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By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

By J. D. Lubahn

The Bauschinger effect, or rounding of the corner of the stress-strain curve upon reloading, represents a temporary apparent softness that is more pronounced at large strains than small and for complete unloading than for partial unloading. Interrupted creep tests on copper exhibit a similar temporary softness (high creep rate) upon reloading. The fact that the strainwise dying-out time of these effects is the same in both tensile and creep tests shows that they are related. Thus, the term Bauschinger effect appears to embrace behavior following partial or complete unloading and reloading in addition to behavior following reversed loading. It is suggested that the term may properly apply also to certain creep behaviors following a small load decrement. INTERRUPTED tensile tests at low temperatures show1 a rounding of the corner of the stress-strain curve for reloading, which indicates a temporarily low deformation resistance. In the absence of recovery, the curve soon rises to the value that would have prevailed if the test had not been interrupted. The rounding of the reloading tensile curve has sometimes been referred to1 as the Bauschinger effect, although the term is more commonly applied to low deformation resistance in compression following tensile prestrain. The unusually broad usage of the term Bauschinger eflect in ref. 1 seems justified by the obvious interconnection of the various behaviors to which it has been applied.' In fact, the following discussion will indicate that still broader usage might be desirable. The Bauschinger effect is common at room temperature but apparently disappears at higher temperatures.2 Interrupted creep tests and tensile tests were made on certified OFHC copper (nongaseous impurities exclusive of silver were 0.004 pct), cold drawn 84 pct to ½ in. diam, and annealed at 600" (about 0.025 mm grains) or 850°C (about 0.2 mm grains). The tests were made in standard creep or tensile machines, using an O.S. Peters microformer-type extensometer or, for the small plastic strains, a special arrangement employing General Electric magnetic gage heads.' Interrupted creep tests at room temperature show3,4 an initial softness after reloading, manifested by an initial creep rate that is higher than that which would have prevailed if the test had not been interrupted. Fig. 1 shows some typical examples. This effect is apparently temporary (as is that in tensile tests): in four of the five tests shown, the log rate vs strain curve becomes parallel to an

Jan 1, 1956

By H. M. Morse

Tinsley Oil Field.—Mississippi joined the oil-producing states when on Sept. 13, 1939, the Union Producing Company's G. C. Woodruff well No. 1, sec. 13, T. 10 N., R. 3 W., Yazoo County, was completed after drilling plug at 4540 ft. in the Woodruff sand of the Eutaw formation of Cretaceous, producing 300 bbl. per day of 34.4" gravity oil through a ¼-in. choke, with a gas-oil ratio of 80 to 1 and bottom-hole pressure of 2045 lb. This was the discovery well in the Tinsley oil field. The well was drilled to a total depth of 4567 ft. and no salt water was encountered. The sand underlies the Selma chalk formation. Nine producing oil wells and one dry hole were drilled and completed by the end of 1939. Two producing sands have been found in the Eutaw and a third sand in the top of the Tuscaloosa formation, called the Woodbine sand in Louisiana and Texas. Faulting is an important factor in the Tinsley field. Total oil production has been approximately 250,000 bbl. from the nine flowing wells. Total depth to top of productive zone was 4540 ft.; to bottoms of productive wells, 4580 ft. Net thickness of the producing formation is 20 to 40 ft., and its porosity is 24 per cent. The deepest zone tested was the Tuscaloosa, in which the depth of hole was 6112 feet. Six hundred and forty acres has been proved for oil production. Jackson Gas Field.—The Jackson gas field has shown a steady decline in the number of wells but the pressure has been maintained. This field is a perfect example of a water-driven field and the time of wells going to salt water is predictable. Five wells were drilled in the Jackson field, of which only one produced. Amory Gas Field.—Interest was renewed in the Amory gas field, where a new well was started in the fall of 1939. Geological Formations.—The deepest well drilled in 1939 was the Willmut Gas and Oil Company's Cleve Love S. F. Johnson No. 1, sec. 29, T. 6 N., R. 1 W., Hinds County. This well encountered the Lower Cretaceous, Trinity series from 3770 to 6422 ft.; Lower Mesozoic from 6422 to 6484 ft. The geological correlations and nomenclature of the formations in Mississippi are shown in the accompanying strati-graphic section.

Jan 1, 1940

By Frederick H. Williams

THE object of this paper is to bring to the attention of those members of the Institute who are interested in the subject, a method for the estimation of manganese, which has been frequently used in the laboratory of the Vulcan Steel Works during the last eight months, and which is deemed worthy of more general use. It is simply an adaptation of well-known processes, for the purpose of determining this element in pig iron and steel. In general, the method consists in precipitating the manganese as binoxide, dissolving in dilute sulphuric acid in the presence of an excess of a standardized solution of oxalic acid, and titrating the remainder of the oxalic acid left unoxidized with permanganate of potash. For this method, therefore,. two standardized solutions are needed, viz., a permanganate solution and an oxalic acid solution. The permanganate solution is made so that 1 c.c. is equivalent to 1 mgr. of iron. By using so weak a solution and keeping the bulk of the solution to be titrated down to 75 c.c. or a little less, the accuracy of the process is greatly increased, since the final reaction is almost if not quite as sharp as if a stronger solution were used. The oxalic acid' may be of almost any strength, but if made so that 1 c.c. requires 3 c.c. of the permanganate to oxidize it, it will auswer well. The process is then, as follows : from 1 to 2 grams of pig iron or steel are dissolved in 40 to 50 c.c. of concentrated nitric acid with the aid of heat. As soon as solution is effected, in the case of steel, add gradually and cautiously, the solution being kept boiling, sufficient pulverized chlorate of potash to precipitate the manganese as binoxide. Two grams will be a great abundance. In the me of pig iron, first remove the carbon and silica by filtering the solution through asbestos and washing with concentrated nitric acid. Filter the strong acid solution in which the binoxide has been precipitated, through asbestos with the aid. of the filter pump. When it has entirely passed through wash well with water. Blow the contents: of the funnel into the beaker in which the precipitation was made and rinse the funnel with a little water.

Jan 1, 1882

By Frederick H. Williams

The object of this paper is to bring to the attention of those members of the Institute who are interested in the subject, a method for the estimation of manganese, which has been frequently used in the labratory of the Vulcan Steel Works during he last eight months, and which is deemed worthy of more general use. It is simply an adaptation of well-known processes, for the purpose of determining this element in pig iron and steel. In general, the method consists in precipitating the manganese as binoxide dissolving in dilute sulphuric acid in the presence of an excess of a standardized solution of oxalic acid, and titrating the remainder of the oxalic acid left unoxidized with permanganate of potash. For this method, therefore, two standardized solutions are needed, viz., a permanganate solution and an oxalic acid solution. The permanganate solution is made so that 1 C.C. is equivalent to 1 mgr. of iron. By using so weak a solution and keeping tile bulk of the solution to be titrated down to 75 C.C. or a little leas, the accuracy of the process is greatly increased, since the final reaction is almost if not quite as sharp as if a stronger solution were used. The oxalic acid may be of almost any strength, but if made so that 1 c.c. requires 3 O.C. of the permanganate to oxidize it, it will auswer well. The process is then, as follows: from 1 to 2 grams of. pig iron or steel ate dissolved in 40 to 50 C.C. of concentrated nitric acid with the aid of heat. As soon as solution is erected, in the awe of steel, add gradually and cautiously, the solution being kept boiling, sufficient pulverized chlorate of potash to precipitate the manganese as binoxide. Two grams will be a great abundance. In the case of pig iron, first remove the carbon and silica by filtering the solution through asbestos and washing with concentrated nitric acid. Filter the strong acid solution in which the binoxide has been precipitated, through asbestos with the aid of the filter pump. When it has entirely passed through wash well with water. Blow the contents of the funnel into the beaker in which the precipitation was made and rinse the funnel with a little water.

Jan 1, 1882

The 139th meeting* of the American Institute of Mining and Metallurgical Engineers was held at New York, February 17 to 20, 1930, the attendance totaling approximately 1800. The meeting consisted of the annual business session, 34 technical sessions at which were presented 166 papers, two meetings of the Board of Directors, two meetings of Section Delegates, two formal lectures and one special lecture, five group dinners and one group luncheon, luncheon daily for members and guests, fourteen committee meetings and conferences, the President's reception, the dinner-dance, an informal dance, a smoker, an exhibition of rare minerals and metals, two meetings of the Woman's Auxiliary and a special program of entertainment for the ladies. The Petroleum Division held seven sessions, including two general sessions featuring, respectively, a symposium on unit operation of oil pools and reports on developments in the petroleum industry during the previous year. The Iron and Steel Division held four sessions, at one of which Dr. Zay Jeffries delivered the Howe Memorial Lecture, the title of which was "The Future of the American Iron and Steel Industry." The Institute of Metals Division held six sessions, including two devoted to a symposium on the Melting and Casting of Metals, and the general session at which Dr. S. L. Hoyt delivered the annual Institute of Metals Lecture. The title of his lecture was "Hard Metal Carbides and Cemented Tungsten Carbide." The Coal and Coal Products Committee devoted one session and the greater part of another to Coal Classification and at a third session organized as the Coal Division of the Institute. The Committees on Mining Methods and Ground Movement and Subsidence each held a session, besides which they met jointly. Sessions were held by other Technical Committees as follows: Nonferrous Metallurgy, 1; Geophysical Prospecting, 2; Nonmetallic Minerals, 2; Milling Methods, 1; Rare Minerals and Metals, 1; Mining Geology, 2; Mine Ventilation, 2; Engineering Education, 1. At the annual business meeting on February 18, the following ticket was elected, and the reports of the President, Treasurer and Secretary were presented: William H. Bassett, President; Scott Turner, Vice-president; Henry Krumb, Vice-president; R. C. Allen, Cadwallader Evans, Jr., John M. Lovejoy, John A. Mathews and Milnor Roberts, Directors. At an executive session of the Directors on Tuesday afternoon, H. A. Guess was elected Vice-president to fill the vacancy created by the

Jan 1, 1930

By H. M. Morse

Tinsley Oil Field.—Mississippi joined the oil-producing states when on Sept. 13, 1939, the Union Producing Company's G. C. Woodruff well No. 1, sec. 13, T. 10 N., R. 3 W., Yazoo County, was completed after drilling plug at 4540 ft. in the Woodruff sand of the Eutaw formation of Cretaceous, producing 300 bbl. per day of 34.4" gravity oil through a ¼-in. choke, with a gas-oil ratio of 80 to 1 and bottom-hole pressure of 2045 lb. This was the discovery well in the Tinsley oil field. The well was drilled to a total depth of 4567 ft. and no salt water was encountered. The sand underlies the Selma chalk formation. Nine producing oil wells and one dry hole were drilled and completed by the end of 1939. Two producing sands have been found in the Eutaw and a third sand in the top of the Tuscaloosa formation, called the Woodbine sand in Louisiana and Texas. Faulting is an important factor in the Tinsley field. Total oil production has been approximately 250,000 bbl. from the nine flowing wells. Total depth to top of productive zone was 4540 ft.; to bottoms of productive wells, 4580 ft. Net thickness of the producing formation is 20 to 40 ft., and its porosity is 24 per cent. The deepest zone tested was the Tuscaloosa, in which the depth of hole was 6112 feet. Six hundred and forty acres has been proved for oil production. Jackson Gas Field.—The Jackson gas field has shown a steady decline in the number of wells but the pressure has been maintained. This field is a perfect example of a water-driven field and the time of wells going to salt water is predictable. Five wells were drilled in the Jackson field, of which only one produced. Amory Gas Field.—Interest was renewed in the Amory gas field, where a new well was started in the fall of 1939. Geological Formations.—The deepest well drilled in 1939 was the Willmut Gas and Oil Company's Cleve Love S. F. Johnson No. 1, sec. 29, T. 6 N., R. 1 W., Hinds County. This well encountered the Lower Cretaceous, Trinity series from 3770 to 6422 ft.; Lower Mesozoic from 6422 to 6484 ft. The geological correlations and nomenclature of the formations in Mississippi are shown in the accompanying strati-graphic section.

Jan 1, 1940

By W. R. Clough, M. E. Shank

IT has been noted in a study of the flow and fracture of nodular cast iron under biaxial stress conditions (complete results of which will be published later) that when this metal is subjected to stress it may undergo a striking density change. Such behavior was first determined by strain gage measurements made on tensile test specimens, and has since been substantiated by other types of measurement. The chemical analyses and mechanical properties of several nodular irons to be discussed here are given in Tables I and 11. Tensile data for iron A was obtained from a hollow cylindrical combined stress specimen of the same dimension as those used by L. F. Coffin, Jr.1 in his investigation of gray iron properties. Standard 0.505 in. solid tensile-test bars were used for irons B and C. On each specimen type, A-8 wire resistance strain gages were used—two diametrically opposing gages in the axial direction, two in the tangential or hoop direction. By subtracting elastic strains from the measured strains, the plastic strains could be calculated. By assuming that radial and tangential strains are numerically equal, a measure of permanent volume change can be obtained by summing the plastic strains. This appears to be a good assumption, since the metal either fractured, iron A, or readings were discontinued, irons B and C, long before necking took place. This calculated variation of volume increase with stress is given for irons A and B in Fig. 1. Data for iron C is almost identical with that for iron B. The volume change indicated by Fig. 1 has been substantiated by a more direct type of density measurement. A method developed by S. G. Fletcher and' Morris Cohen,' and completely described in the discussion of their article, has been used. The accuracy of specific volume measurement has been estimated as 0.00002 cu cm per gram. Essentially the method consists of weighing a sample in air and then immersed in water. Measurements were made before and after straining the material. The results shown in Table I11 were obtained by means of half-size (0.252 in. diameter, 1 in. gage length, 3/8-16 threads) tensile specimens. Initial measurements were made on the whole specimen before stressing. After stress-

Jan 1, 1955

The Year Book of the Institute will be mailed with, the May Bulletin. Its membership lists, both alphabetic and geographic, are corrected to Mar. 1, and the lists of officers and committees are corrected to date.

Jan 4, 1919

On June 1, the offices of the Engineering Division of the National Research Council were moved from Washington to the sixteenth floor of the Engineering Societies Building, 29 W. 39th St., New York City.

Jan 7, 1919

By Larry Kaufman, Martin Schatz

The effect of pressure on the extension of the ? loop in the FeSi system has been determined by means of metallogvaphic studies and hardness measurements performed on a series of high-purity Fe-Si alloys containing 7.5, 11.0, and 13.9 at. pct Si, respectively. These mensurements, performed at 42 kbar and temperatures up to 1200oC, indicate that the ? loop is expanded to about 10 at. pct Si at 42 kbar as opposed to a maximum extension of 4 at. pct Si at 1 atm. Comparison of the experimental results with thermodynamic predictions of the pressure shifts yields satisfnctory results. DURING the past few years, several studies have been performed in our laboratory1-' in order to determine the effect of high pressure on phase equilibrium in pure iron and iron-base alloys. The purpose of these studies has been to elucidate the effects of high pressure experimentally and to compare the observed results with predicted pressure effects derived on the basis of known thermody-namic and volumetric data at 1 atm. These studies have included work on pure iron2,5,7 as well as Fe-Ni,1,5 Fe-cr,l,5 and Fe-c4-6 alloys. In addition, Tanner and Kulin3 have reported results of pressure studies on two Fe-Si alloys containing 2.0 and 6.25 at. pct Si. At the time of this latter study, no detailed information was available concerning the difference in volume between the a (bcc) and ? (fcc) phases in the Fe-Si system as a function of silicon content. In order to compare their observations with calculated pressure shifts, Tanner and Kulin were forced to assume that silicon had no effect on the difference in volume between a and ? iron. The resulting discrepancy between their calculation of the a/? phase boundary at 42 kbar and the observed results led them to the conclusion that silicon additions probably decrease the difference in volume between a and ? iron. Recently: Cockett and Davis8,9 have reported de- tailed studies of the lattice parameters of a series of Fe-Si alloys at temperatures ranging from 20" to 1150°C. These measurements, performed on alloys in the bcc and fcc range, show that silicon does indeed decrease the difference in volume between a and ? iron. By correcting the calculations of Tanner and Kulin in line with the observed effect of silicon they were able to show improved agreement between computed and observed pressure shifts.' The present measurements were undertaken to provide additional corroboration of this effect, by extending the range of composition, in addition to exploring a situation where large extensions of a ? loop could result in impingement of the ? field with an ordered bcc phase (based on Feo.75Sio.25). I) EXPERIMENTAL PROCEDURES AND RESULTS The alloys investigated were obtained from Dr. F. Kayser of M.I.T. They were prepared at the Ford Scientific Laboratory by vacuum melting electrolytic iron and high-purity silicon. The melts were poured under an argon atmosphere into hot-topped steel molds. Subsequently the ingots were hot-worked down to 1/2-in.-diam rods. Three alloys containing 7.5, 11.0, and 13.9 pct Si were studied. Carbon, regarded as the principal impurity, analyzed at, or below, 0.001 wt pct for all of the alloys. Prior to pressure-temperature treatment, the rod was annealed for 24 hr in vacuum at 1000°C, water-quenched, and subsequently machined into 0.100-in.-diam by 0.100-in.-long specimens. Subsequent to machining, the specimens were again annealed and then examined metallographically. They were found to exhibit a clear coarse-grained ferrite similar to Figs. 10 and 110 of Ref. 1 and Fig. 2 of Ref. 3. Subsequently, specimens of each alloy were equilibrated at 42 kbar at various temperatures in supported piston apparatus.1,3,4,6 Three specimens, one of each alloy, were wrapped in platinum and exposed simultaneously. The pressure-temperature cycle consisted of increasing the pressure from ambient to 42 kbar at 25oC, heating rapidly to the desired temperature, holding for 15 min, and quenching to 100°C, followed by slower cooling to 25°C and pressure release. The temperature was measured with a Pt/Pt-13 pct Rh thermocouple which was not corrected for pressure effects. Subsequently, specimens were examined metallographically and by

Jan 1, 1964

By Charles F. Hickey, Eric B. Kula

Thermomechanical treatments applied to the maraging steels include a) cold working in the austenitic condition at 650°F, followed by transformation to martensite and aging, b) cold working in the murtensitic condition and aging, and c) cold working in the aged condition with and without subsequent reaging. The strength increases in these steels are very small compared to the increases observed in conventional carbon and alloy steels. The changes that are observed are compatible with the strengthening mechanisms operative during thermomechanical treatment of conventional steels, however. Differences are caused by the absence of a carbide precipitate and the low work-hardening rate in both the solution-treated and the aged conditions. ThE 18 pct Ni maraging steels represent a class of steels which are finding great interest for high-strength applications.1~2 They are essentially carbon-free, and contain 7 to 9 pct Co, 3 to 5 pct Mo, and 0.2 to 0.8 pct Ti. Although austenitic at elevated temperatures, they can be air-cooled to room temperature to form a martensite, which because of the absence of carbon is relatively soft. On subsequent reheating age hardening occurs and strength levels of 250 to 300 ksi yield strength can be attained. These steels appear to be particularly suitable for studying the response to various thermome-chanical treatments for additional reasons other than the obvious one of attempting to improve their already attractive properties. Thermomechanical treatments can be defined as treatments whereby plastic deformation, generally below the recrystal-lization temperature, is introduced into the heat-treatment cycle of a steel in order to improve the properties. With an absence of intermediate transformation products on air cooling the maraging steels have good hardenability and hence can readily be cold-worked in the austenitic condition prior to transformation to martensite. Further, they can be worked in the martensitic condition prior to aging, and even can be deformed in the fully aged condition. Finally, it is of interest to compare their re- sponse to that of the more conventional alloy and carbon steels, where the role of carbides is important in the strength increase by thermomechani-cal treatments. The thermomechanical treatment of conventional steels has been the subject of a recent review.' I) MATERIALS AND PROCEDURE The steel used in this investigation was a commercially produced vacuum-melt heat, which had been rolled to 0.090 in. and mill-annealed. The composition of the alloy was as follows: 0.02 C, 0.08 Mn, 0.10 Si, 0.009 P, 0.009 S, 18.96 Ni, 7.34 Co, 5.04 Mo, 0.29 Ti, 0.05 Al, 0.004 B, 0.01 Zr, and 0.05 Ca. Unless otherwise stated the heat treatments used were the standai-d solution treatment at 1500°F for 1 hr, air cool, followed by a 900°F, 3 hr age. In this condition, the material exhibited 232 ksi yield strength and 239 ksi tensile strength. Mechanical properties were determined by Vicker's hardness measurement (20 kg) and by tensile tests on standard 1/2-in.-wide, 2-in.-gage-length sheet tensile specimens. Notch tensile tests were run using the 1-in.-wide NASA type, edge-notched specimen.4 Fracture-toughness determinations were made on 3-in.-wide, center-notched, fatigue-cracked specimens, following the recommendations of the ASTM Committee on Fracture-Toughness Testing.4 An electric-potential technique was used for measuring the crack size at the onset of rapid crack propagation5 which is necessary for calculations of Kc, the critical stress-intensity factor under plane-stress conditions. The critical stress-intensity factor under plane-strain conditions KI, was also calculated, using the stress at which the first observable crack growth occurred. 11) RESULTS A) Cold-Worked in the Austenitic Condition. The reported M, temperature for the 18 pct Ni maraging steel is about 310°F.1 Therefore, a temperature of 650°F was selected as suitable for rolling in the austenitic condition. Specimens were solution-treated at 1500°F for 1 hr, air-cooled to 650°F, and rolled varying percentages from 0 to 60 pct, at 20 pct reduction per pass. Tensile and hardness properties after aging at 900°F for 3 hr are shown in Fig. 1. The tensile strength increases from 253 to 271 ksi and the yield strength from 247 to 265 ksi as a result of a reduc-

Jan 1, 1964

By Raymond C. Boettner

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

Jan 1, 1968

Vol. 54 will be sent about February 1 to members who have paid their dues for the current year. Members who do not receive copies within a reasonable time are asked to notify the Secretary.

Jan 2, 1917

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By W. S. Hyler, L. W. Berger, R. I. Jaffee

Hydrogen additions of 390 ppm to A-55 titanium and 368 ppm to Ti-8 pet Mn have no deleterious Hydrogenadditionseffect on the unnotched and notched rotating-beam fatigue properties of these materials. 'These amounts of hydrogen, however, are sufficient to cause severe notch-impact thesematerials.embrittlement in A-55 titanium and pronounced loss of tensile ductility in Ti-8 pet Mn. The lack of embrittling effect in fatigue in the latter alloy is consistent with the postulated strain-aging mechanism of hydrogen embrittlement in a-ß alloys. There is a significant strain-agingincrease in the unnotched endurance limit of A-55 titanium with the addition of hydrogen. This increase may be explained as the result of internal heating effects which would dissolve the hydride and cause solid-solution strengthening. TITANIUM and its alloys may be seriously embrittled by relatively small amounts of hydrogen. The form which this embrittlement takes has been shown to vary with alloy type. The a alloys, for example, suffer most strongly from loss of notch-bend impact toughness' when sufficient hydrogen is added, and this effect has generally been associated with the presence of hydride phase in the micro-structure. In a-ß alloys, on the other hand, hydrogen is most detrimental to tensile ductility in slow-speed tests,2-1 and the embrittlement may be detected in a most convincing manner by means of rupture tests at room temperature. This particular kind of embrittlement has not been associated with a change in microstructure, but has been classified rather generally as associated with a strain-aging type of mechanism.' In the present paper, the effect of an embrittling amount of hydrogen on the rotating-beam fatigue properties of both an a and an a-ß titanium alloy is covered. For this study, annealed commercially pure (A-55) titanium was chosen as an a alloy, and equilibrated and stabilized Ti-8 pet Mn as representative of a typical a-ß alloy. Nominal hydrogen levels of 20 and 400 ppm were evaluated, the latter amount having been shown previously to be severely detrimental to the impact toughness of commercially pure titanium and to cause pronounced strain-aging embrittlement in the Ti-8 pet Mn alloy. The only report of the effect of hydrogen on the fatigue properties of titanium is given by Anderson et al.,° in which a push-pull type of fatigue test was conducted on as-received commercial-purity titanium sheet. Much scatter was found in the results, but generally the presence of hydrides slightly decreased the fatigue strength of unnotched specimens in the longitudinal direction. The results of notched tests were masked too greatly by scatter to be significant. Experimental Procedure Preparation of Materials—Analyses of the A-55 titanium and the Ti-8 pet Mn alloy used in this investigation are given in Table I, which indicates the 8 pet Mn alloy to be more nearly a 6 pet Mn alloy. This alloy will be referred to as Ti-8 pet Mn, however, since this is the commercially designated composition. Both alloys were received in the form of5/8-in. diam rod and, after suitable surface preparation, 5-in. lengths were vacuum annealed at 820°C. Half of the rods for each material were then hydrogenated at 820°C to a nominal hydrogen content of 400 ppm. The hydrogenated and vacuum-annealed A-55 rods were hot swaged at 700°C from 5/8-in. diam to 1/4-in. diam, and then annealed 1 hr at 800°C and air cooled prior to preparation into test specimens. Fabrication of the Ti-8 pet Mn alloy was by hot swaging to 3/8-in. diam at 760" and then 1/4-in. diam at 704°C. This material was then annealed 1 hr at 704", followed by furnace cooling to 593"C, and finally air cooling to room temperature. Evaluation—In order to examine more completely the effects of hydrogen on the particular materials studied, slow-speed tensile and notch-bend impact properties were determined in addition to fatigue data. Tensile specimens were of the standard ASTM type with a reduced section of 1/8-in. diam and a gage length of 1/2 in. A subsize cylindrical Izod specimen was used for impact tests. These specimens had a 45" notch with a 0.005-in. radius and a 0.150-in. root diam, and the stress concentration factor of this notch in bending was Kr = 3. Both the ten-

Jan 1, 1959

By A. Lubinski

In drilling operations, attention generally is given to hole angles rather than to changes of angle, in spite of the fact that the latter are responsible for drilling and production troubles. The paper presents means for specifying maximum permissible changes of hole angle to insure a trouble-free hole, using a minimum amount of surveys. It is expected that the paper will result in a decrease of drilling costs, not only by avoiding troubles, but also by removing the fear of such troubles. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS Excessive dog-legs result in such troubles as fatigue failures of drill pipe, fatigue failures of drill-collar connections, worn tool joints and drill pipe, key seats, grooved casing, etc. Most of these detrimental effects greatly increase with the amount of tension to which drill pipe is subjected in the dog-leg. Therefore, the closer a dog-leg is to the total anticipated depth, the greater becomes its acceptable severity. Very large collar-to-hole clearances will cause fatigue of drill-collar connections and shorten their life, even in very mild dog-legs. Another finding regarding fatiguing of collar connections in dog-legs is that rotating with the bit off bottom sometimes may be worse than drilling with the full weight of drill collars on the bit, mainly in highly inclined holes when the inclination decreases with depth in the dog-leg. Means are given for specifying maximum dog-legs compatible with trouble-free holes. An inexpensive technique proposed is to take inclinometer or directional surveys far apart; then, if an excessive dog-leg is detected in some interval, intermediate close-spaced surveys are run in this interval. The application of the findings should result in a decrease of drilling costs, not only by avoiding troubles, but mainly by removing the fear of such troubles. The result would be much more frequent drilling with heavy weights on bit, regardless of hole deviation. Because of errors inherent to their use, presently available surveys are not very suitable for detecting dog-legs. There is a need for instruments especially adapted to dog-leg surveys. Crooked hole drilling rules should fall into two distinct categories—(1) those whose purpose is to bottom the hole as desired, and (2) those whose purpose is to insure a trouble-free hole. Three kinds of first-category rules in usage today are as follows. 1. A means to bottom the hole as desired is to prevent the bottom of the hole from being horizontally too far from the surface location; this may be achieved by keeping the hole inclination below some maximum permissible value such as, for instance, 5. 2. Another means to achieve the same goal is to limit the rate at which the inclination is allowed to increase with depth. A frequently used rate is 1/1,000 ft. In other words, a maximum deviation of l° is allowed at 1,000 ft, 2 at 2,000 ft, 3 at 3,000 ft, etc. 3. Whenever application of the first two means precludes carrying the full weight on bit required for most economical drilling, then the best course is to take advantage of the natural tendency of the hole to drift updip, displace the surface location accordingly and impose a target area within which the hole should be bottomed. This method has already been successfully applied,'.' and its usage probably will become more frequent in the future. Means for calculating the amount of necessary surface location displacement are avail-able.3'5'6 If in high-dip formations the full weight on bit should result in unreasonably great deviations, the situation could be remedied by increasing the size of collars and (if needed) the size of both hole and collars,351 or in some cases by using several stabilizers. Rules which would fall into the second category (i.e., rules whose purpose is to insure a trouble-free hole) are seldom specified today. It is vaguely believed that following Rules 1 and 2 of the first category will automatically prevent troubles. Actually, this is not true. If at some depth the only specified rule is that the hole inclination must be less than 4", the hole may be lost if the deviation suddenly drops from 4 to 2, or if the direction of the drift changes, etc. Rule 3 of the first category is generally used in conjunction with a rule belonging to the second category, namely, that the hole curvature' (dog-leg severity) must not exceed the arbitrarily chosen value of 1½ /100 ft. Moreover, when using this rule, the industry is not clear over what depth intervals the hole curvature should be measured. All this results in a frequent fear

By P. N. Richards, M. K. Ormay

The present Paper extends the previous work on cold reduced, low carbon steels to preferred orientations developed after various heat treatments. In recrystal-lized rimmed steel, cube-on-comer orientations increased with cold reductions up to 80 pct. Above that {111}<112> and a partial fiber texture with (1,6,11) in the rolling direction dominated. During grain growth, cube-on-corner orientations have been observed to grow at the expense of {210}<00l>. In re-crystallized Si-Fe (111) (112) and cube-on-edge type orientations are dominant near the surface and the (1,6,11) texture near the midplane for reductions up to 60 pct. With larger reductions {111)}<112> and the (1,6,11) texture are dominant. In cross rolled capped steel a relationship of 30 deg rotation was observed between the (100)[011] of the rolling texture and the main orientations after re crystallization. Most orientations present in recrystallized specimens can be related to components of the rolling texture by one of the following rotations: a) 25 to 35 deg about a (110) b) 55 deg about a (110) C) 30 deg about a (Ill) THE orientation texture of recrystallized steel is of interest where the product is to be deep drawn, because preferred orientation is related to anisotropy of mechanical properties such as the plastic strain ratio (r value);1,2 and in electrical steel applications where a high concentration of [loo] directions in the plane of the sheet improves the magnetic properties of the material. It is interesting to note that both these aims are to a large extent achieved commercially, even though the orientation texture of cold rolled steel does not show large variation3 and the recrystallized orientations are generally given as being related to the as rolled orientations mostly by 25 to 35 deg rotations about common (110) directions.4-6 There is, as yet, no single completely accepted theory on recrystallization. The three mechanisms that have been investigated and discussed are: a) Oriented growth b) Oriented nucleation c) Oriented nucleation, selective growth Largely from the observations of the recrystalliza-tion process by means of the electron microscope,7-11 there is now considerable evidence that the "nucleus" of the recrystallized grain is produced by the coalescence of a few subgrains to form a larger composite subgrain, which finally grows by high angle boundary migration into the deformed matrix. From the intensive work on the recrystallization of rolled single crystals of iron, Fe-A1 and Fe-Si al-loys4-" he following observations have been made: 1) The change in orientation during primary recrys-tallization can usually be described as a rotation of 25 to 36 deg about one of the (110) directions. 2) The (110) axes of rotation often coincide with poles of active (110) slip planes. 3) If several orientations are present in the cold rolled structure, the (110) axis of rotation will preferably be a (110) direction that is common to two or more of the orientations. 4) With larger amounts of cold reduction (70 pct or more) departure from these observations became more frequent. 5) After larger cold reductions, rotations on re-crystallization about (111) and (100) directions have been observed. K. Detert12 infers that a rotation relationship of 55 deg about (110) directions is also possible, by stating that the recrystallized orientation {111}<112> can form from the orientation {100}<011> of cold reduced partial fiber texture A.3 The observation by Michalak and schoone13 that (lll)[l10] formed during recrys-tallization in fully killed steel containing (111)[112],— as well as (001)[ 110] which is related to the {111}<011> by a 55 deg rotation about <110>-implies a possible 30 deg rotation relationship about the common [Ill]. Heyer, McCabe, and Elias14 have recrystallized rimmed steel after various amounts of cold reduction, by a rapid and by a slow heating cycle and found that the preferred orientations strengthened with increased cold reduction. The most pronounced orientation up to about 70 pct cold reduction was found to be {1 11}< 110>, after 80 pct cold reduction both {111}<110> and {111}<112>, after 85 and 90 pct cold reduction, {111}<112>, and after 97.5 pct cold reduction it was {111}<112> and (100)(012). In the present work, the orientation textures of the recrystallized specimens are examined under various conditions of steel composition, amount and method of cold reduction, and method of recrystallization. The relationships between the preferred orientations of the as rolled and recrystallized specimens, and the conditions for the formation of the various orientations during recrystallization are investigated.

Jan 1, 1970

By J. B. Clark, A. J. McEvily, R. L. Snyder

The nonuniform distribution of precipitate particles has been recognized as a leading factor contributing to the relatively low fatigue resistance of aluminum alloys. The structure of many of these alloys is characterized by narrow precipitate-free zones adjacent to the grain boundaries. Alloys with such zones exhibit a tendency for brittle inter crystalline fracture. The interrelation between this type of structure and mechanical properties was investigated in an Al-10 wt pct Mg alloy. It was found that deformation during fatigue occurs preferentially along these zones and cracks initiate there. In Al-10wt pct Mg, the zones were found to be supersaturated even after extensive general precipitation and are due to the absence of proper precipitate nuclei in the region near the grain boundaries. Cold working the alloy prior to aging improves the mechanical properties by inducing precipitation within the zones and also by jogging of grain boundaries. The mode of fracture is changed from brittle inter crystalline to more ductile trans granular fracture. THE process of fatigue is highly structure sensitive, with the strength of the whole often dependent upon some localized discontinuity, either geometrical or metallurgical in nature. Much has been learned about the role of geometrical discontinuities, e.g., notches, in fatigue, but with the exception of the effects of inclusions or the shapes of carbides, relatively little is known about the specific effects of discontinuities in metallurgical structure such as nonuniform precipitation. In most age-hardening aluminum alloys, metallo-graphic studies have shown that the extent of precipitation adjacent to grain boundaries is much less than that which occurs in the interior of the grains. The width of these almost precipitate-free regions, which are sometimes called denuded zones, and the extent of solute depletion within them, are dependent upon the particular alloy and its aging treatment. It has been observed1 that these zones are relatively soft with the result that plastic deformation takes place preferentially within them. It has also been shown 2-4 that there exists a tendency for intercrys- talline cracking in fatigue when such zones are present. It is of interest to note that Broom et al.2,3 were able to reduce the incidence of this type of failure in an A1-4 wt pct Cu alloy by stretching the material 10 pct prior to aging. In the present study, the effects of precipitate-free regions on the fatigue properties of an A1-10 wt pct Mg alloy were studied in detail, and the effects of deformation prior to aging on the nature of the precipitation process as well as on fatigue properties were also investigated. MATERIAL AND PROCESSING An A1-10 wt pct Mg alloy was selected for this study, because it was known that well-defined precipitate-free regions along the grain boundaries are readily obtained in this alloy after aging at 200oC.5 The starting materials were 99.998 pct A1 and singly sublimed magnesium of about 99.9 pct purity. The aluminum was induction melted in a graphite crucible, and then the magnesium addition was immersed until dissolved. Chlorine gas was then bubbled through the molten alloy for 4 min to degas the melt, after which the melt was cast at a pouring temperature of 730" to 760°C into a cold, graphite-coated, tapered steel mold. Since A1-Mg alloys are difficult to homogenize,5 special care was taken to obtain a uniform composition. Two-in. cubes were cut from the ingot and heated at 446°C for 30 min. These cubes were then hot forged approximately 35 pct in each of the three cube directions and homogenized for 16 hr at 446°C. Sheet specimens were then obtained by pressing 40 pct and rolling 35 pct per pass with reheating between reduction steps to a final thickness of approximately 0.10 in. The sheet was then solution treated for 16 hr at 446°C and water quenched. The age hardening behavior of this material at 200°C was then determined, and the results are shown in Fig. 1. The age hardening of this alloy when subjected to cold work prior to aging is also shown in this figure. Preliminary work indicated that extensive deformation after quenching was required to affect drastically the precipitate-free regions in this alloy, and a rolling reduction of 50 pct was chosen. For purposes of comparison the following three conditions were studied: a) Solution treated, quenched, and aged 20 hr at 200°C

Jan 1, 1963

By J. D. Hunt, D. T. J. Hurle

A uariety of eutectic structures are formed in faceted/nonfaceted eutectics. The various structures are explained in terms of the absence or presence of small facets in the liquid groove. Regular structures are produced when, for purely geometric reasons facels cannot form. The presence of a facet in the liquid groove leads to the formation of an irregular or a cell-like complex regular structure, due to the relative immobility of the groove. A classification of eutectics was proposed by Hunt and jackson, based on the presence or absence of facets on the primary phases (the absence of facets may be predicted from the dimensionless entropy of melting2). Eutectics were divided into three groups: 1) eutectics in which both phases grow in a nonfaceted manner; 2) eutectics in which one phase grows faceted, the other nonfaceted; 3) eutectics in which both phases grow faceted. It was suggested that regular1 rodlike or lamellar structures1 should be formed in the first group, that irregular or complex regular structures1 should be formed in the&apos; second, and that irregular structures1 should be formed in the third. Recently it has been shown that the structural classification is incomplete. Regular rodlike structures (InSb-NiSb eutectic3), or broken lamellar structure (Bi-Zn eutectic, Fig. 8), are formed in alloys of the second group when the faceted phase has a large volume fraction. Hunt and jackson&apos; argued that regular structures could form in faceted/nonfaceted systems, but that such structures would be unstable in the presence of microfacets on the lamella of the faceting phase, because the growth rate at a point on such a facet would depend on the kinetic undercooling at the point of nu-cleation on the facet, and not on the local kinetic undercooling. In these circumstances it would not be possible to consistently balance the compositional and kinetic undercooling over a lamellar structure and thus obtain a stable isothermal interface. In this paper we discuss in detail the origin of the various structures formed in faceted/nonfaceted systems, pointing out that the most important factor promoting the formation of a regular structure is the absence of a facet in the liquid groove. 1) FACET FORMATION IN SINGLE-PHASE MATERIALS Facets form when there is an energy barrier for the addition of a new solid layer on an existing solid. When a barrier is present,2 growth proceeds by the lateral movement of steps across a crystallographic plane. The rate-controlling stage of the process occurs when the step is first formed. Hulme and Mullin6 have shown that faceting in single-phase materials can only occur when both interface curvatures are convex with respect to the solid and when the surface is tangential to the facet plane. When even one of the curvatures is concave a facet does not form because new layers of solid from adjacent regions can always feed the facet plane, Fig. 1. Growth under these conditions is then as easy as elsewhere. Similar considerations will apply to eutectic growth; consequently the shape of the faceted phase is extremely important. 2) LAMELLAR SPACING CHANGES IN EUTECTICS Jackson and Hunt7 have shown that the interface undercooling AT of a growing lamellar interface (neglecting kinetic undercooling) is related to the lamellar spacing, A, and growth velocity, v, by an expression of the form: where m, Ql, and nL are constants of the system given in Ref. 7. Eq. [I] is plotted for fixed v in Fig. 2. Jackson and Hunt postulate that a regular eutectic grows near, but to the right of the minimum in the AT vs A curve. They argue that the spacing cannot be to the left of the minimum because the interface is then unstable to fluctuations in A. It cannot grow too far to the right, because when the spacing becomes too wide an isothermal interface can no longer be maintained over the large-volume-fraction phase.7 It is argued that during any change in growth rate the lamellar spacing remains in the permitted range by the movement of lamellar faults. When the spacing is too wide, the fault, shown in Fig. 3, moves to the left; when the spacing is too narrow it moves to the right. The faults, however, have to be formed. heir formation has been shown to occur when local regions deviate considerably from the spacing defined by the lamellar When the spacing is locally too narrow (it passes to the left of the minimum, Fig. 2), pinching off of the narrow phase occurs. When the spacing is locally too wide, the interface on the large volume-fraction phase can no longer be maintained as an iso-

Jan 1, 1969