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

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

Jan 1, 1969

By H. N. Hall

Reservoir and producing characteristics can govern the decision to use either a one-, two- or three-dimensional model for making predictions for gravity-drainage reservoirs. Examples of conditions requiring one-, two- and three-dimensional calculations are given. In 1961 the author presented a method for predicting one-dimensional gravity-drainage performance. This work has been exrendcd to obtain a three-dimensional model, which is described and for which a sample problem is presented. Introduction Many papers on gravity drainage or gas-cap drive'-3 have been presented for conditions where the reservoir is treated as a single areal segment so that, in effect, only one-dimen-sional flow is considered. Other authors'-Q ave given evidence showing that the one-dimensional concept would be unsatisfactory to predict reservoir performance for certain types of reservoirs. Experience has indicated that specific reservoir and producing conditions govern whether one-, two- or three-dimensional concepts must be used as a basis for reliable reservoir performance predictioils. Previously the author presented a paper outlining a method for predicting the performance of gravity-drainage reservoirs.' That paper treated the reservoir as a single areal segment so that it was applicable for only one-dimensional flow. The work has been extended to obtain a three-dimensional model that can be used to predict performance of gravity-drainage reservoirs. Although capable of being three-dimensional, it can be used equally well for one- and two-dimensional predictions. This paper discusses those reservoir and producing conditions governing the choice of model, and also describes a three-dimensional model suitable for predicting reservoir performance in the more complex situations. Discussion The Choice of Model To predict reservoir performance, it is necessary to represent the reservoir by a physical model. A mathematical model, based on the assumed physical model, then is used to predict the movement of oil and gas within the reservoir. The word "model" is used here to connote the combination of both a physical model and a mathematical model based on the physical model. Certain types of reservoir situations may be predicted suitably with a one-dimensional model, whereas two- and three-dimensional models may be required for other situations. This section illustrates reservoir conditions associated with the use of a specific type of model. Many types of reservoir structures are such that gravity drainage possibly could be an important factor in oil production. Production practices, as well as the nature of the structure. can influence the type of model that should be used. obviously, it is impossible to discuss all combinations of reservoir structure and production practices that might be encountered in gravity-drainage reservoirs. The following are typical examples of conditions where a choice must be made among a one-, two- or three-dimensional model to predict reservoir performance satisfactorily. Conditions Requiring a One-Dimensional Model Fig. la shows contours for an asymmetrical anticline in which gravity drainage might be expected to be important. Fig. Ib depicts a cross-section along Line A-A in Fig. la. Existence of a gas cap is a good clue that gravity drainage will be an important factor in producing oil from this type of reservoir. However, it is not essential since a gas cap will form as oil is produced from the reservoir. If the proper combination of reservoir permeability and withdrawal rates is present, the reservoir will behave like a

Jan 1, 1969

By R. A. Vandermeer, J. C. Ogle

The preferred crystallographic orientations (texture) developed in randomly oriented, poly crystalline niobium during rolling were studied by means of X-ray diflraction techniques. The evolution of texture at both the surface and center regions of the rolled strip was carefully examined as a function of increasing defamation throughout the range 43 to 99.5 pct reduction in thickness. Certain aspects of the center texture development in niobium are in agreement with the predictions of a theory by Dillamore and Roberts, but others cannot be explained by the theory in its present form. Above 87 pct reduction by rolling, a distinctly different texture appeared in the surface layers which was unlike the center texture. The present results are compared with previous results obtained from other bcc metals and alloys. RANDOMLY oriented, poly crystalline metal aggregates when plastically deformed to a sufficiently large extent develop preferred orientations or textures. In a recent review article, Dillamore and Roberts1 pointed out that the nature of the developed texture may be influenced by a large number of variables. These include both material variables such as crystal structure and composition and treatment variables such as stress system, amount of deformation, deformation temperature, strain rate, prior thermal-mechanical history, and so forth. From a practical point of view, the control of preferred orientation may often be important for the successful fabrication of metals into usable components. During the past few decades many experiments have been devoted to the study of deformation textures. This work, however, has been confined in large part to metals and alloys that have an fcc crystal lattice. By comparison, bcc metals and alloys have received much less attention, and consequently our understanding of preferred orientations in these materials is only shallow. This state of affairs worsens when it is realized that almost all of our present howledge about this class of materials derives from studies on irons and steels.' The bcc refractory metals, which are relative newcomers to the industrial world, have, on the other hand, been given at best only passing glances in the area of texture development. Our understanding of the evolution of preferred orientations in bcc metals can only remain fairly limited until systematic studies of metals and alloys other than the irons and steels have been carried out and the influence of the many variables has been determined. To that end a program was initiated to investigate in detail texture development in niobium. The present paper reports some of the results of this study. Textures were determined at both the center and surface of strips rolled variously to as much as 99.5 pct reduction in thickness at subzero temperatures. Emphasis in this paper is on texture description and on texture evolution during rolling to progressively heavier deformation. EXPERIMENTAL PROCEDURE The niobium was purchased from the Wah Chang Corp. as a 3-in.-diam electron-beam-melted billet. Chemical analysis indicated the impurities to be less than 300 ppm Ta, 40 ppm C, 10 ppm H, 170 ppm 0, and 110 ppm N. All other impurities were below the limits of detection by spectrochemical analysis. This large-grained billet was fabricated into specimen stock so that a fine-grained randomly oriented grain structure resulted. This was accomplished in three deformation steps alternated with recrystalli-zation anneals of 1 hr at 1200°C in a vacuum of low 10"6 Torr range after each deformation step. The first step was to alternately compress the billet 10 to 20 pct in each of three orthogonal directions. The second step was to compress in only two directions 90 deg apart to produce a 2-in.-sq bar. The final step was to roll this bar 50 pct to give a 1-in. by 2-in. cross section. After the final anneal, metallo-graphic examination showed the material to have an average grain size equivalent to ASTM No. 5 at 100 times (i.e., 0.065 in. diam). Specimens cut from the center and edges of this bar gave no indication of detectable preferred orientation when examined by X-ray diffraction. Samples 1.5 in. long, either 0.625 or 0.750 in. wide, and approximately 0.400 in. thick were machined from this fabricated ingot. The surfaces corresponding to the rolling planes were ground so as to be parallel. The samples were chemically polished in a solution of 60 pct nitric acid and 40 pct hydrofluoric acid (48 pct solution) prior to rolling to remove any cold work introduced in the machining operations. Rolling was accomplished with a 2-high hand-operated laboratory rolling mill that had 2.72-in.-diam rolls. Prior to operation, the rolls were polished with 600 grit paper, cleaned with acetone, and then soaked in a container of liquid nitrogen for several hours. The samples were also soaked in liquid nitrogen prior to rolling and were recooled between each pass. While some slight heating of the samples occurred during rolling, this procedure maintained the sample temperature well below 0°C at all times. The samples were rolled unidirectionally, and the rolling plane surfaces were not inverted during any phase of the operation. The draft per pass averaged between 0.010 to 0.012 in. After 96 or 97 pct reduction the draft was reduced to 0.001 to 0.002 in. per pass. Samples were rolled to various reductions in thickness between 43 and 99.5 pct.

Jan 1, 1969

By E. Miller, K. Komarek, W. Johnson

The activity of aluminum in solid Cr-A1 alloys has been measured by an isopiestic technique between Cr-A1890' and 1126" and 13 and 80 at. pct Al. The integral free energy of mixing has a minimum value of —5600 cal per g-atom at 59 at. pct Al. The maximum solid solubility of aluminum in chromium was determined to be 43 at. pct Al, and the composition limits of the compounds CrA14, Cr4A19, and Cr5Al, at 1000"~ were found to be 79 to 80, 66 to 70, and 59 to 63 at. pct Al, respectively. The thermodynamic properties of the Cr-A1 system have been investigated as part of a thermodynamic study of aluminum-transition metal systems.172 Little information is available on the equilibrium properties of the Cr-A1 system. The heats of formation of solid Cr-A1 alloys have been determined by Kubaschewski and Haymer at 600" and low-temperature specific heat data have also been obtained.~ More extensive work has been performed on the phase diagram, and a compilation has been provided by Hansen and Anderko,~ their phase diagram at elevated temperatures being essentially based on the work of Bradley and LU.~ The high-temperature portion of the phase diagram shows an intermediate phase CrA14 decomposing peritectically at 1018°C and existing at 82 at. pct A1 at 1000°C. They also identified the compounds with solubility limits of 72 to 75 at. pct A1 at 1000°C, and Cr5A1,, existing at 61 at. pct A1 at 1000°C. The maximum solid solubility of aluminum in chromium at 1000°C was found to be 46 at. pct Al. These elevated-temperature data were obtained by examination of quenched samples and were considered as less precise than the lower-temperature data. Koester, Wachtel, and Grube7 have revised the phase diagram as a result of their magnetic susceptibility and X-ray study. The results of this work differ appreciably from those of Bradley and Lu at temperatures above 800°C. The CrA1, compound is given as existing between 79 and 81 at. pct A1 at 1000°C, and they do not indicate the presence of a CrA13 phase reported by Bradley and Lu. They also report the compound Cr4Alg as having solubility limits of 66 to 70 at. pct A1 at 1000°C, while Bradley and Lu show this compound stable only up to 870°C. Koester et al. state that the high-temperature modification of the compound Cr5A18 is stable down to 1125"C, and not 980°C as stated by Bradley and Lu, and that the low-temperature modification of Cr5Al, has a range of homogeneity of 58 to 63 at. pct A1 at 1000°C. They also report that the maximum solid solubility of aluminum in chromium is 43 at. pct A1 at 1000°C. APPARATUS AND EXPERIMENTAL PROCEDURE An isopiestic method was employed which has been successfully applied to the determination of aluminum activities in solid ~e-All and Ni-Al alloys. Alloy specimens were held at different positions in a temperature gradient and were equilibrated with aluminum vapor from an aluminum reservoir kept at the temperature minimum of an impressed thermal gradient in a closed alumina system. Diffusion of aluminum into the specimens occurred until equilibrium was reached, at which the partial pressure of aluminum in each of the specimens was given by the vapor pressure of the pure aluminum reservoir. The activity of aluminum referred to liquid aluminum as the standard state in a given equilibrated sample at temperature T could therefore be expressed by: vapor pressure of pure aluminum at _ the temperature of the reservoir Vapor pressure of pure liquid aluminum, at specimen temperature T Since both the temperature of the aluminum reservoir and the specimen temperatures were determined experimentally, and the vapor pressure of pure aluminum is known as a function of temperature,' the activity of aluminum in a given aluminum alloy of known composition could be calculated. Initial runs were made with samples consisting of pure chromium chips placed in alumina crucibles. These runs exhibited large inconsistencies, indicating that equilibrium was not attained. High aluminum content Cr-A1 alloy powders were therefore substituted for the pure chromium specimens. The starting composition of the alloys was adjusted through experimentation until the concentration change necessary to attain equilibrium was small. In this manner, consistent results were obtained in reasonable times. SPECIMEN PREPARATION Alloy specimens were prepared from chromium of 99.997 pct minimum metallic purity: with 0.028 to 0.038 pct H, 0.0002 pct N, and 0.27 to 0.46 pct 0 (Aviquipo, Inc.). The aluminum had a purity of 99.99+ pct and the following impurities: 0.003 pct Cu; 0.002 pct S; 0.002 pct Fe; 0.001 pct Pb; 0.001 pct Ga (Aluminum Corp. of America). Alloy powders were prepared from weighed mixtures of chromium and aluminum by double-arc melt-

Jan 1, 1969

By Carl Altstetter, Roy Adams

Measurements of enthalpy changes and transformation temperatures me reported for the fcc -hcp marten-sitic transformation in pure cobalt single and multi-variant crystals andpolycrystalline specimens. From these measurements the free-energy difference between the two phases was calculated for both heating and cooling and for repeated cycles through the transformation. For heating of single crystals the average value of enthalpy change was 113 cal per mole but on cooling it was 84 cal per mole. This difference is interpreted in terms of lattice imperfections which are introduced during transformation. A calorimeter suitable for measurement of enthalpy changes of athertnal transformations is described. COBALT exhibits an allotropic phase transformation at around 417°C' where an hcp phase (a = 2.507, c = 4.0686, c/a = 1.6228)~ stable at low temperatures transforms to an fcc phase stable up to 1495°C. The transformation has a hysteresis of about 30°C— the exact magnitude of the hysteresis depending on the number of transformation cycles, grain size, impurity content, and prior treatment.'-6 The athermal character of the transformation and surface relief due to transformation shear indicate that the transformation is martensitic. Pole mechanisms for the transformation have been discussed by Sebilleau and Bibrin, Bilby, Seeger,' and Basinski and Christian. These authors have proposed that the cooling transformation is effected by rotation of a Shockley partial dislocation around a pole dislocation with a screw component of 2a/3(111). Such a rotation would change the stacking of close-packed planes from the abcabc fcc stacking to the ababab hcp stacking sequence. This mechanism would predict a lattice correspondence of {111}fcc~~(0002~cp, have been observed. One would expect the heating transformation to occur similarly, involving dislocation movements on the (0002)hcp. However, a high density of pole dislocations and high dislocation ve- locity are required to account for microscopic observations. Furthermore, the high back stress developed on the Shockley partial dislocation as it rotates toward the sessile dislocation associated with it makes it doubtful that this is in fact the transformation mechanism. A mechanism for spontaneous nucleation of partial dislocations1*l2 seems more reasonable. If a single crystal of cobalt is cycled through the transformation but never heated above 600°C, it will remain single."13 However, if the specimen is heated through the transformation and held for a short time at or above 1000°C before cooling, the cooling transformation usually involves all four {lll}fcc habits, resulting in neighboring orientations of hcp differing by 70.5 deg. This condition is termed multivariance and has been observed by Bibring and sebilleau5 and Nelson and ~ltstetter.' The latter authors used single crystals of cobalt grown in an electron beam zone refiner. They proposed that the strongly directional cooling caused the initial cooling transformation to occur on the {lll)fcc most nearly perpendicular to the temperature gradient. Transformation shear on one set of {lll}fcc planes immobilized dislocations on the other {lll}fcc planes involved in the initial transformation. Since there is only one (0002)hcp plane orientation, the product of subsequent heating transformations could have no more than two variants—the original fcc orientation or its twin. If, however, the specimen was annealed at a high temperature, such as 1000°C, there would be relaxation of dislocations into low-energy configurations, and in the absence of a sharp temperature gradient transformation on all four (111 Ifcc planes could occur. If a dislocation mechanism is responsible for the transformation, the perfection of the lattice should affect the reversibility of the transformation. Mutual constraints of neighboring grains in polycrystalline material would inhibit dislocation movement resulting in increasingly sluggish transformation. Indeed, Nelson and Altstetter found the M, to decrease and the A, to increase in going from single crystals to multi-variant specimens to polycrystals. The effect is enhanced by decreasing the grain size of a solid specimen or a powder.6'14 Data on the free-energy difference necessary to initiate the transformation gives information about the driving force of the transformation. This is an important consideration in the understanding of the transformation mechanism. The free-energy change associated with the transformation of the hcp phase to the fcc phase at some temperature T different from the equi-

Jan 1, 1969

By P. K. Strangway, H. U. Ross

Briquets consisting of pure artificial magnetite, pure artificial hematite, and mixtures of the two were reduced by hydrogen in a loss-in-weight furnace at temperatures in the range 500° to 1000° . The rate of reduction of the pure hematite briquets increased continuously with increased temperature. In contrast, the pure nmgnetite briquets exhibited a pronounced rate ninimutn at about 700°C. Metallographic studies of partially reduced briquets rerlealed that, at this temperature, the he.matite samples reduced in a topo-chemical manner while the magnetite ones reduced uniformly throughout, and after partial reduction their cross sections contained a mixture of iron and unreacted wustite grains. No iron shells could be detected on the surfices of any of these uwstite grains. X-ray diffraction investigations indicated that these grains had a rzinimum lattice parameter when they had been formed at the rate rninimum temperature. Also, it was found that an activation energy of 41,000 cal per mole zoas required for reduction when only these wustite grains were present. Thus, it is suggested that the overall reduction rate of the rnagnetile su?nples at temperatures in the range influenced by the rate nzinirnum phenomenon was limited by the rate qf iron ion diffusion in the unreacted wustite grains. THE rate minimum phenomenon, which has often been observed when reducing iron oxides at a temperature of about 700°C, is one of the most interesting, yet unresolved, problems in the field of reduction kinetics. Basic principles of chemical kinetics and 'In some instance, a second rate minimum has been observed at about 900°C. Since most investigators are in agreement that this minimum is directly related to the transformation from a to y iron (which takes place at 911°C) and since it was not encountered during the present reduction tests, it will not be referred to in this vaver. fundamental laws of diffusion all agree that, as the temperature is increased, the rate of reduction should also increase. However, with certain ores, it has been found that their reduction rate actually decreases with an increase in temperature up to some value X where a minimum reduction rate is reached. With further temperature increases beyond X the rate becomes more rapid again. Temperature X is usually referred to as the "rate minimum temperature", while the overall type of behavior constitutes the "rate minimum phenomenon". This phenomenon has been reported by numerous investigators. They have found rate minima during the reduction of both artifiial' and natural374 magnetites and artificia15j6 and natural5" hematites. Rate minima have been observed when reducing high-purity material2 or low-grade ores,3'4 when studying particles in the micronsize range5 or relatively large agglomerates,g10 and during reduction with either hydrogen7 or carbon monoxide.11"2 Previously, this phenomenon has been attributed to many factors; these include sintering and recrystallization of the iron formed during reduction374 changes in microporosity of the ore upon redction,"" formation of dense iron shells around retained wustite grains,11716 and chem-isorption,17 to name only a few. However, most investigators who have reported a rate minimum merely speculated as to what seemed to influence it and they did not examine the fundamental causes. Consequently, the present experimental study was initiated in order to evaluate the basic factors which could be associated with this phenomenon. MATERIALS AND METHODS The experimental techniques, followed during this investigation, are similar to those which have been described previously.18 The chemically pure magnetic powder was prepared by partially reducing Fisher reagent-grade hematite with a gaseous mixture of carbon monoxide and carbon dioxide in a rotating-drum furnace. Three-quarter-inch diam cylindrical briquets which weighed about 12 g were formed from this magnetite powder and pure hematite powder. All of the briquets were sintered while they were slowly raised through the 1200°C hot zone of a vertical tube furnace. An argon stream was continually flushed through this furnace in order to prevent oxidation of the magnetite briquets, while in the case of the pure hematite briquets sintering was carried out in air. The sintered hematite briquets had a density of 5.06 g per cu cm while the density of the sintered magnetite briquets was 4.27 g per cu cm. The sintered briquets were reduced by purified hydrogen in a loss-in-weight furnace at temperatures in the range 500" to 1000°C. In all instances, the critical reducing gas velocity was exceeded and, in order to ensure that the results were reproducible, duplicate briquets of each type were reduced under each set of experimental conditions. A continuous record of the weight loss during reduction was obtained with the aid of a Statham transducer. The present experimental setup was capable of detecting a change in weight as small as 10 mg. Since a weight loss of over 2 g usually occurred during each reduction test, an accuracy of better than 0.5 pct of the total weight loss could be achieved. RESULTS AND DISCUSSION Reducibility Tests. In the first set of experiments, pure hematite and pure magnetite briquets were used.

Jan 1, 1969

By H. Conrad, V. Damiano, J. Hanafee, N. Inoue

The effects of hydrostatic pressure up to 400 ksi at 25" to 300°C on the mechanical properties of three forms of commercial beryllium (hot-pressed block, extruded rod and cross-rolled sheet) were investigated. Three effects of pressure were studied: mechanical beharior under pressure, the effect of pressure-cycling, and the effect of tensile prestraining under hydrostatic pressure on the subsequent tensile properties at atmospheric pressure. For all three materials the ductility increased with pressure whereas the flow stress did not appear to be significantly influenced by pressure. An increase in the subsequent atmospheric pressure yield strength generally occurred as a result of pressure-cycling or prestraining under pressure, whereas either no change or a decrease in ductility occurred. The only exception to this was sheet material, which exhibited some improvement in ductility following a pressure-cycle treatment of 304 ksi pressure. The effects of pressure-cycling and prestraining were relatively independent of the temperature at which they were conducted. Stabilized cracks of the (0001) type were found in hot-pressed specimens and {1120) type in extruded and sheet specimens following straining under pressure. Also, pyramidal slip with a vector out of the basal plane, presumably c + a, was identified by electron transmission microscopy for extruded rod and for sheet strained under pressure. Small loops similar to those previously reported were found after straining at pressures of the order of 300 ksi. THE use of beryllium in structures is limited because of its poor ductility under certain conditions. Therefore, one objective of the present research was to determine if the ductility of beryllium at atmospheric pressure could be improved by prior pressure-cycling or prestraining under hydrostatic pressure. Another objective was to study the mechanisms associated with the plastic flow and fracture of the polycrystalline form of this metal with pressure as an additional variable. Since the early work of Bridgman,1 it has been recognized that many materials which are brittle at atmospheric pressure exhibit appreciable ductility when strained under high hydrostatic pressure. This effect has been reported for beryllium by Stack and Bob-rowsky2 and by Carpentier et al.3 and has been attributed to the operation of pyramidal slip systems with slip vectors inclined to the basal plane while cleavage or fracture is suppressed.4 That such slip may occur simply by the application of pressure alone without external straining (pressure-cycling) is suggested by the results on polycrystalline zinc5 and polycrystalline beryllium,6 where nonbasal dislocations with a vector (1123) were reported. A significant improvement in the ductility of the bee metal chromium by pressure-cycling has been reported.7 On the other hand, limited studies on the pressure-cycling of the hcp metals zinc67819 and beryllium6 indicated no improvement in ductility; there only occurred an increase in the yield and ultimate strengths. The study on beryllium was limited to hot-pressed material. Consequently, additional studies on the effects of pressure-cycling on other forms of beryllium seemed desirable, especially since for chromium some authors10 have been unable to detect any improvement in ductility while others find a large improvement.7 That the ductility of polycrystalline beryllium at atmospheric pressure might be improved by prior straining under hydrostatic pressure was suggested by the known beneficial effects of cold work on the ductile-to-brittle transition temperature in the bee metals. It was reasoned that, by straining under hydrostatic pressure, fracture would be suppressed, and during the propagation of slip from one grain to its neighbor dislocations with a vector inclined to the basal plane"-'4 would operate. Upon subsequent straining at atmospheric pressure, these dislocations with a nonbasal vector would continue to operate and thereby reduce the tendency for fracture to occur, by assisting in the propagation of slip across grain boundaries and by interacting with any cracks that may develop. It was recognized that maximum improvement in ductility would probably occur at some optimum amount of prestrain under hydrostatic pressure. If the pre-strain was too small, an insufficient number of dislocations with a nonbasal vector would be activated; if it was too large, internal stresses (work hardening) might increase the flow stress more than the fracture stress, or incipient cracks or other damage could develop. EXPERIMENTAL PROCEDURE 1) Materials and Specimen Preparation. The materials employed in this investigation consisted of hot-pressed block (General Astrometals, CR grade), extruded rod (General Astrometals, GB-2 grade with a reduction ratio of 8:1), and cross-rolled sheet (Brush S200, 0.065 in. thick). The analyses of these materials and mechanical properties at room temperature and atmospheric pressure are given in Table I. The grain size of the hot-pressed block was 15 to 16 µ, that of the extruded rod 10 to 11 µ, and that of the sheet 7 to 10 µ in the rolling plane and 5 to 6 µ in the thickness, all determined by the linear intercept method. Al-

Jan 1, 1969

By J. Weijdema, D. N. Dietz

In the conventional underground combustion process (dry combustion) much heat is left behind in the swept formation and goes to rva.rte. Econonmy can be improved by heat recuperation through water injection. This is most advantageous if done at the earliest opportunity before much heat is dissiputed to cap and base rock. Water injected simultaneously with the air will flash to superheated steam, which passes through the combustion front together with the nitrogen from the air. A condensation front traveling up to three times as fast as the combustion front drives out the oil. In this type of wet combustion, the water evaporates before it reaches the combustion zone. The evaporation front travels more slowly than the combustion zone. If so much water is injected that the evaporation front overrun the combustion front, combustion in that spot will be quenched and some unburned fuel will be left behind. Air reacts with the oil farther down-stream where steam temperatures occur; at steam temperature, the air reacts rapidly with the oil. Velocity of the combustion front is increased thereby and is governed essentially by the water-injection rate. In the extreme case of high water-injection rate, a short heat wave of constant length is driven through the formation by water injection. Once this wave has been established, no more heat need be generated than that required to make up the heat losses from the short heat wave; a relatively low rate of air injection will suffice. The feasibility of partially quenched combustion has been confirmed in tube experiments. A heat wave at steam temperature is observed. Chemical analyses of flue gas indicate preferential burning of hydrogen while a carbonaceous residue is left in the formation. Introduction A disadvantage of so-called dry in situ combustion is that air-compression costs are rather high. An air consumption of about 400 std cu m/cu m (400 scf/cu ft) of formation swept is an accepted figure. This high consumption is mostly wasted since much heat is left behind in the depleted oil sand. Methods were investigated for recuperating as much as possible of the heat left behind. This paper deals only with basic principles and is confined mainly to one-dimen- sional flow without lateral heat losses; experiments were conducted in relatively narrow, well insulated tubes. If some water is injected with the air, it will turn to superheated steam in an evaporation front, which should travel behind the combustion front. The steam having passed the combustion front causes a steam drive by a condensation front that can travel faster than the combustion front. The latter needs to travel only part of the distance covered by the oil-displacing condensation front, and thus consumes less air. The water-air ratio would seem limited to that at which cold water overruns the combustion. This limitation was deliberately exceeded considerably in theory and experiments. It was found that combustion is then indeed quenched, but only locally. Farther downstream, the oxygen finds residual oil at steam temperature, which is suficiently high to ensure rapid oxidation. Thus, the combustion front uses only part of the available fuel because it is chased through the formation faster than its normal velocity. No heat is left behind. This new process is called "partially quenched combustion". At the upper limit of the water-air ratio, a small heat slug is moved through the formation by the flow of water and steam. Only a small flow of air is needed since it has only to generate sufficient heat to make up for the lateral heat losses of the short heat slug. Theory Although many factors complicate underground combustion, the processes will be presented in their simplest form. For this reason, one-dimensional flow without lateral heat losses is assumed. Heat conduction in the direction of flow also is disregarded. Under these conditions, dry combustion causes very high temperatures. The heat-carrying capacity of the gas stream is small. Heat generated by oxidation of a residual oil saturation is retained in the sand. The available fuel determines the air requirement and the temperature obtained. Accepting the often-mentioned air consumption of 400 std cu m/cu m (400 scf/cu ft) formation, we calculate a temperature of the swept sand of 1,200C (2,192F) (Fig, I). If water is injected at a modest rate with the air, it will flash to superheated steam upon contact with the heated sand. One cu m (35.31 cu ft) of hot formation will evaporate about 0.5 cu m (17.66 cu ft) of water, and thereafter will accommodate (at an estimated 0.80 saturation and an assumed 0.40 porosity) another 0.3 cu m (10.59 cu ft) of water in cold condition. As long as less than 0.5 + 0.3 = 0.8 cu m (28.25 cu ft) of water is injected for every 400 std cu m (14,125 scf) of air (water-

Jan 1, 1969

By K. E. Gray, M. S. Seth

Equations of elasticity for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure were formulated. Using an analogy between thermal and porous body stresses, it was shown that the solution for a transversely isotropic porous body may be obtained by incorporating body forces and the stresses due to a boundary load into the corresponding solution for the thermal stress problem. Equations of elasticity ad the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant pressure or a constant rate of flow is maintained at the wellbore. The vertical and tangential displacements are zero from the conditions of the problem. A numerical analysis was made of the solutions obtained by using a digital computer to determine the relative influence of each system variable. Considering rock as a porous body with internal fluid pressure generally gives results significantly different than considering the rock to be nonporous; the directional character of rocks leads to significant differences as compared to results based upon the common assumption of isotropy. Stress gradients are high near the wellbore but die out away from the well. Radial stresses are compressive or neutral, whereas tangential stresses are tensile, neutral or compressive, depending upon the boundary conditions and physical properties of the system Vertical stresses are compressive for an unbounded system. For constant wellbore injection rate, the vertical stress is proportional to the rate of fluid injection and decreases with time, whereas the radial and tangential stresses increase with time. At a given location, the radial displacement generally is very dependent upon time. INTRODUCTION A realistic appraisal of the state of stress in subsurface rock formations would be of considerable interest and use to the petroleum industry. For example, knowing the state of stress in proximity to a wellbore would be of fundamental importance in designing a fracturing operation or, more important, of clearly understanding the conditions necessary to produce rock failure of desired dimensions and geometry. Understanding conditions necessary for rock failure at the wellbore would also be of utility in a preventive sense. For example, borehole stability is an important consideration for many rock formations, and knowledge of the stress state at and near the wellbore under conditions of substantial pressure gradient due to fluid flow would be of great value. When fluid flows through a porous body which is initially at some uniform stress level, the following forces generate stresses at any point in the body. (1) Forces due to nonuniform pressure distribution. With increasing pressure the elements of a body are compressed. Such compression cannot proceed freely in a continuum when the pressure is not uniform throughout, and thus, stresses due to flow of fluid are set up. (2) Pore fluid pressure. This gives rise to normal stresses whose value at any point is the product of areal porosity and the fluid pressure. Although the fluid exerts uniform pressure, the stresses it creates in an anisotropic body may not be the same in all directions since the areal porosity in an anisotropic porous body is a direction-dependent quantity. This consideration leads to the concept of directional porosity. (3) Body Forces. The flow of the moving fluid imparts a force to the rock matrix, the magnitude of which depends upon the pressure

Jan 1, 1969

By Edwin B. Wilson, Charles F. Cockrell

The application of evolutionary operation is proposed for the cleaning of coal by the heavy media process. Analysis of the data given suggests some benefits that may not be immediately appreciated unless evolutionary operation is applied. For example, while it may seem obvious to increase specific gravity when the ash and sulfur content of the clean coal is lower than that allowed, evolutionary operation may show that an increase in feed rate or an increase in both feed rate and specific gravity would be a more profitable alternative. In addition, by using evolutionary operation, up-to-date knowledge of the effect of change of feed rate or specific gravity on yield and product quality is available. This information facilitates confidence about decisions made in regard to the day-to-day operation of these units. A number of other applications in the minerals industry are proposed. An application of evolutionary operation in a related field is also given where a large number of variables were required to be optimized.

Jan 1, 1969

By Jacques Steininger, Robert E. England

Single crystals of ZnTe and ZnTe1-,Sex with x up to 0.13 have been grown from the elements by temperature gradient solution zoning using excess tellurium as a solvent. Best results have been obtained with charges with the compositions 45/55 at. pct Zn, Te, for ZnTe and increasing amounts of selenium for ZnTe1-xSex. The temperature in the molten zone was maintained at about 1070°C with a gradient of about 10°C per cm. Chemical analyses of quenched ZnTe ingots show tellurium concentrations in the molten zone as high as 70 pct with concentration differences across the zone of 1 to 2 at. pct Dark dots which are observed by transmitted light microscopy in as-grown crystals can be removed by annealing in zinc vapor at 900 C. INTEREST in wide band gap semiconductors has led to a new study of ZnTe and ZnTel-xSex crystal growth. ZnTe is the only II-VI compound with a wide band gap (2.3 ev) that can be made p type with low resistivity. Attempts to make it n type with low enough resistivity to be useful for p-n junctions have so far been unsuccessful.1 ZnSe has a band gap of 2.65 ev but can be made n type only. However, ZnTel-xSex solid solutions with x as low as 0.36 have been made both highly n and p type2 with a minimum band gap around 2.12 ev3 at room temperature and appear to hold the best promise for efficient injection electroluminescence in the visible. ZnTe has the lowest melting point of the zinc chal-cogenides (1295°C) and consequently attempts have been made to grow crystals from both the liquid and the vapor phase.4 Complicated apparatus is required for growth from stoichiometric melts because of the high vapor pressures of the elements at the melting point of ZnTe and because of the problem of quartz devitrification. Small crystals have thus been grown in high-pressure equipment by Fischer5 and by Narita et a1.6 with pressures of the order of 50 atm of argon to prevent excessive evaporation from the melt. Large crystals of ZnTe can be obtained by growth from the vapor phase4 but they often present numerous dislocations and inclusions. An improvement in the quality of vapor- grown ZnTe crystals was reported by Albers and Aten7 by equilibration of mixtures of small crystals with compositions lying on either side of the solid single-phase field at fixed temperature. The same technique was later applied by Aten8 to the growth of ZnTe1-xSex crystals with less than 1 pct inhomo-geneity. Because of the higher liquidus temperatures of the solid solutions and the high vapor pressure of selenium, previous attempts to grow ZnTel-xSex from the melt have been limited and unsuccessful.9 The phase diagram of the Zn- Te system is reproduced in Fig. 1, based on data from Kobayashi10 and Kulwicki.11 Carides and Fishher12 have reported lower liquidus temperatures on the tellurium-rich side, but their data would require confirmation. The liquidus temperature on the tellurium-rich side decreases rapidly with increasing tellurium concentration and the Te2 vapor pressure over the liquidus also decreases accordingly.'3 The decrease in liquidus temperature and vapor pressure therefore makes it possible to use conventional apparatus if there is a sufficient excess of tellurium in the melt. Single crystals of ZnTe have thus been grown by Kucza,14 in a modified Bridgman technique, from solutions containing up to 60 at. pct of Te by lowering unsupported quartz ampoules through a temperature gradient at about 1200°C. Under these conditions, the phase diagram indicates that the entire charge is initially molten. Crystal growth can therefore proceed by normal freezing and rejection of excess tellurium into the melt. The modified Bridgman technique has several major limitations. Because of the rejection of excess tellurium into the melt during freezing, the melt composition and the temperature at the growth interface vary continuously. They tend to follow the liquidus until the eutectic which is very close to pure tellurium (447°C, >99 pct Te). Since the solidus composition also varies with temperature,15 crystals grown by this method are inhomogeneous. They present small variations from stoichiometry which may affect their structure and physical properties. The simultaneous increase in tellurium content and decrease in melt temperature also combine to reduce the rate of diffusion of tellurium away from the growth interface, thereby causing constitutional supercooling and possibly dendritic growth. To minimize these effects, the initial melt composition is in practice kept relatively close to stoichiometry (less than 60 pct Te). This however limits the possibilities of operating at low temperatures and pressures. This paper describes a modified method of crystal growth by temperature gradient solution zoning (TGSZ) which is an adaptation of the temperature gradient zone-melting technique developed by pfann16 and of the traveling solvent method of Mlavsky and weinstein.I7 The TGSZ method now applied to the growth of ZnTe and ZnTel-xSex crystals is characterized by its very simple experimental arrangement and sample preparation technique. Unlike the modified Bridgman technique, there is no increase in the tellurium concentration in the melt and therefore it is possible to operate at lower temperatures and pressures. This method is also suitable for maintaining a constant temperature at the growth interface.

Jan 1, 1969

By R. K. Agarwal

In this paper, a new technique developed to analyze two-dimensional nonhomogeneous models is described. A simple three-layered medium with a circular hole centrally located in the intermediate layer is considered. The layered sheet is loaded uniaxially perpendicular to the stratification. The Young's modulus of the intermediate layer is lower than that of the outer layers. The stress distribution around the circular hole in a stratified medium is significantly different when compared to the case of a continuous homogeneous medium. The distribution depends upon the ratio of the height of the intermediate layer and the hole diameter. A comparison of stress distribution and procedures for preparation and testing of the model are given. The potential of the technique is outlined. In the process of applying the techniques of stress analysis to problems of rock mechanics, the recent discernible trend has been to postulate highly idealized models of physical situations. As new techniques have been developed, more complicated models have been conceived to simulate mote accurately the physical environment to which the analysis results are eventually applied. In this investigation, a new technique is developed to analyze two-dimensional nonhomogeneous models. The technique is used to determine the stress concentration around a circular hole in a soft material overlain and underlain by a hard material. In mining practice, such situations arise commonly in coal deposits and frequently in bedded or vein-type metallic mineral deposits. DEFINITION OF THE PROBLEM A plate, consisting of three layers with a circular hole in the intermediate layer, is loaded uniaxially, Fig. 1. The variable in the experimental investigation is the height of the intermediate layer, H. The diameter of the hole, D, is kept constant. The stress concentration factors around the periphery of the hole, for various values of H/D, are evaluated using the technique of photoelasticity, Table I. TECHNIQUE OF EXPLORATION Photoelastic analyses of composite models have hitherto been limited to the study of lap and butt joints between glued metals and dissimilar materials.1-3 In mining, Haber and Oudenhoven used composite models to study the stress distribution around a circular hole in two-layered media and the behavior of elastic liners in shallow underground openings.4-5 They used the stress freezing technique devised by Dally et a1.6 The procedure used in this investigation is outlined below: Casting of Layer A: Flat sheets of plastic were cast in a silicon-coated mold using Araldite 502 with hardener 951 in the ratio of 100:8 by weight. After

Jan 1, 1969

By T. N. Dixon, J. E. Briggs

A study was made of numerical techniques for solving the large sets of simultaneous equations that arise in the mathematical mode ling of oil reservoir behavior. It was found that noniterative techniques, such as the Alternating Direction Implicit (ADI) method, as well as some other finite difference approximations, produce oscillatory or unsmooth results for large time steps. Estimates of time step sizes sufficient to avoid such behavior are given. A comparison was made of the Point Successive Over-Relaxation (PSOR), Two-Line Cyclic Chebyshev Semi-Iterative SOR (2LCC), and iterative ADI methods, with respect to speed of solution of a test problem. It was found that, when applicable, iterative ADI is fastest for problems involving many points, while 2LCC is preferable for smaller problems. INTRODUCTION With the advent of high speed, large memory, digital computers, there has been an increasing emphasis on the development of improved methods for simulating and predicting reservoir performance. Two-dimensional, three-phase reservoir models with various combinations of PVT effects, as well as gravity and capillary forces, are common throughout the industry. Such models are also available through consulting firms, to anyone desiring to use them. Three-dimensional models will probably be practical in only a few years. We conducted a study of some of the numerical methods used for solving the large sets of simultaneous equations that arise in such models. A typical set of equations for a reservoir model is shown below:

Jan 1, 1969

By W. A. Backofen, G. Mayer

Single crystals of iron, copper, and a Cu-7 wt pct A1 alloy were pulled through conical dies to simulate the constraint in a polycrystalline aggregate undergoing axisymmetric reduction. With Taylor-type hardening, dependence of the drawing stress, od, on the Taylor orientation factor, M, is predictable from the polycrystal stress-strain curve; in particular, for a power-law relationship, it should follow that d log od/d log M = (1 + n). A first-order agreement with analysis was found in the data from iron. For copper, the implied n from the observed d log od/d l°g M was -0, while for Cu-7Al it was negative. The trend was in the direction of random polycrystal behavior. Thus the idea of hardening only in response to the amount of prior slip loses validity as stacking fault energy (SFE) is lowered. Two possible explanations have been suggested: as stacking fault ribbons are widened, barriers from dislocation reactions become increasingly effective in dispersing slip and reducing the orientation dependence of the total glide strain dm that appears in alternatively, or conjointly, the polyslip shear stress, 7, acquires an orientation dependence of a kind which has the same leveling effect on M. The problem of relating the strain hardening of polycrystalline material to that of an isolated single crystal is still largely unsolved. In a new experimental approach from recent work, single crystals of different orientations have been deformed under the constraints found in an aggregate while measuring their deformation resistance. Procedures have involved drawing cylindrical crystals through conical dies1 and compressing slab-shaped crystals in plane strain.2'3 Predictions for the outcome of such experiments were made first by Taylor~ and later, in more general form, by Bishop and Hill.5'6 Taylor's example was the axisymmetric extension of an fcc crystal slipping on the usual {111}(110) systems or, equivalently, a bcc crystal undergoing 'kestricted" slip on {110}(111). In his solution, the deformation work supplied was equated to that dissipated internally in slip on all active systems. With o the single applied tensile stress, dc the resulting axial strain, and dyT the total glide strain on systems operating at resolved shear stress, 7: The orientation dependence of M was found by minimizing dyT for each orientation while activating five independent systems, Fig. l(a).? The Bishop and Hill analysis, based on a principle of maximum work, leads to essentially the same conclusion; the need for at least five active systems is recognized in the finding that either six or eight are actually brought into operation. The mean value from the entire stereo-graphic triangle in either case is M - 3.06. More recently, Hutchinson8 made a Taylor-type analysis for pencil glide in a bcc structure, from which piehlerg prepared Fig. l(b) as the counterpart in Fig. l(a); here M = 2.75. The obvious weakness in such analyses is the indifference to slip-system interactions. A condition of what might be termed "independent"

Jan 1, 1969

By Moshe Sheinkin, Burke O. Trafton

This paper describes the use of a computer in analyzing the expected return on a mining venture. The computer program is designed to incorporate all aspects of a mining project, including the mine, mill, smelter, and refinery. Data input may consist of the operating variables in each phase such as the mining rate, grades, reserves at the mine, and the technical operating characteristics of the mine, mill, smelter, and refinery. Detailed tax computations are shown for a domestic operating company, for a foreign company and for a foreign subsidiary. In addition, the use of the various options that are available such as expense write-offs or deferments to create tax credits during preproduction years are considered, and its effect on the DCF. The program is also constructed to accommodate changes in metal prices, and escalation of capital requirements and operating costs. Output consists of profit and loss statements for entire projects using different methods of depreciation, cash flows, discounted cash flows, net present value and returns on investment. Returns on investment are computed for equity investment, total investment, and total investment less tax credits. Allowances are made for bank and guaranteed loans. Additional financial statements can be made for the following: a) A mine-mill segment with a concentrate selling schedule b) A mine-mill-smelter complex with a smelter product selling schedule c) Profitability of the smelter separately d) Profitability of the refinery separately

Jan 1, 1969

Jan 1, 1969

By I. H. Pratt

The results of a study on the preparation of thin-film capacitor structures are discussed. The dietectric source material was quartz which was sputtered and deposited onto aluminum electrodes and counter-electroded to complete the metal-oxide-metal structures. This configuration was utilized to evaluate the dielectric, the device characteristics, and related process parameters. The effect of gas sputtering pressure, magnetic field strength, source-to-substrate distance, and power density on the rate of deposition is shown. Increased film thickness uniformity over a 3 by 3 in. area by optimum substrate positioning is indicated. Dielectric constant, dissipation factor, dielectric breakdown strength, insulation resistance, heat treatment, capacitance, and dissipation over the range 400 Hz to 5 MHz are reported. In the fabrication of silicon-integrated circuits, silicon dioxide has found use as a material suitable as a diffusion mask, for surface passivation of the silicon, and for protection of conductive films used for interconnections. Its use as a dielectric for thin-film capacitors in film hybrid circuits has been limited, to a degree, for lack of a compatible processing technique and because of its relatively low dielectric constant. With the recent advent of practical metal-oxide-semiconductor (MOS) field effect devices, the material is now being used to insulate the gate electrode from the conducting channel in the silicon. In this latter application, more stringent requirements have been imposed on .the oxide. A comprehensive resume of the use of silicon dioxide in integrated silicon device technology has been compiled including oxide film and bulk properties, method of oxide formations, and their applications.' A relatively new process to deposit SiO, and other dieIectrics is by rf sputtering, and the purpose of this paper is to describe the behavior of capacitors fabricated with a dielectric which has been sputtered from a quartz target and to indicate the relative effect of several of the process parameters on the film deposition. Work on rf sputtering of SiO2 and other dielectrics has been reported utilizing a triode type of sputtering system as described herein or a diode self-sustained glow discharge system. 2-8 SPUTTERING The process occurs during an electrical discharge in a gas plasma which provides the ions for acceleration to the target to produce the desired sputtering. The necessary plasma can be generated by a dc glow discharge through application of a high potential between two electrodes at approximately 2 to 10 x 10-2

Jan 1, 1969

By Hansheinz Portisch, Harold Margolin

A surface expansion was found to occur sometime after etching in Ti-A1 alloys containing 9.5 to 12.5 wt pct Al. The structure formed, grew, and disappeared with tzrrze. The surface expansion was followed by microscope observations and interferometric and lattice parameter measurements. Activation energy measurements for the growth of the "expansion structure" and chemical analysis indicated that the phenomenon occurred as a result of hydrogen pzckup during etching. It is proposed that hydrogen initially enters octahedral sites of Ti3Al coherent with a Ti and later shifts to the tetrahedral sites. It is postulated that expansion occurs when hydrogen enters the tetrahedral sites. The expansion structure disappeared, it is proposed, because of diffusion of hydrogen from the surface into the body of the alloy and because of loss of coherency of Ti3Al. In examining Ti-A1 alloys, Ence and arolinl observed markings on the surface of specimens. These markings did not appear after electropolishing only, but rather appeared only after etching. The markings appeared to grow as a function of time after etching and later seemed to disappear. Although the markings had some similarity to precipitates, showing, frequently, a Widmanstatten type of arrangement, the observation that other microstructural markings continue to be seen within the new structure suggested that it was actually not a precipitate. The source of this structure was unknown and an attempt was made in the present investigation to develop some understanding of its nature. It has been labeled expansion structure. 1) EXPERIMENTAL PROCEDURE A) Alloys. Alloys in the range 6.5 to 14.5 wt. pct A1 were studied. Bars, 4 in. sq, forged from Bureau of Mines (73 Bhn) titanium consumably arc-melted 4-lb ingots,' as well as 50-g arc-melted buttons of desired aluminum contents were used. The 50-g buttons also used Bureau of Mines titanium (73 Bhn) and aluminum of 99.99 pct purity. Buttons containing up to 8.5 wt pct A1 were hot-rolled from a furnace at 900' . Those with higher aluminum contents were hand-forged on a titanium anvil, and heated with an oxygen-hydrogen torch in the region of 1200" to 1300°c. Frequent reheating kept the samples at the desired temperature range. After a reduction of about 30 pct, the samples were water-quenched. To eliminate any contamination picked up either during hot rolling or forging, at least 1 mil of the surface of the sample was taken off. B) Heat Treatment. Prior to heat treatment all alloys were vacuum-annealed to remove hydrogen. Samples were annealed at 900' until a vacuum of 10'5 mm Hg was established. After this treatment, the samples were wrapped in molybdenum sheet and heat-treated in argon-filled quartz capsules, which were broken under water or iced brine at the conclusion of the heat treatment. All heat treatments under dynamic vacuum were performed in a rapid-quench furnace. This consisted of a molybdenum-lined quartz tube attached to a vacuum system and through a stopcock to a beaker of water. At the completion of the heat treatment the vacuum stopcock was closed, the furnace shut off, and dropped below the quartz tube. Then immediately the inlet stopcock was opened and water admitted until the tube was filled. The steam formed was allowed to escape through the inlet stopcock. This method was used in heat treatments up to llOO°C. C) Metallography. Specimens for metallographic examination were ground, then electropolished using a Disa Electropol machine with a perchloric acid electr01te. Specimens were etched with R-etch.3 A standard etching time of 3 min was used, with the specimen being agitated during immersion. D) Sample Preparation for X-ray Analysis. Samples 0.2 to 0.5 mm in diam were produced from heat-treated rods which were turned to 2 mm diam on a lathe and then rotation-etched. An etchant consisting of 1 pt HF, 7 pt HN03, and 12 pt HzO was satisfactory. With the rod rotating in a vertical position at 50 to 100 rpm, a needle with uniform dimensions could be obtained. Care had to be taken to insure that the rod was at the center of rotation, otherwise cavitation developed. If a small unevenness developed, it was possible to grind it off with a fine emery paper. E) X-ray Diffraction. All X-ray work was done on a North American Phillips X-ray diffraction apparatus and a Jarrell Ash microfocus X-ray unit. The Phillips unit was used with a copper target and nickel filter. The Jarrell Ash unit was fitted with a cobalt target and iron filter. For the Phillips unit 35 kva and 20 ma were used, whereas for the microfocus unit with the 100-p fixed-focus gun 40 kv and 1.5 ma were used. It was found that alignment of cameras on the Jarre11 Ash unit was very critical. The X-ray beam contains an intense area which is not the beam center. The cameras were aligned with the intense region by monitoring the beam coming out of the camera with a Geiger counter. Adjustments were made until a maximum intensity was obtained. A Phillips diffractometer with a Brown chart recorder furnished some of the lattice parameter data. The divergence slit up to 80 deg 28 was I deg; above 80 deg, a 4-deg opening was used, while the scatter slit was1 deg and the receiving slit had a 0.003-in. opening. The general scanning rate was 1 deg per min, while peaks of special interest were rescanned at -j deg per min. For elevated-temperature X-ray diffraction a Uni-cam High Temperature Camera with a film diameter

Jan 1, 1969

By D. A. Woodford

A number of observations have now been reported where the steady-state creep rate is apparently linearly dependent on the applied stress at high temperature and low stresses. This results in a creep rate greater than that predicted by extrapolation of high-stress data and has obvious practical implications. However, some of these observations are open to question. For example, the analysis by Harris and Partridge17 of the data of Greenfield et a1.18 was dependent on strain rates which, according to the original authors, were too low to be measured. Dr. Bernstein appears to have demonstrated a linear stress dependence at low stresses in two zirconium alloys. There are, however, a number of discrepancies in his treatment of the data and the subsequent theoretical analysis which require clarification. 1) It is incorrectly stated that steady-state conditions are revealed by a slope of unity on a plot of log i vs log (time). This objection is trivial if the author meant to say a slope of zero, although it is unclear how subsequent extrapolation was made to determine the steady-state creep rates at low stresses for the zircaloy-2. If the plot used was actually log c vs log (time), it is unlikely that a slope of unity would represent a constant creep rate. A plot of log (c - co) vs log (time), where c0 is the extrapolated intercept sf the steady-state creep rate on the strain axis, would have a slope of unity during steady-state creep. However, eo cannot be determined unless is is already known. 2) The author chooses to interpret his results based on the equation: where A, and B, are structure-sensitive parameters, Ql and Q, are the activation energies for the particular creep process, and n describes the sensitivity of the creep rate on stress. The first term represents a slip creep process and the second a diffusion creep process. However, it is stated later that "two distinct processes acting in parallel are involved". Eq. [I] surely represents two processes in series since each reacts to the total applied stress and t, is the sum of the individual creep rates. If the processes are acting in parallel, then the effective stress in each would be less than the applied stress. The component stresses would be given by sl + s2 = a but it is not clear how the magnitude of either, or the corresponding stress exponent, could be determined.

Jan 1, 1969

By R. O. Williams

The concept of biaxial pole figures which completely represent sheel textures is defined and an iterative least-squares solution given. The method has been applied to rolled copper, aluminum, and brass. The results show that the prior ideal textures are reasonably correct but incomplete. The major components in all three cases consist of a continuous range of orienta-tions roughly described as starting from (211) [111] continuing to (110) [112] to (110) [001], the details dif- THIS paper considers the problem of representing rolling textures in the most useful and comprehensible manner possible. A representation called a biaxial pole figure which completely represents such textures fering in all cases. For brass, in particular, the last part of the range is the most important. A minor cube component is established for the copper and aluminurn. The results were also analyzed by means of sets of three axial (inverse) pole figures to give similar, less-detailed results. The method of analysis is outlined. Such a representation is significantly less powerful than the biaxial method, but it has considerable utility in the calculation of anisotropic properties. is defined and an iterative least-squares solution is given. Such textures may be approximated by treating the principal directions as fiber axes to give three axial (inverse) pole figures. This representation is very useful for calculating anisotropic properties. New data for rolled copper, brass, and aluminum are given by both methods. In an axial pole figure the relative frequency or probability of a given physical direction (normally the

Jan 1, 1969