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By A. W. Ruff

In the last ten years large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now-prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. In the last ten years, large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. EXPANDING-GAS-BUBBLE THEORY There has been an outstanding change in the conception of how an explosive produces rock failure. The early theory which explained rock breakage was correct for some of the first force-producing agents such as quicklime. When a drillhole was filled with quicklime and water added, the material expanded and steam was generated. The expanding material and the steam exerted a slowly increasing pressure on the sides of the drillhole. The force broke the rock by splitting. Because a great quantity of gas was produced by the deflagration of gunpowder, the same process of the gas pressure splitting the rock was assumed to take place. Even after 80 years of use, the rock-breaking action of all high explosives was thought to be caused entirely by the expanding gas bubble which tore and split the rock. Fig. 1 shows a vertical section through an exploding spherical charge of high explosive. It illustrates the early theory which attributed the entire breakage to the expanding gas bubble. The basic idea of this theory is that the breakage started at the explosive charge and progressed toward the free face. REFLECTED-WAVE THEORY me expanding-gas- bubble theory has gradually been replaced by the reflected-wave theory. The reflected-wave theory explains rock failure by explosives in the following manner: The enormously high gas pressure in the drillhole produces fracturing of the rock on the sides of the drillhole. The fracturing around a 1 1/2-in. diam drillhole is usually confined to an area with about a 6-in. diam. In the fractured area, the pressure of the gas is reduced until the force on the walls is no longer capable of fracturing the rock. Although the gas pressure does not continue to fracture the rock, the pressure imposes a high impact stress on the wall rock. In addition, a pressure or seismic pulse is produced in the rock. The pulse is probably entirely a compression pulse when originally produced in the rock. But, with distance, part of the energy of the compression pulse is transformed into a tension pulse which follows the compression pulse. The explosive charges and burdens used in conventional mine blasting are such that the tension pulse of the original wave is probably too small to be considered in a practical evaluation of the theory. The compression pulse is transmitted through the rock with no associated fracturing.

Jan 1, 1961

By Henry A. Stiff, J. P. Hammond, A. B. Westerman, H. C. 195-000-000-014 Cross, and Lawrence E. Davis

The phases in Cr-Fe-Mo alloys have been investigated with homo-genization, aging temperature, composition range, and alloy addition as variables. Metallography, three X-ray methods, and hardness were used as methods of study. The behavior of s, M23,C8, and Z phase are reported for cornpasition range 60 pct Cr-15 to 25 pct Fe-15 to 25 pct Mo-<0.005 to 0.36 pct C with aging at 1400º to 2000°F. With 2 pct Ti, Tic and TiC-TiC are formed; with nitrogen Cr2N. THE recently developed class of chromium-base heat-resistant alloys shows appreciably higher strength than commercially used high temperature alloys. However, further developmental work is required to impart needed shock resistance and some degree of room-temperature ductility to these alloys. Extensive exploratory work on chromium-base alloys was begun in a program initiated by the War Metallurgy Committee of the National Defense Research Council at the Climax Molybdenum Co. in the early part of 1942.&apos; Alloys were sought for gas-turbine blades for use at 1600°F. A minimum of 5 pct elongation in the stress-rupture test was a requirement. From the Climax work, ternary alloys of chromium, iron, and molybdenum appeared to show the greatest promise as materials for gas-turbine blades. The composition line in the ternary diagram joining the 60 pct Cr-15 pct Fe-25 pct Mo and 60 pct Cr-25 pct Fe-15 pct Mo alloys was indicated as representing the most useful combination of strength and ductility.&apos; Strength increased while ductility decreased as molybdenum was raised in this composition range.&apos; The 60 pct Cr-15 pct Fe-25 pct Mo type alloy was thought to have the most suitable properties for gas-turbine blades.&apos; Concurrent with the study reported here, other investigations were being made on Cr-Fe-Mo alloys. The liquidus temperatures on a series of low carbon, ternary alloys were being determined, and isothermal sections drawn at 2370°, 2010°, and 1650°F (1300°, 1100°, and 900°C).2 Also, various methods of preparation and some mechanical and physical properties of chromium-base alloys, particularly the 60 pct Cr-15 pct Fe-25 pct Mo type, were being investigated., At the inception of the present program, only a limited study had been made of etchants for developing the microstructures of chromium-base alloys; X-ray analysis of the microconstituents had not been made. A review of the literature revealed that no phase-diagram work had been reported on the Cr-Fe-Mo system. Scope of Work The work on chromium-base alloys includes the following: 1—The development of etching methods for differentiating between the microconstituents; 2—The identification of microconstituents by X-ray diffraction methods; and 3—A comprehensive metallographic and hardness study after various heat treatments. The phases were studied by three standard X-ray techniques: 1—The block-sample focusing-camera method; 2—The powder-diffraction method on elec-trolytically separated residues; and 3—The powder-diffraction method on cold-worked aggregate samples. The results by the first two methods were correlated with the metallographic data. The third method was used largely to study conditions approaching equilibrium, since cold working prior to heat treating accelerated precipitation. Seven types of alloys were investigated: 50 pct Cr-50 pct Fe, 40 pct Cr-40 pct Fe-20 pct Mo, 55 pct

Jan 1, 1953

By A. E. Powers

YEARS of experience and research have shown that molybdenum, tungsten, and vanadium are among the most useful and effective elements in augmenting the high-temperature strength of heat-treatable, ferritic steels. Grün, for example, in conducting an early survey of the strengthening effects of various elements in annealed, low-carbon steel at 750° and 930°F (400° and 500°C), found molybdenum and vanadium to be the most effective.&apos; Holtmann comprehensively studied the strengthening effects of molybdenum and vanadium in quenched and tempered steels at 930°F as a function of microstructure and carbon content.&apos; He found creep strength to be related to the saturation of the austenite at the austenitizing temperature, such that strength is increased by alloying until the y loop is reached—the terminus of complete austenitization. Beyond this degree of alloying, the inability to heat treat will result in lower strength, at least for low and moderate creep temperatures. Tungsten, owing to higher cost than molybdenum, has been little used in ferritic high-temperature steels. As a result, very few investigations have been made of its high-temperature strengthening ability, and reliable data on its effectiveness are not available. Grün rated tungsten far less effective than molybdenum at 930°F (500°C) on a weight-percentage basis.&apos; However, Tammann has found that tungsten is as effective as molybdenum in raising the recrystallization temperature of iron. For this reason Smith, in a review of the subject, has advocated a re-examination of the influence of tungsten on the high-temperature strength of steel.&apos; In any study of the effects of alloying additions on high-temperature properties, recognition must be made of the many variables involved, some of which can be controlled but have been ignored in innumerable investigations of the past, and some of which are difficult or even impossible to control. One cannot, for example, assign a definite strengthening index to any one alloying element, for this will be dependent upon the microstructure (heat treatment and mechanical treatment), testing con- ditions (temperature, time, and stress), and the complete composition of the steel (accompanying alloying elements, impurities, etc.). One ever-appear ing variable, hardness or tensile strength at room temperature, may be eliminated by heat treating all of the alloys to a single hardness level. An attempt may be made to control the variable of primary quenched structure by oil or water quenching the test specimen. The control of such variables may not be possible in cases of widely varying compositions, but at least such deviations should be recognized. Material and Procedure The alloys, made as 30-lb ingots in an induction furnace, all had the same base composition of about 0.18 pct C, 0.85 pct Mn, and 0.48 pct Si. They were grouped as follows: Mo Group—Containing up to 5.2 pct Mo. W Group-Containing up to 6.0 pct W. V Group—Containing up to 3.3 pct V. Mo-V Group—Containing up to 2.7 pct Mo and up to 1.4 pct V. Mo-W Group—Containing up to 2.5 pct Mo and up to 2.5 pct W. The steels, listed in Table I, were forged to ¾ in. sq bars and the material for the high-temperature, rupture-test specimens was further swaged to %-in. round bars.

Jan 1, 1957

By C. G. Dunn, F. W. Daniels

IN recent publications1-5 the existence and behavior of subgrain boundaries in high-purity metals has been clearly brought to light. Lacombe and Beaujardl by means of special etching methods disclosed in polycrystalline sheets of aluminum the existence of substructures differing in orientation by small amounts (about 1/4"). Boundaries of these structures at relatively high temperatures had the remarkable property&apos; of moving about while the ordinary boundaries remained stationary. Cahn2 also observed substructures in bent and annealed single crystals of aluminum, zinc, magnesium, and rock salt. The position of subboundaries could be explained in terms of a dislocation mechanism of polygonization in which dislocations move into lines at right angles to the bent glide planes thereby relieving elastic stresses in these planes. Guinier and Tennevin8,6 disclosed the further interesting feature that polygonized structures coarsened significantly upon prolonged annealing. Somewhat similar subgrain phenomena have been observed in silicon iron of commercial purity. Although some evidence for the development of macro-mosaic structures in silicon iron already has been reported by one of the authors6,7 under the phenom-enological term "crystal recovery," much better evidence recently has been obtained due to improved etching techniques. In addition, phenomena regarding structural changes have been uncovered. The present investigation is divided into three parts: (1) The phenomenon of Laue spot sharpening on annealing cold-rolled crystals, (2) the phenomena of polygonization and subgrain coarsening The material used in the present investigation was high-grade commercial silicon iron sheet of nominal composition, 3.3 pct Si, 0.004 C, 0.011 P, 0.010 S, 0.04 Mn, 0.01 Al, 0.04 Cu, 0.01 Sn. Large single crystals of this material Were prepared for cold-rolling or bending as scheduled. Cold-rolling of 12 pct was carried out on a laboratory 8-in, diam rolling mill. The bending deformations were performed by pressing the crystals between a solid Fig. 2—lllustrative foue patterns to show Laue spot sharpening. a (Left)—Specimen as cold rolled, b (right)—After 48 hr at 1400°C. round bar and a mating half cylinder, both heavily greased. Individual specimens were cut from the deformed crystals, and the cut edges were deeply etched prior to annealing. Laue photographs were made using 40-kv tungsten radiation. The technique used to disclose the various subboundaries was an electropolish and electroetch in a bath of chrome-acetic acid.&apos; The anodic polishing done at 22 v was immediately followed by etching at a reduced voltage, which was dependent upon the nature of the subboundaries. Phenomenon of Laue Spot Sharpening on Annealing Cold-Rolled Crystals Fig. 1 gives the initial and final orientations of the specimens cold-rolled 12 pct. Each specimen was annealed at a temperature and for a time which caused significant structural changes as evidenced by alterations in Laue patterns. Representative Laue patterns and micrographs showing the essential changes are given in Figs. 2, 3, and 4. The essential points to be derived from these illustrations follow: 1. Annealing at 950°C clearly develops a substructure with the orientation of the cold-rolled specimen. 2. The subboundaries formed obviously separate regions of nearly the same orientation. Some of the subboundaries appear as a sequence of dots similar to those observed in aluminum by Lacombe and Beaujard,&apos; but whether this is due to extremely small differences in orientation is not known at present. 3. The substructure coarsens upon prolonged annealing. 4. Prolonged annealing also causes a decrease in orientation spread according to Laue spot sharpening&apos;

Jan 1, 1952

By Henry Rawdon

ONE of the most vital problems in the manufacture of steel at present is the occurrence of the defects that have been popularly termed "snow flakes," "flakes," or "scabs." Particularly is this the problem of many manufacturers who during the past 2 yr. have undertaken large-scale production for the first time. A study of the microstructure of such defective material throws considerable light upon the nature of these defects and is essential before measures may be taken for the elimination of the defects. Flakes do not appear to be found in the plain carbon steels; they have been found, however, in abundance in some of the simple alloy steels that are being used in such vast quantities; viz., nickel steel of the approximate composition, 0.40 carbon and 3.5 per cent. nickel, and in the chrome-nickel type. The present article summarizes the characteristic features of defective steel of the flaky type as they have been found by laboratory study of numerous specimens, and it aims to show the conditions within the metal that are favorable to the occurrence of this type of defect without entering into the details of mill practice (size of ingot, design of molds, rate of cooling, distribution of cooling stresses, etc.), all of which conditions appear to play a role in the production of these defects.

Jan 2, 1919

By P. Bardzil, J. Gurland

An experimental study of the variation of transverse-rupture strength with composition Anexperimentaland grain studysize has shown that the strength reaches a maximum for values of the mean free path between carbide particles of 0.3 to 0.6 microns. The fracture oforiginates in and proceeds through the carbide grains mainly. Impact strength and hardness also were recorded. MOST of the physical properties of sintered carbides vary linearly with composition. The transverse-rupture strength, however, shows a unique behavior. As the amount of binder metal is varied from 6 to 25 pct by weight, the strength at first increases; then, between 15 and 20 pct Co, it reaches a maximum of nearly 400,000 psi, and finally decreases with further additions of binder metal. This behavior of the transverse-rupture strength has been reported, among others, by Englel and Sandford and Trent.&apos; The significance of these observations has not been discussed in the literature. That it may be of more than specific importance is indicated by the very similar variation of strength with composition encountered in other systems sintered in the presence of a liquid phase, such as Tic-Ni3 and Fe-Cu.&apos; Experimental Details All compacts were prepared and sintered according to normal industrial practice. The average diameter of WC grains and the mean free path between grains were measured on metallographically prepared samples by a method of linear and planar analysis sing the relations where d is the average diameter of dispersed grains; Nl is the number of noncontiguous grains intersected on a metallographic plane by a line of unit length; N, is the number of noncontiguous grains per unit area; P is the mean free path between grains of dispersed phase; and f is the volume fraction of dispersed phase. Approximately 1000 grains were counted on each sample. For each composition d2 was plotted against P, the resulting straight lines serving as a check on the measurements. The distribution curves of the WC powders of different average diameters were homologous, and no attempt was made to influence the grain size by blending powders, adjusting the sintering conditions, or otherwise altering the particle size distribution. Densities were measured by differential weighings in air and water. The degree of densification did not vary consistently with either composition or grain size. The density is influenced by slight amounts of impurities, specifically by 0.1 to 0.2 pct Fe which enters the powders during ball milling. As an illus- -tration of the experimental variations, a number of measured densities are listed in Table I. They are expressed in percentage of theoretical density, as calculated from the published X-ray densities of WC and Co.&apos; For the purpose of determining the transverse-rupture strength, rectangular test specimens (3/16x 3/8x3/4 in.) were broken by loading at the center of a 9/16 in. span. The average strength of five or more samples is reported for each composition and grain size. The compacts were ground on two parallel surfaces only. The load was applied at an average rate of 6,800 psi per sec. Since the elongation after fracture of the alloys is very small, it was assumed that the compacts deform elastically to failure and the fracture stress was calculated by the conventional beam formula. The data for one alloy are presented in Table II as an example of the results and scattering ranges encountered. The precision of the test, as measured by the average difference between duplicates, is of the order of 15,000 psi. The results are strictly comparable only to compacts prepared and tested in the manner described and of similar chemical composition and grain size characteristics. Unnotched Charpy specimens were used for impact testing. Each point represents the average of 3 to 20 samples, the larger number being used in an attempt to determine the influence of grain size. Considerable scatter was encountered, the range from lowest to highest value often amounting to 30 pct of the impact strength. The hardness is reported as a Ra reading, using a 60 kg load with diamond brale indenter. Compositions are given in weight percent.

Jan 1, 1956

By B. L. Averbach

Recovery and primary recrystalliza-tion in cold worked metals are usually considered as two competing processes. Some of the effects which usually accompany recovery are: alleviation of stress corrosion tendencies, changes in thermal emf,1 damping capacity,2 electrical resistivity,2 and magnetic properties,3 and only minor changes in hardness or the related strength properties. During primary recrystalliza-tion new unstrained grains are formed at the expense of the strained matrix. These new grains eventually become visible metallographically, and nucle-ation and growth kinetics have been indicated for this process.4,5 Frequent attempts have been made to study the cold-working phenomenon by observations on the line broadening by X ray diffraction patterns. Relatively few measurements of line intensities have been made, although Brind-ley and his collaborators, 6,7,8 by means of film techniques, compared the intensities of cold worked Cu, Ni, and Rh patterns with those from chemically precipitated powders. These precipitated powders were presumed to be strain free, and it was found that the intensities for the cold-worked materials progressively decreased as the Bragg angle increased except for the first line, where there was an increase due to reduction in extinction. This was interpreted as a randomness in atomic position induced by cold work. Such randomness is similar to that caused by thermal agitation and has been described as "frozen heat" displacement of 0.08-0.10 A from the mean atomic position. In a recent study9 on the effect of cold work in metals on their powder pattern intensities, the changes in integrated intensity for heavily cold worked alpha brass were observed as a function of the annealing temperature. These measurements were made with a manually operated Geiger-counter spectrometer using CuKa radiation monochromated with a rock salt crystal. Intensity measurements were made with a scaling meter over small intervals of angle, and the equipment was so arranged that the diffracted and incident beams made equal angles with the specimen. Intensities could be compared directly by simply interchanging specimens, and comparisons from day to day were made with a standard whose line intensities did not change on aging. It was shown that a cold worked alpha brass standard was stable for at least a year. Table 1 indicates the results of the integrated intensity measurements on a 70 Cu-30 Zn brass. In the sample preparation, a brass plate was first cold rolled 50 pct and then filed, screened to —325 mesh, compacted into briquettes at a pressure of 60,000 psi and finally annealed for one hour at various temperatures up to 400°C. The briquetting pressure did not seem to influence the integrated intensities, and most of the cold work was introduced by the filing. Although this method of cold work is not quantitative, it was used to obtain random orientation (and thus uniform diffraction lines) in order to make accurate measurements of integrated intensity. Back reflection patterns were taken in each case to check the uniformity of the lines, and from the observed line broadening it was apparent that this type of plastic deformation was quite severe. Care was taken to traverse the entire background of the pattern and to assign to each peak the total intensity above this background. The bases of the diffraction lines were quite broad and spread out over several degrees, even for the narrow peaks. The theoretical intensities were calculated to include a temperature correction, a dispersion correction, and a Lorenz- polarization factor corrected for the crystal monochromated beam. In Table 1 it was necessary to match the calculated and observed values at only one point, and the rest of the experimental values were converted directly to this arbitrary scale. The integrated intensities in Table 1 are listed in arbitrary units, and the accuracy was sufficient to reproduce any of the measured line intensities to within + 1.5 units. It is evident that the percentage error on the strongest line (111) was quite low. The calculated values and the observed intensities for the cold worked material matched reasonably well. As the annealing temperature was raised, however, the intensity of the strongest reflections, particularly the (lll), decreased measurably. Since the background intensities of all of these patterns were identical, such behavior could be interpreted as a primary

Jan 1, 1950

By F. V. Lenel, G. S. Ansell, J. A. Dromsky

The growth of aluminum oxide particles in a nickel matrix was studied eve?. the temperature vange of 2140° to 2470°F. The instability of the dispersed alumina was shown to be independent of the crystal structure of the alumina. The activation energy for the growth of the dispersed alumina was found to be 84.7 1 2.0 kcal. The particle radius increased as a function of time. These results indicate that the growth is not diffusion controlled. It is believed that the rate controlling mechanism is the dissolution of the aluminum and oxygen atoms into the nickel lattice. THE strength properties of alloys which consist of a finely dispersed second phase in a metallic matrix depend upon the spacing between the second phase particles. It is therefore desirable to achieve very fine dispersions in these alloys. Furthermore, to retain the properties these very fine dispersions must be stable during fabrication and service of the alloys. The best known of the dispersion strengthened materials, the SAP type alloys, which consist of a dispersion of aluminurn oxide in aluminum, have exceptionally good stability up to the melting point of aluminum. There is evidence, however, that other dispersion strengthened alloys, even those consisting of refractory oxides in a metal matrix, may be less stable. This investigation is concerned with the stability of Ni-Al2O3 alloys in the temperature range in which these alloys are usually fabricated. The mechanical properties of Ni-Al2O3 alloys at elevated temperatures have been previously investigated by Crelnens and rant,&apos; and Gregory and Goetzel.2 The behavior of these alloys in stress rupture tests appears to indicate that at temperatures below 1800°F they are highly stable. There is some doubt, however, as to their stability at the higher temperatures used during the conventional fabrication. Cremens and Grant, in preparing their test alloys, cousolidated, by powder metallurgical techniques, nickel powders as fine as 0.13 µ diam and alumina powders as fine as 0.018 µ. Metallo- graphic examination of the alloys following fabrication revealed that none had interparticle spacings of less than 2 µ. Considering the size of the original component powder particles, it is likely that the dispersions coarsened during fabrication. Gregory and Goetzel, in their studies of extruded alloys of 80 pct Ni—-20 pct Cr matrixes with nonmetallic dispersion, observed a definite coarsening of the alumina dispersions in alloys sintered at 2280°F as cantrasted to those sintered at 2000oF. Similar observations on the spheroidization and growth of thoria particles finely dispersed in a nickel matrix were made by D. K. Worn and S. F. Marton.3 As a result of such coarsening, much of the effort expended in the preparation of very fine powder mixtures would be lost. The mechanical properties of the alloys which had experienced coarsening would be expected to be poorer than if the original dispersions had been retained. EXPERIMENTAL PROCEDURE Ni-Al2O3 alloys were produced from powder prepared by a coprecipitation technique. Aluminum hydroxide and nickel hydroxide were coprecipitated from chloride solutions of the metals. The mixed hydroxides were calcined to form metal oxides and the nickel oxide in the mixture was selectively reduced to nickel by treating it in hydrogen. Specimens were compacted from the resultant powder which consisted of a fine, uniform mixture of aluminum oxide and nickel particles. The compacts were sintered by resistance hot pressing4, a densification technique which requires exposure times of the order of only a second or less at elevated temperatures. A conventional sintering process was not used, since the temperature required for densification would have to be in the region in which the stability of the dispersion was to be studied. A series of hot pressed specimens were treated in hydrogen at temperatures from 2140o to 2470°F (1171o to 1355oC, for times up to 120 hr. Changes in the microstructures were studied by electron microscopy using the two-stage preshadowed carbon replica method.5 In performing a lineal analysis on a series of micrographs from each specimen it was found more convenient to determine the mean free path between alumina particles rather than particle radii as the parameter of growth. Although these quantities are directly proportional for only spherical particles, the alumina particles in these alloys

Jan 1, 1962

By H. E. Cline, E. F. Koch, J. L. Walter

It has been postulated and, in a few instances shown, that some kind of dislocation structure will be present at semicoherent interfaces to accommodate small lattice mismatches. In the present study of the NiAl-Cr eutectic, regular arrays of interface dislocations are observed at the boundary between the chromium-rich rods and the NiAl-rich matrix. The networks were examined by transmission electron microscopy and selected area diffraction. The rods and the matrix have a crystallographic relationship in which all directions and planes of the two phases are parallel. The dislocation networks are cmposed of a<100> dislocations lying on the intersections of the cylinders with (100) planes. Dislocations forming hexagonal rather than square arrays are also observed at certain areas of the network. The morphology of the network is consistent with the interpretation of mismatch being accommodated by interface dislocations in the cylindrical geometry. The measured spacing between dislocations was used to calculate an apparent lattice mismatch between the phases (˜0.35 PCt)interface network energy (-140 ergs per sq cm), and network strengthening (-10,000 psi). It has been proposed by Frank and Van der Merwe1 that dislocations should be present at the boundary between two semicoherent crystallographically related phases. The role of the interface dislocations would be to reduce the internal stresses, caused by the mismatch in atomic spacing across the interface. Such dislocations have been observed at the interface between expitaxially grown films and Substrates.2-4 Interfacial dislocations have also been observed at precipitate-matrix interfaces.&apos;-&apos; Directionally solidified eutectics have been shown to have semicoherent phases1&apos; and would, therefore, be expected to have interfacial dislocations as found by Weatherly at a lamellar fault in A1-A12Cu.11 The NiAl-Cr eutectic appeared to be a promising system to examine because both phases are cubic, the lattice mismatch is small, and the phases are crys-tallographically related. Furthermore, the eutectic is easily thinned for transmission microscopy. Indeed, interfacial dislocations were observed and this report describes the nature of the dislocation networks in the boundary between the NiAl-rich ma-trix-phase and the fine chromium-rich rods.21 I) EXPERIMENTAL PROCEDURE Ingots, 3/4 in. in diam and 6 in. long were made by melting in vacuum and casting under argon using 99.9 pct pure material. The composition, in at. pct, was 33 pct Ni, 33 pct Al, and 34 pct Cr. The ingots were then placed in A1203 crucibles on a water-cooled base, melted by means of induction, and withdrawn from the hot zone at the rate of 1 in per hr under argon.* * T his material was first directionally solidified in this laboratory by E. R. Stover Slices were taken perpendicular to the growth direction of the directionally solidified ingot for metallography and for transmission electron microscopy. The electron transmission samples were thinned mechanically, then thinned electrolytically in A-2 electrolyte* *A-2 electrolyte: 62 ml perchloric acid, 700 ml ethanol, 100 ml butylcellosolve, 137 ml distilled H20. until a hole appeared in the foil. 11) EXPERIMENTAL RESULTS A) Optical Microscopy. The microstructure, viewed on a plane perpendicular to the growth direction, is shown in Fig. 1. The structure consists of cells or colonies of parallel chromium-rich rods in the NiAl matrix. The cells occur when there are impurities present12 or, in a ternary eutectic, if the composition is slightly off the eutectic composition. The axis of the chromium-rich rods is parallel to the growth direction except near the cell boundaries. Here the rods may assume angles to the growth direction; however, examination shows that the crystallographic relationship between the rod and the matrix remains the same. Fig. 1 includes cell boundaries where the rods formed at a large angle to the growth direction. The variation of rod position across the cells made it possible to Fig. 1-Structure on plane perpendicular to growth direction. Rods near cell walls are at large angle to growth direction. Magnification 315 times.

Jan 1, 1970

By M. J. Marcinkowski, E. N. Hopkins

An investigation has been made of the ß(fcc) — a(hexagonal) transformation which occurs in lanthanum using both electrical resistivity and transmission electron microscopy techniques. It has been shown that the ß phase can be retained below the transformation temperature by rapid quenching but that the sample immediately begins to transform to the a phase. The transformation is observed to nucleate in the vicinity of inclusions. Based on the above observations, a detailed model of the transformation has been advanced which involves the nucleation of an extrinsic stacking fault bounded by a pair of Shockley partial dislocations in the vicinity of some heterogeneity, i.e., an inclusion. The stress field of the resultant dislocation pair acts to nucleate extrinsic faults in adjacent planes and leads quite naturally to the B-a conversion with a minimum of strain energy induced in the crystal. LANTHANUM possesses an fcc structure ß) (8) upon cooling transforms to a hexagonal modification (a) in much the same way as cobalt. The one exception, however, is that the stacking sequence of the closest packed planes in a La is ABAC ABAC, and so forth,1 whereas in cobalt it is ABAB, and so forth, i.e., hep. Mainly on the basis of transmission electron microscopy techniques, there seems to be little doubt that the 0 — a transformation in cobalt involves a dislocation mechanism2 although its exact nature still remains obscure. Although the ß - a transformation in lanthanum is somewhat more complex than that occurring in cobalt, it was thought that its very uniqueness would be helpful in understanding fcc — hexagonal transformations in general. Such a general understanding of these transformations is important since they represent what are perhaps the simplest of the martensitic class of transformations. The experimental techniques used were those of electrical resistivity and transmission electron microscopy. EXPERIMENTAL PROCEDURE The lanthanum used in this investigation was prepared by the calcium reduction of lanthanum fluoride in a tantalum crucible under an argon atmosphere as described by Spedding et al. The residual calcium was removed by vacuum remelting in a tantalum container. Portions of the metal were then analyzed by emission spectroscopy as well as vacuum fusion. The amounts of the various impurities that were found are listed in Table I. A portion of the lanthanum ingot was swaged at room temperature into 0.030-in.-diam rod for the resistivity samples while the remainder was rolled into 0.010-in.-thick sheet for the transmission electron microscopy phase of this investigation. In order to eliminate the plastic deformation induced in the samples during fabrication, they were sealed in evacuated tantalum lined quartz capsules and annealed for 1 hr at 700° C. Specimen resistances were measured using the conventional "four-wire" technique described by MacDonald, 4 employing a type K-3 Universal Potentiometer and a standard 0.001-ohm resistor, both manufactured by Leeds and Northrup Co. By taking into account all of the possible errors in the apparatus, it was felt that the absolute resistivities of the approximately 0.87-in.-long specimens measured are reliable to 3 pct. Resistances from room temperature to 700°C were measured using a vacuum furnace. In order to avoid sample contamination by the thermocouple, chromel-alumel leads were spot-welded into a tantalum shield which in turn was welded to the lanthanum specimen. Resistances below room temperature were obtained by transferring the sample to a helium gas-filled quench tube and slowly dripping liquid nitrogen into a surrounding dewar flask. A steady reduction of temperature to about —190°C was completed in about 23 hr, and the resistances were measured at various temperature intervals. As will be shown shortly, rapid quenching from above about 350°C was sufficient to suppress the B -a transformation initially but subsequent annealing at lower temperatures leads to a partial ß --a conversion. To investigate this aspect of the transformation, the samples were suspended in the hot zone of a helium-filled furnace from which they could be rapidly dropped into the quench tube mentioned previously which was now

Jan 1, 1969

By M. E. Shank, J. Wulff

In view of the current interest in magnetic materials having rectangular hysteresis loops, as for example those obtained with the grain oriented 50 nickel 50 iron alloys,t we wish to call attention again to the results obtainable with the perminvar (Co-Ni-Fe) alloys heat treated in a magnetic field. Data taken from direct current measurements made prior to and during World War II give the typical values shown below for two of the perrninvar alloys. Fig 1 and 2 show- the hysteresis loops for these samples. The first sample above consisted of small rings punched from 0.014 in. sheet stock. These rings were heat treated at 1000°C for one hour in a hydrogen atmosphere and then cooled with the furnace to 750°C at which point they were subjected to a magnetic field of 15 oersteds maintained during cooling to room telmperature. The molybdenum perminvar sample consisted of a spirally wound core of 0.001 in. tape. The heat treatment was the same except that box annealing methods were used and no hydrogen atmosphere was employed. Even better properties might be expected using hydrogen. The heat treating temperatures and cooling rates are not critical. Rectangular hysteresis loops produced in other perminvar alloys by heat treatment in a magnetic field were described earlier.&apos;,? Properties similar to those described above are realized in perminvars manufactured by conventional methods. Drastic cold working which in practice limits the final thickness and is gen- erally expensive may thus be avoided. This information may be of interest to those concerned with magnetic alloys and the development of contact rectifiers, magnetic amplifiers and so on.

Jan 1, 1950

By Charles C. Fatino, Joel S. Hirschhorn

Loose compacts of strained and annealed stainless-steel powders were sintered at various temperatures and times to determine the effect of residual strains on the sintering behavior. The atomized powders were prepared by annealing, ball milling, and rean-nealing. The residual strains and domain size were determined by a Fourier analysis of X-ray diffvaction dala. The specimens were prepared by siwzultaneously sintering cylinders of both strained and unstrained powder. The evaluation of the sintered compacts included density measurements, metallographic examinations, and analyses of X- ray diffraction data. The results of these studies reveal a definite increase in sintered density and sintering rate for the strained powders. THE pressure compacting of metal powders causes deformation of the particles, mechanical interlocking, and increased contact area. After the deformation, severe residual strains remain in these particles. The subsequent contributions of these strains to the sintering process have been considered to be negligible, since the recovery and recrystallization temperatures usually occur prior to the temperature required for the sintering process. Sintering is con-sidered to be the process by which the powders are transformed into solid compacts at temperatures below their melting points. The sintering operation for stainless steel usually takes place in the range of 2050" to 2400°F (0.84 to 0.95 T,, where T, is the absolute melting point or liquidus temperature) while the temperature required for recovery is approximately 1800°F (0.75 T,). However, it has been shown for several metal powders that densification becomes significant in the range of 0.35 to 0.45 T,.&apos; It is the purpose of this study to determine what effect residual strains have upon the sintering behavior of stainless-steel compacts. Loose compacts were selected for study in order to isolate the strain contributions and eliminate the variables inherent in sintering of pressure-formed compacts. Additional variables were minimized by using only one mesh size, one composition, one particle shape, and also by simultaneously sintering both types of powder. Very little work has been carried out previous to the present study to delineate the effect of strains on sintering behavior. Lenel et 01.2 observed that residual stresses in copper compacts caused shrinkage at comparatively low temperatures. Delisle3 loose-sintered ball-milled electrolytic iron and observed that bonding among particles began at a lower temperature as compared to the behavior of annealed powder. Increased densification of ball-milled oxide powders has also been noted.4&apos;5 EXPERIMENTAL PROCEDURES Powder Preparation. The powder used for this study was a commercial-type 316L stainless steel made by the atomization process. A typical chemical analysis is: C- 0.025 pct Mo- 2.2 pct Cr-18.6 pct Ni-12.5 pct Fe—Balance The atomizing process is essentially the rapid freezing of liquid droplets. This nonequilibrium cooling causes coring to occur and two distinct phases are present within the solid particle, the austenitic phase and the ferritic phase. Due to the presence of this ferritic phase, the particles tended to fracture as well as become cold-worked during the subsequent ball-milling operation. (It was also found that this type of cooling produced a broadened and shifted

Jan 1, 1968

By V. A. Phillips, M. Safdar Ali

The tensile properties of Cu-0.20 pct Al, Cu-0.45 pct Mg, Cu-0.27 pct Cr, and Cu-0.22 pct Be solid-solution alloys were studied at -196°, 18°, 2509 and 500°C on wires internally oxidized at 900°and 1000°C. Internal oxidation produced marked increases in yield strength relative to pure copper, particularly at low temperature. The yield strength decreased with increase in temperature to a much greater extent than predicted by current theories of dispersion hardening. The strengthening effect of internal oxidation persisted throughout the entire stress-strain curve, but since a marked loss of ductility occurred at all test temperatures, only modest increases in tensile strength were realized. INTERNAL oxidation involves the preferential oxidation of a baser solute in a relatively noble solvent by diffusion of oxygen into the solid. Since the process is diffusion controlled, it is expedient to carry it out at a high temperature often approaching the melting point. The amount of solute is limited and the oxidation conditions adjusted so that oxygen diffuses inwards to meet the solute causing reaction to progress inwards and form subscale instead of only sur face scale. The reaction can be made to occur throughout the thickness of thin material producing a fine dispersion of oxide inside the metal. C. S. Smith1"3 appears to have been the first to recognize the true nature of the process of internal oxidation. Although extensive kinetic and metal-lographic studies followed by Rhines and coworkers,4-5 Chaston7 andMeijering and Druyvesteyn8 working independently were the first to report hardening effects due to internal oxidation. These results prompted detailed studies of the effects of internal oxidation on the hardness, tensile, creep, and fatigue properties of a number of alloys by G. C. Smith and coworkers9-12 in England, on hardness by Gottardi13 in Italy, and on hardness and tensile properties by wood14 in the U.S.A. Publications dealing with other aspects of internal oxidation will not be reviewed here. Internal oxidation of solutes having a high affinity for oxygen provides a means of obtaining very fine dispersions stable in a suitable atmosphere at temperatures well above those at which most age harden ing precipitates coalesce. The process therefore offers a method of producing thin sheet and wire of possibly outstanding creep resistance. The size limitation might be overcome by internally oxidizing porous powder compacts made from alloy powder before final sintering. PREPARATION OF ALLOYS The alloy ingots, which were approximately 5 1/2 in. long by 1 in. diam, were made up in a high-frequency furnace, using as raw materials OFHC copper, 99.99 + pct Al, high-purity magnesium, and master alloys of Cu-4.19 pct Be and Cu-10 pct Cr. The alloys containing aluminum and magnesium were melted ii closed high-purity graphite crucibles and solidified in the crucible which was lowered partly Out of the coil to give a hot-top effect. The alloys containing beryllium and chromium were made by melting in vacuo in alumina-lined sillimanite crucibles. The magnesium, chromium, and beryllium

Jan 1, 1960

By Rex B. McLellan, M. L. Rudee, T. Ishibachi

A modelfor dilute quasi-regular interstitial solid solutions is proposed in which the solute atoms can occupy both the octahedral and tetrahedral interstices in the bee solvent lattice. The distribution function, according to which the solute atoms are apportioned between the two kinds of sites, is calculated. The partial thermodynamic functions of the solution are calculated from the distribution function. It is shown that such a solution model can explain the deviation from linearity of the Arrhenius plot of the temperature variation of the diffusivity of carbon through a iron. The published difiusivity data is analyzed to obtain numerical values for the distribution function. Finally it is shown from the numerical values of the distribution function that the possibility of dual-site occupancy will have a negligible effect on the solution thermodynamics for this system. DeSPITE the large amount of experimental data available on the thermodynamics and diffusion kinetics of dilute solid solutions of carbon in a iron, many of the elementary properties of these solutions are not understood due to real or apparent discrepancies in the experimental data. Basically there is a lack of agreement between the solubility and diffusion data obtained by anelastic damping techniques and by bulk chemical thermodynamic methods. SPecifically the heat of solution of cementite in ferrite estimated from thermodynamic measurement1, 2 is about twice as high as that determined from anelastic damping measurements.3 Furthermore the diffusion coefficient D of carbon in a iron in the range -40" to about 150°C (covering about ten orders of magnitude) determined from anelastic damping techniques is such that an Arrhenius plot of In D vs 1/T is linear. However in the range of about 300o to 850°C where mass flow measurements of D have been made (covering about four orders of magnitude), although the data merges with the low-temperature data, the Arrhenius plot departs from linearity. The object of this paper is to present a more refined model of dilute ferrite solutions in which the solute atoms can occupy two kinds of interstitial sites. The experimental data is analyzed in the light of this model and it is believed that thereby some of the anomalies can be resolved. snoek4 explained the room-temperature internal-friction peak (usually referred to as the Snoek peak) in iron as the stress-induced ordering of interstitial carbon and nitrogen atoms occupying the octahedral (0, 0, 1/2) interstices in the bee lattice. From the consideration of a hard-sphere lattice model the (0, 1/4, 1/4) tetrahedral interstices are larger than the octahedrons but their symmetry would not produce the strain dipole necessary to give rise to the Snoek peak. Thus the presence of the Snoek peak is direct evidence that the octahedrons are occupied. Since the publication of Snoek&apos;s explanation, most workers have assumed that all of the carbon and nitrogen in the a solid solution was located in the octahedral sites. This assumption of universal octahedral occupancy has been implicit in the theory of wert5 for interstitial

Jan 1, 1965

By I. S. Levy, J. L. Brimhall, B. Mastel

Specimens of&apos; Hastelloy X-280, a low-cobalt version of the solid-solution- hardened nickel-base alloy Hastelloy X, were given a series of thermomechanical treatttzents. They were then Lensile-tested at room temperature and 1350°F. The Microstructures of the specimens tested at 1350°F were studied by electron Microscopy. Microscopy showed that dislocation tangling, caused by the cold working, mas still in evidence after aging-for 24 hr to temperatures as high as 1550oF. (Cr, Mo)23 C6, (Fe, Mo)6 C&apos;. as well us an unidentifiable phase precipitale due to the combination of the thermomechanical treatments and subsequent tensile strain. The room -temperature and 1350°F tensile properties show a general increase ill strength and decreccse in ductility with increusing cold-work level. This is due to the dislocation taangling-. PerLurbatiot~s to this general trend occur- due to solid-solution weakening at the higher cold-work levels as a direct result of the preciplitation reactions. THE requirements for corrosion resistance and high-temperature strength place nickel-base alloys among the more promising materials for advanced nuclear reactor applications. However, when these alloys are irradiated at service temperatures, they generally suffer severe embrittlement&apos;" and reduction in rupture life.3 Certain experimental treatments resulted in improvements in the tensile and stress-rupture properties of Hastelloy X-280, a solution-hardened nickel-base alloy.&apos; To provide a basis for understanding these improvements, unirradiated tensile specimens were examined by electron microscopy. The results are reported in this paper. EXPERIMENTAL DETAILS Material. Hastelloy X-280, a low-cobalt version of Hastelloy X, is a member of the solution-hardened class of nickel-base alloys. The Hastelloy X-280 was obtained from 4- and 1-in: thick plates in the mill -annealed condition. Table I gives the chemical composition of the material as reported by the National Spectrographic Laboratories. ~x~erimental Treatments. Plates of suitable size, 12 by 3 by 1 in., or by + in., were cut under a water jet from the stock material and examined ultrasonic -ally for homogeneity of grain size and absence of voids. The acceptable plates were solution-treated at 2150°Ffor 1 hr and air-cooled. These plates were then reduced in thickness by cold rolling 0, 10, 15: or 20 pct along the original rolling direction. The plates were machined into buttonhead tensile specimens with a gage diameter of 0.125 in., with a gage length of 1.125 in., and with their tensile axes parallel to the rolling direction. The specimens were examined for quality of finish with a penetrant dye, ultra son ically checked for voids, and finally given a dimensional tolerance check with an optical comparator. The acceptable specimens were aged for 24 hr at either 1000" or 1500 F and air-cooled. These specimens were then held at 540°F in a water loop for approximately 18 days to qualify as controls for similar specimens irradiated under the same conditions of time, temperature, water chemistry, and flow rate. Table U summarizes the treatments. These treatments were investigated to establish whether prior precipitation and stabilization of carbide phases at strain sites within the matrix could reduce the amount of carbides available for precipitation at grain boundaries during service. Tensile-Test Conditions. Specimens were tested to fracture at room temperature or 1350 F in air on an Instron tensile-testing machine at a crosshead speed of 0.05 in. per min. The time for the furnace to reach equilibrium at 1350°F was approximately 30 min; soak time prior to testing was 15 min; and test duration was approximately 5 min.

Jan 1, 1968

By H. C. Chang, N. J. Grant

Creep of very coarse grained, high purity aluminum was studied at 400° to 1100°F with an initial stress range of 50 to 1200 psi. The process of boundary sliding and migration was studied. The driving force of boundary migration under creep conditions is shown to be a combination of strain energy migrationand surface energy. A theory is presented regarding the strainenergyrole the grain boundaries play under creep conditions. From this thetheory intercrystalline failure of commercial alloys can be explained. Also from this theory an optimum grain size should exist for good high temperature properties of high purity materials. IN the investigation of the creep of very coarse grained, high purity aluminum previously reported,&apos; the cyclic nature of the process of grain boundary sliding and migration has been established by microscopic observation of the actual creep process as well as metallographically. It was also substantiated by measuring localized strains across the grain boundaries. In addition, it was shown how extensive subgrain and fold formation may result from boundary sliding and how the slid grain boundary may become sharply wavy as a result of subgrain formation. Since the publication of those results, additional information on the process of grain boundary sliding and migration has been obtained. It is the purpose of this paper to report on the direction and driving force of boundary sliding and migration, the effect of grain size, and the effect of temperature. Finally the effect of decreasing purity (alloys 2s and 3s) on the process of boundary sliding and migration is noted. From these results, an explanation is presented for the intercrystalline failure of alloys under creep conditions. The effects of grain size on the creep properties of impure and high purity materials are discussed in the same light. The experimental procedures and technique have been presented elsewhere.&apos; It is only necessary to state how the 2s and 3s aluminum specimens are prepared. Machined specimens were first annealed at 600°F for about 12 hr. In order to produce a large grain size the specimens were then stretched 3 to 8 pct. The specimens were marked with reference marks, electropolished, annealed at 900°F for 24 hr and at 1150°F for 12 hr, and repolished. The grain size of 2s aluminum produced by this treatment is comparable to that of high purity aluminum in the direction of its width of the specimen, i.e., there are 2 to 4 grains across the width of the specimen. However, the grains of 2s aluminum are 3 to 10 times longer in the direction of the specimen axis. On the other hand, the grain size of coarse grained 3s aluminum ranges from 10 to 20 grains across the width of the specimen due to the treatment just outlined and therefore is much smaller than that of both high purity and 2s aluminum. As in 2s aluminum, the grains are about 3 to 10 times longer in the direction of the specimen axis than in the direction of the width of the specimen. The arrangements of the grains in 2s and 3s aluminum were generally irregular; therefore it was difficult to follow the course of the grain boundaries. Results Method of Presentation: In order to show the arrangement of the grains, especially the direction and positions of the grain boundaries, traces of the grain boundaries on the four surfaces of the specimens were unfolded and mapped out after macroetching. Figs. 1 and 2 show the structural development drawings of specimens P-3 and P-8 respectively. The two flat surfaces (of which the front one faces the microscope) and the round-edged surfaces will be called the "front surface" and "back surface" and

Jan 1, 1954

By W. D. Robertson, E. G. Grenier, V. F. Nole

The electrical, mechanical, and corrosion cracking properties of an age-hardenable Cu-Ni-Si alloy have been studied over a range of time, temperature, and deformation states for the purpose of determining the relationship between the properties and the structural state. The precifitate has been identi3ed as and the sites of preferred precipitation have been located by electron microscope studies of the structures developed by various combinations of heat treatment and plastic deformation. An extreme form of deformation banding has been observed in the aged alloy that results in high strain concentration in bands lying parallel to {111} planes. These bands are the structural paths along which transcrys-talline cracks propagate in the deformed alloy. The observations provide a basis for a general mechanism of transgranu-lar corrosion cracking of face-centered cubic alloys in terms of stacking fault probability. AMONG the age-hardening copper alloys the copper-nickel-silicon (Silnic Bronze) type is outstanding in exhibiting a high strength combined with a considerable capacity for cold working, a relatively high conductivity, and a low to negligible susceptibility to stress corrosion cracking. It is not a new alloy and it has been the subject of a number of investigations,1-5 which were made primarily to establish practical composition and heat treatment limits. The structural characteristics of the aging processes in this alloy have not previously been studied in detail. This particular investigation was undertaken to explore, in detail, and over a wide range of conditions, the properties obtainable by various combinations of working and heat treatment and to correlate structural changes with the observed mechanical, electrical and corrosion properties. MATERIAL AND PROCESSING Eight different commercial heats of the alloy were made and used in the investigation. The range of composition among the eight heats is shown in Table I. Billets, 8 by 24 in., were cast into water-cooled molds, extruded to 1.687-in. rod, and quenched in water after extrusion. Extruded material was rod rolled to 0.750 in., annealed at 1450° F for 2.5 hr, and quenched in water. Subsequent working operations were performed by tandem rolling to various sizes depending on the degree of reduction required. Final cold-working operations were performed by drawing to a uniform size of 0.187 in. diam and straightening by a roller straightening machine (Lewis). The combinations of heat treatment, working and aging that were investigated are summarized in Table 11; the various treatments were performed in the order given in each row of the table, and they will be subsequently identified by the symbols shown in the first column. SOLUTION TREATMENT All material investigated in the cold-worked condition, or cold worked prior to aging, was solution

Jan 1, 1962

By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.&apos; If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By F. W. Jessen, John C. Miller

In many areas where carbonate rocks form important parts of the stratigraphic sequence, stratigraphers have experienced varying degrees of difficulty in differentiating and correlating limestone and dolomite units in both surface and subsurface work. With early Paleozoic rocks of the Mid-Continent, insoluble residues yield a remarkable amount of strati-graphic data and relatively good correlations may be carried over broad distances.&apos; Unfortunately, neither such information nor electric logs and radioactive logs have been particularly helpful in interpreting the limestone sections of the Permian Basin of West Texas. This is because: (1) the variations in the sections may be very slight; (2) no completely satisfactory method of interpretation has been developed; and (3) the measurements themselves are not sensitive enough for small variations. Also, such logs are influenced by the fluid content. Paleontology and micro-paleontology remain the ultimate arbiters. As a routine tool, however, paleontol-ogical examination is slow and tedious. Chemical analysis may be used, but this, too, is extremely slow. Although rocks are not classified according to chemical composition, there is considerable variation with rock types. Correlation by chemical composition has two advantages, first, the characteristics determined are subject to minimum human error and interpretation, and secondly, the lithologic changes are not masked by fluid content as in the case of electric and radioactive logs. Some fossils concentrate certain elements which tentatively might be used to date rock units.&apos; Rapid chemical analysis by spec-trographic means could be used as an adjunct to other means employed in correlation work, or might, in itself, present a suitable method. PURPOSE OF THIS INVESTIGATION Sloss and Cooke&apos; have published data concerning spectrographic analysis of limestone rocks specifically for purposes of direct correlation of a single formation. These authors found satisfactory evidence that differences in percentage of four elements (Mg, Fe, Al, and Sr) in the Mississippian limestones of northern Montana were useful in carrying out correlation of this formation over a distance of approximately 50 miles. It was concluded from the preliminary work that the spectrochemical method offered possibilities of solution of some problems of correlation heretofore not possible. Since the work of Sloss and Cooke&apos; was confined to one particular limestone zone, extension of the use of the method to examine two or more geologic formations would aid materially in the over-all problem of correlation of such rocks. Equipment is now available commercially with which very rapid spectrographic analyses may be made, and hence the problem was to determine whether the variations existing in the minor constituents of limestones were sufficient for use in possible correlation. Qualitative and semi-quantitative investigations were made to determine whether significant changes in the chemical condition occurred. It was a further purpose to investigate the geologic time-boundaries to see whether significant chemical variation could be found corresponding to the paleontological breaks. It was desirable to attempt correlation of a thick section of limestone or dolomite rock and to have as much information as possible on the section. Furthermore, it was felt that examination of formations more difficult to correlate by other means would enhance the value of the method should definite points of correlation be found. Samples were chosen from the Chapman-McFarlin Cogdell No. 25 well in the Cogdell field, Kent County, Tex., and from the General Crude Oil Co., Coleman No. 193-2 well in the Salt Creek field, Kent County, Tex. These fields belong to the famous series of "Canyon" reef fields of West Texas. Cores from the above wells were available from the United States Geological Survey, Austin, Tex. THE SPECTROGRAPHIC METHOD The choice of procedure to be followed in this investigation was based on the anticipated requirements peculiar to the problem. Since the problem was primarily to investigate the possibilities of applying the spec-trograph to problems of correlation in thick carbonate sections, a precise quantitative analysis did not appear necessary. A qualitative analysis to show the possible absence of presence of any element, or a semi-quantitative analysis of the elements present to show the relative changes in magnitude of selected elements was required. Both types of analysis were employed. The two most widely applied methods of semi-quantitative estimates are those of Harvey and of Slavin4,5 though various other procedures have been described.6 while the Harvey method has been modified by Addink,7 this refinement did not seem necessary to the present problem. Essentially, the procedure employed is a variation of the total energy method of Slavin with two exceptions: (1) stressing matrix effect, and (2) using densitometer measurements. As measured by a densito-

Jan 1, 1956