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By N. E. Grosvenor

Several methods have been proposed for determining the tensile strength of rock. These have been tried out over the past several years, but the results have been erratic and of doubtful value. The tensile strength of rock is its weakest property, and this property apparently enters into all failure phenomena, whether underground or on the slope of an open pit. Therefore, it is essential that detailed quantitative information is known about the tensile strength of rock if the design engineer is going to select the proper pit slope, pit orientation, or orientation of underground workings so as to give the most economical and safest mining condition. This quantitative information may be used to orient the pit in such a manner as to allow steep slopes along two sides. This information possibly may be used to orient the direction of either underground workings or open pits so as to decrease powder consumption and to increase blasting efficiency. Hence it is of prime importance that a method of determining accurately the tensile strength of rocks be developed. The U. S. Bureau of Mines states' that no standard methods have been proposed by the ASTM for testing the tensile strength of rock. The method described in the Bureau publication is said by them to be unsatisfactory. A similar test that has been used in our laboratory in place of the USBM test is shown in Figs. 1 and 2. h this test the core is placed in a set of grips that has been designed for one particular size core. The grips are designed to distribute the stress around the core if they are tightened correctly. A universal joint or a flexible cable may be used in conjunction with the apparatus to prevent bending or twisting of the specimen. The main difficulty encountered with the system shown is the failure of the specimen within the grips. The possible cause of the failure within the grips may be due to a stress concentration set up by the uneven tightening of the grips. This method can be used only for tests on cores, and even then has been found to be totally unsatisfactory because of the failure within the grips. The U. S. Bureau of Reclamation has been using a test similar to the sketch shown in Fig. 3. Sulfur is cast around each end of the specimen to form a bearing surface and then a ring grip is used to apply a tensile stress. The grips are in contact with the sulfur cast and do not touch the specimen. This method is unsatisfactory, apparently because a large number of the specimens appear to break within the sulfur cast. Professor Wuerker of the University of Illinois uses the test shown in Fig. 4.' Professor Wuerker states2 that this method has given definite and reproducible results with the weakest as well as with the strongest rocks. The test is a supplement in all cases where cores cannot be obtained. The principle and equipment are the same as for the test for tensile strength of hydraulic-cement mortar. Soft

Jan 1, 1961

By R. D. Pehlke, J. F. Elliott

The equilibrium pressure of nitrogen gas over pure silicon metal and silicon nitride has been measured in the temperature range 1400° to 1700°C. From the experimental data, the standard free energies and enthalpies of formation of Si3N4(a) have been calculated as functions of temperature over the above temperature range. Utilizing data in the literature and the results of this investigation, the specific heat, molar enthalpy, molar entropy, standard enthalpy of fornation, and standard free energy of fornation are estimated for the temperature range 298° to 1400°C. THE high-temperature thermodynamic properties of many metallic nitrides are not well established at present. This is a serious deficiency because nitrogen and nitride-forming metals are important alloying additions to steels, and knowledge of the interaction between nitrogen and these elements is essential to a better understanding of the behavior of steels. Metallic nitrides also are used as refractory materials. Consequently, the investigation reported here was undertaken to provide more complete information on the standard entropy and free energy of formation of silicon nitride. The experimental technique provided a direct measurement of the equilibrium pressure of nitrogen gas in the range of 1413 to 1700°C for the reaction: 3 Si(1) + 2N2 (g) = Si3N4 (a) [ 1 ] and below 1413oC for the reaction: 3Si(c) + 2N2(g) = Si3N4(a) [2] APPARATUS The experimental system consisted of a crucible assembly, a reaction chamber, and a gas supply and vacuum system. The Crucible Assembly which contained the equilibration specimen and molybdenum radiation shields with a susceptor for induction heating is shown in Fig. 1. Two covered, high-purity alumina crucibles, one nested within the other, contained the susceptor, shields and specimen. Central openings in the upper shield and crucible covers permitted on optical pyrometer to be sighted into the central cavity of the specimen. The specimen itself was a 5/8 OD by 1-in.

Jan 1, 1960

By A. G. Metcalfe, R. P. Elliott, F. A. Crossley

THE texture method (utilizing monochromatic copper radiation) was applied to determine the orientation of the columnar grains of two vacuum cast beryllium ingots of 3 in. diam. Samples were mounted in a fixture as illustrated in Fig. 1, which permitted rotation and translation in order to approximate the method used for wires. The specimens were aligned so that the major axes of the columnar grains were parallel. Rotation was around the growth direction. After each translation the specimen holder was rotated 2 deg (1 deg for the samples from the second ingot) until a range of 30 deg on either side of the vertical was covered. The speed of translation was 1 mm per sec. A representative Debye pattern is shown in Fig. 2. The pattern was compared with theoretical patterns for various orientations. Also shown in Fig. 2 is the disposition of reflections on the (10i0), (0002), and (1011) Debye rings for the two possibilities that growth is either in the <10i0> or <ll30> direction. It is apparent that no significant preference for the direction of columnar growth is indicated. It is considered that the lack of a preferred orientation is due to the occurrence of the phase transformation (reported by Martin and oore&apos; to occur above 1250 "C) which masked the original solidification orientation. This research was supported by the United States Air Force under Contract No. AF 33(616)-5911, monitored by the Materials Central, WADD, Wright-Patterson Air Force Base.

Jan 1, 1962

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By Jean-Jacques Prompsy, J. S. Rinehart

The purpose of the present study was to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the drill bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. This paper covers one phase of a broad study involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, arange commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a velocity range in which the dynamic effects are greatly exaggerated and made more identifiable. Specifically, fracturing which develops at the end of a cylindrical bar undergoing a shock produced by impact was experimentally investigated, the impacted area being the face of a truncated cone terminating the cylindrical bar. Fracture characteristics were looked at as a function of impact velocity, area of impacted face and cone angle — parameters of considerable importance in the design of drill bit. EXPERIMENTS The specimens were made of Plexiglas, which enabled the fracture pattern to be easily observed. In Plexiglas, the velocity of a longitudinal wave is about 8,700 ft/sec, and the velocity of the transverse wave about 4,200 ft/sec. The specimens were impacted by a steel cylinder whose lower face was parallel to the terminal face of the experimental bit, as shown in Fig. 1. The impacting mass was shifted up and down on two steel rods, dropping from a maximum height of 11 ft, with the velocity varied between 0 and 6.5 m/sec. The initial mass of the cylinder was 4.1 kg, which could be increased by steps up to 8.8 kg by addition of steel plates. The velocity of the steel cylinder was determined by using an electric circuit; as the cylinder dropped, it contacted two steel wires, the first one starting and the second one stopping an electronic counter. Two similar counters connected in parallel were used to corroborate each other. The velocity was checked at each drop as it had been observed to vary somewhat from drop to drop. The two contact wires were located just above the top of the specimen so as to give a value of the instantaneous velocity of the steel cylinder at impact. The distance between the wires was 40 ± 0.5 mm and the discrepancy between the counters was never more than 0.1 m/sec. Thus the velocity was known to within 3.25 per cent. This precision was sufficient with respect to the precision of the machining of the specimens. A very small lack of parallelism between the face of a specimen and that of the impacting hammer resulted in an oblique impact which required a much lower velocity to break the specimen. The experiments had a twofold purpose — (1) to observe the fracture pattern, and (2) to find relationships between the minimum velocity required to generate a fracture within a specimen and the

The Lake Superior Mining Institute, Ishpeming, Mich. A. J. Yungbluth, Secretary. An Annual Volume of Proceedings, carrying papers presented during the year, has been published since 1S83, with the exception of the years 1S97, 1899, 1907, 1916, 1918, 1919, 1920, 1921, 1924 and 1927. No meetings were held during those years and conse-

Jan 1, 1933

By D. F. Kaufman, E. D. Levine, L. R. Aronin

ThE primary slip plane in hcp metal crystals can usually be inferred from the c/a ratio. Basal slip is the primary system at room temperature for zinc, cadmium, magnesium, cobalt, and rhenium, all of which have a c/a ratio greater than 1.60. Zirconium and titanium, on the other hand, each with a c/a ratio of 1.59, deform primarily by (1010) [ll20] prismatic slip. The increasing tendency toward prismatic slip in these materials is generally thought to be associated with the increase in atomic density on (10i0) as c/a is reduced. Beryllium, with a c/a ratio of 1.57, would, according to the above scheme, be expected to exhibit prismatic slip. However, in beryllium of commercial purity, the primary deformation mode at room temperature is basal slip.&apos; The ratio of critical shear stress for prismatic to that for basal slip at room temperature is approximately 5:l. The critical shear stress for prismatic slip decreases quite rapidly with increasing temperature, however, and at 500°C the ratio is approximately unity. The apparently anomalous behavior of beryllium has led to speculation that prismatic slip in this material may be restricted by an anisotropic effect of impurities,&apos; and that, if beryllium could be purified to a sufficient extent, prismatic slip might predominate at room temperature. In such a case, the conditions under which basal cleavage can occur would be suppressed, and enhanced low-temperature ductility might result. With the advent of the floating-zone method for purification of beryllium,3 it has become possible to determine experimentally the effects of purification on basal and prismatic slip. Tensile tests were performed at room temperature on single crystals oriented favorably either for basal or prismatic slip. The crystals had been purified to various extents by zone-refining, employing procedures that have been described elsewhere.4 Relative purities of the crystals were estimated by measuring the ratio of electrical resistance at 4.2"K to that at 298°K. Typical values ranged from 0.40 for commercial-purity material to 7.7 X 10"4 for crystals prepared from vacuum-distilled beryllium and subjected to six zone-refining passes. The purity dependence of the critical shear stresses for basal and prismatic slip is shown in Fig. 1. In the purity range studied, the critical shear stress for basal slip is decreased from 1.4 to 0.14 kg per sq mm. The critical shear stress for prismatic slip is decreased from 6.7 to 5.3 kg per sq mm. The decreases in critical shear stress for each deformation mode, therefore, are approximately equivalent. No purification anisotropy is observed. Because of the absolute magnitudes of the critical stresses, the ratio of the critical shear stress for prismatic slip to that for basal slip actually increases from 5:l to 38:l at the highest purity level studied. It is evident, therefore, that basal slip is the primary deformation mode in high-purity beryllium. This fact must be accounted for in any rationalization of the deformation behavior of hcp metals. This work was performed at Nuclear Metals, Inc., under the sponsorship of the U.S. Atomic Energy Commission.

Jan 1, 1964

By R. B. Snow

This paper describes a technique of polishing and etching specimens of open-hearth furnace slags or hearth aggregates for identification of the crystalline constituents —lime (CaO), tricalcium silicate (3CaO.SiO2), dicalcium silicate (2CaO.-SiO2), rnonticellite (CaO.MgO.SiO2), or forsterile (2MgO.SiO2), with especial em-phasis on the mineral merwinite (3CaO.-MgO.2SiO2). With proper standardization, this identification does not require the use of the petrographic microscope. The composition of basic open-hearth slags and furnace bottoms falls, almost without exception, within systems containing CaO, MgO, &apos;IFeO,,, MnO and SiOz, in which the number of basic molecules so greatly exceeds the orthosilicate ratio (two molecules of base to one of silica) that free basic oxides, and combinations between them such as alumi-nates or ferrites, are present in cooled specimens. Orthosilicates of (CaO + NgO) are the most common in such specimens, since in nearly all cases, except premelt slags, the molecular ratio of (CaO + MgO) to SiO, is more than 2 to I. When sufficient lime is available it combines with the silica to form dicalcium silicate (2Ca0.Si02), which contains little, if any, IvfgO, FeO or MnO in solid solution whereas the latter oxides combine to form the oxide solid solution known as periclase. If the lime present is insufficient to form dicalcium silicate (2Ca0.Si02) it combines with Mgo to form either merwillite or moIlticellite (SiOz); these minerals take little if any FeO or MnO into solid solution and the remaining MgO, FeO and hInO combine as periclase. This generalization seems to be valid for basic slags and furnace bottoms, since minerals such as Ca0.MnOSi02 and CaO.FeO.SiOz are found only in slags in which the lime-silica ratio is less than 2 and are not observed in &apos;pecimens from furnace bottoms. The identification of crystalline constituents in such materials, especially of fine crystals in the groundmass, is difficult under the petrographic microscope. They are often masked by their neighbors because of their small size in relation to the thickness of the thin section and because of the presence of Opaque Or colored constituents. The indices of refraction and the optical sign of the mineral are sometimes difficult to determine because of the small size or because Of twinning or of inclusions within the crystal. Moreover, the positive identification of merwinite (3Ca0.Mg0.2Si02) from its optical properties is usually difficult in the presence of dicalcium silicate (zCaO.SiO2). CaO, MgO, jCa0.Si02 and 2Ca0.SiOz in open-hearth &apos;lags have been identified for a number of years in the U.S. Steel Corporation Laboratory by the usual

Jan 1, 1948

By R. B. Snow

This paper describes a technique of polishing and etching specimens of open-hearth furnace slags or hearth aggregates for identification of the crystalline constituents —lime (CaO), tricalcium silicate (3CaO.SiO2), dicalcium silicate (2CaO.-SiO2), rnonticellite (CaO.MgO.SiO2), or forsterile (2MgO.SiO2), with especial em-phasis on the mineral merwinite (3CaO.-MgO.2SiO2). With proper standardization, this identification does not require the use of the petrographic microscope. The composition of basic open-hearth slags and furnace bottoms falls, almost without exception, within systems containing CaO, MgO, &apos;IFeO,,, MnO and SiOz, in which the number of basic molecules so greatly exceeds the orthosilicate ratio (two molecules of base to one of silica) that free basic oxides, and combinations between them such as alumi-nates or ferrites, are present in cooled specimens. Orthosilicates of (CaO + NgO) are the most common in such specimens, since in nearly all cases, except premelt slags, the molecular ratio of (CaO + MgO) to SiO, is more than 2 to I. When sufficient lime is available it combines with the silica to form dicalcium silicate (2Ca0.Si02), which contains little, if any, IvfgO, FeO or MnO in solid solution whereas the latter oxides combine to form the oxide solid solution known as periclase. If the lime present is insufficient to form dicalcium silicate (2Ca0.Si02) it combines with Mgo to form either merwillite or moIlticellite (SiOz); these minerals take little if any FeO or MnO into solid solution and the remaining MgO, FeO and hInO combine as periclase. This generalization seems to be valid for basic slags and furnace bottoms, since minerals such as Ca0.MnOSi02 and CaO.FeO.SiOz are found only in slags in which the lime-silica ratio is less than 2 and are not observed in &apos;pecimens from furnace bottoms. The identification of crystalline constituents in such materials, especially of fine crystals in the groundmass, is difficult under the petrographic microscope. They are often masked by their neighbors because of their small size in relation to the thickness of the thin section and because of the presence of Opaque Or colored constituents. The indices of refraction and the optical sign of the mineral are sometimes difficult to determine because of the small size or because Of twinning or of inclusions within the crystal. Moreover, the positive identification of merwinite (3Ca0.Mg0.2Si02) from its optical properties is usually difficult in the presence of dicalcium silicate (zCaO.SiO2). CaO, MgO, jCa0.Si02 and 2Ca0.SiOz in open-hearth &apos;lags have been identified for a number of years in the U.S. Steel Corporation Laboratory by the usual

Jan 1, 1948

By B. S. Hickman

Using primarily quantitative single crystal X-ray techniques studies have been made of the precipitation of the metastable w phase in alloys of titanium with Mo, Mn, Fe, Cr, and Nb. It is shown that, in agreement with earlier work on the Ti-V system, the composition of the w phase during aging approaches a constant; the value varies from one system to another in a systematic manner with the electron concentmtion. Results relevant to the mechanism of w precipitation during quenching and during aging are presented and discussed. Results are presented to confirm that the w phase is coherent and the nzorphology of the Necipitates is described and discussed. PRECIPITATION of the metastable w phase in alloys of titanium is of interest because of its severe embrittling effect and also because of the enhancement of the superconducting properties which accompanies precipitation.1 The general features of w phase precipitation have been discussed by cuillan and by Bagaratskii et d3 The work described in this paper forms part of a general study of w phase precipitation which was undertaken to elucidate various unknown or controversial features of the process, namely: i) What is the mechanism of formation of the phase ii) How does its composition, morphology, volume fraction, and particle size vary with the type and content of the alloying element and with the heat treatment conditions? iii) What is the relation between the w phase and the equilibrium a phase? In a previous paper4 the results of a detailed study of w phase in Ti-V alloys were presented. It was shown that: U During aging the composition of the w phase approached a saturation value of 13.5 to 14.0 at. pct V. ii) w precipitated as cube shaped particles and once precipitation was complete, particle coarsening did not occur. iii) a phase formed initially by direct conversion of w-phase precipitates. In this paper similar measurements are reported on Ti-Mo alloys and some more limited data given on the Ti-Cr, Ti-Fe, Ti-Mn, and Ti-Nb systems. The results i.1 the six systems are then compared. It has been shown previously by electron microscopy that the w precipitates as ellipsoids in both the Ti-Nb system,&apos; and in i-o.&apos; Blackburn and williamsz3 have reported the precipitates in Ti-Fe, Ti-Cr, and Ti-Mn are cubic, i.e., similar to the Ti-V system.476 EXPERIMENTAL METHODS 1) Specimen Preparation. Samples of the compositions shown in Table I were prepared by arc melting. High purity electron beam zone refined titanium (Materials Research Corporation Grade I—total impurity content =250 ppm) was used; the other source materials are given in the table. A commercial Ti-8 wt pct Mn alloy was used for studies of this system. After homogenization the materials were rolled or cut into strip approximately 1/4 in. by 2 in.; the strip was then heated at temperatures of 1200" to 1300°C for several hours by passage of a direct current through the strip in an ultra high vacuum system (<10-torr) and then quenched by admitting high purity helium and switching off the current. This treatment resulted in crystals up to 2 in. by 2 in. by A in., almost all of which had a [100] direction nearly perpendicular to the plane of the strip. The crystals were cut from the strip by spark machining and their composition checked by lattice parameter measurements supported by chemical analysis. 2) X-Ray Diffraction Methods. Lattice parameter measurements were made using a modification of the single crystal spectrometer described by ond. In this technique the crystal angles for reflection on either side of a highly collimated primary beam are measured. Generally the 400 CuK, or the 400 CuKp reflections of the bcc lattice were used. In the as-quenched crystals a precision of 1 in 105 was obtained, but due to line broadening the parameters in aged materials could only be measured to 1 in lo4. This accuracy was, however, quite adequate for the purposes of these experiments and enabled the composition of the p phase to be obtained to 10.1 pct in all systems except Ti-Nb where the lattice parameter change with composition is very small. The precipitation and growth of the w phase was examined using a single crystal goniometer attached to a Phillips diffractometer. The relative intensities and line shapes of b-phase and w-phase reflections

Jan 1, 1970

By C. S. Roberts

Microstructural studies of a Mg-10.3 pct Al alloy showed that discontinuous precipitation during aging multiplies the grain boundary area available for easy deformation in elevated temperature creep. An increase of strain rate for a 6.2 pct Al alloy at 400°F, where precipitation and creep are concurrent, caused an increase in the volume percentage discontinuously precipitated at the completion of the process. The relatively poor elevated temperature creep resistance of heat treated alloys of the Mg-AI-Zn type was explained in these structural terms. C resistance of the heat treatable Mg-A1 based alloys is poor compared to that of Mg-Ce based alloys. While the latter show a continuous precipitate, Mg-A1 alloys prefer a discontinuous precipitate at grain boundaries. &apos;.:&apos; It has been concluded that the excellent creep resistance of Mg-Ce alloys was primarily due to the continuous precipitation which especially localized at the grain boundaries.&apos; The purpose of the present investigation was to obtain a parallel correlation, if such exists, between the poor creep resistance and the state of precipitation in Mg-A1 alloys. Discontinuous precipitation produces about three times as many true grain boundaries as originally existed. This microstructure would be expected to have a marked influence in creep, where quantity of grain boundary area is important. Experimental Procedure The two experimental alloys contained 6.2 and 10.3 pct Al. They were made from electrolytic magnesium by alloying under flux and casting in 3 in. diam permanent molds. The ingots were extruded into 1 1/4 x 1/8 in. flat stock under the following conditions: billet preheat 700°F (2 hr), container and die temperature 700°F, speed 3 fpm, and area reduction ratio 45:1. The creep specimens were machined from blanks which had been solution heat treated 24 hr at 770°F and aged 16 hr at 400°F. Attempts were made to control the grain size as closely as possible for extruded stock. The grain size after solution heat treatment was about two thousandths of an inch for the 6.2 and five thousandths for the 10.3 pct Al alloy.

Jan 1, 1957

By W. Hurst

What is entailed here is the extension of the sinzplified material balance formulas to encompass interference between oil fields. As previously reported, the ex-plicitness as so revealed for the cunzulative pressure drop as a function of all factors contributing to its change in the material balance equation, is now transcribed through the inter-conzmunicating aquifer to effect an increased pressure drop on an adjoining field by interference. Such is performed by mathematical analyses and the application of the Laplace transformations. What is accomplished is that the reiteration problems previously associated with interference studies are nullified, since volumetric changes for the fluids in situ are automatically adjusted by the explicitness so expressed, and what pertains to the superposition principle applies only to the impeded water drive upon a su.bject field, which is likewise incorporated in the over-all pressure drop that results. The mathematics treats with the rigorous solution of the problem, as well as with methods easily amenable to numerical interpretation by the practicing engineer. In all cases, however, what is deduced for areal extents, reveal interference between wells when time becomes large that further substantiate the analyses. Probably of equal significance, all variables and for/nation characteristics are accounted for. This applies to the differences in PVT analyses that occur from field to field and the physical parameters associated with the lithology of the reservoirs. The latter is deduced from a rigorous interpretation of the unsteady-state flow problem for sands of different permeabilities in series. Thus, what purports to be a trial-and-error calculation to include variations in sand conditions within the intercommunicating aquifer to define water drive has little importance compared to the designation of such paranzeters at the reservoir to constitute the essential criteria. INTRODUCTION In a recent publication, the reader has been introduced to the simplified material balance formulas,&apos; It has been shown that the complexities formerly associated for identifying and determining reservoir pressure in the material balance relationship can be resolved by treating with the Laplace transformations, the inversion of which reveals pressure as an explicit function of all factors contributing to its change. For an under saturated oil reservoir, this constitutes an integrated effect from the inception of production; and for a saturated oil reservoir, such represents a survey traverse. However, what is most important, for the first time we are able to express the pressure change in a reservoir directly to the oil, gas and water produced, and to the physical parameters of the formation, in the same manner that reservoir pressure has served in the past to define well interference — which opens up this avenue of endeavor for investigating interference between oil fields. The occurrence of interference is by virtue of the juxtaposition of two or more oil reservoirs producing in the same aquifer. Thus, in any one field, the extended production so incurred creates a pressure lowering in the field, as well as in the aquifer, which can now be transcribed by these simplified material balance formulas to the adjoining reservoir to observe the increased pressure change so induced. These effects are retroactive from field to field, to reveal a pressure drop far in excess of normal depletion to evidence the interference pattern that can result. Such is the purpose for the present undertaking — to develop the mathematical physics treating with this phenomenon of interference between oil fields, employing the simplified material balance formulas. Since Ref. 1 often will be referred to in the text, it is identified as "The Simplification", in the same connotation that another paper has been referred to as the "Laplace Trans-formation. However, the amount of material to be covered in these passages is substantial; therefore, the total emphasis will be placed upon developing these fundamental ideas treating with interference rather than attempting to offer work curves, which always can be prepared. For the practical application of these simplified material balance formulas that form the framework of the present development, the reader will find a comprehensive treatment in the Appendix of Ref. 1, illustrating a factual field example. In essence, what is proposed by this presentation is to make available to the practicing engineer a simplified means to treat with interference between oil fields, independent of the complex machine computations that have attended such undertakings in the past. As the problem unfolds, a common pattern will be discernible, whereby the many reiteration processes that previously required computing devices are eliminated.

By D. G. Russell

Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary eflects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estitnates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. On the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. INTRODUCTION The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottom-hole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + ?t)/ ?t (where At is shut-in time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "afterproduction" or "fill-up" portion of the pressure build-up. During the period that the well fill-up effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the afterproduction period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the afterproduction period is a paper by Gladfelter, Tracy and Wilsey.1 In the approach of these authors it is necessary to measure the rate of influx into the well during the afterproduction period. This is done through sonic measurements or through measurement of tubing-head and casing-head pressures simultaneously with

Jan 1, 1967

By M. J. Marcinkowski, A. Szirmae, R. M. Fisher

Room -temperature hardness measurements obtained from single and polycrystalline samples of a 47.8 at, pet Cr-Fe alloy which were aged for various times al 500°C show a two-fold increase over that of the unaged alloy after annealing for 1000 hr. A detailed examination of the deformation markings in the neighborhood of the hardness imbressions reveals that twinning becomes an increasingly more important mode of deformation as aging proceeds. this observation is shown to be inconsistent with the Proposals that the transformation is eve of order-disorder On the other hand, the results are in agreement with previous observations of Fisher et al. of a coherent chromium-rich precipitate which forms in an iron-rich matrix as a result of a miscibility gap in this alloy system as proposed by Williams . Using the coherent precipitate hypotlzesis as a model, a detailed analysis of the various possible strengthening contributions to both the slip mid twinning stresses is made. In the case of&apos; slip, lattice friction within the chromium-rich phase and the chemical energy associated with the interface between the two phases contribute about 60pet to the total strength. The contributions from coherency strains and modulus differences are thought to contribute the remaining 40 pet of the strength but are difficult to evaluate because of uncertainties regarding the flexibility of the dislocation line. All of the factors have nearly the same or else a smaller effect on the twinning stress in the aged alloy. Twinning is never observed in the unaged alloy because the twinning stress is much higher- than that for slip. With increased aging times, the various contributions to the total stress for both twinning and slip increase, but most of those for slip increase much more rapidly, so that, in the fully aged alloy, it surpasses the stress for twin propagation. When a twin is nucleated by the chance occurrence of an internal stress concentration during a test, the subsequent twin burst results in a low hardness reading. FeRNTIC Fe-Cr alloys from about 15 to 80 at. pet Cr content show considerable change in properties such as hardness, electrical resistivity, saturation magnetization, and so forth, after aging in the vicinity of 500°C.* The most marked change is a large increase in hardness accompanied by a sharp decrease in ductility, so the phenomenon has often been referred to as the 475°C (885°F) em-brittlement problem. Changes in microstructure are rather subtle and most investigators have not been able to observe any X-ray diffraction or metal-lographic changes during aging. There is little doubt that the phenomenon is inherent to the Fe-Cr binary system and is not directly related to the formation of a phase. Two distinct schools of thought have developed during the past decade concerning this problem. Masumoto, Saito, and sugiharal have concluded, from their own specific-heat measurements, that atomic ordering occurs in this temperature range. Pomey and Bastien2 have also attributed the changes in physical properties with aging in the neighborhood of 500°C to atomic ordering. In addition, Takeda and Nagai3 claimed to have found X-ray verification for superlattices corresponding to the compositions FesCr, FeCr, and FeCr3. However, all known attempts to observe superlattices in Fe-Cr alloys using neutron diffraction, which should be much more sensitive, have been unsuccessful. These have been reported by Shull et al.4 for 25 at. pet Cr, williams5 for 75 at. pet Cr, and Tisinai and samans6 for a 28.5 at. pet Cr. steel. The second and more prevalent opinion ascribes the 475°C embrittlement phenomenon to the formation of a coherent precipitate due to the occurrence of a miscibility gap in the Fe-Cr system below about 550°C. This latter concept was first indicated by the results of Fisher, Dulis, and Carroll,7 who were able to extract fine particles about 200Å in diameter from samples of 28.5 at. pet Cr steels aged from 1 to 3 years at 475°C. The extracted material was found to be nonmagnetic, to have a bee structure with a lattice parameter between that of iron and chromium, and to contain about 80 at. pet Cr. Williams and paxton8 and williams5 confirmed these results and first explicitly proposed the existence of a miscibility gap below the a region in the equilibrium diagram. Alloys aged within this gap

Jan 1, 1964

By AIME AIME

TWO weeks ago the writer was lunching in the Engineers` Club in New York with a man who has perhaps the widest acquaintance among engineers of anyone in the country a member of another of the Founder engineering societies. "By the way," lie asked. "who have they nominated for your next president."&apos; "Doctor Becket," I told him- "Oh. that&apos;s line," he replied, in a heartfelt tone that rang with sincerity. "I have come in contact with him occasionally and he is just the right type.&apos; And that is the way Dr. Frederick M. Becket impresses everybody. The right type. Most Institute members of the western group of hard-rock minors do not know him, but then they meet him in his swing around the circle next year they will not require a long acquaintance to sense his kindly and outstanding personality, to realize that he is a gentleman in the bet meaning o1 that word, a man of wide sympathies and interests.

Jan 1, 1932

By A. H. Willis

In this paper the results of an exploratory study conducted by personnel of the Knolls Atomic Power Laboratory on 18.6, 22, and 40 wt pct uranium-zirconium alloy will be presented. LARGE power output and long life or endurance from small, compact nuclear reactors require the use of enriched uranium for a fuel material. However, the ability to remove heat from the element, the tolerable fission product concentration, or some physical limitation of the system can limit the allowable fuel enrichment, or the volume of the fuel. In such an event, the fuel-element designer must find a suitable diluent for the uranium. Zirconium is an attractive material for such a purpose as it has good nuclear properties and a low absorption cross section. Because it has a good corrosion resistance in water, zirconium is a suitable cladding and the uranium-zirconium alloy makes a good core material. The alloy has a high thermal conductivity, a low elastic modulus, and a low thermal-expansion coefficient, all of which tend to minimize the thermal stresses in the core. Furthermore, the unirradiated material is reasonably ductile and has adequate strength. DESCRIPTION OF SAMPLES Two types of cylindrical samples were used in this study 1) short, 1/2-to 1-in.-long samples to test the irradiation stability of the alloy and 2) 2-ft-long samples to investigate the resistance of an element to longitudinal deformation. Composite samples having 0.060-to 0.140-in. core diameters and clad with a 0.010-in. thick zirconium jacket were fabricated by coextrusion and by hydrostatic pressure bonding of the cladding to the preformed core material. Both fabrication processes produced the uniform metallurgical core-to-cladding bond which was felt necessary to minimize the uncertainty of the central core temperature. Both consumable-arc and induction-melting techniques were used to melt the uranium-sponge zirconium core alloy. Since a graphite crucible was used in induction-melting this alloy contained more carbon impurity, which resulted in a finer grain size than the arc-melted alloy. The core to cladding interface was uniform in elements coextruded from the fine-grain, induction-melted core material, while those elements fabricated using arc-melted core material had very irregular interfaces because of the coarser grain size. Both cold-worked and heat-treated fuel materials were irradiation tested. Cold-worked alloys were swaged to about a 5 pct final reduction in area without subsequent annealing. The heat-treated alloys were heated to 800°C, held at temperature for 15 min and furnace-cooled to about room temperature. This

Jan 1, 1960

By W. T. Roberts, N. G. Turner

A study of the fatigue properties of several grades of commercially pure titanium has established that the strain-aging process is of minor importance in the development of a fatigue limit and a relatively high fatigue strength ratio. Metallographic observations and damping measurements at room temperature indicate that striations are able to spread from grain to grain only at stress levels above the fatigue limit. This suggests that the fatigue limit represents the stress above which large-scale dislocation unlocking takes place. Fatigue tests on annealed material at - 60" and - 196" c showed that under conditions when a thermally activated diffusion process would be suppressed the fatigue limit is not eliminated. Prestraining at room temperature did not have a detrimental effect on fatigue strength at room temperature but a decrease was recorded at — 60°C. This is further evidence that initial dislocation locking is a important strengthening mechanism. TITANIUM and titanium alloys have S-N curves with a definite fatigue limit, and a high ratio of fatigue limit to UTS can be attained. Other materials which show similar fatigue characteristics are mild steel and some Al-Mg alloys. The fatigue limit of these materials has been associated with their strain-aging capacity. It is well-known that commercial-purity titanium contains interstitial impurities which can give rise to a sharp yield point, and a small strain-aging effect following static strain has been demonstrated.7 This type of aging reaction is differentiated from the dynamic aging process when aging occurs during plastic deformation, and which is generally observed at elevated temperatures. In a titanium at room temperature, dislocation locking is associated with the interaction of interstitial oxygen, nitrogen, and carbon atoms with dislocations. Ehr-lich has shown that the distortion produced by introduction of these atoms into the hcp lattice has no shear stress component and hence there is no interaction between the stress field and the screw component of a dislocation. Thus the dislocations as a whole are only weakly locked. It is clear that strain-aging effects in hcp a titanium will be much less pronounced than those observed in bcc iron and steel. In recent years, the attribution of the fatigue limit solely to strain aging has been questioned. It has been pointed out that a definite fatigue limit is observed at temperatures as low as -196°C in some titanium alloys,&apos; and strain aging is not expected to be effective at this temperature. The role of initial locking of dislocations in determining fatigue behavior has been examined in low-carbon steel by Oates and Wilson. They showed that under conditions in which the aging potential is low the factors which control the buildup of local stresses and hence affect dislocation unlocking, e.g., grain size, are important. There are indications that other metals can have a definite fatigue limit with no established strain-aging capacity, an example being magnesium12 which has the same crystal structure as a titanium. The spread of plasticity from grain to grain in hexagonal metals may be more difficult than in cubic metals because of the limited number of slip systems in the former, and this may account in part for their fatigue behavior. The present work was undertaken to elucidate the relative importance of crystal structure, strain aging, and initial dislocation locking in determining the properties of commercially pure titanium when subjected to cyclic stressing. 1) EXPERIMENTAL METHODS Three grades of commercial-purity titanium were used and a material of lower interstitial content was prepared by melting high-purity Japanese sponge titanium (referred to as H.P. Ti). The compositions and typical mechanical properties of the materials are shown in Table I. Fatigue tests were made in push-pull (zero mean stress) using an Amsler Vibraphore machine at a frequency of about 160 cps. Two types of fatigue specimen were used—one with a waisted gage length for determination of S-N curves and the other with a parallel gage length for metallographic studies and damping measurements. After careful machining and mechanical polishing, all specimens were electropolished prior to fatigue testing. The electrolyte consisted of 10 parts methyl alcohol, 6 parts 2-butoxyethanol, and 1 part perchloric acid (SG 1.54) and it was maintained at a temperature of -10" to -20°C during polishing. Tests at room temperature were normally carried out with the specimen immersed in a silicone oil bath which could be heated for elevated-temperature tests.

Jan 1, 1969

By John S. Johnson, Thomas Fraser

SIZING is the process of separating mixed particles into groups of particles all of the same size, or into groups in which all particles L range between certain definite maximum and minimum sizes. In coal preparation, sizing is generally accomplished by passing the coal over screens. Separation by differential settling in air or water currents has been adapted to the special field of separating very fine sizes, and these processes are in commercial use to a relatively small extent in the coal industry. Separation with screens is a very old industrial practice. Agricola 1 described the use of screens for ore treatment in the middle ages. In the literature of the British coal industry references were made to the screening of coal as early as 1589, but the practice of extensive sizing for the market did not become general until the last half of the nineteenth century. In America, the practice of sizing developed first in the Pennsylvania anthracite region, beginning with the use of rakes2 in the mine working places to recover coarse coal. This mining procedure left the fines in the mine. Preparation outside the mine started with the installation of stationary cast-iron plates with 4 to 6-in. square holes. The run-of-mine coal was dumped upon the platforms, the large pieces of rock were picked out by hand, and the large lumps of coal were broken with hammers. The term "breaker," which still applies to the anthracite-preparation plant, originated with this practice, but the term is no longer descriptive of the entire function of the plant. In 1884, the first power-operated anthracite coal breaker3 was erected by Gideon Bart at his colliery at Wolf Creek near Minersville, Pa. This plant utilized a system of rolls for breaking the coal and revolving screens for sizing. The plant was driven by a steam engine. It could handle

Jan 1, 1943

By H. F. Bishop, F. A. Brandt, W. S. Pellini

The solidification mechanism of experimental steel ingots (7x7x20 in.) was studied by thermal analysis. It was determined that solidification proceeds in wave-like fashion at rates which are determined by the carbon level, superheat, and mold thickness. The thermal cycles of the mold walls were related to the course of solidification. ESPITE marked advances in the field of solid state transformation, metallurgical research has contributed comparatively little exact quantitative data on the mechanism of solidification of metals. There is, therefore, a great need for such data in the various metallurgical industries. The mechanics of solidification of ingots have been investigated in the past primarily by studies of the rate of skin formation as indicated by bleeding or "pour out" tests. The "pour out" method, however, is a tool which gives only approximate information. In the case of alloys with wide solidification ranges, such as irons and certain nonferrous alloys, the method will not work at all; in the case of alloys of intermediate solidification ranges, such as commercial steels, the information may be misleading. Thus, the general adoption of this method has resulted in divergent conclusions regarding the solidification process. Chipman and Fondersmith1 by means of bleeding tests have shown that the linear growth of a solidifying ingot wall follows a parabola of the general form, D = K C, with the start of solidification delayed until superheat is exhausted, as indicated by the constant C. These tests were carried only to a wall thickness of about 5 in. using an ingot of approximately 17x39 in. in cross-section; hence the latter stages of solidification were not studied. Matuschka2-3 indicated that linear solidification of ingots is rapid at first, then slow, but toward the end of solidification the rate becomes extremely rapid again. Spretnak&apos;s4 bleeding studies indicated that, wall growth is expressed more rigorously by two parabolas, and that their point of intersection corresponds to a change of solidification mode from columnar to equiaxed. Spretnak also showed that the K values of the first parabola are always the same regardless of superheat. Nelson bled ingots of square cross-section and found that linear wall growth is initially rapid but decreases continually until the end of solidification. He also concluded that rate of solidification in ingots of square cross-section increases 2.15 pct for every 10 pct increase in cross-sectional area of the mold. The mold ratios considered (ratio of cross-sectional area of the mold to cross-sectional area of the ingot) were all less than 2 to 1. The subject of solidification has also been treated mathematically in many cases, but because of the lack of accurate thermal constants and the simplifying assumptions required, as their authors generally acknowledge, they represent only approaches to the actual conditions of ingot solidification. A third method of studying solidification is the electrical analogue method promulgated by Pasch-kis6-7 and by Jackson and coworkers.8 This method treats solidification as a heat transfer problem with the solidification cycle synthesized on an electrical circuit. Paschkis in his treatment of solidification considered the fact, which was generally ignored, that solidification of steel is not simply the growth of a plane solid wall but a more complex process occurring over a temperature range as indicated by the constitution diagram. Undoubtedly, the anomalous results obtained by bleeding tests arise from the inability to measure quantitatively this mushy condition. The shape of Paschkis&apos; solidification curves are more nearly in accord with those of Matuschka, in that they indicate rapid linear solidification at the beginning and end of solidification with intermediate solidification occurring at a slower rate. Paschkis indicates a definite lengthening of solidification time with increasing superheat. Thermal analysis is a direct method providing exact information for all types of metals regardless of solidification range and was thus adopted in the present program to follow the entire course of solidification from the surface to the centerline of the ingots. The method has the added advantage of being adaptable to following the thermal cycle of the ingot mold during the course of solidification. Test Methods The ingots studied were of square cross-section, 20 in. long, tapered from 71/4 in. at the top to 63/4 in. at the bottom, and fed with a hot top 7 in. in diam and 12 in. high. The molds were uniform in wall

Jan 1, 1953

By FRANK COLE

THE territory covered in this discussion includes all the states west of the Mississippi river. Agriculture is expanding each year in this section, but until recent years the application of commercial fertilizers as an aid to crop production was not practised to any great extent. The use of commercial fertilizers has increased somewhat, but is still on a small basis as compared with the tonnages used else- where in the United States. During 1928 these western states used 665,100 tons of all classes of fertilizer as compared &apos;with 7,933,600 tons used in the whole United States; or this western area, compromising near- ly two-thirds the land area, uses about 5 per cent of the total fertilizer. To show how large a tonnage one state may consume, North Carolina for the year 192s used 1,349,360 tons of commercial fertilizer or about twice the amount used by 22 western states.

Jan 1, 1930