Search Documents

By B. A. Wilcox

ThERE are several reports in the literature which indicate that both solid-solution hydrogen and hydride precipitates can promote low-temperature em-brittlement of tantalum.1-3 For example, Imgram et al.2 showed that hydrogen additions in the range of 140 to 580 ppm promoted a ductile-to-brittle transition at slightly above room temperature in both wrought and recrystallized tantalum. This contrasts with the observation that tantalum of norma1 purity is very ductile, even at liquid-nitrogen temperature. Imgram et al. also found that hydrogen additions caused a deterioration of notch tensile properties of tantalum. The purpose of this communication is to present some limited evidence that hydrogen can also cause fatigue embrittlement of tantalum. The material used in this investigation was wrought, stress-relieved (1000°C, 1 hr), are-melted tantalum rod (5/8-in. diameter) containing the following impurities in weight percent: 0.005 C, 0.007 02, 0.0005 H2, 0.003 N2, 0.08 Cb, 0.01 W, and 0.01 Fe. Hydrogen charging was done in an atmosphere of flowing dry hydrogen for 3 hr at 600°C, followed by an homogenizing anneal in purified argon for 15 min at 600°C, and cooling in an argon atmosphere. Typical micro-structures of the hydrogen-free and the hydrogen-charged materials are shown in Fig. 1(a) and Fig. 1(b), respectively. Fig. 1(b) shows the appearance of hydride precipitates which, in many cases, formed preferentially parallel to the rod axis. The hydride dispersion was uniform across the diameter of the specimen. The fact that the precipitate was a tantalum hydride was tentatively confirmed by X-ray diffraction on a metallographically prepared surface. After hydrogen charging, chemical analyses by vacuum fusion revealed the hydrogen content to be 0.0295 wt pct. In addition, the oxygen and nitrogen contents were slightly raised to 0.0095 O2 and 0.005 N2.

Jan 1, 1964

By W. A. Backofen, M. L. Ebner

SINCE the early work of Gough with Hanson and Wright,l-3 the study of fatigue has been characterized by experiments on single crystals only in recent times.9-10 Now, increasing attention is given to this aspect of fatigue research for the insight that it may provide into details of mechanism. The investigations have concentrated to a large extent on the development of deformation markings on fatigued crystals, and have shown the cracks to originate in slip bands possibly preceded or accompanied by slip-band extrusions. Experiments of special interest to the present work were conducted by paterson5 on copper crystals and involved both metallographic examination and measurement of change in flow stress. Crystals were cycled in alternating tens ion-compress ion with a constant plastic shear-strain amplitude of approximately 0.8 pct, and were particularly revealing for their demonstration of hardening with accumulated strain similar to that in unidirectional straining, through an easy-glide stage I followed by a stage II of rapid hardening; deformation was not continued beyond 40 cycles, however, so that the eventual course of the hardening curve could not be decided. For the conditions used by Paterson, surface slip markings were similar to those observed in unidirectional straining, but there were no X-ray asterisms and no deformation bands on the surface. In current thinking about the nature of fracture in fatigue, two views relative to mechanism are generally acknowledged, with the reservation that both could apply simultaneously in some measure. As one possibility, fracturing across a slip plane is regarded as a result of loss of cohesion from the creation of many point defects by dislocation movement under the cyclic loading.'' On the other hand, fracture has also been taken to follow as a consequence only of the geometry of slip at a free surface, consisting of offsets and crevices which eventually become fatigue cracks.12, l3 The work of McCammon and Rosenbergl4 showing fatigue in polycrystals at 4.2oK makes clear that any long-range diffusion of point defects is unnecessary, yet studies such as those of Forsyth and stubington15 show that accelerated diffusion may be a characteristic of deformation under fatigue loading. Interest in obtaining data of possible use for resolving such questions led to the experiments described below. Copper crystals were conveniently loaded in alternating four-point bending at constant deflection, a test condition shown to approximate a constant plastic strain amplitude for a wide range of axial orientations. The method of testing was not readily adapted to extensive study of temperature effects, but an investigation of the geometry of crack formation could simply be made by orienting,the slip direction at different angles to the surface. EXPERIMENTAL PROCEDURES Single crystals were grown by a modified Bridgman method in a stationary gradient furnace under an atmosphere of purified dry nitrogen. Purity of as-grown crystals was 99.999 pct as determined by spectrographic analysis plus vacuum fusion and gravimetric analyses for oxygen and sulfur, respectively. Crystals were of reasonable perfection as evidenced by a critical resolved shear stress at 10 deg from (110) of 60 g per sq mm and half-width of a (400) X-ray diffraction line from one crystal of

Jan 1, 1960

By C. S. Barrett

W. Hofmann, J. Ziegler, and H. Hanemann—Having dealt with the same alloys in the winter 1941 to 1942, we want to give a short report on the generating of the hexagonal kappa phase by deforming the supersaturated alpha phase, which we then observed. This work was delivered as a Doctor of Engineering dissertation to the Technical University of Berlin by J. Ziegler in 1942. It still exists in two copies, somewhat damaged, a brief publication of it having been issued in Fiat-Review. Our work was started from the alloy Tombasil with 4.5 to 5 pct Si, 14.5 to 14 pct Zn, the rest Cu. Torpedo propellers were die cast from this alloy in Germany during the war. In order to improve this alloy, annealing was tried. By this treatment the alloy became at the same time harder and more brittle. A further research of this process was made in the Got-tingen University30 and the "Institut fÜr Metallkunde" of the Technical University of Berlin. It soon was apparent that the Cu-Si diagram at our disposal15,31,32 would not fit the observations. For this reason the pith of the matter became from then on the Cu-Si system. At that time we did not know of Smith's* and Andersen'sm latest diagrams. We first knew of them from Dr. Barrett's publication. Twenty-two alloys containing 2 to 11 pct Si were melted in a nitrogen atmosphere and generally homogenized for 2 to 4 hr at 800 °C. Part of the samples were then annealed at 700°, 600° and 500°. Annealing was followed by quenching in water. The phases corresponding to the various temperatures were identified by X-ray and microscopy. The Debye-Scherrer photographs generally were made of filings. The latter were produced after the last anneal of the samples, then equally annealed another 30 min in evacuated glass tubes and quenched in water. In the region of concentrations examined, the Cu-Si phases already known to us were observed: alpha, kappa (then called beta by us), gamma. By hot exposing an alloy of 7.69 pct Si at 800" and 750°,

Jan 1, 1951

By K. L. Moazed, G. M. Pound

An investigation was made of the deposition of silver from a thermal beam onto tungsten field-emitter tips at 300°K. "Island"-type nuclei were observed to form and grow. The nucleation of silver crystals occurs preferentially on non-close -packed planes of a tungsten tip at a critical volume free-energy change of about —2900 cal per cc. The adatom population which is critical for appreciable nucleation rate of silver crystals is about 0.2 of a monolayer and is essentially independent of beam flux, time, and source temperature. This result is strong evidence that a metastable equilibrium exists between adatoms and critical nuclei, as assumed in the present theory. SOME of the more significant studies of nucleation in deposition of metals from vapor beams have been conducted by measuring the thermal beam flux which is critical for appreciable rate of nucleation on a substrate surface held at a given temperature.'2 The observed critical supersaturations may be described in terms of Eq. [7] which was derived3'3a on the model of an adsorption, surface migration, and statistical fluctuation mechanism. However there usually made with a low-power optical microscope, a fairly insensitive method of detection. The object of the present study was to overcome some of these difficulties by measuring the critical supersaturation for condensation of a thermal beam of silver onto a tungsten field-emitter tip. Such a tip may be cleaned by electrically heating it to a high temperature in situ, and the high vacuum obtainable in a field-emission tube (10-10 torr) precludes adsorption of residual gases for convenient periods of time. Furthermore, the degree of cleanliness, the orientation, and the state of imperfection of the tip may be ascertained from the field-emission pattern. Detailed explanations of theoretical considerations and experimental procedures relating to the field-emission microscope may be found in a number of excellent review articles12'13 and thus only a brief description will be given here. The electronic work function of a metal is defined as the energy that an electron needs to escape from the potential field of the solid. By applying a large field between the surface of the solid and a suitable collector, it is possible to free the electrons by the tunnel effect. Fields of approximately 30 million v per cm are needed to produce this effect, and such fields are obtained in practice by using microscopic surfaces of high curvature (tips). Because the work function of a metal is a function of surface orientation, the emission from the various planes is different, and thus it is possible to obtain a representation of the surface in the emission microscope. In general, the work function is higher for the more densely packed planes. Fig. 1 shows a pattern for "clean" tungsten in which the central dark region represents the (110)

Jan 1, 1964

By E. Buehler, E. Berry

HE magnetic properties of dilute palladium alloys are of fundamental interest.''' Neutron diffraction studies3 have indicated that a better understanding of the behavior of these alloys could be realized with the availability of high-purity single crystals of palladium. Crucible melts of 99.999 pct pure palladium were found inadequate for such research. In a successful effort to fill this need, floating zone refining of palladium was undertaken. In this note the results of the initial experiments are reported. Zoning was accomplished in an argon atmosphere using 450 kc rf generator for an energy source. Samples 5 to 6 mm in diam were suspended in a gastight quartz envelope which could be moved vertically through the rf coil. A nominal upward traverse rate of 1.5 mm per min was maintained during a pass. Close coupling was found to be essential for stable retention of the liquid in the zone. Single crystals averaging 3.5 cm in length were obtained. Laue photography showed them to be continuous single crystals without gross imperfections. Several criteria were used for evaluation of the purity of the zoned material: magnetic behavior, low-temperature specific heat and residual resistivity ratios. Table I shows the residual resistance ratios obtained for two samples, one subjected to a single pass, the other zoned four times. It is appilrent that palladium can be zone refined with the electrically active impurities being transported toward the tail end. A decrease in susceptibility for zone-melted specimens over any previously measured material from 1.5" to 80'~ has been obserted by H. J. Williams and R. C. Sherwood4 substantiating the residual resistance data. The specific heat measurements are currently being made3 and will be published at some later date. Discussions with J. H. Wernick and S. C. Abrahams are acknowledged. We also wish to thank G. F. Brennert for the residual resistance measure ments.

Jan 1, 1962

By G. Sachs, C. C. Chow, L. J. Klingler

Most structural parts which are heat treated are designed using strength properties which have been determined in the principal direction of the wrought material. For example, for rolled or drawn materials, properties are given for the rolling or drawing direction. The structures, however, may be loaded so that the critical stress is in some direction other than that for which the properties of the material are known. Investigations of forged products,123 have shown that while the yield strength and tensile strength of carbon steel billets and bars vary little with the direction of the test specimen in relation to the fiber, the contraction in area in tension tests and the impact strength in notched bar impact tests decrease in the transverse direction. The contraction in area and, consequently, the fracture stress of hard aluminum and magnesium alloy forg-ings have also been found to be lower in the transverse direction. An investigation on aluminum alloy plate4 likewise has shown the dependence of the fracturing characteristics upon the direction* of the test specimens, the longitudinal direction being considerably stronger than the transverse direction and the normal direction, with the normal direction being the least strong. The variation of properties with direction has been explained by a type of anisotropy called mechanical anisot-ropy. This anisotropy results from the elongation, in the direction of the principal strain, of certain phases, inclusions, and/or cavities in the metal during working. A mechanical fibering is thus produced which seems to persist through annealing and heat treatment. This investigation was initiated to determine the flow stress and fracture stress, at high hardness levels, at 90° to the rolling direction in a round steel bar. It is this direction which receives the critical stress in drawing dies machined from round bars. Preliminary tests showed a large difference in properties between the 0° and 90° directions. Consequently, it was felt that a more complete investigation, utilizing several types of tests, was warranted to determine the flow and fracture characteristics of a steel at various orientations, for a number of hardness levels. This investigation was conducted on an air hardening nondeform-ing die steel. Material and Procedure The distribution of properties was made on a 3-in. round bar of annealed high-carbon, high chromium steel of the following analysis: Pct Carbon................... 1.53 Manganese................ 0.39 Silicon.................... 0.27 Chromium................ 11.76 Vanadium................. 0.25 Molybdenum.............. 0.81 The 3-in. bar was produced from an 8-in. ingot, which was annealed and forged to a 4-in. square billet. The billet was annealed and rolled to a 3-in. round which was then annealed and straightened. This steel is an air hardening die steel which has very good dimensional stability on hardening; therefore, the residual stresses resulting from hardening would be expected to be low. A hardness survey across the diameter of the annealed bar showed no difference in hardness from the center to the outside. However, the test sections of all the specimens were taken approximately half way between the center of the bar and the surface to avoid any surface effect or possible porosity at the center. Tension, compression and bend tests were made on specimens hardened and tempered at six different temperatures. The tension test specimens, Fig 1, were machined from the bar at orientations of 0, 22.5, 45, 67.5 and 90° from the axis of the steel bar. The specimens were rough machined, heat treated and then ground to size. The test section on each specimen was lapped in a direction parallel to the axis of the specimen to remove any transverse scratches which might act as stress raisers. The specimens were tested in fixtures which insured concentricity of loading of less than 0.001 in.5 The transverse strains were measured with a radial strain gauge,5 the least count of which was 0.0001 in. change in diam. The compression specimens, Fig 1, were machined from the bar at ori-

Jan 1, 1950

By E. J. Ripling, S. I. Liu

IT has been shown in a number of recent publications that much information on the mechanical behavior of metals can be gleaned by first deforming test specimens under one set of conditions, and then evaluating the effect of this deformation by means of a subsequent tensile test. A straining procedure of this type has been applied to study the flow behaviors of a number of metals.1, 2 In these studies the prestraining and testing were both tensile strains, while the straining temperature was varied between the prestraining and testing steps. These data indicate that there is a more or less general flow behavior exhibited by all metals which are pre-stretched at one temperature and then tested in tension at a second temperature. Prestraining a metal at a high temperature produces a lower yield strength during the subsequent low temperature strain than would the same total strain at the lower temperature. On reversing the order of the strains, low temperature prestraining produces a higher yield strength during the subsequent high temperature straining than would a single high temperature strain of the same magnitude. Unlike the flow behaviors, the fracturing characteristics of metals when prestrained under one set of conditions and tested under a second set of conditions is quite material dependent. The fracture behavior of a number of steels2" as well as of a commercially pure zinc,4 have been investigated by these two-step tests and was found to depend upon the position of the transition temperature with respect to the prestraining and testing conditions. Since these fracturing phenomena are complicated by the appearance of the transition temperature, it has been difficult to reliably define the basic effect of a two-step straining procedure in fracturing. Metals crystallizing in the face-centered cubic system do not exhibit transition temperature effects so that the mechanical characteristics obtained on these materials could serve as a base for two-step straining behaviors. Consequently groups of specimens of the aluminum alloy 24s-T4 were prestrained various amounts at room temperature in either tension or compression after which these strained specimens were further strained to failure, or tested in tension, at either room or some lower temperature. Other groups of 24S-T4 specimens were prestretched at various low temperatures after which these were tested in tension at room temperature. These straining techniques then made it possible to compare the behaviors of aluminum with the behaviors previously presented for steels. Material and Procedure The commercial aluminum alloy 24S-T4 in the form of 3/4 in. rods was used in this investigation. The material was subjected to the following treatments before machining: 1—resolution treating at 920" & 10°F for 45 min, 2—quenching in water at room temperature, and 3—aging at room temperature for four days. The re-heat treated material was then machined to either of the specimen shapes shown in Fig. 1. Fig. la shows the threaded-end specimen used for prestraining in compression. Fig. 1b shows the specimen used for both prestrain in tension and final testing. The material subjected to precompression in the form of the specimen shown in Fig. la was re-machined to the specimen shape in Fig. 1b for final testing. Prestraining in tension and final testing were done without any intermediate machining. All straining was performed on a 10,000 1b Riehle tensile testing machine. Tensile strains were conducted in a specially designed concentric fixture which produced an eccentricity of less than 0.001 in." The change in diameter at the minimum section of

Jan 1, 1954

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

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By S. A. Bradford

Internal-oxide precipitates in decarburized a iron alloys were studied by microscopic and X-ray methods. Diffusion of oxygen is primarily trans-granular, although large amounts of manganese or PhosPhorus cause preferred grain boundary dimsion at temperatures below 1450OF. Transgvanular internal oxidation follows the parabolic rate law with an apparent activation energy of 60 kcal per g-atom for decarburized rimmed steel and around 50 kcal per g-atom for higher alloy contents. The internal oxide is (Fe,Mn)0. Evidence was found for a miscibility gap in the FeO-MnO system. UNTIL very recently, the internal oxidation of metals was studied primarily as a scientific curiosity or, in a few cases, as a means of strengthening alloys by precipitation hardening. However, with the recent development of low-carbon enameling sheet steel, internal oxidation has become a problem of practical importance to the steel industry. For example, in 1961 it was reported1 that internal oxidation of steel can occur during decar-burization by open-coil annealing and will reduce the notch ductility of the sheet unless the process is carefully controlled. The present study was therefore undertaken to learn more about the rates and mechanism of oxygen diffusion and oxide formation in iron alloys. BACKGROUND The process of internal oxidation has been well-defined in the literature:',' oxygen dissolves in an alloy, diffuses inward from the surface of the metal, and reacts to form a precipitate with the alloying element that will provide the most stable oxide. he growth of the finely divided so-called subscale, i.e., the internal-oxidation zone, depends on the diffusion rates of both the oxygen and the reactive element.4 Investigators have generally found that increasing the temperature increases the size of the oxide particles, the rate of subscale growth, and the tendency to transgranular diffusion. With very few exceptions, the square of the thickness of the internal oxide layer is directly proportional to the reaction time. Given two conditions easily satisfied for iron systems— a) an oxygen solubility much less than the concentration of the alloying metal and b) an oxygen-diffusion rate to the oxide boundary much faster than that of the alloying element—then the general expression developed by Rhines and co-workers5 for the parabolic growth rate of the internal-oxide zone can be simplified to the following form: where Co and CM are, respectively, the solubility of oxygen and the concentration of the alloying element, DO is the diffusion coefficient of oxygen, O/M is the weight ratio of oxygen to metal in the precipitated oxide, and x is the thickness of the internal-oxide zone after an annealing time t. Both the oxygen solubility and diffusion coefficient can be approximately expressed as functions of temperature by Arrhenius-type equations: in which H and Q are, respectively, the heat of solution and the activation energy of diffusion. Consequently, the apparent activation energies calculated from Arrhenius plots are the sum of the heat of solution of oxygen in iron and the activation energy for diffusion of oxygen. The data, if not the interpretation, of Schenck et al.8 bear out the fact that oxygen diffuses in the atomic form. The general rate law for atomic diffusion is: the reaction rate being proportional to the square root of the pressure at low pressures. Benard and Moreau8 studied both the surface oxidation of Fe-Ni alloys and the gradual penetration of oxygen into the metal. They observed that oxide particles first form along grain boundaries and then grow to form continuous films that eventually envelop the grains. The parabolic rate law does not usually apply in these cases, especially at the higher temperatures. The oxide formed is wustite which gradually transforms into Fe3O4 and finally into Kennedy and coauthors8 examined Fe-Ni alloys with 26, 75, and 84 pct Ni oxidized at 800°C and

Jan 1, 1964

By R. I. Jaffee, J. W. Roberts, D. N. Williams

DISPERSION hardening as an alloying process has aroused increasing interest in the past few years. This alloying procedure, in which an insoluble phase is dispersed randomly through a metal or alloy, is believed to be especially suited for the attainment of creep strength at elevated temperatures since the dispersed phase is metallurgically stable. Another advantage is that the physical properties of the matrix phase, such as electrical conductivity, remain relatively unaffected by alloying. These two characteristics resulted in interest in the applicability of dispersion hardening to copper and copper alloys. A study of copper alloys prepared by powder metallurgy methods has shown some strengthening from oxide dispersions.' However, powder metallurgy processing would not be economical for large scale production of dispersion hardened copper-base alloys. Therefore, the research described in this article was initiated to examine methods of forming dispersion alloys which would not require powder metallurgy processing. If powder metallurgy processing is to be avoided, a method must be found by which the dispersion material can be introduced into and dispersed through the melt before casting. When the dispersed phase is an oxide or similar nonmetallic, it is extremely difficult to form a satisfactory liquid: solid dispersion since successful mixing requires that the melt wet the dispersed phase. It is almost impossible to force a nonwetted particle beneath the melt surface. This difficulty can be avoided, however, if the oxide particles are produced in molten copper by reaction within the melt. The problem would then reduce to maintaining randomness until solidification. Four procedures were considered for producing an oxide particle within molten copper by reaction. In all cases, the intent was to react oxygen (0) with a reactive metal (X) to form an oxide (XO) within the copper melt. These reactions were as follows: 1) (Cu-X), + (O)g (Cu)1 + (XO)S [1] 2) (Cu-X)1 + (Cu2O)s (Cu)x + (XO)S [2] 3) (Cu-OK)1 + (Cu-X)1 (Cu)1+(XO)9 [3] 4) (Cu-OK)1 +(X)s (Cu)1 +(XO)s [4] The reactions were carried out in an 8-lb melt of 99.98 pct Cu maintained in the vicinity of 2200oF by induction heating. Where possible the amount of the reactants was controlled to give 1 to 5 vol pct oxide. Mechanical stirring during the reaction period was used to minimize agglomeration of the reaction product. The presence of a reaction product was determined metallographically by study of an ingot cast from the melt at the end of the reaction period. Reaction [I] was studied by dissolving aluminum in the melt followed by forcing oxygen through the melt. The melts became quite sluggish during the reaction period suggesting that A12O3 was formed. However, the reaction product rose out of the melt rapidly, possibly due to the flushing action of the oxygen stream, and little dispersed phase was formed. Reaction [2] was examined by dissolving aluminum, silicon, or nickel i; the melt and then adding Cu20 (melting point 2250F). This procedure was unsuccessful. Although Cu2O was easily stirred into cop-

Jan 1, 1961

By D. J. Schmatz

DISCUSSION OF RESULTS The qualitative correlation between low-temperature ductility and prior high-temperature creep strain in nickel obtained in this investigation confirms the result obtained on high-purity brass by Chen and Machlin. However, the quantitative effect is much smaller in nickel. Comparison can be made on the basis of a prior high-temperature strain that is a certain percentage of the total high-temperature elongation to rupture. In the research of Chen and machlin, the prior high-temperature strain of 1/2 pct equaled 8.5 pct of the total high-temperature elongation at rupture. For nickel, in our experiments, 8.5 pct of 21.2 pct equals 1.8 pct. For eh = 1.8 pct, the loss in ductility in percent equals x 100 = b.5 pct. That is, for equivalent bo Formation of Beta Manganese-Type Structure in Iron-Aluminum-Manganese Alloys D. J. Schmatz IRON-aluminum alloys have gained much interest in the past few years for use as a base material for elevated-temperature alloys because of their excel- high-temperature strain the loss in low-temperature ductility is 8.5 pct for nickel as compared to 60 pct for pure a, brass. It is also interesting to note the observation that in nickel the low-temperature fractures, even at the most extreme high-temperature pre-strain, were partly trans crystalline and partly intercrystalline. In the case of a brass, these fractures were completely intercrystalline. According to the data on the percent of the grain boundary area that is cracked, at 22 pct high-temperature elongation, about 12.5 pct of the grain boundary area does not carry load. Thus, the inter-crack areas are carrying a stress that is about 11 pct higher than the nominal stress. A simple model predicts that the overall elongation, which is primarily the elongation in the bulk of the specimen, will correspond to the nominal stress when the stress in the intercrack area equals the tensile strength. Quantitatively this model predicts the equation The form of this equation will agree with that found if the strain-hardening exponent, n, equals unity. Actually this model is too gross an approximation to yield good quantitative results. The question naturally arises as to whether in ordinary hot-working, such as hot-rolling, intercrys-talline cracks are introduced that affect the low-temperature properties. It appears that the answer is that such a possibility cannot be overlooked, if the hot-working induces tensile stresses at temperatures above the equicohesive temperature and if the material tends to be notch sensitive at low temperature. ACKNOWLEDGMENT This research was supported by the Aeronautical Research Laboratory, Directorate of Research, Wright Air Development Center, United States Air Force. REFERENCES lC. Zener: Fracturing of Metals, 1948, Cleveland, ASM. 'H. C. Chang and N. J. Grant: Mechanism of Intercrystalline Fracture. AIME Trans., 1956, voL 8, p. 544; lownal of Metals, May, 1956. 'E. S. Machlin. CreepRupt ure by Vacancy Condensation, AIME Trans., 1956, vol. 8, p. 106; lownd of Metals, February, 1956 'C. Chen and E. S. Machlin: On a Mechanism of High-Temper at ure Inter-crystalline Cracking, lownd of Metals, July. 1957. p. 829. Alloys lent oxidation resistance. Binary alloys of aluminum in iron are ferritic and consequently have poor hot strength. Alloys of iron-aluminum-manganese were made in an attempt to produce an austenitic alloy containing sufficient aluminum to retain the oxidation resistance of binary alloys of iron-alumi-

Jan 1, 1960

By R. Webeler

In order to study the role of work hardening in the fatigue process, use was made of the great sensitivty of the resistivity of AuCu to cold work. A change of the resistivity of AuCu of the order of 1 to 2 pct at the temperature of liquid nitrogen was found to occur as a consequence of severe fatigue. ACCORDING to Orowan's theory,' the process of fatigue In metals 1s associated with the production of a number of small regions which have undergone strain hardening. This phenomenon is supposed to occilr even if the stress applied during fatiguing is always smaller than the yield stress. In an attempt to verity the existence of such regions, Welber and Webeler' undertook to detect the stored energy associated with severe fatigue in copper. Previous experiments" had shown that the energy stored in a sample of copper which has been cold worked by torsion is released in the temperature range between 150" and 250°C when the sample is heated from room temperature and that no more energy is released (or absorbed) between 250" and 450°C. In particular the stored energy amounted to 0.41 cal per g for a case in which the mechanical energy expended in twisting the sample was 11.9 cal per g. In the case of fatigued copper, however, no release of stored energy could be detected between 150" and 250°C, so that the experimental error of &0.02 cal per g represents an upper limit for the amount of energy stored in strain hardening., It seemed desirable to attack the problem in a new fashion. For this purpose, it was decided to make use of the fact that, if an alloy capable of undergoing the order-disorder transition is ordered and then cold worked, the resistivity, p, increases very greatly above the value for the ordered state even if the deformation is very small. Some insight into the nature of the fatigue process may be obtained then by measuring the resistivity of an ordered sample before and after subjecting it to fatigue. For reasons which will become apparent from the following remarks, considerably more can be learned by carrying out the resistivity measurements at two different temperatures. In the case of a material containing impurities, vacancies, dislocations, or other imperfections of essentially atomic dimensions, the resistivity, p, according to Matthiessen's rule, can be represented as a sum of two terms p = p, + p, where p, is the (temperature dependent) resistivity of the pure metal, and p, is the temperature independent contribution of the imperfections. Briefly, the physical basis for this rule is the following: The main contribution of the impurities in question to the resistivity results from the fact that they interrupt the periodicity of the lattice and thus scatter the conduction electrons with a probability which is almost independent of temperature. In order that this be the case, it is necessary that the' extension of the impurities be small enough—roughly less than one electron mean free path—so that their main effect on the resistivity occurs for the foregoing reason. If an alloy like AuCu is partly or completely disordered by quenching from an appropriate temperature, Matthiessen's rule also applies to a very good approximation* with p, representing in this case the resistivity po of the ordered sample and p, the additional (temperature independent) resistivity due to the disorder. In general, the disorder can be represented in terms of atoms which are displaced from their "proper" positions in the superlattice and which thus qualitatively represent the imperfections in the superlattice responsible for the term p,. Since the misplaced atoms are distributed at random throughout the super-lattice, their contribution to the resistivity still can be considered in terms of the scattering of conduction electrons by lattice defects. The situation is somewhat more complex in the case of an alloy disordered by cold work because the process of disordering here does not involve a random redistribution of the atoms; however, Matthiessen's rule also holds in this case. Whenever Matthiessen's rule does apply, the values of the quantity /3 = (p? — /(T, — T,), where p, and p, are the values of the resistivity at two fixed temperatures, T, and T,, respectively, is constant (independent of p,) for a given alloy or metal. In particular, if a sample of AuCu is subjected to ordinary cold work, the value of /3 remains equal to Po, the value for the ordered material. According to Orowan's theory,' as remarked before, a fatigued sample contains a large number of isolated severely cold-worked regions, which make up only a small proportion of the metal. Thus, if a sample of AuCu initially in the ordered state is fatigued, more or less disordered regions will be produced within the ordered material. If these regions are small enough so that Matthiessen's rule applies, then it follows from the previous discussion that /3 again will remain equal to Po. If the effect of fatigue is to produce cold-worked regions which are macroscopic—of the order of at least several electron mean free paths—the effective resistivity, p, has to be computed by use of the ordinary laws of large-scale electrodynamics. For the sake of simplicity, it will be assumed here that the cold-worked regions are completely disordered and have a resistivity, p,. For a given proportion A of disordered regions the effective resistivity, p, for the current in a given direction depends on the geometrical configuration of these regions. In any case, the value of p for such

Jan 1, 1956

By C. Feng, P. Levesque

HE addition of rhenium to molybdenum is known to produce alloys with good workability.&apos; Lawley and Maddin found that the critical stress for twinning in this system was lowered by the addition of 35 pct Re, which suggests that twinning may re- place the usual slip operation as the major element of deformation. The twinning elements in bcc Mo-Re alloys have been reported as the (112) planes and the <111> directions.3 This note represents the continuation of this investigation, in which the authors found that the occurrence of twinning promotes the formation of a bcc tetragonal phase, previously identified as u by Greenfield and Beck.4 Specimens of Mo-35 pct Re alloy, prepared as described previusly, were solution annealed at 2400o, cooled to room temperature, and plastically deformed by compression to induce twinning. After subsequent aging for 8 hr at 1300°C, traces of a were observed along the grain boundaries and at the interfaces between the twins and the matrix, Fig. 1. With increased aging time the cr phase grew into larger clusters and finally occupied the entire twinned area, Fig. 2. Experiments also indicated that if twinning did not precede aging, there was no visible evidence of a in the microstructure.

Jan 1, 1962

By Robert T. Ault

The nature of fracture in unnotched tensile and notched tensile sheet and round specimens and V -notched and precracked Charpy-type sheet specimens of both wrought stress -relieved and re-crystallized molybdenum was investigated over the temperature range of -78° to 300°C. The sharp rise in fracture stress, for unnotched tensile samples, as the temperature is increased above the brittleness transition temperature (Tb), is found to be a result of an increase in flow stress due to plastic constraint and an increased strain rate which results from the onset of necking at Tb . Quasi-brittle fracture in notched tensile samples is found to occur when the tensile stress at the elastic-plastic interface, beneath the root of the notch, reaches a maximum critical value, which is independent of test temperature over the range from —78° to 25°C, but dependent on microstructure. In the temperature range between 150° and 300°C, unnotched tensile and notched tensile samples alike are found to fracture by a ductile fibrous tearing process which is discontinuous in nature, as a result of the competition between the processes of tearing, through continued plastic flow, and local work hardening. Results from the V-notched and fatigue-cracked Charpy-type impact tests demonstrate that crack initiation is the governing factor in the low-temperature (-78° to 25°C) fracture process for molybdenum. In recent years, there has been considerable interest, and a commensurate number of investigations, concerning the duc tile-to-brittle transition in refractory metals. There has not developed, however, a satisfactory explanation for the uniaxial tensile fracture-stress transition which accompanies the well-known ductility transition. This matter therefore warranted investigation. In a similar manner, the increased importance of notched tensile strength values in evaluating materials and in design criteria requires a better understanding of the factors which control the fracture behavior of notched tensile samples. In a previous investigation1 of the nature of initial yielding and fracture in notched sheet molybdenum at room temperature, it was suggested that plastic constraint was the controlling factor in governing the fracture behavior of notched samples. The final portion of this investigation was concerned with the fracture toughness of molybdenum. Of particular interest was the comparison of effective surface energies for fracture in V-notched samples with fatigue-cracked, Charpy-type samples in order to ascertain the relative importance of the initiation and propagation phases of the fracture process. MATERIALS AND TEST PROCEDURE Sheet tensile, notched tensile, and V-notched Charpy specimens were prepared from 50-mil, stress-relieved molybdenum sheet.* Half of these specimens were vacuum-annealed for 1 hr at 1200°C and 7.5 x l0-5 Torr and furnace-cooled to produce a relatively uniform grain size of 0.30 mm diameter. Round notched and unnotched tensile specimens were prepared from warm-rolled and swaged 5/8-in.-diam bar.* These specimens were vacuum-annealed for 1 hr at 1350°C and 5 x lom5 Torr and furnace-cooled to produce a grain diameter of 0.11 mm. Material analyses in ppm were: C N O H Sheet 290 10 4 1 Bar 50 30 30 2 The unnotched tensile sheet specimens had a 1/4-in. gage width and a 1-in. gage length. The unnotched tensile round specimens had a 9/32-in. gage diameter and a 1-1/4-in. gage length. The sheet and round notch tensile specimens are shown in Fig. 1. All of the notched tensile specimens tested were tandem-notched in order to study the location and mode of fracture initiation. The tandem-notched specimens were carefully machined so that the largest variation in notch depth on a single specimen was 0.001 in. Thus, when fracture occurs, the extent of plastic deformation that exists in the un-fractured notch section is that which exists just prior to fracture. All of the tandem-notched sheet specimens were electrolytic ally polished and chemically etched prior to testing. The V-notched Charpy-type specimens machined from the 50-mil sheet material had the standard dimensions of 2.125 in. long, 0.394 in. deep, and a 0.010-in. root radius. The unnotched tensile and notched tensile tests were conducted over the temperature range of -78° to 300°C, in a 10,000-lb Instron Universal Testing Machine, at a constant crosshead speed of 0.020 in. per min. The V-notched Charpy-type

Jan 1, 1964

By C. J. Beevers

Tlze influence of zirconium hydride precipitate mprphology on the fructure of Zr-H alloys tested at strain rates of 10- sec at 20° and - 196°C and at strain rates of -500 sec.-1 at 20°C has been inves-tigated. The critical stage in the embrittlement of these alloys was the fracture of the zirconium hyhide precipitates to form large interval cracks at a stress of 25,000 10 137,000 psi. In specimens con-temping up to 100 ppm H the preciptates existed as isolafed platelets in the zirconium matrix and their fracture as enhanced by low temperature (—196°C) and high strain rate (-500 set-f) loading. These resl~lts lead to the conclusion that the rate of strain hardening of the zirconium metal controls the frac-tzrm of the hydride platelets. Increased hydrogen contents of 500 to 2000 ppm resulted in an increase in the 1)volume fraction and size of precipitates and crlso led to crack propogation in the hydride at both 20 and —196C at the low strain rates (10&apos;* sec-&apos;). Quenching led to refinerment of hydride precipitate size and reduced the degree of embrittlement at — 196°C; this effect is attributed to the absence of fracture of the fine precipitates. The formation of zirconium hydride precipitates has been shown to be the cause of hydrogen embrittlement of zirconium.&apos; Several investigators&apos;-" have studied the problem in broad outline, demonstrating that impact-loading conditions, testing temperatures below room temperature, and increasing hydrogen content produce increased brittleness. For example, Muehlenkamp and schwope2 showed that the transition temperature for notched impact tests was raised from 150" to 350°C on increasing the hydrogen content from 45 to 490 ppm. The degree of embrittlement is also controlled by the morphology of the zirconium hydride precipitates. The solubility of hydrogen in zirconium decreases from 600 ppm at 550°C to 10 ppm at 20"C,~ so that the form of the zirconium hydride precipitates (ZrH2) can be modified by varying the cooling rate through the Zr-aZr + ZrH2 phase boundary.= Forscher showed that quenching a specimen containing 35 ppm H from above 315°C resulted in a reduction in area of 70 pct at -196"C, whereas slowly cooling from above 315°C resulted in a ductility of half this value. The role of the hydride precipitate in the fracture process has been examined by Young and schwartz6 and more recently by westlake.&apos; From metallo-graphic observations on slowly cooled Zr-H alloys they have suggested that cracks are nucleated in the hydride precipitates by the interactions of twins in the zirconium metal with the hydride. The experiments reported in this paper show that crack propagation in the zirconium hydride precipitates is the critical stage in the embrittlement of Zr-H alloys. The factors influencing fracture of the hydride precipitates and crack propagation in the zirconium metal will be related to the problem of embrittlement. EXPERIMENTAL TECHNIQUES The zirconium used in these experiments was produced from an ingot of vacuum arc-melted iodide zirconium forged down to 1 in. diameter at 800&apos; to 850°C. The 1-in.-diameter bar was surface-machined and cold-swaged to 0.375 in. diameter. After a vacuum anneal at 800°C for 1 hr the hardness was 60 to 70 Vdh. The total impurity content was approxi-

Jan 1, 1965

By J. H. Smith, H. W. Paxton

ALTHOUGH many structural and kinetic investigations have been made for alloys of iron and nickel, only meager data exist from thermodynamic investigations. The purpose of this note is to estimate the free energy of the Fe-Ni solid solutions from thermodynamic data available for ternary alloys containing iron and nickel. The lack of a description of the thermodynamic behavior for the Fe-Ni system has required the structural and kinetic analyses of the system to assume some form of solution behavior, usually regular, e.g., the mar-tensite transformation analysis of Kaufman and Cohen, 1 consistent with the limited thermodynamic data. Indications that this system could exhibit ideal solution departures might have been suggested by the large deviations from additivity rules observed in the density and lattice-parameter measurements of Jette and Foote2 who interpreted this in terms of possible solute-solvent interactions. Later Turkdogan et al. 3 and more recently Ward and wright 4 found a minimum in the graphite solubility in liquid Fe-Ni solutions near the concentration of FeNi3 with deviations from linearity persisting at all concentrations. This was interpreted by Ward and wright4 to indicate negative heats of solution and was suggestive of short-range ordering. The infinitely dilute activity coefficient of carbon (?oC) was also observed by smith5 to pass through a maximum near the FeNi3 concentration in Fe-Ni solid solutions. Recent investigations of the liquid solutions over the entire concentration range by Zellars et a1.&apos; and Speiser et a1.," using vapor-pressure determinations, revealed both negative departures from Raoult&apos;s law and a nonregular solution behavior. The solid alloys have been studied by Oriani 8 and Kubaschew-ski and von Goldbeck6 employing gaseous H2/H2O equilibria with Fe and FeO. Both investigations were in substantial agreement, indicating very small departures from ideality. However, Oriani observed the formation of Fe3O4 (instead of FeO) at XFe= 0.441 which severed the equilibrium and precluded experimental investigation of the nickel-rich alloys. Heat-capacity and heat-content measurements have been evaluated by Montgomery10 and found generally unsatisfactory for gleaning thermodynamic information. This is due to the unknown final states of the alloys caused by the interference of the martensite transformation on cooling iron-rich concentrations and superlattice formation, magnetic transformation, and the varied heat treatments used by investigators of nickel-rich concentrations. As an alternative to the experimental difficulties, indirect estimates of the solid-solution behavior have been made by Fleischer and Elliott11 and Smith et a1.12 From their measurements of the solubility of Fe-Ni alloys in liquid lead, Fleischer and Elliott calculated the nickel activity (aNi) (and integrated for aFe) by assuming: 1) liquid lead has no solubility in solid Fe-Ni alloys, 2) Henry&apos;s law is obeyed throughout the liquid lead-rich phase (0— 12 at. pct Nil, and 3) Henry&apos;s law constant is independent of relative iron and nickel concentrations. The estimate of Smith et a1.12 was obtained

Jan 1, 1964

By R. W. Gurry, L. S. Darken

The solubility of cementite in austenite is computed by thermodynamic methods from the observed solubility of graphite. It is found that the solubility of cementite is greater than that of graphite in the entire austenite temperature range. Thus the prior discrepancy between this portion of the phase diagram and the observed metastability of cementite is partially resolved. FOR several years it has been apparent that a serious discrepancy exists in certain observations pertaining to the Fe-C system. Direct experimental data indicate: 1-That the curve representing the solubility of graphite in austenite&apos;" crosses that for cementite4 at about 945°C as shown in Fig. 1. 2— That graphite and austenite saturated therewith are stable1 relative to cementite at all temperatures between the eutectoid, about 723°C, and the eutectic, about 1153°C. These observations are mutually incompatible in view of a well-known consequence of the second law of thermodynamics, namely, that the stable phase (presumably graphite at all temperatures) has a lower solubility than the metastable phase (presumably cementite). Hence either 1 or 2 above must be in error; either the measured solubility of graphite or of cementite, or the observation as to the stability of graphite, is in error. Our present purposes are: 1—To collate the available data on cementite and prepare a table of HO — HO° and of (Fa— HO°)/T. This tabular method seems the best and most convenient way to represent the heat and free energy of formation. 2—To determine whether the measured solubilities of cementite and graphite in austenite are in accord with the above table and the measured thermodynamic properties of austenite, in order to resolve, if possible, the existing paradox of these two solubilities. Enthalpy of Cementite The enthalpy of cementite at 273 °K, H279 — HOcem, was computed by integration of the low temperature heat capacity as measured by Seltz, McDonald, and Wells" 68" to 298 °K) and as given by the Debye functions recommended by them (0" to 68°K); the result is included in Table I. At higher temperature HCem — H,,"" is given by Kelley who used the data of Naeser7 (298" to 1037°K) and of Umino8,9 (273° to 1923°K). We have recalculated Hcem — H273 cem from the data of UminoO in the following way. In the equilibrated alloy at temperature the weight fraction of cementite Pct c -Pct cr is PctC -PctCr designated f(C), and the

Jan 1, 1952

By C. Law McCabe, R. G. Hudson

The Knudsen cell has been employed to determine the free energy of formation of Mn7Cs in the temperature range 800" to 950°C. A value of 66,440 cal was found for hH°o for a-manganese. Measurements of the pressure of manganese over a mixed carbide, (Fe,Mn),C, points to a power relationship between aun7cs and N.4,. RECENTLY Kuo and Perssonl have reported that the carbide of manganese which is in equilibrium with graphite at temperatures up to 1100° C is Mn7Ca. There are no published data on the thermo-dynamic properties of this compound. In order to determine the stability of Mn7Ca, it appeared that, by obtaining the pressure of manganese above 8-manganese and also above Mn,C, in equilibrium with graphite, the free energy of formation of Mn7Ca from 8-manganese and graphite could be obtained. In addition, the vapor pressure of manganese, reported by Kelley From data of Bauer and Brunner,&apos; is subject to some uncertainty and further determinations of the vapor pressure of manganese seemed warranted. In this investigation of the pressure of manganese vapor above pure manganese and also above the carbide of manganese in equilibrium with graphite the apparatus used is the Knudsen orifice cell. The same apparatus, experimental procedure, and method of calculating the pressure was used in this investigation as in one previously reported.~ Care was taken to insure that the cells were at constant weight before using them in a run. The manganese charged in the cell was CP grade powder, carbon free, obtained from the Fisher Scientific Co. A spectroscopic analysis of the manganese after appreciable amounts of it had vaporized from the Knudsen cell showed that no element was present in sufficient quantities to contribute to a weighable weight loss or to decrease the vapor pressure of manganese to any appreciable extent. The spectro-graphic analysis was 0.002 pct Cu, 0.05 pct Fe, 0.002 pct Pb, and 0.002 pct Ni. 8-manganesea is the allo-tropic form of manganese which was present in the cell at temperatures used in this investigation. The manganese carbide, Mn,Ca, was made in the following way: In a closed graphite cell manganese powder was added to graphite powder, which was made from graphite rods for spectrographic use. The manganese powder was the same as that described previously; 5 pct excess graphite was added over that required for the formation of Mn7C,. The mixture was heated in a closed graphite cell for approximately 20 hr at 1350°K under vacuum. X-ray analysis revealed that there was no manganese present after this treatment, but that the lines due to Mn,C, were present. In order to prove that there was no volatile carbide of manganese which was effusing out of the cell, the following experiment was performed: A graphite effusion cell containing graphite power, in excess of that to form Mn,C, of a desired amount, was brought to constant weight on heating at 1228°K. The required amount of manganese was accurately weighed and then added to the graphite effusion cell. The cell was placed in a vacuum at 1228°K for one week, which was the time calculated for the manganese to have effused completely, assuming instantaneous formation of Mn,C8. The cell was then weighed again. This experiment was carried out on two different occasions and both times the weight loss of the cell came within 1 pct of the weight of manganese originally charged minus the weight of manganese left in the cell, as determined by chemical analysis. These data are summarized in Table I. This agreement is considered to be within experimental error and is taken as proof that no carbide of manganese is volatile in this temperature range. It was established, by X-ray analysis, that Mn,C, formed before appreciable amounts of manganese vaporized from the metal powder which was charged. The identification of the carbide of manganese which was present in the Knudsen cell in equilibrium with graphite and manganese vapor was carried out by Kehsin Kuo at the University of Uppsala. He established that the authors&apos; sample, which was submitted to him for analysis, contained the phase

Jan 1, 1958

By Robert A. Rapp

The standard molar free energy of formation of MOO,was determined between 750o to 1050o C in galvanic cell measurements involving the solid electrolyte Zr0.85 Ca0.15 O1.85. Use of the reference electrodes Fe + FexO and Ni + NiO Provided two independent determinations of FoMoo2. The data may be represented by the equation FMoO2 = -137,500 +40.0T(°K) which is in good agreement with previous CO/CO, gas equilibrium measurements of Gleiser and Chipman. The standard molar free energy of formation of molybdenum dioxide has recently been reported over a large range of high temperatures from the calorimetric experiments of King, Weller, and christensen.&apos; Gleiser and chipman2 have also recently determined ?FmoO2 from 926o to 1068oC in CO/CO2 gas equilibrium measurements. Earlier gas equilibrium studies have been made and reviewed by Gokcen.&apos; Over the temperature range studied by Gleiser and Chipman their values for ?FoMoO2 differed from the calorimetric data by about 700 cal. This investigation was undertaken to resolve this difference and thereby establish the two phase mixture of Mo + MOO, as an electrode of well-known oxygen potential for galvanic cell applications at very high temperatures. The galvanic cell technique involving the Zr,.,, Ca,0.15 01.85 solid electrolyte was introduced for the

Jan 1, 1963

By G. Horvay, J. G. Henzel

Nomograms and charts are provided which permit rapid determination of the mold-casting interFace temperature and the speed of solidification when a semiinfinite ingot is cast into a semiinfinite mold. The physical properties of the mold, the frozen metal, and the liquid metal are not assumed to be equal, but they are assumed to be temperature independent. The results are correlated with charts prepared by Paschkis and Hlinka—using Columbia University&apos;s Analog Computer—for the freezing of finite ingot slabs when a constant surface temperature is impressed, and with experimental cooling curves obtained by Pellini in sand and iron molds for 7 in.-sq steel castings. x = coordinate directed to right of zero (freezing direction) y = coordinate directed to left of zero (melting direction) e = position of freezing front (in x direction) ? = position of melting front (in y direction) $ = temperature (function of position and time) ? = fixed temperature 2L = width of finite slab Y = a fixed position in the semiinfinite mold, or the width of a finite mold (see Section 7) Properties y = density, lb per cu ft c = specific heat, Btu per lb deg F k = conductivity, Btu per ft hr deg F X = heat of fusion, Btu per lb k = k/Yc = temperature diffusivity, sq ft per hr* b - = = - heat diffusivity, Btu per sq ft deg F Vhr Subscripts 2 = pertaining to the still-liquid metal (case of freezing), or the medium which furnishes the heat (case of melting) 1 = pertaining to solidified metal (case of freezing), or to molten metal (case of melting)* 0 = pertaining to mold (case of freezing), or to the still-solid metal (case of melting) f = pertaining to fusion condition (eg.,?f - fusion temperature) i = pertaining to the location x = 0 (the mold-ingot "interface")

Jan 1, 1960