo), it was shown that during deformation a surface layer was formed which imposes a back stress, a,, on the moving dislocations. It is reasonable to predict that this surface layer stress, as, should be a function of the specimen diameter and could possibly account for the flow stress size effect. In fact, experimental evidence will be presented to show that this is the case; i.e., the increase in flow stress with decreasing size is equal to the increase in the surface layer stress, as, with size. In addition, data will be presented on the variation with size of and a* where is the back stress associated with the generation of dislocation obstacles in the bulk of the specimen and a* is the net effective stress acting on the mobile dislocations. A limited investigation was carried out on gold specimens to determine the influence of an oxide film. EXPERIMENTAL PROCEDURE The aluminum specimens were prepared from -in. bar stock (99.997 pct purity). The 0.350- and 0.150-in.-diam specimens were machined directly from the bars while the specimens having a diameter of 0.033, 0.020, and 0.015 in. were prepared by swaging and drawing to 0.04 in. and electropolishing almost to final size. The specimens were prepared with a 2-in. gage length. The specimens were annealed in vacuum (-10-4 Torr) at 350°C for 8 hr. The grain diameter of the specimens in the various specimen diameter groups was 0.08 ± 0.02 mm. Gold specimens of two diameters, 0.14 and 0.03 in., were prepared in a similar way and annealed at 650°C for 8 hr. The grain diameter of the gold specimens was 0.2 mm. After annealing the specimens were electrochemically polished to the final size and tested in an Instron tensile machine at a strain rate, E&apos;, of 10- 3 per min. While it was possible to determine the surface layer stress, a,, in the larger-size specimens by measuring the difference, Aa, between the stress before unloading the specimens and the initial flow stress after removal of the surface layer as outlined in detail in Ref. 10, this method is not applicable for small wires because of the difficulty in obtaining a sufficiently accurate measure of the diameter. The values at the various strains were therefore determined by measuring after the specimen had been annealed at 35°C for 4 hr. It has previously been shown" that the two methods give the same results for a provided that the annealing temperature is low enough to affect only the surface layer and not the dislocation barriers in the bulk of the specimen. For the gold specimens a treatment at 150°C for 16 hr was found to be satisfactory for the determination of by the low-temperature annealing method. EXPERIMENTAL RESULTS Determination of a,, and a,. The stress-strain curves for the various diameter aluminum specimens, plotted in terms of the logarithms of the true stress, and true strain, are given in Fig. 1. These curves represent the average data taken from at least ten specimens at each size. Over the range of strains investigated the curves follow the empirical equation

Jan 1, 1968

By N. B. Gray, R. V. Culver, W. S. Boundy, N. W. Stump

The kinetics of sulfation of single crystals of lead sulfide to lead sulfate have been studied between 969" and 1073°K in gas atmospheres of known composition using a thermobalance technique. The data are described by an equation derived on the basis that diffusion outward through the Product layer is the major controlling step. The rate of sulfation is linearly related to the logarithm of the sulfur trioxide partial DESPITE its industrial significance the oxidation of lead sulfide has received limited attention. The oxidation reactions have been studied using beds, briquettes, single crystals, or thin films of lead sulfide. Lead oxide and lead sulfate (PbSO,) were formed when Mclntoshl and Gardner2 roasted beds of galena pressure and the temperature coefficient of reaction is 40 ± 5 kcal per g mole. Gold marker experiments show that the sulfate layer grows by outward movement of ions through the sulfate layer. Initially the PbSO, adheres to the PbS but later forms an irnpewious spheroidal envelope; PbS vaporizes and pb2&apos; ions diffuse through the envelope to react at the external surface. in air at temperatures up to 800°C. In a more extensive investigation, Tchizhykov3 obtained Pb, PbO, and PbS04 in accordance with Eqs. [1] to [4], when a bed of -200 mesh galena was oxidized in O2-N2 mixtures at 700° to 900°C.

Jan 1, 1968

By Winston A. Wong, John J. Jonas

Commercial purity aluminum was deformed by extrusion over the temperature range 320° to 616°C and the strain rate range 0.1 to 10 per sec. Flow stresses and strain rates were calculated from the experimenLa1 ram pressures and speeds. The stress-strain rate-lemperature relationship in extrusion was found to be similar to that in creep. Extrusion, torsion, compression, and creep data extending over ten orders of magnitude of strain rate and over two orders of magnitude of stress were correlated by a single creep equation. It was concluded that hot-working is a thermally activated process, in which the rate-controlling mechanism is either the climb of edge dislocations or [he motion of jogged screw dislocations. The microstructural changes observed during extrusion were consistent with the proposed deformation mechanisms. ALTHOUGH great progress has been made in understanding the technology of extrusion, very little is known about the actual deformation mechanisms operating during flow. Previous accounts describing extrusion have indicated that the relationship between ram speed (V), pressure (P), and temperature (T) can be given as follows:1 V = apb and P = A&apos; exp(-AT). In these equations, a and b are constants which depend on temperature, A&apos; is a constant which depends on ram speed, and A is a "coefficient" with a different value for each metal. Although these equations have fairly wide application, they do not contribute much to a fundamental understanding of the deformation. Furthermore, extrusion has not hitherto been considered as a thermally activated rate process. This lacuna is surprising because hot-working is similar to high-temperature creep in several respects. There is, in fact, a fair body of experimental evidence suggesting that the material response under hot-working conditions is similar to that occurring under creep conditions, in spite of the many orders of magnitude difference in strain rate.2"4 Since creep has been extensively analyzed in terms of dislocation mechanisms, the comparison of hot-working to creep is useful, for it can suggest the possible deformation mechanisms operating during hot-working. In this paper, the hot extrusion of aluminum will be examined from the point of view of thermally activated deformation mechanisms, such as operate during creep. EXPERIMENTAL PROCEDURE The experimental procedure consisted of extruding commercial purity aluminum* over a range of ram velocities and temperatures at constant die reduction by the direct method. Details of the experimental equipment have been published elsewhere.5 Extrusion was carried out at each of the following billet temperatures: 320°, 376°, 445°, 490°, 555°, and 616°C at the following constant ram speeds: 0.002, 0.008, 0.02, 0.1, and 0.2 in. per sec.* All results were obtained using a square-shouldered die with an extrusion ratio of 40:1, giving a reduction in area of 97.5 pct. The ram force was the dependent variable, and was measured by means of strain gages on the ram and was plotted as a function of ram travel. The sequence of events before making an extrusion was duplicated before each run so as to minimize as much as possible variations in experimental conditions. For example, after the equipment had been assembled, the billet was allowed to heat up to temperature inside the insulated container. Once the container attained the desired temperature, a period of 1/2 hr was allowed to elapse before the extrusion was made. This time was found to be required to allow the billet to reach a steady-state temperature, as determined from previous tests. When all was ready, extrusion was carried out without interruption; that is, the billet was upset and extruded in one operation. EXPERIMENTAL RESULTS AND DISCUSSION The two usual experimental approaches for investigating high-temperature deformation exhibit an important common feature. In the first approach, which corresponds to creep, a constant stress (or load) is applied to the material at constant temperature and the resultant strain is recorded against time. After an initial transient stage, a state of constant strain rate exists (secondary creep), in which a steady-state condition is established which is sensitive to variation in either applied stress or temperature. In the second approach, a constant strain rate is applied and the resultant flow stress is recorded. This corresponds to the situation in hot torsion or hot compression, where it is observed that, for a constant test temperature, there is an initial rise in stress to a steady value which is maintained up to very high strains. In tests of this type, a steady-state region is also established in which the stress is sensitive to variation in either the strain rate or the temperature.3,4,6-16 In both types of tests, therefore, a steady-state region is established after an initial transient. In the case of hot-working this region may be called steady-state hot-working, and it is analogous to steady-state creep with which it has many common features. Stress Dependence of the strain Rate in Extrusion. In order to assess the stress dependence of the strain rate under extrusion conditions, and to compare it to that of creep, as well as of hot torsion and hot compression, the extrusion data were analyzed according to power, exponential and hyperbolic sine creep equations.

Jan 1, 1969

By Michael Epstein, Daniel E. Rosner

Fume nucleation sufficiently close to vaporizing suvfaces can augment net vaporization rates into cooler environments. Environmental conditions favoring large vaporization rate enhancements are briefly discussed and a previous theoretical treatment of this nucleation phenomenon is generalized to account for the self-regulating effect of condensalion-heat release within the boundary layer. Despite kinetic limitations on homogeneous nucleation, and latent heat release, non-diffusive condensate removal processes appear to make possible large enhancements in steady-state vaporization rates, provided surface temperatures are well below the boiling point. When condensed phases vaporize (or dissolve) into cooler media, the diffusion-limited mass loss rate can be strongly influenced by the process of nucleation/con-densation (or precipitation) within the thermal boundary layer. This condensation process (which typically leads to mists or fumes in the case of evaporation into cooler gases) has the effect of steepening the vapor pressure profiles near the evaporating surface, since the condensation zone acts as a vapor sink. However. the resulting enhancement in the diffusion-limited evaporation rate can be estimated (as first done by Turkdogan1 for the case of molten iron/nickel alloys evaporating into helium) only if one has independent knowledge of the critical supersaturation, sCrit(T), required to homogeneously nucleate the vapor.* In a recent reformulation and generalization of the theoretical model of Ref. 1 it has been shown that, when log sCrit is approximately linear in reciprocal temperature, rather simple expressions can be derived4 for the ratio of the actual rate of vaporization j" to either the minimum (no condensation) rate j"min, or the maximum (equilibrium condensation) rate j"max In the present communication we wish to briefly report on further developments and implications of the formulation of Ref. 4, with emphasis on i) environmental conditions favoring large enhancements in vaporization rate, and ii) the self-regulatory influence of condensation heat release (neglected in Refs. 1 to 4) on predicted vaporization rates. Additionally, we take this opportunity to correct several misprints appear- ing in Ref. 4, and comment on Elenbaas&apos;s recent criticism5 of Ref. 1. MAXIMUM POSSIBLE VAPORIZATION RATE IN PRESENCE OF CONDENSATION A nonequilibrium theory is of interest because of the very large difference between the minimum (no condensation) and maximum (equilibrium condensation) vaporization rate. The magnitude of this maximum possible enhancement can be shown quite clearly by combining a result of Refs. 3 and 4 with the fact that for most liquids there is a simple relationship between the molar heat of evaporation, A, and its boiling point, i.e., A/(RTBp) = C, where the constant C, often called the Trouton ratio, takes on values not very different from 11.* More generally, for any substance (including The Trouton ratio (which for water is 13, for methane, 10, and so forth) will be recognized as the ratio of the molar entropy change upon vaporization (at TBP or Ttransf) to the unlversal gas constant R. Its near constancy reflects the fact that the change in atomic order upon vaporization depends only weakly on the kinds of molecules involved. those that sublime under ordinary conditions) we can define a characteristic transformation temperature. Ttransf, by a relation of the form Ttransf =A/(CR), and then examine the maximum possible evaporation rates as a function of how far removed from Ttransf are the surface temperature, Tw, and ambient temperature, T. Subject to the assumptions: 1) equilibrium vapor pressure, pv,eq, everywhere small compared to prevailing total pressure, p, and 2) negligible effect of condensation heat on temperature profile, the maximum enhancement ratio was found (Eq. [17], Ref. 4) to be: where, for most vapors, Nu/NuD (the ratio of heat transfer coefficient to mass transfer coefficient for the same configuration) is a number near unity.* Ex- *An alternative derivation of the Nu = NuD special case of this equation. revealing its validity for arbitrary velocity/temperature profiles in a laminar boundary layer, is given in Ref. 3. amining this result for a "Trouton substance", one obtains the results shown in Fig. 1, constructed for C = 11. Since we are concerned with vaporization enhancements (j&apos;max/J"min > 1) at surface temperatures below Ttransf, this area of interest is shown unshaded. One notes that at a fixed ambient temperature (hence, T/TtranSf) there is a unique surface temperature, 2T , at which j"max/j"min attains its peak value; moreover, the peak enhancement ratio, see dashed locus. Fig. 1, is: (NuA/NuD)(C/4)(Ttransf/T,). Hence, if Nu = NuD, when the ambient temperature is less than 1/4 of TtranSf the peak enhancement exceeds the Trouton

Jan 1, 1969

By E. Breinan, M. Salkind

Al3Ni whiskers were chemically extracted from unidirectionally solidified Al-A13Ni eutectic ingots, bent into loops, and heated for 0.1 to 10 hr at 320°, 415", and 510°C. The initial strains ranged from 0.003 to 0.055. In all cases, permanent plastic deformation was noted after heat treatment. The deformation consisted of relatively uniform bending at low stresses and temperatures and short times and kinking followed by fracture at high stresses and temperatures and long times. After kinking, the whisker segments adjacent to the kinks were found to have straightened, which is evidence of a dislocation condensation mechanism. The range of temperatures and strains at which time dependent plastic deformation was found indicates that creep of whiskers probably plays a role in the creep of A13Ni whisker-reinforced aluminum. WHISKERS may be defined as nearly perfect single crystals which exhibit high strength. Because they can support high stresses at relatively low strains, they have been successfully employed in reinforcing metals at both ambient and elevated temperatures. In studying the creep behavior of A13Ni whisker-reinforced aluminum at elevated temperatures,1,2 it was noted that the composites exhibited measurable creep deformation. This investigation of the creep relaxation of individual A13Ni whiskel, extracted chemically from the composite was initiated to determine if creep of whiskers could con. "bute to the overall creep of the composite material. Many observations of plastic deformation of metal and halide whiskers have been made. Brenner3-8 noted that copper, silver, and iron whiskers exhibited heterogeneous plastic deformation at room temperature when strained beyond their yield points. Gyulai9 and Gordon10 observed plastic deformation of relatively large (>3 µ) NaCl and KC1 whiskers, although the smallest, most perfect whiskers were completely elastic. Eisner" noted plastic deformation and microcreep of iron and silicon whiskers at room temperature after straining beyond the yield point. Whiskers reported to exhibit creep at stresses below the yield point were zinc1&apos;-" and Silicon.15 Cabrera and price" observed some zinc whiskers which crept at room temperature after a short incubation period but then stopped creeping after a short time. Because some of their specimens exhibited no creep, they concluded that those whiskers that crept were relatively imperfect. Pearson, Reed, and Feldman15 observed similar creep behavior of silicon whiskers at 800°C. They also concluded that creep of the whiskers was a result of imperfections in their crystals. Brenner16 observed delayed failure of A12O3 whiskers at elevated temperatures but found no evidence of plastic deformation up to 2030°C (99 pct of E.EREINAN and M.SALKIND,JuniorMembers AIME,are Research Scientist and Chief, respectively, Advanced Metallurgy Section, United Aircraft Research Laboratories, East Hartford, Conn. Maunscript submitted April 5, 1968. IMD the melting temperature). Brenner also noted7 that some copper and iron whiskers exhibited delayed kinking above 350°C while others did not. One can conclude from these observations that small relatively perfect whiskers could exhibit completely elastic behavior during sustained elevated-temperature loading of composites. Since A13Ni whiskers tested in both bending and tension were found to exhibit no evidence of plastic deformation at room temperature&apos;7&apos;18 this study was initiated to determine whether or not creep of A13Ni whiskers occurred at the elevated temperatures at which creep in the composites was observed. Whiskers were chemically extracted from ingots of unidirectionally solidified A1-A13Ni eutectic, constrained in bending to various elastic strains and heat-treated. The bending constraints were removed after heat treatment and the amount of permanent set was taken as a measure of the time-dependent plastic deformation. EXPERIMENTAL PROCEDURES Ingots of eutectic Al-A13Ni containing nominally 6.2 wt pet Ni were unidirectionally solidified at approximately 11 cm per hr using a process described elsewhere.19,20 The starting materials were 99.99 pct pure. Cylindrical sections cut from the center of each ingot were placed in a 3 pct aqueous solution of hydrochloric acid and the whiskers were extracted as described previously.17 The whiskers nearest the surface were blackened somewhat due to overexposure to the acid while the center of the ingot was being dissolved These partially attacked whiskers were discarded. An intermediate zone of silver-gray-colored whiskers was collected and stored in methanol for use in relaxation experiments. Individual long pieces of A13Ni whiskers were placed on Fisher Precleaned Microscope Slides. These normally straight whiskers were bent elastically into arcs or loops of varying radii by manipulating their ends with a slender probe. The mass attraction between the whisker and the probe was sufficient to cause the whisker to follow the probe. The whiskers were retained in the elastic bend by the surface tension of a fine residual film on the slides. By using long whiskers, the action of the surface tension on the unlooped ends of the whisker allowed high elastic strains to be maintained in the loops. After each whisker was bent, a photomicrograph was taken for use in measuring the bending strain. The range of strains studied was 0.003 to 0.055. The bent whiskers were then encapsulated in Pyrex tubes at pressures between 10"6 and 5 x 10"6 mm of mercury and heat-treated at 320°, 415°, and 510°C (respectively 53, 61, and 70 pct of the peritectic decomposition temperature). After each heat treatment, the liquid film on the slides was found to have dried, but the whiskers were held in their original shapes by a residue on the slide. The minimum radius of curvature of each bent whisker was measured before and

Jan 1, 1969

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