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By F. L. Fayers, J. W. Sheldon

It has been a matter of concern to the petroleum industry to determine what effect the capillary term has on saturation profiles, since these profiles determine ultimate economic oil recovery. In their original solution of the non-capillary two-phase flow problem, Buckley and Leverett&apos; showed that solutions of the two-phase flow equations became multiple-valued in saturation. Since it is physically unrealistic for saturation to have more than one value at a given position, Buckley and Leverett resolved this difficulty by introducing a saturation discontinuity or "shock". They evaluated the strength and position of the shock from material balance considerations. Recently Sheldon, Zondek and Cardwell&apos; have demonstrated that the method of characteristics can be used to solve this and related problems. Owing to capillarity it is physically unlikely that saturation shocks occur in an oil reservoir. Buckley and Leverett suggested that the effects of interfacial tensions should be included in the fluid flow equations, if the solutions are to give continuous single-valued saturation distributions. An analogy to this problem is encountered in the theory of wpersonic compressible flow where the introduction of the viscous term eliminates shock behavior. However, the mathematical form of the capillary term in the porous medium fluid flow equations differs from the viscosity term in the Navier-Stokes equation. This paper demons~rates that capillarity does eliminate the triple-valued behavior and indicates the magnitude of capillary and gravity effects on the saturation profile for a variety of systems. DERIVATION OF LAGRANGIAN AND EULERIAN FORMS OF THE DISPLACEMENT EQUATION The equations representing capillary, two-phase flow are given by applying Darcy&apos;s law and a material balance condition for each phase. The familiar Darcy and material balance equations are as follows. ^U*^0......<3, ^^r=°......c« S is the saturation of the water phase, and B the inclination of the porous medium. Pressures in the oil and water phases differ by the capillary pressure associated with the interfacial tensions, P.-P.=pAS)..........(5) where p, is determined experimentally. The porous medium is said to be oil-wet if P, > Po and water-wet if P, < Po. If the fluids are incompressible and the total volumetric flow rate, q, is constant, then v, f v,, = q...........(6) By eliminating P.. /»,, and v, from Eqs. 1, 2, 5 and 6 it follows that It is convenient to normalize the variables in the problem after the manner of Handy and Hadley% so that Eqs. 3 and 7 become where j,, = —, the fractional flow of water; (F, is a capillary pressure normalizing constant.) Substitution of Eq. 9 into Eq. 8 gives In this partial differential equation for an initial value

By G. Sachs, G. Espey

It is well known that high residual stresses are created in tubing by the sinking process, in which no internal tool or mandrel is used.l-4 In this process, the wall thickness is usually slightly increased.4,5 In tube drawing with a plug, the residual stresses are gradually reduced with increasing reduction of wall, and, by the conventional approximation methods of stress measurement, no stress is detected in tubing in which the wall reduction is over 50 per cent of the total reduction in cross-sectional area.l,6 It has also been observed that higher stresses are set up by the use of wide-angle dies than by acute dies.? &apos;he actual stress distribution in drawn tubing has been investigated by a few workers,7"9 but has not been related to the conditions of the drawing process. Some attempts have been made to correlate accelerated cracking tests for stresses in brass products with the magnitude of the circumferential stresses and the condition of the metal. l-10 Materials and Preparation The material used in this experiment was commercial cartridge-brass (70 per cent Cu, 30 per cent Zn) tubing in the straightened and annealed condition.† This tubing was of various outside diameters and had a wall thickness of 0.032 in. It was sunk to 1/2-in. outside diameter by means of an experimental 10,000-lb. hydraulic draw-bench, with a maximum drawing speed of 8 ft. per minute. All dies were of 1/2-in. diameter. Various die materials and contours were used in order to study the effect of die design on residual stresses in the tubing; the specifications for the dies are given in Fig. I. Castor oil was used throughout as lubricant. Chattering occurred in sinking some of the tubing, particularly when dies having the more acute angles were used, but the tubes showing chatter marks did not differ markedly from those with a smooth surface regarding the magnitude of residual stress. The source of the chattering has not yet been revealed. The wall of the tubing becomes thicker during s nking, as previously observed.4,5 The increases in wall thickness were 3, 7 and 9.5 per cent on the average for 6, 20 and 33 per cent reductions in diameter, no effect of the contour being noticeable. The reductions mentioned throughout this investigation do not consider this fact, but are reductions of the outside diameter. For the evaluation of the residual stress two fundamentally different methods were used. The approximation methodl,ll of splitting a certain length of tubing was employed to obtain a bird&apos;s-eye view of the effect of various drawing conditions on the circumferential stress measured by the diameter change occurring On splitting. For

Jan 1, 1942

By G. Sachs, G. Espey

It is well known that high residual stresses are created in tubing by the sinking process, in which no internal tool or mandrel is used.l-4 In this process, the wall thickness is usually slightly increased.4,5 In tube drawing with a plug, the residual stresses are gradually reduced with increasing reduction of wall, and, by the conventional approximation methods of stress measurement, no stress is detected in tubing in which the wall reduction is over 50 per cent of the total reduction in cross-sectional area.l,6 It has also been observed that higher stresses are set up by the use of wide-angle dies than by acute dies.? &apos;he actual stress distribution in drawn tubing has been investigated by a few workers,7"9 but has not been related to the conditions of the drawing process. Some attempts have been made to correlate accelerated cracking tests for stresses in brass products with the magnitude of the circumferential stresses and the condition of the metal. l-10 Materials and Preparation The material used in this experiment was commercial cartridge-brass (70 per cent Cu, 30 per cent Zn) tubing in the straightened and annealed condition.† This tubing was of various outside diameters and had a wall thickness of 0.032 in. It was sunk to 1/2-in. outside diameter by means of an experimental 10,000-lb. hydraulic draw-bench, with a maximum drawing speed of 8 ft. per minute. All dies were of 1/2-in. diameter. Various die materials and contours were used in order to study the effect of die design on residual stresses in the tubing; the specifications for the dies are given in Fig. I. Castor oil was used throughout as lubricant. Chattering occurred in sinking some of the tubing, particularly when dies having the more acute angles were used, but the tubes showing chatter marks did not differ markedly from those with a smooth surface regarding the magnitude of residual stress. The source of the chattering has not yet been revealed. The wall of the tubing becomes thicker during s nking, as previously observed.4,5 The increases in wall thickness were 3, 7 and 9.5 per cent on the average for 6, 20 and 33 per cent reductions in diameter, no effect of the contour being noticeable. The reductions mentioned throughout this investigation do not consider this fact, but are reductions of the outside diameter. For the evaluation of the residual stress two fundamentally different methods were used. The approximation methodl,ll of splitting a certain length of tubing was employed to obtain a bird&apos;s-eye view of the effect of various drawing conditions on the circumferential stress measured by the diameter change occurring On splitting. For

Jan 1, 1942

By C. R. Dodson, D. Goodwill, E. H. Mayer

The paper summarizes the historical background of the pressure-volume-temperature analyses of reservoir fluids, the errors involved in both the sampling and testing of reservoir fluids, the type of information required of a PVT determination, and the field conditions that limit the application of any one analysis. Particular emphasis is placed on the necessity for approximating as closely as possible the liberation sequence occurring in the producing formation, flow string, and surface separators. A combined differential and flash or "composite" liberation is suggested as the best means of approximating this liberation sequence. HISTORICAL BACKGROUND Petroleum reservoir engineering commonly is considered to be one of the newest fields of petroleum science, yet much work of a theoretical and intuitive nature was done many years before the modern techniques of reservoir analyses were developed. The period 1910-1924 saw considerable work in the field of reservoir behavior done by the U. S. Bureau of Mines. This work:.&apos; although entirely theoretical, pointed out the importance of gas in the recovery of oil from the reservoir. The statement by J. 0. Lewis that 20 per cent or less of the oil originally in place in a pool was recovered from the ground under uncurtailed production conditions caused some operators to re-examine and modify their production methods. However, though these works showed methods of production that have subsequently resulted in greater oil recoveries, they in general went unnoticed, even though there was a fear that the nation&apos;s petroleum resources were being exhausted. The period 1924-1933 saw the industry take considerably more interest in reservoir behavior because of an unfounded fear of its inability to replace oil reserves, the possibility of government regulation, and the energy of one man, Henry L. Doherty. Doherty aroused heated discussions in the industry concerning conservation. To prove or disprove his theories the first experimental work on the reservoir behavior of petroleum was undertaken. The papers of Dow and Calkin,&apos; Beecher and Parkhurst," and Mills and Heitheckere are classics although their experimental procedures were crude. These papers proved that the properties of petroleum in the reservoir are quite dissimilar to the properties measured at the well head. Gas dissolved in the oil phase was recognized as having considerable importance as had been predicted by the earlier theorists. Slightly later Miller and his co-workers assembled the first text correlating all the known data on the reservoir behavior of petroleum and used, these data to show the economic value of conservation. Quantitative application of pressure-volume-temperature analyses of reservoir fluids was given in the paper of Coleman, Wilde, and Moore"; this work showed that with sufficient laboratory and production data prediction of reservoir behavior was possible. The refined sampling and labora-

Jan 1, 1953

By G. Sachs, G. Espey

IT is well known that high residual stresses are created in tubing by the sinking process, in which no internal tool or mandrel is used.1-4 In this process, the wall thickness is usually slightly increased.4,5 In tube drawing with a plug, the residual stresses are gradually reduced with increasing reduction of wall, and, by the conventional approximation methods of stress measurement, no stress is detected in tubing in which the wall reduction is over 50 per cent of the total reduction in cross-sectional area.1-6, It has also been observed that higher stresses are set up by the use of wide-angle dies than by the use of acute dies.2 The actual stress distribution in drawn .tubing has been investigated by a few workers,7-9 but has not been related to the conditions of the drawing process: Some attempts have been made to correlate accelerated cracking tests for stresses in brass products with the magnitude of the circumferential stresses and the condition of the metal.1-10 MATERIALS AND PREPARATION The material used in this experiment was commercial cartridge-brass (70 per cent Cu, 30 per cent Zn) tubing in the straightened and annealed condition.‡ This tubing was of various outside diameters and had a wall thickness of 0.032 in. It was sunk to 1/2-in. outside diameter by means of an experimental 10,000-lb. hydraulic draw-bench, with a maximum drawing speed of 8 ft. per minute. All dies were of 1/2 -in. diameter. Various die materials and contours were used in order to study the effect of die design on residual stresses in the tubing; the specifications for the dies are given in Fig. I. Castor oil was used throughout as lubricant. Chattering occurred in sinking some of the tubing, particularly when dies having the more acute angles were used, but the tubes showing chatter marks did not differ markedly from those with a smooth surface regarding the magnitude of residual stress. The source of the chattering has not yet been revealed. The wall of the tubing becomes thicker during sinking, as previously observed 4,5 The increases in wall thickness were 3, 7 and 9.5 per cent on the average for 6, 20 and 33 per cent reductions in diameter, no effect of the contour being noticeable. The reductions mentioned throughout this investigation do not consider this fact, but are reductions of the outside diameter. For the evaluation of the residual stress two fundamentally different methods were used. The approximation method1,11 of splitting a certain length of tubing was employed to obtain a bird&apos;s-eye view of the effect of various drawing conditions on the circumferential stress measured by the diameter change occurring on splitting. For the determination of the complete stress

Jan 1, 1941

By R. T. Webber, R. B. Owen

The vapor phase deposition of molybdenum and tungsten from the hexacar-bonyls has been thoroughly investigated by Lander and Germerl, and shown to yield well-bonded coatings on a variety of hot metallic surfaces. They also demonstrated that chromium coatings2&apos;3 could be similarly deposited, but did not investigate this metal extensively. Recently, conditions have been described by which this compound can be prepared in quantities sufficient for laboratory scale plating experiments, and it is the purpose of the present communication to outline the results of preliminary experiments upon the plating of chromium from its carbonyl. Apparatus and Technique The apparatus used in these experiments is shown in Fig I. At one end, connected by a short length of rubber tubing, is a Cenco Hypervac 20 pumping continuously. At the opposite end is a needle valve which allows a small stream of purified hydrogen to flow through the apparatus. Connected in series are a trap T1, maintained at the temperature of dry ice and acetone, the plating chamber, and two traps T² and T3 containing crystals of the carbonyl. T² is kept in a constant temperature bath (not shown), while T³ is at room temperature. Stopcock S6 allows the hydrogen flow to by-pass the carbonyl traps. A McLeod gauge is connected so that it can measure the pressure at the pump through Se, or the pressure at the plating chamber through S9 and S6. The standard (12 liter) volume connected by Sb is used to determine the volume included by S4, S6, SB, Slot the needle valve and the McLeod gauge. Knowledge of this volume allows calibration of the flow of hydrogen. The apparatus* is built entirely of pyrex, except for the needle valve, the rubber connection to the Hypervac, and the cover of the plating chamber. The plating chamber is water-jacketed, with a large brass top allowing insertion of the specimen to be plated. Set into the brass top is a ground glass stopper through which thermocouple leads are sealed. The thermocouple wires (pure Pt, and 87 pct Pt-13 pct Rh) serve the double purpose of measuring the specimen temperature and suspending it in the chamber. Surrounding the chamber is the coil of an induction heater, H. The apparatus is designed to allow variation of the following conditions: (I) the specimen temperature, from room temperature to about 1000°C, (2) the carbonyl vapor pressure, from 40 to 220 microns, and (3) the hydrogen flow. In several runs, 0.8 to 1.8 PCt of hydrogen sulfide was introuced through a needle valve that replaced S4. The vapor pressure of the carbonyl is

Jan 1, 1949

By A. H. Daane, B. J. Beaudry

The Sc-Ti system was studied by thermal, metal-lographic, and X-ray methods. Scandium was found to transform at 1334 °C from a (hexagonal) to ß which was concluded to be bee since a continuous series of solid solutions is formed between ß scandium and ß titanium at elevated temperatures. There is a minimum in the solidus at 51 wt pet Ti and 1300°C, a monotectoid at 1050°C and 49 wt pet Ti, and a eutectoid at 875°C and 91.5 wt pet Ti. The maximum solubility of titanium in a scandium is 13.5 wt pet at the monotectoid temperature, while the maximum solubility of scandium in a titanium is 6.5 wt pet at 875°C. SCANDIUM, a member of Group 111 A of the periodic table, and now called a rare-earth metal,&apos; has become of interest recently due to its low density (2.99 g per cc) and relatively high melting point (1539°C).Spedding,&apos; et al. have described a method of preparation of pure scandium metal and have made a study of its basic properties. Since scandium is approximately 10 to 12 pet smaller in at. diam than the other rare earths while its electronegativity and valence are the same, a knowledge of its alloying behavior in contrast to these elements should be very helpful to fundamental alloy theory. Since scandium is quite scarce and difficult to prepare in pure form, its use as a structural material by itself seems quite unlikely. However, its use in special cases as an alloying addi- tive to other low-density materials is a possible application; the Sc-Ti system was chosen for this reason and for others of fundamental interest. Scandium was suspected of having a high temperature bee form as do some of the other rare-earth metals.3&apos;4 Since titanium has a high-temperature bee form, a continuous series of solid solutions at elevated temperatures between ß scandium and ß titanium would prove the existence and structure of the high-temperature form of scandium. The existence of a continuous series of hexagonal solid solutions at room temperature was predicted by Burkhanov and Savitskiy,5 but Hias shown to be incorrect in early X-ray studies. EXPERIMENTAL METHODS Materials. The metals employed in this investigation were crystal bar titanium and distilled scandium prepared by the method described by Spedding,2 et al. The major impurities are listed in Table I in PPm. Alloy Preparation. All the alloys examined were initially formed in a nonconsumable electrode are-melting furnace under an atmosphere of purified helium or argon. A curve based on the observed weight loss of 0.6 pet* when titanium was melted

Jan 1, 1962

By A. G. H. Andersen, A. W. Kingsbury

SILICON bronzes containing iron are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 determined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at 1100°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. Of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West7 have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,12, 7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. PREPARATION OF SAMPLES Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 3 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1942

By J. P. Hirth, G. M. Pound

The flux of evaporation J from {loo) , {111), and (110) planes of silver single crystals and from poly crystalline specimens was measured at 744°C under a high vacuum using a time average weight loss method. The evaporation coefficient a was computed from the measured flux and vapor pressure data through the relationship J = aPe/21rmkT. The evaporation coefficients for the close packed planes and the poly crystalline specimens were found to be about 0.4 providing tentative confirmation of the theoretical limiting law for evaporation of metal crystals, a = 73(P/Pe) + % . The (110) planes faceted to form (111) planes, resulting in a greater evaporating area and larger a . The evaporation morphology of the plane surfaces and the surfaces of spherical single crystals is described in some detail. RECENTLY a detailed theoretical analysis of the mechanism and kinetics of metal crystal evaporation was made.1&apos;2 A mechanism for vaporization involving the recession of monatomic ledges across a metal surface was deduced, and evaporation rate equations were derived by considering the dynamics of these ledges. In most metals, the process of evaporation is one of dissociation of atoms from ledges, surface diffusion, and desorption. The gross vaporization rate is controlled by the surface diffusion and desorption rates. It was shown that the monatomic ledges, under the action of surface diffusion gradients, tend to assume a terminal velocity and spacing. Further, it was shown that crystal edges and grain boundaries are a ready source for monatomic ledges. In the case of evaporation of large, perfect crystals with clean, low-index surfaces, the kinetic treatment1 leads to a limiting law for crystal evaporation: where J is the gross flux of vaporization, a is the evaporation coefficient, Pe the equilibrium vapor pressure, m the atomic mass, k Boltzmann&apos;s constant, T the absolute temperature, and P the actual pressure of vapor over the crystal surface. Imperfections such as grain boundaries, pores, cracks, and macroscopic steps should have the effect of causing positive departures from this limiting law. Such an imperfection is a source for monatomic ledges, which, near their origin, are closely spaced and thus give rise to higher evaporation rates there. However, under many experimental conditions,&apos; this effect should be negligible due to the relatively low concentration of imperfections. In general, a more important cause of positive departure should be screw dislocations, and the effect of these has been considered in some detai1.2,3 Monatomic ledges emanate from points where the surface is intersected by a dislocation with a screw component normal to the surface. The dynamics of ledges arising from a screw dislocation are similar to those of ledges arising from a crystal edge. There is a perturbed region near the origin where the monatomic ledges are, under certain experimental conditions, closely spaced and the

Jan 1, 1960

By Benjamin Lustman, Robert F. Mehl

The study of the high-temperature oxidation of pure metals, intensively pursued experimentally since the pioneer work of Pilling and Bedworth1 and supplemented by the recent theoretical work of Wagner2 is now well advanced. The important field of low-temperature oxidation—i.e., oxidation extending only through the temper color range of thicknesses with the formation of thin oxide layers in the range from 0 to 1000-2000 ?ngstroms—has not, however, reached so satisfactory a state, owing largely to the experimental difficulties that attend the formation and study of thin films; most of the work has been performed on abraded specimens whose surface irregularities approximated the thickness of the films formed. It has been pointed out that the rates of oxidation of different crystal faces are different and that the difierence may be related to the orientation relationships that obtain between the metal crystal and the superimposed oxide crystal; it has also been suggested that this orientation dependence should manifest itself in rates of oxidation and perhaps also of corrosion in aggregates bearing preferred orientations.3&apos;4 An attempt to measure the rates of oxidation of different crystal faces of alpha iron demonstrated this difference in rate,4 but the dependence of rate on orientation was not simple; the method of measuring thickness, consisting of a color comparison with barium stearate multi-films of known thickness, was not wholly satisfactory. For these reasons it was felt that a study of the rate of oxidation of single crystals prepared with surfaces as smooth as possible, using a sensitive method giving true film thickness, should be profitable. Copper was chosen because of the ease of reduction of the primary oxide film and because the orientation relationships between metal and oxide and the composition of the oxide films formed at low temperatures are known; for thin films formed at low temperatures, Cu2O alone occurs.22-24 Experimental Procedure Various methods of surface preparation were attempted in order to obtain a surface that would oxidize uniformly and repro-ducibly. Electrolytic polishing by the method of Jacquet5 and electrolytic and mechanical polishing followed by annealing in vacuum and in purified hydrogen at various temperatures were tested. The procedure finally adopted consisted in a fine metallographic polish followed by an anneal in purified hydrogen at temperatures of 900° to 1000°C. for 12 hr. or more. The surface so produced was very bright and smooth, with no trace of specular etching (though some grain-boundary etching was observed); indeed, fine scratches produced by the final polish were entirely removed by the high-temperature anneal. After this treatment, the specimens were cooled in hydrogen to room temperature and placed in the oxidation furnace, where

Jan 1, 1941

By Benjamin Lustman, Robert F. Mehl

The study of the high-temperature oxidation of pure metals, intensively pursued experimentally since the pioneer work of Pilling and Bedworth1 and supplemented by the recent theoretical work of Wagner2 is now well advanced. The important field of low-temperature oxidation—i.e., oxidation extending only through the temper color range of thicknesses with the formation of thin oxide layers in the range from 0 to 1000-2000 ?ngstroms—has not, however, reached so satisfactory a state, owing largely to the experimental difficulties that attend the formation and study of thin films; most of the work has been performed on abraded specimens whose surface irregularities approximated the thickness of the films formed. It has been pointed out that the rates of oxidation of different crystal faces are different and that the difierence may be related to the orientation relationships that obtain between the metal crystal and the superimposed oxide crystal; it has also been suggested that this orientation dependence should manifest itself in rates of oxidation and perhaps also of corrosion in aggregates bearing preferred orientations.3&apos;4 An attempt to measure the rates of oxidation of different crystal faces of alpha iron demonstrated this difference in rate,4 but the dependence of rate on orientation was not simple; the method of measuring thickness, consisting of a color comparison with barium stearate multi-films of known thickness, was not wholly satisfactory. For these reasons it was felt that a study of the rate of oxidation of single crystals prepared with surfaces as smooth as possible, using a sensitive method giving true film thickness, should be profitable. Copper was chosen because of the ease of reduction of the primary oxide film and because the orientation relationships between metal and oxide and the composition of the oxide films formed at low temperatures are known; for thin films formed at low temperatures, Cu2O alone occurs.22-24 Experimental Procedure Various methods of surface preparation were attempted in order to obtain a surface that would oxidize uniformly and repro-ducibly. Electrolytic polishing by the method of Jacquet5 and electrolytic and mechanical polishing followed by annealing in vacuum and in purified hydrogen at various temperatures were tested. The procedure finally adopted consisted in a fine metallographic polish followed by an anneal in purified hydrogen at temperatures of 900° to 1000°C. for 12 hr. or more. The surface so produced was very bright and smooth, with no trace of specular etching (though some grain-boundary etching was observed); indeed, fine scratches produced by the final polish were entirely removed by the high-temperature anneal. After this treatment, the specimens were cooled in hydrogen to room temperature and placed in the oxidation furnace, where

Jan 1, 1941

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough &apos;0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough &apos;0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By C. G. Durdaller, W. H. Robinson, G. M. Pound

The nucleation rate of the a (pay) to 0 (white) tin transformation was measured as a function of temperature and a tin particle size using an X-ray diffraction technique. The powder specimens of a tin were essentially monodisperse and the small dinzension of the particles of these specimens was varied from 13 to 75 p. Several types of nucleation sites of differing potency were fbund to be operative in the nucleation process, but it could not be determined whether these sites were on the free surface of the tin particles or within the volume. Assuming that they were on the free surface, the average density of the most potent sites was calculated to be 2.5 to 5.3 x 10&apos; sites per sq cnz through the application of a Poisson distribztion finction to the isothermal data. Analysis of the temperature dependence&apos; of the rate constmts at a given fraction transformed suggests that the active sites are regions of higher free energy and not catalytic interfaces. Appreciable induction periods were observed at the lower temperatures of transformation. Experimental studies1 of solid-solid phase transformations have led to the belief that the new phase nucleates at structural imperfections. The purpose of the present work was to learn more about the mechanism of nucleation in solids and the nature of the singularities at which nucleation occurs. In this investigation nucleation rates in the isothermal transformation of gray to white tin were measured by an X-ray diffraction technique using essentially monodisperse powders of gray tin. This particular phase transformation was chosen for study because it presented fewer experimental difficulties than most others. The experimental temperature-control problems were minimal because the two phases coexist in equilibrium at 13.3"C, and measurable transformation rates occur at temperatures only slightly above room temperature. The growth rate of the P phase into the a2 is sufficiently fast to make the measured transformation rate equivalent to the nucleation rate, provided that the particle size of the samples is small enough; for the experimental temperatures used in this study, the particle diameter must be less than 100 p. EXPERIMENTAL TECHNIQUE The P tin used in this study was obtained from Capper Pass and Son Ltd., North Ferriby, Yorkshire, England, and was of 99.999 pct purity. It was transformedS to the a phase and ground into a fine powder in an agate mortar. This powder was separated by a Roller air classifier into seven fractions whose dimensions, as determined by microscopic measurement of many thousands of particles, are given in Table I and whose distribution of size within each fraction is given in Figs. 1 and 2. The shape of the particles was roughly that of an oblate spheroid,

Jan 1, 1964

By Walter Crafts, C. M. Offenhauer

IN the course of study of the heat-treatment of low-alloy steels, the behavior of alloy carbides at subcritical temperatures was found to vary from that indicated by published investigations. In order to establish the ranges of formation of carbides in low-chromium steels, a series of steels containing up to 0.60 per cent carbon and 7.5 per cent chromium has been investigated with respect to the type of carbide formed after quenching and tempering at subcritical temperatures. The types of carbide formed as products of austenite transformation to pearlitic and pseudomartensitic structures have also been determined. There have been numerous investigations of the carbides in chromium steels and diagrams of the iron-chromium-carbon system.1 Westgren, Phragmén and Negresco2 identified the following carbides in chromium steels: [Cementite Fe3C (containing up to about 15 per cent Cr) Trigonal carbide Cr7C3 (containing up to about 55 per cent Fe) Cubic carbide Cr4C (or Cr23C3) (containing up to about 25 per cent Fe) Orthorhombic carbide . Cr3C2 (containing only a few per cent Fe)] The most complete information on the iron-chromium-carbon system was supplied by Tofaute, Sponheuer and Bennek3 and by Tofaute, Küttner and Büttinghaus.4 By means of dilatometric and microscopic studies, sections of the diagram were established. This diagram showed the presence of the special carbide Cr7Ca in steels containing about 2.5 per cent to 12 per cent chromium in low-carbon steels and from about 5 to 20 per cent chromium in r per cent carbon alloys from A1 to room temperature. The present investigation has shown that a carbide inversion from Fe3C to Cr7Ca occurs in chromium steels containing more than about 1 per cent chromium after hardening and tempering at subcritical temperatures above about 500°C. The type of carbide observed to be more stable in quenched and tempered specimens was also found to be produced by direct austenite transformation in corresponding ranges of temperature and composition. EXPERIMENTAL PROCEDURE The steels used in these experiments were made in magnesia-lined crucibles in high-frequency furnaces and were poured into 2-in. ingots. The ingots were forged into 1-in. round bars, and all heat-treatments were conducted on specimens of this section .size. Sections of the bar stock 8 in. long were hardened in air, oil or water depending on the composition, after heating to a temperature sufficiently high to dissolve the carbides. The low-carbon and low-chromium steels were not entirely martensitic after quenching, and contained some ferrite and pseudomartensite. No pearlite was observed in the microstructures after auenchine. The quenched bars were cut into

Jan 1, 1942

By J. B. Hess, C. S. Barrett

Single crystal rods of cadmium collapse under uniaxial compression into peculiar kinks if the (0001) glide plane is nearly parallel to the axis of compression. In his report first describing this behavior, Orowan1 proposed that these "kink bands" do not develop entirely by ordinary gliding and twinning but by a special mechanism in which glide lamellae of uniform thickness snap abruptly to a tilted position that permits lattice continuity across the glide planes. He concluded that a portion of each boundary of a kink band consists of a plane (non-crystallo-graphic) which bisects the angle between the glide planes on the two sides of it, and along which the bending and the dislocations are concentrated. The data presented by Orowan seemed to us to be insuffcient to conclude that a wholly new mechanism of deformation was responsible for the kinks. Therefore, we have investigated zinc, which is hexagonal close-packed and has an axial ratio near to cadmium, to see whether similar bands are produced, and whether the ordinary mechanisms of glide, bend-gliding, twinning, and the formation of deformation bands can account for its mode of deformation. We find that kinks form profusely in zinc as shown in Fig 1. The structure of these kinks, reported below, seems to require no new mechanism for their explanation, but indicates that kink bands are a special form of deformation bands and develop gradually, solely from basal glide. A theory covering the formation and structure of the bands is presented in detail because it is seldom possible to study deformation bands under such simple conditions, yet many principles applying to these kinks should also apply to deformation bands in general. Experimental Procedures Single crystal rods of 2-3 mm diam and 10-15 cm length were grown by the Brideman technique from swaged wire of Horsehead Special zinc in un-coated pyrex tubes. Orientations of the rods were determined with an optical goniometer after cleaving the rods at liquid air temperature. Crystals of desired orientations were then selected and used as "seeds" to grow additional crystals approximately 4 ft in length from which all specimens were cut. The wires were compressed in two ways: in a simple hydraulic handpress —a "soft" machine—and in a Riehle hydraulic testing machine modified to produce very "stiff" action by the simple expedient of inserting lengths of steel bars at the sides of the zinc crystals between the compression plates. For metallographic examination, the specimens were mounted in sealing wax. Hand polishing was employed, with no grits coarser than No. 1 paper; following the abrasives about 0.025 in. was removed by an etch-polishing reagent.* Final etching to reveal ori-

Jan 1, 1950

By C. V. Millikan

Temperature measurement in wells is an old practice and geothermal gradients have been of interest to geologists for many years.le2 Their application to the operation of oil wells is a more recent practice. It has long been recognized that temperature anomalies occur in drilling and producing wells but thermometers that could obtain a satisfactory record of the anomalies were not available. The normal geothermal gradient is con-sidered as being about one degree Fahren-heit for each 60 ft. of depth.4 This "nor-mal " gradient varies in different areas, but whatever it may be in an area there is little variation from the surface to as deep as the : drill penetrates. The normal gradient is appreciably changed by gas expanding ; from the reservoir into the borehole or by the movement of fluid through a borehole : while drilling, producing, or circulating. It is the resulting anomalies and abnormal gradients from which conditions in wells can be interpreted. Some of the applications of such interpretations are locating the position of oil or gas sands, permeable strata in a reservoir zone, gas-oil contact, source of water, casing leaks, and the top of cement behind casing. Thermometers A thermometer for use in wells must be sensitive and have a low thermal lag. The sensitivity should permit recording 0.2OF. or less for differential temperatures although the actual temperature need not be more accurate than 1°F. The thermal lag should be as low as rugged construction will permit in order to allow surveys to be made in a minimum of time. Of the several kinds of thermometers, these requirements are most easily obtained with the vapor-pressure, expansion, and electric-resistance types. Thermometers for use in wells may be self-contained—that is, the complete instrument is lowered into the well and a record made of the temperature—or the thermal element only may be lowered into the well and the temperature recorded at the surface. The vapor-pressure and expansion types are more adaptable for a self-contained instrument while the electric-resistance thermometer is more suitable for surface recording of temperatures. The self-contained instrument can be run against high pressure on a single wire line with only one operator required. The instrument and its hoisting equipment is easily portable and can be mounted on a small car. The disadvantages are a somewhat greater thermal lag and the necessity of completing a run before any temperature or temperature anomaly is known. A surface-recording thermometer has the advantage of being somewhat more sensitive and of having a lower thermal lag. The Operator can see what anomalies are encountered and can immediately change the running conditions of the instrument or the well conditions in order to obtain the most

Jan 1, 1941

By C. V. Millikan

Temperature measurement in wells is an old practice and geothermal gradients have been of interest to geologists for many years.le2 Their application to the operation of oil wells is a more recent practice. It has long been recognized that temperature anomalies occur in drilling and producing wells but thermometers that could obtain a satisfactory record of the anomalies were not available. The normal geothermal gradient is con-sidered as being about one degree Fahren-heit for each 60 ft. of depth.4 This "nor-mal " gradient varies in different areas, but whatever it may be in an area there is little variation from the surface to as deep as the : drill penetrates. The normal gradient is appreciably changed by gas expanding ; from the reservoir into the borehole or by the movement of fluid through a borehole : while drilling, producing, or circulating. It is the resulting anomalies and abnormal gradients from which conditions in wells can be interpreted. Some of the applications of such interpretations are locating the position of oil or gas sands, permeable strata in a reservoir zone, gas-oil contact, source of water, casing leaks, and the top of cement behind casing. Thermometers A thermometer for use in wells must be sensitive and have a low thermal lag. The sensitivity should permit recording 0.2OF. or less for differential temperatures although the actual temperature need not be more accurate than 1°F. The thermal lag should be as low as rugged construction will permit in order to allow surveys to be made in a minimum of time. Of the several kinds of thermometers, these requirements are most easily obtained with the vapor-pressure, expansion, and electric-resistance types. Thermometers for use in wells may be self-contained—that is, the complete instrument is lowered into the well and a record made of the temperature—or the thermal element only may be lowered into the well and the temperature recorded at the surface. The vapor-pressure and expansion types are more adaptable for a self-contained instrument while the electric-resistance thermometer is more suitable for surface recording of temperatures. The self-contained instrument can be run against high pressure on a single wire line with only one operator required. The instrument and its hoisting equipment is easily portable and can be mounted on a small car. The disadvantages are a somewhat greater thermal lag and the necessity of completing a run before any temperature or temperature anomaly is known. A surface-recording thermometer has the advantage of being somewhat more sensitive and of having a lower thermal lag. The Operator can see what anomalies are encountered and can immediately change the running conditions of the instrument or the well conditions in order to obtain the most

Jan 1, 1941

By John Wulff, J. H. Hollomon

THE opinion has been widely held that the corrosion of alpha brass occurs by the selective solution of zinc. As late as 1939, Fink1 and Evans2 suggested that in the initial stage of the corrosion the selective solution of zinc produces copper-rich areas, which subsequently act as cathodes that facilitate the deposition of copper. Previously Abrams3 had shown that most of the copper found on corroded brass was redeposited and not residual, although he did not consider the nature of the initiation of the corrosion process. Enough data exist to indicate that any metal surface is sufliciently heterogeneous to provide the anodes and cathodes necessary for the initiation of corrosion .4,5 Thus, for alpha brass we need postulate not an initial selective solution of zinc, but only the existence of local differences in electrochemical potential. The heterogeneity responsible for potential differences may arise from oxide and other films as well as from alloy concentration gradients. Even though selective corrosion may be possible in some alloy systems, previous data on alpha brass as well as the experimental work reported in this paper do not require this supposition. Bengough and May,6 in a discussion of Abrams&apos; paper, first suggested the addition of small amounts of arsenic (0.03 per cent) to alpha brass to prevent the redeposition of copper (dezincification). This suggestion was later substantiated by Nixon.7 In their studies of the inhibiting influence of arsenic, Evans and Fink were led to the selective-solution hypothesis in order to explain the initial corrosion of such alloys. "I hey believed that an arsenic film covered anode areas and prevented the formation of copper-rich spots capable of acting as cathodes for the deposition of copper. They (lid not consider, however, the mechanism by which the arsenical film was formed. Bengough and May,8 in another publication, suggested that the commonly found gray or black arsenical film may act to: (1) carry oxygen to the brass surface, (2) increase the discharge potential of copper on brass, (3) precipitate cuprous chloride from colloidal suspension in chloride solutions. Masing9 assumed that the film found upon arsenical brass was metallic arsenic. His measurements of hydrogen overvoltage of bulk arsenic led hint to believe that the inhibition of dezincification occurs because the overvoltage of a brass surface is lowered by the arsenic film. He reasoned that this film would permit the more rapid reduction of hydrogen at the cathode, which would prevent the redeposition of copper. In a recent paper,10 we have pointed out that the film formed (luring the corrosion of arsenical brass and copper in stagnant solutions is essentially arsenious oxide (AS208)

Jan 1, 1942

By J. B. Cheatham

An analysis of indexing is given for an idealized plastic rock. Indexing refers to chipping from a bit tooth to a previously formed crater. A method is indicated for computing the dependence of chip size and shape as well as force on the tooth for various tooth shapes as a function of crater configuration and distance to the previous crater. Pressure on the tooth is found to vary with depth of penetration after a critical depth has been reached. Damp sand model experiments indicate that simple solutions using linear and logarithmic spiral slip-line fields for Coulomb plastic materials give reasonable approximations to the failure patterns. Both idealized roller cone bits and fixed blade or drag bits are considered, and methods are presented for approximating the force on the bit and the chip volume when the rock is subjected to sufficiently high pressure to behave plastically. One of the primary objectives of drilling research investigations is to develop theoretical equations which can be used to predict the behavior of rock under drilling loading conditions. Since rocks usually fail in a brittle manner at atmospheric conditions, much current research is directed to studies of the brittle failure of rock under the action of drilling too1s. 1,2 The results of triaxial test on rocks indicate that both rock strength and ductility increase at high confining pressures.3 Recent results from single bit-tooth indentation experiments on dry rocks indicate that the transition from brittle to ductile failure under a bit tooth can occur at pressures sufficiently low to be of interest in oil well drilling.4 Single bit tooth experiments and analyses are not directly applicable to the drilling process since one of the important facets in drilling is the interaction between a bit-tooth and the previously formed crater. This interaction is referred to as indexing.&apos; The purpose of the present paper is to indicate how plasticity theory can be applied to the analysis of indexing for plastic rock. Drag bit or fixed-blade drilling is considered and a discussion is given of the drilling action of an idealized roller cone bit. Results of simple experimental studies using a damp sand model are given as a method of visualizing the failure patterns in rocks under high confining pressures. These results are compared with plasticity theory using simple solutions based on linear and logarithmic spiral slip-lines. Discontinuous stress fields are proposed for drag bit drilling based upon the soil mechanics analysis of Shields. SINGLE BIT TOOTH RESULTS Single bit tooth indentation experiments using dry rocks under pressures from 0 to 5000 psi have indicated a correlation between the shape of a force-displacement curve and the nature of the rock failure beneath the tool.4 Continuous linear curves are in-

Jan 1, 1965