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By Thomas R. Bur

The order of identification and in same cases the magnitude of the elastic constants of an anisotropic material depends on the orientation of the cartesian coordinate axes with respect to a set of reference coordinate axes within the material; thus confusion will result unless standard orientations are used. In this paper the relationship between the cause (the internal fabric) and the effect (the elastic properties in this case) is discussed for single crystals and for polycrystalline and amorphous materials. While reference axes based on the cause are used in the IRE (Institute of Radio Engineers) standard for piezoelectric crystals) it is shown that a reference coordinate system that would be suitable and practical for all anisotropic polycrystalline and amorphous materials must be based directly on a three-dimensional expression of the effect. The conventions offered are similar to the IRE standards for piezoelectric crystals) but use the elastic coordinates of the wave surface which can be quite readily established experimentally as the reference coordinates.

Jan 1, 1969

By Wolfgang Pitsch

INVESTIGATIONS on the above topic have recently been published by Shapiro and Kraussl and Jana and wayman in this journal and by Kessler and Pitsch.- Parts of the results in these papers are in good agreement with each other but there are also some results which are substantially different. The main points of these differences shall be briefly discussed in this communication. Shapiro and Krauss' measured single-surface traces of the habit planes of reversed austenite plates formed within the martensite crystals and deduced from these measurements two distinct habit planes A = (0.174; 0.309; 0.935) and B = (0.375; 0.545; 0.749) within 3 deg. Kessler and pitsch4 found instead by two-surface analysis7 one habit plane n = {0.23; 0.62: 0.75) with a real scatter of 6 deg. The latter observation of a single habit plane apart from a certain scatter is in agreement with most of the investigations of martensite transformations. The differences between these two results are so great that they cannot be explained by experimental error. The purpose of this communication is to show that the A- and B-poles of Shapiro and Krauss are due to an erroneous interpretation of a single-surface trace analysis. The difficulties in the interpretation of such single-surface trace analyses are due to the high symmetry of cubic lattices, from which it follows that there are in general twenty-four equivalent possibilities of plotting a single-surface trace in a pole figure. All these possibilities must be taken into account, when putting different traces from different plates together in order to construct the habit plane. Alternatively the poles of all the traces may be plotted in a unit triangle. This is done in Fig. 1 with twenty-nine traces of different reversed austenite plates, all of this were measured by Shapiro and Krauss in the same plane of a single martensite ther traces taken from Fig. 13 in the Shapiro and Krauss paper' which were determined by electron diffraction. The traces in Figs. 1 and 2 have to be compared with the habits A, B, and n which are under discussion. Therefore the great circles of the poles A, B, and n are plotted in Figs. 3, 4, and 5 together with a 3-deg scatter region for poles A, B and a 6-deg scatter region for pole n. Comparing Figs. 1 and 2 with Figs. 3, 4, and 5 one finds the statements which

Jan 1, 1969

By N. A. D. Parlee, I. D. Shah

The solubilities of oxygen in liquid Ag-Au, Ag-Pt, and Ag-Pd alloys have been determined in the range of 940° to 1200°C at 1 atm pressure of oxygen using an improved Sieverts technique. The additions of gold (0 to 57 pct), platinum (0 to 27 pct), and palladium (0 to 22 pct) to liquid silver continuously decrease the solubility of oxygen in liquid silver. Activity coefficients and interaction coefficients of oxygen in these alloys and have been calculated. The interaction coefficientscan be described by the following equations: Approximate second-order interaction coefficients (pM have been calculated. The contribution of the product, pMxNM, to In yo only becomes significant at high alloy concentrations. RECENTLY several investigators1"3 have redeter-mined the solubility of oxygen in liquid silver. In general the recent findings1" for Po, = 1 atm are in good agreement with the equation:4 log %O = 695.4/T + 1.086 [1] It is established1, 2 that the solubility of oxygen follows Sieverts' law reasonably well, at least up to 1 atm partial pressure of oxygen. It should be noted that a very slight deviation from Sieverts' law has been reported by Lupis and Elliott.3 Only recently has the solubility of oxygen in Ag-X binary liquid systems received much attention, and only the Ag-Cu, Ag-Au, Ag-Pt, and Ag-Pd systems have been studied. Par lee, Sacris, and zoellners reported that the solubility of oxygen in liquid silver increases progressively with the small additions of copper (0 to 0.5 pct) up to the point where the copper oxide phase appears. Lupis and ~lliott~ have reported that the solubilities of oxygen in liquid silver decrease progressively with the additions of gold, platinum, and palladium. However, their investigation was limited to 0 to 5 pct of these alloying elements, a range too limited to satisfy the requirements of the research program of this laboratory, where the solubilities of oxygen in the range of 0 to 30 pct were required for the calculation of chemical diffusion coefficients of oxygen in these alloys. The present paper deals only with the solubilities of oxygen in these alloys while another paper will deal with the diffusion of oxygen in these alloys. EXPERIMENTAL METHOD A Sieverts technique was employed which involved an improved design of the reaction tube, Fig. 1, as described briefly in a previous communication.4 Liquid melts (70 to 100 g) were held in Norton Alun-dum crucibles. The induction furnace used had a maximum output of 2.5 kw with very fine control. This induction system had excellent stability and the final equilibrium temperatures measured by calibrated Pt-Pt, 10 pct Rh thermocouples are believed to be within ±2C. These thermocouples were checked against the melting point of pure gold wire, and the results agreed with standard tables (±l°C). Each run involved a careful sequence of operations. The sample was heated to and held at about 900°C in vacuum for 3 to 4 hr with the thermocouple in a retracted position. After melting, the melts were usually exposed to a small amount of oxygen (0.5 to 2.0 cu cm) and then degassed slowly for 1 to 2 min to remove any oxidizable volatile impurities such as carbon and sulfur as CO, CO2, SO2, and SO forth. Argon gas was then allowed to enter the system. The protection tube containing the thermocouple was then

Jan 1, 1969

By Prakash C. Kapur

A principal first order and a minor summation term contribute to the solution of the discretized batch grinding equation when formulated in cumulative retained mode. Depending on the interrelationships between the selection and breakage parameters, the minor term may be advantageously modified in a number of ways. The reduced grinding equations thus obtained are solved by iterations to give relatively simple solutions which are tested against experimental data. The implications and advantages of the reduced grinding equations are briefly discussed.

Jan 1, 1969

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe' using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"' pure silwer and Ag-0.5 at. pct ~n;' and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l' Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele'~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,'~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,' Gallaher,' and Gallagher and Wash-burn.' Ives and Ruff' found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By Michael Epstein, Daniel E. Rosner

Fume nucleation sufficiently close to vaporizing suvfaces can augment net vaporization rates into cooler environments. Environmental conditions favoring large vaporization rate enhancements are briefly discussed and a previous theoretical treatment of this nucleation phenomenon is generalized to account for the self-regulating effect of condensalion-heat release within the boundary layer. Despite kinetic limitations on homogeneous nucleation, and latent heat release, non-diffusive condensate removal processes appear to make possible large enhancements in steady-state vaporization rates, provided surface temperatures are well below the boiling point. When condensed phases vaporize (or dissolve) into cooler media, the diffusion-limited mass loss rate can be strongly influenced by the process of nucleation/con-densation (or precipitation) within the thermal boundary layer. This condensation process (which typically leads to mists or fumes in the case of evaporation into cooler gases) has the effect of steepening the vapor pressure profiles near the evaporating surface, since the condensation zone acts as a vapor sink. However. the resulting enhancement in the diffusion-limited evaporation rate can be estimated (as first done by Turkdogan1 for the case of molten iron/nickel alloys evaporating into helium) only if one has independent knowledge of the critical supersaturation, sCrit(T), required to homogeneously nucleate the vapor.* In a recent reformulation and generalization of the theoretical model of Ref. 1 it has been shown that, when log sCrit is approximately linear in reciprocal temperature, rather simple expressions can be derived4 for the ratio of the actual rate of vaporization j" to either the minimum (no condensation) rate j"min, or the maximum (equilibrium condensation) rate j"max In the present communication we wish to briefly report on further developments and implications of the formulation of Ref. 4, with emphasis on i) environmental conditions favoring large enhancements in vaporization rate, and ii) the self-regulatory influence of condensation heat release (neglected in Refs. 1 to 4) on predicted vaporization rates. Additionally, we take this opportunity to correct several misprints appear- ing in Ref. 4, and comment on Elenbaas's recent criticism5 of Ref. 1. MAXIMUM POSSIBLE VAPORIZATION RATE IN PRESENCE OF CONDENSATION A nonequilibrium theory is of interest because of the very large difference between the minimum (no condensation) and maximum (equilibrium condensation) vaporization rate. The magnitude of this maximum possible enhancement can be shown quite clearly by combining a result of Refs. 3 and 4 with the fact that for most liquids there is a simple relationship between the molar heat of evaporation, A, and its boiling point, i.e., A/(RTBp) = C, where the constant C, often called the Trouton ratio, takes on values not very different from 11.* More generally, for any substance (including The Trouton ratio (which for water is 13, for methane, 10, and so forth) will be recognized as the ratio of the molar entropy change upon vaporization (at TBP or Ttransf) to the unlversal gas constant R. Its near constancy reflects the fact that the change in atomic order upon vaporization depends only weakly on the kinds of molecules involved. those that sublime under ordinary conditions) we can define a characteristic transformation temperature. Ttransf, by a relation of the form Ttransf =A/(CR), and then examine the maximum possible evaporation rates as a function of how far removed from Ttransf are the surface temperature, Tw, and ambient temperature, T. Subject to the assumptions: 1) equilibrium vapor pressure, pv,eq, everywhere small compared to prevailing total pressure, p, and 2) negligible effect of condensation heat on temperature profile, the maximum enhancement ratio was found (Eq. [17], Ref. 4) to be: where, for most vapors, Nu/NuD (the ratio of heat transfer coefficient to mass transfer coefficient for the same configuration) is a number near unity.* Ex- *An alternative derivation of the Nu = NuD special case of this equation. revealing its validity for arbitrary velocity/temperature profiles in a laminar boundary layer, is given in Ref. 3. amining this result for a "Trouton substance", one obtains the results shown in Fig. 1, constructed for C = 11. Since we are concerned with vaporization enhancements (j'max/J"min > 1) at surface temperatures below Ttransf, this area of interest is shown unshaded. One notes that at a fixed ambient temperature (hence, T/TtranSf) there is a unique surface temperature, 2T , at which j"max/j"min attains its peak value; moreover, the peak enhancement ratio, see dashed locus. Fig. 1, is: (NuA/NuD)(C/4)(Ttransf/T,). Hence, if Nu = NuD, when the ambient temperature is less than 1/4 of TtranSf the peak enhancement exceeds the Trouton

Jan 1, 1969

By J. Szekely, Robert G. Lee

Calculations are presented for the prediction of the combined radiative-convective heat loss from molten steel held in a ladle, covered by initially molten slag. A mathematical formulation is given and numerical solutions are presented of the resultant partial differential equation. It is shown that a slag layer of about 2 to 3 in. thick would prevent any significant heat loss from the top metal surface for Periods of up to 1 hr. For thinner slag layers (or in the absence of the protective slag) appreciable heat losses would occur; plots given in the paper allow the quantitative evaluation of the fall in the metal temperature due to this heat loss. The ironmaking-steel processing operation involves several intermediate steps where the molten metal is held or transfered in ladles. The quantitative assessment of the heat losses occurring under these conditions is of considerable importance in process design considerations since the temperature of the metal may have to meet rigid specifications in any given part of the processing sequence. While the metal is held in a ladle, heat is lost by two mechanisms: i) by conduction into the ladle walls; ii) by radiation and convection from the top surface. Calculations relating to the conductive heat loss, are readily made and information may be found in the literature both on data pertaining to metallurgical situations and on the techniques that are available for performing additional computations.'-3 The evaluation of the combined convective-radiative heat loss is less straightforward, especially when there exists a protective slag layer covering the metal. In this latter case, as the top slag surface loses heat partial solidification may occur and the latent heat thus given up by the slag may represent an effective barrier to the heat loss from the metal. A semiquantitative assessment of the role played by the slag in preventing heat loss from the metal has been made in a previous paper,4 where it was shown that a slag layer 6 in. thick would act as a near-perfect insulator for periods of up to 2 hr. However, this first paper reported on an essentially preliminary investigation that considered only one slag layer thickness; furthermore, the boundary conditions used for the calculations were somewhat restrictive since no allowance was made for changes in the metal temperature. The purpose of this second paper is to extend the scope of the preliminary investigation previously reported by: i) considering several slag layer thicknesses; ii) allowing for variations in the metal temperature; and finally iii) by performing calculations on the net loss from the metal rather than from the slag surface. FORMULATION Consider a slag phase extending from y = 0 to y = L1, covering a metal phase that occupies the region extending from y = Ll to y = L, as illustrated in Fig. 1. Denote the slag and metal temperatures by TS and Tm and assume that initially both slag and metal are molten, having a uniform temperature Ti. At time = zero the surface represented by the y = 0 plane (top slag surface) is brought into contact with cold air, the temperature of which is given as T Thus for time > zero, heat will be transfered from the slag to the air by natural convection and thermal radiation; as a result of this heat loss the slag temperature will fall and after some time a solid phase is formed and a solidification boundary (more realistically described as a zone) will move progressively from y = 0 toward y = L1. Once the region of temperature gradients, moving ahead of the solidification zone, reach the slag-metal interface (y = L1) there will be a net transfer of heat from the metal through the slag to the cold air, across the y = 0 plane. In the formulation of moving boundary problems, involving phase changes that require computer solution, it is convenient to represent both phases by a single equation, making allowance for the latent heat of solidification by assigning an appropriate temperature dependence to the specific heat content. Thus the energy equation for the whole of the slag may be written as follows:

Jan 1, 1969

By R. E. Robbins, H. R. Brager

THIS note describes an unusual result obtained in an electron microscope investigation of cavities produced in commercial type 304 stainless steel irradiated in a thermal reactor (ETR) at 290°C to a high neutron flu-ence, 6 x loz1 n per sq cm. The analysis of the steel used is given in Table I. The unusual result is that the calculated quantity of helium gas produced by transmutation during the irradiation, 12 ppm, is less than one-tenth the amount of gas necessary to balance the surface tension of the observed cavities produced in the steel during ETR irradiation. Therefore, the cavities would be expected to behave like voids; however, they behave like "gas filled" bubbles. The maximum quantity of helium produced in the steel by B" transmutation was 8 ppm. In addition, the amount of helium formed by (n, (1) fast neutron reactions with the major alloy constituents and nitrogen was calculated to be 4 ppm based on the tabulated differential or effective fission-averaged cross sections of elements in type 304 stainless steel irradiated in typical thermal reactors.', In previous investigations concerning commercial austenitic stainless steel irradiated in a thermal reactor, the amount of helium gas calculated to be produced by transmutation has always been significantly greater than the amount calculated on the basis that the bubbles were gas filled, PPs= 2y/R. The balance of the gas was assumed to be in bubbles smaller than could be detected on the electron micrographs. Accordingly, the bubbles were attributed to helium produced from transmutation of impurity boron by thermal neutrons. These bubbles were not uniformly dispersed in the matrix but were located principally at grain boundaries, or were radially positioned around a few precipitates located in the matrix and at the grain bundaries., 4 Voids have also been observed in austenitic stainless steel irradiated at high temperature to high neutron fluences in the EBR-I1 and Dounreay Fast Reactors. The voids were uniformly distributed throughout the matrix. The amounts of helium gas produced by transmutation during these irradiations were less than one-tenth the amounts needed to balance the surface tension of the voids formed by the fast reactor irradiation. The fast reactor results are quite analogous to those reported here for the ETR irradiated steel. Electron microscope examination of the fast reactor irradiated material after a 1 hr postirradiation annealing at 900°C disclosed that essentially all the voids had been eliminated. The authors stated that the voids had developed due to the high concentration of vacancies produced during irradiatin., 6, ' The microstructure of the ETR irradiated material as-tested at 75O°C, Fig. 1, contained about 2 X lot5 cavities per cm3 with an average diameter of 110A. With the Van der Waals b correction and y = 1500 ergs per cm2, 300 ppm He would balance the surface tension of the observed cavities. Stereoscopic examination of the electron micrographs showed that the cavities were neither preferentially located near the grain boundaries nor highly concentrated at specific regions or precipitates. The cavities were nearly uniformly distributed throughout the matrix, on dislocations and at grain boundaries. These observations imply that the cavities were not the sole results of B'O

Jan 1, 1969

By C. T. Liu, J. Gurland

The deformation behavior in tension of spheroidized carbon steels was studied at room temperature as a function of carbon content, 0.065 to 1.46 wt Pct, and carbide particle size, 0.88 to 2.77 p. It was found that the Hall-Petch strength-grain size relation is directly applicable to the yield and flow stresses of the two lower-carbon steels , 0.065 and 0.30 pct C. The strength data for the medium- and high-carbon steels, 0.55 to 1.46 pct C, also satisfied the Hall-Petch relation, provided that these data are based upon the particle spacing. Beyond 4 pct strain, the flow stress data of all the steels studied could be represented by the same Hall-Petch relation with dinerent spacings for grain boundary and particle strengthening. The behavior of the higher-carbon steels was consistent with the postulated formation of a dislocation cell network during processing and initial deformation (up to 4 pct strain). The cell size was assumed to be equal to the planar particle spacing. The true stress at the ultimate tensile strength was also found to be a function of the particle spacing. At a given temperature and strain rate, the yield and flow stresses of carbon steels depend on the type and dimensions of the microstructure. Starting with the work of Gensamer et al. in 1942,' experimental studies on pearlitic and spheroidized carbon steels revealed that the strength of steels is a function of two main parameters: the ferrite grain size2'3 and the carbide particle spacing;1'4'5 on this basis, two different strengthening mechanisms have been developed to apply to steels of low and high carbon contents, respectively. In polycrystalline iron and mild steels the grain boundaries are regarded as the major structural barriers to slip. The relation between strength and grain size is generally represented by the Hall-Petch equation which is based on a linear proportionality between strength and the inverse square root of the average grain size.2'3y677 However, Gensamer et al.' and Roberts et related the yield strength of medium -and high-carbon steels to the carbide particle spacing alone, and they found a linear relation between the logarithm of the mean free path in the ferrite and the yield strength in both spheroidized and pearlitic steels. By means of the electron microscope, Turkalo and LOW' extended the study to finer structures; they concluded that the logarithmic relation is not valid for the entire range of microstructures unless grain boundaries are also included in the measurement of the mean free path. For the specific case of spheroidized steels, Ansell and aenel' found that the yield strength data,4'5 when plotted as a function of mean free path, fit the Hall-Petch equation; however, T'ysong found that the same data fit the 0rowanl0 relation if a planar inter-particle spacing is used. Recently Kossowsky and ~rown" studied the strength of prestrained spheroidized steels, 0.48 and 0.95 pct C, and concluded that the strength due to the carbide dispersions varies linearly with the reciprocal of the square root of the mean free path between carbide particles and dislocation networks. Such networks were first observed by Turkalo." The conclusion common to all these studies is that the available slip distance in the ferrite is the most important variable in determining strendh. Previous work on carbon steels is restricted to limited composition and strain ranges. The mechanism which governs the flow properties is not clearly understood, and, in particular, little is known about the composition dependence of the transition between grain boundary strengthening and particle hardening. The purpose of the present work is to investigate the strengthening mechanism in spheroidized steels over a wide range of carbon content, 0.065 to 1.46 wt pct, and plastic strain, yielding to necking. The spheroidized structure was chosen because of its relative simplicity and the relative ease of control and measurement of the structural parameters. The experimental work is limited to tensile testing at room temperature at constant extension rate. The effects of the carbide particles on the fracture behavior of spheroidized steels are discussed elsewhere.13 EXPERIMENTAL PROCEDURE Eight different grades of vacuum-cast carbon steels were supplied in the form of forged and rolled plate by the Applied Research Laboratory of the U.S. Steel Corp. The compositions furnished with these steels are given in Table I; the carbon content ranges from 0.065 to 1.46 wt pct, or from 1.0 to 22.3 vol pct of carbide. The steel plates were cut transversely into rods a little larger than the test specimens, 1 in. gage length, i in. diam. The rods were austenitized in air (enriched with CO by a consumable carbon-rich muffle) at 50° C above theA, orA., temperature for 2 hr and then quenched in oil with vigorous stirring. The as-quenched rods were tempered in two stages in order to obtain the desired distributions and sizes of carbide particles. The rods were first tempered at 460° C for 10 hr and then at 700" C for periods ranging from 4 hr to 3 days, in vacuum. After final machining, all specimens were vacuum-annealed again at 650°C for 1 hr in order to relieve residual stresses. The tension tests were carried out in two steps. The initial part of the load-strain curve, up to about 2 pct strain, was determined on a Riehle testing machine with an extensometer of small strain range, 4 pct strain, in order to obtain the yield and initial flow piopertiesi As soon as the first part of the test was finished, the specimen was placed in an Instron testing machine equipped with a strain gage extensometer with a maximum strain range of 50 pct. The load-strain curve to fracture was

Jan 1, 1969

Jan 1, 1969

By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection' at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969

The metals titanium and zirconium and their alloys occupy individually unique positions in the catalogue of metallic materials available for engineering applications. Because of the uniqueness of their usage in the aerospace industry, in the case of titanium, and in the nuclear industry, in the case of zirconium, the except- ional resistance of both the metals to the majority of corrosive media is often overlooked. The cost factor in the application of these more exotic metals has, in the past, been a major considerat- ion in the rejection of titanium and zirconium as constructional materials in areas of usage where their superior corrosion resistance strongly favoured them over more conventional metals and alloys. The cost differential, vis-a-vis austenitic stainless steels, for example, is not a trifling matter, being of the order of 6 : 1, when compared on a weight basis. However, if one considers the cost, for, say, sheet product on an area basis, the ratio is redgced to approximately 3.4:1. If one also takes into account the enhanced performance of the more expensive material and the sub- sequent increase in service life and decrease in plant down-time, the economics of the usage of materials such as titanium becomes much more attractive and, indeed, highly competitive,

Jan 1, 1969

By C. Wert, G. Mah

A relaxation peak thought to be due to the presence of C-C pairs in cobalt has been observed. It exists both above 420"C, where cobalt has the fcc structure, and below 420"C, where cobalt has the hcp structure at equilibrium. The effect is thought, however, to be caused by motion of C-C pairs in the fcc phase in both instances; enough retained fcc phase was deduced to be present at temperatures below 420°C to make the phenomenon possible. Measurements of the aniso-tropy of the effect in single crystals of various orientations of fcc phase showed the effect to have a maximum value in longitudinal strain for a [loo] crystal and a minimum value for a [Ill] crystal. This observation seems to rule out the possibility of (110) nn pairs being responsible for the effect. From measurements of the strength of the relaxation in the alloys, we reach the conclusion that both the binding energy of the pairs and the specific relaxation per pair are smaller than corresponding quantities for interstitial pairs in bcc metals. DETERMINATION of the details of atom placement of small atoms such as carbon, nitrogen, oxygen, and hydrogen in metals has been a difficult problem. In certain alloys such as martensite extensive departure from random placement of the interstitials can be deduced from X-ray diffraction off the atoms of the host metal, but such diffraction techniques are of small help for small departures from randomness. A technique which does offer promise in the latter instance is the anelasticity of these interstitial alloys. Most previous investigations using this property have utilized alloys in which the solvent is one of the bcc metals, alloys such as These studies have been interpreted to show that an interaction exists between interstitials which causes them to form clusters in more than random numbers; the binding energy of interstitials in such clusters has been deduced to be about 0.1 ev per atom (for small clusters of size two to four atoms). Similar investigations have been carried out on close-packed solvent metals, Ni-C by and Diamond and Ag-O by Papazian.8- In both of these svstems. no relaxation of the singly dissolved interstitial is expected, so an-elastic behavior of the interstitials must be caused by their association in some cluster or complex of non-cubic symmetry. Since relaxations in these alloys were observed to have a strength which varied about as the square of the interstitial concentration, the effect was deduced to be caused predominately by motion of i-i pairs in the crystal. A striking difference is observed in relaxation strength of interstitial alloys between the bcc and fcc systems. The specific effect per interstitial atom is much larger for the alloys in the bcc crystals than for those in fcc crystals. Comparing clusters of size two in the Nb-O system4 and the Ni-C system,7 one finds the magnitude of the anelastic effect per interstitial atom in the former to be some 100 times greater than that in the latter. Such a difference in relaxation strength might be caused by a difference in concentration of the pairs (this means a higher binding energy in the bcc crystals). It might also be caused by a large difference in shape factor of the elastic strain field about the pairs between the two cases (a much more noncubic shape factor would be required for the bcc crystals). This investigation was undertaken to examine the possibility of C-C pair formation in alloys of cobalt and carbon using anelastic effects. Since cobalt has both fcc and hep phases, it seemed to offer the chance that measurements over a range of frequency might permit comparison of properties of pairs in the two crystal types. Although this goal was not reached, several significant facts were deduced from the observations. 1) An anelastic phenomenon believed to be associated with the presence of C-C pairs in cobalt exists. It has many features in common with that observed in nickel. 2) The effect is thought to be caused by pair motion in the fcc phase. 3) Calculations of the relaxation strength A, which includes as a parameter the product of the pair concentration, C, and the square of the shape factor ', show that this parameter is much smaller in the CO-C alloy system than in the interstitial alloys in the bcc systems. 4) From this finding, we reach the conclusion that both the binding energy of C-C pairs in cobalt and the specific relaxation strength per pair are small compared to corresponding values for such pairs in the bcc systems. 5) The crystalline anisotropy of the effect permits the identification of reasonable geometrical models of close C-C pairs. I) EXPERIMENTAL PROCEDURE A) Method of Measurement. The anelastic measurements-—all of which were constant frequency measurements of internal friction—were designed to study the expected phenomenon in both the hcp and fcc structures in cobalt. Knowledge of similar measurements in Ni-C alloys led us to believe that the damping peak should occur below the transformation temperature for frequencies near 1 cps and above for frequencies near 100 kcps. This surmise was correct. The low-frequency measurements were made on wire specimens using a vacuum torsion pendulum; the damping peak was found at about 2'70°C at a frequency of 1 cps. Because of large superimposed damping of magnetic origin at this temperature, a longitudinal magnetic field of about 1500 oe was applied to the

Jan 1, 1969

By Hillary W. St. Clair

This report describes a mathematical procedure for analyzing size distribution data by the method of moments. The method was applied to Andreasen's data on a variety of grinding mill products. It was found that the observed size distributions could be represented by gamma and beta distribution functions over a wide range of sizes. A computer program, written in BASIC, is described for calculating moments, distribution parameters, and the weight fraction in any size range.

Jan 1, 1969

Standard petrographic profiles for many Permian seams from New South Wales and Queensland have been drawn up. The standard profiles of seams of the same age and from one or more coalfields were used to compile an idealized or type seam sequence for those coals in which more than half the seam profiles were similar to one another. A marked similarity existed between at least 7 of the 10 type seam sequences formed. The configurations of the vitrite-plus-clarite contents of the plies of 95 per cent of the seams could be formed from different arrangements of 3 basic sequences: (i) a two-ply sequence with a lower vitrite-rich and an upper vitrite-poor ply; (ii) a two-ply sequence with a lower vitrite-poor and an upper vitrite-rich ply; and (iii) a four-ply sequence of 3 plies with vitrite-plus- clarite decreasing upwards, terminating in a vitrite- rich ply. The third basic sequence was very similar to a succession described for some British Carboniferous coals. Eighty per cent of the Australian Permian coal seams studied began with the first (i) basic type of sequence and are interpreted as originating in peat- forming areas which became progressively drier. More than half the seams were formed in an area with a stable depositional surface level which was subject to oscillations of small amplitude.. Many (30%) were formed in an area with a steadily rising depositional surface level.

Jan 1, 1969

The Wednesday morning session was opened by President Stanley Shuhart at 9-30 a.m. He called the Chairman of the Auditing Committee. Kenneth Eaton, to report on the financial statement. Mr. Eaton read the data and asked for its approval. It was made, seconded and approved. John Turner, Chairman of the Resolutions Committee, submitted the following: RESOLVED: Whereas, in the year since the last convention of the Rocky Mountain Coal mining Institute, the Institute and the cool mining industry generally have suffered the loss through death of the services of: Walter M. Bellairs F. V. Colombo, M.D. George R. Delamater J. H. East, Jr. E. W. Felegy Hugo H. Machin Archie M. Morrison George E. Mills Veloy K. Piccioni

Jan 1, 1969

By R. K. Dann, L. W. Roberts, R. B. Benson

The mechanical properties of 300-series stainless steels were investigated in both high-pressure hydrogen and helium environments at ambient temperatures. An auslenitic steel which is unstable with respect to formation of strain-induced a (bee) and € (hcp) mar-tensile is embrittled when plastically strained in a hydrogen environment. A stable austenitic steel is not embriltled when tested under the same conditions. The presence of hydrogen causes embrittlement at the mar-lensitic structure and a definite change in the general fracture mode from a ductile to a quasicleavage type. The embrittled martensitic facets are surrounded by a more ductile type fracture which suggests that the presence of hydrogen initiates microcracks at the martensitic structure. If a steel is unstable with respecl to fortnation of strain induced martensile, plastic deformation in a hydrogen environment will produce rapid embrittlement of a notched specimen in comparison to an unnotched one. FERRITIC and martensitic steels can be embrittled by hydrogen that has been introduced into the alloys, either by thermal or cathodic charging prior to testing.1-5 However, conflicting reports exist as to whether austenitic steels that are stable or unstable with respect to formation of strain-induced martensite can be embrittled by hydrogen.8-12 A recent investigation has shown that cathodically-charged thin foils of a stable austenitic steel can be embrittled.13 An earlier investigation of a thermally charged 18-10 stainless steel revealed a significant decrease in the ductility only at the lowest test temperature of -78°C, although strain-induced bee martensite was shown to be present in one specimen tested at ambient temperatures.' When martensitic steels are tested in a hydrogen atmosphere, they are embrittled.'4-'7 It has been observed in this Laboratory that 304L steel, which is unstable with respect to formation of strain induced martensite, forms surface cracks when plastically strained in a high-pressure hydrogen environment. Work in progress elsewhere concurrent with this investigation has also established that 304L is embrittled when tested in a high-pressure hydrogen atmosphere." The objective of this investigation was to study the effect of a high-pressure hydrogen environment on the tensile properties of a stainless steel that contained strain-induced martensite (304L) and one that did not (310). EXPERIMENTAL TECHNIQUES Notched and unnotched cylindrical specimens were machined from 304L* and 310 rods that were heat- treated at 1000°C in argon for 1 hr followed by a water quench. The chemical analyses of these steels are given in Table I. The unnotched specimens had a reduced section diameter of 0.184 & 0.001 in., a gage length of 0.7 in., and were threaded with a 0.5-in.-diam. thread on each end. The notched specimens had a reduced section diameter of 0.260 * 0.001 in. and a 0.75-in. gage length, with a 30 pct 60 deg v-notch at the center. The notch had a maximum root radius of 0.002 in. The tensile bars were fractured in a hydrogen or helium atmosphere of 104 psi at ambient temperatures. The system used for mechanically testing the specimens is to be described in detail elsewhere.19 Several specimens of each type were tested in air using an Instron testing machine. The same yield strength and ultimate tensile strength were obtained in 104 psi helium with the above system as with the conventional testing machine. Magnetic analysis was employed to determine that there was a (bee) martensite in plastically deformed 304L and that it was not present in plastically deformed 310. The magnetic technique depended on allowing the material being studied to serve as the core between a primary and secondary coil. Thus, any change in the amount of magnetic material present between the annealed and plastically deformed steels will be indicated by corresponding changes in the induced voltage in the secondary circuit." The ratio of the output signal of a nonmagnetic stainless steel to a completely magnetic maraging steel was 2000 to I. Several unnotched 304L bars tested in hydrogen were analyzed for hydrogen by vacuum fusion analysis. There was an increase in the hydrogen content to approximately 2 ppm for the specimens tested in hydrogen, as compared to less than 1 ppm for the as-received material. Several thin sections cut from notched areas of 304L specimens tested in hydrogen and containing the fracture surface contained approximately 1.5 ppm H. The accuracy of these determinations was estimated to be ± 50 pct.

Jan 1, 1969

By Richards R. Vandervoot

T HE creep behavior of many polycrystalline metals at moderate stresses can be described by the empirical relationship: where Em is the minimum creep rate, A is a constant, a is the applied stress, E is the average elastic modulus at the test temperature, and D is the self-diffusion coefficient.&apos; This equation is generally applicable for strain rates of less than around 10-5 per sec and temperatures greater than about one-half the melting point in absolute units. Under these conditions atomic mobility plays an important role in the deformation process, and steady-state creep occurs when a dynamic equilibrium is reached between the generation and recovery of dislocation substructure. Although several theoretical mechanisms have been proposed to explain the creep of polycrystalline solids,2"4 the dislocation climb model2 is in accord with most experimental observations. The majority of creep data used to develop Eq. [1] came from metals with either the fcc or hcp crystal structures. However, on the basis of results for a and 7 iron as well as those for a and a thallium, Sherby concluded that the high-temperature deformation behavior of close-packed metals and bcc metals is probably the same.&apos; The greater creep resistance of fcc and hcp metals and alloys on a relative temperature scale was attributed to lower diffusivities in the close-packed structures. To further compare the creep properties of fcc, hcp, and bcc metals, creep data for all six bcc refractory metals were analyzed according to Eq. [I]. The results are shown in Fig. 1. The sources of information for the quantities used to prepare this figure are listed in Table I, except for high-temperature elastic moduli. The latter data were obtained from Refs. 28 and 29. The dashed lines in the figure represent the range and breadth of data analyzed by Sherby for fcc and hcp metals. In general, the deformation behavior of all of the refractory metals, ex- cept possibly that of tungsten, can be represented by Eq. [1]. This correlation is strong evidence of the similarity that exists between creep of pure close-packed metals and creep of pure bcc metals. At (Em/D) < 108, the results of Flagella and Tarr on tungsten (W-1 in Fig. 1) agree with the five-power stress law, while those of Green (W-5 in Fig. 1) show a seven-power stress dependence. Where (Em/D) > 108, the stress exponents for other data on tungsten were in the range 10 to 15. It is possible that the creep rate dependence on stress in this region is not a power law but exponential (i.e., Em - eßo). However, it was not feasible to differentiate between these two cases because of the steep slope and scatter in the data. Note the inflection point in the curve for the data of Flagella and Tarr (W-1 in Fig. 1). The slope of the line changes from 5 to around 10 at Em/D = 108. The breakdown of the fifty-power stress law at high stresses is not uncommon in other metals, and this phenomenon may result from nonequilibrium conditions in the material such as excess lattice vacancies produced by rapid straining.30 The mechanical strength of a polycrystalline metal is related to its microstructure. Attempts to establish the influence of grain size on the creep rate of metals and alloys have led to a wide variety of results. For example, the following effects have been observed: creep rate decreases as grain size increases;31&apos;32 creep rate decreases as grain size decreases;&apos;,33 creep rate is a minimum at some critical grain size and increases with either an increase or decrease in

Jan 1, 1969

By H. K. Kutter

The pressure pulse generated by an underwater spark \vas investigated in relation to its potential use for rock fragmentation. The study established (1) the relation between the peak discharge current and the peak wave pressure; (2) the relationships among the peak wave pressure, the discharge voltage, and the spark gap width; (3) the type and pulse duration of the generated wave; (4) the percentage of energy transmitted in the spark as a function of spark gap width and discharge voltage; and (5) the percentage of energy converted into the pressure wave as a function of gap width and discharge voltage. Spark-generated fractures were studied in two-and three-dimensional rock and plastic specimens. The laboratory results indicated that the pressure pulse generated by an underwater spark is a potential practical tool for rock fragmentation. The paper contains an appendix describing the capacitive pressure gage specially developed for the laboratory tests.

Jan 1, 1969

By G. Gutierrez, D. A. Elgillani, M. C. Fuerstenau

The zero-points-of-charge of apatite, calcite, and fluorite are pH 6.4, 10.8, and 10.0, respectively. Scheelite is negatively charged above at least pH 3. In this article, the flotation responses of these minerals in the presence of potassium oleate and sodium silicate are described and compared with electrokinetic data. Colloidal silica appears to be the species principally responsible for calcite depression, while silicate anion is the species responsible for fluorite depression. Additions as high as 1 x 10-3 mole/liter silicate have no effect on the flotation responses of apatite and scheelite. Selective flotation of nonmetallic minerals is difficult to achieve with fatty acids or soaps by themselves. As a result, specific reagents are added to aid these separations, and one of the reagents commonly employed for this purpose is sodium silicate. Flotation separations of various calcium-bearing minerals such as fluorite from calcite1-3 and scheelite from calcite2,4 and apatite,2,5 for example, almost always involve the use of sodium silicate. The mechanisms by which sodium silicate functions as a depressant are still not understood, probably for a number of reasons. For one thing, the dissolution process of sodium silicate is complex, giving rise to a number of ionic and colloidal species.&apos; Moreover, the type and concentration of these species depend on the ratio of Na2O to SiO2, the concentration of sodium silicate, and the pH of the system.&apos; At the present time, it is not known which species, colloidal silica or silicate anion, is responsible for depression. If colloidal silica is the species that is adsorbing, then adsorption must occur by electrostatic attraction between the colloid and the mineral surface. Silicate anion, on the other hand, may adsorb either physically or chemically. The objective of this paper is to determine first the active species of sodium silicate and then the conditions under which this species will adsorb and function as a depressant. EXPERIMENTAL MATERIALS AND METHODS Pure samples of apatite (Durango), calcite (Iceland-spar), fluorite, and scheelite were used in this investigation. Pure potassium oleate was used as collector, while reagent-grade HC1 and KOH were employed for pH adjustment. The sodium silicates used were samples obtained from the Philadelphia Quartz Co. In one series of experiments, various sodium silicates containing different ratios of SiO2 to Na2O were added to calcite systems. These sodium silicates contained SiO2-to-Na2O ratios of 3.75 to 1, 3.22 to 1, 2.40 to 1, and 1.60 to 1. All other experiments were conducted with the sodium silicate containing the ratio of 3.22 to 1, which is the one that is normally used in industry. Flotation experiments were conducted with 21/2-g charges of 48 x 150-mesh material in conductivity water with an apparatus and technique described previously. Electrokinetic experiments were conducted with both a Zeta Meter and streaming potential apparatus. Particle size was 48 x 65 mesh for the streaming potential experiments. EXPERIMENTAL RESULTS The first series of experiments involved flotation of scheelite in the absence and presence of sodium silicate. As shown in Fig. 1, flotation response was not affected with even the relatively high addition of 1 x 10-3 mole per liter sodium silicate. Interestingly though, no flotation was effected below pH 6 with this collector addition. The responses of apatite to flotation under these same conditions are given in Fig. 2. Similarly, no depression was obtained in basic media under these conditions. Similar experiments were conducted with fluorite, and in this case, depression was noted above about pH 11 with 1 x 10-3 mole per liter sodium silicate (Fig. 3). When calcite was floated with these same levels of addition of sodium silicate, essentially no flotation was possible above pH 7 (Fig. 4). The effect of collector addition with a constant addition of sodium

Jan 1, 1969