Search Documents

By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy's law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy's law' has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy's law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.'s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.' To others,' turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy's law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.' In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy's law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy's law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy's law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy's law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy's law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By Charles Wert

THE diffusion and precipitation of carbon and nitrogen in a iron have previously been investigated using the internal friction as a measuring tool.' Most of this work has been done on rather pure iron; no effect was observed which would indicate that either of these phenomena is affected by the rather small amounts of impurity found in these samples of iron. Fastz observed, however, that both the diffusion rate and the aging properties of nitrogen in iron were sensibly changed by the addition of Vz pet Mn. The diffusion rate at a given temperature is reduced and the nucleation of nitrides is apparently changed somewhat. He observed no such changes for carbon in this alloy. Later Dijkstra and Sladek" extended these observations on nitrogen to other alloys of iron. They found that metals other than manganese also influence the behavior of nitrogen in iron; chromium, molybdenum and especially vanadium affect the diffusion and precipitation of nitrogen even more than manganese does. Their results have been verified in all essential details by this author, who finds in addition that small additions of nickel have about the same effect on the diffusion of nitrogen as the same amount of manganese. The present work was undertaken to study the effect on carbon in iron of these alloying elements. The alloys used had two sources. The material used as a "standard" (designated Fe in this paper) in the measurements was some iron supplied by J. K. Stanley, of Westinghouse Electric Corp., who reported 0.01 pct 0, as the only major impurity. He also made up an alloy of 0.26 pct Ni and one of 0.9 pct Mo using this same iron as a base. They were supplied by him in 2 lb billets, which were sawed into rods and cold formed into 0.030 in. wires for measurement. The alloys of chromium, manganese, and vanadium were prepared by the metallurgy section of the Institute for the Study of Metals, University of Chicago, by adding these metals in turn to vacuum melts of National Research Corp. iron. The small castings prepared in this way were also cold formed into 0.030 in. wires. After these wires had been prepared they were decarburized for 30 min at 730°C in wet Hz. After this treatment, no trace of carbon (as measured by internal friction) could be found. All specimens were then carburized for about 15 min at 710°C and water quenched. By this treatment the internal friction at 40°C was raised to a Q-' ~ 0.015. The diffusion of carbon in these alloys was studied by observing the shape and position of the internal friction peak at 0.9 cycles per sec. These measurements were made using a torsional pendulum in a manner described earlier.' The data are plotted in Fig. 1. It is seen that there is no apparent difference in internal friction between the various alloys. This is in marked distinction to the broadening and shift-

Jan 1, 1953

By L. D. Hall, S. J. Rothman

DIFFUSION coefficients of RaD (PD) and RaE (Bi) in a Bi-0.255 atomic pct Pb alloy have been measured by the methods outlined in a previous paper.' The following changes were made in the experimental procedures: the bath was made up of about 400 to 500 g Bi; and no correction was made for the volume change of bismuth on melting. The data are presented in Table I and Fig. 1. A least-squares analysis of the data yielded D = (0.120 t 0.09) exp ( -9680 + 1070/RT) D- (0.0465 0.001) exp (-8100 + 466/RT). Statistical analysis of the data indicated that the activation energies are significantly different at the 50 pct level, but not at the 75 pct level, while the D values are significantly different at the 97.5 pct level, but not at the 99 pct level. The differences are thus not as clear-cut as they were for lead. However, bismuth diffuses faster than lead in high bismuth alloys as well as in lead. The high activation energies, more than twice the value calculated from viscosities, are in good agreement with the results of Grace and Derge.' No data were obtained at higher temperatures because of gas bubble formation in the capillary. Acknowledgments This work was supported by the Office of Ordinance Research under contract DA-04-200-ORD-178. The authors thank 0. P. Vieria and M. Volpe for help in the experimental work.

Jan 1, 1957

By P. E. Busby, C. Wells

FURTHER study of data used in determinations of 1—rates of diffusion of boron in austenite and 2—solubilities of boron in the a and phases of iron and steel' has provided an equation for the diffusion of boron in a iron. In brief, the previously published data were accumulated from the results of deboron-izing (and decarburizing) experiments carried out in the range of 700° to 1300°C. Diffusion coefficients (D?) for boron in austenite were calculated using the Grube solution of Fick's law. However, only solubility values were estimated from the discontinuous concentration-penetration curves, Fig. 1, which are characteristic of diffusion in two phases. Dr. Carl Wagner' has recently provided a solution for calculating D values from penetration curves of this type as follows: Cl1.1 —C8/C8- C11.1 = vp ? e ? erf (?) and D = ?/4?2 t where C11,12, C8, C11, and E have the values shown in Fig. 1. D is the diffusion coefficient, sq cm per sec; t is time of deboronizing anneal, see; and ? is a di-mensionless parameter. For a given diffusion experiment, the value of ? can be readily obtained by graphical solution from a plot of y vs the right-hand part of Eq. 1. D may then be evaluated from Eq. 2. The avplication of this solution to previously re-ported results, of which excerpts are given in Table I, permits the calculation of diffusion coefficients for boron in a iron. On the basis of these meager data, it is tentatively concluded that the diffusion of boron in a may be represented by the equation Da = 1011 e-92,900/RT where R is the gas constant, cal X 0C-1 X mol-1; and T is the absolute temperature, OK. Although the frequency factor, 106 sq cm per sec, is admittedly several orders of magnitude higher than expected, the value of Q, 62,000 cal per mol, appears reasonable and is, in fact, very similar to that for the self-diffusion of iron. It is pertinent to mention at this point that the value of Q obtained for the diffusion of boron in austenite by means of the Wagner solution is 19,000 cal per mol and is in excellent agreement with the value previously reported1 in the equation DT = 2xl0-3 e-21,000/RT [4] which was determined by the application of the Grube solution to other data. The fact that determined constants A and Q in the equation D? = A e-Q/RT were practically the same, independent of whether the Wagner or Grube solutions were used in determinations of D values, strengthened the authors' belief that the computed values of D (Table I) using the Wagner solution are reliable. The relative values in Eqs. 3 and 4 for the diffusion of boron in the a and ? phases, respectively, suggest that boron forms a substitutional solid solution in a iron and an interstitial solid solution in ? iron. The same tentative conclusion has been reached by McBride et al.3 on the basis of relative solubilities, atom diameter, and the size of the interstitial hole in a and ? iron. In connection with the data for test 14 listed in Table I, it is of interest to calculate the solubility of boron in a iron using the D value given by Eq. 3. As might be anticipated from the small movement of the interface in test 14, proper substitutions in Eqs. 2 and 1 give a low value, approximately 0.0004 pct B, at 850°C. Apparently at 835°C (test 13) it is possible to obtain 0.0018 pct B, and at 850°C only 0.0004 pct B into solution in the a phase before a second phase appears. These observations are consistent with the Fe-B constitution diagram proposed by McBride, Spretnak, and Speiser.3 References P. E. Busby, M. E. Warga, and C. Wells: Diffusion and Solubility of Boron in Iron and Steel. Trans. AIME (1953) 197, p. 1463; Journal of Metals (November 1953). 'W. Jost: Diffusion in Solids, Liquids, Gases. (1952) pp. 69-71. New York. Academic Press Inc. "C. C. McBride, J. W. Spretnak, and R. Speiser: A Study of the Fe-Fe2B System. Trans. ASM (1954) 46, p. 499.

Jan 1, 1955

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION of cobalt has been investigated by Ruder and Birchenall,1, 2 Nix and Jaumot,3 and Gruzin.4 The results for a given tem- perature differ by a factor of about six in the extreme cases with no really close agreement between any two sets of data. The first two groups of investigators employed the decrease of surface activity method. Since Ruder and Birchenall have shown that the values obtained from this method are sensitive to the surface preparation, it seemed desirable to perform a few check experiments by a method not open to this objection.

Jan 1, 1956

By C. E. Birchenall, W. Batz, H. W. Mean

AT temperatures between 1095' and 1347ºC, 13 runs have been made on the diffusion of silicon in iron. In two of the runs the couple compositions were entirely within the loop of the Fe-Si system; the base alloys contained 0.0 and 1.0 wt pct Si. The other runs in which the couples consisted of a 2.3 wt pct Si alloy welded to a 3.7 pct Si alloy were a phase throughout. The alloys were made by melting electrolytic iron and commercially pure silicon. Trace impurities were not determined. The butt welded couples were diffused in an inert atmosphere of argon or hydrogen. After cooling, cuts of two mils or greater thickness were machined parallel to the weld interface. The chips were analyzed for silicon. When the concentration and distance data were examined on the conventional probability plot,' no marked variation of the diffusion coefficient with concentration was indicated over the narrow composition ranges employed. Therefore, a single diffusion coefficient is recorded for each run in Table I. The temperatures and atmospheres of the diffusion anneal are listed along with the compositions of the base alloys. For a iron the silicon diffusion coefficient is given by the equation: D = 0.44 e-48,000/RT where R is the gas Constant and T, the absolute temperature. However, since the scatter in the data is fairly large, the activation energy may be in error by as much as 6000 cal per g-atom. The two ? iron points do not permit estimation of the activation energy with any reasonable certainty. They do indicate that the coefficients reported by Smithells2 and Jost,3 based on the work of Fry,4 are much too high. Although very dilute solutions in iron of manganese,5 nickel,8 cobalt,7 and molybdenum8 give dif- fusion coefficients quite close to those obtained for self-diffusion in iron, the silicon values are considerably higher, though of the same order of magnitude. This seems to be consistent with the fact that the silicon atom is the only one of those listed here which is appreciably smaller than iron. The authors are grateful to the Office of Naval Research for their support of this work under Contract N6ori-47, Task order IV, Project NR 031-184, to J. K. Stanley and the Westinghouse Research Laboratories for the silicon alloys used, to several steel companies for the silicon analyses, and to C. Wells, of the Metals Research Laboratory, Carnegie Institute of Technology, for numerous suggestions during the course of the work. References 'C. Wells: Atom Movements (1951) Chapter 2. A.S.M. 2C. J. Smithells: Metals Reference Book (1949) p. 405. Interscience. Pub. Co. 3W. Jost: Diffusion (1952) p. 223. Academic Press. 4 A. Fry: Stahl und Eisen (1923) 43, p. 1039. T. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 315. "C. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 329. 7M. F. Hawkes and R. F. Mehl: Trans. AIME (1947) 172, p. 467; Metals Technology (August 1947). .J. L. Ham: Trans. A.S.M. (1945) 35, p. 331.

Jan 1, 1953

By L. D. Jaffe, H. C. Mann, E. L. Reed

It has been generally believed that fracture originates at a point and, if the stress is suficient, propagates across the material from this point. Evidence to the contrary is given in Fig 1. This micrograph shows an area close to the fracture of a steel containing The material had been quenched from 1675°F and tempered at 1150°F as a round about 10 in, in diam, and had a static tensile strength of 132,000 psi and a static yield strength of 105,000 psi. The steel was broken in 3000 cycles of reversed bending at a nominal max. fiber stress of 110,000 psi at a speed of 10,000 rpm. It was in the form of a standard R.R. Moore specimen with 45" V-notch, 0.015 in. radius and 0.220 in. diam at base of notch. The fractured edge in Fig 1 is part of the central portion of the specimen which broke during the final sudden fracture. Attention is directed to the short cracks which appear as dark lines within the specimen. Similar cracks were found in another specimen of the material, broken in 1,798,000 cycles at a nominal stress of 40,000 psi. The cracks were found in several areas close to the path of the final sudden fracture. This final fracture appeared microscopically to be wholly brittle and transcrystalline. Closer to the surface of the specimens, near the path of progressive fracture, which presumably advanced gradually during many cycles, there was microscopic evidence of some local deformation, but no microcracks. Neither were microcracks observed in areas distant from the main fracture path. The following explanation is offered: In the sudden fracture of the specimen, a crack propagates along a crystallo-graphic plane, with little or no plastic deformation of the adjacent material, until it reaches a grain boundary or a particle of carbide or inclusion which stops its advance. (The particle or boundary may be outside the plane of polish and not visible in the micrograph.) A stress concentration occurs about the end of the stopped crack. One or more new cracks are likely to start in the zone of this stress concentration. They may lie in the same grain as the first crack or in an adjacent grain. New cracks may occasionally start in a nearby but not adjacent grain whose orientation with respect to the stress leads to more ready fracture than does that of the grain between. Once started, these cracks propagate along crystallographic planes in their grains and the process repeats. This leads to discontinuous, branching chains of microcracks. As the process continues, microcracks probably tend to link up by fracture of intermediate material under the influence of increasing stress concentration. Occasionally, too, there may be a series of nearby grains of similar orientation so that there is a certain continuity of fracture across them. In either case the effective size of a crack is increased, resulting in greater stress concentration at its ends and a greater likelihood of further increase of size of the continuously-fractured region. When one continuous crack crosses the entire specimen, macroscopic fracture has occurred. The fractured edge of the specimen in Fig 1 represents a series of microcracks which became continuous across the entire specimen. The short, dark-appearing cracks in the figure did not become continuous over a large area. The row of microscopic stress concentrations at their ends may link up with those of the "main crack" outside the plane of polish. The above explanation does not imply that microcracks develop at the same rate in all portions of the specimen. They will develop most rapidly where the macroscopic tensile stress and macroscopic stress concentration are greatest. Viewed on a scale large compared to the grains, the fracture would appear to progress continuously across the specimen. Although Fig 1 shows a specimen broken in a fatigue test, it is believed that the microcracks discussed do not depend on the repetitive nature of the stressing used, since they are in the region where "sudden" fracture occurred, presumably in a single stress cycle. The whole process of microcrack propagation outlined above is thought to have occurred during this single cycle. It is believed that discontinuous crack propagation may be universal in brittle transgranular fracture of crystalline solids. Further experiments are under way.

Jan 1, 1950

By P. A. Beck

ACCORDING to the traditional definition,1 re-x crystallization is a process taking place upon annealing of cold worked metals, characterized by the appearance of new strain-free grains, growing at the expense of the cold worked grains until ultimately the new crystals completely replace the cold worked structure. In metals like brass this process was observed long ago to take place simultaneously with the return of the mechanical properties to those characteristic of well annealed material. The above definition implicitly assumes that the matrix in which the new grains are growing is essentially still in the cold worked condition at the time it is absorbed by the new grains, i.e., that the energy stored in the metal during cold working is not greatly decreased by recovery, prior to recrystallization. Accordingly, the bulk of this energy is assumed to serve as the driving force for the process of recrystallization. Recently, a great deal of evidence accumulated, indicating that the traditional concept may be considerably in error. Suzuki' found that by far the largest portion of the stored energy of cold work in compressed polycrystalline copper is released in the early stages of annealing, well in advance of recrystallization. Thus, the new recrystallized grains are undoubtedly growing in a matrix which is, at least energetically, no longer in the cold worked condition, but has nearly returned to the annealed state. It is true that in Suzuki's experiments the major hardness changes due to annealing were observed to take place concurrently with the formation and growth of the new grains, but this process apparently involved the release of only a minor residual fraction of the stored energy of cold work. Confirming in this respect the views of Wood," several recent investigations by various techniques lead to the conclusion that the grains of many, if not all, metals in the cold worked condition consist of small, slightly disoriented "crystallites" or "sub-grains".* (After appreciable deformation at room temperature, the subgrain size in copper appears to be about 7.104 cm and in high purity aluminum about 2.10-4 cm.) Recent investigations which demonstrated this phenomenon most convincingly are those of Heidenreich8 with hammered high purity aluminum, of P. B. Hirsch and collaborators7,8 with cold worked polycrystalline aluminum, copper, nickel, iron, gold, etc., and of Warren and Averbach9 with a rolled copper plus 2 pct Si single crystal. In addition to the existence of slightly disoriented sub-grains, the cumulative evidence from these investigations also shows that in the cold worked condition the subgrains themselves are severely strained. With regard to the early stages of annealing, Heiden-reich's results indicate that within the subarains of hammered high purity aluminum the strain gradually disappears, without discernible migration of the subboundaries. This recovery process presumably accounts for the major portion of the energy release

Jan 1, 1953

By A. D. K. Laird, C. A. Johnson

Drag coefficients for a cylinder being towed through water at constant velocity and also at constant linear acceleration were measured. Drag coefficients for constant velocity towing showed reasonable agreement with previous results. The drag coefficients found for constant acceleration showed little correlation with either the magnitude of the acceleration or the value of the modulus AD/V2 and tended to be slightly lower than those for constant velocity. INTRODUCTION For the design of offshore structures, wave forces acting on immersed cylinders are of importance. Several investigations have been made of these forces and of how they can be predicted from wave theories. A paper by Crooke' summarizes much of the work already done. More recent research by the Wave Research Laboratory at the University of California, Berkeley, has added much to the body of data collected under ocean wave conditions, but has not found a reliable method of force prediction from basic theories of wave motion. The present investigation is part of a long-range program to collect data with which to test current and future theories and correlations. The immediate objective was to measure drag forces on a circular cylinder subjected to linear accelerations over the range of Reynolds numbers between l04 and 105 where the drag coefficient was a constant for constant velocities. In particular, the effect of constant acceleration from rest and from uniform motion was to be investigated. The effect of acceleration may be evaluated in terms of drag coefficients. A useful resistance coefficient, C, is defined by the equation for total drag force, D, exerted by the fluid on the cylinder. DT =CSp V2/2.........(1) The coefficient C may be plotted as a function of the parameter AD/V2. Here D is the diameter and S is the projected area of the cylinder. The acceleration and velocity are A and V. The mass density of the fluid is p. An alternate drag coefficient, C, corresponds to the total force of the fluid opposing the motion minus the virtual mass force. This drag coefficient, arising from the velocity of the fluid, may be compared with that for the same cylinder in uniform motion. The similarities and differences between this coefficient as calculated for accelerated and for steady motion are of interest in the inverse process of predicting drag forces on cylinders under arbitrary conditions. One serious difficulty in this method is the specification of the virtual mass which depends also on the flow picture about the cylinder.1 EXPERIMENTAL EQUIPMENT The experiment was performed in the combination wave and towing tank at the Engineering Field Station of the University of California. The tank is 200 ft long, 8 ft wide, and 6 ft deep. The tow carriage is externally propelled by a cable, and the velocity of the carriage is maintained essentially constant by means of an am-plidyne. For the purpose of the present investigation, the speed control of the amplidyne was modified by inserting a linear speed control rheostat, which was rotated at a constant speed by a small d-c motor equipped with a slip-clutch. Accelerations which were constant over a reasonable length of time were thus produced. The magnitude of the acceleration depended upon the speed of the d-c motor and the limiting speed of the carriage. Data were obtained for a range of accelerations of 2 to 10 ft/sec,2 and a range of velocities of 2 to 15 ft/sec. An accelerometer (Statham Type C-2-350) with a range of ±2g was attached to the carriage and connected to a Brush analyzer and penmotor. A continuous coil of wire with 10 turns/ft wound around a fixed wooden form extending for a distance of 40 ft along the length of the tank was connected by an electrical contact mounted on the carriage to a Brush analyzer and penmotor, to give the time-position history for each run. The test cylinder was machined from solid aluminum alloy, 17-ST. to a diameter of 1.250 in., and could be

Jan 1, 1957

By G. K. Manning, W. E. Few

WORK on the effect of vacuum heat treatment of 0.040 in. diam sintered and wrought molybdenum wires has been sponsored by the Office of Naval Research at Battelle for the past several years. An electrical resistance furnace' capable of maintaining a vacuum of less than 0.1 micron of mercury at temperatures as high as 4000 °F was used for heat treating the wires. Early in the work, it was found that the introduction of a few microns pressure of oxygen into the furnace resulted in a rapid increase in the oxygen content of the wire specimens and the appearance of a discrete oxide phase. Subsequent elimination of the oxygen atmosphere caused the disappearance of the oxide phase. This was used to determine the solid solubility of oxygen in molybdenum over the temperature range of 2000" to 3000°F.2 It was observed that, with the disappearance of the oxide phase, the wires regained some ductility. Single-phased wires possessed from 5 to as much as 40 pct elongation in 2 in. Later, attention became centered on determining the cause of this wide range in ductility. Wires containing less than 0.002 pct C, less than 0.0007 pct 0, less than 0.0005 pct N, and less than 0.00003 pct H exhibited the erratic ductility noted above. These percentages represent approximately the limit of accuracy of presently available methods of analysis and thus it became apparent that chemical analysis would be of little help in the study. A number of possible explanations for the wide range in ductility were suggested during the course of the work. It was first suspected that variations in the grain size of the recrystallized wire specimens might be responsible. Wire from several lots of material was available. One of these lots tended to develop very large grains when recrystallized, the others all developed an ASTM grain size of 3 to 4 when heated above 2700°F. No correlation between grain size and ductility could be found. It was thought that back diffusion of oil from the diffusion pump might cause contamination of the wire, principally with carbon, but when wires were treated without cooling the cold trap in the pumping system,

Jan 1, 1956

By J. J. Gilman

RECENT experiments have shown that the mar-tensite reaction in a standard tool steel is influenced by the history of the reacting austenite. The martensite reaction proceeds to a given extent at a higher temperature in austenite formed from an annealed spheroidal structure than it does in austenite formed from tempered martensite: that is to say, a prequench lowers the temperature range of the martensite reaction in this steel. Furthermore, a prequench alters the appearance of the martensite as compared to martensite formed from "virgin" austenite. The steel used for this work was a manganese nondeforming tool steel of the following composition: C, 0.85 pct; Mn, 1.43; Si, 0.23; Ni, 0.12; Cr, 0.59; and W, 0.59. A piece from a rolled bar was forged to Vz in. sq and annealed to a spheroidal structure. Disks 1/8 in. thick were used in the experiments. Several sets of the specimens were prepared and austenitized in lead at 1475°F. Three sets were held at 1475°F for 15 min, quenched in water, and immediately reheated to 1475°F. After this quench the three sets were held for 5 min, 30 min, and 3 hr, respectively, at 1475°F and then the individual specimens in each set were quenched in molten baths to 325", 300°, and 275ºF, respectively, and held for 15 sec. Immediately after the quenching treatments? the specimens were tempered at 600°F for 30 sec to darken the martensite and then were quenched in water. The holding times were short enough to avoid isothermal transformation. Three other sets of specimens were given the same final quenching treatments as the first three, but they were austenitized at 1475°F for 20 min, 35 min, and 3 hr and 15 min, respectively, without an intermediate water quench. The two individual specimens from each set were quenched together in order to eliminate quenching errors. Several experiments were run in this way but only the six sets referred to are described in detail because they all yielded essentially the same results. By means of the stated heat treatments the martensite reaction was investigated for: 1—austenite formed from an annealed structure, and 2— austenite formed from tempered martensite. The martensite reactions of the two types of austenite differed significantly. This is shown by Figs. 1 and 2. Comparison of the photographs on the left in Figs. 1 and 2 with those on the right shows that less martensite was formed by a quench to a given temperature from prequenched austenite than from austenite formed from an annealed structure, that is, the prequench suppressed the martensite reaction. The effect was observed for specimens austenitized 20 min, 35 min, and 3 hr and 15 min. A comparison of Figs. 1 and 2 shows that the martensite reactions in both sets of specimens occurred at lower temperatures with increased austenitization time. This was caused by the increased dissolution of residual carbides with time at 1475°F. However, the difference in amount of martensite formed in prequenched austenite as compared to virgin austenite was approximately the same for all three austenitization times. One further observation should be noted. The needles of the martensite formed from virgin austenite are somewhat longer on the average and show less of a tendency to cluster than those of martensite formed from prequenched austenite. This causes the martensite on the right in Figs. 1 and 2 to have a more acicular appearance than the martensite on the left. Since the sets of specimens used in this work were austenitized for identical total lengths of time and the effect of a prequench on the martensite reaction existed for specimens held at the austenitizing tem-

Jan 1, 1953

By J. W. Spretnak, R. Speiser, A. M. Adair

THERE are sufficient arguments and evidence to indicate that boron should be adsorbed to existing austenite grain boundaries during the austen-itizing treatment. Accordingly, it is possible that boron contributes to the hardenability of heat-treatable steels by the reduction of the interf acial energy of austenite grain boundaries, at which sites are nucleated heterogeneously the decomposition products of austenite. Such a reduction in interfacial energy would reduce the total energy that can be borrowed in these heterogeneous nudeation processes and thus retard the initiation of transformation. This investigation was undertaken in an attempt to determine the effect of boron on this interfacial

Jan 1, 1956

By L. D. Jaffe, W. P. Clancy, D. C. Buffum

Many earlier workers have suggested that the temper brittleness of steel is associated with the presence of carbon or nitrogen. Nevertheless, no investigations on the effect of removal of these elements upon susceptibility to temper brittleness have been published. It was therefore decided to determine whether temper brittleness would develop in an iron alloy ...__, ing very little carbon and nitrogen. The alloy, in the form of a 10-lb ingot, was prepared by melting purified materials under . argon. Its composition, in per cent, was: This analysis, except for carbon content, is within the specified range for SAE 3140, which has been demonstrated by previous work at this laboratory2 to be markedly susceptible to

Jan 1, 1950

By P. Payson

EMBRITTLEMENT of hard-tempered martensite (500°F embrittlement) appears to be coincident with the beginning of the third stage of tempering. During the first stage, primary martensite of steels containing over 0.25 pct C decomposes to a mixture of c carbide and martensite of appreciably constant carbon content close to 0.25 pct.' During the third stage of tempering, cementite forms. In steels with

Jan 1, 1955

By C. S. Roberts

THE advent of a sensitive X-ray method of analysis recently has allowed the determination of retained austenite in amounts as low as 0.3 pct.' As a result this phase has been found in quenched low carbon steels where its presence has not been generally suspected. In the course of a study of the tempering process,' retained austenite determinations were made by the X-ray method on a series of high purity Fe-C alloys and plain carbon steels. The chemical analyses of these materials and details of the hardening procedure are given in Table I. Results were obtained after quenching to 72°F (22°C) and — 321 °F (—196°C). Austenitizing temperatures were between 100" and 150°F above A, or Acm. All proeutec-toid cementite or ferrite was in solution. The combination of the results with those of Averbach, Castleman, and Cohen,' and earlier results of Esser

Jan 1, 1954

By J. H. Kittel

THE properties of the metal molybdenum have been the subject of recent investigations1,2 = which have included studies of the changes that occur in the metal when it is annealed after having been cold worked. Most of the data which have been reported have pertained to only one aspect of annealing, that is, the conditions under which recrys-tallization has been observecl. The process of recovery which may precede recrystallization docs not appear to have been investigated, and it is the purpose of this note to report observations on the recovery process in cold-worked molybdenum as determined by changes ill the thermoelectric power which occur as the metal is annealed. The measurements were made on commercially pure molybdenum wires which, after annealing at 1035°C in dried hydrogen for 1 hr, were swaged to give a series of reductions up to a maximum of 84.5 pct. The variously cold-worked wires were then annea1c.d in dried hydrogen for periods of 16 hr at progrc:ssively highel. temperatures from 200" to 1000 c with a final annealing treatment of 70 hr at. 1100°C. After each annealing treatment the ther.ma1 emf's were determined against a length of original unwo~,ked material that had received the initial hydrogen anrit,aling treatment. The difference in temperature between the hot and cold junctions was maintained at about 75'C. and. the thermal emf's were measured with a potentiometer that could be read. to 0.01 microvolt. Fig. 1 shows the thermoelectric power. (dE/dT) in microvolts per C between annclalcd and cold-worked molybdenum as a function of the degree of cold work. The effect of annealing is shown in Fig. 2. The general shape of the curves in both figures is similar to results which have been obtained for copper." It was observed that after annealing at temperatures as low as 200°C recovery was well under way. The rapid changes irt thermoelectric power observed near 900 C are probably associated with recrystallization, since such a relation has been observed with copper. Beyond 900°C the thermal emf's changed in polarity. indicating that from this point or1 the specimens were more highly annealed than the standard. Annealing treatments could not be given at temperatures higher than 1100°C due to limitations of the furnace, and it is evident that, since equilibrium values of thermoelectric powers were far from having been attained, temperatures considerably higher are required to fully anneal molybdenum. References Robert M. Parke: Molybdenum, A New High-Temperature Material. Metal Progress (1951) 60, pp. 81-96. * R. A. Long, K. C. Dike, and H. R. Bear: Some Properties of High-Purity Sintered Wrought Molybdenum Metal at Temperatures up to 2400 °F. NACA TN 2319 (March 1951): G. W. Brindley: A Thern-io-Electric Study of the Cold-Rolling and Heat-Treatment of Copper, Report of a Conference on the Strength of Solids. Physical Society, London (1948) pp. 95-106.

Jan 1, 1953

By W. R. Hibbard

It has been proposed1 on the basis of slip and flow that the ideal deformation texture of drawn wire for face-centered cubic metals is a (111) direction parallel to the wire axis. Under these considerations, an intermediate [loo] texture is permissible but should eventually change to the stable [Ill] orientation. This theory does not explain why copper and its alloys containing up to about 30 pct nickel, 5 pct zinc and 1 pct aluminum were found to have a double [Ill], [100] texture, while alloys with at least 8 pct zinc and 2 pct aluminum developed essentially a single [Ill] texture.1,2 It does suggest, however, that the [loo] component of the former alloys should disappear with additional deformation.3 Some evidence exists to support this suggestion. Howald4 reported that annealed copper wire previously drawn 93.8 pct and 98.5 pct developed a single [Ill] texture. Since, in wire, the drawn and annealed textures are similar, these wires probably had a single [Ill] deformation texture before annealing. In addition, although cold rolled polycrystalline copper and 80-20 brass were found to form different types of pole figures,5,6 single crystals of these metals when rolled from the stable (110) [112] orientation were found to produce essentially the same polo figure.7.8 It may be, therefore, that while the addition of solute elements changes the path by which the final texture is obtained, the final texture is not changed. Experimental Results The wires remaining from the previous investigation1 already drawn about 50 pct reduction in diameter were further drawn to 86 pct and then to 96.4 pct total reduction in diameter. The textures were determined after these stages by transmission X ray photograms taken with a copper K-alpha beam rotated 0 degrees toward the wire axis. It was found that the ratio of the [111].] and [100] intensities of the double texture in copper and its alloys containing 0.94 pct aluminum, 30.70 pct nickel, 2.61 pct zinc and 4.99 pct zinc increased from about 3:l for the 50 pct reduction to about 9:l for the 86 pct reduction. After 96.4 pct reduction, these wires exhibited essentially a single [lll] texture. Summary Thus, the drawn wire deformation texture of copper and its alpha solid solution alloys containing aluminum, nickel or zinc is essentially a single [Ill] texture as predicted by theoretical considerations of slip and flow.' For copper and its alloys containing up to about 1 pct aluminum, 5 pct zinc and at least 30 pct nickel, an intermediate [loo] component is found after about 50 pct reduction in diameter, but disappears after about 95 pct reduction in diameter. For alpha solid solution alloys containing at least about 2 pct aluminum and 8 pct zinc the single [Ill] texture is developed considerably more easily and is found after about 50 pct reduction in diameter. No explanation of this compositional effect is apparent. Similar work is contemplated for cold rolled and cold compressed alloys. References 1. w. R. Hibbard, Jr. and M. K. Yen: Trans. AIME 175, 126. Metals Tech., Feb. 1948, TP 2334. 2. W. R. Hibbard, Jr. and D. E. Trout, 11: Trans. AIME 185, 620. Jnl. of Melals, Sept. 1949, TN 18. 3. W. R. Hibbard. Jr.: Disc. of R. M. Brick's paper on Deformation Textures, ASM Symp. on Cold Working of Metals, Oct. 1948. 4. T. S. Howald: Disc. of Ref. 1. Trans. AIME, 175, 126. Melals Tech. Aug. 1948, TP 2449. 5. R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675. 6. 0. Dahl and F. Pawlek: Zlsch. Melall. (1936) 28, 266. 7. C. S. Barrett and F. W. Steadman: Trans. AIME (1942) 147, 57. 8. J. E. Burke and C. S. Barrett: Trans. AIME 175, 106. Melals Tech., Feb. 1948. TP 2327.

Jan 1, 1950

By Howard Martens

HARDNESS behavior of commercial titanium alloys following various heat treating processes has been studied for some time. However, the hardness of such alloys following a definite measured cooling rate from the single phase region has not been reported. Therefore, a series of experiments was conducted on the three alloys: 150A, 130A, and 130B. The manufacturers gave the following compositions for these alloys: Ti 150A: 0.045 pct C, 0.069 pctN, 1.32 pct Fe, and 2.68 pct Cr; RC 130A: 0.13 pct C, and 7.9 pct Mn: RC 130B: 0.11 pct C, 3.5 pct Mn, and 3.2 pct Al. A method similar to that described by Greninger was used, and the cooling rate varied from 6" to 9200°F per sec. The cooling curves were recorded on a Speedomax or a recording oscillograph, and the hardness was measured on a Tukon hardness tester using a Knoop indentor with a 500 g load. The curves of Fig. 1 show the variation of the Knoop hardness with the cooling rate for these three alloys. The alloys 150A and 130B behave in a similar manner, as shown by the curves. In neither of these alloys was it; possible to retain the high temperature ß phases, even by the most rapid cooling rate. The slow cooling rates produced a typical ß structure in these two alloys. As the cooling was increased, these phalses became more finely dispersed and the hardness increased. This increase in hardness with cooling rate continued for the 150A alloy until a rate of approximately 1000°F per sec was reached. At this cooling rate, the structure showed the result of the dif-fusionless transformation of the ß solid solution to the supersaturated a solid solution which is referred as a'. At higher cooling rates, the structure showed no change and the hardness showed no great change, as indicated by the dotted portion of the curve in Fig. 1. The increase in hardness with cooling rate for the 130B alloy continued until a rate of approximately 300°F per sec was reached. At this rate the structure was produced and the maximum hardness was reached. Higher cooling rates caused no marked changes in hardness or structure. The alloy 130A behaved in a different manner, as shown by the curve of Fig. 1. The structure produced by the slow cooling rates was a typical a+ß structure, which became finely dispersed as the cooling rate increased. The hardness increased with cooling rate and reached a maximum at approximately 120°F per sec. At this maximum hardness, the structure showed the result of the decomposition of the ß phase into the ß + phase structure. As the cooling rate was increased, smaller amounts of the at phase were formed and the alloy became softer. For cooling rates of 3000°F per sec and above, the high temperature ß phase was retained and the hardness of the alloy did not change markedly. Acknowledgment This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. DA-04-495-0rd 18, sponsored by the Dept. of the Army, Ordnance Corps.

Jan 1, 1957

By Paul B. Crawford, Bobby L. Landrum

Electrical model studies have been made of the effect of drainhole drilling on production capacity. Drain holes are those lateral holes which are sometimes drilled to assist in increasing the oil drainage into the main wellbore. The studies indicate that if the drainhole length i.r near 0.2 of the drainage radius, the increase in production capacity may be approximately 1.8, 2.08, trnd 2.33 for the case of one, two and four drain holes, respectively. If multiple drain holes are drilled, shorter holes are required to achieve a specific increase in production capacity than if one or two holes are drilled. To achieve increases in production capacities by factors near three it is shown that the drainhole lengths divided by the drainage radii must be approximately 0.64, 0.48, cnd 0.37 for the case of one, two and four drain holes, respectively. IN T RO DUCTION Kecent developments in drilling techniques have permitted the drilling of lateral or horizontal holes to increase the rate of production. The number of these drain holes may vary from 1 to 10, and they have been drilled laterally as much as 100 ft. Drainhole drilling at substantial depths is of recent origin but has been used in the Spraberry field of West Texas, the La Pas field in Western Venezuela, and certain fields in California. The diameter of the drain holes has been approximately 6 in. In drilling drain holes it is desired to know how much increase in production capacity may be expected, what additional benefit may be gained by drilling more than one drain hole, and what increase in production capacity may be brought about by lengthening the existing drain holes. In realization of the importance of lateral drilling, electrical model studies were made to provide quantitative estimates on the effect of drain holes on production capacity. ANALYSIS An electrical model was used in studying this problem. A wooden circular reservoir approximately 30 in. in diameter and 2 in. deep was filled with a dilute salt solution to a depth of 1 in. A copper band formed the periphery of the tank, and a copper wire was inserted in the center of the tank to represent the well. The drainage radius divided by the well radius was equal to 500. A diagram of this type model is shown in the inset of Fig. 1. An electrical potential was applied to the wire well and copper band at the periphery to determine the flow of current. Following this measurement copper wires of various length were soldered to the vertical wire well in such a manner as to simulate lateral wells drilled into the reservoir. Multiple lateral holes of various lengths were studied by varying the number and length of copper wires soldered to the vertical wire well. All multiple lateral wells were located symmetrically about the vertical well. The effect on production capacity by drilling an infinite number of lateral holes was studied by replacing the lateral hole with a copper disk. For each condition the flow of current was measured and compared with the flow of the vertical well only. The model which is thus described provides the steady state increases in production capacity which may be expected in some cases. The data conform to those which would be observed for a uniform homogeneous reservoir. The data may have primary application to those reservoirs producing above the bubble point. It is realized that few lateral holes are drilled in reservoirs of this type, but the data may be of some value in guiding future work or aiding to explain observed phenomena.

Jan 1, 1956

By J. M. W. Mackenzie, C. J. Wood

In attempting to describe the size classification performance of a hydrocyclone, most workers have elected to use either an equilibrium orbit theory or an non-equilibrium orbit theory. The equilibrium orbit theory has been used by the majority of workers including Lilge,' Bradley; and Yoshioka and Hotta. In applying this theory, it is argued that particles in the body of a hydrocyclone attain an equilibrium radial position where the drag force on the particle resulting from the inward radial fluid velocity is balanced by the outward centrifugal force caused by the tangential component of fluid flow. When considered over the full height of the hydrocy-clone, attainment of this radial equilibrium orbit results in the particle following a conical equilibrium envelope. It is then argued that if this envelope lies outside the envelope of "zero vertical velocity," the particle will report to the underflow, while if the equilibrium envelope lies inside the envelope of "zero vertical velocity," the particle will report to the overflow or vortex finder product. The d50-sized particle which reports in equal quantities to the underflow and overflow is assumed to correspond to particles whose equilibrium envelope is coincident with the envelope of "zero vertical velocity." In considering the equilibrium orbit theory, it is apparent that the horizontal position of the particles in the feed inlet pipe should have no effect on their ultimate destination on the hydrocyclone. Each particle should attain an equilibrium position which depends on the density, size, and shape of the particle; the density and viscosity of the fluid; and the flow patterns within the hydrocy-clone. The nonequilibrium orbit or unsteady state theory has been largely developed by Rietema4 and Mizrahi.6 Mizrahi has listed four main objections to the equilibrium orbit theory. These objections center on the short residence time in the hydrocyclone, the fact that the experimental classification curve is much less sharp than is theoretically predicted, and the absence of negative efficiency conditions in hydro cyclones operating on a feed material which is much finer in size than d50. Proponents of the nonequilibrium orbit theory argue that for a particle to discharge with the underflow it must have sufficient outward radial velocity to reach the downward-flowing region close to the hydrocyclone wall in which the flow lines are parallel to the wall and the ratio of vertical to radial velocity is constant. It is then postulated that a d50 particle entering the cyclone at the center of the feed inlet will just reach this downward-flowing region as it reaches the apex. Thus for uniform distribution of particles across the feed inlet, half the d50 particles—that is, those injected in the half of the inlet area nearest the cyclone wall —will report to the underflow while those injected in the other half will not reach the downward-flowing region and will be carried inward to the center of the cyclone and thus report in the overflow. The exact thickness of the down-ward-flowing region of fluid adjacent to the outer wall of the hydrocyclone is uncertain but Mizrahi considers it to be equal to the apex radius minus the air core radius. Particles larger than d50 have a greater outward centrifugal force acting on them than the d50 particles and may reach the wall even if injected at a distance from the wall greater than Di/2 (Di is inlet diameter). Conversely, particles smaller than d50 may not reach the wall even if injected at a distance less than Di/2 from the cyclone wall. Since the equations put forward by the proponents of both theories yield approximately the same values of d50, it is not possible to decide between these theories by measurement of d50. It should be possible however to examine the theories by injecting a small stream of solids into the feed inlet of a hydrocyclone running on clear water. If the efficiency or classification curve is measured for various horizontal injection positions, then the curves should be coincident if the equilibrium orbit theory holds. If, however, the unsteady state theory describes the cyclone operation, then the classification curves should show finer d50 sizes for particles injected close to the cyclone wall. Experimental A 6-in.-diam hydrocyclone with geometry as in Figs. 1 and 2 was used. Quartz particles were injected as a 50% by wt pulp via an 1/8-in. steel probe. For each in-

Jan 1, 1971