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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 Frank Doxey

AT Dominion Steel & Coal Corp. it has long been recognized that continued mechanization of mine operations is necessary in the Pictou, Cumberland, and Sidney coal fields of Nova Scotia. The varied physical conditions in these fields call for special consideration of individual cases before planning is finalized. Because standard equipment cannot be procured which would operate successfully, many experiments have been necessary over the years to keep pace with the progress made in other countries. There are two mines, producing 2000 tpd, located in the Pictou coal field. The field is badly distorted and crossed by many faults. Seams are highly inclined and irregular and vary in thickness from 5 to 40 ft. Entries are difficult to maintain because of squeezing of the coal. ribs and movement of the roof and pavement. Output from the three operating mines in the Cumberland field is 3000 tpd. The field is highly inclined, inclination varying from 12° to 32°. Overlying beds consist of shales and massive sandstone lenses of extreme toughness and are responsible for bumps when the stresses are relieved by extraction. At greatest depth these are among the deepest coal workings in the world. Depth of cover ranges from 2300 to 4000 ft. This prohibits room-and-pillar working and necessitates longwall operation. Working of contiguous seams concurrently to maintain output increases the already difficult conditions. The Sydney field, with a frontage of about 30 miles, is the most important of the Nova Scotia coal fields. With the exception of one small area it is now wholly submarine. Output is approximately 21,000 tpd. Seams are 21/2 to 8 ft thick, and cover in the areas varies from 600 to 2300 ft, with an average of 1500 ft from sea bottom to the top of the seam. The seams dip in a seaward direction, pitches ranging from 6" to 4.0". The shoreline is the last place of entry to the seams and distance from the bank to the working faces is generally over 3½ miles, in some cases as much as 6½ miles. Ventilation is a problem and requires the construction of large permanent airways. Getting and Loading Coal: In 1925, in view of heavy pressures exerted by thickness of cover overlying the seams, roadways and pillars of the room-and-pillar system being worked began to break up and coal was lost. It was decided that a change in the method of extraction in areas with heavy cover was necessary, and experiments were made with many short walls and longwalls varying between 90 and 250 ft. Trial and error proved that the best operating length was between 400 and 500 ft, delivering all coal to the dip, with roadways to the face following a level course. The change-over was gradual, and the technique of roof control developed with the system, so that falls to the face are now very infrequent. An advantage of longwall mining is that it yields 95 pct extraction, especially important in coal seams of high quality or in seams where faults or disturbances restrict the workable areas. This percentage of extraction is based on the fact that the longwall advancing system takes development faces where pitch permits instead of driving headings and leaving roadway pillars. This system yields high tonnage during development and limits loss in extraction to duff left during operations. Accompanying disadvantages, on the other hand, are the heavy construction cost of main roadways and the necessity of driving all new flank face roadways through the gob. If the main roadways are driven through the solid, and large enough pillars are left on each side for protection against flank face weights, then the width of solid coal is approximately 1700 ft. This represents 10.6 pct of the coal available, or 89.4 pct extraction of the whole. These pillars, however, are of such size that they provide a useful pillar drawing area as a final operation of the mine. It may be that although the seam cannot be generally mined by the room-and-pillar method, it can be adapted to

Jan 1, 1955

By Nicholas J. Grant, A. W. Mullendore

Measurements of grain boundary sliding were made on polycrystal and bicrystal tensile creep specimens of Al-2 pct Mg at 500oand 700oF. Grain and pain boundary orientation factors were studied with respect to their effect on the magnitude and direction of grain boundary sliding. It was concluded that a large part of the observed sliding may be caused by the operation of slip crossing the grain boundaries. Supporting evidence for this model from other investigations is also given. GRAIN boundary sliding in metals during elevated temperature deformation has frequently been thought of as an independent mechanism with its own characteristic stress, temperature, and structure dependence. Further, it is common to regard the grain boundary as the weak link during creep deformation since: 1) the strength of apolycrystallinemetal, as meas-sured by creep rate or rupture life, decreases at\a more rapid rate when sliding comes into action, and 2) grain boundary sliding, as revealed by "boundary darkening" and fold formation is often the first visible deformation. On the other hand, more quantitative observations, in both polycrystals and bicrystals, have shown boundary deformation to be closely related to the over-all deformation of the specimen. The curve of grain boundary contribution to elongation vs time takes a shape similar to that of the total creep curve,',' and the apparent activation energy for sliding appears in most cases to have the same value as that for total creep.3 In order to reconcile these observations, one is left with these possibilities: 1) The grain boundary and grain deformation rates are both controlled by the same rate limiting processes. 2) The rate of sliding is limited by accommodation deformation in the grains. 3) Sliding is the consequence of grain deformation. 4) Grain deformation is dependent on prior grain boundary deformation. Alternatives 2) and 3) would view grain boundary sliding as occurring in series with another deformation process which could be rate controlling. McLean prefers item 3) as the sliding basis,4 where subgrain rotation results from dislocation accumulation in the substructure at the grain boundary. Crussard and Friedel's5 treatment of grain boundary migration considers that dislocations are forced into the grain boundary and are dissociated into dislocations with Burgers' vectors nearly parallel to the grain boundary. The movement of these partial grain boundary dislocations then produces the sliding. The results of this investigation have indicated alternative 3) to be the most appropriate and it is this aspect of grain boundary sliding which will be analyzed. EXPERIMENTAL PROCEDURE Three types of tensile creep tests were employed in this study: (I) A constant load test of one very coarsegrained polycrystalline specimen at 500° F, 3600 psi, 1 pct per/hr strain rate to examine the grain and grain boundary orientation factors in grain boundary sliding. (II) Constant strain rate tests of polycrystalline specimens at 510o and 715o F, 2 pct per/hr strain rate to determine the grain boundary contribution to elongation at very low total strains. (m) Constant strain rate tests of bicrystals of various grain and grain boundary orientations at 500°F, 2 pct per/hr strain rate to obtain further information on the orientation effects in grain boundary sliding. The material used in the tests was a high-purity Al-1'.92 mg alloy, kindly furnished by Alcoa. Its composition is given in Table I. The alloy is a solid solution at the test temperatures. The coarse grained polycrystalline specimen for test (I) was prepared by recrystallizingthe machined specimen, straining it about 1pct intension at room temperature and annealing at 900°F for 8hr. The constant strain rate specimens (11), with an 178 in. sq. by 1/2 in. long gage section, were cut from 1/8 in. thick sheet of cold rolled and annealed (8 hr at 1000oF) material. The latter specimens were supported in a special jig during the milling operations to avoid any bending, and the gage section was subsequently heavily electropolished to remove the cold-worked surface layer. The bicrystals (ID) were machined in the same

Jan 1, 1963

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By T. E. Davidson, A. P. Lee

It is known from the early work of Bridgman that the two lowest-pressure transitions (I-II and II-III) are accompanied by substantial and abrupt changes in resistivity and Volume. However, unlike the temperature -induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of the pressure-in&ced transitions. This current work involves an examination of the structural and transformation characteristics of the bismuth I-II and II-III transitions under hydrostatic pressures. The relationship of initial structure to the transformation pressure, rate, resistivity change, and resultant structure is discussed. It is shown that the transition pressure and transformation rate are independent of the presence of grain boundaries and associated anisotropy-induced deformation. An observed hysteresis in both the I-II and II-III transitions is shown. BISMUTH is one of the most interesting of the elements exhibiting pressure-induced polymorphs since it undergoes several allotropic transformations at pressures below 90,000 atm. It is known from the early work of bridman1,2 that the two lowest-pressure transitions (1-11 and 11-111) are accompanied by substantial and abrupt changes in resistance and volume. However, unlike the temperature-induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of these pressure-induced transitions. It is the purpose of this work to examine some of the structural and transformation characteristics of the bismuth 1-11 and 11-111 transitions under hydrostatic pressures. Another interesting characteristic of bismuth is that, in its polycrystalline form, hydrostatic pressures of sufficient magnitude will induce severe progressive plastic deformation in the region of the grain boundaries.3 This deformation, which has also been observed in several other metals, is attributed to the high degree of anisotropy in the linear compressibility of bismuth, resulting in shear stresses in the grain boundaries when it is exposed to hydrostatic pressure. Most thermally induced allotropic transformations in metals, whether of the diffusionless ather-ma1 (martensitic) or isothermal nucleation and growth types, are dependent upon structure and prior history,4 viz., grain boundaries, deformation, and so forth. One logically wonders then whether the transformation characteristics of the pressure-induced polymorphs in bismuth might also depend upon initial structure, particularly with respect to the presence of grain boundaries and associated plastic deformation. In this investigation, the role of grain boundaries and plastic deformation on the characteristics of the bismuth I-II and 11-111 transitions will be established. The rather unique residual microstruc-tural changes associated with these transitions will be presented and discussed. The occurrence of a measurable hysteresis in both the I-II and 11-111 transitions will be demonstrated. The type of transformation mechanism based on the observed transformation rate will be discussed. EXPERIMENTAL PROCEDURE A) Apparatus. The hydrostatic pressure system utilized in this investigation is similar to that previously reported by Bridgman' and Birch and Robertson,5 and has been previously described.3 For the purpose of this work, the pressure medium utilized was a 1:l mixture of pentane and isopentane. Pressure measurement was by means of a manganin coil in conjunction with a Foxboro Recorder. The manganin coil was mounted in the bottom closure and inserted inside the pressure cavity. Based on calibration against a controlled clearance piston gage at approximately 10,000 atm, the estimated error in the pressure measurement was +2 pct. Assuming the nonlinearity in the pressure coefficient of resistivity between 10,000 and 28,000 atm to be not greater than 1 pct, then the estimated error in the range of the I-II and 11-111 transitions was +3 pct. B) specimen Material and Preparation. The bismuth utilized throughout this investigation was of

Jan 1, 1964

By M. R. J. Wyllie, F. Morgan, P. F. Fulton

The importance of formation factor, F, not only in electric logging but as a fundamental rock parameter has recently been stressed.',: The desirability of investigating the range of variation of the resistivity index exponent, n, in the relationship I = S ;", where I is the resistivity index and Sw the water saturation as a fraction of the void volume of a porous medium, has also been urged.3 The magnitude and variation of n with saturation and rock texture is a subject not only of theoretical interest but also one of prime importance in the interpretation of electric logs. A simple technique has recently been developed which enables both F and u to he measured with high accuracy and which may also find acceptance as a convenient method for the determination of irreducible saturation attainment in the restored state method of core analysis. Experience has taught that reproducible measurements of F are possible only if the resistance measuring electrodes are so arranged with respect to a plane face on a porous medium that they are able to make electrical contact with substantially all entry pores in that plane. In practice this may be achieved by using a platinized-platinum gauze electrode backed by some absorbent material (such as felt) which has been saturated with a fluid identical with that used to saturate the porous medium. Applicatiorl of pressure to the electrode and absorbent material then forces the gauze against the plane face of the porous medium and simultaneously squeezes saline solution through the meshes of the gauze. By this means the electrode is in continuous aqueous contact with all pores and satisfactory and reproducible low resistance contact with the porous medium is achieved. Clearly this method, although satisfactory for measurements of F, cannot be applied to the making of continuous resistance measurements on a porous medium while capillary pressure desaturation is being carried out. However, accepting the principle that for satisfactory results electrical contact must be made between a measuring electrode and all pores adja- cent to that electrude, methods of bringing electrodes into intimate contact with the surfaces of porous media were investigated. Two methods were ultimately found to be satisfactory: in the one, the metal electrode is formed on the required portion of the porous medium by the use of a metal spray gun, while in the second the electrode is painted on with an ordinary camel's hair brush. The first method has the advantage of permitting the use of any metal which can be sprayed, but has the disadvantage of requiring rather elaborate and expensive equipment. The second method is presently limited to silver electrodes although in principle other metals, e.g. platinum or gold, could be used. Moreover, the method is so simple and cheap, and has been found to be so satisfactory that it will be described in some detail. The core being investigated is cut into a right circular cylinder and is extracted and dried in the usual manner. The ends are then lightly painted with silver conducting paint* of the type used in printed electrical circuits. The quantity of paint used is not critical but the recommended, minimum compatible with entirely coating the core ends is recommended, particularly on the end that contacts the barrier. The core is then dried at atmospheric temperature for one hour or for shorter periods at any suitable elevated temperature up to about 110°C. It will be found that silver coatings so prepared are not only strongly adherent but also permeable and the core may be the core may be desaturated by the ordinary capillary pressure technique through one of the coated faces. The same permeability is characteristic also of thin metal coatings formed using the spray-gun technique. An ordinary Lucite capillary pressure desaturation cell has been adapted to a form suitable for measuring the resistivity of the saturated silver faced cores both at 100 per cent saturation (i.e., F) and at intermediate saturations down to the irreducible minimum. This has been achieved as follows: A Coors porcelain barrier, having a displacement pressure of c 30 psi was grooved across a diameter. Dimensions of this groove were c 1 mm deep and 1 mm wide at the top. The groove was then painted thickly with silver conducting paint, the paint in the groove being extended lightly over the edges of the groove for a distance of c 1 mm on each side. A 30 gauge silver wire was then arranged in the groove in a form of a spring bow, each end of the silver being held at diamet~ically opposite ends of the groove by means of plastic cement. The arc of the bow at its highest point was arranged to be a millimeter or so above the face of the barrier, while one end of the bow wire was led by means of a pressure-tight connection through the wall of the capillary pressure cell. The groove in the barrier was then Surrounded by suitably cut portions of Kleenex in the conventional manner so as to ensure capillary continuity from core to barrier, and the core placed on the barrier. The weight of the core distorted the silver spring bow and good electrical contact was thereby made between the outside of the cell and the lower painted silver electrode. Electrical connection to tile top painted silver

Jan 1, 1951

By J. R. Bell, W. J. Childs, J. H. Bucher, G. A. Wilber

A technique for determining recrystallization times as short as 0.10 sec was developed utilizing the "Gleeble", a commercially available testing system designed for the study of short-time, high-temperaLure themal and mechanical processes. The procedure consisted of heating a small tensile specimen to a given temperature of hot deformation, loading to a given reduction in area, unloading, delaying various intervals at temperature, and then reloading- to failure. The magnitude of the ultimate load obtained upon reloading decreased with delay lime as recrys-lallization proceeded. The technique was applied to austenite recrystallization in AISI 1010 and AISI 1010 uith 0.02 pct Cb steels. For each steel the reduction in area given the specimen on the first pull was mainlairred at 30 ± 5 pct and recrystallization times deterntined at various temperatures. The results indicaled a significantly slower rate of recrystallization for the columbium-modified composition, suggested the presence of- a recovery stage in the softening process , and indicated a greatly increased softening rate at a temperatuve where significant allotropic transformation to a partially ferritic Structure could occur. In recent years increasing attention has been paid to the fact that the process of recrystallization of austenite deformed at elevated temperatures is far from instantaneous at many practical hot-working temperatures.1-3 This realization has given rise to such terms as hot cold-working1 or warm-working,2 These terms generally describe processes where the recrystallization rate at the temperature of deformation is slow enough to have an appreciable effect on mechanical properties despite a relatively high deformation ternperature. The mechanical properties of interest can be either the properties at the deformation temperature as in hot-workability studies4 or the room-temperature properties after cooling as in the many recent studies of various thermomechanical processes172 where heat treatment and deformation are intentionally combined to give a unique set of room-temperature properties. Because of this interest in processes where the austenite recrystallization kinetics can be an important variable, the development of quantitative methods of following the course of short-time, high-temperature recrystallization has received increasing attention.l,3,5 The experimental methods to date have, in general, relied upon rapidly deforming the austenite, holding at temperature for various brief intervals, quenching as G.A.WILBER and W. J. CHILDS, Members AIME,are Research-Fellow and Professor, respectively, Rensselaer Polytechnic Institute, Troy, N. Y. J. R. BELL and J. H. BUCHER, Member AIME, are Research Engineer and Research Supervisor, respectively, Graham Research Laboratory, Jones & Laughlin Steel Co., Pittsburgh, Pa. Manuscript submitted March 13, 1968. IMD. rapidly as possible, and then using room-temperature measurements to follow the recrystallization process. Although such methods can be successfully applied to certain alloy steels, the existence of the allotropic transformation during cooling of plain-carbon or low-alloy steels tends to obscure the results. Thus, such room-temperature measurements as hardness and X-ray line widths do not correlate well with the extent of austenite recrystallization before quenching,5 and results based on room-temperature microstruc-tural observations are dependent upon the success in correlating the observed structure with the prior aus-tenitic grain structure.1,3,5 The purpose of the present work was to develop a quantitative method for the determination of short-time, high-temperature recrystallization rates, based on measurements made at the temperature of deformation. EXPERIMENTAL TECHNIQUE The basic technique consisted of heating a small tensile specimen to a given temperature of hot deformation, loading to a given reduction in area, unloading, delaying various intervals at temperature, and then reloading to failure. The data were obtained in the form of traces of load and elongation as a function of time. Due to the high deformation temperature, the strain hardening introduced during initial loading was progressively annealed out with holding time after unloading and the loads obtained upon reloading decreased as this softening proceeded. Although the value of the second load at any Consistent point On the load-elongation curve could have been used as a measure of the degree of softening, the most convenient to use was the ultimate load. The softening indicated by the decrease in the second ultimate load with time is essentially a process of annealing of cold-worked material at a high deformation temperature. Although some recovery grain growth may contribute to such a softening process, it is generally considered that the major softening which must take place to achieve complete removal of substantial Strain hardening will occur by the formation of new, stress-free grains. As the results of this work indicate that essentially complete removal of strain hardening did in fact occur. the primary softening process will be attributed to recrystallization, and specific reference made where it appears that other mechanisms may be contributing to the total observed softening. It would, of course, be of interest to attempt to correlate the results of this work with the actual austenite fraction recrystallized as determined by other techniques. This was not attempted in the present work because it would have required running a large number of additional specimens and, as discussed previously, there is limited assurance that the results would accurately reflect the prior austenite fraction recrys-

Jan 1, 1969

By M. R. J. Wyllie, F. Morgan, P. F. Fulton

The importance of formation factor, F, not only in electric logging but as a fundamental rock parameter has recently been stressed.',: The desirability of investigating the range of variation of the resistivity index exponent, n, in the relationship I = S ;", where I is the resistivity index and Sw the water saturation as a fraction of the void volume of a porous medium, has also been urged.3 The magnitude and variation of n with saturation and rock texture is a subject not only of theoretical interest but also one of prime importance in the interpretation of electric logs. A simple technique has recently been developed which enables both F and u to he measured with high accuracy and which may also find acceptance as a convenient method for the determination of irreducible saturation attainment in the restored state method of core analysis. Experience has taught that reproducible measurements of F are possible only if the resistance measuring electrodes are so arranged with respect to a plane face on a porous medium that they are able to make electrical contact with substantially all entry pores in that plane. In practice this may be achieved by using a platinized-platinum gauze electrode backed by some absorbent material (such as felt) which has been saturated with a fluid identical with that used to saturate the porous medium. Applicatiorl of pressure to the electrode and absorbent material then forces the gauze against the plane face of the porous medium and simultaneously squeezes saline solution through the meshes of the gauze. By this means the electrode is in continuous aqueous contact with all pores and satisfactory and reproducible low resistance contact with the porous medium is achieved. Clearly this method, although satisfactory for measurements of F, cannot be applied to the making of continuous resistance measurements on a porous medium while capillary pressure desaturation is being carried out. However, accepting the principle that for satisfactory results electrical contact must be made between a measuring electrode and all pores adja- cent to that electrude, methods of bringing electrodes into intimate contact with the surfaces of porous media were investigated. Two methods were ultimately found to be satisfactory: in the one, the metal electrode is formed on the required portion of the porous medium by the use of a metal spray gun, while in the second the electrode is painted on with an ordinary camel's hair brush. The first method has the advantage of permitting the use of any metal which can be sprayed, but has the disadvantage of requiring rather elaborate and expensive equipment. The second method is presently limited to silver electrodes although in principle other metals, e.g. platinum or gold, could be used. Moreover, the method is so simple and cheap, and has been found to be so satisfactory that it will be described in some detail. The core being investigated is cut into a right circular cylinder and is extracted and dried in the usual manner. The ends are then lightly painted with silver conducting paint* of the type used in printed electrical circuits. The quantity of paint used is not critical but the recommended, minimum compatible with entirely coating the core ends is recommended, particularly on the end that contacts the barrier. The core is then dried at atmospheric temperature for one hour or for shorter periods at any suitable elevated temperature up to about 110°C. It will be found that silver coatings so prepared are not only strongly adherent but also permeable and the core may be the core may be desaturated by the ordinary capillary pressure technique through one of the coated faces. The same permeability is characteristic also of thin metal coatings formed using the spray-gun technique. An ordinary Lucite capillary pressure desaturation cell has been adapted to a form suitable for measuring the resistivity of the saturated silver faced cores both at 100 per cent saturation (i.e., F) and at intermediate saturations down to the irreducible minimum. This has been achieved as follows: A Coors porcelain barrier, having a displacement pressure of c 30 psi was grooved across a diameter. Dimensions of this groove were c 1 mm deep and 1 mm wide at the top. The groove was then painted thickly with silver conducting paint, the paint in the groove being extended lightly over the edges of the groove for a distance of c 1 mm on each side. A 30 gauge silver wire was then arranged in the groove in a form of a spring bow, each end of the silver being held at diamet~ically opposite ends of the groove by means of plastic cement. The arc of the bow at its highest point was arranged to be a millimeter or so above the face of the barrier, while one end of the bow wire was led by means of a pressure-tight connection through the wall of the capillary pressure cell. The groove in the barrier was then Surrounded by suitably cut portions of Kleenex in the conventional manner so as to ensure capillary continuity from core to barrier, and the core placed on the barrier. The weight of the core distorted the silver spring bow and good electrical contact was thereby made between the outside of the cell and the lower painted silver electrode. Electrical connection to tile top painted silver

Jan 1, 1951

By Raymond C. Boettner

The present work had for its purpose: 1) the identification of crack nucleation sites in AISI 4340, quenched to martensite and tempered over a range of 'temperatures; and 2) the comparison of fatigue processes in AISI 4340 with processes observed previously in pure metals From constant def1ection-bending fatigue tests, martensite boundaries were identified as the favored crack nucleation sites in quenched and tempered AISI 4340. It, also, was concluded that the fatigue processes operating- in this lous-alloy steel were similar to Processes observed in pure tnetals. ALTHOUGH much engineering data has been accumulated on the fatigue properties of quenched and tempered martensitic steels,' fatigue as a process is not as well understood in martensite as it is in pure metals.' Important features of the fatigue process, such as the identity of the nucleation sites, have not been determined in the commercially important high-strength low-alloy structural steels. The present work had for its purpose: 1) the identification of crack nucleation sites in a low-alloy steel, i.e., AISI 4340, which had been quenched to martensite and tempered over a range of temperatures; and 2) the comparison of fatigue processes in the AISI 4340 with processes observed previously in pure metals. This comparison of the fatigue processes in the different tempers was restricted to the high-strain low-cycle part of the S-N curve. Under these test conditions, previous work on a number of metals has shown that a large number of cracks are nucleated in less than 30 pct of the fatigue life.3 Furthermore, crack nucleation sites are not restricted to inclusions but are also associated with intrinsic structural characteristics of the metal. MATERIAL A 20-lb ingot of vacuum-melted AISI 4340 (for composition see Table I) was hot-rolled to 1-in.-diam rod and then cold-rolled to a 1-in.-wide strip, 0.08 in. thick. Fatigue specimens, see insert of Fig. 1, were machined from the strip with the long dimension parallel to the rolling direction. m this orientation, the stringers of 1 to 2 p inclusions present in the sheet lay parallel to the stress axis in the specimens. The specimens were austenitited at 2050°F in order to obtain a large prior austenite grain size, i.e., 2 mm, which facilitated the subsequent identification of the prior austenite boundaries. A helium atmosphere was used to minimize decarburization. After austenitiza-tion at 2050°F, the specimens were transferred to a 1450°F furnace so that specimen distortion was held to a minimum in the subsequent oil quench. Previous work4 indicated that refrigeration in liquid nitrogen prior to tempering reduced the percentage of retained austenite in the quenched specimens to less than 5 pct. Tempering was carried out in air over the temperature interval of 200°to 800°F to produce a range of mechanical properties, Table I. The preparation of the fatigue specimen was completed by grinding about 0.005 in. from each surface and electropolishing in a chrome trioxide-acetic acid solution for 30 min. Examination of etched cross sections of specimens prepared in this fashion showed the foregoing specimen preparation to be adequate for the removal of the decarburized layer present after the heat treatment. Transmission electron microscopy showed that the as-quenched microstructure of this alloy consisted of a mixture of martensite plates containing either a high density of dislocations or microtwins. Previous work5'6 indicated that in the course of oil quenching autotem-pering resulted in the formation of E carbide on the martensite and microtwin boundaries. Tempering for 2 hr at temperatures up to about 400°F resulted in further precipitation of the E carbide. Finally, at about 400°F, cementite began to replace the E carbide on the martensite and microtwin boundaries in addition to forming a Widmanstatten structure within the plate matrix. EXPERIMENTAL S-N curves were obtained using electropolished specimens cycled at 1800 cpm as cantilever beams in fully reversed bending at selected constant deflections. The deflections were translated into surface strains by means of a calibration curve obtained through the use of strain gages. An argon atmosphere was used to minimize environmental effects. To investigate the development of fatigue slip bands, the specimens of the different tempers were unidirec-tionally bent to a surface strain of 0.005 to 0.007, photographed to record the location and appearance of slip bands so introduced, and then cycled to failure

Jan 1, 1968

By K. G. Kreider, J. H. Brophy, J. Wulff

The technology of nickel-activated sintering of tungsten powder has been successfully applied to the densification of plasma-sprayed tungsten. Nickel was added by infiltration in a zinc solution followed by evaporation of the solvent. After sintering one hour at 1300°C density 95 pct of theoretical and transverse rupture strength of 74,000 psi were obtained. Shrinkage was found to be anisotropic and the mechanism of densification was comparable to that found in the nickel-activated sintering of tungsten powder. 1 HE use of a plasma spray gun for the fabrication of massive tungsten parts has become increasingly interesting. Applications now exist where a deposit in the as-sprayed condition is satisfactory. However, these deposits are generally characterized by a lamellar anisotropic microstructure containing 15 pct porosity of which, typically, two-thirds is open to the surface. Mechanically, the as-sprayed deposits fail at relatively low stress levels with a biscuit-like fracture. As a result of these problems the possibility of improving structure and strength by sintering treatments subsequent to spraying is particularly attractive. Preferably this sintering treatment should be adaptable to large bodies of sprayed metal. The similarity between the as-sprayed tungsten structure and that of a powder compact suggests that the relatively low-temperature activated sintering technique1 might be profitably employed in the densification of plasma-sprayed tungsten. It was the purpose of the present investigation to develop a technique for introducing the nickel-activating agent into the sprayed structure, to evaluate the amount and mechanism of densification obtained as a function of time and temperature, and to obtain an indication of the relative strength before and after sintering. EXPERIMENTAL PROCEDURE Powder used for spraying was purchased from the Wah Chang Corp. in several size fractions ranging from an average size of 4 to 150 . These powders were sized further for an explicit study of the influence of average feed size on densification. All powders were dried at 200°C before use. Spraying was accomplished with a Plasma Flame unit manufactured by Thermal Dynamics Corp. Several modifications of the unit were helpful in conducting the investigation. A variable speed auger feed mechanism coupled with the carrier gas mecha nism facilitated the use of fine particle sizes. A coil of ten turns of copper tubing in series with the arc power and concentrically would around the nozzle improved nozzle life and extended the range of operating currents available. The function of the auxiliary coil was to cause the arc to spin and to prevent impingement at only one point in the nozzle. Normally air sprayed deposits were made with an arc maintained at 400 amp at 50 to 70 v. The arc was blown by a gas mixture containing from 5 pct H, 95 pct N for the finest powder feed sizes ranging to 20 pct H, 80 pct N for the coarsest size. The flow rate was maintained at 100 cu ft per hr NTP through a nozzle of 0.25 in. ID. When apraying in air, the powder stream was directed toward an aluminum substrate for ease of mechanical removal of the deposit. The substrate was cooled by diverting the plasma flame with an air jet, and a second jet was directed on the deposit surface. In this configuration a gun-to-work distance of 2 to 3 in. was found to be satisfactory. Fig. 1 represents a typical as-sprayed deposit micro-structure. Laboratory studies of protective atmosphere spraying were carried out in cylindrical chamber 8 in. in diam by 18 in. in length. In operating the nozzle attached to such a chamber, particular care was required to avoid nozzle burn out due to reduced gas flow. The structure and density of the chamber sprayed deposits varied over wide ranges depending on substrate temperature. For the purposes of this investigation, flat deposits were made approximately 2 in. sq by 3/8 in. thick. From these deposits individual samples were cut an ground to a rectangular shape typically 1 1/2 in. by 1/8 in. sq such that the long dimension was perpendicular to the spraying direction. For the study of shrinkage anisotropy deposits up to one inch thick were produced. From these, rectangular samples were cut having a longer dimension parallel to the spraying axis. Prior to the addition of activating agent, the samples were deoxidized in hydrogen at 800°C for 20 min. No detectable dimensional or microstructural change was observed after this treatment. The addition of nickel was accomplished by infil-

Jan 1, 1963

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970

By Charles Barrett

RECRYSTALLIZATION textures-the orientations of grains after recrys-tallization-have been studied extensively not only because of their metallurgical importance but also because of the information they yield regarding the atomic movements during recrystallization. Recrystallized grains must possess the same orientations as the submicroscopic nuclei from which they have grown, and thus they offer a direct road by which experimenters can penetrate the submicroscopic realm. Many perplexing results have come of these studies, but one of the most striking has been the apparent difference in behavior between single crystals and polycrystalline grains. For example, Burgers and Louwerse have shown&apos; that when single crystals of aluminum are deformed by compression and are recrystallized (at 600° C.) the new grains appear with orientations that are different from the orientations of the deformed crystal in which they grew; but polycrystalline specimens, on the other hand, appear to have a [110] fiber texture both before and after recrystal-lization and thus to retain their texture during recrystallization. This apparent difference between the habits of single crystals and small grains is the subject of the first part of the present research and has been explained by findings reported herein. A similar situation appears to exist for aluminum when elongated or drawn into wires, for single crystals alter their orientation2,3 and polycrystalline wires retain their texture 4,1 6 upon recrystallization after elongation (at least with high-purity alumi-num), and it is possible that the explanation found in this paper for compression can be extended to cover elongation and other types of deformation as well. The second part of this paper deals with the theory of recrystallization textures. In the most successful theory for aluminum recrystallized after compression,1 much weight is given to the orientation of highly stressed nuclei in the deformed material. Taylor&apos;s "local distortions" are assumed to exist along the slip planes where displacement has occurred, consisting of fragments rotated in a specific way with reference to the slip plane and slip direction; namely, about an axis lying in the slip plane perpendicular to the slip direction. 1,7,8,9

Jan 1, 1940

By Hugh H. Waesche

Of all the military services, the Signal Corps is the most concerned with piezoelectric minerals because of its function as a supply service to the strategic and tactical military forces. Consequently this paper is written from the point of view of one associated with that organization. The Signal Corps is responsible for the research, development, and supply of communications, radar, and components to the using services of the Department of the Army and to some extent the Other branches of the National Defense Department. Their work therefore includes the study of the sources* characteristics, and application of quartz and other piezoelectric materials. These materials have become a vital consideration in strategic planning and are essential for efficient tactical operation by all the Armed Forces. The Signal Corps at the beginning of world War 11 Was respon-sible for both Army Ground and Air Force electronic equipment. Since that time this Army service organization has probably done more in the development of frequency control devices using piezoelectric materials than any other group. The U.S. Department of the Interior, Bureau of Mines, Minerals yearbook of 1945, shows that during the four war years, 1942 through 1945, 9,598,-410 Ib of quartz crystal were imported for all uses and of this total, 5,168,000 lb were consumed to produce 78,320,-000 crystal units for electronic application. Other government records confirm these data which conclusively show that approximately 53 pct of the crystalline quartz imported was consumed in the production of electronically applied quartz crystal units. It may be assumed that some effort was made to maintain a stockpile over demands for all purposes. and this would mean that the actual percentage of quartz used electronically was considerably over the 53 pct figure. These data only emphasize that electronic application of crystalline quartz was the greatest requirement, and per- haps the actual value in this application to national defense is many times greater in importance than is apparent on first inspection. Current electronic research and development programs of the Armed Forces are planned around the fundamental use of piezoelectric minerals for frequency control and this at present, at least, means quartz. Definition and Early Development The word piezoelectricity is formed from combination of the Greek word "piezein". meaning "to press," and "electricity." It is that property shown by numerous crystalline substances whereby electrical charges of equal and opposite value are produced on certain surfaces when the crystal is subjected to mechanical stress. It appears to be intimately associated with the better known property, pyro-electricity and in fact, the two may be manifestations of the same phenomeuon. This property was discovered by Pierre and Jacques Curie in quartz, tourmaline, and other minerals in 1880 while studying the symmetry of crystals. The converse effect, that is, mechanical strain in the crystal when placed in an electrical field, was predicted by the French physicist, G. Lippman, in 1881, and verified by the Curies almost immediately. As has been the case with many discoveries of similar character in the basic sciences, not much attention was paid to this property for man)- years except as an entertaining curiosity. Between 1890 and 1892 a series of papers was published by W. voigt in which the theoretical physical properties were put into mathematical form. The first practical application of piezoelectricity occurred during World War I when professor P. Langevin of France used quartz mosaics to produce underwater sound waves. The same mosaics were used to pick up the sound reflections from submerged objects which were in turn, amplified by electronic means and used to determine the distances to such objects. This device was intended for use as a submarine detector but development was not completed in time for war service although it was used later for determining ocean depths. About the same time, A. M. Nicholson, of Bell Telephone Laboratories, developed microphones and phonograph pickups using Rochelle salt crystals. A major step in the application of piezoelectric quartz came in 1921, when professor W. G. Cady, of wesleyan university, showed that a radio oscillator could be controlled by a quartz crystal; from that date, this use of quartz has increased steadily, reaching its peak in world war 11 as is shown by the figures previously given. Essentially all American electronic equipment for communication, navigation, and radar, utilized quartz crystals for the exacting frequency control required. Crystalline Minerals with piezoelectric Properties QUARTZ Hundreds of piezoelectric crystalline materials are known, most of which are water soluble. Of these, quartz appears to be without a peer for electronic frequency control. Unfortunately, the quartz must be of superior quality. It must be free of mechanical flaws, essen-tially optically clear, free of both Brazil and Dauphiné twinning and must be, for average uses, over 100 g in weight. Because of these stringent requirements, raw quartz of the quality desired is of rare occurrence. In addition to quartz, several other naturally occurring crystalline materials are known to have the piezoelectric property and could perhaps be substituted for quartz in some applications. These

Jan 1, 1950

By J. C. Bierlein, R. A. Dodd

Endurance strengths at 10&apos; cycles, fatigue-hardening rates, and endurance strength/0.2 pct proof stress ratios have been determined jbr a range of Cu(Ni), Cu(Si), and S.R.0. Cu(Au) solid solutions. Some douht is cast on simple cross slip models of fatigue hardening in view of opposite composition dependencies of hardening displayed by Cu(Si) and Cu(Au). The temperature dependencies of hardening also are the opposite of predictions made on the basis of a cross slip model. A correlation apparently exists between the fatigue strength/0.2 Pc~ proof s1.re.s~ ratios and rates of fatigue hardening. An increase in PS/PS due to alloying or temperature change is accompanied by a decrease in hardening rate, and vice versa. In recent years there has been much interest in the determination of the dislocation structure of fatigued metals and alloys. The accumulated evidence, e.g., Refs. 1 to 5, suggests that the structure may be dependent on the stacking fault energy, 7, of the fatigued metal in the same way that fatigue hardening rates have also been shown to apparently depend on u .6&apos; 7 The above research followed the various earlier theories relating crack nucleation to ease of cross slip, e.g., Refs. 8 to 131 so "ggesting that y may indeed be the parameter of principal significance in all facets of the fatigue process. However, comparatively little attention has been paid to correlating engineering fatigue data with observations of the above type. Certainly, it would be useful if potential engineering fatigue performance could be assessed from a knowledge of easily determined alloy properties, and the present research originated from this standpoint. TO investigate the widest Possible range of 7 would require the use of two solvent bases, e.g., aluminum and copper, but a reasonable coverage can be provided by copper-based solutions alone. Therefore, it was decided to work with Cu(Ni) and Cu(Si) solid solutions, the approximate stackillg fault energies of which are given in Table I. The y range extends from low, Cu(7.5 at- Pet Si), to moderately high in Cu(2-5 at. ~ct ~i) and two of the Cu(Ni) alloys. The values listed in Table I should be regarded as qualitative only, being derived as follows. Dillamore and smallman14 quote a value of 85 i 30 erg.cm-2 for the stacking fault energy of pure copper, based on an earlier value due to Howie and swannl5 corrected by Brown&apos;s formula.&apos;&apos; Since the ratios (alloy)h(pure copper) have been reported17,18 for Cu(Ni) alloys containing up to 30 pct Ni, approximate ) values for these alloys can be computed, and a rough estimate of 7 for Cu(50 at. pct Ni) obtained by extrapolation. The relatively low y value obtained in this way for Cu(50 at. pct Ni) coincides with the observation of Nakajima19 that the stacking fault probability is a maximum at this composition. Likewise, the y values for the three ~u(~i) alloys are estimates based on values given by Swann and Nuttingo corrected on the basis Of Brown&apos;s estimate that the true 7 values are probably 2.3 times greater than those originally computed. In addition to the above alloys it was decided to investigate short-range ordered (s.R.O.) CU(AU) alloys containing up to 25 at. pct Au. This last alloy has been shown to have a well-defined planar arrangement of dislocations when deformed,21,22 probably due to cross slip being restricted by the S.R.O. Engineering fatigue data was to be represented by the determination of endurance strengths, and these were to be correlated with fatigue hardening and mechanical property data. EXPERIMENTAL I, order to study the desired properties and property changes, the following alloys were prepared: Cu(2.5 at. pct Si), Cu(5.0 at. pct Si), Cu(7.5 at. pct Si), Cu(5.0 at. pct Ni), Cu(25.0 at. pct Nil, Cu(50.0 at. pct Ni), Cu(5.0 at. pct AU), Cu(15.0 at. pct AU), Cu(25.0 at. pct AU). The copper and gold were zone-refined, while the silicon was semiconductor grade. The nickel was of 99.95 p,t. purity.* All alloys were induction-melted in a *Kindly supplied by the International Nickel co. helium atmosphere, appropriate precautions being taken to avoid segregation in the Cu-Au series. Rod stock was obtained by rolling and swag,ng. A few Bridgman single crystals were grown for fatigue-hardening studies, but most material was machined into polycrystalline fatigue speciments of the design shown in Fig. 1, and into polycrystalline tensile and fatigue-hardening specimens of simple cylindrical design. All specimens except Cu(Au) were annealed; the latter were quenched from above T, to produce short-range order. A few of the quenched alloys were examined for long-range order by step-scanning over

Jan 1, 1969

By E. A. Ernst, N. F. Carpenter

The benefits derived from an acidizing treatment are a function of the penetration achieved by the acid before complete spending. Additional penetration may be achieved by (1) controlling acid leak-08 into formation pores in the channel faces, and (2) retarding the reaction rate of the acid. A recently developed chemical additive consists of a synthetic polymeric material which absorbs hydrochloric-acid solutions, when suspended therein, swelling up to 40 times its original volume. These swollen particles have the ability to deform and seal-08 formation pores, providing fluid-loss control. In addition, they provide a diffusion barrier between the fracture face and the acid solution, prolonging the spending time of the acid. Field applications of this new technique have shown promising results. A method of conducting acid fluid-loss tests, using carbonate cores, is believed to provide fluid-loss data that are more representative of formation conditions than the conventional filter-paper determinations. INTRODUCTION The concept of oilwell acidizing has changed since its first commercial application, 30 years ago. Originally, it was visualized that the acid penetrated thousands of tiny pores and flow channels in the matrix rock, enlarging them by dissolving the carbonate walls. The resultant permeability increase was assumed to be the responsible factor in increasing production from the well. Recent laboratory studies,&apos; however, have shown that this does not provide the complete picture. Although this type of individual pore penetration by the acid does take place during acid "soaks", designed to overcome "skin effect" due to mud invasion in the immediate vicinity of the wellbore, many years of experience have shown that considerable pressure is required to attain any appreciable injection rate into the fine capillary pores of the rock. During most acidizing treatments, the bottom-hole pressure build-up due to the restriction of flow into the formation exceeds the "breakdown" pressure of the rock so that a fracture is induced. In most cases, such fractures open up along natural, incipient fissures and zones of weakness in the rock and, therefore, tend to follow the natural stress pattern of the rock—whether it be horizontal, vertical or inclined. Because of the comparatively greater permeability of the channel in relation to that of the matrix, the bulk of the acid volume is diverted into the newly opened fracture. Here it quickly penetrates the formation, opening and ex- tending the fracture in much the same manner as a conventional fracturing fluid. Unlike the fracturing fluid, however, most acidizing solutions contain no propping agent; thus, the open fracture will again close when the injection pressure is relieved. Laboratory studies2 have shown that in many cases the etching of the fracture faces, resulting from the reaction between the acidizing solution and the carbonate rock, is nonuniform due to the heterogeneity of the rock structure. As a result, the two fracture faces no longer match when pressure is released, and support pillars and intermediate voids remain, forming a high-conductivity channel for well fluids. Unfortunately, this is not true over the entire area of the fracture, but only over that portion of the fracture where the rock has been partially dissolved by the acid. The acid solution spends as its travels away from the wellbore; once it has completely spent, even though it may provide additional mechanical fracture extension, no additional benefit due to etching of fracture faces can be expected. Studies of acid reaction rates under formation conditions,3 observing the effect of different variables upon spending time, have shown that the reaction was often so rapid that very little penetration of the formation occurred before the acid was spent. Study was undertaken to devise methods of increasing the penetration of the acid before spending, so as to provide greater benefit from the acidizing treatment by etching a greater portion of the fracture faces. Several techniques were devised to accomplish this purpose. First, chemical additives were developed which were designed to retard the reaction rate of the acid, causing it to penetrate a greater distance from the wellbore before finally becoming spent. Another method was to increase the injection rate of the acid. However, it was found that the resultant increased shear tended to accelerate the reaction rate of the acid, partially offsetting the benefits of the higher injection rate insofar as achieving increased penetration before spending was concerned.&apos; Another approach to the problem of achieving increased penetration was the development of fluid-loss additives for acid solutions, which would minimize the volume of acid lost into formation pores in the fracture faces and provide maximum fracture extension for the volume of acid injected during the treatment. The use of fluid-loss additives is now considered the most effective method of providing maximum fracturing-fluid efficiency.~ Unfortunately, this latter technique does not solve the problem of rapid reaction rate, with consequent limitation of the fracture area benefited by reaction with unspent acid. A newly developed acid additive overcomes many of these limitations by providing the dual benefits of fluid-loss control and mechanical retardation of acid reaction

By H. B. Probst

Mechanical twins were produced in zone-refined tungsten single crystals by explosive working at room temperature. These twins are parallel to (112) planes and have irregular boundaries rather than the classical plane twin boundaries. These boundaries aye grooved surfaces in which the grooves themselves are parallel to a <111> direction and the sides of the grooves appear to be par-allel to (110) planes. TWINS were produced in tungsten single crystals by explosive working at room temperature. These twins differ in character from any previously reported for tungsten; however, they are similar to those found in molybdenum after compression at -196°C.1 Deformation twins "resembling Neumann bands in ingot iron" have been observed in tungsten by Bech-told and Shewmon.2 This observation was made with sintered polycrystalline tungsten pulled in tension to fracture at 100°C and using a strain rate of 2.8 x 10-4 sec-1. More recently Schadler3 found deformation twins in zone-refined tungsten single crystals pulled in tension at -196"&apos; and -253°C. These tests were conducted using a strain rate of 3.3 x l0-4 sec-1, and the twin bands were found to be parallel to a (112) plane. Deformation twins in tungsten&apos;s sister metal, molybdenum, were observed by Cahn.4 These twins were produced by compressing small (0.7 mm) vapor-deproducedposited molybdenum single crystals at -183°C. The compression was performed &apos;by impact." By the use of precession X-ray techniques, Cahn was able to identify the twin plane as {112} and the shear direction as <1ll>. Mueller and Parker1 produced deformation twins in polycrystalline electron-beam-melted molybdenum by compression at -196°C. Their "loading rate" was 5000 psi per min which, judging from their stress-strain curve, corresponds to a strain rate of approximately 0.3 x 10-4 sec-1. These twin bands were found to be parallel to (1 12) planes; however, they differed in appearance from previously observed twins. In place of straight and parallel twin boundaries they were found to be irregular, jagged, and sawtoothed. The sides of the saw teeth were identified as (110) planes and irrational planes of a (111) zone. The twins observed in the present work in tungsten single crystals are similar in appearance to those of Mueller and Parker in polycrystalline molybdenum. The starting material used in this investigation was 3/16-in. diam commercial tungsten rod produced by powder-metallurgy techniques. This material was converted to a single crystal by the electron-bombardment floating-zone technique.= The process was carried out in a vacuum of 10-5 mm of Hg using a traversing speed of 4 mm per min. Segments (=2 in. long and 3/16 in. in diam) of two crystals (A and B) produced in this manner were studied. Crystal A received one zoning pass, while crystal B received two passes. The two crystals were explosively worked at Bat-telle Memorial Institute in the following manner. A 1/2-in.-thick layer of plastic was applied to the crystals to serve as a buffer in an attempt to prevent cracking. The composite, crystal and buffer, was then wrapped with 1/8-in.-thick DuPont sheet explosive EL506A2 and detonated in water at room temperature. Metallographic samples of the worked crystals were prepared, and back-reflection Laue X-ray patterns were obtained using unfiltered molybdenum radiation. RESULTS AND DISCUSSION Blasting the crystals as described above failed to prevent cracking. The crystals fractured into several fragments about 3/16 to 1/2 in. long; however, the fragments were of sufficient size to be useful for the subsequent study. The diamond pyramid hardness of the crystals after blasting was in the range 430 to 450 as compared with 340 for the as-melted material, which shows a definite hardening resulting from plastic deformation. These hardness values were obtained using a 1000-g load and taking readings only in sound portions of the crystals free of cracks. The crystals exhibited profuse twinning as shown in Fig. 1. No such structure is present in the as-melted condition. Most of these twins have jagged twin boundaries and are similar in appearance to those found in molybdenum by Mueller and Parker. The twins in both crystals were found to be parallel to {112} planes. This identification was made by using the conventional two-trace method. Subsequent efforts to describe these twins more fully were carried out on crystal A. If the longitudinal axis of crystal A is placed in the (001)-(011)-(Il l) basic triangle of the standard cubic stereographic projection, as in Fig. 2, then the two sets of twins shown in Fig. 1 are parallel to the (112) and (121) planes. Fig. 3 shows a schematic representation of a twin with jagged boundaries. This type of twin with a <111>

Jan 1, 1962

By R. L. Bell, T. G. Langdon

A technique was developed- for determining the grain strain, and hence the grain boundary sliding contribution, occurring during the high- temperature creep of a magnesium alloy, from the distortion of a grid photographically printed on the specimen surface. The results were compared with those obtained from measurements of grain shape, both at the surface and interrwlly, and it was concluded that the grain shape technique may substantially underestimate the grain strain and overestimate the sliding contribution due to the tendency for migration to spheroidize the grains. ALTHOUGH a considerable volume of work has been published on the role of grain boundary sliding in high-temperature creep, many of the estimates of Egb (the contribution of grain boundary sliding to the total strain) have been in error due to the use of incorrect formulas or inadequate averaging procedures.&apos; One of the most easy and convenient measurements from which to compute Egb is that of v, the step normal to the surface where a grain boundary is incident. Unfortunately, this parameter is also the one associated with the treatest number of pitfalls. Values of v have been used to calculate Egb from the equation: egb =knrVr [1] where k is a geometrical averaging factor, n is the number of grains per unit length before deformation, v is the average value of v, and the subscript ,r denotes the procedure of averaging along a number of randomly directed lines. If the dependence of sliding on stress were assumed, it would be possible, in principle, to calculate k from the known distribution of angles between boundaries and the surface. This in itself is difficult because the distribution depends on the history of the surface,&apos; but the problem is even further complicated by the fact that v depends on other factors such as the unbalanced pressure from subsurface grains.3 However, the great simplicity of the measurement procedure for v makes it highly desirable that this problem of k determination should be overcome. In the present experiments, this was achieved by the use of an indirect empirical method in which the grain strain, eg, at the surface was determined by the use of a photographically printed grid. The assumption here is that the total strain, et, is simply the sum of that due to grain boundary sliding, egb, and that due to slip or other processes within the grains, eg. SO that: Et = Eg + Egb [2] Thus k is given by: In practice, it is customary to indicate the importance of sliding by expressing it as a percentage of the total creep strain; this quantity is termed y (= 100Egb/Et). The determination of Eg from a printed grid within the grains avoids the difficulties due to boundary migration which should be considered when the grain strain is calculated from measurements of the average grain shape before and after deformation. As first pointed out by Rachinger,4,5 however, this latter technique has the particular advantage that it can also be applied in the interior of a polycrystal. Recently, several workers have produced evidence on a variety of materials6-&apos;&apos; to support the observation, first made by Rachinger on aluminum,4,5 that 7 can be very high, 70 to 100 pct, in the interior, even when the surface value, determined from boundary offsets, is very much lower.10&apos;11 Although there have been criticisms both of the shortcomings of the grain shape technique&apos;&apos; and of the different procedures used to determine y at the surface,&apos; it seemed important to check whether measurements of sliding by grain shape gave values of y which were truly representative of the material. In the present experiments, grain shape measurements were therefore made both at the surface and in the interior for comparison with one another and with the independent measurements of grain strain using the surface grid technique. EXPERIMENTAL TECHNIQUES The material used in this investigation was Magnox AL80, a Mg-0.78 wt pct A1 alloy supplied by Magnesium Elektron Ltd., Manchester. Tensile specimens, about 7 cm in length, were prepared from a 1.27-cm-diam rod, with two parallel longitudinal flat faces each approximately 3 cm in length. The specimens were annealed for 2 hr in an oxygen-free capsule, at temperatures in the range 430° to 540°C, to give varying grain sizes, and, prior to testing, the grain size of each was carefully determined using the linear intercept method. This revealed that the grains were elongated -0.5 to 5 pct in the longitudinal direction. Testing was carried out in Dennison Model T47E machines under constant load at temperatures in the range 150" to 300°C. At temperatures of 200°C and below, tests were conducted in air with the polished flat faces coated with a thin film of silicone oil to prevent oxidation; at higher temperatures, an argon atmosphere was used. To determine v,, each test was interrupted at regular increments of strain and the specimen removed from the machine. At the lower strains, when v, was less than about 1 pm, measurements were taken on a Zeiss Linnik interference microscope;

Jan 1, 1969

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-B alloys has been measured up to the solubility limit for the formation of boron nitride. The activity coefficient of nitrogen increases with increasing boron content in the range 0 to 7 wt pct B. From experimen -tal data, values have been calculated for the B-N interaction parameter e3 at temperatures in the range 1550" to 1750°C. A value of 0.038 has been estimated for the boron self-interaction parameter eg at 1550°C. The standard free energy of decomposition of boron nitride into the elements dissolved in liquid iron has been determined to be: ?F° = 45,900 -21.25T in the range from 1550° to 1750°C. The nitride is assumed to be of composition BN. BORON nitride has an unusual combination of properties which make it appear attractive in a wide range of engineering applications. Some of its more important and most recent applications are in the nuclear area, particularly in connection with the liquid-metal cooled reactor concept now receiving considerable emphasis. Boron nitride has a high degree of stability at elevated temperatures. It also has excellent ma-chinability and the ease with which its crystals deform suggests applications as a lubricant. These properties stem from a hexagonal layer-type structure similar to the structure of graphite. One of its primary uses to date has been for seals in liquid-metal pumping systems. It is also used in nuclear reactors as an insulating layer to separate two solid metals which are not themselves compatible under the conditions of temperature and atmosphere in which they are used. Its inertness to liquid metals has also suggested use as a mold-release agent in casting processes. In addition to its excellent machinability and reported inertness to liquid metals such as iron, silicon, aluminum, copper, and zinc, boron nitride has high thermal conductivity and excellent thermal shock resistance. This combination of properties would make it appear ideal as a refractory crucible material for refining of high-purity liquid metals, for example high-quality steels. However, since it is known that concentrations of boron as low as 50 ppm can have a marked effect on the physical properties of certain steels,&apos; in particular on the creep and stress-rupture properties, an investigation was undertaken to define accurately the chemical equilibrium among boron, nitrogen, and liquid iron in the range of steelmaking temperatures. EXPERIMENTAL PROCEDURE Two experimental approaches to this problem were employed: a Sieverts&apos; method and a quenching method. In the first method, the Sieverts&apos; technique was used to measure the equilibrium nitrogen solubility in liquid Fe-B alloys of 0 to 7 pct B as a function of nitrogen gas pressure over the melt. The solubility limit of the boron nitride phase formed was determined by the point of departure of the nitrogen absorption from Sieverts&apos; Law. This technique has been applied to liquid Fe-Ti alloys by Rao and parlee,&apos; to liquid Fe-A1 alloys by Evans and Pehlke,3 and to solid Fe-V alloys by Fountain and Chipman.4 In the second method a melt of liquid iron was held in a crucible of boron nitride under a known partial pressure of nitrogen gas. After thermodynamic equilibrium was attained, the melt was quenched in a stream of helium and then analyzed by wet-chemical methods for boron and nitrogen. The Sieverts&apos; apparatus used in the first method was essentially of the same design as the one described by Pehlke and Elliott.5 The charge materials were vacuum-melted high-purity iron (Ferro-vac E) supplied by the Crucible Steel Co. and -325 mesh boron powder supplied by Cooper Metallurgical Associates of Cleveland, Ohio. The boron contained less than 0.02 wt pct O, according to supplier&apos;s analysis. Recrystallized alumina crucibles were used to contain the melt. Examination of solidified melts showed these crucibles to be satisfactory with no evidence of any reaction or physical penetration of the crucible wall by the melt. The melt temperature was measured by a disappearing filament-type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diam sight hole in the crucible lid. The pyrometer was calibrated against the melting point of pure iron in the same apparatus, taking the emissivity of

Jan 1, 1964

By S. Feuerstein, L. Rice

The effect of low pressures on the flow and fracture behavior of molybdenum is described. For poly crystalline samples, room-temperature tensile tests indicate greater ductility under 10 Torr than under intermediate pressures up to and including atmospheric pressure (760 Torr). In addition, tests conducted at 760 Torr under atmospheres of air, dry nitrogen, and purified argon exhibited no apparent difference in mechanical properties. Critical tests involving baking in situ as well as those involving single-crystal deformation further imply that the ductility effect is a pressure-dependent phenomenon related only to the fracture process. This dependency is discussed in terms of adsorption and diffusion contributions. THE effect of very low pressures on material properties has heretofore been presumed to be important only for substances possessing relatively high vapor pressures at ambient temperatures. Research has therefore been concentrated primarily on organic solids and liquids, and in some instances on metals such as zinc and cadmium. Most vacuum-effect studies&apos; on the mechanical behavior of metals have been performed under conditions of either cyclic loading or creep rupture at elevated temperatures, i.e., over extended time periods. These studies were not restricted to high vapor pressure materials but also encompassed such metals as gold, copper, and nickel. Very little concern, however, was placed upon the importance of a vacuum environment on the mechanical behavior of metals subjected to a simple unidirectional deformation at ambient temperatures. A tension test is generally of short duration as compared to a creep test, and at room temperature vacuum effects if any would be expected to be surface-limited. In early 1963, Kramer and podlaseck2 reported a change in the bulk flow behavior of aluminum single crystals during room-temperature tension tests. The deformations were performed under pressure conditions of 760 to 3.4 X 10-8 Torr and indicated for the first time a vacuum surface effect contributing to the bulk tensile behavior of metal specimens. As a consequence, an experimental program was initiated in this Laboratory to study the effects of ultrahigh-vacuum conditions on the mechanical behavior of metals. The results of a preliminary study on poly-crystalline molybdenum3 revealed, unlike Kramer&apos;s observations of changes in the stress-strain behavior, only an increased ductility under ultrahigh vacuum. Flow behaviors were nearly identical for all tests re- gardless of pressure. This paper presents comprehensive results obtained in this area of research. 1) EXPERIMENTAL PROCEDURE Three material categories were used in this study: sintered and are-cast polycrystalline molybdenum of nominal purity 99.93+ pct and single-pass electron-beam zone-refined molybdenum single crystals having a nominal purity level of 99.99+ pct. The interstitial levels (weight percent) as determined by the Materials Testing Laboratories, Division of Magnaflux Corp., were as follows: sintered molybdenum (C— 0.005, H—0.0004, O—0.015, N—0.008); and arc-cast molybdenum (C-0.0038, H-0.0003, O-0.015, N-0.023). Single-crystal molybdenum obtained from Materials Research Corp. had a typical interstitial analysis of C-0.0015, H-0.00007, O—0.00045, and N-0.0001. Tensile specimens having a 5 mm diam by 50.8 mm length were prepared from these materials. An average grain diameter of 0.059 mm was obtained for the sintered specimens following a 4-hr, 1600°C heat treatment. Grain sizes from 0.019 to 0.149 mm were obtained in the arc-cast specimens following heat treatments from 1100° to 1600°C for 1 hr. This series of specimens was used exclusively for the grain-size effect studies. All samples were electrolytically polished in 97 pct sulfuric acid solution prior to testing. Experiments were performed at room temperature in an ion-pumped ultrahigh-vacuum system positioned in an Instron tensile machine, Fig. 1. A constant strain rate of 4.2 x 10-4 sec-1 as derived from crosshead displacement was assumed for the deformations. Starting vacuums ranged from 2 to 0.5 X 10-10 Torr. These pressure measurements were made using corrected values4 of an NRC Redhead gage. Comparative readings were also made against a G.E. triggered dis-

Jan 1, 1967