Search Documents

By J. W. Spretnak, D. A. Chatfield, G. W. Powell, J. R. Eifert

In nzost cases, the driving force for a lattice transformation is produced by supercooling below the equilibriunz transformation temperature. The interfnce reaction in isothermally annealed, multiphase diffusion couples may involve a luttice transformation which also requires a driving force. Direct experinzental evidence has been obtained for the existence of the driring force in the form of a supersaturated phase at the aocc)-0@cc) interface in Cu:Cu-12.5 ult pct A1 couples; the super saturation is equivalent to an excess free energy of approximately 3 cal per mol at 905. A tentatiue interpretation of the dynanzic situation a1 the interface based on the free energy-composition diagram is proposed. THE presently accepted theory of diffusion in multiphase couples1 states that there will be a phase layer in the diffusion zone for every region which has three degrees of freedom and which is crossed by the diffusion path in the equilibrium phase diagram. For binary systems, this restriction excludes all but single-phase fields and, for ternary systems, only one- and two-phase fields are included. In addition, Rhines"~ as well as other investigators3 6 have reported that the compositions of the various phases adjacent to the interfaces are, for all practical purposes, the compositions given by the intersections of the diffusion path with the solubility limits of the single-phase fields of the equilibrium phase diagram. Some studies of the rate of thickening of these intermediate diffusion layers indicate that the thickness of the layer changes para-bolically with time, or: where x is the position of the interface relative to an origin xo, t is the diffusion time, and k is a temperature-dependent factor. crank7 shows mathematically that, if the compositions at an interface are independent of time and the motion of the interface is controlled by the diffusion of the elements to and from the interface, then the segments of the concentration penetration curve for a semi-infinite step-function couple will be described by an equation of the form: hence, Eq. [l] follows from Eq. (21 if the interface compositions are fixed and if the motion of the interface is diffusion-controlled. Although the concept of local equilibrium being attained at interfaces has assumed a prominent role in the theory of diffusion in multiphase couples, experimental evidence and theoretical discussions which challenge the general validity of this concept have been reported in the literature. arkeen' has stated that strict obedience to the conditions set by the equilibrium phase diagram cannot be expected in any system in which diffusion is occurring because diffusion takes place only in the presence of an activity gradient. Darken also noted that it is usually assumed that equilibrium is attained locally at the interface although the system as a whole is not at equilibrium, the implication being that the transformation at the interface is rapid in comparison with the rate of supply of the elements by diffusion. ISirkaldy3 indicates agreement with Darken in that he believes the concept of local equilibrium is at best an approximation because the motion of the phase boundary requires that there be a free-energy difference and, hence, a departure from the equilibrium composition at the interface. Seebold and Birks9 have stated that diffusion couples cannot be in true equilibrium, but the results obtained are often in good agreement with the phase diagram. The initial deviation from equilibrium in a diffusion couple will be quite large because alloys of significantly different compositions are usually joined together. Kirkaldy feels that the transition time for the attainment of constant interface compositions (essentially the equilibrium values) will be small, although in some cases finite. Castleman and sieglelo observed such transition times in multiphase A1-Ni couples, but at low annealing temperatures these times were quite long. Similarly, ~asing" found departures, which persisted for more than 20 hr, at phase interfaces in Au-Ni and Fe-Mo diffusion couples. Braun and Powell's12 measurements of the solubility limits of the intermediate phases in the Au-In system as determined by microprobe analysis of diffusion couples do not agree with the limits reported by Hiscocks and Hume-Rothery13 who used equilibrated samples. Finally, Borovskii and ~archukova'~ have stated that the determination of the solubility limits of phase diagrams using high-resolution micro-analyzer measurements at the interfaces of multiphase couples is not an accurate technique because of deviations from the equilibrium compositions at a moving interface; diffusion couples may be used to map out the phase boundaries in the equilibrium diagram, but the final determination of the solubility iimits should be made with equilibrated samples. The purpose of this work was to investigate the conditions prevailing at an interface in a multiphase diffusion couple and to compare the interface compositions with those associated with true thermodynamic equilibrium between the two phases. Microanalyzer techniques were used to measure interface compositions in two-phase Cu-A1 diffusion couples annealed at 80@, 905", and 1000°C for various times.

Jan 1, 1969

By W. C. Clarke

An empirical study of the nature of the embrittle-ment which occurs in martensitic and semiaustenitic precipitation hardening stainless steels upon exposure at temperatures of from about 550" to 875°F has been undertaken. This work was aimed at determining cazusation and means of controlling this phenomenon. A commercial copper bearing precipitation hardening alloy was used as a basic material for study. The effect of heat treatment variables was studied as was the effect of variations in analysis. It is concluded from the evidence that martensitic and semiaustenitic precipitation hardening stainless steels are subject to 885°F ernbrittlement similar to that observed in the straight chromium stainless steels. A characteristic of precipitation hardening stainless steels which has limited their use in certain applications is that they embrittle when held at temperatures in the range of from about 550" to 900°F. This is true to a more or less degree in all currently available alloys, either the basically martensitic type or the semiaustenitic type. The rate of embrittlement varies markedly with exposure temperature, being low at 550" to 600°F and in-creasing as the temperature increases. In spite of this embrittlement, these alloys with their unique combination of high mechanical strength, reasonable toughness, and good corrosion resistance are used in many hundreds of applications. Nevertheless, there are potential applications where the embrittle-ment described is a limiting factor. The purpose of this investigation was to study the embrittlement of these alloys and to find a way to control or eliminate it. GUIDELINES USED IN PRESENT WORK The work reported in this paper is based on a study of 17-4 PH*, a very widely used alloy. It has been used *Trademark of Armco Steel Corp., licensor. in pressurized water and boiling water atomic reactors operating at about 550°F for a number of years. As the life of such equipment is extended or operating temperatures are raised, the possibility of embrit-tlement becomes of increasing concern to materials engineers. Much investigation work was done with respect to the use of 17-4 PH at 550°F. K. C. Antony' states "Such estimation" (of an activation energy for the diffusion of chromium in iron) "would indicate W. C. CLARKE, Jr. is Senior Research Engineer, Advanced Materials Division, Armco Steel Corp., Baltimore. Md. This manuscript is based on a talk presented at the symposium on New Developments in Stainless Steel, sponsored by the IMD Corrosion Resistant Metals Committee, Detroit, Mich., October 14-15, 1968. significant secondary aging is improbable at temperatures less than 700°F within normal component service life". This statement is modified however by the recognition of the accelerating tendencies of applied stress and internal stress as well as the possible effect of irradiation. In this investigation of 17-4 PH, the H 1100 (1900°F-1 hr oil quench or air cool + 1100°F-4 hr-air cool) condition was used, partly because this condition is normally used in atomic reactors. As shown later, the precipitation hardening temperature has no real bearing on the rate of embrittlement. An exposure temperature of 800°F was selected since embrittlement at 800°F is rapid, permitting development of relative data in time periods of 400 to 500 hr. For those not familiar, a nominal present day analysis of 17-4 PH is: C Mn P S SiCrNiCuCbN 0.04 0.30 0.015 0.015 0.60 16.00 4.30 3.25 0.23 0.030 TYPICAL BEHAVIOR OF 17-4 PH Figs. 1 and 2 show the behavior of a commercial heat of 17-4 PH under the conditions defined. Characteristically, 800°F exposure causes a rapid drop in Charpy V-notch impact strength. Tensile and yield strengths gradually increase and a gradual loss of elongation and reduction of area occur, accompanied by an increase in hardness. Notched tensile strength increases to 125 hr exposure and then sharply decreases after exposure for 500 hr. The notched vs un-notched tensile ratio remains virtually constant to exposure for 125 hr (1.67 to 1.56) but drops to 1.15 after 500 hr. Tensile ductility is not alarmingly affected even after much longer exposure times than these. For example, samples aged at 1100°F for 1 hr exposed at 800°F for 4000 hr showed a drop in elonga-tion of from 13 to 11 pct and in reduction of area of from 58 to 37 pct. Notched impact is the property SmIgth KSI 3JJ[/__________^UTS-Nrteh 260 ;/- 240 —^ 200 UTS-Smooth________._, o ioo mo Sob" m Too Hours Exposure Fig. 1—Effect of exposure at 800°F for various times on notched tensile strength and smooth tensile and 0.2 pct yield strength of 17-4 PH in the H 1100 condition.

Jan 1, 1970

By Robin O. Williams

AN investigation has been made of the Ni-Cr system for the purpose of elucidating certain points, namely the nature of aging in both terminal solid solutions and the nature of the phase diagram. Information pertaining to solubilities and precipitation has been obtained. Experimentation Five alloys, Table I, were arc melted in a cold copper crucible using electrolytic chromium and car-bony1 nickel, both dry hydrogen treated. These 100 g buttons were homogenized 24 hr at 1300°C in dry hydrogen and air cooled. Powders were prepared by filing or pulverizing and subsequent heat treatment was done in vacuum or helium using titanium chips as a getter. Powder of —80 mesh was filed from the 60 pct Ni alloy quenched from 1000°C and was sealed in silica under vacuum using a 250 °C outgassing. After aging as indicated in Table I1 the lattice parameters were measured on the quenched samples using the standard cos" 6 extrapolation. These parameters are considered accurate to roughly 0.0001A. In all cases chromium lines of 2.8812 ± 0.0005Å at 30°C were found. Drastic quenching from sufficiently high temperatures produced very sharp body-centered-cubic lines in the first four alloys without indications of transformations. Temperatures to 1250°C were used. Solid samples less than 1/16 in. thick were quenched in water without transformation and the powders could be adequately quenched in small helium filled thin wall silica tubing using a water quench. For those powder samples which were quenched from the two phase field the relative intensity of the body-centered-cubic lines and the face-centered-cubic lines were estimated and extrapolated to give the indicated solubility data in Fig. 1. The data for the two higher alloys were somewhat limited, the plotted points being the lowest temperature where no nickel phase was found. Neither filing, abrading, pulverizing, nor cooling to —190°C produced any new diffraction lines for solid samples quenched from the single phase region, nor did the character of the body-centered-cubic lines change Single phase body-centered-cubic powders likewise did not change on cooling to —190°C. Also, samples which had some precipitation due to inadequate quenching showed no additional changes under these conditions. The first change apparent by X-ray diffraction form samples quenched almost fast enough to prevent precipitation was the diffuseness of the body-centered-cubic lines, particularly on the low angle side, For slower cooling rates the diffuse face-centered-cubic lines appeared. Work on the large grained castings showed profuse streaking through some of the Laue spots while oscillating patterns showed broad body-centered-cubic and face-cen-tered-cubic lines as well as some new lines. For the 23.6 pct Ni alloy the new lines corresponded to 2.16, 1.96, and 1.86A and were more similar in character to the face-centered-cubic lines than the body-centered-cubic lines. Samples which were air cooled gave only face-centered-cubic and body-centered-cubic lines which were still broad. One pattern indicated that face-centered-cubic (111) plane was parallel to a body-centered-cubic (110) plane. For those samples which were examined by light microscopy there were details which were not resolved. However, varied and beautiful structures were obtained. Fig. 2 is of an alloy quenched in a helium filled silica tube from the single phase region and shows particles associated apparently with dislocations which are arranged in low angle boundaries. Finer, general precipitation has also taken place within the grains. Figs. 3 to 5 show the variety of structures produced in these alloys on continuous cooling. It appears that there are four distinct modes of precipitation as evidenced by these, figures. Annealing these structures at higher tem-peratures in the two phase field gives structures as shown in Fig. 6, which shows nickel plates in the chromium matrix which reprecipitated nickel on a much finer scale of the final quench. Lower annealing temperatures and shorter times naturally give finer plates of the nickel-rich phase. Samples of the first four alloys were annealed for appreciable times between 900º and 1250°C and gave structures like Fig. 6. The relative amounts of the two phases were measured and extrapolated to give solubility data as indicated in Fig. 1. The point at 1250°C was deduced from data of Oxx.1 These and most of the other samples were checked for ferromagnetism but none was apparent. In fact, it appeared that the magnetic susceptibilities were not more than three times that for paramagnetic chromium. Discussion In Fig. 1 it is seen that the solubility of nickel in chromium can be represented by a slightly curved line on the usual log X vs 1/T plot, These data are believed to be accurate to roughly 5 to 10º. There is only fair agreement with the data of Taylor and

Jan 1, 1958

By H. E. Cline

Calculations of the formation and growth of faults caused by a variation in lumellar widths were made for a two-dimensioml three-plate problem. The angle between the a-ß boundary and the growth direction was allowed to vary and the time evolution was studied using a quasisteady state approach. At spacings smaller than a critical spacing given by X V = AO variations in the larrlellar widths grow in time to produce faults that coarsen the structure, while at spac-ings larger than this critical spacing, variations in the lamellar widths decay in time. If small plates are introduced into the structure they may grow only at large spacings to refine the structure. The time evolution and shape of faults were calculated for the three plate-problem and then the three dimensional problem and rod-like eutectic were qualitatively discussed. UNDERSTANDING of the mechanism by which the spacing of directionally solidified eutectics is determined may allow one to control their structure better. Steady state solutions for the growth of lamellar structures have been found for a range of lamellar spacings A and growth velocities V. To obtain a unique solution for the isothermal growth of pearlite, Zener1 assumed that growth occurs at a maximum velocity, while Tiller2 assumed that a eutectic alloy, grown under an imposed velocity, will choose a spacing corresponding to minimum undercooling. These assumptions are equivalent and have been referred to as "extremum growth". The extremum condition predicts the observed relation between velocity and spacing as given by V = constant [I] but does not provide a mechanism for changing the lamellar spacing. Jackson and Hunt3 calculated the interface shape by using solutions to the diffusion equation for a planar interface and a relation of the interface composition to the local curvature. If the spacing is much larger than the extremum spacing, the interface breaks down catastrophically to form forked plates. However, the catastrophic breakdown cannot account for the small adjustments in spacing that must occur in practice..3 Direct observations during the growth of organic eutectics4 and the Pb-Sn eutectic5 show that spacing changes occur by the formation of faults. A fault in a plate-like eutectic is the edge of a plate. Once the faults form, they may move to make small adjustments in the spacing.6,3 The motion of faults intersecting the growing interface was shown by an approximate analysis to give Eq. [I].6 A perfectly regular lamellar structure should be able to persist over a range of lamellar spacings. However, during growth small perturbations in the structure may occur. If the amplitude of the perturbation increases in time the structure is unstable, while if all possible perturbations decrease in time the structure is stable. In a previous paper7 variations in the shape of the solid-liquid interface were considered, while this paper considers only variations in lamellar widths while maintaining a macroscopically planar solid-liquid interface. Previously, theories of lamellar growth1"3 have artificially contrained the growth to give a regular periodic structure. To allow for a variation in spacing, the three phase intersections and groove angles were allowed to change with time as determined by assuming local equilibrium. THREE-PLATE PROBLEM Since the spacing changes in eutectics by local formation of faults,4'5 it is suggested that local variations in spacing are responsible. The interaction between neighboring plates will be greatest because they have the smallest diffusion distance. For simplicity, as a nearest neighbor approximation, a three-plate problem will be considered, as illustrated in Fig. 1. The structure consists of a periodic array in which all the plates are allowed to vary in width. As in steady state growth it is assumed that the average composition in the solid remains constant. A variation in plate widths, that maintains the composition in the solid, was introduced by making the first a-phase plate thinner by an amount A, keeping the width of the second B-phase plate constant, and increasing the width of the third a-phase plate. If the structure were not perturbed, as in the regular two-plate problem previously described,' then the groove angles at the three-phase junctions are the equilibrium angles, 0, and ? B, and the solid-solid boundary is normal to the interface. In the three-plate problem with a variation in plate widths the phase boundaries are assumed to be related to the three-phase junction by equilibrium angles, but the a/B boundaries may be rotated by an angle 0 from the growth direction. The angle H be-tween the tangent to the a/B boundary and the growth direction may vary during growth and determine the —> — — —.A_ Q-0 / 0 x, X2 Fig. 1—Schematic of the three-plate problem showing a variation in the spacing and the effect on the angles at the three phase intersections.

Jan 1, 1970

By L. F. Bryant, J. P. Hirth, R. Speiser

The surface, gain boundary, and twin boundary energies, as well as the surface diffusion coefficient, of cobalt were determined from tests at 1354°C in pure hydrogen. A value of 1970 ergs per sq cm was calculated for the surface energy, using the zero creep method. It was possible to measure the creep strains at room temperature because the phase transformation was accompanied by negligible irreversible strain and no kinking. Established techniques based on interference microscopy were used to obtain values for the other three properties. The gain boundary and twin boundary energies were 650 ad 12.7 ergs per sq cm, respectively, while a value of 2.75 x l0 sq cm per sec was determined for the surface dufusion coefficient. In the course of a general study of cobalt and cobalt-base alloys, information was required about the surface energy of cobalt. Hence, the present program was undertaken to measure the interfacial free energy, or, briefly, the surface energy, of the solid-vapor interface of cobalt. The microcreep method was selected for this measurement because other surface properties could also be determined from the accompanying thermal grooving at grain boundaries and twin boundaries. A brief summary of the methods for determining the various surface properties follows. At very high temperatures and under applied stresses too small to initiate slip, small-diameter wires will change in length by the process of diffu-sional creep described by Herring.1 The wires acquire the familiar bamboo structure and increase or decrease in length in direct proportion to the net force on the specimen. For a specimen experiencing a zero creep rate, the applied load, wo, necessary to offset the effects of the surface energy, y,, and grain boundary energy, y b, is given by the relation: where r is the wire radius and n is the number of grains per unit length of wire. The first results obtained from wire specimens were reported by Udin, Shaler, and Wulff.' udin3 later corrected these results for the effect of grain boundary energy. The grain boundary energy is determined from measurements of the dihedral angle 8 of the groove which develops by thermal etching at the grain boundary-free surface junction. For an equilibrium configuration: Measurements of the angle 8 can be made on the creep specimens4'5 or on sheet material, as was done in this investigation by a method employing interference microscopy.= If the vapor pressure is low, the rate at which grain boundary grooves widen is determined primarily by surface diffusion and, to a lesser extent, by bulk diffusion. The surface diffusion coefficient, D,, is obtained from interferometric measurements of the groove width as a function of the annealing time, t. As predicted by Mullins~ and verified by experiment, the distance, w,, between the maxima of the humps formed on either side of the grain boundary increases in proportion to if grooving proceeds by surface diffusion alone. For this case: where fl is the atomic volume and n is the number of atoms per square centimeter of surface. When volume diffusion also contributes to the widening, the surface diffusion contribution can be extracted from the data by the method described by Mullins and shewmon.8 Where a pair of twin boundaries intersects a free surface, a groove with an included angle of A + B (using the groove figure and notations of Robertson and shewmong) forms by thermal etching at one twin boundary-free surface junction. If the "torque terms", i.e., the terms in the Herring10 equations describing the orientation dependence of the surface energy, are sufficiently large, an "inverted groove" with an included angle of 360 deg-A'-B' develops at the other intersection. The angles A + B and A' + B' are measured interferometrically. When the angle, , between the twinning plane and the macroscopic surface plane is near 90 deg, the twin boundary energy is calculated from the relation: 1) EXPERIMENTAL TECHNIQUES Five-mil-diam wire containing 56 parts per million impurities was used for making ten creep specimens. These specimens had about 15 mm gage lengths with appended loops of wire and carried loads (the specimen weight below the midpoint of the gage length) ranging from 3.7 to 149.8 mg. The wires were hung inside a can made from 99.6 pct pure cobalt sheet. Beneath the wires were placed small specimens of 20-mil-thick, 99.9982 pct pure cobalt sheet from which the relative twin boundary and grain boundary energies and the surface diffusion coefficient were measured. All the specimens were annealed at a temperature of 1354" i 3°C which is 92 pct of the absolute melting point of cobalt. The furnace atmosphere was 99.9 pct pure hydrogen that was purified further by a Deoxo catalytic unit, magnesium perchlorate, and a liquid-nitrogen cold trap. As a precautionary measure the gas was then passed through titanium alloy turnings which were heated to 280" to 420°C and replaced after every test period. The hydrogen was maintained at a

Jan 1, 1969

By E. R. Russell, N. E. Richards

The current ejyiciency of aluminum cells was derived from the metal produced over a period of time and the theoretical faradaic yield. The difference in the actual amount of aluminum in the cathode at the beginning and end of the period must be determined. The weight of aluminum in the cathode was calculated from the dilution of an added quantity of impurity metal. Use of multiple indicator metals, copper, manganese, and titanium, demonstrated that the weight of aluminum in cells can be determined to within 1 pct with routine but careful chemical analyses. Over intervals of the order of 30 days, current efficiencies reliable to within 1 pct can be obtained. INVESTIGATIONS beginning with those of Pearson and waddington ,' through the most recent published work of Georgievskii,9-11 illustrate the direct relationship between the composition of the anode gas and the applicability of analysis of anode gases to the control of alumina reduction cells. McMinn12 noted the lack of an independent method for measuring cell production efficiency over the short term. There is no doubt that changes in the current efficiency are immediately reflected in the composition of anode gases. However, the accuracy of faradaic yields calculated from gas analyses depends upon the degree of interaction between primary anode gas and Carbon.6 A conventional industrial practice of obtaining long-term current efficiency for production units from mass balances and quantity of electricity is generally insensitive to the impact of planned control of any one or more of the influential reduction cell parameters such as temperature, alumina concentration, and mean interelectrode distance. Consequently, there is a real need in the aluminum industry for a procedure to obtain the absolute cell current efficiency over a short term—10 to 30 days—both for the calibration of values obtained from gas analysis6 and for evaluating the effect of controlling specific parameters in the reduction process. The amount of aluminum produced may be determined by considering the cathode pool as a reduction of an impurity metal in aluminum. Analyses over a period will show a decreasing concentration of the impurity due to the accumulation of aluminum solvent. The increase in aluminum inferred from analyses is the amount produced by the cell during the period. Combining weights of the cell aluminum in the cathode at the beginning and end of a specific period, weights of aluminum tapped and the quantity of electricity passed during the interval will yield the current efficiency. Smart,I3 Lange;4 Rempel,15 Beletskii and Mashovets,16 and winkhaus17 have used dilution techniques to determine aluminum inventory in alumina reduction cells. A technique for determining the weight of aluminum in production cells by addition of small amounts of copper to the aluminum cathode was described by smart.13 The precision in values of the aluminum reservoir through dilution of copper in the cathode ranged from about 1 to 3 pct depending upon the quantity of copper added in the range 0.2 to 0.01 wt pct, respectively. Because the method appears so direct and apparently simple, one would not anticipate difficulties in application to industrial cells. The objective of this study was to resolve this problem associated with the trace metal dilution technique for determining the amount of aluminum in a cell. The approach in evaluating trace metal dilution as a basic factor in determining the weight of aluminum in the cell reservoir, and the absolute current efficiency of the Hall-Heroult cell, was to dilute more than one trace metal in the aluminum cathode so that we could discriminate among complications arising from physical mixing, the possibility of separation of intermetallic compounds, loss of the added elements, and chemical detection. EXPERIMENTAL METHODS These experiments are not complex but require standardized procedures. The technique involves addition of the trace metals to the cathode, knowing when these metals are homogeneously distributed in the liquid cathode, timing of the sampling, employing accurate and precise analytical methods, using reliable procedures for monitoring the amount of electricity passed through the cell, and accurate weighing of aluminum removed from the cell during the particular period. More accurate results might be obtained if the increment in concentration of the added indicator metals were of the order of 0.1 to 0.2 wt pct. The method must be applicable to production units and, hence, the contamination of the aluminum minimized. For this reason, the concentration of trace metals in the cathode was kept below 0.07 wt pct and generally at 0.04 wt pct level. Trace quantities of copper, manganese, titanium, and silicon are already present in virgin aluminum and are suitable as additives from electrochemical and analytical points of view. Concentration of silicon is quite dependent upon the characteristics of the raw materials and was not used extensively in this work. Chemical Analyses. All instrumental analyses require calibration against an absolute technique such as a gravimetric, volumetric, or spectrophotometric method which represents the ultimate in sensitivity, precision, and accuracy. On review, the best methods for copper appeared to be optical absorption without

Jan 1, 1969

By W. B. Lilienthal, J. C. Melrose

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By M. Cohen, D. J. Blickwede

Quantitative observations concerning the carbide phases in high speed steel are of importance for two general reasons: (1) the carbides, being inevitable constituents of the final structure, exert a direct influence on the properties of the steel; and (2) a substantial proportion of the total alloy content is tied-up in the carbides, and hence the extent of their solution on austenitizing governs the composition of the steel matrix. The latter relationship has a vital bearing on the response of the steel to tempering as well as on its performance in subsequent service. Accordingly, in the course of a long-term study of the behavior of high speed steels, the authors were confronted with the problem of securing quantitative data on the carbide phases. The obvious method for acquiring such information is to isolate the car-bides from the steel and subject them to chemical, X ray diffraction and other measurements. There are well-known extraction techniques which involve the chemical or electrolytic solution of the less noble matrix (ferrite, marten-site or austenite), thus leaving a residue of the carbide phases. However, the results obtained must be scrutinized carefully1,2 since the carbides may be affected by the chemical or electrolytic action. It is the purpose of the present paper to describe the experiments leading to an electrolytic-extraction technique for quantitatively isolating the carbides from both I and hardened high speed steel. Particular attention is paid to the amount, as well as the composition, of the carbides so that the matrix analysis becomes ascertainable by subtraction from the overall steel composition. Illustrative results are given for the M-2 grade of tungsten-molybdenum steel. Review of the Literature The chemical method of dissolving the matrix selectively with respect to the carbides makes use of dilute non- oxidizing reagents such as hydrochloric or sulphuric acid. Although this simple procedure has led to the determination of the cementite composition,3,4 it achieved only limited success because of the interaction between the acid and the carbide residue. Some of the carbides may not only be destroyed in this way, but the hydrogen released is likely to remove part of their carbon as hydrocarbon gases. The electrolytic technique of isolating carbides has the advantage of rapidly dissolving the specimen (anode) in the presence of less reactive solutions than are practicable with the chemical method. This reduces the possibility of chemical attack on the carbides, and furthermore, the hydrogen evolved during the electrolysis is released at the cathode which is not in close proximity to the carbides. The common electrolytes adopted for this purpose are hydrochloric and sulphuric acids.5-l1 Aqueous solutions of ferrous salts have also been used.12,13 A considerable advance in experimental technique was introduced by Treje and Benedicks14 who developed a double-compartment cell for electrolytic extraction, the anode and cathode chambers being separated by a porous diaphragm. A solution of 15 pct sodium citrate, 2 pct potassium bromide and 1 pct potassium iodide was selected for the anolyte, while the catholyte consisted of a 10 pct solution of copper sulphate, with copper serving as the cathode. This type of cell has a number of desirable characteristics: 1. The anolyte has a pH value close to 7, at least at the beginning of the run. 2. The iron that dissolves from the anode-specimen forms a water-soluble complex ion with the citrate, thereby preventing the precipitation of iron hydroxide (which would contaminate the carbide residue) despite the neutrality of the solution. 3. Copper deposition instead of hydrogen evolution occurs at the cathode, and this avoids an increasing concentration of hy-droxyl ions which (in an otherwise neutral solution) might cause the precipitation of insoluble hydroxides. 4. Contamination of the anode chamber by copper sulphate is inhibited by the porous diaphragm. Houdremont and coworkers15 applied the above method (with the further refinement of excluding oxygen during the electrolysis, washing and drying) to the extraction of carbides from a series of plain carbon steels after various heat treatments. They had quantitative success only with specimens in the annealed condition, and concluded that the size and shape of the carbide particles play an important role in the isolation process, with large spheroids exhibiting the least tendency to decompose during the electrolysis. Up to the present time, the citrate double-cell has not been used to any extent for isolating the carbides of high alloy steels, apparently on the grounds that the complex carbides are more resistant than cementite to attack in the simpler acid electrolytes. In particular, Bain and Grossmann7 and Gulyaev10.10a have employed the hydrochloric acid cell for their investigations of the carbides in high speed steel.* It will be demonstrated here that this type of cell is capable of yielding quantitative results in the case of high speed steel, and actually has certain advantages over the more complicated double cell. However, in order to provide a rigorous test of the quanti-tativeness of electrolytic procedures for the problem at hand, both methods were studied in considerable detail.

Jan 1, 1950

By J. C. Melrose, W. B. Lilienthal

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By H. Conrad, V. V. Damiano, G. J. London

A method is described for producing single crystals of high-purity beryllium, Be-4.37pct Cu, and Be-5.24 pct Ni. These crystals were prepared for testing in compression parallel to the [0001] by orienting and lapping to within ±3' of arc of the (0001). Microstrain testing apparatus is described along with c axis compression results for ingot purity beryllium, twelve-zone-pass material, and the above-mentioned alloys. Results show no measurable plasticity for the ingot purity material from -196" to 400°C, although some surface traces of (1122) slip was observed at 200°C and above. The twelve-zone-pass material shows substantial microstrain plasticity at 220°C with slip on (1122). Both alloys show significant plasticity at room temperature and above with slip also on (1122) planes. THE two slip systems which normally operate during the plastic deformation of beryllium in the vicinity of room temperature are:' basal slip (0001)(1120) and prism slip . Pyramidal slip with a vector inclined to the basal plane has been reported for elevated temperatures,'-a but occurs near room temperature only at very high stresses.~ A summary of the available data on the effect of temperature on the critical resolved shear stress for slip on these systems has been compiled by Conrad and Perlmutter.~ It has been postulated6'7 that one of the principal factors contributing to the brittleness of poly crystalline beryllium at temperatures below about 200°C is the difficulty of operating pyramidal slip with a vector inclined to the basal plane. Hence, detailed information on the operation of such a slip system is important to understanding the brittleness of beryllium. The operation of pyramidal slip with a vector inclined to the basal plane is best accomplished in beryllium by compressing single crystals in a direction parallel to the c axis. In such a test the resolved macroscopic shear strzss on the basal and prism planes is zero and (1012) twinning which is favored by tension along the c axis does not occur. Hence, in c axis compression of beryllium the normal deformation modes are inhibited and the operation of pyramidal slip with a vector inclined to the basal plane is favored. In the present investigation, c axis compression tests were performed on beryllium single crystal as a function of temperature (77" to 700°K), purity (commercial and twelve zone pass), and alloy content (4.37 wt pct Cu and 5.24 wt pct Ni). Presented here is a description of the test techniques employed and the gross mechanical behavior observed. A detailed analysis of the slip traces developed on the surfaces of the deformed specimens during these tests and the results of electron transmission studies of the deformed crystals are given in a separate paper.B PROCEDURE 1) Materials and Preparation. Single crystals about 1 in. diam were prepared of the following materials: commercial-purity beryllium, high-purity beryllium, and two beryllium alloys, one with 4.37 wt pct Cu and the other with 5.24 wt pct Ni. The commercial-purity single crystals were obtained by cutting specimens from large-grained ingot of Pechiney SR material, which is approximately 99.98 pct pure. The high-purity crystals were prepared by floating-zone refining (twelve passes) a rod (7 in. by 1 in, diam) of Pechiney SR grade cast and extruded beryllium. Although an absolute chemical analysis of the zone-refined material was not established, mass spectro-graphic analysis, emission spectrographic analysis, and y activation analysis indicated that it contained in atomic fractions about 5 to 10 ppm each of carbon and oxygen, 1 to 5 ppm each of nickel and iron, and about 1 to 2 ppm of copper, with the remaining residual impurities being less than 1 ppm. Further indication of the purity of this material is provided by the critical resolved shear stress for basal slip, which was approximately 300 psi. The starting material for the alloy single crystals was 1-in.-diam floating-zone-refined (six passes) rod of Pechiney SR grade beryllium. Two such rods were wrapped respectively with sufficient weight of wire of high-purity copper (99.999 pct) or nickel (99.999 pct) to yield a 5 wt pct alloy. A seventh floating-zone pass was then applied to each of the rods to accomplish the initial alloying and an eighth pass for homogenization. Analytical samples were taken from regions of the rod immediately adjacent to where the mechanical test specimens were cut; these indicated 4.37 wt pct Cu and 5.24 wt pct Ni. 2) Crystal Orientation. To avoid the occurrence of basal slip during c axis compression testing, it is necessary to load the crystals as nearly parallel to the c axis as possible. Preliminary c axis compression tests indicated that plastic flow and/or fracture occurred at stresses of the order of 300,000 psi; hence on the basis of a critical resolved shear stress for basal slip of 300 to 400 psi, the maximum crystal misorientation permitted is about 4 to 5' of arc. Since this accuracy cannot be obtained using the usual back-

Jan 1, 1969

By M. I. Jacobson, A. S. Yue, A. E. Vidoz, F. W. Crossman

An equation governing the concept of constitutional supercooling under the combined effect of concentration and temperature gradients was used to produce platelike Al-CuAl2 eutectic composites for mechanical properties studies. Compression specimens were prepared from a single-colony Al-CuA12 eutectic composite ingot, 2 in. in diam and 12 in. long. The specirrzens were cut such that the platelets were oriented parallel, 45 deg, and perpendicular to the compression direction. Since the ingot was of eutectic composition, The aluminum-rich matrix could dissolve 5. 7 wt pct Cu in solid solution, and therefore could be strengthened by precipitation hardening. Specimens were tested at room temperature and elevated temperatures in the unidirectionally solidified, solution-treated, and solution-treated plus aged conditions. The results were compared with those for the conventionally cast and extruded specimens. For the controlled material, the highest strengths were obtained with platelets oriented parallel to the compression axis. In the unidirectionally solidified condition, 0.2 pct offset yield strength was 32,000 psi; however, this was increased to 59,000 psi by solution treatment, and further increased to 90,500 psi by solution treatment and aging. The attainment of high compressive strengths in the Al-CuAl2 eutectic composites was interpreted in terms of the buckling of elastic CuAl2 platelets in the plastically deformed a aluminum matrix. SINCE the discovery of high-strength whiskers,' scientists and engineers have made significant progress toward incorporating these whiskers into metallic matrices, forming composites for basic studies and structural application. The general procedure is to produce the whiskers first and then to bind them together with a ductile matrix. The production of whisker-reinforced composites requires tedious handling techniques,, particularly when it is desired to align the whiskers unidirectionally. Furthermore, the interfacial bond between the whisker and the matrix is frequently poor3 so that the resulting composite has strengths lower than expected. These disadvantages are generally true for any metallic composite produced by physically mixing the components. It is possible to eliminate these shortcomings by growing whiskers directly in the matrix material by eutectic solidification.4-8 In eutectic solidification, the matrix phase and a whisker phase are grown approximately simultaneously from a liquid of the same overall composition at the eutectic temperature. If the solidification process is controlled by varying the freezing rate, the temperature gradient, and the impurity content, platelike or filamentlike whiskers are produced parallel to the growth direction. The morphology of the grown-in reinforcement, i.e.. plates or rods, generally depends on the volume fraction9 of the dispersed phase present in the eutectic mixture. Since the unidirectional eutectic solidification is a one-step process, i.e., the liquid-solid transformation process, an excellent interfacial bond between the matrix and whisker is obtained. An additional advantage is that no special handling technique for whiskers is needed. In recent years, many investigators10-13 have studied the effects of growth variables on the micromorpholo-gies of binary eutectic alloys produced by controlled solidification. The study of their mechanical properties was initiated by Kraft and coworkers14-16 who found that the strength of cast A1-CuA12 eutectic alloy can be increased threefold by unidirectional solidification. In the A1-AL3Ni system, a strength of 50,000 lb per sq in, was reported for the unidirectionally solidified eutectic alloy, a value five times higher than for conventionally cast material. Thus, the unidirectionally solidified eutectics can be used as fiber-reinforced composite materials. In this paper, we shall first use an equation17 as a guide for the production of eutectic composites in general and the Al-33 wt pct Cu eutectic in particular. Experimental data supporting the theoretical prediction are given. Second, the compressive properties of the grown A1-33 wt pct Cu eutectic were thoroughly investigated in terms of platelet orientations, thermo-mechanical treatment, and temperature. The experimental data are interpreted in terms of a buckling model of fibers in elastic fiber-plastic matrix metallic composites. EXPERIMENTAL PROCEDURE Crystal Growth. The following experimental procedure was adopted for the production of controlled microstructures in the A1-33 wt pct Cu eutectic alloy. The controlled solidification was accomplished with a movable resistance-wound radiation furnace. Fig. 1 is a schematic drawing of the solidification apparatus. A water-cooled chiller was placed into a degassed high-purity graphite crucible containing the charge. Rubber stoppers wrapped with aluminum foil were used to seal both ends of the quartz tube through which a dried argon atmosphere was passed under a slight positive pressure. At both ends of the quartz tube, radiation shields were used to minimize heat loss. The quartz tube was held in place by two steel clamps and the furnace was drawn vertically by means of a steel cable against the steel truss which permits the furnace to move without touching the tube. The drive mechanism consisted of two pulleys, a counter weight.

Jan 1, 1969

By R. K. McGeary, B. Lustman

The textures produced in zirconium by cold and hot rolling, and by recrystallization above and below the transformation temperature were determined. Thermal expansivities were measured in the thickness, transverse, and rolling directions of preferentially oriented zirconium and were correlated with the texture scatter in these directions. REVIOUS investigations have indicated that minor differences between hexagonal close-packed metals of similar axial ratio may appear with respect to the textures produced both on cold rolling and on subsequent recrystallization. In the case of magnesium, beryllium, and titanium, metals of axial ratio similar to that of zirconium, the ideal orientations produced by rolling are fundamentally the same, although marked variance is reported in the degree and type of scatter about the mean orientation; in those instances where recrystallization textures were observed, they were reported to be similar to the rolling textures. Measurement of the anisot-ropy of thermal expansion of both rolled and re-crystallized zirconium could not be correlated satisfactorily with the textures reported for the above metals, and therefore a study was made of the preferred orientations produced in zirconium. Reported below are the textures produced in zirconium by cold and hot rolling, and recrystallization above and below the transformation temperature, together with the results of thermal expansion measurements. Determination of Preferred Orientation Two types of zirconium were investigated: 1— "crystal bar" zirconium obtained from the Foote Mineral Co., produced by the thermal decomposition of zirconium tetraiodide, and 2—zirconium ingot obtained from the Bureau of Mines prepared by melting sponge zirconium in a graphite resistor vacuum furnace in a graphite crucible. The major impurities present in the two materials used are listed in Table I. Several of the pole figures were later checked with 0.03 pct hafnium crystal bar material and the results were identical with those to be shown for the 1.5 pct hafnium material. The materials were cold rolled to 0.014 in. in thickness as shown in Table 11. Specimens were cut from the 0.014 in. thick rolled sheets and etched to thicknesses of 0.002 to 0.010 in. Such specimens were used for exposures up to a 50' to 60" angle between the beam and plane of the specimen; for higher angles a wire shape, similar to that described by Bakarian,' was formed on an end of the original 0.014 in. sheet. A fine-bladed abrasive cut-off wheel was used to slot the sheet and to form the cylindrical cross-section. The wire shaped ends were then etched to 0.006 to 0.010 in. in diam. Although absorption of X-rays in the wire-shaped specimens does not vary with angle of rotation, the line width around the diffraction rings was not uniform, because the wire was narrower than the X-ray beam, and this condition caused some uncertainty in the estimation of azimuthal intensities. Furthermore, scanning was not practicable with this type of specimen so that spottiness of the rings due to large grain size was excessive for specimens which had been heated above about 650°C. Nevertheless, satisfactory information could be obtained for high angle exposures from the negatives by the use of both types of specimens. Transmission Laue photograms were taken using unfiltered molybdenum radiation (47.5 kv, 18 ma) and a 0.025 in. pinhole. With the film 8 cm from a 0.005 in. thick specimen exposures of about 30 min were adequate. For specimens with a coarse grain size, a device that scanned about 0.15 sq in. of sheet surface was used. An attempt was made to plot the pole figures by use of an X-ray spectrometer as described by Norton.' However, for the particular technique used, the intensity variations obtained were not considered definite enough to give reliable results, especially for the large grained recrystallized and transformed specimens. This method was therefore abandoned in favor of the standard photographic method. Nine exposures were taken of each specimen: seven exposures with the beam perpendicular to the rolling direction and at 0°, 10°, 20°, 35", 50°, 65", and 80" to the transverse direction, and two exposures with the beam perpendicular to the transverse direction and at 60" and 80" to the rolling direction. Additional exposures were then made where necessary. The intensity variations of the diffraction rings were estimated by eye. It was usually possible to estimate 3 degrees of intensity from the photograms but in some cases 2, 4, or 5 degrees were estimated. Experimental Results The preferred orientation was determined for the following treatments: 1—cold-rolled, 2—low temperature rolled, 3—cold-rolled surface layer, 4— cross-rolled, 5—hot-rolled, 6—recrystallized below the transformation temperature, and 7-—recrystallized above the transformation temperature. I—Cold-Rolled Textures: The slip plane in hexag-

Jan 1, 1952

By J. W. Spretnak, J. N. Cordea

The gain boundary relaxation in high-purity aluminum, nickel, copper, and silver was studied by means of a low-frequency torsion pendulum. Both internal friction and creep at constant stress tests were conducted. A lognormal distribution in relaxation times was found to account for the relatively wide experimental internal friction peaks and the gradual relaxation behavior during the creep tests. This distribution was separated further into a lognormal distribution of relaxation time constants and a normal distribution in activation energies. A spread of up to ±6 kcal per mole in the activation energies accounted for the major part of the distribution. A "double-peak" internal friction phenomenon was observed in silver. The activation energies in kcal per mole derived from the grain boundary relaxation phenomena are 34.5 for aluminum, 73.5 for nickel, 31.5 for copper, and 41.5 for silver. It was found that the rain boundary relaxation strength in these metals increases with the reported stacking-fault energy. GRAIN boundary relaxation phenomena have been observed in a large number of polycrystalline metals and alloys. Numerous investigations have been conducted to study the structure of the grain boundary through this relaxation process. One of the first investigators was Ke1-4 who observed that the activation energy for grain boundary relaxation in aluminum, a brass, and a iron was about the same as that for volume diffusion. He concluded that the grain boundary behaved as if it were a thin liquid layer with neighboring grains sliding over one another. Leak5 conducted experiments on iron of a higher purity and observed that the grain boundary activation energy is comparable with that of grain boundary diffusion. He suggested that, in metals where this relationship holds, the damping may be caused by a reversible migration of grain boundaries into adjoining grains. Nowick6 has presented an interesting view of inter-facial relaxation with his "sphere of relaxation" model. A relaxed interface is represented as one where the shear stress is greater than the normal value along the edges and zero in the interior of the interface. The region of the stress relaxation is pictured as a sphere surrounding the interface. From his calculations Nowick concluded that the slip along an interface is directly proportional to its length. Therefore, the time of relaxation, T, depends on the size of the relaxation interface. This means that in the Arrhenius relationship, t = TO exp[H/RT], valid for atom movements, the relaxation time T is predicted to be proportional to the grain diameter through the pre-exponential term, TO. Since the internal friction can be given as Q-1 = ?j wt/(1 + w2r2), where ?J is the relaxation strength and w is the angular frequency, an increase in grain size at a constant frequency will shift the peak to a higher temperature. A great deal of work has been done to determine the exact relationship between the internal friction and grain size.1,5,7,8 In metals, the grain boundary peaks are found to be lower and broader than predicted theoretically.' The above model can explain this by a distribution in the size of the interface areas, represented by a distribution in the parameter tO, and an overlap of spheres of relaxation, represented by a distribution in activation energies. Both these phenomena result in an over-all distribution in the relaxation time, which could affect the internal friction peak height, breadth, and also position. This relationship between the experimental data and theoretical calculations appears very promising in the study of interfacial relaxation mechanisms. THEORY A lognormal distribution in t can sometimes be used to adequately describe the spectrum of relaxation times governing an anelastic relaxation. wiechert9 originally suggested such a distribution to explain the elastic after-effect in solids. This choice is particularly applicable to grain boundary relaxation when considering Saltykov's work.'' He found a lognormal distribution in the grain sizes within a metal. Recently Nowick and Berry11 have introduced a log-normal distribution in T into the theoretical internal friction equations. The form of the distribution function is where z = In(r/rm), and Tm is the mean value of t. The parameter ß is a measure of the distribution and is the half-width of the distribution when is l/e of its maximum, IC/(O). Nowick and Berry have described the methods to obtain the parameters Tm, ß, and ?,J from experimental internal friction and creep test data. In the idealized case, where only one relaxation event occurs with one relaxation time, only ?J and T are necessary to completely describe the event, and 0 = 0. For the broader internal friction curves 6 is some positive number greater than zero. The larger the 6, the greater is the half-width of the distribution in In t.

Jan 1, 1967

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite 'aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou'e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.'" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, ''' and ativity'-' data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,'"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener''% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil'' (on the basis of a previous study by ohansson'), and subsequently rede-rived correctly by Speiser and retnak,' in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, ' in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener's method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967

By R. A. Wattenbarger, H. J. Ramey

The trend in gas well testing has been to rely more on the early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modern gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks. It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore. Russell and Truittl published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark2 applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis. The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz3 presented the drawdown equations for *Now with Scientific Software Corp., Denver. ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice. Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore. The Mathematical Model The geometry of our mathematical model is similar to that used by Prats.4 The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through the wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model. The equation for the flow of real gas in a porous medium with uniform porosity, permeability and thickness is5-7

Jan 1, 1970

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961

By W. M. Ross

AMONG the comparatively few A radical changes in mining equipment in recent years is the introduction and use to an ever greater degree of detachable bits for rock drills. Just how great the possible field for economic application of this innovation is, and to what ex- tent detachable bits are used instead of the conventional type of drill steel, are matters of conjecture. Just as a rough approximation, one might conceive that at least three-quarters of the drilling done in mines today could better be performed by steel with detachable bits, instead of only about one-quarter as at present.

Jan 1, 1939

By C. P. Proctor

WESTERN Pennsylvania, eastern Ohio, and Illinois are carrying out experiments wherein much more slate and other impurities are loaded with the coal in the mine and hauled to the surface preparation plant for removal. In general everything is sent to the cleaning plant although there may be some gobbing in the mine. No conclusions have been announced as to the effect of such a mining system on clean coal costs. Such factors as ability of the surface plant to handle the impurities, land and facilities for disposing of the impurities, and the transportation facilities underground should be considered.

Jan 1, 1942

By John G. Hall

The pumping operations at the Chief mine have been unique in the respect that for many years the entire flow of water into the mine has been disposed of by pumping into natural underground " caverns" or "sinks." Volumes up to 4000 gpm have been pumped into these caverns with no apparent tendency for the caverns to fill with water, and it has never been proven that any of the water returns to the mine workings. Major pumping operations have been carried on during two periods, the first from 1918 to 1927, and the second from 1942 to the present time.

Jan 1, 1949

By AIME AIME

ONE hundred and eighty-three A.I.M.E. members, W. S. Morris with an excellent technical program, John Suman, "oil" President of the Institute, and a Texas norther blew into Dallas for the fall meeting of the Petroleum Division at the Adolphus Hotel, Oct. 16-18. and the most successful result will give future meeting committees a high mark to equal. People were still talking of the terrific heat the week before and it was quite noticeable that with the lowered temperatures, the members were in fine fettle for the technical sessions. The total attendance on Friday noon was

Jan 1, 1941