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By P. K. Koh, H. A. Lewis, H. F. Graff

New data on the distribution of silicon between slag and carbon-saturated iron at 1600Oand 1700OC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1'700°C for slags containing up to 20 pct A12O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A12O3-SiO, slags over a range from zero pct Al2O3 to saturation with Al2O3, or CaO.2Al2O3. The upper limit of SiO2 is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/Al203 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al,O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al0 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al2O3 and of Al20,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO2 (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2. The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960

By J. Clair, H. Mirabel

The determination of the temperature and electrical potential distributicms in the cathodes of aluminum electrolytic cells is difficult. The reascms come from the various nature and the intricate three-dimensional geometry of the materials; besides thermal and electrical phenomena react upon each other. A method of calculation using a computer program applied to a mathematical model, figuring the cathode, is developed. Both of the thermal and electrical phenomena are simultaneously considered. Temperature and electrical potential distributions are finally obtained by successive iterations. Results are compared with measurements on industrial cells. Theoretical and practical applications of these studies are given. Up to the present time the study of the distribution of the temperatures and electric potentials in the electrodes, anode and cathode, of the electrolytic cells used for the production of aluminum was limited to one of the two aspects of the phenomena because of lack of a simultaneous method of calculation. For example, the anode or cathode drop was studied assuming that the temperatures in the iron and carbon are known, a method that obviously is very approximate since iron resistivity, in particular, greatly varies with temperature, which in turn depends on current density. Consequently we tried to find a method of calculation simultaneously taking into account both thermal and electrical phenomena. We proceeded to the study of the cathodes as an initial approach to the problem. Although the cathode and surrounding materials may have varied forms and particularly very heterogeneous characteristics, their structures are simpler than that of the Sijderberg anode and boundary conditions are more easily represented than in the case of anodes even though they are prebaked. The study was in two parts: a) development of a model schematizing the true geometry of a cathode and defining the thermal and electrical boundary conditions, and b) working out a method of calculation of the temperatures and potentials by means of an electronic computer. To facilitate solution of the problem, a model was used initially much simplified in comparison with an actual cathode. This model permitted development of the method of calculation. In a second phase, this model was adjusted to the study of actual cathodes and applied to different types of cells: low- or high-intensity cells, cells set up at ground level or above ground level, cells with cathodes more or less heat-insulated. Simultaneously measurements were made with cells equipped with cathodes of the types studied to compare the values resulting from calculation. The initial model was also used for general studies, in particular for studying the effects of current density in the carbon and iron. The results were confirmed or made precise by the model of the true cathodes. This report successively describes: a) the manner in which the model representing a cathode was worked out, with the simplifications and/or the hypotheses used, b) the method of solution of the problem by means of the electronic computer, and c) an example, stating the extent to which the results obtained may be realistic. Further the possibilities offered by such a study are examined. 1) CATHODE REPRESENTATION The purpose of this phase is to represent the cathode in the form of a so-called "mathematical model", that is with a simplified geometrical configuration, in order to meet the subsequent calculation requirements, while keeping to the true facts as closely as possible. This model further includes the thermal and electric conductivities with regard to temperature for the varied materials composing the cathode, as well as the thermal and electrical conditions at the model boundaries. 1.1) Guiding Principles. For calculating the temperatures and potentials the model is divided by trior-thogonal planes into a network of small elementary parallelepipeds. At the summit of these parallelepipeds' so-called mesh points, the temperatures and potentials are computed. The number of mesh points is of course limited by the capabilities of the computer, since 1) the number of equations to be solved depends on the number of mesh points selected, and 2) the amount of time spent by the computer considerably increases with increasing this number. These conditions call for the following requirements as concerns the model: a) Dimensional requirements: the calculation will be all the more accurate as the network is more closely meshed. Since the number of mesh points is limited in practice, it is necessary to restrict the dimensions of the model. b) Geometrical requirements: so as to make things easier in working out the network, the model must be given a simple geometry. In particular, it will be convenient to have the cathode so constituted that the surfaces limiting the cathode and the surfaces within the cathodes separating the different materials consist of triorthogonal planes. 1.2) Schematization of the Cathodes. After the tech-

Jan 1, 1968

By R. T. Keyes, R. B. Clay, L. L. Udy, V. O. Cook, M. A. Cook

Based on compressibility and stress wave velocity in rock, initial explosive loading conditions, the thermochemistry of the explosive and reasonable description of the pressure-distance relations behind the shock front, the distribution of energy between the products of detonation and the burden are estimated as a function of time for various loading conditions. These include 'powder factor', loading density A (fraction of borehole occupied by explosive), and the explosive itself. Factors responsible for rock fragmentation are discussed in terms of: 1) 'release wave fracturing', 2) 'shear wave fracturing', and 3) 'release of loading fracturing' or 'rock bursting'. Release wave fracturing appears to occur only in the immediate vicinity of free faces, and shear wave fracturing only adjacent to the borehole under normal blasting conditions. Rock bursting is thus considered to be the most important means of rock fracturing in blasting. Means for maximizing it are considered. The most important factors to consider include maximum available energy A, explosive density p1, loading density A and 'powder factor'. Maximum efficiency is attained in general by maximizing the A . p1 product. This is achieved by using high density explosives at a loading density of unity (A = 1.0). Ways for achieving this condition are discussed. The bulk-handled aluminized slurry blasting agents have the desired properties for achieving optimum conditions for high blasting efficiency based on the theory outlined herein. Factors considered most important in the blasting of rock are: 1) The maximum available energy A, determined by the heat of explosion Q and the mechanical efficiency ?, a factor intimately associated with the mode of application (A = Q at highest gas concentrations). 2) The 'borehole pressure', pb, or the maximum pressure developed in the borehole after passage of the detonation wave and before the burden has had time to move or become compressed appreciably. (Owing to the short duration of the detonation wave at any particular point in the borehole, the fact that the explosive may not always fill the borehole completely and the further fact that the burden may not actually see the detonation pressure, the borehole pressure is considered more significant than the detonation pressure p2 as a performance factor in borehole blasting.) The borehole pressure is determined by the explosion or adiabatic pressure, p3 , and the loading density, A, or the fraction of the borehole filled by explosive. 3) The physical conditions important in the application of the explosive are: a) The 'powder factor,' (We/Wr), or the ratio of the wt of the explosive to that of the rock being blasted expressed as lb per ton or more generally in lb/cu yd. b) The bulk density, p1 ?. c) The 'burden' or 'line of least resistance,' the spacing between boreholes, the geometry of the borehole pattern and sequence of firing. d) The physical and chemical properties of the rock, most significant of which are possible heterogeneties, such as faulting, prefracture, and greater than micro-scale chemical heterogeneities. (This factor is not considered here but deserves a great deal of careful consideration.) All of these factors need to be carefully considered in the most economical engineering of a blast. Here is considered firstly an outline of the present status of dynamic rock mechanics, particularly as it pertains to blasting. The factors pertaining to the most efficient application of blasting agents are also considered, followed by a discussion of methods of application to achieve optimum explosives performance. ROCK MECHANICS Dynamic rock mechanics is currently a rapidly developing science contributing greatly to a better understanding and consequently the more effective application of explosives in blasting of rock.1-22 Basic to the development of the science of dynamic rock mechanics were the advances of Goransen23 and the Los Alamos and NOL groups24-28 concerning rock and stress wave phenomena and the transmission and reflection characteristics of stress waves at interfaces between different media. Basing considerations on this new knowledge as well as new experimental methods of study (ultra-high speed streak and framing cameras and electronic timers) the theory of fracture and failure of solids under impulsive loading by stress waves developed rapidly.14,16,27-29 Also the

Jan 1, 1967

By M. Metzger, T. A. Read

The strengthening effects of hydroxide and synthetic plastic films in the creep of cadmium crystals were studied. The results were broadly consistent with the naive mechanical model. The dislocation-film reactions and the significance of the macroscopic stresses associated with certain films are discussed in the paper. ALTHOUGH a number of studies have been made of the strengthening of metal single crystals produced by surface films usually less than Ir in thickness, the mechanisms underlying this phenomenon are still not well established. Roscoe' first noted the critical shear stress and the stress-strain curve of cadmium-crystal wires to be raised markedly by the presence of oxide films. Subsequent investigators2-' have confirmed the effect for several metals and films including a number of plated poly-crystalline metal films. Harper and Cottrel1" with a thin film on zinc presumed to have formed as a result of etching and washing treatments) did not detect a strengthening at a rate of extension of 10 ' sec-' although at lo-' sec-' the film raised the flow stress by 7 pct at 0.0005 extension and by 22 pct at 0.01. The marked strengthening at moderate strains thus appeared to be the result of a dynamical effect dependent on the rate and amount of plastic flow. Other observations'. " are consistent with this view. The large effects of films on the tensile creep rate of single crystals were demonstrated when the observation of Andrade and Randall," that the creep rate of cadmium crystals increased on immersion in aaueous solutions of certain cadmium salts. was shown' * to hold only when a film was present initially and was explained by the attack of the solution on the film and the removal of its strengthening effect. Changes in the creep rate interpretable in terms of the removal or formation of various films have been observed by other investigators.3,8,10,31 Certain other experiments have been reported in which surface films or liquid environments have affected the plastic behavior of metals, but these are not within the scope of the present work which deals with the effect of solid films on single-crystal slip. Possible Mechanisms—The film does not significantly reduce the load on the crystal in the elastic range (the elastic moduli of film and crystal are not too greatly different and the area of the film is so small that its share of the load is negligible) so that the initial operation of internal Frank-Read sources is not affected. However, as Fisher" has pointed out, a source terminating on the crystal surface requires only half the critical stress for activation as an internal source of the same length and a relatively strong film (even a very thin one) would pin the free ends of the surface sources so that, if surface sources are responsible for plastic flow in a clean crystal. such a film would increase by roughly a factor of 2 the stress necessary for generation of dislocation loops at a given rate. The other general possibility is that the film resists the passage to the crystal surface of internally generated dislocations. If the film is adherent and if the specimen is to exhibit slip of the same general character as a film-free specimen, the film must deform or fail in shear at the active slip planes. The naive mechanical model, where shear-stress relaxation across the active slip plane in the metal transfers load to the film until it deforms and slip can

Jan 1, 1959

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute's influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger's argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.' Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute's influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute's influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By W. F. Domis, F. von Gemmingen, R. W. Whitmore, F. Garofalo

Constant-load creep-rupture tests at 1100°, 1300° and 1500°F were made on a Type-316, 18 Cr-8 Ni-ZMo, austenitic stainless steel to determine the relationship between ruptzire life and other aspects of creep behavior, The test program was designed on a statistical basis to check the variability of various creep properties and to determine emprically the dependence of minimutn creep rate and ruptzire life on initial stress, The dependence of the rupture life, tn, on the initial stress, a,, is found to be related to the stress dependence of the wrinimum creep rate, i,, and secondary creep strain, The instabilities or breaks found in the conventionual log - logt, plots can be traced to either a change in the linear dependence of log i, on log a, or to a change in secondary creep strain. In the alloy tested, rupture is found to be predowmanantly of the inter crystalline type, For this material, the secondary creep strain is -found to depend on the nature of the grain boundary precipitate, which affects grain boundary migration. It has been shown for a variety of metals and al tested at elevated temperatures under creep conditions that the empirical relationship exists between rupture life, tr, and minimum creep rate, i,. This relationship, in which C and a are in some cases independent of stress or temperature, shows in a general way that creep rupture depends on creep behavior prior to tertiary creep stage. To determine more fully the factors which control creep rupture requires, therefore, more knowledge of the relationship between rupture and creep behavior. To obtain such information, constant-load creep-rupture tests have been made on a Type-316, 18 Cr-8 Ni-2 Mo, austenitic stainless steel at 11000, 1300°, and 1500°F. These tests were designed on a statistical basis to determine the variability of the various creep properties measured and to determine empirically the stress dependence of minimum creep rate and rupture life. As a result of this work, various empirical relations have been established defining more closely the factor, C, in the relation between rupture life and minimum creep rate. This factor is found to be proportional to the amount of strain during secondary creep. The variation of secondary creep strain with rupture life and temperature is determined and its effect on rupture behavior discussed. The variability in minimum creep rate and rupture life is also dis- cussed and the dependence of these quantities on initial stress is interpreted. TEST MATERIAL AND TEST PROCEDURES The material tested is an austenitic stainless steel, AISI Type 316, of the following composition: C, 0.07 pct; Mn, 1.94 pct; P, 0.01 pct; S, 0.021 pct; Si, 0.38 pct; Cr, 18 pct; Ni, 11.4 pct; Mo, 2.15 pct; All 0.003 pct and N, 0.043 pct. The material was received as a hot-rolled 0.5-in. diam bar which was sectioned into 3.25 in. long blanks. Each blank was heat treated by holding 1/2 hr at 2000° F followed by water quenching. A 3/8-in. coupon was removed from each heat-treated blank and the microstructure was examined, the grain size determined, and the hardness measured. The microstructure was found to be uniform from blank to blank and the grain size was found to range from 4 to 6 ASTM numbers. Hardness, measured using a 20-kg load, varied between 127 and 148 Vpn. Tensile creep-rupture specimens having a 0.25 in. diam within a 1.5-in. reduced section were machined from the heat-treated blanks. Constant-load tests were made on these specimens at 1100°, 1300°, and 1500 F. Six specimens were tested at each stress level. Three creep-rupture machines were employed for tests at each temperature, two specimens being tested in each machine for each stress level. To minimize any effect due to local inhomogeneities along the length of the as-received bar the specimens were randomized before test. Each specimen was tested to rupture and in most cases an autographic extension-time curve was obtained. For very low stress levels at 1500°F no auto-

Jan 1, 1962

By W. D. Forgeng, R. L. Folkman, D. C. Hilty

The solubility of oxygen in molten Fe-Cr alloys has been determined at 1550° , 1600°, and 1650°C for alloys containing up to alloyshasbeenabout 50 pct Cr and found to decrease as chromium increases to 6 pet and then to increase gradually. Phase relations in the Fe-Cr-0 system at steelmaking temperatures have been evaluated and two previously unreported oxides have been identified. OPERATIONS in the melting and refining of chromium steels are dependent to a major degree on the reactions of chromium and iron with oxygen and are primarily directed toward controlling and modifying these reactions to secure maximum advantage in the utilization of chromium. Although fairly effective practices have been developed empirically, understanding of the specific reactions is limited. Moreover, the ability of molten steel to dissolve oxygen that subsequently precipitates as oxide inclusions during solidification is well known, so that clarification of the effect of chromium on the nature and mechanism of formation of these inclusions is desirable. Study of the problem indicated that increased knowledge of the fundamental Fe-Cr-0 system is essential to further technical and economic improvement. Consequently, an investigation of the influence of chromium on the solubility of oxygen in molten iron and of phases and phase relations in the Fe-Cr-0 system was undertaken at the Metals Research Laboratories of the Electro Metallurgical Co. as part of a general program on the effective utilization of chromium in chromium steel production. Experimental Procedure All of the experimental runs made during this investigation were carried out in the rotating crucible induction furnace which has been described in detail in a previous publication.' In review, the principle underlying this furnace is that rotational forces in the crucible cause the molten metal to assume a concave shape in such a manner that the slag is contained in the molten metal cup, thereby minimizing slag/crucible contact and subsequent reaction. Practically all of the heats were melted in commercial-quality magnesia crucibles of the type usually furnished for laboratory induction furnaces. All of the runs were made under an argon atmosphere after the furnace chamber had been degassed. Bath temperatures were controlled by Pt—Pt-10 pct Rh thermocouples. The basic furnace charge consisted of a premelted 12 to 15 lb electrolytic iron slug which had been cast to a shape convenient for fitting into the rotating furnace crucible. A typical analysis of the electrolytic iron slugs is given in Table I. For certain runs, it was desirable to melt down charges containing high initial chromium contents. In these cases the chromium was added to the electrolytic iron during the premelting operations. Chromium was added to the rotating furnace bath in the form of electrolytic chromium of the analysis given in Table 11. In all of the constant temperature runs, the standard procedure was to melt down the electrolytic iron or alloy slug under vacuum, admit argon to slightly greater than atmospheric pressure, and adjust rotational speed to develop a well formed "cup" on the bath surface. The melt was then saturated with oxygen by an addition of ferric oxide and the temperature of the bath adjusted to within +5°C of the desired level. At this point the heat was permitted to come to equilibrium prior to sampling or further addition. This time interval was varied from 15 min to 2 hr but generally was about 20 min. After sampling, the desired chromium addition was made and the bath again equilibrated prior to subsequent sampling. This cycle of addition and sampling continued for the duration of the run which lasted from 4 to 8 hr. At the end of this period, power was shut off and the bath allowed to solidify in the furnace. Quenched metal samples were taken from the equilibrated melts by means of the "Taylor sampler" which has been described by Taylor and Chipman.' Before being submitted to chemical analysis, all samples were carefully examined for surface slag occlusions and cold shuts. Later in the study, each sample was radiographed and examined metal-lographically in cross-section to determine the presence of internal defects. On the basis of these examinations, sound and apparently clean specimens were selected from the Taylor samples for chemical analysis.

Jan 1, 1956

By C. J. Guntner, R. P. Reed

A commercial 18Cr-8Ni iron alloy (AISI 304L) was examined in tension at 300°, 76°, 20°, and 4°K. Continuous stress-strain recordings were made, X-ray analyses at periodic stress (strain) intervals were obtained, and the magnetic measurements were taken. From this data the percentage of martensitic products [bcc(a) and hcp (E)] was computed as a function of stress (strain). It was found thatup to 15 pct E phase forms at low temperntures. The amount of E formed increases to a maximum at about 5 pct strain, then decreases. This decrease indicates the additional transformation of E to a'. The total amount of E and a' was suppressed at constant stress (strain) at 4°K as compared to 76°K. It is proposed that the suppression of E and a' is associated with the decreased mobility of extended dislocations at very low temperatures. The yield strength decreased as the temperature was depressed below room temperature and then increased rapidly near 4°K. SOME ferrous alloys which are austenitic (fcc ?) at room temperature appear to be unique in that two martensitic products (hcp e and bcc a') may form on cooling to lower temperatures or on application of mechanical stress. The most common room-temperature austenitic ferrous alloys are 18Cr, 8Ni stainless steels. Most aspects of the spontaneous transformations have been previously described for these steels.' Several previous papers have described special aspects of the stress-induced transformations at low temperatures for the stainless steels, such as the existence of the hcp phase (c) after straining at 76oK,2-7 the morphology after straining using electron microscopy,7 and the decrease in E at higher strains at 76oK.4 However, for a complete representation, one must know the stress-strain characteristics and the dependence of both martensitic products on applied stress and temperature. It is the intention of this paper to provide that documentation. To accomplish this, continuous stress vs strain recordings were made at four temperatures: 300°, 76", 20°, and 4°K for annealed AISI 304L (a commercial 18Cr-8Ni alloy). At periodic stress intervals at each temperature the integrated X-ray line intensity of a selected peak for each phase (y, E, and a') was measured. In addition, photomicrographs of the strained surfaces were taken and magnetic measurements were made. The magnetic readings can be directly converted into percent a'.',e With these measurements the percentage of each phase may be plotted as a function of stress (or strain) and test temperature. It was found that up to 15 pct E phase forms upon stressing the AISI 304L alloy at low temperatures. The E percentage increases abruptly after the alloy yields, but then decreases gradually at higher stresses. The rapid increase in e at 76°K is associated with an "easy-glide" portion of the stress-strain curve. The total amount of a' + .G is suppressed below 76°K at a constant stress or strain. The yield strength decreases down to 76°K but increases rapidly below 20°K. EXPERIMENTAL PROCEDURE Tensile test specimens were cut parallel to the rolling direction from 0.1-in.-thick sheet. Continuous stress vs strain recordings were obtained at each test temperature (300°, 76o, 20°, and 4°K) using equipment and methods described elsewhere.' The specimens which were used in the X-ray analysis were stressed to successive increments of strain at each temperature, analyzed at room temperature, then restressed at the test temperature. This procedure was repeated until approximately ten X-ray analyses had been performed with approximately 1.0 pct strain increments. The specimens had a reduced section 1 in. long, 1.2 in. wide, and 0.1 in. thick. They were electro polished prior to testing and after each strain increment. Table I lists the chemical composition, grain size, and hardness for the alloy which was used. This is the same alloy for which extensive mechanical-property tests3 and morphological studies of the spontaneous transformations' have previously been made. For the low-temperature tests (76o and 4°K) below the Ms temperature the specimens were initially cooled to the test temperature, held for 1/2 hr, then warmed and X-rayed at room temperature. The results are listed in Table 11. From earlier work8 it was known that additional transformation on the second cycle would be considerably less (-0.1 pct

Jan 1, 1964

By L. W. Holm

This study shows that in the presence of foam, gas and liquid flow separately through porous media representative of reservoir rock. These results were obtained by using tracer techniques to measure the flow of the gas and liquid comprising the foam. Foam does not flow through the porous medium as a body even when the liquid and gas are combined outside the system and injected as foam. Instead, the liquid and gas forming the foam separate as the foam films break and then re-form in the porous system. Liquid moves through the porous medium via the film network of the bubbles and gas moves progressively through the system by breaking and re-forming bubbles throughout the length of the flow path. The flow rates of the gas and liquid are a function of the number and strength of the films in the porous medium. There is no free flow of gas; i.e., no continuous gas phase. On the basis of these results, foam can be expected to improve a water flood or gas drive by decreasing the permeability of the reseruoir rock to a displacing liquid or gas. This improves the mobility ratio and thus the conformance of the flood. INTRODUCTION Foam is formed when gas and a solution of a surface active agent are injected into a porous medium either simultaneously or intermittently. During the past few years, several papers have been published on the subject of foam flow in Dorous media. Foam has been used successfully in the removal of capillary water blocks from producing formations.''2 The use of foam in gas storage reservoirs to reduce gas leaks and to increase storage capacity has been considered in recent years. Foam has also been investigated as an oil displacing agent,3-5 and as an agent to improve the mobility ratio in a waterflood.6-10 However, the mechanism by which the gas and liquid phases comprising the foam flow through a porous medium has nor been described adequately. Normally, when two immiscible phases (gas and liquid) flow concurrently through a porous medium, each phase follows separate paths or channels. At given saturations of the two phases, a certain number of channels are available to each phase, and as saturations change, the number and configuration of the channels available for each phase also change. The effective permeability of each phase is a function of the saturation of that phase only, and the flow of each phase can be described by Darcy's law. When foam is present, the effective permeability of the porous medium to each phase is greatly reduced compaced with permeabilities measured in the absence of foam.6,11-13 Based upon the observed flow of surfactant solutions and gas in capillaries, it has been concluded that the gas and liquid may flow separately or they may flow combined as foam. At least four mechanisms have been postulated to explain how fluids flow with foam present: 1. A large portion of the gas is trapped in the porous medium and a small fraction flows as free gas, following Darcy's law.9 2. The foam structure moves as a body; the rate of gas flow is the same as the rate of liquid flow. 6,13 3. Gas flows as a discontinuous phase by breaking and re-forming films. Liquid flows as a free phase.12 4. A portion of the liquid and gas move as a foam body while excess surfactant solution moves as a free phase.14 It also has been suggested that different flow mechanisms exist for high quality (dry) foams made from dilute surfactant solutions and for foams made from more concentrated solutions. Studies conducted on the flow of foam through capillaries have shown that a plug-type flow occurs and that foam flows as a body.6,15 Fried also has described the flow of foam through porous media as

Jan 1, 1969

By W. B. Gogarty, W. C. Tosch

A new recovery process for producing oil under both secondary and tertiary conditions utilizes the unique properties of micellar solutions (also known as microemulsions, swollen micelles, and soluble oils). These solutions, which displace 100 percent of the oil in the reservoir contacted, can be driven through the reservoir with water and are stable in the presence of reservoir water and rock. Basic components of micellar solutions are surfactant, hydrocarbon and water. They may also contain small amounts of electrolytes and co surfactants such as a1cohol.r. The specific reservoir application dictates the type and concentration of each component. A salient feature of [he process is the capability for mobility control. Micellar solution slug mobility, by way of viscosity control, is made equal to or less than the combined oil and water mobility. Mobility control continues with a mobility buffer that prevents drive water from contacting the micellar solution. Laboratory and field flooding have proven that the process is technically feasible and that surfactant losses by adsorption on porous media are small. Introduction projects are under way to recover the maximum amount of oil under the most favorable economic conditions.' : New techniques are being developed to increase oil recovery,3" Polymer solutions are becoming an important means of controlling mobility in a waterflood. Thermal methods such as in-situ combustion and steam injection are being used in reservoirs containing highly viscous crudes. Surfactant flooding is receiving attention as a method of reducing interfacial tension to increase recovery.*'" Exotic recovery processes have been considered primarily for ' perations. Economics are unfavorable in most cases for tertiary recovery. studies at the Denver Research Center of the Marathon oil CO. have led to a new oil recovery method.* Micellar solutions (sometimes called microemulsions, swollen micelles, and soluble oils) are used to recover oil by miscible-type waterflooding. Basically, these solutions contain surfactant, hydrocarbon, and water. The method can be used in either secondary or tertiary operations. First, thc concept of thc process is considered in terms of the requirements for an effective miscible waterflood ing operation. Next, micellar solution properties are described including structure, composition, and phase behavior with reservoir fluids. Fluid characteristics are then considered as related to mobility control, and, finally, laboratory and field results are presented to illustrate the efficiency of the process. Concept of the Process Unit displacement efficiency and conformance determine the effectiveness of any oil recovery mechanism. In theory, a miscible waterflood should be capable of a 100-percent unit displacement efficiency with a correspondingly high conformance. Requirements for the slug of a miscible waterflood include (1) 100-percent displacement of oil in the reservoir contacted, (2) controllable mobility, (3) the capability of being driven through the reservoir with water, (4) a low unit cost to enhance economics, and (5) the ability to remain stable in the presence of reservoir water and rock. Micellar solutions satisfy requirements for the slug of a miscible waterflood process. Our discovery that these solutions acted as though they were miscible by displacing all fluids in the reservoir and by being displaced by water solved the miscibility problem. Adequate mobility control is possible by variations in solution viscosity through compositional changes. Economic requirements are met since micellar solution costs below $6/bbl appear possible, Mi cellar solutions stabilize surfactant in the presence of reservoir rock and water, thus reducing the importance of the problem of surfactant loss by adsorption. Fig. 1 illustrates schematically how these solutions are used. Operations start with injection of a micellar solution slug that serves as the oil displacing agent. Next, a mobility buffer of either a water-external emulsion or water solution containing polymer (thickened water) is injected to protect the slug from water invasion. Finally, drive water (water used in a regular waterflood) is injected to propel the slug and mobility buffer through the reservoir. Reservoir oil and water are displaced ahead of the slug, and a stabilized oil and water bank develops as shown in Fig. 1. Stabilized bank saturations are independent of original oil and water saturations. This means that, for a particular type of reservoir, the displacement mechanism is the same under secondary and tertiary recovery conditions. Oil is produced first in a secondary operation. For tertiary conditions, water is produced first. Movement of the slug through the reservoir is stabilized by the mobility buffer. An unfavorable mobility ratio usually exists at the interface between the buffer and drive

Jan 1, 1969

By I. R. Kramer

Studies of the effect of size of the specimen on the change of slopes of Stages I and 11 by surface removal showed that the change of Stage I was independent of size with respect to the polishing rate; however, the change in the slope of Stage 11 with polishing rate increased directly in proportion to the surface area. The removal of the surface during the test affected the plastic deformation characteristics of gold, aluminum, and zinc single crystals and polycrystalline aluminum. The apparent activation energy of aluminum was found to be decreased markedly by removing the surface during the deformation process. In previous papers1-3 it was shown that the surface played an important role in the plastic deformation of metals. By removing the surface layers of a crystal of aluminum by electrolytic polishing during tensile deformation, it was found that the slopes of Stages I, II, and III were decreased and the extents of Stages I and II were increased when the rate of metal removal was increased. By removing a sufficient amount of the surface layer after a specimen had been deformed into the Stage I region, upon reloading, the flow stress was the same as the original critical resolved shear stress and the extent of Stage I was the same as if the specimen had not been deformed previously. The slope of Stage I was decreased 50 pct and that of Stage 11 decreased 25 pct when the rate of metal removal was 50 X 10"5 ipm. These data show that in Stage I the work hardening is controlled almost entirely by the surface conditions, while in Stages 11 and III both surface conditions and internal obstacles to dislocation motion are important. It appears that during the egress of dislocations from the crystal, a fraction of them becomes stuck or trapped in the surface regions and a layer of a high dislocation concentration is formed. This layer would not only impede the motion of dislocations, but would provide a barrier against which dislocations may pile up. In this case, there will be a stress, opposite to that of the applied stress, imposed on the dislocation source and dislocations moving in the region beyond this layer. It has been found convenient to refer to this layer as a "debris" layer. The "debris" layer may be similar to the dislocation tangle observed by thin-film electron microscope techniques.4 Reported in this paper are the results of studies on the effects of removing the surface during plastic deformation on aluminum crystals of various sizes. The effects of the surface on the yield point behavior of gold and high-purity aluminum crystals as well as the creep behavior were also determined. The effects of surface removal on polycrystalline aluminum (1100-0 and 7075-T6) are also reported. EXPERIMENTAL PROCEDURE For those portions of the investigation involving creep and tensile specimens, single crystals, having a 3-in. gage length and a nominal 1/8-in. sq cross section, were prepared by a modified Bridgman technique using a multiple-cavity graphite mold. The single crystals were prepared from materials which had initial purities of 99.997, 99.999, 99.999, and 99.999 pct for Al, Cu, Zn, and Au, respectively. The aluminum specimens for the size effect studies were prepared through the use of a three-tier mold in which crystals having a cross section of 1/8, 1/4, and 1/2 in. were grown from a common seed. The mold design was arranged so that one 1/2-in. crystal, two 1/4-in. crystals, and four 1/8-in, crystals of the same orientation could be cast. With this technique, it was possible to obtain only one set of crystals with the same orientation. Because of this limitation, it was not possible to determine both the changes of extent and slope of the various stages since a large number of crystals of the same orientation would have been required. Instead, only the change of slope as a function of the rate of metal removal was studied by abruptly altering the current density of the electrolytic polishing bath at various strains within the regions of Stages I and 11. The experimental techniques used for the tensile studies were essentially the same as those used previously.1,3 The specimens were deformed in a 200-lb Instron tensile machine, usually at a rate of 10-5 sec-5. A methyl alcohol-nitric acid solution was used as the polishing bath for aluminum. The temperature was maintained constant within ±0.l°C by means of a water bath. The tensile machine was

Jan 1, 1963

By Francis R. Conley, John A. Sievert, John N. Dew

A brief review is presented of the past performance of a number of large, thin, highly permeable reservoirs with low dips in the Bolivar Coastal fields of Venezuela. The performance of these reservoirs indicates that the fluids are segregated vertically within the sand section by gravity. With this assumption, equations are developed which describe the performance under pressure maintenance operations. Methods of solving these equations and results of simple example calculations are presented. Example calculations indicate that under pressure maintenance conditions injected gas tends to {tow preferentially along the top of the sands and that encroaching water has a tendency to flow preferentially along the bottom. The expected performance of segregated fluids is discussed and compared with that of fluids which are uniformly distributed in any sand section. INTRODUCTION The field performance of a number of reservoirs described herein indicates that the fluids are segregated vertically within the sand section by the force of gravity. Thus, it was felt that any method used to predict the future performance of these reservoirs should consider the effects of segregation in the sand sections. A study of the available information on some of the reservoirs suggests that increased recoveries may be expected if the reservoir pressure is maintained by either crestal gas injection or flank water injection. To predict future performance of reservoirs under pressure maintenance operations, a method of analysis was needed which would account for segregation of fluids in the sand sections. Several methods of analysis have been developed to take into account the segregation of fluids in the reservoir as a whole1,3 To our knowledge no method considers segregation of the fluids within sand sections in the manner indicated by the past performance of several reservoirs in the Mara-caibo Basin. This paper outlines part of the work done in studying some of these reservoirs and contains a description of their performance characteristics. The analysis presented is restricted to pressure maintenance conditions, since space limitations prevent a full discus- sion of the development of the mathematical relations and the various methods of solving them. Only a sketch of the development of the mathematical relations is given. The various methods of solving these relations are pointed out, but the actual determination of solutions to various problems are omitted except for one example. It is felt that these results may aid in the study of reservoirs outside the Maracaibo Basin. Some concepts on which the present analysis is based are outlined by D. N. Dietz. However, the analysis presented herein includes several factors not considered by Dietz: (1) variations in permeability and in the cross section, (2) various shapes of the cross section, and (3) the production of fluids. Also, the mathematical development presented by Dietz differs considerably from our corresponding analysis. RESERVOIR CHARACTERISTICS The reservoirs under consideration, large and thin, with low dip and high permeability, are large to the extent that they contain from 0.5 to over four billion bbl of oil initially in place. The section thicknesses vary from 100 to 400 ft and the lengths from 10,000 to 40,000 ft. Thus, a length-wise cross section of the producing formation appears to be long and thin. The dip angles vary from 0 to 6 degrees and the average permeabilities vary from 0.5 to over three darcies. The reservoirs contain from 20 to 50 per cent shale inter-laminated with the productive sands. Most shale breaks within the major sands do not correlate from one well to the next, and correlation is often difficult, even between wells drilled from the same location. However, it is often possible to correlate the shale breaks between major sands for some distance. Herein we are concerned with the performance of reservoirs containing oil of gravities over 20" API. Past reservoir performance indicates good pressure communication and, in cases where pressure sinks have developed, large amounts of fluid migration have occurred. Few of the reservoirs have had initial gas caps, but also, few have been found to be highly under-saturated. Due to gravity segregation, secondary gas caps usually form before the pressure has been reduced more than 25 per cent of its initial value. The effect of gravity has not only been apparent on a reservoir-wide basis, but has also caused segregation of the reservoir fluids in productive sections. Proof of this is found from the results of selective well tests, workovers, and electric and various other types of logs. Evidence that

By D. Harrington

ALTHOUGH statistical data are not at hand to justify definite statements as to progress in health, and safety in the mining and allied industries during 1935, it now appears probable that in both coal mining and in metal- mining the rate of accident occurrence as well as the absolute number of accidents will show slight increases for the year. Much: of the responsibility for this increase lies with the large number of relatively. small mines that have more or less recently come into existence, partly because of 'the lack of opportunity for work in the larger mines for large numbers of unemployed miners, and partly due to increased prices for some of the mineral products, especially gold. In general, the larger long-established nines show downward accident trends and this is decidedly encouraging as it shows that where mines are operated with real efficiency, mining can be done in relative safety.

Jan 1, 1936

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By R. W. Heckel, R. L. DeGregorio

The DeHoff method of determining the size distribution of ellipsoid-shaped, second-phase particles has been applied to the spheroidization of cementite in a eutectoid steel. The surface area of Precipitates determined from the various size fractions in the distribution was correlated with surface-area measurements based on the number of intersected interfaces on a random lest line. The precipitate particles were found to be oblate ellipsoids with an axial ratio of about 0.90. The size distributions were found to be log-normal. A method is proposed whereby the shrinkage of small particles and growth of large ones can be determined from the experimental data. The experimental data are compared to previously proposed mathematical models describing diffusion-controlled kinetics and various types of interface-controlled kinetics. The experimental growth and shrinkage rates are considerably slower than those predicted by diffusion-controlled kinetics. The best fit is obtained for a model describing interface-controlled kinetics limited by the rate of formation of cementite at the growing interfaces where the interfacial reaction rate is proportional to the solute thermodynamic activity gradient across the surface. THE subject of spheroidization of second-phase particles has been considered previously by other investigators. Livingston1 has studied the precipitation of the cobalt-rich phase from copper alloys containing 0.7 to 3.2 wt pet Co. His results indicate that the average particle size increases as the cube root of the heat treatment time in accord with diffusion-controlled kinetics.'-' Komatsu and rant' in their studies of the growth of SiO2 in a dispersion-strengthened copper-silica alloy found that the initial growth of SiO2 proceeded by diffusion-controlled growth and later stages were limited by interface-controlled growth. The values of the activation energy obtained for the interface- controlled process led them to the conclusion that the process was limited by the dissociation of SiO2 at the shrinking interface. The transition from diffusion-controlled growth to interface-controlled growth was characterized by a particle size which varied with the heat-treatment temperature. It is also interesting to note that the particle-size distribution as found by Komatsu and Grant exhibits log-normal behavior when replotted on log-probability coordinates. Dromsky, Lenel, and Ansell9 have observed the growth of Al2O3 particles having a mean free path of about 1.5 to 13 µ. Their photomicrographs indicate that the Al2O3 particle sizes were larger than those observed by Komatsu and Grant. Dromsky, Lenel, and Ansell concluded that the Al2O3 coarsened by an interface-controlled growth mechanism limited by the solution of A12O3 at the shrinking interfaces. Bannyh, Modin, and Modin10 have studied the spheroidization of a eutectoid steel (0.83 wt pet C). Their spheroidization (tempering) treatments were carried out in the range from 210o to 700°C for times between 1.5 sec and 20 hr. Measurements of mean particle size as a function of time indicated a cube root of time dependence of size at 700°C, in agreement with previous analyses of diffusion-controlled kinetics.2°7 At lower temperatures, the time dependence was less than the one-third power. It is important to note that, although mathematical models of growth* considering particle-size distribution have been available, measurements of only mean particle size have been carried out. DeHoff11 has presented a quantitative metallography technique which is applicable to the determination of the size distribution of ellipsoids of constant shape. This method is applicable to both oblate and prolate ellipsoids of all ratios of minor to major axis and is based upon an extension of Saltykov's analysis12 of the distribution of spheres of varying size. DeHoff's analysis is based upon measurements of the minor axis of the particles on a random plane of polish in a unit area. This method provides a measure of the number of ellipsoids in various size ranges per unit area. As pointed out by DeHoff, such measurements may be used to obtain surface area and total precipitate volume data. Thus, the accuracy of the distribution analysis may be checked by comparison of the surface and volume

Jan 1, 1965

By J. C. Melrose

The contact angle is one of the boundary conditions for the differential equation specilying the configuration of fluid-fluid interfaces. Hence, applying knowledge concerning the wettability of a solid surface to problems of fluid distribution in porous solids, it is important to consider the complexity of the geometrical shapes of the individual, interconnected pores. As an approach to this problem, the ideal soil model introduced by soil physicists is discussed in detail. This model predicts that the pore structure of typical porous solids will lead to hysteresis effects in capillary pressure, even if a zero value of the contact angle is maintained. The model is generalized to situations in which the contact angle takes on values between zero and 40 degrees. For the imbibition branch of the capillary- pressure function, the model predicts a considerable departme ftom the usually assumed cos 0 relationship. In fact, according to the model, it is possible that a displaced wetting phase will not be able to reimbibe, even when the contact angle does not exhibit hysteresis. INTRODUCTION The subject of capillarity in porous media has long been of interest in many branches of engineering and applied science. The earlier investigators were those concerned with the physics of soils. 1-5 More recently, petroleum engineers and others dealing with the problems of petroleum production from reservoir rock have given much attention to the subject.6-10 Also, important additions to the literature of capillarity have been contributed from the field of chemical engineering.11-12 These attest to the wide range of industrial applications in which capillary phenomena play a role. The present paper is concerned with the role which wettability plays in capillary action in porous media. As is well known, capillary-rise (or capillary pressure) phenomena have frequently been interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This approach has enjoyed a certain degree of success in correlating experimental results.13 The generalization of this model, however, to situations which involve varying wettability, has not been established and, in fact, is likely to be unsuccessful. In this paper another approach to this problem will be discussed. A considerable literature relating to this approach exists in the field of soil science, where it is referred to as the ideal soil model. Certain features of this model have also been discussed by Purcel114 in relation to variable wettability. The application of this model, however, to studying the role of wettability in capillary phenomena has not previously been attempted in detail. In the present paper, additional features of the model are introduced. These features are critical in determining the quantitative behavior of the model. GENERAL FEATURES OF CAPILLARY HYDROSTATICS BASIC PRINCIPLES When the interstices of a typical porous solid are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. Hence, fluid-fluid interfaces are found within a certain fraction of the pore openings. The fundamental equation of capillarity specifies the configuration of these fluid-fluid interfaces. This is known as the Laplace equation, when derived from mechanics, and as the Gibbs-Kelvin equation when derived thermodynamically.15 Given two fluid phases, a and ß, in hydrostatic equilibrium, the Laplace equation states that the respective fluid pressures in regions close to the interface are related by Here oaß is the surface or interfacial tension and rl and r2 are the principal radii of curvature of the surface or interface. The pressure difference, Pa-Pß, is the capillary pressure, PC. As Buff15 has shown, Eq. 1 states the condition for hydrostatic equilibrium within the two-phase confluent region, which is referred to as the interface. It thus can

Jan 1, 1966

By C. G. Bieber, J. R. Mihalisin, R. T. Grant

A growing demand for longer service life of gas turbines has placed increasingly rigorous requiret~rents upon superalloys employed for that application. Long-titne testing at high temperature has revealed that phase transformations occur in all superalloys. A common one of particular interest is o formation. Presented here are studies made to identify a and to characterize its formation and effect on properties in three cast nickel-base superalloys—IN 100 alloy, alloy 713C, and alloy 713LC. Methods are discussed by which o can be eliminated or inhibited in IN 100 alloy and alloy 713C. Evidence was obtained to indicate that some types of o may be more detrimental than others. Limitations in the electron vacancy approach to o prevention are pointed out, and it is shown how alternative approaches, such as reducing a complex superalloy matrix to the form of a pseudo-ternary system permitting equilibrium diagram treatment, lead to additional insights into the formation of in these alloys. AROUND 1960. Beiber1 developed IN 100 alloy, which still remains one of the strongest commercially available nickel-base superalloys. The principle used in the design of this alloy was to produce large quantities of y' phase in a y matrix through the use of copious amounts of aluminum and titanium. In 1963, ROSS' showed that when certain heats of this alloy were held for a long time at 1650°F they formed an acicular phase, subsequently identified as a.3 a is a hard and brittle phase first discovered in the Fe-Cr system by Bain and Griffiths.4 They termed it the "B" constituent. Subsequently this same phase was found in other systems, primarily those of the transition elements, and acquired the name "a" by which it is now known. The crystal structure of the a phase was first determined in the Fe-Cr system in 1950.5 It was shown to be tetragonal with a c/a ratio of about 0.52. as is the case with a found in other systems. This characteristic crystal structure is now the means by which a is identified. In superalloys, such as IN 100 alloy. large amounts of o impair the high-temperature creep strength and drastically reduce room-temperature tensile ductility. Discovery of o phase in some heats of IN 100 alloy quickly led to investigations of other superalloys for similar transformations. It was found that many of the stronger, more highly alloyed. super-alloys were indeed susceptible to o formation. This investigation has been concentrated on three commercial alloys: IN 100 alloy, alloy 713C, and alloy 713LC. J.R.MIHALISIN,MemberAIME, and C.G.BIEBER are with The International Nickel Co., Inc., Paul D. Merica Research Laboratory, Sterling Forest, Suffern, N. Y. R. T. GRANT, Member AIME, is with The International Nickel Co., Inc., Pittsburgh, Pa. Manuscript submitted May 22. 1968. IMD A detailed study has been made of the phase transformations and their relation to a formation along with a consideration of electron vacancy approaches for predicting a-forming propensity in these alloys. EXPERIMENTAL PROCEDURE Phase transformations were studied by light and electron microscopy, electron diffraction, microprobe investigations, and X-ray diffraction. Specimens for light micrographic examination were prepared by conventional grinding and polishing followed by etching with glyceregia (2:l HC1/HNO3 + 3 glycerine by volume). Photomicrographs of stress-rupture specimens were taken adjacent to the fracture unless otherwise noted in the text. Negative replicas for electron microscopy were taken from surfaces electropolished with a solution of 15 pct H2SO4 in methanol. For carbon extraction replication, a solution of 10 pct HC1 in methanol was used. A Siemens Elmiskop I was used for all electron microscopy. Selected-area diffraction studies were made at 80 kv using evaporated aluminum for standardizing the patterns. A nondispersive electron microprobe attachment was used to analyze the extracted precipitates chemically. The fluorescent X-rays were recorded using a flow counter containing P10 gas (90 pct Ar-10 pct methane) with a beryllium window and a single-channel pulse-height analyzer. The pulses from the analyzer were passed to a scaler-ratemeter and differential curves of counting rate vs pulse amplitude were obtained. The base line of the analyzer was driven with a synchronous motor at 0.5 v per min and a channel width of 0.5 v. The time for 105 counts was printed out for each 0.5-v increment. The microscope was operated at 80 kv with beam currents of 1 to 20 pa. This equipment detects elements from atomic number 13 to 40. X-ray diffraction studies were usually made on residues electrolytically extracted in 10 pct HC1 in H2O, although in one case a pattern was obtained from an etched surface of a metallographic specimen. A Siemens Crystalloflex IV was used with iron-filtered CoKa radiation. X-ray patterns were recorded using a goniometer speed of : deg per min. The scintillation counter and pulse-height analyzer operated at a channel height of 10 v and a channel width of 12 v. The equipment was calibrated with a powdered gold standard. The residues usually contained a number of phases. several of which could not be found in the ASTM card file. In addition, as is shown for the case of a phase in IN 100 alloy, other phases had a somewhat different lattice parameter from that reported in the ASTM card file, making it difficult to separate and identify constituents by comparison with ASTM d spacings. For these reasons, phases were identified on the basis of the lattice parameter obtained by indexing the ob-

Jan 1, 1969

By M. H. Waxman, L. J. M. Smits

A simple physical model was used to develop an equation that relates the electrical conductivity of a water-saturatedshaly sand to the water conductivity and the cation-exchange capacity per unit pore volume of the rock. This equation fits both the experimental data of Hill and Milburn and data obtained recently on selected shaly sands with a wide range of cation-exchange capacities. This model was extended to cases where both oil and water are present in the shaly sand. This results in an additional expression, relating the resistivity ratio to water saturation, water conductivity and cation-exchange capacity per unit pore volume. The effect of shale content on the resistivity index - water saturation function is demonstrated by several numerical examples. INTRODUCTION A principal aim of well logging is to provide quantitative information concerning porosity and oil saturation of the permeable formations penetrated by the borehole. For clean sands, the relationships between measured physical quantities and porosity or saturation are well known. However, the presence of clay minerals greatly complicates log interpretation, particularly the electrical resistivity and SP logs, and considerably affects evaluation of hydrocarbon-bearing formations. The conductance and electrochemical behavior of shaly sands and their relation to log interpretation have been studied by many workers. wylliel and Lunch2 reviewed this work in some detail. Virtually all laboratory measurements of electrical resistivity and electrochemical potential of shaly sands published to date are the work of Hill and Milburn.3 Their measurements were made on about 300 cores covering a large variety of sedimentary rocks, and a wide range of equilibrating NaCl solution concentrations. Hill and Milburn described their conductivity data by an empirical equation in which the shaly sand conductivity Co was expressed as a function of the solution conductivity C and two parameters b and F01 . The quantity b was shown to be a measure of the effective clay content of the rock, being approximately proportional to the cation-exchange capacity of the rock divided by its pore volume. The latter ratio is designated as 9, in this paper and has the dimensions meq/ml or equiv/liter. Qv is identical with the term representing the concentration of fixed charges in the Meyer-Sieved and Teorel15 theory of permselective membrane behavior. F01 is a formation resistivity factor referred to a hypothetical equilibrating solution resistivity of 0.01 ohm m at 25C,* where clay effects presumably are minimized. F01 was correlated to porosity by an Archie-type equation.6 The Hill-Milburn equation describes their data with a standard deviation of approximately 1 percent and a maximum deviation of + 10 percent. Shaly sands behave as permselective cation-exchange membranes, their electrochemical efficiencies increasing with increasing clay content. The electrochemical potential data of Hill and Milburn were expressed graphically, and demonstrate that the membrane efficiency (or cation transport number) of these sands is a function only of the b value (i.e., Qv) and the respective salt concentrations of the two solutions forming the liquid junction in the sand. The diffusion potentials are not dependent on F01 or any parameter relating to the porosity or pore geometry of the rock. The Hill-Milburn resistivity equation correctly predicts a decreasing sand conductivity Co with decreasing solution conductivity C?. However, at some low value of C,, the calculated Co-C, function goes through a minimum; with further decrease in C?, the predicted sand conductivity increases sharply. As pointed out by Hill and Milburn, an increasing value of Co with decreasing C, is physically meaningless. Since this occurs below the range of practical values of C,, the usefulness of the empirical equation is not affected when

Jan 1, 1969

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By F. C. Langenberg

It is the purpose of this paper to present a limited amount of experimental data obtained on the Charpy impact machine. Several concrete examples will be given showing the relation existing between the results obtained upon the Charpy impact machine and the behavior of the parts tested when in service. Although it is pointed out by G. Charpy and A. Cornu-Thenard1 that it is first necessary to determine a satisfactory working process before studying the correlation between the results of these tests and the behavior of the parts tested in service, this ideal course cannot be strictly adhered to. If a certain part repeatedly fails in service and the available tests give no indication of its cause, advantage must be taken of any possible means that will solve the problem; therefore, even though the reliability of the results obtained by the Charpy impact machine have been questioned by many, it was necessary to use this instrument without giving careful consideration to its possible sources of error. It would seem that the conclusions arrived at by Charpy -and Cornu-Thenard justify the assumption that the precision obtained by this machine is comparable to that obtained by the other more common forms of testing. The second general conclusion arrived at by them, namely, that the impact test upon notching does not offer any direct correlation to the ordinary tests, is also borne out by many hundred determinations made in the laboratories at Watertown Arsenal. This statement, however, should be qualified as follows: Other ordinary tests include the static tensile test from bars taken in a longitudinal direction and the Brinell hardness. The author agrees that no law is yet known for the computation of the energy absorbed in the rupture of bars of the same material but of different dimensions. Although Charpy and Cofnu-Thenard do not refer in their valuable article to the use of the Charpy machine in industrial practice, it should be stated that this instrument has been in constant use in the laboratory at Watertown Arsenal for several years, and is now employed for both routine and experimental testing.

Jan 1, 1920